The role of solutal convection in protein crystal growth-A new dimensionless number to evaluate the effects of convection on protein crystal growth

According to the experiments by Vekilov et al., the crystal growth rate, Gc of tetragonal lysozyme crystal initially increases up to 200 μm/s with increasing flow velocity, um and then decreases monotonically. While in the lower supersaturated solution, Gc decreases monotonically with increasing um, and the growth cessation occurs at um=1450 μm/s. In this paper, we propose a new theory to explain these complicated experimental results. We consider one protein molecule near the crystal surface and define a dimensionless number r, the ratio of the velocity of convective flow to the diffusion velocity of a protein molecule. When convection occurs along the crystal surface and a molecule diffuses toward the crystal surface, r indicates the moving direction of the molecule and is closely related with crystal growth rate. We derive the equation to calculate r from experimental parameters. Analyzing the experimental results in the literatures, we find that the dependence of Gc on um is related with r and there exist three critical r-values, r1≈4-8, r2≈0.01-0.02, r3≈0.004. When r>r1, crystal growth cession occurs; when r1>r>r2, Gc decreases with um; when r2>r>r3, Gc increases with um; when r