Accurate Calculations of Binding, Folding, and Transfer Free Energies by a Scaled Generalized Born Method

Abstract

The Poisson-Boltzmann (PB) equation is widely used for modeling solvation effects. The computational cost of PB has restricted its applications largely to single-conformation calculations. The generalized Born (GB) model provides an approximation at substantially reduced cost. Currently the best GB methods reproduce PB results for electrostatic solvation energies with errors at ~5 kcal/mol. When two proteins form a complex, the net electrostatic contributions to the binding free energy are typically of the order of 5 to 10 kcal/mol. Similarly, the net contributions of individual residues to protein folding free energy are < 5 kcal/mol. Clearly in these applications the accuracy of current GB methods is insufficient. Here we present a simple scaling scheme that allows our GB method, GBr6, to reproduce PB results for binding, folding, and transfer free energies with high accuracy. From an ensemble of conformations sampled from molecular dynamics simulations, five were judiciously selected for PB calculations. These PB results were used for scaling GBr6. Tests on the binding free energies of the barnase-barstar, GTPase-WASp, and U1A-U1hpII complexes and on the folding free energy of FKBP show that the effects of point mutations calculated by scaled GBr6 are accurate to within 0.3 kcal/mol of PB results. Similar accuracy was also achieved for the free energies of transfer for ribonuclease Sa and insulin from the crystalline phase to the solution phase at various pH's. This method makes it possible to thoroughly sample the transient-complex ensemble in predicting protein binding rate constants and to incorporate conformational sampling in electrostatic modeling (such as done in the MM-GBSA approach) without loss of accuracy.