Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories

Abstract

Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many nonequilibrium 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, 70, 97–110] to generate equilibrium trajectory ensembles and extract nonequilibrium 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 nonequilibrium 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.

Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations [Article v1.0]

“…The final set of trajectories can be visualized as a tree structure based on the occasional replication and pruning events. WE is an unbiased method that can be used to sample rare transient behavior [71] as well as steady states [72] including equilibrium [73]. …”

WESTPA: An Interoperable, Highly Scalable Software Package for Weighted Ensemble Simulation and Analysis

“…19,23,27 Here we consider in more explicit detail how WESTPA can be used to calculate dynamic and distributional quantities from a molecular system, focusing on key elements of a typical workflow and highlighting important capabilities provided by the software package.…”

“…16 The efficiency of WE simulations can be further increased, particularly in the presence of metastable intermediates, by the use of reweighting procedures that determine global thermodynamic properties in terms of local kinetic properties. 17,27 …”

Technical advances in molecular simulation since the 1980s

“…TPS methods are computationally expensive but they allow, in principle, the computation of both the free energies and rate constants of a process. Other algorithms of similar type include milestoning [86,87], weighted ensemble path sampling [88], and generalizations of the string method [89].…”