Recent Developments in Integral Equation Theory for Solvation to Treat Density Inhomogeneity at Solute–Solvent Interface

The integration equation theory (IET) provides highly efficient tools for the calculation of structural and thermodynamic properties of molecular liquids. In recent years, the 3D reference interaction site model (3DRISM), the most developed IET for solvation, has been widely applied to study protein solvation, aggregation, and drug-receptor binding. However, hydrophobic solutes with sufficient size (>nm) can induce water density depletion at the solute–solvent interface. This density depletion is not considered in the original 3DRISM theory. The authors here review the recent developments of 3DRISM at hydrophobic surfaces and related theories to address this challenge. At hydrophobic surfaces, an additional hydrophobicity-induced density inhomogeneity equation is introduced to 3DRISM theory to consider this density depletion. Accordingly, several new closures equations including D2 closure and D2MSA closures are developed to enable stable numerical solutions of 3DRISM equations. These newly developed theories hold great promise for an accurate and rapid calculation of the solvation effect for complex molecular systems such as proteins. At the end of the report, the authors also provide a perspective on other challenges of the IETs as an efficient solvation model.