Smith-Waterman.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 305,
   "id": "bccc361a-9996-4bff-8b5d-7fb89c34009d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import blosum as bl\n",
    "import random\n",
    "import itertools\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "score = bl.BLOSUM(62)\n",
    "colors = ['white', 'green', 'red', 'blue']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "id": "12f16e8c-06b0-4e95-82fa-f19a8bc4717a",
   "metadata": {},
   "outputs": [],
   "source": [
    "alphabet = \"ABCDEFGHIJKLMNPQRSTVWXYZ\"\n",
    "n = 15\n",
    "m = 14\n",
    "def mut(c):\n",
    "    if random.random() < 0.7:\n",
    "        return random.choice(alphabet)\n",
    "    else:\n",
    "        return c\n",
    "\n",
    "s1 = ''.join(random.choices(alphabet, k=n))\n",
    "chars = list(s1)\n",
    "for i in reversed(random.choices(range(n), k=n-m)):\n",
    "    chars.pop(i)   \n",
    "s2 = ''.join([mut(c) for c in chars])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "id": "d6993be8-c616-4692-bdad-d1fb1e4ed2de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('GDEEFQNRLTDXMIQ', 'BBEXFGKLWMXXBQ')"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1, s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "id": "b66880a7-2614-4400-82cc-38820c7171fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "dp = np.zeros((n + 1, m + 1), np.int64)\n",
    "bt = np.zeros((n + 1, m + 1), np.int64)\n",
    "bg = np.zeros((n + 1, m + 1), np.int64)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba867071-f5b7-4528-aa36-3c325145a94d",
   "metadata": {},
   "source": [
    "Fill in the dynamic programming matrix `dp`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "id": "0de21ea7-15af-415a-b6b1-2dab9db00a1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "maxij = (0,0)\n",
    "for i, j in itertools.product(range(1, n+1), range(1, m+1)):\n",
    "        if dp[i - 1, j - 1] + score[s1[i - 1] + s2[j - 1]] > dp[i,j]:\n",
    "            dp[i,j] = dp[i - 1, j - 1] + score[s1[i - 1] + s2[j - 1]]\n",
    "            bt[i,j] = 1\n",
    "        if dp[i - 1, j] + score[s1[i - 1] + '*']  > dp[i,j]:\n",
    "            dp[i,j] = dp[i - 1, j] + score[s1[i - 1] + '*']\n",
    "            bt[i,j] = 2\n",
    "        if dp[i, j - 1] + score[\"*\" + s2[j - 1]] > dp[i,j]:\n",
    "            dp[i,j] = dp[i, j - 1] + score[\"*\" + s2[j - 1]]\n",
    "            bt[i,j] = 3\n",
    "        if dp[i,j] > dp[maxij]:\n",
    "            maxij = (i,j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "056f2045-e0fe-44c1-b915-3a4b7fa5e510",
   "metadata": {},
   "source": [
    "And compute the actual optimal alignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "id": "0b671a13-df9f-4327-a7ba-20d04c7b5916",
   "metadata": {},
   "outputs": [],
   "source": [
    "ij = maxij\n",
    "alignment = []\n",
    "while dp[ij] > 0:\n",
    "    bg[ij] = 2\n",
    "    (i,j) = (ij[0] - 1, ij[1] - 1)\n",
    "    if bt[ij] == 1:\n",
    "        if s1[i] == s2[j]:\n",
    "            alignment.append((s1[i], '=', s2[j]))\n",
    "        else:\n",
    "            alignment.append((s1[i], 'X', s2[j]))\n",
    "        ij = (ij[0] - 1, ij[1] - 1)\n",
    "    elif bt[ij] == 2:\n",
    "        alignment.append((s1[i], ' ', '*'))\n",
    "        ij = (ij[0] - 1, ij[1])\n",
    "    elif bt[ij] == 3:\n",
    "        alignment.append((' ', '*', s2[j]))\n",
    "        ij = (ij[0], ij[1] - 1)\n",
    "bg[maxij] = 1    \n",
    "bg[ij] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "id": "e733ca65-e7a4-4f06-a5fa-8987becd7abb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DEEFQNRL\n",
      "X=X= XX=\n",
      "BEXF*GKL\n"
     ]
    }
   ],
   "source": [
    "for row in list(map(list, zip(*alignment))):\n",
    "    print(''.join(reversed(row)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "id": "02419220-8160-40eb-b294-34b0b846cf54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fdb5647a620>"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(clear = True)\n",
    "for i in range(n+1):\n",
    "    for j in range(m+1):\n",
    "        plt.text(j, i, str(dp[i,j]), va='center', ha='center', backgroundcolor = colors[bg[i,j]])\n",
    "plt.imshow(bg)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}