Expanded ensemble and replica exchange methods for simulation of protein-like systems

Abstract

Extended state methods are powerful tools for studying the conformational equilibria of proteins. This study focuses on three aspects of their implementation. First, existing approaches for determining importance weights (namely, recursion, random walk, and transition probability schemes) are compared in the context of their use with the method of expanded ensembles (EXE). Second, a combined scheme (REXE) involving EXE and replica exchange (REX) updates is developed for simulating a small number of replicas within a much larger macrostate space. Finally, variants of the extended state methods are considered for accelerating folding, either through special-purpose ensembles which target specific force-field parameters, or through biased sampling of extended macrostates that favor structural fluctuations. All methods are applied to a three-dimensional lattice protein model. Overall, it is found that transition probability approaches employing multiple system replicas perform naturally better than methods that intrinsically require macrostate equilibration by a single replica; the transition probability approaches need about an order of magnitude fewer steps to reach the same degree of convergence in the importance weights. The specific REXE protocol implemented is observed to have an efficiency intermediate to that of EXE and REX schemes at high temperatures, but to outperform them at more glassy conditions. Finally, special-purpose and locally enhanced tempering ensembles are shown to promote faster folding than conventional tempering.