Size dependence of transfer free energies: A hard-sphere-chain- based formalism

Abstract

The main purpose of this paper is to present a theoretical scheme which describes the solvation and transfer free energies of small molecules and relate them to solvent contributions in the biomolecular processes. Several proposals, based originally on Flory–Huggins theory, have been made recently that there is a non-negligible solute’s volume-proportional term in solvation free energy and the term should be subtracted to obtain solute/solvent contact free energy for biochemical applications. These proposals have resulted in the revision of the magnitude of the hydrophobic effect in biomolecules. The validity has been controversial, since the existence, physical origin, and magnitude of the volume-proportional term have been model dependent. In this paper, we cleared up this problem by using an accurate fused-hard sphere model and a perturbation scheme in which the compensation between the repulsive and attractive interactions has been clarified. The solvation free energy is shown to be dependent on the solute’s surface area and curvature: the volume-proportional term is shown to be negligibly small. This disproves the basic assumption of the previous theories whose purpose is to “correct” the magnitude of the solvation free energy by subtracting volume-proportional terms. The relationship of our theory to previous theories is also discussed.