Liver Freezing Response of the Freeze-Tolerant Wood Frog, Rana sylvatica, in the Presence and Absence of Glucose. II. Mathematical Modeling

The “two-step” low-temperature microscopy (equilibrium and dynamic) freezing methods and a differential scanning calorimetry (DSC) technique were used to assess the equilibrium and dynamic cell volumes in Rana sylvatica liver tissue during freezing, in Part I of this study. In this study, the experimentally determined dynamic water transport data are curve fit to a model of water transport using a standard Krogh cylinder geometry (Model 1) to predict the biophysical parameters of water transport: L_pg = 1.76 μm/min-atm and E_Lp = 75.5 kcal/mol for control liver cells and L_pg[cpa] = 1.18 μm/min-atm and E_Lp[cpa] = 69.0 kcal/mol for liver cells equilibrated with 0.4 M glucose. The DSC technique confirmed that R. sylvatica cells in control liver tissue do not dehydrate completely when cooled at 5°C/min but do so when cooled at 2°C/min. Cells also retained twice as much intracellular fluid in the presence of 0.4 M glucose than in control tissue when cooled at 5°C/min. The ability of R. sylvatica liver cells to retain water during fast cooling (≥5°C/min) appears to be primarily due to its liver tissue architecture and not to a dramatically lower permeability to water, in comparison to mammalian (rat) liver cells which do dehydrate completely when cooled at 5°C/min. A modified Krogh model (Model 2) was constructed to account for the cell–cell contact in frog liver architecture. Using the same biophysical permeability parameters obtained with Model 1, the modified Krogh model (Model 2) is used in this study to qualitatively explain the experimentally measured water retention in some cells during freezing on the basis of different volumetric responses by cells directly adjacent to vascular space versus cells at least one cell removed from the vascular space. However, at much slower cooling rates (1–2°C/h) experienced by the frog in nature, the deciding factor in water retention is the presence of glucose and the maintenance of a sufficiently high subzero temperature (≥−8°C).