Metastable states of water and ice during pressure-supported freezing of potato tissue

Different ice modifications were obtained during freezing processes at several pressure levels from atmospheric pressure up to 300 MPa. In the pressure range between 210 and 240 MPa, a metastable ice I modification area was observed, as the nucleation of ice I crystals in the thermodynamically stable region of ice III was reached. A significant degree of supercooling was obtained before freezing the tissue water to ice III, which has to be considered when designing pressure-supported freezing processes. The effect of supercooling phenomenon on the phase transition time is discussed using a mathematical model based on the solution of the heat transfer governing differential equations. Phase transition and freezing times for the different freezing paths experimented are compared for the processes: freezing at atmospheric pressure, pressure-assisted freezing, and pressure-shift freezing. Different metastable states of liquid water are defined according to their process-dependent stability.     

The effect of undissolved air on isochoric freezing

This study evaluates the effect of undissolved air on isochoric freezing of aqueous solutions. Isochoric freezing is concerned with freezing in a constant volume thermodynamic system. A possible advantage of the process is that it substantially reduces the percentage of ice in the system at every subzero temperature, relative to atmospheric freezing. At the pressures generated by isochoric freezing, or high pressure isobaric freezing, air cannot be considered an incompressible substance and the presence of undissolved air substantially increases the amount of ice that forms at any subfreezing temperature. This effect is measurable at air volumes as low as 1%. Therefore eliminating the undissolved air, or any separate gaseous phase, from the system is essential for retaining the properties of isochoric freezing.     

High-pressure shift freezing. Part 1. Amount of ice instantaneously formed in the process

A mathematical model to calculate the amount of ice formed instantaneously after a rapid expansion in high-pressure shift processes (HPSF) was developed. It considers that when water is expanded it does not extend over its melting curve but reaches a metastable state (supercooled water), which also occurs in practice. Theoretical results appear to agree with experimental data.     

Pressurized freezing for retarding shrinkage after drying: a quantitative interpretation

Certain gases, when dissolved at high pressure in foods and biological materials, give a structure of gas bubbles inflating cells after freezing, depressurization, and thawing. This phenomenon has been found to reduce shrinkage after subsequent drying. The effect is interpreted quantitatively in terms of the needs for (a) a sufficient solubility of the gas in the water of the tissue at high pressure so that the Bunsen coefficient is high enough (at least 1.5 cm³/cm³ for maximum effect), and (b) a sufficiently low permeability, expressed as the product of atmospheric solubility and diffusivity in water (equal to or less that of air for maximum effect).     

Ultrastructure of Kurloff body proteoglycans after high pressure freezing, cryosubstitution and postembedding staining with cuprolinic blue

Very high pressure freezing and cryosubstitutlon of Kurloffcells preserves the ultrastructural morphology of Kurloff bodies,particularly the myelin figures, as shown by embedding in epoxyresin and conventional postembedding staining. It also preservesthe Kurloff body proteoglycans as more expanded spindle-likeshapes than does fixation with formaldehyde at atmospheric pressure.But., proteoglycans were not discernible in the Kurloff bodymatrix on either unstained or conventionally stained thin sections.The Kurloff body skeleton of proteoglycans in their native expandedshape was stained with the electron-dense cationic ministaincuprolinic blue, using thin sections embedded in LR white. Themean equatorial diameter of the spindles was 20–30 nm,while the collapsed filaments produced by aldehyde fixationwere about 10–15 nm wide. The spindles were often about200–300 nm long but could be much longer, depending onthe plane of the section. Thus, high pressure freezing, freezesubstitution, embedding in LR white, and staining with cationicdyes such as phthalocyanins seems to be a convenient way ofvisualizing intracellular proteoglycans that are well preservedand in very much like their native expanded state. cuprolinic blue high pressure freezing Kurloff cell proteoglycans ultrastructure     

Influence of the freezing process upon fluoride binding to hemeproteins.

