Kinetic analysis of protein crystal nucleation in gel matrix

Abstract

The effect of agarose on nucleation of hen egg white lysozyme crystal was examined quantitatively using a temperature-jumping technique. For the first time, to our knowledge, the inhibition of agarose during the nucleation of lysozyme was quantified in two respects: a), the effect of increasing interfacial nucleation barrier, described by the so-called interfacial correlation parameter f(m); and b), the ratio of diffusion to interfacial kinetics obtained from dynamic surface tension measurements. It follows from a dynamic surface tension analysis that the agarose network inhibits the nucleation of lysozyme by means of an enhancement of the repulsion and interfacial structure mismatch between foreign bodies and lysozyme crystals, slowing down the diffusion process of the protein molecules and clusters toward the crystal-fluid interface and inhibiting the rearrangement of protein molecules at the interface. Our results, based on ultraviolet-visible spectroscopy, also show no evidence of the supersaturation enhancement effect in protein agarose gels. The effects of nucleation suppression and transport limitation in gels result in bigger, fewer, and perhaps better quality protein crystals. The understandings obtained in this study will improve our knowledge in controlling the crystallization of proteins and other biomolecules.

FIGURE 1

Temperature T₁ and corresponding supersaturation () for lysozyme nucleation during the time Temperature T₂ and corresponding supersaturation () for developing the crystals to detectable dimensions.

FIGURE 2

Time dependence of the mean number of crystals per microliter at the supersaturation of 9.33 at 6°C.

FIGURE 3

Effect of additives on the interfacial correlation factor and the nucleation kinetics. A promotion or inhibition effect will increase or decrease the interfacial correlation parameter in the plot of ln J ∼

FIGURE 4

Protein 2D interface assembly kinetics. (a) The diffusion of protein molecules to the interface. (b) The penetration of protein molecules through the interface film from subsurface (a thickness of a few molecular diameters next to surface) to the surface (28). (c) Molecular rearrangements of adsorbed molecules in the film.

FIGURE 5

Influence of agarose on the nucleation kinetics of lysozyme at pH = 4.5, 6°C. Schematic plot of lnJ ∼ 1/[ln(1 + σ)]² with error bar.

FIGURE 6

Schematic drawing of structural match between the nucleating phase and foreign bodies (a) in gel-free solution and (b) in gel solution. The gel fibers separate the foreign bodies and nuclei and lead to the structure mismatch between the two phases.

FIGURE 7

Typical figure of surface tension of lysozyme solution at the air/water interface as a function of time at 6°Cfor selected values of supersaturation

FIGURE 8

as a function of time for lysozyme with and without 0.2% agarose. The rate constants for different steps can be obtained from the slope of the linear regression parts.

FIGURE 9

Lysozyme crystals in gel-free (a) and gelled (b) 0.4 μl microbatch drops under oil.

FIGURE 10

UV-Vis spectra of diluted lysozyme solution in the presence of 0.2% agarose gel and in the absence of agarose gel.