doc/source/examples/analysis/structure/elastic_network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Elastic network analysis\n",
    "\n",
    "Here we use a Gaussian network model to characterise conformational states of a trajectory.\n",
    "\n",
    "**Last executed:** Dec 27, 2020 with MDAnalysis 1.0.0\n",
    "\n",
    "**Last updated:** January 2020\n",
    "\n",
    "**Minimum version of MDAnalysis:** 1.0.0\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",
    "<div class=\"alert alert-info\">\n",
    "    \n",
    "**Note**\n",
    "\n",
    "The elastic network analysis follows the approach of (<a data-cite=\"hall_characterization_2007\" href=\"https://doi.org/10.1021/ja071797y\">Hall *et al.*, 2007</a>). Please cite them when using the ``MDAnalysis.analysis.gnm`` module in published work.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:10.907984Z",
     "iopub.status.busy": "2021-05-19T05:58:10.907144Z",
     "iopub.status.idle": "2021-05-19T05:58:11.621995Z",
     "shell.execute_reply": "2021-05-19T05:58:11.622470Z"
    }
   },
   "outputs": [],
   "source": [
    "import MDAnalysis as mda\n",
    "from MDAnalysis.tests.datafiles import PSF, DCD, DCD2\n",
    "from MDAnalysis.analysis import gnm\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>)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:11.626135Z",
     "iopub.status.busy": "2021-05-19T05:58:11.625593Z",
     "iopub.status.idle": "2021-05-19T05:58:11.919487Z",
     "shell.execute_reply": "2021-05-19T05:58:11.919074Z"
    }
   },
   "outputs": [],
   "source": [
    "u1 = mda.Universe(PSF, DCD)\n",
    "u2 = mda.Universe(PSF, DCD2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a Gaussian network model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a Gaussian network model to represent a molecule as an elastic network, we can characterise the concerted motions of a protein, and the dominance of these motions, over a trajectory. The analysis is applied to the atoms in the `selection`. If two atoms are within the `cutoff` distance (default: 7 ångström), they are considered to be bound by a spring. This analysis is reasonably robust to the choice of cutoff (between 5-9 Å), but the singular value decomposition may not converge with a lower cutoff.\n",
    "\n",
    "We use the GNMAnalysis class ([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/gnm.html#MDAnalysis.analysis.gnm.GNMAnalysis)) for the analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:11.923601Z",
     "iopub.status.busy": "2021-05-19T05:58:11.922947Z",
     "iopub.status.idle": "2021-05-19T05:58:16.214927Z",
     "shell.execute_reply": "2021-05-19T05:58:16.215674Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lily/anaconda3/envs/mda-user-guide/lib/python3.7/site-packages/MDAnalysis/analysis/gnm.py:294: DeprecationWarning: The structure of the `results` list will change in MDAnalysis version 2.0.\n",
      "  category=DeprecationWarning\n"
     ]
    }
   ],
   "source": [
    "nma1 = gnm.GNMAnalysis(u1,\n",
    "                      select='name CA',\n",
    "                      cutoff=7.0)\n",
    "nma1.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is saved in `nma1.results`: the time in picoseconds, the first eigenvalue, and the first eigenvector, associated with each frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:16.222738Z",
     "iopub.status.busy": "2021-05-19T05:58:16.221853Z",
     "iopub.status.idle": "2021-05-19T05:58:16.225058Z",
     "shell.execute_reply": "2021-05-19T05:58:16.225568Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "98"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nma1.results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:16.230286Z",
     "iopub.status.busy": "2021-05-19T05:58:16.229530Z",
     "iopub.status.idle": "2021-05-19T05:58:21.279527Z",
     "shell.execute_reply": "2021-05-19T05:58:21.280142Z"
    }
   },
   "outputs": [],
   "source": [
    "nma2 = gnm.GNMAnalysis(u2,\n",
    "                      select='name CA',\n",
    "                      cutoff=7.0)\n",
    "nma2.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike normal mode analysis, Gaussian network model analysis uses only a single eigenvalue to represent the rotation and translation of each frame. The motion with the lowest positive eigenvalue represents the dominant motion of a structure. The frequency of this motion is the square root of the eigenvalue.\n",
    "\n",
    "Plotting the probability distribution of the frequency for the first eigenvector can highlight variation in the probability distribution, which can indicate trajectories in different states.\n",
    "\n",
