Relationship between Solvation Thermodynamics from IST and DFT Perspectives.

Inhomogeneous solvation theory (IST) and classical density functional theory (DFT) each provide a framework for relating distribution functions of solutions to their thermodynamic properties. As reviewed in this work, both IST and DFT can be formulated in a way that use two "end point" simulations, one of the pure solvent and the other of the solution, to determine the solute chemical potential and other thermodynamic properties of the solution and of subvolumes in regions local to the solute containing hydrating waters. In contrast to IST, where expressions for the excess energy and entropy of solution are the object of analysis, in the DFT end point formulation of the problem, the solute-solvent potential of mean force (PMF) plays a central role. The indirect part of the PMF corresponds to the lowest order (1-body) truncation of the IST expression. Because the PMF is a free energy function, powerful numerical methods can be used to estimate it. We show that the DFT expressions for the solute excess chemical potential can be written in a form which is local, involving integrals only over regions proximate to the solute. The DFT end point route to estimating solvation free energies provides an alternative path to that of IST for analyzing solvation effects on molecular recognition and conformational changes in solution, which can lead to new insights. In order to illustrate the kind of information that is contained in the solute-solvent PMF, we have carried out simulations of β-cyclodextrin in water. This solute is a well studied "host" molecule to which "guest" molecules bind; host-guest systems serve as models for molecular recognition. We illustrate the range of values the direct and indirect parts of the solute-solvent PMF can have as a water molecule is brought to the interface of β-cyclodextrin from the bulk; we discuss the "competition" between these two terms, and the role it plays in molecular recognition.