{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Helix analysis\n", "\n", "We look at protein helices with HELANAL.\n", "\n", "**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n", "\n", "**Minimum version of MDAnalysis:** 2.0.0\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "\n", "**Optional packages for visualisation:**\n", "\n", "* [matplotlib](https://matplotlib.org)\n", "* [nglview](http://nglviewer.org/nglview/latest/)\n", "\n", "
\n", " \n", "**Note**\n", "\n", "`MDAnalysis.analysis.helix_analysis.HELANAL` implements the HELANAL algorithm from Bansal *et al.*, 2000, which itself uses the method of Sugeta and Miyazawa, 1967 to characterise each local axis. Please cite them when using this module in published work.\n", "\n", "
\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T11:56:12.985716Z", "start_time": "2020-12-27T11:56:12.979131Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f3395796f39d4e409c0934ae05766543", "version_major": 2, "version_minor": 0 }, "text/plain": [] }, "metadata": {}, "output_type": "display_data" } ], "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. (Beckstein *et al.*, 2009)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T11:56:13.711285Z", "start_time": "2020-12-27T11:56:13.607121Z" } }, "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": [ "## 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 (Sugeta and Miyazawa, 1967) 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", "
\n", "
\n", "\n", "![local properties](helanal_images/local_properties.png)\n", " \n", "
\n", "
\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", "
\n", "
\n", "\n", "![local axes](helanal_images/local_axes_properties.png)\n", " \n", "
\n", "
\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", "
\n", "
\n", "\n", "![screw angles](helanal_images/screw_angles.png)\n", " \n", "
\n", "
\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": 3, "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()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "The properties described above are stored as attributes in `h.results`. 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": 4, "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": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.results.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": 5, "metadata": {}, "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": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.results.summary.keys()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T11:56:22.520664Z", "start_time": "2020-12-27T11:56:22.516082Z" }, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean: 86.121\n", "sample_sd: 2.011\n", "abs_dev: 1.715\n" ] } ], "source": [ "for key, val in h.results.summary['global_tilts'].items():\n", " print(f\"{key}: {val:.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the data is stored as arrays, it can easily be plotted." ] }, { "cell_type": "code", "execution_count": 7, "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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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(h.results.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": 8, "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": 9, "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": "15f27001e0db48e1858b5dbabdc33a4b", "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. Bansal, S. Kumar, and R. Velavan.\n", "HELANAL: a program to characterize helix geometry in proteins.\n", "Journal of Biomolecular Structure & Dynamics, 17(5):811–819, April 2000.\n", "00175.\n", "doi:10.1080/07391102.2000.10506570.\n", "\n", "[2] Oliver Beckstein, Elizabeth J. Denning, Juan R. Perilla, and Thomas B. Woolf.\n", "Zipping and Unzipping of Adenylate Kinase: Atomistic Insights into the Ensemble of Open↔Closed Transitions.\n", "Journal of Molecular Biology, 394(1):160–176, November 2009.\n", "00107.\n", "URL: https://linkinghub.elsevier.com/retrieve/pii/S0022283609011164, doi:10.1016/j.jmb.2009.09.009.\n", "\n", "[3] Richard J. Gowers, Max Linke, Jonathan Barnoud, Tyler J. E. Reddy, Manuel N. Melo, Sean L. Seyler, Jan DomaÅ„ski, David L. Dotson, Sébastien Buchoux, Ian M. Kenney, and Oliver Beckstein.\n", "MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations.\n", "Proceedings of the 15th Python in Science Conference, pages 98–105, 2016.\n", "00152.\n", "URL: https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html, doi:10.25080/Majora-629e541a-00e.\n", "\n", "[4] Naveen Michaud-Agrawal, Elizabeth J. Denning, Thomas B. Woolf, and Oliver Beckstein.\n", "MDAnalysis: A toolkit for the analysis of molecular dynamics simulations.\n", "Journal of Computational Chemistry, 32(10):2319–2327, July 2011.\n", "00778.\n", "URL: http://doi.wiley.com/10.1002/jcc.21787, doi:10.1002/jcc.21787." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.15 ('mda-user-guide')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.15" }, "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 }, "vscode": { "interpreter": { "hash": 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