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

Abstract

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 solution 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 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.

Crystallization of Proteins on Chip by Microdialysis for <i>In Situ</i> X-ray Diffraction Studies

“…Use the supernatant for the crystallization experiment. 51 , and it might take more time for the nucleation to start. In order to prevent evaporation, if any, during this period, place the chip in a humidity saturated atmosphere at 293 K. 2.…”

Role of solutal free convection on interdiffusion in a horizontal microfluidic channel

“…Appendix A: Buoyancy-driven flow at early stage for the case of a slit After a transient corresponding to the diffusion of the momentum across the slit, the velocity field is solution of the Stokes equation Eq. (20). Introducing the stream function ψ(x, z) defined by:…”

“…Furthermore, although these buoyancy-induced flows could have little impact on the solute concentration gradients that generate them, they still do exist, and are able to effectively disperse less mobile species in the fluid mixture, such as macromolecules or colloids [8]. These buoyancy-driven flows may also have an influence in protein crystallization experiments [18][19][20][21], for evaluating colloidal diffusio-phoresis induced by solute gradients [6], or even in the context of biological systems for the motility of microorganisms [22]. It is therefore necessary to quantify these flows as a function of the density gradients that generate them for predicting their possible role on other species in the case of complex fluid mixtures.…”

High-Throughput Protein Crystallization <em>via</em> Microdialysis

“…This way, the protein solution is slowly brought into equilibrium, with the precipitant reaching the necessary concentration to crystallize. The system's kinetics depends on temperature, precipitant concentration, and the cellulose membrane molecular weight cut-off (MWCO) 19 . To date, the most popular crystallization setup by dialysis has been using microdialysis buttons made of transparent acrylic sheets.…”