Bayesian Maximum Entropy Ensemble Refinement

Abstract

The principle of maximum entropy provides a canonical way to include measurement results into a thermodynamic ensemble. Observable features of a thermodynamic system, which are measured as averages over an ensemble are included into the partition function by using Lagrange multipliers. Applying this principle to the systems energy leads to the well-known exponential form of the Boltzmann probability density. Here, we present a Bayesian approach to the estimation of maximum entropy parameters from nuclear Overhauser effect measurements in order to achieve a refined ensemble in molecular dynamics simulations. To achieve this goal, we leverage advances in the treatment of doubly intractable Bayesian inference problems by adaptive Markov Chain Monte Carlo methods. We illustrate the properties and viability of our method for alanine dipeptide as a simple model system and trp-cage as an example for a more complex peptide.