The pathway elaboration method for mean first passage time estimation in large continuous-time Markov chains with applications to nucleic acid kinetics

Abstract

For predicting the kinetics of nucleic acid reactions, continuous-time Markov chains (CTMCs) are widely used. The rate of a reaction can be obtained through the mean first passage time (MFPT) of its CTMC. However, a typical issue in CTMCs is that the number of states could be large, making MFPT estimation challenging, particularly for events that happen on a long time scale (rare events). We propose the pathway elaboration method, a time-efficient probabilistic truncation-based approach for detailed-balance CTMCs. It can be used for estimating the MFPT for rare events in addition to rapidly evaluating perturbed parameters without expensive recomputations. We demonstrate that pathway elaboration is suitable for predicting nucleic acid kinetics by conducting computational experiments on 267 measurements that cover a wide range of rates for different types of reactions. We utilize pathway elaboration to gain insight on the kinetics of two contrasting reactions, one being a rare event. We then compare the performance of pathway elaboration with the stochastic simulation algorithm (SSA) for MFPT estimation on 237 of the reactions for which SSA is feasible. We further build truncated CTMCs with SSA and transition path sampling (TPS) to compare with pathway elaboration. Finally, we use pathway elaboration to rapidly evaluate perturbed model parameters during optimization with respect to experimentally measured rates for these 237 reactions. The testing error on the remaining 30 reactions, which involved rare events and were not feasible to simulate with SSA, improved comparably with the training error. Our framework and dataset are available at https://github.com/ DNA-and-Natural-Algorithms-Group/PathwayElaboration.