Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations

Bayesian inference is used to obtain self-consistent estimates of free energies and position-dependent diffusion coefficients along complex reaction coordinates from molecular dynamics simulation trajectories. Effectively, exact solutions for the dynamics of a diffusive model are matched globally to the observed molecular dynamics data. The approach is first tested for a simple one-dimensional diffusion model, and then applied to the dihedral-angle dynamics of a peptide fragment dissolved in water. Both long equilibrium molecular dynamics simulations and short, appropriately initialized, replica simulations are used to sample the short-time dynamics of the peptide-water system. In both cases, accurate estimates of free energies and diffusion coefficients are obtained.