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+{"Unnamed: 0":2413,"id":"journal.pcbi.1006222","year":2018,"title":"Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions","sections":"RNAs can fold into complex three-dimensional ( 3D ) structures to carry out their various biological functions 1 ., An RNA pseudoknot represents a very common structure motif , which is not only one of the fundamental structure elements in various classes of RNAs such as human telomerase RNA , self-splicing introns of ribozyme and S-adenosylmethionine-responsive riboswitches , but also involved in many biological functions , including regulation and catalysis 2 , 3 ., For instance , an RNA pseudoknot can be present within the coding regions of an mRNA , where it stimulates programmed -1 ribosomal frameshifting to control the relative expression levels of proteins 2\u20134 ., Generally , an RNA pseudoknot is formed when a sequence of nucleotides within a single-stranded loop region forms base pairs with a complementary sequence outside that loop 2 , 3 , 5 , 6 ., Many experiments have shown that this special 3D topology is key to realize the various functions of RNA pseudoknots 2\u20134 ., In addition , the stability of RNA pseudoknots can also play important roles in modulating their biological functions , and structure changes of RNA pseudoknots could cause diseases such as dyskeratosis 3 , 7 , 8 ., Thus , to determine 3D structures and quantify stability of RNA pseudoknots is essential to unveil the mechanisms of their functions and to further aid the related drug design 5 , 9 ., There have been several successful experimental methods to obtain 3D structures of RNAs , such as X-ray crystallography , nuclear magnetic resonance spectroscopy , and newly developed cryo-electron microscopy 9\u201312 ., However , it is still very time-consuming and expensive to derive high-resolution 3D structures of RNAs and the RNA structures deposited in Protein Data Bank ( PDB ) are still limited 9 , 12 ., To complement experimental measurements , some computational models have been developed to predict 3D structures for RNAs 13\u201322 ., The knowledge-based models 23\u201334 such as MC-Fold\/MC-Sym pipeline 24 , FARNA 25 , 3dRNA 29 , 35 , 36 , RNAComposer 30 and pk3D 31 are rather successful and efficient in constructing 3D structures for RNA pseudoknots through fragments assembly based on limited experimental structures\/fragments or reliable secondary structures , while it is still a problem to exactly predict secondary structures of RNA pseudoknots 11 , 20 ., Furthermore , most of the above methods cannot give reliable predictions for the thermodynamic properties of RNA pseudoknots from their sequences 9\u201311 ., Simultaneously , some coarse-grained ( CG ) models have been developed to predict the thermodynamic stability of RNAs including pseudoknots 37\u201346 ., The Vfold model enables predictions for the structure , stability , and the free energy landscape for RNA pseudoknots from sequences through enumerating loop conformations on a diamond lattice 37 , 38 ., The model is applicable to secondary structure folding while the 3D structures need to be built through fragment assembly based on secondary structures 47 ., Several other CG models such as the iFoldRNA 39 , the HiRE-RNA 40 and the oxRNA 42 have been used to predict 3D structure and stability for a few RNA pseudoknots , but the parameters of these models may need further validation for quantifying RNA thermodynamics to accord with experiments ., In addition , due to the polyanionic nature of RNAs , metal ions ( e . g . , Na+ and Mg2+ ) in solutions can play an essential role in RNA folding 48\u201353 , and Mg2+ can play a more special role in stabilizing the compact folded structures of RNA pseudoknots 54\u201357 ., However , the above structure prediction models seldom consider the conditions departing from the high salt ( e . g . , 1M NaCl ) ., Although all-atomic molecular dynamics simulations can be used to probe ion-RNA interactions , it is still difficult to simulate RNA structure folding at present due to the huge computation cost 56 , 57 ., In simplified CG models , the effect of ions ( especially Mg2+ ) is seldom properly involved due to the interplay between ion binding and structure deformation as well as the particularly efficient role of Mg2+ beyond mean-field description 51\u201353 ., Recently , a G\u00f6-like CG model has been introduced to reproduce the folding thermodynamics of several RNA pseudoknots in the presence of monovalent ions 46 , 58 , 59 , and another structure-based model can well capture the ion atmosphere around RNAs with an explicit treatment of divalent ions 60 ., However , the two structure-based models could not be used to predict 3D structures for RNA pseudoknots solely from the sequences 11 , 20 , 46 , 60 ., Therefore , it still remains an important problem to predict 3D structures and thermodynamic stability for RNA pseudoknots especially in monovalent\/divalent ion solutions only from the sequences ., In this study , we focused on predicting 3D structures and stability for extensive RNA pseudoknots in monovalent and divalent ion solutions from their sequences through our previously developed three-bead CG model 61 , 62 ., In the following , we first revisited the key features of our CG model such as the CG representation and the implicit-solvent\/salt force field for RNAs ., We then employed the model to predict 3D structures for various RNA pseudoknots from their respective sequences ., Afterward , we made the prediction for the stability of typical pseudoknots with different lengths and sequences over a wide range of monovalent\/divalent ion concentrations ., Finally , we made the comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions and examined the effect of monovalent\/divalent ions on the unfolding pathway of RNA pseudoknots ., Throughout the article , we have made the comparisons between the predictions and the extensive experimental data as well as the comparisons with the existing models ., In our model , an RNA is represented as a chain of nucleotides , where each nucleotide is reduced to three beads retaining the key structure features of an RNA chain 46 , 47 , 61 , 62 ., As shown in Fig 1A , the backbone phosphate bead ( P ) and sugar bead ( C ) coincide with the phosphate and C4\u2019 atoms of a nucleotide , and the base beads ( N ) are placed at the base atoms linked to the sugar , that is N1 atom for pyrimidine or the N9 atom for purine 61 , 62 ., The P , C and N beads are treated as spheres with van der Waals radii of 1 . 9\u00c5 , 1 . 7\u00c5 and 2 . 2 \u00c5 , respectively , and each P bead has a charge of\u2013e on its center 61 , 63 ., In the CG model , the effective potential energy of an RNA conformation is given by 61 , 62, U=Ub+Ua+Ud+Uexc+Ubp+Ubs+Ucs+Uel ,, ( 1 ), where bond length energy Ub , bond angle energy Ua and dihedral energy Ud account for chain connectivity and angular rotation for an RNA chain , and Uexc represents for excluded volume interactions between two CG beads ., Ubp and Ubs are the base-pairing and base-stacking interactions , and Ucs is the coaxial stacking interaction between two neighbor stems ., The last term Uel corresponds to electrostatic interactions between phosphate groups , which are ignored by most of the existing predictive models for RNA 3D structures 11 , 20 ., The detailed description of the potentials in Eq 1 and the determination of the potential parameters have been described in S1 Text and also in Refs ., 61 , 62 ., Briefly , two sets of parameters of the bonded potentials ( Ub , Ua and Ud ) , Paranonhelical used in RNA folding process and Parahelical used only in structure refinement for helical stems , are derived respectively from single strands\/loops and stems in the PDB 12 , 61 , 64 ., The sequence-dependent strength of base-staking energy is derived from the combination of the experimental thermodynamic parameters 65\u201367 ., In most occurring pseudoknots with interhelix loop length \u2264 1nt , two helical stems can be often coaxially stacked to form a quasi-continuous double helix ( Fig 1 ) , and the strength of Ucs depends on sequences of two interfaced base pairs 65 ., The coaxial stacking could stimulate high levels of -1 frameshifting 3 , 4 , and consequently , could be important for stabilizing functional structures of RNA pseudoknots ., The electrostatic interaction Uel is taken into account through the combination of the Debye-H\u00fcckel approximation and the concept of counterion condensation ( CC ) 68 ., Notably , based on the tightly bound ion ( TBI ) model 51 , 52 , 69 , the competition between monovalent and divalent ions was also taken into account in Uel to enable the CG model to simulate RNA pseudoknot folding in mixed monovalent\/divalent ion solutions 61 , 62 ., Although the present model has been described by us in Refs ., 61 and 62 , the model is still not employed for 3D structure predictions of extensive RNA pseudoknots and it has never been used to predict the stability of RNA pseudoknot in ion solutions , especially in the presence of divalent ions 61 , 62 ., Here , the model will be tested by extensive RNA pseudoknots on 3D structure prediction , and be further used to predict thermodynamic stability and the unfolding pathway for various RNA pseudoknots over the wide range of monovalent\/divalent ion conditions ., Based on the CG force field , the Monte Carlo ( MC ) simulations with simulated annealing algorithm are used to predict 3D structures of RNA pseudoknot 43 , 61 , 62 , where an initial simulation is started at a high temperature and a given solution condition from a totally random chain configuration generated from an RNA sequence ., The system is then gradually cooled in steps , and the ion condition is fixed during the cooling process ., At each temperature , RNA conformational changes are accomplished via the pivot moves which have been demonstrated to be rather efficient in sampling conformations of polymers 63 , and the changes are accepted or rejected according to the standard Metropolis algorithm 43 , 61 ., The final structures obtained at the lowest target temperature ( e . g . , room\/body temperature ) are the folded conformations of the RNA predicted by the CG model ., Notably , the recorded trajectories at different temperatures during the cooling process allow us to analyze the stability of the RNAs 61 , 62 ., Beyond 3D structure prediction , the present model was also employed to predict the stability of RNA pseudoknots in monovalent and divalent salt solutions ., Since intermediate states of RNAs can be important to their biological functions 5 , 76 , 80\u201385 , unfolding pathway of RNAs including some pseudoknots has been studied through theoretical modeling and experiments 75\u201377 , 81\u201388 ., To examine the unfolding pathway of RNA pseudoknots , we made comprehensive analyses for six RNA pseudoknots; see Fig 7 and S4 Fig . Based on the simulations for each pseudoknot at a given solution condition , beyond the fractions of states F and U , the fractions of different intermediate hairpin states ( named as S1 and S2 for intermediate states reserving one of Stem 1 and Stem 2 , respectively ) at different temperatures can also be calculated; see Figs 7 and 8 and S4 and S6 Figs ., Furthermore , we employed the model to predict the unfolding pathway for various RNA pseudoknots in monovalent\/divalent ion solutions and examined the effect of monovalent\/divalent ions on the unfolding pathway of RNA pseudoknots , which was seldom covered in previous studies since the effect of divalent ions is generally difficult to be involved ., It is important to predict 3D structures and stability of RNA pseudoknots in monovalent\/divalent ion solutions from their sequences ., In this work , we employed our previously developed model to address this problem ., Beyond mainly focusing on reproducing structures , as many previous structure prediction models have done , the present model enables us to predict and analyze 3D structure stability for RNA pseudoknots in different monovalent\/divalent ion solutions ., The following are the major conclusions: Despite the extensive agreements between our predictions and experiments , the present model has several limitations that should be overcome in future model development ., First , the present model does not treat possible noncanonical interactions such as base triple interactions between loops and stems , self-stacking in loop nucleotides and special hydrogen bonds involving phosphates and sugars , which could be important for some more complex pseudoknotted structures 7 , 17 , 38 ., Beyond the common H-type pseudoknots ( \u2264 56nt ) used in this work , larger RNAs with complex structures should be incorporated in to further improve the present model 19 , 90\u201394 ., Second , the effect of monovalent\/divalent salts is implicitly accounted for in the present model by the combination of CC theory and the TBI model ., Such implicit-salt treatment may be responsible for the underestimation on the stability of RNA pseudoknots at high Mg2+ ., Mg2+ can play an efficient and special role in stabilizing compact RNA structures 51\u201354 , 79 , and further development may need to involve Mg2+ explicitly in our model ., Third , in this work , we mainly focused on the 3D structures and thermodynamic stability of RNA pseudoknots , and did not involve the stability under mechanical force ., Mechanical forces can be not only considered as a useful probe for RNA stability , but also important for the functions of some RNA pseudoknots 3 , 81 , 86 , 95\u201397 ., For example , the frameshifting efficiency may be affected by the magnitude of unfolding force for RNA pseudoknots 3 , 81 , 96 ., Fortunately , the present model can be extended to study the mechanical stability of RNA pseudoknots by including external force in the energy functions of the model 67 , 86 , 95 ., Finally , the 3D structure predicted by the present model is at the CG level , and it is still necessary to develop the model to reconstruct all-atomistic structures based on the CG structures for further practical applications ., Nevertheless , the present model could be a reliable predictive model for predicting 3D structures and stability of RNA pseudoknots in ion solutions from their sequences and the analyses can be helpful to understand the physical mechanism for the unfolding pathway of RNA structures .","headings":"Introduction, Materials and methods, Results, Discussion","abstract":"RNA pseudoknots are a kind of minimal RNA tertiary structural motifs , and their three-dimensional ( 3D ) structures and stability play essential roles in a variety of biological functions ., Therefore , to predict 3D structures and stability of RNA pseudoknots is essential for understanding their functions ., In the work , we employed our previously developed coarse-grained model with implicit salt to make extensive predictions and comprehensive analyses on the 3D structures and stability for RNA pseudoknots in monovalent\/divalent ion solutions ., The comparisons with available experimental data show that our model can successfully predict the 3D structures of RNA pseudoknots from their sequences , and can also make reliable predictions for the stability of RNA pseudoknots with different lengths and sequences over a wide range of monovalent\/divalent ion concentrations ., Furthermore , we made comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions ., Our analyses for extensive pseudokonts and the wide range of monovalent\/divalent ion concentrations verify that the unfolding pathway of RNA pseudoknots is mainly dependent on the relative stability of unfolded intermediate states , and show that the unfolding pathway of RNA pseudoknots can be significantly modulated by their sequences and solution ion conditions .","summary":"RNA pseudoknotted structures and their stability can play important roles in RNA cellular functions such as transcription , splicing and translation ., Due to the polyanionic nature of RNAs , metal ions such as Na+ and Mg2+ in solutions can play an essential role in RNA folding ., Although several computational models have been developed to predict 3D structures for RNA pseudoknots to further unveil the mechanisms of their functions , these structure prediction models seldom consider ion conditions departing from the high salt ( e . g . , 1M NaCl ) and temperatures from the room temperature ., In this work , we employed our coarse-grained model to predict 3D structures and thermodynamic stability for various RNA pseudoknots in monovalent\/divalent ion solutions from their sequences , and made comparisons with extensive experimental data and existing models ., In addition , based on our comprehensive analyses for extensive pseudoknots and the wide range of monovalent\/divalent ion conditions , we confirmed that the thermally unfolding pathway of RNA pseudoknots is mainly determined by the relative stability of intermediate states , which has been proposed by Thirumalai et al . Our analyses also show that the thermally unfolding pathway of RNA pseudoknots could be apparently modulated by the sequences and ion conditions .","keywords":"rna structure prediction, condensed matter physics, rna stability, sequence motif analysis, thermodynamics, research and analysis methods, sequence analysis, rna structure, bioinformatics, gene expression, melting, phase transitions, molecular biology, physics, biochemistry, rna, rna folding, nucleic acids, pseudoknots, database and informatics methods, genetics, biology and life sciences, physical sciences, macromolecular structure analysis","toc":null}
+{"Unnamed: 0":556,"id":"journal.pgen.1004776","year":2014,"title":"Dissemination of Cephalosporin Resistance Genes between Escherichia coli Strains from Farm Animals and Humans by Specific Plasmid Lineages","sections":"Antibiotic resistance among opportunistic pathogens is rapidly rising globally , hampering treatment of infections and increasing morbidity , mortality and health care costs 1 , 2 ., Of particular concern is the increased incidence of infections caused by Escherichia coli isolates producing extended-spectrum \u03b2-lactamases ( ESBLs ) , which has rendered the use of third generation cephalosporins increasingly ineffective against this pathogen 3 ., During the 1990s , the most commonly encountered ESBL genes were blaTEM and blaSHV , and their spread occurred mainly through cross-transmission in hospitals ., However , the epidemiology of ESBL-producing E . coli has changed ., Nowadays , the most prevalent ESBL gene type is blaCTX-M 4 and infections with ESBL-producing E . coli also occur in the community 5 , 6 ., The intestinal tracts of mammals and birds are important reservoirs for ESBL-producing E . coli 7 , but it is unclear to what extent these bacteria can spread to humans ., Food may be an important source , since ESBL genes have been detected in food-producing animals , especially poultry 8 , 9 , and on retail meat 10 ., The presence of ESBL-producing bacteria in food has been attributed to widespread use of antimicrobials , including third generation cephalosporins , in industrial farming practices 11 ., In The Netherlands , antibiotic use and prevalence of antibiotic resistance in humans are among the lowest in Europe 12 , whereas antibiotic use in food-producing animals ranks among the highest in Europe 13 ., These circumstances render The Netherlands particularly suitable to study the transfer of third-generation cephalosporin-resistant bacteria through the food-chain ., Recent studies performed in The Netherlands suggested clonal transfer of ESBL-producing E . coli from poultry to humans 14\u201316 ., However , these interpretations were based on typing methods that target a limited number of genes , and which may not have provided sufficient resolution to accurately monitor the epidemiology of pathogens 17 ., In this study , we have therefore sequenced 28 ESBL-producing and four ESBL-negative E . coli strains that had previously been collected from humans , poultry , retail chicken meat and pigs and tested whether previous claims on the relationship between strains from different reservoirs could be confirmed at the whole-genome sequence level ., Furthermore , we investigated the relatedness of cephalosporin resistance gene-carrying plasmids , which were derived from different backgrounds and reservoirs , at the genomic level ., We assessed the relatedness of ESBL-producing E . coli from humans , animals and food by using Whole-Genome Sequencing ( WGS ) ., The genomes of 32 , mostly ESBL-producing , E . coli strains isolated in The Netherlands in the period 2006\u20132011 were sequenced ( Table 1 ) ., One set of isolates ( n\\u200a=\\u200a24 ) included five pairs of human and poultry-associated strains that had previously been found indistinguishable based on Multi Locus Sequence Typing ( MLST ) , plasmid typing ( pMLST ) and ESBL gene sequencing 15 , 18 ., This set also included 11 human and poultry-associated isolates that carried an AmpC-type \u03b2-lactamase gene on an IncK plasmid 18 ., The second set of isolates contained eight ESBL-producing strains that were isolated from pigs ( n\\u200a=\\u200a4 ) and their farmers ( n\\u200a=\\u200a4 ) ( Table 1 ) ., Illumina sequencing yielded draft genomes with an average assembly size of 5 . 2 Mbp ( \u00b10 . 17 Mbp ) , consisting of an average number of 133 scaffolds ( \u00b141 ) of size \u2265500 bp and a mean N50 of 153 kbp ( \u00b147 . 9 kbp ) ( S1 Table ) ., WGS-based MLST and ESBL gene analysis provided good agreement with previous typing data ., Previously obtained MLST profiles and WGS-based MLST profiles were in complete agreement with each other ., Although ESBL genes had previously been detected by both microarray-based methods and Sanger sequencing 15 , the previously typed ESBL genes of four ( out of 28 ) strains were absent from their assembled genomes ., In three of these cases ( strains 681 , 320 and 38 . 34 ) , we detected a blaTEM-1 or blaTEM-20 gene in the assembled genome , whereas a blaTEM-52 gene should have been found according to the typing data ., Mapping the Illumina reads of these strains against their own assemblies showed that the assembled blaTEM genes contained several ambiguous positions pointing to the presence of more than one type of blaTEM gene ( most likely a combination of blaTEM-1 and blaTEM-52 ) in these strains ( S2 Table ) ., In comparison , no ambiguous positions were found in the assembled blaTEM genes of other strains using the same mapping approach ., In addition , the relative coverage of the assembled blaTEM genes of strains 681 , 320 and 38 . 34 was higher than that of the assembled blaTEM genes of other strains ( S2 Table ) ., These findings suggested that strains 681 , 320 and 38 . 34 contain multiple nearly identical blaTEM genes ( i . e . blaTEM-1 and blaTEM-52 ) that hampered the correct assembly of these genes ., The fourth inconsistency between WGS and typing data was the absence of blaCTX-M-1 from the assembly of strain 435 ., Mapping the reads of strain 435 against the blaCTX-M-1 gene sequence did suggest the presence of this gene in the WGS data , but with a depth of around 1\/10th the average genomic sequencing depth ., Possible explanations include a relatively poor isolation efficiency of the blaCTX-M-1-carrying plasmid and\/or the loss of this plasmid from the bacterial cells during culturing in the absence of antibiotics ., The previous AmpC typing data 18 and our WGS data were in complete agreement ., To assess the phylogenetic context of the sequenced strains within the genus Escherichia and Shigella , we used publicly available genome sequences of Escherichia ( n\\u200a=\\u200a126 ) and Shigella ( n\\u200a=\\u200a12 ) strains ., Based on COG assignments , we identified 215 core proteins in the 170 analysed genomes , from which a concatenated core genome alignment of 170461 bp was built ., A phylogenetic tree based on the 18169 variable positions in this alignment confirmed previous clustering based around phylogroups A , B1 , B2 , D , E and F ( Fig ., 1 ) 19 ., The sequenced strains clustered together in accordance with their ST . Strains did not cluster based on isolation source , year , plasmid or ESBL gene ., The ESBL-producing strains were spread throughout the tree , indicating that acquisition of ESBLs arises in different E . coli genetic backgrounds and has occurred multiple times during evolution ( Fig . 1 ) ., There were four clusters of ESBL-producing strains isolated from humans and animals\/meat ( clusters I\u2013IV , Fig . 1 ) ., Cluster I contained human and pig isolates from two pig farms , with strains from farm A being particularly closely related ., The other three clusters contained the five pairs of human and chicken isolates that had previously been considered indistinguishable based on traditional typing methods 15 ., Among the five pairs of human and chicken isolates , the most closely related pairs were in cluster IV ., The COG-based core genome alignment showed 171 SNPs between these strains , corresponding to 1003 SNPs\/Mbp ., To better elucidate the minimum number of SNPs between human and chicken isolates , we performed a core genome analysis using OrthoMCL 20 on the strains in cluster IV ., For comparison , ten clonal O104:H4 strains from the 2011 German EHEC outbreak 21 and the four strains from pig farm A ( cluster I ) were included in this analysis ( Fig . 1 ) ., We identified 3574 core proteins in this dataset translating to a concatenated nucleotide alignment of 3 . 34 Mbp ., Within cluster IV there were 4216 SNPs between the most closely related isolates , corresponding to 1263 SNPs\/Mbp ., In contrast , only 0\u20136 SNPs ( 0\u20131 . 8 SNPs\/Mbp ) were found between any two strains in the German EHEC outbreak and only 6 SNPs were found between farmer isolate FAH2 and any of its two related pig isolates , suggesting recent clonal transmission of E . coli between pig and human in farm A ( Fig . 2 ) ., Given an estimated E . coli mutation rate of 2 . 3\u00d710\u22127 to 3 . 0\u00d710\u22126 substitutions per site per year 21 , 22 and an average E . coli genome size of 5 . 2 Mbp , the number of SNPs ( 1263\/Mbp ) between the two most closely related human and chicken isolates largely exceeded the number of 3\u201341 SNPs that is expected to arise in 2 . 6 years ( the difference in isolation dates between both strains , Table 1 ) ., Even if 10% of the detected SNPs were due to recombination , which is considerably more than the reported upper limit for recombinant DNA ( \u223c3 . 5% ) in E . coli 19 , the number of SNPs due to mutation would exceed the expected maximum number of SNPs in case of recent clonal transmission ., As the genetic distance between all other pairs of human and poultry isolates was even larger , our findings do not support a scenario of recent clonal transmission of ESBL-producing E . coli strains between humans and poultry ., To investigate the possibility of horizontal spread of ESBLs via plasmids , we employed a Plasmid Constellation Networks ( PLACNET ) approach to reconstruct plasmids from WGS data 23 ., Application of this approach resulted in the reconstruction of 147 plasmids ( average of 4 . 6\u00b12 . 1 plasmids per strain ) , with plasmid sizes ranging from 1 . 1 kbp to 290 . 4 kbp ( Table 2 ) ., The plasmid sizes showed a trimodal distribution ( Fig . 3 ) that was similar to the distribution previously reported for plasmids from a wide range of bacterial taxa 24 ., The median size of large ( conjugative ) plasmids was 93 . 6 kbp ( n\\u200a=\\u200a91 ) ., Small plasmids could be further subdivided into two groups: one with a median size of 5 . 9 kbp ( n\\u200a=\\u200a41 ) , predominated by mobilizable plasmids ( i . e . containing MOB genes ) and one with a median size of 1 . 7 kbp ( n\\u200a=\\u200a15 ) , predominated by non-mobilizable plasmids ., Based on the classification of their MOB genes 25 and using a hierarchical clustering analysis of gene content ( Fig . 4 ) , reconstructed plasmids belonged to a limited number of plasmid families , of which the most abundant ones were IncF-MOBF12 ( n\\u200a=\\u200a38; average size of 107 . 4\u00b157 . 7 kbp ) and IncI1-MOBP12 ( n\\u200a=\\u200a26; average size of 95 . 7\u00b120 . 0 kbp ) ., Other abundant families included MOBP5 ( n\\u200a=\\u200a25 ) , IncK ( n\\u200a=\\u200a12 ) and MOBQ ( n\\u200a=\\u200a11 ) ., Finally , there were 18 , mostly small-sized , plasmids ( median size of 1 . 6 kbp; range of 1 . 1\u2013106 . 3 kbp ) that were scattered throughout the dendrogram and could not be clearly subdivided into any family ., A comparison between previous typing data and the PLACNET reconstructions showed that both data types were in excellent agreement with each other ., First of all , the 11 strains that were previously found to contain an IncI1 plasmid were also found to contain such a plasmid using PLACNET ., The sizes of these 11 reconstructed plasmids ( average size of 92 . 7 kbp\u00b15 . 7 kbp ) were also in agreement with their previously estimated sizes on the basis of gel electrophoresis ( average size of 97 . 7 kbp\u00b13 . 8 kbp ) 15 ., Furthermore , the reconstructed plasmids for ten of these 11 strains had exactly the same ST as was previously found using pMLST ., The only inconsistency was found for strain 38 . 34 , which should contain an IncI1\/ST10 plasmid according to pMLST , whereas we reconstructed an IncI1\/ST36 plasmid ., However , IncI1\/ST10 and IncI1\/ST36 are single locus variants that differ by only one SNP ( http:\/\/pubmlst . org\/plasmid\/ ) , indicating that this inconsistency was not a result of PLACNET , but was likely due to typing errors ., Of the 11 strains that had previously been found to contain an IncK plasmid , ten were also found to contain such a plasmid using PLACNET , the only exception being strain 1047 ., We also examined to what extent we were able to correctly connect ESBL and AmpC genes to reconstructed plasmids ., Of the 28 previously typed ESBL genes , 24 were correctly identified in their genomes ( Table, 1 ) and among these , 15 were connected to a reconstructed plasmid ., Four of the remaining nine unconnected ESBL genes ( blaCTX-M-1 in strains 1350 , 1365 , 1047 and 38 . 52 ) should have been connected to an IncI1 plasmid according to previous typing data ( Tables 1\u20132 ) ., The reason that these ESBL genes remained unassigned was because they were located on relatively small scaffolds ( average size of 6 . 6 kbp ) that did not contain enough genetic information to unequivocally match them to a single plasmid using our reference database ., For the 15 cases where we were able to connect an ESBL gene to a reconstructed plasmid , typing data indicating where the ESBL gene should be located was available for four cases ( strains 148 , 897 , 38 . 16 and 38 . 27 ) and for all these cases we had connected the ESBL gene ( blaCTX-M-1 ) to the correct plasmid ( IncI1\/ST7 ) ( Tables 1\u20132 ) ., Of the 11 AmpC ( blaCMY-2 ) genes , ten were connected to their correct plasmid ( IncK ) ., The only exception was found again for strain 1047 for which we could not reconstruct an IncK plasmid ( Table 2 ) ., The above findings show that PLACNET worked efficiently to assemble plasmids from WGS data , although the assignment of small scaffolds to plasmids can be problematic , as is illustrated above by the ESBL genes that were not linked to a specific reconstructed plasmid ( see also discussion below and in 23 ) ., Fifteen ESBL genes were connected to a reconstructed plasmid , of which 13 were connected to an IncI1 plasmid ., Frequently ( eight out of 13 ) , these IncI1 plasmids were also unequivocally linked to other antibiotic resistance genes , such as sul , dfrA , aadA or tet ., We also found IncK plasmids that were commonly ( ten out of 12 plasmids ) associated with the AmpC \u03b2-lactamase-encoding gene blaCMY-2 ( Fig . 4 ) ., As IncI1 and IncK were the only plasmid families that included reconstructed ESBL-\/AmpC-containing plasmids in strains from both humans and animals\/meat , we further investigated their potential role in the transfer of resistance genes through the food-chain ., To this aim we built a gene content-based dendrogram that also included closely related and publicly available plasmid sequences ., In the resulting dendrogram , all reconstructed ESBL-containing IncI1 plasmids , except the blaSHV-12-carrying plasmids p1A_2 and p9B_1 , clustered into one specific branch that did not contain any other previously sequenced plasmid ( Fig . 5 ) ., This branch also contained 12 of the 13 reconstructed IncI1 plasmids that did not include an ESBL gene ., Similarly , all of the reconstructed IncK plasmids , except p87A_5 , clustered into one specific branch that did not include any previously sequenced plasmid ., These findings suggest the existence of IncI1 and IncK plasmids with a genetic profile distinct from previously characterised plasmids ., We did not find any single gene that unequivocally explained the formation of the IncK branch , pointing to a delicate configuration of genes that gives these plasmids their unique genetic profile ., However , for the IncI1 branch , we found a characteristic shufflon-related gene ( UniProt P10487 ) that was present in all 26 reconstructed IncI1 plasmids , but which was absent from related IncI1 plasmids ( Fig . 5 ) ., To further characterise the IncI1 and IncK resistance plasmids , phylogenetic trees were built from the sequences of the reconstructed plasmids and their closest plasmid relatives ., For the IncI1 phylogenetic reconstruction , the 23 plasmids belonging to the specific IncI1 branch as well as 27 related plasmids were included ., An OrthoMCL analysis of these plasmids resulted in 8 core proteins ( S3 Table ) , corresponding to a concatenated nucleotide alignment of 8 . 6 kbp , including 763 variable positions ., In the phylogenetic tree built from these variable positions the reconstructed IncI1 plasmids were assigned to four distinct branches ( Fig . 6A ) , each of which also contained previously characterised plasmids ., However , the reconstructed plasmids within each branch were always more similar to each other than to any of these previously characterised plasmids ., Two of the four branches , corresponding to IncI1\/ST3 and IncI1\/ST7 , contained reconstructed ESBL-harbouring plasmids from both humans and animals or meat ., Further rounds of OrthoMCL analyses showed that the reconstructed plasmids within each of these two sets were highly similar to each other: a maximum of only four SNPs ( all attributable to p53C_2 ) was found in the 40 kbp plasmid core of the IncI1\/ST3 subset , whereas no SNPs were found in the almost 50 kbp plasmid core of the IncI1\/ST7 subset ( Fig . 6A ) ., Similarly , a subset of the blaCMY-2-carrying IncK plasmids contained a plasmid core of almost 37 kbp with a maximum of 27 SNPs ( Fig . 6B ) , which were mostly attributable to p435_1 ., Leaving out p435_1 from the comparisons revealed a maximum of only seven SNPs ., These data strongly support the existence of ESBL-associated IncI1 and AmpC-associated IncK plasmids that have spread through phylogenetically distinct E . coli populations , possibly contributing to the dissemination of ESBLs and AmpC-type \u03b2-lactamases through the food-chain ., To validate the conclusions drawn from the PLACNET reconstructions , we sequenced two strains ( 53C and FAP1 ) using long-read DNA sequencing technology ( Pacific Biosciences ) ., Strain 53C was selected because it has both an IncI1 and an IncK plasmid , carrying blaCTX-M-1 and blaCMY-2 , respectively ., Strain FAP1 was selected because it contained an IncI1 plasmid of the same lineage as the one in strain 53C ( Fig . 6A ) ., The total amount of reconstructed plasmid sequence for strains 53C and FAP1 was 338 kbp and 319 kbp , respectively ( Table 2 ) ., Genomes were assembled to an average depth of 66 . 7- and 77 . 0-fold , respectively , resulting in 11 contigs for strain 53C and five contigs for strain FAP1 ( S4 Table ) ., Inspection of the contig sequences showed the presence of four large plasmids in both strains ., These were assigned to Inc groups F , I1 ( carrying blaCTX-M-1 ) , I2 , and K ( carrying blaCMY-2 ) in strain 53C and F , I1 ( carrying blaCTX-M-1 ) , and I2 , in strain FAP1 ., A single plasmid in strain FAP1 could not be assigned to an Inc group ., Except for the IncI1 plasmid of FAP1 , all plasmid contigs could be circularized ( S4 Table ) ., The plasmid content was in agreement with our reconstructions , except for two inconsistencies in strain FAP1:, ( i ) PLACNET did not assign a blaCTX-M-1 gene to its IncI1 plasmid , and, ( ii ) PLACNET reconstructed two IncF plasmids ., Blast analysis of both reconstructed IncF plasmids against the FAP1 long-read assembly suggested that they should indeed have been merged into one single plasmid ., The reason for this incorrect prediction by PLACNET is unclear , but in the constellation network the two plasmids were relatively far away from each other , suggesting that the IncF plasmid in FAP1 is a fusion between previously observed IncF plasmids present in the reference database ., These data show that caution must be taken in case PLACNET predicts multiple plasmids of the same Inc group in one strain ., For the remaining plasmids , blast analysis showed that the precision rate of PLACNET was high , ranging from 97\u2013100% ( Table 3 ) ., Also in terms of sensitivity , PLACNET performed well being able to recover 72 . 1\u201399 . 7% of the plasmids ( Table 3 ) ., The plasmid regions that were not reconstructed by PLACNET mostly aligned with small scaffolds ( average size of 2 . 0\u00b11 . 9 kbp , n\\u200a=\\u200a33 ) in the assemblies built from Illumina short-read data , which indicates that these regions are difficult to assemble ., Notably , these small scaffolds encoded many mobile element- , phage- , transposon- and integrase-associated proteins ( 29 . 7% of all predicted proteins in these scaffolds ) as compared to the correctly assigned scaffolds , where only 6 . 7% of the proteins had these predicted roles ., These observations are in line with results obtained from the PLACNET validation analyses described in 23 and show that PLACNET efficiently reconstructs plasmids from WGS data ., Finally , the PLACNET-based prediction that both IncI1 plasmids from strains 53C and FAP1 are highly similar ( Fig . 6A ) was confirmed by aligning the two complete IncI1 plasmid sequences assembled from the long-read sequencing data ., Filtering out repetitively aligning regions resulted in a pairwise alignment of 94 . 8 kbp containing only 4 SNPs ., These data further substantiate our conclusions regarding highly successful plasmid lineages disseminating cephalosporin resistance ., We assessed the epidemiology of ESBL-producing E . coli from humans , animals and food using WGS ., Our findings strongly suggest the existence of highly successful ESBL-carrying plasmids facilitating transmission of ESBL genes between different reservoirs ., This has important implications for our understanding of the dynamics of the spread of ESBL genes and for evaluating control measures ., Several strains that were sequenced in this study and which originated from humans and poultry had previously been considered indistinguishable based on MLST , plasmid and ESBL gene typing , suggesting clonal transfer of these strains through the food-chain , to humans 15 ., The claim that ESBL-producing E . coli strains from humans and poultry are frequently identical was also made in other studies that made use of traditional sequence-based typing methods 14 , 16 ., However , as has been demonstrated for different bacterial pathogens and in varied contexts , especially bacterial outbreak investigations , WGS provides superior resolution over traditional typing methods in terms of ruling in and out epidemiological connections between strains 26\u201328 ., Similarly , we demonstrate that conclusions on the clonal spread of ESBL-producing E . coli through the food-chain cannot realistically be drawn on the basis of traditional sequence-based typing methods , due to their insufficient discriminative power ., More specifically , we found that none of the five pairs of human and poultry-associated isolates , previously typed as indistinguishable , were particularly closely related ., The most similar pair of isolates differed by 1263 SNPs\/Mbp compared to a difference of 1 . 8 SNPs\/Mbp for known\/expected clonally related isolates ., Hence , inferences from classical typing-based studies regarding the extent of transfer of ESBL-producing E . coli strains from animals via food to humans and the burden of disease and mortality due to the use of third-generation cephalosporins in food production must be considered as highly speculative 11 ., In fact , our findings strongly suggest that distinct plasmids disproportionately contribute to the spread of antibiotic resistance between different reservoirs ., We have demonstrated the existence of highly similar cephalosporin resistance-encoding IncI1\/ST3 ( 40 . 0 kbp core , 0\u20134 SNPs ) , IncI1\/ST7 ( 49 . 7 kbp core , 0 SNPs ) , and IncK ( 36 . 9 kbp core , 0\u201327 SNPs ) plasmids in different reservoirs ., Reconstructed blaCTX-M-1-carrying IncI1\/ST3 plasmids were found in one human and two poultry isolates , blaCTX-M-1-carrying IncI1\/ST7 plasmids were found in three human , two poultry , and one pig isolate; and blaCMY-2-carrying IncK plasmids were found in five human and four poultry isolates ., The isolates carrying these plasmids belonged to evolutionarily distinct backgrounds ( IncI1 in phylogroups A , B1 and B2; IncK in phylogroups A , B1 , B2 , D and F ) , suggesting that these plasmids efficiently spread through E . coli populations and play an important role in the dissemination of ESBL and AmpC-type \u03b2-lactamases between different reservoirs ., Based on their genetic content , the IncI1 and IncK plasmids in our dataset clustered into specific sub-branches that did not contain any previously characterised plasmid ., However , phylogenetic analyses revealed that these sub-branches could be split into evolutionarily distinct plasmids , some of them being distantly related to previously sequenced plasmids ., These findings suggest that evolutionarily distinct plasmids have been accumulating genes from the same genetic reservoir , resulting in plasmids with a similar genetic inventory ., The reconstructed IncI1 plasmids all harboured a characteristic shufflon-related gene that was absent from previously characterised IncI1 plasmids ., Shufflons are site-specific recombination systems that produce variable C-terminal extensions of the PilV adhesin , resulting in variations of recipient ability in IncI1 plasmid mating 29 ., Whether this shufflon explains the promiscuous nature of ESBL-carrying IncI1 plasmids remains to be determined ., One important question is to what extent the IncI1 and IncK resistance plasmids found in this study have spread beyond The Netherlands ., Given the trees in Fig . 6 , it is clear that currently available plasmid sequences in public databases do not contain any plasmids that are particularly closely related to our reconstructed IncI1 and IncK plasmids ., The pMLST repository ( http:\/\/pubmlst . org\/plasmid\/ ) shows that blaCTX-M-1-carrying IncI1\/ST3 plasmids have been isolated from six different European countries , whereas blaCTX-M-1-carrying IncI1\/ST7 plasmids have until now been isolated only from The Netherlands and Germany ., The location of blaCMY-2 on an IncK plasmid , as found here , has only been occasionally reported before , in The Netherlands 30 , 31 , but also in Sweden 32 and Canada 33 ., Future sequencing projects are needed to determine whether the previously identified plasmids isolated outside The Netherlands are closely related to those described here ., We found that none of the human E . coli strains in our dataset were closely related to strains from poultry ., In contrast , nine out of 17 human isolates ( 53% ) contained a blaCTX-M-1 or a blaCMY-2 gene located on plasmids that were highly similar to those found in poultry ., These data cannot be interpreted to mean that clonal transfer of antibiotic resistant E . coli strains between poultry and humans does not occur , but rather that such transfer occurs less frequently than the transfer of resistance plasmids between both reservoirs ., One drawback of our study is that we have used a relatively small sample size ( 32 strains ) ., Future studies , using larger sample sizes , are needed in order to make more accurate estimates of the relative ( and absolute ) contributions of clonal versus plasmid transfer towards the spread of antibiotic resistance and the associated health-care burden ., In addition , our study focuses on IncI1 and IncK plasmids ., Future studies are needed that also focus on other plasmid families , such as IncF plasmids , which are commonly detected in E . coli from human infections and are associated with the dissemination of many virulence and antibiotic resistance determinants 34 , 35 ., Conjugal transfer of plasmids carrying antibiotic resistance genes has been shown to frequently occur among Enterobacteriaceae in different environments , including milk , meat , and feces , even in the absence of antibiotic pressure 36 , 37 ., Moreover , it has been shown that bla-carrying plasmids are readily transferred from invading Enterobacteriaceae to Enterobacteriaceae that are indigenous to the animal and human intestine and that the invading clone itself generally does not persist in the intestine 38 , 39 ., Nonetheless , it is difficult to infer to what extent the reservoir of bla-type resistance genes in poultry contributes to the carriage of such genes by human E . coli strains ., If successful plasmids are largely responsible for the rising prevalence of ESBL- and AmpC-producing E . coli in healthy humans , their emergence in poultry and humans may simply be a reflection of selection of strains carrying these plasmids due to antibiotic usage in human and veterinary medicine ., A better understanding of the dynamics of ESBLs and other resistance genes in different hosts is needed to design effective control measures , both in the community and within health care settings ., Our findings strongly suggest the occurrence of clonal transfer of ESBL-producing E . coli between pigs and pig farmers , which may well occur through direct contact or through aerosols ., Whether such events represent a public health threat remains to be determined ., The occurrence of transmission of ESBL-producing E . coli from poultry through the food-chain is less evident ., The occurrence of highly-related plasmids that carry ESBL- and AmpC-type resistance genes among genotypically distinct E . coli strains from different sources is cause for concern because this suggests that plasmids can spread with relative ease between the different reservoirs and the spread of these plasmids may be exceedingly difficult to control ., Clearly , there still remains an urgent need to minimize the use of third-generation cephalosporins in animal husbandry as this is an important selective pressure for the occurrence of ESBL- and AmpC-producing E . coli in animals raised for food production ., The genomes of 32 , mostly ESBL-producing , E . coli strains isolated from different reservoirs in The Netherlands in the period 2006\u20132011 , were sequenced ., One set of isolates ( n\\u200a=\\u200a24 ) has been studied previously using classical typing methods 15 , 18 ., This set contained strains from human clinical infections ( n\\u200a=\\u200a13 ) which had been obtained from geographically dispersed laboratories in The Netherlands , servicing secondary and tertiary care hospitals , general practitioners and long-term care facilities ., Additional isolates were from chickens raised on production farms ( n\\u200a=\\u200a4 ) and chicken retail meat ( n\\u200a=\\u200a7 ) ( Table 1 ) ., All 24 isolates were previously genotyped by MLST 40 ( http:\/\/mlst . warwick . ac . uk\/mlst\/dbs\/Ecoli ) and plasmid characterization was previously performed using PCR-based replicon typing 31 , 41 and additional pMLST for IncI1 plasmids 42 , 43 ( http:\/\/pubmlst . org\/plasmid\/ ) ., Detection of ESBL genes had been performed for all 24 strains using microarray analysis and gene sequencing 44 ., In addition , detection of AmpC-type \u03b2-lactamase-encoding genes had been performed for 11 strains , using gene sequencing 18 ., The association between ESBL\/AmpC genes and plasmids was previously determined by both Southern blot hybridization and transformation 31 ., Four non-ESBL-producing isolates were included as controls and were analysed for the carriage of plasmids that can incorporate ESBL genes via horizontal gene transfer ., The second set of isolates contained eight ESBL-producing strains that had been isolated from three different pig farms in The Netherlands in 2011 ( Table 1 ) ., These farm strains were part of a larger cohort that will be described in detail elsewhere ( Dohmen et al . , unpublished data ) ., For one farm ( farm A ) , four strains were collected , two from different fecal pools of six unique pigs and two from the feces of different farmers ., For each of the other two farms ( farms B and C ) , one strain was collected from a fecal pool of six pigs and one from the feces of a farmer ., Detection of the ESBL ( blaCTX-M-1 ) gene was performed using a CTX-M-1 group-specific PCR and additional gene sequencing ( Dohmen et al . , unpublished data ) ., Genomic DNA was isolated from cell pellets using the Ultraclean Microbial DNA isolation kit ( Mo Bio Laboratories , Inc . , Carlsbad , CA , USA ) according to the manufacturers instructions ., Strains were sequenced using Illumina HiSeq 2000 sequencing technology ( Illumina , Inc . , San Diego , CA , USA ) generating 90 bp paired-end reads from a library with an average insert size of 500 bp and a total amount of quality-filtered raw sequence of over 600 Mbp per strain ., Quality filtering included the removal of duplicate reads","headings":"Introduction, Results, Discussion, Materials and Methods","abstract":"Third-generation cephalosporins are a class of \u03b2-lactam antibiotics that are often used for the treatment of human infections caused by Gram-negative bacteria , especially Escherichia coli ., Worryingly , the incidence of human infections caused by third-generation cephalosporin-resistant E . coli is increasing worldwide ., Recent studies have suggested that these E . coli strains , and their antibiotic resistance genes , can spread from food-producing animals , via the food-chain , to humans ., However , these studies used traditional typing methods , which may not have provided sufficient resolution to reliably assess the relatedness of these strains ., We therefore used whole-genome sequencing ( WGS ) to study the relatedness of cephalosporin-resistant E . coli from humans , chicken meat , poultry and pigs ., One strain collection included pairs of human and poultry-associated strains that had previously been considered to be identical based on Multi-Locus Sequence Typing , plasmid typing and antibiotic resistance gene sequencing ., The second collection included isolates from farmers and their pigs ., WGS analysis revealed considerable heterogeneity between human and poultry-associated isolates ., The most closely related pairs of strains from both sources carried 1263 Single-Nucleotide Polymorphisms ( SNPs ) per Mbp core genome ., In contrast , epidemiologically linked strains from humans and pigs differed by only 1 . 8 SNPs per Mbp core genome ., WGS-based plasmid reconstructions revealed three distinct plasmid lineages ( IncI1- and IncK-type ) that carried cephalosporin resistance genes of the Extended-Spectrum Beta-Lactamase ( ESBL ) - and AmpC-types ., The plasmid backbones within each lineage were virtually identical and were shared by genetically unrelated human and animal isolates ., Plasmid reconstructions from short-read sequencing data were validated by long-read DNA sequencing for two strains ., Our findings failed to demonstrate evidence for recent clonal transmission of cephalosporin-resistant E . coli strains from poultry to humans , as has been suggested based on traditional , low-resolution typing methods ., Instead , our data suggest that cephalosporin resistance genes are mainly disseminated in animals and humans via distinct plasmids .","summary":"The rapid global rise of infections caused by Escherichia coli that are resistant to clinically relevant antimicrobials , including third-generation cephalosporins , is cause for concern ., The intestinal tract of livestock , in particular poultry , is an important reservoir for drug resistant E . coli , but it is unknown to what extent these bacteria can spread to humans ., Food is thought to be an important source because drug-resistant E . coli have been detected in animals raised for meat consumption and in meat products ., Previous studies that used traditional , low-resolution , genetic typing methods found that drug resistant E . coli present in humans and poultry were indistinguishable from each other , suggesting dissemination of these bacteria through the food-chain to humans ., However , by applying high-resolution , whole-genome sequencing methods , we did not find evidence for such transmission of bacteria through the food-chain ., Instead , by employing a novel approach for the reconstruction of mobile genetic elements from whole-genome sequence data , we discovered that genetically unrelated E . coli isolates from both humans and animal sources carried nearly identical plasmids that encode third-generation cephalosporin resistance determinants ., Our data suggest that cephalosporin resistance is mainly disseminated via the transfer of mobile genetic elements between animals and humans .","keywords":"bacteriology, antimicrobials, gram negative bacteria, medicine and health sciences, genome evolution, evolutionary biology, food chains, infectious disease epidemiology, plasmids, population genetics, microbiology, gene transfer, antibiotic resistance, plant science, antibiotics, genome analysis, genetic elements, forms of dna, plant pathology, dna, microbial genomics, veterinary science, bacterial genomics, antimicrobial resistance, genetic polymorphism, veterinary microbiology, medical microbiology, epidemiology, molecular evolution, comparative genomics, biochemistry, ecology, genetics, microbial control, biology and life sciences, genomics, mobile genetic elements, computational biology","toc":null}
+{"Unnamed: 0":675,"id":"journal.pcbi.1003851","year":2014,"title":"A Novel Model to Combine Clinical and Pathway-Based Transcriptomic Information for the Prognosis Prediction of Breast Cancer","sections":"Breast cancer is the second ( after skin cancer ) most frequently diagnosed cancer in women , and ranks second ( after lung cancer ) in the deaths of women in year 2013 1 ., Most clinical studies categorize breast cancer into four molecular subtypes: Luminal A , Luminal B , Triple Negative\/Basal like and Her2 2 , 3 ., The survival outcomes differ significantly among the clinical subtypes ., Luminal A and B subtypes have a relatively good prognosis , whereas triple negative or basal like tumors , and Her2 tumors have very poor prognosis with much higher recurrence and metastasis rates 2\u20134 ., Furthermore , it is increasingly being realized that breast cancers are much more heterogeneous diseases than what is determined by the clinical subtypes , and that better prediction of prognosis is needed early on for more personalized treatment and management ., Towards this goal , prognosis biomarkers of breast cancers have been investigated in many studies 5\u20137 , based on signatures from high-throughput platforms such as gene expression profiles ., Some signature panels such as the NKI 70 test are currently in commercial use with decent prediction of metastasis 8 ., However , transcriptomic data are usually poorly dimensioned with many more genes than the number of samples , thus methods that reduce the dimension by incorporating higher-order information of functional units , such as gene sets , pathways and network modules , have been recently explored 9\u201316 ., This methodology is based on the observation that multiple genes involved in the same biological processes are often dysfunctional all together in cancers 17 , therefore features selected from representative functional units are presumably more robust with better biological annotations 10 , 17 ., Currently , two main approaches to define functional units have been proposed ., One approach is to identify de novo functional units from the data ., For example , van Vliet used an unsupervised module discovery method to identify gene modules , scored them and use them as features in a Bayes classifier 18 ., Teschendorff et al . reported improved prognostic classification of breast cancers via a novel strategy to discover the activated pathways from the modules of \u201cexpression relevance network\u201d 12 ., Similarly , network analysis with combination of all the useful gene information has been developed and utilized to measure the coordination among the genes 13 ., The other main approach uses the existing pathway information to build functional units ., For example , Lee et al used the MsigDB C2 gene sets to select feature sets using the t-test , and represented the pathway activity level by a subset of genes whose combined expression delivered optimal discriminative power for the disease phenotype 14 ., Abraham et ., al used a set statistic that aggregated the expression levels of all genes in a set , and constructed prognostic gene sets that were as predictive as individual genes , yet more stable and interpretable within the biological context 9 ., However , most of these methods model the prognosis as binary outcomes , and post hoc analyze the performance of the methods using survival information; or individualized information of pathway deregulation is lost during information extraction before deriving statistical metrics ., More importantly , the merits of combining clinical features and genomic features together have not been adequately addressed in most studies , where the models were only built upon the genomic information ., In this study , we use a novel pathway-based deregulation scoring matrix to transform the gene-based genomic features in combination with the Cox regression and L1-LASSO regularization to model survivals ., With this pathway deregulation score matrix as inputs , we constructed a pathway-based genomic model consisting of fifteen cancer relevant pathways that successfully predicted relapse difference ( log rank p-value\\u200a=\\u200a6 . 25e-12 , and AUC\\u200a=\\u200a0 . 80 ) and validated them on three breast cancer data sets with diversified clinical profiles ( log rank p-value<0 . 0005 , and average AUC\\u200a=\\u200a0 . 68 ) ., The pathway-based genomic models consistently performed better than gene-based models on all four data sets ., Moreover , combining genomic level information with clinical information improved prognosis prediction and classification by at least three orders of magnitudes of p-values , in comparison to either genomic or clinical information alone ., We used four individual gene expression microarray data sets for the testing and validation of the pathway-based prognosis model ( Table 1 ) , all of which were measured by Affymetrix HG-U133A array and had relapse and survival information ., We used the data set of 236 patients in Miller et . al . 19 as the training data mainly because this data set contains the most abundant clinical information , including ER status , PG status , tumor size , grade , lymph node status and P53 mutation ., PAM50 is a list of 50 genes initially proposed to successfully differentiate the breast cancer subtypes and it was later found that PAM50 also harbors good prognosis information on breast cancer 20 ., Therefore , we first present the testing data summary results and correlate relapse with PAM50 and other clinical factors ( Figure 1 ) ., Although tumor molecular subtypes are unknown due to the missing Her2 marker information , we nevertheless observed a good correlation between PAM50 matrix and relapse ., Based on the hierarchical clustering results of PAM50 heatmap , we dichotomized the samples into high and low risk groups , This grouping approach , without any supervised learning , results in a fairly good association to relapse status ( Chi-square test p\\u200a=\\u200a7 . 46e-5 ) ., Additionally , grade and lymph node have significant associations to relapse , with Chi-square test p-values of 0 . 018 and 9 . 146e-6 respectively ., Single clinical factor based survival analysis also confirms such significant relevance to relapse: p-values of Wilcoxon log rank tests for the p53 , grade , tumor size and lymph node status based survival differences are 0 . 0152 , 0 . 00181 , 1 . 92e-7 and 4 . 93e-8 , respectively ., Similar to previous observations 21 , ER and PG status are not good prognosis indicators , with the log rank test p-values of 0 . 819 and 0 . 227 , respectively ., There are a total of around 600 samples in the three testing data sets , 2 . 5 times the size of samples in the training set ., Testing set 1 ( Ivshina data ) 22 and testing set 2 ( Pawitan data ) 23 have very similar distribution pattern to the training data ( Miller data ) 19 ., However testing set 3 ( Desmedt data ) 24 has very different distribution compared to other three data sets , as the samples were all lymph node negative tumors ., We include set 3 as an extension to the other two testing data sets to exam the performance of the pathway-based genomic model for prognosis ., We have developed a novel pathway-based prognosis prediction model , unlike most other models that are gene-based ( Figure 2 ) ., We transformed a conventional gene-based matrix into a new pathway-based matrix of reduced numbers of rows , where each row represents a KEGG or BIOCARTA pathway-based scores over all samples ( columns ) ., Instead of using log2 transformed intensities as elements of the matrix , we used Pathway Dysregulation Scores ( PDS ) 25 that measure the distance of a particular pathway to the \u201cnormal condition\u201d curve in a hyperspace ., PDS ranges from 0 to 1 , and the higher PDS score signifies more \u201cabnormity\u201d ., This pathway-based PDS matrix was used as the initial input to select featuring pathways that are predictive of survival , based on the multi-variate Cox-PH model 26 ., We used L1-LASSO penalization method 27\u201329 to constrain the featuring pathways to be selected ., To be consistent , we conducted 250 simulations to select the best set of pathways ., We first evaluated the featuring pathways selected by the model , in relation to other clinical factors and relapse status in the training data set ( Figure 3 ) ., Comparing the heatmap of selected featuring pathways to that of the PAM 50 genes ( Figure 3A ) , the selected pathways are more prognostic for relapse ., This is supported by two observations: ( 1 ) Dichotomized samples of high risk and low risk groups through hierarchical clustering of PDS scores have a higher correlation to relapse status ( Chi-square test p\\u200a=\\u200a1 . 99e-6 ) , compared to those of PAM50 gene matrix ( Chi-square test p\\u200a=\\u200a7 . 46e-5 ) and ( 2 ) The median PDS scores over fifteen selected pathways have a correlation coefficient of 0 . 17 to relapse , in comparison to 0 . 08 for the median expression intensities over PAM50 genes ., Thus the selected pathways by our model are better prognostic features than PAM50 genes , in terms of the correlation to disease relapse ., To investigate the performance of the model , we used the PI value which is the logarithm of hazard ratio from the fitted Cox-PH model to dichotomize the samples , similar to others 21 30 ., We divided the samples into higher and lower risk groups with a 3 to 1 ratio ( 3rd quartile in PI ) , in order to match the relapse versus non-relapse sample ratio in the training data ., Samples with larger PDS scores are expected to have higher PI scores , and are more likely to have relapsed diseases ., The same PI threshold was applied to dichotomize the training data set as well as multiple independent testing data sets ., The performance of the genomic model was then evaluated by two approaches: ( 1 ) the Wilcoxon log rank test p-values of the Kaplan-Meier survival curves from the two risk groups in each data set , and ( 2 ) the AUCs of ROC curve based on binary classification ., Instead of combining all four data sets for meta-analysis , we kept them as individual data sets to validate the robustness of our model ., As expected , the pathway-based genomic model is highly accurate at differentiating the risks of breast cancer relapse within the training data , with a Wilcoxon log rank p-value of 6 . 25e-12 ( Figure 4A ) ., The model yields very decent predictive results with the p-value of 1 . 52e-4 in testing set 1 and 3 . 91e-5 in testing set 2 ( Figure 4B and 4C ) ., The predictive performances are expected to drop in the testing data sets , since they have different patient populations and clinical characteristics from the training set ( Table 1 ) ., Impressively , the model gives a very significant p-value of 3 . 73e-4 for testing data set 3 ( Figure 4D ) , which are all early stage lymph node negative tumors whose prognosis is very difficult to predict ., Additionally , we evaluated the performance of models using binary classification ., We used the relapse\/non-relapse information in the data sets as truth measures , and the models high vs . low risk classification as predictions ., As shown in Figure 4E , the ROC curve in the training set gives an AUC value of 0 . 80 , and AUCs of 0 . 73 ( testing set 1 , Pawitan data ) , 0 . 67 ( testing set 2 , Ivshina data ) , 0 . 65 ( testing set 3 , Desmedt data ) , consistent with the results in Kaplan-Meier curves ( Figure 4A\u2013D ) ., To examine the effect of total number of input pathways on model performance , we randomly kept 1\/2 , 1\/4 , 1\/8 and 1\/16 of all input KEGG and BioCarta pathways in the training dataset , and then generated the PDS Matrices for 18 simulations under each scenario ., For each simulation , we built the model with the same workflow as in Figure 2 and computed the Wilcoxon log-rank test p-value between the survival curves of the two risk groups , as well as the AUCs of the classification results ., The boxplot in Figure S1 shows a gradual decrease of AUCs due to the input pathways , in the order of 1\/2>1\/4>1\/8>1\/16 pathway-based models ., The difference between 1\/2 and 1\/4 pathways is significant ( p-value<0 . 05 ) ., All AUCs , however , are in the range between 0 . 69 and 0 . 81 ., Our earlier results of selected pathway features vs . PAM 50 genes suggested that pathway-based features may be better than gene-based features ., To validate this , we trained the four data sets individually and compared within the same data set the performance of pathway-based models and gene-based genomic models which do not have the PDS matrix generation step ( Figure 2 ) ., In order to test the risk differentiation power of the model , the cutoff PI value in each data set was set to match the ratio of relapse vs . non-relapse patients in that particular set ., The results of Kaplan-Meier survival curves and ROC plots based on classification all consistently show that pathway-based genomic models are superior to the gene-based models ( Figure 5A\u2013H ) ., For example , in Miller data set the log-rank p-value is 6 . 25e-12 for the pathway-based model ( Figure 5B ) , compared to that of 1 . 75e-9 for the gene-based model ( Figure 5A ) ., In the Desmedt data set , the p-value of the pathway-based model is even more significant than that of gene-based model ( 5 . 12e-36 vs . 8 . 84e-12 , Figure 5H and 5G ) ., Similarly , pathway-based genomic models have better ROC curves than gene-based genomic models ( Figure 5I ) , with AUCs of 0 . 