dwhswenson/contact_map.ipynb

## contact_map.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contact Maps\n",
    "\n",
    "The file `contact_map.py` includes some tricks to study contact maps in protein dynamics, based on tools in MDTraj. This notebook shows examples as serves as documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import mdtraj as md\n",
    "traj = md.load(\"no-h20.xtc\", top=\"no-h20.pdb\")\n",
    "topology = traj.topology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from contact_map import ContactMap, ContactFrequency, ContactDifference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look at a single frame: `ContactMap`\n",
    "\n",
    "First we make the contact map for the 0th frame. For default parameters (and how to change them) see section \"Changing the defaults\" below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 78.6 ms, sys: 4.21 ms, total: 82.8 ms\n",
      "Wall time: 82 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "frame_contacts = ContactMap(traj[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.07 s, sys: 34.6 ms, total: 1.1 s\n",
      "Wall time: 1.1 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec35410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(frame_contacts.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you wanted to, you could also plot all the atom-atom contacts. But that takes a lot longer, so it is commented out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%time frame_contacts.atom_contacts\n",
    "#%time df = frame_contacts.atom_contacts.df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%%time\n",
    "#plt.axis([0, topology.n_atoms]*2)\n",
    "#plt.pcolor(df, cmap='RdBu', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look at a trajectory: `ContactFrequency`\n",
    "\n",
    "`ContactFrequency` finds the fraction of frames where each contact exists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.45 s, sys: 27.2 ms, total: 4.47 s\n",
      "Wall time: 4.49 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "trajectory_contacts = ContactFrequency(traj[::100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# if you want to save this for later analysis\n",
    "trajectory_contacts.save_to_file(\"traj_contacts.p\")\n",
    "# then load with ContactFrequency.from_file(\"traj_contacts.p\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.12 s, sys: 26.8 ms, total: 1.15 s\n",
      "Wall time: 1.15 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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zaNEYIyOZz+DTFTt2AOedV3QtuqNbMU/jYeCyjTTi0Lupa4L9d7qXQ4yx2ZrL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\nIEEnCIKoCCToBEEQFeH/A23f648Xf6rfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fffb390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(trajectory_contacts.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare two: `ContactDifference`\n",
    "\n",
    "If you want to compare two frequencies, you can use the `ContactDifference` class (or the shortcut for it, which is to subtract a contact frequency/map from another.)\n",
    "\n",
    "The example below will compare the trajectory to its first frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.32 ms, sys: 647 µs, total: 1.97 ms\n",
      "Wall time: 1.55 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "diff = trajectory_contacts - frame_contacts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A contact that appears in trajectory, but not in the frame, will be at +1 and will be shown in red below. A contact that appears in the frame, but not the trajectory, will be at -1 and will be shown in blue below. The values are the difference in the frequencies (of course, for a single frame, the frequency is always 0 or 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.35 s, sys: 44 ms, total: 1.39 s\n",
      "Wall time: 1.4 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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ibjoGvTn09/ejf8cOX9v69aFPgfChv8v+fQuAP3LOb2GMLQUwgXO+lDH2IQCf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\nJ5CgEwRB5IT/Dwmez6UV912DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11072e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(diff.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List the residue contacts that show the most difference\n",
    "\n",
    "First we look at the frames that are much more important in the trajectory than the frame. Then we look at the frames that are more important in the frame than the trajectory.\n",
    "\n",
    "The `.most_common()` method gives a list of the contact pairs and the frequency, sorted by frequency. See also `collections.Counter.most_common()` in the standard Python `collections` module.\n",
    "\n",
    "Here we do this with the `ContactDifference` we created, although it works the same for `ContactFrequency` and `ContactMap` (with the single-frame contact map, the ordering is a bit nonsensical, since every entry is either 0 or 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.38 ms, sys: 559 µs, total: 4.94 ms\n",
      "Wall time: 4.87 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[([SER17, THR20], 0.9900990099009901),\n",
       " ([VAL81, ASN116], 0.9801980198019802),\n",
       " ([LEU19, VAL152], 0.9801980198019802),\n",
       " ([ALA18, GTP201], 0.9702970297029703),\n",
       " ([THR20, LYS16], 0.9603960396039604),\n",
       " ([ASP57, MG202], 0.9504950495049505),\n",
       " ([ILE163, GLU76], 0.9504950495049505),\n",
       " ([GLU162, HIS166], 0.9504950495049505),\n",
       " ([THR20, VAL8], 0.9405940594059405),\n",
       " ([ASP57, THR20], 0.9405940594059405)]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "# residue contact more important in trajectory than in frame (near +1)\n",
    "diff.residue_contacts.most_common()[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[([CL6864, ASP47], -0.9900990099009901),\n",
       " ([VAL29, ILE21], -0.9900990099009901),\n",
       " ([GLU162, NA6838], -0.9900990099009901),\n",
       " ([LYS165, NA6838], -0.9900990099009901),\n",
       " ([NA6816, SER106], -0.9900990099009901),\n",
       " ([ARG161, CL6864], -0.9900990099009901),\n",
       " ([CL6848, NA6845], -0.9900990099009901),\n",
       " ([GLU107, NA6821], -0.9900990099009901),\n",
       " ([CL6854, NA6830], -0.9900990099009901),\n",
       " ([ASP153, GLN22], -0.9801980198019802)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# residue contact more important in frame than in trajectory (near -1)\n",
    "list(reversed(diff.residue_contacts.most_common()))[:10]\n",
    "# alternate: diff.residue_contacts.most_common()[:-10:-1] # (thanks Sander!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List the atoms contacts most common within a given residue contact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VAL81 ASN116\n"
     ]
    }
   ],
   "source": [
    "val81 = topology.residue(80)\n",
    "asn116 = topology.residue(115)\n",
    "print val81, asn116\n",
    "gtp201 = topology.residue(166)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We extended the standard `.most_common()` to take an optional argument. When the argument is given, it will filter the output to only include the ones where that argument is part of the contact. For example, the following gives the residues most commonly in contact with GTP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([VAL14, GTP201], 1.0)\n",
      "([GLY13, GTP201], 1.0)\n",
      "([ALA146, GTP201], 1.0)\n",
      "([SER145, GTP201], 1.0)\n",
      "([GTP201, LEU120], 1.0)\n",
      "([GTP201, GLY15], 1.0)\n",
