From 144d65949a3bfe76efefba3789247632700ceebe Mon Sep 17 00:00:00 2001
From: Lily Wang <lily@minium.com.au>
Date: Sun, 27 Dec 2020 22:56:46 +1100
Subject: [PATCH] add helanal

---
 .../examples/analysis/structure/README.rst    |    1 +
 .../examples/analysis/structure/helanal.ipynb | 2848 +++++++++++++++++
 .../helanal_images/local_axes_properties.png  |  Bin 0 -> 32346 bytes
 .../helanal_images/local_heights.png          |  Bin 0 -> 17921 bytes
 .../helanal_images/local_properties.png       |  Bin 0 -> 102457 bytes
 .../local_window_properties.png               |  Bin 0 -> 66389 bytes
 .../structure/helanal_images/screw_angles.png |  Bin 0 -> 16210 bytes
 7 files changed, 2849 insertions(+)
 create mode 100644 doc/source/examples/analysis/structure/helanal.ipynb
 create mode 100644 doc/source/examples/analysis/structure/helanal_images/local_axes_properties.png
 create mode 100644 doc/source/examples/analysis/structure/helanal_images/local_heights.png
 create mode 100644 doc/source/examples/analysis/structure/helanal_images/local_properties.png
 create mode 100644 doc/source/examples/analysis/structure/helanal_images/local_window_properties.png
 create mode 100644 doc/source/examples/analysis/structure/helanal_images/screw_angles.png

diff --git a/doc/source/examples/analysis/structure/README.rst b/doc/source/examples/analysis/structure/README.rst
index bda002056..3043c26a8 100644
--- a/doc/source/examples/analysis/structure/README.rst
+++ b/doc/source/examples/analysis/structure/README.rst
@@ -12,3 +12,4 @@ Structure
    /examples/analysis/structure/average_rdf
    /examples/analysis/structure/site_specific_rdf
    /examples/analysis/structure/dihedrals
+   /examples/analysis/structure/helanal
diff --git a/doc/source/examples/analysis/structure/helanal.ipynb b/doc/source/examples/analysis/structure/helanal.ipynb
new file mode 100644
index 000000000..17804d5a4
--- /dev/null
+++ b/doc/source/examples/analysis/structure/helanal.ipynb
@@ -0,0 +1,2848 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Helix analysis\n",
+    "\n",
+    "We look at protein helices with HELANAL.\n",
+    "\n",
+    "**Last executed:** Dec 27, 2020 with MDAnalysis 2.0.0-dev0\n",
+    "\n",
+    "**Last updated:** March 2020\n",
+    "\n",
+    "**Minimum version of MDAnalysis:** 2.0.0\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",
+    "* [nglview](http://nglviewer.org/nglview/latest/)\n",
+    "\n",
+    "<div class=\"alert alert-info\">\n",
+    "    \n",
+    "**Note**\n",
+    "\n",
+    "`MDAnalysis.analysis.helix_analysis.HELANAL` implements the HELANAL algorithm from <a data-cite=\"bansal_helanal_2000\" href=\"https://doi.org/10.1080/07391102.2000.10506570\">Bansal *et al.*, 2000</a>, which itself uses the method of <a data-cite=\"sugeta_general_1967\" href=\"https://doi.org/10.1002/bip.1967.360050708\">Sugeta and Miyazawa, 1967</a> to characterise each local axis. Please cite them when using this module in published work.\n",
+    "\n",
+    "</div>\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:12.985716Z",
+     "start_time": "2020-12-27T11:56:12.979131Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import MDAnalysis as mda\n",
+    "from MDAnalysis.tests.datafiles import PSF, DCD\n",
+    "from MDAnalysis.analysis import helix_analysis as hel\n",
+    "import matplotlib.pyplot as plt\n",
+    "import nglview as nv\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "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>)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:13.711285Z",
+     "start_time": "2020-12-27T11:56:13.607121Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "u = mda.Universe(PSF, DCD)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Helix analysis\n",
+    "\n",
+    "HELANAL can be used to characterize the geometry of helices with at least 9 residues. The geometry of an alpha helix is characterized by computing local helix axes and local helix origins for four contiguous C-alpha atoms, using the procedure of Sugeta and Miyazawa (<a data-cite=\"sugeta_general_1967\" href=\"https://doi.org/10.1002/bip.1967.360050708\">Sugeta and Miyazawa, 1967</a>) and sliding this window over the length of the helix in steps of one C-alpha atom.\n",
+    "\n",
+    "``HELANAL`` computes a number of properties.\n",
+    "\n",
+    "<center>\n",
+    "<div style=\"width: 600px; text-align: center;\">\n",
+    "\n",
+    "![local properties](helanal_images/local_properties.png)\n",
+    "   \n",
+    "</div>\n",
+    "</center>\n",
+    "\n",
+    "\n",
+    "For each sliding window, it calculates:\n",
+    "\n",
+    "* ``local_rotation_vectors``: the vectors bisecting the angles of the middle 2 atoms\n",
+    "* ``local_origins``: the projected origins of the helix\n",
+    "* ``local_twists``: the twist of each window ($\\theta$)\n",
+    "* ``residues_per_turn``: how many residues would fit in a turn, based on ``local_twist``\n",
+    "* ``local_axes``: the axis of each local helix\n",
+    "* ``local_heights``: the rise of each helix\n",
+    "\n",
+    "HELANAL calculates the bends between each ``local_axes`` and fits the vector ``global_axes`` to the ``local_origins``.\n",
+    "\n",
+    "<center>\n",
+    "<div style=\"width: 150px; text-align: center;\">\n",
+    "\n",
+    "![local axes](helanal_images/local_axes_properties.png)\n",
+    "   \n",