80 vs . 0 . 78 in Miller data , 0 . 85 vs . 0 . 77 in Pawitan data , 0 . 74 vs . 0 . 70 in Ivshina data , and 0 . 92 vs . 0 . 76 in Desmedt data ., To estimate the statistical significance of comparisons among the pathway-based and gene-based models , we performed leave-one-out cross validation ( LOOCV ) simulations to compute the Wilcoxon log-rank test p-values and AUCs of ROC classification curves ., The cross validation results show that statistically the pathway-based models perform better than the gene-based models ( Figure S2 , all t-test p-values<0 . 001 ) ., These results are consistent with the observations from previous studies 12 , 14 , and support the hypothesis that including higher-order secondary information yields better prognostic values ., NKI70 ( Mammaprint ) is one of the most commonly used model for breast cancer prognosis prediction , and it has been approved by FDA for commercially use in clinics ., To demonstrate the potential clinical utilities of our model , we compared the NKI70 method with ours , and applied the NKI70 method to our training data set ( Miller data ) ., We first mapped the NKI70 gene signatures 8 to the genes in the U133A array , then correlated the gene-expression profile with the good-prognosis\/poor prognosis data from the NKI study and classified the samples into good and poor clusters as done previously 7 ., The NKI70 test gives a Wilcoxon log-rank test p-value of 2 . 58e-3 for the survival analysis , in contrast to the p-value of 6 . 25e-12 obtained by our pathway-based model; it only yields an AUC of 0 . 62 for classification , in contrast to 0 . 80 from our model ( Figure S3 ) ., Previous studies suggested that clinical information of breast cancers provides additional values to a genomic model that was built on lists of genes 21 ., To test if such merit of clinical information also applies to our genomic model of fifteen pathway features , we investigated the performances of the genomic , clinical and genomic-clinical combined models ., Since the scales of PDS and clinical features vary significantly , we re- normalized PDS and clinical features independently to have the standard normal distribution , so that they are subject to the same selection criteria ., The resulting clinical model is composed of four selected features: grade , tumor size , p53 and lymph node ., This is not surprising , as they are also significant factors in the univariate Cox-PH models ( Table 2 and Figure 1B\u2013E ) ., The combined model keeps ten of the fifteen pathways ( Table, 2 ) and about 60% of genes that were selected by the genomic model ., It also selects tumor size and lymph node status as additional features ( Table 2 ) ., This is expected given their highly significant p-values ( 1 . 92e-7 and 4 . 93e-8 , respectively ) in the univariate Cox-PH models ( Figure 1B and 1E ) , as well as relatively large coefficients in the clinical model ( 0 . 27 and 0 . 36 , respectively ) ., Since only testing data set 2 has both tumor size and lymph node information , we used this data set and the testing data set to demonstrate the performances of genomic , clinical , and combined models ., The comparisons present the compelling advantage of combining clinical and genomic information in a model ( Figure 6 ) ., As shown in the training data , selected clinical features are undoubtedly important: the Wilcoxon log rank test p-value of the clinical model is 2 . 21e-10 ( Figure 6E ) , slightly less significant than the pathway-based genomic features by two orders of magnitude ., Most importantly , the combined model is much better than either genomic model ( p-value\\u200a=\\u200a6 . 25e-12 ) or clinical model alone , with a p-value of 1 . 88e-24 ( Figure 6C ) ., This trend of significances is consistent in the testing set 2 , with the p-values of 1 . 12e-7 in the combined model ( Figure 6D ) , 1 . 52e-4 in the genomic model ( Figure 6B ) , and 2 . 7e-3 in the clinical model ( Figure 6F ) ., Moreover , the ROC curve comparisons of these three models also show the same order of performances: combined model>genomic model>clinical model , with AUCs of 0 . 83 , 0 . 80 , and 0 . 74 in the training set , and 0 . 71 , 0 . 68 and 0 . 65 in the testing set 2 ( Figure 6G ) ., To demonstrate the statistical significance of comparisons among the pathway-based , clinical and combined model in the training set and the testing set 2 , we performed leave-one-out cross validation ( LOOCV ) simulations to compute the Wilcoxon log-rank test p-values and AUCs of ROC classification curves ., The cross validation results show that statistically the combined model performs better than the pathway-based model , and the pathway-based model performs better than the clinic model ( Figure S4 , all p-values<0 . 001 between pathway-base\/clinical models and combined models ) ., We expect that the consensus pathways selected both in our genomic model and combined model convey important cancer-related functions ., To test this we examed the annotations of this subset of ten pathways ( Table 2 ) ., Interestingly , KEGG_MELANOGENESIS is selected as a feature , probably due to inclusion of many cancer relevant genes in this pathway: such as protein kinase genes PRKACB , PRKACG , PRKCB , PRKCA; phosphorylase kinase genes CALM1 , CALM2 , CALM3; G-protein related gene GNAQ , HRAS; mitogen-activated protein kinases MAPK1 , MAPK3 , MAP2K1; and other oncogenes like RAS 31 , 32 ., Many of these genes have been shown to function in breast cancer progression 31 ., Impressively , multiple signaling pathways are selected , including BIOCARTA_P53_PATHWAY , BIOCARTA_SRCRPTP_PATHWAY , BIOCARTA_PYK2_PATHWAY , BIOCARTA_VIP_PATHWAY , BIOCARTA_RARRXR_PATHWAY , and BIOCARTA_AKAP13_PATHWAY ., They are well-known to be associated with breast cancers prognosis 33\u201339 ., The best example is BIOCARTA_P53_PATHWAY , the dysregulation of p53 Signaling Pathway is well-documented , and the tumor-suppressor gene p53 has one of the highest mutation rates in breast cancer 5 , 19 ., In addition , some pathways related to basic cell functions are selected as prognostic features ., For example , G1_PATHWAY is selected , and the G1\/S cell cycle checkpoint controls are well known to be dysfunctional in many cancers including breast cancer 40 ., FATTY_ACID_METABOLISM is also selected by the model , and many studies have showed that fatty acid metabolism is involved in breast cancer 41 ., In particular , Fatty acid synthase ( FASN ) is highly expressed in breast cancer with a poor prognosis compared to others 41 ., Interestingly , BIOCARTA_RNA_PATHWAY is also selected , largely due to its members TP53 and MAP3K14 that are closely related to breast cancer ., A total of 265 genes are overlapped between the selected pathways of the genomic model and the combined model ., Table 3 summarizes the top 30 genes that are involved in the selected pathways ., They are ranked by weighted sum of both occurrences in selected pathways ( counts ) and weights measured by the hazard ratio of each pathway ., Among them , many genes encode protein kinases that are well-known to be involved in breast cancers , such as PRKACB , PRKACG , MAPK1 and CALM1 ., Some other genes encode transcription factors that are well-known for their close relationship to cancer , such TP53 , RB1 , HRAS , RAF1 , GRB2 , E2F1 , and SRC 32 , 42\u201344 ., We therefore conclude that the selected pathways are prognostic features of significant cancer relevance ., The heterogeneity of cancers is being increasingly recognized , suggesting more personalized care decisions with treatment for individual patients are needed ., As a result , prognosis prediction of breast cancers with high-throughput data has been a growing topic in recent years ., Many statistical and machine learning methods have been developed to analyze various types of high-throughput cancer genomics data , by taking advantage of higher-order relationships among genes ., The hypothesis is that the highly correlated gene-based markers often represent identical biological processes; therefore by including higher-order representative features , such as Gene Ontology sets , pathways and network modules , the prediction will be more stable 9\u201314 , 45 ., Our novel method of prognosis prediction presented in this study belongs to this class of methods ., However , unlike some other methods where individual pathway information is lost due to summarization or transformation , the pathway features proposed in this study explicitly measure the degrees of pathway dysregulation for cancer recurrence ., Comparing selected pathways and the PAM50 genes which were demonstrated to be prognostic 20 , the PDS-based pathway approach has better correlation to breast cancer relapses ., Moreover , when comparing gene-based with the pathway-based genomic models , where the only difference between them was the input matrix , pathway-based models uniformly performed better than gene-based models in all the data sets we tested ., Our results are consistent with several other gene-set\/pathway-based models 9 , 14 , where different summarization metrics were used ., It will be very interesting to compare the prediction results based on these different metrics in a follow-up study ., To demonstrate the robustness in predicting differential risks of relapse from the pathway-based genomic model , we chose to train and test on independent study samples , rather than combining them together as a large data set 21 , 46 , which would diminish the effect of population heterogeneity ., Despite population difference and much bigger testing data size relative to the training data size , the method still achieved good performance on all three testing data sets , including a data set of all early stage lymph node negative tumors where prognosis is particularly difficult to predict ., Another merit of our method is that it enables combining the important clinical information with the pathway-based genomic information ., Even though the clinical model by itself is the least predictive , compared to the genomic model and the combined model , it is nevertheless significant and informative , as shown by tumor size and lymph node status ., The genomic model is better than clinical model alone ., However , the combined model of clinical and genomic features performs the best ., Our conclusions agree and extend the earlier work from Fan et al . 21 who focused on prognosis prediction of all node-negative and systemically untreated breast cancer patients , since we include both node-negative and node-positive samples ., The results of the genomic model ( AUC\\u200a=\\u200a0 . 80 and p-value\\u200a=\\u200a6 . 25e-12 in training data , and AUC\\u200a=\\u200a0 . 68 and p-value\\u200a=\\u200a1 . 52e-4 in test data 2 ) and the combined model ( AUC\\u200a=\\u200a0 . 83 and p-value\\u200a=\\u200a1 . 88e-24 in the training set , and AUC\\u200a=\\u200a0 . 79 and p-value\\u200a=\\u200a1 . 12e-7 in test data set 2 ) are better than what was recently reported by Vilinia S et al 47 ., They obtained an AUC\\u200a=\\u200a0 . 74 for the training set and 0 . 65 for the testing set , in a model that combined signatures of mRNA and microRNAs deriving from the TCGA IDC cohort sequencing data ., This suggests the advantages of combining PDS based pathway score inputs with a Cox-PH model and LASSO penalization approach: even though the genomic data in our study are based on microarrays that have more noise and smaller sample sizes , they still yield better predictive results in comparison to the combined mRNA and microRNA sequencing signatures obtained from a larger sample size ., It will be of great interest to apply our models to the TCGA breast cancer mRNA and microRNA sequencing data in the future ., The pathways selected by the model show biological relevance to breast cancer prognosis ., The fatty acid metabolism pathway is found to be crucial to maintain the cancer cell malignant phenotype , and higher expression of fatty acid synthase has been discovered as a common phenotype in breast cancer with a poorer prognosis 41; As another example , Src kinase activation by protein tyrosine phosphatase alpha ( SRCRPTP_PATHWAY ) , has been discovered in invasive breast cancer with compelling evidences ., Src inhibitors are being considered as potential therapy to treat invasive breast cancers , as inhibition of c-src was recently found to be involved in E2-induced stress which would finally result in apoptosis in breast cancer cells 33 ., Increasing evidence shows that vasoactive intestinal peptide ( VIP ) in BIOCARTA_VIP_PATHWAY is highly expressed in breast cancer cells along with its receptor 33 , and VIP-targeted nanomedicine is under study as therapy for breast cancer 34 ., Pyk2 in BIOCARTA_PYK2_PATHWAY is linked to map kinases MAPK , which has wealthy records in breast cancer studies 35 ., RARRXR_PATHWAY is the RAR\/RAR nuclear receptor complex that is co-activators to facilitate initiation of transcription in carcinoma cells 37 ., And BRX , the truncated form of Rho-Selective Guanine Exchange Factor AKAP13 in the BIOCARTA_AKAP13_PATHWAY , has been identified to function as an ER cofactor 39 ., Although the workflow proposed in this study is generic and the pathway features are clearly significant , we should point out a few potential limitations of the model ., First of all , the pathway-based model is trained and tested on gene expression data from the U133A platform ., We suspect that direct application of the model to other platforms , such as RNA-Seq , is not desirable , and some additional re-processing work has to be done additionally ., The reason is that data distributions maybe very different between various platforms ., One notorious example is that biomarkers identified by high-throughput microarray platform often had poor correlations in qPCR platform ., Thus we recommend that when researchers use the workflow in Figure 2 on different data types , they may increase the predictive power by retraining the model with their own data ., Another limit of our approach is that we only used the information from genes that compose the 403 pathways that we considered , thus some gene-level information is unavoidably lost ., In our case , over 4500 genes were enlisted in the pathways , and among them over 3200 genes are probably expressed ( averaged log 2 expression intensities >7 ) ., On the other hand , the raw U133A array has results of over 14 , 000 genes within which over 10 , 000 genes are probably expressed ., Therefore our model captures about 1\/3 of the gene-level information overall ., One can certainly use other curated gene sets , such as the MsigDB C2 gene sets , to increase the coverage of the genes by the pathways ., However , from the sensitivity analysis that we have performed ( Figure S1 ) , we only observed a slight decrease of model performance based on AUCs , which are in the range of 0 . 69 and 0 . 81 ., In conclusion , we propose a novel pathway-based genomic model that measures the pathway-based deregulation score and shows significant prognosis values ., This pathway-based genomic model performs better than the gene-based genomic model ., Additionally , we found that combining the clinical information of lymph node status and tumor size improves the performance of the prognosis model ., Many selected pathways in our study present values for breast cancer prognosis prediction , and they are also promising therapeutic targets for future investigations ., We used four publicly available data sets of breast cancer samples from National Center for Biotechnology Information ( NCBI ) Gene Expression Omnibus ( GEO ) GSE4922 22 , GSE1456 23 , GSE3494 19 and GSE7390 24 ., All four data sets are based on Affymetrix HG-U133A microarray platform , and have relapse-free survival information as well as some other clinical information , as shown in Table 1 ., For data set GSE7390 24 , all patients are lymph node negative ., The GSE3494 data set was used as the training set as it has more clinical information , and all others were used as testing data sets ., We mapped original probe IDs to Gene IDs using R package biomaRt 48 ., In order to relate the probe ID to the Gene ID , we downloaded the array annotation file and used the RefSeq IDs as the intermediates to map to the Gene ID ., When a gene has multiple probes , we computed the geometric mean of log2 transformed probe intensities as the gene expression ., All the data sets were normalized independently between array using limma package 49 ., To minimize batch effects across different data sets , we used the CONOR package with the Bayesian method 50 ., We generated the PAM50 heatmap of the gene expression data and the correlation heatmap with hierarchical clustering , where Euclidean distance measure was employed ., For the clinical factors , we correlated their associations with the relapse in the training data set with both Chi-square test and Wilcoxon log-rank test for survival curves ., The pathway information was obtained from the GSEA ( http:\/\/www . broadinstitute . org\/gsea\/ ) curated gene sets that include a total of 403 pathways from Biocarta ( http:\/\/www . biocarta . com ) 51and KEGG 52 ., To perform gene sets analysis , we used R package Pathifier 25 , an algorithm that transforms the information from the gene level to pathway level and infers pathway deregulation scores for each pathway within each sample ., The pathway deregulation score ( PDS ) in each sample is a measure of degrees of the deviation of a specific pathway from the \u201cnormal status\u201d located on the principle curve ., The concept of principle curve was proposed by Hastie and Stuetzle 53 as a nonparametric nonlinear extension of the PCA ( Principle Component Analysis ) in which the assumptions of dependence in the data are avoided ., A principle curve is a one-dimensional curve that is derived from the local average of p-dimensional points and goes through the cluster of p-dimensional principle components ., It sensibly captures the information of variation in all the samples ., Specifically , the single parameter \u03bb varies tracing the whole data along the curve 53 ., The curve f ( \u03bb ) is defined to be a principal curve if for arbitrary \u03bb ., The principle curve is built through iterations of smoothed procedure in the local average of data points ., If one sample differs from others in one specific pathway , the distance to the curve is further and it leads to a higher PDS score and vice versa ., In the model selection stage , we used Cox-Proportional Hazards ( Cox-PH ) model based on L1 \u2013 penalized ( LASSO ) estimation 27\u201329 , with the R package penalized 29 ., With the input of both PDS score containing the gene sets information and survival information of time and relapse , a tuning parameter lambda was used to restrict the number of paramete","headings":"Introduction, Results, Discussion, Materials and Methods","abstract":"Breast cancer is the most common malignancy in women worldwide ., With the increasing awareness of heterogeneity in breast cancers , better prediction of breast cancer prognosis is much needed for more personalized treatment and disease management ., Towards this goal , we have developed a novel computational model for breast cancer prognosis by combining the Pathway Deregulation Score ( PDS ) based pathifier algorithm , Cox regression and L1-LASSO penalization method ., We trained the model on a set of 236 patients with gene expression data and clinical information , and validated the performance on three diversified testing data sets of 606 patients ., To evaluate the performance of the model , we conducted survival analysis of the dichotomized groups , and compared the areas under the curve based on the binary classification ., The resulting prognosis genomic model is composed of fifteen pathways ( e . g . P53 pathway ) that had previously reported cancer relevance , and it successfully differentiated relapse in the training set ( log rank p-value\\u200a=\\u200a6 . 25e-12 ) and three testing data sets ( log rank p-value<0 . 0005 ) ., Moreover , the pathway-based genomic models consistently performed better than gene-based models on all four data sets ., We also find strong evidence that combining genomic information with clinical information improved the p-values of prognosis prediction by at least three orders of magnitude in comparison to using either genomic or clinical information alone ., In summary , we propose a novel prognosis model that harnesses the pathway-based dysregulation as well as valuable clinical information ., The selected pathways in our prognosis model are promising targets for therapeutic intervention .","summary":"With the increasing awareness of heterogeneity in breast cancers , better prediction of breast cancer prognosis is much needed early on for more personalized treatment and management ., Towards this goal we propose in this study a novel pathway-based prognosis prediction model , which emphasizes on individualized pathway-based risk measurement using the pathway dysregulation score ( PDS ) ., In combination with the L1-LASSO penalized feature selection and the COX-Proportional Hazards regression model , we have identified fifteen cancer relevant pathways using the pathway-based genomic model that successfully differentiated the relapse in the training set as well as three diversified test sets ., Moreover , given the debate whether higher-order representative features , such as GO sets , pathways and network modules are superior to the gene-level features in the genomic models , we demonstrate that pathway-based genomic models consistently performed better than gene-based models in all four data sets ., Last but not least , we show strong evidence that models that combine genomic information with clinical information improves the prognosis prediction significantly , in comparison to models that use either genomic or clinical information alone .","keywords":"medicine and health sciences, bioinformatics, epidemiology, database and informatics methods, biology and life sciences, computational biology, disease informatics, research and analysis methods","toc":null}
+{"Unnamed: 0":1666,"id":"journal.pcbi.1000500","year":2009,"title":"Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields","sections":"Neurons possess highly branched , complex dendritic trees , but the relationship between the structure of the dendritic arbor and underlying neural function is poorly understood 1 ., Recent studies suggest that dendritic branches form independent computational subunits: Individual branches function as single integrative compartments 2 , 3 , generate isolated dendritic spikes 4 , 5 linking together neighbouring groups of synapses by local plasticity rules 6\u20138 ., Coupling between dendritic branches and the soma is regulated in a branch-specific manner through local mechanisms 9 , and the homeostatic scaling of the neurotransmitter release probability is also regulated by the local dendritic activation 10 ., The computational power of active dendrites had already been demonstrated by several computational studies 11\u201316 , but how local events influence the output of the neuron remained an open question ., Using the cable equation 17 or compartmental modelling tools one can calculate the current or voltage attenuation between arbitrary points in a dendritic tree 14 , which is in good agreement with in vitro recordings ., However , cortical networks in vivo are believed to operate in a balanced state 18 , 19 , where the inhibitory drive is continuously adjusted such that the mean activity of the population is nearly constant 20 , 21 ., In this case , the firing of an individual neuron is determined , beyond its own input , by the activity distribution of the population ., A simple cascade model 22 incorporating numerous dendritic compartments allowed us the statistical estimation of the activity distribution of neurons within the population ., We used this model to study how localized dendritic computations influence the output of the neuron ., The present study focuses on hippocampal granule cells ., Compared to pyramidal neurons granule cells have relatively simpler dendritic arborization: They lack the apical trunk and the basal dendrites , but are characterized by several , equivalent dendritic branches , extended into the molecular layer 23 ( Figure 1A ) ., Recordings from freely moving rats revealed that like pyramidal neurons , granule cells exhibit clear spatially selective discharge 24 , 25 ., However , granule cells had smaller place fields than pyramidal cells , and had multiple distinct subfields 24 , 26 ., It has also been recently shown that these subfields are independent , i . e . , their distribution was irregular and the transformation of the environment resulted in incoherent rate change in the subfields 26 ., The dendritic morphology of granule cells suggest that parallel dendritic computations could contribute to the generation of multiple , distinct subfields of these neurons ., In the present study we analyzed how synaptic input arriving to dendritic subunits influence the neuronal output ., First , we introduce the model used in this study and we define statistical criteria to measure if a dendritic branch alone is able to trigger somatic spiking ., We show , that generally neurons perform input strength encoding i . e . , input to the whole dendritic tree but not activation of a single branch is encoded in the somatic firing ., Next we demonstrate that if the local response is enhanced by active mechanisms ( dendritic spiking and synaptic plasticity ) then neurons switch to feature detection mode during which the firing of the neuron is usually triggered by the activation of a single dendritic branch ., Furthermore we show that moderately branched dendritic tree of granule cells is optimal for this computation as large number of branches favor local plasticity by isolating dendritic compartments , while reliable detection of individual dendritic spikes in the soma requires low branch number ., Dendritic branches of dentate granule cells could therefore learn different inputs; and the cell , activated through different dendritic branches , could selectively respond to distinct features ( locations ) , participating in different memories ., Finally using spatially organized input we illustrate that our model explains the multiple independent place fields of granule cells and these dendritic computations increase the pattern separation capacity of the dentate gyrus ., Supposing that firing rates of presynaptic neurons ( uj ) are independent and identically distributed we assume that the total input of the dendritic branches Ui\\u200a=\\u200a\u03a3jwijuj is drawn randomly from a Gaussian distribution with mean \u03bc and variance \u03c32: ( 5 ) where pU indicates a probability distribution over U ( Figure 1C; see Eq . 17 in Methods for parameters specific to hippocampal granule cells ) ., More specifically , indicates the distribution of the magnitude of possible total inputs to a single dendrite over many different instances ., Based on the distribution of the total input , we can compute the distribution of the somatic activation and determine the firing threshold ( \u03b2 ) according to the proportion of simultaneously active cells ( the sparseness of the representation , spDG ) in the DG 24 ., First , we rearrange Eq ., 3 using the input distribution to express the distribution of : ( 6 ) where indicates that the inputs of the dendritic branches are randomly sampled from a Gaussian distribution ., We substitute Eq ., 6 into Eq ., 4 , and we get ( 7 ) We can assume again , that the inputs ( Ui ) of the dendritic branches are independent and identically distributed variables ., ( Note , that while the activations are not independent because of the back-propagation of currents from the soma , the inputs are . ), If N is high enough , we can approximate the sum in Eq ., 7 with a Gaussian distribution , and rewrite the equation: ( 8 ) where indicates a probability distribution over , while \u03bcF and are the expected value and the variance of the dendritic integration function F ( U ) given the input distribution : ( 9 ) ( 10 ) We calculated the integrals 9\u201310 with two different forms of dendritic integration of synaptic inputs: a linear and a quadratic function ( Figure 1C ) ., The details of these calculations are in the Supporting Information ( Text S4 ) ., In this paper we do not model inhibitory neurons in the dentate gyrus , however , we assume , that they play a substantial role in continuously adjusting the firing threshold of principal neurons and regulating the activity of the network 20 , 21 ., As a result of this regulation always the most depolarized neurons are able to fire , and the proportion of simultaneously active neurons is characteristic for different hippocampal areas 24 , 29 ., Given that all neurons share a common input statistics and have similar internal dynamics , equation 8 also describes the distribution of across the granule cell population at a given time ., If only the most depolarized 1\u20135% of the population are able to fire 29 , this also means that only those neurons exceed their firing threshold whose activation is within the uppermost 1\u20135% of the distribution described by Eq ., 8 ., Therefore , the proportion of simultaneously active neurons within the dentate gyrus spDG 24 , 29 also determine the firing threshold \u03b2 for granule cells ., We approach the dendritic independence by focusing on the statistical distributions of the input to dendritic branches , as these branches form the basic computational subunits in our model ., We ask whether the input of a single branch could be sufficiently large to significantly depolarize not only the given branch but also the soma of the neuron ., We defined two conditions to study whether the spiking of the neuron is caused by the activation of a single dendritic branch or by the simultaneous depolarization of multiple branches ., First , the conditional probability is the probability of firing given that any branch k has total input Uk\\u200a=\\u200a\u03a3jwkjuj , while inputs to all other branches are random and independent samples from the distribution of ( Figure 2A ) ., At those Uk values where this probability is close to 1 the cell tends to fire when any of the dendritic branches gets that input ., Second , the conditional distribution is the distribution of the synaptic input of the most active branch at the time the depolarization of the soma exceeds the firing threshold ( \u03b2 ) , where U* is the total synaptic input arriving to the most active branch ( Figure 2A ) ., K ( U* ) can be regarded as the marginal distribution of above the firing threshold ( Figure 2B ) ., The probability mass of this function shows the typical maximal input ( U* ) values when the neuron fires ., These two conditions together determine whether a single branch can be sufficiently depolarized to trigger somatic spike or not ., If the probability of firing is high ( H ( U ) \u22481 ) at typical input values ( K ( U* ) ) then the firing of the cell is caused by a single branch ., With the definition of Gasparini and Magee 30 we call this form of information processing as independent feature detection ., On the other hand , if the firing probability is low ( H ( U ) \u226a1 ) even if one of the branches receive extremely large input ( U* is high ) then the cell mostly fires when the overall dendritic activation is high , and even the most depolarized branch usually fails to make the neuron fire ., We use the expression input strength encoding 30 to denote this second type of computation ., The calculation of the two functions H ( U ) and K ( U* ) is described in the Methods section ., First we chose unstructured synaptic input , i . e . , the firing of entorhinal neurons were independent and the strength of all synapses were equal ., In this case we approximated the total synaptic input U to a branch with a Gaussian distribution ( Eq . 5 , Figure 1C ) ., Given the input distribution we asked whether the excitation of single branches can be sufficiently large to cause significant depolarization in the soma ., The typical largest input values , indicated by the probability mass of K ( U* ) ( Figure 2C\u2013D ) are unable to sufficiently depolarize the soma and determine the neuronal output ( indicated by the low H ( U ) values ) in the case of both the linear ( Figure 2C ) and the quadratic ( Figure 2D ) integration functions ., Wherever K ( U* ) has high values , H ( U ) is low in both cases , which indicate , that these branches are not able to independently influence the output of the neuron ., Only coactivation of several branches could make the neuron fire in this case , and the output of the neuron encodes the strength of all dendritic inputs ., As H ( U ) converges to 1 for high input values extremely high inputs to a single dendrite could reliably trigger somatic firing ., In the next sections , however , we study how synaptic plasticity selectively modifies individual synapses and contributes to the sparse occurrence of extraordinarily high input values ., During Hebbian learning synapses contributing to postsynaptic activation are potentiated while other synapses may experience compensatory depression 31 , 32 ., We simulated the learning process by showing a finite number of uncorrelated samples from the input distribution ( see Methods ) to the model neuron initiated with uniform synaptic weights ., The synaptic weights of those dendritic branches where the activation exceeded a threshold , \u03b2d were modified according to the following Hebbian plasticity rule 33 that incorporates heterosynaptic depression 31: ( 11 ) where is the local dendritic activation , uj is the presynaptic firing rate and wij is the synaptic strength ., is the Heaviside function and \u03b3<1 is a constant learning parameter ., Note , that the learning rule is local to the dendritic branches: the synaptic change depends on the local activation but not on the somatic firing ., Next , we calculated the total input to the branches Ui\\u200a=\\u200a\u03a3jwijuj after modification of synapses ( Figure 3A ) , and recalculated the two functions H ( U ) and K ( U* ) defined previously with the new input distribution ( Eq . 18 ) ., As shown on Figure 3A the total synaptic input in response to a learned pattern increases significantly after learning ( compare blue and grey curves on Figure 3A ) , while untrained patterns generate smaller synaptic inputs ( compare grey and black curves on Figure 3A ) ., The main consequence of synaptic plasticity is that the trained patterns generate much larger local response than untrained patterns , which raise the possibility of their detection in the soma ., Note , that an unspecific increase of synaptic weights would result in an upward shift of both the input distribution ( Eq . 5 ) and the firing threshold , but would not affect the somatic detection of individual dendritic events ., The neuron is able to selectively respond to the dendritically learned patterns if a single branch , when facing with its preferred input , is able to induce significantly more depolarization at the site of the action potential initiation compared with the case when all of the branches get random , not learned input ., Figure 3B\u2013E shows the dendritic input and the activation of the soma after learning ., If the maximal input U* is small ( left bumps on Figure 3B , D ) and none of the branches got its preferred input then the somatic activation is usually small ., If U* is high ( Figure 3B , D; right bumps ) , which means that one of the branches receives its preferred input pattern , then the somatic activation is increased ., The increase of the somatic activation with learned input is only moderate in the linear case ( Figure 3B , C ) resulting in an incomplete separation of learned and not learned inputs by the somatic firing threshold ., However , if synaptic inputs are supra-linearly ( quadratically ) integrated within the dendritic branches , efficient separation is possible: the probability that the presentation of a learned pattern elicits subthreshold somatic response , called dendritic spike detection probability was over 95% ( Figure 3D , E ) ., In this case the output of the neuron encodes whether or not one of the stored features was present in the neurons input and not simply the strength of the total input arriving to the whole dendritic tree ., In other words , if dendritic nonlinearity enhance the response of a given branch to its preferred input , then this branch alone is able to trigger somatic spiking ., In the following sections we use the term dendritic spiking to refer to these supra-linear dendritic events ., Although there is no data available on the synaptic induction of local dendritic spiking in hippocampal granule cells , voltage dependent Ca2+ currents are present in the membrane of granule cells 34 , 35 and whole-cell recordings from these neurons suggest that T-type Ca2+ channels can generate dendritic action potentials at least in young neurons 36 or under hyper-excitable conditions 34 , 37 ., Next , we explored how the independent feature detection ability of the model depends on the resistance between the somatic and dendritic compartments with nonlinear dendritic integration ., In the passive cable model of dendritic trees the space constant of the membrane \u03bbm\u2248 ( Rm\/Ri ) 1\/2 plays a substantial role in determining the voltage attenuation among two sites ., Consequently , an increase in the intracellular resistivity Ri or a similar decrease in the membrane resistance Rm will contribute to the separation of dendritic subunits by decreasing the membranes space constant \u03bbm ., In the present study we used the inverse of the space constant R\u2248Ri\/Rm to characterize the degree of electrical resistivity between the somatic and dendritic compartments ., Indeed , an increased resistivity ( R ) between the compartments ( smaller space constant ) induced larger degree of electrical isolation as the somatic response to the same amount of dendritically applied current decreased ( compare Figure 4A left and right panels ) ., However , this isolation did not modify the dendritic spike detection probability in the soma: Large dendritic spikes localized to a single compartment could be reliably separated from subthreshold events with a somatic firing threshold at a large range of resistances R ( Figure 4A\u2013B ) ., This was also true for the selective alternation of the somatic or the dendritic membrane resistance ( Figure 4B ) ., On the other hand , the resistance parameter had a substantial impact on the isolation of different dendritic compartments which might be necessary for the independence of synaptic plasticity ., To measure the isolation of the dendritic subunits we calculated the influence of other compartments on the activation of a given branch ( external influence ) quantified by the standard deviation of ., Figure 4C shows the activation of a dendritic branch in the function of its input at different R values ., If the resistance is small ( , Figure 4C , left ) , then the local activation depends only slightly on the local input and the external influence is high ( Figure 4D ) ., In this case the local input spread out to the entire dendritic tree and activates similarly all branches ., On the other hand , if the resistance is high ( R\\u200a=\\u200a1 , Figure 4C , right ) then the external influence is small , and the depolarization of a dendritic branch depends mostly on the local input ., Interestingly , decreasing the resistance of the perisomatic membrane ( ) alone was more efficient in separating the dendritic subunits than decreasing the resistance of the dendritic membrane or both ( Figure 4D ) ., The extensive GABAergic 38 , 39 and glutamatergic 40 innervation of the proximal dendritic and perisomatic region of granule cells may therefore contribute significantly to the isolation of the dendritic compartments ., The impact of a single branch on the somatic activation , and also the coupling between dendritic branches may depend highly on the structure of the dendritic tree ., Therefore we varied the number of dendritic subunits , N , and calculated the probability of detecting dendritic spikes in the soma and the external influence on the dendritic subunits ( Figure 5 ) ., The probability of detecting a dendritic spike in the soma decreased gradually after a few ( N\u224830 ) number of branches from 1 to 0 . 3 ( N\u22481000 , Figure 5A\u2013B ) ., If the number of branches was low , then the effect of a single branch on the soma was relatively high , and the somatic detection of single dendritic events was reliable ., Conversely , one out of hundreds of branches had relatively low impact on the neurons output even if the local depolarization was significant ., The electrical coupling between the dendritic subunits characterized by the external influence on the local activation also decreased with the number of branches , ( Figure 5C\u2013D ) ., In the model the branches are connected through the somatic compartment , and because the variance of the somatic activation decreases if N increases ( Eq . 8 ) , the external influence will also decrease ., However , in a complex dendritic tree containing higher number of subunits the branches are electronically more isolated which is required for local plasticity ., To keep the probability of dendritic spike detection high and the dendritic coupling low at the same time , the number of branches should therefore be as high as possible , but not higher than N\u224860 ., As we showed on Figure 4 , the dendritic coupling depends on the resistance R , as high resistance separates better the subunits ., Therefore we conclude , that a medium number of branches with relatively high resistance is ideal for parallel dendritic computations ., The optimal number of dendritic subunits , however , depends on the size of the dendritic event determined by the local integration of the synaptic inputs ( Figure 5B ) ., Appropriate detection of dendritic responses to learned patterns with linear integration is possible only in very small dendritic trees , whereas supra-linear integration allows the detection of individual dendritic events also in a larger dendritic arbor ., Nonlinear integration by dendritic spiking therefore permits the neuron to selectively respond to a larger number of distinct input pattern ., During the calculation above we assumed , that the activity of the presynaptic neurons are independent and that the samples from the distribution are uncorrelated ., It is known , however , that the firing of entorhinal neurons are not independent: At least half of layer II cells in the medial entorhinal cortex ( EC ) are grid cells , whose firing depend mostly on the position of the animal 27 ., Moreover , in reality animals do not face with discrete uncorrelated samples , but they experience the continuous change of their environment which is mirrored by the activity of the entorhinal neurons ., In order to test our model under more realistic conditions , we simulated the activity of the rodents EC during exploratory behavior as input to our modeled granule cell ., The EC consisted of two neuron population: A population of grid cells ( 1000 neurons , 5 spacing , 5 orientations ) representing a path integrator system 41 and a population of visual cells ( 1200 units ) , representing highly processed sensory information available in the EC 42 ., In these simulations we used the Webots mobile robot simulator 43 ., The firing statistics of the entorhinal neurons was the same as used in the analytical calculation except that the activity of the neurons was location dependent ., Moreover , as we simulated the trajectory of the rat during continuous foraging for randomly tossed food pellets 26 the subsequent input patterns were highly correlated ., We simulated a single granule cell with N\\u200a=\\u200a20 dendritic branches each of them receiving a total number of M\\u200a=\\u200a100 synaptic contacts from entorhinal neurons ., The resistance was R\\u200a=\\u200a1 , we used the quadratic integration function and the neuron was tested in 5 different environments ., During the 5 min . learning period ( while 2000 spatial locations was sampled with an average running speed of 0 . 22 m\/s ) 0\u20138 branches learned usually at different spatial locations in each of the 5 environments ., In most of the time synaptic plasticity in different branches occurred at different places , therefore the subunits were able to learn independently ., Moreover , learning occurred only in naive branches , i . e . , each branch learned only in one environment at a specific location and synapses of trained branches did not engage in learning at a different location ., After the training period the synaptic weights of those branches that were subthreshold for synaptic plasticity ( \u03b2d\\u200a=\\u200a1 . 11 ) in all environments were scaled down manually ., Next we studied the spatial activity pattern of the somatic and dendritic compartments while the robot was moving on a different track in the same environments ., The dendritic branches responded with high activation ( \u201cdendritic spikes\u201d ) to subsequent visit of places close to their preferred locations leading to the formation of dendritic place fields ( Figure 6 ) ., Moreover , since the activation of the soma was substantially increased in each of these dendritic place fields , the neuron had a multi-peaked activity map in several environments ( Figure 6 ) ., Finally we explored the effect of the size of the dendritic tree on the spatial firing pattern of the neuron ( Figure 7 ) ., If there were only a few functional dendritic subunit than the neuron obviously had a small number of dendritic place fields ( Figure 7A ) , but the individual branches had strong influence on the somatic activity ., Therefore the correlation between the somatic activation as and the maximal dendritic input U* was high ( Figure 7B , C ) , as predicted by the analytical calculations ., On the other hand , in neurons with large number of dendritic subunits there were more dendritic place fields ( Figure 7A ) , but a single branch had only a little impact on the activity of the neuron ( Figure 7D ) ., Accordingly , the correlation between the maximal dendritic input and somatic activation was reduced ( Figure 7B ) ., In these cases the cell fired when the overall excitation was high or when more than one branch were simultaneously excited ., Therefore , the moderately branching dendritic tree of granule cells seems optimal for parallel dendritic computations since extensive branching inhibits the detection of individual dendritic events ., We conclude , that clustered plasticity together with dendritic spiking may be an adequate cellular mechanism to explain the generation of multiple place fields in the DG 24 , 26 ., Dendritically generated spikes mediated by voltage-gated Na+ 3 and\/or Ca2+ channels 44 as well as glutamate-activated N-methyl-D-aspartate ( NMDA ) channels 45 have been described in a variety of neurons ( for a review see 46 or 47 ) including hippocampal granule cells 34\u201337 ., We used a quadratic integration function in order to analytically model supra-linear dendritic integration 15 which differs from the sigmoid form of nonlinearity realized by dendritic spiking ( Text S1 , 3 , 4 , 45 ) ., We believe , however , that at this level of abstraction the exact form of nonlinearity does not affect our results: As that is the difference between the dendritic responses to learned and not learned patterns that influence the somatic detection of dendritic events , a sigmoid integration function give qualitatively similar results ( Text S2 ) ., Moreover , we studied only passive interactions between individual dendritic events as the effect of voltage and calcium dependent currents ( including A-type and Ca2+-dependent potassium 48 and the H-current 49 ) regulating the propagation of dendritic spikes were not included in the model ., Future studies using a compartmental model equipped with dendritic spiking could support our results and clarify further details ., Our analysis has revealed that a moderately branched dendritic tree is optimal for the independent branches model , and we have shown that this mechanism could contribute to the spatial firing properties of granule cells in the DG ., The dendritic tree of cerebellar Purkinje cells as well as the apical dendrites of hippocampal and neocortical pyramidal cells is typically larger , and more ramifying 50 ., Their morphology is suitable for local plasticity within single branches 6 , 8 , and although it seems that individual branches may function as single integrative compartments 3 , 4 , 51 , 52 , dendritic spikes localized to these compartments fail to propagate to the soma and directly influence the neurons output 53 ., Larger dendritic events , active spread of dendritic spikes towards the soma or interactions among dendritic subunits could contribute to the generation of somatic action potentials in this case ., The dendritic tree of pyramidal neurons is , however , far more complex than that of granule cells: it has several morphological and functional subregions with different afferent inputs and membrane excitability 50 ., Understanding how their spatial firing characteristics arise from their cellular properties would require at least a different model structure and is beyond the scope of this paper ., Whether individual dendritic events influence the output of the neuron depends - beyond the structure of the dendritic tree - on the size and the frequency of the large dendritic events and the output sparsity ., The size of the events depends on the exact form of the dendritic integration function and the plasticity rule while the input statistics determine the frequency of such events ., We have shown that given the sparseness of the output , sufficiently large , localized dendritic events arriving with appropriate frequency are able to separately determine the output of the neuron ., Whether a local event is sufficiently large depends on the geometry of the dendritic tree: A smaller event may be sufficient if there are only a few subunits , or if the events actively propagate to a large part of the entire dendritic tree ( e . g , the apical tuft in pyramidal neurons , 54 ) ., Conversely , in neurons such as cerebellar Purkinje cells with large , ramifying dendritic tree , where individual events are localized to small branches , very large dendritic spikes would be required to influence the output ., Indeed , detailed compartmental modelling of dendritic morphology revealed that the forward propagation of the action potential initiated in the apical trunk of pyramidal neurons was very effective , while in Purkinje cells dendritic action potentials were rapidly attenuated 53 ., Clustered plasticity allows the neuron to simultaneously learn several different patterns but requires the electrical and\/or biochemical isolation of the dendritic compartments 47 , 55 ., However , the intracellular resistance ( ) in dentate granule cells is relatively low and granule cells are usually regarded as electrically compact neurons 28 ., Indeed , signal propagation from somata into dendrites in vitro is more efficient in granule cells compared with CA1 pyramidal cells and distal synaptic inputs from entorhinal fibers can efficiently depolarize the somatic membrane of granule cells 28 ., However , in vitro studies do not take into account that neurons are embedded in a network of spontaneously active cells ., As thousands of synapses bombard the dendritic tree in vivo , the dendritic membrane becomes \u201cleakier\u201d and , consequently , the membranes space constant decreases significantly 56 ., Moreover perisomatic inhibition 57 and feed-back excitation ( via hilar mossy cells 40 ) further decrease the resistance of the proximal membrane contributing to the separation of the somatic and dendritic compartments 54 , 58 ., More specifically , we predict , that the membrane resistance of granule cells is considerably smaller at the perisomatic region than in the distal dendrites ., Indeed , computational studies predict a 7\u201330 fold increase in the somatic leak conductance due to the synaptic background activity 59 ., On the other hand , large space constant at long terminal branches facilitate interactions among synapses distributed on the same branch ., Therefore the long dendritic branches of dentate granule cells may act as single integrative computational subunits , separated from each other by the perisomatic region of the cell ., Furthermore , in the present paper we used steady-state approximations and we neglected temporal characteristics of the input and the integration ., For rapidly varying inputs the coupling between dendritic sites and the soma is much smaller than for slowly varying currents since the distributed capacitance throughout the tree will absorb the charge before it reaches the soma 14 ., Therefore dendritic compartments in a passive tree are more isolated for transient events such as dendritic spikes than for steady-state current ., Finally , biochemical compartmentalization is likely to play a substantial role in the cooperative induction of LTP in both hippocampal 60 and neocortical neurons 7 ., If , on the other hand , dendritic branches are not isolated during the learning process and synapses across the whole dendritic tree are modified simultaneously then different dendritic branches will be sensitive for different component ( modalities ) of the same episode ., A new episode with partial overlap with the previously learned one may trigger dendritic spiking in the corresponding dendritic branch ., As the somatic detection probability of dendritic spikes does not depend on the degree of electrical isolation ( Figure 4 ) , individual branches trigger somatic spiking , and , in this way the dentate gyrus contributes to the associative recall of the previously encoded episode in the hippocampus ., Since the first description of LTP at perforant path - granule cell synapses 61 synaptic plasticity has become widely accepted as the physiological basis of memory 62 ., As Hebbian plasticity is intrinsically unstable , simply because it is a positive feed-back mechanism multiple stability-promoting mechanisms h","headings":"Introduction, Model, Results, Discussion, Methods","abstract":"A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron ., Different forms of integration of neighbouring and distributed synaptic inputs , isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits ., In the present paper , we study how these local computations influence the output of the neuron ., Using a simple cascade model , we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity ., The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments , while reliable detection of individual dendritic spikes in the soma requires a low branch number ., Finally , we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells .","summary":"Neurons were originally divided into three morphologically distinct compartments: the dendrites receive the synaptic input , the soma integrates it and communicates the output of the cell to other neurons via the axon ., Although several lines of evidence challenged this oversimplified view , neurons are still considered to be the basic information processing units of the nervous system as their output reflects the computations performed by the entire dendritic tree ., In the present study , the authors build a simplified computational model and calculate that , in certain neurons , relatively small dendritic branches are able to independently trigger somatic firing ., Therefore , in these cells , an action potential mirrors the activity of a small dendritic subunit rather than the input arriving to the whole dendritic tree ., These neurons can be regarded as a network of a few independent integrator units connected to a common output unit ., The authors demonstrate that a moderately branched dendritic tree of hippocampal granule cells may be optimized for these parallel computations ., Finally the authors show that these parallel dendritic computations could explain some aspects of the location dependent activity of hippocampal granule cells .","keywords":"neuroscience\/theoretical neuroscience, computational biology\/computational neuroscience","toc":null}
+{"Unnamed: 0":1656,"id":"journal.pcbi.1006359","year":2018,"title":"A multi-scale layer-resolved spiking network model of resting-state dynamics in macaque visual cortical areas","sections":"Cortical activity has distinct but interdependent features on local and global scales , molded by multi-scale connectivity ., Data from multiple species including macaque indicate that the ground state of cortex locally features asynchronous irregular spiking with low pairwise correlations 1 and low , layer-specific spike rates 2 , 3 with inhibitory rates exceeding excitatory ones 4\u20136 , and activity fluctuations on multiple timescales 7 ., Globally , resting-state activity has characteristic patterns of inter-area correlations 8 , 9 and propagation 10 ., These interactions are layer-specific and distinct between feedback and feedforward directions 11\u201313 ., We present a full-density multi-scale spiking network model in which these features emerge from its detailed structure ., Most cortical models concentrate on either the local or the global scale , using two basic approaches ., The first approach represents each neuron explicitly in networks ranging from local microcircuits to small numbers of areas 14 , 15 ., The second describes large-scale cortical dynamics by simplifying ensemble dynamics to few differential equations ., These models predict resting-state oscillations in a metastable regime 16\u201319 and reproduce the frequency specificity of inter-area interactions 20 ., Cortical processing is not restricted to one or few areas , but results from complex multi-area interactions 21 , 22 ., Simultaneously , dense within-area connectivity 23 , 24 suggests the importance of local processing , where the population-specific connectivity underlies multidimensional functional properties 25 and supports a set of computational principles that underlie sensory processing across the cortex 26 , 27 ., Capturing both aspects requires combining detailed features of local microcircuits with realistic inter-area connectivity ., Modeling at cellular resolution enables testing the equivalence with population models instead of assuming it a priori ., Two main obstacles of multi-scale simulations are gradually being overcome ., First , recent progress in simulation technology enables the efficient use of supercomputers 28 ., Second , systematic connectivity data is increasingly available 29 , 30 ., However , statistical predictions remain necessary to fully specify large cortical network models ., Consequently , few large-scale spiking network models have been simulated to date , and existing ones heavily downscale the number of synapses per neuron 31 , 32 ( but see 33 ) , affecting network dynamics 34 ., We here investigate a spiking multi-area network model of macaque visual cortex , covering the scales of single neurons , microcircuits , and cortical areas ., The connectivity map , derived in 35 , customizes that of the microcircuit model of 36 to each area based on its architecture and adds layer-specific inter-area connections ., Each area is represented by a 1 mm2 microcircuit with the full density of neurons and synapses ., A mean-field method 37 refines the connectivity to fulfill the basic dynamical constraint of nonzero and non-saturated activity ., By combining simple single-neuron dynamics with complex connectivity , the model enables studying the influence of the connectivity itself on the network dynamics ., We first describe the refinement of the connectivity by dynamical constraints , leading to plausible spike rates ., Next , we vary cortico-cortical synaptic strengths and find that with increased coupling , connections onto inhibitory neurons must outbalance connections onto excitatory neurons for stability at low rates ., The resulting network state reproduces spiking statistics of V1 resting-state data 38 and yields population bursts reflecting a metastable regime 39\u201342 ., Outside this metastable regime , the spiking statistics deviate considerably from the experimental data ., Our findings thus extend previous works demonstrating metastability of cortical networks via modeling 16\u201319 by unifying microscopic and macroscopic descriptions and supporting the hypothesis that plausible spiking statistics require cortex to be poised in a metastable regime ., Analyzing the order of activation of the areas reveals that the population bursts propagate mainly in the feedback direction ., Subsequently we show that , for intermediate cortico-cortical synaptic strengths , inter-area correlation patterns resemble fMRI functional connectivity 43 ., Finally , we observe directional differences in laminar patterns of inter-area communication that reflect both structural relationships and dynamical states ., Our work provides a platform for future studies addressing spiking-level functional properties and for the development of analogous models of other cortical regions ., Preliminary results have been presented in abstract form 44 ., We performed simulations on the JUQUEEN supercomputer 75 with NEST version 2 . 8 . 0 76 with optimizations for the use on the supercomputer which were subsequently released in NEST version 2 . 12 . 0 77 ., The simulations use 1024 compute nodes ( corresponding to 1 rack of JUQUEEN ) with 1 MPI process per node and 64 threads per MPI process ., A model instance requires about 2GB of working memory on each compute node and takes about 5 minutes for the creation of the network and approximately 12 minutes per 1 s biological time for propagation of the dynamical state ., All simulations use a time step of 0 . 1 ms and exact integration for the subthreshold dynamics of the leaky integrate-and-fire neuron model 78 ., Simulations are run for 100 . 5 s ( \u03c7 = 1 . 9 ) , 50 . 5 s ( \u03c7 \u2208 1 . 8 , 2 . 0 , 2 . 1 ) , and 10 . 5 s ( \u03c7 \u2208 1 . , 1 . 4 , 1 . 5 , 1 . 6 , 1 . 7 , 1 . 75 , 1 . 8 , 2 . 5 ) biological time discarding the first 500 ms . Spike times of all neurons are recorded , except for the simulations shown in Fig 2A and 2B , where 1000 neurons per population are recorded ., The digitized workflow reproducing all results and figures of this work was created in compliance with 79 and is available as Python code from https:\/\/github . com\/INM-6\/multi-area-model ., The simulation data presented in this manuscript is available from https:\/\/web . gin . g-node . org\/maximilian . schmidt\/multi-area-model-data ., Instantaneous firing rates are determined as spike histograms with bin width 1 ms averaged over the entire population or area ., In Figs 3G and 5G we convolve the histograms with Gaussian kernels of optimal width using the method of 80 , implemented in the Elephant package 81 ., Spike-train irregularity is quantified for each population by the revised local variation LvR 82 averaged over a subsample of 2000 neurons ., The cross-correlation coefficient is computed with bin width 1 ms on single-cell spike histograms of a subsample of 2000 neurons per population with at least one emitted spike per neuron ., Both measures are computed on the entire population if it contains fewer than 2000 neurons ., To compare the simulated with the experimental power spectrum in Fig 6K , we use the simulated spiking data from 140 neurons ( equal to the number of neurons identified in the experimental data ) , distributed across populations in V1 in proportion to the population sizes ., We compute the power spectrogram and power spectral densities using Welch\u2019s method ( signal . welch of the Python SciPy library 83 with a \u2018boxcar\u2019 window , segment length of 1024 data points and 1000 overlapping points between segments ) ., To make our results as comparable as possible with 38 , we follow these authors and disregard neurons with an average spiking rate < 0 . 56 spikes\/s ., We employ analytical mean-field theory to predict the stationary population-averaged firing rates of the model ., In the diffusion approximation , which is valid for large numbers of sufficiently independent inputs with small synaptic weights , the dynamics of the membrane potential V and synaptic current Is of the leaky integrate-and-fire model neurons used in our model are described by 84, \u03c4 m d V d t = - V + I s ( t ) \u03c4 s d I s d t = - I s + \u03bc + \u03c3 \u03c4 m \u03be ( t ) ,, where the input spike trains are replaced by a current fluctuating around the mean \u03bc with variance \u03c3 with fluctuations drawn from a random Gaussian process \u03be ( t ) with \u2329\u03be ( t ) \u232a = 0 and \u2329\u03be ( t ) \u03be ( t\u2032 ) \u232a = \u03b4 ( t \u2212 t\u2032 ) ., Going from the single-neuron level to a description at the population level , we define the population-averaged firing rate \u03bdi due to the population-specific input \u03bci , \u03c3i ., The stationary firing rates \u03bdi are then given by 84, 1 \u03bd i = \u03c4 r + \u03c4 m \u03c0 \u222b V r \u2212 \u03bc i \u03c3 i + \u03b3 \u03c4 s \u03c4 m \u0398 \u2212 \u03bc i \u03c3 i + \u03b3 \u03c4 s \u03c4 m e x 2 ( 1 + erf ( x ) ) d x \u2255 1 \/ \u03a6 i ( \u03bd ) \u03bc i = \u03c4 m \u2211 j K i j J i j \u03bd j + \u03c4 m K ext J ext \u03bd ext \u03c3 i 2 = \u03c4 m \u2211 j K i j J i j 2 \u03bd j + \u03c4 m K ext J ext 2 \u03bd ext , ( 1 ), which holds up to linear order in \u03c4 s \/ \u03c4 m and where \u03b3 = | \u03b6 ( 1 \/ 2 ) | \/ 2 , with \u03b6 denoting the Riemann zeta function 85 ., We solve this equation for our high-dimensional network by finding the fixed points of the first-order differential equation 86, \u03bd \u02d9 \u2254 d \u03bd d s = \u03a6 ( \u03bd ) - \u03bd , ( 2 ), for different initial conditions \u03bd0 using the continuous-time dynamics framework of NEST 87 , which uses the exponential Euler algorithm , with step size h = 0 . 1 , where s denotes a dimensionless pseudo-time ., To investigate the local stability of the fixed point , we study the evolution of a small perturbation \u03b4\u03bd around the fixed point \u03bd* to linear order ,, \u03bd i = \u03bd i * + \u03b4 \u03bd \u02dc i = \u03a6 i ( \u03bd * + \u03b4 \u03bd ) = \u03a6 i ( \u03bd * ) + d \u03a6 i d \u03bd \u03b4 \u03bd = \u03bd i * + \u2202 \u03a6 i \u2202 \u03bc i \u2211 j d \u03bc i d \u03bd j \u03b4 \u03bd j + \u2202 \u03a6 \u2202 \u03c3 i 2 \u2211 j d \u03c3 i 2 d \u03bd j \u03b4 \u03bd j = \u03bd i * + \u2211 j G i j \u03b4 \u03bd j \u21d2 \u03b4 \u03bd \u02dc i = \u2211 j G i j \u03b4 \u03bd j \u03b4 \u03bd \u02dc = G \u03b4 \u03bd ., ( 3 ), The perturbation decays to zero if the maximal real value of the eigenvalues of the effective connectivity matrix G , the Jacobian of \u03a6 , is smaller than 1 ., To investigate inter-area propagation , we determine the temporal order of spiking based on the location of the extremum of the correlation function for each pair of areas ., This measure is chosen to characterize the relative timing of activity fluctuations across areas , as opposed to measures of causal interactions like Granger causality and the directed transfer function 88 ., In an analysis of the lag structure of resting-state fMRI , Mitra et al . 