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.