Measurement and modeling of protein crystal nucleation kinetics

Nucleation kinetics of tetragonal hen egg-white lysozyme obtained by the method of initial rates are reported. Sodium chloride (NaCl), ranging in concentration from 2% (w/v) to 7% (w/v), was used as the precipitant. Data are modeled using an empirical kinetic expression based on classical nucleation theory. The expression contains a preexponential factor, A, and an exponential factor, B, related to the surface energy between crystal and solution. The parameters A and B were evaluated from the experimental data using standard nonlinear regression techniques. The trends in the experimental data suggest that two nucleation mechanisms may exist: heterogeneous nucleation at lower protein concentrations and homogeneous nucleation at higher protein concentrations. Accordingly, the data were split into two regions and the model parameters were estimated separately in individual regions. Within both regions, parameter B varied little with ionic strength. In the homogeneous range, the preexponential factor, A, increased monotonically with salt concentration and correlated with trends observed in osmotic second virial coefficients and solubility. The implications of such a correlation to globular protein nucleation kinetics are discussed.