{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Principal component analysis of a trajectory\n", "\n", "Here we compute the principal component analysis of a trajectory.\n", "\n", "**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n", "\n", "**Minimum version of MDAnalysis:** 1.0.0\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", "* [nglview](http://nglviewer.org/nglview/latest/api.html)\n", "\n", "Throughout this tutorial we will include cells for visualising Universes with the [NGLView](http://nglviewer.org/nglview/latest/api.html) library. However, these will be commented out, and we will show the expected images generated instead of the interactive widgets." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:19:58.481105Z", "start_time": "2020-12-27T02:19:57.039201Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import PSF, DCD\n", "from MDAnalysis.analysis import pca, align\n", "# import nglview as nv\n", "\n", "import warnings\n", "# suppress some MDAnalysis warnings about writing PDB files\n", "warnings.filterwarnings('ignore')" ] }, { "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": "2020-12-27T02:19:58.572962Z", "start_time": "2020-12-27T02:19:58.483786Z" } }, "outputs": [], "source": [ "u = mda.Universe(PSF, DCD)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Principal component analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Principal component analysis is a common linear dimensionality reduction technique that maps the coordinates in each frame of your trajectory to a linear combination of orthogonal vectors. The vectors are called **principal components**, and they are ordered such that the first principal component accounts for the most variance in the original data (i.e. the largest uncorrelated motion in your trajectory), and each successive component accounts for less and less variance. The frame-by-frame conformational fluctuation can be considered a linear combination of the essential dynamics yielded by the PCA. Please see Amadei *et al.*, 1993, Jolliffe, 2002, Sittel *et al.*, 2014, or Sittel and Stock, 2018 for a more in-depth introduction to PCA.\n", "\n", "Trajectory coordinates can be transformed onto a lower-dimensional space (*essential subspace*) constructed from these principal components in order to compare conformations. You can thereby visualise the motion described by that component.\n", "\n", "In MDAnalysis, the method implemented in the PCA class ([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/pca.html)) is as follows:\n", "\n", "1. Optionally align each frame in your trajectory to the first frame.\n", "2. Construct a 3N x 3N covariance for the N atoms in your trajectory. Optionally, you can provide a mean; otherwise the covariance is to the averaged structure over the trajectory.\n", "3. Diagonalise the covariance matrix. The eigenvectors are the principal components, and their eigenvalues are the associated variance.\n", "4. Sort the eigenvalues so that the principal components are ordered by variance.\n", "\n", "
\n", " \n", "**Note**\n", " \n", "Principal component analysis algorithms are deterministic, but the solutions are not unique. For example, you could easily change the sign of an eigenvector without altering the PCA. Different algorithms are likely to produce different answers, due to variations in implementation. `MDAnalysis` may not return the same values as another package.\n", "\n", "
\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-01-05T02:46:35.986463Z", "start_time": "2021-01-05T02:46:35.885643Z" } }, "outputs": [], "source": [ "aligner = align.AlignTraj(u, u, select='backbone',\n", " in_memory=True).run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can choose how many principal components to save from the analysis with `n_components`. The default value is `None`, which saves all of them. You can also pass a `mean` reference structure to be used in calculating the covariance matrix. With the default value of `None`, the covariance uses the mean coordinates of the trajectory." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:07.656913Z", "start_time": "2020-12-27T02:19:58.577563Z" } }, "outputs": [], "source": [ "pc = pca.PCA(u, select='backbone', \n", " align=True, mean=None,\n", " n_components=None).run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The principal components are saved in `pc.p_components`. If you kept all the components, you should have an array of shape $(n_{atoms}\\times3, n_{atoms}\\times3)$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:16.649872Z", "start_time": "2020-12-27T02:20:16.634649Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There are 855 backbone atoms in the analysis\n", "(2565, 2565)\n" ] } ], "source": [ "backbone = u.select_atoms('backbone')\n", "n_bb = len(backbone)\n", "print('There are {} backbone atoms in the analysis'.format(n_bb))\n", "print(pc.p_components.