Fluoride association with ferric myoglobins and hemoglobins in aqueous buffers above freezing has been well studied. We chose this reaction to investigate the feasibility of observing titration intermediates and estimating dissociation constants at the freezing temperature by electron paramagnetic resonance spectroscopy at cryogenic temperatures. Dependence of apparent dissociation constant upon protein concentration was observed, a factor of four decrease in protein accompanied by about a fourfold increase in the apparent tightness of binding in the range of protein concentration studied. Binding was also found to depend upon cooling rate and concentration of additives (serum albumin, sucrose, glycerol). These effects appear to be associated with freezing-induced concentration of ligand, a process described in the literature. Bands of high concentration of electrolyte accompany solute rejection during ice growth, sweeping by slowing moving macromolecules. Thus, just before being trapped in the solid, the protein can experience a greater concentration of salt than in the original liquid. A mathematical model of this process, based upon simplifying assumptions about nucleation and ice-crystal growth rates in super-cooled solution, shows how the average concentration of mobile solute species can depend upon the concentration of all species present. Semiquantitative computer simulations of the actual, more complex, freezing are also presented and lead to estimates of ice particle size which are then compared with estimates from the former model.     

Osmotic response of individual cells during freezing. II. Membrane permeability analysis

An analytical model is presented to simulate the freezing of individual yeast cells. In addition the model is solved numerically on a digital computer to obtain values for cell volume as a function of temperature, based on the thermal protocol during freezing, and the transport parameters of the cell membrane. The numerical procedure was modified to enable values for the membrane hydraulic permeability reference coefficient, Lpg, and activation energy, ELp, to be deduced by nonlinear analysis of complementary experimental data (10). It was observed that the apparent values of both Lpg and ELp increase with cooling rate, from Lpg = 0.0116 micrometer 3 micrometers-2 atm-1 min-1 and ELp = 19.4 kJ mol-1 for 9 degrees K/min to Lpg = 2.11 micrometers 3 micrometer-2 atm-1 min-1 and ELp = 101 kJ mol-1 for 35 degrees K/min. The deduced permeabilities fall within the range of values determined in a prior study by Levin (6). Analysis with the model also indicates that the turgor pressure exerts a negligible effect on yeast exposed to freezing stress.     

Negative pressures produced in an artificial osmotic cell by extracellular freezing

A rigid artificial osmotic cell has been constructed using reverse osmosis membranes that were supported by metal grids from both sides to yield a high elastic modulus of the system. The cell could be subjected to changes of external water potential either by evaporation or by application of hypertonic solutions so that negative internal pressures or tensions (i.e. pressures smaller than atmospheric) could be built up. Negative pressures were also obtained by freeze-induced dehydration when the cell was cooled to −1.5°C and ice was formed on the outer surface. Tensions of up to −0.7 megapascals (−7 bars) could be established in the different types of experiments. Smaller tensions could be kept in the cell for several hours. Cavitations caused the pressure to increase instantaneously to values of about −0.1 megapascals (relative to atmospheric pressure) as theoretically expected. Cavitations could be reversed by pressurizing the system. The cell could be cooled to subzero temperatures while the cell solution was under tension. Intracellular freezing could be easily detected from an instantaneous increase in pressure. When the membrane was not supported by a grid from the inside (analogous to the situation in plant cells), no tensions could be built up in the system. The results support the idea of the incidence of negative pressures during freezing, if the wall is sufficiently rigid to prevent cell collapse and if the membrane does not separate from the cell wall.     

Biphasic investigation of tissue mechanical response during freezing front propagation

Cryopreservation of engineered tissue (ET) has achieved limited success due to limited understanding of freezing-induced biophysical phenomena in ETs, especially fluid-matrix interaction within ETs. To further our understanding of the freezing-induced fluid-matrix interaction, we have developed a biphasic model formulation that simulates the transient heat transfer and volumetric expansion during freezing, its resulting fluid movement in the ET, elastic deformation of the solid matrix, and the corresponding pressure redistribution within. Treated as a biphasic material, the ET consists of a porous solid matrix fully saturated with interstitial fluid. Temperature-dependent material properties were employed, and phase change was included by incorporating the latent heat of phase change into an effective specific heat term. Model-predicted temperature distribution, the location of the moving freezing front, and the ET deformation rates through the time course compare reasonably well with experiments reported previously. Results from our theoretical model show that behind the marching freezing front, the ET undergoes expansion due to phase change of its fluid contents. It compresses the region preceding the freezing front leading to its fluid expulsion and reduced regional fluid volume fractions. The expelled fluid is forced forward and upward into the region further ahead of the compression zone causing a secondary expansion zone, which then compresses the region further downstream with much reduced intensity. Overall, it forms an alternating expansion-compression pattern, which moves with the marching freezing front. The present biphasic model helps us to gain insights into some facets of the freezing process and cryopreservation treatment that could not be gleaned experimentally. Its resulting understanding will ultimately be useful to design and improve cryopreservation protocols for ETs.     

