Optimal Temperature Set for Replica Exchange Sampling

Abstract

Replica Exchange Monte Carlo method has been introduced to improve sampling of a rugged energy landscape for such systems as polymers, biopolymers and spin glasses. Efficiency of the method however critically depends on the set of replica temperatures used for simulations. A novel method selecting these parameters has been recently proposed1, which numerically evaluates the probability of replica swap between temperatures based on estimated density of states for a system under study. Here we extend this method and prove it provides the optimal set of temperatures i.e. temperatures that guarantee the fastest flow of replicas from the lowest to the highest temperature.During an initial phase of the protocol, energy distributions are collected at different temperatures. Based on these observations, the density of states for the system is computed by the multihistogram method. Knowing the density, improved temperature set is established by minimizing the mean first passage time of replicas in the temperature space. The procedure has been illustrated with a coarse-grained protein folding simulation and all-atom dynamics in AMBER force field. The method has been implemented in BioShell package.2,31 D. Gront and A. Kolinski “Efficient scheme for optimization of parallel tempering Monte Carlo method” Journal of Physics: Condensed Matter 2007 19(3) 036225 http://dx.doi.org/10.1088/0953-8984/19/3/0362252 D. Gront and A. Kolinski “BioShell - a package of tools for structural biology computations” Bioinformatics 2006 22(5):621-6223D. Gront and A. Kolinski “Utility library for structural bioinformatics” Bioinformatics 2008 24(4):584-585