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

Abstract

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.