2001 by Xytex Corporation. All rights reserved. This document may be viewed and copied from www.xytex.com.

1

CRYOBIOLOGY 2001 FOR MAMMALIAN EMBRYOLOGISTS

Armand M. Karow, Ph.D. Xytex Corporation

Augusta, Georgia, USA

Introduction 1

Heat 3

Properties of Pure Water/Phase Separation 5

Aqueous Solutions/Phase Separation 11

Crystal Development and Growth 17

Vitrification 20

Living Cells at Cryogenic Temperatures 22

References 32

Acknowledgment 38

INTRODUCTION

Just as embryology has grown beyond a descriptive discipline into a molecular science, cryobiology is very much part of biophysics, a quantitative science. For any embryologist to make a substantive contribution to cryopreservation of reproductive tissues, it is essential to understand that modem cryobiology no longer recognizes a “witch’s cauldron” as a laboratory device. Clearly, there are important advances to be made in cryopreservation of reproductive tissues, including tissues from

humans. Human sperm survive cryopreservation very poorly. A random ejaculate from the general population is unlikely to have 50 percent motile cells when thawed. But five percent of the general population has an excellent postthaw semen analysis. What is different genetically about this five percent and their cell biology? And how can technology improve the results for everyone? Postthaw survival of human embryos is only marginally better, and for unknown reasons. Even more dramatic is the lack of knowledge that obstructs postthaw survival of oocytes sufficient for fertilization,

Cryobiology 2001

2

implantation, and ultimately, live births. Also frustrating is the lack of explanation for species variability. Every clinical embryologist would benefit from knowing why sperm from murine or porcine sources is more resistant to present cryopreservation procedures than human sperm or why bovine sperm is more tolerant. A major factor contributing to these poor results is that much of the cryobiology being done by embryologists is empirical, based on “rules of thumb” rather than basic principles and solid knowledge. The purpose of this review is to serve as a literature guide for embryologists wanting fundamental knowledge of cryobiology relevant to cryopreservation of reproductive tissues. Much of this literature is based on physical chemistry and is therefore mathematical. Regardless of the effort needed to acquire this knowledge, an embryologist wanting to make a substantive contribution to cryobiology will be rewarded by mastering it. Since cryopreservation fundamentally is about the removal of energy from living systems, a study of cryobiology necessarily begins with a consideration of energy, thermodynamics. Since a major consequence of the energy fluctuation in cryobiology is the solidification of liquid water, this process is considered early on, for both pure water and mixtures. All of this is a necessary prelude to understanding the cryobiology of cells (spermatozoa), tissues (oocyte-cumulus complex; embryo), and vascularized organs (gonads). Furthermore, the embryologist is strongly encouraged to learn from the successes and failures of others attempting to cryopreserve their cells, tissues or organs. Clearly, the volume of information cannot be presented in a short paper. The objective of this document is to present a narrative overview with selected references to published literature providing the scientific foundations.

Karow, A.M., Critser, A.M. editors. Reproductive Tissue Banking. Scientific Principles. San Diego. Academic Press, 1997.

Mandelbaum, J., Menezo, Y.J.R.

Cryopreservation of human embryos. In Textbook of Assisted Reproductive Techniques

(ed D. Garner). 2001. Pegg, D.E., Karow, A.M. editors. The

Biophysics of Organ Cryopreservation. New York: Plenum, 1987.

Cryobiology 2001

3

HEAT

Heat is, of course, a form of electromagnetic energy, radiation. Heat is certainly manifested by radiation, but in biological systems, heat is usually manifested by its effect on molecular motion: translational, rotational and vibrational. Heat is expressed in SI nomenclature as joules. Joules are related to calories in that 1 calorie = 4.184 joule. One calorie is the amount of heat required to raise the temperature of 1g water at 15°C by 1°C. Temperature is a manifestation of the average translational kinetic energy of molecules due to heat. Temperature (T) is expressed in SI as degree Kelvin (°K) where absolute zero is 0°K. Since the degree intervals for Kelvin and Celsius scales are identical, absolute zero is -273°C and 0°C is set as the temperature of melting ice under standard atmospheric pressure (101 x 103 Pascals). Heat energy can do work only through a change of temperature. Free energy (Gibbs free energy; thermodynamic potential) can do work at constant temperature and pressure. Entropy is energy in a state of randomness, unavailable to do work. Changes in heat (T), free energy (∆G) and entropy (∆S) in a system at constant temperature and pressure, are related to each other by

∆G = ∆H - T∆S

where ∆H is the change in heat content, namely, enthalpy. Units of measurement for ∆G and ∆H are joules mole-1 and for ∆S, joules degree-1. Specific heat, like enthalpy, is a measure of heat content. Chemical potential is a property of a substance equivalent to its molar free energy. Chemical potential determines whether a

Cryobiology 2001

4

chemical reaction or physical process (such as diffusion) will take place. A substance will tend to pass spontaneously to a state or condition of lower chemical potential. The chemical potential is influenced by pressure and temperature. For molecules to participate in a reaction, whether chemical or physical (e.g. phase transition), they must possess energy equal to or greater than the activation energy (Ea) for that event (Figure 1). The temperature of a space (a volume) containing molecules will determine the proportion of molecules that exceed Ea. Living cells obtain their free energy from nutrient molecules or from light (e.g. the sun). Alberty, R.A. Physical Chemistry 7th Edition.

New York: John Wiley & Sons, 1987. Atkins, P. Physical Chemistry 6th Edition.

New York: W. H. Freeman, 1998. Maron, S.H., Lando, J.B. Fundamentals of

Physical Chemistry. New York: MacMillan, 1974.

Figure 1. Energy Distribution Curves for a Population of Molecules at Two Different Temperatures (T). The average energy of the molecules (dashed lines) is indicated by the temperature of the population. Molecules having energies equal or greater than the activation energy (Ea) are reactive as indicated by the shaded area; there are more of these molecules in the high T population.

Cryobiology 2001

5

PROPERTIES OF PURE WATER/PHASE

SEPARATION

Liquid water (HOH) is a bipolar molecule with strong intermolecular attractive force. Electrostatic forces create hydrogen bonds (H-bonds) between water molecules and other species such as sugars and alcohols and those with electrical charges such as ions and proteins. H-bonds between water molecules give water an usually high viscosity (Figure 2) and give rise to “flickering clusters” so that water behaves as if it had a molecular mass greater than 18. Water molecules dissociate into hydronium and hydroxyl ions:

2HOH ⇔ H3O+ + OH−

Considering the isotopes of hydrogen and oxygen, there are at least 33 chemical derivatives of HOH. Water exists in three phases: gas (vapor), liquid and crystalline. Each phase is determined by temperatures and pressure (Figure 3). At 101 x 103 Pa (atmospheric pressure), liquid water and crystalline ice co-exist at 0°C. The phase diagram of pure water illustrates that pressure alters the freezing point (line CO) and the boiling point (line AO) of water. When pressure is applied to liquid water, the ability of water molecules to escape as vapor is decreased. The temperature must be raised to provide energy for liquid to vaporize. At temperatures above 374°C, the “critical temperature,” water

Figure 2. Viscosity of Pure Water as a Function of Temperature (T). As the temperature is increased, the liquid becomes more fluid. Note the viscosity of supercooled water, liquid to -10°C.

Figure 3. Phase Diagram of Frozen Pure Water. See text for discussion.

Cryobiology 2001

6

Phase Transitions for Pure Water Pressure Boiling Point Freezing Point(Pa x 103) (0oC) (oC)

0.6 0.0098 +0.0098 101 100 0.0

22,100 374 ca. –2.0 193,100 374 -20

molecules have sufficient energy that they will not liquify regardless of pressure (A); the meniscus disappears!

Vapor pressure is, of course, the

pressure at a given temperature that the vapor phase co-exists in equilibrium with either the liquid or solid phases. Crystalline ice will vaporize (sublimate) therefore, it has a vapor pressure (line BO). Water can remain liquid at temperatures below 0°C and so it too has a vapor pressure (line DO) higher than that of ice.

