Quantitative analysis of the probability of intracellular ice formation during freezing of isolated protoplasts.

(i) A quantitative prediction of the temperature and cooling-rate dependence of IIF requires information on the probability distribution for IIF temperature; the super-cooling tolerance; and membrane permeability, initial cell size, Boyle-van't Hoff relation, and other parameters associated with the thermodynamic description of cell volumetric behavior. (ii) A probabilistic analysis of IIF was developed on the basis that IIF occurs if the underlying potential IIF temperature T* falls within the range of temperatures over which the cell is supercooled beyond its tolerance delta T*. The "location" of the transition range of cooling rates, in which the Pr(IIF) increases from 0 to 1, depends on the mean of T* and delta T*. The breadth of the transition range increases strongly with variability in T*. (iii) Cryomicroscopic studies of IIF in rye protoplasts isolated from cold acclimated and nonacclimated leaves showed that the range of IIF temperatures and the incidence of IIF are strongly dependent on the solute used to manipulate osmolality in the suspending medium. The ionic solutes used in this study (NaCl + CaCl2, KCl + CaCl2, KNO3 + CaCl2) generally yielded median IIF temperatures lower than those of the nonionic solutes (sucrose, sorbitol, proline). Cold acclimation reduced the median IIF temperature for all suspending media and reduced the incidence of IIF for KCl + CaCl2, sorbitol, and proline. A Weibull distribution was found to describe adequately the distribution of IIF temperatures at the highest cooling rate. (iv) Estimates of the supercooling tolerance were generally from 1.0 to 1.5 degrees C based on the location of the transition range of cooling rates and on the estimates of Lp and delta E from (6). The breadth of the transition range of cooling rates could mostly be attributed to random variability in the underlying potential IIF temperature. The rise in median IIF temperature with higher cooling rates was correctly predicted by the model when the supercooling tolerance was also assumed to be random. For rye protoplasts, both the model and the data showed that cooling-rate dependence in median IIF temperatures occurs within the transition range of cooling rates.