  Continuous-time Markov chains (CTMCs) are widely used in many applications,
including in modeling nucleic acid kinetics (non-equilibrium dynamics). A
typical issue in CTMCs is that the number of states could be large, making mean
first passage time (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 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 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.
