{ "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": {}, "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": {}, "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": {}, "outputs": [], "source": [ "hbonds = HydrogenBondAnalysis(universe=u)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e9a342112e4f4caa9c008d2e0a38491f", "version_major": 2, "version_minor": 0 }, "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": {}, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "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": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": {}, "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": {}, "outputs": [], "source": [ "params, fit_t, fit_ac = fit_biexponential(tau_frames, hbond_lifetime)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "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": {}, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1\n", "intermittencies = [0, 1, 10, 100]\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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 10 most prevalent hydrogen bonds." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "hbonds = HydrogenBondAnalysis(universe=u)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "41f14e4748cf41b9a0e13ac189a7758d", "version_major": 2, "version_minor": 0 }, "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": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ARG-71-NH2\tHH22\tASP-76-OD1\tcount=98\n", "TYR-193-OH\tHH\tGLU-108-OE1\tcount=97\n", "ARG-2-NH1\tHH11\tASP-104-OD1\tcount=96\n", "THR-199-OG1\tHG1\tASP-197-OD1\tcount=95\n", "TYR-24-OH\tHH\tGLY-214-OT2\tcount=95\n", "TYR-133-OH\tHH\tASP-146-OD1\tcount=95\n", "ARG-206-NE\tHE\tGLU-210-OE1\tcount=93\n", "ARG-124-NH2\tHH22\tGLU-143-OE1\tcount=93\n", "LYS-200-NZ\tHZ2\tASP-208-OD2\tcount=93\n", "LYS-211-NZ\tHZ3\tGLU-204-OE1\tcount=92\n" ] } ], "source": [ "# Print donor, hydrogen, acceptor and count info for these hbonds\n", "counts = hbonds.count_by_ids()\n", "for donor, hydrogen, acceptor, count in counts[:10]:\n", " d, h, a = u.atoms[donor], u.atoms[hydrogen], u.atoms[acceptor]\n", " print(f\"{d.resname}-{d.resid}-{d.name}\\t{h.name}\\t{a.resname}-{a.resid}-{a.name}\\tcount={count}\")" ] }, { "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": {}, "outputs": [], "source": [ "tau_max = 25\n", "window_step = 1\n", "intermittency = 0" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "hbond_lifetimes = []\n", "labels = [] # for plotting\n", "\n", "for hbond in counts[:10]:\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": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "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 3.9.15 ('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": "7b52aa17ef4e9358c0e91ff3f0bf50d10667bb8b55636d4b9fb967a2ff94bd8c" } }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "046bce8d09354bdf9628178fb9adefbe": { "model_module": 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