SESSION 9

CRYOBIOLOGY - III

Chairman: T.C. Hua


NON-LINEAR MICROSCALE ALTERATIONS IN MEMBRANE
TRANSPORT BY ELECTROPERMEABILIZATIONa

T. R. Gowrrishankar, Wei Chen, and Raphael C. Lee
Electrical Trauma Research Program, Department of Surgery
The University of Chicago, Chicago, IL 60637

INTRODUCTION

Membrane permeabilization occurs when a strong electric field disrupts the structural integrity of the membrane and causes transmembrane defects or gaps.1,2 Electropores, as these openings are commonly called, are believed to occur on the sub-microsecond time scale and expand in size during the electrical exposure.3,4,1,5 For low magnitude and short duration pulses, the pores shrink and disappear following the removal of the pulse and thus the electrical breakdown of the membrane can be reversed.6,5,7 When a sufficiently strong electric field is imposed, the pores continue to conduct long after the removal of the pulse leading to irreversible damage of cell membrane.8,9

Recently, Winterhalter et al.10 showed that the initial process of pore formation in planar lipid bilayers starts a few microseconds after the onset of the pulse, and the breakdown of the membrane occurs within a millisecond. O'Neill and Tung11 used voltage clamp measurements of membrane patches from frog ventricular cells to show large step increases in membrane conductance that occurred on a time scale of less than 30 ms at transmembrane potentials of 0.1-1 V/msec. Chen and Lee12 showed that the increase in membrane conductance in response to a positive pulse is 3 to 4 times larger than in response to a negative pulse of the same magnitude. The dynamics of the underlying molecular events that cause an increase in membrane conductance are not well understood. The purpose of this study was to precisely characterize the changes in cell membrane conductance in response to electropermeabilization using a high-speed, space-clamp and voltage-clamp experimental configuration.

MATERIALS AND METHODS

A double Vaseline gap voltage clamp was used to study the changes in membrane properties resulting from supraphysiologic transmembrane potentials imposed by an external electric field.13 The voltage clamp technique involves clamping transmembrane potential while simultaneously measuring the transmembrane current. This method also makes it possible to differentiate the transmembrane leakage current due to membrane electroporation from current passed through ion channels. The voltage clamp technique enables study of rapid dynamics of electroporation.

A single twitch muscle fiber from the semitendinosus of an English frog (Rana temperoria) was hand-dissected in a high K+ relaxing solution. The fiber was mounted in a chamber filled with a relaxing solution and isolated across the three distinct pools by two Vaseline seals. Membranes of fiber segments in the two end pools were chemically permeabilized by treatment with 0.01% saponin for 2 minutes in order to ensure that electrical and ionic transfer could take place between the interior and exterior of the cell. The solution in the two end pools was then replaced by an "internal solution'' which mimicked the composition of the cytoplasmic fluid. The central pool was filled with normal Ringer's solution containing both Na+ and K+ channel blockers, tetrodotoxin (TTX) and tetraethanoammonia (TEA). Six agar bridges and six Ag-AgCl pellets were used to connect the solutions in the chamber to the external circuit.

Membrane was exposed to by a series of square wave pulses ranging from -150 to - 400 mV in steps of 10 mV. Simultaneously, the resulting transient transmembrane current was recorded. The dynamics of membrane conductance changes was characterized using the transmembrane current data. Under resting conditions, the transmembrane current was found to be approximately 2.5(+-)0.03 nA corresponding to a membrane conductance of 27.9(+-)3.5 nS.

RESULTS

The transmembrane current increased from approximately -2.5 nA to -550 nA when the membrane potential is increased from -90 mV to -300 mV. The changes in membrane properties that occured in this range of transmembrane potential (-200 to -300 mV) were transient and fully reversible. The resealing process, following a 50 ms pulse, was shown to have a rapid phase with a time constant of 350 ns and a slow phase with a time constant of approximately 2 ms. The fast phase could not be measured accurately because of the limitation on the sampling frequency. In addition, the time constant of decay of transmembrane potential to the resting value was approximately 30 ms, which limited the accuracy of measuring the rapid phase of the decay of transmembrane current. The drop is essentially due to the abrupt resealing of small pores when the driving force is removed. An increase in membrane potential beyond -400 mV led to stable alterations in membrane electrical properties. Our results indicate that muscle membrane electrical properties were very nonlinear above physiologic transmembrane potential. Both in designing bio-technology tools and in treating electric field mediated membrane injury, it is crucial to understand the role of pulse parameters on membrane alteration.