      "([GLY12, GTP201], 1.0)\n",
      "([ALA11, GTP201], 1.0)\n",
      "([GTP201, LYS16], 1.0)\n",
      "([ASN116, GTP201], 1.0)\n",
      "([LYS147, GTP201], 1.0)\n",
      "([SER17, GTP201], 1.0)\n",
      "([LYS117, GTP201], 1.0)\n",
      "([GTP201, ASP119], 1.0)\n",
      "([ALA18, GTP201], 0.9702970297029703)\n",
      "([GTP201, GLU63], 0.5247524752475248)\n",
      "([ASP57, GTP201], 0.42574257425742573)\n",
      "([ASP33, GTP201], 0.22772277227722773)\n",
      "([GTP201, THR144], 0.13861386138613863)\n"
     ]
    }
   ],
   "source": [
    "for contact in trajectory_contacts.residue_contacts.most_common(gtp201):\n",
    "    if contact[1] > 0.1:\n",
    "        print contact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also find all the atoms, for all residue contacts, that are in contact with a given residue, and return that sorted by frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[([ALA18-CB, GTP201-N7], 0.9702970297029703),\n",
       " ([GTP201-O2B, VAL14-CG1], 0.9702970297029703),\n",
       " ([GTP201-C8, ALA18-CB], 0.9702970297029703),\n",
       " ([SER17-N, GTP201-O2A], 0.9405940594059405),\n",
       " ([SER17-C, GTP201-O2A], 0.9405940594059405),\n",
       " ([GTP201-O2A, ALA18-CA], 0.9405940594059405),\n",
       " ([SER17-CA, GTP201-O2A], 0.9405940594059405),\n",
       " ([ALA18-N, GTP201-O2A], 0.9405940594059405),\n",
       " ([ALA18-CB, GTP201-O2A], 0.9405940594059405),\n",
       " ([SER17-N, GTP201-PB], 0.9306930693069307),\n",
       " ([GLY15-C, GTP201-O2A], 0.9306930693069307),\n",
       " ([GLY15-O, GTP201-O2A], 0.9108910891089109),\n",
       " ([LYS16-N, GTP201-O2A], 0.8811881188118812),\n",
       " ([GTP201-C2, LYS147-CB], 0.8514851485148515),\n",
       " ([GLY15-C, GTP201-PA], 0.8316831683168316)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff.most_common_atoms_for_residue(gtp201)[:15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can look at which atoms are most commonly in contact within a given residue contact pair."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[([ASN116-CB, VAL81-CG1], 0.9801980198019802),\n",
       " ([ASN116-CG, VAL81-CG1], 0.3465346534653465),\n",
       " ([VAL81-CG1, ASN116-ND2], 0.2079207920792079),\n",
       " ([VAL81-CG1, ASN116-N], 0.13861386138613863),\n",
       " ([VAL81-CG1, ASN116-CA], 0.019801980198019802)]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trajectory_contacts.most_common_atoms_for_contact([val81, asn116])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Changing the defaults\n",
    "\n",
    "This sections covers several options that you can modify to make the contact maps faster, and to focus on what you're most interested in.\n",
    "\n",
    "The first three options change which atoms are included as possible contacts. The query atoms are the atoms which appear on the y-axis of the plot. The haystack atoms are those along the x-axis of the plot. In general, you should choose a query that is smaller than the haystack.\n",
    "\n",
    "Both of these options take a list of atom index numbers. These are most easily created using MDTraj's atom selection language."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1408\n"
     ]
    }
   ],
   "source": [
    "# the default selection is\n",
    "default_selection = topology.select(\"not water and not symbol == 'H'\")\n",
    "print len(default_selection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a different query"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "switch1 = topology.select(\"resSeq 32 to 38 and not symbol == 'H'\")\n",
    "switch2 = topology.select(\"resSeq 59 to 67 and not symbol == 'H'\")\n",
    "gtp = topology.select(\"resname GTP and not symbol == 'H'\")\n",
    "mg = topology.select(\"element Mg\")\n",
    "cations = topology.select(\"resname NA or resname MG\")\n",
    "sodium = topology.select(\"resname NA\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.82 s, sys: 11.8 ms, total: 1.83 s\n",
      "Wall time: 1.82 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "sw1_contacts = ContactFrequency(trajectory=traj[::100], query=switch1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XktaJgVwPPSKuBvZm5o7q+W4gM/O22jIGvCT1YFXvKRoRI8CzwHuB/wUeAz6Wmcf7vjJJ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110831610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(sw1_contacts.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a different haystack\n",
    "\n",
    "Currently, changing the haystack has essentially no effect on the performance. However, I expect to change that in the  future (requires making some modifications to MDTraj)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.83 s, sys: 16.2 ms, total: 1.84 s\n",
      "Wall time: 1.87 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "cations_switch1 = ContactFrequency(trajectory=traj[::100], query=cations, haystack=switch1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PAAcmUYdpfgE3ACeBn9EL8gNd+buAJ7q2+3fgnZOu64Tb6SF6PaD/A54HvgRctVwb0Tu7\n6r+BnwM3T7r+U9JeDwLPdMfbI/TGhxeXP9i112ng1knXfwLt9XHgYt9n8ekuu5b9HE76GPPCIklq\nhI+gk6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXi/wFUsir325wClgAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110940650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(cations_switch1.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Changing how many neighboring residues are ignored\n",
    "\n",
    "By default, we ignore atoms from 2 residues on either side of the given residue (and in the same `chain`). This is easily changed. However, even when you say to ignore no neighbors, you still ignore the residue's interactions with itself.\n",
    "\n",
    "Note: for non-protein contact, the `chain` is often poorly defined. In this example, the GTP and the Mg are listed sequentially in residue order, and therefore they are considered \"neighbors\" and their contacts are ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6 s, sys: 34.4 ms, total: 6.04 s\n",
      "Wall time: 6.04 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ignore_none = ContactFrequency(trajectory=traj[::100], n_neighbors_ignored=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FGeUcvCLXTZ+78z2tXLfK/wzAcRU5ntoR5ivXLXRbyly1TtBCN1n3ccTf5KIB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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110903050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(ignore_none.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a different cutoff\n",
    "\n",
    "The size of the cutoff has a large effect on the performance. The default is (currently) 0.45nm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2min 19s, sys: 1.78 s, total: 2min 21s\n",
      "Wall time: 2min 21s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "large_cutoff = ContactFrequency(trajectory=traj[::100], cutoff=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FRx+Hk43SIwen/VIy8NIPGQA/ThSW7D0qzJJPTwLW384RX/OQFNscBWqxPRHOydB/MkDi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OlSy9bILhwCwvFkMzko2yQS4cYTrENu7g+I5oEzbIwXOZast7Wvs8XtzVlFPk1z5sTzgyaRQPPm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\nsrs7kB54ZtYszIth4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee60610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0, topology.n_residues]*2)\n",
    "plt.pcolor(large_cutoff.residue_contacts.df, cmap='seismic', vmin=-1, vmax=1);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
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   "pygments_lexer": "ipython2",
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 },
 "nbformat": 4,
 "nbformat_minor": 0
}

