Mathematical model for diffusion of a protein and a precipitant about a growing protein crystal in microgravity

Equations are presented that model diffusion of a protein to the surface of a growing crystal in a convection-free environment. The equations apply to crystal growth solutions that contain both a protein and a protein precipitant. The solutions are assumed ternary and the equations include all four diffusion coefficients necessary for the full description of the diffusion process. The four diffusion coefficients are assumed constant. Effects of crystal/solution moving boundary and the effect of a protein adsorption barrier at the crystal interface are included. The equations were applied to the system lysozyme chloride + NaCl + H2O, which has served as the primary model system for the study of crystal growth of proteins and for which there are now published ternary diffusion coefficients. Calculated results with and without the inclusion of cross-term diffusion coefficients are compared.