Topics in Crystal Growth Kinetics

Viral capsomere structure, surface processes and growth kinetics in the crystallization of macromolecular crystals visualized by in situ atomic force microscopy

“…Similar values for the kinetic coefficient were found for the crystallization of several other macromolecules [31,[36][37][38]. The lower values of b for macromolecular crystallization compared with inorganic crystallization [35] has been attributed to the necessity of the pre-kink selection of the proper orientation of an incoming macromolecule for incorporation into the growth step [28]. At lower supersaturation a non-linear dependency of tangential step rate was observed (Fig.…”

“…where O ¼ 4:8 Â 10 À19 is the specific volume of a glucose isomerase tetramer in the crystal, c and c e ¼ 2:1 Â 10 15 cm À3 are initial and equilibrium concentrations of protein, respectively, and b is the step kinetic coefficient [35]. From the linear portion of vðc À c e Þ dependencies for ðc À c e Þ > 10 14 cm À3 (Fig.…”

Diffusion-limited kinetics of the solution–solid phase transition of molecular substances

“…The figure of merit for the discussion here is the net growth of two molecules for 128 s, leading to an average net flux (j ϩ Ϫ j Ϫ ) ϭ 0.054 s Ϫ1 into the growth sites distributed with mean density n k Ϫ1 ϭ 0.28. Because there are no sources or sinks of molecules at the step other than the attachment sites, the step growth rate v should equal an k Ϫ1 (j ϩ Ϫ j Ϫ ) (7,12). At (C͞C e Ϫ 1) ϭ 1, at which all data in Fig.…”

“…For the kinetics of the phase transitions in solutions, it is generally accepted that colloid particles follow the diffusion-limited model, whereas the growth rates of new phases of small molecules are thought to be governed by a transition state (3)(4)(5)(6)(7). For the intermediate case of protein solid phases, the growth kinetics largely resemble those of small molecules, and it was assumed that transition-state laws apply (8).…”

“…In the transition-state kinetics, the rate coefficients are (i) mass-dependent (12,13), (ii) independent on the diffusivity (2), and (iii) faster for high-symmetry molecules because of the transition-state entropy (7). Hence, for tests of the mechanism of growth of the new phase during a solution-solid phase transition, we selected the crystallization of ferritin͞ apoferritin, a unique pair of proteins that share a nearspherical protein shell, consisting of 24 identical subunits (14,15).…”