## Measuring the Effects of Non-additivity in Interaction Energy Calculations

**Pairwise additivity of energy components in protein-ligand binding: The HIV II protease-Indinavir case**

An energy expansion (binding energy decomposition into

*n*-body interaction terms for

*n*≥ 2) to express the receptor-ligand binding energy for the fragmented HIV II protease-Indinavir system is described to address the role of cooperativity in ligand binding. The outcome of this energy expansion is compared to the total receptor-ligand binding energy at the Hartree-Fock, density functional theory, and semi-empirical levels of theory. We find that the sum of the pairwise interaction energies approximates the total binding energy to ∼82% for HF and to >95% for both the M06-L density functional and PM6-DH2 semiempirical method. The contribution of the three-body interactions amounts to 18.7%, 3.8%, and 1.4% for HF, M06-L, and PM6-DH2, respectively. We find that the expansion can be safely truncated after

*n*= 3. That is, the contribution of the interactions involving more than three parties to the total binding energy of Indinavir to the HIV II protease receptor is negligible. Overall, we find that the two-body terms represent a good approximation to the total binding energy of the system, which points to pairwise additivity in the present case. This basic principle of pairwise additivity is utilized in fragment-based drug design approaches and our results support its continued use. The present results can also aid in the validation of non-bonded terms contained within common force fields and in the correction of systematic errors in physics-based score functions.