Using the fast fourier transform in binding free energy calculations

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. The authors demonstrate the feasibility of using the fast Fourier transform to calculate binding free energies between proteins and small molecules. A key part of the algorithm involves calculating interaction energies when the small molecule is translated across the binding site on the receptor (lower right inset). On averaging over the interaction energies and over multiple protein conformations, the resulting binding free energy is consistent with those from more expensive alchemical methods (scatter plot).