4_affine_gaps_global.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Affine Gap Penalties\n",
    "\n",
    "Instead of linear gap penalties, we can modify gap penalties such that an opening gap is taxed more heavily than an extended gap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import pandas as pd\n",
    "import sequence_alignment as seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_2 = \"KKASKASPKKKK\"\n",
    "seq_1 = \"KKSPKMLHKK\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Initialization\n",
    "\n",
    "When working with affine gap penalties we need to consider two gap penalty values — one for opening up a gap and one for extending a gap. Therefore the initialized scoring matrix ($M$) looks slightly different from the initialized scoring matrix in the linear gap penalty case. <br>\n",
    "$$ M_{(0,0)} = 0 $$ <br>\n",
    "$$M_{(0,j)} = g_{open} + (j-1)g_{ext}\\  \\forall j>0$$ <br>\n",
    "$$M_{(i,0)} = g_{open} + (i-1)g_{ext}\\  \\forall i>0$$\n",
    "\n",
    "where $g_{open}$ is the opening gap penalty and $g_{ext}$ is the extension gap penalty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_open = -6; g_ext = -2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = len(seq_1); n = len(seq_2)\n",
    "M = np.zeros([m+1,n+1])\n",
    "#initialize the matrix\n",
    "M[0,1:] = g_open + g_ext*np.arange(0,n,1)\n",
    "M[1:,0] = g_open + g_ext*np.arange(0,m,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 396x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5.5,5.5))\n",
    "sns.heatmap(M,linecolor='white',linewidth=1,square=True,annot=True,cbar=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For implementing global dynamic programming with affine gap penalties, we need to introduce two *helper* scoring matrices, let's call them $U$ and $L$. These matrices have to be initialized in a slightly different fashion from $M.$ <br>\n",
    "$$U_{(0,0)} = L_{(0,0)} = 0$$ <br>\n",
    "$$U_{(0,j)} = 2g_{open} + (j-1)g_{ext}\\  \\forall j>0$$ <br>\n",
    "$$L_{(i,0)} = 2g_{open} + (i-1)g_{ext}\\  \\forall i>0$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialize helpers\n",
    "L = np.copy(M); U = np.copy(M)\n",
    "L[1:,0] = L[1:,0]+g_open; U[0,1:] = U[0,1:]+g_open #avoiding Gotoh's error (see reference 2.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Fill Step\n",
    "\n",
    "To fill the matrix with scores, we need to iterate over the elements of the matrix and fill in values according to the following recursive relations: <br>\n",
    "$$U_{(i,j)} = \\max \\{ (U_{(i-1,j)} + g_{ext}), \\ (M_{(i-1,j)} + g_{open)} \\}$$ <br>\n",
    "$$L_{(i,j)} = \\max \\{ (L_{(i,j-1)} + g_{ext}), \\ (M_{(i,j-1)} + g_{open)} \\}$$ <br>\n",
    "$$M_{(i,j)} = \\max \\{ (M_{(i-1,j-1)} + S_{(i,j)}), \\ L_{(i,j)}, \\ U_{(i,j)} \\}$$\n",
    "\n",
    "Where $M$ is the scoring matrix, $S$ is the substitution matrix, $g_{open}$ is the opening gap penalty, $g_{ext}$ is the extension gap penalty and $U$, $L$ are the upper and leftward helper matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Substitution Matrix\n",
    "\n",
    "We will use the BLOSUM62 matrix for obtaining substitution scores for protein sequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = pd.read_csv('blosum62.csv',index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filling up the $M,$ $U$ and $L$ matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialize tracer\n",
    "tracer = np.zeros([np.shape(M)[0],np.shape(M)[1],7])\n",
    "\n",
    "for i in range(1,m+1):\n",
    "    for j in range(1,n+1):\n",
    "        l_arr = np.array([M[i,j-1]+g_open,L[i,j-1]+g_ext])\n",
    "        L[i,j] = np.max(l_arr)\n",
    "        l_where = l_arr==np.max(l_arr)\n",
    "                        \n",
    "        u_arr = np.array([M[i-1,j]+g_open,U[i-1,j]+g_ext])\n",
    "        U[i,j] = np.max(u_arr)\n",
    "        u_where = u_arr==np.max(u_arr)\n",
    "                        \n",
    "        m_arr = np.array([M[i-1,j-1]+(S[seq_1[i-1]][seq_2[j-1]]),U[i,j],L[i,j]])\n",
    "        M[i,j] = np.max(m_arr)\n",
    "        m_where = m_arr==np.max(m_arr)\n",
    "            \n",
