Biomolecular Structure Refinement & Prediction using Dead-End Elimination with a Polarizable Force Field

Abstract

Global optimization of protein side-chains using discrete rotamer libraries is a challenging problem due to the large number of permutations that exist. For example, a small protein with 100 amino acid residues, each with 3 energetically favorable conformations, gives 3100 (or 1047) permutations to be searched. A systematic search over all permutations is computationally intractable, even in this simple case. To reduce the search space, rigorous inequalities have been described that eliminate high-energy rotamers, rotamer pairs, and so on (i.e. dead-end elimination), based on the assumption of a pairwise decomposable energy function. However, important biomolecular driving forces, including the hydrophobic effect and electronic polarization, are fundamentally many-body in nature. Neglect of higher order many-body forces has unduly limited the accuracy protein side-chain optimization and its applications to protein structure refinement, protein design and drug discovery. Here we present new rotamer elimination criteria that make possible the provable global optimization of protein side-chains using a polarizable (many-body) force field. Our many-body elimination criteria are only modestly more complex than the earlier pairwise versions when truncated at 3- or 4-body interactions. This opens the door to the rigorous use of not only polarizable force fields, which are now widely available for protein simulations, but also quantum mechanical potentials and/or implicit solvents such as Poisson-Boltzmann. Application to the protein “Proliferating Cell Nuclear Antigen” (PCNA) will be presented, which is a eukaryotic sliding clamp involved in numerous DNA processing pathways.