Using voltage clamp measurements of transmembrane current, we showed that the onset of transient electroporation occurs at a transmembrane potential of approximately - 240 mV in a frog skeletal muscle cell. The transmembrane potential threshold for electroporation that we observed is lower than those reported for other types of membranes. It is low in comparison with transmembrane potentials exceeding 0.5-1.0 V required to cause pore formation in artificial lipid membranes.14 In cardiac cells, the onset of electroporation was found to occur at approximately 300-400 mV for 5-10 msec pulses.20 According to Hibino et al5, the membrane was porated and started to conduct current when the transmembrane potential reached a critical value of about 1V following an external electric field application.

The lower threshold for electroporation observed in the voltage clamp experiments may be due to the experimental design. We used a double Vaseline gap voltage clamp wherein the cell was held at a spatially uniform and accurately measured transmembrane current. In the traditional configuration of voltage clamp, a large part of the cell experiences a potential that is lower than the applied potential. Thus, a larger membrane potential is required to cause the same level of electroporation as with our voltage clamp setup. In studies that used external electrodes to apply an electric field, transmembrane potential was estimated from analytical expressions.16 The actual membrane potential may differ considerably from theoretical estimates and may be spatially non-uniform.

The membrane conductance transiently increases by over 400 times above its resting value when the membrane potential is increased to -450 mV. In contrast, for a -200 mV pulse, the increase is less than 20-fold of its value at -90 mV.

Both the rate of pore creation and the energy required to expand existing pores were non-linear functions of transmembrane potential.

DISCUSSION

An increase in transmembrane potential favors both creation and expansion of pores causing an increase in the fraction of membrane area occupied by pores and consequently the membrane conductance, because higher transmembrane potentials overwhelm diffusion-limited process of pore contraction. The consequent shift in pore distribution causes an increasingly rapid rise in transmembrane current at higher transmembrane potentials. This is evident from the decrease in electroporation time constant from 0.65 msec to 0.25 msec when the transmembrane potential is increased from -300 mV to -440 mV. Theoretical models of electroporation1,7,17 describe pore creation in terms of an Arrhenius function of transmembrane potential suggesting a non-linear change in pore distribution with changes in transmembrane potential. Our measurements show that both peak conductance during the pulse and residual conductance following the pulse are non- linear functions of transmembrane potential.

An applied electric field causes lipid molecules of the membrane to reorient while creating hydrophilic pores. The molecular dynamics of these events involve changes in conformation of lipid molecules and rearrangement of the lipid bilayer.15 Under quiescent conditions, membrane defects fluctuate in time scales of picoseconds to minutes.18 The highly cooperative structural rearrangements of lipids occur in milliseconds to minutes, while the rotation of lipid molecules occurs in microseconds. However, in the presence of an electric field, the rate of reorientation of an electric dipole associated with the lipid molecules is enhanced. When the external field is turned off, the lipids return to their initial configuration. The relaxation of transmembrane current following the pulse occured with a time constant of 0.16 msec. This value relates to a diffusion coefficient of lipids which is two orders of magnitude lower than that for reorientation of lipids in pure bilayer lipid membrane. This suggests that the resealing process is not completely determined by lateral lipid movement as is the case in a pure lipid bilayer membrane. One possible explanation is that the reoriented lipid molecules of a pore wall may form a quasi-stable complex with membrane proteins when pores expand during a pulse. Lipid molecules in such a complex may find it difficult to re-orient after the pulse, which leads to sustained conduction through aqueous pathways.