10 similarly characterize temporal order using the time-delay matrix derived from the lagged cross-covariance functions ., Our method also resembles the assessment of propagation using the relative timing of slow waves in EEG and LFP recordings in different areas 89\u201391 ., In analogy to structural hierarchies based on pairwise connection patterns 92 , 93 , we look for a temporal hierarchy that best reflects the order of activations for all pairs of areas ., This overall characterization of temporal order extracts the essence of the more complex picture provided by the pairwise delays ., The hierarchy is based on the cross-covariance function computed between area-averaged firing rates and subsequently convolved with Gaussian kernels with \u03c3 = 2 ms to obtain smoother curves ., We use a wavelet-smoothing algorithm ( signal . find_peaks_cwt of the Python SciPy library 83 with peak width \u0394 = 5 ms ) to detect extrema for \u03c4 \u2208 \u2212100 , 100 and take the location of the extremum with the largest absolute value as the time lag ., To order areas hierarchically , we determine the peak locations \u03c4AB of the cross-correlation function for each pair of areas A , B . We then define a function for the deviation between the distance of hierarchical levels h ( A ) , h ( B ) and peak locations ,, f ( A , B ) = h ( A ) - h ( B ) - \u03c4 A B ., To determine the hierarchical levels , we minimize the sum of f ( A , B ) over all pairs of areas ,, S = \u2211 A , B f ( A , B ) ,, using the optimize . minimize function of the scipy library 83 with random initial hierarchical levels ., We verified that the initial choice of hierarchical levels does not influence the final result ., We obtain hierarchical levels on an arbitrary scale , which we normalize to values h ( A ) \u2208 0 , 1\u2200A ., In the context of our spiking network model we define functional connectivity ( FC ) as the zero-time lag cross-correlation coefficient of the area-averaged synaptic inputs , which we approximate as, I A ( t ) = 1 N A \u2211 i \u2208 A N i | I i ( t ) | = 1 N A \u2211 i \u2208 A N i \u2211 j K i j | J i j | ( \u03bd j * P S C j ) ( t ) ,, with the normalized post-synaptic current PSCj ( t ) = exp\u2212t\/\u03c4s , * indicating convolution , synaptic time constant \u03c4s , the population firing rate \u03bdj of source population j , mean indegree Kij , and mean synaptic weight Jij of the connection from j to target population i containing Ni neurons ., The population firing rate \u03bdj is defined as the spike histogram with bin width 1 ms averaged over the entire population , thus time t is in discrete increments of 1 ms . We compute a BOLD signal from the simulated area-averaged synaptic inputs using the Balloon model 94 , implemented in the neuRosim 95 package of R . Synaptic inputs IA ( t ) drive the responses of cerebral blood flow ( CBF ) f ( t ) and cerebral metabolic rate of oxygen ( CMRO2 ) m ( t ) by linear convolutions, f ( t ) = 1 + ( f 1 - 1 ) h ( t - \u03b4 t ) * I A ( t ) m ( t ) = 1 + ( m 1 - 1 ) h ( t ) * I A ( t ) with h ( t ) = 1 k \u03c4 h ( k - 1 ) !, ( t \u03c4 h ) k e - t \/ \u03c4 h \u03c4 f = 4 s , \u03c4 h = 0 ., 242 \u03c4 f , f 1 = 1 ., 5 , ( m 1 - 1 ) = ( f 1 - 1 ) \/ 2 , \u03b4 t = 1 s ., These responses then feed into the Balloon model which is characterized by two dynamical variables q ( t ) , v ( t ) :, d q d t = 1 \u03c4 MTT  f ( t ) E ( t ) E 0 - q ( t ) v ( t ) f out ( v , t )  d v d t = 1 \u03c4 MTT  f ( t ) - f out ( v , t )  with f out ( v , t ) = v 1 \/ \u03b1 + \u03c4 d v d t E ( t ) = E 0 m ( t ) f ( t ), with \u03c4MTT = 3 s , \u03c4 = 10 s , \u03b1 = 0 . 4 , E0 = 0 . 4 ., These two variables determine the relative change of the BOLD signal S:, \u0394 S S = V 0  a 1 ( 1 - q ) - a 2 ( 1 - v ) , with a1 = 3 . 4 , a2 = 1V0 = 0 . 03 ., The parameters are chosen as in 94 ., Clusters in the FC matrices are detected by optimizing the modularity of the weighted , undirected FC graph 96 ., We use the function modularity_louvain_und_sign of the Brain Connectivity Toolbox ( BCT; http:\/\/www . brain-connectivity-toolbox . net ) with the Q* option , which weights positive weights more strongly than negative weights , as introduced by 97 ., The clustering of the structural connectivity is performed with the map equation method 98 , which can handle directed connections but no negative weights ., In this clustering algorithm , an agent performs random walks between graph nodes according to their degree of connectivity and a certain probability of jumping to a random network node ., We choose the probability for a certain target node to be selected to be proportional to the outdegree of the connection , and p = 0 . 15 as the probability of a random jump ., The algorithm detects clusters in the graph by minimizing the length of a binary description of the network using a Huffman code ., To investigate causal relations in the network , we compute the conditional Granger causality 99 between pairs of populations ., To reduce computational load , we restrict the set of source populations for each target population i to those that form a connection with on average more than 1 synapse per target neuron ., A vector autoregressive model ( VAR ) describes the target firing rate \u03bdi ( t ) based on the firing rates of other populations with a maximal time lag of 25 ms corresponding to the rounded maximal delay between any two areas in the network ., For each source population j , we perform two fits: one using the set of all source populations , yielding VAR{j\u2032} , and one using all source populations except j , yielding VAR{j\u2032|j\u2032 \u2260 j} ., To determine the causal influence j \u2192 i , we test whether the residual variances of the two VARs are significantly different using Levene\u2019s test 100 , which is more robust against non-normally distributed residuals than the F-test ., To study dominant paths in the network , we construct the weighted and directed gain matrix G with G i j = K i j | J i j | d \u03bc i d \u03bd j + K i j J i j 2 d \u03c3 i 2 d \u03bd j of the network at the population level , where we evaluate the terms d \u03bc i d \u03bd j , d \u03c3 i 2 d \u03bd i j at the simulated population-averaged firing rates of the model with \u03c7 = 1 . 9 ., We denote the eigenvalues of G by \u03bb and define \u03bbmax as the eigenvalue with the largest real part ., To reflect the near-criticality of the brain , we perform an element-wise division by the real part of \u03bbmax: G\u2032 = G\/Re ( \u03bbmax )  , so that the maximal real part of the eigenvalues \u03bb\u2032 of the resulting matrix G\u2032 is maxRe ( \u03bb\u2032 )  = 1 ., This scaling modulates the relative strengths of direct and indirect paths: a larger value of maxRe ( \u03bb\u2032 )  increases the relative weighting of indirect paths ., Subsequently we use the same method as 35 and denote the weight of the edge from population j to i as g i j \u2032 ., The logarithm of the reciprocal of the weight , dij = log ( 1\/wij ) , defines the distance between two nodes in the graph so that summing the distances corresponds to a multiplication of the corresponding weights ., Next , the Bellman-Ford algorithm 101\u2013103 finds the shortest paths between any two nodes of the graph ., This algorithm determines the shortest paths emanating from vertex i on a graph with N vertices in an iterative manner: it initially assigns an infinite path length to all other nodes k of the graph ., Then , the algorithm loops through all edges ( j , k ) of the graph , tests if the path length pij plus the distance of the edge djk is smaller than the currently stored path length pik , and , if so , assigns pik \u2190 pij + djk ., By repeating the loop over all edges N \u2212 1 times , the algorithm considers paths of increasing length on every iteration and ultimately uncovers the shortest paths between each pair of vertices ., In contrast to Dijkstra\u2019s algorithm Bellman-Ford copes with edges with negative distance values ., The experimental recordings are described in 38 and are publicly available 104 ., The data consist of sorted spike trains from a 64-electrode array implanted into primary visual area V1 of a lightly anesthetized macaque monkey ., The array has 8 electrodes , called shanks , with 8 contacts sites per shank , spanning 1 . 4 \u00d7 1 . 4 mm horizontally and in depth at 200 \u03bcm spacing , covering all cortical layers ., For the analysis in Fig 6 , we used the 15 minutes of spontaneous activity , where no visual stimulation was provided to the animal ., To obtain single-neuron spike trains , 38 performed super-paramagnetic clustering 105 on the high-frequency component ( 400\u20135000 Hz ) of the recorded signal ., Details of the experimental procedures are given in 38 ., In our analysis , we distinguish between low-fluctuation and high-fluctuation phases , with low vs . high activity in the frequency range up to 40 Hz ., We defined these phases from the power spectrum |C ( \u03c9 ) |2 of the spike histogram for all neurons combined at subsequent intervals of 10 s duration and assign the interval to the low-fluctuation phase if \u222b 0 Hz 40 Hz | C ( \u03c9 ) | 2 d \u03c9 \u2264 \u03b8 , with an empirically determined threshold \u03b8 = 0 . 8 \u22c5 108 ., This leads to 77 intervals being classified as low-fluctuation and 15 intervals as high-fluctuation ., Data were acquired from six male macaque monkeys ( 4 Macaca mulatta and 2 Macaca fascicularis ) ., All experimental protocols were approved by the Animal Use Subcommittee of the University of Western Ontario Council on Animal Care and in accordance with the guidelines of the Canadian Council on Animal Care ., Data acquisition , image preprocessing and a subset of subjects ( 5 of 6 ) were previously described 106 ., Briefly , 10 5-min resting-state fMRI scans ( TR: 2 s; voxel size: 1 mm isotropic ) were acquired from each subject under light anesthesia ( 1 . 5% isoflurane ) ., Nuisance variables ( six motion parameters as well as the global white matter and CSF signals ) were regressed using the AFNI software package ( afni . nimh . nih . gov\/afni ) ., The global mean signal was not regressed ., The FV91 parcellation was drawn on the F99 macaque standard cortical surface template 47 and transformed to volumetric space with a 2 mm extrusion using the Caret software package ( http:\/\/www . nitrc . org\/projects\/caret ) ., The parcellation was applied to the fMRI data and functional connectivity computed as the Pearson correlation coefficients between probabilistically weighted ROI timeseries for each scan 43 ., Correlation coefficients were Fisher z-transformed and correlation matrices were averaged within animals and then across animals before transforming back to Pearson coefficients ., From a dynamical systems perspective , we define a state of the network as a set of mean firing rates for all populations ., An attractor is a state towards which the network tends to evolve for many different initial conditions ., Since the network receives stochastic external input , individual neurons fluctuate around their mean firing rate ., An attractor is locally stable if all eigenvalues of the effective connectivity matrix , defined as the Jacobian of the population-level transfer function obtained from mean-field theory ( Eq ( 1 ) ) , have real values < 1 ., The global stability of an attractor is assessed by the size of its basin of attraction in phase space ., This volume is measured by discretizing the phase space into a grid of initial conditions and defining the global stability of an attractor A as the proportion of initial conditions leading the system to evolve to A . An analysis based on mean-field theory 37 and simulations reveals that across a wide range of configurations of the external input rate \u03bdext and the relative inhibitory synaptic strength g , the network possesses a bistable activity landscape with two coexisting locally stable fixed points ( Fig 2 ) ., In view of the high dimensionality of the system with 254 populations , the bistability in the mean-field theory is found numerically from a pseudo-time integration that yields the stable fixed points 37 , in which the set of firing rates for the full set of populations consistently converges to one of two possible states for each combination of \u03bdext and g ., The simulation results are qualitatively consistent with these mean-field results ., We identify the stable fixed points based on the fact that , after a short initial simulation phase ( typically \u223c100 ms ) and regardless of the initial condition , the network settles in either of these states ., The first attractor exhibits asynchronous , irregular activity at moderate firing rates except for populations 5E and 6E , which are nearly silent ( Fig 2A ) , while the second features highly synchronized and regular firing with excessive rates ( Fig 2B ) in almost all populations ., Depending on the parameter configuration , either the low-activity fixed point has a sufficiently large basin of attraction for the simulated activity to remain near it , or fluctuations drive the network to the high-activity fixed point ., To counter the shortcoming of vanishing infragranular firing rates , we define an additional parameter \u03ba which increases the external drive onto 5E by a factor \u03ba = Kext , 5E\/Kext compared to the external drive of the other cell types ., Since the rates in population 6E are even lower , we increase the external drive onto 6E linearly with \u03ba such that \u03ba = 1 . 15 results in K6E , ext\/Kext = 1 . 5 ., However , even a small increase in \u03ba already drives the network into the undesired high-activity fixed point ( Fig 2B ) ., The stabilization procedure described by 37 uses mean-field theory to determine the population-averaged firing rates characterizing the fixed points of the system ( cf ., Eqs ( 1 ) and ( 2 ) ) ., By linearizing the population dynamics around the fixed points , the technique identifies connectivity components that are most critical to the global stability of the fixed points and yields targeted modifications of the connectivity within the margins of uncertainty of the anatomical data ., The resulting average relative change in total indegrees ( summed over source populations ) is 11 . 3% ., This allows us to increase \u03ba while retaining the global stability of the low-activity fixed point ., In the following , we choose \u03ba = 1 . 125 , which gives K6E , ext\/Kext = 1 . 417 , and g = 11 , \u03bdext = 10 spikes\/s , yielding reasonable firing rates in populations 5E and 6E ( Fig 2C ) with sufficient global stability of the low-activity fixed point 37 ., The stabilization renders the intrinsic connectivity of the areas more heterogeneous ., Cortico-cortical connection densities similarly undergo small changes , but with a notable reduction in the mutual connectivity between areas 46 and FEF ., For more details on the connectivity changes , see 37 ., In total , the 4 . 13 million neurons are interconnected via 2 . 42 \u22c5 1010 synapses in the stabilized model ., The network displays a reasonable ground state of activity with low spiking rates between 0 . 05 and 11 spikes\/s ( Fig 3 ) ., Inhibitory populations are generally more active than excitatory ones across layers and areas despite the identical intrinsic properties of the two cell types ., This behavior , first found and discussed in detail in 36 , is thus caused by the network connectivity which leads to a high excitation-inhibition ratio onto inhibitory cells ., Spiking activity is asynchronous irregular across populations ., Population activity fluctuates around its stationary point with small amplitude ., Pairwise correlations are low throughout the network ( Fig 3E ) ., Excitatory neurons are less synchronized than inhibitory cells in the same layer , except for L4 ., Spiking irregularity is close to that of a Poisson process across areas and populations ( Fig 3F ) ., The only exception is population 6E , which features very low firing rates , so that the measure probably suffers from insufficient spiking data in single cells ., To control interactions between areas , we scale cortico-cortical synaptic weights onto excitatory neurons by a factor \u03c7 = J cc E \/ J and provide balance by increasing the weights J cc I onto inhibitory neurons by twice this factor , J cc I = \u03c7 I \u03c7 J = 2 \u03c7 J . For increasing \u03c7 , we observe growing fluctuations of the population spiking rates ., At \u03c7 = 2 and beyond , the network enters a high-activity state at some time point in the simulation , where most populations spike at unrealistically high rates ( Fig 4A ) ., Predictions of mean-field theory show that for increasing \u03c7 , a growing proportion of initial conditions ( in Eq ( 2 ) ) result in states with increased activity ( Fig 4B ) ., We explain this behavior with the global phase space of the model ., At any time , there are two stable attractors with basins of attraction divided by the separatrix , a hyperplane in the phase space that contains unstable fixed points ., The low-activity fixed point remains locally stable for increasing \u03c7 , as determined by the maximal real part of the eigenvalues of the effective connectivity matrix which is below one for all configurations ( Fig 4C ) ., At the same time , its global stability , determined by the proportion of initial conditions leading the system to evolve to it , decreases ( Fig 4B and 4D ) ., The effect is that fluctuations around the stationary state , which are evident in a stochastic system , let the system approach the separatrix more closely ., Close to the unstable fixed points , the dynamics of the system slow down , which causes the rate fluctuations to appear ., From \u03c7 = 2 , the system is likely to enter the high-activity state within a short amount of simulation time ., In the following , we choose \u03c7 = 1 . 9 as the parameter configuration where slow fluctuations coincide with a sufficient global stability of the LA fixed point so that the system does not enter the HA fixed point during the simulation ., The corresponding activity is irregular with plausible firing rates ( Fig 5A\u20135C ) ., Irregularly occurring population bursts of different lengths up to several seconds ( Fig 5G ) arise from the asynchronous baseline activity ( Fig 5A\u20135C ) and propagate across the network ., The time scales of the population bursts arise from network interactions rather than directly reflecting axonal delays or membrane and synaptic time constants , which only cover a range of 100 \u223c 101 ms . The firing rates differ across areas and layers and are generally low in L2\/3 and L6 and higher in L4 and L5 , partly due to the cortico-cortical interactions ( Fig 5D ) ., The overall average firing rate is 14 . 6 spikes\/s , with the inhibitory populations tending to have higher rates than the excitatory populations ., However , the strong participation of L5E neurons in the cortico-cortical interaction bursts causes these to fire more rapidly than L5I neurons ., Pairwise correlations are low throughout the network ( Fig 3E ) ., Unlike in the model without population bursts , excitatory neurons are more synchronized than inhibitory cells in the same layer , except for L6 ., Spiking irregularity is close to that of a Poisson process across areas and populations , with excitatory neurons tending to fire more irregularly than inhibitory cells ( Fig 3F ) ., Higher areas exhibit bursty spiking , as illustrated by the raster plot for area FEF ( Fig 5C ) ., We compare the simulated spiking activity with experimental data from 38 , who recorded spiking activity in 140 neurons of macaque primary visual cortex in the spontaneous condition ., The experimental activity shows activity phases differing in their low-frequency power ( Fig 6A ) ., In the early stage of the recording , the population activity exhibits only small fluctuations ( Fig 6B ) , while in later stages , the population activity fluctuates on different time scales up to the order of a second ( Fig 6C ) ., We therefore split the recorded data into low-fluctuation and high-fluctuation phases ( see Materials and methods for details ) , distinguished by their power at frequencies up to 40 Hz ( Fig 6E ) ., To compare simulated with recorded power spectra , we compute the spike rates of 140 cells in V1 distributed across populations in proportion to the population sizes ( see Materials and methods for details ) ., We compare three different simulations with low fluctuations ( \u03c7 = 1 , Fig 3 ) , meta-stable dynamics ( \u03c7 = 1 . 9 ) and unrealistically high activity ( \u03c7 = 2 . 5 ) in Fig 6D ., The power spectral densities ( PSD ) of the simulations with \u03c7 = 1 , 2 . 5 are flat while for \u03c7 = 1 . 9 the PSD clearly reflects the slow oscillations in the spiking activity ( cf . Fig 5 ) ., We compare the PSD of this simulation with the experimental results ., Overall , the simulated activity in V1 to a good approximation reproduces both the spectrum from the entire recording period and that from the low-fluctuation phase , differing mainly in its increased power between 20 and 40 Hz ., The sum of squared deviations ( SSD ) of the logarithmized spectrum from the logarithmized experimental spectrum for the entire recording period is SSD = 44 ( \u03c7 = 1 . 9 ) , compared to SSD = 793 for weak cortico-cortical synapses ( \u03c7 = 1 ) and SSD = 2180 for strong cortico-cortical synapses ( \u03c7 = 2 . 5 ) , showing that this match is unique to the metastable case ., For the entire frequency range , the metastable case ( \u03c7 = 1 . 9 ) best matches the low-fluctuation phase ( SSD = 42 vs . SSD = 89 for the high-fluctuation phase ) ., At frequencies below 3 Hz , the power spectrum of the simulations closely matches that of the high-fluctuation phase ( \u03c7 = 1 . 9: SSD = 3 . 2 vs . SSD = 6 . 8 for the low-fluctuation phase ) ., The horizontal stripes in Fig 5I and 5J may to some extent be due to the mixing of spike trains from excitatory and inhibitory neurons , as the spike sorting does not distinguish between these ., This interpretation is supported by the fact that the simulated activity across all layers and populations of V1 closely reproduces the broad distribution of spike rates across cells ( Fig 5L ) ., The model with weak cortico-cortical synapses has","headings":"Introduction, Materials and methods, Results, Discussion","abstract":"Cortical activity has distinct features across scales , from the spiking statistics of individual cells to global resting-state networks ., We here describe the first full-density multi-area spiking network model of cortex , using macaque visual cortex as a test system ., The model represents each area by a microcircuit with area-specific architecture and features layer- and population-resolved connectivity between areas ., Simulations reveal a structured asynchronous irregular ground state ., In a metastable regime , the network reproduces spiking statistics from electrophysiological recordings and cortico-cortical interaction patterns in fMRI functional connectivity under resting-state conditions ., Stable inter-area propagation is supported by cortico-cortical synapses that are moderately strong onto excitatory neurons and stronger onto inhibitory neurons ., Causal interactions depend on both cortical structure and the dynamical state of populations ., Activity propagates mainly in the feedback direction , similar to experimental results associated with visual imagery and sleep ., The model unifies local and large-scale accounts of cortex , and clarifies how the detailed connectivity of cortex shapes its dynamics on multiple scales ., Based on our simulations , we hypothesize that in the spontaneous condition the brain operates in a metastable regime where cortico-cortical projections target excitatory and inhibitory populations in a balanced manner that produces substantial inter-area interactions while maintaining global stability .","summary":"The mammalian cortex fulfills its complex tasks by operating on multiple temporal and spatial scales from single cells to entire areas comprising millions of cells ., These multi-scale dynamics are supported by specific network structures at all levels of organization ., Since models of cortex hitherto tend to concentrate on a single scale , little is known about how cortical structure shapes the multi-scale dynamics of the network ., We here present dynamical simulations of a multi-area network model at neuronal and synaptic resolution with population-specific connectivity based on extensive experimental data which accounts for a wide range of dynamical phenomena ., Our model elucidates relationships between local and global scales in cortex and provides a platform for future studies of cortical function .","keywords":"action potentials, medicine and health sciences, diagnostic radiology, functional magnetic resonance imaging, neural networks, nervous system, membrane potential, vertebrates, electrophysiology, neuroscience, animals, mammals, magnetic resonance imaging, primates, brain mapping, computational neuroscience, neuronal dendrites, neuroimaging, old world monkeys, research and analysis methods, computer and information sciences, imaging techniques, monkeys, animal cells, macaque, cellular neuroscience, radiology and imaging, eukaryota, diagnostic medicine, cell biology, anatomy, synapses, physiology, neurons, single neuron function, biology and life sciences, cellular types, computational biology, amniotes, neurophysiology, organisms","toc":null}
+{"Unnamed: 0":2253,"id":"journal.pcbi.1005885","year":2017,"title":"Novel linear motif filtering protocol reveals the role of the LC8 dynein light chain in the Hippo pathway","sections":"A large number of protein-protein interactions ( PPIs ) are mediated by short linear motifs ( SLiMs ) that are recognized by specific globular domains 1 ., SLiM-mediated interactions are involved in a wide range of biological functions and can regulate the formation of transient protein complexes , orchestrate subcellular localization , modulate post-translational modification state , and determine the fate of proteins 1 ., Such interactions emerged as key mediators of complex regulatory processes in higher eukaryotic cells and their aberrant functioning can contribute to various diseases as well 2 ., The key to the essential nature of SLiMs in biological systems lies in their specific properties ., SLiMs correspond to a stretch of approximately 3\u201310 residues that generally reside within intrinsically disordered regions ( IDRs ) ., As a result , they usually form transient , weak interactions with micromolar binding affinity 3 ., Due to these specific properties , the identification of linear motif sites is challenging both experimentally and computationally 4 ., Currently , the most comprehensive collection , the Eukaryotic Linear Motif database ( ELM ) holds only 200\u2013300 motif patterns with a few thousands of experimentally verified instances 5 ., This number pales in comparison to the expected number of linear motif mediated interactions in the human proteome , estimated to number at least several hundred thousand 6 ., Linear binding peptides have been systematically analyzed only for a few specific interaction domains , such as SH2 , PTB , 14-3-3 , PDZ and SH3 domains 7 , 8 ., However , for most motif binding domains , the interaction network is largely incomplete ., The identification of linear motif mediated interactions is usually divided into two phases ., The first phase is the characterization of the common consensus sequence motif that is shared among the diverse set of binding partners of a common domain , i . e . defining the motif class 9 , 10 ., The core motif that mediates interactions with a given domain is usually represented by a sequence pattern or a position specific scoring matrix ( PSSM ) ., In the second phase , the core motif is used to identify additional candidate binding sites in the proteome , i . e . finding novel motif instances ., However , as the information content of consensus motifs is usually low , predicted motif matches are overwhelmingly dominated by false positive matches that occur purely by chance 3 , 11 ., Therefore , this phase involves additional filtering steps to remove matches that are unlikely to be functional and to prioritize motif hits for further experimental characterization ., Various computational tools such as ELM , QuasiMotifFinder , MiniMotifMiner , SLiMSearch , ScanProsite or DOReMi 5 , 12\u201316 have been developed to overcome this problem ., These tools scan a defined set of proteins with a single consensus motif and utilize various discriminatory attributes to prioritize motif hits , including structural context , protein disorder , functional ontology , evidence for PPIs and shared cellular localization ., Evolutionary conservation can highlight functionally relevant positions in proteins and have been used for globular domains to identify conserved motif-like patterns that are indicative of the function of a protein 12 ., However , linear motif sites generally reside within IDRs that are generally less conserved 17 ., Within these regions , SLiMs often show a specific pattern of evolutionary conservation that are characterized by a higher relative conservation of the key motif residues compared to their flanking regions 18 , 19 , and this information can be used to highlight true binding motifs ., Using various sequence attributes , specific filtering pipelines were constructed to identify novel motif instances for several domains 20\u201324 ., However , the strength and optimality of the filtering steps have never been systematically tested ., In order to build optimal filtering protocols , a more systematic approach is needed that can take into account the specific trade-off between reducing false positive hits while capturing biologically relevant motif matches , which is likely to be specific to individual binding domains ., In this study , we focused on LC8 dynein light chain and its binding partners as a case study , and explored how the interaction network of a specific linear motif binding protein can be expanded in an optimal way ., LC8 is a remarkably conserved eukaryotic hub protein 22 ., Although LC8 was originally suggested to function as a cargo adaptor for the dynein motor complex , its extensive interaction network suggests a more general role , independent of dynein 22 , 25 ., Recently , the prevailing view has become that LC8 functions as a dimerization or oligomerization engine for various proteins 25 , 26 ., Known interaction partners link LC8 to processes such as nuclear transport , tumor suppression , viral replication , DNA damage repair , apoptosis , mitosis and signaling 22 , 25 ., In contrast to their functional heterogeneity , LC8 binding partners generally share a common binding mechanism 22 , 27 ., The known structures of complexes between LC8 and various bound partners show that the binding groove is formed at the dimerization interface of the homodimeric LC8 , favoring binding partners that are also dimerized 28 , 29 , often promoted by coiled coil ( CC ) regions 20 , 30 ., The recognition SLiMs are generally located within intrinsically disordered regions 25 and undergo a disorder-to-order transition upon complex formation ., In their bound form , these segments adopt highly similar conformations that augment the central beta sheet of LC8 on each side of the dimer 27 ., Many of the binding segments contain a Thr-Gln-Thr ( TQT ) motif with additional positions showing larger variations ., Apart from the canonical TQT motif , there are also non-canonical binding motif instances , in which the central Gln is replaced by Met or Asn 22 ., An even more unusual Thr-Ser-Pro ( TSP ) binding motif mediates the interaction between Pak1 and LC8 ., Altogether , more than 50 LC8 binding motif instances were collected from various eukaryotic species 22 ., To reveal the optimal binding motif , a phage display study was also carried out , identifying further LC8 binding motif instances 20 ., The suggested general role for LC8 raises the possibility of many additional binding partners in the human proteome ., In this work we expanded the interaction network of dynein light chain LC8 using a combination of computational and experimental methods ., We introduced a novel measure based on information gain that enabled us to build an optimal bioinformatic pipeline by combining various attributes predicted from the amino acid sequence ., We also incorporated known binding partners from PPI databases and exploited the specific evolutionary conservation of binding motifs to increase the likelihood that the motif hit is biologically relevant ., The resulting procedure enabled us to drastically reduce false positive predictions among putative novel linear motif instances and to expand the interaction network of LC8 with high-confidence predictions ., We experimentally verified the binding of several novel motif instances to LC8 using surface plasmon resonance ( SPR ) assay ., One of the most interesting outcomes of the extended interaction network of LC8 revealed a possible new function of the LC8 protein in the Hippo pathway through interaction with WWC and AMOT protein family members ., The presented study significantly contributes to the better understanding of the functional and evolutionary properties of the LC8 interactome ., Beyond this specific hub protein , it also offers general guidelines for the exploration of additional linear motif-mediated interaction networks ., LC8 recognizes a short linear motif in its partner proteins ., In this case , the binding involves both polypeptide chains of the homodimer LC8 ., However , to emphasize the similar binding mode to many single modular domains that also bind short linear motifs , LC8 is also referred to as a \u201cbinding domain\u201d in this article ., We assembled a manually curated database of LC8 interaction partners based on literature search , in which LC8 binding was verified at the motif level ( see Materials and Methods and S1 Table ) ., The final dataset contained 53 partners with 67 motif instances and covered multiple eukaryotic species and viruses ., 40 motifs in 33 proteins belonged to human or could be directly mapped to a human protein based on close homology ., The length of the core binding motif was taken as 8 amino acids ( S1 Fig; for details , see S1 Text ) ., The ELM database describes the LC8 binding motif using the regular expression \u201c^P . K . TQT\u201d ., From the 67 known motif instances , only 13 matched this regular expression , and 24 further motifs contained only the canonical \u201cTQT\u201d motif core ., Considering human partners only , the corresponding numbers were 7 and 17 , respectively ., These numbers indicate that the definition in the ELM database is too restrictive to capture the majority of known instances ., To better describe the common sequential properties of known LC8 binding sites , we used a position specific scoring matrix ., The calculated PSSM is shown in Fig 1 ., Positive scores indicate amino acid residues that are favored at a given position ., The PSSM clearly captures the frequent occurrence of the canonical \u201cTQT\u201d motif ., However , with the exception of Gln in position 0 , there are additional favored amino acids in every position ., The strong preference for Lys at position -3 from the central Gln is not supported by the current collection of known partners , as neighboring positions have stronger preferences according to the bitscore ., Using the obtained PSSM , we scanned the whole human proteome to score every overlapping eight amino acid long peptide segment ( S2 Fig ) ., As expected , all known LC8 binding peptides had a positive score ., While only 2% of human peptides had a positive score , these still represented more than one hundred thousand cases ., This indicates that on the one hand , positive PSSM scores are strongly associated with true binding motifs and can serve as a valid starting point for novel LC8-binding motif discovery ., On the other hand , the very large number of initial motif hits underscore the need for that additional filtering steps ., In order to establish additional filtering criteria , we gathered various predicted features of the PSSM-identified peptides ., The methods we used included PFAM annotations 31 , average disorder prediction scores ( using IUPred , PONDR VSL2 , Espritz and DISOPRED3 ) 32\u201335 , average score to be part of disordered binding regions ( using ANCHOR , MORF-CHIBI and DISOPRED3-BR ) 35\u201337 , and secondary structure prediction scores using PSIPRED 38 ., At the protein level , information about predicted cellular localization 20 , 39 and the presence of coiled coil regions was also collected ( See Materials and Methods ) ., The various data for all known true positive motifs from human and other species are available at http:\/\/gerdos . web . elte . hu\/data\/LC8\/known_results . html ., These various features can be associated with known motifs to different extents ., The main challenge is to find the best tools and parameter settings that enable the prioritization of peptide segments that are the most likely to be biologically relevant motif hits in an optimal way ., We introduced a metric based on weighted information gain derived from the Shannon entropy to globally attest the discriminatory power of each criterion ., On a dataset containing 40 known human binding partners and 10 , 000 random human segments from the proteome with a higher than zero PSSM score , the weighted information gain was calculated for each criterion ., The suggested measure enabled not only to rank the attributes in terms of their discriminatory power , but also to choose the best parameter settings ., According to this protocol , the strongest criterion based on the information gain was the predicted intracellular localization , which was fulfilled by all known motifs , but only 85 . 53% of random peptides ., The next strongest filtering criterion was based on PFAM annotations ., Using annotation strictly based on the domain type PFAM families , it was possible to filter out 15% of random motifs , while retaining all known motifs ., The third strongest criterion was based on PSSM scores ., The highest information gain was achieved with the cutoff value of 3 . 3 ., This cutoff value was not met by only three known human motifs ( PAK1 , NRF1 , MYZAP ) ., At the next level , disorder prediction methods produced the highest information gain ., Four methods were tested with different cutoff values corresponding to different false positive rates ., The optimal choice was IUPred with the cutoff value of 0 . 42 , which was fulfilled by all but one known motifs ., We also tested three methods ( ANCHOR , MoRFchibi , DISOPRED3 ) 35\u201337 for predicting disordered binding regions also known as molecular recognition features ( MoRFs ) ., The information gain was much lower , compared to previous criteria ., The optimal information gain was reached using the ANCHOR method with a cutoff value of 0 . 57 ., However , even this criterion would filter out 57 . 5% of the positive examples ., An additional criterion considered was secondary structure prediction ., Based on known structures of the complexes , the binding motif is expected to adopt a beta-strand conformation ., Surprisingly , predicted beta-strands occurred in only four out of 40 cases , and even in these cases only very short segments were predicted to be in beta conformation ., Helical segments were predicted in five cases , including MYO5A , which has been shown to have helical tendencies in the unbound form 40 ., However , the lack of residues predicted to be in helix did not perform well as a filtering criterion as the majority of random hits were also predicted to lack regular secondary structural elements , and the overall information gain was below that of predicting disordered binding regions ., Similarly , the presence of coiled coil regions in the partner proteins predicted by NCoils 41 did not have a strong discriminatory power either ., As these criteria filtered out many known motifs , they were not included in our filtering protocol ., The resulting filtering protocol is shown on Fig 2 , indicating the proportion of random hits and known motifs that were eliminated at each step ., By the stepwise application of the four filtering steps , a drastic reduction of random hits could be achieved , while still retaining the majority of known motifs: 90% of known motifs were kept while 99 . 78% of random hits were filtered out ( i . e . only 0 . 22% was kept ) ., By applying the filtering protocol for the complete human proteome , 335 candidate motifs remained ., We carried out a 3-fold cross validation to measure the generality of the obtained filtering protocol ( see Materials and Methods ) ., On average , we were able to correctly categorize 34 examples from the 40 experimentally validated human binding motifs ., This was only marginally worse compared to using the complete database where 36 motifs were categorized correctly ., The cut-off values for the PSSM and IUPred scores also did not change largely ., This indicates that the protocol is robust and can correctly describe the general attributes of the binding event between LC8 and its known binding partners ., Given the extreme conservation of LC8 , it is of special interest how the interaction motifs are conserved in partner proteins ., To study this , we generated multiple sequence alignments of orthologous proteins harboring known LC8 binding motifs and categorized them into 5 taxonomic groups: Mammalia , Vertebrata , Metazoa , Fungi and Eukarya ., The conservation at the level of protein and motif was tested based on the obtained alignments in each taxonomic group ., The definition of motif conservation applied here depends on the PSSM score of the motif ( see Materials and Methods ) ., Consequently , this approach cannot be applied to motifs that significantly differ from canonical motifs , i . e . their binding motif had a PSSM value below the threshold ., These three examples were excluded from the analysis ., Nevertheless , this strict criterion ensured that not only the general sequence similarity is maintained , but also the similarity to known human LC8 motifs is preserved ., The results of the conservation analysis for the known human motifs are presented in Fig 3 ., Among the known partners , the LC8 binding sites located within dynein intermediate chains ( DYNC1|1 , DYNC1|2 ) exhibited the most pronounced conservation , spreading across a wide range of eukaryotic species ( e . g . starlet sea anemone , C . elegans , slime mold ) ., In contrast , other motifs identified in human or other mammalian species were generally not conserved beyond Vertebrata ( e . g . , BMF , DLGAP1 , MTCL1 ) ., In the majority of cases , not only the LC8 binding motif but the complete protein was lost beyond this evolutionary distance ( e . g . BMF , BSN , SNPH ) ., Similarly , limited conservation of LC8 motifs was observed for binding regions experimentally verified in other species ( S3 Fig ) ., For example , the EGL protein from Drosophila melanogaster had orthologues at each level , but its binding motif showed conservation only in metazoan species ., While the centriole duplication functionality is conserved across metazoan species , the LC8 binding protein ANA2 involved in this process is specific to Drosophila species 42 ., Lowering the PSSM cutoff value used to define the conservation of the motifs perturbed the results only in three cases: NRF1 , FAM83D and MYO5A , but had no major impact on the overall trends ( S4A and S4B Fig ) ., We can conclude from this analysis of motif conservation that while the LC8 binding interface is highly conserved , known partners and especially the binding motifs located within them are significantly less conserved ., We tested the specific conservation pattern of motif binding sites using the SLiMPrints algorithm 19 ., This method identifies short stretches of residues within disordered regions that show high relative conservation compared to their flanking region as calculated from multiple sequence alignments of orthologous sequences ., In our dataset , 13 out of the 40 known human motifs exhibited high relative conservation , which is only 32 . 5% of all cases ., This suggests that the approach based on the island-like conservation identified by SLiMPrints has a limited ability to highlight putative functional binding motifs and overall it is not a good filtering criterion , as it misses the majority of functional motifs ., Here , we suggest an alternative filtering criterion based on the observation that known motifs are generally conserved within their own taxonomic group even if they lack motif level conservation over wider evolutionary distances ., For the majority of the cases , known motifs in human sequences were conserved in at least 80% of mammalian species ., The exceptions included only the three cases that had a PSSM value below our cutoff , and two additional examples ( the MAP4 motif and the second motif of FAM83D at position 405 ) ., In contrast , randomly chosen motif hits located within disordered regions generally did not possess this property ., Applying this discriminatory technique ( see Materials and Methods ) , we could filter out 163 of the possible candidate peptides , reducing the number of candidate motifs to 172 ., Therefore , for human sequences the conservation within mammalian species can be used as an efficient filter to further reduce likely false positives ., The predicted motif hits were also analyzed in relation to experimental data in PPI databases ., Known interaction partners of LC8 were collected using the integrative PSICQUIC approach 43 , which enabled us to search multiple databases simultaneously and to group the experiments based on detection methods and association types ( see Materials and Methods ) ., Altogether , 381 LC8 interaction partners were collected ( S2 Table ) ., Several of these interaction partners were supported by multiple lines of evidence , with a total of 782 independent experiments ., Known motif partners were well represented in current PPI databases , with only three missing out of these 33 partners ., The comparison of interaction partners collected from PPI databases with those that contained known motifs indicated that there is no single criterion that can identify biologically relevant interactions from candidates in PPI databases ., However , PPIs from low-throughput and direct experiments are more likely to be biologically relevant , especially when they are supported by multiple independent measurements ( see S5 Fig ) ., Overall , there were a large number of potential partners recorded in PPI databases ( 323 ) that contained neither known nor predicted LC8 binding motif instances ., By looking at the distribution of partners over the number of supporting experiments , we can see that partners with known and predicted motifs were largely evenly distributed , similarly to the partners detected by direct methods ( Fig 4A ) ., Known and predicted motifs dominated in partners with at least 7 supporting measurements , with a single exception corresponding to KANK2 , in which no motif-like segments could be identified ., In contrast , most of the partners without a likely motif candidate were detected by only a single , indirect method ., Although it cannot be ruled out that some of these interactions represent an alternative binding mechanism to LC8 , the large number of PPIs that are not compatible with the existing binding mode underlines that data from PPI databases should be treated with caution as they may contain several false positives ., Among the 172 predicted motifs in 152 proteins that satisfied our filtering criteria , there were 43 novel motif instances predicted by our pipeline that had corresponding PPI data ., While most of these interactions were based on indirect , high-throughput experiments , many of them were supported by multiple measurements ., 8 of these motifs represented additional instances in proteins that already contained an experimentally verified binding motif ., In 35 cases , the likely binding region for LC8 could be identified for proteins whose interaction were studied only at the level of the protein ( see S2 Table ) ., Furthermore , the presence of PPIs lends support to the biological relevance of the predicted motifs in these cases ., By considering motif hits located in proteins with corresponding PPI data , we created a dataset that contained a list of high confidence motif instances for LC8 ., In addition to PPIs , the presence of island-like conservation was also taken as an indication of likely motif hits ., Altogether , we collected 71 high confidence motif instances , supported by PPI data ( 29 cases ) , the presence of island-like conservation ( 27 cases ) , or both ( 15 cases ) ( Fig 4B ) ., Using these complementary information , the number of interaction partners of LC8 could be practically doubled ( S3 Table ) ., The high confidence motifs are available at http:\/\/gerdos . web . elte . hu\/data\/LC8\/HUMAN\/high_confidence_hits . html ., The high confidence set together with the already known motif hits was used to carry out a GO enrichment analysis against the human proteome with the DAVID server 44 ., The analysis showed an enrichment of multiple functionalities previously associated with LC8 , such as cytoskeletal organization , microtubule binding or cell morphogenesis ( Fig 5 ) ., Besides the already known activities , the enrichment analysis revealed a highly over-represented , yet previously undiscovered function of LC8 that links the protein to the regulation of cell and tissue growth , and in particular , to the Hippo pathway ., This result suggests that LC8 might play a critical role in the regulation of the Hippo pathway ., In order to understand how LC8 is connected to the Hippo pathway , we took a closer look at the relevant partners ., The motif hits highlighted two families involved in the upstream regulation of the Hippo pathway , the WWC ( WWC1 , WWC2 and WWC3 ) and angiomotin ( AMOT , AMOTL1 , AMOTL2 ) families 45 , 46 , 47 ., The WWC family member WWC1 , also known as KIBRA , was shown previously to interact with LC8 48 , and two binding motifs were also identified , located at positions 278 and 887 ( highlighted in Table 1 ) 49 ., However , no binding sites have been previously identified in the other two members of the family , WWC2 and WWC3 ., Interactions between LC8 and the AMOT family members were previously reported in high-throughput studies to be LC8 interactors 50 , but the binding motif has not been located in any of these proteins as of yet ., Here , we identified the likely LC8 binding regions in all WWC and AMOT family members and analyzed their evolutionary conservation ., The binding of these peptides was verified and quantitatively characterized by SPR ( Table 1 ) ., The list of putative LC8 binding peptides identified by our protocol are shown in Table 1 , together with the measured binding constants , which confirmed the binding of the selected peptides to LC8 ., As an example , results are shown for the motif in AMOTL2 in Fig 6 ., Although the apparent Kd values indicate weak interactions , these binding affinities are similar to other LC8 interactions 25 , 20 , and in biological settings they can increase in strength due to avidity caused by dimerization 30 ., Besides the canonical TQT motifs these peptides also contain SQT and TNT motifs ., Additional peptides that further expand the repertoire of compatible amino acids at various positions were also tested for their binding to LC8 ( S4 Table ) ., In order to properly assess the conservation of LC8 binding motifs in WWC and AMOT family members , we traced the evolutionary history of these proteins and their identified binding regions and additional functional modules ., Almost all vertebrate species have three paralogs of both the WWC and AMOT family members ( Figs 7 and 8 ) ., For both families , the multiple paralogs observed at the level of vertebrates could be traced back to a single common ancestor gene , as shown in the case of Florida lancelet ., KIBRA orthologs were detected beyond the level of chordates , not only in arthropods , but also in cnidaria ( Fig 7 ) ., AMOT was also present in arthropods , but it was missing in the fruit fly ( Fig 8 ) ., The most likely explanation for this is that the angiomotin was originally present in all bilaterian animals , but was lost relatively recently in the dipteran lineage that includes Drosophila 51 ., Altogether , the WWC family members seem to have a more ancient evolutionary origin compared to angiomotins ., Both WWC and AMOT family members showed a highly conserved domain and linear motif organization across a wide range of species ( Figs 7 and 8 ) ., While most LC8 binding motifs verified in human sequences are not conserved beyond vertebrates , KIBRA and the other WWC family members represent an important exception in this regard ., The two LC8 binding motifs of this protein family are well conserved in all three paralogs in vertebrates , lancelet and fruit fly ., Furthermore , one of the motifs is also present in a sea anemone , matching the strong evolutionary conservation of the WW and C2 domains , the defining functional modules of this family ( Fig 7 ) ., The AMOT family members contained a single LC8 binding motif , which seems to have emerged more recently ., While orthologous sequences could be detected in non-vertebrate species based on the conserved coiled coil region together with the angiomotin domain , these sequences lacked the LC8 binding motif ( Fig 8 ) ., The LC8 motif , similarly to the PDZ and WW binding motifs , has become conserved within vertebrate species ., In both of these families , the redundancy and conservation underline the functional importance of LC8 binding motifs in the upstream regulation of the Hippo pathway ., In this work , we established a systematic filtering protocol that can be used to expand the interaction network of a given linear motif binding domain with high confidence motif hits and reduce the number of random motif matches ., While similar bioinformatic pipelines have been used before 14 , the optimality of the applied filtering steps could not be guaranteed or even assessed due to the lack of appropriate measures ., Here , we offered a solution to this problem by introducing a decision tree-like filtering procedure together with the weighted information gain that enabled the construction of an optimal bioinformatic pipeline ., The presented approach was applied to expand the interaction network of LC8 , a highly conserved eukaryotic hub protein that binds its partners via a specific linear motif 22 ., By combining our motif filtering protocol with data collected from protein-protein interaction databases and the information on the presence of island-like conservation , we created a dataset of 71 novel high confidence motif instances ( S3 Table ) ., These novel binding sites significantly enriched the interaction network of LC8 with novel partners and highlighted a previously unknown , important function of LC8 in the Hippo pathway ., A list of predicted LC8 binding motifs was also created in an earlier work 20 ., In this case , the PSSM was calculated based on a library of binding motifs evolved through phage selection instead of using the collection of naturally occurring motif instances ., Although some of the filtering criteria , like IUPred based disorder prediction or intracellular localization were used in both studies , the details of implementation differed significantly , including the optimal cutoff for the PSSM score ., The comparison of the two sets showed that among the top 83 hits identified based on the in vitro evolution and absent from the list of known naturally occurring motifs , 58 ( 70% ) were also uncovered by our presented motif discovery pipeline ., However , our evolutionary filtering criteria reduced this overlap to 38 ( 46% ) ., While to some extent , the limited overlap could be due to the technical differences in the implementation , a more appealing explanation is that binding motifs selected by phage display are optimized for binding strength , while the sequence of naturally occurring motifs were shaped by various evolutionary requirements in the cell , from which strength is just one , and not necessarily the dominant constraint ., Despite these differences , in vitro evolution by phage selection 20 , 52 represent a complementary approach to predict potential motif instances for specific binding domains and to explore the binding preferences of such domains ., While the filtering protocol implemented here is specific to LC8 , the presented work also has important implications beyond this system ., We suggested here a general framework to find the optimal selection of methods for the filtering steps ., The importance of this optimization can be best demonstrated through the example of disorder prediction methods ., Several methods , such as DISOPRED3 , PONDR VSL2 or ESpritz Disprot 33\u201335 , that were tested in this work , perform better on specific datasets of ordered and disordered proteins 53\u201355 ., Nevertheless , IUPred achieved the best results for this specific problem , supporting the choice of this approach in motif-centric application of protein disorder 4 , 14 , 19 ., The pipeline applied here also enabled us to identify features that had limited discriminatory power and therefore were not incorporated into the current pipeline ., For example , all known LC8 binding motifs adopt a \u03b2-strand conformation upon binding , but the current tools are not capab","headings":"Introduction, Results, Discussion, Materials and methods","abstract":"Protein-protein interactions ( PPIs ) formed between short linear motifs and globular domains play important roles in many regulatory and signaling processes but are highly underrepresented in current protein-protein interaction databases ., These types of interactions are usually characterized by a specific binding motif that captures the key amino acids shared among the interaction partners ., However , the computational proteome-level identification of interaction partners based on the known motif is hindered by the huge number of randomly occurring matches from which biologically relevant motif hits need to be extracted ., In this work , we established a novel bioinformatic filtering protocol to efficiently explore interaction network of a hub protein ., We introduced a novel measure that enabled the optimization of the elements and parameter settings of the pipeline which was built from multiple sequence-based prediction methods ., In addition , data collected from PPI databases and evolutionary analyses were also incorporated to further increase the biological relevance of the identified motif hits ., The approach was applied to the dynein light chain LC8 , a ubiquitous eukaryotic hub protein that has been suggested to be involved in motor-related functions as well as promoting the dimerization of various proteins by recognizing linear motifs in its partners ., From the list of putative binding motifs collected by our protocol , several novel peptides were experimentally verified to bind LC8 ., Altogether 71 potential new motif instances were identified ., The expanded list of LC8 binding partners revealed the evolutionary plasticity of binding partners despite the highly conserved binding interface ., In addition , it also highlighted a novel , conserved function of LC8 in the upstream regulation of the Hippo signaling pathway ., Beyond the LC8 system , our work also provides general guidelines that can be applied to explore the interaction network of other linear motif binding proteins or protein domains .","summary":"Fine-tuning of many cellular processes relies on weak , transient protein-protein interactions ., Such interactions often involve compact functional modules , called short linear motifs ( SLiMs ) that can bind to specific globular domains ., SLiM-mediated interactions can carry out diverse molecular functions by targeting proteins to specific cellular locations , regulating the activity and binding preferences of proteins , or aiding the assembly of macromolecular complexes ., The key to the function of SLiMs is their small size and highly flexible nature ., At the same time , these properties make their experimental identification challenging ., Consequently , only a small portion of SLiM-mediated interactions is currently known ., This underlies the importance of novel computational methods that can reliably identify candidate sites involved in binding to linear motif binding domains ., Here we present a novel bioinformatic approach that efficiently predicts new binding partners for SLiM-binding domains ., We applied this method to the dynein light chain LC8 , a protein that was already known to bind many partners in a wide range of organisms ., With this method , we not only significantly expanded the interaction network of LC8 , but also identified a novel function of LC8 in a highly important pathway controlling organ size in animals .","keywords":"protein interactions, protein interaction networks, dyneins, molecular motors, network analysis, sequence motif analysis, research and analysis methods, sequence analysis, computer and information sciences, network motifs, bioinformatics, proteins, biological databases, proteomics, biochemistry, cytoskeletal proteins, sequence databases, cell biology, proteomes, database and informatics methods, protein domains, biology and life sciences, microtubule motors","toc":null}
