Dynamical reweighting: Improved estimates of dynamical properties from simulations at multiple temperatures

Abstract

Dynamical averages based on functionals of dynamical trajectories, such as time-correlation functions, play an important role in determining kinetic or transport properties of matter. At temperatures of interest, the expectations of these quantities are often dominated by contributions from rare events, making the precise calculation of these quantities by molecular dynamics simulation difficult. Here, we present a reweighting method for combining simulations from multiple temperatures (or from simulated or parallel tempering simulations) to compute an optimal estimate of the dynamical properties at the temperature of interest without the need to invoke an approximate kinetic model (such as the Arrhenius law). Continuous and differentiable estimates of these expectations at any temperature in the sampled range can also be computed, along with an assessment of the associated statistical uncertainty. For rare events, aggregating data from multiple temperatures can produce an estimate with the desired precision at greatly reduced computational cost compared with simulations conducted at a single temperature. Here, we describe use of the method for the canonical (NVT) ensemble using four common models of dynamics (canonical distribution of Hamiltonian trajectories, Andersen thermostatting, Langevin, and overdamped Langevin or Brownian dynamics), but it can be applied to any thermodynamic ensemble provided the ratio of path probabilities at different temperatures can be computed. To illustrate the method, we compute a time-correlation function for solvated terminallyblocked alanine peptide across a range of temperatures using trajectories harvested using a modified parallel tempering protocol.

Markov State Models for Rare Events in Molecular Dynamics

“…Therefore we could obtain K by sampling in the same way we obtained P τ through Equation (19) in Section 5. This is difficult, however, due to recrossing problems for small τ ; see e.g., [44]. Finally, let us note in passing that we can drastically simplify k v if the cells, A i , are boxes of length h. Denote the elementary lattice vectors by e n .…”

Girsanov reweighting for path ensembles and Markov state models

“…In the reweighting scheme for parallel tempering simulations 43,44 , the path probability density is defined for time discretized paths at a reference temperature and then reweighted to different temperatures using statistically optimal estimators 45,46 . Like the Girsanov reweighting scheme, this method relies on the random forces at each integration time step and reweights the contribution of each path to the estimate of the transition probability individually.…”

Using Markov state models to study self-assembly

“…[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93] In cases where a set of collective coordinates describing all of the slow degrees of freedom is known (or guessed) a priori, biased sampling can be used to determine the free energy landscape as a function of these coordinates. States can then be defined based on local free energy minima (e.g., Refs.…”

“…While such MSMs have been extensively developed in the context of protein folding, [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] existing approaches cannot describe the assembly of disconnected, permutable subunits. Here, we present a method to construct MSMs that is applicable to a wide variety of such assembly reactions.…”