REFERENCES

  1. Barnett, A. & J. C. Weaver. 1991. Electroporation: a unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes. Bioelectrochem Bioenerg. 25: 163-182.
  2. Lee, R. C. 1991. Physical mechanisms of tissue injury in electrical trauma. IEEE Trans Educ. 14: 221-230.
  3. Kinosita, K. & T. Y. Tsong. 1979. Voltage-induced conductance of human erythrocyte membranes. Biochim Biophys Acta. 554: 479-97.
  4. Benz, R., F. Beckers & U. Zimmermann. 1979. Reversible electrical breakdown of lipid bilayer membranes: charge-pulse relaxation study. J Membr Biol. 48: 181-204.
  5. Freeman, S. A., M. A. Wang & J. C. Weaver. 1994. Theory of electroporation of planar bilayer membranes: Predictions of the aqueous area, change in capacitance, and pore-pore separation. Biophys J. 67: 42-56.
  6. Zimmermann, U. 1975. Electrical breakdown: electropermeabilization and electrofusion. Rev Physiol Biochem Pharmacol. 105:176-256.
  7. Abidor, I. G., V. B. Arakelyan, L. V. Chernomordik, Y. A. Chizmadzhev, V. F. Pastushenko & M. R. Tarasevich. 1979. Electric breakdown of bilayer membranes: 1. The main experimental facts and their qualitative discussion. Bioelectrochem Bioenerg. 6: 37-52.
  8. Prausnitz, M. R., J. D. Corbett, J. A. Gimm, D. E. Golan, R. Langer & J. C. Weaver. 1995. Millisecond measurement of transport during and after an electroporation pulse. Biophys J. 68: 1864-70.
  9. Glaser, R. W., S. L. Leikin, L. V. Chernomordik, V. F. Pastushenko & A. I. Sokirko. 1988. Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. Biochem Biophys Acta. 940: 275-87.
  10. Winterhalter, M., K-H. Klotz, R. Benz & W. M. Arnold. 1996. On the dynamics of the electric field induced breakdown in lipid membranes. IEEE Trans Ind Applns. 32: 125-30.
  11. O'Neill, R. J. & L. Tung. 1991. Cell-attached patch clamp study of the electropermeabilization of amphibian cardiac cells. Biophys J. 59: 1028-1039.
  12. Chen, W. & R. C. Lee. 1994a. Electromediated permeabilization of frog skeletal muscle cell membrane. Bioelectrochem Bioenerg. 34: 157-167.
  13. Chen W. & R. C. Lee. 1994b. An improved double vaseline gap voltage clamp to study electroporated skeletal muscle fibers. Biophys J. 66: 700-709.
  14. Tsong, T. Y. 1991. Electroporation of cell membranes. Biophys J. 60: 297-306.
  15. Tung, L., O. Tovar, M. Neunlist, S. K. Jain & R. J. O'Neill. 1994. Effects of strong electrical shock on cardiac muscle tissue. Ann. N. Y. Acad. Sci. 720: 160-175.
  16. Kinosita, K., J. Ashikawa, S. Nobuyuri, H. Hoshimura, H. Itoh, K. Nagayama & A. Ikegami. 1988. Electroporation of cell membrane visualized under a pulsed-laser fluorescence microscope. Biophys J. 53: 1015-1019.
  17. Lee, R. C. & K. Prakah-Asante. 1992. Theory of nonlinear conduction in cell membranes under strong electric fields. In Electrical trauma: The pathophysiology, manifestations and clinical management. Lee, R. C., E. G. Cravalho & J. F. Burke, Eds.: 426-434. Cambridge University Press. Cambridge.
  18. Caffrey, M. 1989. The study of lipid phase transition kinetics by time-resolved x-ray diffraction. Annu Rev Biophys Biophys Chem. 18: 159-186.

a This work was supported in part by grants from Electric Power Research Institute, Commonwealth Edison, Empire State Electric Energy Research Company, New York State Electric and Gas Company, Niagara Mohawk Power Corporation, Northeast Utilities Services Company, Public Service Company of Oklahoma, Shell Oil Foundation and Amoco Oil Foundation.


EFFECTS OF GLYCEROL ON INTRACELLULAR ICE FORMATION AND
DEHYDRATION OF ONION EPIDERMIS

Takaharu Tsuruta, Yuko Ishimoto, and Takashi Masuoka
Department of Mechanical Engineering, Kyushu lnstitute of Technology,
1-I, Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan

INTRODUCTION

Intracellular ice formation and cell dehydration are very important for a cryopreservation of large living tissue. Concerning the ice formation in the tissue cells, our previous study conducted using a high-speed and high-magnified observation system confirmed that the plasma membrane initiates the ice formation due to the surface-catalyzed nucleation (SCN). Since the membrane also blocks the growth of ice crystals, the freezing propagates cell by cell. It was also observed that a decrease of the cooling rate raises the dehydration and reduces the fraction of frozen cells.

In the present study, effects of glycerol on the intracellular ice formation and dehydration were examined, and the results were compared with the theoretical estimations for the freezing temperature and the dehydration rate, which are made based on the SCN theory developed by Toner et al. and the dehydration theory by Mazur.

