Analysis of cryopreservation media thermophysical characteristics after ultra-rapid cooling through differential scanning calorimetry.

Cryoprotective agents play a critical role in minimizing cell damage caused by ice formation during cryopreservation. However, high concentrations of CPAs are toxic to cells and tissues. Required concentrations of CPAs can be reduced by utilizing higher cooling and warming rates, but insight into the thermophysical properties of biological solutions in the vitrification method is necessary for the development of cryopreservation protocols. Most studies on thermophysical properties under ultra-rapid cooling conditions have been qualitatively based on visualization. Differential scanning calorimetry methods are ideal for studying the behavior of biomaterials in various freezing conditions quantitatively and accurately, though previous studies have been predominantly restricted to slower cooling rates. Here, we developed an ultra-rapid cooling method for DSC that can achieve minimal cooling rates exceeding 2000 °C/min. We investigated the thermophysical vitrification behavior of ternary solutions of phosphate buffer saline (1X), dimethyl sulfoxide or glycerol and ice blocking polymers (X-1000 or Z-1000). We quantified the impact of solute concentration on ice crystal formation during rapid cooling. Our findings support the expectation that increasing the solute concentration reduces the amount of ice formation, including devitrification. Devitrification increases from 0% to 40% (v/v) Me2SO and then reduces significantly. The relative amounts of devitrification to the total ice formation are 0%, 60%, 0% in 20%, 40%, 60% (v/v) Me2SO, and 2%, 48%, 49% in 20%, 40%, 60% (v/v) glycerol, respectively. The results suggest that at low concentrations, such as below 20% (v/v) for Me2SO or glycerol, increasing the warming rate after ultra-rapid freezing is not essential to eliminate devitrification. Furthermore, ice blocking polymers do not reduce ice formation substantially and cannot eliminate devitrification under ultra-rapid cooling conditions. In conclusion, our results provide insights into the impact of solute concentration on ice formation and devitrification during rapid cooling, which can be practical for optimizing cryopreservation protocols.

Comparison of liquid nitrogen-free slow freezing protocols toward enabling a practical option for centralized cryobanking of ovarian tissue.

Geographically distributed ovarian tissue cryobanks remain limited due to the high facility and staff costs, and cold transportation to centers is associated with ischemia-induced tissue damage that increases with transport distance. It is ideal to perform the cryopreservation procedure at a tissue removal site or local hospital before shipment to cost-effective centralized cryobanks. However, conventional liquid nitrogen-based freezers are not portable and require expensive infrastructure. To study the possibility of an ovarian tissue cryopreservation network not dependent on liquid nitrogen, we cryopreserved bovine ovarian tissue using three cooling techniques: a controlled rate freezer using liquid nitrogen, a liquid nitrogen-free controlled rate freezer, and liquid nitrogen-free passive cooling. Upon thawing, we evaluated a panel of viability metrics in frozen and fresh groups to examine the potency of the portable liquid nitrogen-free controlled and uncontrolled rate freezers in preserving the ovarian tissue compared to the non-portable conventional controlled rate freezer. We found similar outcomes for reactive oxygen species (ROS), total antioxidant capacity (TAC), follicular morphology, tissue viability, and fibrosis in the controlled rate freezer groups. However, passive slow cooling was associated with the lowest tissue viability, follicle morphology, and TAC, and the highest tissue fibrosis and ROS levels compared to all other groups. A stronger correlation was found between follicle morphology, ovarian tissue viability, and fibrosis with the TAC/ROS ratio compared to ROS and TAC alone. The current study undergirds the possibility of centralized cryobanks using a controlled rate liquid nitrogen-free freezer to prevent ischemia-induced damage during ovarian tissue shipment.

Ovarian tissue cryopreservation and transplantation: a review on reactive oxygen species generation and antioxidant therapy.

