title: A Stochastic Solution to the Unbinned WHAM Equations.
abstract: The weighted histogram analysis method (WHAM) and unbinned versions such as the multistate Bennett acceptance ratio (MBAR) and unbinned WHAM (UWHAM) are widely used to compute free energies and expectations from data generated by independent or coupled parallel simulations. Here we introduce a replica exchange-like algorithm (RE-SWHAM) that can be used to solve the UWHAM equations stochastically. This method is capable of analyzing large data sets generated by hundreds or even thousands of parallel simulations that are too large to be "WHAMMED" using standard methods. We illustrate the method by applying it to obtain free energy weights for each of the 240 states in a simulation of host-guest ligand binding containing ∼3.5 × 10(7) data elements collected from 16 parallel Hamiltonian replica exchange simulations, performed at 15 temperatures. In addition to using much less memory, RE-SWHAM showed a nearly 80-fold improvement in computational time compared with UWHAM.
authors.affiliation: Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States.
authors.forename: Bin W
authors.initials: BW
authors.lastname: Zhang
authors.affiliation: Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States.
authors.forename: Junchao
authors.initials: J
authors.lastname: Xia
authors.affiliation: Department of Statistics, Rutgers University , Piscataway, New Jersey 08854, United States.
authors.forename: Zhiqiang
authors.initials: Z
authors.lastname: Tan
authors.affiliation: Center for Biophysics and Computational Biology, Department of Chemistry, and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States.
authors.forename: Ronald M
authors.initials: RM
authors.lastname: Levy
mesh_terms: D000465:Algorithms; D013269:Stochastic Processes; D013816:Thermodynamics
keywords: MBAR; UWHAM; free energy; parallel simulations; stochastic reweighting