Umbrella Refinement of Ensembles-An Alternative View of Ensemble Optimization

The elucidation of protein dynamics, especially in the context of intrinsically disordered proteins, is challenging and requires cooperation between experimental studies and computational analysis. Molecular dynamics simulations are an essential investigation tool but often struggle to accurately quantify the conformational preferences of flexible proteins. To create a quantitatively validated conformational ensemble, such simulations may be refined with experimental data using Bayesian and maximum entropy methods. In this study, we present a method to optimize a conformational ensemble using Bayes' theorem in connection with a methodology derived from Umbrella Sampling. The resulting method, called the Umbrella Refinement of Ensembles (URE), reduces the number of parameters to be optimized in comparison to the classical Bayesian Ensemble Refinement and remains methodologically suitable for use with the forward formulated Kullback-Leibler divergence. The method is validated using two established systems, an alanine-alanine zwitterion and the chignolin peptide, using nuclear magnetic resonance data from the literature.