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THESIS

C ‘\

 

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3 1293 10704 7015

 

 

 

This is to certify that the
thesis entitled
CRYOMICROSCOPE INVESTIGATION AND

THERMODYNAMIC MODELING OF THE
FREEZING OF UNFERTILIZED HAMS'I‘ER OVA

presented by

Mohsen Shabana

has been accepted towards fulfillment
of the requirements for

 

M.S. degree in Mechanical Eng.

Qflm Q-M‘W

/ Méjér professor
V

Date “Ibo/33

0.7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

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RETURNING MATERIALS:
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CRYOMICROSCOPE INVESTIGATION AND
THERMODYNAMIC MODELING OF THE FREEZING
OF UNFERTILIZED HAMSTER OVA

BY

Mohsen Shabana

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1983

ABSTRACT
CRYOMICROSCOPE INVESTIGATION AND

THERMODYNAMIC MODELING OF THE FREEZING
OF UNFERTILIZED HAMSTER OVA

BY

Mohsen Shabana

Thermodynamic computer modeling was used to predict
the freezing response of single—celled unfertilized
hamster ova. The cell membrane transport characteristics
were investigated, using a microsc0pe diffusion chamber
system. The osmotically-inactive cell volume was experi-
mentally determined to be 21.6% of the initial cell volume.
An overall mean value of 0.8 um3/um2°min°atm°(518 um/d)
was determined for the membrane water permeabilityin.
The effect of the extracellular solute concentration on
Lp was determined at room temperature (~23°C). An existing
thermodynamic computer model was used to predict the
cell response to freezing. The predicted response was
compared to the actual volumetric response observed during
freezing on a temperature-controlled cryomicroscope
conduction stage. The effect of cooling rate on the
nucleation temperature of unprotected ova, and protected ova
suspended in a 1.5 M DMSO solution was investigated.
Overall mean nucleation temperatures of -13°C and -57.l°C

were observed for unprotected and protected ova, respectively.

Shabana, Moshen
Finally, cell survival was correlated to the internal

ice formation.

£\

r‘r .- ”HI/u"
' r’ ' IN
/f. r/. ' .f I/( I /.

In the name of Allah the most merciful

<

‘

and the most beneficient

ii

ACKNOWLEDGEMENTS

I gratefully acknowledge the patient guidance,
the friendship and the help of my major advisor,
Dr. John McGrath, throughout this work.

I would like to express my appreciation to the
members of the Endocrine Research Unit, especially
Dr. Dukelow, for his support and Dr. DeMayo, for his
effort in supplying the biological material required
for this research.

I am deeply grateful to the members of my family

who have patiently supported me during hard times.

iii

TABLE OF CONTENTS

CHAPTER PAGE
LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . Vi
NOMENCLATURE. . . . . . . . . . . . . . . . . . . . . . .ix
1 INTRODUCTION. . . . . . . . . . . . . . . 1
l. l Freezing of Biological Materials. . . . . l

1.2 Ova and Embryo Freezing. . . . . . . . . .11
1.3 Goals of the Present Work. . . . . . . . .13

2 THERMODYNAMIC AND MATHEMATICAL MODELING. . . . 14
2.1 Introduction. . . . . . . . . . . . . . . 14
2.2 The Extracellular Solution. . . . . . . . 16
2 3 The Intracellular Solution. . . . . . . . 18
2 4 Water Transport Model. . . . . . . . . . .20
2 5 Membrane Water Permeability. . . . . . . .21
3 EXPERIMENTAL TECHNIQUES. . . . . . . . . . . . 26
3.1 Cell Sample Preparation. . . . . . . . . .26
3.2 The Diffusion Chamber System. . . . . . . 27
3.3 Measurement of "Osmotically Inactive
Volume". . . . . . . . . . . . . . . . .35
3.4 Measurement of Cell Membrane Water
Permeability. . . . . . . . . . . . . . . 39
3.5 The Cryomicroscope System. . . . . . . . .39
3.5.1 Error Introduced in the
Measurement of Sample
Temperature. . . . . . . . . . . .47
4 ULTS AND DISCUSSION- - . - - . - . . . . . .52

Cell Membrane Water Permeability. . . . . 56

RES
4.1 The Osmotically Inactive Cell Volume. . . 52
4 2
4 3 Computer Simulation of the Cell

Osmotic Behavior During Freezing. . . . . 66
4.3.1 Assumptions. . . . . . . . . . . .66
4.3.2 Effect of Cooling Rate on

Predicted Cell Volume. . . . . . .63

Water Permeability Effect. . . . .70
Activation Energy Effect. . . . . 72
Comparison Between Predicted

and Observed Cell Response

During Freezing. . . . . . . . . .74

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O O
01.5w

iv

CHAPTER PAGE

4.4 Nucleation Temperature as a Function
Of COOling Rate. 0 O O I O O O O O O O O O 0 .78

5 CONCLUSIONS. . . . . . . . . . . . . . . . . . . .88
6 SUGGESIONS FOR FUTURE WORK. . . . . . . . . . . . .91
APPENDIX A. . . . . . . . . . . . . . . . . . . . . . . 93
APPENDIX B. . . . . . . . . . . . . . . . . . . . . . . 96
APPENDIX C. . . . . . . . . . . . . . . . . . . . . . . 99

LIST OF REFERENCES. . . . . . . . . . . . . . . . . . .103

FIGURE

1

5a

5b
5c

10
ll

12

13

LIST OF FIGURES

A schematic of the two—factor hypothesis
(Reproduced from McGrath (8)). . . . . . . . . . 4

Cell survival as a function of cooling

rate for several cell types. (Reproduced

from Mazur et a1. (7)). . . . . . . . . . . . . .5
A model describing cell water transport

during freezing. (Reproduced from

McGrath (8)). . . . . . . . . . . . . . . . . . .6

Alternative methods for a supercooled
cell to achieve equilibrium. (Reproduced
from McGrath (8)). . . . . . . . . . . . . . . . 8

Exploded view of the diffusion chamber.
(Reproduced from Nowlen (36)). . . . . . . . . .28

Schematic of the diffusion chamber. . . . . . . 29

Layout of the diffusion chamber connected
to the flushing mechanism. . . . . . . . . . . .31

A photograph of the diffusion chamber
mounted on the microsc0pe stage. . . . . . . . .34

Sequence of photographs of equilibrium cell
volume in increasingly concentrated NaCl
solutions. [a-0.3, b-0.4, c-0.5, d-0.6,

e-0.8, f—1.5 Osm]. . . . . . . . . . . . . . . .37

Typical equilibrium volumes of a single
ovum when exposed to hypertonic solute
concentrations. . . . . . . . . . . . . . . . . 38

Layout of the cryomicroscope system. . . . . . .41
Schematic of cryomicroscope conduction stage. . 42

Schematic of cryomicroscope temperature

controller. . . . . . . . . . . . . . . . . . . 43
Photograph of cryostage mounted on the

microscope. . . . . . . . . . . . . . . . . . . 45
Assembly of the thermocouple sandwich. . . . . .46

vi

FIGURE

14

15
16

17

18

19

20

21

22

23

24

25

26

27

PAGE

The estimated temperature error in the
x-direction in the viewing area of the
cryostage. . . . . . . . . . . . . . . . . . . .50

Boyle-Van't Hoff plot. . . . . . . . . . . . . .53

Representative shrinkage pattern of three
hamster ova in a hypertonic NaCl solution
as a function of time. . . . . . . . . . . . . .55

Representative correlation of experimental
data in the form of Terwilliger and
Solomon. . . . . . . . . . . . . . . . . . . . .58

Normalized water loss from experiments
compared to the mathematical model where
Lp==0.7317 um3/um2'min°atm (516.39 um/sec). . . 60

Water permeability as a function of the
extracellular impermeable solute concen-
tration (NaCl only). . . . . . . . . . . . . . .64

Water permeability as a function of the
extracellular solute concentration
(NaCl only). . . . . . . . . . . . . . . . . . .65

Effect of cooling rate on predicted cell
volume change during freezing
[Lp==0.732 um3/um2-minvatm (216.4 um/sec]. . . .69

Effect of membrane hydraulic permeability
(Lp) on predicted cell volume response
during freezing. . . . . . . . . . . . . . . . .71

Effect of activation energy (Ea) on
predicted cell volume response during
freezing [cooling rate (B)==8°C/min]. . . . . . 73

Comparison between predicted and observed
cell volume response during freezing. . . . . . 75

Schematic representing the fit of the

experimental data to the computer model

with initial volume defined at a) 0.0°C

(before external ice appearance); b) at

the moment when external ice surrounds

the cell. . . . . . . . . . . . . . . . . . . . 76

Nucleation temperature of unprotected
unfertilized hamster ova as a function
of cooling rate. . . . . . . . . . . . . . . . .80

Probability of internal ice formation as
a function of cooling rate for unprotected
hamster ova. . . . . . . . . . . . . . . . . . .82

vii

FIGURE

28

29

30

PAGE
Unprotected hamster ova survival as
a function of cooling rate. . . . . . . . . . . 83
Probability of internal ice and cell
survival both as a function of cooling
rate. 0 O O O O O O O O O O O O O O I O O O O O 84

Nucleation temperature at protected
unfertilized hamster ova in 1.5 M DMSO
as a function of cooling rate. . . . . . . . . .86

viii

NOMENCLATURE

 

A surface area, cm3

a activity

B cooling rate, °C/min

Ea Activation energy, Kcal/mole
AGfus molar free energy of fusion, Kcal/mole
AHfus latent heat of fusion, Kcal/mole
J molar flux, moles/cmz/sec

E water conductivity, um/sec

Lp water permeability, um3/um2-min°atm
n number of moles

p pressure, dyne/cm2

R gas constant, dyne-cm/mole-°K

T Temperature, °K

t time, sec

V volume, cm2

5 partial molar volume, cm3/mole

x mole fraction

Subscripts

b bound

f final

i isotonic

J solute

ix

0 initial

 

v volume

w water

Superscript

1 inside

L liquid

0 outside

s solid

* reference state

Greek

n osmolality, Osm/kg

u chemical potential dyne-cm/mole
v dissociation coefficient

CHAPTER 1

INTRODUCTION

1.1 Freezing of Biological Materials

 

Cryopreservation of biological materials is an area
of growing interest for a variety of peOple working in
both academic and applied disciplines. Blood and tissue
banking, genetic development of frost-resistent crops,
spermatozoa and ova storage for the purposes of scientific
research, protection of scarce animal species and breeding
of expensive laboratory and domestic animals are among
the numerous advantages of cryopreservation of biomaterials.

In 1949 Polge and colleagues (1) reported a major
breakthrough in cryobiology. They accidentally discovered
that glycerol and pr0pylene glycol protected spermatozoa
against the injurious consequences of exposure to low
subzero temperatures.

Since that time, many workers have succeeded in
freezing different biological materials and for extended
periods of time. Some biomaterials are routinely
cryopreserved with excellent recovery, such as erythrocytes

and lymphocytes. Others are still fragile and yield a low

2

percentage of survival after thawing,such as human
granulocytes.

However, most of the optimal freezing protocols are
defined by an entirely empirical approach to the experimen-
tal work. This can be attributed to a lack of understanding
of the basic mechanisms involved in cell damage during
freezing.

A number of theories that describe the cell damage
mechanism have been presented most of which lack adequate
experimental evidence.

Lovelock (2,3) proposed that the increased concentra-
tion of electrolytes in the cell suspension during
freezing could break down the membrane components. In
addition the dilution of the cell suspension during
thawing could produce an osmotic shock that could also
damage the cell.

Others proposed that during freezing a certain
critical amount of so-called "bound" water is removed from
vital cellular components such as membranes and proteins,
which causes cell death (4).

Meryman (5) suggested that cell dehydration during
freezing, results in a fatal increase in the membrane
permeability for normally impermeable solutes.

