Estimating Full Path Lengths and Kinetics from Partial Path Transition Interface Sampling Simulations

Assessing the time scale of biological processes using molecular dynamics (MD) simulations with sufficient statistical accuracy is a challenging task, as processes are often rare and/or slow events, which may extend largely beyond the time scale of what is accessible with modern day high performance computational infrastructure. Recently, the replica exchange partial path transition interface sampling (REPPTIS) algorithm was developed to study rare and slow events involving metastable states along their reactive pathways. REPPTIS is a path sampling method where paths are cut short to reduce the computational cost, while combining this with the efficiency offered by replica exchange between the partial path ensembles. However, REPPTIS still lacks a formalism to extract time-dependent properties, such as mean first passage times, fluxes, and rates, from the short partial paths. In this work, we introduce a Markov state model (MSM) framework to estimate full path lengths and kinetic properties from the overlapping partial paths generated by REPPTIS. The framework results in newly derived closed formulas for the REPPTIS crossing probability, mean first passage times (MFPTs), flux, and rate constant. Our approach is then validated using simulations of Brownian and Langevin particles on a series of one-dimensional potential energy profiles as well as the dissociation of KCl in solution, demonstrating that REPPTIS accurately reproduces the exact kinetics benchmark. The MSM framework is further applied to the trypsin-benzamidine complex to compute the dissociation rate as a test case of a biological system, albeit the computed rate underestimates the experimental value. In conclusion, our MSM framework equips REPPTIS simulations with a robust theoretical and practical foundation for extracting kinetic information from computationally efficient partial paths.