Analysis of the protein-salt coupled transport: precision measurements of multicomponent diffusion coefficients for aqueous lysozyme solutions containing chloride salts at 25°C and in conditions relevant for crystal growth

Abstract

Accurate models of protein diffusion are important in a number of applications, including 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 elements of the multicomponent diffusion coefficient matrix, D ij , for the extensively investigated protein lysozyme in aqueous chloride salts at 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. The behavior of the multicomponent diffusion coefficients is described in terms of protein charge, medium viscosity, excluded volume effect, and salting-out interactions. For ternary systems, a method is presented for using measured values of the four ternary diffusion coefficients and the Onsager Reciprocal Relations to extract derivatives of solute chemical potentials with respect to solute molar concentrations. The method is applicable to systems in which the molar concentration of one solute is very small compared to that of the other. These conditions apply to a large number of aqueous systems involving macromolecules of biological interest. Unlike other techniques, the present method can be used to study undersaturated and supersaturated solutions. The behavior of the lysozyme chemical potential as a function of pH and salt concentration was obtained. This method also permits the estimation of the effective protein charge. The salting-out effectiveness of various salts (NaCl, KCl, NH 4 Cl, MgCl 2 and CaCl 2 ) discussed. At high CaCl 2 concentration a decrease of the lysozyme chemical potential was observed (salting-in). The transport properties of the quaternary system lysozyme-NaCl-PEG have been experimentally investigated as a function of the polymer molecular weight and concentration. Those measurements are more precise and accurate than any results that have been reported so far for a quaternary system. Transport models are presented for concentration profiles (1) around a spherical crystal and (2) related to counter-diffusion experiments. Diffusion coefficients from dynamic light scattering are measured on the ternary lysozyme-NaCl-water system and reported for comparison. They closely follow the behavior of the smaller eigenvalue of the ternary diffusion coefficient matrix.