Vapor Pressure (Pa) for Pure Water Temperature Ice Liquid

(°C) -90 0.01 ---- -80 0.53 ---- -70 .027 ---- -60 1.33 ---- -50 4.00 ---- -40 13.30 ---- -30 40.00 ---- -20 107.0 ---- -15 165.0 192.0 -10 260.0 287.0 -5 401.0 427.0 0 611.0 611.0 10 ---- 1,230.0 20 ---- 2,330.0 30 ---- 4,240.0

Cryobiology 2001

7

Ice depicted in Figure 3 is ice I, there being at least six other distinct types, depending upon temperature (-100 to 100°C) and pressure (ranging through 10,000 atm). These are discussed by Fletcher and by Hobbs.

Although 0°C is commonly called “freezing point” (FP) of pure water at atmospheric pressure, crystallization of the liquid is initiated at a lower temperature. It is essential to understand that 0°C is the “equilibrium freezing point,” meaning the temperature at which ice crystals and water co-exist in equilibrium. Adding heat to this mixture will increase the amount of liquid; removing heat will increase the amount of ice. The “equilibrium” is between the solid and liquid phases. Therefore it is acceptable, speak of “equilibrium melting point.”

For pure water at atmospheric pressure to crystallize, it must be cooled below the equilibrium freezing point. At some temperature below 0°C crystallization will initiate. When crystallization of pure water commences, the temperature of the solid-liquid mixture rises to 0°C . The temperature difference (∆T) between 0°C and the temperature at which crystallization begins is the extent of supercooling (also called undercooling) (Figure 4). Once crystallization begins, the latent heat of fusion (334 joule for each g) is released causing the temperature to rise to the equilibrium freezing point (0°C) and the temperature remains at 0°C until all of the water is converted to ice. Further removal of heat (dependent upon the specific heat of ice) results in lowering the temperature of ice.

A freezing curve as shown in Figure 4 can be obtained only with small volumes (less than 1 mL) of water; larger volumes obscure details because of difference in thermal conductivity of ice and liquid water.

Figure 4. Freezing Curve of Pure Water. See text for discussion.

Cryobiology 2001

8

Temperatures in such small volumes can be measured reliably with thermocouple instrumentation (copper-constantan) in association with an electronic read-out device that compensates for non-linearity. The cooling rate and the freezing rate are two different measurements. The cooling rate is the rate of temperature change, i.e. °T min.-1. The freezing rate is the rate of ice formation, i.e. g min.-1. For pure water, freezing occurs at one temperature. For aqueous solutions, as discussed in the next section, freezing occurs over a range of temperatures. The freezing rate can be calculated from direct observation with a cryomicroscope (Cosman et al.) or from calorimetry (MacFarlane et al.). Thermal conductivity is important to cryobiologists because heat must move through both liquid and crystals during cooling and warming of samples. As shown in Figure 5, the thermal conductivity of ice changes with temperature and is considerably greater than that of liquid water, which acts as a thermal insulator. Thermal conductivity profoundly influences the mechanical integrity of aqueous samples undergoing freezing or thawing. More will be said about sample size in the discussion of living tissues. Crystallization of a solid phase from a liquid phase requires the presence of centers (“nuclei”) onto which the solid phase can condense. An effective nucleus is one consisting of molecules resembling the solid (crystalline) phase. In pure water, clusters of H-bonded water molecules serve as nuclei; this process is called homogenous nucleation. Obviously an energy barrier (activation energy) must be surmounted to initiate nucleation: the free energy of activation (∆G*) for nucleation at the temperature under consideration. A cluster of water molecules with a size corresponding to ∆G* is said to

Figure 5. Thermal Conductivity of Pure Water as Crystalline Ice and as Liquid. See text for discussion.

Figure 6. Energy of Activation (Ea = ∆G*) to Nucleate Sustainable Crystals (r>r*). See text for discussion.

Cryobiology 2001

9

have a “critical radius” (r*), one with an equal probability of growing or shrinking (Figure 6). Nuclei are clusters that will grow; embryos disintegrate. The main factor influencing the critical radius is extent of supercooling (Figure 7). Clearly, r* grows smaller as the extent of supercooling increases. The likelihood of small nuclei (clusters of water molecules) to be present in a given volume is greater than the likelihood of large nuclei. In fact, r* at 0°C would be infinite. Franks (1985) has calculated the number (n) of r* nuclei expected for each gram of supercooled water; temperatures of nucleation is dependent upon sample volume.

Concentration of Critical Nuclei in Supercooled Water

Temperature r* Nuclei Droplets (r=10nm) (°C) (n/g) Containing a Nucleus -10 2.3 x 10-315 8.4 x 10-449 -20 1.5 x 10-60 3.4 x 10-92 -30 3.8 x 10-14 1.1 x 10-35 -40 6.3 x 102 2.6 x 10-17 -50 7.1 x 109 ------

In pure water the limit of supercooling (at equilibrium) is -39°C because at this temperature the probability of nucleation is unity. If pure water is cooled at an exceptionally rapid rate (106°Cs-1), a temperature will be reached that thermodynamically precludes rearrangement of water molecules into crystals (Uhlmann, 1972), and therefore, an amorphous solid, a glass, forms. Nucleation can also be initiated by factors that add energy to the liquid, such as mechanical agitation, electric field or irradiation; the mechanism is unknown. Even the wall of the container can nucleate the crystallization of water. In reality it is extremely difficult to supercool a large volume of water (e.g. > 1mL) regardless of the purity.

Figure 7. Critical Radius (r*) as a Function of Temperature.

Cryobiology 2001

10

For cryobiologists the ability to control nucleation of ice crystals is important. For reasons that will become apparent in subsequent discussion of living cells, a cryobiologist may prefer to have a few large crystals rather than numerous small crystals. Nucleation at high (warm) subzero temperatures will favor the former; nucleation at low (cold) subzero temperatures will favor the latter. Initiation of crystallization can be done by touching the external container wall (if thin enough) with forceps or other small object chilled to the temperature of liquid nitrogen. This process of focal cooling, called seeding, allows even very small nuclei to grow to critical radius and then to become self sustaining crystals. Angell, C.A. Supercooled water. In Water. A

Comprehensive Treatise Vol. 7 (ed. F. Franks). New York: Plenum Press, 1982. Pp 1 – 81.

Cosman, M.D., Cravalho, E.G., Kandel, J.,

Toner, M. (1989). An integrated Cryomicroscopy system. Cryo-Letters, 10:17-38.

Eisenberg, D., Kauzmann, W. The Structure

and Properties of Water. New York: Oxford University, 1969.

Fennema, O.R., Powrie, W.D., Marth, E.H..

Low-Temperature Preservation of Foods and Living Matter. New

York: Marcel Dekker, 1973. 598 pp. Fletcher, N.H. The Chemical Physics of Ice.

Cambridge University Press, 271 pp. Franks, F. The properties of ice. In Water. A

Comprehensive Treatise. Vol. 7 (ed. F. Franks) New York: Plenum Press, 1982. Pp 115 – 149.

Franks, F. Biophysics and Biochemistry at Low Temperatures. Cambridge: Cambridge University Press, 1985.

Hobbs, P.V. Ice Physics. Oxford: Oxford University Press, 1974.

MacFarlane, D.R. Kadiayala, R.K., Angell,

C.A. (1983). Homogeneous nucleation and growth of ice from solutions. TTT curves, the nucleation rate and the stable glass criterion. J. Chem. Phys.

79: 3921 – 3927. Uhlmann, D.R., Chalmers, B. (1965). The

Energetics of Nucleation. Indust. Chem. September 1965.

Uhlmann, D.R. (1972). The kinetic theory of

glass formation. J. Non-crystalline Solids. 7:337.

Zettlemoyer, A.C. Nucleation. New York:

Marcel Dekker, 1969.

Cryobiology 2001

11

AQUEOUS SOLUTIONS/PHASE

SEPARATION

Dissolving substances (solutes) in water (solvent) greatly alters thermal properties of the solution. This is of obvious importance to cryobiology since life exists in aqueous solutions rather than pure water. The chemical potential of the pure liquid is greater than the chemical potential of the liquid solvent. The equilibrium freezing point is depressed by solutes in water as given by Raoult’s law. Solutes lower chemical potential and vapor pressure of a solvent. Solute molecules compete with solvent molecules for the phase interface (e.g. liquid/vapor), decreasing the opportunity for solvent molecules to escape as vapor. Solute molecules also interfere with access of solvent molecules to the crystal surface. In these ways vapor pressure of solvent is decreased by solute, an effect that results in depression of the equilibrium freezing point. To illustrate the depression of the equilibrium freezing point, Figure 3 may be redrawn as shown in Figure 8. As the temperature of pure water decreases, its vapor pressure also decreases. At the equilibrium freezing point of water (To), ice formation occurs and the vapor pressure curve becomes that of ice (AB). The vapor pressure of the solution, lower than that of the solvent, also decreases with temperature. The vapor pressure curve of the solvent intersects the vapor pressure curve of ice at temperature Ts at which point the solution begins to freeze. The solute has depressed the freezing point by To – Ts, or ∆T. For dilute aqueous solutions, that is with a solute concentration less than 0.01M, the molal freezing-point constant (Kf) is 1.86 so that

∆T = Kfm

Figure 8. Vapor Pressure of Pure Water and of an Aqueous Solution as a Function of Temperature. See text for discussion.

