{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating the pairwise RMSD of a trajectory\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", "* matplotlib\n", "\n", "**See also**\n", "\n", "* [1D RMSD](rmsd.ipynb)\n", "* [RMSF](rmsf.ipynb)\n", "\n", "\n", "
\n", " \n", "**Note**\n", "\n", "MDAnalysis implements RMSD calculation using the fast QCP algorithm (Theobald, 2005). Please cite (Theobald, 2005) when using the ``MDAnalysis.analysis.align`` module in published work.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:38.028738Z", "iopub.status.busy": "2021-05-19T05:56:38.028068Z", "iopub.status.idle": "2021-05-19T05:56:38.930418Z", "shell.execute_reply": "2021-05-19T05:56:38.930952Z" } }, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import PSF, DCD, CRD, DCD2\n", "from MDAnalysis.analysis import diffusionmap, align, rms\n", "import numpy as np\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. (Beckstein *et al.*, 2009) The trajectories sample a transition from a closed to an open conformation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:38.934786Z", "iopub.status.busy": "2021-05-19T05:56:38.933805Z", "iopub.status.idle": "2021-05-19T05:56:39.152721Z", "shell.execute_reply": "2021-05-19T05:56:39.153222Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pbarletta/mambaforge/envs/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 behavior will be changed in 3.0 to be the same as other readers. Read more at https://github.com/MDAnalysis/mdanalysis/issues/3889 to learn if this change in behavior might affect you.\n", " warnings.warn(\"DCDReader currently makes independent timesteps\"\n" ] } ], "source": [ "adk_open = mda.Universe(CRD, DCD2)\n", "adk_closed = mda.Universe(PSF, DCD)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background\n", "\n", "While [1-dimensional RMSD](rmsd.ipynb) is a quick way to estimate how much a structure changes over time, it can be a misleading measure. It is easy to think that two structures with the same RMSD from a reference frame are also similar; but in fact, they can be very different. Instead, calculating the RMSD of each frame in the trajectory to all other frames in the other trajectory can contain much more information. This measure is often called the pairwise, all-to-all, or 2D RMSD.\n", "\n", "The other, or reference, trajectory in pairwise RMSD can either be the first trajectory, or another one. If the pairwise RMSD of a trajectory is calculated to itself, it can be used to gain insight into the conformational convergence of the simulation. The diagonal of the plot will be zero in this case (as this represents the RMSD of a structure to itself). Blocks of low RMSD values *along* the diagonal indicate similar structures, suggesting the occupation of a given state. Blocks of low RMSD values *off* the diagonal indicate that the trajectory is revisiting an earlier state. Please see the living guide [Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations by Grossfield et *al.*](https://github.com/dmzuckerman/Sampling-Uncertainty) for more on using 2D RMSD as a measure of convergence. MDAnalysis provides a [DistanceMatrix](#Pairwise-RMSD-of-a-trajectory-to-itself) class for easy calculation of the pairwise RMSD of a trajectory to itself.\n", "\n", "When the other trajectory in pairwise RMSD is a different trajectory, the pairwise RMSD can be used to compare the similarity of the two conformational ensembles. There is no requirement that the two trajectories be the same length. In this case, the diagonal is no longer necessarily zero. Blocks of low RMSD values anywhere indicate that the two trajectories are sampling similar states. [Pairwise RMSDs with different trajectories must be manually calculated in MDAnalysis](#Pairwise-RMSD-between-two-trajectories)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pairwise RMSD of a trajectory to itself" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to calculate the pairwise RMSD of a trajectory to itself, you should begin by aligning the trajectory in order to minimise the resulting RMSD. You may not have enough memory to do this `in_memory`, in which case you can write out the aligned trajectory to a file (please see [the aligning tutorials](aligning_trajectory.ipynb#Aligning-a-trajectory-with-AlignTraj) for more)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.157245Z", "iopub.status.busy": "2021-05-19T05:56:39.156727Z", "iopub.status.idle": "2021-05-19T05:56:39.240283Z", "shell.execute_reply": "2021-05-19T05:56:39.239511Z" } }, "outputs": [], "source": [ "aligner = align.AlignTraj(adk_open, adk_open, select='name CA', \n", " in_memory=True).run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then calculate a pairwise RMSD matrix with the [diffusionmap.DistanceMatrix](https://docs.mdanalysis.org/stable/documentation_pages/analysis/diffusionmap.html#MDAnalysis.analysis.diffusionmap.DistanceMatrix) class, by using the default the [rms.rmsd](https://docs.mdanalysis.org/stable/documentation_pages/analysis/rms.html#MDAnalysis.analysis.rms.rmsd) metric. