The Needleman-Wunsch algorithm is a way to align sequences in a way that optimizes "similarity". Usually, a grid is generated and then you follow a path down the grid (based off the largest value) to compute the optimal alignment between two sequences. I have created a Python program, that given two strings, will create the resulting matrix for the Needleman-Wunsch algorithm. Currently, the program when ran will generate two random sequences of DNA and then print out the resulting Needleman-Wunsch matrix.


import random
from tabulate import tabulate

class NeedlemanWunsch:
    Class used for generating Needleman-Wunsch matrices.

    def _compute_block(self, result, i, j):
        Given a block (corresponding to a 2 x 2 matrix), calculate the value o-
        f the bottom right corner.
        (Based on the equation:
                               M_{i,j} = max(M_{i-1,j-1} + S_{i,j},
                                             M_{i,j-1} + W,
                                             M_{i-1,j} + W)
         Found here: https://vlab.amrita.edu/?sub=3&brch=274&sim=1431&cnt=1)

            result : The current matrix that is being computed.
            i : The right most part of the block being computed.
            j : The bottom most part of the block being computed.

            The value for the right bottom corner of a particular block.
        return max(result[i-1][j-1] +
                   result[i-1][j] + self.gap,
                   result[i][j-1] + self.gap)

    def _calc_weight(self, first_char, second_char):
        Helper function, given two characters determines (based on the sc-
        oring scheme) what the score for the particular characters can be.

            first_char : A character to compare.
            second_char : A character to compare.

            Either self.match or self.mismatch.
        if first_char == second_char:
            return self.match
            return self.mismatch

    def generate(self, first_seq, second_seq):
        Generates a matrix corresponding to the scores to the Needleman-Wu-
        nsch algorithm.

            first_seq : One of the sequences to be compared for similarity.
            second_seq : One of the sequences to be compared for

            A 2D list corresponding to the resulting matrix of the Needlem-
            an-Wunsch algorithm.
        # Internally requies that the first sequence is longer.
        if len(second_seq) > len(first_seq):
            first_seq, second_seq = second_seq, first_seq
        self._first_seq = first_seq
        self._second_seq = second_seq
        # Adjust sequence with "intial space"
        # Initialize the resulting matrix with the initial row.
        result = [list(range(0, -len(first_seq) - 1, -1))]
        # Create initial columns.
        for i in range(-1, -len(second_seq) - 1, -1):
            row = [i]
        # Sweep through and compute each new cell row-wise.
        for i in range(1, len(result)):
            for j in range(1, len(result[0])):
                result[i][j] = self._compute_block(result, i, j)
        # Format for prettier printing.
        for index, letter in enumerate(second_seq):
            result[index + 1].insert(0, letter)
        result[0].insert(0, ' ')
        result.insert(0, list("  " + first_seq))
        return result

    def __init__(self, match=1, mismatch=-1, gap=-1):
        Initialize the Needleman-Wunsch class so that it provides weights for
        match (default 1), mismatch (default -1), and gap (default -1).
        self.match = match
        self.mismatch = mismatch
        self.gap = gap
        self._first_seq = ""
        self._second_seq = ""

def deletion(seq, pos):
    Deletes a random base pair from a sequence at a specified position.

        seq : Sequence to perform deletion on.
        pos : Location of deletion.

        seq with character removed at pos.
    return seq[:pos] + seq[pos:]

def base_change(seq, pos):
    Changes a random base pair to another base pair at a specified position.

        seq : Sequence to perform base change on.
        pos : Locaion of base change.

        seq with character changed at pos.
    new_base = random.choice("ACTG".replace(seq[pos], ""))
    return seq[:pos] + new_base + seq[pos:]

def mutate(seq, rounds=3):
    Mutates a piece of DNA by randomly applying a deletion or base change

        seq : The sequence to be mutated.
        rounds : Defaults to 3, the number of mutations to be made.

        A mutated sequence.
    mutations = (deletion, base_change)
    for _ in range(rounds):
        pos = random.randrange(len(seq))
        seq = random.choice(mutations)(seq, pos)
    return seq

def main():
    Creates a random couple of strings and creates the corresponding Needleman
    -Wunsch matrix associated with them.
    needleman_wunsch = NeedlemanWunsch()
    first_seq = ''.join(random.choices("ACTG", k=5))
    second_seq = mutate(first_seq)
    data = needleman_wunsch.generate(first_seq, second_seq)
    print(tabulate(data, headers="firstrow"))

if __name__ == '__main__':

I ended up using a NeedlemanWunsch class, because using only function resulted in a lot DRY for the parameters match, mismatch, and gap.

I am not particularly fond of the code. I haven't used numpy or any related libraries because I couldn't see any way that it would significantly shorten the code, however, I would be willing to use numpy if there is a significantly shorter way of expressing the matrix generation. However, the code seems frail, and very prone to off by one errors.


1 Answer 1



  • base_change is not good name for function. It's suggest change. At wikipedia they use Indel (INsertion or DELetion) names.
  • first_seq and second_seq strings could be lists. In this case mutate/deletion/base_change function can do its stuff in-place
  • _first_seq and _second_seq changes after every call generate method. No need to cache these variables, because of they not use in future by public method of class
  • numpy simplify code


  • you have two main public functionalities: mutate and generate methods. generate mess presentation layer and logic one. Generally it's not good idea. Imho better design generate (needleman_wunsch) to calc only logic (without first row and column with first_seq, second_seq). Additional method print_needleman_wunsch_matrix could add these lines if needed.

Example code (without design warning, additionally i exchange tabulate for pandas but this no needed)

import numpy as np
import pandas as pd
from random import choice, choices, randrange

def needleman_wunsch(first, second, match=1, mismatch=-1, gap=-1):
    tab = np.full((len(second) + 2, len(first) + 2), ' ', dtype=object)
    tab[0, 2:] = first
    tab[1, 1:] = list(range(0, -len(first) - 1, -1))
    tab[2:, 0] = second
    tab[1:, 1] = list(range(0, -len(second) - 1, -1))
    is_equal = {True: match, False: mismatch}
    for f in range(2, len(first) + 2):
        for s in range(2, len(second) + 2):
            tab[s, f] = max(tab[s - 1][f - 1] + is_equal[first[f - 2] == second[s - 2]],
                            tab[s - 1][f] + gap,
                            tab[s][f - 1] + gap)
    return tab

def mutate(seq, rounds=3):
    mutate_seq = seq.copy()
    for change in choices((deletion, insertion), k=rounds):
        pos = randrange(len(mutate_seq))
        change(mutate_seq, pos)
    return mutate_seq

def deletion(seq, idx):

def insertion(seq, idx):
    seq.insert(idx, choice("ACTG".replace(seq[idx], "")))

def main():
    first_seq = choices("ACTG", k=5)
    second_seq = mutate(first_seq)
    data = needleman_wunsch(first_seq, second_seq)

if __name__ == '__main__':

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