## contact_map.py
"""
Contact map analysis.
"""
# Maintainer: David W.H. Swenson (dwhs@hyperblazer.net)
# Licensed under LGPL, version 2.1 or greater
import collections
import itertools
import scipy
import pandas as pd
import mdtraj as md
import pickle

# TODO:
# * switch to something where you can define the haystack -- the trick is to
#   replace the current mdtraj._compute_neighbors with something that
#   build a voxel list for the haystack, and then checks the voxel for each
#   query atom. Doesn't look like anything is doing that now: neighbors
#   doesn't use voxels, neighborlist doesn't limit the haystack
# * (dream) parallelization: map-reduce like himach should work great for
#   this

def residue_neighborhood(residue, n=1):
    """Find n nearest neighbor residues

    Parameters
    ----------
    residue : mdtraj.Residue
        this residue
    n : positive int
        number of neighbors to find

    Returns
    -------
    list of int
        neighbor residue numbers
    """
    neighborhood = set([residue.index+i for i in range(-n, n+1)])
    chain = set([res.index for res in residue.chain.residues])
    # we could probably choose an faster approach here, but this is pretty
    # good, and it only gets run once per residue
    return [idx for idx in neighborhood if idx in chain]


class ContactCount(object):
    def __init__(self, counter, object_f, n_x, n_y):
        self._counter = counter
        self._object_f = object_f
        self.n_x = n_x
        self.n_y = n_y

    @property
    def counter(self):
        return self._counter

    @property
    def sparse_matrix(self):
        mtx = scipy.sparse.dok_matrix((self.n_x, self.n_y))
        for (k, v) in self._counter.items():
            key = list(k)
            mtx[key[0], key[1]] = v
            mtx[key[1], key[0]] = v
        return mtx

    @property
    def df(self):
        return pd.SparseDataFrame(self.sparse_matrix.todense())

    def most_common(self, obj=None):
        if obj is None:
            result = [
                ([self._object_f(idx) for idx in common[0]], common[1])
                for common in self.most_common_idx()
            ]
        else:
            obj_idx = obj.index
            result = [
                ([self._object_f(idx) for idx in common[0]], common[1])
                for common in self.most_common_idx()
                if obj_idx in common[0]
            ]
        return result


    def most_common_idx(self):
        return self._counter.most_common()

class ContactObject(object):
    """
    Generic object for contact map related analysis. Effectively abstract.

