Combining the Fragment Molecular Orbital and GRID Approaches for the Prediction of Ligand–Metalloenzyme Binding Affinity: The Case Study of hCA II Inhibitors

Polarization and charge-transfer interactions play an important role in ligand–receptor complexes containing metals, and only quantum mechanics methods can adequately describe their contribution to the binding energy. In this work, we selected a set of benzenesulfonamide ligands of human Carbonic Anhydrase II (hCA II)—an important druggable target containing a Zn²⁺ ion in the active site—as a case study to predict the binding free energy in metalloprotein–ligand complexes and designed specialized computational methods that combine the ab initio fragment molecular orbital (FMO) method and GRID approach. To reproduce the experimental binding free energy in these systems, we adopted a machine-learning approach, here named formula generator (FG), considering different FMO energy terms, the hydrophobic interaction energy (computed by GRID) and logP. The main advantage of the FG approach is that it can find nonlinear relations between the energy terms used to predict the binding free energy, explicitly showing their mathematical relation. This work showed the effectiveness of the FG approach, and therefore, it might represent an important tool for the development of new scoring functions. Indeed, our scoring function showed a high correlation with the experimental binding free energy (R² = 0.76–0.95, RMSE = 0.34–0.18), revealing a nonlinear relation between energy terms and highlighting the relevant role played by hydrophobic contacts. These results, along with the FMO characterization of ligand–receptor interactions, represent important information to support the design of new and potent hCA II inhibitors.