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) freezin g 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 experi mentally determined dynamic water transport data are curve fit to a model o f water transport using a standard Krogh cylinder geometry (Model 1) to pre dict the biophysical parameters of water transport: L-pg = 1.76 mu m/min-at m and E-Lp = 75.5 kcal/mol for control liver cells and L-pg[cpa] = 1.18 mu m/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 contro l liver tissue do not dehydrate completely when cooled at 5 degrees C/min b ut do so when cooled at 2 degrees 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 degrees C/min. The ability of R. sylvatica liver cells to retain water during fast cooling (greater than or equal to 5 degrees 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 degrees C/min. A modified Krogh model (Model 2) was constructed to account for the cell-ce ll contact in frog liver architecture. Using the same biophysical permeabil ity parameters obtained with Model 1, the modified Krogh model (Model 2) is used in this study to qualitatively explain the experimentally measured wa ter retention in some cells during freezing on the basis of different volum etric responses by cells directly adjacent to vascular space versus cells a t least one cell removed from the vascular space. However, at much slower c ooling rates (1-2 degrees C/h) experienced by the frog in nature, the decid ing factor in water retention is the presence of glucose and the maintenanc e of a sufficiently high subzero temperature (greater than or equal to-8 de grees C). (C) 1999 Academic Press.