    Much of what we need to do the contact map analysis is the same for all
    analyses. It's in here.
    """
    def __init__(self, topology, query, haystack, cutoff, n_neighbors_ignored):
        # all inits required: no defaults for abstract class!
        self._topology = topology
        if query is None:
            query = topology.select("not water and not symbol == 'H'")
        if haystack is None:
            haystack = topology.select("not water and not symbol == 'H'")
        # make things private and accessible through read-only properties so
        # they don't get accidentally changed after analysis
        self._cutoff = cutoff
        self._query = set(query)
        self._haystack = set(haystack)
        self._n_neighbors_ignored = n_neighbors_ignored
        self._atom_idx_to_residue_idx = {atom.index: atom.residue.index
                                         for atom in self.topology.atoms}

    def save_to_file(self, filename, mode="w"):
        """Save this object to the given file.

        Parameters
        ----------
        filename : string
            the file to write to
        mode : 'w' or 'a'
            file writing mode. Use 'w' to overwrite, 'a' to append.
        """
        f = open(filename, mode)
        pickle.dump(self, f)
        f.close()

    @classmethod
    def from_file(cls, filename):
        f = open(filename, "r")
        return pickle.load(f)

    def __sub__(self, other):
        return ContactDifference(positive=self, negative=other)

    @property
    def cutoff(self):
        return self._cutoff

    @property
    def n_neighbors_ignored(self):
        return self._n_neighbors_ignored

    @property
    def query(self):
        return list(self._query)

    @property
    def haystack(self):
        return list(self._haystack)

    @property
    def topology(self):
        return self._topology

    @property
    def residue_query_atom_idxs(self):
        result = {}
        for atom_idx in self._query:
            residue_idx = self.topology.atom(atom_idx).residue.index
            try:
                result[residue_idx] += [atom_idx]
            except KeyError:
                result[residue_idx] = [atom_idx]
        return result


    @property
    def residue_ignore_atom_idxs(self):
        result = {}
        for residue_idx in self.residue_query_atom_idxs.keys():
            residue = self.topology.residue(residue_idx)
            # Several steps to go residue indices -> atom indices
            ignore_residue_idxs = residue_neighborhood(residue,
                                                       self._n_neighbors_ignored)
            ignore_residues = [self.topology.residue(idx)
                               for idx in ignore_residue_idxs]
            ignore_atoms = sum([list(res.atoms)
                                for res in ignore_residues], [])
            ignore_atom_idxs = set([atom.index for atom in ignore_atoms])
            result[residue_idx] = ignore_atom_idxs
        return result

    def most_common_atoms_for_residue(self, residue):
        try:
            residue_idx = residue.index
        except AttributeError:
            residue_idx = residue
            residue = self.topology.residue(residue_idx)

        residue_atoms = set(atom.index for atom in residue.atoms)
        results = []
        for contact in self.atom_contacts.most_common_idx():
            atoms = contact[0]
            number = contact[1]
            for atom in atoms:
                if atom in residue_atoms:
                    results.append(([self.topology.atom(a) for a in atoms],
                                    number))
        return results

    def most_common_atoms_for_contact(self, contact_pair):
        contact_pair = frozenset(contact_pair)
        res_A = list(contact_pair)[0]
        res_B = list(contact_pair)[1]
        try:
            res_A_idx = res_A.index
        except AttributeError:
            res_A_idx = res_A
            res_A = self.topology.residue(res_A_idx)
        try:
            res_B_idx = res_B.index
        except AttributeError:
            resB_idx = res_B
            res_B = self.topology.residue(res_B_idx)
        atom_idxs_A = set(atom.index for atom in res_A.atoms)
        atom_idxs_B = set(atom.index for atom in res_B.atoms)
        all_atom_pairs = [
            frozenset(pair)
            for pair in itertools.product(atom_idxs_A, atom_idxs_B)
        ]
        result = [([self.topology.atom(idx) for idx in contact[0]], contact[1])
                  for contact in self.atom_contacts.most_common_idx()
                  if frozenset(contact[0]) in all_atom_pairs]
        return result


    def contact_map(self, trajectory, frame_number, residue_query_atom_idxs,
                    residue_ignore_atom_idxs):
        """
        Returns atom and residue contact maps for the given frame.

        Parameters
        ----------
        frame : mdtraj.Trajectory
            the desired frame (uses the first frame in this trajectory)
        residue_query_atom_idxs : dict
        residue_ignore_atom_idxs : dict

