Precision Measurements of Binary and Multicomponent Diffusion Coefficients in Protein Solutions Relevant to Crystal Growth: Lysozyme Chloride in Water and Aqueous NaCl at pH 4.5 and 25 °C

Abstract

Accurate models of protein diffusion are important in a number of applications, including liquid−liquid phase separation and growth of protein crystals for X-ray diffraction studies. In concentrated multicomponent protein systems, significant deviations from pseudobinary behavior can be expected. Rayleigh interferometry is used to measure the four elements (Dij)v of the ternary diffusion coefficient matrix for the extensively investigated protein, hen egg-white lysozyme (component 1) in aqueous NaCl (component 2) at pH 4.5 and 25 °C. These are the first multicomponent diffusion coefficients measured for any protein system at concentrations high enough to be relevant to modeling and prediction of crystal growth or other phase transitions, and the first for a system involving lysozyme at any concentration. The four ternary diffusion coefficients for the system lysozyme chloride/NaCl/water are reported for lysozyme chloride at 0.60 mM (8.6 mg/mL) and NaCl at concentrations of 0.25, 0.50, 0.65, 0.90, and 1.30 M (1.4, 2.8, 3.7, 5.1, and 7.2 wt %), with the latter two compositions being supersaturated. One cross-term, (D21)v, is 80−259 times larger than the main term (D11)v and 7−18 times larger than (D22)v. Standard interferometric diagnostic tests indicate that aggregation is unimportant in our experiments. We also present binary diffusion coefficients Dv for lysozyme chloride/water at concentrations from 0.43 to 3.08 mM (6.2−44.1 mg/mL), at the same pH and temperature. The precision of the results is about 0.1% for the binary diffusion coefficients and diagonal ternary diffusion coefficients, and about 1−2% for the cross-terms. For the ternary systems investigated, we show that a single pseudobinary diffusion coefficient does not accurately describe diffusive transport, and predictions by simple models such as the Nernst−Hartley equations are inaccurate at the higher concentrations considered here. Finally, dynamic light-scattering diffusion coefficients, differing from both our interferometrically measured (Dij)v and a theoretical prediction of light-scattering diffusion coefficients in multicomponent systems, are reported for the same solutions used for the ternary experiments at 1.30 M.