Simultaneous computation of dynamical and equilibrium information using a weighted ensemble of trajectories

TL;DR

This paper introduces a weighted ensemble simulation method that simultaneously computes equilibrium and non-equilibrium kinetic and thermodynamic properties without predefining states, validated on molecular systems.

Contribution

It presents a novel approach combining weighted ensemble simulations with a matrix procedure to estimate kinetic and equilibrium observables in complex systems.

Findings

Successfully applied to methane association and Ala4 peptide systems

Able to estimate kinetic rates and equilibrium populations post-simulation

Addresses challenges in weighted ensemble calculations

Abstract

Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many non-equilibrium processes can be described by suitable subsets of the equilibrium ensemble. Here, we employ the "weighted ensemble" (WE) simulation protocol [Huber and Kim, Biophys. J., 1996] to generate equilibrium trajectory ensembles and extract non-equilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance. The procedure formally allows estimation of kinetic rates between arbitrary states chosen after the simulation, along with their equilibrium populations. We also describe a related history-dependent matrix procedure for estimating equilibrium and non-equilibrium observables when phase space has been divided into arbitrary non-Markovian regions, whether in WE or ordinary simulation. In this proof-of-principle study, these methods are successfully applied and validated on two molecular systems: explicitly solvated methane association and the implicitly solvated Ala4 peptide. We comment on challenges remaining in WE calculations.