{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Non-linear dimension reduction to diffusion maps\n", "\n", "Here we reduce the dimensions of a trajectory into a diffusion map.\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 (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "\n", "
\n", " \n", "**Note**\n", "\n", "Please cite Coifman and Lafon, 2006 if you use the ``MDAnalysis.analysis.diffusionmap.DiffusionMap`` in published work.\n", "\n", "
\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:42.555038Z", "start_time": "2021-01-05T02:45:41.747445Z" } }, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import PSF, DCD\n", "from MDAnalysis.analysis import diffusionmap\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\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). The trajectory ``DCD`` samples a transition from a closed to an open conformation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:42.762521Z", "start_time": "2021-01-05T02:45:42.556396Z" } }, "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": [ "## Diffusion maps\n", "\n", "Diffusion maps are a non-linear dimensionality reduction technique that embeds the coordinates of each frame onto a lower-dimensional space, such that the distance between each frame in the lower-dimensional space represents their “diffusion distance”, or similarity. It integrates local information about the similarity of each point to its neighours, into a global geometry of the intrinsic manifold. This means that this technique is not suitable for trajectories where the transitions between conformational states are not well-sampled (e.g. replica exchange simulations), as the regions may become disconnected and a meaningful global geometry cannot be approximated. Unlike [principal component analysis](pca.ipynb), there is no explicit mapping between the components of the lower-dimensional space and the original atomic coordinates; no physical interpretation of the eigenvectors is immediately available. \n", "Please see Coifman and Lafon, 2006, Porte *et al.*, 2008, Rohrdanz *et al.*, 2011 and Ferguson *et al.*, 2011 for more information.\n", "\n", "The default distance metric implemented in MDAnalysis' DiffusionMap class is RMSD.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "MDAnalysis implements RMSD calculation using the fast QCP algorithm (Theobald, 2005). Please cite Theobald, 2005 if you use the default distance metric in published work.\n", "\n", "
\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.118650Z", "start_time": "2021-01-05T02:45:42.765100Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dmap = diffusionmap.DiffusionMap(u, select='backbone', epsilon=2)\n", "dmap.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first eigenvector in a diffusion map is always essentially all ones (when divided by a constant):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.121585Z", "start_time": "2021-01-05T02:45:41.752Z" } }, "outputs": [ { "data": { "text/plain": [ "array([-0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525, -0.10101525, -0.10101525,\n", " -0.10101525, -0.10101525, -0.10101525])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dmap._eigenvectors[:, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore, when we embed the trajectory onto the dominant eigenvectors, we ignore the first eigenvector. In order to determine which vectors are dominant, we can examine the eigenvalues for a **spectral gap**: where the eigenvalues stop decreasing constantly in value." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.122785Z", "start_time": "2021-01-05T02:45:41.753Z" }, "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(dmap.eigenvalues[1:16]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this plot, we take the first *k* dominant eigenvectors to be the first five. Below, we transform the trajectory onto these eigenvectors. The ``time`` argument is the exponent that the eigenvalues are raised to for embedding. As values increase for ``time``, more dominant eigenvectors (with lower eigenvalues) dominate the diffusion distance more. The ``transform`` method returns an array of shape (# frames, # eigenvectors)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.124022Z", "start_time": "2021-01-05T02:45:41.755Z" } }, "outputs": [ { "data": { "text/plain": [ "(98, 5)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "transformed = dmap.transform(5, # number of eigenvectors\n", " time=1)\n", "transformed.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For easier analysis and plotting we can turn the array into a DataFrame." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.125160Z", "start_time": "2021-01-05T02:45:41.758Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Mode2 Mode3 Mode4 Mode5 Mode6 Time (ps)\n", "0 -0.094795 -0.075950 -0.054708 -0.035526 -0.022757 0.0\n", "1 -0.166068 -0.132017 -0.094409 -0.060914 -0.038667 1.0\n", "2 -0.199960 -0.154475 -0.107425 -0.067632 -0.041445 2.0\n", "3 0.228815 0.168694 0.111460 0.067112 0.038469 3.0\n", "4 0.250384 0.171873 0.103407 0.057143 0.028398 4.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(transformed, \n", " columns=['Mode{}'.format(i+2) for i in range(5)])\n", "df['Time (ps)'] = df.index * u.trajectory.dt\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several ways we can visualise the data. Using the Seaborn's `PairGrid` tool is the quickest and easiest way, if you have seaborn already installed. Each of the subplots below illustrates axes of the lower-dimensional embedding of the higher-dimensional data, such that dots (frames) that are close are kinetically close (connected by a large number of short pathways), whereas greater distance indicates states that are connected by a smaller number of long pathways. Please see Ferguson *et al.*, 2011 for more information.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "You will need to install the data visualisation library [Seaborn](https://seaborn.pydata.org/installing.html) for this function.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:45:52.126187Z", "start_time": "2021-01-05T02:45:41.759Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "\n", "g = sns.PairGrid(df, hue='Time (ps)', \n", " palette=sns.color_palette('Oranges_d',\n", " n_colors=len(df)))\n", "g.map(plt.scatter, marker='.');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] 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 OpenClosed 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", "[2] Ronald R. Coifman and Stéphane Lafon.\n", "Diffusion maps.\n", "Applied and Computational Harmonic Analysis, 21(1):5–30, July 2006.\n", "02271.\n", "doi:10.1016/j.acha.2006.04.006.\n", "\n", "[3] J. de la Porte, B. M. Herbst, W. Hereman, and S. J. van der Walt.\n", "An introduction to diffusion maps.\n", "In In The 19th Symposium of the Pattern Recognition Association of South Africa. 2008.\n", "00038.\n", "\n", "[4] Andrew Ferguson, Athanassios Z. Panagiotopoulos, Ioannis G. Kevrekidis, and Pablo G. Debenedetti.\n", "Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach.\n", "Chemical Physics Letters, 509(1-3):1–11, June 2011.\n", "00085.\n", "doi:10.1016/j.cplett.2011.04.066.\n", "\n", "[5] Richard J. Gowers, Max Linke, Jonathan Barnoud, Tyler J. E. Reddy, Manuel N. Melo, Sean L. Seyler, Jan Domański, 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", "[6] 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.\n", "\n", "[7] Mary A. Rohrdanz, Wenwei Zheng, Mauro Maggioni, and Cecilia Clementi.\n", "Determination of reaction coordinates via locally scaled diffusion map.\n", "The Journal of Chemical Physics, 134(12):124116, March 2011.\n", "00220.\n", "doi:10.1063/1.3569857.\n", "\n", "[8] Douglas L. Theobald.\n", "Rapid calculation of RMSDs using a quaternion-based characteristic polynomial.\n", "Acta Crystallographica Section A Foundations of Crystallography, 61(4):478–480, July 2005.\n", "00127.\n", "URL: http://scripts.iucr.org/cgi-bin/paper?S0108767305015266, doi:10.1107/S0108767305015266." ] } ], "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": false }, "vscode": { "interpreter": { "hash": "7b52aa17ef4e9358c0e91ff3f0bf50d10667bb8b55636d4b9fb967a2ff94bd8c" } } }, "nbformat": 4, "nbformat_minor": 2 }