{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating hydrogen bond lifetimes\n", "\n", "We will calculate the lifetime of intramolecular hydrogen bonds in a protein.\n", "\n", "**Last updated:** December 2022\n", "\n", "**Minimum version of MDAnalysis:** 2.0.0-dev0\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "* [numpy](https://numpy.org)\n", "* [matplotlib](https://matplotlib.org)\n", "\n", "**See also**\n", "\n", "* [Calculating hydrogen bonds: the basics](hbonds.ipynb)\n", "* [Calculating hydrogen bonds: advanced selections](hbonds-selections.ipynb)\n", "\n", "
\n", " \n", "**Note**\n", "\n", "Please cite [Smith et al. (2018)](http://dx.doi.org/10.1039/C9CP01532A) when using HydrogenBondAnaysis in published work.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:15.548416018Z", "start_time": "2023-12-01T16:14:14.429254050Z" } }, "outputs": [], "source": [ "from tqdm.auto import tqdm\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import PSF, DCD\n", "from MDAnalysis.analysis.hydrogenbonds import HydrogenBondAnalysis\n", "\n", "import warnings\n", "# suppress some MDAnalysis warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading files" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:15.771935191Z", "start_time": "2023-12-01T16:14:15.547009929Z" } }, "outputs": [], "source": [ "u = mda.Universe(PSF, DCD)" ] }, { "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)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find all hydrogen bonds\n", "First, find the hydrogen bonds.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:15.779555164Z", "start_time": "2023-12-01T16:14:15.773027167Z" } }, "outputs": [], "source": [ "hbonds = HydrogenBondAnalysis(universe=u)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:27.886484626Z", "start_time": "2023-12-01T16:14:15.778084242Z" } }, "outputs": [ { "data": { "text/plain": " 0%| | 0/98 [00:00" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hbonds.run(verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate hydrogen bond lifetimes\n", "\n", "The hydrogen bond lifetime is calculated via the time autocorrelation function of the presence of a hydrogen bond:\n", "
\n", "$$\n", "C(\\tau) = \\bigg\\langle \\frac{h_{ij}(t_0) h_{ij}(t_0 + \\tau)}{h_{ij}(t_0)^2} \\bigg\\rangle\n", "$$\n", "
\n", "\n", "where $h_{ij}$ indicates the presence of a hydrogen bond between atoms $i$ and $j$:\n", "\n", "* $h_{ij}=1$ if there is a hydrogen bond\n", "* $h_{ij}=0$ if there is no hydrogen bond\n", "\n", "$h_{ij}(t_0)=1$ indicates there is a hydrogen bond between atoms $i$ and $j$ at a time origin $t_0$, and $h_{ij}(t_0+\\tau)=1$ indicates these atoms remain hydrogen bonded throughout the period $t_0$ to $t_0+\\tau$. To improve statistics, multiple time origins, $t_0$, are used in the calculation and the average is taken over all time origins. \n", "\n", "See [Gowers and Carbonne (2015)](https://doi.org/10.1063/1.4922445) for further discussion on hydrogen bonds lifetimes.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " \n", "**Note**\n", " \n", "The period between time origins, $t_0$, should be chosen such that consecutive $t_0$ are uncorrelated.\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `hbonds.lifetime` method calculates the above time autocorrelation function. The period between time origins is set using `window_step`, and the maximum value of $\\tau$ (in frames) is set using `tau_max`. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:27.937552280Z", "start_time": "2023-12-01T16:14:27.883829276Z" } }, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.115325664Z", "start_time": "2023-12-01T16:14:27.926915985Z" } }, "outputs": [], "source": [ "tau_frames, hbond_lifetime = hbonds.lifetime(\n", " tau_max=tau_max,\n", " window_step=window_step\n", ")\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.608070123Z", "start_time": "2023-12-01T16:14:28.121928088Z" } }, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tau_times = tau_frames * u.trajectory.dt\n", "plt.plot(tau_times, hbond_lifetime, lw=2)\n", "\n", "plt.title(r\"Hydrogen bond lifetime\", weight=\"bold\")\n", "plt.xlabel(r\"$\\tau\\ \\rm (ps)$\")\n", "plt.ylabel(r\"$C(\\tau)$\")\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the time constant\n", "\n", "To obtain the hydrogen bond lifetime, you can fit a biexponential to the time autocorrelation curve. We will fit the following biexponential:\n", "\n", "
\n", "$$\n", "A\\exp(-t / \\tau_1) + B\\exp(-t / \\tau_2)\n", "$$\n", "
