Optimization and dynamics of protein-protein complexes using B-splines

A moving-grid approach for optimization and dynamics of protein-protein complexes is introduced, which utilizes cubic B-spline interpolation for rapid energy and force evaluation. The method allows for the efficient use of full electrostatic potentials joined smoothly to multipoles at long distance so that multiprotein simulation is possible. Using a recently published benchmark of 58 protein complexes, we examine the performance and quality of the grid approximation, refining cocrystallized complexes to within 0.68 A RMSD of interface atoms, close to the optimum 0.63 A produced by the underlying MMFF94 force field. We quantify the theoretical statistical advantage of using minimization in a stochastic search in the case of two rigid bodies, and contrast it with the underlying cost of conjugate gradient minimization using B-splines. The volumes of conjugate gradient minimization basins of attraction in cocrystallized systems are generally orders of magnitude larger than well volumes based on energy thresholds needed to discriminate native from nonnative states; nonetheless, computational cost is significant. Molecular dynamics using B-splines is doubly efficient due to the combined advantages of rapid force evaluation and large simulation step sizes. Large basins localized around the native state and other possible binding sites are identifiable during simulations of protein-protein motion. In addition to providing increased modeling detail, B-splines offer new algorithmic possibilities that should be valuable in refining docking candidates and studying global complex behavior.