The thermodynamics of solvent exchange

Abstract

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 H̄ responds directly to the fraction of site occupation. This differs from the free energy Ḡ and preferential interaction Γ₃₂, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while Ḡ and Γ₃₂ are governed by (K − 1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity C̄p 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 experiementalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites n_exp, equilibrium constant K_exp, and enthalpy, Δh_exp), 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, n_exp is greater than the true number of sites and K_exp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogenious 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. © 1994 John Wiley & Sons, Inc.