Intracellular ice formation in yeast cells vs. cooling rate: Predictions from modeling vs. experimental observations by differential scanning calorimetry

To survive freezing, cells must not undergo internal ice formation during cooling. One vital factor is the cooling rate. The faster cells are cooled, the more their contents supercool, and at some subzero temperature that supercooled cytoplasm will freeze. The question is at what temperature? The relation between cooling rate and cell supercooling can be computed. Two important parameters are the water permeability (Lp) and its temperature dependence. To avoid intracellular ice formation (IIF), the supercooling must be eliminated by dehydration before the cell cools to its ice nucleation temperature. With an observed nucleation temperature of −25 °C, the modeling predicts that IIF should not occur in yeast cooled at <20 °C/min and it should occur with near certainty in cells cooled at ?30 °C/min. Experiments with differential scanning calorimetry (DSC) confirmed these predictions closely. The premise with the DSC is that if there is no IIF, one should see only a single exotherm representing the freezing of the external water. If IIF occurs, one should see a second, lower temperature exotherm. A further test of whether this second exotherm is IIF is whether it disappears on repeated freezing. IIF disrupts the plasma membrane; consequently, in a subsequent freeze cycle, the cell can no longer supercool and will not exhibit a second exotherm. This proved to be the case at cooling rates >20 °C/min.     

Kinetics of water loss and the likelihood of intracellular freezing in mouse ova. Influence of the method of calculating the temperature dependence of water permeability

To avoid intracellular freezing and its usually lethal consequences, cells must lose their freezable water before reaching their ice-nucleation temperature. One major factor determining the rate of water loss is the temperature dependence of the water permeability, Lp (hydraulic conductivity). Because of the paucity of water permeability measurements at subzero temperatures, that temperature dependence has usually been extrapolated from above-zero measurements. The extrapolation has often been based on an exponential dependence of Lp on temperature. This paper compares the kinetics of water loss based on that extrapolation with that based on an Arrhenius relation between Lp and temperature, and finds substantial differences below -20 to -25 degrees C. Since the ice-nucleation temperature of mouse ova in the cryoprotectants DMSO and glycerol is usually below -30 degrees C, the Arrhenius form of the water-loss equation was used to compute the extent of supercooling in ova cooled at rates between 1 and 8 degrees C/min and the consequent likelihood of intracellular freezing. The predicted likelihood agrees well with that previously observed. The water-loss equation was also used to compute the volumes of ova as a function of cooling rate and temperature. The computed cell volumes agree qualitatively with previously observed volumes, but differ quantitatively.     

Thermally defined cryomicroscopy and thermodynamic analysis in lymphocyte freezing

A cryomicroscope is described which provides the possibility of quantifying the volume loss of cells during freezing, detection of intracellular ice formation during cooling and warming, as well as the determination of viability as function of (constant) cooling rates. The basic mechanisms occurring in cryopreservation have been studied with this system using the human lymphocyte suspended in pure saline as a biological model system; experimentally observed exosmosis during freezing is compared to predictions from a thermodynamic model. Cell volume loss during freezing has been determined experimentally for cooling rates of 2.4, 12, 48, and 120 degrees K/min. Exosmosis also was calculated corresponding to various assumptions regarding the concentration dependence of the hydraulic permeability of the cells. Further calculations of exosmosis are performed for determining the effects of the initial cell volume. The temperatures and transition cooling rate ranges of intracellular ice formation have been determined. On the basis of exosmosis and a lethal level of intracellular salt concentration, a hypothetical relative optimum of the cooling rate is theoretically predicted and compared to the experiments.     

On the problem of dehydration and intracellular crystallization during freezing of cell suspensions.

The kinetic equation of the process of cell dehydration during freezing has been obtained. It is used to assess the degree of protoplasmic supercooling as a function of the cooling rate and cell parameters.The suggested model of dehydration cannot be applied to cells with permeability coefficients for water molecules more than 10^?5 cm/sec · bar, in particular to erythrocytes.The peculiarities of intracellular crystallization in red cells have been studied. The results show that red cells are likely to start freezing at cooling rates slower than those supposed from calculations of Mazur (9).     