Cryobiology 2001

12

where m is the molality (mol kg-1) of the solution. This relationship approximates reality only for very dilute solutions, of non-dissociating species such as sucrose. For electrolytes, the relationship would hold true only in situations in which there is complete dissociation, and then, each ionic species behaves independently. Therefore, 0.01 mole of NaCl in 1 kg water would behave similarly to 0.02 mole of a non-electrolyte, depressing the freezing point by 0.037 °C. Freezing point depression means that supercooling will occur prior to nucleation, but after nucleation, the temperature will “rebound” to a point colder than the freezing point of pure water (Figure 9). This point, however, will not be a plateau as it is with pure water, rather it will grow increasingly colder as heat is removed. This downward slope occurs because the solute concentration rises in the solvent. Ice forms and decreases the amount of solvent liquid. Vapor-pressure depression, like several other properties of solution (freezing-point depression, boiling-point elevation, osmotic pressure) is dependent upon the number of particles in solution, not their kind. These are called colligative properties. As shall be demonstrated, vapor pressure is as important for cryobiologists as is osmotic pressure for general biologists. Furthermore, the possibility of altering freezing point depression by applying external pressure is an experimental approach of some cryobiologists. Like molality, another means of expressing concentration used frequently in discussion of colligative properties is mole fraction. Mole fraction of a substance in solution is equal to the number of moles of that substance divided by the total number of

Figure 9. Freezing Curve of an Aqueous Solution of a Non-electrolyte (e.g. Monosaccharide). See text for discussion and Fig. 4.

Cryobiology 2001

13

moles in solution including all solutes and solvent. The sum of all the mole fractions of a solution equals unity, of course. Mole fraction is logarithmically related to chemical potential. Unlike molarity, molality and mole fraction are independent of temperature. Nucleation of supercooled water usually occurs in the temperature range of –2 to -10°C because water generally is not pure; it contains solutes or suspended material that serve as nuclei. Many different materials in the liquid may act as nuclei. Some organisms actually synthesize proteins that function to nucleate supercooled water: these are ice nucleating proteins (INP). The radius of this material will be greater than that of H-bonded water clusters, therefore r* will be attained at temperatures warmer than is possible with pure water. This process is termed hetergenous nucleation in contrast to homogeneous nucleation in pure water. As demonstrated for pure water, the temperature at which nucleation actually occurs depends upon several factors, including sample size and rate of cooling. In aqueous mixtures the limit of supercooling is also depressed by solutes and viscosity. In a 50 percent (w/v) aqueous solution of polyvinylpyrrolidone, a sample cooled at 300°Cs-1 will not nucleate; a sample cooled at 80°Cs-1 will nucleate, but crystal growth will be negligble (at temperatures below -60°C); a sample cooled at 20°Cs-1 will nucleate and exhibit crystal growths (at temperatures above -40°C). The viscosity of a liquid is a function of temperature as previously shown for water (Figure 2). The viscosity of water at room temperature is approximately 0.9 x 103 Pa and glycerol, 1410. (These units correspond to centipoise.) As temperature decreases, additional H-bonds form between solute molecules and between solute and solvent, causing an increase in viscosity. The viscosity

Cryobiology 2001

14

of a 1:1 mixture of glycerol and water (v/v) at +20°C is 6.3 and at -20°C, 80 cP. Viscosity of a 1:1 mixture of ethylene gylcol and water at -10°C is 18 cP; -20°C, 32 cP; -30°C, 63 cP; -40°C, 125 cP. The thermal history of an aqueous solution of a generic monosaccharide being frozen in equilibrium conditions illustrates the physical events (Figure 9). As the solution is cooled below 0°C, supercooling occurs (S). When nucleation occurs, latent heat of fusion is released, but the equilibrium freezing point will be cooler than 0°C because of freezing point depression. Furthermore, the temperature of the solution will continue to fall as the freezing process continues and the quantity of ice increases. This is because crystallization ideally excludes extraneous material, namely sugar. Therefore the sugar concentration rises in the remaining liquid, further depressing the freezing point of that liquid. At some temperatures (-15°C in the figure), the extraneous material also crystallizes; this is called the “eutectic temperature” or “eutectic point” (Te). At the eutectic, a form of supercooling called supersaturation (SS) occurs. At Te, the ratio of solute to solvent will be constant. Crystals of pure water and of pure solute (sugar) will intermingle. Cooling below Te will occur only after the solution has solidified completely. The freezing history shown in Figure 9 can be demonstrated only for small sample volumes, i.e., less than 1mL that are cooled slowly enough to maintain equilibrium. Rapid cooling will result in solute inclusion in ice crystals (Figure 10). The phase diagram of an aqueous solution is usually represented as shown in Figure 11. The freezing point for pure solvent (Tf) is at A. The eutectic point (Te) is at B. Although curve AB represents an equilibrium between the liquid solution and crystalline ice, it is referred to as the “freezing

Figure 10. Freezing Curves of Aqueous Solution (see Fig. 9) Cooled Slowly (A), Faster (B) and Even Faster (C).

Cryobiology 2001

15

point curve” or “liquidus” which is dependent of the initial concentration of solute. Of course, this is also the “melting curve.” Clearly, the concentration of solute increases as freezing progresses with the lowering of temperature. It is proper to think of this loss of liquid water as a kind of dehydration. During freezing of electrolyte solutions, these changes can alter pH as discussed by Taylor. Chemical reactions can also occur in the concentrated solution as discussed by Douzou and by Franks (1985). Line BD, representing the equilibrium between the liquid and crystalline sugar hydrate, is called the “solubility curve;” dissolution of high concentrations of solute may require T>Tf. Supersaturation, represented by BC, often occurs in simple systems of high viscosity and is even more likely in complex systems such as cellular cytoplasm. The fact that solutes depress the limit of supercooling, the temperature of homogeneous nucleation (Th), is also illustrated by Figure 11. Methods such as the ones devised by Fahy and by Pegg are available for calculating phase diagrams for more complex solutions. Some solutes are especially difficult to nucleate. Glycerol, for example, has a eutectic of -45°C, but it seldom if ever crystallizes at that temperature. Glycerol simply becomes supersaturated and increasingly viscous as it is cooled below its eutectic. Nucleation of glycerol can be accomplished by seeding with a crystal of glycerol. In the absence of crystallization, vitrification takes place, giving rise to a glass, a process that will be discussed subsequently. Atkins. Op. Cit. Ben-Naim, A. Water and Aqueous Solutions.

Introduction to a Molecular Theory. New York: Plenum, 1974.

Figure 11. Phase Diagram of Frozen Aqueous Solution. See text for discussion and Fig.9.

Cryobiology 2001

16

Douzou, P. Cryobiochemistry. London, Academic Press, 1977.

Fahy, G.M. (1980). Analysis of “solution

effects” injury. Equations for calculating phase diagram information for the ternary systems NaCl – dimethysulfoxide-water and NaCl – glycerol-water. Biophysics J 32: 837-850.

Fennema et al. Op. Cit. Franks, F. Op. Cit., 1985. Pegg, D.E. (1986). Equations for obtaining

melting points and eutectic temperatures for the ternary system dimethyl suplhoxide/sodium

chloride/water. Cryo-Letters 7: 387. Taylor, M.J. (1981). The meaning of pH at

low temperatures. Cryo-Letters, 2: 231-239.