In 1972 Mazur and co-workers (6) presented their
widely accepted theory for cell damage during freezing:
the "Two Factor" hypothesis. They related cell damage to

two competing phenomena, each dominates a specific range

3

of cooling rantes. Specifically these phenomena are,
"formation of internal ice crystals" at fast cooling
rates, and "solution effects" at slow cooling rates.

The schematic in Figure 1 describes Mazur's theory.
Figure l-a shows the effect of intracellular ice formation
on cell survival, while Figure l-b shows the solution
effect. The solid line in Figure 1-c represents the
proposed cell survival when the two modes of damage are
combined. Quantitatively, the experimental observations
shown in Figure 2 support Mazur's theory. This figure
shows cell survival as a function of cooling rate for a
number of different cell types. An optimum cooling rate
where cell survival is maximum is observed for each cell
type. An apparent decrease in cell survival on both
sides of that optimum cooling rate is in strong agreement
with the proposed damage theory schematically described
in Figure l-c.

For a better understanding of the two modes of
cellular damage, the equilibrium aspects of the freezing
process are explained below.

Figure 3 shows the typical elements of a model
describing water transport across the cell membrane during
freezing. When heat is removed from the system, water
starts to solidify in the external medium forming pure
ice, where salts are assumed to be rejected from the ice
to the liquid water phase. The cell membrane is modeled

as a semi—permeable barrier, which prevents the permeation

% Recovery

 

 

% Recovery

% Recovery

 

 

"Intracellular Ice"
Damage

  

Cooling Rate
-a-

"Solution Effects"
Damage

Cooling Rate
-b-

\/
,/‘<;\‘ Resultant of
Combined Effects

   

 

Cooling Rate
-c-

Figure l. A schematic of the TWo-Factor
hypothesis.

(Reproduced from McGrath (8))

70-

63-

8

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20-4

 

 

 

‘0’I . . I '6 '6: - ‘93- 18‘
o "“3.“ng 319.196. COOLING VELOCITY

Figure 2. Cell survival as a function
of cooling rate for several
cell types. -

(Reproduced from Nazur et a1. (7))

System Boundary

Heat Removal Heat Addition
During Freezing During Thawing

 

   

PURE ICE

Net Water Transfer Net Water Transfer
During Solidification During Melting

INTRACELLULAR
SOLUTION:
/ WATER + SOLUTES

Semi-permeable
Cell Membrane

EXTRACEI-LULAR
SOLUTION:

WATER + SOLUTES + ICE-

 

 

 

 

P——-—-_—-———*--‘--——-—-—fi

\

Figure 3. A model describing cell water

transport during freezing.

(Reproduced from McGrath (8))

fl

of solutes into the cell. It also prevents the penetration
of the external ice into the cytoplasm, hence preventing
the intracellular water from freezing. Consequently, two
transient events occur. First the chemical potential of
the external water decreases, creating a state of
chemical non-equilibrium across the cell membrane.
Secondly the cell water supercools and becomes more
likely to form ice. For the cell to regain a state of
equilibrium it has to follow one of the two paths described
in Figure 4. During slow cooling, the difference in
chemical potential drives the intracellular water outside
the cell where it freezes externally. A state of
equilibrium is re-established across the cell membrane,
and the cell shrinks due to dehydration. In this case
the process is said to be mass transfer-dominated. The
cell damage in this process is believed to be due to the
so—called "solution effects” which include all of the
various cell damage theories described above.

At fast cooling rates, despite the rapid increase
in water chemical potential gradient across the membrane,
the water does not have enough time to leave the cell.
The cell water becomes more supercooled and forms ice
inside the cell in order to achieve chemical equilibrium
with the external medium. Here, the process is said
to be heat transfer-dominated.

In this case the cell volume change is minimal if

it occurs at all. The cell damage at fast cooling rates

TEMPERATURE

 

Initial Cell
State

Slow Freezing:
Mass Transfer-Dominated
Proce

Rapid Freezing:
Heat Transfer-
Dominated Process

 

9 £3
63
903
0 Water
9. Flux»»l
Extracellular And Extracellular Ice
Intracellular Ice No Intracellular Ice

A
fl

TIME

Figure 4. Alternative methods for a suprecooled
cell to achieve equilibrium.

(Reproduced from McGrath (8))

9
is commonly attributed to the mechanical deformation
exerted by the intracellular ice crystals on the cell
organelles (9).

As the selective barrier between the inside of the
cell and the outside suspending medium, the cell membrane
is believed to be the primary site of cell damage (2-5).
The problem remains unsolved as to whether physical or
chemical aspects are responsible for cellular death.
However, as described in most theories water transport
across the cell membrane and the amount of water remaining
within the cell play a highly significant role in cell
damage (6). Therefore, the mathematical modeling of the
kinetics of water transport across the cell membrane,
become a logical and a necessary step in developing an
improved understanding of the mechanisms involved.

In 1963 Mazur (10) began a new era in cryobiology.
He introduced the first thermodynamic model describing
the kinetics of water loss from a cell as a function of
various parameters.

Among these parameters, the temperature, the cooling
rate, the ratio of cell surface area to volume, the
membrane hydraulic permeability and its temperature
coefficient were included. However, Mazur's model was
based on a number of simplifying assumptions. These
assumptions include: modeling the cytoplasm as an ideal

dilute solution; no thermal or concentration gradients

10

were allowed in the cooled cell sample; the membrane was
assumed impermeable to solutes and; a state of equilibrium
exists between the solid and liquid water phases. These
assumptions and others were investigated in subsequent
non-equilibrium models (10,11). However the main
structure of Mazur's original model remains intact.

A computer simulation of the freezing process based
on a thermodynamic model can be used to predict the cell
volumetric response to freezing and thawing. The
predicted response can then be compared to actual cell
behavior obtained from cryomicroscopic experiments.

Such comparisons have been used for two purposes:

1) to assess the validity of the mathematica1/thermodynamic
model itself and; 2) to investigate the significance of
various assumptions and parameters included in the model.
However, the real future goal of the modeling process

is to be able to predict the response of experimentally
untested biological cells. Such predictions are not yet
established because of a lack of understanding with

respect to the complicated nature of the biological cells.

In order to test the cell response, and experimentally
investigate different modeling aspects of the problem,
sophisticated equipment is required.

Cryomicroscope systems have been designed and
deveIOped in a number of laboratories (12-15). The basic
features of such a microscope system are: 1) the ability

to cool the cell suSpension to low subzero temperatures;

11

2) the ability to observe the cell sample in real time

at accurately measured temperatures and; 3) the ability to
control both the temperature and the rate of temperature
change (usually linear rates of cooling and warming).

The development and use of such cryomicroscopes has
allowed the determination of the likelihood of intracellular
ice formation, measurements of cell volume during freezing
and thawing, as well as other investigations such as
gas bubble formation inside the cell during freezing

and thawing (38).

1.2 Ova and Embryo Freezing

 

Unfertilized and fertilized mouse ova as well as
preimplantation-stage embryos have been successfully
frozen to -196 or even -296°C. When transferred into
foster mothers they yield live pups (16,17). The
survival was achieved by slow freezing rates (0.2-2.0°C/min)
and moderate warming rates (4-25°C/min). Glycerol and
dimethylsulphoxide (DMSO)(mostly the latter) were used
as cryoprotective agents to protect the embryos against
the deleterious low temperature effects. The same
technique was applied in many laboratories to preserve
embryos from several other mammals, e.g. cattle, sheep,
goats, rabbits and rats (18).

Mammalian embryos have been used for the microsopic
investigation of both intracellular nucleation as well

as volume changes during freezing and thawing. Their

12

relatively large size (~10 times the diameter of human
erythrocytes) and their spherical shape permit volume
changes to be calculated from cross sectional areas.

Several techniques have been reported whereby
membrane permeability can be determined from volume
measurements performed on single cells.

Liebo (19) evaluated the permeability of mouse
ova using the following technique: 1) an ovum was
suspended in a vertical column filled with an osmotically
active solution; 2) as the ovum changed volume by water
flux its density was changed correspondingly; 3) as the
density changed the ovum was forced to rise or fall and;
4) the slowly moving ovum was photographed at small time
intervals and the transient volumes were recorded. A
different technique was used in this thesis. A diffusion
chamber (described below) was used to observe the
transient cell volumes while changing the concentration
of the suspending solution, simultaneously.

Unfertilized, rather than fertilized, hamster ova
were used in the present study for convenience because
microliter volumes of frozen-thawed samples of ova cannot
be quantitatively recovered from the microsc0pe stage.
Therefore, further direct analysis of the treated ova,
such as in-vitro survival assays would not have been
possible. However, the effect of fertilization and
development on the different parameters involved in the

freezing of hamster ova is suggested for future work.

13

1.3 Goals of the Present Thesis Work

 

The goals of this work as guided by the techniques
and results of previous workers are: 1) to determine the
so-called "osmotically-inactive" volume of unfertilized
hamster ova; 2) to determine the plasma membrane hydraulic
permeability (LP) of unfertilized hamster ova; 3) to
determine the effect of the concentration of the suspending
medium on LP; 4) to use the water permeability obtained in
an existing computer model to predict the quantitative
cellular response during freezing; 5) to experimentally
determine the ova volumetric response during freezing and
correlate that response to the model predictions and;

6) to determine the nucleation temperatures of unprotected
as well as protected hamster ova suspended in a DMSO
solution as a function of the cooling rate. This last
factor then determines the effect of DMSO as a
cryoprotective agent on the nucleation temperature of

unfertilized hamster ova.

CHAPTER 2

THERMODYNAMIC AND MATHEMATICAL MODELING

2.1 Introduction

 

In 1963 Mazur (20) derived equations to describe
the kinetics of water loss from a cell during the freezing
process as a function of various parameters. These
parameters include: temperature; cooling rate; the cell
membrane water permeability; the temperature dependency
of the permeability; and the ratio of the cell surface
or membrane area to volume. This was the first thermodyna-
mic model delineating the osmotic response of cells to
freezing. Since that time a number of quantitative models
that share the fundamental framework with Mazur's model
(21-24) have been published.

The fundamental reasons for the development of a
thermodynamic model are: l) to predict cell volume
during freezing and; 2) to predict the thermodynamic state<mf
the intracellular system. Two expressions, one for the con-
centration of the intracellular contents as well as one for
the extracellular medium as a function of the system tempera-
ture are required. The difference between these concentra-

tions represents the thermodynamic potential that drives

14

15

the water into or out of the cell at any given temperature.
The cell membrane is a selective barrier that controls

the water flux, and which is essential for unequal osmotic
pressures inside and outside the cell to exist. Hence,

both the internal and the external concentration expressions
have to be linked through the transport characteristics

of the cell membrane. The resulting expression is the
thermodynamic model that predicts the amount of water
remaining inside a dehydrating cell during freezing at

any subzero temperature and at any given cooling rate.

A typical model for a biological cell suspended in an
isotonic medium is shown in Figure 3. The model consists
of the following elements: 1) The extracellular solution,
consisting of water and solutes; ii) An intracellular
solution of a complicated biological nature that is
simply modeled as water and a single solute; iii) The cell
membrane, which is modeled as a semipermeable membrane
that allows the diffusion of the solvent (water in this
case), but in this model does not allow for the transport
of any solute molecules. In general, this assumption
is not strictly true. However, it is a good approximation
since the permeability of cells to water is several orders
of magnitude higher than to the non-permeating solutes
normally found in protoplasm (20).

For a complete investigation, the water transport
characteristics of the cell membrane must be obtained

either from experimentation or from the literature.

16

The modeling approach used in this work was developed
and modified by Mazur (20), Levin (21), Mansoori (25),
and other researchers. It has been developed in the

present laboratory by Callow (26).

2.2 The Extracellular Solution

 

It is assumed that the external solution behaves as
an ideal solution. Hence, a relationship between the
water mole fraction outside the cell and the temperature
of the system which is assumed to be uniform (25) can
be developed from the basic equation for the chemical

potential of an ideal solution:
Lr'r x) = L'*(T )+RT lnx (2-1)
uw .p, uw .p w

where, u:’* is the chemical potential of pure liquid water,
used as a reference value, xw is the water mole fraction,
and RT and p have their usual meaning.