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.246600Z", "iopub.status.busy": "2021-05-19T05:56:39.245353Z", "iopub.status.idle": "2021-05-19T05:56:39.455932Z", "shell.execute_reply": "2021-05-19T05:56:39.456410Z" } }, "outputs": [], "source": [ "matrix = diffusionmap.DistanceMatrix(adk_open, select='name CA').run()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "The results array is in `results.matrix.dist_matrix` as a square array with the shape (#n_frames, #n_frame)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.462088Z", "iopub.status.busy": "2021-05-19T05:56:39.461547Z", "iopub.status.idle": "2021-05-19T05:56:39.464002Z", "shell.execute_reply": "2021-05-19T05:56:39.464324Z" } }, "outputs": [ { "data": { "text/plain": [ "(102, 102)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix.results.dist_matrix.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the common plotting package [matplotlib](https://matplotlib.org/3.1.1/gallery/index.html) to create a heatmap from this array. For other ways to plot heat maps, you can look at the [seaborn](https://seaborn.pydata.org/generated/seaborn.heatmap.html), [plotly](https://plotly.com/python/heatmaps/) (for interactive images), or [holoviews](http://holoviews.org/reference/elements/bokeh/HeatMap.html) (also interactive) packages." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.480499Z", "iopub.status.busy": "2021-05-19T05:56:39.472917Z", "iopub.status.idle": "2021-05-19T05:56:39.945578Z", "shell.execute_reply": "2021-05-19T05:56:39.946086Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(matrix.results.dist_matrix, cmap='viridis')\n", "plt.xlabel('Frame')\n", "plt.ylabel('Frame')\n", "plt.colorbar(label=r'RMSD ($\\AA$)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pairwise RMSD between two trajectories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculating the 2D RMSD between two trajectories is a bit more finicky; `DistanceMatrix` can only calculate the RMSD of a trajectory to itself. Instead, we do it the long way by simply calculating the RMSD of each frame in the second trajectory, to each frame in the first trajectory.\n", "\n", "First we set up a 2D numpy array a shape corresponding to the length of each of our trajectories to store our results. To start off, it is populated with zeros." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.951516Z", "iopub.status.busy": "2021-05-19T05:56:39.950754Z", "iopub.status.idle": "2021-05-19T05:56:39.952569Z", "shell.execute_reply": "2021-05-19T05:56:39.952922Z" } }, "outputs": [], "source": [ "prmsd = np.zeros((len(adk_open.trajectory), # y-axis\n", " len(adk_closed.trajectory))) # x-axis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we iterate through each frame of the `adk_open` trajectory (our y-axis), and calculate the RMSD of `adk_closed` to each frame, storing it in the `prmsd` array." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:39.957282Z", "iopub.status.busy": "2021-05-19T05:56:39.956729Z", "iopub.status.idle": "2021-05-19T05:56:41.722116Z", "shell.execute_reply": "2021-05-19T05:56:41.722478Z" } }, "outputs": [], "source": [ "for i, frame_open in enumerate(adk_open.trajectory):\n", " r = rms.RMSD(adk_closed, adk_open, select='name CA', \n", " ref_frame=i).run()\n", " prmsd[i] = r.results.rmsd[:, -1] # select 3rd column with RMSD values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot it below. As you can see, there is no longer a line of zero values across the diagonal. Here, the frames of `adk_closed` and `adk_open` are similar but not identical." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:56:41.735834Z", "iopub.status.busy": "2021-05-19T05:56:41.734043Z", "iopub.status.idle": "2021-05-19T05:56:41.919194Z", "shell.execute_reply": "2021-05-19T05:56:41.919838Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(prmsd, cmap='viridis')\n", "plt.xlabel('Frame (adk_closed)')\n", "plt.ylabel('Frame (adk_open)')\n", "plt.colorbar(label=r'RMSD ($\\AA$)')" ] }, { "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] 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", "[3] 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", "[4] 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": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "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": "5edc5d8d8cbc0935a054a8e44024f729bc376180aae27775d15f2ff38c68f892" } } }, "nbformat": 4, "nbformat_minor": 2 }