Statistical potentials for improved structurally constrained evolutionary models

Assessing the influence of three-dimensional protein structure on sequence evolution is a difficult task, mainly because of the assumption of independence between sites required by probabilistic phylogenetic methods. Recently, models that include an explicit treatment of protein structure and site interdependencies have been developed: a statistical potential (an energy-like scoring system for sequence-structure compatibility) is used to evaluate the probability of fixation of a given mutation, assuming a coarse-grained protein structure that is constant through evolution. Yet, due to the novelty of these models and the small degree of overlap between the fields of structural and evolutionary biology, only simple representations of protein structure have been used so far. In this work, we present new forms of statistical potentials using a probabilistic framework recently developed for evolutionary studies. Terms related to pairwise distance interactions, torsion angles, solvent accessibility, and flexibility of the residues are included in the potentials, so as to study the effects of the main factors known to influence protein structure. The new potentials, with a more detailed representation of the protein structure, yield a better fit than the previously used scoring functions, with pairwise interactions contributing to more than half of this improvement. In a phylogenetic context, however, the structurally constrained models are still outperformed by some of the available site-independent models in terms of fit, possibly indicating that alternatives to coarse-grained statistical potentials should be explored in order to better model structural constraints.