    "        idx = np.hstack([m_where,u_where,l_where])\n",
    "        tracer[i,j,idx] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,3,figsize = (15,4))\n",
    "for i,p in enumerate([[M,\"$M$\"],[U,\"$U$\"],[L,\"$L$\"]]):\n",
    "    sns.heatmap(p[0],linecolor='white',linewidth=1,square=True,annot=True,cbar=False,ax=ax[i]);\n",
    "    ax[i].set_title(p[1])\n",
    "fig.suptitle(\"Scoring Matrices\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Traceback\n",
    "The 3D `tracer` matrix saves the tracebacks as shown below — with each sub-matrix corresponding to a particular movement. In the affine gap penalty case, arrows can indicate movement _between_ the scoring matrices $M$, $U$ and $L$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3,3,figsize = (10,8))\n",
    "\n",
    "for i,m in enumerate([[0,0,r\"$\\nwarrow_{M}$\"],[0,1,r\"$\\odot_{U}$\"],[0,2,r\"$\\odot_{L}$\"],\n",
    "                      [1,0,r\"$\\uparrow_{M}$\"],[1,1,r\"$\\uparrow_{U}$\"],\n",
    "                      [2,0,r\"$\\leftarrow_{M}$\"],[2,2,r\"$\\leftarrow_{L}$\"]]):\n",
    "    sns.heatmap(tracer[:,:,i],cmap=\"coolwarm\",vmin=-0.5,vmax=0.6,linecolor='white',\n",
    "                linewidth=1,square=True,cbar=False,ax=ax[m[0]][m[1]])\n",
    "    ax[m[0]][m[1]].set_title(m[2])\n",
    "\n",
    "fig.delaxes(ax[1][2]); fig.delaxes(ax[2][1])\n",
    "fig.suptitle(\"tracer sub-matrices\")\n",
    "fig.tight_layout(rect=[0, 0.03, 1, 0.95]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\nwarrow_\\text{M}$ indicates movement along the $\\text{M}$ matrix in the diagonal direction,\n",
    "$\\odot_\\text{U}$ indicates climbing up to the $\\text{U}$ matrix and $\\odot_\\text{L}$ indicates climbing down to the $\\text{L}$ matrix. $\\leftarrow_\\text{M}$ indicates first hopping onto $\\text{M}$ and then moving diagonally. Similarly, $\\leftarrow_\\text{L}$, $\\uparrow_\\text{M}$ and $\\uparrow_\\text{U}$ indicate how to move and on which matrix.\n",
    "\n",
    "Thus the `tracer` matrix in the affine gap penalty case has 7 sub-matrices as opposed to 3 in the linear gap penalty case. This can be avoided by storing different symbols within a single 1D matrix instead of having a sub-matrix for each symbol."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A traceback function for affine gap penalties\n",
    "\n",
    "The traceback function for the affine gap penalty case takes into account movement _on_ a matrix as well as _between_ matrices. The subscript of the traceback arrow determines which matrix to move on and the direction of the arrow is treated the same way as in the linear gap penalty case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. \n",
      " KK----SPKMLHKK \n",
      " KKASKASPK--KKK \n",
      "\n",
      "2. \n",
      " KK----SPKMLHKK \n",
      " KKASKASPKK--KK \n",
      "\n"
     ]
    }
   ],
   "source": [
    "alignment = seq.traceback_iterator(tracer,seq_1,seq_2,affine=True,high_low=True)\n",
    "for i,e in enumerate(alignment):\n",
    "    print(str(i+1)+\".\",\"\\n\",e[0],\"\\n\",e[1],\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are at least two optimal solutions for the above pair of sequences with maximum score = +15."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Example Alignments\n",
    "\n",
    "Let's try out a few more sequence alignments. <br>\n",
    "\n",
    "### Protein Sequences\n",
    "\n",
    "### 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 200 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = 9.0\n",
      "1. \n",
      " KKSPKML-HK-K \n",
      " KKASKASPKKKK \n",
      "\n",
      "2. \n",
      " KKSPKML-H-KK \n",
      " KKASKASPKKKK \n",
      "\n",
      "3. \n",
      " KKSPKML--HKK \n",
      " KKASKASPKKKK \n",
      "\n",
      "4. \n",
      " KKSPKM--LHKK \n",
      " KKASKASPKKKK \n",
      "\n",
      "5. \n",
      " KKSPKML-HKK- \n",
      " KKASKASPKKKK \n",
      "\n",
      "6. \n",
      " KKSPK-M-LHKK \n",
      " KKASKASPKKKK \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_2 = \"KKASKASPKKKK\"\n",
    "seq_1 = \"KKSPKMLHKK\"\n",
    "g_open = -6; g_ext = -6\n",
    "\n",
