Introduction

Crystallization of proteins, as any other phase transition, occurs through a combination of processes at molecular, mesoscopic, and macroscopic length scales. During phase transitions in solution, molecular-level phenomena include the interactions between the molecules that alter the free energy landscape to cause the formation of the new phase and determine the driving force for the phase transformation; attachment of molecules to the new phase during growth; formation of sites suitable for molecular attachment; and generation of defects. On the mesoscopic length scale, one could consider the nucleation of droplets, clusters, or crystallites of the new phase; generation of new layers of a crystal controlled by capillarity; and interactions between growth steps as they propagate along the crystal's surfaces. Macroscopic length scales govern the fluxes of energy and mass through the interface (i.e., the transport of building blocks to the growing phase and the dissipation of heat away from it), as well as the balance and distribution of stress and strain in a solid and the transition from elastic to plastic deformations.

In this chapter, I focus on the molecular-level processes during the growth of crystals of the pair of proteins ferritin and apoferritin. Ferritin is the main nonheme iron storage protein in cytosol (1-3). The protein shell consists of 24 subunits, arranged in pairs along the 12 facets of a rhombododecahedron (4,5). Ferritins have been extensively studied as an example of biological mineralization occurring in vivo (6,7). The iron-containing core of ferritin can be replaced with other organic, inorganic, and bioorganic compounds for potential applications in the areas of nanoassembly, drug delivery, biomineralization, and so on (8,9). Apoferritin is the protein shell from which the ferrite core has been removed by dissolution into an acidic solution. The structures of the proteins from various species are known down to 1.90 A resolution (5).

In the presence of Cd2+, ferritin and apoferritin crystallize in the cubic F432 group (3,5). Contrary to typical protein crystallization cases, in which the electrolyte serves to screen the repulsion between the similarly charged protein molecules, in the case of apoferritin, Cd2+ is involved in specific bonds between the molecules (5). This specificity makes the case of apoferritin crystallization a relevant first-approximation model of other self-assembling systems, such as viri, protein complexes, and nanoparticles.

The crystals, such as the one in Fig. 1, are typically faceted by octahedral (111) faces pierced by the threefold axis belonging to the symmetry group. The highly symmetric shape of the ferritin and apoferritin molecules makes the approximation of isotropic molecular shape realistic. In addition, the symmetry of the environment of a molecule in a crystal makes quantitative insight easier to obtain and comprehend. Because of these two factors, ferritin and apoferritin crystallization is a particularly appealing system for in-depth investigations of the thermodynamics and kinetics of phase transitions.

Fig. 1. Typical octahedral crystal of apoferritin, resting on cell bottom with a (111) face facing upward. Ferritin crystals appear identical except for the ruby red color.

In this chapter, I first define the methods used to characterize the growth kinetics on the molecular length scale. Then, I discuss tests of the correspondence between discrete approaches to the kinetics of attachment, in which the growth rate and other spatial and temporal characteristics of the growth process are represented as a statistical averages of events involving individual atoms or molecules, and continuous approaches, in which fluxes of matter toward the growth interface are evaluated. Finally, I show that the kinetics of incorporation of the molecules into growth sites on the surface of a crystal are not determined by decay of a high-energy transition state but are only limited by the diffusion of the incoming molecule over a barrier owing to the hydration shells around incoming molecules.

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