Improving the Potential of Mean Force and Nonequilibrium Pulling Simulations by Simultaneous Alchemical Modifications

We present an approach combining alchemical modifications and physical-pathway methods to calculate absolute binding free energies. The employed physical-pathway method is either a stratified umbrella sampling to calculate a potential of mean force or nonequilibrium pulling. We devised two basic approaches: the simultaneous approach (S-approach), where, along the physical unbinding pathway, an alchemical transformation of ligand-protein interactions is installed and deinstalled, and the prior-plus-simultaneous approach (PPS-approach), where, prior to the physical-pathway simulation, an alchemical transformation of ligand-protein interactions is installed in the binding site and deinstalled during the physical-pathway simulation. Using a mutant of T4 lysozyme with a benzene ligand as an example, we show that installation and deinstallation of soft-core interactions concurrent with physical ligand unbinding (S-approach) allow successful potential of mean force calculations and nonequilibrium pulling simulations despite the problems posed by the occluded nature of the lysozyme binding pocket. Good agreement between the potential of the mean-force-based S-approach and double decoupling simulations as well as a remarkable efficiency and accuracy of the nonequilibrium-pulling-based S-approach is found. The latter turned out to be more compute-efficient than the potential of mean force calculation by approximately 70%. Furthermore, we illustrate the merits of reducing ligand-protein interactions prior to potential of mean force calculations using the murine double minute homologue protein MDM2 with a p53-derived peptide ligand (PPS-approach). Here, the problem of breaking strong interactions in the binding pocket is transferred to a prior alchemical transformation that reduces the free-energy barrier between the bound and unbound state in the potential of mean force. Besides, disentangling physical ligand displacement from the deinstallation of ligand-protein interactions was seen to allow a more uniform sampling of distance histograms in the umbrella sampling. In the future, physical ligand unbinding combined with simultaneous alchemical modifications may prove useful in the calculation of protein-protein binding free energies, where sampling problems posed by multiple, possibly sticky interactions and potential steric clashes can thus be reduced.