W0196: Protein Crystal Nucleation Kinetics Mediated Through Solubility

Nucleation kinetics of tetragonal hen egg-white lysozyme (HEWL) were obtained by the method of initial rates at various protein and precipitant (NaCl) concentrations. Nucleation kinetics were measured at a variety of salt concentrations, pH values and temperatures. Data were modeled using an empirical relation based on classical nucleation theory. An apparent correlation of model parameters with osmotic second virial coefficients and subsequently with solubility is discussed.

One can lump the parameters in the classical nucleation kinetic expression into a pre-exponential factor, A, that represents the collisions and inter-molecular interactions and an exponential factor, B, that is indicative of the surface energy between crystal and solution. The data were split into two regions: nucleation rates at lower protein concentrations, where heterogeneous nucleation may be the predominant nucleation mechanism and higher protein concentrations that may be a homogeneous nucleation regime. The model parameters were then estimated in the individual regions using standard non-linear regression techniques. In both regions, parameter B is fairly constant with change in ionic strength, indicating that the surface energy is relatively constant with change in ionic strength. In the homogeneous nucleation range, the pre-exponential parameter, A, of the model correlates with the osmotic second virial coefficient, B₂₂. Wilson et al. has correlated B₂₂with protein solubility of HEWL and other globular proteins¹. Thus, the trend in the pre-exponential factor, A, of the classical nucleation kinetic expression, is expected to correlate directly with HEWL solubility. Equal solubility conditions have been found to produce the same nucleation rates, independent of solution pH and temperature. If the correlation between solubility and second viral coefficients is valid for a wide range of globular proteins, a measure of solubility of a globular protein may provide a method for estimation of the pre-exponential factor, A, and subsequent prediction of homogenous nucleation rates.