Refine
Year of publication
- 2012 (2)
Language
- English (2)
Keywords
Project
- A19 (2)
Application Area
- A (2)
Dynamical averages based on functionals of dynamical trajectories, such as time-correlation func-
tions, 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 prop-
erties 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
of 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 us-
ing 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 terminally-
blocked alanine peptide across a range of temperatures using trajectories harvested using a modified
parallel tempering protocol.
While seemingly straightforward in principle, the reliable estimation of rate constants is seldom easy in practice. Numerous issues, such as the complication of poor reaction coordinates, cause obvious approaches to yield unreliable estimates. When a reliable order parameter is available, the reactive flux theory of Chandler allows the rate constant to be extracted from the plateau region of an appropriate reactive flux correlation function. However, when applied to real data from single- molecule experiments or molecular dynamics simulations, the reactive flux correlation function requires the numerical differentiation of a noisy empirical correlation function, which can result in an unacceptably poor estimate of the rate and pathological dependence on the sampling interval. We present a modified version of this theory which does not require numerical derivatives, allowing rate constants to be robustly estimated from the time-correlation function directly. We illustrate the approach using single-molecule passive force spectroscopy measurements of an RNA hairpin.