Cryobiology 2001

17

CRYSTAL DEVELOPMENT AND

GROWTH

Crystal growth begins as soon as nuclei with r* exist in the supercooled liquid (Fletcher). Ice continues to form while supercooling exists and ends when the equilibrium amount of ice has been formed. The rate of crystal growth depends upon factors including the rate at which water molecules diffuse to and solute molecules diffuse from the ice-liquid interface, the rate of removal of latent heat, and the extent of supercooling. It is helpful to distinguish between equilibrium freezing and perturbed freezing. Equilibrium freezing occurs when the force driving the freezing, namely the environmental temperature, is about the same as the temperature of the freezing system. Perturbed freezing occurs when the temperature difference (∆T) is quite large. The concentration of crystals depends upon the concentration of nuclei, which is dependent upon ∆T. During equilibrium freezing the sample will be at relatively high temperatures for a longer period than with perturbed freezing; at these high temperatures, the rate of nucleation is low so that a few crystals form and then grow quite large. During perturbed freezing the sample is cooled rapidly so that many nuclei form but grow very little because of the intense competition for available energetic (“liquid”) molecules. Crystal growth is often quantified in terms of linear crystallization velocity (Figure 12). Crystallization velocity increases with increased supercooling (∆T prior to initial nucleation) and decreases with increasing solute concentration or solute molecular mass. A disadvantage of linear crystallization velocity measurements is its focus on growth

Figure 12. Linear Crystallization Velocity as a Function of Supercooling (∆T).

Cryobiology 2001

18

of the ice front rather than the growth of individual crystals as found in real systems. An alternative analysis of crystallization rate is the so-called TTT (time-temperature transformation). This relates the time taken to crystallize a given fraction of the supercooled liquid to the temperature (Figure 13). Experimentally, the crystallization rate is measured by quenching the solution at an appropriate temperature (T) and measuring the time for ice to crystallize at T either calorimetrically (MacFarlane et al.) or visually with a microscope (Cosman). Morphology of ice crystals is extremely complex (Hobbs; Luyet). Marginally different experimental conditions will create a variety of habits including needles, feathers, spherulites, dendrites or even “pineapple skin” (Figure 14). Morphology is greatly influenced by rate of cooling, extent of supercooling, and presence of solutes. Solutes affect crystal complexity because they create gradients of concentration and temperature. The advancing ice front ejects solutes that accumulate at the interface, giving rise to a concentration gradient. This results in the local freezing point in front of the interface being lowered and a decrease in the freezing rate. Local areas of supersaturation (constitutional supercooling) develop giving rise to irregular or discontinuous interface (Figure 15). Constitutional supercooling explains how the temperature of the liquid phase can be higher than the interface yet be supercooled in a functional sense. Recrystallization is the formation of larger crystals from smaller ones. Small crystals are thermodynamically less stable than larger. Since small crystals have relatively high surface to volume ratios, they have higher surface free energies than larger crystals. Recrystallization reduces free energy of the frozen systems. Two important mechanisms

Figure 13. Time-Temperature-Transformation Curves of Crystallization in a Generic Aqueous Solution of Electrolyte. Solutions, either high concentration (Curve B) or lower concentration (Curve A) were allowed to freeze at a temperature indicated on the ordinate. The time of crystallization was determined by scanning calorimetry. Note that the time is dependent upon concentration and viscosity. The upper branch of the curve (or “nose”) indicates nucleation limited crystallization; the lower branch, the freezing process.

Figure 14. Morphology of Ice Crystals Grown in Aqueous Solutions. Number 1 – 7: growth of regular hexagonal forms. Number 8 – 14: irregular dendrites. Number 8 illustrates concentric layers of ice. Number 9 – 14 illustrate arborescent structures typical of high cooling rates. Number 15 and 16 represent transitional forms intermediate between irregular dendrites (8 – 14) and spherulites (17 and 18). From Luyet and reproduced by permission of publisher.

Cryobiology 2001

19

of recrystallization are accretion (the joining of two crystals) and migration or Ostwald ripening (small crystal subliming). The rate of Ostwald ripening depends upon viscosity of the liquid. Temperature gradients and fluctuations accentuate recrystallization, making this a prominent component of thawing. Cosman, et al. Op. Cit. Fletcher, Op. Cit.

Hobbs, Op. Cit.

MacFarlane, Kadiyala, Angell, 1983. Op. Cit. Luyet, B.J. Physical changes occurring in

frozen solutions during rewarming and melting. In The Frozen Cell (editors G.E.W. Welstenholm, and M. O’Connor). London: J & A Churchill, Pp. 27 – 50.

Figure 15. Growth of Ice in a Concentrated Aqueous Solution. Solid ice (S) grows into the liquid phase (L). Growth occurs by incorporating “liquid” molecules at the interface into the solid crystal. This causes the concentration of the liquid at the interface to be higher than the concentration in the liquid away from the interface; CG>CC.

Cryobiology 2001

20

VITRIFICATION

The vitreous state is essentially a solidified, amorphous liquid state obtained by cooling the liquid so rapidly that crystallization is precluded (Yannas). Translational and rotational motions of molecules are arrested and the viscosity is very high, perhaps 1014 Pa•s (Viscosity of water at 25°C is 0.8 mPa•s.) The vitreous state is a non-equilibrium (i.e. metastable) state. Attainment of this state is facilitated by the presence of solutes which diminish the required rate of cooling. Since there is no change of phase in vitrification, there is no latent heat. A block of vitrified water is “crystal clear,” transparent rather than opaque (Fahy, 1984). Vitrification is of interest to cryobiologists because it avoids many of the lethal effects of freezing, yet it presents a different set of problems. These will be discussed in the last section (Living Cells); here the physical process of vitrification is outlined. Figure 11 may be drawn with detail relevant to vitrification (Figure 16). Crystallization of solvent is possible in the region between curves Tf and Th. In this region r* for a nucleus decreases from infinite to that of a “flickering cluster” of H-bonded water molecules. Below Th crystallization depends upon recrystallization (Tr), the growth of crystals from clusters of water molecules. As T becomes colder, the likelihood of these molecules attaining Ea decreases and approaches zero. Similarly, the likelihood of crystallization of solute decreases. So at some temperature the solution solidifies as a glass; it vitrifies. Previously formed crystals are imbedded in the glass. The opportunity for vitrification is dependent upon solute concentration and T as represented by Tg, or glass transition curve. To make a glass with a minimum of embedded ice crystals, one must use high

Figure 16. Phase Diagram of Aqueous Solution of Cryoprotectants. See text for discussion and Figure 11.

Cryobiology 2001

21

concentrations of solutes and also to cool as quickly as possible to a temperature below Tg. Embedded ice crystals will grow when the glass warms above Tg. Devitrification (Td) is crystallization in a vitrified system. Nucleation and crystal growth is more rapid during warming through Td than it is during initial cooling to Tg. Devitrification occurs because the optimal temperature for nucleation is colder than that for crystal growth. During initial cooling the temperature for crystal growth is attained before the temperature producing the maximum number of nuclei. During the warming of a glass, the system produces a large number of nuclei, then warms to temperatures supporting crystal growth and to temperatures favorable for recrystallization (Tr). The process of devitrification and recrystallization are so quick that when observed through a microscope the opacification is called “flashing”; these processes can be mathematically modeled (Boutron; Martino). For cryobiologists it is important to note that the application of high pressures (1 – 2,000 atm) depresses Tf and Th. High pressures elevate Tg by enhancing viscosity, forcing molecules closer together. Boutron, P., Mehl, P. (1990). Theoretical

prediction of devitrification tendency: determination of critical warming rates without using finite expansions. Cryobiology 27: 359-377.

Fahy, G.M., MacFarlane, D.R., Angell, C.A., Meryman, H.T. (1984). Vitrification

as an approach to cryopreservation. Cryobiology 21: 407-426.

Franks, F. 1982. Op. Cit. Franks, F. 1985. Op. Cit.

MacFarlane, D.R. (1986) Devitrification in glass-forming aqueous solutions. Cryobiology 23:230-244.

MacFarlane, D.R. (1987) Physical aspects of

vitrification in aqueous solutions. Cryobiology 24:

Martino, M.N., Zaritzky, N.E. (1989). Ice

recrystallization in a model system and in frozen muscle tissue. Cryobiology 26: 138-148.

Uhlmann, D.R., 1972. Op. Cit. Yannas, I. (1968). Vitrification temperature

of water. Science 160: 298-299.