Assuming that the solid/liquid water phases are
in a state of mutual equilibrium, an equality holds for

the chemical potentials of water in both phases (27),
La ) - 5w ) <2-2)
le pPrX — NW 1}?

where, u: and u: are the chemical potentials of liquid
water in solution and pure solid water, respectively.
The above expression includes the assumption that all
the solutes in the solution are rejected from the solid

phase to the liquid water phase. In other words, the

17

solid phase is assumed to be pure water. Substituting
Equation (2-1) into Equation (2-2) yields

5 L,*
uw(T.P) uw (T.p)

1lew = ’ RT (2'3)

 

and substituting the following expression,

AG = us(T p) -uL'*(T P)
fus w ' w ’

where AG is the molar free energy of fusion of pure

fus
water at temperature T (27), into Equation (2-3) results
in,

-AGfus
1.an = T (2-4)

Equation (2—4) can be differentiated with respect
to X at constant pressure. Using the Gibbs-Helmholtz

expression,

8(AG/T) _ AH
IT] ' '7 (2'5)

Equation (2-4) becomes,

 

1 AHfus 8T
E = ‘—T 53: (2‘6)
RT
where, AHfus is the latent heat of fusion of pure water.

Integrating Equation (2—6),

x T AH

dx _ fus _

Ix‘f‘IT—‘é—d'l‘ (27)

w (3 RT

18

where, the lower limit corresponds to pure water, for

which the mole fraction xw==l, and To is the freezing

temperature. The upper limit corresponds to the mole

fraction at any prescribed subzero temperature. Also

assuming that AHfus is independent of temperature over
the experimental temperature range, Equation (2-7)

yields,

 

AH
In x = fus

w R (2-8)

 

 

_1_.._1_
T T
0

Equation (2-8) describes the concentration of the
solute in the extracellular solution as a function of the
temperature of the system. Also, from the assumption of
ideality made above, it is true that the water activity
outside the cell,a$,is identical to the water mole

fraction x3. Thus:

AH
1n a0 = fus
w R

 

 

l l
T'TI (2'9)
0

Equation (2-9) describes the extracellular water

activity as a function of the uniform system temperature.

2.3 The Intracellular Solution

 

The mole fraction of water inside the cell can be

described by the formula,

i
nW
= i - (2.10)
n -+2v.n%
W j j

X

 

J.
W

19
where, ni,£number of water molecules inside the cell,
n? Enumber of molecules of the jth solute inside the cell
and vj E the dissociation coefficient of the jth solute
species.

However, due to the complicated nature of the internal
solution of most biological cells including the ova used
here, and the lack of detailed information about their
constituents, it is virtually impossible to calculate the
internal water mole fraction by means of Equation (2-10).
Instead, for a state of chemical equilibrium to exist
across the cell membrane, the initial mole fraction of the
intracellular water is considered to be equal to that
of the extracellular isotonic solution in which the ova
naturally exist. Using the water transport equations,
the number of moles of water leaving the cell as the
system temperature is lowered can be calculated. Finally,
if it is assumed that the cell membrane is semipermeable
(i.e. no solute molecules can pass across it in either
direction), the instantaneous mole fraction of water
inside the cell can be calculated.

The intracellular solution is modeled as an ideal
solution (20), for which the water activity is equal to

its mole fraction,
x = a (2—11)

i i . . .
where, xw and aw are the water mole fract1on and act1v1ty

inside the cell, respectively.

20
Equations (2-9), (2-11) and the membrane transport
characteristics are essential for the calculation of the
rate of water flow across the cell membrane as a function

of temperature.

2.4 Water Transport Model

 

Levin (21) described the water flux across the cell

membrane as a function of the chemical potential gradient

by,

out

where, Jw is the water mole flux, A is the membrane
surface area, t is time and Lp is the membrane hydraulic
water permeability expressed in (cm3/dyn-sec) or
(umB/umz-min-atm).

The water chemical potential is given in the form

(28),

'k __
“w = uw(T)-+va-+ T hiaw (2-13)

* _
where, “w 15 a reference chemical potential, VW 15 the

molar volume of water and p is the pressure. Neglecting
the hydrostatic pressure gradient across the cell membrane
(23), Equations (2—12) and (2-13) result in,

_‘l _ ’23: (1n a1 - 1n a0) <2-14)
W W

Vw

where, E is the membrane water conductivity (um/sec)

 

 

 

 

OI

n.

21

 

.2 = Lp .53
vw
or,
dnw E-.A i o
-— = _ — 2- 5
dT Vw°B (1n aw lnaw) ( 1 )

where the cooling rate, B, is given as

(2-16)

03

ll
(LID:
r1” *9

Equation (2-15) relates the outward mole flux of
water across the cell membrane as a function of the uniform
subzero temperature to the natural logarithm of the water
activity on both sides of the membrane. To perform
a computer simulation for the cell dehydration during
freezing using Equation (2-15), the membrane water

permeability (LP) has to be obtained.

2.5 Membrane Water Permeability

 

Terwilliger and Solomon (29) described the bulk
volume flow of water, JV, across the cell membrane, in
a state of chemical potential non-equilibrium and in the
absence of a transmembrane hydrostatic pressure difference

as,

I (2-17)

Jv = RT Lp (Hin — IIout

where, Hin’ Hout denote the osmolality of intracellular

and extracellular solutions respectively.

CORE

am

thl

an:

dI'E

cal

I

5011

bcun

 

22
Assuming that the water permeability, Lp, the
effective membrane area, and the temperature T remain
constant during the course of an experiment, Equation

(2-17) can be integrated to produce:

 

H
Bt-L = {I -—f-1 - ln 1-5] (2—18a)
9 Hi
where,
H 2
AIIP( f)
e = _ (2—18b)
(Vi vb)IIi
and,
_ V(t)--Vi
V = W (2'18C)
f 1

where, Vb is the osmotically inactive cell volume, Vi is
the isotonic cell volume, Vf is the final or the
equilibrium cell volume in the non-isotonic solution,
V(t) is the cell volume at time t, (cm3), Hi and Hf are
the osmolalities of the extracellular solution before
and after mixing (osm/cm3), A is the membrane surface
area (cmzh and R is the gas constant (dyn°cm/mole-°k).
An important parameter that is required for the
calculation of Lp is the osmatically inactive cell volume

V That volume can be described as the volume of the

b'
solid material plus the volume of water (within the cell
boundary) that is not free to move across the cell

membrane in response to an osmotic gradient (37).

23

This parameter was obtained experimentally utilizing
the so—called Boyle-Van't Hoff plot (which will be
discussed in Chapter 4).

A number of researchers (20,21) described the

temperature dependence of Lp as:

E
_ a l 1
Lp - LplT eXPEtIt‘T—II ”‘19)

where, LP] corresponds to the water permeability at
T

Tg==293.15°K, and Ea is the apparent activation energy for
the permeation process.

However, Levin (30) mentioned that the above equation
can be applied only to the simplest types of membrane
systems. For more complicated membrane systems (i.e. a
number of parallel membranes resisting the water flow), one
may require a more complicated expression for temperature
and/or solute concentration dependence for the overall
cell water permeability.

Diller and Bradley (31) proposed two possibilities
for the dependence of Lp on the solute concentration.

The first one is an exponential relation expressed in

the form,

_1_.__1_
T

T
g

 

 

1 1
+EC[—fi—-fi—]:l (2-20)

E

a

L = L ] exp[;—

P P T R g

g _
while the second relation shows a linear dependence of

the form,

24

E
_ 3A-}. _1_...1_ -
Lp — Lp]T exp‘.R T TH +EC II II ] (2 21)

g- 9-

 

 

LQ

where, the first part of the right-hand-side of Equations
(2-20) and (2-21) is the temperature dependence shown

in Equation (2-19). EC is the permeability concentration
coefficient and Hg is the reference solute concentration
at the reference temperature Tg. Scheiwe et al. (32,33)

have used another form of equation:

H-—H l 1
Lp = LP]T exp[§(l-+a2 ~7:;g [T-—Tg]yta1[7T-fi;}]

9
(2-22)
where, al and a2 and b are coefficients of the L function.
A discussion of the effect of temperature and solute
concentration on Lp for hamster ova is presented in
Chpater 4 of this thesis.
In summary, cell volume changes during freezing are

determined numerically from:

T dnw
dT (2-23)

V = V -V'lyr 7??
o

o w
where, V0 is the initial cell volume at the freezing
temperature TO (°K),and v& and nw are the apparent molar
volume and the number of moles of water, respectively} where:

dn E-A

_!V_=
dT '".
vw B

 

(1n a;- 1n a3) (2-15)

25
where, A is the membrane surface area, B is the cooling
rate (°C/min), and a: and as are the water activity
inside and outside the cell, respectively. E is the

membrane hydraulic conductivity (um/sec) and is equal to

where Lp is the membrane water permeability obtained from
experiments, by means of Equation (2—18) described
above. The temperature dependence of Lp is in the form

IEaII 1“

L =L] exp -— —-— (2-19)
R T T

p pT _ g

g _

 

where Lp corresponds to the water permeability Lp at
Tg==293.15°K. The activation energy, Ea, in Equation
(2-19) has been determined from the literature (19).

The concentration dependence of Lp described in Equations
(2-20) through (2-22) has been assumed insignificant

due to experimental results to be described in

Chapter 4 in this thesis. The cell membrane is assumed
semi-permeable. The membrane surface is assumed to be
that of a shrinking sphere. No concentration or thermal
gradients are assumed to exist within the cell sample

as well as the cell itself. Hydrostatic pressure
gradients across the membrane are neglected. These
simplifying assumptions and others are discussed in

detail in Chapter 4 of this document.

CHAPTER 3

EXPERIMENTAL TECHNIQUES

3.1 Cell Sample Preparation

 

Hamster ova were obtained by the method described
by DeMayo (1). Hamsters were induced to superovulate
by an intraperitonial (IP) injection of 30 10 pregnant
mare serum (PMS, FolligonR; Intervet Laboratories;
Bar Hill, Cambridge, Great Britain) between 900 hrs and
1200 hrs of age followed 56 to 64 hrs later with an IP
injection of 30 10 human choronic gonadotropin, HCG
(APLR; Ayerst Laboratories Inc., NY). The hamsters were
sacrificed by cervical dislocation, 14 to 16 hrs after
HCG administration. The oviducts were removed, dissected
free of fat and flushed from the fimbrie with 0.3 ml of
either Dulbeccos phosphate buffered saline (PBS) (Gibco
Laboratories, Grand Island, NY) or a modification of the
squirrel monkey in-vitro fertilization medium used by
Kuehl and Dukelow (1979), TC-l99. Cumulous cells were
removed by an addition of 1 mg/ml of hyaluronidase
(Sigma Corp., St. Louis, M0) to the collection medium.

Fresh cells were then washed in 0.3 m1 of medium and

held in an ice bath for no longer than 3 hrs until

26

27

transferred to either the diffusion chamber or the
cryomicroscope stage (both described below).

Cryoprotectant: For the experiments that required

 

the addition of a cryoprotective agent, 0.2 ml of a 3 M
dimethylsulfoxide solution (DMSO; Baker Chemical Co.,
Phillipsburg, PA) were added to an equal volume of cell
medium for a final concentration of 1.5 M solution.
Healthy cells (75 to 80 um dia.) were transferred to

the mixture at room temperature (23°C), where they were
held on ice for at least 10 minutes, allowing them

enough time to equilibrate with the 1.5 M solution before

the transfer to the experimental apparatus.