Kinetics of water loss and the likelihood of intracellular freezing in mouse ova

To avoid intracellular freezing and its usually lethal consequences, cells must lose their freezable water before reaching their ice-nucleation temperature. One major factor determining the rate of water loss in the temperature dependence of the water permeability,L _p (hydraulic conductivity). Because of the paucity of water permeability measurements at subzero temperatures, that temperature dependence has usually been extrapolated from above-zero measurements. The extrapolation has often been based on an exponential dependence ofL _p on temperature. This paper compares the kinetics of water loss based on that extrapolation with that based on an Arrhenius relation betweenL _p and temperature, and finds substantial differences below ?20 to ?25°C. Since the ice-nucleation temperature of mouse ova in the cryoprotectants DMSO and glycerol is usually below ?30°C, the Arrhenius form of the water-loss equation was used to compute the extent of supercooling in ova cooled at rates between 1 and 8°C/min and the consequent likelihood of intracellular freezing. The predicted likelihood agrees well with that previously observed. The water-loss equation was also used to compute the volumes of ova as a function of cooling rate and temperature. The computed cell volumes agree qualitatively with previously observed volumes, but differ quantitatively.     

Basic investigations on the freezing of human lymphocytes

Human lymphocytes were frozen at constant cooling rates in the range 2.4 to 1000 degrees K/min without cryoadditive on the cold stage of a thermally defined cryomicroscope. The volume loss due to water efflux was quantified optically for the cooling rates 2.4, 12, 48, and 120 degrees K/min. The likelihood of the formation of intracellular ice was determined as function of the cooling rate. Intracellular crystallization temperatures were obtained for ice formation during both cooling and rewarming. A theoretical analysis of the cell volume loss during freezing was compared to the experimental data and used for an indirect determination of the water permeability of the cells. A relative optimum of the cooling rate is predicted theoretically under the assumption of a critical level of intracellular salt concentration near the eutectic temperature. The dependence of survival and cooling rate was determined cryomicroscopically by simultaneously applying the FDA/EB fluorescence viability test. The optimal cooling rate of about 35 degrees K/min was also found for 2-ml samples frozen within the range of cooling rates of interest. The results show that for freezing in physiological saline solution (1) the optimum of the cooling rate is theoretically predictable, (2) cryomicroscopical data are significant for freezing of samples of larger volume, and (3) the lethal type of intracellular crystallization is cooling rate dependent and distinguishable from innocuous types.     

Is intracellular ice formation the cause of death of mouse sperm frozen at high cooling rates?

Mouse spermatozoa in 18% raffinose and 3.8% Oxyrase in 0.25 x PBS exhibit high motilities when frozen to -70 degrees C at 20-130 degrees C/min and then rapidly warmed. However, survival is <10% when they are frozen at 260 or 530 degrees C/min, presumably because, at those high rates, intracellular water cannot leave rapidly enough to prevent extensive supercooling and this supercooling leads to nucleation and freezing in situ (intracellular ice formation [IIF]). The probability of IIF as a function of cooling rate can be computed by coupled differential equations that describe the extent of the loss of cell water during freezing and from knowledge of the temperature at which the supercooled protoplasm of the cell can nucleate. Calculation of the kinetics of dehydration requires values for the hydraulic conductivity (Lp) of the cell and for its activation energy (Ea). Using literature values for these parameters in mouse sperm, we calculated curves of water volume versus temperature for four cooling rates between 250 and 2000 degrees C/min. The intracellular nucleation temperature was inferred to be -20 degrees C or above based on the greatly reduced motilities of sperm that underwent rapid cooling to a minimum temperature of between -20 and -70 degrees C. Combining that information regarding nucleation temperature with the computed dehydration curves leads to the conclusion that intracellular freezing should occur only in cells that are cooled at 2000 degrees C/min and not in cells that are cooled at 250-1000 degrees C/min. The calculated rate of 2000 degrees C/min for IIF is approximately eightfold higher than the experimentally inferred value of 260 degrees C/min. Possible reasons for the discrepancy are discussed.     

