Spatial Decomposition of Solvation Free Energy Based on the 3D Integral Equation Theory of Molecular Liquid: Application to Miniproteins

We propose the method of spatial decomposition analysis (SDA) based on three-dimensional integral equation (3D-IE) theory of molecular liquids to study and decompose the thermodynamics of proteins in solution into atomic level contributions. The 3D-IE theory maps the solvation thermodynamic properties, such as the solvation free energy and solvation entropy, onto the 3D space around the solute, including the excluded volume of the solute macromolecule, with the elementary volume contributions expressed in terms of the 3D total and direct correlation functions. The SDA thus breaks down the thermodynamic quantity into partial contributions of the solute fragments (functional groups or residues) by applying the proximity criterion to the 3D-IE mapping onto both the solvation shell outside the solute macromolecule and its excluded volume inside the van der Waals cores, the latter giving a major contribution to the solvation thermodynamics. This is distinct from the previous use of the proximity criterion applied to the 3D distribution functions in the solvation shell only. As SDA does not require perturbing the protein molecule to extract the contributions from the constituent residues, it can become an alternative to the computational "alanine scanning approach". For illustration, we apply SDA to four miniproteins composed of 10-28 amino acid residues (chignolin, CLNO25, Trp-cage, and FSD-1) and decompose their solvation free energy into the partial contributions of each residue. The present results show that SDA is capable of detecting a change in the protein thermodynamics due to mutations and local conformational changes. Furthermore, the SDA exhibits a convincing consistency with the experimental values of the whole-residue transfer free energies from water to 1-octanol. Thus, the SDA provides a meaningful decomposition of the protein thermodynamics which can bear a comparison with experimental measurements and therefore can serve as a valuable sensitive tool to analyze the protein thermodynamics at the atomistic resolution level. We envision that the SDA may also serve as a tool for quantitative structure-activity relationships (QSAR) to correlate and predict various solute properties in a fragment-based manner.