CustomProteinVis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from simtk.openmm.app import *\n",
    "from simtk.openmm import *\n",
    "from simtk.unit import *\n",
    "from sys import stdout\n",
    "import numpy as np\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdb = PDBFile('proteins/6ct4.pdb')\n",
    "forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')\n",
    "modeller = Modeller(pdb.topology, pdb.positions)\n",
    "\n",
    "system = forcefield.createSystem(modeller.topology, nonbondedMethod=CutoffNonPeriodic, nonbondedCutoff=1*nanometer, constraints=HBonds)\n",
    "integrator = LangevinIntegrator(300*kelvin, 1/picosecond, 0.002*picoseconds)\n",
    "simulation = Simulation(modeller.topology, system, integrator)\n",
    "simulation.context.setPositions(modeller.positions)\n",
    "simulation.minimizeEnergy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "class AA:\n",
    "    def __init__(self, residue, context):\n",
    "        self.context = context\n",
    "        self.residue = residue\n",
    "        self.atoms = list(self.residue.atoms())\n",
    "        self.atoms_dict = {atom.name:atom.index for atom in self.atoms}\n",
    "        self.atom_indices = list(self.atoms_dict.values())\n",
    "        self.backbone_names = ['N', 'H', 'CA', 'HA', 'C', 'O', 'H2', 'H3', 'OXT']\n",
    "        \n",
    "    def _get_atom_pos(self):\n",
    "        return self.context.getState(getPositions=True).getPositions(asNumpy=True)\n",
    "    \n",
    "    def get_atom_pos(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        return positions[self.atom_indices]\n",
    "    \n",
    "    def get_pos(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        return positions[self.atoms_dict['CA']]\n",
    "        \n",
    "    def get_backbone_dir(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        backbone_dir = positions[self.atoms_dict['C']] - positions[self.atoms_dict['N']]\n",
    "        return backbone_dir / np.sqrt(np.sum(backbone_dir ** 2))\n",
    "        \n",
    "    def get_avg_side_chain_pos(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        indices = [atom.index for atom in self.atoms if atom.name not in self.backbone_names]\n",
    "        return positions[indices].mean(axis=0)\n",
    "    \n",
    "    def get_side_chain_dir(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        side_chain_dir = self.get_avg_side_chain_pos(positions) - self.get_pos(positions)\n",
    "        return side_chain_dir / np.sqrt(np.sum(side_chain_dir ** 2))\n",
    "    \n",
    "    def get_amino_pos(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        return positions[self.atoms_dict['N']]\n",
    "    \n",
    "    def get_carboxyl_pos(self, positions=None):\n",
    "        if positions is None:\n",
    "            positions = self._get_atom_pos()\n",
    "        return positions[self.atoms_dict['C']]\n",
    "    \n",
    "    def set_pos(self, pos):\n",
    "        positions = self._get_atom_pos()\n",
    "        positions[self.atom_indices] += -self.get_pos(positions) + np.array(pos) * nanometers\n",
    "        self.context.setPositions(positions)\n",
    "            \n",
    "chain = []\n",
    "for i, residue in enumerate(simulation.topology.residues()):\n",
    "    aa = AA(residue, simulation.context)\n",
    "    chain.append(aa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
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       "                    fig.imageObj.src);\n",
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       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"900\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot(aas, all_atoms=False, side_chains=True, aa_connections=True, aa_backbones=True):\n",
    "    def as_array(fun):\n",
    "        return np.array([fun(aa)._value for aa in aas])\n",
    "    \n",
    "    fig = plt.figure(figsize=(9, 6))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    \n",
    "    if all_atoms:\n",
    "        positions = as_array(AA.get_atom_pos)\n",
    "        for pos in positions:\n",
    "            ax.plot(pos[:,0], pos[:,1], pos[:,2], '.', alpha=0.1)\n",
    "    \n",
    "    if side_chains:\n",
    "        pos = as_array(AA.get_pos)\n",
    "        side_chain_dir = as_array(AA.get_side_chain_dir) * 0.15\n",
    "        ax.quiver(pos[:,0], pos[:,1], pos[:,2], side_chain_dir[:,0], side_chain_dir[:,1], side_chain_dir[:,2],\n",
    "                  colors='black', alpha=0.35, linewidth=2)\n",
    "    \n",
    "    if aa_connections:\n",
    "        for i in range(1, len(aas)):\n",
    "            points = np.array([aas[i-1].get_carboxyl_pos()._value, aas[i].get_amino_pos()._value])\n",
    "            ax.plot(points[:,0], points[:,1], points[:,2], c='black', alpha=0.4, linewidth=5)\n",
    "    \n",
    "    if aa_backbones:\n",
    "        for aa in aas:\n",
    "            points = np.array([aa.get_amino_pos()._value, aa.get_pos()._value, aa.get_carboxyl_pos()._value])\n",
    "            ax.plot(points[:,0], points[:,1], points[:,2], linewidth=5)\n",
    "    \n",
    "    ax.axis('off')\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "plot(chain)"
   ]
  }
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