  In comparison to numerous enhanced sampling methods for equilbrium
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 the time reversibility to
accelerate simulations for determining the transition rates between free-ernegy
basins. It converts the difficult up-hill path sampling into an easy down-hill
problem. The 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 by comparison with direct
simulations on 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. The approach is generally applicable to stochatic
processes with microscopic reversibility, no mater whether the variables are
continuous or discrete.