    "Below, we plot the distribution of eigenvalues. The dominant conformation state is represented by the peak at 0.06."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:21.293277Z",
     "iopub.status.busy": "2021-05-19T05:58:21.292108Z",
     "iopub.status.idle": "2021-05-19T05:58:21.614571Z",
     "shell.execute_reply": "2021-05-19T05:58:21.615117Z"
    }
   },
   "outputs": [
    {
     "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": [
    "eigenvalues1 = [res[1] for res in nma1.results]\n",
    "eigenvalues2 = [res[1] for res in nma2.results]\n",
    "\n",
    "histfig, histax = plt.subplots(nrows=2, sharex=True, sharey=True)\n",
    "histax[0].hist(eigenvalues1)\n",
    "histax[1].hist(eigenvalues2)\n",
    "\n",
    "histax[1].set_xlabel('Eigenvalue')\n",
    "histax[0].set_ylabel('Frequency')\n",
    "histax[1].set_ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we plot how the eigenvalue varies with time, we can see that the simulation transitions into the dominant conformation and stays there in both trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:21.626109Z",
     "iopub.status.busy": "2021-05-19T05:58:21.625129Z",
     "iopub.status.idle": "2021-05-19T05:58:21.751749Z",
     "shell.execute_reply": "2021-05-19T05:58:21.752237Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time1 = [res[0] for res in nma1.results]\n",
    "time2 = [res[0] for res in nma2.results]\n",
    "linefig, lineax = plt.subplots()\n",
    "plt.plot(time1, eigenvalues1, label='DCD')\n",
    "plt.plot(time2, eigenvalues2, label='DCD2')\n",
    "lineax.set_xlabel('Time (ps)')\n",
    "lineax.set_ylabel('Eigenvalue')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DCD and DCD2 appear to be in similar conformation states."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a Gaussian network model with only close contacts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `MDAnalysis.analysis.gnm.closeContactGNMAnalysis` class provides a version of the analysis where the Kirchhoff contact matrix is generated from close contacts between individual atoms in different residues, whereas the `GNMAnalysis` class generates it directly from all the atoms. In this close contacts class, you can weight the contact matrix by the number of atoms in the residues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:21.756636Z",
     "iopub.status.busy": "2021-05-19T05:58:21.756105Z",
     "iopub.status.idle": "2021-05-19T05:58:27.825024Z",
     "shell.execute_reply": "2021-05-19T05:58:27.825519Z"
    }
   },
   "outputs": [],
   "source": [
    "nma_close = gnm.closeContactGNMAnalysis(u1,\n",
    "                                        select='name CA',\n",
    "                                        cutoff=7.0,\n",
    "                                        weights='size')\n",
    "nma_close.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:27.835704Z",
     "iopub.status.busy": "2021-05-19T05:58:27.834967Z",
     "iopub.status.idle": "2021-05-19T05:58:27.960946Z",
     "shell.execute_reply": "2021-05-19T05:58:27.961555Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigenvalues_close = [res[1] for res in nma_close.results]\n",
    "\n",
    "plt.hist(eigenvalues_close)\n",
    "plt.xlabel('Eigenvalue')\n",
    "plt.ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-05-19T05:58:27.976945Z",
     "iopub.status.busy": "2021-05-19T05:58:27.976108Z",
     "iopub.status.idle": "2021-05-19T05:58:28.085441Z",
     "shell.execute_reply": "2021-05-19T05:58:28.086050Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_close = [res[0] for res in nma_close.results]\n",
    "ax = plt.plot(time_close, eigenvalues_close)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Eigenvalue');"
   ]
  },
  {
   "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] Benjamin&nbsp;A. Hall, Samantha&nbsp;L. Kaye, Andy Pang, Rafael Perera, and Philip&nbsp;C. Biggin.\n",
    "Characterization of <span class=\"bibtex-protected\">Protein</span> <span class=\"bibtex-protected\">Conformational</span> <span class=\"bibtex-protected\">States</span> by <span class=\"bibtex-protected\">Normal</span>-<span class=\"bibtex-protected\">Mode</span> <span class=\"bibtex-protected\">Frequencies</span>.\n",
    "<em>Journal of the American Chemical Society</em>, 129(37):11394–11401, September 2007.\n",
    "00020.\n",
    "URL: <a href=\"https://doi.org/10.1021/ja071797y\">https://doi.org/10.1021/ja071797y</a>, <a href=\"https://doi.org/10.1021/ja071797y\">doi:10.1021/ja071797y</a>.\n",
    "\n",
    "[4] 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>."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (mda-user-guide)",
   "language": "python",
   "name": "mda-user-guide"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": false,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}