A simple model for solvation in mixed solvents. Applications to the stabilization and destabilization of macromolecular structures

The properties of a simple model for solvation in mixed solvents are explored in this paper. The model is based on the supposition that solvent replacement is a simple one-for-one substitution reaction at macromolecular sites which are independent of one another. This leads to a new form for the binding polynomial in which all terms are associated with ligand interchange rather than ligand addition. The principal solvent acts as one of the ligands. Thermodynamic analysis then shows that thermodynamic binding (i.e., selective interaction) depends on the properties of K'-1, whereas stoichiometric binding (site occupation) depends on K'. K' is a 'practical' interchange equilibrium constant given by (f3/f1)K, where K is the true equilibrium constant for the interchange of components 3 and 1 on the site and f3 and f4 denote their respective activity coefficients on the mole fraction scale. Values of K' less than unity lead to negative selective interaction. It is selective interaction and not occupation number which determines the thermodynamic effects of solvation. When K' greater than 100 on the mole fraction scale or K' greater than 2 on the molality scale (in water), the differences between stoichiometric binding and selective interaction become less than 1%. The theory of this paper is therefore necessary only for very weak binding constants. When K'-1 is small, large concentrations of the added solvent component are required to produce a thermodynamic effect. Under these circumstances the isotherms for the selective interaction and for the excess (or transfer) free energy are strongly dependent on the behavior of the activity coefficients of both solvent components. Two classes of behavior are described depending on whether the components display positive or negative deviations from Raoult's law. Examples which are discussed are aqueous solutions of urea and guanidinium chloride for positive deviations and of sucrose and glucose for negative deviations. Examination of the few studies which have been reported in the literature shows that most of the qualitative features of the stabilization of proteins by sugars and their destabilization by urea and guanidinium chloride are faithfully represented with the model. This includes maxima in the free energy of stabilization and destabilization, decreased and zero selective interaction at high concentrations, etc. These phenomena had no prior explanation. Deficiencies in the model as a representation of solvation in aqueous solution are discussed in the appendix.