Kinetics of protein crystal nucleation and growth in the batch method

We have applied the Johnson-Mehl-Avrami-Kolomogorov (JMAK) theory of crystal nucleation and growth to the problem of protein crystallization in the batch method. Without integrating the JMAK equation explicitly, we use dimensional analysis to derive a general formula for the half-life for decay of the protein supersaturation. This formula includes a dimensioned group and an arbitrary dimensionless function. We integrate the JMAK equation exactly for the special case where the growth rate is independent of the supersaturation 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 half-life in which all arbitrary dimensionless functions are evaluated. The results are consistent not only with Von Weimarn's rule, which asserts that the average size of a crystal increases as the supersaturation decreases, but also with our experimental results for crystallization of lysozyme, in which the half-life at fixed pH decreases with increasing ionic strength and decreasing temperature. (C) 1999 Elsevier Science B.V. All rights reserved.