Quantitative study of the importance of water permeability in plant cold hardiness

The rate of ice formation was measured for Hedera helix L. cv. Thorndale (English ivy) bark exposed to -10 C. The cooling rate of bark exposed to -10 C was 31 C per minute. The water efflux rate required for ice formation to occur extracellularly was calculated from the rate of ice formation and the average cell diameter. The water potential difference driving the efflux of water to sites of extracellular ice was calculated from the sample temperature, osmotic water potential, and fraction of water frozen at a given freezing temperature. From the water efflux rate and water potential difference, the resistance of the barrier controlling movement of intracellular water to sites of extracellular ice was calculated. Comparison of the resistance of this barrier to water movement with the resistance of the cell membrane revealed that the membrane represented only 0.5% of the barrier resistance. Thus, membrane resistance can have little influence on the rate of water efflux and ice formation when bark is cooled at a rate of 31 C per minute. If ice formation occurred at the same rate in ivy bark as it occurred in a 10 mm MnCl(2) solution, the membrane resistance would still have represented only 1% of the resistance of the barrier to ice formation. Therefore, at a cooling rate of 31 C/minute, heat removal plays a large part in determining the rate of ice formation. At slower cooling rates experienced under natural freezing conditions the ability to remove heat would play an even larger role. It is concluded that under natural freezing conditions membrane resistance does not limit water efflux.     

Equilibrium,quasi-equilibrium,and nonequilibrium freezing of mammalian embryos

The first successful freezing of early embryos to −196°C in 1972 required that they be cooled slowly at ∼1°C/min to about −70°C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to −70°C, the result is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/ chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.     

Equilibrium, quasi-equilibrium, and nonequilibrium freezing of mammalian embryos.

The first successful freezing of early embryos to -196 degrees C in 1972 required that they be cooled slowly at approximately 1 degree C/min to about -70 degrees C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to -70 degrees C, the results is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.     

Differing actions of penetrating and nonpenetrating cryoprotective agents.

A two-step freezing technique has been used to examine the role of cryoprotective agents during cooling. Chinese hamster fibroblasts were cooled to various subzero holding temperatures and subsequently thawed or cooled to ?196 °C before thawing. Cells were suspended in various concentrations of dimethylsulfoxide (DMSO) or hydroxyethyl starch (HES) before freezing. The results indicated differing protective actions of DMSO and HES. These differences were verified using glycerol as either a penetrating or a nonpenetrating agent.The results are consistent with the concepts that cryoprotection is based on the avoidance or minimization of intracellular freezing and the minimization of damage to the cell from the environment of concentrated solutes during cooling, and that the colligative action of both penetrating and nonpenetrating agents allows the cells to survive the conditions for a reduction of cell water content during cooling thereby reducing the amount of intracellular freezing. The results indicate that penetrating and nonpenetrating agents accomplish this in different ways. Penetrating agents create the environment for a reduction of cell water content at temperatures sufficiently low to reduce the damaging effect of the concentrated solutes on the cells. Nonpenetrating agents osmotically “squeeze” water from the cells primarily during the initial phases of freezing at temperatures between ?10 and ?20 °C when these additives become concentrated in the extracellular regions.     

Studies on Rapidly Frozen Suspensions of Yeast Cells by Differential Thermal Analysis and Conductometry

Few, if any, yeast cells survived rapid cooling to -196°C and subsequent slow warming. After rapid freezing, the suspensions absorbed latent heat of fusion between -15° and 0°C during warming, and the relation between the amount of heat absorbed and the concentration of cells was the same as that in equivalent KCl solutions, indicating that frozen suspensions behave thermally like frozen solutions. The amount of heat absorbed was such that more than 80 per cent of the intracellular solution had to be frozen. The conductometric behavior of frozen suspensions showed that cell solutes were still inside the cells and surrounded by an intact cell membrane at the time heat was being absorbed. Two models are consistent with these findings. The first assumes that intracellular freezing has taken place; the second that all freezable water has left the cells and frozen externally. The latter model is ruled out because rapidly cooled cells do not shrink by an amount equal to the volume of water that would have to be withdrawn to prevent internal freezing.     

Nonequilibrium freezing of one-cell mouse embryos. Membrane integrity and developmental potential.

