MSU

 

RETURNING MATERIALS:
Place in book drop to

 

'LJBRARJES remove this checkout from
.Anu-(jlzlL your record. FINES wiII

 

 

be charged if book is
returned after the date
stamped below.

 

J

.34

 

 

 

 

 

 

THERMODYNAMIC MODELLING AND
CRYOMICROSCOPY OF LARGE UNILAMELLAR LIPOSOMES

By

Richard Callow

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

THERMODYNAMIC MODELLING AND CRYOMICROSCOPY
OF LARGE UNILAMELLAR LIPOSOMES

By

Richard Callow

Cell—sized, unilamellar, semi—permeable vesicles (lipo-
somes) have been used as a simple model system to study
freezing response. Experimental data obtained from cryo-
microscopy studies indicate that protein-free liposomes mimic
several important types of qualitative freezing behavior
seen in biological cells. Experimental determination has
been made of the equilibrium osmotic properties and the non-
equilibrium water transport properties of the egg lecithin
liposomes used in the freezing studies. These properties
have been used in a computer model to simulate volume
changes resulting from water transport during freezing and
thawing. A parameter study using the computer model has
been made to predict the sensitivity of the liposome re—
sponse to several modelling parameters. In addition, a
comparison between computer model predictions and experi-
mental data of volume response during freezing indicates
reasonable agreement. Computer simulations of volume re-
sponse during thawing does not match experimental data well.
Accurate quantitative comparisons of this type are valuable
but improvement in cryomicroscopic volume determination is

required.

ACKNOWLEDGEMENTS

I would like to express my appreciation to my advisor,
Dr. John McGrath, for his friendship and support during the
course of this work.

In addition I am grateful for the help received from
the members of the BTP lab. Special thanks is due to Amir
Fallahi for his advice and help, and to Mark Melkerson for
assistance in Boyle-van't Hoff and water permeability data

collection.

ii

Page

LIST OF TABLES ...................................... v
LIST OF FIGURES ..................................... vi
NOMENCLATURE ........................................ ix
1.0 Introduction ................................... 1
1.1 Background ................................. 1

1.2 Thermodynamic Water Transport Model ........ 7

1.3 The Liposome Model System .................. 9

1.“ Scope of The Present Work .................. 16

2.0 Water Transport Model .......................... 18
2.1 Introduction ............................... 18

2.2 The Extracellular Solution ................. 19

2.3 The Intracellular Solution ................. 21

2.“ Water Transport Kinetics ................... 2h

2.5 Water Permeability ......................... 25

3.0 Experimental Procedures ........................ 28
3.1 Preparation of Liposomes ................... 28

3.2 The Cryomicroscope System .................. 29

3.3 Measurement of Sample Temperature .......... 3h

3.“ Measurement of Liposome Volume ............. 38

3.5 Measurement of Osmotically Inactive

or "Bound Water" ........................... ho

3.6 Measurement of Water Permeability .......... M3

“.0 Results and Discussion ......................... “7

TABLE OF CONTENTS

“.1 Determination of Liposome Water Permeability M7
“.2 Determination of Liposome Osmotically In-

active Volume .............................. “9
“.3 Percent (%) Internal Ice as a Function of
Cooling Rate .. ............................. 51

“.“ Nucleation Temperature as a Function of

Cooling Rate ............................... 61
“.5 Computer Simulations ...................... 69
“. 5.1 The Effect of Freezing Rate .......... 69

“. 5. 2 The Effect of Different Assumptions
Regarding Membrane Surface Area

During Freezing ...................... 70
“.5.3 Effect of the Reference Water
Permeability ......................... 73
“.5.“ Activation Energy Effect ............. 73
“.5.5 Comparison Between Computer Predictions
and Experimental Data for Volume
Reduction During Freezing ............ 75
“.6 Thawing Response of Liposomes .............. 78
“.7 Possible Mechanisms of Freeze-Thaw Damage .. 80
“.8 General Response of Liposomes During
Freeze-Thaw ................................ 81
5.0 Conclusions ..................................... 88
6.0 Suggestions for Future Work ..................... 89
Appendix A .......................................... 92
Appendix B .......................................... 100
Appendix C .......................................... 10“
Appendix D .......................................... 106
Appendix E .......................................... 107
Appendix F .......................................... 110
Appendix G .......................................... 113
References .......................................... 116

iv

1.

2.

LIST OF TABLES

Experimental Water Permeability Values (um/s)
for Egg Lecithin Liposomes ......................

Nucleation Temperature Data for Liposomes .......

\‘lChU‘l

ll.

12.

13.

