{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All distances between two selections\n",
    "\n",
    "Here we use ``distances.distance_array`` to quantify the distances between each atom of a target set to each atom in a reference set, and show how we can extend that to calculating the distances between the centers-of-mass of residues.\n",
    "\n",
    "**Last executed:** Feb 06, 2020 with MDAnalysis 0.20.2-dev0\n",
    "\n",
    "**Last updated:** January 2020\n",
    "\n",
    "**Minimum version of MDAnalysis:** 0.19.0\n",
    "\n",
    "**Packages required:**\n",
    "    \n",
    "* MDAnalysis (<a data-cite=\"michaud-agrawal_mdanalysis_2011\" href=\"https://doi.org/10.1002/jcc.21787\">Michaud-Agrawal *et al.*, 2011</a>, <a data-cite=\"gowers_mdanalysis_2016\" href=\"https://doi.org/10.25080/Majora-629e541a-00e\">Gowers *et al.*, 2016</a>)\n",
    "* MDAnalysisTests\n",
    "   \n",
    "**Optional packages for visualisation:**\n",
    "\n",
    "* [matplotlib](https://matplotlib.org)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import MDAnalysis as mda\n",
    "from MDAnalysis.tests.datafiles import PDB_small\n",
    "from MDAnalysis.analysis import distances\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading files"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test files we will be working with here feature adenylate kinase (AdK), a phosophotransferase enzyme. (<a data-cite=\"beckstein_zipping_2009\" href=\"https://doi.org/10.1016/j.jmb.2009.09.009\">Beckstein *et al.*, 2009</a>) AdK has three domains: \n",
    "\n",
    "  * CORE\n",
    "  * LID: an ATP-binding domain (residues 122-159)\n",
    "  * NMP: an AMP-binding domain (residues 30-59)\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = mda.Universe(PDB_small)   # open AdK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating atom-to-atom distances between non-matching coordinate arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We select the alpha-carbon atoms of each domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LID has 38 residues and NMP has 30 residues\n"
     ]
    }
   ],
   "source": [
    "LID_ca = u.select_atoms('name CA and resid 122-159')\n",
    "NMP_ca = u.select_atoms('name CA and resid 30-59')\n",
    "\n",
    "n_LID = len(LID_ca)\n",
    "n_NMP = len(NMP_ca)\n",
    "print('LID has {} residues and NMP has {} residues'.format(n_LID, n_NMP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`distances.distance_array` will produce an array with shape `(n, m)` distances if there are `n` positions in the reference array and `m` positions in the other configuration. If you want to calculate distances following the minimum image convention, you *must* pass the universe dimensions into the ``box`` keyword."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(38, 30)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_arr = distances.distance_array(LID_ca.positions, # reference\n",
    "                                    NMP_ca.positions, # configuration\n",
    "                                    box=u.dimensions)\n",
    "dist_arr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting distance as a heatmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Distance (Angstrom)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(dist_arr, origin='upper')\n",
    "\n",
    "# add residue ID labels to axes\n",
    "tick_interval = 5\n",
    "ax.set_yticks(np.arange(n_LID)[::tick_interval])\n",
    "ax.set_xticks(np.arange(n_NMP)[::tick_interval])\n",
    "ax.set_yticklabels(LID_ca.resids[::tick_interval])\n",
    "ax.set_xticklabels(NMP_ca.resids[::tick_interval])\n",
    "\n",
    "# add figure labels and titles\n",
    "plt.ylabel('LID')\n",
    "plt.xlabel('NMP')\n",
    "plt.title('Distance between alpha-carbon')\n",
    "\n",
    "# colorbar\n",
    "cbar = fig.colorbar(im)\n",
    "cbar.ax.set_ylabel('Distance (Angstrom)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating residue-to-residue distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As `distances.distance_array` just takes coordinate arrays as input, it is very flexible in calculating distances between each atom, or centers-of-masses, centers-of-geometries, and so on.\n",
    "\n",