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variance of each principal component is in `pc.variance`. For example, to get the variance explained by the first principal component to 5 decimal places:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:21.823829Z", "start_time": "2020-12-27T02:20:21.816021Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PC1: 4203.19053\n" ] } ], "source": [ "print(f\"PC1: {pc.variance[0]:.5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This variance is somewhat meaningless by itself. It is much more intuitive to consider the variance of a principal component as a percentage of the total variance in the data. MDAnalysis also tracks the percentage cumulative variance in `pc.cumulated_variance`. As shown below, the first principal component contains 90.3% the total trajectory variance. The first three components combined account for 96.4% of the total variance." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:23.692900Z", "start_time": "2020-12-27T02:20:23.687699Z" }, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cumulated variance: 0.903\n", "Cumulated variance: 0.951\n", "Cumulated variance: 0.964\n" ] } ], "source": [ "for i in range(3):\n", " print(f\"Cumulated variance: {pc.cumulated_variance[i]:.3f}\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:24.501694Z", "start_time": "2020-12-27T02:20:24.374964Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(pc.cumulated_variance[:10])\n", "plt.xlabel('Principal component')\n", "plt.ylabel('Cumulative variance')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualising projections into a reduced dimensional space\n", "\n", "The `pc.transform()` method transforms a given atom group into weights $\\mathbf{w}_i$ over each principal component $i$.\n", "\n", "$$ \\mathbf{w}_i(t) = (\\mathbf{r}(t)-\\mathbf{\\overline{r}}) \\cdot \\mathbf{u}_i$$\n", "\n", "$\\mathbf{r}(t)$ are the atom group coordinates at time $t$, $\\mathbf{\\overline{r}}$ are the mean coordinates used in the PCA, and $\\mathbf{u}_i$ is the $i$th principal component eigenvector $\\mathbf{u}$.\n", "\n", "While the given atom group must have the same number of atoms that the principal components were calculated over, it does not have to be the same group.\n", "\n", "Again, passing `n_components=None` will tranform your atom group over every component. Below, we limit the output to projections over 3 principal components only." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:26.034071Z", "start_time": "2020-12-27T02:20:26.002165Z" } }, "outputs": [ { "data": { "text/plain": [ "(98, 3)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "transformed = pc.transform(backbone, n_components=3)\n", "transformed.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output has the shape (n_frames, n_components). For easier analysis and plotting we can turn the array into a DataFrame." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:27.302939Z", "start_time": "2020-12-27T02:20:27.281162Z" } }, "outputs": [ { "data": { "text/html": [ "
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PC1PC2PC3Time (ps)
0118.40841329.08824115.7466240.0
1115.56187926.78679714.6524981.0
2112.67561625.03876612.9202742.0
3110.34146724.30698411.4270983.0
4107.58430223.46415411.6121044.0
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" ], "text/plain": [ " PC1 PC2 PC3 Time (ps)\n", "0 118.408413 29.088241 15.746624 0.0\n", "1 115.561879 26.786797 14.652498 1.0\n", "2 112.675616 25.038766 12.920274 2.0\n", "3 110.341467 24.306984 11.427098 3.0\n", "4 107.584302 23.464154 11.612104 4.0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(transformed, \n", " columns=['PC{}'.format(i+1) for i in range(3)])\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.\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": 11, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:20:43.927184Z", "start_time": "2020-12-27T02:20:28.405274Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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='.')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to investigate the essential motions of the trajectory is to project the original trajectory onto each of the principal components, to visualise the motion of the principal component. The outer product $\\otimes$ of the weights $\\mathbf{w}_i(t)$ for principal component $i$ with the eigenvector $\\mathbf{u}_i$ describes fluctuations around the mean on that axis, so the projected trajectory $\\mathbf{r}_i(t)$ is simply the fluctuations added onto the mean positions $\\mathbf{\\overline{r}}$.\n", "\n", "$$ \\mathbf{r}_i(t) = \\mathbf{w}_i(t) \\otimes \\mathbf{u}_i + \\mathbf{\\overline{r}}$$\n", "\n", "Below, we generate the projected coordinates of the first principal component. The mean positions are stored at `pc.mean`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:21:00.109489Z", "start_time": "2020-12-27T02:21:00.105601Z" } }, "outputs": [], "source": [ "pc1 = pc.p_components[:, 0]\n", "trans1 = transformed[:, 0]\n", "projected = np.outer(trans1, pc1) + pc.mean.flatten()\n", "coordinates = projected.reshape(len(trans1), -1, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can create a new universe from this to visualise the movement over the first principal component." