{ "cells": [ { "cell_type": "markdown", "id": "d36d7e22-b012-44a9-ae68-dffeb173f5f9", "metadata": {}, "source": [ "# Multistate Sampling 2: Expanded Ensemble\n", "\n", "## Introduction\n", "\n", "In the previous tutorial we ran a simulation with replica exchange, a popular algorithm for multistate sampling. In this one we will look at a different algorithm called *expanded ensemble* sampling. Recall the basic algorithm for replica exchange:\n", "\n", "1. Initialize N replicas, each in a different thermodynamic state.\n", "2. Simulate every replica for M steps.\n", "3. Attempt to exchange states between replicas.\n", "\n", "If we look at just a single replica, we see a continuous trajectory that periodically changes to a different thermodynamic state. That is essentially what expanded ensembling sampling does. It dispenses with the multiple replicas and uses a single simulation to sample all of the states.\n", "\n", "1. Initialize a simulation to an initial thermodynamic state.\n", "2. Simulate it for M steps.\n", "3. Attempt to move to a different thermodynamic state.\n", "\n", "Why would you prefer one method over the other? It turns out that expanded ensemble sampling has certain theoretical advantages over replica exchange that make it more efficient. The thermodynamic states can be further apart, allowing you to cover the same range with fewer states. This comes at a cost in complexity and robustness, however. In replica exchange, you are always simulating one replica in every state. It is guaranteed that at the end, you will have an identical amount of sampling for every state. Expanded ensemble does not have that guarantee. It takes careful work to ensure that all states are properly sampled.\n", "\n", "In practice this is done by choosing a *weight* for each thermodynamic state. When attempting to move to a different state, the weights influence the transition probabilities. Our goal is to choose weights that lead to spending approximately equal time in every state. Fortunately, OpenMM can do this for you automatically. It does take time for it to work out what the weights should be, so an expanded ensemble simulation usually begins with an initial period dedicated to choosing weights. This initial period must be discarded when analyzing results.\n", "\n", "## Running the Simulation\n", "\n", "As in the previous tutorial, we will simulate alanine dipeptide in a box of water. This time we will do a different type of simulation, one where thermodynamic states correspond to different values of a force field parameter. We will do an umbrella sampling simulation, using a bias potential to make one dihedral remain close to a particular value. Different states will correspond to different positions of the bias potential. This lets us explore how the free energy varies as a function of that dihedral angle.\n", "\n", "Let's start by creating the `System`, `Integrator`, and `Simulation`. We use a `CustomTorsionForce` to apply a bias whose position depends on a global parameter." ] }, { "cell_type": "code", "execution_count": 1, "id": "9fac69a3-c6f0-428d-957e-54f0f6be37ca", "metadata": {}, "outputs": [], "source": [ "from openmm import *\n", "from openmm.app import *\n", "from openmm.unit import *\n", "\n", "pdb = PDBFile('alanine-dipeptide-water.pdb')\n", "ff = ForceField('amber19-all.xml', 'amber19/tip3pfb.xml')\n", "system = ff.createSystem(pdb.topology, nonbondedMethod=PME, constraints=HBonds, hydrogenMass=1.25*amu)\n", "bias = CustomTorsionForce('100*min(dtheta, 2*pi-dtheta)^2; dtheta = abs(theta-theta0); pi = 3.1415926535')\n", "bias.addGlobalParameter('theta0', 0)\n", "bias.addTorsion(6, 8, 14, 16)\n", "system.addForce(bias)\n", "integrator = LangevinIntegrator(300*kelvin, 1.0/picosecond, 0.004*picoseconds)\n", "simulation = Simulation(pdb.topology, system, integrator)\n", "simulation.context.setPositions(pdb.positions)" ] }, { "cell_type": "markdown", "id": "6c7e3ec2-c254-4900-bfff-43e6e898df0a", "metadata": {}, "source": [ "As with any simulation, we should equilibrate the system before we start the main simulation." ] }, { "cell_type": "code", "execution_count": 2, "id": "8ca214a4-66f7-4dfc-a0db-4a5a1e3756fe", "metadata": {}, "outputs": [], "source": [ "simulation.context.setVelocitiesToTemperature(300*kelvin)\n", "simulation.step(10000)" ] }, { "cell_type": "markdown", "id": "eaf0df3b-7184-4ede-bc2c-4fbb316d7ad9", "metadata": {}, "source": [ "In this case, our thermodynamic states correspond to different values of the global parameter `theta0`. To specify this for multistate sampling, just use the name of the global parameter as the key." ] }, { "cell_type": "code", "execution_count": 3, "id": "5a149f73-b06c-4271-9c16-7dfd23bdf412", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "states = [{'theta0':t} for t in np.linspace(0.0, np.pi, 10)]" ] }, { "cell_type": "markdown", "id": "33a26dd7-ba59-45a8-b046-e9d014cf1bfe", "metadata": {}, "source": [ "Performing expanded ensemble sampling is very similar to replica exchange. We create an `ExpandedEnsembleSampler`, passing it the list of states, the `Simulation` object, and the interval in time steps at which to attempt state changes.