The amount by which the melting point of a curved ice crystal in pure water is suppressed below that of a planar crystal is given by the Kelvin equation, namely,
where v, Tm, rSL, 9, and Lf are the molar volume of water, the melting point of the planar crystal, the interfacial tension between ice and water, the contact angle between ice and the inner wall of the pore (values can be 0-90°), and the latent heat of fusion of ice, respectively. The symbols a and r are the radius of the pore and the radius of curvature of the ice crystal (Fig. 6). Values for all except 9 are known or have been estimated. buy birth control online
Acker et al. state that v should be the molar volume of ice, not water, and that a correction term needs to be added to the equation to correct for situations where the liquid is a solution, not pure water, and they have calculated AT for various pore radii and contact angles using both the original and corrected equations. Table 5 shows the calculations for pore radii of 7.5 and 12 A, and for 9 = 50° and 75°. There is only about a 3°C difference in AT with the two equations, mostly due to substituting the molar volume of ice for the molar volume of liquid water. We observed a mean flash temperature of —23.1°C for the simultaneous freezing of the morulae (Table 3), which is consistent with the AT values calculated for a gap junction pore radius of 7.5 A in Table 5. Additional support for the role of gap junctions in cell-to-cell ice propagation is our finding that the propagation rate is slowed 6-fold by the presence of the gap junction inhibitor GA.
FIG. 6. Configuration of an ice-water interface in a hypothetical cylindrical pore in a cell membrane. See Membrane Changes Associated with Development for a definition of the symbols. (Reprinted in slightly modified form from Mazur with permission from Elsevier.)
One-cell through eight-cell embryos. The mean flash temperature for the one- to eight-cell embryos that flashed simultaneously was —38.2°C (Table 3). These constituted 87% of the two- to eight-cell embryos studied. That temperature is very close to the calculated homogeneous nucleation temperature of —40°C for a volume of 1 M EG equal to the volume of water in mouse oocytes and embryos. We conclude from this that the nucleation is homogeneous; i.e., it is not heterogeneously catalyzed by external ice or intracellular nucleators. That in turn means that the plasma membranes of the blastomeres must remain intact throughout all the cooling prior to IIF. Moreover, their plasma membranes must not contain any pores capable of allowing the passage of extracellular ice and none form during cooling. This interpretation is consistent with the fact that stages two- to eight-cell embryos contain no detectable gap junctions, and stages one- to eight-cell embryos show no evidence of aquaporins in their plasma membranes (other than the possibility of AQP 9 in eight-cell embryos; Table 1).