Accelerated Estimation of Long-Timescale Kinetics from Weighted Ensemble Simulation via Non-Markovian “Microbin” Analysis

Abstract

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 postsimulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community, can yield unbiased kinetics from WE data before steadystate 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.

Gaussian accelerated molecular dynamics with the weighted ensemble method: a hybrid method improves thermodynamics and kinetics sampling

“…Since a long simulation is typically needed to get reasonable estimates of the kinetics, researchers have recently developed methods for the WE method to estimate the actual kinetics faster. 52,103,104 If GaMD-WE is combined with these current methods, more improvements will be seen in obtaining thermodynamic and kinetic properties.…”

“…Suppose a more comprehensive picture of the entire configuration space is needed along with its thermodynamic and kinetic properties. In that case, either one can build a Markov state model (MSM) [41][42][43][44][45][46][47][48] or run the weighted ensemble (WE) method [49][50][51][52][53][54][55][56][57][58][59] on the system of interest. Both methods decompose the configuration space into small volume elements called "macrostates" and run many short simulations to obtain good statistics.…”

#COVIDisAirborne: AI-Enabled Multiscale Computational Microscopy of Delta SARS-CoV-2 in a Respiratory Aerosol

“…First, in contrast to prior manual bins for controlling trajectory replication, we have developed automated and adaptive binning that enables more efficient surmounting of large barriers via early identification of "bottleneck" regions (Torrillo et al, 2021). Second, we have parallelized, memory-optimized, and implemented data streaming for the history-augmented Markov state model (haMSM) analysis scheme (Copperman and Zuckerman, 2020) to enable application to the TB-scale S-opening datasets. The haMSM approach estimates rate constants from simulations that have not yet reached a steady state (Suarez et al, 2014).…”

Markovian Weighted Ensemble Milestoning (M-WEM): Long-time Kinetics from Short Trajectories

“…Many new variants, as well as new analysis schemes for the traditional WE approach, have emerged in recent years, including WExplore, 30 resampling of ensembles by variation optimization (REVO), 31 history augmented Markov State Modeling (haMSM), 32 the RED scheme, 33 minimal adaptive binning (MAB), 34 and micro-bin analysis. 35 Particularly, the WExplore and REVO algorithms have been successfully applied to study the pathways and kinetics of protein-ligand dissociation, 31,36,37 even for systems with residence times as high as seconds to minutes. 38,39 Another popular approach to study the kinetics of biophysical rare events is milestoning, [40][41][42] which belongs to the larger category of trajectory stratification.…”