Exploring the quality of protein structural models from a Bayesian perspective

Abstract

On the present work, we explore how ideas and practices common in Bayesian modeling can be applied in the context of protein structure assessment. We feature two different but related types of models in this work. The first is statistical while the second is related to the 3D structure of proteins. We fit a Bayesian hierarchical linear model to experimental and theoretical 13Cα Chemical Shifts. Based on the premise that evaluation of the Bayesian statistical model’s fit may reveal aspects of the quality of a 3D protein structural model, we propose two complementary approaches for its evaluation: 1) in terms of the expected differences between experimental and posterior predicted values; 2) in terms of the leave-one-out cross validation point-wise predictive accuracy computed from the hierarchical Bayesian models. As the expected differences are unknown from theory alone, empirical reference densities computed from a data set of high quality protein structures are used to provide context for those differences. Finally, we present visualizations that can help interpret all these comparisons. The analyses presented in this article are aimed to aid in detecting problematic residues or regions in protein structures. The code used in this paper is available on: https://github.com/BIOS-IMASL/Hierarchical-Bayes-NMR-Validation. We encourage others to make use of this code to reproduce our analysis, perform a similar analysis on proteins of interest and improve over our proposal, either by expanding the hierarchical linear models or including other observables to complement or replace 13Cα Chemical Shifts.