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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

A three-part, coupled model of cell dehydration, nucleation, and crystal growth was used to study intracellular ice formation (IIF) in cultured hepatocytes frozen in the presence of dimethyl sulfoxide (DMSO). Heterogeneous nucleation temperatures were predicted as a function of DMSO concentration and were in good agreement with experimental data. Simulated freezing protocols correctly predicted and explained experimentally observed effects of cooling rate, warming rate, and storage temperature on hepatocyte function. For cells cooled to -40 degrees C, no IIF occurred for cooling rates less than 10 degrees C/min. IIF did occur at faster cooling rates, and the predicted volume of intracellular ice increased with increasing cooling rate. Cells cooled at 5 degrees C/min to -80 degrees C were shown to undergo nucleation at -46.8 degrees C, with the consequence that storage temperatures above this value resulted in high viability independent of warming rate, whereas colder storage temperatures resulted in cell injury for slow warming rates. Cell damage correlated positively with predicted intracellular ice volume, and an upper limit for the critical ice content was estimated to be 3.7% of the isotonic water content. The power of the model was limited by difficulties in estimating the cytosol viscosity and membrane permeability as functions of DMSO concentration at low temperatures.

Understanding the effects of cell-cell interaction on intracellular ice formation (IIF) is required to design optimized protocols for cryopreservation of tissue. To determine the effects of cell-cell interactions during tissue freezing, without confounding effects from uncontrolled factors (such as time in culture, cell geometry, and cell-substrate interactions), HepG2 cells were cultured in pairs on glass coverslips micropatterned with polyethylene glycol disilane, such that each cell interacted with exactly one adjacent cell. Assuming the cell pair to be a finite state system, being either in an unfrozen state (no ice in either cell), a singlet state (IIF in one cell only), or a doublet state (IIF in both cells), the kinetics of state transitions were theoretically modeled and cryomicroscopically measured. The rate of intercellular ice propagation, estimated from the measured singlet state probability, increased in the first 24 h of culture and remained steady thereafter. In cell pairs cultured for 24 h and treated with the gap junction blocker 18beta-glycyrrhetinic acid before freezing, the intercellular ice propagation rate was lower than in untreated controls (p < 0.001), but significantly greater than zero (p < 0.0001). These results suggest that gap junctions mediate some, but not all, mechanisms of ice propagation in tissue.