        Returns
        -------
        atom_contacts : collections.Counter
        residue_contact : collections.Counter
        """
        neighborlist = md.compute_neighborlist(trajectory, self.cutoff,
                                               frame_number)
        contact_pairs = set([])
        residue_pairs = set([])
        for residue_idx in residue_query_atom_idxs:
            ignore_atom_idxs = set(residue_ignore_atom_idxs[residue_idx])
            query_idxs = residue_query_atom_idxs[residue_idx]
            for atom_idx in query_idxs:
                # sets should make this fast, esp since neighbor_idxs
                # should be small and s-t is avg cost len(s)
                neighbor_idxs = set(neighborlist[atom_idx])
                contact_neighbors = neighbor_idxs - ignore_atom_idxs
                contact_neighbors = contact_neighbors & self._haystack
                # frozenset is unique key independent of order
                # local_pairs = set(frozenset((atom_idx, neighb))
                                  # for neighb in contact_neighbors)
                local_pairs = set(map(
                    frozenset,
                    itertools.product([atom_idx], contact_neighbors)
                ))
                contact_pairs |= local_pairs
                # contact_pairs |= set(frozenset((atom_idx, neighb))
                                     # for neighb in contact_neighbors)
                local_residue_partners = set(self._atom_idx_to_residue_idx[a]
                                             for a in contact_neighbors)
                local_res_pairs = set(map(
                    frozenset,
                    itertools.product([residue_idx], local_residue_partners)
                ))
                residue_pairs |= local_res_pairs

        atom_contacts = collections.Counter(contact_pairs)
        # residue_pairs = set(
            # frozenset(self._atom_idx_to_residue_idx[aa] for aa in pair)
            # for pair in contact_pairs
        # )
        residue_contacts = collections.Counter(residue_pairs)
        return (atom_contacts, residue_contacts)

    @property
    def atom_contacts(self):
        n_atoms = self.topology.n_atoms
        return ContactCount(self._atom_contacts, self.topology.atom,
                            n_atoms, n_atoms)

    @property
    def residue_contacts(self):
        n_res = self.topology.n_residues
        return ContactCount(self._residue_contacts, self.topology.residue,
                            n_res, n_res)


class ContactMap(ContactObject):
    """
    Contact map (atomic and residue) for a single frame.
    """
    def __init__(self, frame, query=None, haystack=None, cutoff=0.45,
                 n_neighbors_ignored=2):
        self._frame = frame
        super(ContactMap, self).__init__(frame.topology, query, haystack,
                                         cutoff, n_neighbors_ignored)
        contact_maps = self.contact_map(frame, 0,
                                        self.residue_query_atom_idxs,
                                        self.residue_ignore_atom_idxs)
        (self._atom_contacts, self._residue_contacts) = contact_maps


class ContactTrajectory(ContactObject):
    """
    Contact map (atomic and residue) for each individual trajectory frame.

    NOT YET IMPLEMENTED. I'm not sure whether this gives appreciable speed
    improvements over running contact map over and over.
    """
    pass


class ContactFrequency(ContactObject):
    """
    Contact frequency (atomic and residue) for a trajectory.

    The contact frequency is defined as fraction of the trajectory that a
    certain contact is made. This object calculates this quantity for all
    contacts with atoms in the `query` residue, with "contact" defined as
    being within a certain cutoff distance.

    Parameters
    ----------
    trajectory : mdtraj.Trajectory
        Trajectory (segment) to analyze
    query_residues : list of int
        Indices of the residues to be included as query. Default `None`
        means all atoms.
    cutoff : float
        Cutoff distance for contacts, in nanometers. Default 0.45.
    n_neighbors_ignored : int
        Number of neighboring residues (in the same chain) to ignore.
        Default 2.
    """
    def __init__(self, trajectory, query=None, haystack=None, cutoff=0.45,
                 n_neighbors_ignored=2):
        self._trajectory = trajectory
        self._n_frames = len(trajectory)
        super(ContactFrequency, self).__init__(trajectory.topology,
                                               query, haystack, cutoff,
                                               n_neighbors_ignored)
        self._build_contact_map()

    def _build_contact_map(self):
        # We actually build the contact map on a per-residue basis, although
        # we save it on a per-atom basis. This allows us ignore
        # n_nearest_neighbor residues.
        # TODO: this whole thing should be cleaned up and should replace
        # MDTraj's really slow old computer_contacts by using MDTraj's new
        # neighborlists (unless the MDTraj people do that first).
        topology = self.topology
        trajectory = self.trajectory
        cutoff = self.cutoff
        self._atom_contacts_count = collections.Counter([])
        self._residue_contacts_count = collections.Counter([])

        # cache things that can be calculated once based on the topology
        # (namely, which atom indices matter for each residue)
        residue_ignore_atom_idxs = self.residue_ignore_atom_idxs
        residue_query_atom_idxs = self.residue_query_atom_idxs
        for frame_num in range(len(trajectory)):
            frame_contacts = self.contact_map(trajectory, frame_num,
                                              residue_query_atom_idxs,
                                              residue_ignore_atom_idxs)
            frame_atom_contacts = frame_contacts[0]
            frame_residue_contacts = frame_contacts[1]
            # self._atom_contacts_count += frame_atom_contacts
            self._atom_contacts_count.update(frame_atom_contacts)
            self._residue_contacts_count += frame_residue_contacts

    @property
    def trajectory(self):
        return self._trajectory

    @property
    def n_frames(self):
        return self._n_frames

    @property
    def atom_contacts(self):
        """Atoms pairs mapped to fraction of trajectory with that contact"""
        n_x = len(self.haystack)
        n_y = len(self.query)
        return ContactCount(collections.Counter({
            item[0]: float(item[1])/self.n_frames
            for item in self._atom_contacts_count.items()
        }), self.topology.atom, n_x, n_y)

    @property
    def residue_contacts(self):
        """Residue pairs mapped to fraction of trajectory with that contact"""
        n_x = self.topology.n_residues
        n_y = self.topology.n_residues
        return ContactCount(collections.Counter({
            item[0]: float(item[1])/self.n_frames
            for item in self._residue_contacts_count.items()
        }), self.topology.residue, n_x, n_y)


class ContactDifference(ContactObject):
    """
    Contact map comparison (atomic and residue).

