dna_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate Random Sequences\n",
    "\n",
    "The following function generate random sequences of bases (A, C G, T) and stores these in a text file. Each sequence is a string or 25 bases with each base chosen randomly with 25% probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random as rnd\n",
    "\n",
    "def generate_seq(outfile, size, rows):\n",
    "    rnd.seed()\n",
    "    f = open(outfile, 'w')\n",
    "    for i in xrange(rows):\n",
    "        dna = ''\n",
    "        for i in xrange(size):\n",
    "            dna += rnd.choice(['A','C','G','T'])\n",
    "\n",
    "        f.write(dna)\n",
    "        f.write('\\n')\n",
    "    \n",
    "    f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# this generates 2500 sequesces of length 25 each\n",
    "generate_seq(\"dna.txt\",25,2500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DNA Sequence Arrangement\n",
    "\n",
    "I've implemented a Monte Carlo method to arrange the DNA sequences on a square grid. It can be thought of as a cooling process. We start by randomly assigning all the sequences to the grid. We then calculate the average distance of sequence in each cell from adjacent cells. Note that the _penalty score_ defined in the challenge is simply the hamming distance between two strings. This average hamming distance for each cell can be thought of temperature at that cell. The Monte Carlo algorithm them seeks an arrangement that lowers the temperature at each cell.\n",
    "\n",
    "This MC algorithm works in the following way\n",
    "- pick two cells on the grid at random \n",
    "- calculate the average local distance of both cells. \n",
    "- swap the contents of the cell \n",
    "- calculate the average local distance of both cells after swap \n",
    "- if the average local distance becomes smaller for both cell after swap, then accept new arrangement, else, discard the change. \n",
    "- repeat for fixed number of iteration \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Case\n",
    "\n",
    "Before running the algorithm for random sequences generated above, I would like to explore the working of the algorithm for a test case where there are only four types of sequences generated by the following function. In this case the the penalty score is either $0$ or $25$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#test case. generate 400 sequences\n",
    "\n",
    "f = open('test.txt', 'w')\n",
    "for i in xrange(100):\n",
    "    f.write('AAAAAAAAAAAAAAAAAAAAAAAAA\\n')\n",
    "    f.write('CCCCCCCCCCCCCCCCCCCCCCCCC\\n')\n",
    "    f.write('GGGGGGGGGGGGGGGGGGGGGGGGG\\n')\n",
    "    f.write('TTTTTTTTTTTTTTTTTTTTTTTTT\\n')\n",
    "    \n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.0\n"
     ]
    },
    {
     "data": {
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6/tY+dZLsvPT8brV2d6uUXNPpM+7ae6BLnaTvuuqp17j2d1xXew7e361Wz7/BXvZd+cpu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\n0EgBYAEaKQAsQCMFgAVopACwgP8HBqu+BVYhFm8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9038f58950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a dna object using test data\n",
    "from dna import DNA\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "dtest = DNA('test.txt')\n",
    "dtest.hamming_dist_all()\n",
    "\n",
    "dtest.plot_heat_map()\n",
    "print np.average(dtest.heat_map()) #average temperature of the heat map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This heat map shows the state of the grid when the sequences are assigned to the cells at random. The average temperature of the heat map is 19. Now, I'll run the MC algorithm to see how the system evolves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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frKrvbq19qaouSfLQ6V74+hfuXKA8AD3YdfWO7Lp6x/HH17/5htVucMDzSHc+5UnZ+ZQn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\nSAFgCQYpACzh/wG4BKERJRs0bQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9036b21b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtest.clusterify(100000)\n",
    "dtest.plot_heat_map()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As one can see from the above heat map, the MC algorithm nicely creates __islands__ of similar sequences, which are shown here in light colors. The average temperate of the heat map is now 3.1.\n",
    "\n",
    "There are disadvantages of this method. In the test case, one would expect four regions only. But the MC algorithm can generate more than four islands, but putting identical sequences in separate islands. Secondly, the shape of these islands is completely random. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.96875\n"
     ]
    }
   ],
   "source": [
    "print np.average(dtest.heat_map()) #average temperature of the heat map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Main Case\n",
    "\n",