+{"Unnamed: 0":2146,"id":"journal.pgen.1006034","year":2016,"title":"Discovery of Genetic Variation on Chromosome 5q22 Associated with Mortality in Heart Failure","sections":"Heart failure ( HF ) is a common clinical condition in which the heart fails to maintain blood circulation adequate to meet the metabolic demands of the body without increased cardiac filling pressures ., HF is the result of chronic ventricular remodelling initiated by myocardial injury , volume\/pressure overload , or intrinsic cardiomyopathic processes ., Progression of HF is a complex process involving many tissues , driven by activation of neurohormonal pathways , which induce gradual myocardial hypertrophy , ventricular dilation , and deterioration of cardiac function , often resulting in death from low cardiac output , arrhythmia , or thromboembolic complications 1 ., Activation of such neurohormonal pathways in the short term increases cardiac output when necessary ., However , long-term activation results in accelerated ventricular remodelling and myocyte death ., Inhibitors of deleterious neurohormonal pathways , including adrenergic 2\u20134 and renin-angiotensin-aldosterone ( RAAS ) 5\u20138 pathways have been shown to improve ventricular function and survival in patients with HF and are the mainstay of current pharmacological treatment of HF 9\u201310 ., Despite advances in therapy with neurohormonal antagonists , mortality after onset of HF remains high 9\u201313 and continued progress to identify additional therapeutic targets is needed ., Genome-wide association ( GWA ) studies have the potential to identify in an agnostic manner genetic variants related to clinical outcomes in humans and has led to the identification of novel pathways 14 and potential treatments 15 for cardiovascular traits ., Heritable factors have been shown to be predictive of mortality in certain heart failure patients 16 ., We therefore implemented a genome-wide association approach to identify novel molecular determinants of mortality in patients with new-onset HF ., We expanded our previously published GWA study 17 of HF mortality with additional samples and extended follow-up in Stage, 1 . Stage 1 included 2 , 828 new-onset HF patients from five community-based cohorts , thus representative of the general population of HF patients , as part of the Cohorts for Heart and Aging Research in Genomic Epidemiology ( CHARGE ) consortium 18: the Atherosclerosis Risk in Communities ( ARIC ) Study , the Cardiovascular Health Study ( CHS ) , the Framingham Heart Study ( FHS ) , the Health , Aging and Body Composition ( Health ABC ) Study , and the Rotterdam Study ( RS ) ., Cohorts are described in detail in S1 Text ., HF was defined using international published criteria as outlined in S1 Table ., Subjects in Stage 1 cohorts were of European ancestry , predominantly male , and approximately 20\u201330% had a history of myocardial infarction at the time of HF diagnosis ., Additional characteristics are shown in Table, 1 . During an average follow-up time of 3 . 5 years , 1 , 798 deaths occurred ., The sample-size weighted average 1-year mortality rate was 28% ., Among deaths , 51% were classified as cardiovascular , 19% were due to neoplasms , 10% were respiratory deaths , and the remaining were due to other miscellaneous causes ., Genotyping using high-density Illumina or Affymetrix single nucleotide polymorphism ( SNP ) arrays , followed by imputation to the HapMap CEU release 22 imputation panel was performed in each cohort ., Population stratification was assessed and corrected in each cohort as described in S1 Text ., Association with time to death following HF diagnosis was examined in each cohort using Cox proportional hazards models with censoring at loss to follow-up ., Mild inflation of test statistics was observed only in the Framingham Heart Study ( FHS ) as shown in S1 Fig ( \u03bbGC = 1 . 07 , other cohorts \u2264 1 . 03 ) , and genomic control was applied in each individual study ., In the meta-analysis of all cohorts , there was no evidence of inflated test statistics overall ( \u03bbGC = 1 . 00 ) as shown in S2 Fig , so no further genomic control was needed ., Results for all SNPs across the genome are plotted in S3 Fig . Single nucleotide polymorphisms ( SNPs ) passing a significance threshold specified a priori as P < 5 . 0x10-7 , as used in our previous article 17 , were carried forward to a second stage of genotyping in independent cohorts ., Five SNPs on chromosome 5q22 and one SNP on chromosome 3p22 passed the pre-specified P-value threshold ., Results for all six SNPs are shown in Table 2 and S3 Table ., The five SNPs on chromosome 5q22 were highly correlated ( pairwise r2 > 0 . 9 ) ., Two sentinel SNPs , rs9885413 and rs12638540 , on chromosomes 5q22 and 3p22 , respectively , were next genotyped in 1 , 870 European-ancestry subjects with new-onset HF from four independent cohorts in Stage 2: Malm\u00f6 Diet and Cancer , Malm\u00f6 Preventive Project , Physicians\u2019 Health Study , and the PROSPER trial ., Characteristics of populations in Stage 2 are shown in S2 Table ., During an average sample-size weighted follow-up of 4 . 3 years in Stage 2 samples , 889 patients died ., We observed evidence of association with mortality for rs9885413 on chromosome 5q22 ( P = 0 . 006 ) but not for the SNP rs12638540 ( P = 0 . 18 ) which reached nominal significance in our previous analysis 17 ., Results for both SNPs are shown in Table, 2 . In the combined results from Stages 1 and 2 , rs9885413 was associated with a 36% relative increase in mortality per minor allele ( P = 2 . 7x10-9 ) ., There was no evidence for effect heterogeneity across cohorts in the two stages ( P for heterogeneity = 0 . 39 ) as shown in S4 Table ., The SNP had a similar minor allele frequency ( MAF = 0 . 07 ) across cohorts ., Information on cause-specific mortality was available from death certificates in a subset of cohorts ( S5 Table ) and was explored descriptively due well-known problems with substantial misclassification in death certificate data and low power for agnostic GWAS of individual causes ., The minor allele frequency was slightly higher for several causes of death associated with heart failure , including renal , pulmonary and endocrine mortality and death from ischemic heart disease ., We next examined whether rs9885413 on chromosome 5q22 that was associated with HF mortality was also associated with differences in myocardial structure and function , which could potentially mediate the association ( S6 Table ) ., In 12 , 612 individuals from the EchoGen Consortium 19 , the SNP was not associated with major echocardiographic characteristics ., The SNP rs9885413 was not associated with incident HF in 20 , 926 individuals from the general population in the CHARGE-HF study 20 , or with cardiac endocrine function , as determined by plasma levels of atrial and B-type natriuretic peptides ( all P > 0 . 05 ) , in a GWA study of 5 , 453 individuals from the population-based Malm\u00f6 Diet and Cancer study 21 ., No association was observed with electrocardiographic measures of cardiac conduction ( n = 39 , 222 ) 22 or repolarization ( n = 74 , 149 ) 23 , which confer risk of ventricular arrhythmia , or with sudden cardiac death in 4 , 496 sudden death cases and over 25 , 000 controls from the general population ( described in S1 Text ) ., The lead SNP rs9885413 on chromosome 5q22 that was associated with mortality is located in an intergenic region , 100 kb downstream of the gene SLC25A46 , 114 kb upstream of TMEM232 , and 230 kb upstream of TSLP as shown in Fig, 1 . The SNP is not in linkage disequilibrium with any known coding SNP in the 1000 Genomes Project database ( no coding SNP with r2 > 0 . 01 to the sentinel SNP ) ., We therefore sought to evaluate gene regulatory functions of this SNP ., In 129 human tissues from the ROADMAP Epigenomics project 24 , we studied whether rs9885413 or strongly correlated SNPs ( a total of 9 at r2 > 0 . 8 ) are located in regulatory regions , as determined by histone modification patterns ., None of the 9 SNPs was located in an active regulatory region in cardiac tissues ( S7 Table ) , but rs9885413 was located in a predicted enhancer in several epithelial or mesenchymal tissues , including keratinocytes , gastrointestinal cell types and adipose cells ( Fig 2 and S7 Table ) ., Regulatory motif annotations in HaploReg indicate that the SNP causes a change in a regulatory motif predicted to bind the transcription factor NHLH1 as shown in S8 Table ., Interestingly , NHLH1-null mice have been shown to be predisposed to premature , adult-onset unexpected death in the absence of signs of cardiac structural or conduction abnormalities , in particular when mice were exposed to stress 25 ., Little is known about the function of NHLH1 , but it is widely expressed in human tissues and has been shown to regulate expression of key inflammatory genes 26 ., To experimentally test the effect of rs9885413 on enhancer activity , the 100 bp region flanking the SNP ( 50 bp on either side ) was cloned into a reporter vector and transfected into HEK293 cells expressing NHLH1 ( S1 Text ) ., Luciferase activity measured after 24 hours was 4-fold higher with a construct corresponding to the risk allele as compared to the wild-type allele ( S4 Fig , P < 0 . 001 ) , indicating that the risk allele of rs9885413 substantially increases enhancer activity ., We next explored the association of rs9885413 with DNA methylation at the locus , providing functional evidence of epigenetic association and regulation of gene expression ., DNA methylation was determined by a microarray assaying in total over 480 000 CpG methylation sites in whole blood samples from 2408 participants of the FHS ., Of the 84 CpG methylation sites on the microarray within +\/- 500 kb of the SNP , two were significantly associated with rs9885413: cg21070081 ( beta 0 . 017 per T allele , P = 9 . 0x10-69 ) and cg02061660 ( beta -0 . 015 per T allele , P = 4 . 5x10-40 ) , thus constituting strong methylation quantitative trait loci ( mQTLs ) at the locus ., Other , correlated SNPs at the locus were more strongly associated with each of these mQTLs as shown in S5 Fig: rs244431 for cg21070081 ( P = 6 . 7x10-369 ) and rs72774805 for cg02061660 ( P = 7 . 0x10-85 ) ., The SNP rs72774805 ( perfect proxy SNP rs3844597 used ) but not rs244431 was associated with heart failure mortality ( P = 3 . 3x10-3 and 0 . 08 , respectively ) , indicating that the methylation site cg02061660 is more strongly related to the underlying signal for heart failure mortality ., The association of rs9885413 with lower probability of methylation at cg02061660 was replicated in 731 participants from the Rotterdam study ( beta -0 . 029 per T allele , P = 1 . 7x10-11 ) ., Adjustment for cell types from direct measurement instead of estimates from methylation patterns did not abolish the association ( beta -0 . 029 per T , P = 1 . 2x10-6 ) ., Interestingly , differential methylation at this CpG site was also correlated with a SNP at the locus previously associated with allergic sensitization 27 ( rs10056340 , P = 4 . 7x10-29 for mQTL ) , suggesting a link to inflammatory disease ., This SNP was also modestly correlated with rs9885413 ( r2 = 0 . 28 ) and associated with heart failure mortality ( P = 0 . 01 ) ., The association of cg02061660 with rs9885413 ( P = 0 . 52 ) and rs10056430 ( P = 0 . 87 ) was abolished in analyses conditioning for rs72774805 , for which the association was also markedly attenuated ( P = 7 . 0x10-33 and 2 . 1x10-46 , respectively ) indicating that these correlated SNPs may reflect the same underlying signal ., We further assessed the association of rs9885413 with gene expression ., No gene was significantly associated with rs9885413 in the diverse tissues from the Gene-Tissue Expression ( GTEx ) project 28 after correction for multiple tests ( S1 Text , S9 Table ) , although conclusions were limited by a small sample size ., We next assessed association of the SNP with gene expression in two large datasets with each of the tissues most relevant for the phenotype under study: heart tissue and whole blood ., We observed no convincing evidence of association ( S1 Text , S10 Table ) with gene expression in 247 left ventricular samples from patients with advanced heart failure ( n = 116 ) undergoing transplantation and from unused donors ( n = 131 ) ., Finally , we tested the association of rs9885413 with the expression of genes at the locus in whole blood from 5257 FHS participants 29 , and with DNA methylation at cg02061660 among 2262 FHS participants ., All five genes at the locus ( Fig 1 ) except TMEM232 were expressed in blood ., We did not observe association of the SNP rs9885413 with any transcript , but expression of one gene ( TSLP ) was significantly associated with the methylation status of cg02061660 ( P = 1 . 1x10-4 ) ., The TSLP gene encodes a cytokine released from epithelial cells that induces release of T cell-attracting chemokines from monocytes , promotes T helper type 2 cell responses , enhances maturation of dendritic cells and activates mast cells ., It has also been linked to angiogenesis and fibrosis ., A monoclonal antibody targeting and inhibiting TSLP is currently in clinical phase III trials for asthma and allergic inflammation after a promising phase II trial 30\u201332 ., In the myocardium , the TSLP gene has very low expression ( S10 Table ) but expression has been described in mature myocardial fibroblasts , which are abundant in the myocardium but of substantially smaller volume than cardiomyocytes and likely contribute little to the overall myocardial RNA pool 31 , 32 ., To examine whether the transcription factor NHLH1 affects the expression of any of the five genes in the locus ( Fig 1 ) , we knocked down NHLH1 in HEK293 cells using siRNAs ., A 50% decrease in NHLH1 mRNA levels was seen 48 hours after transfection , confirming efficient knock down ( p<0 . 05 , S6A Fig ) ., TSLP was the only gene at the locus affected by NHLH1 knock down , showing a 30% decrease compared to cells transfected with negative control siRNA ( p<0 . 05 , S6A Fig ) ., Moreover , we observed a dose-response relation between level of NHLH1 knockdown and expression of TSLP in HEK293 cells ( r2 = 0 . 74 , p<0 . 0001 , S6B Fig ) ., Finally , distribution of the risk allele of rs9885413 in human populations was assessed using data from HapMap phase II ., The derived ( non-ancestral ) T allele ( risk allele for mortality ) was highly differentiated among human populations ( S7 Fig ) having risen to an allele frequency of 0 . 59 in a Nigerian population ( HapMap YRI sample ) but only 0 . 06 in a European population ( CEU sample ) ., The fixation index ( Fst ) , a measure of population differentiation in allele frequencies , for comparison of YRI and CEU was 0 . 48 and more extreme Fst was observed in only 2 . 4% of SNPs in the HapMap phase 2 dataset ., Consistent results were observed for another signature of recent positive selection , based on longer runs of haplotype homozygosity in carriers of the derived allele ( standardized integrated haplotype score -0 . 766 in YRI , where negative score values indicate longer haplotypes on the background of the derived allele ) 33 ., These observations are consistent with positive selection in recent human history , with a selective sweep resulting in high frequency of the derived allele in western African populations ., These findings are of particular interest as HF mortality is well known to be higher in populations of African ancestry , although the current study has not tested for the association with HF mortality in such populations 34 ., We identified a SNP on chromosome 5q22 associated with increased mortality in subjects with HF ., Although previous genome-wide association studies have described hundreds of loci associated with risk of disease onset , few have examined prognosis in subjects with manifest disease ., This approach has the potential to generate targets for novel disease-modifying medications ., Through a series of analyses in silico and in vitro we show that the SNP is located in an enhancer region , and confers increased activity of this enhancer ., Interestingly , mice deficient in the transcription factor NHLH1 predicted to bind a motif in this enhancer region have been reported to be predisposed to premature , adult-onset unexpected death in the absence of signs of cardiac structural or conduction abnormalities ., NHLH1 has also been shown to regulate expression of key inflammatory cytokines such as interleukin-6 and tumor necrosis factor \u03b1 ., The SNP was not associated with any electrocardiographic , endocrine , or echocardiographic marker of increased risk in the general population , suggesting a mechanism specific to heart failure , an extracardiac pathway of importance in cardiac pathophysiology , or interaction with therapy for heart failure which we were unable to further test given the inception cohort design of this study ., We also did not observe any robust eQTL associations for the SNP in heart ., The SNP was however associated with a DNA methylation signature in whole blood that was also associated with a SNP previously associated with allergy , and with expression of the cytokine TSLP in blood ., Knockdown of NHLH1 also resulted in lower expression of TSLP in HEK293 cells ., This non-coding SNP may thus exert an influence on TSLP expression via altered NHLH1 enhancer function and DNA methylation at the methylation site cg02061660 ., Detailed characterization of causal variants and different association signals at the locus would however require finemapping and sequence data ., The TSLP cytokine is released from epithelial cells and fibroblasts and is considered important in initiation of inflammatory responses to tissue damage , particularly in the type 2 T-helper ( Th2 ) pathways ., Th2 pathways are central in the response to extracellular parasites but also play a key role in the pathophysiology of allergies and hypersensitivity reactions ., A small subset of HF is known to be caused by Th2-mediated inflammation ( eosinophilic cardiomyopathy ) , yet Th2 cells have received limited attention in HF pathophysiology ., Recent experimental work implicates an important role of T-helper cells in HF progression for both systolic and diastolic heart failure , but has mainly focused on type 1 T-helper pathways 35 , 36 ., It remains unclear if the mechanism for rs9885413 is through a specific etiology characterized by high mortality such as eosinophilic cardiomyopathy or a pathway involved in outcomes with manifest disease ., The lack of association with HF incidence suggests that it may not act through incidence of a specific etiology , although firm conclusions are limited by sample size ., We did not observe significant associations of the SNP with gene expression in any tissue ., It is possible that adequately powered samples with a specific cell subtype in a specific context is needed to detect such associations , as illustrated by a recent study which only observed certain eQTLs with single-cell but not across averaged cells 37 ., Indeed , baseline expression of TSLP was low in our samples , and is induced by tissue injury , microbes , viruses and proinflammatory cytokines 38 ., Evidence of recent positive selection in individuals of African descent suggests that the HF risk allele may have been beneficial in some environments in recent human history ., Inflammatory pathways are enriched for signals of recent positive selection , reflecting that infectious disease has been an important cause of mortality throughout recent evolution ., Genes such as HBB and APOL1 have also been reported to have been subject to recent positive selection in Africa by conferring protection against infectious diseases such as Malaria and Trypanosomiasis ( sleeping sickness ) 39 , and APOL1 alleles have also been linked to cardiovascular disease 40 ., As cardiovascular disease and heart failure often presents after reproductive age , increased mortality in such patients would not be expected to exert purifying ( negative ) selective pressure ., Whether SNPs at 5q22 contribute to higher mortality in subjects of African ancestry remains to be shown ., Thus , although additional work is needed to further clarify the tissues and pathways perturbed by this genetic variant and the mechanisms linking it to mortality in HF patients , the current findings implicate rs9885413 as a novel marker of increased risk among patients with HF ., Complementary epigenomic evidence demonstrated candidate regions and genes , which may be mediators in cardiac pathophysiology and potential therapeutic targets to improve prognosis in patients with HF ., A genome-wide association ( GWA ) study was performed in a total of 2 , 828 subjects of European ancestry with HF from seven samples collected within five large community-based prospective cohort studies including the Atherosclerosis Risk in Communities ( ARIC and ARIC2 ) Study , the Cardiovascular Health Study ( CHS ) , the Framingham Study ( FHS ) , the Health ABC ( Health ABC ) study and the Rotterdam Study ( RS and RS2 ) ., Sample characteristics , data collection and clinical definitions have been described previously and are summarized in S1 Text ., 41\u201346 First diagnosis of heart failure ( new-onset ) was ascertained using a variety of methods based on international published criteria , as detailed in S1 Table ., Mortality was ascertained from telephone contacts with relatives and from medical records , death certificates and\/or municipal records ( S1 Text ) ., Genotyping was performed using commercially available assays for genome-wide SNP detection ., Imputation of non-genotyped SNPs was performed using CEU reference panels of SNP correlations from the HapMap project phase II ( S1 Text ) , to characterize a total of 2 . 5 million SNPs ., Imputation quality was assessed for each SNP from the ratio of observed over expected variance of allele dosage ., All-cause mortality following initial HF diagnosis was examined for association with additive allele dosage of each genotyped or imputed SNP using Cox proportional hazards models , with censoring at the end of or loss to follow-up ., Models were adjusted for age at diagnosis , sex , and recruitment site in multicenter cohorts ., In the family-based FHS , Cox models were implemented with clustering on pedigree to account for relatedness ., Genomic control was applied to results from each cohort ., Cohort-specific GWA results were combined using fixed effects meta-analysis with inverse variance weights ., SNPs were excluded from cohort-level analyses if exhibiting implausible beta coefficients ( < -5 or > 5 ) and from the meta-analysis for low heterozygosity ( sample size-weighted minor allele frequency \u2264 0 . 03 , corresponding to < 100 minor allele carriers with an endpoint ) ., SNPs passing a P-value threshold defined a priori as P < 5 . 0x10-7 in the genome-wide stage 1 were carried forward to the second stage with targeted genotyping in 1 , 870 HF patients from four independent cohorts ., For 2 . 5 million tests , this threshold limits the expected number of genome-wide false positives to approximately 1 , assuming statistical independence of tests ., The second stage included four independent cohorts; the Malm\u00f6 Diet and Cancer Study ( MDCS ) , the Malm\u00f6 Preventive Project ( MPP ) , the Physicians\u2019 Health Study ( PHS ) and the Prospective Study of Pravastatin in the Elderly at Risk ( PROSPER ) 47\u201350 ., Heart failure ascertainment and time of death in these cohorts was similar to in stage 1 cohorts , as shown in S1 Table and S1 Text ., Genotyping was performed as outlined in S1 Text ., Association analyses and meta-analysis of results were performed as in the first stage ., Meta-analysis of stage 1 and 2 was performed , and a combined P-value < 5 . 0x10-8 was considered significant ., Heterogeneity was assessed across the combined stage 1 and 2 cohorts using Cochran\u2019s Q test for heterogeneity , computed as the sum of the squared deviations of each study\u2019s effect from the weighted mean over the study variance , and the I2 test , the percentage of total variation across studies that is due to heterogeneity rather than chance ( I2 = Q\u2014df \/ Q ) 51 , 52 ., The association of replicated SNPs with measures of cardiac structure and function was evaluated from summary results of the following GWA consortia: EchoGen 19 , CHARGE-HF 20 , CHARGE-QRS 22 , natriuretic peptides in 5453 subjects from the Malm\u00f6 Diet and Cancer study 21 , QT-IGC 23 , and the CHARGE Sudden Cardiac Death consortium ( manuscript in preparation ) ., Each of these consortia is described in S1 Text ., The correlation of replicated SNPs with known coding SNPs was examined in the databases for the 1000 Genomes Project and phase III of the HapMap project , using SNAP 53 ., The location of SNPs in relation to regulatory motifs was explored using histone methylation patterns generated as part of the ROADMAP Epigenomics project 24 ., Enhancers were identified in each of the 129 ROADMAP tissues using the ChromHMM algorithm 54 from patterns of monomethylation ( H3K4Me1 ) of the fourth residue ( lysine ) and acetylation of the 27th residue ( H3K27Ac ) of histone H3 ., The location of SNPs in relation to transcription factor binding sites was assessed in silico using HaploReg version 4 . 1 ( http:\/\/www . broadinstitute . org\/mammals\/haploreg\/haploreg . php ) 55 and the UCSC Genome Browser ( http:\/\/genome . ucsc . edu ) ., In HaploReg , position weight matrices ( PWMs; probabilistic representations of DNA sequence ) were computed with p-values based on literature sources and ENCODE ChIP-Seq experiments as previously described 55 , and only instances where a motif in the sequence passed a threshold of P < 4\u22127 were considered ., The NHLH1-binding motif was retrieved into HaploReg from the manually curated TRANSFAC database ., Complementary DNA oligonucleotides corresponding to the 100 bp genomic region flanking rs9885413 ( 50 bp on either side of the SNP ) were cloned into the luciferase reporter vector pGL3-Promoter ( Promega , Madison , WI ) using the MluI and BglII sites ., Two different sets of oligos were cloned , one corresponding to the major allele of rs9885413 ( pGL3P-G ) and one to the minor allele ( pGL3P-T ) ., Oligonucleotide sequences were as following: major allele sense: CGCGTCCTGCCTCACATAATCTTTTTGTTTGTCCCCCTGAAATGGATTCTCAGCTGTTGCCCAAACATTTCATCTTAGCGTTCCAGGTTTGAACTCGCCCTCACGA , minor allele sense: CGCGTCCTGCCTCACATAATCTTTTTGTTTGTCCCCCTGAAATGTATTC TCAGCTGTTGCCCAAACATTTCATCTTAGCGTTCCAGGTTTGAACTCGCCCTCACGA , and the corresponding antisense sequences ., The reporter vectors were co-transfected with the pRL-null vector at a ratio of 10:1 into HEK293 cells using Lipofectamine LTX ( Life Technologies ) according to the manufacturer\u2019s instructions ., 24 hours post-transfection , luciferase activity was assayed using the Dual-Luciferase Reporter Assay System ( Promega ) and Glomax 20\/20 Luminometer ( Promega ) ., The signal from the reporter vector was normalized to the signal from the pRL-null vector ., Samples of left ventricular cardiac tissue from patients undergoing cardiac surgery were genotyped for the SNP rs9885413 and for all five transcripts within +\/- 500 kb of the SNP ., Samples of cardiac tissue were acquired from patients from the MAGNet consortium ( http:\/\/www . med . upenn . edu\/magnet\/ ) ., Gene expression levels were determined using the Affymetrix ST1 . 1 gene expression array ( Affymetrix , Santa Clara , CA , USA ) in a cohort including 247 heart samples ., Genotyping was performed using the Illumina OmniExpress array ., Left ventricular free-wall tissue was harvested at time of cardiac surgery from subjects with heart failure undergoing transplantation or from unused transplant donors ., In all cases , the heart was perfused with cold cardioplegia prior to cardiectomy to arrest contraction and prevent ischemic damage ., Tissue specimens were then obtained and frozen in liquid nitrogen ., Genomic DNA from left ventricle was extracted using the Gentra Puregene Tissue Kit ( Qiagen ) according to manufacturer\u2019s instruction ., Total RNA was extracted from left ventricle using the miRNeasy Kit ( Qiagen ) including DNAse treatment on column ., RNA concentration and quality was determined using the NanoVue Plus spectrophotometer ( GE Healthcare ) and the Agilent 2100 RNA Nano Chip ( Agilent ) ., For all samples , genome-wide SNP genotypes were generated using the Illumina OmniExpress Array ., Caucasian Ancestry was verified using multi-dimensional scaling of genotypes ., For Gene expression array experiments , the Affymetrix ST1 . 1 Gene array was used ., Data were normalized using the Robust Multi-array Average algorithm and batch effects were adjusted for using ComBat ., Transcript expression levels were considered significantly higher than background noise if expression values from robust multiarray analysis in at least 10% of either cases or controls exceeded of the 80% quantile of expression of genes on the Y-chromosome in female hearts ( 5 . 24 ) ., Associations of expression levels for expressed genes with SNP genotypes were tested using a likelihood ratio test ., Specifically , we fit a linear regression model Y = \u03b20 + \u03b21*D + \u03b22*g + \u03b23* ( g x D ) where Y is the log2 transformed expression level of a given probe , g is the genotype ( coded as 0 , 1 , and, 2 ) of the test SNP , and D is heart failure disease status ( D = 1 for heart failure cases and D = 0 for unused donor controls ) ., Association between the probe and test SNP was assessed by testing H0: \u03b22 = \u03b23 = 0 using a likelihood ratio test ., Significance of the test statistic was evaluated by comparing with a Chi-squared distribution with two degrees of freedom ., All models were additionally adjusted for age , gender , and study site ., The association of the SNP rs9885413 with DNA methylation was examined in 2408 participants from the FHS Offspring cohort ., Methylation at cytosine-guanine dinucleotides ( CpG ) at the 5q22 locus ( +\/-500 kb from rs9885413 ) were ascertained from a gene-centric DNA methylation array ( Infinium HumaMethylation450 BeadChip , Illumina , San Diego , CA , USA ) which allows interrogation of 485 , 512 methylation sites across the genome ., The array has coverage of at least one methylation site near 99% of RefSeq genes and 96% of CpG islands ., Briefly , bisulfite-treated genomic DNA ( 1 \u03bcg ) from peripheral blood samples underwent whole-genome amplification , array hybridization and scanning according to manufacturer instructions ., Genotyping of rs9885413 was performed as described in S1 Text ., Association of rs9885413 and the methylation probe cg02061660 with expression of the five genes at the locus ( +\/-500 kb from rs9885413 ) was examined from microarray data ( Affymetrix Human Exon Array ST 1 . 0 ) in 5257 participants from the FHS Offspring cohort and Third Generation cohort ., Procedures for RNA extraction , processing and analysis have been described previously ( 28 ) ., Linear mixed effect ( LME ) models were fit accounting for familial correlation , cell count heterogeneity and technical covariates to account for batch effects using the pedigreemm package in R 56 ., Specifically , the mQTL model utilized a two-step approach: first , the DNA methylation beta-value ( ratio of methylated probe intensity to total probe intensity ) was residualized with adjustment for age , sex , cell count proportions ( imputed using the Houseman method for granulocytes , monocytes , B-lymphocytes , CD4+ T lymphocytes , CD8+ T lymphocytes and NK cells ) 57 , measured technical covariates ( row , chip , column ) , and the family structure covariance matrix ., Second , DNA methylation residuals were specified as dependent variable , SNP genotype dosage as independent variable with additional adjustment for 558 SVAs ( surrogate variable analysis ) 58 and ten principal components from eigenstrat 59 to account for unmeasured batch effects ., The eQTL models similarly residualized gene expression with adjustment for age , sex , imputed cell count proportions ( imputed in Offspring Cohort participants utilizing gene expression markers of cell count proportions developed from the Third Generation participants with both gene","headings":"Introduction, Results, Discussion, Materials and Methods","abstract":"Failure of the human heart to maintain sufficient output of blood for the demands of the body , heart failure , is a common condition with high mortality even with modern therapeutic alternatives ., To identify molecular determinants of mortality in patients with new-onset heart failure , we performed a meta-analysis of genome-wide association studies and follow-up genotyping in independent populations ., We identified and replicated an association for a genetic variant on chromosome 5q22 with 36% increased risk of death in subjects with heart failure ( rs9885413 , P = 2 . 7x10-9 ) ., We provide evidence from reporter gene assays , computational predictions and epigenomic marks that this polymorphism increases activity of an enhancer region active in multiple human tissues ., The polymorphism was further reproducibly associated with a DNA methylation signature in whole blood ( P = 4 . 5x10-40 ) that also associated with allergic sensitization and expression in blood of the cytokine TSLP ( P = 1 . 1x10-4 ) ., Knockdown of the transcription factor predicted to bind the enhancer region ( NHLH1 ) in a human cell line ( HEK293 ) expressing NHLH1 resulted in lower TSLP expression ., In addition , we observed evidence of recent positive selection acting on the risk allele in populations of African descent ., Our findings provide novel genetic leads to factors that influence mortality in patients with heart failure .","summary":"In this study , we applied a genome-wide mapping approach to study molecular determinants of mortality in subjects with heart failure ., We identified a genetic variant on chromosome 5q22 that was associated with mortality in this group and observed that this variant conferred increased function of an enhancer region active in multiple tissues ., We further observed association of the genetic variant with a DNA methylation signature in blood that in turn is associated with allergy and expression of the gene TSLP ( Thymic stromal lymphoprotein ) in blood ., Knockdown of the transcription factor predicted to bind the enhancer region also resulted in lower TSLP expression ., The TSLP gene encodes a cytokine that induces release of T-cell attracting chemokines from monocytes , promotes T helper type 2 cell responses , enhances maturation of dendritic cells and activates mast cells ., Development of TSLP inhibiting therapeutics are underway and currently in phase III clinical trials for asthma and allergy ., These findings provide novel genetic leads to factors that influence mortality in patients with heart failure and in the longer term may result in novel therapies .","keywords":"death rates, genome-wide association studies, medicine and health sciences, body fluids, demography, genome analysis, epigenetics, dna, population biology, dna methylation, chromatin, cardiology, genomics, chromosome biology, gene expression, chromatin modification, dna modification, heart failure, genetic loci, hematology, people and places, biochemistry, population metrics, blood, cell biology, nucleic acids, anatomy, physiology, genetics, biology and life sciences, computational biology, chromosomes, human genetics","toc":null}
+{"Unnamed: 0":2007,"id":"journal.pcbi.1002544","year":2012,"title":"Sarcomeric Pattern Formation by Actin Cluster Coalescence","sections":"Several groups have proposed polarity sorting of actin filaments by myosin activity 30 , 31 ., However , those mechanisms localize myosin filaments close to actin filament plus-ends , which is opposite to the myosin localization observed in striated stress fibers and myofibrils , where myosin resides in the mid region between neighboring crosslinks that attach to the actin plus-ends , see figure 1 ., In simulations of a generic bundle of polar filaments crosslinked by populations of both plus- and minus-end directed motors , Zemel et al . demonstrated sarcomeric ordering with correct polarity sorting if applied to actin bundles 32 , see also 33 ., However , in the context of actin bundles , there is little evidence for an unconventional , minus-end directed myosin 34 ., The concept of a plus-end tracking crosslinker as put forward here has been introduced earlier in the framework of a mean field description 35 ., Recently , the group of Joanny proposed a description for the establishment of striated order by stress-induced polarity sorting in terms of a one-dimensional , active gel 36 ., However , this mechanism relies on a phenomenological coupling term and as such does not provide insight into the microscopic mechanisms that eventually underlie this coupling ., To describe the transition from an unstriated actin bundle to a striated one , we consider in our simulations a single , long bundle that consists of parallel actin filaments aligned with the long axis of the fiber ( chosen to be the -axis ) ., In biological cells , striated fibers have an extension in the transverse direction of only a few hundred nanometers ., In our computational model , we therefore ignore the transverse position of the individual actin filaments and assume that each filament can interact with any other provided their projections on the fiber axis overlap ., This assumption corresponds to a mean-field treatment of the transverse degrees of freedom ., For simplicity , filaments are assumed to be rigid and incompressible with respective lengths , ., For figures 2 , 3 , 4 , filament lengths are monodisperse with for all ; whereas for figure 4 filament length are chosen from a log-normal distribution that satisfies and , see also the Supporting Information ( SI ) ., Actin filaments are structurally polar and filaments ends are referred to as either the plus-end or the minus end , see figure 2A ., We distinguish actin filaments with plus-ends that face either the positive -direction ( orientation , blue in figures ) , or the negative -direction ( , red in figures ) ., Actin filament polymerization is a non-equilibrium process and polymerization and depolymerization rates differ for the plus- and minus-ends , respectively ., In a deterministic description of filament polymerization dynamics at steady state , we assume that the individual actin filaments possess a net polymerization speed at their plus-ends whose absolute magnitude is equal to the net depolymerization speed at their minus ends ., ( The corresponding polymerization rate is thus , where denotes actin monomer length . ), The broken symmetry of the polymerization dynamics results in a velocity difference between the current plus-end position of the -th filament ( with a lab-frame velocity ) and its individual monomers ( velocity ) ., This phenomenon is commonly referred to as filament treadmilling 2 , see figure 2A ., For an actin filament that is subject only to a friction force for motion relative to the cytosol , the plus-end advances with velocity , while the monomers are at rest , , and the friction force is zero due to force balance ., Here , is an effective friction coefficient that accounts for rapid binding and unbinding interactions with the surrounding actin gel , and , possibly , integrin-mediated interactions with a substrate ., This situation changes , if rigid crosslinks between actin filaments constrain their motion ., In addition to treadmilling actin filaments , the second key ingredient of our model is a processive , plus-end tracking actin crosslinker that effectively describes the concerted action of several Z-body proteins , see figure 2A ., In our simulations , actin filaments become irreversibly crosslinked with a rate , if their respective plus-end positions and are close ., The precise functional form of affects results only slightly and we chose with and ( measured in units of ) ., A case of reversible plus-end crosslinking for which actin filaments can spontaneously dissociate again is considered in the SI text S1 ., Subsequent crosslinking results in the formation of \u2018actin filament clusters\u2019 that consist of many actin filaments whose respective plus-ends are aligned and which are permanently crosslinked by effective plus-end tracking crosslinkers ., Such an actin cluster will move as a whole subject to the sum of forces acting on its constituent actin filaments ., These crosslinked actin clusters can grow by fusion ., If two actin filaments belonging to two small clusters establish a new crosslink , the new -coordinate of the merged cluster is taken as the weighted average of the respective -coordinates of the two clusters ., In real nascent striated fibers , the longitudinal alignment of plus-ends of crosslinked filaments supposedly involves a dynamic reorganization of the crosslinking Z-band on a time-scale of several minutes 27 , which is not included in our minimal model ., Importantly , the proposed plus-end tracking crosslinkers are assumed to be processive , i . e . they always remain locally attached to the filament plus-ends , even in the presence of actin treadmilling of the crosslinked filaments , see figure 2A ., As a consequence , the center of an actin cluster is subject to polymerization forces of its constituent actin filaments and moves with a velocity that is determined by a local force-balance of cytosolic friction forces ., This force balance is spelled out below in the paragraph \u2018Active motion of a single actin cluster\u2019 ., For figure 2 only , a generic friction force for the relative sliding of two actin filaments is introduced , which is proportional to the mutual length overlap of the two filaments ., Here , denotes a friction coefficient ., Finally , the motion of actin clusters is determined in each time-step in a self-consistent manner by a balance of forces ., We employ periodic boundary conditions with a system size ; a case of static boundary conditions is discussed in the SI text S1 ., Total filament numbers were for actin filaments and for myosin filaments ( for figure 2 ) ., In the premyofibrils of developing muscle cells as well as in stress fibers of non-muscle cells , the molecular motor myosin II polymerizes into bipolar filaments of a few hundred nanometers length that have numerous myosin heads at either end 37 ., Individual myosin heads change conformations via ATP-dependent cycles , while synchronously attaching to ( and pushing on ) actin filaments ., Despite the low duty ratio of individual myosin heads , the large number of these heads ensures a processive and significant myosin-actin interaction ., In our simulations , we employ a coarse-grained description of bipolar myosin filaments of length , in which the individual myosin heads at the two ends of a myosin filament are described as a pair of \u2018actin binding sites\u2019 , see figure 3D ., Each of these two actin binding sites can bind one actin filament in a polarity-specific way ., Attachment and detachment to actin filaments are described as simple Poisson processes with constant rates ., Once a myosin filament is attached to an actin filament , we assume a linear force-velocity relation for myosin walking past the actin filament , see also SI text S1 for details ., Myosin walking speed is directly related to an active myosin force ( that also equals the myosin stall force ) ., While myosin filaments tend to walk towards actin filament plus-ends , a strong backward force acting on the actin filament can push both the actin and myosin filaments in the opposite direction ., In our simulations , actin treadmilling and associated polymerization forces indeed cause such a motion of myosin filaments towards actin filament minus-ends ., For sake of illustration , consider an isolated actin cluster that comprises a total number of filaments of positive orientation that treadmill towards the -direction ( blue in figures ) as well as a number of filaments of negative orientation ( treadmilling towards the -direction , red in figures ) ., In our deterministic description of filament treadmilling , the monomers of the filaments with positive orientation all move with the same velocity , whereas those of the filaments of negative orientation all move with velocity ., Here is treadmilling speed and the ( yet unknown ) velocity of the crosslinking Z-band ., The two sets of filaments exert respective friction forces on the cytosol , and , where is actin filament length and a cytosolic friction coefficient per actin filament unit length , see above ., By Newtons third law , the counter forces of these cytosolic friction forces act on the Z-band and amount in this case exactly to the polymerization forces of the treadmilling actin filaments ., Local force balance at the Z-band , , determines the velocity of this single cluster as ., The structure factor is a standard measure used in condensed matter physics to quantify the regularity of periodic order 38; it is defined as the squared amplitude of the Fourier transformed density-density correlation function ., We can adopt the structure factor to quantify sarcomeric order in our simulations: We characterize the crosslinked clusters by their respective plus-ends positions and total filament number ., We then define ., Examples of this structure factor as a function of wave vector are shown in figure 3A ., Periodic order is characterized by a series of very sharp , so-called Bragg peaks ., The height of the principal Bragg peak ( red point ) defines a sarcomeric order parameter ., Our computational model primarily serves as a proof of physical principle ., The emergence of striated order in the framework of this model is a robust process that is not sensitive to the parameter choices ., A sensitivity analysis can be found in the SI text S1 ., Since the parameters in the model represent effective quantities ( which , in particular , average out transverse degrees of freedom ) , numerical estimation of these parameters is difficult ., Therefore , our simulation results are presented assuming specific ratios of parameters only , without specifying their absolute values in physical units ., Nevertheless , we now present a rough guide to these parameter values ., In unstriated stress fibers , actin filament length range from , myosin filaments have a length of about 39 ., Thus , the length-scale , which sets the mean length of actin filaments in our simulations , may be chosen as ., Actin polymerization speeds of up to about have been observed in vitro , while filopodia protrusion driven by actin polymerization can be as fast as , see 40 and references therein ., In stereocilia , actin polymerization is highly regulated and polymerization speeds can be as low as 41 ., While in general the polymerization speed of an actin filament is force-dependent with a stall force in the pico Newton range 37 , 42 , we assume here a constant mean polymerization speed ., The ratio sets the primary time-scale of sarcomeric pattern formation in our simulations , and it is shown below that sarcomeric ordering in established within for typical parameter choices ., Experimentally , sarcomeric pattern formation evolves on a time-scale of hours 5 , which corresponds to an actin polymerization speed in our simulations ., This estimated actin polymerization speed would be lower than that in filopodia , but significantly larger than the speed measured e . g . in stereocilia ., Myosin filaments may exert pico Newton forces on actin filament at full activation ., Decoration of actin filaments with troponin\/tropomyosin reduces myosin walking , which would correspond to lower values for the active myosin force in our simulations ., Below , we argue that myosin walking towards actin filaments impedes the correct , sarcomeric polarity sorting , which is established in our model by actin treadmilling ., The effective friction for an actin filament moving within a dense bundle is presumably dominated by binding-unbinding interactions with the surrounding actin gel as well as integrin-mediated interactions with the substrate ., The corresponding effective friction coefficient is expected to be orders of magnitude larger than the hydrodynamic friction coefficient for motion in water 43 , ., Assuming a friction coefficient for single actin filaments ( per unit length ) in the range , we would find for a filament of length moving at a speed of friction forces in the range , i . e . well below both the stall force of actin polymerization and the buckling force of single actin filaments ., We did not incorporate filament diffusion explicitly in our model , as thermal motion will be small in a dense bundle ., Note , however , that dynamic myosin forces with short correlation time can induce stochastic , bidirectional motion of filaments ., Several studies pointed out the effect of integrin-mediated anchorage of Z-lines for myofibrillogenesis 44: Although , initial I-Z-I complexes did form even in the presence of RNAi against integrin , Z-body stability was apparently reduced and bundle integrity was impaired in these experiments 28 ., Presumably , integrins play multiple roles starting with the stabilization of I-Z-I-complexes , which corresponds in our model to a reduced rate of dissociation of single filaments from an actin cluster ( see also SI text S1 ) ., Secondly , anchorage reduces the mobility of I-Z-I complexes , which would correspond to an increased total friction coefficient of actin clusters ., As anchored I-Z-I complexes still showed some residual mobility , anchorage must be dynamic and allow for slippage ., Thus , dynamic anchorage affects the effective parameters in our model , but does not change its basic , qualitative features ., Finally , stable anchorage at the two terminal ends of an acto-myosin bundle specifies its boundary conditions; a simulation case of static boundary conditions is shown in the SI to mimic a bundle whose terminal ends are grafted by focal complexes to a substrate ., In our simulations , we consider a minimal , one-dimensional model of a bundle of treadmilling actin filaments ., Actin filaments with nearby plus-ends can form a stable crosslink by a complex of molecules ( that eventually become the Z bodies ) that holds the plus-end of the two actin filaments , but still allows for actin polymerization at the plus-end , see section \u2018The computational model\u2019 and figure 2A ., Subsequent crosslinking gives rise to the formation of actin clusters that consist of several actin filaments whose respective plus-ends are aligned and which are permanently crosslinked by effective plus-end tracking crosslinkers ., Each actin cluster will move as a whole subject to the sum of forces acting on its constituent actin filaments ., These crosslinked actin clusters can grow by fusion and eventually self-organize into sarcomeric order , thus representing precursors of the I-Z-I complexes observed during early myofibrillogenesis 45 ., To gain basic insight into the process of actin cluster formation and coalescence , we first simulated bundles of treadmilling actin filaments and crosslinks without myosin filaments; the effect of myosin filaments is discussed in the next section ., We observe the formation and coalescence of clusters of crosslinked actin filaments , see figure 2B ., In each actin cluster , the constituent actin filaments polymerize at their plus-ends , thereby pushing against the processive crosslinkers of the Z-band ., The growing actin filaments themselves move away from the Z-band in a form of \u2018local retrograde flow\u2019 ., The polymerization forces exerted by the polymerizing actin filaments on the Z-band are counter-balanced by friction forces that constrain the motion of the actin filaments ., Any imbalance in the number of filaments of the two orientations will result in a net polymerization force and thus net motion of the cluster ., The collision of two clusters can result in their mutual coalescence and the formation of a larger cluster ., If actin filaments slide past each other without any friction , all filaments would eventually coalesce into a small number of very large clusters , see figure 2B ., If we assume , however , a hypothetical , effective friction between moving actin filaments , coalescence of actin clusters above a critical size is dynamically impeded and sarcomeric order results ., The arrest of actin cluster coalescence due to our proposed inter-filament friction can be understood on qualitative grounds as follows: The active motion of a single actin cluster is driven by an imbalance of polymerization forces acting on the Z body that can arise from an imbalance between the respective numbers of the constituent filaments of the two different filament orientations ., This net polymerization force is balanced by the total friction force of the actin cluster ( and possibly additional forces due to interactions with neighboring clusters ) ., Since this total friction is proportional to the total number of filaments in the actin cluster , whereas the net polymerization force ( due to statistical imbalance ) roughly scales only as the square root of this number , smaller actin clusters move faster than larger clusters ., Furthermore , the mutual friction force between two overlapping actin clusters adds a friction term to the force balance that scales as the product of the respective filament numbers and therefore will eventually stall the approach of actin clusters above a certain size ., In the more complex case of an actin bundle , the force balance for all actin clusters has to be considered ., Friction between sliding actin filaments may be provided by fast , dynamic crosslinking along the entire lengths of the actin filaments by a second set of crosslinkers ., Next , we discuss the possibility that myosin filaments serve as such a dynamic actin crosslinker , which mediates an effective repulsion between neighboring actin clusters ., We now augment the simple actin bundle model by adding bipolar myosin filaments that can dynamically attach to actin filaments in a polarity-specific way , see figure 3D ., The relative motion of actin and myosin filaments is governed by a linear force-velocity relation for myosin walking , see section \u2018The computational model\u2019 ., While myosin activity leads to \u2018walking\u2019 of the myosin towards the actin plus-ends , the local retrograde flow of treadmilling actin filaments transports the myosin in the opposite direction as in figure 3A ., For the case shown , actin treadmilling outpaces active myosin walking towards actin plus-ends , resulting in highly regular sarcomeric patterns with myosin localized near the actin minus-ends ., Any actin filament , which is grafted at its plus-end in a Z-band has to polymerize against this obstacle , and is pushed away from the cluster center in a form of \u2018local retrograde flow\u2019 , see figure 3C ., For weak active myosin forces and thus slow active myosin walking , myosin filaments attached to such an actin filament are dragged along with this retrograde flow towards the depolymerizing minus-end of the actin filament ., This \u2018actin conveyor belt\u2019 not only transports myosin filaments to the future A-band , but also generates an effective repulsion between neighboring I-Z-I clusters mediated by crosslinking actin filaments , which ensures a regular sarcomeric spacing of actin clusters ., Stronger active myosin forces drive the myosin towards the actin plus-ends and therefore slow down sarcomeric ordering , see figure 3D ., Above a critical force level , active myosin walking dominates actin treadmilling , and a wrong polarity sorting results that localizes myosin at the plus-ends and thus impedes sarcomeric ordering ., To account for a distribution of actin filament lengths , we simulated bundles comprising actin filaments of different lengths ., For simplicity , we chose a static polydispersity for the actin length given by a unimodular distribution of fixed mean length and tunable width ., Remarkably , sarcomeric ordering occurred even for considerable length variability , though with a sarcomeric order parameter that decreased monotonically with , see figure 4 . Sarcomeric spacing increased as a function of length variability , showing that the longest actin filaments set sarcomere spacing ., Using an exponential distribution for actin filament length instead of a unimodular distribution resulted in no apparent sarcomeric ordering ( not shown ) ., Assuming static filament lengths allows us to study separately the mechanisms that result in actin filament length control and actin turnover , which we now discuss ., Actin filament length control and turnover of filaments both depend crucially on the polymerization and depolymerization dynamics of actin filaments ., Thus , length control and filament turnover are in principle inseparable ., This being said , we nonetheless aimed at isolating the qualitative effect of actin turnover ., To this end , we augmented our computational model by including prototypical actin dynamics that differentiates between idealized dynamic regimes of either, ( i ) steady-state treadmilling with constant actin filament length ,, ( ii ) \u2018actin catastrophies\u2019 characterized by fast and complete depolymerization of filaments that occur with rate , and, ( iii ) rapid de novo polymerization of new actin filaments 46 ., These simple limits are not intended to realistically depict actin dynamics ., Rather they allow us to study the qualitative effects of actin filament turnover , without changing the filament length distribution ., As expected , actin filament turnover interferes with the formation of large actin clusters and results in reduced sarcomeric order , see figure 5 . Surprisingly , myosin is still sorted into regular A-bands even for considerable actin turnover rates ., We conclude that partial polarity sorting of actin filaments is sufficient to sort myosin into A-bands ., This may provide an explanation for experimental observations in which myosin ordering was observed to precede the formation of large , periodically spaced I-Z-I complexes ., Our simulations suggest that sarcomere spacing is set by the length of actin filaments at early stages of striated ordering ., How is actin filament length controlled within a pool of highly dynamic actin filaments ?, Capping proteins regulate filament polymerization and depolymerization rates ., However , on their own , these proteins do not provide a means to tune the average filament length to a set point since they act locally in a manner that is not sensitive to the total length of a filament ., Energetically favorable crosslinking or attraction of actin filaments all along their length can result in a unimodular length distribution as this ensures maximal mutual overlap of filaments 47 ., However , to allow for filament sliding and sorting , such crosslinking would have to be highly dynamic ., Alternatively , severing agents ( such as ADF\/cofilin-like UNC-60B 23 ) are recruited by actin filaments in a length-dependent manner and can provide a generic feedback mechanism that controls actin filament length 48\u201350 ., We consider a simple implementation of actin filament severing assuming that filaments elongate by polymerization at their plus-end with constant polymerization speed , whereas the minus-end is stable ., A generic severing agent can bind with constant rate anywhere along the filament and cut it there ., Since the minus-end facing fragment of a cut actin filament comprises mainly ADP-bound actin monomers and thus is less stable , we assume that this fragment rapidly depolymerizes after severing , see figure 6A ., This simple severing mechanism results in a unimodular length distribution at steady state , see figure 6B as well as SI text S1 ., For an intuitive explanation for this length control mechanism , note that longer filaments with more monomers have a higher probability to recruit a severing agent within a certain time interval compared with shorter filaments: In this scenario , filaments act as \u2018binding antennas\u2019 for severing agents ., Figure 6 shows the emergence of sarcomeric order from an initially unstriated bundle for which actin filaments polymerize and are cut by severing agents ., Here , we proposed a simple , generic , and robust mechanism for striated pattern formation in a crosslinked bundle of aligned actin filaments ., This physical mechanism of sarcomeric ordering is based on the formation of small actin clusters by the plus-end crosslinking of single actin filaments and the subsequent coalescence of these smaller actin clusters into larger ones , which are reminiscent of the I-Z-I complexes observed during early myofibrillogenesis 45 ., This mechanism represents a way to establish cytoskeletal order on length-scales of tens of microns from micron-size building blocks independent of any external scaffolding ., Termination of cluster coalescence and stabilization of sarcomeric units requires a repulsive force between actin clusters ., In mature myofibrils , the giant protein titin acts like an elastic spring and could serve this function ., However , it is questionable if titin could play its role as a spacer between Z-bodies already at these early stages ., While the N-terminal domain of titin is involved in early Z-body formation 28 , the M-line epitope of titin associated to its C-terminal domain is established only after a delay 51 and ligand binding may be required to stretch the titin protein so that it spans the sarcomere; thus , at early times , titin may not set the initial sarcomere spacing 20 ., Here , we studied polymerization forces from polymerizing actin filaments as a possible mechanism to generate repelling forces between actin clusters ., A similar mechanism may apply to stress fibers in adherent , non-muscle cells as well as to stress-fiber like structures in developing muscle cells ., The assembly of mature myofibrils in striated muscle cells has been proposed to be a multi-step process 8 that starts with the formation of unstriated , stress fiber-like acto-myosin bundles near the plasma membrane , followed by the establishment of sarcomeric order within these bundles 10 , possibly by actin cluster formation and coalescence as proposed here ., These striated bundles represent an important intermediate in the assembly of mature myofibrils and are termed nascent myofibrils ., Nascent myofibrils can grow by incorporating free actin and myosin filaments in a mechanism of \u201cself-templating\u201d ., Additionally , they can fuse with each other into a single fiber of increased diameter after aligning their respective periodic patterns 5 , 52 ., Finally , maturation processes and actin length fine-tuning regularizes sarcomeric order resulting in mature myofibrillar \u201ccrystals\u201d ., This myofibrillogenesis pathway represents a succession of hierarchical ordered states ., We speculate that the assembly of striated stress fibers in non-muscle cells may follow a partial sequence of myofibrillar steps ., Initial sarcomeric pattern formation in unstriated bundles would be a key step in this pathway and could rely on similar physical mechanisms both in muscle and non-muscle cells ., Experimental visualization of early sarcomeric pattern formation including actin filament length distribution , polymerization dynamics and their associated forces is technically challenging , but may be essential to test theoretical models of sarcomere formation ., Little is known about the dynamics of actin filaments at early stages of sarcomeric pattern formation ., In mature myofibrils , actin polymerization dynamics has been observed at both the plus- and the minus end 6 , 29 ., These experiments show that actin filaments are highly dynamic even in these apparently stable striated bundles and that Z-bodies may act as plus-end tracking actin crosslinkers ., It should be noted that at these late stages , actin filament treadmilling was not observed; thus , actin treadmilling may be limited to the early stages of striated ordering ., In vitro experiments with reconstituted actin stress fibers 53 might serve as an accessible experimental system to study sarcomeric pattern formation and actin polarity sorting ., Additionally , filament treadmilling in the presence of crosslinkers is a source of expansive stress and should reduce any contractile prestress in the bundle , or even give rise to an overall expansive stress ., This prediction could be tested in future experiments , possibly by laser nano-surgery of unstriated bundles ., Myosin filaments walk towards actin plus-ends ., Unless counter-acted by other mechanisms , myosin walking would result in a wrong localization of myosin at nascent Z-bodies and thus impair sarcomeric ordering ., In our model , actin treadmilling counter-acts myosin walking and transports myosin towards the future M-band , provided active myosin forces are not too strong ., It has been suggested that in some species , the early establishment of sarcomeric patterning involves a non-muscle isoform of myosin II , which is later replaced by muscle-specific myosin II 8 ., It is tempting to speculate that muscle myosin allows for maximal force generation , whereas non-myosin filaments play a role as structural elements during the early establishment of striated order , for which , according to our model predictions , strong myosin forces could be obstructive ., Alternatively , the decoration of actin filaments with tropomyosin may limit myosin walking during the early stages of sarcomeric pattern formation and thus prevent the active myosin forces from disrupting the treadmilling imposed myosin localization as we suggest ., This is consistent with a recent study by Rui et al . , which showed that sarcomeric pattern formation was impaired in the presence of RNAi against tropomyosin and troponin 28 ., In conclusion , we put forward a model that includes a minimal number of generic mechanisms that results in sarcomeric polarity sorting in in silicio acto-myosin bundles ., We acknowledge the possibility that the mechanism presented here is only partial and that other mechanisms also contribute to sarcomeric pattern formation that can be tested experimentally ., In particular , details of our computational model can differ from the genesis of sarcomeres in developing muscle cells: Actin filament buckling as observed in reconstituted in vitro systems 12 , 53 may reduce the myosin mediated repulsion force between neighboring actin clusters ., Also , adhesive linkage of nascent Z-bodies to an extra-cellular substrate could reduce actin cluster motility 7 , 44 ., We believe , however , that our theoretical study helps identify key elements of sarcomeric pattern formation ., We propose that the length of sarcomere constituents such as actin filaments must be tightly controlled as it is expected to set sarcomere length at early stages of striated ordering ., The emergence of sarcomeric order from the active condensation of actin clusters fits into the general framework of cytoskeletal pattern formation by active self-organization , which provides an alternative to external templating mechanisms .","headings":"Introduction, Model, Results, Discussion","abstract":"Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils , but the physical mechanisms that lead to myofibril assembly remains ill-defined ., Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible , suggesting a pivotal role of active processes in sarcomeric pattern formation ., Using a one-dimensional computational model of an initially unstriated actin bundle , we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments ., We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation ., In our simulations , sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation ., The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells .","summary":"Muscle contraction driving voluntary movements and the beating of the heart relies on the contraction of highly regular bundles of actin and myosin filaments , which share a periodic , sarcomeric pattern ., We know little about the mechanisms by which these \u2018biological crystals\u2019 are assembled and it is a general question how order on a scale of 100 micrometers can emerge from the interactions of micrometer-sized building blocks , such as actin and myosin filaments ., In our paper , we consider a computational model for a bundle of actin filaments and discuss physical mechanisms by which periodic order emerges spontaneously ., Mutual crosslinking of actin filaments results in the formation and coalescence of growing actin clusters ., Active elongation and shrinkage dynamics of actin filaments generates polymerization forces and causes local actin flow that can act like a conveyor belt to sort myosin filaments in place .","keywords":"physics, biophysic al simulations, biophysics theory, biology, cell mechanics, biophysics simulations, biophysics, biomechanics, computational biology","toc":null}