\n", "\n", "where $\\tau_1$ and $\\tau_2$ represent two time constants - one corresponding to a short-timescale process and the other to a longer timescale process. $A$ and $B$ will sum to $1$, and they represent the relative importance of the short- and longer-timescale processes in the overall autocorrelation curve.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.658299780Z", "start_time": "2023-12-01T16:14:28.613760144Z" } }, "outputs": [], "source": [ "def fit_biexponential(tau_timeseries, ac_timeseries):\n", " \"\"\"Fit a biexponential function to a hydrogen bond time autocorrelation function\n", " \n", " Return the two time constants\n", " \"\"\"\n", " from scipy.optimize import curve_fit\n", " \n", " def model(t, A, tau1, B, tau2):\n", " \"\"\"Fit data to a biexponential function.\n", " \"\"\"\n", " return A * np.exp(-t / tau1) + B * np.exp(-t / tau2)\n", "\n", " params, params_covariance = curve_fit(model, tau_timeseries, ac_timeseries, [1, 0.5, 1, 2])\n", " \n", " fit_t = np.linspace(tau_timeseries[0], tau_timeseries[-1], 1000)\n", " fit_ac = model(fit_t, *params)\n", "\n", " return params, fit_t, fit_ac\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.658765843Z", "start_time": "2023-12-01T16:14:28.654973996Z" } }, "outputs": [], "source": [ "params, fit_t, fit_ac = fit_biexponential(tau_times, hbond_lifetime)" ] }, { "cell_type": "code", "execution_count": 10, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the fit\n", "plt.plot(tau_times, hbond_lifetime, label=\"data\")\n", "plt.plot(fit_t, fit_ac, label=\"fit\")\n", "\n", "plt.title(r\"Hydrogen bond lifetime\", weight=\"bold\")\n", "plt.xlabel(r\"$\\tau\\ \\rm (ps)$\")\n", "plt.ylabel(r\"$C(\\tau)$\")\n", "\n", "plt.legend()\n", "plt.show()\n" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-12-01T16:14:28.907165265Z", "start_time": "2023-12-01T16:14:28.655354640Z" } } }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.921583492Z", "start_time": "2023-12-01T16:14:28.909114150Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time_constant = 6.14 ps\n" ] } ], "source": [ "# Check the decay time constant\n", "A, tau1, B, tau2 = params\n", "time_constant = A * tau1 + B * tau2\n", "print(f\"time_constant = {time_constant:.2f} ps\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intermittent lifetime\n", "\n", "The above example shows you how to calculate the continuous hydrogen bond lifetime. This means that the hydrogen bond must be present at every frame from $t_0$ to $t_0 + \\tau$. To allow for small fluctuations in the DA distance or DHA angle, the intermittent hydrogen bond lifetime may be calculated. This allows a hydrogen bond to break for up to a specified number of frames and still be considered present.\n", "\n", "In the `lifetime` method, the `intermittency` argument is used to set the maxium number of frames for which a hydrogen bond is allowed to break. The default is `intermittency=0`, which means that if a hydrogen bond is missing at any frame between $t_0$ and $t_0 + \\tau$, it will not be considered present at $t_0+\\tau$. This is equivalent to the continuous lifetime. However, with a value of `intermittency=2`, all hydrogen bonds are allowed to break for up to a maximum of consecutive two frames.\n", "\n", "Below we see how changing the intermittency affects the hydrogen bond lifetime.\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:28.981790832Z", "start_time": "2023-12-01T16:14:28.914348229Z" } }, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1\n", "intermittencies = [0, 1, 10, 100]\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:31.981537902Z", "start_time": "2023-12-01T16:14:28.958972801Z" } }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for intermittency in intermittencies:\n", " \n", " tau_frames, hbond_lifetime = hbonds.lifetime(\n", " tau_max=tau_max,\n", " window_step=window_step,\n", " intermittency=intermittency\n", " )\n", " \n", " times_times = tau_frames * u.trajectory.dt\n", " plt.plot(times_times, hbond_lifetime, lw=2, label=intermittency)\n", " \n", "plt.title(r\"Hydrogen bond lifetime\", weight=\"bold\")\n", "plt.xlabel(r\"$\\tau\\ \\rm (ps)$\")\n", "plt.ylabel(r\"$C(\\tau)$\")\n", " \n", "plt.legend(title=\"Intermittency=\", loc=(1.02, 0.0))\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hydrogen bond lifetime of individual hydrogen bonds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first find the 3 most prevalent hydrogen bonds." