The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations

We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na⁺/Cl^- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.