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, G_c of tetragonal lysozyme crystal initially increases up to 200 μm/s with increasing flow velocity, u_m and then decreases monotonically. While in the lower supersaturated solution, G_c decreases monotonically with increasing u_m, and the growth cessation occurs at u_m=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 G_c on u_m is related with r and there exist three critical r-values, r₁≈4-8, r₂≈0.01-0.02, r₃≈0.004. When r>r_1, crystal growth cession occurs; when r₁>r>r₂, G_c decreases with u_m; when r₂>r>r₃, G_c increases with u_m; when r<r₃, G_c is independent of u_m. Though our model is very simple, the dimensionless number r can explain the effects of convection on crystal growth rate consistently.