3.2 The Diffusion Chamber System

 

Figures 5a and 5b show a schematic of the diffusion
chamber designed by Ligon (35). The system consists of
two compartments separated by a dialysis membrane. A
drop of cell suSpension is held stagnant in the upper
compartment. The lower compartment is initially filled
with a solution isotonic with the cell suspension. The
volume of the lower compartment is extremely large
compared to that of the upper compartment. Hence, the
lower compartment can be considered as an infinite
reservoir. This allows the extracellular solution in the
upper sample space to attain a final equilibrium
concentration equal to that of the bulk solution in the

lower compartment. At time equal to zero the lower

 

Top Fitting

View Hole -
95"
/.—Circu1ar Coverglass

on bottom

@ Spacing Ring
"- (variable diameter;

Duty“; ' 35 cell dis.)
Henbrene ..._.. thicknes
. Membrane
rheteiner

 

//-\ /;k '10.!

rautlet Port

 

 

 

Bulk Flow
Plastic
Bulk Plow Brass

 

 

 

 

Channel
.a1\\ ‘j3;7

Plastic Sheet

/ /

Figure 58.Exploded view of the diffusion chamber.

 

 

 

(Reproduced from Nowlen(56))

29

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30
compartment is flushed with a new solution whose concentra-
tion is either hypotonic or hypertonic with respect to the
cell suspension. If the solution in the lower compartment
has a concentration higher than that of the cell suspension
in the upper compartment, solutes will diffuse upward
across the dialysis membrane from the lower to the upper
compartment and vice versa.

As shown in Figure 5c, two pressurized bottles
(1000 cc) are connected to two small single pumps. The
outlet of each pump is connected with plastic tubing to
the inlet ports of a two-way switch. The outlet of the
switch is connected with plastic tubing to the inlet at
the lower compartment of the diffusion chamber. The
outlet of the lower compartment is connected to a
discharge container. The entire mechanism is used to
regulate the bulk flow in the lower compartment. It
is also used to facilitate changing the osmolality of
the bulk flow from isotonic to non-isotonic and vice versa.
This will in turn change the osmolality of the extracellular
solution in the upper compartment. The system can be
modified to include more solution bottles.

Once the lower compartment is filled with a non-
isotonic solution, e.g. hypertonic, the solutes will
gradually diffuse across the dialysis membrane to the
upper sample region. Consequently, the concentration of
the solution in the upper compartment will increase in
some fashion. A certain amount of time will elapse

until a state of transmembrane chemical equilibrium is

31

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32

established. This time constant will depend primarily
on the transport characteristics of the dialysis membrane
for each of the solutes present.

Preliminary analytical studies by Ligon (35)
suggested that for NaCl, a typical solute of interest,
the sample region will have negligible concentration
gradients. Hence it can be characterized by a single
concentration. Ligon could also show, both analytically
and optically, that the time constant required for the
solution in the sample region to equilibrate with that
in the lower compartment ranges from 3 to 6 seconds.

Nowlen (36) assumed that concentration gradients
within the sample compartment are negligible and concluded
from a simple analytical model that the concentration of
the solute in the sample region is expressed as an
exponential function of various parameters. These
parameters are: the concentration of the bulk solution;
the initial concentration of the sample region; the
permeability of the dialysis membrane to that solute;
the volume of the sample region; the effective area of
dialysis membrane available for transfer, and time.

Nowlen found that using a Cuprophan 80 pm dialysis
membrane and a sodium chloride solution, the time delay
is approximately 59 seconds for 95% response time. This
is a significantly long time compared to the 3-4 minute

period during which the hamster ova were observed to shrink.

33

The major difference between Ligon's case and
Nowlen's was the fact that Ligon's model was for a chamber
thickness of 12 um whereas Nowlen's model was for a chamber
thickness of approximately 250 um.

Experimental results of the present work, using
hypertonic NaCl solutions and a Cuprophan 80 m membrane
(Membrana GmbH, Wuppenal, West Germany) showed a time
lag of approximately 6 seconds. The effect of such a time
lag was considered insignificant in the calculation of
the water permeability of hamster ova in the present
study. The reason for the insignificance of the time
lag is explained in Chapter 4 of this thesis.

The chamber design with top and bottom glass covers
allowed a real-time recording of the cell volumetric
behavior using a microscope-mounted video camera. The
entire chamber fits on a typical microscope stage as
shown in Figure 6.

A circular plastic spacer L~150 um thick], with a
hole in the middle [~1/8" I.D.] was inserted in the upper
compartment. The thickness of the spacer protected the
hamster ova [75-80 um diameter] from being crushed between
the dialysis membrane and the top cover glass. The
spacer also decreased the volume of the upper compartment.
This volume reduction increased the probability of finding
a good ovum, since few ova were available for

experimentation.

34

 

Figure 6. A photograph of the diffusion chamber
mounted on the microscope stage.

35

3.3 Measurement of "Osmotically Inactive Volume"

 

The concept of osmotically inactive volume was
first proposed by Luké and McCutcheon (37). They
modified the Boyle Van't Hoff law (see Appendix A) to
account for the amount of solids and water inside the
cell that is unavailable for transport across the cell
membrane in response to an osmotic gradient. This
amount of water and solids is usually defined as the
"osmotically inactive volume".

The diffusion chamber described above was used
in the present work to determine the osmotically inactive
volume of unfertilized hamster ova. A small drop
(~3 uL) of cell suspension containing 5 to 10 ova was
placed inside the upper compartment. The upper compartment
consists of 3 parts: 1) an upper bound, which is a cover
glass; 2) a lower bound (an appropriate piece of dialysis
membrane which was immersed for several minutes, before
an experimental run, in a solution isotonic to the cell
suspension [300 mOsm NaCl]) and; 3) the circular spacer
described above, surrounding the sample region.

Next, the lower compartment of the chamber was
mounted on the microscope and filled with isotonic NaCl
solution [300 mOsm]. The assembled upper fixture was
then press-fitted on top of the lower compartment (see
Figure 5b). All experiments were conducted at room

temperature [~23°C].

36

A healthy ovum was located in the microscopic
field of View. The initial isotonic cell volume was
recorded. The spherical nature of the hamster ova
facilitated volume measurements from the circular
projected area. Two or three diameters of the same ovum
were measured. The mean of these diameters was used to
calculate the volume of the spherical ovum.

The lower compartment was then flushed with a
hypertonic sodium chloride solution. The ovum was
observed to shrink until a new state of chemical
equilibrium was established across the cell membrane.
This was judged by observing no further change in the cell
volume. At this point the new volume was recorded as
mentioned above. The preceding procedures were repeated
for the same ovum in a number of increasingly concentrated
NaCl solutions. The new equilibrium volume was recorded
each time. Figure 7 shows a sequence of photographs of
typical microscopic observations of the equilibrium
volumes of a single cell in increasingly concentrated
NaCl solutions.

Figure 8 shows the typical behavior of a single
ovum during osmotic shrinkage in hypertonic solutions.
The linear relation between the inverse of the external
solute concentration and the normalized equilibrium cell
volume indicates the applicability of the so-called

Boyle-Van't Hoff law (see Appendix A).

 

 

Figure 7. Sequence of photographs of equilibrium cell
volume in increasingly concentrated NaCl
solutions.(a-O.3, b-O.4, c-0.5, d-O.6,
e-O.8 and f-l.5 Osm

Normalized Cell Volume (%)

( Vcell / Vinitial )

100~

80 -

60 _

4O -

20-

38

 

 

Figure 8. Typical equilibrium volumes

1 1 1

1 2 3
1 / Concentration (Kg/0am)

of a single ovum when
exposed to hypertonic
solute concentrations.

421

39
In order to generate a Boyle-Van't Hoff plot, the
experiment as described above was repeated for several
ova. The osmotically inactive volume of unfertilized
hamster ova, was obtained by extrapolating the linear

dependence to infinite solute concentration.

3.4 Measurement of Cell Membrane_Water Permeability

 

The same diffusion chamber described above was used
to determine the water permeability of hamster ova. The
cell sample was placed in the chamber as explained in
detail in the previous section. The initial volume was
recorded. The bulk flow region was flushed with a
hypertonic NaCl solution, using the flushing system
described above. The moment at which flushing occurred
was defined as time zero.

The actual transient cell response to the hypertonic
salt solution was recorded on video tape. The tape
was replayed and the cell volume was measured every
5-10 seconds, until the cell reached a final equilibrium
volume in the concentrated salt solution. Substituting
these measured volumes into Equation (2-18c), the
normalized cell volume V was obtained. Then using
Equations (2-18a) and (2-18b) the membrane hydraulic

conductivity Lp was calculated.

3.5 The Cryomicroscope System

 

A temperature-controlled cryomicroscope conduction

stage was used to observe the behavior of both protected

40

and unprotected hamster ova during the freezing process.
The system is based on the designs of Diller and

Cravalho (12) and McGrath et a1. (14). It is essentially
the same system used by Morris and McGrath (38) and
Callow (26) with slight modifications (Appendix B).

As shown by Figure 9 the system consists of a
specially designed heat conduction stage mounted on a
commercial research light microscope (Zeiss Universal)
to which a color video camera or a 35 mm camera can be
attached. The video camera is connected to a video
cassette recorder as well as to a color monitor. This
allows the real-time observation of the sample behavior
while simultaneously recording the same response on
video tape. A refrigeration source, namely a liquid
nitrogen (~196°C) dewar is connected to the conduction
stage. A stream of two-phase nitrogen (vapor and liquid)
is circulated in an annular cavity inside the copper
stage (see Figure 10). A thermocouple and an electrical
heater which exist on top of the copper block are both
wired to an analog controller.

As shown in Figure 11, the controller mainly consists
of an amplifier, a power supply, and a digital temperature
display. The controller input is a programmed analog
signal provided by a PDP-ll minicomputer through a
digital-analog converter. A strip chart recorder is
used to record the actual sample temperature profile.

The stage and the microsc0pe optical elements are

enclosed in an environmental glove box to minimize

41

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42

 

NOT TO SCALE

Thermocouple

/ Re fregerant

Refregerant \
Out

In

         

To Power
Supply

ScrOVI

Glass Heater
Slide

Copper
F°il Plastic
I. 4 Clamp

 

 

 

 

 

 

 

 

 

 

Insulating'—\ I I
M” t—I-‘H—l‘l'
Copper
L’fl-‘IT —'—-' "— Block
Ill
‘\—-Refregerant

Annular Cavity

Figure 10. Schematic of cryomicroscope
conduction stage.

43

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DARLINGTON
TRANSISTOR
PAIR

 

 

 

POWER
SUPPLY
DESIRED TEMPERATURE
SIGNAL CONDITIONING
csnsnaron stscrnonrcs INERHOCOUPLE 4‘
IN
V(deaired
temperature) V(actual
temperature)
antarcsaanr "5‘75“
a
COMPARATOR

 

 

 

HEAT TRANSFER STAGE

 

 

ERROR SIGNAL

Figure 11. Schematic of cryomicroscope temperature

controller.

 

44
condensation on the cryostage during freezing. The
assembly of the conduction stage is shown in Figure 10.
The body of the stage is a copper block that fits in
place of the regular microscope stage (Fig. 12). Interior
to the block is a circular channel of rectangular cross
section with inlet and outlet ports. The channel acts
as a passage for the refrigerant. A small hole is drilled
in the middle of the copper block to allow the transmission
of light through the metal base. The top surface of the
stage is covered with a thin layer of insulating tape.
A tiny copper-constantan thermocouple (copper wire n9.
TFCP-003, Constantan wire n9.TFCC-003, Omega Engineering
Inc., Stamford, CT) is sandwiched in between a regular
no. cover glass and the non-conductive surface of an
electrically conductive coated glass slide (1" X1%" X0.02",
E-C coated glass, n2. 7059 Alkali Free, Corning, NY). An
epoxy glue (5 minute epoxy, Devcon Corporation, Danvers,
MA) or G.E. clear silicon rubber glue is used to hold
the thermocouple between the two surfaces. The entire
assembly is shown in Figure 13. The thermocouple-glass
sandwich is placed on the stage with the electrically-
conductive surface facing down, towards the insulating
tape. Two small pieces of thin c0pper foil contact
the edges of the lower surface of the sandwich to
facilitate supplying power across the thin film on the
bottom surface of the glass heater. The glass slide
is held on top of the stage by means of plastic clamps

at either end (see Figure 10).

