Revisiting the estimation of relative free energies from a single ensemble

COMP 169

Daniel J. Price, Department of Molecular Biology, The Scripps Research Institute, 10550 N. Torrey Pines Rd., TPC 6, La Jolla, CA 92037 and Charles L. Brooks III, Department of Molecular Biology, TPC6, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, CA 92037.
Techniques for performing conventional single-topology free energy perturbations (FEP) are adapted to obtain relative free energies of hydration and binding for a congeneric series of compounds from a single simulation of a pseudo-chemical reference state. Convergence of the calculations benefit from using a modern generalized Born solvation model (GBMV) to reduce configurational space, the GASP procedure for performing the transformation from the reference state to the chemical end points, and by limiting the transformations considered to relatively isosteric mutations. The protocol is validated by calculating relative free energies of hydration for a series of substituted benzenes, with errors of 0.5 kcal/mol when compared to estimates obtained with conventional FEP in explicit solvent. The method is then applied to the calculation of relative free energies of binding for two model systems which have both received previous theoretical efforts: beta-cyclodextrin bound to a series of monosubstituted benzenes and trypsin bound to several p-substituted benzamidines. There is good accord with experiment in both cases (average error = 0.3 kcal/mol with cyclodextrin and 0.7 kcal/mol with trypsin), and a novel explanation for the ranking of the trypsin series is presented.