  Molecular dynamics (MD) and enhanced sampling simulations have become
fundamental tools for studying biomolecular events. A significant challenge in
these simulations is ensuring that sampled configurations and transitions
converge to the stationary distribution of interest, whether equilibrium or
nonequilibrium. Lack of convergence constrains the estimation of mechanisms,
free energy, and rates of complex molecular events. Here, we introduce the
"Randomized Iterative Trajectory Reweighting" (RiteWeight) algorithm to
estimate a stationary distribution from unconverged simulation data. This
method iteratively reweights trajectories in a self-consistent way by solving
for the stationary distribution using a discrete-state transition matrix,
employing a new random clustering in each iteration. The iterative random
clustering mitigates the phase-space discretization error inherent in existing
trajectory reweighting techniques based on one-shot clustering and ultimately
yields numerically unbiased, quasi-continuous configuration-space distributions
and estimates of observables. We demonstrate the efficacy of RiteWeight using
Trp-Cage synthetic MD trajectories.