45

 

Figure 12. Photograph of cryostage mounted on the
microsc0pe.

46

 

 

 

 

square
thermocouple cover 51“”
junction '———\\
epoxy or
-”-—_—‘ silicon ruber
glue

 

electrically -—d//

conductive film

(transparent) teflon coated
l thermocouple wires

 

 

‘r—fl

 

-.

 

 

 

 

 

 

rectangular
Klass slide

 

NOT TO SCALE

 

Figure 13. Assembly of the thermocouple
sandwich. I

47

The manner in which the sample temperature is
controlled is as follows. The sample is placed on top
of the cover glass at the center of the viewing area as
close as possible to the junction of the thermocouple.
Saturated nitrogen vapor at approximately -l96?C is
passed through the conduction stage, which acts as a
thermal sink for the conduction of heat from the sample.
A PDP-ll minicomputer provides an analog signal equal
to the voltage equivalent of the desired temperature to
the comparator of the control circuit. Simultaneously,
the voltage equivalent to the actual temperature measured
by the thermocouple is linearized, amplified and is
input to the comparator. Measuring the difference
between the desired and the actual voltages, the
comparator induces the power supply to generate an amount
of electrical power across the glass heater disk, which
tends to drive the instantaneous temperature difference
to zero. The digital temperature meter displays the
actual temperature, while the strip chart recorded.

traces the temperature history of the sample.

3.5.1 Error Introduced in the Measurement of Sample

 

 

Temperature

 

Two major sources of error in temperature measurements
are introduced due to the configuration of the conduction
stage. The sample is vertically displaced from the
thermocouple by the thickness of the glue layer and the

coverslip above the thermocouple itself. This introduces

48

an amount of error that is estimated by Tu (39) to be less
than 1.0°C. The second and the most important source of
error is the horizontal displacement of the sample from
the thermocouple. Due to the normal operating mode of
the conduction type of cryomicroscope, a horizontal
temperature gradient is expected (40). While the
thermocouple is measuring the temperature at the very
local domain surrounding its junction, the sample
could be located anywhere in the viewing area of the
conduction stage. Consequently, due to the non-uniformity
of the temperature profile across the viewing hole, an
error in temperature reading could result from the
difference in temperature between the thermocouple
location and the sample location. This type of error
was studied in detail by Tu (39), who used a numerical
heat transfer analysis to determine the temperature
gradients in the vicinity of the thermocouple. However,
Tu used a different stage configuration than the one
used in this work. Callow (26) described an experimental
method for the determination of the total magnitude of
temperature error (in x and y directions). Callow
estimated that error to be as large as 8-9°C between
the thermocouple and the edge of the viewing hole
(~2 mm) at steady state.

The method used in the present work to estimate
the amount of temperature error in the horizontal

direction can be described as follows:

49
As shown in Figure 14a, an electrically conductive

coated glass slide is prepared as described above (see
Figure 13), with two more copper-constantan thermo-
couples sandwiched between the cover glass and the non-
conductive surface of the heater slide. The distance
between the middle thermocouple and each of the two
additional thermocouples is 1.5 mm. The entire assembly
was mounted on the conduction stage. The middle
thermocouple was connected to the analog controller,

so that the temperature of the center point in the
viewing area can be controlled. Each of the other two
thermocouples was connected to a digital voltmeter (DVM).
The end of the copper thermocouple wire was connected
directly to the positive pole of the DVM. The end of

the constantan wire was connected to the negative pole of
the DVM by means of a copper cable. The connection between
the constantan wire and the copper cable was immersed

in an ice bath for a reference. The temperature of the
center point was set at values in the temperature range
of (0 to -100°C) through thermocouple number 1. The
voltages equivalent to the steady state temperatures at
thermocouples 2 and 3 were recorded. The voltages were
transformed into temperatures using the tables in the
Temperature Measurement Handbook [Omega Engineering, Inc.,
Stamford, CT]. The generated plot in Figure 14b was
produced from the measured values over the temperature

range of 0 C to -100 C.

50

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ruonowsonuo on» no ache
In, - h b P

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. % oaasooosaone ...... II ..o

 

 

 

 

(3°) 8? pay 2# satanooomraq; JO Sutteaa

51

The steady state results shown in Fig. 14b give an
amount of error ranging from 4°C to 10°C for a point
displaced from the center of the viewing hole by 1.5 mm.
This is in agreement with the results of Callow (26).

The fact that all data are below the theoretical line
shown in Figure 14 indicates that thermocouple number one
is always warmer than thermocouple number two and number
three as expected.

The fact that thermocouple number two and number three
data are not coincident on Figure 14 suggests that an
undesirable asymmetry exists in the system. The most likely
source of this asymmetry is the inaccurate positioning
of the thermocouples relative to the center point of the
viewing area and relative to each other.

To eliminate the horizontal type of temperature error
as much as possible a cell very close to the thermocouple
(no more than 0.3 mm away) was always chosen for
observation. Hence, the overall steady state temperature

uncertainty was estimated to range from 1.0°C to 3.0°C.

CHAPTER 4

RESULTS AND DISCUSSION

4.1 The Osmotically Inactive Cell_Volume

 

Figure 15 is a Boyle-Van't Hoff plot, that shows the

normalized cell volume [V l/V. ] as a function of

cel initial

the inverse of the solute concentration for ova. The

data were gathered at room temperature [~23°C]. The

data shown are the result of seven experimental runs. Each
run was performed on a different ovum. The diffusion
chamber was used as described in Chapter 3. During each
run, a small drop of cell suSpension was placed in the
upper compartment of the diffusion chamber. A healthy
ovum was located under the microscope objective, and

its isotonic volume was recorded. The lower compartment
of the chamber was filled initially with NaCl solution
isotonic to the cell suspending medium [300 mOsm]. By
changing the solution in the lower compartment, the single
ovum was exposed to a number of increasingly hypertonic
NaCl solutions [0.4, 0.5, 0.6, 0.8 and 1.5 Osm NaCl].

The ovum was allowed enough time to equilibrate in each

hypertonic solution [~5 minutes]. The equilibrium cell

52

NORMALIZED CELL VOLUME

53

 

 

 

t0_. a
0.0 ._
0.0 __
0.7 _
0.0 _ /
0.5 __ I
0.0 _

.r I

/

0.: __ ,’ reap. a 23 'c

- // * 300 mOSM

}/ 21.0% 2
0.2.. ‘— r = 97.79.
= 3.3 %
Limits 18.22-27.12 I s“. o".
0.1 —' I lelta
0.0 I I I I 7| I 1 I
C) t 2. 3
l/CONCENTRATIOqu/osu)
Figure 15. Boyle-van't Hoff plot

Each point is the mean of 7 ova suspended in

NaCl 5
method

olution. The data were fitted using the
of the least squares.

 

54

volume was recorded in each case and divided by the
initial isotonic volume.

The ova seem to behave as perfect osometers, since
the data show a highly linear relationship as expected
from the Boyle-Van't Hoff law [see Appendix A]. The
typical behavior of a single cell is shown in Figure 8,
which also indicates a linear relationship for an
individual ovum.

The line shown in Figure 15 is a least squares fit
to the experimental data with a determination coefficient
of 97.7%. The thinner "band" about each point represents
the limits of the collected data, while the heavy marks
represent the standard deviation with circles at the mean
values. The fitted line is extrapolated to infinite
concentration to yield an average osmotically inactive
volume, Vb’ of 21.6%, with a standard deviation of
3.3% and values ranging from 18.2% to 27.1%. At this
time, there are no other values published for the
osmotically inactive volume of hamster ova. But for a
similar biological system, which possesses approximately
the same volume (mouse ova) the published values are
18.2% [by Leibo (19)], and 20-21% [by Rall; see Leibo
(19) for the values obtained by Rall]. This suggests

that the present values are reasonable.

55

.mswp to compocst m we cowuzpom _omz sweepnngc
m cw m>o Layman; m to :tmpumq mmsxcmngm m>wpeucmmmtamm

 

 

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3.3: m2.»
n.» 0.... m a 0d a p 0.— n0 0.0
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.50 «.9 H _: m file...

00 an N .050».

56

4.2 Cell Membrane Water Permeability

 

Figure 16 shows the normalized cell volume as a
function of time for 3 hamster ova, when exposed to a
hypertonic NaCl solution [500 mOsm NaCl].

The diffusion chamber described in Chapter 3 was
used to generate the data in Figure 16. A small drop
[~2 uL] of cell suspension was placed in the upper sample
region. The lower bulk flow region was filled with a
sodium chloride solution isotonic to the cell medium
[300 mOsm]. A healthy ovum was located under the microscope
objective. The initial cell volume was recorded as
described above. The bulk solution region was then flushed
with a hypertonic NaCl solution [500 mOsm], using the
flushing mechanism described above. The moment at which
the flushing occurred was marked as time equal to zero.
The ovum responded to the hypertonic extracellular medium
by shrinking. The transient cell response from time equal
to zero until the cell reached equilibrium with the
hypertonic external medium was recorded on a video tape.
The equilibrium volume was judged by observing no
further change in the cell volume. The video tape was
replayed and the transient cell volume was measured from
the projected area every 10 to 15 seconds. The transient
volumes were normalized and plotted as shown in Figure 16.
The same procedure was repeated for each one of 18

different unfertilized hamster ova examined in this

57

experiment. However, different final solute concentrations
were examined (Hf==0.5, 0.8, 1.5 and 1.76 Osm). All
experimental runs were conducted at room temperature
(T5E23°C). Substituting the observed cell volume as a
function of time into the equation develOped by Terwilliger
and Solomon (29) (Equation 2-18), Figure 17 was obtained.
The solid line in Figure 17 is a least squares fit to the
experimental data represented by circles. The slope of
this line is equal to the water permeability Lp multiplied
by the constant B, from which Lp was obtained for each
single cell.

The x-intercept of Figure 17 represents the
summation of two time lag factors. Due to the design of
the flushing mechanism described above (see Chapter 3),
the hypertonic solution will take some time to replace
the isotonic solution first in the plastic tubing then
in the bulk flow region. The second lag is the time
constant associated with the solute diffusion across the
dialysis membrane (this subject is discussed in detail
in Chapter 3). The total time lag observed was typically
5 to 10 seconds. Fortunately, that lag did not affect
the calculations of Lp, because as shown from Figure 17
Lp was calculated from the slope of the line, which should
not change even if the line passes through the origin.
However, it should be noticed that for perfect
instantaneous mixing at time t =0, the value of the

y-variable of Figure 17 should be zero. The calculated

58

 

TOMp-z 23 'c

I _ / Ilia-308m
11': .8 n

{VKH,/fl.l-1]_ln(1_\7) }
to
I

 

 

0.0 0.5 10 1.5 20
TIME ( min.)

Figure 17. Representative correlation of experimental data in
the form of Terwilliger and Solomon.

Calculated Lp 0.8l5 umB/umZ-min-atm
K 18.26 INTI/SEC

59

values of Lp were substituted back into the Terwilliger
and Solomon equation, to produce the solid line shown in
Figure 18. The line shows a good fit to the average
experimental shrinkage pattern of 4 representative ova.
This indicates that the dynamics of the osmotic shrinkage
of hamster ova correlates to the mathematical model of
Terwilliger and Solomon (29), and to the osmotic behavior

of other biological cells, like human red blood cells

'_—_ — _I

which were examined by the same authors. Lp values

ranging from 0.65-+1.00 um3/um2-minoatm (corresponding

to water conductivity E values from 16.3-+22.4 um/sec) were
obtained with an overall mean value of 0.8 um3/um2-min-atm
(E==18.0 um/sec), at room temperature (T 523°C).

