Self-assembly of apoferritin molecules into crystals: thermodynamics and kinetics of molecular level processes

Abstract

Aside from the biological, biomedical and materials importance of ferritin and apoferritin, the self-assembly of these molecules into crystals is of interest because it is a suitable model for protein crystallization and aggregation that impact many fundamental and applied fields. We use the atomic force microscope in-situ, during the crystallization of apoferritin to visualize and quantify at the molecular level the processes responsible for crystal growth. We image the configuration of the incorporation sites, “kinks”, on the surface of a growing crystal. We show that the kinks are due to thermal fluctuations of the molecules at the crystal-solution interface. This allows evaluation of the free energy of the intermolecular bond φ = 3.0 k B T = 7.3 kJ/mol. The crystallization free energy, extracted from the protein solubility, is − 42 kJ/mol. Thermodynamics analyses based on these two values suggest that the main component in the crystallization driving force is the entropy gain of the waters bound to the protein molecules in solution and released upon crystallization. Furthermore, we determine the characteristic frequency of attachment of individual molecules into the kinks at one set of conditions. We show that the macroscopic step growth velocity, scaled by the molecular size, equals the product of independently determined kink density and attachment frequency, i.e., these are the molecular-level parameters for crystallization. Finally, we show that although new crystal layers are generated by intrinsically stochastic surface nucleation, for crystals > 200 μm layer generation predominantly occurs at the crystal edges. Numerical simulations of the concentration fields in the solution allow us to assign this localization to higher interfacial concentration at the edges. As the steps propagate to cover the crystal face, step density waves, or bunches, develop and may lead to non-uniformity and lower quality and utility of the growing crystal.