Extraction of Thermodynamic Data from Ternary Diffusion Coefficients. Use of Precision Diffusion Measurements for Aqueous Lysozyme Chloride−NaCl at 25 °C To Determine the Change of Lysozyme Chloride Chemical Potential with Increasing NaCl Concentration Well into the Supersaturated Region†

For ternary systems, we present a method for using measured values of the four ternary diffusion coeffs. and the Onsager reciprocal relations to ext. derivs. of solute chem. potentials with respect to solute molar concns. The method is applicable to systems in which the molar concn. of one solute is very small compared to that of the other, and also small enough that an inverse concn. dependence dominates certain activity coeff. derivs. These conditions apply to a large no. of aq. systems involving macromols. of biol. interest. Unlike other techniques, the present method can be used to study undersatd. and supersatd. solns. The approach is illustrated for the lysozyme chloride-NaCl-H2O system at 25°, 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, and 1.30 M (1.4, 2.8, 3.7, 5.1, and 7.2 wt %) NaCl concns., and our earlier data for pH 4.5 at the same concns. We use these solute chem. potential derivs. to compute the protein cation charge approx., and to construct a function approximating the deriv. of the lysozyme chloride chem. potential with respect to NaCl concn., which we integrate over a range of NaCl concns. This provides the change of the lysozyme chloride chem. potential with NaCl concn. well into the supersatd. region, and hence provides the driving force for nucleation and crystal growth of lysozyme chloride as a function of the extent of supersatn. We also compute the diffusion Onsager coeffs. (Lij)0 for each compn. at pH 4.5 and 6.0. Binary diffusion coeffs. of aq. lysozyme chloride at 0.89 mM (12.7 mg/mL) for pH values from 4.0 to 6.0, and at pH 6.0 for concns. from 0.25 to 1.95 mM (3.6-27.9 mg/mL) are also reported.