For critical tests of whether diffusion-limited kinetics is an option for the solution-solid phase transition of molecular substances or whether they are determined exclusively by a transition state, we performed crystallization experiments with ferritin and apoferritin, a unique pair of proteins with identical shells but different molecular masses. We find that the kinetic coefficient for crystallization is identical (accuracy <7%) for the pair, indicating diffusion-limited kinetics of crystallization. Data on the kinetics of this phase transition in systems ranging from small-molecule ionic to protein and viri suggest that the kinetics of solution-phase transitions for broad classes of small-molecule and protein materials are diffusion-limited.T he kinetics of the reactions in solutions are either limited only by the rate of diffusion of the species (1) or additionally slowed down by a transition state (2). 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 (3-7). 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). Although rate laws reminiscent of diffusionlimited mechanisms have been postulated for small-molecule phase transitions (9-11), they were viewed as equivalent to respective transition-state expressions (10, 11), and no critical tests to discriminate between the two mechanisms were suggested or performed.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). The crystals of ferritin and apoferritin are typically faceted by octahedral [111] faces and have been shown to grow by the lateral spreading of layers generated by two-dimensional nucleation (16, 17). For apoferritin, it was shown that the edges of the unfinished layers, called growth steps, propagate by the incorporation of single protein molecules at the growth sites, kinks (16,18). In the face-centered cubic lattice that ferritin and apoferritin share, kinks are defined as the termination points of three independent ͗011͘ rows of molecules belonging to the unfinished layer (19). Thus, the step velocity equals the product of the molecular diameter a, mean kink density n k Ϫ1 , and net molecular f lux into a kink (j ϩ Ϫ j Ϫ ) (16, 18).
Methods
Characterization of the Molecular Masses and Pair Interactions ofFerritin and Apoferritin. We performed static light scattering (20) in 0.2 M NaOOCCH 3 solutions....