Extraction of thermodynamic data from ternary diffusion coefficients. Use of precision diffusion measurements for aqueous lysozyme chloride-NaCl at 25 degrees C to determine the change of lysozyme chloride chemical potentialwith increasing NaCl concentration well into the supersaturated region

For ternary systems, we present a method for using measured values of the f our ternary diffusion coefficients and the Onsager reciprocal relations to extract derivatives of solute chemical potentials with respect to solute mo lar concentrations. The method is applicable to systems in which the molar concentration of one solute is very small compared to that of the other, an d also small enough that an inverse concentration dependence dominates cert ain activity coefficient derivatives. These conditions apply to a large num ber of aqueous systems involving macromolecules of biological interest. Unl ike other techniques, the present method can be used to study undersaturate d and supersaturated solutions. The approach is illustrated for the lysozym e chloride NaCl-H2O system at 25 degrees C, using data reported here for pH 6.0 at 0.60 mM (8.6 mg/mL) lysozyme chloride and 0.25, 0.50, 0.65, 0.90, a nd 1.30 M (1.4, 2.8, 3.7, 5.1, and 7.2 wt %) NaCl concentrations, and our e arlier data for pH 4.5 at the same concentrations. We use these solute chem ical potential derivatives to compute the protein cation charge approximate ly, and to construct a function approximating the derivative of the lysozym e chloride chemical potential with respect to NaCl concentration, which we integrate over a range of NaCl concentrations. This provides the change of the lysozyme chloride chemical potential with NaCl concentration well into the supersaturated region, and hence provides the driving force for nucleat ion and crystal growth of lysozyme chloride as a function of the extent of supersaturation. We also compute the diffusion Onsager coefficients (L-ij)( 0) for each composition at pH 4.5 and 6.0. Binary diffusion coefficients of aqueous lysozyme chloride at 0.89 mM (12.7 mg/mL) for pH values from 4.0 t o 6.0, and at pH 6.0 for concentrations from 0.25 to 1.95 mM (3.6-27.9 mg/m L) are also reported.