EXPERIMENTAL APPARATUS AND PROCEDURE

Figure 1 shows schematics of the directional solidification stage arranged in a microscope. The stage consists of two bases made of copper kept at a constant but different temperatures by a temperature control equipment with liquid-nitrogen vapor and heating elements. Temperatures of the copper bases are measured with Pt-resistance thermometers of 1.8 mm diameter and set in the ranges of 15~30 C and

-30 ~ -60 C, respectively. Setting a glass microslide on the two copper bases, almost a linear temperature profile is formed in the microslide between the bases. By moving the microslide with a constant velocity along the direction of temperature gradient the specimen on the microslide is cooled at a constant cooling rate and the directional solidification is achieved in the mieroscope system.

Epidermal tissues of onion bulbs were used as the biological material. Since the onion epidermis consists of a monolayer ( ~90 mm thick) of relatively large cells ( 50~800 mm ) containing much water above 70 %, we can observe the freezing and dehydration processes clearly with the light microscope. In the experiments, a layer of the epidermal tissue was sandwiched between thin layers of glycerol solution, which simulates the extracellular freezing observed in the tissues. The concentrations of glycerol were 5wt%, 10wt%, and 20wt%. Before the cooling tests, we could observe a protoplasmic movement showing a proof of living cells.

RESULTS AND DISCUSSIONS

First, a comparison between experimental and theoretical dehydration rate under the slow cooling conditions have been made. Figure 2 shows the volume changes of cells during the cooling for different glycerol concentrations together with a photograph showing a typical cell shrinkage due to the dehydration. It is seen that an increase of glycerol concentration reduces the dehydration rate. The theoretical lines in the figure were drawn based on Mazur's theory for aconstant cooling rate H:

where nw is the molar volume of pure water. The vapor pressure ratio between extra and intracellular water is given by the Clausius-Clapeyron equation and the Raoult' s law:

Lf is the molar latent heat of fusion, Vw the volume of water in the cell and ns the moles of solute. The protoplasmic permeability coefficient Lp for water (hydraulic conductivity) were measured from the transient osmotic volume changes of the cells in the hypertonic sucrose solution and it is expressed in a form of Arrhenius-type equation:

where E*=44.71 (kJ/mol) and Lpg=0.597x10-12 m3/(Nmin) at Tg=298.15 K.


Concerning for the intracellular ice formation, the SCN theory by Toner et al. was applied to the experiments.

where PIF denotes an probability of intracellular ice formation, Woscn and koscn are the thermodynamic and kinetic parameters for the SCN obtained by comparing with the rate of homogeneous nucleation. The both parameters can be expressed as the ratios of the concentration-dependent terms like viscosity with their values under isotonic conditions. In this study, the values of Woscn=1.3x108 (m2s)-1 and koscn=1.2x1010 (K5) are used as the parameters under the isotonic conditions for the onion epidermis. The results for the cases of glycerol of 5wt% and 20wt% are presenfed in Fig. 3 with some experimental data. The ordinate of the figure indicates the cumulative fraction of frozen cells above a given temperature. We can see that the freezing temperature decreases with increasing concentration of glycerol and it is found that the glycerol suppresses the intracellular ice formation by reducing the amount of unbounded water.

Although the figures show a relatively good agreement between the theoretical and experimental results, we can see some differences in the higher temperature regions. This is because that the propagative ice formation through the connected cells is not considered in the theory. The difference in the lower temperature region for 20% glycerol is due to the dehydration.

CONCLUSIONS

Experimental observations were made to examine the effects of glycerol on the intracellular ice formation and the dehydration. It is found that the use of glycerol reduces the probability of ice formation but can not prevent the dehydration under the very slow cooling condition. The dehydration rate during the slow cooling can be estimated by the theories if we know some physicochemical properties such as permeability coefficient. For the intracellular ice formation, the SCN theory can predict the spontaneous temperature for cell freezing but can not estimate the propagative freezing occurred in the higher temperature region. Also, under the lower temperature conditions attained by the rapid cooling, some different freezing phenomena from the SCN occurs and this can keep the cell morphology in a same state before the freezing.


THINGS WE D0 N0T KNOW ABOUT
CRYOPRESERVATION OF BIOLOGICAL ORGANS

Ichiro Tanasawa
Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan

INTRODUCTION

The technique of cryopreservation of living cells, organs and tissues has been pursed for more than sixty years. As the consequence, cryopreservation of cell suspensions, such as spermatozoon, fertilized ovum, erythrocyte, bone marrow, etc. has been succeeded. However, cryopreservation of some of blood elements, such as stem and progenitor cells, has not been successful yet. Cryopreservation of massive organs and tissues has not always been successful either . This means that we do not understand completely what is happening during the process of cryopreservation and that we have not yet developed fully the art of cryopreservation.