Cryobiology 2001

22

LIVING CELLS AT CRYOGENIC TEMPERATURES

Cryopreservation of living cells,

including those of interest to a mammalian embryologist, involves chilling and even freezing or vitrifying cells in order to put their life “on hold.” For either freezing or vitrification to maintain vital functions of the cells, cooling, warming and solute concentrations must be managed in a way to favor survival and to minimize injury. Management is considerably benefited by application of physical knowledge. First some general concepts will be considered. Living cells can be injured by reduction in temperature, by ice crystals, by osmotic forces, and by chemical toxicity. The effect of heat, or its loss, from simple physical systems has been the focus of this discussion so far. Now, living systems are included in that focus including the complication of metabolism. The thermal influence on chemical reactions is more complex than that of physical processes – such as water diffusion, osmotic pressure, thermal linear expansion and ice formation. The change in the rate of such physical processes as a result of change in temperature is proportional to the fractional change in absolute temperature. For example, a physical reaction cooled from 37°C (310°K) to 27°C (300°K) is reduced by a factor of 100 x (310 – 300)/310, or about 3 percent. On the other hand, metabolic reactions depend upon Ea, the energy of activation (Figure 1). For every 10°C reduction, there is about a 50 percent decrease in the rate of these reactions in accordance with the Arrhenius relationships (Atkins). Chilling alone has profound effects on cells, and freezing may be lethal.

Cellular metabolism is organized in a complex aqueous gel within a cell membrane. The cell membrane, composed primarily of a

Cryobiology 2001

23

bimolecular layer of phospholipids, is metabolically active, the function of which in large measure is to regulate the cellular content. Quantitatively the major component of cells is water. Proteins are a major component of cellular gel. The membrane controls a bi-directional flux of materials, including water, other electrolytes and nonelectrolytes. In turn, the structural integrity of the membrane is determined by temperature and composition of the solution on either side. Similar membranes define intracellular structures, especially the nucleus and mitochondria; they also form the endoplasmic reticulum. Membranes are complex and dynamic (Hammerstedt; Parks). Embedded in the lipid bilayer are proteinaceous channels, pores (aquaporin; glycerol pores), transporters, enzymes, and receptors (Fu; Karow; Yang). The cell membrane is asymmetric, its outer surface coated with a glycocalyx and absorbed protein. Membranes are polymorphic in that the cell membrane, usually in a planar configuration, can also take on a localized polycylindrical form (hexagonal, HII) during fusion, vesiculation, or instances of “stress.” Nuclear membranes actually dissolve during mitotic events. The polymorphism is sensitive to temperature and salt concentrations (Drobnis; Giraud; Hammerstedt; Morris; Parks; Wolf; Zenes). Additionally, chilling lipids results in their “hardening,” becoming mechanically brittle. Thermal injury, chilling injury, or thermal shock are terms referring to adverse effects of cooling alone on cell membranes. These effects may be studied by calorimetry (Morris). Cell membranes are adversely affected by osmotic shock. If relatively simple cells such as erythrocytes are thought of as semipermeable balloons filled with an isotonic liquid and also suspended in an isotonic

Cryobiology 2001

24

medium, they would shrink (“deflate”) when frozen. This is because the external solution becomes hypertonic during freezing (Figure 17). The viscous, proteinaceous intracellular solution is less likely to crystallize than the fluid extracellular medium. Since the vapor pressure of the intracellular material, being a liquid, is greater than the vapor pressure of extracellular ice, it forces intracellular water into the extracellular space where it freezes; the cells shrink. A portion of intracellular water, bound to protein, is unfreezable. Any freezable water remaining in the cell will freeze. Shrunken cells are trapped between extracellular ice crystals (Figure 18). Upon rewarming, ice melts diluting the extracellular medium and allowing reexpansion of cells. Cytolysis usually takes place. These osmotic events can be experimentally followed by microscopy or simulated mathematically. The flow of water across each unit of cell surface as a function of time (hydraulic conductivity or hydraulic coefficient; Lp) can be calculated based upon measurements of cell volume. Cell volume can be easily measured with an optical densitometer, an electronic particle counter, or by microperfusion (Agca; Gao; Paynter), or microscopically (McGrath, 1997) or by microperfusion (Agca; Gao, 1996; Paynter) or by stopped-flow fluorescence (Cury). Volume measurements made in several hyperosmotic strengths, when plotted against the reciprocal of the osmolarity (Figure 19), gives the osmotically inactive volume of the cell its “b” value. Measurements must be repeated for various temperatures. Since experimental conditions affect cell permeability, measurements under these conditions are important for validity. Furthermore, there is great variability in permeability between cell

Figure 17. Water in Cellular System Converted to Ice As a Function of Temperature. Note that upon the initiation of ice formation in a cellular system, a large amount of liquid is converted to ice at very high temperatures.

Figure 18. Freezing and Thawing Erythrocytes Without Cryoprotectants. Upper panel: Cooling cells from -1°C to -10°C. At -1°C the cells suspended in supercooled medium. At -3°C ice formation begins; the cells are located in liquid filled channels between ice crystals. At -7°C cells are visable distorted by exosmosis intracellular water. Some original cells are no longer in the field. Lower panel: Warming cells from -7°C to 0°C. Cells cytolyse during rehydration.

Cryobiology 2001

25

types and even species among mammals. In fact, fertilization alters oocyte permeability. The cell volume and the “b” value are used to solve for Lp using classical diffusion equations (Karow, 1997; Rule).

The biological definition of “slow cooling” is cooling that results in ice crystallization only in extracellular spaces. The complete reason that intracellular crystallization is precluded by slow cooling is not known; maybe cellular freezing occurs so rarely that it is not observed or that no evidence remains after its occurrence. The biological definition of “fast cooling” is cooling that results in intracellular freezing or intracellular ice formation (IIF). IIF is considered to be lethal, perhaps because of disruption of cytoarchitecture. Conceivably IIF consisting of only homogeneous nuclei would be non-lethal, but such crystals are predisposed to grow. The generation of such “crystals” would be tantamount to vitrification. Perhaps this is happening when human crythrocytes suspended in a simple medium survive as droplets sprayed on the surface of liquid nitrogen (Rowe).

Mathematics allows simulation of

cellular freezing. Going from a non-frozen system to a frozen system requires consideration of the molar heat of vaporization provided by the Clausius – Clapeyron equation (Mazur, 84). The process may be followed experimentally by calorimetry (Devireddy) or with a cryomicroscope (Cosman; McGrath; Porsche). Classical nucleation theory can also predict the probability of intracellular ice (Pitt; Toner, 1990).

A major contributing factor to freezing injury is the concentration of solutes resulting from freezing. Solutes may precipitate. Concentrated electrolytes adversely affect protein conformation and consequently metabolic function. Equally important but often overlooked is the effect

Figure 19. Determination of Osmotically Inactive Cell Volume (b). Cell volume measurements at several osmolalities are extrapolated to the ordinate to obtain the b value.

Cryobiology 2001

26

of concentrating lipids and proteins. Bringing these molecules into close proximity facilitates intramolecular and intermolecular reactions, including the irreversible formation of disulfide bonds from free sulfhydryl groups. Such events causing freezing injury are frequently called “solution effects.” They could also be called “dehydration effects.” Even at subzero temperatures in the range of –1 to -5°C, the amount of liquid water converted to ice is exceptionally high (Figure 17).

Extracellular ice in a cellular system

causes injury and death by several mechanisms. Already mentioned are the osmotic consequences to cells in a frozen aqueous solution. Also of importance is the mechanical effect of ice (Figure 20). Although ice crystals probably do not “spear” or lacerate cells, ice possibly fractures cells. Lipoid cell membranes lose flexibility during chilling; they are “hardened” and resistant to deformation. Osmotic forces act to deform cells during freezing, and so do mechanical forces of ice crystals that are growing (Figure 18). These forces of deformation have not been mathematically modeled for cellular systems.

Formation of extracellular ice has greater adverse consequence for tissue and organs than for cells in suspension. Cells organized into tissue such as the cumulus-oocyte complex and embryos are bound together by cellular junctions and interact dynamically. Specialized functions of cells in tissues generally cannot be accomplished when the cells are isolated. Ice in the extracellular space of tissues and organs disrupts cellular junctions and, therefore, communication. In vascularized tissues ice forms in the micro-vasculatures causing wall lesions and, ultimately, extravasation (Fahy; Hunt; Pegg, 1987).

Figure 20. Ice Formation in Tissue in the Absence of a Cryoprotectant. See text for discussion.