+{"Unnamed: 0":195,"id":"journal.pcbi.1002505","year":2012,"title":"Insights into the Fold Organization of TIM Barrel from Interaction Energy Based Structure Networks","sections":"Proteins are amino\u2013acid polymers capable of folding into unique three\u2013dimensional functional states ., The information for the structure formation is contained within their amino\u2013acid sequence 1 ., With an enormous amount of data available on genomic sequences in organisms and the structures of the proteins they encode , it has become evident that despite the large sequence space , the structure space is rather limited 2\u20134 ., It has been predicted that merely a few thousand protein folds are needed to generate the entire repertoire of the multimillion strong protein universe 5 , 6 ., The limited number of folds has been explained as a result of optimization of backbone packing 7 , 8 ., A recent analysis of the fold space showed that the atomic interaction network in the solvent\u2013unexposed core of protein domains are fold\u2013conserved , and that the network is significantly distinguishable across different folds , providing a \u201csignature\u201d of a native fold 9 ., As a common rule , homologous sequences generally take up similar folds and the sequence divergences are concomitantly accompanied by structural variations 10 ., However , increasing number of identified sequences and folds show a significant departure from this rule , i . e the same fold is able to house highly dissimilar protein sequences 11\u201314 ., Folds like the TIM ( Triosephosphate Isomerase ) barrel , Rossmann , \u03b1\u03b2\u2013plait , and all \u03b2\u2013immunoglobins are taken up by divergent sequences thereby underscoring the availability of limited fold space ., These folds with their simple and symmetric architectures seem to be favorable folds for a large number of non\u2013homologous sequences ., Such folds are of special interest since their investigation would provide profound insights into the principles governing protein folding and stability ., Although functional variations are related to structural variations , it has been established that proteins with disparate structures may retain their function during the course of their evolution as long as the local active site geometry is maintained 10 , 15 ., Triosephosphate Isomerase ( TIM ) Barrel is one the ancient folds with considerable sequence diversity 2 ., It is also one of the ubiquitously occurring enzymatic folds and hosts the most diverse enzymatic reactions catalyzing five of the six classes of biochemical reactions 16 , 17 ., Thus TIM barrel , possessing both structural and functional diversity , has appealed both structural biologists and biochemists equally over the years ., Factors responsible for its structural maintenance and functional diversity have been investigated in detail since its first structural discovery in 1975 16 , 18\u201324 ., The fold consists of an alternating helix\u2013loop\u2013strand secondary structure motif , where the strands assemble into the core \u03b2\u2013barrel ., This \u03b2\u2013barrel is therefore formed by parallel strands , which is a rarity in fold space 24 ., The outer rim of the barrel is maintained by helix\u2013sheet and helix\u2013helix interactions ., Evolutionary studies suggest that there are evidences for both divergent 23 and convergent 20 evolution of the TIM barrel proteins , and hence , its evolution is being highly debated ., A large number of computational studies have been carried on this fold , focusing mainly on their prevalence in the enzymes of various organisms catalyzing different functions , their structural and evolutionary properties 16 , 21\u201326 ., In this study we have explored the factors responsible for the stability of TIM fold taken up by dissimilar sequences ., Unlike earlier studies that focus on residue conservation , we have focused on interaction conservation as the basis of understanding the underlying structural determinants of the TIM fold ., Although this is a novel method , several concepts related to protein sequence-structure-function relationship have been explored and quantitative results have been presented in the literature ., For instance , evolutionary concepts were implemented in identifying pair-wise 27 and sets of residues , called as a \u201csectors\u201d , that have undergone correlated mutations 28 in the protein sequences ., At the structure-dynamics level , coarse-grained network models have shown that proteins with similar architecture exhibit similar large-scale dynamic behavior 29 and the differences usually occur in regions where specific functions are localized ., Energetic coupling between residues has been investigated both experimentally by mutation followed by biochemical measurements 30 and from computational methods 31 ., The classical problem of studying the structure-function relationship in allostery has been addressed from protein structure network point of view 32\u201336 ., In essence the protein sequence-structure relationship and the structural changes accommodating their biological function have been investigated by a variety of methods ., Here , we have made the preliminary attempt to study the role of conserved interactions in stabilizing a fold by, ( a ) analyzing residue\u2013residue interactions obtained from atomistic force fields;, ( b ) investigating the interactions and their threshold energy values at a global level by constructing Protein Energy Networks ( PEN ) ;, ( c ) obtaining a common PEN for a family of proteins ( f\u2013PEN ) by structure based alignment followed by the construction of a common energy\u2013weighted interaction matrix;, ( d ) using the f\u2013PENs to study the conserved interactions responsible maintaining the fold and, ( e ) exploiting the conservation of interactions ( obtained from f\u2013PENs ) to deduce phylogenetic relationship ( trees ) as opposed to the commonly practiced sequence based methods ., PENs are structure networks where the constituent amino\u2013acids are the nodes and the edges represent the non\u2013covalent interactions among them ., By representing the interactions as interaction energies ( obtained from molecular mechanics force fields ) , both the chemistry and the geometry of the amino\u2013acids are better represented than other contact\u2013based structure networks 37 , 38 ., We have used structural similarities between the remote homologues of TIM barrel fold to align their PENs to obtain information on the extent of interaction conservation among them ., The analysis of f\u2013PENs has provided us a wealth of information in terms of the strength of interactions and their conservation ( at pair\u2013wise as well as at the level of a collection of multiple interactions ) ., We have been able to identify the factors responsible for the stability of the different secondary structural interfaces in the TIM fold ., In general we have observed that the residues involved in high\u2013energy interactions to have more conservation than the residues forming low\u2013energy vdW dominated interactions ., We have seen that high\u2013energy conserved interactions are present in the central \u03b2\u2013barrel stabilizing it and in the catalytic loop regions helping in the functioning of the protein ., The interface between helices and sheets are dominated exclusively by low\u2013energy interactions between non\u2013conserved residues , thus contributing much to the sequence diversity ., We also observed that interaction conservation based phylogeny represents the structural and functional evolution better than those derived from sequence conservation ., The new outlook from \u201cinteraction conservation\u201d has shed more light on the factors behind the fold organization of TIM fold by sequentially diverse homologues ., Such observations are unique and we believe that this method will pave an alternate way for understanding the basis of organization of other folds as well ., Furthermore , the information on interaction conservation can enable more controlled engineering of new proteins with enhanced structural\/functional properties ., The TIM fold comprises three major secondary structural interfaces: the central \u03b2\u2013barrel , \u03b1\/\u03b2 and \u03b1\/\u03b1 ( Figure 1a ) ., The central \u03b2\u2013barrel is formed by staggered parallel \u03b2 sheets forming the \u03b2\/\u03b2 interface and makes up the core of the fold ( Figure 1b ) ., The \u03b1\/\u03b2 interface flanks the barrel and is formed by the most common \u03b1\u2013X\u2013\u03b2 motif ( where X can be any secondary structure like loops and \u03b2 turns or even separate motifs ) ., The helices interact with each other to form the \u03b1\/\u03b1 interface facing the exterior ., It has been shown that the face of the fold with the C\u2013terminal ends of the barrel and the adjoining loops contain the active\u2013site residues , thus forming the catalytic face of the fold ( Figure 1b ) 18 ., As mentioned earlier TIM fold is rich in both sequential and functional diversity marking it a viable system for studying sequence\u2013structure\u2013function relationship ., The analysis of the Protein Energy Networks ( PENs ) provides a rationale to investigate the non\u2013covalent interactions in proteins at various levels such as the interacting pairs ( edges ) , network of connected residues ( clusters ) , nodes connected by a large number of interactions ( hubs ) as a function of interaction energy ., The domains of the TIM barrel fold in the dataset ( Table S1 ) are represented as energy weighted structure networks ( PENs ) , in which the constituent amino\u2013acids are considered as nodes and the edges are weighted based on the non\u2013covalent interaction energies among the amino\u2013acids ( Eq 3 , Methods Section ) ., Such a representation of PEN , capturing the non\u2013covalent interaction energies at the atomic level , is capable of providing a consolidated view of the forces stabilizing the fold of the protein , yet retaining the details of individual interactions ., It is to be noted that highly favorable interactions ( for example , \u221225 kJ\/mol ) will be referred to as \u201chigh\u2013energy\u201d interactions , whereas less favorable interactions ( for example , \u221210 kJ\/mol ) will be referred to as \u201clow\u2013energy\u201d interactions ., A range of unweighted PENes can be generated from the PEN using specific maximum energy cutoffs ( e ) to define the edges ( Eq 4 , Materials and Methods ) ., It was earlier noted from the PENs of a set of globular proteins that at low energies ( e>\u221210 kJ\/mol ) the network is dominated by hydrophobic vdW interactions and above this value ( e<\u221210 kJ\/mol ) , the electrostatic interactions starts dominating the edges in the PENs 38 ., The ljPENs are generated to focus exclusively on the vdW interactions by excluding the dominant terms of electrostatic interactions ., The largest cluster ( LC , see Materials and Methods ) profiles as a function of \u2018e\u2019 for both PENs and ljPENs are provided for the present dataset of 81 TIM barrel domains ( Figure S1 ) ., It is clear that the domains show three distinct network behaviors as a function of \u2018e\u2019 ( Figure S1a ) ., In the high\u2013energy region ( e<\u221220 kJ\/mol , henceforth denoted as pre\u2013transition region ) , the LC size is small with the network connected by electrostatic interactions ., The size of the LC increases in the intermediate energy region ( \u221220<e<\u221210 kJ\/mol , transition region ) following a sigmoidal profile by accruing low\u2013energy vdW interactions and to encampass the whole protein in the low\u2013energy region ( e>\u221210 kJ\/mol , post\u2013transition region ) , where the vdW interactions are dominant , tethering together local pockets of high\u2013energy interactions ., The LC profile of ljPENs is similar to PENs except that the mid\u2013transition point is around \u22127 kJ\/mol ( Figure S1b ) , due to the absence of high\u2013energy electrostatic interactions ., The TIM barrel domain is a common fold adopted by a large number of diverse sequences ., Here we ask the question whether these domains are stabilized by similar patterns of interactions ., Despite high sequence diversity we find common patterns of interactions of equivalent energies emerged when investigated at the family level ., The family level classification of the TIM fold was obtained from the SCOP database 39 ., We constructed family specific PENs for a chosen \u2018e\u2019 value ( f\u2013PENes ) ( Figure, 2 ) and obtained the equivalent node\/edge\/network information from the multiple structural alignments of the constituent members ( Materials and Methods ) ., Each edge in the family specific network is given a commonality coefficient ( ccij ) value indicating the frequency of occurrence of that edge\/interaction in the f\u2013PENe ( Eq 5 and Figure 2f ) ., A \u2018cc\u2019 value of one corresponds to the presence and a \u2018cc\u2019 value zero represents the absence of interaction within a spatially similar position of the fold in all the members of a TIM family ., Thus various f\u2013PENe ( cc ) can be generated for a specific family where f\u2013PENe ( 1 . 0 ) represents interactions that are present in all the members of the fold and f\u2013PENe ( 0 . 5 ) represents interactions that are present in at least half the members of the family ., In order to determine the role of an amino\u2013acid ( node ) type in maintaining an interaction ( edge ) , we have used an Entropy based Conservation score ( EC ) for each node in the f\u2013PEN ( see Methods Section 3 . 6 ) ., Generally if EC is greater than zero then there is a degree of conservation of that residue in the family , while a negative EC score shows that the residue is not conserved in that position ., Therefore , cc is a measure of \u201cinteraction conservation\u201d between two nodes and EC is a measure of \u201cresidue conservation\u201d of the nodes ., We have analyzed f\u2013PENes in the dataset for edge distribution in different secondary structural interfaces namely the central \u03b2\u2013barrel , \u03b1\/\u03b2 and \u03b1\/\u03b1 interfaces ., We further explore the network parameters like clusters and hubs in PENs and f\u2013PENs to determine the maintenance of the fold architecture in the TIM fold despite low sequence homology ., In our analysis we principally focus on f\u2013PENs at the pre\u2013transition region ( \u223ce<\u221218 kJ\/mol , Figure S1a ) for studying the electrostatic contribution to the fold and the post\u2013transition region of f\u2013ljPENs ( \u223ce<\u22128 kJ\/mol , Figure S1b ) for obtaining the vdW contribution ., By analyzing the distribution of the conserved edges across different interfaces it is possible to determine how the fold is maintained irrespective of the residue conservation ., While the interaction\u2013based studies discussed so far is a step above the residue level investigation , the network parameters like clusters and hubs go beyond pair\u2013wise , by providing a collective view of multiple interacting residues ., For instance , even if common interacting pairs in a family of structures are not obvious , a collection of residues interacting at a threshold energy level at similar structural locations can be detected as clusters ., Therefore , we have utilized the PENs and f\u2013PENs to study certain network properties like hubs and clusters to further understand the formation and stabilization of the fold ., One of the major implications in understanding protein sequence\u2013structure\u2013function relationship is that we can obtain a variety of evolutionary information ., Classically , existing phylogenetic methods exploit sequence conservation information to infer relationships and recent increase in structural data has resulted in the inclusion of structural features to deduce relationships between proteins 43 ., The most commonly used sequence conservation based methods fail to obtain correct relationships between remote homologues due to the misgivings of sequence alignment techniques in the \u201ctwilight region\u201d of the sequence\u2013structure space ., Here we deduce improved similarity relationships between remote homologues of the TIM fold through quantification of the similarity of interactions ( edges ) from their PENs ( details described in Materials and Methods ) ., Figure 6 shows the comparison of the cladograms ( a map of the hierarchical clusters ) obtained from the interaction based and sequence based techniques ., It can be readily seen that the interaction conservation based method clusters proteins of the same family under the same clade better than the sequence conservation based method ., It should be noted that the SCOP classification of families is based on sequence or structure or functional similarities ., The interaction based phylogeny matches very well with the SCOP classification than the sequence based method for the same dataset ., Despite low sequence identity ( \u226430% ) we were able to find domains that exhibited as high as \u223c85% interaction conservation ( between d1r0ma1 and d1muca1 from DGDL family ) ., These observations show that the interaction based phylogenetic tree may be able to cluster the members of the family better than a residue based classification scheme ., Lockless and Rangathan 27 introduced a sequence-based method to investigate statistical interactions between residues ( Statistical Coupling Analysis ( SCA ) ) ., Later Halabi et al . , grouped these statistically correlated amino-acids into quasi-independent groups called sectors and studied their characteristics in Serine proteases 28 ., Here we have made the preliminary attempt to compare the interaction-energy based approach with the sequence based SCA approach ., We selected \u03b2-glycanase family of TIM fold for this comparison ., The interactions ( \u2264\u221210 kJ\/mol ) common to this family were identified and cross verified with correlated mutations obtained from SCA ., Although the correlation appeared to be weak at the pair-wise level , significant correlations are identified when the collective behavior of these correlated pairs are examined ., In other words , there is a significant match between the residues of the sector from SCA and the clusters obtained from the present energy based analysis ., The results have been pictorially depicted in Figure 7 ( details of the underlying calculations and comparison are provided in Table S2 and Table S3 ) ., Interestingly , the agreement is more in the regions stabilizing the structure ., The residues located more towards the function are identified by SCA and the PEN clusters encompass more of the residues required for the structural integrity ., Based on this reasonable correlation of the SCA sectors and PEN clusters , we emphasize the fact that the protein structures should be viewed as a collective entity and an examination of individual residues and pair interactions in isolation may not always provide a holistic view of the structure and function of proteins ., This feature was also reiterated by the coarse-grained network model studies on Rossmann-like domain proteins 29 ., A weak agreement of pair-wise correlations from SCA predictions with the biochemical experiments on double mutants of PDZ domain perhaps may be attributed to this reason ., Furthermore , fundamental issues like divergent 23 or convergent 20 evolution of proteins like TIM barrel , whose sequences are so diverse , has always been debated 16 ., Extensive investigation by complimentary approaches such as PEN , SCA and essential mode dynamics should be able to provide more clarity into such systems ., The sequence\u2013structure relationship is a well\u2013researched area , however , the factors that drive highly diverse sequences to fold into the same structure has not been well understood because of the apparent absence of consensus information from sequence similarity analyses ., Here we have taken an alternative approach in which we consider \u201cinteraction conservation\u201d and analyze whether the preservation of interactions is an essential driving force in the formation of the fold rather than sequence conservation ., TIM barrel fold is one of the most popular folds that have a high sequence variability and functional diversity ., In this study we have analyzed non\u2013homologous members of different families of the TIM fold and investigated various factors that contribute to the formation of the fold ., We have adapted the concept of interaction networks in order to study these protein structures from a global perspective ., Also , by using interaction energies we have realistically represented the residue\u2013residue relationships in the network ., The subsequent methodology that exploits structural alignment to align the Protein Energy Networks ( PENs ) in a family of TIM fold has provided us with valuable information on the conservation of interactions in the family ., It was evident from our analyses of conserved interactions that the central \u03b2 barrel is being stabilized by, ( a ) sequentially long\u2013range conserved high\u2013energy interactions and, ( b ) low\u2013energy vdW interactions from residues of the neighboring strands interacting in tandem , in addition to the hydrogen\u2013bonding network in the sheet ., Also , the analysis of the other interfaces like the \u03b1\/\u03b2 and the \u03b1\/\u03b1 show an absence of any high\u2013energy conserved interactions , and being maintained exclusively by low\u2013energy interactions ., In general we found that the residues involved in high\u2013energy interactions are better conserved than low\u2013energy interactions ., From our cluster analysis it was seen that the conserved interactions are not segregated into isolated interacting pairs but rather coalesce together to form a sub\u2013network of interactions ., Our hub analysis has shown that the charged and the conserved residues are favorable to be hubs at higher energies , while hydrophobic residues with less conservation act as hubs at lower energies ., All these results suggest that, ( a ) the \u03b2 barrel formation driven by high\u2013energy interactions ( with the participating residues being conserved ) seem to be an important step in the organization of the TIM barrel;, ( b ) the formation of the other interfaces mainly by low\u2013energy interactions ( with residue conservation being immaterial ) is a more canonical step in the fold formation common to all the folds of the \u03b1\/\u03b2 class , and can be taken up by a variety of sequences , thus contributing the high sequence diversity ., These conclusions concur with several experimental observations that suggest that while the \u03b1\/\u03b2 interfaces in TIM are resilient to mutations the \u03b2 barrel is sensitive 18 , 40 , 41 , 44 ., We have analyzed the structural and functional relevance of conserved interactions in the regions involving loops in various TIM barrel families ., We found that loop based high\u2013energy conserved interactions ( e<\u221220 kJ\/mol ) are present near the active sites of a number of TIM barrel families ., This suggests that the loop based interactions are conserved during evolution to maintain the active site geometry for successful enzymatic functioning of the TIM proteins ., Therefore this method can be used in functional annotation of hypothetical proteins in cases where there are structural homologues but no sequence homologues ., Finally we exploited the concept of \u201cinteraction conservation\u201d to construct a cladogram and compare it with the sequence based cladogram ., The outcome of analysis reinforces our assumption that it may be interaction conservation and not necessarily sequence conservation that determines the fold organization ., Our attempt to correlate our method with that of SCA suggests that there may be significant correlation between the sector residues and cluster residues ., However , extensive investigation by complimentary approaches such as PEN , SCA and Elastic Network Models ( ENM ) should be carried out and such an analysis will be able to provide more clarity to studying such protein systems ., The methodology of representing the protein structures as interaction energy based networks and using structural alignments to align these networks has provided us a very convenient handle to study structure homology among sequentially diverse proteins , from a network point of view ., We were able to study the salient features that stabilize the TIM fold using this method , and also analyze how interaction conservation can play an important role in the formation of this fold ., We believe that this methodology can shed valuable knowledge on the fold maintenance by remote homologues and pave way for useful de novo design and analysis of protein folds ., The dataset used in this analysis is composed of domains from the TIM fold given by Structural Classification Of Proteins ( SCOP ) 39 ., The coordinates for the domains are obtained from ASTRAL 45 ., The domains are sorted into their respective families as given in SCOP ., The sequence identity within the members of each family is less than 30% ., The culling of domains with higher sequence identity was done using cd\u2013hit 46 ., All the families constitute at least three members ( except HMGL like domains ( HMGL ) and Adenosine\/AMP deaminase ( ADA ) families , ( see Table S1 ) ) ., The dataset consisting of 19 families with 81 domains is presented in Table S1 ., The secondary structural elements ( SSE ) for each domain were assigned using DSSP 47 ., Structure network construction requires the coordinates of the interacting amino acids ( nodes ) and a criterion to define the interactions ( edges ) ., A purely geometry based all-atom interaction can be deduced from the crystal structure , which we had used to describe the Protein Structure Networks ( PSNs ) 48 ., Recently , we have considered the chemistry in greater detail by explicitly considering the interaction energy between residues 38 ., Although qualitative results are expected to be similar from both formalisms , PEN has the advantage of capturing subtle details of importance , whereas the PSN approach has the advantage of being simple to adopt ( Figure S7 ) ., The interaction energies can be obtained on a single structure or on an ensemble of structures of a given protein ., The set of structures can be obtained from experiments ( X-ray crystallography , Nuclear Magnetic Resonance ) under different environment or by simulations from a single starting conformation ., In the case where the conformational changes are small , a set of conformations will provide a statistically relevant average structure and in the case of large conformational change , it is advantageous to study them independently to characterize the structural variations in different states of the same protein , for example to understand the effect of ligand binding ., In this study we have used Molecular Dynamics ( MD ) simulations to obtain the structure ensemble for each of the TIM domains ., We have considered the crystal structures for all the proteins in the dataset ( Table S1 ) and subjected them to minimization and Molecular Dynamics simulations for a brief time interval ( 20 ps ) to obtain interaction energies in equilibrium ., In our earlier studies we have shown that the correlation between interaction energies calculated using the equilibrated structures from 2 ns simulations and 20 ps simulations was around 90% 38 ., The MD simulations were performed using GROMACS ( GROningen MAChine for Simulations ) 49 for just 20 ps and structure ensemble for each domain is obtained by sampling its trajectory every 1 ps ., The average interaction energies among the amino\u2013acids are computed using the structure ensemble thus obtained ., Selenomethionines ( MSE ) present in certain domains like d1pbga_ and d1uwsa_ from Glycosyl hydrolase family ( F1GH ) were converted to Methionine and missing atoms in the residues were generated using Swiss PDB viewer 50 ., The best conformations for both the modified and the built residues recommended by the Swiss PDB viewer from its rotamer library were used ., The details of the construction of PEN are given in Vijayabaskar and Vishveshwara 38 ., Briefly , the non\u2013bonded interaction energies ( Eij , Eq, 1 ) between all pairs of residues were obtained as a summation of the electrostatic ( given by columbic potential , Eq, 2 ) and van der Waals ( given by the Lennard Jones ( LJ ) potential , Eq, 3 ) interaction energies averaged over the structure ensemble ., PEN is constructed with amino\u2013acids as nodes , and with edges drawn between all pairs of residues except the sequential neighbors ., The edges are weighted with the calculated Eij ., ljPENs take into account only the van der Waals ( vdW ) interactions ( i . e Eij\\u200a=\\u200aVLJ ) ., Unweighted networks ( PENe and ljPENe ) can be obtained for a specific maximum energy cutoff \u2018e\u2019 as given in Eq 4 ., ( 1 ) ( 2 ) ( 3 ) ( 4 ) Steps involved in the construction of the family specific PEN ( f\u2013PEN ) by alignment of the PENes of its members is given in detail in Figure 2 ., Domains in a family are structurally aligned using MUSTANG ( MUltiple STructural AligNment AlGorithm ) 51 ( Figure 2b ) ., A family specific Multiple Structure based Sequence Alignment ( MSSA ) was obtained for all the members of a given family and the residues that are aligned in the MSSA are referred to as Equivalent residues ., Residues that were not structurally super\u2013imposable were compensated within the alignment using gaps ( Figure 2c ) ., The PENes are remapped using the equivalent node information obtained from the MSSA ( Figure 2d ) ., The gaps in the MSSA are introduced as virtual nodes in the corresponding PENes , such that the edge weights of a virtual node to all other nodes in the PEN were highly unfavorable ( Eij\\u200a=\\u200a100 kJ\/mol where either i or j is a virtual node ) ( Figure 2d ) ., The remapped PENes are then aligned to form the family specific PEN ( f\u2013PENe ) ( Figure 2e ) such that the nodes are equivalent and edges exists only if they were present in any of the realigned PENes ( Figure 2f ) ., In a f\u2013PENe , the values ( X , Eq, 5 ) of the edges can vary from 0 to M , where 0 represents the absence of an edge in all the members of the f\u2013PENe and M represents the edge being present in all members ., Therefore each edge is given a commonality coefficient ( ccij , Eq 5 ) , and it represents the measure of the frequency of occurrence of an edge between equivalent nodes within the members of a family ., ( 5 ) where X is the total number of members having the edge between nodes \u2018i\u2019 and \u2018j\u2019 with interaction energy better than \u2018e\u2019 , Aeij is the element of the adjacency matrix of the remapped PENe and M is the total number of members in the family ( Figure 2e ) ., Thus , a family specific PEN can be denoted as f\u2013PENe ( cc ) where \u2018e\u2019 is the interaction energy cutoff used to generate PENes for all the members of the family and edges are constructed only if their ccij is better than \u2018cc\u2019 ., The f\u2013PENe ( cc ) consists of both equivalent and virtual nodes and represents spatially conserved interactions across the members of that family ., In fact both the \u2018e\u2019 and \u2018cc\u2019 values can be used as weights in order to construct a weighted matrix ., However , in this study , we have considered un-weighted matrix at given values of \u2018e\u2019 and \u2018cc\u2019 ., Entropy based Conservation scores ( EC ) for each alignment position in the MSSA were obtained using AL2CO 52 ., In this method the entropy is normalized with the mean and standard deviation ., Thus better the entropy score , the more conserved the amino\u2013acids are at that position ., A network similarity matrix ( S ) for any two members \u2018a\u2019 and \u2018b\u2019 in the dataset is constructed as given in Eq, 6 . S is an adjacency matrix which takes a value of 1 if the interaction energies between equivalent residues in the MSSA are similar ., The Similarity Score ( SSab ) between the PENs of any two members in the dataset is derived as given in Eq, 7 . This value is the fraction of edges that is conserved between the two members ., The distance matrix ( D , Eq 8 ) with each row and column representing a domain in the dataset , is used to construct the phylogenetic tree ., ( 6 ) ( 7 ) ( 8 ) where Ea and Eb are PENs of any two members in the dataset that are remapped based on their pairwise MSSA , and N is the total number of nodes in the remapped PENs ., The concept of structure conservation is often used in structural alignment methods 53 , 54 ., For instance , an alignment based on dynamic characteristics of structurally similar but functionally distinct proteins have been reported earlier 29 ., The identification of energetically similar edges in two proteins done in the present study , can also serve as a basis for alternate method of structural alignment , although it is not pursued in this study ., Clusters were generated using Depth First Search ( DFS ) algorithm 55 ., Family specific clusters in a family of TIM fold are ","headings":"Introduction, Results\/Discussion, Materials and Methods","abstract":"There are many well-known examples of proteins with low sequence similarity , adopting the same structural fold ., This aspect of sequence-structure relationship has been extensively studied both experimentally and theoretically , however with limited success ., Most of the studies consider remote homology or \u201csequence conservation\u201d as the basis for their understanding ., Recently \u201cinteraction energy\u201d based network formalism ( Protein Energy Networks ( PENs ) ) was developed to understand the determinants of protein structures ., In this paper we have used these PENs to investigate the common non-covalent interactions and their collective features which stabilize the TIM barrel fold ., We have also developed a method of aligning PENs in order to understand the spatial conservation of interactions in the fold ., We have identified key common interactions responsible for the conservation of the TIM fold , despite high sequence dissimilarity ., For instance , the central beta barrel of the TIM fold is stabilized by long-range high energy electrostatic interactions and low-energy contiguous vdW interactions in certain families ., The other interfaces like the helix-sheet or the helix-helix seem to be devoid of any high energy conserved interactions ., Conserved interactions in the loop regions around the catalytic site of the TIM fold have also been identified , pointing out their significance in both structural and functional evolution ., Based on these investigations , we have developed a novel network based phylogenetic analysis for remote homologues , which can perform better than sequence based phylogeny ., Such an analysis is more meaningful from both structural and functional evolutionary perspective ., We believe that the information obtained through the \u201cinteraction conservation\u201d viewpoint and the subsequently developed method of structure network alignment , can shed new light in the fields of fold organization and de novo computational protein design .","summary":"Proteins are polymers of amino-acids that fold into unique three-dimensional structures to perform cellular functions ., This structure formation has been shown to depend on the amino-acid sequences ., But examples of proteins with diverse sequences retaining a similar structural fold are quite substantial that we can no longer consider such phenomenon as exceptions ., Therefore , this non-canonical relationship has been studied extensively mostly by studying the remote sequence similarities between proteins ., Here we have attempted to address the above-mentioned problem by analyzing the similarities in the spatial interactions among amino-acids ., Since the protein structure is a resultant of different interactions , we have considered the proteins as networks of interacting amino-acids to derive the common interactions within a popular structural fold called the TIM barrel fold ., We were able to find common interactions among different families of the TIM fold and generalize the patterns of interactions by which the fold is being maintained despite sequence diversity ., The results substantiate our hypothesis that interaction conservation might by a driving factor in fold formation and this new outlook can be used extensively in engineering proteins with better biophysical characteristics .","keywords":"protein structure, biology, computational biology, macromolecular structure analysis","toc":null}
+{"Unnamed: 0":1416,"id":"journal.pcbi.1005497","year":2017,"title":"Robust information propagation through noisy neural circuits","sections":"Neurons in sensory systems gather information about the environment , and transmit that information to other parts of the nervous system ., This information is encoded in the activity of neural populations , and that activity is variable: repeated presentations of the same stimulus lead to different neuronal responses 1\u20137 ., This variability can degrade the ability of neural populations to encode information about stimuli , leading to the question: which features of population codes help to combat\u2014or exacerbate\u2014information loss ?, This question is typically addressed by assessing the amount of information that is encoded in the periphery as a function of the covariance structure 6 , 8\u201324 , the shapes of the tuning curves 25 , 26 , or both 27 , 28 ., However , the informativeness of the population responses at the periphery is not the only relevant quantity for understanding sensory coding; of potentially equal importance is the amount of information that propagates through the neural circuit to downstream structures 29 , 30 ., To illustrate the ideas , consider the case of retinal ganglion cells transmitting information about visual stimuli to the cortex via the thalamus , as shown in Fig 1 ., To quantify the performance of the retina , one must consider not only the informativeness of the optic nerve responses ( Ix ( s ) in Fig 1A ) , but also how much of that information is transmitted by the lateral geniculate nucleus ( LGN ) to the cortex ( Iy ( s ) in Fig 1A ) 31 ., The two may be very different , as only information that survives the LGN\u2019s spike-generating nonlinearity and noise corruption will propagate to downstream cortical structures ., Despite its importance , the ability of information to propagate through neural circuits remains relatively unexplored 31 ., One notable exception is the literature on how synchrony among the spikes of different cells affects responses in downstream populations 32\u201336 ., This is , however , distinct from the information propagation question we consider here , as there is no guarantee that those downstream spikes will be informative ., Other work 25 , 29 , 30 , 37 , 38 investigated the question of optimal network properties ( tuning curves and connection matrices ) for information propagation in the presence of noise ., No prior work , however , has isolated the impact of correlations on the ability of population-coded information to propagate ., Given the frequent observations of correlations in the sensory periphery 6 , 8 , 17 , 39\u201345 , and the importance of the information propagation problem , this is a significant gap in our knowledge ., To fill that gap , we consider a model ( Fig 1B; described in more detail below ) , in which there are two layers ( retina and LGN , for example ) ., The first layer contains a fixed amount of information , Ix ( s ) , which is encoded in the noisy , stimulus-dependent responses of the cells in that layer ., The information is passed to the second layer via feedforward connections followed by a nonlinearity , with noise added along the way ., We ask how the covariance structure of the trial-to-trial variability in the first layer affects the amount of information in the second ., Although we focus on information propagation , the problem we consider applies to more general scenarios ., In essence , we are asking: how does the noise in the input to a network interact with noise added to the output ?, Because we consider linear feedforward weights followed by a nonlinearity , the possible transformations from input to output , and thus the computations the network could perform , is quite broad 46 ., Thus , the conclusions we draw apply not just to information propagation , but also to many computations ., Moreover , it may be possible to extend our analysis to recurrent , time-dependent neural networks ., That is , however , beyond the scope of this work ., Our results indicate that the amount of information that successfully propagates to the second layer depends strongly on the structure of correlated responses in the first ., For linear neural gain functions , and some classes of nonlinear ones , we identify analytically the covariance structures that optimize information propagation through noisy downstream circuits ., Within the optimal family of covariance structures , we find variability with so-called differential correlations 22\u2014correlations that are proven to minimize the information in neural population activity ., Thus , covariance structures that maximize the information content of neural population codes , and those that maximize the ability of this information to propagate , can be very different ., Importantly , we also find that redundancy is neither necessary nor sufficient for the population code to be robust against corruption by noise ., Consequently , to understand how correlated neural activity affects the function of neural systems , we must not only consider the impact of those correlations on information , but also the ability of the encoded information to propagate robustly through multi-layer circuits ., We consider a model in which a vector of \u201cperipheral\u201d neural population responses , x , is determined by two components ., The first is the set of tuning curves , f ( s ) , which define the cells\u2019 mean responses to any particular stimulus ( typical tuning curves are shown in Fig 2A ) ., Here we consider a one dimensional stimulus , denoted s , which may represent , for example , the direction of motion of a visual object ., In that case , a natural interpretation of our model is that it describes the transmission of motion information by direction selective retinal ganglion cells to the visual cortex ( Fig 1 ) 5 , 6 , 47 ., Extension to multi-dimensional stimuli is straightforward ., The second component of the neural population responses , \u03be , represents the trial-to-trial variability ., This results in the usual \u201ctuning curve plus noise\u201d model ,, x = f ( s ) + \u03be , ( 1 ), where \u03be is a zero mean random variable with covariance \u03a3\u03be ., The neural activity , x , propagates to the second layer via feed-forward weights , W , as in the model of 38 ., The activity in the second layer is given by passing the input , W \u00b7 x , through a nonlinearity , g ( \u22c5 ) , and then corrupting it with noise , \u03b7 ( Fig 1B ) ,, y = g ( W \u00b7 x ) + \u03b7 , ( 2 ), where the nonlinearity is taken component by component , and \u03b7 is zero mean noise with covariance matrix \u03a3\u03b7 ., The function g ( \u22c5 ) need not be invertible , so this model can include spike generation ., While we have , in Fig 1 , given one explicit interpretation of our model , the model itself is quite general ., This means that our results apply more broadly than just to circuits in the peripheral visual system ., Moreover , while our analysis ( below ) focuses on information loss between layers , this should not be taken to mean that there is no meaningful computation happening within the circuit: because we have considered arbitrary nonlinear transformations between layers , the same model can describe a wide range of possible computations 46 ., Our results apply to information loss during those computations ., In the standard fashion 6 , 12 , 20\u201322 , we quantify the information in the neural responses using the linear Fisher information ., This measure quantifies the precision ( inverse of the mean squared error ) with which a locally optimal linear estimator can recover the stimulus from the neural responses 48 , 49 ., The linear Fisher information in the first and second layers , denoted Ix ( s ) and Iy ( s ) , respectively , is given by, I x ( s ) = f \u2032 ( s ) \u00b7 \u03a3 \u03be \u2212 1 \u00b7 f \u2032 ( s ) ( 3a ) I y ( s ) = f \u2032 ( s ) \u00b7  \u03a3 \u03be + ( W eff T \u00b7 \u03a3 eff , \u03b7 \u2212 1 \u00b7 W eff ) \u2212 1  \u2212 1 \u00b7 f \u2032 ( s ) ( 3b ), where a prime denotes a derivative ., Here Weff are the effective weights\u2014basically , the weights , W , multiplied by the average slope of the gain function , g ( \u22c5 ) \u2014and \u03a3eff , \u03b7 includes contributions from the noise in the second layer , \u03b7 , and , if g ( \u22c5 ) is nonlinear , from the noise in the first layer ., ( If g is linear , \u03a3eff , \u03b7 = \u03a3\u03b7 , so in this case \u03a3eff , \u03b7 depends only on the noise in the second layer ) ., This expression is valid if W eff T \u00b7 \u03a3 eff , \u03b7 - 1 \u00b7 W eff is invertible; so long as there are more cells in the second layer than the first , this is typically the case ., See Methods for details ( section titled \u201cInformation in the output layer\u201d ) ., Eq ( 3b ) is somewhat intuitive , at least at a gross level: both large effective noise ( \u03a3eff , \u03b7 ) and small effective weights ( Weff ) reduce the amount of information at the second layer ., At a finer level , the relationship between the two covariance structures\u2014corresponding to the first and second terms in brackets in Eq ( 3b ) \u2014can have a large effect on Iy ( s ) , as we will see shortly ., We begin with an example to highlight the difference between the information contained in neural population codes and the information that propagates through subsequent layers ., Here , we consider two different neuronal populations with identical tuning curves ( Fig 2A ) , nearly-identical levels of trial-to-trial neural variability , and identical amounts of stimulus information encoded in their firing-rate responses; the populations\u2019 correlational structures , however , differ ., We then corrupt these two populations\u2019 response patterns with noise , to mimic corruption that might arise in subsequent processing stages , and ask how much of the stimulus information remains ., Surprisingly , the two population codes can show very different amounts of information after corruption by even modest amounts of noise ( Fig 2B ) ., In more detail , there are 100 neurons in the first layer; those neurons encode an angle , denoted s , via their randomly-shaped and located tuning curves ( Fig 2A ) ., We consider two separate model populations ., Both have the same tuning curves , but different covariance matrices ., For reasons we discuss below , those covariance matrices , denoted \u03a3 \u03be blue and \u03a3 \u03be green ( blue and green correspond to the colors in Fig 2B and 2C ) , are given by, \u03a3 \u03be blue = \u03a3 0 + \u03f5 f \u2032 ( s ) f \u2032 ( s ) ( 4a ) \u03a3 \u03be green = \u03a3 0 + \u03f5 u u ( s ) u ( s ) ( 4b ), where \u03a30 is a diagonal matrix with elements equal to the mean response ,, \u03a3 0 , i j = f i ( s ) \u03b4 i j ., ( 5 ) Here \u03b4ij is the Kronecker delta ( \u03b4ij = 1 if i = j and 0 otherwise ) , and we use the convention that two adjacent vectors denote an outer product; for instance , the ijth element if uu is ui uj ., The vector u has the same magnitude as f\u2032 , but points in a slightly different direction ( it makes an angle \u03b8u with f\u2032 ) , and \u03f5 and \u03f5u are chosen so that the information in the two populations , Ix ( s ) , is the same ( \u03f5u also depends on s; we suppress that dependence for clarity ) ., In our simulations , both \u03f5 and \u03f5u are small ( on the order of 10\u22123; see Methods ) , so the variance of the ith neuron is approximately equal to its mean ., This makes the variability Poisson-like , as is typically observed when counting neural spikes in finite time windows 1\u20136 ., ( More precisely , the average Fano factors\u2014averaged over neurons and stimuli\u2014were 1 . 01 for the \u201cblue\u201d population and 1 . 04 for the \u201cgreen\u201d one . ), Both model populations also have the same average correlation coefficients , which are near-zero ( see Methods , section titled \u201cDetails for Numerical Examples\u201d ) ., To determine how much of the information in the two populations propagates to the second layer , we computed Iy ( s ) for both populations using Eq ( 3b ) ., For simplicity , we used the identity matrix for the feed-forward weights , W , a linear gain function , g ( \u22c5 ) , and independently and identically distributed ( iid ) noise with variance \u03c32 ., Later we consider the more general case: arbitrary feedforward weights , nonlinear gain functions , and arbitrary covariance for the second layer noise ., Those complications don\u2019t , however , change the basic story ., Fig 2B shows the information in the output layer versus the level of output noise , \u03c32 , for the two populations ., Blue and green curves correspond to the different covariance structures ., Although the two populations have identical tuning curves , nearly-identical levels of trial-to-trial neural variability , and contain identical amounts of information about the stimulus , they differ markedly in the robustness of that information to corruption by noise in the second layer ., Thus , quantifying the information content of neural population codes is not sufficient to characterize them: recordings from the first-layer cells of the two example populations in Fig 2 would yield identical information about the stimulus , but the blue population has a greater ability to propagate that information downstream ., One possible explanation for the difference in robustness is that the information in the green population relies heavily on correlations , which are destroyed by a small amount of noise ., To check this , we compared the information of the correlated neural populations to the information that would be obtained with the same tuning curves and levels of single neuron trial-to-trial variability , but no inter-neuronal correlations 11 , 50 , 51 ( Fig 2C ) ., We find that removing the correlations actually increases the information in both populations ( Fig 2C; \u201cTrial-Shuffled\u201d ) , and by about the same amount , so this possible explanation cannot account for the difference in robustness ., We also considered the case where the correlated responses carry more information than would be obtained from independent cells ., We again found ( similar to Fig 2C ) that there could be substantial differences in the amount of information propagated by equally informative population codes ( see Methods , section titled \u201cDetails for numerical examples\u201d , and the figure therein ) ., These examples illustrate that merely knowing the amount of information in a population , or how that information depends on correlations in neural responses , doesn\u2019t tell us how much of that information will propagate to the next layer ., In the remainder of this paper , we provide a theoretical explanation of this observation , and identify the covariance structures at the first layer that maximize robustness to information loss during propagation through downstream circuits ., To understand , from a geometrical point of view , why some population codes are more sensitive to noise than others , we need to consider the relationship between the noise covariance ellipse and the \u201csignal direction , \u201d f\u2032 ( s ) \u2014the direction the mean neural response changes when the stimulus s changes by a small amount ., Fig 3A and 3B show this relationship for two different populations ., The noise distribution in the first layer is indicated by the magenta ellipses , and the signal direction by the green arrows ., The uncertainty in the stimulus after observing the neural response is indicated by the overlap of the green line with the magenta ellipse ., Because the overlap is the same for the two populations , they have the same amount of stimulus uncertainty , and thus the same amount of information\u2014at least in the first layer ., Although the two populations have the same amount of information , the covariance ellipses are very different: one long and skinny but slightly tilted relative to the signal direction ( Fig 3A ) , the other shorter and fatter and parallel to the signal direction ( Fig 3B ) ., Consequently , when iid noise is added , as indicated by the dashed lines , stimulus uncertainty increases by very different amounts: there\u2019s a much larger increase for the long skinny ellipse than for the short fat one ., This makes the population code in Fig 3A much more sensitive to added noise than the one in Fig 3B ., To more rigorously support this intuition , in Methods , section titled \u201cAnalysis behind the geometry of information loss\u201d , we derive explicit expressions for the stimulus uncertainty in the first and second layers as a function of the angle between the long axis of the covariance ellipse and the signal direction ., Those expressions corroborate the phenomenon shown in Fig 3 ., The geometrical picture in the previous section tells us that a code is robust against added noise if the covariance ellipse lines up with the signal direction ., Taken to its extreme , this suggests that when all the noise is concentrated along the f\u2032 ( s ) direction , so that the covariance matrix is given by, \u03a3 \u03be ( s ) \u221d f \u2032 ( s ) f \u2032 ( s ) , ( 6 ), the resulting code should be optimally robust ., While this may be intuitively appealing , the arguments that led to it were based on several assumptions: iid noise added in the second layer , feedforward weights , W , set to the identity matrix , and a linear neural response function g ( \u22c5 ) ., In real neural circuits , none of these assumptions hold ., It turns out , though , that the only one that matters is the linearity of g ( \u22c5 ) ., In this section we demonstrate that the covariance matrix given by Eq ( 6 ) optimizes information transmission for neurons with linear gain functions ( although we find , perhaps surprisingly , that this optimum is not unique ) ., In the next section we consider nonlinear gain functions; for that case the covariance matrix given by Eq ( 6 ) can be , but is not always guaranteed to be , optimal ., To determine what covariance structures maximize information propagation , we simply maximize information in the second layer , Iy ( s ) , with respect to the noise covariance matrix in the first layer , \u03a3\u03be , with the information in the first layer held fixed ., When the gain function , g ( \u22c5 ) , is linear ( the focus of this section ) , this is relatively straightforward ., Details of the calculation are given in Methods , section titled \u201cIdentifying the family of optimal covariance matrices\u201d; here we summarize the results ., The main finding is that there exists a family of first-layer covariance matrices \u03a3\u03be , not just one , that maximizes the information in the second layer ., That family , parameterized by \u03b1 , is given by, \u03a3 \u03be ( s ) = \u03b1 I x ( s ) I \u03b7 ( s ) \u03a3 y + 1 - \u03b1 I x ( s ) f \u2032 ( s ) f \u2032 ( s ) , ( 7 ), where \u03a3y is the effective covariance matrix in the second layer ,, \u03a3 y \u2261 ( W eff T \u00b7 \u03a3 \u03b7 - 1 \u00b7 W eff ) - 1 , ( 8 ), and I\u03b7 ( s ) is the information the second layer would have if there were no noise in the first layer ,, I \u03b7 ( s ) = f \u2032 ( s ) \u00b7 \u03a3 y - 1 \u00b7 f \u2032 ( s ) ( 9 ), ( see in particular Methods , Eq ( 46 ) ) ., For this whole family of distributions\u2014that is , for any value of \u03b1 for which \u03a3\u03be is positive semi-definite\u2014the output information , Iy ( s ) , has exactly the same value ,, I y ( s ) = I x ( s ) 1 + I x ( s ) \/ I \u03b7 ( s ) ( 10 ), ( see Methods , Eq ( 76 ) ) ., This is the maximum possible output information given the input information , Ix ( s ) ., Two members of this family are of particular interest ., One is \u03b1 = 0 , for which the covariance matrix corresponds to differential correlations ( Eq ( 6 ) ) ; that covariance matrix is illustrated in Fig 4A ., This covariance matrix aligns the noise direction with the signal direction ., Accordingly , as for the geometrical picture in Fig 3 , it makes the encoded information maximally robust ., The other family member we highlight is \u03b1 = 1 , for which \u03a3\u03be \u221d \u03a3y ., For this case , the covariance matrix in the first layer matches the effective covariance matrix in the second layer; we thus refer to this as \u201cmatched covariance\u201d ., To understand why this covariance optimizes information in the second layer , we start with the observation that the population activities can be decomposed into their principal components: each principal component corresponds to a different axis along with the population activities can be projected ., The information contained in each such projection ( principal component ) adds up to give the total Fisher information ( see Methods , Eq 71 ) ., The most informative of these projections are those that have low noise variance , and which align somewhat with the signal curve\u2014like the blue line in Fig 4B ., When \u03a3\u03be \u221d \u03a3y , the projections that are most informative in the first layer are corrupted by relatively little noise in the second layer ., Consequently , this configuration enables robust information propagation ., In contrast , when the covariance structures in the first and second layers are less well matched , all projections are heavily corrupted by noise at some point ( i . e . , either in the first or the second layer ) , and hence very little information propagates ( Fig 4C ) ., The family of optima interpolates between the two configurations shown in Fig 4A and 4B ( see also Eq ( 7 ) ) ., Almost all members of this optimal covariance family depend on the details of the downstream circuit: for \u03b1 \u2260 0 in Eq ( 7 ) , the optimal noise covariance at the first layer depends on the feed-forward weights , W , and the structure of the downstream noise ., The one exception to this is the covariance matrix given by Eq ( 6 ) : that one is optimal regardless of the downstream circuit ., These are so-called \u201cdifferential correlations\u201d\u2014the only correlations that lead to information saturation in large populations 22 , and the correlations that minimize information in general ( see Methods , section titled \u201cMinimum information\u201d , for proof ) ., The fact that correlations can minimize information content and at the same time maximize robustness highlights the fact that optimizing the amount of information in a population code versus optimizing the ability of that information to be transmitted put very different constraints on neural population codes ., The existence of an optimum where the covariance matrices are matched across layers emphasizes that not all optimally robust population codes are necessarily redundant ., ( By redundant we mean the population encodes less information than would be encoded by a population of independent cells with the same tuning curves and levels of single neuron trial-to-trial variability 12 , 21; see Fig 2 ) ., Notably , if the effective second layer covariance matrix , \u03a3y , admits a synergistic population code\u2014wherein more information is encoded in the correlated population versus an uncorrelated one with the same tuning curves and levels of trial-to-trial response variability\u2014then the matched case , \u03a3\u03be \u221d \u03a3y , will also admit a synergistic population code , and be optimally robust ., Optimally robust , however , does not necessarily mean the majority of the information is transmitted; for that we need another condition ., We show in the Methods section titled \u201cVariances of neural responses , and robustness to added noise , for different coding strategies\u201d that for non-redundant codes , a large fraction of the information is transmitted only if there are many more neurons in the second layer than in the first ., This is typically the case in the periphery ., For differential correlations , that condition is not necessary\u2014so long as there are a large number of neurons in both the input and output layers , most of the information is transmitted ., So far we have focused on linear gain functions g ( \u22c5 ) ; here we consider nonlinear ones ., This case is much harder to analyze , as the effective covariance structure in the second layer , \u03a3eff , \u03b7 , depends on the noise in the first layer ( see Methods , Eq ( 22 ) ) ., We therefore leave the analysis to Methods ( section titled \u201cNonlinear gain functions\u201d ) ; here we briefly summarize the main results ., After that we consider two examples of nonlinear gain functions\u2014both involving a thresholding nonlinearity to mimic spike generation ., For linear gain functions we were able to find a whole family of optimal covariance structures , for nonlinear ones we did not even try ., Instead , we asked: under what circumstances are differential correlations optimal ?, Even for this simplified question a definitive answer does not appear to exist ., Nevertheless , we can make progress in special cases ., When there is no added noise in the second layer ( e . g . , \u03b7 = 0 for the model in Fig 1B ) , differential correlations maximize the amount of information that propagates through the nonlinearity , so long as the tuning curves are sufficiently dense relative to the steepness of the tuning curves ( meaning that whenever the stimulus changes , the average stimulus-evoked response of at least one neuron also changes; see Methods ) ., If there is added noise at the second layer , differential correlations tend to be optimal in cases where the addition of noise at the first layer , \u03be , causes reductions in information , Ix ( s ) ., ( This means that , so long as there are no stochastic resonance effects causing added noise to increase information , then differential correlations are optimal . ), We first check , with simulations , the prediction that differential correlations are optimal if there is no added noise ., For that we use a thresholding nonlinearity , chosen for two reasons: it is an extreme nonlinearity , and so should be a strong test of our theory , and it is somewhat realistic in that it mimics spike generation ., For this model , the responses at that second layer , yi , are given by, y i = \u0398 ( x i - \u03b8 i ) ( 11 ), where \u0398 is the Heaviside step function ( \u0398 ( x ) = 1 if x \u2265 0 and 0 otherwise ) , and \u03b8i is the spiking threshold of the ith neuron ., This is the popular dichotomized Gaussian model 52\u201356 , which has been shown to provide a good description of population responses in visual cortex , at least in short time windows 54 , and to provide high-fidelity descriptions of the responses of integrate-and-fire neurons , again in short time windows 57 ., In our simulations with the step function nonlinearity , as for all of the other cases we considered above , the first layer responses are given by the tuning curve plus noise model ( Eq ( 1 ) ) ., The tuning curves , f ( s ) , of the 100-neuron population are again heterogeneous ( similar to those in Fig 2A but with a different random draw from the tuning curve distribution ) , and the trial-to-trial variability is given by, \u03a3 \u03be = \u03b3 u \u03a3 0 + \u03f5 u u ( s ) u ( s ) ( 12 ), with \u03a30 given by Eq ( 5 ) ., This is the same covariance matrix as in Eq ( 4b ) , except that we have included an overall scale factor , \u03b3u , chosen to ensure that the information in the input layer is independent of both \u03f5u and u ( s ) ( see Methods , Eq ( 99 ) ) ., Because these ( step function ) nonlinearities are infinitely steep , the tuning curves are not sufficiently dense for our mathematical analysis to guarantee that differential correlations are optimal for information propagation ., However , we argue in Methods ( section titled \u201cNonlinear gain functions\u201d ) , that this should be approximately true for large populations ., And indeed , that\u2019s what we find with our numerical simulation , as shown in Fig 5B ., When \u03b8u = 0 ( recall that \u03b8u is the angle between u ( s ) and f\u2032 ( s ) ) , so that u ( s ) = f\u2032 ( s ) , the second term in Eq ( 12 ) corresponds to differential correlations; in this case , information increases monotonically with \u03f5u ., In other words , information propagated through the step function nonlinearity increases as \u201cupstream\u201d correlations become more like pure differential correlations ., In contrast , when \u03b8u is nonzero ( as in Fig 3A ) , information does not propagate well: information decreases as \u03f5u increases ., This is consistent with our findings for the linear gain function considered in Fig 2 ., Thus , differential correlations can optimize information transmission even for a nonlinearity as extreme as a step function ., The lack of explicit added noise at the second layer makes this case somewhat unrealistic ., In neural circuits , we expect noise to be added at each stage of processing\u2014if nothing else , due to synaptic failures ., We thus considered a model in which noise is added before the spike-generation process ,, y i = \u0398 ( x i + \u03b6 i - \u03b8 i ) ( 13 ), where \u03b6i is zero-mean noise with covariance matrix \u03a3\u03b6 ., We computed information for this model using the same input tuning curves , spike thresholds , and covariance matrix , \u03a3\u03be , as without the additional noise ( i . e . , as in Fig 5 ) ., To mimic the kind of independent noise expected from synaptic failures , we chose the \u03b6i to be iid , and for simplicity we took them to be Gaussian distributed with variance \u03c3 \u03b6 2 ., We computed the amount of stimulus information , Iy ( s ) , for several different levels of the added input noise \u03c3 \u03b6 2 ., We found that for all levels of noise , differential correlations increase information transmission ( Iy ( s ) increases monotonically with \u03f5u in Fig 6A , for which \u03b8u = 0 ) ., And we again found that when the long axis of the covariance ellipse makes a small angle with the signal direction , information propagates poorly ( Fig 6B , for which \u03b8u = 0 . 1 rad . ) ., These numerical findings for a spike-generating nonlinearity with added noise are similar to the previous cases of a linear transfer function , g ( \u22c5 ) , with added input noise ( Figs 2 and 3 ) , for which we have analytical results , or a spike generating nonlinearity with no added input noise ( Fig 5 ) , for which we do not ., We further argue in Methods ( section titled \u201cNonlinear gain functions\u201d ) , that for nonlinear gain functions differential correlations are likely to be optimal if the tuning curves are optimal ( in the case of Eq ( 13 ) , if the thresholds \u03b8i are chosen optimally ) ., Taken together , our findings demonstrate that differential correlations in upstream populations generally increase the information that can be propagated downstream through noisy , nonlinear neural circuits ., Much work in systems neuroscience has investigated the factors that influence the amount of information about a stimulus that is encoded in neural population activity patterns ., Here we addressed a related question that is often overlooked: how do correlations between neurons affect the ability of information to propagate robustly through subsequent stages of neural circuitry ?, The question of robustness is potentially quite important , as the ability of information to propagate determines how much information from the periphery will reach the deeper neural structures that affect decision making and behavior ., To investigate this issue , we considered a model with two cell layers ., We varied the covariance matrix of the noise in the first layer ( while keeping the tuning curves and information in the first layer fixed ) , and asked how much information could propagate to the second layer ., Our main findings were threefold ., First , population codes with different covariance structures but identical tuning curves and equal amounts of encoded information can differ substantially in their robustness to corruption by additional noise ( Figs 2 , 5 , 6 and 7 ) ., Consequently , measurements of information at the sensory periphery are insufficient to understand the ability of those peripheral structures to propagate information to the brain , as that propagation process inevitably adds noise ., For instance , populations of independent neurons can be much worse at transmitting information than can populations displaying correlated variability ( Fig 5B ) ., Thus , to understand how the brain efficiently encodes information , we must concern ourselves not just with the amount of information in a population code , but also with the robustness of that encoded information against corruption by noise ., Second , for linear gain functions , or noise-free nonlinear ones with sufficiently dense tuning curves , populations with so-called differential correlations 22 are maximally robust against noise induced by information propagation ., This fact may seem surprising given that differential correlations are the only ones that lead to information saturation in large populations 22 , and the correlations that minimize information in general ., However , in hindsight it makes sense: differential correlations correspond to a covariance ellipse aligned with the signal direction ( see Fig 3B ) , and added noise simply doesn\u2019t make it much longer ., For nonlinear gain ","headings":"Introduction, Results, Discussion, Methods","abstract":"Sensory neurons give highly variable responses to stimulation , which can limit the amount of stimulus information available to downstream circuits ., Much work has investigated the factors that affect the amount of information encoded in these population responses , leading to insights about the role of covariability among neurons , tuning curve shape , etc ., However , the informativeness of neural responses is not the only relevant feature of population codes; of potentially equal importance is how robustly that information propagates to downstream structures ., For instance , to quantify the retina\u2019s performance , one must consider not only the informativeness of the optic nerve responses , but also the amount of information that survives the spike-generating nonlinearity and noise corruption in the next stage of processing , the lateral geniculate nucleus ., Our study identifies the set of covariance structures for the upstream cells that optimize the ability of information to propagate through noisy , nonlinear circuits ., Within this optimal family are covariances with \u201cdifferential correlations\u201d , which are known to reduce the information encoded in neural population activities ., Thus , covariance structures that maximize information in neural population codes , and those that maximize the ability of this information to propagate , can be very different ., Moreover , redundancy is neither necessary nor sufficient to make population codes robust against corruption by noise: redundant codes can be very fragile , and synergistic codes can\u2014in some cases\u2014optimize robustness against noise .","summary":"Information about the outside world , which originates in sensory neurons , propagates through multiple stages of processing before reaching the neural structures that control behavior ., While much work in neuroscience has investigated the factors that affect the amount of information contained in peripheral sensory areas , very little work has asked how much of that information makes it through subsequent processing stages ., That\u2019s the focus of this paper , and it\u2019s an important issue because information that fails to propagate cannot be used to affect decision-making ., We find a tradeoff between information content and information transmission: neural codes which contain a large amount of information can transmit that information poorly to subsequent processing stages ., Thus , the problem of robust information propagation\u2014which has largely been overlooked in previous research\u2014may be critical for determining how our sensory organs communicate with our brains ., We identify the conditions under which information propagates well\u2014or poorly\u2014through multiple stages of neural processing .","keywords":"medicine and health sciences, statistical noise, ellipses, nervous system, random variables, geometry, neuroscience, covariance, mathematics, statistics (mathematics), algebra, computational neuroscience, neuronal tuning, coding mechanisms, gaussian noise, animal cells, neural pathways, probability theory, cellular neuroscience, neuroanatomy, cell biology, linear algebra, anatomy, neurons, biology and life sciences, cellular types, physical sciences, computational biology, eigenvalues","toc":null}