+    "</div>\n",
+    "</center>\n",
+    "\n",
+    "``all_bends`` contains the angles between every `local_axes` ($\\alpha$) in a pairwise matrix, whereas ``local_bends`` contains the angles between ``local_axes`` that are calculated 3 windows apart ($\\beta$). The ``global_tilts`` ($\\gamma$) are calculated as the angle between the ``global_axes`` and the user-given reference ``ref_axis``.\n",
+    "\n",
+    "<center>\n",
+    "<div style=\"width: 200px; text-align: center;\">\n",
+    "\n",
+    "![screw angles](helanal_images/screw_angles.png)\n",
+    "   \n",
+    "</div>\n",
+    "</center>\n",
+    "\n",
+    "Finally, ``local_screw`` angles are computed between the ``local_rotation_vectors`` and the normal plane of the ``global_axes``."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Running the analysis\n",
+    "\n",
+    "As with most other analysis classes in MDAnalysis, pass in the universe and selection that you would to like to operate on. The default reference axis is the z-axis. You can also pass in a list of selection strings to run HELANAL on multiple helices at once."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:15.019676Z",
+     "start_time": "2020-12-27T11:56:14.929127Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "h = hel.HELANAL(u, select='name CA and resnum 161-187',\n",
+    "                ref_axis=[0, 0, 1]).run()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The properties described above are stored as attributes in `h`. For example, the ``all_bends`` matrix contains the bends in a `(n_frames, n_residues-3, n_residues-3)` array."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:18.524268Z",
+     "start_time": "2020-12-27T11:56:18.517882Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(98, 24, 24)"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "h.all_bends.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Each property is also summarised with a mean value, the sample standard deviation, and the average deviation from the mean."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:22.055549Z",
+     "start_time": "2020-12-27T11:56:22.049626Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "dict_keys(['local_twists', 'local_bends', 'local_heights', 'local_nres_per_turn', 'local_origins', 'local_axes', 'local_helix_directions', 'local_screw_angles', 'global_axis', 'global_tilts', 'all_bends'])"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "h.summary.keys()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:22.520664Z",
+     "start_time": "2020-12-27T11:56:22.516082Z"
+    },
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'mean': 86.12100441254297,\n",
+       " 'sample_sd': 2.0108377345768065,\n",
+       " 'abs_dev': 1.7152381351099988}"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "h.summary['global_tilts']"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As the data is stored as arrays, it can easily be plotted."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:24.061616Z",
+     "start_time": "2020-12-27T11:56:23.950283Z"
+    }
+   },
+   "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": [
+    "plt.plot(h.local_twists.mean(axis=1))\n",
+    "plt.xlabel('Frame')\n",
+    "plt.ylabel('Average twist (degrees)');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can also create a Universe from the ``local_origins`` if you would like to save it as a file and visualise it in programs such as VMD."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:25.706533Z",
+     "start_time": "2020-12-27T11:56:25.697091Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "origins = h.universe_from_origins()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-12-27T11:56:26.348022Z",
+     "start_time": "2020-12-27T11:56:26.286571Z"
+    },
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "756baa7f7a0e4360b062ef9a104ab750",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "NGLWidget(max_frame=97)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "view = nv.show_mdanalysis(h.atomgroups[0])\n",
+    "view.add_trajectory(origins)\n",
+    "view"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "\n",
+    "[1] M.&nbsp;Bansal, S.&nbsp;Kumar, and R.&nbsp;Velavan.\n",
+    "<span class=\"bibtex-protected\">HELANAL</span>: a program to characterize helix geometry in proteins.\n",
+    "<em>Journal of Biomolecular Structure &amp; Dynamics</em>, 17(5):811–819, April 2000.\n",
+    "00175.\n",
+    "<a href=\"https://doi.org/10.1080/07391102.2000.10506570\">doi:10.1080/07391102.2000.10506570</a>.\n",
+    "\n",
+    "[2] 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",
+    "[3] 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",
+    "[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-dev)",
+   "language": "python",
+   "name": "mda-dev"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  },
+  "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": true
+  },
+  "widgets": {
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+       "max": 97,
+       "style": "IPY_MODEL_eede91af3ba246a6990646571b15adf8"
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diff --git a/doc/source/examples/analysis/structure/helanal_images/local_heights.png b/doc/source/examples/analysis/structure/helanal_images/local_heights.png
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