First-order phase transitions of matter, such as condensation and crystallization, proceed through the formation and subsequent growth of 'critical nuclei' of the new phase. The thermodynamics and kinetics of the formation of these critical nuclei depend on their structure, which is often assumed to be a compact, three-dimensional arrangement of the constituent molecules or atoms. Recent molecular dynamics simulations have predicted compact nucleus structures for matter made up of building blocks with a spherical interaction field, whereas strongly anisotropic, dipolar molecules may form nuclei consisting of single chains of molecules. Here we show, using direct atomic force microscopy observations, that the near-critical-size clusters formed during the crystallization of apoferritin, a quasi-spherical protein, and which are representative of the critical nucleus of this system, consist of planar arrays of one or two monomolecular layers that contain 5-10 rods of up to 7 molecules each. We find that these clusters contain between 20 and 50 molecules each, and that the arrangement of the constituent molecules is identical to that found in apoferritin crystals. We anticipate that similarly unexpected critical nucleus structures may be quite common, particularly with anisotropic molecules, suggesting that advanced nucleation theories should treat the critical nucleus structure as a variable.

We have studied the structure of the protein species and the protein-protein interactions in solutions containing two apoferritin molecular forms, monomers and dimers, in the presence of Na(+) and Cd(2+) ions. We used chromatographic, and static and dynamic light scattering techniques, and atomic force microscopy (AFM). Size-exclusion chromatography was used to isolate these two protein fractions. The sizes and shapes of the monomers and dimers were determined by dynamic light scattering and AFM. Although the monomer is an apparent sphere with a diameter corresponding to previous x-ray crystallography determinations, the dimer shape corresponds to two, bound monomer spheres. Static light scattering was applied to characterize the interactions between solute molecules of monomers and dimers in terms of the second osmotic virial coefficients. The results for the monomers indicate that Na(+) ions cause strong intermolecular repulsion even at concentrations higher than 0.15 M, contrary to the predictions of the commonly applied Derjaguin-Landau-Verwey-Overbeek theory. We argue that the reason for such behavior is hydration force due to the formation of a water shell around the protein molecules with the help of the sodium ions. The addition of even small amounts of Cd(2+) changes the repulsive interactions to attractive but does not lead to oligomer formation, at least at the protein concentrations used. Thus, the two ions provide examples of strong specificity of their interactions with the protein molecules. In solutions of the apoferritin dimer, the molecules attract even in the presence of Na(+) only, indicating a change in the surface of the apoferritin molecule. In view of the strong repulsion between the monomers, this indicates that the dimers and higher oligomers form only after partial denaturation of some of the apoferritin monomers. These observations suggest that aggregation and self-assembly of protein molecules or molecular subunits may be driven by forces other than those responsible for crystallization and other phase transitions in the protein solution.

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We show with three proteins that trapping and release of the water molecules upon crystallization is a determinant of the crystallization thermodynamics. With HbC, a strong retrograde solubility dependence on temperature yields a high positive enthalpy of 155 kJ mol -1 , i.e., crystallization is only possible because of the huge entropy gain of 610 J mol, stemming from the release of up to 10 water molecules per protein intermolecular contact. With apoferritin, the enthalpy of crystallization is close to zero. The main component in the crystallization driving force is the entropy gain due to the release upon crystallization of two water molecules bound to one protein molecules in solution. With both proteins, the density of the growth sites imaged by AFM is in excellent agreement with a calculation using the crystallization free energy. With lysozyme, the entropy effect due to the restructuring of the water molecules is negative. This leads to higher solubility.

Using the atomic force microscope (AFM) in situ during the crystallization of the protein apoferritin, we show that for this system the kink density along the steps is an equilibrium property that, multiplied by the frequency of molecular attachment, fully determines the propagation of growth steps. The intermolecular bond energy is 3.2k(B)T. Point defects are nonequilibrial and are caused by incorporation of impurity molecules, and replicate in subsequent layers due to the strain they cause. Using single-molecule manipulation with the AFM tip, the defects can be healed to restore the regular lattice.