+{"Unnamed: 0":1632,"id":"journal.pcbi.1005926","year":2018,"title":"A theory of how active behavior stabilises neural activity: Neural gain modulation by closed-loop environmental feedback","sections":"Neural response are strongly sensitive to behavioural state ., The onset of movement such as running and whisking is coincident with prominent modulations in neural activity in sensory areas 1\u20133 ., The rodent whisker system has become a key model system within which to investigate these changes 4\u20136 ., The onset of active whisking in a previously quiet but attentive rodent is correlated with a marked reduction in endogenous synchronous neural activity of neurons in sensory areas; quantified as a reduction in low frequency fluctuations and a decrease in correlations between the membrane potentials of neurons in the barrel cortex 4 ., Furthermore , membrane potential responses to experimentally induced perturbations of the whisker are also reduced by the presence of whisking 6 ., These changes suggest that movement reduces neural gain 7 , 8 in the barrel cortex suppressing neural fluctuations and sensory response ., Several internal pathways have been implicated in this gain regulation including various neuromodulatory pathways 9 , 10 , intracortical feedback modulation by motor areas 11 or they could be directly triggered by changes in sensory input 12 , 13 via thalamo-cortical projections 14 ., Despite this gain reduction , robust responses to sensory input occur during active contact events when the whisker collides with an object placed in the whisk field 5 , 6 ., Thus , a whisking-induced gain reduction cannot by itself account for the difference in sensory responses to whisker perturbations and active contact events without appeal to additional mechanisms 15 ., The reafference principle ( RP ) 16 also does not straightforwardly explain these differences ., The RP explains the amplitude of sensory response by a mismatch between the actual sensory input and its prediction , where the prediction is based on an efference copy ( an internal copy of motor command ) ., But the RP does not explain why sensory responses to whisker perturbations , which are always unpredicted , are suppressed during movement ., Active behaviours are defined by closed-loop feedback interactions between brain\/body\/environment which are central to motor control and , it has been argued , pivotal to account of perceptual processes 17\u201319 ., During active whisking reafferent sensory input ( sensory input resulting from ones own actions ) conveys information about proprioceptive sensory feedback of whisking and which informs the subsequent motor control of the vibrissae 20 , 21 ., Repeated cycles of reafferent sensory input followed by motor output constitute a closed-loop feedback interaction between cells in the barrel cortex and the vibrissae 22 ., In this work , we show that in this system closed-loop feedback mediated by whisking vibrissae can:, 1 . Suppress synchronous endogenous neural fluctuations and passive sensory responses ,, 2 . Account for large response to active touch events because of a transient interruption of this feedback ., The results provide a nuanced view of predictive coding where neurons represent predictions errors about consequences of motor actions rather than the difference between the predicted and actual sensory input ., More generally these results strongly support the centrality of closed-loop interaction in perceptual apparatus 17 by suggesting a specific role they play in event detection ., To support a key prediction of this theory we examine how closed-loop interactions in a motor control behaviour impact on neuronal fluctuations ., Specifically , we re-analysed data from a second system , a larval zebrafish behaving in a virtual reality where fictive water flow is simulated by a grating ( striped image ) drifting across the fish retina 23 ., In this set up zebrafish larvae are immobilised with a neuromuscular blocker ., The fishs attempted movements relative to the grating are monitored through motor neuron activity and translated into appropriate modulation of the velocity of the grating 23 ., With data from this setup we show that the presence of closed-loop interactions between neurons and fictive swim speed causes the suppression of synchronous neural fluctuations across the fish brain in a manner analogous with the rodent whisker system ., Further we show that the amount of this suppression for each neuron is correlated with the strength of its involvement in the optomotor signaling ., Together , these results suggest that understanding changes in neural activity across the brain caused by the onset of movement requires the study of closed-loop brain\/body\/environment interactions beyond open-loop sensory paradigms ., Thus we strongly support the argument that a full understanding of phenomenology of neural circuits during active behaviors requires moving away from the idealisation of the brain as an input\/output information processor toward its role as a dynamic control system regulating behaviour 19 ., In moving animals , the brain receives sensory input that originates in the external environment , or exafferent sensory input ( Fig 1A , blue arc ) ., In addition , efferent motor commands ( Fig 1A , green arc ) drive the body and environment and induce reafferent ( self-generated ) sensory input ( Fig 1A , red arc ) 16 , 24 ., To develop an intuition of how closed-loop feedback , mediated by reafferent input , could impact on neural activity we introduce two model conditions ., First , we assume that when an animal is not moving the brain receives only exafferent input , we describe this as an open-loop condition ( Fig 1B , top ) ., Second , when the animal begins to move the brain interacts with the environment coupling motor action and reafferent sensory input , we refer to this as a closed-loop condition ( Fig 1C top ) ., Note: it is likely that some reafferent input is always present but our focus here is on the effect that the onset of a previously absent reafferent sensory pathway could have on neural activity ., We examine these two conditions in a simple idealized model , see 17 for a similar idealisation , where brain variable B ( which describes collective neural activity , e . g . , membrane potential activity ) receive input from , or interacts with , the body and environment ., In the open-loop condition the collective neural activity , Bo ( t ) , is assumed to be described in term of a first-order linear differential equation ,, dBo ( t ) dt=\u2212Bo ( t ) \u03c4+I ( t ) +\u03beo ( t ) ,, ( 1 ), where \u03beo is white noise of instantaneous variance \u03c32 generated inside the brain , t is time , \u03c4 is the time constant of the system and I ( t ) is exafferent input ., Essentially , in the absence of input , we represent collective neural activity as a simple leaky integrator system with leak timescale \u03c4 driven by endogenous noise ( see Fig 1B , bottom , for traces ) ., Of interest here is the magnitude of fluctuations which can be calculated as the autocorrelation peak ( instantaneous variance ) of variable Bo which is Peako = \u03c32 \u03c4\/2 , and the gain of the response to sensory input ( calculated as the ratio between a static input and an equilibrium response ) , which is simply Gaino = \u03c4 ., Thus in this simple system both the gain and the fluctuations are determined by the timescale of the endogenous dynamics ., However , during the closed-loop condition we write the dynamics of the brain variable ,, dBc ( t ) dt=\u2212Bc ( t ) \u03c4+wBc ( t ) +I ( t ) +\u03bec ( t ) ,, ( 2 ), where we have idealised reafferent input as a simple self-feedback signal with strength w , i . e . , we have assumed this feedback is linear and instantaneous ( we will relax this assumption later ) ., In this condition , the continuous cycles of reafferent input constitute a closed-loop feedback signal to the brain ., The presence of this feedback changes the effective time constant to \u03c4eff = \u03c4\/ ( 1\u2212w\u03c4 ) ., The magnitude of the fluctuations is now characterized by autocorrelation peak Peakc = Peako\/ ( 1\u2212w\u03c4 ) and the effective gain of the system is Gainc = Gaino\/ ( 1\u2212w\u03c4 ) ., In particular , if this feedback is negative ( w < 0 ) , it will suppress both fluctuations and the gain of sensory responses , see Fig 1B and 1C ( bottom panels ) ., This very simple model suggests that , in principle , closed-loop feedback mediated by the body\/environment could have a direct impact on neural activity ., One way to accentuate sensory responses is described in Fig 1D ., Here the brain initially has low closed-loop gain ( Gainc = \u03c4\/ ( 1\u2212w\u03c4 ) ) and thus exhibits suppressed fluctuations ., However , if during a sensory event ( Fig 1D , grey bar ) closed-loop feedback is interrupted , e . g . , if whisking is interrupted by contact with an object ( see below ) , then brain will have temporarily high open-loop gain ( Gaino = \u03c4 ) ., Thus the combination of a large sensory response and suppressed background fluctuations prior to sensory event can accentuate signal-to-noise ratios ., In the following , we explain how these three conditions can be realized in the rodent whisker system ., In this study we proposed the idea that negative closed-loop sensory feedback during active behavior reduces network gain , which in turn , suppresses synchronous neural fluctuations and modulates sensory responses ., We supported this with modelling and data analysis in the whisker system and in a behaving zebrafish , see summary Fig 7 ., The formal component of our theory , i . e . , that closed-loop sensory feedback can modulate a systems gain , is well documented in dynamical systems theory and control theory 32 , 33 ., This gain control occurs even though the pathways mediating feedback are purely additive ( c . f . Eqs 1 and 2; i . e . , effectively repeated cycles of feedback accumulate over time and produce a multiplicative effect ) ., Thus , a constitutively active closed-loop feedback that mediates action-perception cycles is essential for the form of gain control we propose ., This means that discrete and intermittent involvement of reafferent input does not imply gain modulation ., For example , the classical reafference principle explains neural responses by a one-time detection of the mismatch between an efference copy ( predicted ) and reafferent ( actual ) input 16 ., However , this situation is likely an inaccurate idealization to describe the closed-loop systems studied here ., For example , in the zebrafish system , swim bouts typically occur every 700 ms and this interval closely overlapped with the peak of the estimated sensory feedback interaction ( Fig 6B ) ., Hence , the neural responses in the fish experiment suggest a more dynamic system , where neural activity evoked by many cycles of action and sensation are continuously and mutually interacting ., The idea that closed-loop feedback is central to cognition is not new and has early precedents in behavioral psychology 19 , resonate with a movement in embodied cognitive science 18 , 34 , 35 and has recently been proposed as concrete alternative to input\/output conception of perceptual processing 17 , 36 ., Our work shares the view of these proposals and provides a specific example where brain function is contingent on closed-loop interactions between brain\/body\/environment ., Furthermore , we provided a mathematical model showing why neural dynamics underlying cognitive states cannot be recapitulated even if the sensory input during active behavior is identically repeated , i . e . , a replay condition 37 ., The presence of continuous negative closed-loop sensory feedback during active behavior is fundamental for our theory ., In our rodent study we assumed negative closed-loop sensory feedback was mediated directly by a cortical-whisker circuit ., However , our theory is agnostic to the detail of the neural implementation and several other schemes are possible ( see S2 Appendix ) ., This assumption is consistent with the idea that the barrel cortex comprises a nested set of servo control loops that regulate various aspects of whisker dynamics 22 ., At the level of the whole vibrissa system multiple parallel and nested feedback loops both positive and negative most likely exist 22 ., In zebrafish , the presence of negative feedback during swimming behavior is a priori necessary for optic-flow stabilization behavior because the fish must act in opposition to perceived optic flow in order to minimize horizontal displacement 38 , 39 ., Interestingly , neurons that received strong negative feedback and were substantially stabilized were located in the cerebellum ( Fig 6D ) ., This is consistent with the theoretical viewpoint that the cerebellum is strongly involved in the action-perception cycle 40\u201342 ., We suggest that closed-loop sensory feedback plays a major role in brain state control ., However , importantly , we do not propose this mechanism is mutually exclusive with other mechanisms , such as thalamo-cortical input 25 or neuromodulation 10 , 43 , 44 because brain state transitions also occur in the absence of sensory feedback e . g . , the onset of running that does not change the visual input 3 , 45 , during sleep 46 , 47 , or by dissection of the sensory nerve 5 , 25 ., Mechanisms underlying brain state transitions are likely to be redundant and occur even in the absence of mechanisms , such as thalamo-cortical input 25 or corollary discharge 26 , albeit involving further delay ( see S1 ) ., Such functional redundancy may help to maintain the stability of brain state 44 , 48 , 49 ., Furthermore , the relative importance of internal and external mechanisms might adaptively change in an experience-dependent manner 50 ., In the whisking model , we proposed that the regulation of cortical gain by closed-loop sensory feedback could explain enhanced active touch ., Specifically , negative sensory feedback during whisking reproduces suppressed fluctuations and reduces responses to passive whisker stimulation ( see Figs 2 and 3 ) ., Moreover , robust neural response to active touch events could be explained by the interruption of this feedback when the whisker is driven into an external object ., These interruptions transiently release the cortex from a low gain state and enhancing sensory responses to salient sensory stimuli ., This mechanism for active touch contrasts with the account of sensory processing suggested by the reafference principle 16 , which postulates that motor efference is discounted from sensory input , allowing animals to sense exafferent signals ( externally caused sensory input ) without being confounded by the consequences of their own motor actions ., In contrast , our theory suggests that the sensory system is insensitive to pure exafference during active sensing 4; see Fig 3 , but sensitive to the interruption of reafference which may allow animals to focus attention on the consequences of their own motor actions ., This idea is supportive of other work that has cast doubt on the role of efference copy during active sensing 51 ., This mechanism is also distinct from the most common form of predictive coding 52 , where neural activity represents the error between the actual and the brain\u2019s prediction of sensory input ., Instead our suggestion could be viewed as a more specific form of predictive coding where neurons represent predictions errors about consequences of motor actions , in this sense it is closer to the idea of active inference 53 , 54 ., While it is straightforward to generalize this sensory mechanism to other tactile systems , its implication for other modalities is less clear ., However , in theory , closed-loop sensory feedback could be interrupted anywhere along the action-perception cycle , thus dynamically regulating neural gain ., The timely interruption of this feedback , possibly related to transient freezing of behavior , could serve as a general mechanism for temporarily accentuating neural responses against a background of reduced noise ., For example , closed-loop sensory feedback could be gated by the frequency of miniature eye movements 55 a hypothesis that complements a previous proposal suggesting such movements are under active closed-loop control 56 ., Furthermore , cerebellum neurons , which are strongly involved in the sensory-motor cycle , could be suppressed in anticipation of salient sensory events by a relevant brain area , such as the reticular formation 31 , 57 ., The importance of using naturalistic sensory stimuli to study and manipulate brain state dynamics is widely demonstrated 58 ., However , an important prediction of our theory ( Fig 4 ) , supported by our experimental findings is that brain dynamics during active sensing cannot be fully recapitulated or re-encoded , even if the same sensory input is precisely recorded and replayed back into a passive brain ., These results provide evidence that brain state during active behaviors can only be accurately understood by a quantitative account of ongoing brain-environment interactions 18 ., To investigate the \u2018in principle\u2019 feedback between barrel cortex and whiskers we model a simple cortical circuit that interacts with a single whisker , see Fig 2A ., Our cortical circuit comprises of N excitatory and N inhibitory neurons ( i = 1\u2026N are excitatory and i = N+1 , \u2026 , 2N are inhibitory , N = 100 ) modeled as a linear dynamical system by ,, x . i=\u2212xi+\u2211j=12Nwijxj\u2212ai\u2212wx\u03b8\u03b8p+\u03bei+I ,, which is numerically simulated by a Euler forward integration method with time-bin dt = 0 . 5 ms . Hereafter , all time derivatives are taken to represent single-step differences divided by dt ( e . g . x ., ( t ) =x ( t+dt ) \u2212x ( t ) \/dt ) , but we omit the ms time unit ., wij is the synaptic strength from neuron j to i , ai is an adaptation current described below , \u03b8p is the whisker protraction angle interacting with neurons with weight wx\u03b8 = 0 . 002 , I is exafferent input that takes I = 0 . 035 upon whisker stimulation and otherwise zero , and \u03bei is independent white noise of unit variance added to each neuron ., We interpret xi as both the firing rate and membrane potential , assuming a roughly linear relationship between the two ., Entries in the connectivity matrix are assigned as wij = bijJ + b\u2032ijg for excitatory synapses ( j = 1\u2026 , N ) and wij = \u2212b\u2033ijg for inhibitory synapses ( j = N + 1 , \u2026 , 2N ) , where bij , b\u2032ij , b\u2033ij are all random binary values that take b0 > 0 with probability p = 0 . 1 and 0 with probability 1 \u2212 p , respectively ., The weights are scaled by J=1pN and g=g0\u221a2Np ( 1\u2212p ) , so that dynamics are insensitive to the parameter values of p and N . Note that the eigenvalue spectrum of the connectivity matrix wij is centered around b0 and spread with the radius b0g0 in the limit of large N . Hence , the network is excitation dominated ., The variability of weight values across neurons is controlled by the magnitude b0g0 of the excitatory-inhibitory-balanced component and this variability is controlled by the parameter g0 = 0 . 05 , which reproduces highly synchronized up\/down-like fluctuations during the quiet state ., To promote significant network fluctuations observed in the barrel cortex we scale of the connectivity matrix b0 such that the lead eigenvalue of this matrix is close to unity ( \u2248 0 . 975 and the dynamics are close to instability ., We include an adaptation current that gives these fluctuations a low frequency ( ca . 1 Hz ) component modelling up\/down-like oscillations 59\u201361 in the absence of neuron\/whisker interactions ., The adaptation current is integrated as, ai\u02d9=\u22120 . 07ai+0 . 008xi, Over time , the adaptation variable slowly builds upon neural activity and suppresses neurons , resulting in the ca ., 1-Hz oscillation ., Consequently , in the absence of interactions with the whisker , implemented by setting wx\u03b8 = 0 , this simple network reproduces the power spectrum and cross-correlogram of neurons in the barrel cortex 5 , 6 , see Fig 2B and 2C ., We model a simple flexible vibrissa as two hinged sections ( with bending angle \u03b8h ) connected at the base ( with protraction angle \u03b8p to the body ) of unit length which are constrained by simple torsion springs with spring constant k1 and k2 respectively , see Fig 2A ., We assume the whisker is light and frictionless and simulated it by numerically minimising the energy of the system ,, E=k1 ( \u03b8p\u2212\u03b8eq ) 2+k22\u03b8h2 ,, where \u03b8eq equilibrium value of the base spring ., Here , only the ratio k1\/k2 is important for the results and , without losing generality , we set k1 = 1 ., The central hinge spring has an equilibrium value of zero angular displacement and thus tends to align both sections ., Whisking is driven both by the cortex and a central a pattern generator ( CPG ) 62 ., Specifically , the equilibrium value of the base spring , \u03b8eq is set as ,, \u03b8eq\u02d9=\u22120 . 93\u03b8eq+w\u03b8xN\u2211i=1Nxi+u ,, where the second term on the right-hand side is the sum of activity in the cortical excitatory population and the third term is the external CPG activity ., Here u is modeled as simple stochastic oscillator , given by, u\u02d9=\u2212 . 98u+2\u03c0Fwhiskv+\u03beu, v\u02d9=\u2212 . 98v\u22122\u03c0Fwhisku+\u03bev ,, where Fwhisk = 10Hz is the frequency of the oscillator and \u03beu , \u03bev are independent Gaussian white noise ., w\u03b8x = 0 . 085 describes the relative strength of the cortex versus the CPG in driving the whisker variable ., With this parameter , the whisker is mainly driven by the CPG and is only modulated by cortical activity ., In this model , most excitatory neurons respond to whisker retraction and drive whisker protraction ., Adding a separate counterpart population that responds to whisker protraction and drives whisker retraction in a similar manner does not change the model\u2019s behavior ., We simulate a passive deflection of the whisker by a brief injection of input of I = 0 . 035 to the cortical neurons for c . a 25 ms . The magnitude of this input approximately matches the evoked change over the standard deviation of the membrane potential ( \u0394Vm\/\u03c3Vm ) in response to magnetic whisker deflection during the whisking condition 5 ., Contact events are simulated by simulating a horizontal solid wall is placed above the whisker ( 1 unit length away ) ., To simulate contact with the wall we solve the energy equation subject to the length constraint in the vertical direction ,, sin ( \u03b8p ) +sin ( \u03b8p\u2212\u03b8h ) <1 ., Thus , as the whisker collides with the wall it deforms accordingly , see Fig 2A ., By adjusting the relative stiffness of each torsion spring ( i . e . k2\/k1 ) , we can control the degree to which the protraction angle is affected by contact events , e . g . , if the whisker is very flexible , the protraction angle will change continuously , despite contact of the tip ., During contact we also inject an input ( I = 0 . 035 ) to the cortical neurons for the duration of the contact event , but for no longer than 25 ms to simulate contact-detection signal that results from the stereotypical response of pressure sensitive cells in the trigeminal ganglion 27 ., The model was run for 200 s in the closed loop , open-loop , and sustained period of active touch to calculate all quantitative measures ., To quantify the discriminability of whisker contact events we calculated an information theoretic measure of generalized signal-to-noise-ratio ., Specifically , we calculated the Chernoff distance 63\u201365 between probability distributions , p1 ( x ) and p0 ( x ) , in the presence or absence of a sensory event , respectively ., Specifically , this measure, \u03a8 ( p1\u2225p0 ) \u2261\u2212min0<\u03bb<1log\u222bp1\u03bb ( x ) p01\u2212\u03bb ( x ) dx, summarises the detectability of whisker stimulation based on population responses and , unlike a naive calculation of signal-to-noise ratio , is applicable even when p1 ( x ) and p0 ( x ) are very different distributions ., For our model , the probability distribution for each condition is well described by a Gaussian distribution ,, p0\/1 ( x ) =|2\u03c0C0\/1|\u22121\/2exp ( \u221212 ( x\u2212\u03bc0\/1 ) C0\/1\u22121 ( x\u2212\u03bc0\/1 ) ) ,, where C0\/1 and \u03bc0\/1 are covariance matrix and vector of means , respectively , in the presence ( with subscript 1 ) or absence ( with subscript 0 ) of a sensory event ., By substituting this into the expression for Chernoff distance and employing the Gaussian integral identity and expressing the Chernoff distance in terms of C0 , C1 , and \u03bc0 , \u03bc1 , we calculate the covariance and mean between a small number of neurons ( here three ) , randomly selected from the cortical network described above ., We calculate covariance\u2019s across ensembles of 500 networks every 10 ms for a period of 1 s , starting at the onset of the sensory event ., Minimization with respect to \u03bb is computed numerically ., In a transgenic fish expressing the calcium indicator GCaMP2 brain-wide calcium activity was monitored using a two-photon microscope to scan single planes in the brain ., We analyzed the calcium signal ( \u0394F\/F ) at various sample frequencies ( ca . 2\u22123 Hz ) across 1908 cells in 32 fish , see 23 and electrical recordings of swim power ., We analyzed data taken from a 6-min recording of 1\u22126 prominent calcium sources per fish , putative neurons , across 600 trials ., In the first 3 min , the fish performed the closed-loop optomotor behavior ., For the subsequent 3 min , each fish was presented with the stimulus received in the closed-loop stimulus which is a repeat of what the animal experienced in the previous 3 min , the replay condition ., In the original study , the gain ( i . e . , the multiplicative factor between fictive swim power , and the speed of visual feedback ) was alternated between a high and low gain condition every 30 s ., This gain alternating protocol is not relevant to the current study ., To reduce this variability in data , we subtracted the mean activity level in each gain setting in our analysis ( from both brain and behavior variables ) ., Notably , our main results were qualitatively the same , even without such subtraction of the means ., We distinguish variables in the closed loop condition ( Bc and Ec ) and replay condition ( Br and Er ) , see Fig 5B ., Specifically , we assume that the closed-loop dynamics in the frequency domain are described by the following equations ,, Bc ( \u03c9 ) =F ( \u03c9 ) Ec ( \u03c9 ) +RBc ( \u03c9 ), ( 4 ), Ec ( \u03c9 ) =G ( \u03c9 ) Bc ( \u03c9 ), where F ( \u03c9 ) is an afferent filter describing the interaction from the environment to the brain ( i . e . , the Ec \u2192 Bc filter , see Fig 5B dashed blue arrow ) and G ( \u03c9 ) is an efferent filter from the brain to the environment ( i . e . , the Bc \u2192 Ec filter , see Fig 5B dashed green arrow ) , respectively , and RBc ( \u03c9 ) is the residual inputs not accounted of by the filters ., Note: we have assumed that the noise on the environment is negligible , this is a reasonable assumption given that visual flow is directly modulated by motor nerve activity ., Similarly , we also write the replay dynamics in the frequency domain as ,, Br ( \u03c9 ) =F ( \u03c9 ) Ec ( \u03c9 ) +RBr ( \u03c9 ), ( 5 ), Er ( \u03c9 ) =G ( \u03c9 ) Br ( \u03c9 ) ., In the replay condition , neurons are driven by the recorded visual stimulus in the closed-loop condition , which is determined by fish\u2019s motor activity in the closed-loop condition Ec ., Note: we have made the assumption that F ( \u03c9 ) and G ( \u03c9 ) are the same filter in the both conditions ( i . e . , the interactions with the same color in Fig 6A have the same property ) because the sensory and motor circuits in the brain remain the same between the conditions ., We use Eq 5 in the replay condition to fit the linear filters F ( \u03c9 ) and G ( \u03c9 ) because the computation would be more involved in the closed-loop condition than the replay condition ., We first calculate linear filter F ( Fig 6A , solid blue arrow ) that minimizes the mean square error between the observed variable Br and the convolution F * Ec over time ., Next , we determine G ( t ) by first calculating the residual variability of neural activity in the replay condition that cannot be accounted for by the closed-loop environment , i . e . , RBr ( \u03c9 ) =Br ( \u03c9 ) \u2212F ( \u03c9 ) Ec ( \u03c9 ) and subsequently calculating how RBr drives the environment in the replay condition Er , effectively determining the Br \u2192 Er interaction ( Fig 6A , solid green arrow ) ., The filters were constrained as a superposition of Laguere functions ., We use Laguere functions up to the order that best satisfied the Akaike Information Criterion 66 ., Almost all filters had an order that was mid-range between 1 and 15 ., The Ec \u2192 Br \u2192 Er interaction ( Fig 6A solid orange arrow ) is then straightforwardly computed by the convolution of both filters , H ( \u03c9 ) = F ( \u03c9 ) G ( \u03c9 ) ., Based on the assumption that the filters are the same in the two conditions , we assume that self-feedback in the closed-loop condition ( Fig 6A , dashed orange arrow ) is the same as H ( \u03c9 ) ., In our investigation , we calculated the ratio of the low frequency power of neural fluctuations between the closed-loop and replay conditions ., We then compare this empirical ratio with the theoretically expected ratio based on the estimated filters ., To derive this theoretically expected ratio , we write the dynamics of neural activity in the closed- and replay conditions in the frequency domain as ,, Closed\u2011loop:Bc ( \u03c9 ) =H ( \u03c9 ) Bc ( \u03c9 ) +RBc ( \u03c9 ) = ( 1\u2212H ( \u03c9 ) ) \u22121RBc ( \u03c9 ) Replay:Br ( \u03c9 ) =H ( \u03c9 ) Bc ( \u03c9 ) +RBr ( \u03c9 ) ,, where H ( \u03c9 ) = F ( \u03c9 ) G ( \u03c9 ) is the estimated combined filter in the frequency domain and we assume the noise in the closed- and replay conditions have the same power spectrum , i . e . , RBc ( \u03c9 ) 2=RBr ( \u03c9 ) 2 ., The ratio of the power between each condition is then ,, Bc ( \u03c9 ) 2Br ( \u03c9 ) 2=1H ( \u03c9 ) 2+1\u2212H ( \u03c9 ) 2 ., We also investigated the effect of accumulative cycles of feedback on brain dynamics by comparing the full closed-loop effect with a control effect that includes only one-time feedback ., Namely , we can expand the contribution of each cycle in a geometric series as, Bc ( \u03c9 ) = ( 1\u2212H ( \u03c9 ) ) \u22121RBc ( \u03c9 ) = ( 1+H ( \u03c9 ) +H2 ( \u03c9 ) +H3 ( \u03c9 ) \u22ef ) RBc ( \u03c9 ), where the O ( Hn ) term in the above Taylor expansion describes the effect from signal propagation along the feedback loop for n times ., By neglecting the contributions with n>1 , we can write the effect of a single cycle of feedback effect as ,, B1 ( \u03c9 ) = ( 1+H ( \u03c9 ) ) RBc ( \u03c9 ) ., This yields an alternative expression for the ratio of the power between each condition that only includes one-time effect of feedback as ,, B1 ( \u03c9 ) 2Br ( \u03c9 ) 2=1H ( \u03c9 ) 2+1+H ( \u03c9 ) \u22122 ., To further investigate how the effective interaction between the brain and the environment depends on the closed-loop feedback , we compare Ec \u2192 Br filter in the replay condition and the Ec \u2192 Bc filter in the closed-loop condition naively computed by neglecting closed-loop effects ., Notably , the na\u00efve Ec \u2192 Bc filter in the closed-loop condition generally has an acausal component , because the brain Bc and the environment Ec are mutually interacting ( see below ) ., Thus to calculate these filters we use Hermite rather than the Laguere functions to capture the acausal ( t<0 ) side of the filter ., To quantify the difference between these filters , using Eq 4 , we write, Ec ( \u03c9 ) = ( 1\u2212H ( \u03c9 ) ) \u22121 ( G ( \u03c9 ) RBc ( \u03c9 ) ) ,, and thus the na\u00efve Ec \u2192 Bc filter in the closed-loop condition is, Bc ( \u03c9 ) Ec* ( \u03c9 ) Ec ( \u03c9 ) Ec* ( \u03c9 ) =F ( \u03c9 ) + ( Ec ( \u03c9 ) RBc* ( \u03c9 ) Ec ( \u03c9 ) Ec* ( \u03c9 ) ) *=F ( \u03c9 ) + ( G ( \u03c9 ) 1\u2212H ( \u03c9 ) ) *|RBc ( \u03c9 ) |2|Ec ( \u03c9 ) |2, where * describes complex conjugate ., Hence , this filter is different from the corresponding filter F ( \u03c9 ) in the replay condition by the second term ., To predict the second term without knowing RBc , we again assume |RBc ( \u03c9 ) |2\u2248|RBr ( \u03c9 ) |2 , where the latter spectrum is based on the residual RBr computed in the replay condition .","headings":"Introduction, Results, Discussion, Material and methods","abstract":"During active behaviours like running , swimming , whisking or sniffing , motor actions shape sensory input and sensory percepts guide future motor commands ., Ongoing cycles of sensory and motor processing constitute a closed-loop feedback system which is central to motor control and , it has been argued , for perceptual processes ., This closed-loop feedback is mediated by brainwide neural circuits but how the presence of feedback signals impacts on the dynamics and function of neurons is not well understood ., Here we present a simple theory suggesting that closed-loop feedback between the brain\/body\/environment can modulate neural gain and , consequently , change endogenous neural fluctuations and responses to sensory input ., We support this theory with modeling and data analysis in two vertebrate systems ., First , in a model of rodent whisking we show that negative feedback mediated by whisking vibrissa can suppress coherent neural fluctuations and neural responses to sensory input in the barrel cortex ., We argue this suppression provides an appealing account of a brain state transition ( a marked change in global brain activity ) coincident with the onset of whisking in rodents ., Moreover , this mechanism suggests a novel signal detection mechanism that selectively accentuates active , rather than passive , whisker touch signals ., This mechanism is consistent with a predictive coding strategy that is sensitive to the consequences of motor actions rather than the difference between the predicted and actual sensory input ., We further support the theory by re-analysing previously published two-photon data recorded in zebrafish larvae performing closed-loop optomotor behaviour in a virtual swim simulator ., We show , as predicted by this theory , that the degree to which each cell contributes in linking sensory and motor signals well explains how much its neural fluctuations are suppressed by closed-loop optomotor behaviour ., More generally we argue that our results demonstrate the dependence of neural fluctuations , across the brain , on closed-loop brain\/body\/environment interactions strongly supporting the idea that brain function cannot be fully understood through open-loop approaches alone .","summary":"Animals actively exploring or interacting with their surroundings must process a cyclical flow of information from the environment through sensory receptors , the central nervous system , the musculoskeletal system and back to the environment ., This closed-loop sensorimotor system is essential for an animals ability to adapt and survive in complex environments ., Importantly , closed loop feedback signals also regulate brainwide neural circuits for behavior ., Specifically , the activity of coherent populations of neurons inform motor behaviours and in turn are influenced by sensory feedback signals mediated by the environment ., We develop a theory that suggests that this feedback can explain the marked changes in large-scale neural dynamics and sensory processing ( together referred to as brain state ) that coincide with the onset of active behaviours ., This feedback may contribute to flexible context dependent neural computations in brain systems .","keywords":"control theory, medicine and health sciences, fish, swimming, engineering and technology, membrane potential, vertebrates, electrophysiology, social sciences, neuroscience, animals, biological locomotion, motor neurons, control engineering, animal anatomy, systems science, mathematics, zoology, computer and information sciences, animal cells, touch, animal physiology, cellular neuroscience, psychology, eukaryota, cell biology, vibrissae, physiology, neurons, biology and life sciences, cellular types, physical sciences, sensory perception, organisms","toc":null}
+{"Unnamed: 0":2008,"id":"journal.pcbi.1002912","year":2013,"title":"The Timing and Targeting of Treatment in Influenza Pandemics Influences the Emergence of Resistance in Structured Populations","sections":"The use of chemotherapy in the treatment of pathogenic disease places selective pressures on the pathogen to develop resistance to the treatment 1 ., Since failure of chemotherapeutic agents in the treatment of influenza can cause large morbidity and mortality , much work has been done to understand the biology of \u2013 and assess the public policy regarding \u2013 resistance 2\u20135 , this is especially important in the light of recent studies on the evolution of transmissibility of highly pathogenic avian influenza ( H5N1 ) 6\u20139 ., The most widely used antiviral agents , neuraminidase inhibitors ( NIs ) oseltamivir and zanamivir have demonstrated beneficial effects on pandemic and seasonal influenza strains , and thus play key roles in the planning of mitigation of epidemics 3 , 5 , 10\u201313 ., Though fundamentally important to the transmission dynamics of infectious disease , the bulk of current studies examining the effects of treatment on resistance to therapies have ignored contact structure 14 and timing of treatment 15 , 16 ., Given the surprising and largely unpredictable evolutionary trajectories exhibited by influenza 6 , the role of structure in populations may have significant effects on these trajectories ., Here we employ network models of influenza transmission extending previous work 2 to incorporate the effects of contact structure and timing of antiviral treatment ., Network models are a robust framework for studying the transmission dynamics of infectious diseases in structured populations 17 , 18 ., Read & Keeling ( 2003 ) 14 examined the evolution of a pathogen on networks with varying contact structures , without the effects of treatment ., They find differential levels of virulence depending on the clustering of the contact network ., Previous studies have examined the role of treatments on networks of disease transmission ., Pastor-Satorras ( 2002 ) 19 suggested targeting vaccination by node degree ., While extremely effective in theory , identifying high degree individuals a priori is practically impossible ., Cohen et al . ( 2003 ) 20 extended this idea to vaccinate an individual and one of the individuals contacts at random ., Thus by design , the probability of identifying high degree individuals is greatly increased ., This method has been shown empirically to be more effective at detecting influenza transmission early than by using a randomly selected group 21 ., In addition to the problem of identifying individuals for efficient treatment , the timing of treatment plays directly into the evolution of resistance ., Wu et al . ( 2009 ) 15 found that in a pandemic scenario with limited supplies of antivirals , it was beneficial to use a small amount of a secondary drug early in the epidemic to \u2018hedge\u2019 against the evolution of resistance ., Hansen and Day ( 2011 ) 16 use optimal control theory to explore the effects of changing treatment over the course of an epidemic ., They find that in a well-mixed , homogenous population it is optimal to fully treat a population as long as the timing is correct as they derive ., While much important work has been done , the bulk of studies to this point have either ignored stochasticity 22 , 23 or contact structure 14 , 24 or both 25 , the effects of which have been previously shown to be significant 26 ., The goal of the present work is to combine network simulation models of evolution of pathogen resistance under chemotherapy and explore the effects of treatment timing and treatment regimes ( targeted versus non-targeted ) on the development and persistence of resistance ., We focus on influenza and as we model resistance explicitly , we wish to answer three questions: one , to minimize resistance , should treatment be initiated at all in epidemics ?, two , if treatment is initiated , how does its timing affect the emergence and persistence of resistance in structured populations ?, and three , which treatment regime , targeted by degree or not , leads to the least amount of resistance ?, The approach taken here is novel in that our model combines stochasticity and population structure in assessing the role of treatment , and find results contrary to previous studies ., We extend an ordinary differential equation ( ODE ) model of treatment and resistance to influenza antivirals developed by Lipsitch et al . ( 2007 ) 2 ., Whereas they considered both prophylactic and therapeutic treatment in well-mixed , homogenous populations , we consider only reactive treatment in structured populations ., We limit our exploration to treatment because current guidelines suggest limiting prophylactic use of antivirals to individuals at high risk 5 ., Our model features five possible states for individuals: susceptible ( ) , infectious and untreated ( ) , infectious and effectively treated ( ) , infectious with a resistant strain ( ) , or recovered ( ) ., The dynamics then obey the following rules: susceptibles become infected at rates , , and from untreated , treated and resistant individuals , respectively; wild-type infection ( from or individuals ) is treated with probability ; those treated develop de novo resistance with probability ; resistant infections ( transmitted by ) transmit only this strain ( i . e . , no reverse mutation ) ; and infectious individuals recover at rates , respectively ., We assume treatment reduces transmissibility but does not affect the rate of recovery ., Disease propagation has been the subject of massive modeling efforts in recent network theory spanning multiple approaches and disease models 17 , 27\u201329 ., While the standard ODE treatment of epidemics is essentially a coarse-grained mean-field model of disease propagation in a population with homogeneous mixing , it has two main shortcomings in relation to realistic models of disease transmission: It neglects individual heterogeneity ( i . e . , the variance of the node degree distribution ) 27 as well as state correlations between neighboring nodes ( i . e . , an infectious node is more likely to be connected to other infectious nodes ) 30 , 31 ., To include individual heterogeneity we employ a network model of disease transmission ., Here , in contrast to the standard 5-states modeled in the ODE system , one typically needs to introduce a higher-order compartmentalization where nodes are distinguished not only by their state , but also by their degree ., Hence , instead of one equation for the fraction of susceptible individuals at time , an infinite number of equations describes the fraction of susceptible nodes of degree , , at time ., Correlations between nodes are then taken into account by coupling this system of equations to another system describing the evolution of the density of links stemming from susceptible nodes ., To accurately reproduce features of real networks , we consider networks with heavy-tail degree distributions 32 , 33 ., Specifically , we use a binomial distribution leading into a power-law tail with exponential cut-off to avoid unrealistically high degree and infinite average excess degree ( see Text S1 ) ., Such a heterogeneous distribution is more realistic in modeling influenza pandemics where there exists large variation in numbers of individual contacts across a population 34 ., This is opposed to modeling outbreaks within small communities or schools , where there are natural lower and upper bounds to the numbers of possible contacts , not representing the variation seen across an entire population ., Even so , in modeling transmission within small communities , it is still debated whether contact structure should feature heavy-tailed degree distributions 35\u201337 or not 38; and , while several studies have indicated that networks with low coefficients of variation may be better for modeling influenza 38 , others have not 34 , 36 ., Finally , heterogeneous distributions as employed here have been shown to influence the outcome of epidemics 27 and the efficiency of targeted treatment 19 , 20 ., The full mean-field model and ODE model equations and details of the degree distributions are given in ., Integrating the ODEs resulting from the mean-field analysis yields the possible final states of the dynamics ., But such an analysis neglects the inherent stochastic nature of disease transmission ., Standard epidemic models often only consider stochastic extinctions of a disease ., When the contact structure of the population is known , the probability of extinction can be calculated 17 ., However , in addition to stochastic extinction , our model dynamics also depend on the probability of treatment and mutation ., Thus even though the mean-field model predicts a final state dominated by the resistant strain , a randomly picked trajectory will reach this state only if a mutation occurs ( with probability ) , i . e . , infections must occur , then resistance is able to appear ., This becomes especially important if the resistant strain has a higher force of infection than the treated wild-type strain ( e . g . , ) 39 , 40 ., In this case , even below the epidemic threshold of the treated wild-type strain , the development of resistance can occur and propagate ., From the expected number of secondary infections caused by a quantity of initial infectious individuals and the total probability of transmission , 17 , one can calculate the probability , , that an individual infected with a wild-type strain develops de novo resistance ( details in Text S1 ) : ( 1 ) where and are the average degree and excess degree of the network , respectively 41 ., Hence , Eq ., ( 1 ) equals the probability of reaching a state where the resistant strain has emerged ( assuming such a state is possible according to our mean-field analysis ) ., Since the epidemic threshold is given by , we set for ., Note that Eq ., ( 1 ) assumes that is such that , but ., Finally , we note the generality of our model: parameter values chosen here are to illustrate and exaggerate the phenomena observed ., We are interested in assessing the effects of the timing of antiviral treatment ., If the resistant strain is less transmissible than the treated wild-type strain ( ) , treatment will always be a good option and one must then concentrate on optimizing treatment efficiency ( Figure 1 ) ., If the resistant strain is at least as transmissible as the treated wild-type strain ( ) , timing of treatment is crucial 15 ., Figure 2 shows the final epidemic size ( proportion recovered ) as a function of the untreated force of infection , , and corresponds to a situation when the resistant strain is more transmissible than the treated wild-type infections ., For increasing values of we see an expected increase in final epidemic size ., However , the first bifurcation creates a regime of bistability where two final states can be reached for the same in stochastic simulations ., Between the two possible branches , there exists a critical manifold corresponding to the curve of initial conditions ( initial number infected , ) yielding equal expected epidemic sizes whether treatment is implemented or not ( details in Text S1 ) ., Thus , depending on the number of infected individuals when treatment is initiated , we encounter one of three scenarios: one , where treatment is effective , de novo resistance is unlikely and there are few infections which eventually die out ( this is the green area \u2013 \u201cEfficient Treatment\u201d \u2013 in Figure 2 , panel b ) ., In the second and third scenario ( the red area \u2013 \u201cDangerous Treatment\u201d \u2013 in Figure 2 ) , treatment will most likely fail and result in either large incidence of resistant infections or a small outbreak of resistance in a depleted susceptible population ( depending on the timing of this dangerous treatment ) ., The derivation of the critical manifold is detailed in Text S1 ., Figure 3 demonstrates the behavior of the system in the regimes defined by this critical manifold ., We see similar behavior for epidemics from both regimes when no treatment is applied ( panels b and e ) ., As observed in previous work 16 , late treatment can be somewhat efficient if implemented after the peak of infections , such that the wild-type strain has depleted the pool of susceptibles to limit propagation of the resistant strain ( panels d and g ) ., However , since this implies that the bulk of the original epidemic has passed , this does not qualify as a truly efficient treatment regime ., On the other hand , simulations ( Figure 3 , points ) for early treatment of an epidemic with low initial number of infectious individuals appear significantly more efficient than predicted by the ODEs ( Figure 3 , solid lines , panels c and, f ) ., This discrepancy is caused by the stochasticity of this system , or more precisely , by the mutation probability , ., Such mathematical models based on mean-field approximations consider infinite populations in which a finite fraction of infectious individuals cause an infinite number of infections , resulting in an infinite number of treatments and an inevitable emergence of resistance ., In finite populations , early treatment with low initial infections will cause only a small number of interventions resulting in a small probability of resistance emergence , ., This is why the expected value of the prevalence of resistance is below one individual for all time in the simulations ., Importantly , models without stochasticity would have not indicated treatment and failed to identify this efficient treatment regime ( Figure 3 ) ., We note that presenting the per-epidemic average number of cases would have allowed the mean-field approximations to better align with simulations ., This however would have ignored the role of stochastic extinctions including those due to successful treatment ., Assuming treatment is expected to be efficient , we can explore two different forms of treatment: non-targeted , where is a percentage of the population selected at random for treatment , and targeted , where is a function of node degree ( ) , similar to Cohen et al . where an individuals probability of being treated depends on its degree 20 ., We focus on scenarios where treatment would be indicated a priori; i . e . , when there is a fitness cost to resistance ( ) ., In the case when there is no cost of resistance ( as explored above ) treatment may or may not be optimal , however the results are qualitatively similar ., Similar to previous studies 2 , 4 , we see a transition from wild type to resistant infections as treatment levels increase , and find a minimum in disease prevalence at intermediate levels of treatment ., Interestingly , we see higher levels of resistance at lower treatment percentages in the targeted treatment regime ., Figure 4 shows that under the non-targeted treatment regime , the resistant strain dominates when , whereas under the targeted treatment regime , resistance is dominant when ., This happens because targeted treatment increases the chances of resistance occurring in high-degree nodes ., Once resistant mutants arise in highly connected nodes , they will have a high probability of being widely transmitted ., In addition to the take over of the resistant strain in the targeted treatment regime , we see high levels of total infection with increasing percentage treated due to treatment failure in the resistant cases ., Finally , we find the effects of treatment targeting to be robust to the network structure ., Under a more homogenous degree distribution ( binomially distributed ) we find the difference between high- and low-degree individuals to be less than in the heterogeneous network , and thus targeting treatment by degree has a smaller effect ., However , the results are qualitatively the same , with targeted treatment leading to higher levels of resistance at lower levels of treatment than non-targeted treatment ( see Text S1 ) ., This finding is reassuring given the uncertainty in actual contact structures relevant to influenza transmission 34 , 36 , 38 ., In the current study we wanted to answer three questions: one , to minimize resistance , should treatment be initiated at all in epidemics ?, two , if treatment is initiated , how does its timing affect the emergence and amount of resistance in structured populations ?, and three , which treatment regime , targeted by degree or not , leads to the least amount of resistance ?, We find potential bistability in the final epidemic size and deviations from mean-field approximations which would have misidentified optimal treatment timing ., We find two scenarios: one , when the initial number infected is low ( early in an epidemic ) , early treatment is preferable to late treatment , and two , when the initial number infected is high , treatment after the peak of epidemic is optimal to keep resistance low ., Interestingly , this occurs at identical values of the force of infection ( values of ) , and indicates a strong dependence on initial conditions ( number of cases at the onset of treatment ) and thus on the timing of treatment ., Given the uncertainty inherent in estimating epidemic prevalence , especially in emerging infections 42 , caution must be taken when deciding to implement mass treatment ., In addition to the presence of this bifurcation and strong dependence on initial conditions we find large differences depending on the method used to allocate treatment ., In accordance with previous results , we find a minimum in the total number of infections at intermediate levels of antiviral use ., Surprisingly however , we find higher levels of resistance at lower levels of treatment in the targeted treatment case ., This is due to the heterogeneity in contact structure wherein if those that are preferentially targeted for treatment ( due to their high number of secondary contacts ) develop de novo resistance , they have a large opportunity to spread the resistant strain ., This is counter to previous results demonstrating that targeted treatment is optimal to keep absolute numbers of infecteds low ., Thus , in structured populations , non-targeted treatment is preferable if resistance is to be minimized ., This implies that in populations where the development of resistance is of concern , resources do not need to be spent on targeting treatment ., We note two things: first , in cases where drugs are scarce , the amount of resistance expected to appear is low ( Figure 4 ) and treatment targeted by node degree and factors not considered here ( i . e . , treating teachers , healthcare workers , first-responders , etc . ) is preferable to no treatment or non-targeted treatment ., Second , non-targeted , or random treatment may be complicated by additional clinical factors also not considered here ( i . e . , age , severity of illness , pregnancy , etc . ) ; however , our results indicate that in cases where antivirals can be provided to a large fraction of the infected population , resource-intensive targeting by degree need not be employed and treatment should be initiated based on clinical factors alone ., The current work highlights the importance of including stochasticity and contact structure in epidemic models ., Due to the bistability in final epidemic sizes , the mean-field approximation overestimated the number of resistant cases when treatment was initiated early and missed the efficient treatment when the initial numbers of infected are low ., Additionally , we have shown that targeted treatment is not optimal due to the heterogeneous contact structure of the population ., This is contrary to earlier studies demonstrating the efficiency of targeted treatment ., While our results are qualitatively valid , and hold over multiple network types ( see Text S1 ) , more detailed models can and should be developed to study the effects of contact structure heterogeneity on the development of resistance ., Parameters were chosen to be general , and give qualitative results , more accurate statistical estimation could be employed to improve the realism of the model ., The timing and targeting of antivirals for the treatment of influenza has important policy implications ., Recent studies have demonstrated the facility with which highly pathogenic H5N1 can mutate to spread efficiently from human-to-human 6\u20139 ., The development of resistance of H5N1 to common antiviral treatments , could have devastating consequences ., We have demonstrated the danger of initiating treatment when the number of infected cases have surpassed a certain threshold ( above and below the critical manifold ) , but have also demonstrated that spending resources on targeting treatment may not be necessary .","headings":"Introduction, Methods, Results, Discussion","abstract":"Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality ., Previous models have identified treatment regimes to minimize total infections and keep resistance low ., However , the bulk of these studies have ignored stochasticity and heterogeneous contact structures ., Here we develop a network model of influenza transmission with treatment and resistance , and present both standard mean-field approximations as well as simulated dynamics ., We find differences in the final epidemic sizes for identical transmission parameters ( bistability ) leading to different optimal treatment timing depending on the number initially infected ., We also find , contrary to previous results , that treatment targeted by number of contacts per individual ( node degree ) gives rise to more resistance at lower levels of treatment than non-targeted treatment ., Finally we highlight important differences between the two methods of analysis ( mean-field versus stochastic simulations ) , and show where traditional mean-field approximations fail ., Our results have important implications not only for the timing and distribution of influenza chemotherapy , but also for mathematical epidemiological modeling in general ., Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts , and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations .","summary":"Resistance of influenza to common antiviral agents carries the possibility of causing large morbidity and mortality through failure of treatment and should be taken into account when planning public health interventions focused on stopping transmission ., Here we present a mathematical model of influenza transmission which incorporates heterogeneous contact structure and stochastic transmission events ., We find scenarios when treatment either induces large levels of resistance or no resistance at identical values of transmission rates depending on the number initially infected ., We also find , contrary to previous results , that targeted treatment causes more resistance at lower treatment levels than non-targeted treatment ., Our results have important implications for the timing and distribution of antivirals in epidemics and highlight important differences in how transmission is modeled and where assumptions made in previous models cause them to lead to erroneous conclusions .","keywords":"medicine, organismal evolution, social and behavioral sciences, influenza, applied mathematics, sociology, microbiology, mathematics, microbial evolution, social networks, population biology, infectious diseases, evolutionary modeling, biology, infectious disease modeling, population ecology, viral evolution, ecology, virology, viral diseases, computational biology, evolutionary biology","toc":null}
