Residue-Level Affinity Decomposition via Quantum Electron Density: A Multivariable Framework Applied to HIV-1 Protease Inhibitors

Understanding the molecular determinants that govern protein–ligand binding remains a central challenge in computational chemistry and rational drug design. Here, we introduce a quantum-informed, residue-level affinity decomposition framework that integrates experimental thermodynamic data with multivariable modeling of electron-density descriptors. Using a unified computational workflow combining molecular dynamics simulations, semiempirical hydrogen refinement, Density Functional Theory single-point calculations, and QTAIM analysis, we quantified noncovalent interactions between HIV-1 protease and six clinically approved inhibitors. Although the total electron density at bond critical points showed no direct correlation with experimental binding enthalpies, residue-specific multivariate models revealed that affinity is primarily governed by the nature of individual contacts rather than by their overall number or density. This statistical decomposition is further supported by Hessian-based electron-density descriptors and NCI index, which provide a physical interpretation of stabilizing and destabilizing residue-level interactions. The models clearly distinguished between stabilizing (cooperative) and destabilizing (anticooperative) residue contributions, highlighting the mechanistic influence of structured water. Comparison with MM-PBSA per-residue energies further supported the predictive value of the quantum descriptors. Importantly, the analysis is independent of the structural relatedness of the ligands, underscoring its applicability to chemically diverse scaffolds. Overall, this study presents a transferable, quantum-topological framework for mechanistic protein–ligand affinity analysis, offering a generalizable strategy for structure-guided optimization of inhibitors targeting a common binding site.