    "_,_,_,_,_, = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True,max_i=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Affine vs. Linear Alignment\n",
    "\n",
    "We should expect that for equal costs of gap opening and extension, affine penalties should reduce to linear penalties. In **example 1.1** we called the `seq.affine_global_dp` function with $g_{open} = g_{ext} = -6$. In **1.2**, we will call the `seq.global_dp` function with $g = -6$ for the same pair of sequences.\n",
    "\n",
    "### 1.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 200 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = 9.0\n",
      "1. \n",
      " KKSPKML-HK-K \n",
      " KKASKASPKKKK \n",
      "\n",
      "2. \n",
      " KKSPKML--HKK \n",
      " KKASKASPKKKK \n",
      "\n",
      "3. \n",
      " KKSPKML-H-KK \n",
      " KKASKASPKKKK \n",
      "\n",
      "4. \n",
      " KKSPKM--LHKK \n",
      " KKASKASPKKKK \n",
      "\n",
      "5. \n",
      " KKSPKML-HKK- \n",
      " KKASKASPKKKK \n",
      "\n",
      "6. \n",
      " KKSPK-M-LHKK \n",
      " KKASKASPKKKK \n",
      "\n"
     ]
    }
   ],
   "source": [
    "_,_,_ = seq.global_dp(seq_1,seq_2,S,-6,\n",
    "                                  disp_alignments=True,max_i=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 100 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = 39.0\n",
      "1. \n",
      " KMNKPSQRTTTS \n",
      " KMNKPLQR--TS \n",
      "\n",
      "2. \n",
      " KMNKPSQRTTTS \n",
      " KMNKPLQRT--S \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_2 = \"KMNKPLQRTS\"\n",
    "seq_1 = \"KMNKPSQRTTTS\"\n",
    "g_open = -5; g_ext = -1\n",
    "\n",
    "_,_,_,_,_, = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DNA Sequences\n",
    "\n",
    "We choose to align pairs of sequences for which all optimal alignments have been described in the literature.\n",
    "\n",
    "### 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 100 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = -15.0\n",
      "1. \n",
      " TTAAAAGGGGTT \n",
      " AAA------GGG \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_2 = \"AAAGGG\"\n",
    "seq_1 = \"TTAAAAGGGGTT\"\n",
    "g_open = -6; g_ext = -1\n",
    "S = pd.read_csv('dna_identity.csv',index_col=0)\n",
    "S[S==0] = -1\n",
    "S[S==1] = 0\n",
    "_,_,_,_,_, = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 100 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = -5.0\n",
      "1. \n",
      " TGAGTT \n",
      " --AG-T \n",
      "\n",
      "2. \n",
      " TGAGTT \n",
      " --AGT- \n",
      "\n",
      "3. \n",
      " TGAGTT \n",
      " AG---T \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_2 = \"AGT\"\n",
    "seq_1 = \"TGAGTT\"\n",
    "g_open = -2; g_ext = -1\n",
    "S = pd.read_csv('dna_identity.csv',index_col=0)\n",
    "S[S==0] = -1\n",
    "S[S==1] = 0\n",
    "\n",
    "_,_,_,_,_, = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 100 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = -62.0\n",
      "1. \n",
      " ------TAAATTTGC \n",
      " TCGCCTTA------C \n",
      "\n",
      "2. \n",
      " T------AAATTTGC \n",
      " TCGCCTTA------C \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_1 = \"TAAATTTGC\"\n",
    "seq_2 = \"TCGCCTTAC\"\n",
    "g_open = -41; g_ext = -1\n",
    "S = pd.read_csv('dna_identity.csv',index_col=0)\n",
    "S[S==0] = -30\n",
    "S[S==1] = 10\n",
    "\n",
    "_,_,_,_,_ = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: 100 iterations exceeded; <10 alignments found: to continue searching, increase max_i.\n",
      "Max. score = -7.0\n",
      "1. \n",
      " --CC \n",
      " ACCT \n",
      "\n",
      "2. \n",
      " CC-- \n",
      " ACCT \n",
      "\n"
     ]
    }
   ],
   "source": [
    "seq_1 = \"CC\"\n",
    "seq_2 = \"ACCT\"\n",
    "g_open = -5; g_ext = -1\n",
    "S = pd.read_csv('dna_identity.csv',index_col=0)\n",
    "S[S==0] = -1\n",
    "S[S==1] = 0\n",
    "\n",
    "_,_,_,_,_ = seq.affine_global_dp(seq_1,seq_2,S,g_open,g_ext,\n",
    "                                  disp_alignments=True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}