Using stochastic models calibrated from nanosecond nonequilibrium simulations to approximate mesoscale information

doi:10.1063/1.3106225We demonstrate how the surrogate process approximation (SPA) method can be used to compute both the potential of mean force along a reaction coordinate and the associated diffusion coefficient using a relatively small number (10-20) of bidirectional nonequilibrium trajectories coming from a complex system. Our method provides confidence bands which take the variability of the initial configuration of the high-dimensional system, continuous nature of the work paths, and thermal fluctuations into account. Maximum-likelihood-type methods are used to estimate a stochastic differential equation (SDE) approximating the dynamics. For each observed time series, we estimate a new SDE resulting in a collection of SPA models. The physical significance of the collection of SPA models is discussed and methods for exploiting information in the population of estimated SPA models are demonstrated and suggested. Molecular dynamics simulations of potassium ion dynamics inside a gramicidin A channel are used to demonstrate the methodology, although SPA-type modeling has also proven useful in analyzing single-molecule experimental time series.C.P.C. thanks Benoît Roux for providing comments on this paper, Riccardo Chelli for helpful discussions related to PMF computations, a referee for helpful comments on the first version, and NIH Grant No. T90 DK070121-04. L.J. and I.K. gratefully acknowledge the computer time provided by the University of Missouri Bioinformatics Consortium. Partial computational support was obtained from the Rice Computational Research Cluster funded by NSF under Grant No. CNS-0421109 and a partnership between Rice University, AMD, and Cray