A thermodynamic model was used to evaluate and optimize a rapid three-step nonequilibrium freezing protocol for one-cell mouse embryos in the absence of cryoprotectants (CPAs) that avoided lethal intracellular ice formation (IIF). Biophysical parameters of one-cell mouse embryos were determined at subzero temperatures using cryomicroscopic investigations (i.e., the water permeability of the plasma membrane, its temperature dependence, and the parameters for heterogeneous IIF). The parameters were then incorporated into the thermodynamic model, which predicted the likelihood of IIF. Model predictions showed that IIF could be prevented at a cooling rate of 120 degrees C/min when a 5-min holding period was inserted at -10 degrees C to assure cellular dehydration. This predicted freezing protocol, which avoided IIF in the absence of CPAs, was two orders of magnitude faster than conventional embryo cryopreservation cooling rates of between 0.5 and 1 degree C/min. At slow cooling rates, embryos predominantly follow the equilibrium phase diagram and do not undergo IIF, but mechanisms other than IIF (e.g., high electrolyte concentrations, mechanical effects, and others) cause cellular damage. We tested the predictions of our thermodynamic model using a programmable freezer and confirmed the theoretical predictions. The membrane integrity of one-cell mouse embryos, as assessed by fluorescein diacetate retention, was approximately 80% after freezing down to -45 degrees C by the rapid nonequilibrium protocol derived from our model. The fact that embryos could be rapidly frozen in the absence of CPAs without damage to the plasma membrane as assessed by fluorescein diacetate retention is a new and exciting finding. Further refinements of this protocol is necessary to retain the developmental competence of the embryos.     

A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures

Thermodynamic models show that the loss of intracellular water from human erythrocytes during freezing depends heavily upon the water conductivity of the erythrocyte membrane. These calculations, which are based on the simple extrapolation of ambient conductivity data to subzero temperatures, show that more than 95% of cell water is transferable during freezing, whereas experiments show that at least 20% of cell water is retained. A study of the effects of different published values for the membrane water conductivity on cell water retained during freezing shows that this discrepancy may be a consequence of the simple extrapolation procedure.For a homogeneous membrane system, absolute reaction rate theory was used to develop a surface-limited permeation model that includes the resistance to the flow of water not only through the interior region of the membrane but also across possible rate-limiting barriers at the solution-membrane interfaces. The model shows that it is unlikely that a single ratelimiting process dominates water transport in the red cell as it is being cooled from ambient to subzero temperatures. The effective membrane conductivity at subzero temperatures could possibly be much lower than a simple extrapolation of existing data would predict. With the aid of this model analytical predictions of intracellular water during freezing are more consistent with experimental observations.     

Manifestations of cell damage after freezing and thawing

The nature of the primary lesions suffered by cells during freezing and thawing is unclear, although the plasma membrane is often considered the primary site for freezing injury. This study was designed to investigate the nature of damage immediately after thawing, by monitoring several functional tests of the cell and the plasma membrane. Hamster fibroblasts, human lymphocytes, and human granulocytes were subjected to a graded freeze-thaw stress in the absence of cryoprotective compound by cooling at -1 degree C/min to a temperature between -10 and -40 degrees C, and then were either warmed directly in water at 37 degrees C or cooled rapidly to -196 degrees C before rapid warming. Mitochondrial function in the cells was then assessed using 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyl-tetrazolium bromide (MTT), fluorescein diacetate (FDA), colony growth, and osmometric response in a hypertonic solution. Cells behaved as osmometers after cooling at -1 degree C/min to low temperatures at which there were no responses measured by other assays, indicating that the plasma membrane is not a primary site for injury sustained during slow cooling. These results also indicate that the FDA test does not measure membrane integrity, but reflects the permeability of the channels through which fluorescein leaves the cells. Fewer cells could respond osmotically after cooling under conditions where intracellular freezing was likely, implying that the plasma membrane is directly damaged by the conditions leading to intracellular freezing. A general model of freezing injury to nucleated mammalian cells is proposed in which disruption of the lysosomes constitutes the primary lesion in cells cooled under conditions where the cells are dehydrated at low temperatures.     

