# Markov chain Monte Carlo (MCMC)¶

openmmtools provides an extensible Markov chain Monte Carlo simulation framework.

This module provides a framework for equilibrium sampling from a given thermodynamic state of a biomolecule using a Markov chain Monte Carlo scheme.

It currently offer supports for

• Langevin dynamics (assumed to be free of integration error; use at your own risk]),
• hybrid Monte Carlo,
• generalized hybrid Monte Carlo, and
• Monte Carlo barostat moves,

which can be combined through the SequenceMove and WeightedMove classes.

By default, the MCMCMoves use the fastest OpenMM platform available and a shared global ContextCache that minimizes the number of OpenMM Context objects that must be maintained at once. The examples below show how to configure these aspects.

Note

To use the ContextCache on the CUDA platform, the NVIDIA driver must be set to shared mode to allow the process to create multiple GPU contexts.

Using the MCMC framework requires importing ThermodynamicState and SamplerState from openmmtools.states:

from simtk import unit
from openmmtools import testsystems, cache
from openmmtools.states import ThermodynamicState, SamplerState


Create the initial state (thermodynamic and microscopic) for an alanine dipeptide system in vacuum.

test = testsystems.AlanineDipeptideVacuum()
thermodynamic_state = ThermodynamicState(system=test.system, temperature=298*unit.kelvin)
sampler_state = SamplerState(positions=test.positions)


Create an MCMC move to perform at every iteration of the simulation, and initialize a sampler instance.

ghmc_move = GHMCMove(timestep=1.0*unit.femtosecond, n_steps=50)
langevin_move = LangevinDynamicsMove(n_steps=10)
sampler = MCMCSampler(thermodynamic_state, sampler_state, move=ghmc_move)


You can combine them to form a sequence of moves

sequence_move = SequenceMove([ghmc_move, langevin_move])
sampler = MCMCSampler(thermodynamic_state, sampler_state, move=sequence_move)


or create a move that selects one of them at random with given probability at each iteration.

weighted_move = WeightedMove([(ghmc_move, 0.5), (langevin_move, 0.5)])
sampler = MCMCSampler(thermodynamic_state, sampler_state, move=weighted_move)


By default the MCMCMove use a global ContextCache that creates Context on the fastest available OpenMM platform. You can configure the default platform to use before starting the simulation

reference_platform = openmm.Platform.getPlatformByName('Reference')
cache.global_context_cache.platform = reference_platform
cache.global_context_cache.time_to_live = 10  # number of read/write operations


Minimize and run the simulation for few iterations.

sampler.minimize()
sampler.run(n_iterations=2)


If you don’t want to use a global cache, you can create local ones.

local_cache1 = cache.ContextCache(capacity=5, time_to_live=50)
local_cache2 = cache.ContextCache(platform=reference_platform, capacity=1)
sequence_move = SequenceMove([HMCMove(), LangevinDynamicsMove()], context_cache=local_cache1)
ghmc_move = GHMCMove(context_cache=local_cache2)


If you don’t want to cache Context at all but create one every time, you can use the DummyCache.

dummy_cache = cache.DummyContextCache(platform=reference_platform)
ghmc_move = GHMCMove(context_cache=dummy_cache)


This book by Jun Liu is an excellent overview of Markov chain Monte Carlo:

Jun S. Liu. Monte Carlo Strategies in Scientific Computing. Springer, 2008.

## MCMC samplers¶

An MCMC sampler driver is provided that can either utilize a programmed sequence of moves or draw from a weighted set of moves.

 MCMCSampler Basic Markov chain Monte Carlo sampler. SequenceMove A sequence of MCMC moves. WeightedMove Pick an MCMC move out of set with given probability at each iteration.

## MCMC move types¶

A number of MCMC component move types that can be arranged into groups or subclassed are provided.

 MCMCMove Markov chain Monte Carlo (MCMC) move abstraction. BaseIntegratorMove A general MCMC move that applies an integrator. MetropolizedMove A base class for metropolized moves. IntegratorMove An MCMCMove that propagate the system with an integrator. LangevinDynamicsMove Langevin dynamics segment as a (pseudo) Monte Carlo move. LangevinSplittingDynamicsMove Langevin dynamics segment with custom splitting of the operators and optional Metropolized Monte Carlo validation. GHMCMove Generalized hybrid Monte Carlo (GHMC) Markov chain Monte Carlo move. HMCMove Hybrid Monte Carlo dynamics. MonteCarloBarostatMove Monte Carlo barostat move. MCDisplacementMove A metropolized move that randomly displace a subset of atoms. MCRotationMove A metropolized move that randomly rotate a subset of atoms.