Standard free energies of binding of solute to proteins in aqueous medium .1. Thermodynamic analysis for multicomponent system

Using an equilibrium dialysis technique, moles (Gamma(2)(1)) of cationic and anionic surfactants bound per kilogram of proteins of various types in aqueous media have been measured previously in this laboratory under different physicochemical conditions. From a thermodynamic analysis in the present paper, Gamma(2)(1) has been shown to be equal to the Gibbs relative excess of surfactant per kilogram of protein at a measured value of solute activity, a(2). The values of relative solvent excesses, Gamma(1)(2) (which are negative for surfactants) can be estimated from values of Gamma(2)(1) and a(2). Using the Gibbs-Duhem relationship for protein solution inside the dialysis bag and dialysate solutions respectively at equilibrium, an integrated expression for the standard free energy change, Delta G degrees (in kilojoules per kilogram of protein for binding with ligand as a result of the change of a(2) from zero to unity) can be calculated from experimental data. The isopiestic vapour pressure technique was used extensively for evaluation of negative binding (-Gamma(2)(1)) of inorganic salts to proteins of different types for various values of a(2) of salts present in the bulk media. With some modifications of our derived equations for free energy of binding in such a system, Delta G degrees has been evaluated for the change of mean activity of electrolyte from zero to unity in the rational scale. Delta G degrees is positive since Gamma(2)(1) is negative and Gamma(1)(2) is positive for such ionic systems. Delta G degrees in all cases, however, are expressed in terms of the standard state of reference of unit activity so that their magnitudes and sign can be related to the relative affinities of a solute for binding with proteins in aqueous media.