Elimination of Finite-Size Effects on Binding Free Energies via the Warp-Drive Method

The accurate calculation of protein-ligand binding free energies is necessary for computer-aided drug design. The alchemical perturbation method frequently used for binding free energy calculations under periodic boundary conditions suffers from finite-size effects related to the cell-size dependence of the charging free energy at different cell sizes. The finite-size effect on the binding free energy of charged ligands is not negligible in comparison to the binding free energy itself. In this study, we propose an effective perturbation protocol for calculating the binding free energy termed the "warp-drive" method for eliminating the finite-size effect. When the warp-drive method is applied, a solution system consisting of a protein-ligand complex and an unbound ligand located at a distant position is used. Diminished partial charges of the bound ligand simultaneously emerge in the other unbound ligand, and in turn, the total charge of the system does not change at all intermediate states. To assess the performance of the warp-drive method, charging free energies for systematically varied cell sizes are examined and compared to those calculated via alchemical perturbation. In contrast to that of alchemical perturbation, the charging free energy obtained via the warp-drive method does not exhibit finite-size effects, even for typical cell sizes without any corrections, and this result is in good agreement with that calculated on the basis of alchemical perturbation levels measured from large cells with full corrections of the finite-size effect. This finding reveals an advantage of the warp-drive method, as alchemical perturbation is computationally costly due to the large cell sizes and specificities involved in correction schemes depending on the total charge of proteins and components of solvent molecules.