Abstract
The weighted ensemble (WE) simulation strategy can provide unbiased sampling
of non-equilibrium processes, such as molecular folding or binding. Unbiased
kinetic rates can be extracted from any discrete clustering of the
configuration space based on a history-augmented Markov state model (haMSM) at
any lag time, in the steady-state. However, the convergence of WE to
steady-state may require unaffordably long simulations in complex systems. Here
we show that by clustering molecular configurations into many (thousands of)
microbins using methods developed in the Markov State Modeling (MSM) community,
unbiased kinetics can be obtained from WE data using history-augmented Markov
State Models (haMSMs) before steady-state convergence of the WE simulation
itself. Because arbitrarily small lag times can be used within the exact haMSM
formulation, accurate kinetics can be obtained with significantly less
trajectory data than traditional MSMs, while bypassing the often prohibitive
convergence requirements of the non-equilibrium weighted ensemble. We validate
the method in a simple diffusive process on a 2D random energy landscape, and
apply the method to atomistic protein folding simulations using WE molecular
dynamics. We report significant progress towards the unbiased estimation of
protein folding times and pathways, though key challenges remain.
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