Various contributions to the osmotic second virial coefficient in protein-water-cosolvent solutions

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water-protein-cosolvent mixtures is developed. The Kirkwood-Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water-protein-cosolvent mixtures. These properties can be divided into two groups: (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water-cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions: (1) one due to the protein-solvent interactions B2(p-s), which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B2(p-p)), and (3) a third one representing an ideal mixture contribution (B2(id)). The cosolvent composition dependencies of these three contributions were examined for several water-protein-cosolvent mixtures using experimental data regarding the OSVC and the preferential binding parameter. For the water-lysozyme-arginine mixture, it was found that OSVC exhibits the behavior of an ideal mixture and that B2(id) provides the main contribution to the OSVC. For the other mixtures considered (water-Hm MalDH-NaCl, water-Hm MalDH-(NH4)2SO4, and water-lysozyme-NaCl mixtures), it was found that the contribution of the protein-solvent interactions B2(p-s) is responsible for the composition dependence of the OSVC on the cosolvent concentration, whereas the two remaining contributions (B2(p-p)) and B2(id)) are almost composition independent.