Capillarity Effects on Crystallization Kinetics:  Insulin

Abstract

During layerwise growth of crystals, capillarity governs the generation of new crystal layers. Theory predicts that the line tension of the layer edge determines, via the characteristic two-dimensional capillary length L(c), the rates of generation and initial growth of the new layers. To test the correlation between L(c) and the rate of layer generation, we used in situ Tapping Mode Atomic Force Microscopy (TM-AFM) to study the generation and spreading of layers during crystallization of rhombohedral, R3, porcine insulin. We show that crystallization of this insulin form is uniquely suitable for such an investigation due to the linear kinetics of step growth it exhibits. This linear kinetics reflects the abundance of the incorporation sites along the rough steps, the lack of long-range step-step interactions, and the transport control of the growth kinetics. The kinetic coefficients are 7 x 10(-)(3) and 4 x 10(-)(2) cm s(-)(1), respectively, in the absence and presence of the cosolvent acetone-somewhat high for proteins and comparable to values for inorganic systems. We show that (i). the relevant capillary length, the size of a critical quadrangular 2D nucleus L(c), is the main scaling factor for the density of growth steps, while (ii). all steps longer than L(c) grow with a rate determined only by the supersaturation and independent of their length. We explain the divergence of (ii). from theoretical predictions with the high supersaturations typical of the growth of this protein system.

A fast response mechanism for insulin storage in crystals may involve kink generation by association of 2D clusters

“…Previous studies of insulin crystallization at Ͼ 0.2 revealed kink density n k Ϫ1 Ϸ 0.3, which was difficult to quantify exactly because of fast step motion (16,33). To understand the transition between low values of n k Ϫ1 at Յ 0.05 and n k Ϫ1 at higher values of we monitored the step edge at Ϸ 0.1 at earlier times of observation.…”

“…The crystals grow exclusively by generation of layers on screw dislocations piercing the {100} faces (13,16). Because the crystals grow by the association of hexamers and they are the dominant species in the solution, we refer to them as molecules.…”

“…Either of the two functions of crystallization requires that the rate of growth of the crystals be fast and readily responsive to inevitable fluctuations in the rate of conversion. In contrast, like many other faceted crystals, Zn-insulin crystals grow by spreading of layers (13)(14)(15)(16). Zn-insulin hexamers join the edges of the growing layers, the steps, at sites of specific configuration, kinks (17).…”

Role of molecular charge and hydrophilicity in regulating the kinetics of crystal growth

“…A Langmuirtype adsorption isotherm best predicts this distribution between the bulk solution and the surface fractional coverage of impurities (8,33,34). Nevertheless, the relatively low amounts of biomolecules needed to affect growth rates likely reflect the much larger sizes of the biomolecules compared with the solute ions and thus the biomolecules greater ability to perturb the solvation environment of the solute ions compared with smaller impurities (35). These enhancements are thus expected to scale with the concentration C i of biomolecules [i.e., ␤(C i )], in the growth solution up until the point of onset of inhibition as is indeed experimentally observed (Fig.…”

The Use of Scanning Probe Microscopy to Investigate Crystal-Fluid Interfaces

“…Quantitative measurements of velocity versus supersaturation are found in the literature for a variety of solution grown crystals including minerals such as calcite [33,34], barite [35,36], hydroxyapatite [37]; optical crystals such as ammonium dihydrogen phosphate (ADP) [38] and potassium dihydrogen phosphate (KDP) [39]; several proteins [40][41][42][43][44]; and organic crystals such as hydrogen bonded tapes [45] and uric acid [46]. Land and De Yoreo tabulate kinetic coefficients for several systems [41] demonstrating that they vary over several orders of magnitude.…”