Replica exchange and expanded ensemble simulations as Gibbs sampling: Simple improvements for enhanced mixing

TL;DR

This paper reinterprets replica exchange and expanded ensemble algorithms as Gibbs sampling within MCMC, proposing simple, cost-effective improvements to enhance phase space mixing and reduce simulation times in molecular simulations.

Contribution

It introduces a novel perspective of these algorithms as Gibbs sampling and proposes new state update methods to improve mixing efficiency.

Findings

Enhanced mixing with simple state update schemes

Reduced simulation times for molecular sampling

Effective in various applications like parallel tempering

Abstract

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus improving their efficiency. Here, we demonstrate how both of these classes of algorithms can be considered a form of Gibbs sampling within a Markov chain Monte Carlo (MCMC) framework. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices---corresponding to thermodynamic parameters such as temperature or alchemical coupling variables---associated with these configurations can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.