    This can compare single frames or entire trajectories (or even mix the
    two!)
    """
    def __init__(self, positive, negative):
        self.positive = positive
        self.negative = negative
        # TODO: verify that the combination is compatible: same topol, etc
        super(ContactDifference, self).__init__(positive.topology,
                                                positive.query,
                                                positive.haystack,
                                                positive.cutoff,
                                                positive.n_neighbors_ignored)

    def __sub__(self, other):
        raise NotImplementedError

    def contact_map(self, *args, **kwargs):
        raise NotImplementedError

    @property
    def atom_contacts(self):
        n_x = self.topology.n_atoms
        n_y = self.topology.n_atoms
        diff = collections.Counter(self.positive.atom_contacts.counter)
        diff.subtract(self.negative.atom_contacts.counter)
        return ContactCount(diff, self.topology.atom, n_x, n_y)

    @property
    def residue_contacts(self):
        n_x = self.topology.n_residues
        n_y = self.topology.n_residues
        diff = collections.Counter(self.positive.residue_contacts.counter)
        diff.subtract(self.negative.residue_contacts.counter)
        return ContactCount(diff, self.topology.residue, n_x, n_y)
	"""
	Contact map analysis.
	"""
	# Maintainer: David W.H. Swenson (dwhs@hyperblazer.net)
	# Licensed under LGPL, version 2.1 or greater
	import collections
	import itertools
	import scipy
	import pandas as pd
	import mdtraj as md
	import pickle

	# TODO:
	# * switch to something where you can define the haystack -- the trick is to
	# replace the current mdtraj._compute_neighbors with something that
	# build a voxel list for the haystack, and then checks the voxel for each
	# query atom. Doesn't look like anything is doing that now: neighbors
	# doesn't use voxels, neighborlist doesn't limit the haystack
	# * (dream) parallelization: map-reduce like himach should work great for
	# this

	def residue_neighborhood(residue, n=1):
	"""Find n nearest neighbor residues

	Parameters
	----------
	residue : mdtraj.Residue
	this residue
	n : positive int
	number of neighbors to find

	Returns
	-------
	list of int
	neighbor residue numbers
	"""
	neighborhood = set([residue.index+i for i in range(-n, n+1)])
	chain = set([res.index for res in residue.chain.residues])
	# we could probably choose an faster approach here, but this is pretty
	# good, and it only gets run once per residue
	return [idx for idx in neighborhood if idx in chain]


	class ContactCount(object):
	def __init__(self, counter, object_f, n_x, n_y):
	self._counter = counter
	self._object_f = object_f
	self.n_x = n_x
	self.n_y = n_y

	@property
	def counter(self):
	return self._counter

	@property
	def sparse_matrix(self):
	mtx = scipy.sparse.dok_matrix((self.n_x, self.n_y))
	for (k, v) in self._counter.items():
	key = list(k)
	mtx[key[0], key[1]] = v
	mtx[key[1], key[0]] = v
	return mtx

	@property
	def df(self):
	return pd.SparseDataFrame(self.sparse_matrix.todense())

	def most_common(self, obj=None):
	if obj is None:
	result = [
	([self._object_f(idx) for idx in common[0]], common[1])
	for common in self.most_common_idx()
	]
	else:
	obj_idx = obj.index
	result = [
	([self._object_f(idx) for idx in common[0]], common[1])
	for common in self.most_common_idx()
	if obj_idx in common[0]
	]
	return result



	def most_common_idx(self):
	return self._counter.most_common()

	class ContactObject(object):
	"""
	Generic object for contact map related analysis. Effectively abstract.

	Much of what we need to do the contact map analysis is the same for all
	analyses. It's in here.
	"""
	def __init__(self, topology, query, haystack, cutoff, n_neighbors_ignored):
	# all inits required: no defaults for abstract class!
	self._topology = topology
	if query is None:
	query = topology.select("not water and not symbol == 'H'")
	if haystack is None:
	haystack = topology.select("not water and not symbol == 'H'")
	# make things private and accessible through read-only properties so
	# they don't get accidentally changed after analysis
	self._cutoff = cutoff
	self._query = set(query)
	self._haystack = set(haystack)
	self._n_neighbors_ignored = n_neighbors_ignored
	self._atom_idx_to_residue_idx = {atom.index: atom.residue.index
	for atom in self.topology.atoms}

	def save_to_file(self, filename, mode="w"):
	"""Save this object to the given file.