+{"Unnamed: 0":527,"id":"journal.pcbi.1000719","year":2010,"title":"Specialization Can Drive the Evolution of Modularity","sections":"For our study we consider a network of genes ., Each genes activity state is regulated by other genes in the network ., The genotype of an individual is defined as the set of the interactions among its genes ., We represent this set of interactions as a matrix ., Non-zero elements in indicate activation ( ) or repression ( ) of gene exerted by gene ., The state of the network at time is described by a vector ., A certain gene at time can be either active ( ) or inactive ( ) ., We model the change in the activity of the genes in the network according to the difference equation ( 1 ) where equals if , and it equals in all other cases ., Despite its simplicity , variants of this model have been successfully used to study how robustness can evolve in gene regulatory networks 22\u201324 , how robustness can aid in evolutionary innovation 25 , 26 , and how recombination can produce negative epistasis 27 ., Moreover , similar models have been successfully used to predict the dynamics of developmental processes in plants and animals 28 , 29 ., For our purpose , we consider that a phenotypic trait is defined by an attractor , a stable gene activity pattern resulting from the dynamics of a gene regulatory network ., Attractors are often associated with developmental end-states and \u2018outputs\u2019 of developmental mechanisms 22 , 30\u201332 ., In order to study the evolution of modularity in gene regulatory networks , we implemented evolutionary simulations that consisted of iterative rounds of mutation and selection in populations of networks ., In these simulations , we compared a set of reference gene activity patterns to actual network attractors , so that networks with attractors that were similar to the selected activity patterns had higher fitness than others ( see Methods ) ., To quantify the modularity of networks in our model , we used an algorithm 33 that identifies modules as non-overlapping densely connected groups of nodes with sparser connections between groups ( see Methods ) ., Thus , if genes in individual modules interact with many genes outside their module , the autonomy of the modules decreases , which would be reflected in a lowered modularity score ., To find out whether specialization can increase modularity , we studied 200 independent evolving populations of gene regulatory networks ( eq . 1 ) ., Each of these populations was started with identical networks , and was subject to 500 generation cycles of mutations and selection towards attainment of a fixed-point attractor I ( see Methods for details ) ., The number of generations was chosen to ensure that networks that stably attain I can arise in the population ., After gene activity pattern I had evolved , we allowed the population to evolve for 1500 more generations , but selecting for attainment of gene activity pattern I and a new pattern II during this time ., Under this selection regime , the fittest networks were those capable of stably attaining I and II from different initial conditions that may occur in different parts of a multicellular organism ., In other words , selection maintained the ability to attain I while at the same time favoring acquisition of II ., Pattern II was chosen such that half of the network genes had identical ( shared ) expression states in I and II , and the other half differed in their activity state ( Figure 1A ) ., We chose such activity patterns because we hypothesized that interactions between genes with shared activity states and the rest of the genes would obstruct either, i ) the constant activity state of the former , or, ii ) the capacity of the latter to acquire different activity states independently of genes with constant activity states ., If so , interactions between the different sets of genes may be selected against , thus resulting in two sets of genes with only sparse connections between them ., In most of the 200 evolving populations , modularity increased after evolving towards the attainment of both I and II ., We observe this increase both in the networks with the highest fitness in the population ( Figure 1B; Wilcoxon signed-rank test; ; ) , and when averaged over all networks in a population ( Figure 1C; Wilcoxon signed-rank test; ; ) ., Figures 1D , E show an example of how modularity increases after selection for attainment of activity patterns I and II ., Modularity does not increase when selection for II is absent , nor when networks evolve in the absence of selection ( Figure S2 ) ., The increase in modularity is not transient because it is maintained around the same level , at least for 10 , 000 additional generations , when selecting for both I and II ( Figure 2 ) ., We next verified that our results were insensitive to changes in model assumptions and parameters ., We first decreased the mutation rate , and even though the time required to evolve activity patterns I and II then increases , modularity still increases significantly ( ; Figure S3A ) ., Modularity increases as well when is increased ( ; Figure S3B ) ., We next asked whether our observations were sensitive to the assumption that individual gene activity patterns contribute to fitness additively ., Changing this assumption to multiplicative fitness contributions still leads to a significant increase in modularity ( Figure S4 ) ., In addition , the increase in modularity also occurs for networks containing more genes ( ; Figure S5 ) , suggesting that such behavior does not depend on the number of genes in a network ., In a next analysis , we asked whether the increase in modularity depends on the identity of gene activity states I and II ., We found that it does not , as long as some genes have the same activity state in the two patterns ., For example , modularity also increases when the activity patterns differ in the activity of either three or seven genes ( Figure S6A , B ) ., Moreover , modularity increases when both the first and the second gene activity patterns are randomly chosen , except that pairs with fewer than two different activity states are discarded ( Figure S6C , based on 100 populations with different pairs of activity patterns ) ., In contrast , modularity does not increase when all genes in the activity states I and II differ in their expression ( Figure S6D ) ., This result is not due to a lack of adaptation , since networks able to attain both activity patterns arise in all evolving populations ., Taken together , these observations show that modularity does not only increase for specific gene activity patterns , but that it is a generic evolutionary response ., Moreover , the distinction between two sets of genes , those with identical and those with different activity in both expression patterns , is essential for the evolution of modularity ., That modularity increases only in this case suggests that modules arise as a means of diminishing the effects of genes with unchanging activity on genes with changing expression in I and II , and vice versa ., If so , modules should correspond to sets of genes that are required to switch their activity in a concerted manner ., The following section shows that this is the case ., Having established that the evolution of modularity requires genes with both shared and different activity states , we next asked whether the partitioning of modules is congruent with these two sets of genes ., In other words , does one module tend to involve the genes with shared activity states , whereas another involves genes with different activity states in I and II ?, We evolved 300 network populations , first towards activity pattern I and later towards both I and II , depicted in Figure 1A ., Throughout evolution , we determined for one of the best adapted networks in each population:, i ) the frequency at which two genes with activity states shared in I and II occur within the same module ,, ii ) the frequency at which two genes with different activity states in I and II occur within the same module ,, iii ) the frequency with which a specific gene with a shared activity state and a gene with a non-shared activity state are in the same module ( Figure 3A ) ., As selection for I and II occurs , and increase , while decreases ( Figure 3B ) ., This observation tells us that genes with activity states that change concertedly throughout all the selected activity patterns \u2013 be they shared or not \u2013 will tend to be included in the same module , and kept apart from other genes ., This is exemplified in Figure 1D , E , which compares one of the optimal networks after selection for I with one of the optimal networks after selection for both I and II ., The latter is partitioned into modules in which genes with shared and distinct activity states in I and II lie apart ., Thus , the structure of modules reflects the manner in which selection has molded the traits , as has been previously suggested 2 ., We also tested whether modularity arises only where selection favors the attainment of two gene activity patterns , or whether it increases further with even more gene activity patterns ., To this end , we analyzed 100 evolving populations in which selection first favored a gene activity pattern I ( 500 generations ) , then an additional pattern II ( I+II , next 1 , 500 generations ) , and then a third pattern III ( I+II+III , last 3 , 000 generations ) ., The patterns share the activity of some genes and differ in others ., As selection for the third pattern begins , more and smaller groups of genes arise whose activity changes in a concerted manner ( Figure 4A ) ., Interactions between different such groups would obstruct evolutionary adaptation ., Such interactions should thus be selected against , resulting in a further increase in modularity ., Our observations confirm this hypothesis ., After selection for patterns I and II , we observed a significant first increase in modularity ( Wilcoxon signed-rank test; ; ) ., Modularity increased further after selection for pattern III ( Figure 4B; Wilcoxon signed-rank test; ; ) ., In addition , we observed an increased number of modules in networks with high fitness after selection for patterns I and II ., Moreover , this number increases further after selection for patterns I , II and III ( Figure S8B ) ., This result suggests that the increase in modularity after selection for the three patterns occurs because of the appearance of new modules , and is not a mere consequence of the consolidation and refinement of previously evolved modules ., We also analyzed how the probability of two genes being part of the same module changes across evolution ., We found that the frequency of two genes occurring in the same module in the fittest networks of each evolving population changes according to whether those genes change their activity concertedly across the selected patterns ( Figure S8C ) ., For example , as we depict in Figures 4 and S8A , the activity of genes 5 and 6 changes concertedly across all activity patterns: if in one pattern gene 5 is active , then gene 6 is inactive in that same pattern , and vice versa ., The frequency with which those genes lie in the same module increases across evolution ., In contrast , the activity of genes 0 and 6 changes concertedly when selecting for patterns I and II , but not when also selecting for activity pattern III ., Thus , the probability of those genes occurring in the same module increases prior to selection for pattern III ., After selection for pattern III starts , the probability that genes 0 and 6 lie in the same module decreases abruptly ( Figure S8C ) ., These results show that the modules that arise after selection for the third pattern also tend to coincide with sets of genes whose activity states change concertedly throughout the selected patterns ., Computational cost did not allow exploration of further increases in modularity via selection of additional gene activity patterns ., However , our observations already suggest that modularity will increase as long as there is an increase in the number of gene groups for which concerted activity changes are favored ., A question recurring in the literature is how modularity may increase evolvability by facilitating co-option , the combination of previously evolved modules to perform new functions 19\u201321 , 34\u201336 ., We addressed how the previous evolution of modules in gene regulatory networks biases future evolutionary potential by asking whether gene networks acquire new gene activity patterns faster if these patterns use gene activity states associated with previously evolved modules ., Specifically , we selected networks for their ability to stably attain three gene activity patterns I , II and III ( Figure 5A ) ., We chose the specific combination of patterns in Figure 5A because:, i ) it promotes the evolution of a module including genes 0\u20134 and another module including genes 5\u20139 , as shown above , and ,, ii ) it allows the inclusion of an additional activity pattern ( IV ) that is composed entirely of activity states associated with previously evolved modules ( Figure 5A , B ) ., After 3 , 000 generations , we subjected networks in 100 evolving populations to selection favoring such an additional gene activity pattern IV ( Figure 5B ) ., Importantly , this pattern shares the activity states of genes 0\u20134 with III , and the activity state of genes 5\u20139 with II ., Thus , gene activity pattern IV may evolve by combining previously evolved modules in a new manner ., In addition , we repeated this approach in 100 \u201ccontrol\u201d populations where the fourth favored gene activity pattern was randomly chosen with equal probability for genes being active and inactive ., Notice that we do not expect that selection for activity pattern IV increases modularity , because the inclusion of this pattern does not cause an increase in the number of gene groups with concerted activity changes ., Rather , we hypothesize that modularity facilitates the evolutionary acquisition of such an activity pattern , as compared to other activity patterns ., We found that networks with high fitness arise much more rapidly when IV is the new gene activity pattern ., This indicates that pattern IV is much easier to attain than random gene activity patterns in populations of networks that have previously been selected for their ability to attain I , II and III ( Figure 5C ) ., The same trend occurs when not just the networks with highest fitness are considered , but also when we analyze mean population fitness ( Figure S7 ) ., We note that in our analysis selection favors the attainment of IV to the same extent as the attainment of any one random gene activity pattern in the control populations ., This means that our observations are not simply caused by a greater increase in fitness conveyed by IV ., The fitness increase rather depends on how easily the new gene activity patterns can be constructed: it is easier to evolve gene activity patterns that combine activity states of previously evolved modules ., In sum , we showed here that modularity arises in gene networks when they acquire the ability to attain new activity patterns that share the activity state of some genes with old patterns ., Our observations indicate that selection to attain the new activity patterns can cause modularity to arise in gene regulatory networks when pleiotropic effects obstruct adaptation 2 , 8 , 11 ., Such pleiotropic effects are caused by interactions between, ( i ) genes whose activity is shared between different patterns , and, ( ii ) genes whose activity is specific to one pattern: If changes in the latter affect the former , evolutionary acquisition of the new pattern is hindered ., Thus , the scenario we propose favors networks with few interactions between genes with an unchanging activity state and genes that adopt new regulatory functions ., In this way , genes that have correlated activity states come to lie in the same network module ( Figures 3 and S8C ) ., Our results suggest that modularity increases as long as selection favors new activity patterns involving more and smaller groups of genes whose activity changes in a concerted manner ( Figures 4 and S8 ) ., Empirical falsification ( or validation ) of the mechanism that we propose ideally requires comparative analyses of the structure of gene regulatory networks in several related species ., Such information might not be available soon ., However , existing information from various sources suggests that the mechanism we propose could be important ., Specifically , the evolutionary acquisition of new gene activity states by regulatory networks is ubiquitous in evolution , and nowhere more than in the evolution of development ., It occurs wherever new cell types , organs , or body structures , arise from previously undifferentiated ones ., Many examples in the literature suggest that some genes exhibit specialized activity in different parts of an organism , whereas others present shared activity patterns ., Indeed , gene functions may be inferred via correlated gene expression patterns in conventional or high-throughput expression analyses 37\u201339 ., For example , the activity of the same genes patterns both vegetative and floral meristems in the plant Arabidopsis thaliana ., Floral identity genes are active exclusively in floral meristems , so that the floral structure is determined by both the floral identity genes and the shared patterning genes 40\u201342 ., In the sea urchin Strongylocentrus purpuratus , some differentiation genes are active in the micromer lineage that produces the euechinoid exclusive embryonic skeleton and also in the independently derived juvenile skeletogenic centers that produce the adult skeleton 43 ., Some other genes of the gene network that specifies the skeletogenic micromere lineage are active in those cells but not in the juvenile skeletogenic centers ., Examples include genes involved in induction of neighbouring cells or in triggering the initial stages of micromere specification 43 , 44 ., Another example involves the cellular level ., Mammalian brown fat cells share some traits and gene activity patterns with white fat cells , and others with muscle cells 45 ., More generally , evolutionarily derived cell types usually perform just a fraction of the functions that ancestral cell types performed 46 , a trend that will lead to similar activity states for some genes and different states for others in sister cell types ., In a similar vein , evolutionary specialization of initially homogeneous metameric units is likely to occur mainly by modifications ( such as changes in the transcriptional circuitry ) that result in metamers with different activity states of some genes but not of others; otherwise , differentiated metameric units would be hardly recognizable as such ., For example , in D . melanogaster , limbs are positioned and patterned by mechanisms that are reiterated along the body , however limb identity relies on segment-specific mechanisms 47 ., Moreover , in heteronomous arthropods , in which the morphology of segments along an individual is very distinct , processes underlying segmentation and limb differentiation interact less than in homonomous arthropods , in which the segments along a body are very similar 47 ., Segment formation is performed throughout the organism ( shared ) , and , in heteronomous taxa , limb identity determination is specialized according to the place where a limb develops ., Thus , when there is specialization in limb identity , the two processes are more independent , in contrast to taxa that lack this specialization ., Co-option , the recruitment of previously evolved modules to perform new functions , is a common feature of evolutionary innovations 20 , 21 , 34 , 36 , 43 ., A case in point regards the gene network regulating pharyngeal dentition in fish , which is co-opted to also generate oral dentition 36 ., Another example is the gene network that patterns the insect wing blade ., It is co-opted to determine the localization of eyespots in butterfly wings 34 ., Our work shows that a modular network may readily generate new gene activity patterns that make use of gene activity states of previously evolved modules ., The existence of such structured , or \u201cfacilitated\u201d variation has been known for a long time 48\u201351 ., Our work provides a candidate mechanism to create such variation , namely via network modularity that results from specialization in gene activity ., Our observations could thus help explain the repetitive co-option of several modules , such as that responsible for proximal-distal polarity in lateral appendages and body outgrowths 20 , 21 , or the achaete and scute module that operates in a wide range of developmental processes in animals 19 ., An alternative hypothesis for the evolution of modularity is the \u2018modularly-varying goals\u2019 scenario 10 ., This scenario requires that populations are exposed to evolutionary goals that fluctuate over time , so that modularity can arise and be maintained ., In contrast , our scenario requires specialization of gene activity , that is , new gene activity patterns must be attained while old activity patterns are preserved ., Relatedly , the modularly-varying goals scenario requires genetic changes for evolutionary adaptation after an evolutionary goal changes ., In contrast , our mechanism requires one genotype to produce different activity patterns under different conditions , conditions that may occur in different parts of a multicellular organism ., In other words , in our scenario , modularity arises to avoid obstruction to attain different selected patterns within the same genotype ., Our scenario may thus be more appropriate for traits where environmental demands are not constantly fluctuating , such as in the development of many morphological traits in plants and animals ., Thus far , we motivated our approach with the development of multicellular organisms ., However , the approach could also explain modularity in unicellular organisms ., For example , the metabolic networks of bacteria living in changing environments tend to be more modular than those of bacteria living in stable environments 12 ., Similar patterns may exist for gene regulatory networks ., If so , the modularly varying goals scenario is not their only possible explanation ., Unicellular organisms respond to changing environments by tuning their gene activity pattern ., In other words , they usually have adaptively plastic phenotypes ., For example , different sets of genes are activated or repressed when yeast cells are exposed to different environments 52\u201354 ., Evolving the ability to switch gene expression according to the environment requires producing several alternative activity patterns , as we propose here ., Importantly , some yeast genes change their expression concertedly in several environments , whereas others have responses that are specific to any one environment 52\u201354 ., This observation suggests that the activity of some genes is shared across alternative activity patterns while the activity of other genes is particular to certain environments , as our model demands ., In sum , because organisms in changing environments are required to produce different gene activity patterns according to the environment , our scenario can explain the evolution of modularity both in fluctuating and non-fluctuating environments ., A question that remains unanswered is whether our model applies to genotype-phenotype maps different from those of gene regulatory networks ., A prominent example is metabolic networks , whose phenotypes are patterns of metabolic fluxes through network reactions ., Our framework may apply to some instances of modularity in metabolic systems , as the following example illustrates ., The main requirement of our model is an increase in the number of functions that a network must perform ( i . e . in the number of selected gene activity patterns ) ., The appearance of new functions in a metabolic network usually involves the production of new metabolites ., Hintze and Adami 55 performed evolutionary simulations of an artificial metabolism in which the fittest metabolic networks were able to produce an increasingly diverse spectrum of metabolites ., This selection regime resulted in increased modularity of metabolic networks , an observation consistent with the mechanism that we propose for gene regulatory networks ., Our work aimed at conceptual clarity by using only few essential assumptions in explaining the evolution of modularity ., We therefore neglected many processes that doubtlessly play a major role in the evolution of regulatory gene networks ., For example , we did not consider mutations changing the number of genes in a network , even though processes such as gene loss or duplication may be frequently involved in the appearance of new gene activity patterns ., Similarly , the appearance of new body structures or cell types requires interactions among cells , tissues and organs ., Such interactions ensure the proper placement of cells with the combination of general and specialized gene activity that is characteristic of specialization ., The incorporation of these and other processes in future work will deepen our understanding of the evolution of modularity , and thus of evolvability ., We here identify modularity using one 33 , 56 of several algorithms aimed at identifying structural modules , densely connected groups of nodes with sparser connections between groups ., The measure of modularity in this algorithm is a score that compares the abundance of intra-module connections between a given network to that of random networks with the same degree distribution 57 ., is defined as: ( 2 ) where denotes one of the prospective modules in a network , stands for the total number of edges in the network , represents the number of edges within module , and is the sum of the number of connections that each node in module has 33 , 56\u201358 ., The algorithm we use 33 identifies a partitioning of networks into modules that maximizes ., We use this algorithm because of its computational efficiency and accuracy 33 , 56 ., We also explored different algorithms 57 , 58 and found that our results hold regardless of these choices ., Typical values of partitions that maximize intra-module connections in random networks vary depending on the number of nodes , edges and connectivity distribution 59 ., For example , the maximum value of a network varies as a function of the total number of edges in it 60 ., Hence , a fair comparison of modularity in different networks requires first addressing how atypical is in the best partition of each network when compared with random networks with the same attributes ., Following 10 we use for normalization the equation: ( 3 ) where is the modularity returned by the Newman algorithm 33 , 56 for a certain network , stands for the average value of 1 , 000 random networks with the same number of genes and edges and the same degree distribution as the original network ., values for these random networks are also calculated using the Newman algorithm ., is the maximal value in these 1 , 000 random networks ., The normalized modularity tells us how modular a network is in comparison to random networks with the same attributes ., Non-normalized and normalized values render equivalent results in our analysis ( Figure S1 ) ., Therefore , we restrict ourselves to report results for normalized modularity ., The fitness function we use compares a set of reference gene activity patterns to actual network attractors ., Our fitness measure also incorporates the likelihood that an attractor is attained in the face of perturbations ., In doing so , it takes into account not only the identity of an attractor but also its robustness , an important feature for the stability and reproducibility of developmental processes 13 , 18 , 61\u201363 ., For each gene activity pattern that contributes to fitness and for each network in our analysis , evaluation of fitness involved the following steps:, i ) The initial state of the gene network at time 0 was chosen to be a perturbation of the target pattern , drawn from a probability distribution where the initial state of each gene differs from that of with probability ., ii ) We carried out network dynamics ( eq . 1 ) until some new attractor was reached;, iii ) We recorded the Hamming distance ( ) separating from , and calculated the contribution to fitness of this developmental trajectory as ; modifications of by varying the exponent produce equivalent results ., iv ) We repeated steps, i ) \u2013iii ) 500 times to determine 500 values ( ) ., Notice that several of such 500 values would correspond to the same initial condition , and that the distribution of possible initial conditions is biased towards gene activity patterns similar to the reference pattern ., This reflects our assumption , for the sake of simplicity , that selection favors similar initial conditions leading to the same selected activity pattern ., We also assumed that gene activity patterns that are similar to the reference pattern are more likely to be required as initial conditions ., Relaxation of such assumptions by variation in did not modify our results ., We then calculated the networks fitness as ( 4 ) where is the arithmetic mean of all ., Wherever fitness needed to be evaluated for multiple gene activity patterns , we calculated the arithmetic mean of over these multiple patterns ., Notice that selection is pushing the acquisition of different gene activity patterns that would appear under different conditions ( such as different parts of the organism ) ., Hence , the optimal networks will be those with dynamics that lead to different attractors matching the reference activity patterns , and not those with a single attractor that is a combination of the reference patterns ., Had we used multiplicative contributions to fitness then the benefits that result from attaining a gene activity pattern would have depended on the acquisition of all other activity patterns ., Because our simulations start with selection for a single activity pattern , it was preferable to assume otherwise ., Using additive contributions to fitness guarantees that networks that are not able to attain the new gene activity pattern still have a chance to contribute to the next generation ., However , usage of multiplicative fitness contributions does not affect our results qualitatively ., For each simulation of gene network evolution , we first built a 10 node network and added 20 interactions at random to its interaction matrix ., These interactions were activating or repressing , with equal probability ., To construct the initial population we exposed 100 copies of this initial network to random mutation ., Mutations occurred independently among different genes ., A mutation of a gene either added a positive or negative interaction affecting the genes activity , or eliminated one of the interactions that regulated the gene ., Such mutations can be interpreted as changes in the regulatory regions of a gene , adding or eliminating cis-regulatory elements ., Most of our results are based on a probability of a mutation occurring in a gene ( ) of 0 . 05 ., This value of allowed adaptation within a tractable number of generations ., Variation in did not affect our results , but only affected the time required for adaptation ., For a gene undergoing mutation , we defined the probability of losing an interaction as ( 5 ) and the probability of acquiring a new interaction as ., Here represents the number of regulators of the gene , and equals the number of genes in the network , and hence , the maximum number of regulators of any gene ., This procedure results in networks that evolve towards low connectivities of 2\u20133 regulators per gene ., Such low connectivity is often observed in transcriptional regulation networks of plants , animals , fungi and bacteria 64 ., Loss of interactions may also help explain the observation that loss of gene expression is more common than acquiring new expre","headings":"Introduction, Results, Discussion, Methods","abstract":"Organismal development and many cell biological processes are organized in a modular fashion , where regulatory molecules form groups with many interactions within a group and few interactions between groups ., Thus , the activity of elements within a module depends little on elements outside of it ., Modularity facilitates the production of heritable variation and of evolutionary innovations ., There is no consensus on how modularity might evolve , especially for modules in development ., We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity ., Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition ., Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities ., This and other observations suggest that modularity evolves because it decreases interference between different groups of genes ., Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change ., We also show how modularity can facilitate co-option , the utilization of existing gene activity to build new gene activity patterns , a frequent feature of evolutionary innovations .","summary":"Throughout lifes history , organisms have produced evolutionary innovations , features that are useful when facing new ecological and environmental challenges ., A property that aids in the production of such innovations is modularity ., Modular systems consist of groups of molecules with many interactions within a group but fewer interactions between groups ., Such modularity increases the chances of innovation , because it allows changes inside one module without perturbing others , and because it permits redeployment of modules to create new biological functions ., We simulate the evolution of gene networks known to be important in development to show that modularity increases when selection favors specialization in gene activity ., Specialization occurs wherever new cell types , organs , or other body structures arise ., In the course of this process gene networks acquire the ability to produce new gene activity patterns specific to these structures ., We also demonstrate how modularity favors the evolution of new gene activity patterns that make use of already existing modules ., Because specialization in gene activity is very common in evolution , the mechanism that we put forward may be important for the origins of modularity in gene regulatory networks .","keywords":"computational biology\/evolutionary modeling, developmental biology\/developmental evolution, evolutionary biology\/developmental evolution","toc":null}
+{"Unnamed: 0":1189,"id":"journal.pcbi.1000701","year":2010,"title":"Non-Linear Neuronal Responses as an Emergent Property of Afferent Networks: A Case Study of the Locust Lobula Giant Movement Detector","sections":"Since the introduction of the neuron doctrine about 100 years ago , a central question has become what local operations the primitive elements of nervous systems can perform ., So far , the only operation that has clear experimental support is the threshold operation that converts the depolarization of the membrane into action potentials ., However , also other local non-linear operations such as multiplications and divisions have been proposed ., For instance , the Elementary Motion Detector ( EMD ) , a well-established model of motion detection in the fly visual system that relies on multiplication in order to explain the neural responses of the Horizontal and Vertical System ( HS , VS ) visual interneurons 1 ., In addition , it has been proposed that attentional modulation can result in a multiplicative gain of neuronal response to sensory stimuli 2 ., Another example is the divisive inhibition that is assumed to underlie some of the non-linear adaptation properties of cortical neurons 3 , 4 , while several other studies have investigated how neuronal noise or dendritic saturation could contribute to divisive gain control 5 , 6 ., Moreover , theoretical studies on neocortical pyramidal cells have suggested that multiplicative dendritic integration could account for non-linear sensory processing enhancing stimulus classification 7 , 8 ., Despite the above examples , its computational attractiveness and the fact that some data can be satisfactorily described in non-linear terms , it remains unclear how the biophysics of single neurons could implement these operations ., One particular case in point is the Lobula Giant Movement Detector ( LGMD ) visual interneuron of the locust ., Recently it has been shown that the responses of this visual interneuron can be explained in terms of a local product of two high-level features of visual stimuli , their angular size and angular speed by means of a non-linear transfer function of the neuron 9 , 10 ., If correct , this is the most explicit case reported in the experimental literature that supports the notion of local non-linear neuronal operations and it will have important consequences for our understanding of the computations that the nervous system can perform , as it significantly increases the computational power we can ascribe to single neurons ., Hence , given the implications of this finding , it is important to investigate whether the non-linear relationship between the responses of the LGMD neuron and the visual stimuli it is exposed to can be understood in alternative terms , yet consistent with our current knowledge of the system ., Here we investigated the alternative hypothesis that the non-linear responses of the LGMD can be explained in terms of an emergent non-linear operation that results from the integration of distributed computations performed by the neurons of the processing architecture as a whole as opposed to being a multiplication operation that is local to a single unit , i . e . the LGMD ., The LGMD neuron is a wide-field neuron that is known to respond preferentially to looming stimuli 11 , 12 ., Initially , it was first thought to be an on-off neuron due to its integration of neuronal responses generated in the afferent medulla layer that correlate with the onset and offset of local visual features 13\u201315 ., More recently the relationship between properties of looming stimuli and the firing rate of the LGMD have been extensively documented , including the non-linear relationship between firing rate and time to collision ( TTC ) , the constant relation between peak firing rate and angular size , the independence of the peak firing rate of the stimulus speed , shape and texture , and the linear relationship between the TTC of the LGMD peak firing rate and the apparent looming stimulus speed 9 , 16\u201318 ., The LGMD has been the target of a number of theoretical studies that either investigated its collision detection capabilities 19\u201322 , or its putative non-linear integration properties 9 , 16\u201318 ., The first model was published in the late 90s 22 ., Rind et al . have shown that the integration of on- and off-channels by a LGMD model can account for aspects of its looming sensitivity and subsequently this model has been applied to collision avoidance by roving robots 22\u201326 ., Recently , it has been shown that all of the known response properties of the LGMD can be accounted for in terms of the multiplication of the angular velocity ( \u03b8\u2032 ) with the angular size ( \u03b8 ) of a looming stimulus 9 , where \u03b8 and log ( \u03b8\u2032 ) are directly conveyed to the LGMD via separate inhibitory and excitatory pathways ( Figure 1 ) ., The membrane potential ( Vm ) deflection is subsequently assumed to be proportional to this multiplication that is subsequently expressed in a firing rate , f\u2212l , via an exponential mapping: ( 1 ) where , ( 2 ) and \u03b8threshold is an animal and species dependent parameter that specifies the approaching objects angular size at which the LGMD firing rate is maximal 27 ., Hence , by performing an exponential on the summed inputs an effective multiplication occurs ., This model indeed provides for an excellent fit of the LGMD responses to looming stimuli , and as such constitutes a useful benchmark for any model of the LGMD 10 ., Nevertheless , this local multiplicative model makes a number of strong assumptions and overlooks the role of the neurons pre-synaptic to the LGMD ., More concretely: how does the fan-in to the LGMD delineate an \u201cobject\u201d of which \u03b8\u2032 and \u03b8 can be assessed , given that an \u201cobject\u201d has been defined , how are log ( \u03b8\u2032 ) and \u03b8 computed , how is this high-level information represented by the massive fan-in to the LGMD , and how are the parameters related to the approaching stimulus ( \u03b8\u2032 and \u03b8 ) extracted and conveyed to the LGMD in the early visual system of the locust ?, Moreover , this proposal assumes that the excitatory and inhibitory inputs to the LGMD respond to high level information about the visual stimulus ( \u03b8\u2032 and \u03b8 ) and that the role of the LGMD is to compute a functional multiplication on those ., By definition , the functional multiplication attributed to the LGMD heavily depends on having the two above mentioned features reliably computed and delivered to distinct pathways ., However , in mathematical terms , there is not a unique combination of input signals to the LGMD that could give rise to the above described firing rate pattern ( eq . 1 ) , and thus , no reason to exclude this possibility ., Indeed , our model suggests that this is the case ( Figure 1 , layers C\u2013D right panel ) ., Would the LGMD in that case still perform a functional multiplication or just a non-linear mapping of its inputs ?, In fact , the putative multiplicative properties of the LGMD have already been a matter of debate 28\u201330 ., In this study we approach the above mentioned points from a system and architectural point of view ., We evaluate the alternative hypothesis that the non-linear relationship between the responses of the LGMD neuron and the stimuli the organism is exposed to result from the interaction of many neurons in the sensory processing architecture , i . e . it is an emergent non-linearity that is read-out by the LGMD ., In particular , we will assess the contribution of each processing layer in the visual processing hierarchy of the locust , how and what information is conveyed to the LGMD , and the resulting integration at the LGMD level ., The empirical validation of this alternative hypothesis , however , is currently unpractical since it requires simultaneous in-vivo measurements from large numbers of neurons under well-controlled behavioural conditions ., Hence , to assess the validity of our alternative \u201cemergent non-linearity\u201d hypothesis we resort to a computational approach and use a computational model that is consistent with the anatomy and physiology of the locust visual processing hierarchy , including the ommatidia , medulla , lobula , LGMD and the Descending Contra-lateral Movement Detector ( DCMD ) ., Using this model we show that all properties of the LGMD neuron that can be described in terms of a local non-linear operation can be explained as emerging from the structure of the network as a whole ., Above all , we show that the inputs to the LGMD are directly driven by the stimulus dynamics rather than resulting from a process of segmentation or computation of the speed of the approaching objects ., Despite the differences with Gabbianis et al . model , the model proposed here displays identical responses to its biological counterpart on all standard stimulation protocols reported in the literature ., We demonstrate that the emergent non-linear operations are strongly dependent on the details of the synaptic organization of the locusts visual system ., In addition , we apply our model to a high-speed mobile vehicle and show that it reliably stabilizes the movement trajectory and robustly avoids collisions ., Hence , our model not only suggests that the functional non-linear response properties of the LGMD emerge out of the network as a whole but also shows robust and realistic real-world properties ., The structure of our model consists of four layers that capture the most relevant processes involved in the pathway to the LGMD , and both the output of the LGMD and the population responses for each layer are considered ( Figure 1 ) ., We model the photoreceptor layer with Linear Threshold ( LT ) units that are driven by a CCD camera with automatic gain control ( see Experimental Procedures ) ( Figure 1A ) ., The lamina is modelled with a centre\/surround connectivity that produces an edge enhancement 31 ( Figure 1B ) ., Subsequently , neurons in the medulla layer produce onset and offset sensitive responses 13\u201315 ( Figure 1C ) ., The connectivity between the medulla and the lobula layer transduces the excitatory input to the LGMD ( Figure 1D ) ., Post-synaptic inhibition onto the LGMD is modelled through the integration of the activity of the onset and offset sensitive neurons in the medulla where the summed activity inhibits the excitatory projections onto the LGMD from the second chiasma ., The LGMD is modelled as an Integrate and Fire ( I&F ) neuron that integrates the above mentioned excitatory and inhibitory inputs from the medulla and produces spikes ( Figure 1E ) ., All neurons in our model are standard leaky I&F or leaky LT neurons 32 , 33 ( see Experimental Procedures for model details and dynamic equations ) ., In the context of this study , we present an exhaustive analysis of the responses of our model to a set of standard LGMD stimulation protocols that allow us to validate our model with respect to the biological system ., Additionally , the contribution of each neural layer of the model to the LGMD responses properties is assessed experimentally ( Figure 1A\u2013E ) as well as analytically , and its real-world properties are evaluated using a fast moving robot ., In our first experiment we evaluate the model by using a looming stimulus consisting of a solid square with 10 to 21 repetitions performed per each l\/|v| pair ( where l stands for the half length of the object and v for its linear velocity ) ( see the Experimental Procedures for further details ) ., This ratio determines the time course of the angular size ( \u03b8 ) of the looming stimulus in an independent fashion from the actual stimulus properties ( eq . 3 ) ., This experiment replicates the protocol used in 17 ., Our model of the LGMD displays the typical response of this neuron to an approaching stimulus ( Figure 2A ) ; as the angular size of the retinal projection of the stimulus increases , the firing rate increases , peaks and decays before the collision occurs ., This response closely resembles that of the biological data with the multiplicative model ( r\\u200a=\\u200a0 . 98 ) ( Figure 2A , middle panel ) ., We observe that the fit of the peak firing rate and the TTC versus the l\/|v| ratio is consistent with that observed in the biological system , and is well captured by the multiplicative model that was derived from LGMD recordings ( eq . 1 ) ( Figure 2B ) ., The response of the LGMD neuron has been shown to peak when the angular size of the projection of the looming stimuli onto the retina of the insect reaches a specific size , known as the angular threshold 9 , 10 , 16 , 17 , 34 , 35 ., Moreover , the time at which the response of the LGMD peaks , that is , when the stimulus reaches the angular threshold , depends linearly on the l\/|v| ratio ., This reflects a robust detection of the angular threshold over a wide range of l\/|v| ratios since the time at which the response of the LGMD peaks is proportional to l\/|v| ., The linear relationship between TTC of the peak firing rate and the l\/|v| ratio is a known property of the LGMD 17 , 18 ( eq . 2 ) , that is reliably replicated by our model ( r>0 . 99 ) ( Figure 2C ) ., We propose a specific connectivity for the LGMD pre-synaptic fan-in such that the projections from the medulla to the lobula integrate oriented contrast boundaries ( see Experimental Procedures ) ., These projections are retinotopic and integrate the activity of a set of on-off neurons of the medulla that surround its location at distances \u03b4x and \u03b4y ( surround excitation ) ., Consequently , \u03b4x and \u03b4y define the width and height of the region within which the boundaries of a looming stimulus have to fall in order to achieve maximal excitation , what defines the angular threshold ., To further test this aspect of the model , we performed a control experiment in which we varied \u03b4x and \u03b4y to define a surround receptive field of 25 , 29 and 36 degrees of the cameras field of view ., The predicted behaviour of our model is that the changes in \u03b4x and \u03b4y would affect the angle of the peak firing rate , and therefore the TTC ., Indeed , we obtained a change of the slope of the linear regression between the frequency peak and the l\/|v| ratio which correlates with the changes in \u03b4x and \u03b4y; the bigger \u03b4x and \u03b4y , and hence the angular threshold ., The later the LGMD response firing rate reaches its maximum and the flatter the slope is ( Figure 2C ) ., In conclusion , our model is consistent with the known properties of the LGMD 9 , 16 , 17 and shows that the response peak is defined by the topology of the projections from the medulla to the LGMD ., It was shown that the responses of the LGMD are largely independent of the shape of the stimulus and its texture 17 ., In a series of experiments , we assessed whether our model shows similar invariant properties ( Figure 3 ) ., To do so , consistent with previous experiments 17 , we used four different shapes ., For all stimuli tested , and over the whole range of l\/|v| ratios ( from 5ms to 50ms ) , the models responses show the same linear relationship with the TTC as reported for the biological system , with a correlation coefficient between the models responses and the regression lines of r>0 . 99 ( Figure 3C ) ., The response invariance to the approach angle of looming stimuli is biologically highly relevant in a system that can serve to detect potential predators , as is the LGMD ., This reported property of the LGMD was investigated in the last set of experiments ., The invariance was assessed by using the same experimental protocol as previously employed , but now aligning the camera at different angular orientations with respect to the projection screen as was reported in 17 ., In the following we refer to 0% of the visual field when there is a complete alignment of the camera orientation and screen , and to 100% when the centre of the screen is at the edge of the cameras visual field ( Figure 4B , insertion ) ., We found that our LGMD model shows a robust response invariant to the approach angle up to an angle that represents approximately 75% of the visual field ( Figure 4 ) ., A one-way ANOVA analysis of the distribution of the model responses revealed that a significant difference in the mean number of spikes only occurs at an angle exceeding 75% of the total visual field of the camera ( approximately 30\u00b0 ) ( p<0 . 05 ) , i . e . when the stimulus was partially lying outside of the visual field of the camera ., Although the fields of view of the locust eye and our camera are not equivalent , yet we have designed it to have a similar angular resolution of 2 . 33\u00b0 per pixel 36 ., Additionally , the fraction of field of view where the response is invariant is comparable to the one of the biological system 16 ( Figure 4A ) ., Subsequently , we investigated the linear relationship of the TTC of our LGMD model over a wide range of l\/|v| ratios and approach angles ., Our results show that the invariance of the response properties can be seen as well in the TTC domain ( Figure 4B ) ., Here , the correlation coefficients of the data and its linear regression are above 0 . 9 for both a perfect alignment between the camera and the screen and in case of a misalignment of 75% of the visual field ., Thus , even though the activity of the neural model is significantly reduced due to the loss of stimulation by the looming stimulus at a very shallow approach angle ( Figure 4A ) , the intrinsic linear dependence of the TTC with respect to the l\/|v| of the LGMD is preserved ( Figure 4B ) ., In order to understand better and to be more specific about the nature of the inputs to the LGMD , we propose the use of additional stimulation protocols that can be applied to the locust using currently available experimental technologies ., For instance , in the multiplicative model , the firing rate of the LGMD is defined by the product of the angular speed ( \u03b8\u2032 ) and a value related to the objects angular size ( \u03b8 ) ( eq . 1 ) ., If those two variables were indeed the input to the LGMD , it would imply that for an object that is approaching at a constant angular speed the LGMD should display a completely different time response ., In fact , since the angular approaching speed of the stimulus ( \u03b8\u2032 ) would be constant , the predicted output by the multiplicative model would be an exponentially decreasing firing rate ., Hence , we explicitly evaluate the different responses between our model for each neural layer and the multiplicative one by using objects that show a uniform increase in size ( Figure 5 , layers A\u2013E left panel ) ., We observe that , whereas the multiplicative model displays the expected exponential decreasing response , our emergent non-linearity model still displays a peak at the preferred angular size ., This stimulation protocol was previously used by Hatsopoulos et al . showing a response profile consisting of a fast increase of the firing rate , a peak and subsequently followed by a slower decrease of the activity 18 ., Although some of the data could eventually be approximated by an exponential function , a more quantitative analysis of the LGMD responses is required in order to find the relationship between stimuli and rising , peak and decay properties of the responses of the LGMD under this protocol ., Additionally , we see that the predicted excitatory input to the LGMD with our model differs from the constant factor predicted by the multiplicative fit ( Figure 5 , layer D left panel ) ., Thus , a further examination of the LGMD responses under this protocol is essential to unveil what the real input to the LGMD is , and therefore to understand whether it computes a product of the objects angular size ( \u03b8 ) and angular speed ( \u03b8\u2032 ) or responds to a different processing as suggested by our results ., Next , we analyze the activity of each layer of our model to identify the relationship between receding stimuli and the intensity of the LGMD response ( Figure 5 , layers A\u2013E right panel ) ., The responses are consistent with a number of experiments of stimulus selectivity of the LGMD that showed a preference for looming stimuli and its diminished response to receding ones 11 , 12 , 35 ., Two hypothetical peaks in the TTC curve to receding stimulus are predicted depending on the weighting of the post-synaptic inhibition ( Figure 5 , right panel ) ., We show that the specific amplitude-time course of this response depends on the gain of the inhibitory projections onto the LGMD ., So far we have shown that we can account for all known aspects of the responses of the LGMD neuron to looming stimuli with a model that relies on the transformations performed in the complete pathway from the photoreceptors to the LGMD as opposed to a local multiplication ., We now want to assess the behavioural validity of our model by applying it to a high-speed impeller driven based robot called \u201cStrider\u201d ., Given its structure , the Strider is highly sensitive to inertia and friction forces , yet it delivers high-speeds ., For the robot to be sensitive to shallow approach angles , its camera was equipped with a wide angle lens ( 190 deg . field of view ) ., Although the aim of the robot is to have dynamics comparable to that of a flying insect , our robot has longer reaction times due to its increased mass , i . e . it operates at a higher Reynolds number than a flying insect ., We therefore use a course stabilization system to guarantee that the robot is able to follow straight trajectories ., This course stabilization system is based on the flys Elementary Motion Detectors ( EMD ) and uses directional motion information from the visual input to correct for drifts , and has been previously deployed on flying vehicles 37 ., The real-world behavioural task of the robot is to drive forward on a straight course until an imminent collision is detected ., The modelled LGMD neuron will detect this upcoming collision and induce a collision avoidance reaction that consists of two phases: first deceleration of the robot , and then change of heading direction ., To deal with the inertia of the robot , the braking manoeuvre is realized by driving the impellers backwards at full speed for one second ., The change in heading direction is achieved by a turn-in-place manoeuvre of 1 . 25s duration ., The LGMD model reports the detection of an imminent collision when its firing rate exceeds a specific threshold , and will trigger avoidance actions until its firing rate decreases below the above mentioned threshold value ., The following analysis is based on 16 experiments in a confined environment of 3 . 5 by 4 . 5 meters that lasted approximately 3 minutes each , where both course stabilization and collision avoidance systems were active ., Additionally , we performed 5 control experiments where the LGMD neuron model was active but the course stabilization system was disabled ., The experimental results confirm the necessity of a course stabilization system: when the robot is solely controlled by the LGMD model it displayed an erratic behaviour dominated by multiple loops in either one direction or the other ( Figure 6A , right panel ) ., When the LGMD model is combined with the EMD-based course stabilization system , the robot exhibited longer periods of translation exploring a larger area , and had a less variable heading direction ( Figure 6A , polar plots ) ., The nearly uniform distribution of the variation of the heading direction during the control experiments ( Figure 6A , right panel polar histogram ) is the result of the continuous changes that result from the complex dynamics of the Strider robot ., When both the LGMD model and the course stabilization system were combined , this distribution was significantly different and reduced to a few preferred heading directions ( Figure 6A , left panel polar histogram ) ( p<0 . 01 , Kolmogorov-Smirnov ) ., To further demonstrate the effect of the course stabilization system in the control of the behaviour of the robot , a linear segmental fitting of the behavioural traces , consisting of finding a sequence of linear segments that keep the Mean Square Error ( MSE ) of the fit below a threshold value , was performed ( Figure 6A ) ., This measure allows quantifying the straightness of the trajectory ., That is , the longer the segments are on average , the straighter the overall trajectories are ( Figure 6D ) ., In order to assess the dependency of the fit upon the threshold value , different threshold values were tested ., All tested values yielded comparable results ., Although it is not the objective of this study to evaluate our course stabilization model , these data serve to illustrate the complex dynamics of the Strider robot ., A statistical analysis of the segment length distribution ( two-sample Kolmogorov-Smirnov ) showed that in case of the combined system , the distributions of the linear segments were significantly different ( p<0 . 01 ) ., Longer segments and a higher variance were obtained for the combined system ( Figure 6D ) ; concluding that the stabilization system contributes significantly to the straightness of the trajectory ., Therefore , the course stabilization system we included is an essential component in order to deal with the dynamics of the Strider , and allows us to perform and evaluate the collision avoidance task with a high-speed robot ., To evaluate the performance of the LGMD component of the robot system , all collision detections were classified into three groups: correctly detected , false negatives ( missed ) , and false positives ., These data have to be read in the context of this fast moving robot , that on average detects a collision 0 . 5m away from a wall while moving at a mean speed of 1 . 2m\/s ., Hence , if the robot does not dramatically change its speed at the moment of detection , it collides in less than half a second ., Collisions detected 20\u2013100cm away from the walls were considered as correct , while all collisions detected closer than 20cm from the wall were considered to be detected too late , and thus missed ( false negative ) ., Conversely , collisions detected farther than 100cm from the walls , were considered false positives ( Figure 6A , grey dashed region ) ., In total , 87 . 8% of the detections were correct , 4 . 9% were false positives and 7 . 3% were missed ( Figure 6B ) ., The distribution of the number of detections vs . the distance to the wall at the time of detection peaked at 0 . 5m , and decreased exponentially further away from the wall ( Figure 6C ) ., Thus , the behaviour of the robot directly results from the non-linear nature of the response of the LGMD model ( Figure 2 ) ., Since the responses of the DCMD neuron feed directly into the thoracic motor ganglia of the locust that control the wing muscles , this seems to suggest that the amplitude-time course of the LGMD defines a particular collision avoidance strategy that minimizes the number of false positives as the distance to objects increases ., In conclusion , these behavioural experiments suggest that the exponential transfer function of the LGMD neuron 9 is more related to its role in the regulation of behaviour rather than to the computation of object approach per se ., The question whether neurons can perform non-linear operations is of great relevance to answer what computations neuronal systems can be expected to perform ., It has been argued , on the basis of the physiology of the LGMD neuron , that these neurons can perform a multiplication of high-level features of visual stimuli in order to detect pending collisions 9 , 10 , 16\u201318 ., Gabbiani et al . proposed a model that provides for an excellent fit of the LGMD responses to looming stimuli , and as such constitutes a useful benchmark for any model of the LGMD ., Using a biologically constrained model of the locust visual system , we have demonstrated that an alternative interpretation can not be excluded ., In this alternative view , the local non-linear transfer function of the LGMD neuron can be accounted for in terms of the physiological and anatomical properties of its afferent visual processing hierarchy ., We tested our model using simulated analogues of the locust experiments reported in the literature and assessed the real-world validity of our model using a high-speed robot ., We showed that our model is able to account for all reported properties of the LGMD neuron without assuming any non-linearities other than thresholding that is intrinsic to standard leaky I&F and leaky LT neural models 32 , 33 ( see Materials and Methods ) ., Consistent with our model , recent findings support the existence of a retinotopic mapping of the LGMD pre-synaptic network and suggest that a topographic map would be used to magnify the dendritic sampling of the acute zone 38 ., Our model proposes an alternative view that suggests that a non-linear transfer function between stimulus and response can emerge out of the interaction of many distributed neuronal operations and their specific mapping through synaptic topologies ., Moreover , our simulations show that the computation of angular speed and angular size pre-synaptic to the LGMD is not necessary to explain its properties ., It has been reported that the LGMD shows an exponential relationship between the membrane potential and the firing frequency 9 , 17 ., Such properties are standard to integrate and fire neurons and can be explained in terms of their sigmoid transfer function 39 ., As such , we believe that the LGMD has a similar transfer function and we have included it in our model ., Additionally , our experiments reveal that this non-linear transfer function does not play a significant computational role in the detection of a collision , but rather that it shapes the LGMD response with respect to the behaviour requirements of collision avoidance , as demonstrated with our robot experiments ., In our analysis we have presented a plausible model of how motion selective responses can arise from the interaction between on-set and off-set sensitive neurons ., The idea of having selective motion detection via delayed on-off interactions has been previously used to model visual motion-selective neurons in the mammalian neocortex 40 ., The analysis of our \u201cemergent non-linearity\u201d hypothesis shows that the non-linear responses of the LGMD are caused mainly by the particular connectivity through the second chiasma and the parameters of the neurons in the network ., It is the contribution of the restricted and local non-linearities in the medulla and structures pre-synaptic to the LGMD that give rise to the non-linear responses of our model ., This mechanism is akin to the way a multilayer perceptron can approximate any continuous function with an arbitrary accuracy based on a distributed set of non-linearities 41\u201343 ., Nonetheless , ours is not the first connectionist model proposed to explain the responses of the LGMD neuron to visual stimuli ., In fact , Rind and Bramwell proposed a model that accounts for the looming sensitivity and selectivity when stimulated with approaching , translating or receding objects over a decade ago 44 ., Consistent with ours , Rind and Bramwells model is a feed-forward model with transient detectors ( on and off-set sensitive neurons ) and a feed-forward inhibition that brings the LGMD activity back to baseline ., Moreover , Rind and Bramwells model has been successfully applied to mobile robots 23\u201325 , 45 ., Although the model has been shown to provide a similar functionality to that of its biological counterpart , there are a number of aspects of LGMD computation that it does not account for since this model was proposed before many of the properties of the LGMD were unveiled ., Thus , it does not address aspects such as the emergence of the angular threshold or the non-linear responses of the biological LGMD with respect to the specific properties of the visual stimulus ( angular size and angular velocity ) ., Our model goes a step beyond Rinds model , making clear anatomical predictions on how the specific properties of the LGMD arise and showing that a non-linear interaction in the form of a multiplication between stimulus angular size and velocity is not required to account for the known properties of the LGMD neuron ., In our predictions , we test new stimulation protocols that would help us to better understand the f","headings":"Introduction, Results, Discussion, Materials and Methods","abstract":"In principle it appears advantageous for single neurons to perform non-linear operations ., Indeed it has been reported that some neurons show signatures of such operations in their electrophysiological response ., A particular case in point is the Lobula Giant Movement Detector ( LGMD ) neuron of the locust , which is reported to locally perform a functional multiplication ., Given the wide ramifications of this suggestion with respect to our understanding of neuronal computations , it is essential that this interpretation of the LGMD as a local multiplication unit is thoroughly tested ., Here we evaluate an alternative model that tests the hypothesis that the non-linear responses of the LGMD neuron emerge from the interactions of many neurons in the opto-motor processing structure of the locust ., We show , by exposing our model to standard LGMD stimulation protocols , that the properties of the LGMD that were seen as a hallmark of local non-linear operations can be explained as emerging from the dynamics of the pre-synaptic network ., Moreover , we demonstrate that these properties strongly depend on the details of the synaptic projections from the medulla to the LGMD ., From these observations we deduce a number of testable predictions ., To assess the real-time properties of our model we applied it to a high-speed robot ., These robot results show that our model of the locust opto-motor system is able to reliably stabilize the movement trajectory of the robot and can robustly support collision avoidance ., In addition , these behavioural experiments suggest that the emergent non-linear responses of the LGMD neuron enhance the systems collision detection acuity ., We show how all reported properties of this neuron are consistently reproduced by this alternative model , and how they emerge from the overall opto-motor processing structure of the locust ., Hence , our results propose an alternative view on neuronal computation that emphasizes the network properties as opposed to the local transformations that can be performed by single neurons .","summary":"The tiny brains of insects of about 1mm3 smoothly control a flying platform while avoiding obstacles , regulating its distance to objects and search for objects of interest ., This is largely achieved through a complex hierarchical processing of signals from the multitude of ommatidia in their eye to a set of highly specialized neurons that are optimized to respond to specific properties of the visual world ., One of these neurons , the Lobula Giant Movement Detector ( LGMD ) of the locust , has been recently shown to perform a functional multiplication of its synaptic inputs ., If true , that would make the LGMD neuron a unique and highly sophisticated neuron that raises questions about the non-linear operations other neurons in other neuronal systems would be able to perform ., Hence it is crucial to understand its properties , its role in behaviour and to evaluate whether its responses can be explained in simpler terms ., Our results emphasize the role of network architecture and distributed computation as opposed to local complex non-linear computation ., We show that our model reliably reproduces the known properties of the LGMD and can be used to control a high-speed robot .","keywords":"computer science\/natural and synthetic vision, computational biology\/synthetic biology, computer science\/applications, neuroscience\/motor systems, biophysics\/theory and simulation, computer science\/systems and control theory, computational biology\/computational neuroscience, evolutionary biology\/animal behavior, computer science\/numerical analysis and theoretical computing, biochemistry\/bioinformatics, neuroscience\/natural and synthetic vision, biotechnology\/bioengineering, biochemistry\/theory and simulation, computer science\/information technology, computational biology\/systems biology","toc":null}