The water permeability calculated above is approximately
twice the published value for the permeability of
unfertilized mouse ova (0.44 pm3/um2-min-atm (19)). This
indicates that unfertilized hamster ova are more permeable
to water than mouse ova. Hence, during freezing, a
hamster ova is expected to dehydrate faster than a mouse
ova cooled to the same subzero temperature and at the
same cooling rate.

Thus, according to Mazur's two-factor hypothesis (6),
hamster ova have to be frozen at a faster cooling rate
in order to observe the same probability of internal ice
formation as that observed for mouse ova.

The effect of both temperature and solute osmolality

on the water permeability of biological cells has been

6O

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61

studied by a number of workers (19,30,41-47). There is
an agreement by most workers that the hydraulic permeability
Lp is highly dependent on temperature; this dependency
is usually presented in an exponential form as given by

Equation (2-19)

L —L] ex FEEL-i“ (2-19)
p‘pT p__RT T_

g 9
The apparent activation energy, Ea' which describes the
temperature dependence of the hydraulic permeability
coefficient, Lp, for hamster ova was not determined in
the present study.

The computer simulation to be described later in
this thesis was performed using an activation energy
value of 14.5 kcal/mol. This value was obtained by Leibo
(19), for unfertilized mouse ova, and is the only
published value of activation energy for any ova. The
appropriateness of using this value for hamster ova will
be discussed later in this chapter.

Farmer and Macey (48), and Outhred and Colon (49)
reported that Lp is independent of the osmolality of
the suspending solution. Diller and Bradley (31)
suggested two forms for the solute concentration
dependence of LP: exponential and linear as illustrated
by Equations (2-20) and (2—21),

1 1 l l
F‘T] +Ec['n“fi—fl (2'20)
9 9 ‘

 

E
a
L = L ex ——
p 9].]? pI:R
g

62

l l l l
T—---T-]] +EC[—n”n'g—] (2’21)

 

Both equations when fitted to the experimental data obtained
by the same authors (31) revealed poor statistical fits.
Scheiwe et al. (47) proposed another exponential form
as shown by Equation (2-22),
H-H

= 9 _ _l_-__1_ -
Lp LP] exp[b(1-+a2 H [T Tg]+al[H H I] (2 22)
T9 - 9 9

 

where al and a2 are functional parameters that can be
adjusted to obtain the best possible fit to the experimental
data. However, Scheiwe et al. (31) concluded that this
method is rather approximate and that the values of al

and a2 should be established independently in respective
experiments.

Rich et al. (45) reported that the Lp of red blood
cells decreases with increasing osmolality. Farmer and
Macey (48) and Outhred and Colon (49) disagreed with the
conclusions of Rich et al., where they reported that Lp
is independent of the osmolality of the suspending
medium. On the other hand Forster (50) fully supported
the findings of Rich et al.

In this work, both the linear and exponential
relationships between the hydraulic permeability of
unfertilized hamster ova and the external solute

concentration were investigated.

63

Figure 19 shows a linear fit to the data obtained
for Lp at room temperature (~23°C) for different solute
osmolalities [0.5, 0.8, 1.5 and 1.76 Osm NaCl]. The
extracellular solute concentration is expressed in a form
similar to Equation (2-21), [l/ni-—l/n]. The light marks
represent the range of Lp values at each solute concentra-
tion, while the heavy marks represent the standard
deviation, with a circle at the mean value. The coefficient
of determination is 66.3%. Figure 20 illustrates an
exponential fit to the same data presented in Figure 19
with the same meaning of the drawn lines. The coefficient
of determination for the exponential fit is 65%.
Obviously, it can be noticed that the correlation
coefficients of both the linear and the exponential fits
are almost identical and that they are relatively low.
This poor correlation can be attributed to the wide
distribution of the measured values of Lp relative to the
510pe of the best fit line.

By means of a statistical test of hypothesis the
slope of the best fit line in Figure 19 was found to be
significantly different than zero at the 99% confidence
level (see Appendix C). This means that the water perme-
ability of hamster ova is dependent on the extracellular
solute concentration in some fashion. However, it is not
possible to assess the applicability of both suggested
forms of dependence shown by Equations (2-20) and (2-21) due

to the low correlation coefficients obtained above.

64

 

1.1

 

 

 

 

 

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(V-3 —'/U) Kg/Ogm

Figure 19, Water permeability as a function
of the extracellular impermeable
solute concentration (NaCl only).

65

 

 

 

 

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E r
‘ c Overall Inn: 18 Urn/fie:
- 1.5 __.L .
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03 l T l I l I l 1 1
1O 15 10 25 30 35

(Ma — l/n) Kg/Osm

Figure 20. Water permeability as a function of the extracellular
impermeable solute concentration (NaCl only).

66

The water permeability of hamster ova decreased by a
factor of approximately 1.5 when the external solute
osmolality increased from 0.5 to 1.76 Osm/kg. Since
the solute osmolality increases to very high values during
freezing, it was necessary to estimate the permeability
values at such high solute concentration.

Extrapolating the statistical fit lines in Figures
19 and 20 to infinite solute concentration, where the
value (l/O.3-—l/H) is limited to 3.33 when H-*un the
estimated values of Lp were found to be 0.607 and 0.627
(um3/um2-min-atm) for both linear and exponential
relations respectively. These values are very close to
the range of Lp values obtained in the present work
(from 0.65 to 1.0 um3/um2-min-atm). However, over the
same range of solute concentration [(1/0.3-—1/H) ranging
from 0 to 3 kg/Osm], Schwartz and Diller (43) showed that
the water permeability of granulocytes will decrease
by at least an order of magnitude. Therefore, the
external solute concentration dependence of L , for
unfertilized hamster ova was considered insignificant.
Hence, this concentration dependence of Lp was not accounted

for in the computer model to be presented.

4.3 Computer Simulation of The Cell Osmotic Behavior

 

During Freezing

 

4.3.1. Assumptions

 

Several assumptions concerning the modeling of the

osmotic behavior of biological cells during freezing are

 

67

regarded in this work. As reviewed by McGrath (8), one
major problem involved in such models is the extrapolation
of the numerical value of the membrane permeability at
higher temperatures to lower subzero temperatures. Although
some experimental evidence suggests that the extrapolation
is valid, some researchers have suggested that it should
be undertaken with care. Since physical and chemical
events may alter the membrane transport characteristics
at low subzero temperatures, the water permeability could
undergo significant non-linear changes. However, in this
work, the linear extrapolation was considered a reasonable
assumption. An activation energy, Ea' of 14.5 kcal is
chosen from the literature, as reported by Leibo (19)
for unfertilized mouse ova. This value has been used
unless otherwise noted. Some workers proposed that the
concentration of the suspending medium affects the membrane
permeability. However, from the experimental data
presented above, the membrane hydraulic permeability is
assumed to be independent of the solute concentration.
It is also assumed that the solute concentration is
uniform within the cell during freezing, which is
generally accepted except for cells with very high
water permeability (20,51,52).

Two cases may be considered for the cell membrane
surface area during freezing: 1) it can be assumed to
remain constant as assumed by Mazur (20) or; 2) it can

be considered to behave like a shrinking sphere.

68

McGrath (53) mentioned that membrane material could be
lost during freezing. However, Callow (26) showed that
the difference in the predicted cell response during
freezing, due to the surface area assumptions is not
critical. Hence, the cell membrane surface area is
assumed in the present work to be that of a shrinking
sphere. This assumption is supported by Luke et al. (54).
The membrane is assumed nonpermeable to solutes, hence,
only water transport is accounted for in the dehydration
model. A good approximation that is supported by
analytical work (10,25,55), assumes that both the
internal and external solutions behave like ideal
solutions, and that the cell is in thermal equilibrium
with its surrounding medium. Hence, no thermal gradient
is assumed to exist within the cell boundary or in its
local environment. Finally, it is assumed that the
latent heat of fusion remains constant over the experimental
range of temperature.

The computer model used in the present study is
summarized at the end of Chapter 2 of this thesis. The
initial solute concentration is taken to be that of the
cell suspending medium [300 mOsm]. The inactive cell

volume is taken to be 21.6%.

4.3.2 Effect of Cooling Rate on Predicted Cell Volume

 

Figure 21 shows the effect of changing the cooling

rate, B (°C/min), on the predicted osmotic response of

JEI

0.8

13

0.6I

IA 0

NOWL IZED CELL VCLUHE

0.20

69

Glynn

 

 

 

0J0

Figure 21.

a1711111[1111 [11 1111 111' 1111l111 111111 I111 r]

-m m .2030 - an. no -4 p. on
TEPFERATLRE (° C.)

Effect of cooling rate on predicted cell volume

3
change during freezing [Lp= 0.732 Tm—" l6. 4 's—m—ec]
pm -min-atm

70

unfertilized hamster ova. A typical Lp value of

0.732 um3/um2-min-atm obtained from the experiments
performed as part of this work has been used, with an
activation energy of 14.5 kcal/mol. The figure illustrates
the highly significant effect of the cooling rate on the
water content of an ovum at any intermediate subzero
temperature. At'~-13°C the volume of a cell cooled at
3°C/min is about 45% of the volume of the same cell if
cooled at 20°C/min. Consequently, at the same intermediate
temperature the predicted volume of a cell cooled at a
relatively faster rate is more displaced from the
equilibrium volume. Hence, the cell is more likely to

form ice internally. This correlates to the experimental
results of increased probability of internal ice formation

at higher cooling rates, as presented below.

4.3.3 Water Permeability Effect

 

 

Figure 22 shows the effect of the water permeability
coefficient, LP, on the predicted cell response during
freezing. The solid lines represent the predicted
response at cooling rates of 5 and 8°C/min using
Lp==0.73 um3/um2-min-atm (516.35 um/sec), while the
dotted lines represent the response of the same cells using
Lp==0.89 um3/um2-min°atm (519.94 um/sec). Both Lp
values are typical values obtained from the experiments
performed for this thesis. Although these values are

not the extreme limits observed for Lp (0.65-+1.0 um3/um2

NORMALIZED CELL VCLUME

71

 

 

 

 

 

1.00 _‘

-------- 1180.73 ’"emz-mlnatm

“‘3‘“. “:009
131313 '3. "~”.
nas- ‘

" ' ,a 4 O'chun
6.40 a- "3".“ ‘ 5 Wm.” ............................
0.20 "4 “MA “”1“!“
0.00
11111111111111111111111111111111111111111
0.00 -mm -2000 -3000 -4000

TEMPERATURE (° C.)

Figure 22. Effect of membrane hydraulic permeability (Lp) on
predicted cell volume response during freezing.

[l um3/pm2-min-atm 5 22.4 um/sec].

72

-min-atm), it can be noticed that these values represent
a major part of the total range of Lp values and these
values have a slight effect on the predicted cell response.

At an intermediate subzero temperature (-lO‘~-15°C),
an increase of about 6% in the predicted volume is
associated with the indicated decrease in LP' which
represents about 50% of the experimental range of Lp

values.

4.3.4 Activation Energy Affect

 

Figure 23 demonstrates the significance of the
activation energy, Ea, in predicting the cell osmotic
response during freezing. The solid line represents
the equilibrium cell volume as a function of subzero
temperature, and the predicted cell volume if it is
cooled at a rate of 8°C/min, using an activation energy
of 14.5 kcal/mol. This Ea value is reported in the
literature (19) for the unfertilized mouse ova system.
This value was chosen because of the lack of information
concerning the membrane transport characteristics of
the unfertilized hamster ova system, and because of the
biological and volumetric similarities between both
systems.

The dotted line represents the predicted response
of the same cell cooled at the same rate (8°C/min),
if the activation energy of the permeation process is

assumed to be 20 kcal/mol. This value was reported in

NORMAL IZED CEL L V0. UHE

1.00

0.8 I

\‘

 

0.6I

0.4 0

0.20

 
   

73

"---..._. Eg=20Kallmol

.-
...o‘
...-'.O -oo....-o...........