	Parameters
	----------
	filename : string
	the file to write to
	mode : 'w' or 'a'
	file writing mode. Use 'w' to overwrite, 'a' to append.
	"""
	f = open(filename, mode)
	pickle.dump(self, f)
	f.close()

	@classmethod
	def from_file(cls, filename):
	f = open(filename, "r")
	return pickle.load(f)

	def __sub__(self, other):
	return ContactDifference(positive=self, negative=other)

	@property
	def cutoff(self):
	return self._cutoff

	@property
	def n_neighbors_ignored(self):
	return self._n_neighbors_ignored

	@property
	def query(self):
	return list(self._query)

	@property
	def haystack(self):
	return list(self._haystack)

	@property
	def topology(self):
	return self._topology

	@property
	def residue_query_atom_idxs(self):
	result = {}
	for atom_idx in self._query:
	residue_idx = self.topology.atom(atom_idx).residue.index
	try:
	result[residue_idx] += [atom_idx]
	except KeyError:
	result[residue_idx] = [atom_idx]
	return result


	@property
	def residue_ignore_atom_idxs(self):
	result = {}
	for residue_idx in self.residue_query_atom_idxs.keys():
	residue = self.topology.residue(residue_idx)
	# Several steps to go residue indices -> atom indices
	ignore_residue_idxs = residue_neighborhood(residue,
	self._n_neighbors_ignored)
	ignore_residues = [self.topology.residue(idx)
	for idx in ignore_residue_idxs]
	ignore_atoms = sum([list(res.atoms)
	for res in ignore_residues], [])
	ignore_atom_idxs = set([atom.index for atom in ignore_atoms])
	result[residue_idx] = ignore_atom_idxs
	return result

	def most_common_atoms_for_residue(self, residue):
	try:
	residue_idx = residue.index
	except AttributeError:
	residue_idx = residue
	residue = self.topology.residue(residue_idx)

	residue_atoms = set(atom.index for atom in residue.atoms)
	results = []
	for contact in self.atom_contacts.most_common_idx():
	atoms = contact[0]
	number = contact[1]
	for atom in atoms:
	if atom in residue_atoms:
	results.append(([self.topology.atom(a) for a in atoms],
	number))
	return results

	def most_common_atoms_for_contact(self, contact_pair):
	contact_pair = frozenset(contact_pair)
	res_A = list(contact_pair)[0]
	res_B = list(contact_pair)[1]
	try:
	res_A_idx = res_A.index
	except AttributeError:
	res_A_idx = res_A
	res_A = self.topology.residue(res_A_idx)
	try:
	res_B_idx = res_B.index
	except AttributeError:
	resB_idx = res_B
	res_B = self.topology.residue(res_B_idx)
	atom_idxs_A = set(atom.index for atom in res_A.atoms)
	atom_idxs_B = set(atom.index for atom in res_B.atoms)
	all_atom_pairs = [
	frozenset(pair)
	for pair in itertools.product(atom_idxs_A, atom_idxs_B)
	]
	result = [([self.topology.atom(idx) for idx in contact[0]], contact[1])
	for contact in self.atom_contacts.most_common_idx()
	if frozenset(contact[0]) in all_atom_pairs]
	return result


	def contact_map(self, trajectory, frame_number, residue_query_atom_idxs,
	residue_ignore_atom_idxs):
	"""
	Returns atom and residue contact maps for the given frame.

	Parameters
	----------
	frame : mdtraj.Trajectory
	the desired frame (uses the first frame in this trajectory)
	residue_query_atom_idxs : dict
	residue_ignore_atom_idxs : dict

	Returns
	-------
	atom_contacts : collections.Counter
	residue_contact : collections.Counter
	"""
	neighborlist = md.compute_neighborlist(trajectory, self.cutoff,
	frame_number)
	contact_pairs = set([])
	residue_pairs = set([])
	for residue_idx in residue_query_atom_idxs:
	ignore_atom_idxs = set(residue_ignore_atom_idxs[residue_idx])
	query_idxs = residue_query_atom_idxs[residue_idx]
	for atom_idx in query_idxs:
	# sets should make this fast, esp since neighbor_idxs
	# should be small and s-t is avg cost len(s)
	neighbor_idxs = set(neighborlist[atom_idx])
	contact_neighbors = neighbor_idxs - ignore_atom_idxs
	contact_neighbors = contact_neighbors & self._haystack
	# frozenset is unique key independent of order
	# local_pairs = set(frozenset((atom_idx, neighb))
	# for neighb in contact_neighbors)
	local_pairs = set(map(
	frozenset,
	itertools.product([atom_idx], contact_neighbors)
	))
	contact_pairs \|= local_pairs
	# contact_pairs \|= set(frozenset((atom_idx, neighb))
	# for neighb in contact_neighbors)
	local_residue_partners = set(self._atom_idx_to_residue_idx[a]
	for a in contact_neighbors)
	local_res_pairs = set(map(
	frozenset,
	itertools.product([residue_idx], local_residue_partners)
	))
	residue_pairs \|= local_res_pairs

	atom_contacts = collections.Counter(contact_pairs)
	# residue_pairs = set(
	# frozenset(self._atom_idx_to_residue_idx[aa] for aa in pair)
	# for pair in contact_pairs
	# )
	residue_contacts = collections.Counter(residue_pairs)
	return (atom_contacts, residue_contacts)

	@property
	def atom_contacts(self):
	n_atoms = self.topology.n_atoms
	return ContactCount(self._atom_contacts, self.topology.atom,
	n_atoms, n_atoms)

	@property
	def residue_contacts(self):
	n_res = self.topology.n_residues
	return ContactCount(self._residue_contacts, self.topology.residue,
	n_res, n_res)


	class ContactMap(ContactObject):
	"""
	Contact map (atomic and residue) for a single frame.
	"""
	def __init__(self, frame, query=None, haystack=None, cutoff=0.45,
	n_neighbors_ignored=2):
	self._frame = frame
	super(ContactMap, self).__init__(frame.topology, query, haystack,
	cutoff, n_neighbors_ignored)
	contact_maps = self.contact_map(frame, 0,
	self.residue_query_atom_idxs,
	self.residue_ignore_atom_idxs)
	(self._atom_contacts, self._residue_contacts) = contact_maps


	class ContactTrajectory(ContactObject):
	"""
	Contact map (atomic and residue) for each individual trajectory frame.

