Model selection using replica averaging with Bayesian inference of conformational populations

Bayesian Inference of Conformational Populations (BICePs) is a reweighting algorithm that reconciles simulated ensembles with sparse and/or noisy observables, by sampling the full posterior distribution of conformational populations in the presence of experimental restraints. By modifying BICePs to use replica-averaging in its forward model, BICePs becomes similar to other MaxEnt approaches, but with the significant advantages of (1) being able to sample over the posterior distribution of uncertainties due to random and systematic error, with improved likelihoods to deal with outliers, and (2) having an objective score for model selection, a free energy-like quantity called the BICePs score. To demonstrate the power of our approach, we used BICePs to reweight conformational ensembles of the mini-protein chignolin simulated in nine different force fields with TIP3P water, using a set of 158 experimental measurements (139 NOE distances, 13 chemical shifts, and 6 vicinal $J$-coupling constants for H$^{\text{N}}$ and H$^{\alpha}$. In all cases, reweighted populations favor the correctly folded conformation. The BICePs score, which reports the free energy of "turning on" conformational populations along with experimental restraints, provides a metric to evaluate each force field. For the nine force fields tested (A14SB, A99SB-ildn, A99, A99SBnmr1-ildn, A99SB, C22star, C27, C36, OPLS-aa), we obtain results consistent with previous work that used a conventional $\chi^{2}$ metric for model selection for small polypeptides and ubiquitin (Beauchamp et al 2012). These results suggest a powerful role for BICePs in future applications requiring ensemble reweighting and model selection.