Cancer is the leading cause of death worldwide. Fortunately, the survival rate of cancer continues to rise, owing to advances in cancer treatments. However, these treatments are gonadotoxic and cause infertility. Ovarian tissue cryopreservation and transplantation (OTCT) is the most flexible option to preserve fertility in women and children with cancer. However, OTCT is associated with significant follicle loss and an accompanying short lifespan of the grafts. There has been a decade of research in cryopreservation-induced oxidative stress in single cells with significant successes in mitigating this major source of loss of viability. However, despite its success elsewhere and beyond a few promising experiments, little attention has been paid to this key aspect of OTCT-induced damage. As more and more clinical practices adopt OTCT for fertility preservation, it is a critical time to review oxidative stress as a cause of damage and to outline potential ameliorative interventions. Here we give an overview of the application of OTCT for female fertility preservation and existing challenges; clarify the potential contribution of oxidative stress in ovarian follicle loss; and highlight potential ability of antioxidant treatments to mitigate the OTCT-induced injuries that might be of interest to cryobiologists and reproductive clinicians.

Meta-analysis of the Boyle van 't Hoff relation: Turgor and leak models explain non-ideal volume equilibrium.

There has been much recent attention paid to the interaction of cell volume, its regulation, and the molecular biology of the cell. Cells are generally assumed to behave as linear osmometers, with their water volume linearly proportionate to the inverse of osmotic pressure as described by the Boyle van 't Hoff (BvH) relation. This study evaluates the generality of this and other long-standing assumptions about cell responses to anisotonic conditions. We present alternative models that account for osmoregulation including mechanical resistance to volumetric expansion (the turgor model) and ion-osmolyte leakage (the leak model). To evaluate the generality of the BvH relation and determine the suitability of alternative models, we performed a comprehensive survey of the literature and a careful analysis of the resulting data, and then we used these data to compare among models. We identified 137 articles published from 1964 to 2019 spanning 14 animal species and 26 cell types and determined the BvH relation is not an appropriate general model but is adequate when restricted to the hypertonic region. In contrast, models that account for either mechanical resistance or ion-osmolyte leakage fit well to almost all collected data. The leak model has fitted parameters that are in the same range as the current literature estimate, while the turgor model typically requires an elastic modulus value of one or multiple orders of magnitude larger than literature values. However, confirmation of the underlying mechanism of osmotic regulation is required at the cell-specific level and cannot be assumed a priori.

Silymarin mediated osmotic responses and damage in HepG2 cell suspensions and monolayers.

Maintenance of cells within a volume range compatible with their functional integrity is a critical determinant of cell survival after cryopreservation, and quantifying this osmotically induced damage is a part of the rational design of improved cryopreservation protocols. The degree that cells tolerate osmotic stress significantly impacts applicable cryoprotocols, but there has been little research on the time dependence of this osmotic stress. Additionally, the flavonoid silymarin has been shown to be hepatoprotective. Therefore, here we test the hypotheses that osmotic damage is time-dependent and that flavonoid inclusion reduces osmotic damage. In our first experiment, cells were exposed to a series of anisosmotic solutions of graded hypo- and hypertonicity for 10-40 min, resulting in a conclusion that osmotically induced damage is time dependent. In the next experiment, adherent cells preincubated with silymarin at the concentration of 10-4 mol/L and 10-5 mol/L showed a significant increase in cell proliferation and metabolic activity after osmotic stress compared to untreated matched controls. For instance, when adherent cells preincubated with 10-5 mol/L silymarin were tested, resistance to osmotic damage and a significant increase (15%) in membrane integrity was observed in hypo-osmotic media and a 22% increase in hyperosmotic conditions. Similarly, significant protection from osmotic damage was observed in suspended HepG2 cells in the presence of silymarin. Our study concludes that osmotic damage is time dependent, and the addition of silymarin leads to elevated resistance to osmotic stress and a potential increase in the cryosurvival of HepG2 cells.

Permeation of individual cryoprotectants and their different combinations into mouse liver tissue.

Development of successful tissue cryopreservation methods requires specific knowledge regarding tissue permeation of individual cryoprotective agents (CPAs) and their combinations. The present study assessed the permeation of dimethyl sulfoxide, ethylene glycol, and propylene glycol into liver tissue, and addressed whether the diffusion coefficient of individual CPAs changes when combining CPAs. To do this, mouse liver slices were exposed at room temperature to 3.5 mol/L concentrations of CPAs individually or in combination for 15, 30, 45, and 60 min. Subsequently, tissue CPA concentrations were determined using a gas chromatography/mass spectrometry (GC/MS) method. Our results show that (1) the GC/MS method allows measurement of multiple CPA concentrations in a single small tissue sample, (2) dimethyl sulfoxide has a higher diffusion coefficient than ethylene glycol and propylene glycol, and (3) the CPA diffusivity appears to decrease in mixtures with multiple CPAs. These findings may help the development of effective tissue cryopreservation methods.

