A model of diffusion-limited ice growth inside biological cells during freezing

Abstract

Articles you may be interested inThe effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation Modeling the cell-type dependence of diffusion-limited intracellular ice nucleation and growth during both vitrification and slow freezing A theoretical model for predicting the kinetics of ice crystallization inside cells during cryopreservation was developed, and applied to mouse oocytes, by coupling separate models of (1) water transport across the cell membrane, (2) ice nucleation, and (3) crystal growth. The instantaneous cell volume and cytosol composition during continuous cooling in the presence of glycerol were predicted using the water transport model. Classical nucleation theory was used to predict ice nucleation rates, and a nonisothermal diffusion-limited crystal-growth model was used to compute the resulting crystallization kinetics. The model requires knowledge of the nucleation rate parameters a and K, as well as the viscosity 11 of a water-NaCl-glycerol solution as a function of both the composition and temperature of the solution. These dependences were estimated from data available in the literature. Cell-specific biophysical parameters were obtained from previous studies on mouse oocytes. A sensitivity analysis showed that the model was most sensitive to the values of K and 7. The coupled model was used to study the effect of cooling rate and initial glycerol concentration on intracellular crystal growth. The extent of crystallization, as well as the crystal size distribution, were predicted as functions of time. For rapid cooling at low to intermediate glycerol concentrations, the cells crystallized completely, while at high concentrations of glycerol, partial or total vitrification was observed. As expected, the cooling rate necessary for vitrification dropped with increasing glycerol concentration; when cells initially contained -7.5 M glycerol, vitrification was achieved independent of cooling rate. For slow cooling protocols, water transport significantly affected the results. At glycerol concentrations greater than -3 M, the final intracellular ice content decreased with increasing glycerol concentration at a fixed cooling rate. In this regime, the cooling rate at which a critical amount of ice was formed increased as more glycerol was used. When less than -3 M glycerol was initially present in the cell, an increase in glycerol concentration was predicted to cause an increase in the final intracellular ice content at agiven cooling rate. In this regime, the critical cooling rate decreased with increasing glycerol concentration. These predictions clarify previous empirical observations of slo< freezing phenomena. 4442

The effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation

“…6 In general, IIF has been recognized as a lethal event to living cells. [7][8][9][10] Therefore, a quantitative understanding of the process of IIF which includes ice nucleation (IN) and the subsequent ice crystal growth (ICG) is crucial for optimizing cryopreservation protocols to maximize cell survival.…”

Preservation of Embryonic Stem Cells

“…Therefore, water enclosed in the microcapsules can be preferentially vitrified in the presence of 1.4 M DMSO while more than 2.1 M DMSO is required to vitrify the same amount of water in the bulk solution, indicating the capability of alginate microcapsules in enhancing vitrification of the enclosed water even at a cooling rate of 100 o C/min. The preferential vitrification of water enclosed in the microcapsule is due to its higher viscosity (Ahearne et al 2005;Qin 2008;Zhang et al 2006) and small volume (sub-nanoliter) and is expected to be much more significant at much higher cooling rates (e.g., > 10,000 o C/min) (Chen and Li 2008;Karlsson et al 1994;Yang et al 2009;Zhang et al 2010;Zhao et al 2006). The preferential vitrification of water enclosed in small alginate microcapsules demonstrated in Fig.…”

“…3 should be able to enhance vitrification of living cells encapsulated in the microcapsules at high cooling rates (e.g., > 10,000 o C/min). This is because it can not only depress ice formation and growth in the microcapsule but also prevent ice (if any) propagation into cells from the bulk solution where ice is usually formed first (because of its much bigger volume) (Berejnov et al 2006;Fahy et al 1987;Franks et al 1983;He et al 2008b;Karlsson et al 1994;Mazur et al 2005a;Mazur et al 2005b;Toner 1993;Toner et al 1990;Yavin and Arav 2007). This hypothesis is confirmed by a recent study where the C3H10T1/2 mouse mesenchymal stem cells encapsulated in ~100 µm alginate microcapsules were vitrified using a 400 µm, thin-walled quartz microcapillary at a low-CPA concentration (1.4 M DMSO) (Zhang et al 2010).…”

“…When cooling cells/tissue with much higher cooling rates and/or a high concentration of intracellular CPA (e.g., during vitrification and after significant cell dehydration during slow-freezing), the rate limitingstep of IIF is the growth of the ice nuclei. The IIF under these conditions is said to be diffusion-limited for which more complicated models are needed to predict the amount of intracellular ice (Chen and Li 2008;Karlsson et al 1993;Karlsson et al 1994;Yang et al 2009;Zhao et al 2006). To better predict the diffusion-limited ice nucleation and growth, an advanced model such as the free volume model that can account for the effect of glass transition on solution viscosity and diffusion coefficient might be necessary.…”

“…In order to predict the probability of IIF using the above model during slow-freezing where freeze concentration induced cell dehydration is significant, information on the cell volume, V (or cell surface area, A, related to the diameter of the cells when the cells assume a spherical geometry), during freezing is required. The following model has been commonly used to predict the cell volume change during freezing (Karlsson et al 1994;Mazur 1963):…”