Freezing-induced cellular and membrane dehydration in the presence of cryoprotective agents

Abstract

FTIR and cryomicroscopy have been used to study mouse embryonic fibroblast cells (3T3) during freezing in the absence and presence of DMSO and glycerol. The results show that cell volume changes as observed by cryomicroscopy typically end at temperatures above ?15°C, whereas membrane phase changes may continue until temperatures as low as ?30°C. This implies that cellular dehydration precedes dehydration of the bound water surrounding the phospholipid head groups. Both DMSO and glycerol increase the membrane hydraulic permeability at subzero temperature and reduce the activation energy for water transport. Cryoprotective agents facilitate dehydration to continue at low subzero temperatures thereby decreasing the incidence of intracellular ice formation. The increased subzero membrane hydraulic permeability likely plays an important role in the cryoprotective action of DMSO and glycerol. In the presence of DMSO water permeability was found to be greater compared to that in the presence of glycerol. Two temperature regimes were identified in an Arrhenius plot of the membrane hydraulic permeability. The activation energy for water transport at temperature ranging from 0 to ?10°C was found to be greater than that below ?10°C. The non-linear Arrhenius behavior of Lp has been implemented in the water transport model to simulate cell volume changes during freezing. At a cooling rate of 1°C min^-1, ～5% of the initial osmotically active water volume is trapped inside the cells at ?30°C.     

Water transport and cell survival in cryobiological procedures.

Living cells may be cooled to 77 K (liquid nitrogen) either to destroy them selectively or to store them for long periods. Water transport across the cell membranes during freezing and thawing is a primary factor determining whether the cells survive. These water movements are controlled by phase changes both intracellular and extracellular and by other factors such as the nature of any cryoprotective agent present, and the rates of cooling and thawing. The relation between cooling procedure, water transport and cell survival is discussed. In particular, the crucial r?le of dilution shock is emphasized: this is the damage to cells induced during the dilution that occurs both as ice melts during rewarming and when any cryoprotective additives are removed after thawing. Apart from the usefulness of understanding these processes for maximizing preservation or controlling selective destruction, the diverse responses of cells to different combinations of water transport and temperature changes appear likely to provide basic information on the properties of cell membranes.     

Thermal stresses from large volumetric expansion during freezing of biomaterials.

Thermal stresses were studied in freezing of biomaterials containing significant amounts of water. An apparent specific heat formulation of the energy equation and a viscoelastic model for the mechanics problem were used to analyze the transient axi-symmetric freezing of a long cylinder. Viscoelastic properties were measured in an Instron machine. Results show that, before phase change occurs at any location, both radial and circumferential stresses are tensile and keep increasing until phase change begins. The maximum principal tensile stress during phase change increases with a decrease in boundary temperature (faster cooling). This is consistent with experimentally observed fractures at a lower boundary temperature. Large volumetric expansion during water to ice transformation was shown to be the primary contributor to large stress development. For very rapid freezing, relaxation may not be significant, and an elastic model may be sufficient.     

Water transport and IIF parameters for a connective tissue equivalent

Understanding the biophysical processes that govern freezing injury of a tissue equivalent (TE) is an important step in characterizing and improving the cryopreservation of these systems. TEs were formed by entrapping human dermal fibroblasts (HDFs) in collagen or in fibrin gels. Freezing studies were conducted using a Linkam cryostage fitted to an optical microscope allowing observation of the TEs cooled under controlled rates between 5 and 130 degrees C/min. Typically, freezing of cellular systems results in two biophysical processes that are both dependent on the cooling rate: dehydration and/or intracellular ice formation (IIF). Both these processes can potentially be destructive to cells. In this study, the biophysics of freezing cells in collagen and fibrin TEs have been quantified and compared to freezing cells in suspension. Experimental data were fitted in numerical models to extract parameters that governed water permeability, E(Lp) and L(pg), and intracellular ice nucleation, omega(o) and kappa(o). Results indicate that major differences exist between freezing HDFs in suspension and in a tissue equivalent. During freezing, 55% of the HDFs in suspension formed IIF as compared to 100% of HDFs forming IIF in collagen and fibrin TE at a cooling rate of 130 degrees C/min. Also, both the water permeability and the IIF parameters were determined to be higher for HDFs in TEs as compared to cell suspensions. Between the TEs, HDFs in fibrin TE exhibited higher values for the biophysical parameters as compared to HDFs in collagen TE. The observed biophysics seems to indicate that cell-cell and cell-matrix interactions play a major role in ice propagation in TEs.