Real-time computer assisted measurement of oocyte and embryo volume for assessment of transport parameters.

Cryopreservation of gametes has revolutionized both animal agriculture and human reproductive medicine. Although many new technologies have tremendously improved the cryopreservation of oocytes and embryos, osmotic stress encountered during the equilibration process can cause their loss of function. Rational cryoprotective agent (CPA) equilibration strategies can be used to minimize this stress but require trained personnel to monitor the process in individual oocytes or embryos or require the use of suboptimal average transport parameter values in mathematically guided protocols. To enable individually optimized equilibration of CPAs in individual cells, here we establish experimental and computational techniques to track the osmotic behavior of individual bovine oocytes and embryos during CPA equilibration in real time. We designed a microfluidic device to provide a controlled flow of CPA and modified standard image analysis techniques to estimate real-time cell volume changes. In particular, we used a level-set method to define a boundary within a contour plot which could automate the image analysis process. A colour based level set algorithm coupled with contour smoothing not only provided the best fit but also reduced the segmentation time to well under a second per image. The accuracy of the automated method was comparable to human segmented images for both oocytes and embryos. This technology should enable both rapid evaluation of key biophysical parameters in oocytes and embryos undergoing CPA equilibration and the development of real-time feedback-control of CPA equilibration, enabling individual oocyte- and embryo-specific optimal protocols.

Multiple cryoprotectant toxicity model for vitrification solution optimization.

Vitrification is a promising cryopreservation technique for complex specimens such as tissues and organs. However, it is challenging to identify mixtures of cryoprotectants (CPAs) that prevent ice formation without exerting excessive toxicity. In this work, we developed a multi-CPA toxicity model that predicts the toxicity kinetics of mixtures containing five of the most common CPAs used in the field (glycerol, dimethyl sulfoxide (DMSO), propylene glycol, ethylene glycol, and formamide). The model accounts for specific toxicity, non-specific toxicity, and interactions between CPAs. The proposed model shows reasonable agreement with training data for single and binary CPA solutions, as well as ternary CPA solution validation data. Sloppy model analysis was used to examine the model parameters that were most important for predictions, providing clues about mechanisms of toxicity. This analysis revealed that the model terms for non-specific toxicity were particularly important, especially the non-specific toxicity of propylene glycol, as well as model terms for specific toxicity of formamide and interactions between formamide and glycerol. To demonstrate the potential for model-based design of vitrification methods, we paired the multi-CPA toxicity model with a published vitrification/devitrification model to identify vitrifiable CPA mixtures that are predicted to have minimal toxicity. The resulting optimized vitrification solution composition was a mixture of 7.4 molal glycerol, 1.4 molal DMSO, and 2.4 molal formamide. This demonstrates the potential for mathematical optimization of vitrification solution composition and sets the stage for future studies to optimize the complete vitrification process, including CPA mixture composition and CPA addition and removal methods.

General tissue mass transfer model for cryopreservation applications.

Successful cryopreservation of complex specimens, such as tissues and organs, would greatly benefit both the medical and scientific research fields. Vitrification is one of the most promising techniques for complex specimen cryopreservation, but toxicity remains a major challenge because of the high concentration of cryoprotectants (CPAs) needed to vitrify. Our group has approached this problem using mathematical optimization to design less toxic CPA equilibration methods for cells. To extend this approach to tissues, an appropriate mass transfer model is required. Fick's law is commonly used, but this simple modeling framework does not account for the complexity of mass transfer in tissues, such as the effects of fixed charges, tissue size changes, and the interplay between cell membrane transport and transport through the extracellular fluid. Here, we propose a general model for mass transfer in tissues that accounts for all of these phenomena. To create this model, we augmented a previously published acellular model of mass transfer in articular cartilage to account for the effects of cells. We show that the model can accurately predict changes in CPA concentration and tissue size for both articular cartilage and pancreatic islets, tissue types with vastly different properties.

Rapid quantification of multi-cryoprotectant toxicity using an automated liquid handling method.