  

 

 

330 FHIITIIITHHllTiqilfillrlilHIili1W]

0.00

Figure 23.

-1000 -2000 -3000 .4 0.00
TEHFERATUR‘E 1" 0

Effect of activation energy (Ea) on predicted
cell volume response during freezing

[cooling rate (8) = 8 °C/min]

 

74

the literature (56) for Arbacia eggs, and is used here

only to demonstrate the effect of Ea on the cell response.

As can be seen from Figure 23, an increase of approximately
38% in the activation energy of the water permeability

can cause more than a 70% increase in the predicted cell
volume at -20°C, during freezing at a rate of 8°C/min.

This depicts the significant effect of the activation

energy on the predicted response as previously reported (20).
It also suggests that an accurate Ea value is required, in
order to minimize the sources of error in the modeling

process.

4.3.5 Comparison between Predicted and Observed Cell

 

 

Volume Response During Freezing

 

Figure 24 shows the correlation between the predicted
cell response and the experimental data obtained by
freezing for 3 different hamster ova at a rate of 2°C/min.
Each set of data was obtained from the volume change of
one ovum in a separate run.

The normalized volume represents the cell volume at
defined temperatures divided by the initial cell volume.
The schematic in Figure 25 describes the problem associated
with the definition of the initial cell volume. In
Figure 25-a, the initial volume is defined as the volume
at 0°C. The entire set of volume measurements during
the freezing process will be shifted upward from the

computer prediction by approximately a 20-30% increase

NONLIZED CELL VG-LIHE

1.00 o

0.80

0-6I

0.4 0

0.20

75

Cooling I." s 2 'CM

 

4?
o O .
4K. . ‘5
4 0* 0,4.

 

0'60 1111111111fi11111111l1111l111111111lr1fil

0.00

Figure 24.

-1000 -2000 -3000 -4000
TEHF‘ERATLRE 1" 1'.)

Comparison between predicted and observed cell volume
response during freezing.

[cooling rate = 2°C/min]

V = 2l.6°/.
Lb = 0 8006 m3/ mz-min-atm
pmgan - u u
K = 18 um/sec

Average Dia. = 77 um
E6 = l4.5 Kcal/mol

spherical shrinkage

 

 
 
   

76

     
 

 

 

 

 

A
/ \
l b rJZO %
100‘ “ .
I
1
80. ‘
ER
2
60. g 4 computer
g eXperimental model
\ data
40. '3 *‘--0- '0 .
.‘3 1.. 20 96
1-1
20. E .
,g - a - - b -
O 0 10 2

Temperature (°C)

Temperature (°C)

Figure 25. Schematic representing the fit of the

experimental data to the computer

model with initial volume defined as

a) 0.0 °C (before external ice appearance)

b) at the moment when external ice
surrounds the cell.

77

in volume. In Figure 25-b, the initial volume is defined
as the cell volume right at the moment when the external
ice completely surrounds the cell (~-1°C). The volume
measurements in this case will fit the computer model

in an appropriate manner. The reason for the volume
increase in the first case is believed to be due to a
deformation of the cell due to ice layers growing
underneath and/or above the cell. Hence, the second
definition of the initial volume is used here. In which
case the initial volume will not be the volume of a
sphere. However, it is assumed to be a sphere, having the
same diameter of the cell projected area.

Another source of uncertainty in the experimental
measurements is the distortion of the cell boundary by
the growing ice dendrites. Few ova stay spherical after
being surrounded by external ice. Therefore, due to the
small number of ova available for experiments, the number
of experimental runs presented in Figure 24 is not
adequate to justify the comparison between the model and
the actual cell response. Also, the overall steady state
temperature uncertainty is estimated to range from 1.0°C
to 3.0°C at the worst situation.

Other than the mechanical distortion of the cell
boundary by the external ice, the value of the activation
energy could be a second source of uncertainty.

The above discussion suggests that an accurate value

of the activation energy should be obtained. It also

78

suggests that data from a larger number of experimental
runs should be available, in order to justify any
conclusions on a solid statistical basis. In fact,
despite all uncertainties, the experimental data indicate
that the observed cell response is consistent with the
thermodynamic water transport model.

The observed cell response is also consistent with
the nucleation temperature measurements presented below.
At a cooling rate of 2°C/min, where no internal ice
formation was observed, the cells reached the equilibrium
volume at approximately -12°C to -l4°C, while the mean

nucleation temperature is ~13°C.

4.4 Nucleation Temperature as a Function of Cooling Rate

 

During freezing, the cell is initially in thermal
and chemical equilibrium with the surrounding aqueous
medium. As a result of heat removal from the medium,
ice starts to grow within the extracellular solution,
hence lowering the water chemical potential outside the
cell. The difference in chemical potential drives the
water flux out of the cell. The rate of water transport
across the membrane depends on the membrane water
permeability and the rate at which the system is cooled.
If the cooling rate is relatively fast, and the dehydration
rate is not rapid enough for the cell to achieve chemical
equilibrium, the cellular water freezes inside. This

event results in a decrease of the water chemical potential

79

inside the cell which re-establishes the chemical
equilibrium across the membrane. The event of internal
ice formation is commonly termed "nucleation", "flashing",
or "blackening out" (13,57,58,60) because of the physical
appearance. At sufficiently slow rates of cooling, the
cell continues to dehydrate in order to maintain chemical
equilibrium with the surrounding frozen solution. In such
cases, "flashing" is not likely to occur. Nucleation
temperature as a function of the cooling rate was

experimentally determined for:

i) Unprotected Unfertilized Hamster Ova

Figure 26 shows the nucleation temperatures of
unfertilized unprotected hamster ova as a function of
cooling rate. The light bars represent the range of
the data, the heavy bars represent the standard deviation
and the circles represent the mean values with the number
of cells indicated to the right of the mean. The nucleation
temperature was statistically found to be independent of
the cooling rate. At a level of significance of 0.01,
the slope of regression line (not drawn) did not differ
significantly from zero (Appendix C). The overall mean
nucleation temperature for all cases was determined to
be -13°C.

Despite cooling to a minimum temperature of -30°C,
no internal ice formation was observed below the cooling

rate of 4°C/min.

uucusnuou reupennune 1°C)

80

 

 

 

 

 

00
-1o._.
_ 7 a
-20—
-30—
Overall lean -13'C
_ 810.0"-
le118 .—
-4o . , g
i|l|l|l|l|lm 1 | I|1|I
a 4 s e 7 0910 20 so 40 so
COOLING RATE [°C/MIN.]
Figure 26. Nucleation temperature of unprotected

unfertilized hamster ova as a function
of cooling rate.

81

The probability of internal ice formation as a
function of the cooling rate is illustrated in Figure 28.
It shows 100% internal ice formation for cooling rates
of 8°C/min and higher, and zero percent for cooling
rates 3°C/min and lower. The dotted line was not fit
statistically. It only serves to indicate an increase
in the probability of internal ice formation with the
increase in the cooling rate between the limits of
3 to 8°C/min.

Preliminary results of determining survival of
unprotected unfertilized hamster ova as a function of
cooling rate are shown in Figure 28. Morphological
appearance was used to judge the cell survival after a
freeze/thaw protocol. The figure illustrates a linear
dependence between cell survival and cooling rate with
a maximum survival of about 50% at a cooling rate of
3°C/min. For cooling rates of 10°C/min and lower, the
thawing rate is 10°C/min. For cooling rates higher than
10°C/min, the thawing rate is the same as the cooling
rate. The minimum freezing temperature reached was
—30°C in all cases.

When Figures 27 and 28 are combined together
(Figure 29), a number of conclusions can be drawn. At
a cooling rate of 3°C/min, where no internal ice is
observed, the cell "survival" (as judged by morphology),
is maximum. Cell "survival" decreases with the increasing

probability of internal ice formation until it reaches a

l

82

 

 

 

 

 

I (8/8) (11/12) (3/31
— 6
(9/10) ”9””
‘~ OOl-— ’
25 I
— I
g. I
60 — I
E I
.‘e'. -— I
5 I
3 40 —- o I
3. 15/13),
5 — I
g I
ID
2 2° —- I
“ I
- I
.’ (0/10)
0 __F"'T"’| I 1 1 1 I 1 I
O 4 8 12 16 20
Cooling Rate (°C/1nin)
Figure 27. Probability of internal ice formation as a function

of cooling rate for unprotected hampster ova.

Cell Survival (%)

83

 

 

 

 

100
80-
60-
(5/10%
40- '
\.
\
(5/13);
20 -
\1
(0/6) . /
o . L._ 10.17.) ...... ‘. EELS F)
T l 1 1 1
o 8 12 16 20

Cooling Rate (°C/min)

Figure 28. Unprotected hamster ova survival as
a function of cooling rate.

Probability of Internal Ice (%)

84

Internal Ice

 

O J.)

_.._.-__-—o Cell Survival

 

100

 

 

 

 

 

0 o .100
(8/8) fie/12) (e/e)
(9/1o)o 9/10)
80. / .80
/
(5/10 /
40- \0 5/15) .4?
\
(3/15)‘
20- z .20
wm/ \(n/e)
0.‘ "o [--.£9/_73._-_--‘.9E?_-9/9) .o
T 1 1 1 fir
c a e 12 16 20

Cooling Rate (°C/min)

Figure 29. Probability of internal ice and

cell survival both as a function
of cooling rate.

(%) IVAIA-IT‘S 1190

minimum "survival". Hence, it can be concluded that
cell survival is inversely related to the likelihood of
intracellular ice formation. The same observation was
reported for mouse ova suspended in 1 M DMSO (59).

ii) Protected Unfertilized Hamster Ova

Figure 30 shows the nucleation temperature as a
function of cooling rate for unfertilized hamster ova
suspended in 1.5 M DMSO. As can be seen, the collected
data show large fluctuations and a wide range of
nucleation temperatures. However, the overall mean
temperature for all cells examined is shifted down to
-57.1°C, which indicates that the cryoprotective additive
(DMSO) has a significant effect on the nucleation
temperature. Hall et al. (60) reported that permeating
cryoprotective additives decrease the ice nucleation
temperature of cells. The same authors also reported that
intracellular nucleating agents become less effective
in mouse embryos in the presence of glycerol or DMSO. They
added that the nucleating agents become almost completely
ineffective when the concentration of additive reaches
1.5-2.0 M. Rall et al. also reported that the nucleation
temperature of eight-cell mouse embryos decreased from
-10 to -15°C in saline alone to between -38° to -44°C
in 1.0-2.0 M glycerol and DMSO.

The effect of cryoprotectives on hamster ova seems

similar to the effect suggested by the mouse embryo

86

 

 

 

 

 

 

.3
H - 40 —4
m i,
m —J
:1 {a
E — so _ 11
E - I” o.
a .P I:
E - so —- .1
1' I:
Z _ 0 1) a
E .. 1.
< 1211'
m —-I Ji-
_| .-
g .0 Overall lean -57-1
2 81¢. Dev. _
— lelte
- I0
’1 1 I] 1|1l11111 1 1 1 T 1 1 1'1
3 I 5 I 7 I I 10 20 30 40 IO IO

COOLING RATE [°C/MINJ

Figure 30. Nucleation temperature of protected
unfertilized hamster ova in 1.5 M DMSO
as a function of cooling rate.

87

results (60), where the overall mean nucleation temperature
decreased from ~13°C in saline to -57.1°C in 1.5 M DMSO
solution.

The data in Figure 30 also suggest that the nucleation
temperature at slower cooling rates is lower than that
at fast cooling rates. This behavior was not observed
for unprotected ova. It is also unlike that of unfertilized
mouse ova frozen in l M DMSO cell suspension as reported
by Leibo et a1. (59). The minimum cooling rate below
which no internal ice formation was observed was 6°C/min.
This rate is approximately 6 times greater than that
reported for mouse ova (l°C/min) (59). This correlates
reasonably with the results obtained for water
permeability, where the permeability coefficient for
unfertilzied hamster ova is almost twice that reported

for mouse ova (l).

