Kinetic Models of Enhanced Sampling Methods

Abstract

We present kinetic models of enhanced sampling methods such as replica exchange and simulated tempering. With these models we derive analytical expressions for the statistical error and computational efficiency of the sampling methods. As a specific example, we consider two-state protein folding. A main result is that with comparable computational resources used, the relative efficiency of replica exchange molecular dynamics (REMD) and molecular dynamics (MD) simulations is given by the ratio of the number of transitions between the two folding states averaged over all replicas at the different temperatures, and the number of transitions at the single temperature of the MD run. This formula applies if replica exchange is frequent, as compared to the transition times. For simulated tempering (ST) simulations, we obtain a relation for the efficiency that is derived for the limit in which changes in the ST temperature are fast compared to the two-state transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived for replica exchange. Implications on actual protein folding simulations will be discussed.