+{"Unnamed: 0":1165,"id":"journal.pntd.0006588","year":2018,"title":"A real-time medical cartography of epidemic disease (Nodding syndrome) using village-based lay mHealth reporters","sections":"Disease outbreaks in remote rural populations of Africa and elsewhere are often detected late by public health entities ., Reasons include dependence on traditional remedies and healers , low village literacy and knowledge of how to report a disease outbreak , lack of distributed health professionals , poor communication systems and difficulties in transportation of patients to clinics ., Examples abound but come into focus most dramatically from two outbreaks of Ebola hemorrhagic fever ( EHF ) in sub-Saharan countries ., In an example from northern Uganda ( Acholiland ) , several weeks elapsed between the presumptive index case ( August 30 , 2000 ) and virus confirmation ( October 15 , 2000 ) of an outbreak of EHF that persisted for 6 months ( January 9 , 2001 ) and resulted in 425 presumptive case patients 1 ., Second , a major 2014\u20132016 West African EHF epidemic appears to have begun in rural southeastern Guinea but months elapsed before the illness was recognized as EHF , during which the virus spread to multiple neighboring countries ., As of June 2016 , 28 , 616 suspected , probable , and confirmed cases with a total of 11 , 310 deaths were recorded in Guinea , Liberia , and Sierra Leone 2\u20133 ., These examples illustrate the urgent need to develop improved health surveillance of remote rural communities for emerging and extant diseases ., Timely discovery of outbreaks cannot be accomplished by periodic visits by healthcare workers to the scattered villages where disease can begin and spread ., Needed is a health surveillance system that in real-time can pinpoint and track disease cases longitudinally , such that clinical , education and research resources can be rapidly and efficiently dispatched to affected villages ., To this end , we have tested the feasibility of using software-coupled mobile phones operated with minimal training by village-based lay mHealth reporters charged with repeatedly assessing the status of children with a non-infectious and easily recognized idiopathic neurologic disease ( Nodding syndrome ) 4\u20135 ., Their weekly reports , transmitted by simple smartphones , were instantaneously aggregated , analyzed and mapped by data collection centers locally ( Gulu , Uganda ) and remotely ( Oregon , USA ) ., While lay health aides have been used successfully to amplify health coverage in remote regions of Asia ( Nepal , Bangladesh , Indonesia ) 6\u20139 , and mHealth projects are legion 10\u201312 , we are unaware of prior initiatives that have used the reports of lay mHealth operators to populate a real-time medical cartography that can guide clinical , research , and educational interventions to respond to epidemic disease ., We undertook a feasibility study in remote regions of northern Uganda to determine whether minimally trained lay reporters , resident within rural villages , could collect and reliably transmit health-related information at regular intervals using simple smart phones equipped with network-linked software that integrates data sets from multiple settings across time ., The study was not designed or approved to conduct or implement a medical intervention ., This study was conducted in Acholiland , the northernmost region of Uganda ., The region is recovering from a brutal conflict ( 1986\u20132009 ) between the Lord\u2019s Resistance Army and the forces of the Ugandan government , which from approximately 1996 to 2008 required an estimated 2 million people to leave their villages for the relative safety of internal displacement camps ., Focus was placed on families with children with Nodding syndrome ( NS ) , a chronic epileptic encephalopathy of unknown etiology that was regionally epidemic between 1997 and 2012 , with peaks in 2003\u20132005 and 2008 , 5\u20136 years after peaks in the number of wartime conflicts and deaths ., The largest number of NS cases followed 5\u20137 years after the peak of population translocation to internal displacement camps 13 ., Selected for study were 2 rural districts heavily affected by NS , namely Pader and Omoro , including 2 sub-counties , 4 parishes and 10 villages therein ( Table 1 ) ., A manageable sample of households ( n = 240 ) with one or more children with NS was recruited in equal proportion for each district ., Most if not all children had a prior physician-diagnosis of NS that allowed them to receive , under the treatment program of the Ugandan government 14 , a supply of nutritional supplements ( Mamas Nutritional Supplement Ltd , Mbale , Uganda ) and anticonvulsant medication ., A medical diagnostician ( DLK ) physically examined a sample of households reporting existing and newly reported NS cases , the large majority of which had longstanding but unregistered NS ., In agreement with the First International Scientific Meeting of NS in Kampala ( July 30th-August 1st 2012 ) , a probable NS case was identified by an age of onset between 3 and 18 years of age , a frequency on unprovoked head nodding of 5-20\/minute ( triggered by food and\/or cold weather ) and at least one of the following minor criteria:, a ) other neurological abnormalities ( other seizures , cognitive decline\/behavioral problems with or without school dropout , psychiatric symptoms ) ,, b ) developmental abnormalities ( stunting or wasting , delayed sexual or physical development ) and\/or, c ) clustering in space or time with similar cases ., In undertaking this feasibility study , we customized a data collection platform named Magpi that uses mobile phones and real-time cloud-based storage with global positioning system ( GPS ) coordinates and time stamping 15 ., The decision to use Magpi was based on several factors , including its widespread acceptance ( Magpi has been used by organizations such as the WHO , CDC , UNICEF , UNFPA , CARE and the IFRC ) , proven track record and because the software supports:, a ) a wide variety of question types ( text\/numeric entry , multiple choice , etc . ) ;, b ) customized questions;, c ) off-line data collection ( data can be collected off-line and submitted to a central server whenever an active connection becomes available ) ;, d ) GPS stamping and display of data-points on an electronic map; and, e ) instantaneous data integration from multiple users ., In addition , Magpi is, f ) user friendly;, g ) easy to learn;, h ) requires no programing experience ( the software allows non-technically trained users to create data collection forms , messaging systems and interactive reports ) ; and, i ) offers free and paid premium versions with an excellent technical support team ., A pilot study in the USA used Magpi-programmed basic mobile flip phones , while the pilot and feasibility studies in Uganda used similarly programmed smartphones ., The two pilot studies ( USA and Uganda ) were conducted using the free version of Magpi whereas we used the Magpi Pro version ( $500\/month or $417\/month if bought annually ) to operate the feasibility study in Uganda , which required more than 500 survey uploads\/storage per month ., Technical and subject-use issues with Magpi software-enabled equipment were identified by conducting two pilot studies among:, a ) university students in the USA Pacific Northwest and, b ) students attending Uganda\u2019s Gulu University ( GU ) School of Medicine ., Briefly , each student ( n = 12 per study population , with equal numbers of males and females of similar age randomly selected at each site ) was provided with a Magpi-programmed cell phone , instructed on its functions , and asked to respond to a 10-question personal sleep-health survey daily for 14 consecutive days ., After completion , participants were asked to attend a final meeting , share their experiences , return their cell phones , and receive a vendor gift card or small compensation ., While not designed to conduct a scientifically defensible survey of sleep patterns , the data were analyzed using Microsoft Excel to assess sleeping trends across the 14-day span ., Minor technical difficulties ( duplicate questions , duplicate surveys , error messages , etc . ) were referred to Magpi\u2019s technical support team , and modifications were made to the software feature to ensure these issues were eliminated ., The pilot studies also provided valuable information on network connectivity and reporter reliability , perception , and experience in using the application and surveys ., Such information fed into the design of the mHealth feasibility study in Uganda ., The study was carried out in northern Uganda from July to October 2017 ., Eight male and female Ugandan lay mHealth reporters , age 20\u201330 years , were recruited and trained ., The training covered basic concepts of health and disease , the purpose and content of the program , clinical and social aspects of NS , use and maintenance of the equipment ( cell phones , solar batteries , bicycles ) , questionnaire presentation , data collection and submission , home and community entry , informed consent administration and patient confidentiality ., Focus was placed on some typical mistakes , such as mistyping or duplicated forms; time spent collecting and transmitting the surveys; WiFi and Internet accessibility; GPS stamping; and other technical issues such as how to turn off\/on the WiFi\/GPS to help improve cell-phone battery life ., One local field coordinator and two community health nurses ( one from each sub-county ) , in the role of field supervisors , were appointed and registered with the study to closely monitor the training and operations in the field and to provide onsite supervision to each sub-county mHealth team ( 4 reporters per sub-county ) ., mHealth reporters were pilot-tested and evaluated for satisfactory performance before they returned to their respective villages to commence weekly reporting ., Before engaging in data collection , the mHealth reporters signed the Hope for Humans\u2019 Child Protection protocol to ensure adherence with their Child Protection Policy and information confidentiality ., Supportive supervision was made available to mHealth reporters by phone ( 24\/7 ) and in-person every week during the first month of program implementation and biweekly throughout the end of the program ., Biweekly meetings of the lay mHealth operators and field supervisors allowed mHealth staff to share field experiences , lessons learned , challenges , barriers and how they could be overcome ., Payment of mHealth reporters was made in the form of a stipend for training , a regular monthly salary , and small economic incentives ., For instance , provided weekly mHealth data were uploaded on time to the Magpi server , we placed no restrictions on the phones regarding the apps that could be accessed\/installed or the use of airtime for personal communication ., The phones were loaded with a shared bundle ( Kazi , MTN Service Center , Gulu; approx . $97 . 1\/month ) from the local mobile operator MTN which included MTN minutes , minutes to other networks , MTN SMS , SMS to other networks , data\/internet , and free calling among each number in the bundle ., Inexpensive , locally purchased airtime-loaded smartphones ( MTN Smart Mega; approx . $30\/phone ) supported by the local telecommunication company MTN , were individually programmed with Magpi software over 1 week and distributed to the mHealth reporters and field supervisors ., With every phone , a portable power supply consisting of a solar energy panel\/bulb and a battery with dual USB charging ports ( approx . $30\/set ) was also provided ., Paper forms were distributed as a backup alternative to mHealth data collection ( e . g . in case of cell phone loss or failure ) ., In addition , mountain bicycles ( Phoenix single frame , approx . $80\/bike ) and raingear ( raincoats and boots , approx . $11\/set ) were supplied to facilitate access and travel to and within the communities ( typically with poor or no road infrastructure , particularly during the rainy season ) ., Reserve equipment ( two software-equipped smartphones , two solar panels and chargers , and two bicycles ) was also available for immediate use in both sub-counties ., A simple structured questionnaire was designed using the Magpi web-interface to measure the feasibility and practicalities of the Magpi application-based reporting system ., The Magpi application works with the Magpi website to deploy data collection surveys to basic smartphones ., The survey , which was applied once weekly , included information on coded household location , number of NS children\/household , seizure frequency , availability of anti-seizure medication , and injuries and deaths ., After obtaining informed consent from the participant household caregivers , a unique ID code was assigned to each household to preserve confidentiality and anonymity ., Data collection via the Magpi\u2019s mobile platform took place for 12 consecutive weeks , from August 1st throughout October 31st 2017 ., During this period , the mHealth reporters were asked first to complete and store the surveys locally on their mobile devices in the field , and subsequently , depending on WiFi availability , upload them daily or weekly to a secure web-hosted database ., Day-to-day technical support was provided by the local field coordinator and supervisors; support included: troubleshooting the phone system , applications , survey forms and dealing with any queries from the mHealth workers ., Any issues the local research team could not resolve were passed to the program manager at OHSU for investigation ., Online software-integrated village-based survey forms , transmitted by smart phone to the Magpi data management website , were monitored weekly and analyzed by the program manager ( RVA ) located at Oregon Health & Science University ( OHSU ) ., Data were later imported into a local data center established at Gulu University ( GU ) School of Medicine ., During the 12-week data collection period , any mistyping , duplicated reports , data inconsistencies or doubtful information were reported by phone or email to the field coordinator and from there to the corresponding field supervisor for double-checking , fixing , and resending if necessary ., On-site monitoring trips were also organized biweekly during the implementation phase to some randomly chosen households , to ensure compliance with data transmission instructions and consistency across different sites and different data collectors ., While the goal of this intervention was to test the feasibility of NS-related data collection and integration using Magpi , cartographic information from the mHealth syndromic surveillance within the study area was offered to supervisors and health bureaus in support of their public mandate and with the aim of increasing understanding on how convulsive disorders , such as NS , impact families and children ., These data were analyzed qualitatively ( using Magpi and Excel ) and reports were mainly descriptive ., All cell phones were password-protected , and the survey was developed to avoid subject-specific identifiable information ., As mentioned earlier , each household was assigned a specific identification code and each reporter was given a unique identification email ., Hence , the data collected and transmitted daily did not disclose information about specific individuals ., All connections between the cell phone and the server were made using modern encryption methods to transfer data , including Extended Validation Secure Sockets Layer ( EV-SSL ) and AES-256 bit encryption ., In addition , Magpi uses Rackspace Cloud Storage in the U . S . for primary data storage , which has a robust security policy of its own ., Access to the surveys and databases was strictly controlled and only available to authorized personnel ., Administrative rights to view data were given to the leadership at GU ., Neither the analytics dashboard nor the mobile phone forms gave users any access to edit or change data ., This ensured data integrity and eliminated the possibility of data tampering ., A secondary goal of this project was to, a ) incentivize and empower young adults with modest education to raise awareness in their communities of the importance of healthcare , disease early detection and disease monitoring , and, b ) expose GU medical students to community-specific health challenges ., The interaction of mHealth reporters and GU medical students with members of the USA team , GU faculty , and health personnel at the HfH care facility , was expected to raise their interest in pursuing and\/or expanding upon a health-sector career , whether as a research assistant , nurse , or community health worker , thereby helping to alleviate the health-manpower shortage , building capacity and strengthening a weak primary health care system ., Hence , at the end of the program , we evaluated with short questionnaires the impact of this exploratory mHealth study on mHealth reporters ( future healthcare interest ) , medical students ( future research interest ) , and health workers ( acceptability of mHealth and eHealth approaches and compatibility with regional\/national systems ) ., As part of the qualitative evaluation , we sought to elicit the views of participants on their acceptability of the intervention and research procedures , as well as potential demand and integration into primary healthcare settings ., The Ugandan study was reviewed and approved by the Institutional Review Board of St . Mary\u2019s Lacor Hospital in support of Gulu University , the Uganda National Council for Science and Technology , and the Office of the President of Uganda ., The USA and Uganda studies were reviewed and approved by the Institutional Review Board of Oregon Health & Science University ., Written or fingerprinted consent for participation was obtained for each household , and families were informed about their right to withdraw from the study at any time ., At the end of the study , each household received financial compensation ( $10 ) for their time and cooperation ., We used two pilot studies to test the feasibility of using customized network-linked software ( Magpi ) that integrates data sets from multiple geographically dispersed reporters via mobile phones ., The first pilot study employed 12 students from Oregon Health & Science University ( Portland , OR ) and Washington University ( Seattle , WA ) as reporters of their own sleep-related behaviors ., We used Magpi-programmed flip phones to collect and integrate data , develop a real-time sleep pattern topography , and test the hypothesis that 85% of daily sleep surveys , over a 14-day span , would be completed on time ., We reproduced the pilot study in Gulu , northern Uganda , with 12 medical students from Gulu University ( GU ) and basic smartphones locally purchased and supported by the local telecommunication company MTN ., Overall , respondents in the USA completed a mean of 77% of surveys administered , compared to a 96% survey completion rate for Ugandan respondents ., Completion percentages in the USA dropped in the middle of each week and were strongest at the beginning and end of each trial ., In Uganda , completion percentages remained high throughout the entire trial ., The American students averaged 7 . 5 hours of sleep per night , felt well rested on 53% of days , used sleeping aids 21% of nights , and 27% of them reported caffeine use ., Participants in Uganda averaged 6 . 4 hours of sleep per night , felt well rested over 85% of the time , none reported using a sleeping aid , and only 3% reported caffeine use ., Both pilot studies allowed us to conclude that Magpi is an effective and powerful tool to build a real-time geography of health data ., In addition , these studies provided valuable information on reporter consistency and desirable training , as well as detecting minor technical issues that were referred , troubleshot and eliminated by Magpi\u2019s technical support team ., We next used Magpi in combination with the lay operator mHealth network of eight village-based lay mHealth reporters ( vide supra ) to develop a real-time electronic map of child health , injury and illness relating to NS in northern Uganda ., Surveillance data were collected for three consecutive months ( August to October 2017 ) in a convenient sample of villages ( n = 10 ) from two rural sub-counties ( Odek in Omoro District and Awere in Pader District ) heavily affected by NS ( Table 1 ) ., The accuracy and completeness of the surveys submitted were assessed by, a ) daily remote data monitoring and, b ) periodic quality-control visits made to a randomly selected sub-set of households ., One of the major advantages of using Magpi was the ability to visualize , through the Magpi web-interface , outputs such as survey start and end times , average survey completion time , survey completion count , etc . ( Fig 1 ) ., Survey quality checks were thus performed in real-time and inconsistencies were detected , reported , rectified , and cleaned in a timely manner ., The monitoring potential of Magpi also allowed for the rapid recognition of fabricated data , based upon our expectations about the amount of time it would reasonably take to move from household to household , obtain informed consent and complete the survey ., All mHealth workers were informed their movements and data authenticity could be tracked ., Almost all mHealth reporters had experience using smartphone devices prior to the surveillance feasibility project and were not intimidated by the technology ., Half of them felt comfortable using the Magpi app within a week , and none of them found it difficult to use after a month ., Despite the many implementation challenges described below , data collection proceeded in a timely and efficient manner ., Overall , a total of 240 households ( 30 households per mHealth reporter ) and an average of 326 children with NS ( 40 . 7 \u00b1 4 . 57 children per mHealth reporter ) were monitored every week by the mHealth team ., With the exception of one reporter ( targeting Ludok and Olam villages ) who abandoned the program on week 6 due to health-related issues , the mHealth team completed a mean of 97 . 3% of surveys administered per week ( 29 . 2 \u00b1 0 . 63 of 30 surveys assigned per mHealth reporter ) ., All data acquired and integrated into the Magpi database could be exported , with no particular conversion problems , from the platform into statistical ( Excel ) or spatial ( Magpi maps ) analysis software ., To illustrate the system\u2019s interoperability and quality , Fig 2 displays the surveillance area and includes a close-up of two villages ( Paikat Akidi and Bolo Lapeta ) at week-6 of data collection ., With the map interface , it is possible to zoom in and observe the geographic distribution of NS health-related data in a particular village , and even in a specific household ., For instance , the close-up in Fig 2 highlights those households with at least one child with NS that did not have anti-seizure medication ( Fig 2E1 , green color ) , was injured ( Fig 2E2 , green color ) or died ( Fig 2E3 ) that week ., The Magpi interface also made it possible to visualize NS health-related data over a defined period of time ( Fig 3 ) with the goal to assess fluctuations and carry out temporal interpretations ., However , after comparing our maps ( Fig 3 ) and the data collected ( Table 2 ) , it became readily apparent that many geotracers malfunctioned or , most likely , many remote areas had weak or no coverage of cellular communication , causing limitations in acquiring GPS stamps and compromising the ability to produce maps using GPS coordinates ., While the purpose of this study was to test the feasibility of NS-related data collection and integration using Magpi , we used descriptive statistical analyses to assess the health impact of NS with the aim of guiding future clinical , educational and research interventions ., Of the 326 affected children monitored by the mHealth team , 17 died over the 12-week study time frame and 22 siblings were reported to have nodding spells for the first time ., Lack of appropriate anti-seizure medication and injuries were also registered on Magpi 688 times and 186 times , respectively ( S1 Tables ) ., After normalizing the number of NS children monitored per village to 100% for comparison purposes ( Fig 4 , red section in each pie chart ) , several findings emerged ., For instance , access to anti-seizure medication was extremely limited in Awere sub-county , particularly in Paikat Akidi , Bolo Juklebi\/Bolo Agweng , and Bolo Lapeta , where the percentage of children without medication ( Fig 4 , blue section in each pie chart ) was 585 . 1% , 341 . 6% , and 233 . 3% , respectively ., We would like to highlight that the pie charts in Fig 4 display health-related information across the 12-week study and percentages above 100% are indicative of repeated ( the sum of ) health outcomes ., For instance , the blue pie chart sections with percentages above 100% in the Paikat Akidi , Bolo Juklebi\/Bolo Agweng , and Bolo Lapeta graphs denote that several children with NS in those villages did not have access to medication for a number of weeks ., However , the charts do not allow the reader to discern whether , for example , 10 children did not have medication for 1 week or whether 1 child did not have medication for 10 weeks ( this information is made available in the weekly S1 Tables ) ., The goal of the pie charts was simply to provide a quick snap shot of those villages that required immediate attention ., In the particular case of lack of anti-seizure medication , higher percentages indicated a greater need for medication supply ., Along the same lines , villages like Paikat Akidi and Ajan\/Akoyo had the highest percentage of injured children ( 146 . 3% and 75 . 1% , respectively ) , compared to only 11 . 8% in Lukee ., The highest mortality percentages were associated with Atede West ( 28 . 4% ) and Ajan ( 7 . 3% ) ., Ajan was also the village where respondents reported a surprisingly large percentage of children with nodding spells for the first time ( 16 . 9% ) , alongside Paikat Akidi ( 16 . 0% ) and Lukee ( 8 . 8% ) ., While most of these newly identified subjects proved to be longstanding NS cases in the sample given a medical evaluation , there is a possibility that the one potentially new case portends others ., The possibility that the NS epidemic has not ended merits prioritized study ., While we noticed some improvement on a few health outcomes ( e . g . provision of medication , reduction of injuries , clinical referrals , etc . ) across the 12-week study , such progress resulted exclusively from the cooperative effort by individuals on the mHealth team ( including members of the local non-profit organization Hope for Humans ) , who organized themselves to further serve their communities beyond the scope of the mHealth project ., Physical examination of the sample of newly reported and existing NS cases confirmed a diagnosis of NS ., On examination , children newly reported by mHealth workers to have NS were found to have longstanding disease ., Only one new case of Suspected NS was found in the sample , a boy aged 3 years with an older brother with registered NS ., Around 2 . 5 years of age , at the sight of food , the new case developed episodes of head nodding lasting for minutes ., The child was unresponsive during these periods and usually fatigued and irritable thereafter ., Otherwise , on examination , he was grossly neurologically intact ., The boy was registered with the Ministry of Health as a Suspected NS case and started on anti-seizure medication by a government healthcare worker ., Other children that had not been registered with NS and who were identified as newly reported cases in the mHealth survey were referred to a primary health center for observation , NS confirmation and treatment ., The foregoing observations were made in the face of numerous technical , logistical and institutional problems that were met with innovative solutions but nevertheless substantially delayed progress ., The most common technical issues were frequent power cuts , poor network coverage , slow upload speeds and unreliable GPS satellites ., Inconsistent connectivity led to difficulties in survey uploading ( e . g . , some mHealth workers reported traveling to a specific hotspot or even climbing a particular tree to access satisfactory signal strength and network coverage ) ., Instrument charging issues were traceable to an inability to charge phones in the field , failure to charge overnight , and short battery life of cell phones possibly exacerbated by heat ., On the first day of September , all mobile phones ran out of data because the network provider failed to renew the monthly phone bundle on time ., Although the surveys collected during this period were stored on the memory of the cell phone and could have been uploaded later , some reporters stopped working when they realized their data bundles were exhausted ., Other reporters used hard-copy forms and entered the data in the Magpi app later ., This last practice resulted in no data loss but large single entries ( e . g . , > 10 households ) with only one GPS stamp ., Thanks to ongoing remote monitoring , the program manager discovered there were no entries on the Magpi server that day and notified the problem to the field coordinator for immediate clarification ., Occasional technical problems with Magpi software and human errors ( e . g . , duplicates , outliers , etc . ) during daily data collection and transmission were also detected and rapidly addressed ., Some technical problems were exacerbated by logistical challenges ., Some monitored households had to be replaced due to accessibility issues and poor road conditions during the rainy season ., Others were replaced because of outdated household records ( deceased children , relocation ) ., A handful of householders showed some reluctance to consent and required a follow-up visit by the field supervisor ., Family absences during the harvest season forced mHealth reporters to follow the subjects to their gardens ., This not only slowed the process of data collection but also changed some GPS coordinates , introducing undesired variability and therefore hindering the ability to produce maps using GPS stamps ., In addition , our research partner Hope for Humans ceased Ugandan operations on December 30th , 2017 ., Lastly , research performed by U . S . researchers abroad poses many administrative challenges including registration , research ethics training , acquisition of research approvals from university human subjects review boards , approvals from local ( Gulu ) , national ( Uganda ) and international ( USA ) agencies , and requirements for foreign investigators that are not user-friendly , lengthy and time-consuming ., Institutional inefficiency and suboptimal cooperation consumed more than half of the 2-year grant that funded this feasibility study ., All mHealth workers rated the intervention , mHealth team , and outcomes very positively ., The resulting gain in skills made them feel confident , enthusiastic and motivated to participate in future healthcare programs ., Everyone ( 100% ) expressed their desire to help people be healthy ( e . g . , as doctors , nurses , community health workers , etc . ) in the future ., Three of 11 ( 27 . 3% ) expressed that they would also like to work in technology ( e . g . , cell phone manufacturing ) ; two of 11 ( 18 . 2% ) stated they would like to \u201csell things\u201d; and the 2 field supervisors indicated a desire for further studies to improve their health careers ( the two field supervisors have been admitted into the Lacor School of Nursing and Midwifery in Gulu ) ., Everyone ( 100% ) stated that money was a barrier to fulfilling their respective dreams ., One mHealth reporter added that she didn\u2019t know where to start , another expressed the lack of inadequate guidance and career mentorship , and a third added he did not have enough time , appropriate means or support from the community ., GU medical students also expressed some interest in research and future research opportunities ., Healthcare providers and professionals from Gulu University , St . Mary Lacor Hospital and Awere Health Center III showed enthusiastic ","headings":"Introduction, Methods, Results, Discussion","abstract":"Disease surveillance in rural regions of many countries is poor , such that prolonged delays ( months ) may intervene between appearance of disease and its recognition by public health authorities ., For infectious disorders , delayed recognition and intervention enables uncontrolled disease spread ., We tested the feasibility in northern Uganda of developing real-time , village-based health surveillance of an epidemic of Nodding syndrome ( NS ) using software-programmed smartphones operated by minimally trained lay mHealth reporters ., We used a customized data collection platform ( Magpi ) that uses mobile phones and real-time cloud-based storage with global positioning system coordinates and time stamping ., Pilot studies on sleep behavior of U . S . and Ugandan medical students identified and resolved Magpi-programmed cell phone issues ., Thereafter , we deployed Magpi in combination with a lay-operator network of eight mHealth reporters to develop a real-time electronic map of child health , injury and illness relating to NS in rural northern Uganda ., Surveillance data were collected for three consecutive months from 10 villages heavily affected by NS ., Overall , a total of 240 NS-affected households and an average of 326 children with NS , representing 30 households and approximately 40 NS children per mHealth reporter , were monitored every week by the lay mHealth team ., Data submitted for analysis in the USA and Uganda remotely pinpointed the household location and number of NS deaths , injuries , newly reported cases of head nodding ( n = 22 ) , and the presence or absence of anti-seizure medication ., This study demonstrates the feasibility of using lay mHealth workers to develop a real-time cartography of epidemic disease in remote rural villages that can facilitate and steer clinical , educational and research interventions in a timely manner .","summary":"Absence of health monitoring of rural populations in low-income countries allows diseases to emerge and spread for months before their detection by public health authorities ., We tested the feasibility of using smartphones operated by lay villagers to report health information in real time from the populations in which they reside ., Eight young lay adults from remote rural regions of northern Uganda were trained to administer questions and transmit answers using pre-programmed mobile phones ., Weekly , over a 3-month period , each lay reporter monitored an average of 40 children suffering from an epileptic disorder known as Nodding syndrome ( NS ) ., For each child , episodes of head nodding , convulsions , injuries , deaths and availability of anti-seizure medication were reported weekly and the data instantaneously assembled by customized software for analysis in Uganda and the USA ., This system not only provided a real-time map of the health status of children with established NS but also discovered children previously unknown to have head nodding ., While logistical hurdles had to be overcome , the study demonstrates the feasibility of using lay workers operating software-equipped mobile smartphones to build a current and continuously updatable medical geography of the rural populations in which they reside ., Wide application of such systems could result in the early detection and control of disease .","keywords":"medicine and health sciences, engineering and technology, geographical locations, uganda, cell phones, pediatrics, research design, surveys, infectious disease control, africa, research and analysis methods, infectious diseases, computer and information sciences, epidemiology, pilot studies, communication equipment, people and places, infectious disease surveillance, survey research, equipment, computer software, disease surveillance","toc":null}
+{"Unnamed: 0":34,"id":"journal.pcbi.1005542","year":2017,"title":"A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements","sections":"Stochastic neural dynamics mediate between the underlying biophysical and physiological properties of a neural system and its computational and cognitive properties ( e . g . 1\u20134 ) ., Hence , from a computational perspective , we are often interested in recovering the neural network dynamics of a given brain region or neural system from experimental measurements ., Yet , experimentally , we commonly have access only to noisy recordings from a relatively small proportion of neurons ( compared to the size of the brain area of interest ) , or to lumped surface signals like local field potentials or the EEG ., Inferring from these the computationally relevant dynamics is therefore not trivial , especially since both the recorded signals ( e . g . , spike sorting errors; 5 ) as well as the neural system dynamics itself ( e . g . , stochastic synaptic release; 6 ) come with a good deal of noise ., The stochastic nature of neural dynamics has , in fact , been deemed crucial for perceptual inference and decision making 7\u20139 , and potentially helps to avoid local minima in task learning or problem solving 10 ., Speaking in statistical terms , model-free techniques which combine delay embedding methods with nonlinear basis expansions and kernel techniques have been one approach to the problem 11; 12 ., These techniques provide informative lower-dimensional visualizations of population trajectories and ( local ) approximations to the neural flow field , but they may highlight only certain , salient aspects of the dynamics ( but see 13 ) and , in any case , do not directly return distribution generating equations or underlying computations ., Alternatively , state space models , a statistical framework particularly popular in engineering and ecology ( e . g . 14 ) , have been adapted to extract lower-dimensional , probabilistic neural trajectory flows from higher-dimensional recordings 15\u201325 ., State space models link a process model of the unobserved ( latent ) underlying dynamics to the experimentally observed time series via observation equations , and differentiate between stochasticity in the process and observation noise ( e . g . 26 ) ., So far , with few exceptions ( e . g . 23; 27 ) , these models assumed linear latent dynamics , however ., Although this may often be sufficient to yield lower-dimensional smoothed trajectories , it implies that the recovered dynamical model may be less apt for capturing highly nonlinear dynamical phenomena in the observations , and will by itself not be powerful enough to reproduce a range of important dynamical and computational processes in the nervous system , among them multi-stability which has been proposed to underlie neural activity during working memory 28\u201332 , limit cycles ( stable oscillations ) , or chaos ( e . g . 33 ) ., Here we derive a new state space algorithm based on piecewise-linear ( PL ) recurrent neural networks ( RNN ) ., It has been shown that RNNs with nonlinear activation functions can , in principle , approximate any dynamical systems trajectory or , in fact , dynamical system itself ( given some general conditions; 34\u201336 ) ., Thus , in theory , they are powerful enough to recover whatever dynamical system is underlying the experimentally observed time series ., Piecewise linear activation functions , in particular , are by now the most popular choice in deep learning algorithms 37\u201339 , and considerably simplify some of the derivations within the state space framework ( as shown later ) ., They may also be more apt for producing working memory-type activity with longer delays if for some units the transfer function happens to coincide with the bisectrix ( cf . 40 ) , and ease the analysis of fixed points and stability ., We then apply this newly derived algorithm to multiple single-unit recordings from the rat prefrontal cortex obtained during a classical delayed alternation working memory task 41 ., This article considers simple discrete-time piecewise-linear ( PL ) recurrent neural networks ( RNN ) of the form, zt=Azt\u22121+Wmax{0 , zt\u22121\u2212\u03b8}+Cst+\u03b5t , \u03b5t\u223cN ( 0 , \u03a3 ) ,, ( 1 ), where zt = ( z1t\u2026zMt ) T is the ( M\u00d71 ) -dimensional ( latent ) neural state vector at time t = 1\u2026T , A = diag ( a11\u2026aMM ) is an M\u00d7M diagonal matrix of auto-regression weights , W = ( 0 w12\u2026w1M , w21 0 w23\u2026w2M , w31 w32 0 w34\u2026w3M , \u2026 ) is an M\u00d7M off-diagonal matrix of connection weights , \u03b8 = ( \u03b81\u2026\u03b8M ) T is a set of ( constant ) activation thresholds , st is a sequence of ( known ) external K-dimensional inputs , weighted by ( M\u00d7K ) matrix C , and \u03b5t denotes a Gaussian white noise process with diagonal covariance matrix \u03a3=diag ( \u03c3112\u2026\u03c3MM2 ) ., The max-operator is assumed to work element-wise ., In physiological terms , latent variables zmt are often interpreted as a membrane potential ( or current ) which gives rise to spiking activity as soon as firing threshold \u03b8m is exceeded ( e . g . 42 , 43 ) ., According to this interpretation , the diagonal elements in A may be seen as the neurons\u2019 individual membrane time constants , while the off-diagonal elements in W represent the between-neuron synaptic connections which multiply with the presynaptic firing rates ., In statistical terms , ( 1 ) has the form of an auto-regressive model with a nonlinear basis expansion in variables zmt ( e . g . 44;45 ) , which retains linearity in parameters W for ease of estimation ., Restricting model parameters , e . g . \u03a3 , to be of diagonal form , is common in such models to avoid over-specification and help identifiabiliy ( e . g . 26; 46; see also further below ) ., For instance , including a diagonal in W would be partly redundant to parameters A ( strictly so in a pure linear model ) ., For similar reasons , and for ease of presentation , in the following we will focus on a model for which K = M and C = I ( i . e . , no separate scaling of the inputs ) , although the full model as stated above , Eq 1 , was implemented as well ( and code for it is provided; of course , the case K>M could always be accommodated by pre-multiplying st by some predefined matrix C , obtained e . g . by PCA on the input space ) ., While different model formulations are around in the computational neuroscience and machine learning literature , often they may be related by a simple transformation of variables ( see 47 ) and , as long as the model is powerful enough to express the whole spectrum of basic dynamical phenomena , details of model specification may also not be overly crucial for the present purposes ., A particular advantage of the PLRNN model is that all its fixed points can be obtained easily analytically by solving ( in the absence of external input ) the 2M linear equations, z*= ( A+W\u03a9\u2212I ) \u22121W\u03a9\u03b8 ,, ( 2 ), where \u03a9 is to denote the set of indices of units for which we assume zm \u2264 \u03b8m , and W\u03a9 the respective connectivity matrix in which all columns from W corresponding to units in \u03a9 are set to 0 ., Obviously , to make z* a true fixed point of ( 1 ) , the solution to ( 2 ) has to be consistent with the defined set \u03a9 , that is z*m \u2264 \u03b8m has to hold for all m \u2208 \u03a9 and z*m > \u03b8m for all m \u2209 \u03a9 ., For networks of moderate size ( say M<30 ) it is thus computationally feasible to explicitly check for all fixed points and their stability ., For estimation from experimental data , latent state model ( 1 ) is then connected to some N-dimensional observed vector time series X = {xt} via a simple linear-Gaussian model ,, xt=B\u03d5 ( zt ) +\u03b7t , \u03b7t\u223cN ( 0 , \u0393 ) ,, ( 3 ), where \u03d5 ( zt ) \u2254 max{0 , zt\u2212\u03b8} , {\u03b7t} is the ( white Gaussian ) observation noise series with diagonal covariance matrix \u0393=diag ( \u03b3112\u2026\u03b3NN2 ) , and B an N\u00d7M matrix of regression weights ., Thus , the idea is that only the PL-transformed activation \u03d5 ( zt ) reaches the \u2018observation surface\u2019 as , e . g . , with spiking activity when the underlying membrane dynamics itself is not visible ., We further assume for the initial state ,, z1\u223cN ( \u03bc0+s1 , \u03a3 ) ,, ( 4 ), which has , for simplicity , the same covariance matrix as the process noise in general ( reducing the number of to be estimated parameters ) ., In the case of multiple , temporally separated trials , we allow each one to have its own individual initial condition \u03bck , k = 1\u2026K ., The general goal here is to determine both the model\u2019s unknown parameters \u039e = {\u03bc0 , A , W , \u03a3 , B , \u0393} ( assuming fixed thresholds \u03b8 for now ) as well as the unobserved , latent state path Z \u2254 {zt} ( and its second-order moments ) from the experimentally observed time series {xt} ., These could be , for instance , properly transformed multivariate spike time series or neuroimaging data ., This is accomplished here by the Expectation-Maximization ( EM ) algorithm which iterates state ( E ) and parameter ( M ) estimation steps and is developed in detail for model ( 1 ) and ( 3 ) in the Methods ., In the following I will first discuss state and parameter estimation separately for the PLRNN , before describing results from the full EM algorithm in subsequent sections ., This will be done along two toy problems , a higher-order nonlinear oscillation ( stable limit cycle ) , and a simple working memory paradigm in which one of two discrete stimuli had to be retained across a temporal interval ., Finally , the application of the validated PLRNN EM algorithm will be demonstrated on multiple single-unit recordings obtained from rats on a standard working memory task ( delayed alternation; data from 41 , kindly provided by Dr . James Hyman , University of Nevada , Las Vegas ) ., The latent state distribution , as explained in Methods , is a high-dimensional ( piecewise ) Gaussian mixture with the number of components growing as 2T\u00d7M with sequence length T and number of latent states M . Here a semi-analytical , approximate approach was developed that treats state estimation as a combinatorial problem by first searching for the mode of the full distribution ( cf ., 16; 48; in contrast , e . g . , to a recursive filtering-smoothing scheme that makes local ( linear-Gaussian ) approximations , e . g . 15; 26 ) ., This approach amounts to solving a high ( 2M\u00d7T ) -dimensional piecewise linear problem ( due to the piecewise quadratic , in the states Z , log-likelihood Eqs 6 and 7 ) ., Here this was accomplished by alternating between ( 1 ) solving the linear set of equations implied by a given set of linear constraints \u03a9 \u2254 { ( m , t ) |zmt \u2264 \u03b8m} ( cf . Eq 7 in Methods ) and ( 2 ) flipping the sign of the constraints violated by the current solution z* ( \u03a9 ) to the linear equations , thus following a path through the ( M\u00d7T ) -dimensional binary space of linear constraints using Newton-type iterations ( similar as in 49 , see Methods; note that here the \u2018constraints\u2019 are not fixed as in quadratic programming problems ) ., Given the mode and state covariance matrix ( evaluated at the mode from the negative inverse Hessian ) , all other expectations needed for the EM algorithm were then derived analytically , with one exception that was approximated ( see Methods for full details ) ., The toy problems introduced above were used to assess the quality of these approximations ., For the first toy problem , an order-15 limit cycle was produced with a PLRNN consisting of three recurrently coupled units , inputs to units #1 and #2 , and parameter settings as indicated in Fig 1 and provided Matlab file \u2018PLRNNoscParam\u2019 ., The limit cycle was repeated for 50 full cycles ( giving 750 data points ) and corrupted by process noise ( cf . Fig 1 ) ., These noisy states ( arranged in a ( 3 x 750 ) matrix Z ) were then transformed into a ( 3 x 750 ) output matrix X , to which observation noise was added , through a randomly drawn ( 3 x 3 ) regression weight matrix B . State estimation was started from a random initial condition ., True ( but noise-corrupted ) and estimated states for this particular problem are illustrated in Fig 1A , indicating a tight fit ( although some fraction of the linear constraints were still violated , \u22480 . 27% in the present example and <2 . 3% in the working memory example below; see Methods on this issue ) ., To examine more systematically the quality of the approximate-analytical estimates of the first and second order moments of the joint distribution across states z and their piecewise linear transformations \u03d5 ( z ) , samples from p ( Z|X ) were simulated using bootstrap particle filtering ( see Methods ) ., Although these simulated samples are based only on the filtering ( not the smoothing ) steps ( and ( re- ) sampling schemes may have issues of their own; e . g . 26 , analytical and sampling estimates were in tight agreement , correlating almost to 1 for this example , as shown in Fig 2 ., Fig 3A illustrates the setup of the \u2018two-cue working memory task\u2019 , chosen for later comparability with the experimental setup ., A 5-unit PLRNN was first trained by conventional gradient descent ( \u2018real-time recurrent learning\u2019 ( RTRL ) , see 50; 51 ) to produce a series of six 1\u2019s on unit #3 and six 0\u2019s on unit #4 five time steps after an input ( of 1 ) occurred on unit #1 , and the reverse pattern ( six 0\u2019s on unit #3 and six 1\u2019s on unit #4 ) five time steps after an input occurred on unit #2 ., A stable PLRNN with a reasonable solution to this problem was then chosen for further testing the present algorithm ( cf . Fig 3C ) ., ( While the RTRL approach was chosen to derive a working memory circuit with reasonably \u2018realistic\u2019 characteristics like a wider distribution of weights , it is noted that a multi-stable network is relatively straightforward to construct explicitly given the analytical accessibility of fixed points ( see Methods ) ; for instance , choosing \u03b8 = ( 0 . 5 0 . 5 0 . 5 0 . 5 2 ) , A = ( 0 . 9 0 . 9 0 . 9 0 . 9 0 . 5 ) , and W = ( 0 \u03c9 \u2212 \u03c9 \u2212 \u03c9 \u2212 \u03c9 , \u03c9 0 \u2212 \u03c9 \u2212 \u03c9 \u2013 \u03c9 , \u2212 \u03c9 \u2212 \u03c9 0 \u03c9 \u2013 \u03c9 , \u2212 \u03c9 \u2212 \u03c9 \u03c9 0 \u2212 \u03c9 , 11110 ) with \u03c9 = 0 . 2 , yields a tri-stable system ., ) Like for the limit cycle problem before , the number of observations was taken to be equal to the number of latent states , and process and observation noise were added ( see Fig 4 and Matlab file \u2018PLRNNwmParam\u2019 for specification of parameters ) ., The system was simulated for 20 repetitions of each trial type ( i . e . , cue-1 or cue-2 presentations ) with different noise realizations and each \u2018trial\u2019 started from its own initial condition \u03bck ( see Methods ) , resulting in a total series length of T = 20\u00d72\u00d720 = 800 ( although , importantly , in this case the time series consisted of distinct , temporally segregated trials , instead of one continuous series , and was treated as such an ensemble of series by the algorithm ) ., As before , state estimation started from random initial conditions and was provided with the correct parameters , as well as with the observation matrix X . While Fig 3B illustrates the correlation between true ( i . e . , simulated ) and estimated states across all trials and units , Fig 3C shows true and estimated states for a representative cue-1 ( left ) and cue-2 ( right ) trial , respectively ., Again , our procedure for obtaining ( or approximating ) the maximum a-posteriori ( MAP ) estimate of the state distribution appears to work quite well ( in general , only locally optimal or approximate solutions may be achieved , however , and the algorithm may have to be repeated with different state initializations; see Methods ) ., Given the true states , how well would the algorithm retrieve the parameters of the PLRNN ?, To assess this , the actual model states ( which generated the observations X ) from simulation runs of the oscillation and the working memory task described above were provided as initialization for the E-step ., Based on these , the algorithm first estimated the state covariances for z and \u03d5 ( z ) ( see above ) , and then the parameters in a second step ( i . e . , the M-step ) ., Note that the parameters can all be computed analytically given the state distribution ( see Methods ) , and , provided the state covariance matrices ( summed across time ) as required in Eq 17A , 17D and 17F are non-singular , have a unique solution ., Hence , in this case , any misalignment with the true model parameters can only come from one of two sources:, i ) estimation was based on one finite-length noisy realization of the PLRNN process ,, ii ) all second order moments of the state distribution were still estimated based on the true state vectors ., However , as can be appreciated from Fig 1B ( oscillation ) and Fig 4 ( working memory ) , for the two ( relatively low-noise ) example scenarios studied here , all parameter estimates still agreed tightly with those describing the true underlying model ., In the more general case where both the states and the parameters are unknown and only the observations are given , note that the model as stated in Eqs 1 & 3 is over-specified as , for instance , at the level of the observations , additional variance placed into \u03a3 may be compensated for by adjusting \u0393 accordingly , and by rescaling W and , within limits , A ( cf . 52; 53 ) ., In the following we therefore always arbitrarily fixed \u03a3 ( to some scalar; see Methods ) , as common in many latent variable models ( like factor analysis ) , including state space models ( e . g . 27; 46 ) ., It may be worth noting here that the relative size of \u03a3 vs . \u0393 determines how much weight is put on temporal consistency among states ( \u201c\u03a3<\u0393\u201d ) vs . fitting of the observations ( \u201c\u03a3>\u0393\u201d ) within the likelihood , Eq 5 ., The observations above confirm that our algorithm finds satisfactory approximations to the underlying state path and state covariances when started with the right parameters , and\u2014vice versa\u2014identifies the correct parameters when provided with the true states ., Indeed , the M-step , since it is exact , can only increase the expected log-likelihood Eq 5 with the present state expectancies fixed ., However , due to the systems piecewise-defined discrete nature , modifying the parameters may lead to a new set of constraint violations , that is may throw the system into a completely different linear subspace which may imply a decrease in the likelihood in the E-step ., It is thus not guaranteed that a straightforward EM algorithm converges ( cf . 54; 55 ) , or that the likelihood would even monotonically increase with each EM iteration ., To examine this issue , full EM estimation of the WM model ( as specified in Fig 4 , using N = 20 outputs in this case ) was run 240 times , starting from different random , uniformly distributed initializations for the parameters ., Fig 5B ( \u0394t = 0 ) gives , for the five highest likelihood solutions across all 240 runs ( Fig 5A ) , the mean squared error ( MSE ) avg ( xit\u2212x^it ) 2 between actual neural observations xit and model predictions x^it , which is close to 0 ( and , correspondingly , correlations between predicted and actual observations were close to 1 ) ., With respect to the inferred states , note that estimated and true model states may not be in the same order , as any permutation of the latent state indices together with the respective columns of observation matrix B will be equally consistent with the data X ( see also 27 ) ., For the WM model examined here , however , partial order information is implicitly provided to the EM algorithm through the definition of unit-specific inputs sit ., For the present example , true and estimated states for the highest likelihood solution were nicely linearly correlated for all 5 latent variables ( Fig 6 ) , but some of the regression slopes significantly differed from 1 , indicating a degree of freedom in the scaling of the states ., Note that if the system were strictly linear , the states would be identifiable only up to a linear transformation in general , since any multiplication of the latent states by some matrix V could essentially be reversed at the level of the outputs by back-multiplying B with V-1 ( cf . 27 ) ., Likewise , in the present piecewise linear system , one may expect that there is a class of piecewise-linear transformations of the states which is still compatible with the observed outputs , and hence that the model is only identifiable up to this class of transformations ( a general issue with state space models , of course , not particular to the present one; cf . 53 ) ., However , this might not be a too serious issue , if one is primarily interested in the latent dynamics ( rather than in the exact parameters ) ., Fig 7 illustrates the distribution of initial and final parameter estimates around their true values across all 240 runs ( before and after reordering the estimated latent states based on the rotation that would be required for achieving the optimal mapping onto the true states , as determined through Procrustes analysis ) ., Fig 7 reveals that, a ) the EM algorithm does clearly improve the estimates and, b ) these final estimates seemed to be relatively \u2018unbiased\u2019 ( i . e . , with deviations centered around 0 ) ., How do the computational costs of the algorithm grow as the number of latent variables in the model is increased ?, As pointed out in Paninski et al . 16 , exploiting the block-tridiagonal nature of the covariance matrices , the numerical operations within one iteration of the state inference algorithm ( i . e . , solving \u2202Q\u03a9* ( Z ) \/\u2202Z=0 , Eq 7 ) can be done in linear , O ( M\u00d7T ) , time , just like with the Kalman filter ( due to the model\u2019s Markov properties , full inversion of the Hessian is also not necessary to obtain the relevant moments of the posterior state distribution ) ., This leaves open the question of how many more mode search iterations , i . e . linear equation solving ( Eq 7 ) and constraint-flipping ( vector d\u03a9 ) steps , are required as the number of latent variables ( through either M or T ) increases ., The answer is provided in Fig 8A which is based on the experimental data set discussed below ., Although a full computational complexity analysis is beyond the scope of this paper , at least for these example data ( and similar to what has sometimes been reported for the somewhat related Simplex algorithm; 56 ) , the increase with M appears to be at most linear ., Likewise , the total number of iterations within the full EM procedure , i . e . the number of mode-search steps summed across all EM iterations ( thus reflecting the overall scaling of the full algorithm ) , was about linear ( Fig 8B; in this case , single-constraint instead of complete flipping ( see Methods ) was used which , of course , increases the overall number of iterations but may perform more stably; note that in general the absolute number of iterations will also depend on detailed parameter settings of the algorithm , like the EM convergence criterion and error tolerance ) ., Thus , overall , the present state inference algorithm seems to behave quite favorably , with an at most linear increase in the number of iterations required as the number of latent variables is ramped up ., I next was interested in what kind of structure the present PLRNN approach would retrieve from experimental multiple ( N = 19 ) single-unit recordings obtained while rats were performing a simple and well-examined working memory task , namely spatial delayed alternation 41 ( see Methods ) ., ( Note that in the present context this analysis is mainly meant as an exemplification of the current model approach , not as a detailed examination of the working memory issue itself . ), The delay was always initiated by a nose poke of the animal into a port located on the side opposite from the response levers , and had a minimum length of 10 s ., Spike trains were first transformed into kernel density estimates by convolution with a Gaussian kernel ( see Methods ) , as done previously ( e . g . 12; 57; 58 ) , and binned with 500 ms resolution ., This also renders the observed data more suitable to the Gaussian noise assumptions of the present observation model , Eq 3 ., Models with different numbers of latent states were estimated , with M = 5 or M = 10 chosen for the examples below ., Periods of cue presentation were indicated to the model by setting external inputs sit = 1 to units i = 1 ( left lever ) or i = 2 ( right lever ) for three 500 ms time bins surrounding the event ( and sit = 0 otherwise ) , and the response period was indicated by setting s3t = 1 for 3 consecutive time bins irrespective of the correct response side ( i . e . , non-discriminatively ) ., The EM algorithm was started from a range of different initializations of the parameters ( including thresholds \u03b8 ) , and the 5 highest likelihood solutions were considered further for the examples below ., Fig 10A gives the log-likelihoods across EM iterations for these 5 highest-likelihood solutions ( starting from 36 different initializations ) for the M = 5 model ., Interestingly , there were single neurons whose responses were predicted quite well by the estimated model despite large trial-to-trial fluctuations ( Fig 9A , top row ) , while there were others with similar trial-to-trial fluctuations for which the model only captured the general trend ( Fig 9A , bottom row; to put this into context , Fig 9B gives the full distribution of correlations between actual and predicted observations across all 19 neurons ) ., This may potentially indicate that trial-to-trial fluctuations in single neurons could be for very different reasons: For instance , in those cases where strongly varying single unit responses are nevertheless tightly reproduced by the estimated model , a larger proportion of their trial-to-trial fluctuations may have been captured by the latent state dynamics , ultimately rooted in different ( trial-unique ) initializations of the states ( recall that the states are not completely free to vary in accounting for the observations , but are constrained by the model\u2019s temporal consistency requirements ) ., In contrast , when only the average trend is captured , the neuron\u2019s trial-to-trial fluctuations may be more likely to represent true intrinsic ( or measurement ) noise sources that the model\u2019s deterministic part cannot account for ., In practice , such conclusions would have to be examined more carefully to rule out that no other factors in the estimation procedure , like different local maxima , initializations , or over-fitting issues ( see below ) , could account for these differences ., Although this was not further investigated here , this observation nevertheless highlights the potential of ( nonlinear ) state space models to possibly provide new insights also into other long-standing issues in neurophysiology ., Cross-validation is an established means to address over-fitting 45 , although due to the presence of both unknown parameters and unknown states , its application to state space models and its interpretation in this context may be a bit less straightforward ., Here the cross-validation error was first assessed by leaving out each of the 14 experimental trials in turn , estimating model parameters \u039e from the remaining 13 trials , inferring states zt given these parameters on the left-out trial , and computing the squared prediction errors ( xit\u2212x^it ) 2 between actual neural observations xit and model predictions x^it on the left-out trial ., As shown in Fig 10B , this measure steadily ( albeit sub-linearly ) decreases as the number M of latent states in the model is increased ., At first sight , this seems to suggest that with M = 5 or even M = 10 the over-fitting regime is not yet reached ., On the other hand , the latent states are , of course , not completely fixed by the transition equations , but have some freedom to vary as well ( the true effective degrees of freedom for such systems are in fact very hard to determine , cf . 59 ) ., Hence , we also examined the \u0394t-step-ahead prediction errors , that is , when the transition model were iterated \u0394t steps forward in time , and x^i , t+\u0394t=bi\u22c5\u03d5 ( z^t+\u0394t ) estimated from the deterministically predicted states z^t+\u0394t=H\u0394t ( Ezt ) ( with H\u0394t the \u0394t-times iterated map H ( zt ) = Azt + W\u03d5 ( zt ) + Cst ) , not from the directly inferred states ( that is , predictions were made on data points which were neither used to estimate parameters nor to infer the current state ) ., These curves are shown for \u0394t = 1 and \u0394t = 3 in Fig 10C , and confirm that M = 5 might be a reasonable choice at which over-fitting has not yet ensued ., ( Alternatively , the predictive log-likelihood , logp ( Xtest|\u039e^train ) =log\u222bp ( Xtest|Z^ ) p ( Z^|\u039e^train ) dZ^ , may be used for model selection ( i . e . , choice of M ) , with p ( Z^|\u039e^train ) either approximated through the E-step algorithm ( with all X-dependent terms removed ) , or bootstrapped by generating Z^-trajectories from the model with parameters \u039e^train ( note that this is different from particle filtering since p ( Z^|\u039e^train ) does not depend on test observations Xtest ) ., This is of course , however , computationally more costly to evaluate than the \u0394t-step-ahead prediction error ., ) Fig 11 shows trial-averaged latent states for both left- and right-lever trials , illustrated in this case for one of the five highest likelihood solutions ( starting from 100 different initializations ) for the M = 10 model ., Recall that the first 3 PLRNN units received external inputs to indicate left cue ( i = 1 ) , right cue ( i = 2 ) , or response ( i = 3 ) periods , and so , not too surprisingly , reflect these features in their activation ., On the other hand , the cue response is not very prominent in unit i = 1 , indicating that activity in the driven units is not completely dominated by the external regressors either , while unit i = 10 ( not externally driven ) shows a clear left-cue response ., Most importantly , many of the remaining state variables clearly distinguish between the left and right lever options throughout the delay period of the task , in this sense carrying a memory of the cue ( previous response ) within the delay ., Some of the activation profiles appear to systematically climb or decay across the delay period , as reported previously ( e . g . 1; 60 ) , but are a bit harder to read ( at least in the absence of more detailed behavioral information ) , such that one may want to stick with the simpler M = 5 model discussed above ., Either way , for this particular data set , the extracted latent states appear to summarize quite well the most salient computational features of this simple working memory task ., Further insight about the dynamical mechanisms of working memory might be gained by examining the system\u2019s fixed points and their eigenvalue spectrum ., For this purpose , the EM algorithm was started from 400 different initial conditions ( that is , initial parameter estimates and threshold settings \u03b8 ) with maximum absolute eigenvalues ( of the corresponding fixed points ) drawn from a relatively uniform distribution within the interval 0 3 ., Although the estimation process rarely returned truly multi-stable solutions ( just 2 . 5% of all cases ) , one frequently discussed candidate mechanism for working memory ( e . g . 29; 32 ) , there was a clear trend for the final maximum absolute eigenvalues to aggregate around 1 ( Fig 12 ) ., For the discrete-time dynamical system ( 1 ) this implies it is close to a bifurcation , with fixed points on the brink of becoming unstable , and will tend to produce ( very ) slow dynamics as the degree of convergence shrinks to zero along the maximum eigenvalue direction ( strictly , a single eigenvalue near 1 does not yet guarantee a slow approach , but makes it very likely , especially in a ( piecewise ) linear system ) ., Indeed , effectively slow dynamics is all that is needed to bridge the delays ( see also 1 ) , while true multi-stability may perhaps even be the physiologically less likely scenario ( e . g . 61; 62 ) ., ( Reducing the bin width from 500 ms to 100 ms appeared to produce solutions with eigenvalues even closer to 1 while retaining stimulus selectivity across the delay , but this observation was not followed up more systematically here ) ., Linear dynamical systems ( LDS ) have frequently and successfully been used to infer smooth neural trajectories from spike train recordings 15; 16; 20; 22 or other measurement modalities 63 ., However , as noted before , they ","headings":"Introduction, Results, Discussion, Models and methods","abstract":"The computational and cognitive properties of neural systems are often thought to be implemented in terms of their ( stochastic ) network dynamics ., Hence , recovering the system dynamics from experimentally observed neuronal time series , like multiple single-unit recordings or neuroimaging data , is an important step toward understanding its computations ., Ideally , one would not only seek a ( lower-dimensional ) state space representation of the dynamics , but would wish to have access to its statistical properties and their generative equations for in-depth analysis ., Recurrent neural networks ( RNNs ) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective ., Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs ( PLRNNs ) within the statistical framework of state space models , which accounts for noise in both the underlying latent dynamics and the observation process ., The Expectation-Maximization algorithm is used to infer the latent state distribution , through a global Laplace approximation , and the PLRNN parameters iteratively ., After validating the procedure on toy examples , and using inference through particle filters for comparison , the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex ( ACC ) obtained during performance of a classical working memory task , delayed alternation ., Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance , including stimulus-selective delay activity ., The estimated models were rarely multi-stable , however , but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point ., In summary , the present work advances a semi-analytical ( thus reasonably fast ) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series , and directly link these to computational properties .","summary":"Neuronal dynamics mediate between the physiological and anatomical properties of a neural system and the computations it performs , in fact may be seen as the \u2018computational language\u2019 of the brain ., It is therefore of great interest to recover from experimentally recorded time series , like multiple single-unit or neuroimaging data , the underlying stochastic network dynamics and , ideally , even equations governing their statistical evolution ., This is not at all a trivial enterprise , however , since neural systems are very high-dimensional , come with considerable levels of intrinsic ( process ) noise , are usually only partially observable , and these observations may be further corrupted by noise from measurement and preprocessing steps ., The present article embeds piecewise-linear recurrent neural networks ( PLRNNs ) within a state space approach , a statistical estimation framework that deals with both process and observation noise ., PLRNNs are computationally and dynamically powerful nonlinear systems ., Their statistically principled estimation from multivariate neuronal time series thus may provide access to some essential features of the neuronal dynamics , like attractor states , generative equations , and their computational implications ., The approach is exemplified on multiple single-unit recordings from the rat prefrontal cortex during working memory .","keywords":"neural networks, applied mathematics, neuroscience, learning and memory, simulation and modeling, algorithms, cognitive neuroscience, systems science, mathematics, cognition, algebra, memory, research and analysis methods, computer and information sciences, animal cells, dynamical systems, nonlinear dynamics, approximation methods, working memory, cellular neuroscience, cell biology, linear algebra, neurons, biology and life sciences, cellular types, physical sciences, cognitive science, eigenvalues","toc":null}