    "Instead of calculating the distance between the alpha-carbon of each residue, we could look at the distances between the centers-of-mass instead. The process is very similar to the atom-wise distances above, but we give `distances.distance_array` an array of residue center-of-mass coordinates instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LID has 38 residues and NMP has 30 residues\n"
     ]
    }
   ],
   "source": [
    "LID = u.select_atoms('resid 122-159')\n",
    "NMP = u.select_atoms('resid 30-59')\n",
    "\n",
    "LID_com = LID.center_of_mass(compound='residues')\n",
    "NMP_com = NMP.center_of_mass(compound='residues')\n",
    "\n",
    "n_LID = len(LID_com)\n",
    "n_NMP = len(NMP_com)\n",
    "\n",
    "print('LID has {} residues and NMP has {} residues'.format(n_LID, n_NMP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can pass these center-of-mass arrays directly into `distances.distance_array`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_dist = distances.distance_array(LID_com, NMP_com,\n",
    "                                    box=u.dimensions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Distance (Angstrom)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2, ax2 = plt.subplots()\n",
    "im2 = ax2.imshow(res_dist, origin='upper')\n",
    "\n",
    "# add residue ID labels to axes\n",
    "tick_interval = 5\n",
    "ax2.set_yticks(np.arange(n_LID)[::tick_interval])\n",
    "ax2.set_xticks(np.arange(n_NMP)[::tick_interval])\n",
    "ax2.set_yticklabels(LID.residues.resids[::tick_interval])\n",
    "ax2.set_xticklabels(NMP.residues.resids[::tick_interval])\n",
    "\n",
    "# add figure labels and titles\n",
    "plt.ylabel('LID')\n",
    "plt.xlabel('NMP')\n",
    "plt.title('Distance between center-of-mass')\n",
    "\n",
    "# colorbar\n",
    "cbar2 = fig2.colorbar(im)\n",
    "cbar2.ax.set_ylabel('Distance (Angstrom)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Oliver Beckstein, Elizabeth&nbsp;J. Denning, Juan&nbsp;R. Perilla, and Thomas&nbsp;B. Woolf.\n",
    "Zipping and <span class=\"bibtex-protected\">Unzipping</span> of <span class=\"bibtex-protected\">Adenylate</span> <span class=\"bibtex-protected\">Kinase</span>: <span class=\"bibtex-protected\">Atomistic</span> <span class=\"bibtex-protected\">Insights</span> into the <span class=\"bibtex-protected\">Ensemble</span> of <span class=\"bibtex-protected\">Open</span>↔<span class=\"bibtex-protected\">Closed</span> <span class=\"bibtex-protected\">Transitions</span>.\n",
    "<em>Journal of Molecular Biology</em>, 394(1):160–176, November 2009.\n",
    "00107.\n",
    "URL: <a href=\"https://linkinghub.elsevier.com/retrieve/pii/S0022283609011164\">https://linkinghub.elsevier.com/retrieve/pii/S0022283609011164</a>, <a href=\"https://doi.org/10.1016/j.jmb.2009.09.009\">doi:10.1016/j.jmb.2009.09.009</a>.\n",
    "\n",
    "[2] Richard&nbsp;J. Gowers, Max Linke, Jonathan Barnoud, Tyler J.&nbsp;E. Reddy, Manuel&nbsp;N. Melo, Sean&nbsp;L. Seyler, Jan Domański, David&nbsp;L. Dotson, Sébastien Buchoux, Ian&nbsp;M. Kenney, and Oliver Beckstein.\n",
    "<span class=\"bibtex-protected\">MDAnalysis</span>: <span class=\"bibtex-protected\">A</span> <span class=\"bibtex-protected\">Python</span> <span class=\"bibtex-protected\">Package</span> for the <span class=\"bibtex-protected\">Rapid</span> <span class=\"bibtex-protected\">Analysis</span> of <span class=\"bibtex-protected\">Molecular</span> <span class=\"bibtex-protected\">Dynamics</span> <span class=\"bibtex-protected\">Simulations</span>.\n",
    "<em>Proceedings of the 15th Python in Science Conference</em>, pages 98–105, 2016.\n",
    "00152.\n",
    "URL: <a href=\"https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html\">https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html</a>, <a href=\"https://doi.org/10.25080/Majora-629e541a-00e\">doi:10.25080/Majora-629e541a-00e</a>.\n",
    "\n",
    "[3] Naveen Michaud-Agrawal, Elizabeth&nbsp;J. Denning, Thomas&nbsp;B. Woolf, and Oliver Beckstein.\n",
    "<span class=\"bibtex-protected\">MDAnalysis</span>: <span class=\"bibtex-protected\">A</span> toolkit for the analysis of molecular dynamics simulations.\n",
    "<em>Journal of Computational Chemistry</em>, 32(10):2319–2327, July 2011.\n",
    "00778.\n",
    "URL: <a href=\"http://doi.wiley.com/10.1002/jcc.21787\">http://doi.wiley.com/10.1002/jcc.21787</a>, <a href=\"https://doi.org/10.1002/jcc.21787\">doi:10.1002/jcc.21787</a>."
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