# Accelerated estimation of long-timescale kinetics by combining weighted ensemble simulation with Markov model "microstates" using non-Markovian theory

## TL;DR

This paper introduces a method combining weighted ensemble simulation with non-Markovian theory and Markov State Models to efficiently estimate long-timescale kinetics, such as protein folding, without requiring steady-state convergence.

## Contribution

The authors develop a post-simulation clustering approach using haMSM to extract unbiased kinetics from WE data before steady state is reached, improving efficiency.

## Key findings

- Validated on a 2D diffusive process showing unbiased MFPT estimation.
- Applied to protein folding simulations, achieving progress in estimating folding times.
- Demonstrated that the method bypasses convergence issues of traditional WE simulations.

## 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 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.