	NOT YET IMPLEMENTED. I'm not sure whether this gives appreciable speed
	improvements over running contact map over and over.
	"""
	pass


	class ContactFrequency(ContactObject):
	"""
	Contact frequency (atomic and residue) for a trajectory.

	The contact frequency is defined as fraction of the trajectory that a
	certain contact is made. This object calculates this quantity for all
	contacts with atoms in the `query` residue, with "contact" defined as
	being within a certain cutoff distance.

	Parameters
	----------
	trajectory : mdtraj.Trajectory
	Trajectory (segment) to analyze
	query_residues : list of int
	Indices of the residues to be included as query. Default `None`
	means all atoms.
	cutoff : float
	Cutoff distance for contacts, in nanometers. Default 0.45.
	n_neighbors_ignored : int
	Number of neighboring residues (in the same chain) to ignore.
	Default 2.
	"""
	def __init__(self, trajectory, query=None, haystack=None, cutoff=0.45,
	n_neighbors_ignored=2):
	self._trajectory = trajectory
	self._n_frames = len(trajectory)
	super(ContactFrequency, self).__init__(trajectory.topology,
	query, haystack, cutoff,
	n_neighbors_ignored)
	self._build_contact_map()

	def _build_contact_map(self):
	# We actually build the contact map on a per-residue basis, although
	# we save it on a per-atom basis. This allows us ignore
	# n_nearest_neighbor residues.
	# TODO: this whole thing should be cleaned up and should replace
	# MDTraj's really slow old computer_contacts by using MDTraj's new
	# neighborlists (unless the MDTraj people do that first).
	topology = self.topology
	trajectory = self.trajectory
	cutoff = self.cutoff
	self._atom_contacts_count = collections.Counter([])
	self._residue_contacts_count = collections.Counter([])

	# cache things that can be calculated once based on the topology
	# (namely, which atom indices matter for each residue)
	residue_ignore_atom_idxs = self.residue_ignore_atom_idxs
	residue_query_atom_idxs = self.residue_query_atom_idxs
	for frame_num in range(len(trajectory)):
	frame_contacts = self.contact_map(trajectory, frame_num,
	residue_query_atom_idxs,
	residue_ignore_atom_idxs)
	frame_atom_contacts = frame_contacts[0]
	frame_residue_contacts = frame_contacts[1]
	# self._atom_contacts_count += frame_atom_contacts
	self._atom_contacts_count.update(frame_atom_contacts)
	self._residue_contacts_count += frame_residue_contacts

	@property
	def trajectory(self):
	return self._trajectory

	@property
	def n_frames(self):
	return self._n_frames

	@property
	def atom_contacts(self):
	"""Atoms pairs mapped to fraction of trajectory with that contact"""
	n_x = len(self.haystack)
	n_y = len(self.query)
	return ContactCount(collections.Counter({
	item[0]: float(item[1])/self.n_frames
	for item in self._atom_contacts_count.items()
	}), self.topology.atom, n_x, n_y)

	@property
	def residue_contacts(self):
	"""Residue pairs mapped to fraction of trajectory with that contact"""
	n_x = self.topology.n_residues
	n_y = self.topology.n_residues
	return ContactCount(collections.Counter({
	item[0]: float(item[1])/self.n_frames
	for item in self._residue_contacts_count.items()
	}), self.topology.residue, n_x, n_y)


	class ContactDifference(ContactObject):
	"""
	Contact map comparison (atomic and residue).

	This can compare single frames or entire trajectories (or even mix the
	two!)
	"""
	def __init__(self, positive, negative):
	self.positive = positive
	self.negative = negative
	# TODO: verify that the combination is compatible: same topol, etc
	super(ContactDifference, self).__init__(positive.topology,
	positive.query,
	positive.haystack,
	positive.cutoff,
	positive.n_neighbors_ignored)

	def __sub__(self, other):
	raise NotImplementedError

	def contact_map(self, args, *kwargs):
	raise NotImplementedError

	@property
	def atom_contacts(self):
	n_x = self.topology.n_atoms
	n_y = self.topology.n_atoms
	diff = collections.Counter(self.positive.atom_contacts.counter)
	diff.subtract(self.negative.atom_contacts.counter)
	return ContactCount(diff, self.topology.atom, n_x, n_y)

	@property
	def residue_contacts(self):
	n_x = self.topology.n_residues
	n_y = self.topology.n_residues
	diff = collections.Counter(self.positive.residue_contacts.counter)
	diff.subtract(self.negative.residue_contacts.counter)
	return ContactCount(diff, self.topology.residue, n_x, n_y)