Capture of spatially homogeneous chemical reactions in tissue by freezing.

A useful technique in studying the saturation of hemoglobin in erythrocytes or myoglobin in tissue is cryophotometry, in which tissue is frozen for later spectrophotometric analysis. A general question associated with this technique is whether the freezing process alters the chemical state. This paper presents a theoretical analysis of the simplest model relevant to that question. We study the effect of rapid cooling on a spatially homogeneous chemical reaction. The analysis shows that changes during freezing are negligible near the boundary to which the heat sink is applied, but can be significant deeper in the sample. The distance from the boundary at which the changes during freezing become appreciable can be expressed simply in terms of the chemical reaction rates and the thermal diffusivity of the tissue. Detailed results are given for the case of oxygen and myoglobin in skeletal muscle.     

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).     

Company-sponsored egg freezing: an offer you can't refuse?

The aim of this article is to argue that one of the central arguments against company-sponsored non-medical egg freezing, namely that this practice is contrary to the reproductive autonomy of women, can be difficult to sustain under certain conditions. More specifically, we argue that company-sponsored egg freezing is not necessarily in conflict with the most common requirements for autonomous choice. That is, there is no reason to assume that employees cannot be adequately informed beforehand about what is scientifically known about the practice, and/or that they lack the required capacity to understand and process this information. Although they may feel a certain pressure to comply with the wishes of their employer, this concern can plausibly be alleviated through privacy regulations. In any event, such pressure is arguably not stronger than or relevantly different from other types of pressure on the labour market that most people readily accept as being ethically acceptable. Finally, we argue that company-sponsored non-medical egg freezing may mitigate certain types of oppressive socialization, although it may well perpetuate others, and should in any case arguably be dealt with through guidelines and counselling, which would ensure that women make autonomous choices when companies offer egg freezing.     

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.     

Effect of freezing and thawing rates on denaturation of proteins in aqueous solutions

The freeze denaturation of model proteins, LDH, ADH, and catalase, was investigated in absence of cryoprotectants using a microcryostage under well-controlled freezing and thawing rates. Most of the experimental data were obtained from a study using a dilute solution with an enzyme concentration of 0.025 g/l. The dependence of activity recovery of proteins on the freezing and thawing rates showed a reciprocal and independent effect, that is, slow freezing (at a freezing rate about 1 degrees C/min) and fast thawing (at a thawing rate >10 degrees C/min) produced higher activity recovery, whereas fast freezing with slow thawing resulted in more severe damage to proteins. With minimizing the freezing concentration and pH change of buffer solution by using a potassium phosphate buffer, this phenomenon could be ascribed to surface-induced denaturation during freezing and thawing process. Upon the fast freezing (e.g., when the freezing rate >20 degrees C/min), small ice crystals and a relatively large surface area of ice-liquid interface are formed, which increases the exposure of protein molecules to the ice-liquid interface and hence increases the damage to the proteins. During thawing, additional damage to proteins is caused by recrystallization process. Recrystallization exerts additional interfacial tension or shear on the entrapped proteins and hence causes additional damage to the latter. When buffer solutes participated during freezing, the activity recovery of proteins after freezing and thawing decreased due to the change of buffer solution pH during freezing. However, the patterns of the dependence on freezing and thawing rates of activity recovery did not change except for that at extreme low freezing rates (<0.5 degrees C/min). The results exhibited that the freezing damage of protein in aqueous solutions could be reduced by changing the buffer type and composition and by optimizing the freezing-thawing protocol.     