Cryopreservation in a vitrified state has vast potential for long-term storage of tissues and organs that may be damaged by ice formation. However, the toxicity imparted by the high concentration of cryoprotectants (CPAs) required to vitrify these specimens remains a hurdle. To address this challenge, we previously developed a mathematical approach to design less toxic CPA equilibration methods based on the minimization of a toxicity cost function. This approach was used to design improved methods for equilibration of bovine pulmonary artery endothelial cells (BPAEC) with glycerol. To fully capitalize on the toxicity cost function approach, it is critical to describe the toxicity kinetics of additional CPAs, including multi-CPA mixtures that are commonly used for vitrification. In this work, we used automated liquid handling to characterize the toxicity kinetics of five of the most common CPAs (glycerol, dimethyl sulfoxide (DMSO), propylene glycol, ethylene glycol, and formamide), along with their binary and ternary mixtures for BPAEC. In doing so, we developed experimental methods that can be used to determine toxicity kinetics more quickly and accurately. Our results highlight some common CPA toxicity trends, including the relatively low toxicity of ethylene glycol and a general increase in toxicity as the CPA concentration increases. Our results also suggest potential new approaches to reduce toxicity, including a surprising toxicity neutralization effect of glycerol on formamide. In the future, this dataset will serve as the basis to expand our CPA toxicity model, enabling application of the toxicity cost function approach to vitrification solutions containing multiple CPAs.

Robust numerical solution for the two parameter solute solvent transport model.

Prediction of solute and solvent transport in cells is central to developing and testing cryopreservation protocols. As we show here, however, the models used can be difficult to accurately numerically integrate in some key cases, and thus are a challenge to implement when determining the time dependent cell state during cryoprotectant equilibration and cooling. Exact solution techniques exist for overcoming this problem, but their implementation is also challenging: inversion of a nonlinear function is required that negates much of the utility of the approach. This communication describes a simple approach for more robust numerical integration that can be implemented using any numerical differential equation solver, and can facilitate arbitrarily accurate solutions to transport models without the complication of inversion formulae or complicated numerical integration schemes. Further, a simple relevant example of red blood cell equilibration with 40% glycerol is presented with comments on extending the approach to other settings.

Low concentrations of 3-O-methylglucose improve post thaw recovery in cryopreserved bovine spermatozoa.

A number of studies have explored the use of membrane permeable (usually metabolizable) and membrane impermeable saccharides to protect cells in general, and sperm in particular during cryopreservation. Critical concentrations for protective levels of sugars frequently range between 50 mmol/L and 500 mmol/L, where efficacy is attributed to the sugar's membrane stabilizing and glass forming attributes and colligative effects that reduce intra- and extracellular salt concentrations during freezing. Many studies on bull sperm have demonstrated that both permeating and non-permeating sugars have negligible positive effects on post-thaw viability. Recently, however, a non-metabolizable sugar, 3-O-Methylglucose (3-OMG), was shown to protect hepatocytes during liver cryopreservation at 0.1-0.3 mol/L. Because glucose is readily transported into sperm, we hypothesized that 3-OMG could be a new class of cryoprotectant to explore in bull sperm. Here we present positive results demonstrating that 3-OMG improves post thaw viability in bull sperm, and that this effect is not likely due to improved glass forming capabilities. In particular, in experiment 1, 3-OMG was added to the Tris-egg yolk-glycerol base media at levels from 0 mmol/L to 200 mmol/L. Semen from four bulls was collected and diluted with one of the cryopreservation media, cooled, and frozen following industry standard practices. Motility and mitochondrial activity were negatively impacted when concentration of 3-OMG was more than 25 mmol/L. Therefore, we explored lower concentrations in experiment 2, where semen from eight bulls was used to evaluate concentrations 5 mmol/L, 15 mmol/L and 25 mmol/L of 3-OMG compared with control. Motility and progressive motility in 5 mmol/L 3-OMG and in the control were significantly higher than 15 mmol/L and 25 mmol/L 3-OMG, whereas mitochondrial activity and acrosome integrity in 5 mmol/L 3-OMG were significantly better than the control freezing medium. In experiment 3, to evaluate whether the improved effects of 3-OMG are due to its non-metabolizing property, or due to colligative effects, we compared post-thaw viability in semen from four bulls cryopreserved with 5 mmol/L glucose, sucrose, or 3-OMG. Motility and progressive motility was significantly improved in 3-OMG compared to glucose or sucrose groups which were comparable to the EY control. In conclusion, 3-OMG at a concentration of 5 mmol/L in Tris-egg yolk-glycerol medium improves the post thaw motility, progressive motility and viability of bull sperm. The mechanism of action is not understood but because the efficacy is maximal at low concentrations, it is not likely due to improved intra- or extracellular glass forming abilities and may demonstrate a different protective mechanism than was shown in hepatocytes.

