Fast optimization of statistical potentials for structurally constrained phylogenetic models

Contact Potential for Structure Prediction of Proteins and Protein Complexes from Potts Model

The energy function is the key component of protein modeling methodology. This work presents a semianalytical approach to the development of contact potentials for protein structure modeling. Residue-residue and atom-atom contact energies were derived by maximizing the probability of observing native sequences in a nonredundant set of protein structures. The optimization task was formulated as an inverse statistical mechanics problem applied to the Potts model. Its solution by pseudolikelihood maximization provides consistent estimates of coupling constants at atomic and residue levels. The best performance was achieved when interacting atoms were grouped according to their physicochemical properties. For individual protein structures, the performance of the contact potentials in distinguishing near-native structures from the decoys is similar to the top-performing scoring functions. The potentials also yielded significant improvement in the protein docking success rates. The potentials recapitulated experimentally determined protein stability changes upon point mutations and protein-protein binding affinities. The approach offers a different perspective on knowledge-based potentials and may serve as the basis for their further development.

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.