Cryobiology 2001

27

Cooling and warming organs creates substantial thermal gradients (Figure 21). The cooling rate of the core is much slower than that of the surface because of differences in thermal conductivity of liquid and crystalline water (Figure 5). Since the surface freezes first, a hard shell of ice surrounds the non-frozen core. As the liquid core expands prior to freezing, the outer shell will rupture, having profound mechanical consequences: organ fracture (Rabin; Rubinsky, 1986; Webb).

Another consequence of large mass

for organs is that the rate of temperature change experienced by any cell will depend upon the cell’s location within the mass. Since the viability of frozen and thawed cells is predicated in part upon its thermal history, localized cell injury is to be expected when heat transfer is less than uniform. Furthermore, the resistance to water diffusion from a cell to an ice crystal increases with distance. Spatial separation of cells from extracellular ice will alter the probability of IIF (Diller, Raymond). Postthaw viability is also affected by the concentration of cells, a “packing effect” (Pegg, 1984).

Cryoprotectants (CPAs) are pharmaceuticals that ameliorate freezing injury from both mechanical and chemical sources (Karow). Although CPAs are not essential to postthaw survival, they enhance survival. CPAs such as dimethylsulfoxide, ethylene glycol, glycerol or propylene glycol diffuse across cell membranes and, therefore are called penetrating CPAs. These pharmaceuticals not only reduce the extent of crystallization (and therefore solute concentration), they dilute (replace) some of the freezable intracellular water and therefore partially maintain cell volume (Figure 22 and 23). They form H-bonds and can presumably stabilize protein quaternary conformation against dehydration. These drugs are used in osmotically active concentrations (0.5 – 6.0 M) so they have physical (osmotic) and pharmacological (toxic) effects on cells; both

Figure 21. Effect of Ice Formation on Thermal Conductivity of Tissue. Circles represent a sphere or cylinder of tissue. A thermocouple is placed on the surface (A) and another in the center (B) of the tissue and temperature is recorded during cooling (upper panel) and freezing. Initially, as the tissue is cooled to 0°C, the temperature of the surface falls faster than the core. Ice (hatch) forms on the surface while the core remains liquid. Lower panel: warming and thawing. The surface thaws before the core. The liquid layer, having a lower thermal conductivity than ice, acts as an insulator.

Figure 22. Liquid Water in Cellular System Converted to Ice at Different Concentrations of Cryoprotectant (Dimethyl sulfoxide; DMSO). The cryoprotectant substantially decreases the amount of liquid converted to ice.

Cryobiology 2001

28

are temperature dependent. Even with CPA, ultrastructural changes are seen in thawed sperm (Alexander; Woolley). Calculating the flux of a penetrating CPA across the cell membrane (Karow, 1997) is classically accomplished with the Kedem-Katchalsky equations taking into consideration the permeability coefficient (Ps), Ea, and the reflection coefficient (sigma) of the CPA, water and membrane. The need for including sigma in the calculations has been questioned (Katkov, 2000; Kleinhaus, 1998; Mazur, 1974). Osmometric methods for measuring cell volume provide information needed to calculate CPA flux across membrane for cells in suspension (Gao, 1997). These measurements are essential because some cells are much less permeable to penetrating CPAs than other cells. Also, temperature has a profound effect on CPA permeability. A mechanistic, integrated model (Karlsson, 1994) of water flux, intracellular ice nucleation, and crystal growth in the presence of CPA has been demonstrated for mouse oocytes (Karlsson, 1996). Abrupt addition or removal of penetrating CPAs can have adverse consequences for cells. Cells may have a “safe” minimum cell volume which, if exceeded, causes osmotic damage (Meryman). Certainly, cells can be destroyed by excessive expansion, cytolysis. Knowledge of the permeability parameters enables the design of protocols for adding and removing cryoprotectants step-wise in cell suspensions (Gao, 1997) and in perfused tissues (Pegg, 1986; Rubinsky, 1984).

A myth in cryobiology is that CPAs are non-toxic. A distinction must be made between toxicity, a biochemical or pharmacological event, and osmotic injury, a physical event. Certainly CPAs are effective at astoundingly high concentrations, but like all drugs, they are toxic. Toxicity is a function of the agent, its concentration, the time of

Figure 23. CPA Maintains Volume of Frozen Cell. Ventricular myocardium slowly cooled (1-2°C min-1) to -70°C and freeze substituted. Upper: Cardiac muscle compressed between extracellular ice (actually cavities that contained ice prior to freeze substitution) give net-like appearance. Such muscle does not survive thawing. Lower: Cardiac muscle treated with 1.4M dimethyl sulfoxide then cooled as before, frozen and freeze subtituted. The muscle retains its characteristic structure. Ice occupies 45 percent of the field. Muscle treated in this way survives thawing. From Karow and Shlafer and reproduced by permission of publisher.

Cryobiology 2001

29

exposure and temperature. Using CPAs at reduced temperatures, say 4°C rather than 37°C or 20°C may decrease toxicity but contribute to osmotic problems (Fiser). In some instances other pharmaceuticals may ameliorate CPA toxicity (Karow, 1986, 1987, 1997).

Reports of toxicity for penetrating CPAs include dimethylsulfoxide for reproductive tissue (Demirci; Heald; Johnson), and for nonreproductive tissue (Shlafer), glycerol for reproductive tissue (Dobrinsky, 1994; Hunter; Katkov, 1998; Mazur, 2000) and for nonreproductive tissue (Fahy, 1977), and propanediol for reproductive tissue (Demirci; Shaw; Van der Elst). Armitage et al. have reported that all three agents adversely affect intercellular junctions in cultured renal cells. Toxicity, as a chemical phenomenon, will be inhibited by low temperatures in accordance with the Arrhenius relationship. Freezing protocols usually strive to cool slowly enough to allow sufficient time for freezable water to exit cells, then to warm rapidly enough to preclude recrystallization of inadvertant intracellular crystals. An alternative strategy is to use CPAs at concentrations sufficiently high for vitrification. This avoids the problems of eutectic solutions and ice crystals in cellular systems. Vitrification as a means of cryopreservation has been clearly described by Fahy et al. (1984, 1987, 1990). In the absence of CPA, vitrification requires cooling rates that may exceed technological resources. CPAs, however, enable vitrification to occur at practical cooling rates. Usually, however, the required concentrations of conventional CPAs (dimethylsulfoxide; propanediol) are toxic. Some strategies to avoid this toxicity have been presented by Fahy (1986) and by MacFarlane and Forsyth.

Cryobiology 2001

30

One strategy is the use of alternative polyhydric alcohols. Glycerol (and dimethylsulfoxide) will form glasses at “practical” cooling rates only at concentrations > 45 percent. Propanediol requires a concentration of about 40 percent. Butane –2,3 diol will vitrify at concentrations in the range of 31 – 35 percent. A second strategy promoted by Fahy et al. (1984) is the addition of nonpenetrating CPAs, namely, polymers to conventional penatrating CPAs. Protein within cells is believed to limit crystallization, and polymers such as polyvinylpyrrolidone (PVP), dextran, hydroxyethyl starch, or polyethylene glycol (PEG), retained in the extracellular space, may similarly facilitate the action of penetrating CPAs. Some polymers, antifreeze proteins (AFP), block nucleation. A third strategy is the use of pressures up to 2,000 atm to lower Tf and Th and to raise Tg. Although these pressures are ordinarily injurious, compound that act as cryoprotectants also exhibit significant baroprotection. High pressure is required only during vitrification itself; subsequent storage is at ambient pressures. There is no requirement for warming to be done under pressure, but pressure may be beneficial in avoiding devitrification. To avoid devitrification and recrystallization, warming must be relatively rapid. The warming rate required to achieve this is dependent upon the CPA and its concentration:

Critical Warming Rate (°C min-1) Concentration

(% w/w) Butane

–2,3 diol Propane –1,2-diol

DMSO Glycerol

30 30*108 40 130 1.0*104 45 80 80 3330 5.6*108 50 20 50 10 4500 55 10 2100

Courtesy of R. Sutton

Cryobiology 2001

31

The critical warming rate is also influenced by the presence of polymers:

Critical Warming Rate (°C min-1)

Concentration (% w/w)

Without Polymer

+6% PEG 400

+1% AFP

+1% AFP and 6%

PEG 400

30 2.1*108 1680 31800

25000

35 6300 170 110 40

40 160 20 45 20

Courtesy of R. Sutton

Warming protocols for small volume samples (>1mL) can utilize thermal conduction (e.g. water bath). Larger sample sizes probably require use of electromagnetic heating as reviewed by several authors in Pegg and Karow (1987) and by Ruggera.

