  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.
