Pairwise Additivity and Three-Body Contributions for Density Functional Theory-Based Protein–Ligand Interaction Energies

The prediction of protein–ligand binding energies is crucial in computer-assisted drug design. This property can be calculated in a straightforward fashion as the difference in the energies between a binding site–ligand complex and the separated binding site and ligand. Often, though, there is value in knowing how different amino acid residues in the protein binding site interact with the ligand. In this case, the interaction energy can be calculated as the sum of pairwise energies between each amino acid residue in the binding site and the ligand, and the sum of these energies is often equated with the total interaction energy. The validity of this pairwise additivity approximation can be assessed by experimental evidence, such as double-mutant cycles. In this work, we test the pairwise additivity approximation on the sulfotransferase-l-DOPA complex for 16 density functional theory (DFT) methods with varying degrees of exact (Hartree–Fock) exchange. Several "families" of functionals are studied, including BLYP, B3LYP, and CAM-B3LYP, as well as M06L, M06, and M062X. We also calculate the three-body contributions to interaction energy for the same DFT methods and assess when they are significant. We find that the amount of exact exchange or other nonlocal contributions has a direct influence on how closely the sum of pairwise energies approximates the total interaction energy. We also find that three-body interactions can be significant and that their significance can be predicted with good accuracy.