The thermodynamics of solvent exchange

A model for solvation in mixed solvents, which was developed for the free energy and preferential interaction [J. A. Schellman (1987), Biopolymers, Vol. 26, pp. 549-559; (1990), Biophysical Chemistry, Vol. 37, pp. 121-140; (1993), Biophysical Chemistry, Vol. 45, pp. 273-279], is extended in this paper to cover the thermal properties: enthalpy, entropy, and heat capacity. An important result is that the enthalpy of solvation H(ex)2 responds directly to the fraction of site occupation. This differs from the free energy G(ex)2 and preferential interaction gamma 32, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while G(ex)2 and gamma 32 are governed by (K-1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity Cpex2 consists of two term: (1) the intrinsic heat capacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies solvent exchange. Binding to biological macromolecules is heterogeneous but experimentalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites nexp, equilibrium constant Kexp, and enthalpy, delta hexp), when homogeneous formulas are applied to the heterogeneous case. It is shown that the experimental parameters for the occupation and enthalpy are simple functions of the moments of the distribution of equilibrium constants over the sites. In general, nexp is greater than the true number of sites and Kexp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogeneous formula, but the parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencies of this type of thermodynamic model are discussed.