Modeling Tetragonal Lysozyme Crystal Growth Rates

Tetragonal lysozyme 110 face crystal growth rates, measured over 5 orders of magnitude in range, can be described using a model where growth occurs by 2D nucleation on the crystal surface for solution supersaturations of c/c(sub eq) less than or equal to 7 +/- 2. Based upon the model, the step energy per unit length, beta was estimated to be approx. 5.3 +/- 0.4 x 10(exp -7) erg/mol-cm, which for a step height of 56 A corresponds to barrier of approx. 7 +/- 1 k(sub B)T at 300 K. For supersaturations of c/c(sub eq) > 8, the model emphasizing crystal growth by 2D nucleation not only could not predict, but also consistently overestimated, the highest observable crystal growth rates. Kinetic roughening is hypothesized to occur at a cross-over supersaturation of c/c(sub eq) > 8, where crystal growth is postulated to occur by a different process such as adsorption. Under this assumption, all growth rate data indicated that a kinetic roughening transition and subsequent crystal growth by adsorption for all solution conditions, varying in buffer pH, temperature and precipitant concentration, occurs for c/c(sub eq)(T, pH, NaCl) in the range between 5 and 10, with an energy barrier for adsorption estimated to be approx. 20 k(sub B)T at 300 K. Based upon these and other estimates, we determined the size of the critical surface nucleate, at the crossover supersaturation and higher concentrations, to range from 4 to 10 molecules.