{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Visualize protein deformability"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "deletable": true,
    "editable": true,
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. contents:: Table of Contents\n",
    "   :local:\n",
    "   :backlinks: none"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Protein Blocks are great tools to study protein deformability. Indeed, if the block assigned to a residue changes between two frames of a trajectory, it represents a local deformation of the protein rather than the displacement of the residue.\n",
    "\n",
    "The API allows to visualize Protein Block variability throughout a molecular dynamics simulation trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Date & time: 2017-03-13 10:25:36.895583\n",
      "Python version: 3.5.2 (default, Nov 17 2016, 17:05:23) \n",
      "[GCC 5.4.0 20160609]\n",
      "Matplotlib version: 1.5.3\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint\n",
    "from IPython.display import Image, display\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import urllib.request\n",
    "import os\n",
    "\n",
    "# print date & versions\n",
    "import datetime\n",
    "print(\"Date & time:\",datetime.datetime.now())\n",
    "import sys\n",
    "print(\"Python version:\", sys.version)\n",
    "print(\"Matplotlib version:\", matplotlib.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PBxplore version: 1.3.5\n"
     ]
    }
   ],
   "source": [
    "import pbxplore as pbx\n",
    "print(\"PBxplore version:\", pbx.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here we will look at a molecular dynamics simulation of the barstar. As we will analyse Protein Block sequences, we first need to assign these sequences for each frame of the trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pierre/.virtualenvs/pbx-py3-test/lib/python3.5/site-packages/MDAnalysis/coordinates/XDR.py:126: UserWarning: Reload offsets from trajectory\n",
      " ctime or size or n_atoms did not match\n",
      "  warnings.warn(\"Reload offsets from trajectory\\n \"\n",
      "Frame 1/225.\n",
      "Frame 100/225.\n",
      "Frame 200/225.\n",
      "Frame 225/225.\n"
     ]
    }
   ],
   "source": [
    "# Assign PB sequences for all frames of a trajectory\n",
    "topology, _ = urllib.request.urlretrieve('https://raw.githubusercontent.com/pierrepo/PBxplore/master/demo_doc/psi_md_traj.gro', \n",
    "                                         'psi_md_traj.gro')\n",
    "trajectory, _ = urllib.request.urlretrieve('https://raw.githubusercontent.com/pierrepo/PBxplore/master/demo_doc/psi_md_traj.xtc', \n",
    "                                           'psi_md_traj.xtc')\n",
    "sequences = []\n",
    "for chain_name, chain in pbx.chains_from_trajectory(trajectory, topology):\n",
    "    dihedrals = chain.get_phi_psi_angles()\n",
    "    pb_seq = pbx.assign(dihedrals)\n",
    "    sequences.append(pb_seq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Block occurences per position\n",
    "\n",
    "The basic information we need to analyse protein deformability is the count of occurences of each PB for each position throughout the trajectory. This occurence matrix can be calculated with the `pbxplore.analysis.count_matrix()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "count_matrix = pbx.analysis.count_matrix(sequences)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "``count_matrix`` is a numpy array with one row per PB and one column per position. In each cell is the number of time a position was assigned to a PB.\n",
    "\n",
    "We can visualize ``count_matrix`` using Matplotlib as any 2D numpy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f312fce5208>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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TW1iXdPSJxzQaBz8yczkxuQ2zxsrdI2zdBYnHTy0kirL/fZY+YZuZdY572GZm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\ninDCNjOriP8PinefFsoeqEwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3130570240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "im = plt.imshow(count_matrix, interpolation='none', aspect='auto')\n",
    "plt.colorbar(im)\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Block')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "PBxplore provides the `pbxplore.analysis.plot_map()` function to ease the visualization of the occurence matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PE9LHObU2XjRz+qrnI8ZOYOTYCbU2MzMzK52lvXNZ1ju3oW1zDOhaa8dVaZ0k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\n92mO1ZZzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3158404ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.plot_map('map.png', count_matrix)\n",
    "!rm map.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The `pbxplore.analysis.plot_map()` helper has a ``residue_min`` and a ``residue_max`` optional arguments to display only part of the matrix. These two arguments can be pass to all PBxplore functions that produce a figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NH63Dyp7wb5K0bUQMWPMmL0kvAq4jJfpTSecFPinpmoi4ttn2zax1ljU4Dz8i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\nR/w/Rs7OYrKsuugAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f312daadc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.plot_map('map.png', count_matrix,\n",
    "                      residue_min=20, residue_max=30)\n",
    "!rm map.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Note that matrix in the the figure produced by `pbxplore.analysis.plot_map()` is normalized so as the sum of each column is 1. The matrix can be normalized with the `pbxplore.analysis.compute_freq_matrix()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "freq_matrix = pbx.analysis.compute_freq_matrix(count_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f312db38128>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hqqLnmJlZNYk9DpcAu3VwyPKI2LHp+P2Aj0bEweXzE4qQ4oymfX5Y7vMLSUPA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f312d9e9358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "im = plt.imshow(freq_matrix, interpolation='none', aspect='auto')\n",
    "plt.colorbar(im)\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Block')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Protein Block entropy\n",
    "\n",
    "The $N_{eq}$ is a measure of variability based on the count matrix calculated above. It can be computed with the `pbxplore.analysis.compute_neq()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "neq_by_position = pbx.analysis.compute_neq(count_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "``neq_by_position`` is a 1D numpy array with the $N_{eq}$ for each residue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f31308c0828>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eoHpjKXbuTGaJ3CCxy8yZ8OyzrotpY46/dasTiTFNfol5chSbNsHLXz768UWL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f31584190b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(neq_by_position)\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('$N_{eq}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The `pbxplore.analysis.plot_neq()` helper ease the plotting of the $N_{eq}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7PrkTSvP33gvveQ9885vw8MPeLV5u1SpvNDzttHzGl1SrDXXK3Gtb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\nRsFdRESkYP4/Oi5rV/1OJ2wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f312daf3240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.plot_neq('neq.png', neq_by_position)\n",
    "!rm neq.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The ``residue_min`` and ``residue_max`` arguments are available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HkP5Bv5u99vfiqqxdlf16HNgEWAK0n6WtA7xYTIXdExELs6eDSO00AewJ/D5b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\nZjk4LM3McnBYmpnl4LA0M8vh/wEzlQMIp/hNlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f312db07b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.plot_neq('neq.png', neq_by_position,\n",
    "                      residue_min=20, residue_max=30)\n",
    "!rm neq.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Display PB variability as a logo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oMnXYNifVftvEsLsdzoQcBK+PN6FX7VFB/bCKpmLWLnv9fDFmM60OcvbBkSXx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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.generate_weblogo('logo.png', count_matrix)\n",
    "display(Image('logo.png'))\n",
    "!rm logo.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8uL6+vr6+/vSpvc8FB25gwPE9mhhxFvFUK0aWq4q9GnTUL1CyeGmaDodDGCkhOnJBEOR5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\ncuvxixKwEAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbx.analysis.generate_weblogo('logo.png', count_matrix,\n",
    "                              residue_min=20, residue_max=30)\n",
    "display(Image('logo.png'))\n",
    "!rm logo.png"
   ]
  },
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