My attempt in this article is to make clear the things we do not know, at least at present, about cryopreservation of living organs, hoping that the attempt would indicate us the way we should take in our future reserach. The attention is focused on cryopreservation of living organs and tissues of mammals. Cryopreservation of other living things, such as insects, plants, plant seeds is outside the scope of this article, though I notice that strenous efforts have been made and fruitful results have been obtained in those areas .

I raise eight questions to be answered. The questions are limited mainly to those related to cooling/freezing and warming/thawing processes of cryopreservation. I dare not say only the eight questions here represent the most essential issues in cryopreservation, though they seem to me quite important. At the same time, I suspect that some of the questions have been answered already. If it is the case, I would be pleased to change "we"in the title of this article to "I".

Q1: WHAT ARE THE PHYSICO-CHEMICAL AND PHYSIOLOGICAL PRINCIPLES WHICH MAKE CRYOPRESERVATION POSSIBLE?

A seemingly reasonable answer to this question is that cryopreservation is possible because the rates of chemical reactions related to the energy metabolism in living organs decrease with temperature. However, the rate of chemical reactions at low temperatures are unknown. Therefore we are not certain about the upper limit of the temperature for long-term cryopreservation, or we do not know how long we can preserve living organs under a cryogenic temperature.

Q2: WHAT ARE THE FACTORS WHICH WE CAN ( SHOULD ) CONTROL AND WHICH AFFECT THE SURVIVAL RATIO OF CRYOPRESERVED SUBJECTS?

The answers which come to my mind at once are; (1) Rate of cooling (which may be variable with time), (2) Ways of cooling and warming,, (3)Temperature at which the solidified subject is preserved, (4) Choice of cryoprotective agent (CPA), including a mixture, and its initial concentration, (5) Rate and extent of dehydration (and rehy- dration), (6) Rate of warming (which may vary with time), and (7) Method of removing cryoprotectant away from the subject.

A comment to the above answers is that, although we know the factors important for successful cryopreservation, our understanding remains still to be rather qualitative. For example, we know that the rate of cooling is very important. But we do not know exactly what cooling rate is (or cooling program ) is the best. It might be because we do not understand precisely what is happening during the cooling process. Our next step should be to turn the above answers into quantitative ones.

Q3: WHAT ARE THE PHYCO-CHEMICAL AND PHYSIOLOGICAL ROLES OF CRYOPROTECTIVE AGENT (CPA) IN CRYOPRESERVATION?

We use CPAs in the hope of preventing injuries to cell structure (or cell membranes ) from occurring. However, its mechanism is not clearly understood. As the result CPAs are chosen rather empirically and their optimum concentrations are determined by trial and error method.

Q4: WHAT IS THE CRITICAL RATE OF COOLING BY WHICH THE SUBJECT CAN BE VITRIFIED?

Many people believe that vitrification by rapid cooling is the most ideal process for successful cryopreservation. However, it is evident that vitrification is possible only for subjects having small dimensions of the order of 100mm or smaller, because ultrarapid cooling is needed. Conduction of heat is usually the limiting mechanism that controls the rate of cooling.

Some people consider that vitrification is possible even for larger subjects if the concentration of CPA absorbed into the cells is sufficiently high because the glassy state (vitrification) temperature increases with concentration of the solution and finally meets with the homogeneous nucleation temperature or the heterogeneous nucleation temperature. It suggests that vitrification may occur prior to ice nucleation. It should be noted, however, that such a phenomenon occurs only for a very high concentration of the solution. It seems considerably difficult to have a CPA solution absorbed into the cells without causing serious harm to them due to toxity and dehydration.

Q5: HOW CAN WE OBTAIN(OR MEASURE) THERMODYNAMICAL AND TRANSPORT PROPERTIES NECESSARY FOR ANALYZING HEAT AND MASS TRANSFER PROCESSES ENCOUTERED IN CRYOPRESERVATION?

When cooling a cell, heat flows out of the intracellular substance to the outside through the cell membrane. How much heat is transferred is dependent upon the thermal properties (thermal couductivities, densities, specific heats, etc.) of the substances through which the heat flows. When a cell is immersed in a CPA solution, the intracellular free water molecules are transported through the membrane to the extracellular solution due to an osomotic pressure difference. Then, in turn, the CPA molecules enter into the cell. The rate of the mass transport process is dependent upon the transport properties such as diffusion coefficient and penetration coefficient. To know accurate values of thermophysical properties is very important for determining the protocol of cryopreservation.