CHAPTER 5

CONCLUSIONS

Based on the results of the experiments performed
on the unfertilized hamster ova system in the present
work, several conclusions could be made as presented
below.

Unfertilized hamster ova behave as perfect osmometers.
The Boyle van't Hoff law is applicable, and the mean
osmotically inactive volume was found to be 21.6% with
a standard deviation of 3.3%.

The value for the inactive volume agrees with the
published values for mouse ova [18.2% (Leibo) and
20-21% (Rall)] which is approximately the same size as
hamster ova [~75 um dia.].

The dynamics of the osmotic shrinkage of hamster
ova correlates to the mathematical model of Terwilliger
and Solomon (29) and to the behavior of other biological
cells.

The calculated water permeability of unfertilized
hamster ova (0.8 um3/um2-min1atm) is approximately twice
the published value for mouse ova (0.43 um3/um2-min-atm)

obtained by Leibo (19), This suggests that a faster

88

89

freezing rate will be required in order to observe the
same probability of internal ice formation during rapid
freezing.

As predicted from the water permeability results,
internal ice started to form at much higher cooling
rates (4 and 6°C/min for unprotected and protected
hamster ova respectively) than in the case of mouse
ova (~l.O°C/min for protected ova).

The external solute concentration appears to affect
the water permeability, since it decreases the
permeability by a factor of approximately 1.5 when the
external concentration increases from 0.5 to 1.76 osm/kg.
The concentration dependence of the water permeability
is less pronounced than for some other systems. A low
coefficient of determination of (~66%) was obtained as
a result of the wide range of the calculated water
permeability values. This precludes concluding that the
concentration dependence is significant with a high degree
of confidence.

A thermodynamic computer model shows a slight effect
of the range of Lp on the predicted cell response during
freezing. It also shows the large effect of the
activation energy Ea on the predicted response, which
indicates that an accurate value of Ea should be obtained.

The observed cell volume response during freezing
correlates well with the predicted response using a

published value of the activation energy for the mouse

90

ova [14.5 kcal/mol (LeiboJ. The comparison suggests that
Ea for the hamster ova is quite similar but slightly
less than that of the mouse ova.

At the 0.01 level of significance, the nucleation
temperature of unprotected hamster ova was found to be
independent of the cooling rate with an overall mean
of -13°C.

For ova protected in 1.5 M DMSO the system showed
large fluctuations in the nucleation temperature as a
function of the cooling rate. However, the overall
mean is shifted down to -57.1°C. The data suggest
that the nucleation temperature at slower rates is
lower than that at rapid rates. This response is unlike
that of the mouse ova system as reported by Leibo et al.
(11), because for the mouse ova system the experimental
observations suggested that over the range of about
2-40°C/min, the nucleation temperature is relatively

independent of cooling rate (59).

CHAPTER 6

SUGGESTIONS FOR FUTURE WORK

At this point, some suggestions are made for future
work, on the modeling of the freezing response of hamster
ova and, the design of optimal freeze/thaw protocols that
yield maximum survival.

1) Determine the activation energy for the water
permeability of the hamster ova membrane. A low
temperature bath and a modified version of the diffusion
chamber could be used in conjunction with the method
presented here for room temperature experiments to determine
membrane water permeability values at lower temperatures.

2) Develop an accurate method for measuring the cell
volume during freezing. An image analysis technique could
be used to measure the projected area of an ovum. However,
for a more accurate volume measurement a three-dimensional
image has to be constructed.

3) Collect more data regarding the cell response during
freezing. Such data is required to judge the validity of
the thermodynamic model as well as the assumptions included.

4) Characterize the thawing behavior of hamster ova

and correlate that to a consistent thermodynamic model.

91

1

92

5) Minimize the amount of error introduced in the
measurement of temperature due to the thermal gradients
present within the viewing area of the microscope freezing
stage. A modified design for the cryostage based on the
analysis of Tu (39) and other workers could be helpful.

6) Collect more data regarding the survival of
hamster ova and the formation of internal ice, both as
a function of cooling rate. Such data could help define
the mechanism of cell injury during freezing.

7) Use fluorescent markers (FDA) for viability
assays, a technique that has been developed by McGrath
et al. (14). Data is also available from DeMayo (34).

8) Determine the effect of different types and
concentrations of cryoprotective agents on the nucleation
temperature of hamster ova. Data is available from
DeMayo (34).

9) Study the effect of in-vivo and in-vitro
fertilization and development on both the membrane transport

characteristics and the formation of internal ice.

 

APPENDICES

APPENDIX A

E

APPENDIX A

BOYLE VAN'T HOFF LAW AND THE
OSMOTICALLY INACTIVE VOLUME

The cell membrane is assumed to be semipermeable,
which means that it allows for transmembrane water flux
but not for solute transport. This assumption implies

that in the case of osmotic equilibrium,
u = u (A-l)

This means that the chemical potential of water should be
equal on both sides of the cell membrane for the
equilibrium situation.

At this point a distinction should be made between
two independent driving forces each of which can cause
transmembrane water flux. These forces are, Ap, the
hydrostatic pressure difference and, At, the osmotic
pressure difference that results from the difference in
solute concentration on both sides of the membrane.

At equilibrium, An is numerically equal to Ap, however
An is best thought of as a measure of water activity or

concentration since

93

94

-RT ln aW
W = -——————— (A-2)

<|

where, 5“ is the partial molar volume of water.

As summarized by McGrath (8), the Boyle Van't Hoff
law states that the osmotic pressure of a solution varies
inversely with the volume of solvent in which a definite

quantity of the solute is dissolved.
0V = const (A-3)
w

where, Vw represent the volume of water (solvent).

Hence, the total volume of the cell should vary
inversely with the osmotic pressure of the extracellular
solution. The Boyle Van't Hoff law is valid only if there
is no hydrostatic pressure gradient across the cell
membrane, if the temperature is constant, if the intracel-
lular solution can be considered ideal, and if solute
leakage across the membrane does not occur.

The Boyle Van't Hoff law is corrected for any
osmotically inactive volume that may be present within

the cell, hence,

V

b) ) (A—4)

W( = ni(Vi-V

Vcell'- b

is the total cell volume, V is the
cell b

osmotically inactive volume, and the subscripted values

where, V

ti and Vi correspond to a reference intitial state.

95

Rearranging Equation (A-4) results in the final

form of the Boyle Van'tHoff law:

 

i b
+7”:- 1 ”v“.- (A-S)

is the normalized cell volume, and Vb/Vi is
the normalized osmotically inactive volume.

The so-called Boyle-Van't Hoff plot is determined
experimentally by exposing the cell to solutions of
increasing osmotic pressure, and recording the equilibrium
cell volume in each concentrated solution. The resulting
linear relationship between the normalized cell volume
and the inverse solute concentration (l/n) (if it exists)
is extrapolated to infinite solute concentration (l/n==0)
to estimate the normalized osmotically inactive cell

volume.

APPENDIX B

APPENDIX B

DESIGN MODIFICATIONS OF CRYOMICROSCOPE
CONDUCTION STAGE

In previous designs of the crysostage two configura-
tions were used to hold the electrically conductive
heater slide on top of the copper block, while maintaining
good contact with the poles of the heating circuit. The
first configuration used a circular quartz disc of
0.075" thickness. The quartz disc was bonded to the
insulating tape covering the copper block with a commericial
silver based paint. This paint served as both an
electrically conducting medium and an adhesive. However,
in an attempt to increase thermal response times by
decreasing thermal mass, Callow (26) used thinner quartz
discs (0.025" thick). This resulted in frequent breaking
of the quartz disc and/or the breaking of the silver
paint-quartz disc bond. Callow solved this problem by
painting the edges of the quartz disc onto a thin strip
of aluminum foil, and the aluminum foil was painted
down on the insulating tape. Although this arrangement
solved the breakage problem, it decreased the thermal
response time of the quartz disc since the disc is not in

optimal contact with the thermal sink.

96

97

In the present study a rectangular glass slide
(1" Xl%" X0.02") which is coated with a thin transparent
film of electrically conductive material on one surface,
was used instead of the circular quartz disc. The edges
of the glass slide were clamped to the copper block
by means of two plastic clamps screwed in the copper
base (see Figure 10). Two pieces of thin copper foil
were inserted between the conductive surface of the
glass slide and the insulating tape to connect the
conductive surface to the heating circuit. This
arrangement solved the breakage problem resulting from
the thermal stress present in the glass slide during
freezing. It also improved the thermal contact between
the glass slide and the heat sink (the copper block),
hence improving the thermal response time.

In the previous design of the thermcouple sandwich
a bare foil thermocouple was used to measure the sample
temperature. This resulted in a frequent short circuit
between the electrically conductive surface of the glass
slide and the thermocouple wires when moisture condenses
on the cryostage during freezing. To solve this problem
insulated (teflon coated) thermocouple wires were used.

Finally to minimize the disturbance that results
from condensation on the crysostage during freezing, a
plastic condensation box was built around the microsc0pe.
The box has inlet and outlet parts which are used for

flushing with dry nitrogen gas prior to an experimental run.

98

The box proved to be an efficient way for minimizing
the condensation, however it did not prevent condensation

completely.

APPENDIX C

APPENDIX C

Statistical Calculations

l) Membrane Water Permeability Lp as a Function of

Solute Concentration:

To justify the dependence of Lp on the external
solute concentration, the slope of the regression line
in Figure 19 was tested statistically. Chapter 12 of
reference 61 details the required procedure.

The following values were determined from the
experimental data in order to determine the confidence

limits for the slope of regression line.

n = 18 (number at points)
Ex. = 38.13

1
Eyi = 14.41

Exiyi = 29.64

2X? = 86.31
1

2-
Zyi — 11.74
i = 2.12
y = 0.8

99

100

The slope (b) and the y intercept (a) of the least
squares line y==bx~+a are obtained using the following

two expressions:

_ nzxiyi " (2x1) (2Y1)

 

an?-(2x.)2
1 1
a==y-bx
Solving the equations yields
a = 1.14
b = -0.159

In order to calculate whether the slope of -0.159 is
significantly different than zero the following quantities

must be calculated.

 

s =n2xg-(2x.)2=99.9
xx 1 i
_ 2 2 _
Syy — nZyi (Xyi) - 3.78
Sxy = nExiyi-(Exi)(2yi) = -15.89
—s s (s 2 U2
se = XX *1: 31. = 0.066
n(n-2)(SXX)

The confidence limits for the slope b are

b 1 (ta/2 ) (se) /n/SXX

101

At the 99% confidence lvel for 16 degrees of freedom
tel/2 = 2.921

which yields
-O.22 < B=< -0.1

This interval does not include the zero. Hence we
can conclude that at the 99% confidence level the
lepe b is different than zero. A test of this
hypothesis is performed in order to assess the validity
of the above conclusion. The null hypothesis to be
tested is H : B==0 and the appropriate alternative

0
is H1: 8 7‘0. Using the equation

(b-BO) S

_ xx
t _ Se / n
yields
t = 5.675

and since this exceeds 2.921, the value for to/z’ we
can reject the null hypothesis at the 0.01 level of
significance. In other words, we can conclude that
there is a relationship between Lp and the solute

concentration.

102

2) Nucleation Temperature as a Function of Cooling

Rate for Unprotected Hamster Ova:

Following the example given above the following
values were calculated for the experimental data obtained
for nucleation temperatures as a function of cooling

rate:

b = 0.107
S = 13196
xx
S = 5438.24
YY
S = 1416.8
XY
8 = 1.506
e
t0.005 = 2.576 (at 99% level of confidence)

Then the value of the estimator B is

-0.078 < B < 0.292

Threfore, the value of zero slope is included in the
limits, and we can conclude that at the 99% level of
confidence the nucleation temperature is independent of

the cooling rate.

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"ITITJ'TEHE'M'EIM’MM'Hamill