\n", "\n", "We also need to save results for later analysis. Because expanded ensemble involves a single continuous simulation, you can mostly use standard reporters, for example to save a trajectory. In addition, there are certain extra pieces of information specific to the expanded ensemble algorithm that you will often want to save. `ExpandedEnsembleSampler` provides options to write them. In this case we include the `logFile` argument. It saves a CSV file recording what state the simulation is in at each iteration, as well as the values of the weights." ] }, { "cell_type": "code", "execution_count": 4, "id": "32d46568-75ee-4ec2-b9f9-fd0246e539fb", "metadata": {}, "outputs": [], "source": [ "sampler = ExpandedEnsembleSampler(states, simulation, 100, logFile='log.csv', reportInterval=1000)\n", "simulation.reporters.append(XTCReporter('trajectory.xtc', 1000, atomSubset=list(range(22))))" ] }, { "cell_type": "markdown", "id": "af4f576a-4999-4d55-8b44-192491eb36f0", "metadata": {}, "source": [ "Now we're ready to run the simulation." ] }, { "cell_type": "code", "execution_count": 5, "id": "c072543d-d120-408b-82cd-d4711d9a2bbd", "metadata": {}, "outputs": [], "source": [ "simulation.step(2000000)" ] }, { "cell_type": "markdown", "id": "3ae63a0f-8668-49b9-8499-2593361a8e02", "metadata": {}, "source": [ "## Analysis\n", "\n", "Let's load the log and plot the weight factors." ] }, { "cell_type": "code", "execution_count": 6, "id": "fe3bd7d4-4851-4f23-a67f-2b0afabb533b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plot\n", "\n", "log = np.loadtxt('log.csv', delimiter=',', skiprows=1)\n", "plot.plot(log[:,3:])\n", "plot.xlabel('Time')\n", "plot.ylabel('Weight')\n", "plot.show()" ] }, { "cell_type": "markdown", "id": "21d99290-8e73-40e3-a457-dc83e3d7296f", "metadata": {}, "source": [ "We see it took about 800,000 steps (800 reports) for the weights to converge. We therefore should discard everything before that point when doing analysis. It does not reflect a well defined distribution.\n", "\n", "Now let's plot how the state varied over the simulation. If the states were sufficiently close together, there should be frequent transitions to and from all states." ] }, { "cell_type": "code", "execution_count": 7, "id": "fadb7a37-ea6a-49c1-a773-43cdbba52625", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot.plot(log[800:,2])\n", "plot.xlabel('Time')\n", "plot.ylabel('State')\n", "plot.yticks(np.arange(10))\n", "plot.show()" ] }, { "cell_type": "markdown", "id": "a42c9273-ac26-41f9-857a-b08df6e64a3f", "metadata": {}, "source": [ "There are lots of transitions, indicating we have sufficient states. Now let's look at the distribution of states. In replica exchange, we are guaranteed to produce an identical amount of sampling for every state. In expanded ensemble sampling, it depends on how good a job it has done of selecting weights." ] }, { "cell_type": "code", "execution_count": 8, "id": "dafdd54b-6a42-4fb0-ad47-ad18c4054a19", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot.hist(log[800:,2])\n", "plot.show()" ] }, { "cell_type": "markdown", "id": "d2b04b88-78cd-4650-a79b-419bb68954bf", "metadata": {}, "source": [ "The distribution is fairly uniform, indicating it has done a good job of selecting weights. It is not perfectly flat, but all states have a significant level of sampling.\n", "\n", "Let's compute the dihedral angle for every frame in the trajectory and plot a histogram of them for each state. If our biasing potential worked correctly, each state should have a different distribution of angles centered on a different point." ] }, { "cell_type": "code", "execution_count": 9, "id": "36da028d-2ef5-4692-a57b-08bb5313d8bc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.analysis.dihedrals import Dihedral\n", "\n", "u = mda.Universe('alanine-dipeptide.pdb', 'trajectory.xtc')\n", "atoms = mda.AtomGroup([6, 8, 14, 16], u)\n", "dihedral = Dihedral([atoms]).run()\n", "wrapped = dihedral.results.angles + 360*(dihedral.results.angles < -90)\n", "for state in range(len(states)):\n", " angles = [a for i, a in zip(log[800:,2], wrapped[800:,0]) if i == state]\n", " plot.hist(angles)\n", "plot.xlabel('Angle (degrees)')\n", "plot.ylabel('Count')\n", "plot.show()" ] }, { "cell_type": "markdown", "id": "b7a67471-f4fc-48c8-b869-48ae58eff627", "metadata": {}, "source": [ "In an expanded ensemble simulation, the probability of finding the simulation in state $i$ is proportional to $\\mathrm{exp}(w_i-F_i/k_B T_i)$ where $w_i$ is its weight factor, $F_i$ is its free energy, and $T_i$ is its temperature. This means that, if `ExpandedEnsembleSampler` has done a perfect job of picking weights to give every state an equal probability, the free energy of each state is given by $k_B T_i w_i$. Of course, it will not have done a perfect job and accurately computing free energy differences requires a more complicated analysis. Nonetheless, it is still useful as a way of quickly estimating free energies." ] }, { "cell_type": "code", "execution_count": 10, "id": "ad7bf145-30b0-44aa-929a-bab418e4716a", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fe = [MOLAR_GAS_CONSTANT_R*integrator.getTemperature()*w for w in sampler.weights]\n", "plot.plot([x.value_in_unit(kilojoules_per_mole) for x in fe])\n", "plot.xlabel('State')\n", "plot.ylabel('Estimated Free Energy (kJ/mol)')\n", "plot.show()" ] }, { "cell_type": "markdown", "id": "e61dde07-575d-4fc7-8ef5-ddaee9f0cf0f", "metadata": {}, "source": [ "## Next Steps\n", "\n", "Our focus in this tutorial has been on how to use `ExpandedEnsembleSampler`, not on how to analyze an umbrella sampling simulation. If you want to learn more about that, there is another tutorial that goes into much more detail about it.\n", "\n", "## Links\n", "\n", "- Tutorials\n", " - [Umbrella Sampling](https://openmm.github.io/openmm-cookbook/latest/notebooks/tutorials/umbrella_sampling.html)\n", "- API Documentation\n", " - [ExpandedEnsembleSampler](https://docs.openmm.org/latest/api-python/generated/openmm.app.expandedensemblesampler.ExpandedEnsembleSampler.html)" ] } ], "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }