Advancing Binding Affinity Calculations: A Non-Equilibrium Simulations Approach for Calculation of Relative Binding Free Energies in Systems with Trapped Waters

The formation of protein-ligand complexes involves displacement of water molecules that were previously occupying the protein's binding site. In some cases, however, some water molecules may not be displaced by the ligand's binding and they can stabilize the complex by mediating the interactions between the ligand and the protein. A relative binding free energy (RBFE) calculation between two ligands, one of which binds to the protein with an intermediate water while the other ligand displaces it, can yield wrong results if the water fails to rearrange itself within the simulation timescale. Enhanced sampling methods have previously been used to address the sampling of such "trapped" waters, inserting or deleting waters in the protein's binding site during ligand transformation. While sometimes effective, the enhanced sampling methods typically require long simulation times to converge and may lead to differences in RBFE estimates (i.e., hysteresis) based on initial water placement. In this study, we present a non-equilibrium switching (NES) method to calculate RBFEs in systems with trapped waters. Our approach requires the knowledge of the positions of the trapped waters prior to performing the free energy calculation for ligand transformation, and then uses this information to efficiently calculate the RBFE between the ligands. In our simulation protocol, we perform ligand transformation in the binding site of the target protein using three consecutive NES switches. The three NES switches implement restraints, transform the ligand, and then remove the restraints. We demonstrate that our NES simulations-based method results in RBFE estimates within 1.1 kcal/mol of experimental RBFEs, with associated statistical errors under 0.4 kcal/mol, for eight systems involving trapped water displacement. Our method provides a computationally inexpensive alternative for estimating RBFEs for systems involving trapped waters by leveraging distributed computational resources.