Transition path sampling for discrete master equations with absorbing states

Abstract

Transition path sampling (TPS) algorithms have been implemented with deterministic dynamics, with thermostatted dynamics, with Brownian dynamics, and with simple spin flip dynamics. Missing from the TPS repertoire is an implementation with kinetic Monte Carlo (kMC), i.e., with the underlying dynamics coming from a discrete master equation. We present a new hybrid kMC-TPS algorithm and prove that it satisfies detailed balance in the transition path ensemble. The new algorithm is illustrated for a simplified Markov State Model of trp-cage folding. The transition path ensemble from kMC-TPS is consistent with that obtained from brute force kMC simulations. The committor probabilities and local fluxes for the simple model are consistent with those obtained from exact methods for simple master equations. The new kMC-TPS method should be useful for analysis of rare transitions in complex master equations where the individual states cannot be enumerated and therefore where exact solutions cannot be obtained.