Finally, embryologists should

remember that perservation of viability is not essential in some instances. Some investigators are able to fertilize mammalian oocytes with lyophilized (freeze-dried) spermatozoa.

Cryobiology 2001

32

REFERENCES Alexander, N.J. (1976). Surface structure of

spermatozoa for artificial insemination. Andrologia 9: 155. Armitage, W.J., Juss, B.K., Easty, D.L. (1995).

Differing effects of various cryoprotectants on intercellular junctions of epithelial (MDCK) cells. Cryobiology 32: 52-59.

Agca, Y., Liu, J., McGrath, J.J., Peter, A.T.,

Crister, E.S., Crister, J.K. (1998). Membrane permeability characteristics

of metaphase II mouse oocytes at various temperatures in the presence of Me2SO. Cryobiology 36:

287-300. Atkins, Op. Cit. Cosman, M.D., Toner, M., Kandel, J.,

Cravalho, E.G. (1989). An integrated cryomicroscopy system. Cryo-Letters 10: 17-38.

Cury, M.R., Kleinhans, F.W., Watson, P.F.

(2000). Measurement of the water transport during freezing in cell suspensions using a differential scanning calorimetor. Cryobiology

36: 124-155. Demirci, B., Lornage, J., Salle, B., Frappart, L.,

Frank, M., Guerin, F. (2001). Follicular viability and morphology of sheep ovaries after exposure to cryoprotectant and cryopreservation with different freezing protocols.

Fertil Steril 75: 754-762.

Devireddy, R.V., Swanlund, D.J., Roberts,

K.P., Pryor, J.L., Biscof, J.C. (2000). The effect of extracellular ice and cryoprotective agents on the water permeability parameters of human sperm plasma membrane during freezing. Human Reprod. 15: 1125-1135.

Diller, K.R., Raymond, J.F. (1990). Water

transport through a multicellular tissue during freezing: a network thermodynamic modeling analysis. Cryo-Letters 112: 151-162.

Diller, K.R. (1992). Modeling of bioheat

transfer processes at high and low temperatures. Bioeng. Heat Transfer 22: 157-357.

Dobrinsky, J.R., Johnson, L.A. (1994).

Cryopreservation of procine embryos by vitrification: a study of in vitro development. Theriogenology

42: 25-35. Dobrinsky, J.R (1996). Cellular approach to

cryopreservation of embryos. Theriogenology 45: 17-26, 1996. Drobnis, E.Z., Crowe, L.M., Berger, T.,

Anchordoguy, T.J., Overstreet, J.W., Crowe, J.H. (1993). Cold shock damage is due to lipid phase Transitions in cell membranes: a demonstration usuing sperm as a model. J. Exp. Zool. 265: 432-437.

Fahy, G.M., Karow, A.M. (1977).

Ultrastructural-function correlative studies for cardiac cryopreservation. V. Absence of correlation between electrolyte toxicity and cryoinjury in the slowly frozen, cryoprotected rat heart. Cryobiology 14: 418-427.

Cryobiology 2001

33

Fahy, G.M. (1981). Analysis of “solution effects” injury: cooling rate dependence of the functional and morphological sequella of freezing in rabbit renal cortex protected with dimethyl sulfoxide. Cryobiology

18: 550-570. Fahy, G.M., MacFarlane, D.R., Angell, C.A.,

Meryman, H.T. (1984). Op cit. Fahy, G.M. (1986). The relevance of

cryoprotectant “toxicity” to cryobiology. Cryobiology 23: 1-13. Fahy, G.M., Saur, J., Williams, R.J. (1990).

Physical problems with the vitrification of large biological systems. Cryobiology 27: 492-510.

Fahy, G.M., Levy, D.I., Ali, S.E. (1987).

Some emerging principles underlying the physical properties, biological actions, and utility of vitrification

solutions. Cryobiology 24: 196-213. Fiser, P.S., Fairfull, R.W. (1989). The effect

of glycerol-related osmotic changes on post-thaw motility and acrosomal integrity of ram spermatozoa.

Cryobiology 26: 64-69. Fu, D., Libson, A., Miercke, L.J.W.,

Weitzman, C., Nollert, P., Krucinski, J., Stroud, R.M. (2000). Structure of a glycerol-conducting channel and the basis for its selectivity. Science 290: 481-486.

Gao, D., Mazur, P., Critser, J.K.

Fundamental cryobiology of mammalian spermatozoa. In Reproductive Tissue Banking. Scientific Principles. (ed. A.M. Karow, J.K. Critser). San Diego:

Academic Press, 1997.

Gao, D.Y., Benson, C.T., Liu, C., McGrath, J.J., Critser, E.S., Critser, J.K. (1996). Development of a microperfusion chamber for determination of cell membrane transport properties. Biophys. J. 71: 443-450.

Giraud, M.N., Molta, C., Boucher, D.,

Grizard, G. (2000). Membrane fluidity predicts the outcome of cryopreservation of human spermatozoa. Human Reprod. 15: 2160-2164.

Hammerstedt, R.H., Graham, J.K., Nolan, J.P.

(1990). Cryopreservation of mammalian sperm: what we ask them to survive. J. Androl 11: 73-88.

Heald, R., Tournebize, R., Habermann, A.,

Karsenti, E., Hyman, A. (1997). Spindle assembly in Xenopus egg extracts: respective roles of centrosomes and microtubule self-organization. J. Cell Biol. 138: 615-628.

Hunt, C.J. (1984). Studies on cellular structure and ice location in frozen organs and tissues: the use of freeze-substitution and related techniques.

Cryobiology 21: 385-402. Hunter, J.E., Fuller, B.J., Bernard, A., Shaw,

R.W. (1995). The effect of cooling and hypertonic exposure on murine oocyte function, fertilization, and development. Cryobiology 32: 318-326.

Johnson, M.H., Pickering, S.J. (1987). The

effects of dimethyl sulfoxide on the microtubular system of the mouse oocyte. Development 100: 313-324.

Cryobiology 2001

34

Karlsson, J.O.M., Cravalho, E.G., Toner, M. (1994). A model of diffusion-limited

ice growth inside biological cells during freezing. J. Appl. Phys 75: 4442-4455. Karlsson, J.O.M., Eroglu, A., Toth, T.L.,

Cravalho, E.G., Toner, M. (1996). Fertilization and development of mouse oocytes cryopreserved using a theoretically optimized protocol. Human Reprod. 11: 1296-1305.

Karow, A.M., Shlafer, M. (1975).

Ultrastructure-function correlative studies for cardiac cryopreservation. IV. Prethaw ultrastructure of myocardium cooled slowly (≤ 2°C/min) or rapidly (≥ 70°C/sec) with or without dimethyl sulfoxide (DMSO). Cryobiology 12: 130-143.

Karow, A.M., McDonald, M., Dendle, T.,

Rao, R. (1986). Functional preservation of the mammalian kidney. VII. Autologous tranplantation of dog kidneys after treatment with dimethyl sulfoxide (2.8 and 4.2M). Transplantation 41: 669-674.

Karow, A.M. Biological effects of

cryoprotectant perfusion, delivery and removal to nonfrozen organs. In the Biophysics of Organ Cryopreservation (ed. D.E. Pegg, A.M. Karow). New York: Plenum, 1987.

Karow, A.M. Pharmacological interventions

in vitro. In Reproductive Tissue Banking. Scientific Principles. (ed. A.M. Karow, J.K. Critser). San Diego: Academic Press, 1997

Katkov, I.I., Kathova, N., Critser, J.K., Mazur, P. (1998). Mouse spermatozoa in high concentrations of glycerol. Chemical toxicity vs. osmotic shock at normal and reduced oxygen concentrations. Cryobiology 37: 325-338.

Katkov, I.I. (2000). A two-parameter model

of cell membrane permeability for multisolute systems. Cryobiology 40: 64-83.

Kedem, O., Katchalsky, A. (1958).

Thermodynamic analysis of the permeability of biological membranes to nonelectrolytes. Biochem. Biophys. Acta 27: 229-246.

