Mixing salts and polyethylene 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 polyethylene glycol (PEG). Mixing two solutions is a surprisingly complex process, but this complexity has not received much attention by those crystallising proteins, despite crystallisation being notoriously sensitive to solu- tion conditions. We combine experimental data with modelling to improve our ability to predict mixing timescales for conditions typical of protein crystallisation. We look at the effects of convection, and of diffusion through semipermeable membranes. Our experiments are with dialysis chambers, where the crystallisation 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 concentra- tion. Both salt and PEG solutions are denser than dilute protein solutions, and this drives convection, which accelerates mixing. Convection is ow 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