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J Chem Theory Comput. 2014 Jul 8;10(7):2658-2667. Epub 2014 Mar 3.

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

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Department of Computational and Systems Biology, University of Pittsburgh , 4200 Fifth Ave, Pittsburgh, Pennsylvania 15260, United States.
Department of Chemistry, University of Pittsburgh , 4200 Fifth Ave, Pittsburgh, Pennsylvania 15260, United States.
Gatsby Computational Neuroscience Unit, University College London , Gower St, London WC1E 6BT, United Kingdom.


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.

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