Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson-Mehl-Avrami-Kolomogorov (JMAK) theory of crysta l nucleation and growth to the problem of protein crystallization in the ba tch method. Without integrating the JMAK equation explicitly, we use dimens ional analysis to derive a general formula for the half-life for decay of t he protein supersaturation. This formula includes a dimensioned group and a n arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersatur ation and the nucleation rate is proportional to its square. This gives an equation for the time decay of the supersaturation and a formula for the ha lf-life in which all arbitrary dimensionless functions are evaluated. The r esults are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, b ut also with our experimental results for crystallization of lysozyme, in w hich the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature. (C) 1999 Elsevier Science B.V. All rights reserved .