A Contribution to the Theory of Preferential Interaction Coefficients

A simple and complete derivation of the relation between concentration-based preferential interaction coefficients and integrals over the relevant pair correlation functions is presented for the first time. Certain omissions from the original treatment of pair correlation functions in multicomponent thermodynamics are also addressed. Connections between these concentration-based quantities and the more common molality-based preferential interaction coefficients are also derived. The pair correlation functions and preferential interaction coefficients of both solvent (water) and cosolvent (osmolyte) in the neighborhood of a macromolecule contain contributions from short-range repulsions and generic long-range attractions originating from the macromolecule, as well as from osmolyte-solvent exchange reactions beyond the macromolecular surface. These contributions are evaluated via a heuristic analysis that leads to simple insightful expressions for the preferential interaction coefficients in terms of the volumes excluded to the centers of the water and osmolyte molecules and a sum over the contributions of exchanging sites in the surrounding solution. The preferential interaction coefficients are predicted to exhibit the experimentally observed dependence on osmolyte concentration. Molality-based preferential interaction coefficients that were reported for seven different osmolytes interacting with bovine serum albumin are analyzed using the this formulation together with geometrical parameters reckoned from the crystal structure of human serum albumin. In all cases, the excluded volume contribution, which is the volume excluded to osmolyte centers minus that excluded to water centers in units of V¯1, exceeds in magnitude the contribution of the exchange reactions. Under the assumption that the exchange contribution is dominated by sites in the first surface-contiguous layer, the ratio of the average exchange constant to its neutral random value is determined for each osmolyte. These ratios all lie in the range 1.0 ± 0.15, which indicates rather slight deviations from random occupation near the macromolecular surface. Finally, a mechanism is proposed whereby the chemical identity of an osmolyte might be concealed from partially ordered multilayers of water in clefts, grooves, and pits, and its consequences are noted.