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It is a challenge to obtain an accurate model of the state-to-state dynamicsof a complex biological system from molecular dynamics (MD) simulations. Inrecent years, Markov State Models have gained immense popularity for computingstate-to-state dynamics from a pool of short MD simulations. However, theassumption that the underlying dynamics on the reduced space is Markovianinduces a systematic bias in the model, especially in biomolecular systems withcomplicated energy landscapes. To address this problem, we have devised a newapproach we call quasi-stationary distribution kinetic Monte Carlo (QSD-KMC)that gives accurate long time state-to-state evolution while retaining theentire time resolution even when the dynamics is highly non-Markovian. Theproposed method is a kinetic Monte Carlo approach that takes advantage of twoconcepts: (i) the quasi-stationary distribution and (ii) dynamical correctionstheory. Implementation of QSD-KMC imposes stricter requirements on the lengthsof the trajectories than in a Markov State Model approach, as the trajectoriesmust be long enough to dephase. However, the QSD-KMC model producesstate-to-state trajectories that are statistically indistinguishable from an MDtrajectory mapped onto the discrete set of states, for an arbitrary choice ofstate decomposition. Furthermore, the aforementioned concepts can be used toconstruct a Monte Carlo approach to optimize the state boundaries regardless ofthe initial choice of states. We demonstrate the QSD-KMC method on twoone-dimensional model systems, one of which is a driven nonequilibrium system,and on two well-characterized biomolecular systems.

Computing Long Timescale Biomolecular Dynamics using Quasi-Stationary Distribution Kinetic Monte Carlo (QSD-KMC)