A graphical model approach for predicting free energies of association for protein-protein interactions under backbone and side-chain flexibility

Biomolecular systems are governed by changes in free energy, and the ability to predict binding free energies provides both better understanding of biomolecular interactions and the ability to optimize them. We present the first graphical-model based approach, which we call GOBLIN (Graphical mOdel for BiomoLecular INteractions), for predicting binding free energies for all-atom models of protein complexes. Our method is physically sound in that internal energies are computed using standard molecular-mechanics force fields, and free energies are obtained by computing a rigorous approximation to the partition function of the system. Moreover, GOBLIN explicitly models both backbone and side-chain flexibility, and, when desired, employs non-linear regression to optimize force-field parameters. In tests on a benchmark set of more than 700 mutants, we show that our method is fast, running in a few minutes, and accurate, achieving root mean square errors (RMSEs) between predicted and experimental binding free energies of 2.05 kcal/mol. GOBLIN’s RMSEs are 0.55 kcal/mol better than the well-known program ROSETTA, despite the fact that we use the ROSETTA force field for computing internal energies. That is, our increase in accuracy is due to our ability to accurately estimate entropic contributions to the free energy. Finally, using our novel algorithm for optimizing force-field parameters on specific protein complexes reduced GOBLIN’s RMSE by 0.26 kcal/mol on average.