Exploring the quality of protein structural models from a Bayesian perspective

We explore how ideas and practices common in Bayesian modeling can be applied to help assess the quality of 3D protein structural models. As the word model is used in both Bayesian Statistics and Protein Science, throughout this article we deliberately use the word model to discuss statistical models and structure to discuss protein 3D models, thus avoiding potential confusions. The basic premise of our approach, is that the evaluation of a Bayesian statistical model’s fit may reveal aspects of the quality of a structure, when the fitted data are related to protein structural properties. Therefore, we fit a Bayesian hierarchical linear model to experimental and theoretical 13 C α Chemical Shifts. Then, we propose two complementary approaches for the evaluation of such fitting: 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 . Finally, we present visualizations that can help interpret these evaluations. The analyses presented in this article are aimed to aid in detecting problematic residues in protein structures. The code developed for this work is available on: https://github.com/BIOS-IMASL/Hierarchical-Bayes-NMR-Validation .