{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contact analysis: number of contacts within a cutoff\n",
    "\n",
    "We calculate the number of salt bridges in an enzyme as it transitions from a closed to an open conformation.\n",
    "\n",
    "**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n",
    "\n",
    "**Minimum version of MDAnalysis:** 0.17.0\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",
    "* [matplotlib](https://matplotlib.org)\n",
    "* [pandas](https://pandas.pydata.org)\n",
    "\n",
    "**See also**\n",
    "\n",
    "* [Write your own contacts analysis method](contacts_custom.ipynb)\n",
    "* [Q1 vs Q2 contact analysis](contacts_q1q2.ipynb)\n",
    "* [Fraction of native contacts over a trajectory](contacts_native_fraction.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-07-29T05:08:24.953983Z",
     "start_time": "2020-07-29T05:08:21.329652Z"
    },
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:13.080694Z",
     "iopub.status.busy": "2021-05-19T05:57:13.080158Z",
     "iopub.status.idle": "2021-05-19T05:57:14.169643Z",
     "shell.execute_reply": "2021-05-19T05:57:14.170078Z"
    }
   },
   "outputs": [],
   "source": [
    "import MDAnalysis as mda\n",
    "from MDAnalysis.tests.datafiles import PSF, DCD\n",
    "from MDAnalysis.analysis import contacts\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Background\n",
    "\n",
    "Quantifying the number of contacts over a trajectory can give insight into the formation and rearrangements of secondary and tertiary structure. This is closely related to native contacts analysis; where the fraction of native contacts refers to the fraction of contacts retained by a protein from the contacts in a reference frame, the number of contacts simply counts how many residues are within a certain cutoff for each frame. No reference is necessary. Please see the [Fraction of native contacts](contacts_native_fraction.ipynb#Background) for an introduction to native contacts analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading files\n",
    "\n",
    "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>) The trajectory ``DCD`` samples a transition from a closed to an open conformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.173557Z",
     "iopub.status.busy": "2021-05-19T05:57:14.172951Z",
     "iopub.status.idle": "2021-05-19T05:57:14.397389Z",
     "shell.execute_reply": "2021-05-19T05:57:14.396971Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pbarletta/mambaforge/envs/mda-user-guide/lib/python3.9/site-packages/MDAnalysis/coordinates/DCD.py:165: DeprecationWarning: DCDReader currently makes independent timesteps by copying self.ts while other readers update self.ts inplace. This behaviour will be changed in 3.0 to be the same as other readers\n",
      "  warnings.warn(\"DCDReader currently makes independent timesteps\"\n"
     ]
    }
   ],
   "source": [
    "u = mda.Universe(PSF, DCD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the groups for contact analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define salt bridges as contacts between NH/NZ in ARG/LYS and OE\\*/OD\\* in ASP/GLU. It is not recommend to use this overly simplistic definition for real work that you want to publish."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.402746Z",
     "iopub.status.busy": "2021-05-19T05:57:14.401962Z",
     "iopub.status.idle": "2021-05-19T05:57:14.405378Z",
     "shell.execute_reply": "2021-05-19T05:57:14.405760Z"
    }
   },
   "outputs": [],
   "source": [
    "sel_basic = \"(resname ARG LYS) and (name NH* NZ)\"\n",
    "sel_acidic = \"(resname ASP GLU) and (name OE* OD*)\"\n",
    "acidic = u.select_atoms(sel_acidic)\n",
    "basic = u.select_atoms(sel_basic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating number of contacts within a cutoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we define a function that calculates the number of contacts between `group_a` and `group_b` within the `radius` cutoff, for each frame in a trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.410261Z",
     "iopub.status.busy": "2021-05-19T05:57:14.409582Z",
     "iopub.status.idle": "2021-05-19T05:57:14.411114Z",
     "shell.execute_reply": "2021-05-19T05:57:14.411621Z"
    }
   },
   "outputs": [],
   "source": [
    "def contacts_within_cutoff(u, group_a, group_b, radius=4.5):\n",
    "    timeseries = []\n",
    "    for ts in u.trajectory:\n",
    "        # calculate distances between group_a and group_b\n",
    "        dist = contacts.distance_array(group_a.positions, group_b.positions)\n",
    "        # determine which distances <= radius\n",
    "        n_contacts = contacts.contact_matrix(dist, radius).sum()\n",
    "        timeseries.append([ts.frame, n_contacts])\n",
    "    return np.array(timeseries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are returned as a numpy array. The first column is the frame, and the second is the number of contacts present in that frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.414883Z",
     "iopub.status.busy": "2021-05-19T05:57:14.414313Z",
     "iopub.status.idle": "2021-05-19T05:57:14.430769Z",
     "shell.execute_reply": "2021-05-19T05:57:14.431195Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(98, 2)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ca = contacts_within_cutoff(u, acidic, basic, radius=4.5)\n",
    "ca.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.435679Z",
     "iopub.status.busy": "2021-05-19T05:57:14.435146Z",
     "iopub.status.idle": "2021-05-19T05:57:14.441001Z",
     "shell.execute_reply": "2021-05-19T05:57:14.441446Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Frame</th>\n",
       "      <th># Contacts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Frame  # Contacts\n",
       "0      0          69\n",
       "1      1          73\n",
       "2      2          77\n",
       "3      3          77\n",
       "4      4          85"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ca_df = pd.DataFrame(ca, columns=['Frame', \n",
    "                                  '# Contacts'])\n",
    "ca_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:57:14.445711Z",
     "iopub.status.busy": "2021-05-19T05:57:14.444988Z",
     "iopub.status.idle": "2021-05-19T05:57:14.575273Z",
     "shell.execute_reply": "2021-05-19T05:57:14.575913Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
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   "source": [
    "ca_df.plot(x='Frame')\n",
    "plt.ylabel('# salt bridges');"
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    "## 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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