The Thermodynamics of Intracellular Ice Nucleation in the Freezing of Erythrocytes

Abstract

A theoretical model describing the thermodynamics of intracellular ice nucleation is developed for red blood cells as a model biomaterial. Analytical expressions based on current theories of ice nucleation by both homogeneous and heterogeneous nucleation processes are coupled with a thermodynamic model for the loss of intracellular water during freezing. Numerical solutions for both modes of nucleation identify two cooling regions—high cooling rates and low cooling rates—separated by a sharp demarcation zone. The nucleation temperature for high cooling rates is approximately 20° K higher than the nucleation temperature for low cooling rates and is essentially independent of cooling rate in each region. The nucleation temperatures for heterogeneous nucleation are approximately 30° K higher than the nucleation temperatures for homogeneous nucleation in the two regions. For the case of heterogeneous nucleation, it is possible to increase the nucleation temperature by packing of catalysts via the concentration polarization effect. If the cell suspension is allowed to supercool before nucleation occurs in the extracellular medium, the sharp transition from low cooling rates to high cooling rates for heterogeneous nucleation shifts to much lower cooling rates. The dependence of the transition cooling rate on the degree of supercooling has been established for a typical freezing situation.

Phenomena at the advancing ice–liquid interface: solutes, particles and biological cells

“…A similar behaviour was observed for mouse ova and embryos (Leibo, 1977 a, 6;Leibo et al 1978), algae (Morris & McGrath, 1981), liposomes (Callow & McGrath, 1985), and granulocytes (Scheiwe & Korber, 1987). Cooling rates which are independent of intracellular crystallization temperatures were also predicted from a theoretical model (Toscano et al 1975) for the heterogeneous nucleation of ice in red blood cells subjected to freezing induced exosmosis (cf. Section 5.1.1).…”

“…In principal, two possibilities are conceivable, i.e. the induction of intracellular crystallization by nucleating agents present within the cell (Toscano et al 1975;Franks & Bray, 1980;Franks et al 1983) and by extracellular ice (Mazur, 1965(Mazur, , 1966. Rasmussen et al (1975) and Franks and co-workers (Franks & Bray, 1980;Franks et al 1983) have employed an emulsion technique for suppressing extracellular crystallization and detecting the formation of intracellular ice by means of differential scanning calorimetry, but obtained inconclusive results: whereas yeast and human erythrocytes could be supercooled down to the homogeneous nucleation temperature (Rasmussen et al 1975), Franks and coworkers (Franks & Bray, 1980;Franks et al 1983) observed intracellular crystallization above the homogeneous nucleation temperature for yeast, erythrocytes and various culture cells indicating the presence of heterogeneous nucleators.…”

Heat and mass transport in the freezing of apple tissue

“…The dendritic spacing was measured on the micrographs by counting intersections on a circular test line located at random positions (Underwood, 1969). No attempt was made to correct for a non-planar viewing surface, but Howell (1978) showed that the error in using such a parallel projection for measuring distances was on the order of 5% for the working distance of 12mm and magnification of 100 X that was used in most of the measurements in the present work.…”

“…Mazur (1966) has postulated a theory based on the hypothesis that at rapid freezing rates the ice formed extracellularly has a sufficiently small radius of curvature to nucleate the intracellular solution through the pores that exist in cell membranes. Toscano et al (1975) have proposed that there are naturally occurring catalysts in the cell which can trigger heterogeneous nucleation. The calculation of the degree of supercooling for nucleation is complicated, and the pertinent parameters are not readily available.…”

An Improved Model for Nucleation-Limited Ice Formation in Living Cells during Freezing

“…As a result, IIF in the absence of CPAs (e.g., for cryotherapy applications) is nucleation-limited. Therefore, ice nucleation in cells during freezing has been extensively studied in the past decades both experimentally and by modeling [15][16][17][18][19][20][21][22][23][24]. For the latter, the Toner's PIF (Probability of IIF) model [15] has been the most widely used for quantifying IIF that is nucleation-limited [14,25].…”