Accelerating Kinetics with Time-Reversal Path Sampling.

In comparison to numerous enhanced sampling methods for equilibrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here, we derive a time-reversal path sampling (tRPS) method based on time reversibility to accelerate simulations for determining the transition rates between free-energy basins. It converts the difficult uphill path sampling into an easy downhill problem. This method is easy to implement, i.e., forward and backward shooting simulations with opposite initial velocities are conducted from random initial conformations within a transition-state region until they reach the basin minima, which are then assembled to give the distribution of transition paths efficiently. The effects of tRPS are demonstrated using a comparison with direct simulations of protein folding and unfolding, where tRPS is shown to give results consistent with direct simulations and increase the efficiency by up to five orders of magnitude. This approach is generally applicable to stochastic processes with microscopic reversibility, regardless of whether the variables are continuous or discrete.