Foundations of modeling in cryobiology-III: Inward solidification of a ternary solution towards a permeable spherical cell in the dilute limit.

In the previous two manuscripts we outlined the general theory of heat and mass transport in a cell-liquid-ice system with general boundaries and nonideal and nondilute assumptions. Here we simplify the models considerably by presenting a reduction to a spherically symmetric system-a spherical cell with an encroaching spherical ice front. We also reduce to linear approximations of the nonideal nondilute models, essentially assuming dilute and ideal conditions. We derive the resulting nondimensional combined heat and mass transport model for a ternary solution and present numerical solutions. We include an analysis of the effects of varying some nondimensional parameters on rates of ice growth with comments on the necessity of models that account for spatially varying quantities in cryobiology.

Implications of variability in cell membrane permeability for design of methods to remove glycerol from frozen-thawed erythrocytes.

In North America, red blood cells (RBCs) are currently cryopreserved in a solution of 40% glycerol. While glycerol is not inherently toxic to humans, it must be removed prior to transfusion to prevent intravascular osmotic hemolysis. The current deglycerolization procedure requires about 45 min per RBC unit. We previously presented predictions suggesting that glycerol could be safely removed from RBCs in less than 1 min. However, experimental evaluation of these methods resulted in much higher hemolysis than expected. Here we extend our previous study by considering both concentration-dependence of permeability and variability in permeability values in the mathematical optimization algorithm. To establish a model for the concentration dependence of glycerol permeability, we combined literature data with new measurements of permeability in the presence of 40% glycerol. To account for cell-dependent variability we scaled the concentration-dependent permeability model to define a permeability range for optimization. Methods designed using a range extending to 50% of the model-predicted glycerol permeability had a duration of less than 3 min and resulted in hemolysis ranging from 34% to 83%; hemolysis values were highly dependent on the blood donor. Extending the permeability range to 5% of the model-predicted value yielded a 30 min method that resulted in an average hemolysis of 12%. Our results suggest high variability in the glycerol permeability between donors and within a population of cells from the same donor. Such variability has broad implications for design of methods for equilibration of cells with cryoprotectants.

Foundations of modeling in cryobiology-II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces.

Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts-namely, transport in the "bulk phases" away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series.

Concentration dependence of the cell membrane permeability to cryoprotectant and water and implications for design of methods for post-thaw washing of human erythrocytes.

For more than fifty years the human red blood cell (RBC) has been a widely studied model for transmembrane mass transport. Existing literature spans myriad experimental designs with varying results and physiologic interpretations. In this review, we examine the kinetics and mechanisms of membrane transport in the context of RBC cryopreservation. We include a discussion of the pathways for water and glycerol permeation through the cell membrane and the implications for mathematical modeling of the membrane transport process. In particular, we examine the concentration dependence of water and glycerol transport and provide equations for estimating permeability parameters as a function of concentration based on a synthesis of literature data. This concentration-dependent transport model may allow for design of improved methods for post-thaw removal of glycerol from cryopreserved blood. More broadly, the consideration of the concentration dependence of membrane permeability parameters may be important for other cell types as well, especially for design of methods for equilibration with the highly concentrated solutions used for vitrification.

A toxicity cost function approach to optimal CPA equilibration in tissues.

There is growing need for cryopreserved tissue samples that can be used in transplantation and regenerative medicine. While a number of specific tissue types have been successfully cryopreserved, this success is not general, and there is not a uniform approach to cryopreservation of arbitrary tissues. Additionally, while there are a number of long-established approaches towards optimizing cryoprotocols in single cell suspensions, and even plated cell monolayers, computational approaches in tissue cryopreservation have classically been limited to explanatory models. Here we develop a numerical approach to adapt cell-based CPA equilibration damage models for use in a classical tissue mass transport model. To implement this with real-world parameters, we measured CPA diffusivity in three human-sourced tissue types, skin, fibroid and myometrium, yielding propylene glycol diffusivities of 0.6 × 10-6 cm2/s, 1.2 × 10-6 cm2/s and 1.3 × 10-6 cm2/s, respectively. Based on these results, we numerically predict and compare optimal multistep equilibration protocols that minimize the cell-based cumulative toxicity cost function and the damage due to excessive osmotic gradients at the tissue boundary. Our numerical results show that there are fundamental differences between protocols designed to minimize total CPA exposure time in tissues and protocols designed to minimize accumulated CPA toxicity, and that "one size fits all" stepwise approaches are predicted to be more toxic and take considerably longer than needed.

Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes.

BACKGROUND: Simple and effective cryopreservation of human oocytes would have an enormous impact on the financial and ethical constraints of human assisted reproduction. Recently, studies have demonstrated the potential for cryopreservation in an ice-free glassy state by equilibrating oocytes with high concentrations of cryoprotectants (CPAs) and rapidly cooling to liquid nitrogen temperatures. A major difficulty with this approach is that the high concentrations required for the avoidance of crystal formation (vitrification) also increase the risk of osmotic and toxic damage. We recently described a mathematical optimization approach for designing CPA equilibration procedures that avoid osmotic damage and minimize toxicity, and we presented optimized procedures for human oocytes involving continuous changes in solution composition. METHODS: Here we adapt and refine our previous algorithm to predict piecewise-constant changes in extracellular solution concentrations in order to make the predicted procedures easier to implement. Importantly, we investigate the effects of using alternate equilibration endpoints on predicted protocol toxicity. Finally, we compare the resulting procedures to previously described experimental methods, as well as mathematically optimized procedures involving continuous changes in solution composition. RESULTS: For equilibration with CPA, our algorithm predicts an optimal first step consisting of exposure to a solution containing only water and CPA. This is predicted to cause the cells to initially shrink and then swell to the maximum cell volume limit. To reach the target intracellular CPA concentration, the cells are then induced to shrink to the minimum cell volume limit by exposure to a high CPA concentration. For post-thaw equilibration to remove CPA, the optimal procedures involve exposure to CPA-free solutions that are predicted to cause swelling to the maximum volume limit. The toxicity associated with these procedures is predicted to be much less than that of conventional procedures and comparable to that of the corresponding procedures with continuous changes in solution composition. CONCLUSIONS: The piecewise-constant procedures described in this study are experimentally facile and are predicted to be less toxic than conventional procedures for human oocyte cryopreservation. Moreover, the mathematical optimization approach described here will facilitate the design of cryopreservation procedures for other cell types.

Foundations of modeling in cryobiology-I: concentration, Gibbs energy, and chemical potential relationships.

Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and refinement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are significant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from first principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these effects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simplification arguments that are often made in heat and mass transport. In this first part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials.

Rationally optimized cryopreservation of multiple mouse embryonic stem cell lines: II--Mathematical prediction and experimental validation of optimal cryopreservation protocols.

In Part I, we documented differences in cryopreservation success measured by membrane integrity in four mouse embryonic stem cell (mESC) lines from different genetic backgrounds (BALB/c, CBA, FVB, and 129R1), and we demonstrated a potential biophysical basis for these differences through a comparative study characterizing the membrane permeability characteristics and osmotic tolerance limits of each cell line. Here we use these values to predict optimal cryoprotectants, cooling rates, warming rates, and plunge temperatures. We subsequently verified these predictions experimentally for their effects on post-thaw recovery. From this study, we determined that a cryopreservation protocol utilizing 1M propylene glycol, a cooling rate of 1°C/minute, and plunging into liquid nitrogen at -41°C, combined with subsequent warming in a 22°C water bath with agitation, significantly improved post-thaw recovery for three of the four mESC lines, and did not diminish post-thaw recovery for our single exception. It is proposed that this protocol can be successfully applied to most mESC lines beyond those included within this study once the effect of propylene glycol on mESC gene expression, growth characteristics, and germ-line transmission has been determined. Mouse ESC lines with poor survival using current standard cryopreservation protocols or our proposed protocol can be optimized on a case-by-case basis using the method we have outlined over two papers. For our single exception, the CBA cell line, a cooling rate of 5°C/minute in the presence of 1.0M dimethyl sulfoxide or 1.0M propylene glycol, combined with plunge temperature of -80°C was optimal.