Mixing Salts and Poly(ethylene glycol) into Protein Solutions: The Effects of Diffusion across Semipermeable Membranes and of Convection

Growing a protein crystal starts by mixing a solution of the protein, with a solution of a precipitantsuch as a salt or poly­(ethylene glycol) (PEG). Mixing two solutions is a surprisingly complex process, but this complexity has not received much attention by those crystallizing proteins, despite crystallization being notoriously sensitive to solution conditions. We combine experimental data with modeling to improve our ability to predict mixing time scales for conditions typical of protein crystallization. We look at the effects of convection and of diffusion through semipermeable membranes. Our experiments are with dialysis chambers, where the crystallization chamber is separated from a precipitant reservoir by a semipermeable membrane. This membrane slows mixing down by factors that vary from ten, for smaller PEG and salts, to a hundred, for dilute larger PEG. This agrees with our model prediction that for larger polymers diffusion through the membrane is sensitive to both molecular weight and concentration. Both salt and PEG solutions are denser than dilute protein solutions, and this drives convection, which accelerates mixing. Convection is flow due to gravity acting on mass density differences. We show how to determine when convection occurs and how to estimate its effect on mixing times.