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# This script will calculate Shannon entropy from a MSA. |
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# Dependencies: |
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# Biopython, Matplotlib [optionally], Math |
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""" |
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Shannon's entropy equation (latex format): |
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H=-\sum_{i=1}^{M} P_i\,log_2\,P_i |
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Entropy is a measure of the uncertainty of a probability distribution (p1, ..... , pM) |
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https://stepic.org/lesson/Scoring-Motifs-157/step/7?course=Bioinformatics-Algorithms&unit=436 |
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Where, Pi is the fraction of nuleotide bases of nuleotide base type i, |
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and M is the number of nuleotide base types (A, T, G or C) |
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H ranges from 0 (only one base/residue in present at that position) to 4.322 (all 20 residues are equally |
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represented in that position). |
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Typically, positions with H >2.0 are considerered variable, whereas those with H < 2 are consider conserved. |
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Highly conserved positions are those with H <1.0 (Litwin and Jores, 1992). |
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A minimum number of sequences is however required (~100) for H to describe the diversity of a protein family. |
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""" |
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import os |
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import sys |
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import warnings |
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import traceback |
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__author__ = "Joe R. J. Healey" |
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__version__ = "1.0.0" |
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__title__ = "ShannonMSA" |
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__license__ = "GPLv3" |
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__author_email__ = "J.R.J.Healey@warwick.ac.uk" |
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def parseArgs(): |
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"""Parse command line arguments""" |
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import argparse |
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try: |
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parser = argparse.ArgumentParser( |
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description='Compute per base/residue Shannon entropy of a Multiple Sequence Alignment.') |
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parser.add_argument('-a', |
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'--alignment', |
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action='store', |
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required=True, |
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help='The multiple sequence alignment (MSA) in any of the formats supported by Biopython\'s AlignIO.') |
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parser.add_argument('-f', |
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'--alnformat', |
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action='store', |
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default='fasta', |
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help='Specify the format of the input MSA to be passed in to AlignIO.') |
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parser.add_argument('-v', |
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'--verbose', |
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action='count', |
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default=0, |
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help='Verbose behaviour, printing parameters of the script.') |
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parser.add_argument('-m', |
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'--runningmean', |
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action='store', |
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type=int, |
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default=0, |
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help='Return the running mean (a.k.a moving average) of the MSAs Shannon Entropy. Makes for slightly smoother plots. Providing the number of points to average over switches this on.') |
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parser.add_argument('--makeplot', |
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action='store_true', |
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help='Plot the results via Matplotlib.') |
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except: |
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print "An exception occurred with argument parsing. Check your provided options." |
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traceback.print_exc() |
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return parser.parse_args() |
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def parseMSA(msa, alnformat, verbose): |
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"""Parse in the MSA file using Biopython's AlignIO""" |
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from Bio import AlignIO |
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alignment = AlignIO.read(msa, alnformat) |
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# Do a little sanity checking: |
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seq_lengths_list = [] |
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for record in alignment: |
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seq_lengths_list.append(len(record)) |
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seq_lengths = set(seq_lengths_list) |
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if verbose > 0: print("Alignment length is:" + str(list(seq_lengths))) |
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if len(seq_lengths) != 1: |
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sys.stderr.write("Your alignment lengths aren't equal. Check your alignment file.") |
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sys.exit(1) |
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index = range(1, list(seq_lengths)[0]+1) |
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return alignment, list(seq_lengths), index |
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################################################################## |
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# Function to calcuate the Shannon's entropy per alignment column |
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# H=-\sum_{i=1}^{M} P_i\,log_2\,P_i (http://imed.med.ucm.es/Tools/svs_help.html) |
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# Gaps and N's are included in the calculation |
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################################################################## |
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def shannon_entropy(list_input): |
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"""Calculate Shannon's Entropy per column of the alignment (H=-\sum_{i=1}^{M} P_i\,log_2\,P_i)""" |
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import math |
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unique_base = set(list_input) |
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M = len(list_input) |
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entropy_list = [] |
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# Number of residues in column |
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for base in unique_base: |
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n_i = list_input.count(base) # Number of residues of type i |
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P_i = n_i/float(M) # n_i(Number of residues of type i) / M(Number of residues in column) |
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entropy_i = P_i*(math.log(P_i,2)) |
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entropy_list.append(entropy_i) |
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sh_entropy = -(sum(entropy_list)) |
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return sh_entropy |
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def shannon_entropy_list_msa(alignment): |
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"""Calculate Shannon Entropy across the whole MSA""" |
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shannon_entropy_list = [] |
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for col_no in xrange(len(list(alignment[0]))): |
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list_input = list(alignment[:, col_no]) |
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shannon_entropy_list.append(shannon_entropy(list_input)) |
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return shannon_entropy_list |
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def plot(index, sel, verbose): |
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""""Create a quick plot via matplotlib to visualise""" |
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import matplotlib.pyplot as plt |
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if verbose > 0: print("Plotting data...") |
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plt.plot(index, sel) |
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plt.xlabel('MSA Position Index', fontsize=16) |
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plt.ylabel('Shannon Entropy', fontsize=16) |
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plt.show() |
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def running_mean(l, N): |
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sum = 0 |
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result = list(0 for x in l) |
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for i in range( 0, N ): |
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sum = sum + l[i] |
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result[i] = sum / (i+1) |
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for i in range( N, len(l) ): |
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sum = sum - l[i-N] + l[i] |
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result[i] = sum / N |
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return result |
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def main(): |
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"""Compute Shannon Entropy from a provided MSA.""" |
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# Parse arguments |
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args = parseArgs() |
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# Convert object elements to standard variables for functions |
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msa = args.alignment |
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alnformat = args.alnformat |
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verbose = args.verbose |
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makeplot = args.makeplot |
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runningmean = args.runningmean |
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# Start calling functions to do the heavy lifting |
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alignment, seq_lengths, index = parseMSA(msa, alnformat, verbose) |
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sel = shannon_entropy_list_msa(alignment) |
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if runningmean > 0: |
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sel = running_mean(sel, runningmean) |
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if makeplot is True: |
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plot(index, sel, verbose) |
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if verbose > 0: print("Index" + '\t' + "Entropy") |
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for c1, c2 in zip(index, sel): |
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print(str(c1) + '\t' + str(c2)) |
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if __name__ == '__main__': |
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main() |
Would Shannon entropy plot be helpful?
Just a thought.
Entropy From A Multiple Sequence Alignment With Gaps
Link looks helpful, thanks. Interesting idea to quantify the uncertainty instead of the conservation. Kinda the inverse of my initial thought process but would show the same end result I think.