  The weighted ensemble (WE) simulation strategy provides unbiased sampling of
non-equilibrium processes, such as molecular folding or binding, but the
extraction of rate constants relies on characterizing steady state behavior.
Unfortunately, WE simulations of sufficiently complex systems will not relax to
steady state on observed simulation times. Here we show that a post-simulation
clustering of molecular configurations into "microbins" using methods developed
in the Markov State Model (MSM) community, can yield unbiased kinetics from WE
data before steady-state convergence of the WE simulation itself. Because WE
trajectories are directional and not equilibrium-distributed, the
history-augmented MSM (haMSM) formulation can be used, which yields the mean
first-passage time (MFPT) without bias for arbitrarily small lag times.
Accurate kinetics can be obtained 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
then analyze 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.
