Performance of a kinetic model for intracellular ice formation based on the extent of supercooling

Cryomicroscopy was used to study the incidence of intracellular ice formation (IIF) in protoplasts isolated from rye (Secale cereale) leaves during subfreezing isothermal periods and in in vitro mature bovine oocytes during cooling at constant rates. IIF in protoplasts occurred at random times during isothermal periods, and the kinetics of IIF were faster as isothermal temperature decreased. Mean IIF times decreased from approximately 1700 s at -4.0 degrees C to less than 1 s at -18.5 degrees C. Total incidence of IIF after 200 s increased from 4% at -4.0 degrees C to near 100% at -15.5 degrees C. IIF behavior in protoplasts was qualitatively similar to that for Drosophila melanogaster embryos over the same temperature ranges (Myers et al., Cryobiology 26, 472-484, 1989), but the kinetics of IIF were about five times faster in protoplasts. IIF observations in linear cooling of bovine oocytes indicated a median IIF temperature of -11 degrees C at 16 degrees C/min and total incidences of 97%, 50%, and 19% at 16, 8, and 4 degrees C/min, respectively. A stochastic model of IIF was developed which preserved certain features of an earlier model (Pitt et al. Cryobiology 28, 72-86, 1991), namely Weibull behavior in IIF temperatures during rapid linear cooling, but with a departure from the concept of a supercooling tolerance. Instead, the new model uses the osmotic state of the cell, represented by the extent of supercooling, as the independent variable governing the kinetics of IIF. Two kinetic parameters are needed for the model: a scale factor tau 0 dictating the sensitivity to supercooling, and an exponent rho dictating the strength of time dependency. The model was fit to the data presented in this study as well as those from Myers et al. and Pitt et al. for D. melanogaster embryos with and without cryoprotectant, and from Toner et al. (Cryobiology 28, 55-71, 1991) for mouse oocytes. In protoplasts, D. melanogaster embryos, and mouse oocytes, the parameters were estimated from IIF times in the early stages of isothermal periods, while the osmotic state of the cell was relatively constant. In bovine oocytes, the parameters were estimated from linear cooling data. Without further calibration, the model was used to predict total IIF incidence under different cooling regimes. For protoplasts, D. melanogaster embryos, and bovine oocytes, the model's predictions were quite accurate compared to the actual data. In mouse oocytes, adjustment of the hydraulic permeability coefficient (Lp) at 0 degree C was required to yield realistic behavior.(ABSTRACT TRUNCATED AT 400 WORDS)