Ligand Binding Free Energies with Adaptive Water Networks: Two-Dimensional Grand Canonical Alchemical Perturbations

Computational methods to calculate ligand binding affinities are increasing in popularity, due to improvements in simulation algorithms, computational resources, and easy-to-use software. However, issues can arise in relative ligand binding free energy simulations if the ligands considered have different active site water networks, as simulations are typically performed with a predetermined number of water molecules (fixed N ensembles) in preassigned locations. If an alchemical perturbation is attempted where the change should result in a different active site water network, the water molecules may not be able to adapt appropriately within the time scales of the simulations-particularly if the active site is occluded. By combining the grand canonical ensemble (mu VT) to sample active site water molecules, with conventional alchemical free energy methods, the water network is able to dynamically adapt to the changing ligand. We refer to this approach as grand canonical alchemical perturbation (GCAP). In this work we demonstrate GCAP for two systems; Scytalone Dehydratase (SD) and Adenosine A(2A) receptor. For both systems, GCAP is shown to perform well at reproducing experimental binding affinities. Calculating the relative binding affinities with a naive, conventional attempt to solvate the active site illustrates how poor results can be if proper consideration of water molecules in occluded pockets is neglected. GCAP results are shown to be consistent with time-consuming double decoupling simulations. In addition, by obtaining the free energy surface for ligand perturbations, as a function of both the free energy coupling parameter and water chemical potential, it is possible to directly deconvolute the binding energetics in terms of protein-ligand direct interactions and protein binding site hydration.