Rapid Estimation of Solvation Energy for Simulations of Protein-Protein Association

We have formulated the Energy by Linear Superposition of Corrections Approximation (ELSCA) for estimating the electrostatic and apolar solvation energy of bringing two proteins into close proximity or into contact as defined by the linearized Poisson-Boltzmann model and a linear function of the solvent-accessible surface area. ELSCA utilizes potentials of mean force between atom types found in the AMBER ff99 force field, a uniform distance-dependent dielectric, and a potential that mimics the change in solvent accessible surface area for bringing two solvated spheres into contact. ELSCA was trained by a linear least-squares fit on more than 39 000 putative complexes, each formed from pairs of nonhomologous proteins with a range of shapes, sizes, and charges. The training set was also designed to capture various stages of complex formation. ELSCA was tested against over 8000 non-native complexes of 45 enzyme/inhibitor, antibody/antigen, and other systems that are known to form complexes and gives an overall correlation of 0.962 with PBSA-derived energies for these complexes. The predictions have a slope of 0.89 on the actual values with a bias of 11.1 kcal/mol. When applied to native complexes of these 45 protein systems, ELSCA reproduces PBSA results with a correlation of 0.787, a slope of 1.13, and a bias of 13.0 kcal/mol. We report parameters for ELSCA in the context of the AMBER ff99 parameter set. Our model is most useful in macromolecular docking and protein association simulations, where large portions of each molecule may be considered rigid.