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# Copyright 2008 by Norbert Dojer. All rights reserved.
# Adapted by Bartek Wilczynski.
# This code is part of the Biopython distribution and governed by its
# license. Please see the LICENSE file that should have been included
# as part of this package.
"""Approximate calculation of appropriate thresholds for motif finding."""
class ScoreDistribution:
"""Class representing approximate score distribution for a given motif.
Utilizes a dynamic programming approach to calculate the distribution of
scores with a predefined precision. Provides a number of methods for calculating
thresholds for motif occurrences.
"""
def __init__(self, motif=None, precision=10**3, pssm=None, background=None):
"""Initialize the class."""
if pssm is None:
self.min_score = min(0.0, motif.min_score())
self.interval = max(0.0, motif.max_score()) - self.min_score
self.n_points = precision * motif.length
self.ic = motif.ic()
else:
self.min_score = min(0.0, pssm.min)
self.interval = max(0.0, pssm.max) - self.min_score
self.n_points = precision * pssm.length
self.ic = pssm.mean(background)
self.step = self.interval / (self.n_points - 1)
self.mo_density = [0.0] * self.n_points
self.mo_density[-self._index_diff(self.min_score)] = 1.0
self.bg_density = [0.0] * self.n_points
self.bg_density[-self._index_diff(self.min_score)] = 1.0
if pssm is None:
for lo, mo in zip(motif.log_odds(), motif.pwm()):
self.modify(lo, mo, motif.background)
else:
for position in range(pssm.length):
mo_new = [0.0] * self.n_points
bg_new = [0.0] * self.n_points
lo = pssm[:, position]
for letter, score in lo.items():
bg = background[letter]
mo = pow(2, pssm[letter, position]) * bg
d = self._index_diff(score)
for i in range(self.n_points):
mo_new[self._add(i, d)] += self.mo_density[i] * mo
bg_new[self._add(i, d)] += self.bg_density[i] * bg
self.mo_density = mo_new
self.bg_density = bg_new
def _index_diff(self, x, y=0.0):
return int((x - y + 0.5 * self.step) // self.step)
def _add(self, i, j):
return max(0, min(self.n_points - 1, i + j))
def modify(self, scores, mo_probs, bg_probs):
"""Modify motifs and background density."""
mo_new = [0.0] * self.n_points
bg_new = [0.0] * self.n_points
for k, v in scores.items():
d = self._index_diff(v)
for i in range(self.n_points):
mo_new[self._add(i, d)] += self.mo_density[i] * mo_probs[k]
bg_new[self._add(i, d)] += self.bg_density[i] * bg_probs[k]
self.mo_density = mo_new
self.bg_density = bg_new
def threshold_fpr(self, fpr):
"""Approximate the log-odds threshold which makes the type I error (false positive rate)."""
i = self.n_points
prob = 0.0
while prob < fpr:
i -= 1
prob += self.bg_density[i]
return self.min_score + i * self.step
def threshold_fnr(self, fnr):
"""Approximate the log-odds threshold which makes the type II error (false negative rate)."""
i = -1
prob = 0.0
while prob < fnr:
i += 1
prob += self.mo_density[i]
return self.min_score + i * self.step
def threshold_balanced(self, rate_proportion=1.0, return_rate=False):
"""Approximate log-odds threshold making FNR equal to FPR times rate_proportion."""
i = self.n_points
fpr = 0.0
fnr = 1.0
while fpr * rate_proportion < fnr:
i -= 1
fpr += self.bg_density[i]
fnr -= self.mo_density[i]
if return_rate:
return self.min_score + i * self.step, fpr
else:
return self.min_score + i * self.step
def threshold_patser(self):
"""Threshold selection mimicking the behaviour of patser (Hertz, Stormo 1999) software.
It selects such a threshold that the log(fpr)=-ic(M)
note: the actual patser software uses natural logarithms instead of log_2, so the numbers
are not directly comparable.
"""
return self.threshold_fpr(fpr=2**-self.ic)
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