Quite different from a homogeneous material, the thermophysical properties of biological cells, organs and tissues are difficult to define and measure. In the first place, their configurations are complex and structures are heterogeneous. We have to compromize by defining some kind of equivalent parameters, such as equivalent thermal conductivities, equivalent thermal and molecular diffusivities, etc. Difficulty is quite the same when we want to measure those properties. However, such efforts are truely important to establish a firm basis of the science of cryopreservation.

Q6: HOW CAN WE ASSESS IN SITU (IF POSSIBLE) VIABILITY OF CRYOPRESERVED CELLS OR ORGANS THROUGH THE ENTIRE PROCESSES OF COOLING , STORAGE AND WARMING?

We need a technique of in situ observation of cells or organs while they are being cooled, stored and thawed to watch the processes of nucleation and growth of ice crystals and to see if there is any injury caused by these icelets. In addition to this, we have to devise means to know if there occurs any biochemical injury inside the cells or on the cell membranes.

Q7: WHAT IS THE DIFFERENCE IN THE TECHNIQUE BETWEEN CRYOPRESERVATION OF A CELLULAR SOLUTION AND THAT OF A MASSIVE ORGAN?

Characteristic dimensions of biological cells are in the range of 1mm~100mm, whereas those of organs or tissues are in the range of 1mm100mm. There is three or four orders of magnitude difference. Vitrification is relatively easy for cellular solutions, while it is difficult for organs or tissues, because heat conduction is the most dominant process in cooling.

At the same time, CPA is easily absorbed into cells when they are suspended in the aqueous solution. On the other hand, absorption of CPA into cells takes much longer time in the case of a massive organ in which a great number of cells are packed closely. Perfusion of CPA soluition through blood vessels is a possible way to achieve fast and uniform absorption of CPA into an organ. But this kind of technique is feasible only for those organs which have fine networks of circulatory system. We need a new technique for cryopreservation of massive organs.

Q8: VOLUME (NON-CONDUCTIVE) HEATING IS POSSIBLE WITH THE USE OF AN ELECTROMAGNETIC DEVICE. IS THERE ANY POSSIBILITY OF VOLUME COOLING?

When a cellurar solution or an organ is to be cooled, cooling is done from the outer surface. In the case of a small-seized subject, the cooling rate at the outer surface is substantially equal to the cooling rate inside the sujbect. However, in the case of a larger subject the cooling rate inside the subject decreases greatly from the outer surface to the inside. The ultrarapid cooling rate sufficient to obtain amorphous state of the intracellular liquid is difficult to achieve by cooling from the outer surface.

Everybody knows that, in the case of warming, uniform and rapid temperature rise is possible by the use of electromagnetic heating. If a similar (but reverse ) method is available in the case of cooling, vitrification of a large-sized subject becomes possible.

CONCLUDING REMARKS

No definite conclusions are derived from what I have written in this article, because my intention is to make clear that there are still a lot of things we do not know about cryopreservation of living organs. Most of the knowledge we have obtained so far remain rather qualitative.

REFERENCES

  1. Takahashi, T. 1995. Preprint of the 41th Annual Meeting of the Society of Cryobiology and Cryotechnology: 14 (in Japanese).
  2. Steponkus, P. L. Ed. 1992. Advances in Low-Temperature Biology, Vol.1. JAI Press, Greenwich, Conneticut.
  3. Steponkus, P. L. Ed. 1993. Advances in Low-Temperature Biology, Vol.2. JAI Press, Greenwich, Conneticut.
  4. Steponkus, P. L. Ed. 1996. Advances in Low-Temperature Biology, Vol.3. JAI Press, Greenwich, Conneticut.
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  9. Shirakashi, R. and Tanasawa I. 1997. Trans. JSME, Series B, 63: 2793 -2795 (in Japanese)
  10. Shirakashi, R. and Tanasawa I. 1997. Proc. 18th Japan Symposium on Thermophysical Properties, Nara: 21 - 24.
  11. Tanasawa, I., Nagata, S. and Ninomiya, J. 1995. Proc. Symposium on Thermal Science and Engineering in Honor of Chancellor Chang-Lin Tien, Berkeley: 483 - 489.
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  13. Westwater, J. W. 1963. In Theory and Fundamental Reserarch in Heat Transfer . Clark, J. A., Ed. Pergamon Press: 61 - 73.

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