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:21:03.279468Z", "start_time": "2020-12-27T02:21:03.193255Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "proj1 = mda.Merge(backbone)\n", "proj1.load_new(coordinates, order=\"fac\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:21:05.697035Z", "start_time": "2020-12-27T02:21:05.533730Z" } }, "outputs": [], "source": [ "# view = nv.show_mdanalysis(proj1.atoms)\n", "# view" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have `nglview` installed, you can view the trajectory in the notebook. Otherwise, you can write the trajectory out to a file and use another program such as VMD. Below, we create a movie of the component." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2020-12-26T06:51:33.338274Z", "start_time": "2020-12-26T06:51:33.319302Z" }, "scrolled": true, "tags": [ "nbval-ignore-output" ] }, "outputs": [], "source": [ "# from nglview.contrib.movie import MovieMaker\n", "# movie = MovieMaker(\n", "# view,\n", "# step=4, # keep every 4th frame\n", "# output='pc1.gif',\n", "# render_params={\"factor\": 3}, # set to 4 for highest quality\n", "# )\n", "# movie.make()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", " \n", "![pc1 gif](pc1.gif)\n", " \n", "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measuring convergence with cosine content\n", "\n", "The essential modes of a trajectory usually describe global, collective motions. The cosine content of a principal component can be interpreted to determine whether proteins are transitioning between conformational states. However, random diffusion can also appear to produce collective motion. The cosine content can measure the convergence of a trajectory and indicate poor sampling. \n", "\n", "The cosine content of a principal component measures how similar it is to a cosine shape. Values range from 0 (no similarity to a cosine) and 1 (a perfect cosine shape). If the values of the first few principal components are close to 1, this can indicate poor sampling, as the motion of the particles may not be distinguished from random diffusion. Values below 0.7 do not indicate poor sampling.\n", "\n", "For more information, please see Maisuradze *et al.*, 2009.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "Hess, 2002 first published the usage of cosine content to evaluate sampling. Please cite this paper when using the ``MDAnalysis.analysis.pca.cosine_content`` method in published work.\n", "\n", "
\n", "\n", "Below we calculate the cosine content of the first five principal components in the transformed subspace. Note that this is an example only, to dmonstrate how to use the method; the first few principal components of short simulations always represent random diffusion (Hess, 2002)." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:13:58.769516Z", "start_time": "2020-12-27T02:13:58.761494Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cosine content for PC 1 = 0.960\n", "Cosine content for PC 2 = 0.906\n", "Cosine content for PC 3 = 0.723\n" ] } ], "source": [ "for i in range(3):\n", " cc = pca.cosine_content(transformed, i)\n", " print(f\"Cosine content for PC {i+1} = {cc:.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be seen, the cosine content of each component is quite high. If we plot the transformed components over time, we can see that each component does resemble a cosine curve." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2020-12-27T02:11:49.174147Z", "start_time": "2020-12-27T02:11:48.544605Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# melt the dataframe into a tidy format\n", "melted = pd.melt(df, id_vars=[\"Time (ps)\"],\n", " var_name=\"PC\",\n", " value_name=\"Value\")\n", "g = sns.FacetGrid(melted, col=\"PC\")\n", "g.map(sns.lineplot, \n", " \"Time (ps)\", # x-axis\n", " \"Value\", # y-axis\n", " ci=None) # no confidence interval\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] Andrea Amadei, Antonius B. M. Linssen, and Herman J. C. Berendsen.\n", "Essential dynamics of proteins.\n", "Proteins: Structure, Function, and Bioinformatics, 17(4):412–425, 1993.\n", "_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/prot.340170408.\n", "URL: http://onlinelibrary.wiley.com/doi/abs/10.1002/prot.340170408, doi:https://doi.org/10.1002/prot.340170408.\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 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", "[3] 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", "[4] I. T. Jolliffe.\n", "Principal Component Analysis.\n", "Springer Series in Statistics.\n", "Springer-Verlag, New York, 2 edition, 2002.\n", "ISBN 978-0-387-95442-4.\n", "URL: http://www.springer.com/gp/book/9780387954424, doi:10.1007/b98835.\n", "\n", "[5] 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", "[6] Florian Sittel, Abhinav Jain, and Gerhard Stock.\n", "Principal component analysis of molecular dynamics: on the use of Cartesian vs. internal coordinates.\n", "The Journal of Chemical Physics, 141(1):014111, July 2014.\n", "doi:10.1063/1.4885338.\n", "\n", "[7] Florian Sittel and Gerhard Stock.\n", "Perspective: Identification of collective variables and metastable states of protein dynamics.\n", "The Journal of Chemical Physics, 149(15):150901, October 2018.\n", "Publisher: American Institute of Physics.\n", "URL: http://aip.scitation.org/doi/10.1063/1.5049637, doi:10.1063/1.5049637." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.2" }, "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": "5edc5d8d8cbc0935a054a8e44024f729bc376180aae27775d15f2ff38c68f892" } } }, "nbformat": 4, "nbformat_minor": 4 }