Kleinhaus, F.W. (1998). Membrane

permeability modeling: Kadem- Katchalsky vs. two-parameter formalism. Cryobiology 37: 271-289.

MacFarlane, D.R., Forsyth, M. (1990). Recent

insights on the role of cryoprotective agents in vitrification. Cryobiology 27: 345-358.

Mazur, P., Leibo, S.P., Miller, R.H. (1974).

Permeability of bovine red cell to glycerol in hypertonic solutions at various temperatures. J. Memb.

Biol. 15: 107-136. Mazur, R., Rall, W.F., Leibo, S.P. (1984).

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. Cell Biophysiol 6: 197-214.

Cryobiology 2001

35

Mazur, P., Katkov, I.I., Katkova, N., Critser, J.K. (2000). The enhancement of the ability of mouse sperm to survive freezing and thawing by the use of high concentrations of glycerol and the presence of an Escherichia coli membrane preparation (Oxyrase) to lower the oxygen concentration.

Cryobiology 40: 187-209. McGrath, J.J. (1985). A microscope diffusion

chamber for the determination of the equilibrium and non-equilibrium osmotic response of individual cells. J. Micros 139: 249-263.

McGrath, J.J. Temperature-controlled

cryogenic light microscopy – an introduction to cryomicroscopy. In The Effects of Low Temperatures on Biological Systems. (editors B.W.W. Grout, G.J. Morris). London:

Edward Arnold, 1987. Pp. 234-267. McGrath, J.J., Fuller, B.J., Hunter, J.E.,

Paynter, S., Bernard, A..G. (1995). The permeability of fresh preovulatory human oocytes to dimethyl sulfoxide at 3°C. Cryo-Letters 16: 79-84.

McGrath, J.J. (1997). Quantitative

measurement of cell membrane transport. Technology and application. Cryobiology 34: 315-334.

Meryman, H.T. (1968). Modified model for

the mechanism of freezing injury in erythrocytes. Nature 218: 333-336.

Morris, G.J., Clarke, A. Cells at low

temperature. In The effects of Low Temperatures on Biological Systems. (editors B.W.W. Grout, G.J. Morris) London: Edward Arnold, 1987. Pp. 72-118.

Parks, J.E. Hypothermia and mammalian gametes. In Reproductive Tissue Banking. Scientific Principles. (ed. A.M. Karow, J.K. Critser). San Diego: Academic Press, 1997.

Paynter, S.J., Fuller, B.J., Shaw, R.W. (1997).

Temperature dependence of mature mouse oocyte membrane permeabilities in the presence of cryoprotectant. Cryobiology 34: 122-130.

Paynter, S.J., McGrath, J.J., Fuller, B.J., Shaw,

R.W. (1999). A method for differentiating nonunique estimates of membrane transplant properties: mature mouse oocytes exposed to glycerol. Cryobiology 39: 205-214.

Pegg, D.E. Ice crystals in tissues and organs.

In The Biophysics of Organ Cryopreservation (editors D.E. Pegg, A.M. Karow). New York: Plenum, 1987. Pp. 117-136.

Pegg, D.E., Diaper, M.P., Skaer, H. Leb., Hunt, C.J. (1984). The effect of cooling rate and warming rate on the packing effect in human erythrocytes frozen and thawed in the presence of 2 M glycerol. Cryobiology 21: 491-502.

Pegg, D.E., Rubinsky, B., Diaper, M.P., Lee,

C.Y.C. (1986). Analysis of the introduction and removal of glycerol in rabbit kidneys using a Krogh cylinder model. Cryobiology 23: 150- 160. Pitt, R.E., Steponkus, P.L. (1989).

Quantitative analysis of the probability of intracellular ice formation during freezing of isolated protoplasts.

Cryobiology 26: 44-63.

Cryobiology 2001

36

Porsche, A.M., Korber, C., Englich, S., Hartman, U., Rau, G. (1986). Determination of the permeability of human lymphocytes with a microscope diffusion chamber. Cryobiology 23: 302-316.

Rabin, Y., Olson, P., Taylor, M.J., Steif, P.S.,

Julian, T.B., Wolmark, N. (1997). Gross damage accumulation in frozen rabbit liver due to mechanical stress at cryogenic temperatures. Cryobiology 34: 394-405.

Rowe, A.W., Allen, F.H. (1965). Freezing of

blood droplets in liquid nitrogen for use in blood group studies. Transfusion 5: 379.

Rubinsky, B., Cravahlo, E.G., Mikic, B.

(1980). Thermal Stresses in frozen organs. Cryobiology 17: 66-73. Rubinsky, B., Cravahlo, E.G. (1984). An

analytical method to evaluate cooling rates during cryopreservation protocols for organs. Cryobiology

21: 303-320. Rubinsky, B. Heat transfer during

cryopreservation. In The Biophysics of Organ Cryopreservation (editors D.E. Pegg, A.M. Karow). New York: Plenum, 1987. Pp 89-112.

Ruggera, P.S., Fahy, G.M. (1990). Rapid and

uniform electromagnetic heating of aqueous cryoprotectant solutions from cryogenic temperatures. Cryobiology 27: 465-478.

Rule, G.S., Law, P., Kruuv, J., Lepock, J.R.

(1980). Water premeability of mammalian cells as a function of temperature in the presence of dimethylsulfoxide: correlation with the state of membrane lipids.

J. Cell Physiol 103: 407-416.

Shaw, J.M., Trounson, A.O. (1989). Parthenogenics activation of unfertilized mouse ooctyes by exposure to 1,2-propanediol is influenced by temperature, oocyte age and cumulus removal. Gamete Rev. 24: 269-279.

Shlafer, M., Karow, A.M. (1971). Ultra-

structure-function correlative studies for cardiac cryopreservation. I. Hearts perfused with various concentrations of dimethyl sulfoxide (DMSO). Cryobiology 8: 280.

Sutton, R.L. (1992). Critical cooling rates for

aqueous cryoprotectants in the presence of sugars and polysaccharides. Cryobiology 29: 585-598.

Sutton, R.L. (1993). Devitrification in butane

–2,3 diol solutions containing antifreeze peptide. Cryo-Letters 14: 13-20.

Taylor, M.J. (1981). The meaning of pH at

low temperatures. Cryo-Letters 2: 231-239.

Toner, M., Cravalho, E.G., Karel, M. (1990).

Thermodynamics and kinetics of intracellular ice formation during freezing of biological cells. J. Appl. Phys. 67: 1582-1592, erratum 70: 4653

Toner, M., Cravalho, E.G., Stachecki, J.,

Fitzgerald, T., Tompkins, T.G., Yarmugh, M.L., Armant, D.R. (1993). Nonequilibrium freezing of one-cell mouse embryos. Membrane integrity and development potential. Biophys. J. 64: 1908-1921.

Cryobiology 2001

37

Van der Elst, J., Van Den Abbeel, E., Nerinckx, S., Van Steirteghem, A. (1992). Parthenogenetic activation pattern and microtubular organization of the mouse oocyte after exposure to 1,2-propanediol. Cryobiology 29: 549-562.

Viskanta, R., Bianchi, M.V.A., Crister, J.K.,

Gao, D. (1997). Solidification processes of solutions. Cryobiology 34: 348-362.

Webb, W.R., Karow, A.M. (1965).

Hypothermic organ preservation. Comparison of cooling and warming methods. JAMA 191: 1012-1014.

Wolfe, J., Bryant, G. (1999). Freezing, drying,

and/or vitrification of membrane-solute-water systems. Cryobiology 39: 103-129.

Woolley, D.M., Richardson, D.W. (1978).

Ultrastructural injury to human spermatozoa after freezing and thawing. J. Reprod. Fert. 53: 389-394.

Yang, B., Verkman, A.S. (1997). Water and

glycerol permeabilities of aquaporins 1 – 5 and MIP determined quantitatively by expression of epitope-tagged constructs of Xenopus oocytes. J. Biol. Chem. 272: 16140-16146.

Zenzes, M.T., Bielecki, R., Casper, R.F.,

Leibo, S.P. (2001). Effect of chilling to 0°C on the morphology of meiotic spindles in human metaphase II oocytes. Fertil Steril 75: 769-777.

Cryobiology 2001

38

ACKNOWLEDGEMENT

Doctor Robin L. Sutton provided the author with much helpful conceptual guidance in the development of this manuscript. Paula Bond and Julee Bode created the document and its figures.