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:31.995177223Z", "start_time": "2023-12-01T16:14:31.987193038Z" } }, "outputs": [], "source": [ "hbonds = HydrogenBondAnalysis(universe=u)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:43.096309531Z", "start_time": "2023-12-01T16:14:31.993497404Z" } }, "outputs": [ { "data": { "text/plain": " 0%| | 0/98 [00:00" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hbonds.run(verbose=True)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:43.157127118Z", "start_time": "2023-12-01T16:14:43.100859247Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ARG-124-NH2\tHH22\tGLU-143-OE1\tcount=93\n", "ARG-2-NH1\tHH11\tASP-104-OD1\tcount=96\n", "ARG-206-NE\tHE\tGLU-210-OE1\tcount=93\n", "ARG-71-NH2\tHH22\tASP-76-OD1\tcount=98\n", "LYS-200-NZ\tHZ2\tASP-208-OD2\tcount=93\n", "LYS-211-NZ\tHZ3\tGLU-204-OE1\tcount=92\n", "THR-199-OG1\tHG1\tASP-197-OD1\tcount=95\n", "TYR-133-OH\tHH\tASP-146-OD1\tcount=95\n", "TYR-193-OH\tHH\tGLU-108-OE1\tcount=97\n", "TYR-24-OH\tHH\tGLY-214-OT2\tcount=95\n" ] } ], "source": [ "# Print donor, hydrogen, acceptor and count info for these hbonds\n", "counts = hbonds.count_by_ids()\n", "lines = []\n", "for donor, hydrogen, acceptor, count in counts[:10]:\n", " d, h, a = u.atoms[donor], u.atoms[hydrogen], u.atoms[acceptor]\n", " lines.append(f\"{d.resname}-{d.resid}-{d.name}\\t{h.name}\\t{a.resname}-{a.resid}-{a.name}\\tcount={count}\")\n", "for line in sorted(lines):\n", " print(line)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll calculate the lifetime of these hydrogen bonds. To do this, the simplest way is to run `HydrogenBondAnalysis` for each hydrogen bond then use the `lifetime` method. It is very efficient to find hydrogen bonds between two specific atoms, especially with `update_selections=False`." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:43.158453934Z", "start_time": "2023-12-01T16:14:43.143012205Z" } }, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1\n", "intermittency = 0" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:43.305822652Z", "start_time": "2023-12-01T16:14:43.143401161Z" } }, "outputs": [], "source": [ "hbond_lifetimes = []\n", "labels = [] # for plotting\n", "\n", "for hbond in counts[:3]:\n", " \n", " # find hbonds between specific atoms\n", " d_ix, h_ix, a_ix = hbond[:3]\n", " tmp_hbonds = HydrogenBondAnalysis(\n", " universe=u,\n", " hydrogens_sel=f\"index {h_ix}\",\n", " acceptors_sel=f\"index {a_ix}\",\n", " update_selections=False\n", " )\n", " tmp_hbonds.run()\n", " \n", " # calculate lifetime\n", " taus, hbl, = tmp_hbonds.lifetime(\n", " tau_max=tau_max,\n", " intermittency=intermittency\n", " )\n", " hbond_lifetimes.append(hbl)\n", " \n", " # label for plotting\n", " donor, acceptor = u.atoms[d_ix], u.atoms[a_ix]\n", " label = f\"{donor.resname}:{donor.resid} to {acceptor.resname}:{acceptor.resid}\"\n", " labels.append(label)\n", "\n", "hbond_lifetimes = np.array(hbond_lifetimes)\n", "labels = np.array(labels)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T16:14:43.516614932Z", "start_time": "2023-12-01T16:14:43.324301887Z" } }, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the lifetimes\n", "times = taus * u.trajectory.dt\n", "for hbl, label in zip(hbond_lifetimes, labels):\n", " plt.plot(times, hbl, label=label, lw=2)\n", "\n", "plt.title(r\"Hydrogen bond lifetime of specific hbonds\", weight=\"bold\")\n", "plt.xlabel(r\"$\\tau\\ \\rm (ps)$\")\n", "plt.ylabel(r\"$C(\\tau)$\")\n", "\n", "plt.legend(ncol=1, loc=(1.02, 0))\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " \n", "**Note**\n", " \n", "The shape of these curves indicates we have poor statistics in our lifetime calculations - we used only 100 frames and consider a single hydrogen bond.\n", " \n", "The curve should decay smoothly toward 0, as seen in the first hydrogen bond lifetime plot we produced in this notebook. If the curve does not decay smoothly, more statistics are required either by increasing the value of `tau_max`, using a greater number of time origins, or increasing the length of your simulation.\n", " \n", "See [Gowers and Carbonne (2015)](https://doi.org/10.1063/1.4922445) for further discussion on hydrogen bonds lifetimes.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] 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", "[2] 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", "[3] Paul Smith, Robert M. Ziolek, Elena Gazzarrini, Dylan M. Owen, and Christian D. Lorenz.\n", "On the interaction of hyaluronic acid with synovial fluid lipid membranes.\n", "Phys. Chem. Chem. Phys., 21(19):9845-9857, 2018.\n", "URL: http://dx.doi.org/10.1039/C9CP01532A\n", "\n", "[4] 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", "[5] Richard J. Gowers and Paola Carbonne.\n", "A multiscale approach to model hydrogen bonding: The case of polyamide.\n", "J. Chem. Phys., 142:224907, June 2015.\n", "URL: https://doi.org/10.1063/1.4922445" ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "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 }