Accurate Atomic Decomposition Method in 3D-RISM Theory via Multi-Input Linear Correction: Application to the Protein...

Solvation free energy (SFE) is a fundamental thermodynamic quantity governing biomolecular processes in solution. Although the atomic decomposition method derived from the Kirkwood charging formula enables site-resolved evaluation of SFE contributions, its application within the three-dimensional reference interaction site model (3D-RISM) theory suffers from systematic overestimation relative to benchmark values. Here, we developed the Multi-Input Linear Correction for Atomic Decomposition (MILC-AD) framework by extending the original MILC approach to the atomic decomposition scheme within 3D-RISM theory. Unlike the original MILC framework, which relies on the nondecomposable partial molar volume (PMV), the proposed method uses atomically decomposable solute-solvent interaction energies as descriptors. Validated against 628 molecules from the benchmark FreeSolv database, the framework achieves a mean absolute deviation (MAD) of 0.57 kcal/mol relative to the Bennett acceptance ratio (BAR) calculations using ensemble-averaged predictions over ten conformations per molecule. As a representative application, the method is applied to the 36-residue villin headpiece subdomain HP36, revealing the site-resolved balance between intramolecular packing, SFE, and solvation entropy underlying the cooperative assembly of its hydrophobic core. These results demonstrate the potential of the MILC-AD framework as a practical tool for quantitative, site-resolved thermodynamic analyses of complex biomacromolecular systems.