THE THERMODYNAMICS OF SOLVENT EXCHANGE

A model for solvation in mixed solvents, which was developed for the f ree energy and preferential interaction [J. A. Schellman (1987), Biopo lymers, 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, entr opy, and heat capacity. An important result is that the enthalpy of so lvation ($) over bar H-2(ek) responds directly to the fraction of site occupation. This differs from the free energy ($) over bar G(2)(ex) a nd preferential interaction Gamma(32), which are measures of the exces s binding above a random distribution of solvent molecules. In other w ords, the enthalpy is governed by K while ($) over bar G(2)(ex) and Ga mma(32) are governed by (K - 1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity ($) over bar Cp(2)(ex) consists of two term: (1) the intrinsic heat c apacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies so lvent exchange. Binding to biological macromolecules is heterogeneous but experimentalists must use binding isotherms that assume the homoge neity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites n(exp), equilibrium constant K-exp, and enthalpy, Delta h(exp)), when homogeneous formulas are appl ied to the heterogeneous case. It is shown that the experimental param eters for the occupation and enthalpy are simple functions of the mome nts of the distribution of equilibrium constants over the sites. In ge neral, n(exp) is greater than the true number of sites and K-exp is gr eater than the average of the equilibrium constants. The free energy a nd preferential interaction can be fit to a homogeneous formula, but t he parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencie s of this type of thermodynamic model are discussed. (C) 1994 John Wil ey & Sons, Inc.