A mathematical model for the freezing process in biological tissue

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.     

Clinal variation in freezing tolerance among natural accessions of Arabidopsis thaliana

Low temperature represents a form of abiotic stress that varies predictably with latitude and altitude and to which organisms have evolved multiple physiological responses. Plants provide an especially useful experimental system for investigating the ecological and evolutionary dynamics of tolerance to low temperature because of their sessile lifestyle and inability to escape ambient atmospheric conditions. Here, intraspecific variation in freezing tolerance was investigated in Arabidopsis thaliana by conducting freezing tolerance assays on 71 accessions collected from across the native range of the species. Assays were performed at multiple minimum temperatures and on both cold-acclimated and non-cold-acclimated individuals. Considerable variation in freezing tolerance was observed among accessions both with and without a prior cold-acclimation treatment, suggesting that differences among accessions in cold-acclimation capacity as well as differences in intrinsic physiology contribute to variation in this phenotype. A highly significant positive relationship was observed between freezing tolerance and latitude of origin of accessions, consistent with a major role for natural selection in shaping variation in this phenotype. Clinal variation in freezing tolerance in A. thaliana coupled with considerable knowledge of the underlying genetics and physiology of this phenotype should allow evolutionary genetic analysis at multiple levels.     

Prediction of local cooling rates and cell survival during the freezing of a cylindrical specimen

A finite element numerical model was implemented to simulate the freezing process of an aqueous salt solution in a cylindrical container. Local cooling rates within the container were computed for several defined cooling protocols applied at the boundary. Characteristic cell survival signatures were used to predict the associated local survival rates throughout the system. These calculations show that there are two definite time domains during a typical freezing process: (1) while the surface temperature is changing and (2) after the surface temperature reaches a constant storage value. The calculations also show significant spatial variations in the local cooling rates within the container and considerable local deviation from the volumetric average survival for various simulated freezing protocols.     

Reversible inactivation of typhus Rickettsiae. I. Inactivation by freezing

Rickettsiae that have been frozen and thawed in isotonic salt solutions show greatly decreased toxicity for mice, hemolytic activity, respiration, and infectivity for eggs. All these properties can be partially restored by incubation of the rickettsiae in the presence of DPN and coenzyme A for 2 hours at 34°C. The extent of both inactivation and of subsequent reactivation is markedly affected by the presence of low concentrations of sucrose during the process of freezing and thawing. It has been shown that DPN is present in rickettsial suspensions and that in preparations that have not been frozen, the DPN sediments with the rickettsiae. After freezing in isotonic salt solution the DPN becomes non-sedimentable.     

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 cryomicroscope for the analysis of solute polarization during freezing

A better understanding of the freezing process in the extracellular suspension medium implies the consideration of deviations from equilibrium, i.e., unsteady diffusion of heat and mass with a moving phase boundary. Such phenomena, especially solute redistribution in front of the advancing phase interface, can readily be investigated with a special cryomicroscope equipped with a spectrophotometer. A major advantage of this method is the combination of quantitative measurements in conjunction with visual observations, allowing a control of the solid-liquid interface morphology (planar-cellular-dendritic) which is crucial to the solidification process. The freezing stage designed for this purpose produces a temperature field in the sample layer resembling that within a large plate-shaped container, and hence well-defined thermal gradients (having a dominant effect on the shape of the interface). Aqueous solutions of NaMnO₄, exhibiting a maximum absorption at 525 nm and a phase diagram as well as diffusive properties very similar to NaCl in water, turned out to be a particularly suitable model for simulating of solidification of biological solutions. As long as freezing is unidimensional (planar), the concentration profiles can be scanned on-line, while multidimensional (cellular, dendritic) structures require off-line densitometric determination from photomicrographs. The experimental results agree quite well with mathematical models for both types of solidification. The observed transition points between planar freezing and higher-order structures correspond to those resulting from constitutional supercooling, a criterion roughly indicating the conditions for interface instability based on temperature and concentration gradients at the phase boundary.