    "Here I'll use the MC algorithm to analyze the random sequences generated in the first part."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0n8uAV5IsAc6rqkNJpoCJQZ8VwLMzDXIYIpKkn3Xsf7C3bt06p/5dp7Oq6o6qWlFVK4H1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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f90369e5950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = DNA('dna.txt')\n",
    "d.hamming_dist_all() # this step takes a bit long\n",
    "\n",
    "#plot histogram of all possible distances.\n",
    "d.hamming_hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.7645666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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ODr89uoVfiiMaQz91MOw79aPTbltUjk6S5s/7ZdbGnoqf6nXd9Tvdto6bh8K+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f903399ed10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# heat map for the random sequences\n",
    "d.plot_heat_map()\n",
    "print np.average(d.heat_map())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The average temperature of the heat map is 18.7\n",
    "\n",
    "The following plot shows the histogram of the average local distances (temperature) for each cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RrBsu0ayHuV2imZaVLtFc9YusktSX0QlEP66FBxcDfh3o804gTVafz5bWPgN+3fCOIK03\nfo2AJDXKgJekRhnwktQoA16SGmXAS1KjDHhJapQBL0mNMuAlqVEGvCQ1yoCXpEYZ8JLUKANekhrl\nl41Nkd/qKGmaDPip6+sPMkhab1yikaRGGfCS1CgDXpIaZcBLUqMMeElq1EQCPsmdSU4lOZPk4UnM\nIUl9SjL1y0qtesAnuR74V8CdwHbg3UnesNrzTMNwOOy7hDEN+y5gTMO+CxjTsO8CxjDsu4AxDfsu\nYEzDK9ineriszCTO4HcAZ6vqXFW9APwGsHMC80ycAb/ahn0XMKZh3wWMYdh3AWMa9l3AmIZ9FzAR\nk/ig083A83Ounwd+aALzXJGf/umf5dvf/u5YY8+c+RInTpxalXmv89UOSVM2iYDv46OaYzt06Df5\n7ndfGHv82bPPTrAaSZqcVK1uHif5YWCmqu7sru8BXqyqX54zZk0/CEjSWlVVY7/aOomA3wB8Gfjr\nwB8AJ4B3V9VzqzqRJGlJq75EU1UXk/w88BngeuBRw12Spm/Vz+AlSWvDxN/bkeSjSWaTPLPAtn+Q\n5MUkmyddx3IWqjPJTJLzSZ7sLneutRq7/vcmeS7Jl5L88mL7T8sit+VvzLkdv5LkyT5r7GpaqM4d\nSU50dX4uye191tjVtFCdfyXJZ5M8neRwku/vs8aupluSHEvybPe7+FDXvznJ0SSnkxxJsmmN1vkz\nXd93k7x5jdb4K919/YtJPpXkVUseqKomegHeBrwJeGZe/y3AY8BXgM2TruNK6gT2An+/79qWqfHt\nwFHgZd31167FOudt/2fAL67FOhm9IfrHu/Y7gWNrtM7PAW/r2vcB/3QN1HkD8Mau/UpGr8W9Afgw\n8Atd/8PAvjVa523ANuAY8OY1WuOPAdd1/fuWuy0nfgZfVb8HfHOBTf8c+IVJzz+uJepcM38tY5Ea\n/y7wSzX6UBlV9fWpFzbPErclGX3e+h7gwFSLWsAidf4hcOmsaBPw1akWtYBF6ry16wd4HPib063q\nparqQlU91bW/BTzH6HMxdwH7u2H7gbv7qXBkkTpvqqpTVXW6z9ouWaLGo1X1YjfsOPC6pY7Ty8dv\nkuwEzlfV033Mv0Lv7Z4OPdr3U8tF3Ar8tST/JckwyVv6LmgZbwNmq+r3+y5kEbuBX03yP4BfAfb0\nXM9inu3uRwA/w+gZ8ZqR5PWMnnUcB7ZU1Wy3aRbY0lNZLzGvzjVpiRrvB35nqX2nHvBJXg58gNHy\nx+Xuadcxpn8NbAXeyOjM7lf7LWdBG4BXV9UPA+8HDvZcz3LeDXyi7yKW8CjwUFX9APD3gI/2XM9i\n7gceTPJ5Rk/hv9NzPZcleSXwW8D7quqP526r0drCmnhnR1fnJxnV+a2+61nIYjUm+UfAd6pqyftS\nH2fwPwi8Hvhikq8weorxhSR/vodallRVX6sO8GuMvmdnrTkPfAqgqj4HvJjkz/Vb0sK6z0j8FPDv\n+65lCTuq6re79idZm//nVNWXq+rHq+otjL7vaU08I0ryMkbh/vGqOtR1zya5odt+I/C1vuq7ZE6d\n/25OnWvKYjUm+VvATwA/u9wxph7wVfVMVW2pqq1VtZVRQL25qnr/T5+v+2W85KeAl7wTaA04BPwo\nQJJtwMaq+p/9lrSodwDPVdUf9F3IEs4m+ZGu/aPAmliTnS/Ja7t/rwN+kdGzzV51r688Cpysqo/M\n2XQY2NW1dzH6ne3NEnV+z7AplvTSyRepsXsn3/uBnVX1f5c90BReDT7A6BOt/4/Rl5DdN2/7f2Nt\nvIvmUp3f6eq8H/i3wNPAFxn9Um5ZIzVevi2BlwEfZ/Tg8wVgsIZuy+/5Pwc+Bvydvutb4v/8PuAt\njNY6nwI+C7xpDdZ5P/AQo3dWfBn4UN81dnW+FXixu+2e7C53ApsZvRB8GjgCbFqDdb6T0Yu/zwN/\nAlwAfncN1ngG+O9z+h5Z6jh+0EmSGuWX2EpSowx4SWqUAS9JjTLgJalRBrwkNcqAl6RGGfCS1CgD\nXpIa9f8BxE8vGej5weAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9033866c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d.local_avg_hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, I'll run the MC algorithm. I'll also explore how many iterations are needed for the system to reach an equilibrium state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "temp = []\n",
    "for i in range(5000):\n",
    "    d.clusterify(10000)\n",
    "    temp.append(np.average(d.heat_map()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9036ba0790>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9033871510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(range(len(temp)), temp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this plot, we can see how the system cools down. The system almost reaches an equilibrium after 3e7 iterations. It takes almost 20 min to run on single core. Like several other MC algorithms, this is one big disadvantage of this algorithm. It cannot be parallelized to take advantage of multiple processors.\n",
    "\n",
    "Following is the heat map for the equilibrium state. The average temperature has dropped to 14.9 from 18.7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.8965"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hdb0AAGgMRrYAgMYY06vIjGwBABg1RrYAgMaIMX1CipEtAAAjxsgWANAY4zmuXYCTbefa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\nvy8C6D2xcwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9036b33b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d.plot_heat_map()\n",
    "np.average(d.heat_map())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9036baa3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# histogram of temperature in equilibrium state.\n",
    "d.local_avg_hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# write the final configuration to a text file\n",
    "\n",
    "d.write('final_config.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}