Journal of Crystal Growth, Vol.310, No.24, 5370-5374, 2008
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, of tetragonal lysozyme crystal initially increases up to 200 mu m/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 mu m/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, r(1) approximate to 4-8, r(2) approximate to 0.01-0.02, r(3) approximate to 0.004. When r > r(1). crystal growth cession occurs; when r(1) > r > r(2), G(c) decreases with u(m); when r(2) > r > r(3), G(c) increases with u(m); when r < r(3), 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. (C) 2008 Elsevier B.V. All rights reserved.