LIST OF FIGURES

Page
Cell survival as a function of cooling
rate (76) ...................................... 3
A model describing cell water transport during
freezing (“3) .................................. “
Alternate methods for a supercooled cell to
achieve equilibrium (20) ....................... 6

Schematic representation of a lipid bilayer .... 11
Cryomicroscope system schematic (30) ...... - ..... 3O
Schematic of conduction heat transfer stage .... 32

Schematic of cryomicroscope temperature
controller ...... . .............................. 33

Side view diagram of cryomicroscope heat
transfer stage ................................. 35

Diagram of the diffusion chamber ............... “1

Representative plots of liposome radius as a
function of time during water permeability
experiments ......... . .......................... “6

Normalized Boyle—van't Hoff plot ............... 50

Liposome percent internal ice as a function
of cooling rate ....................... . ........ 52

Formation of liposome internal ice. a: onset

of external ice; b: before internal ice nuclea—

tion; c: after internal ice nucleation; d:

after thaw ..................................... 53—5“

1“.

15.

16.

l7.

l8.

19.

20.

21.

22.

23.

2“.

25.

26.

27.

28.

29.

Page

Percent internal ice (right axis) as a function
of cooling rate for several biological cells ... 56

Osmotic shrinkage for cooling rate of 2°C/min.

a-d: during freeze; c—h during thaw ............ 57-60

Nucleation temperature as a function of cooling
rate for liposomes ............................. 62

Nucleation temperature as a function of cooling
rate for HeLa cells (73) ....................... 6“

Nucleation temperature as a function of cooling
rate for Chlamydomonas (7“) .................... 6“

Nucleation temperature as a function of cooling
rate for Spirogyra (51) ........................ 65

Safe internal thermodynamic states with respect
to ice formation for a hypothetical cell (15) .. 68

Effect of freezing rate on predicted volume
response during freezing ....................... 71

Effect of surface area assumptions on predicted
volume response during freezing ................ 71

Effect of reference permeability on predicted
volume response during freezing ................ 7“

Effect of activation energy on predicted
volume response during freezing ................ 7“

Comparison between experimental data and computer
model ...... . .......... . ........................ 76

Comparison between experimental data and computer
model .......................................... 76

Comparison between experimental data and computer
model for freeze-thaw response ................. 79

Comparison between experimental data and computer
model for freeze-thaw response ................. 79

Freezing of liposomes in distilled water. a:
before external ice; b: onset of external ice;
c: liposome embedded in external ice; d: after

destruction of liposome ........................ Ef-87

vii

30.
31.

Osmotic pressure schematic (“3) ................

Experimental apparatus to determine response
time of the DTM ................................

viii

AC

AGfus

AHfus

:3“

a 50 111 'U :3

d

<'.

NOMENCLATURE

Surface area, cm2

Activity

Cooling rate, °C/s

Concentration difference, osm/l
Activation energy, kcal/mole

Molar free energy of fusion, kcal/mole
Latent heat of fusion, kcal/mole

Molar flux, moles/cme/s

Water permeability, cm/s

Water permeability, moles/dyne-cm3-s
Number of moles

Pressure, dyne/cm2

Radius, cm

Gas constant, dyne-cm/mole-K
Temperature, K

Time, 5

Volume, cm3

Partial molar volume, cm3/mole

Mole fraction

ix

Subscripts

b bound

1 solvent

3 solute

r reference

8 solute

t total

w water

Superscripts

f free

1 inside

1 liquid

0 outside

5 solid

* reference state

Greek

u chemical potential, dyne—cm/mole
n osmotic pressure, dyne/cm2
v dissociation coefficient

1.0 Introduction

 

1.1 Background

 

Determining the response of biological cells to freezing
and thawing continues to be an active area of research. The
interest in this area is due largely to the potential
benefit to be derived. An improved understanding
of the mechanisms of freezing damage to biological cells
could lead to advances in such areas as blood-banking,
tissue and organ preservation, cell culture preservation,
cryosurgery, and the genetic development of frost hardiness
in crops.

Efforts thus far have resulted in the successful
cryopreservation of such biological systems as red blood
cells (1), spermatozoa (2), and embryos (3); however,
despite these successes, it is not possible to predict the
conditions required for a successful freeze-thaw protocol of
a given biological system. The design of a successful
freeze-thaw protocol of a given biological system remains,
in general, an empirical art.

Previous work has indicated that at least five factors
affect the likelihood of the survival of biological systems
subjected to freezing:

1) cooling rate

2) thawing rate

3) minimum temperature reached

“) length of storage

5) addition and removal of crypOprotective agents
These factors are interrelated so that information
concerning how they are coupled will be necessary in
deve10ping a model of the mechanisms of freeze-thaw damage.
For a biomaterial being frozen in the absence of
cryOprotectives and stored at sufficiently low temperatures
the important factors affecting survival are cooling rate
and thawing rates. These two factors are coupled such that
the survival of rapidly frozen cells increases if they are
thawed rapidly (“). In addition, it also appears that
slowly frozen cells should be thawed slowly (“L.

For a constant warming rate, the survival of many cell
types is roughly a bell-shaped function of the cooling rate
(Figure 1). The shapes of these curves suggest that there
are at least two competing phenomena which determine
survival. Mazur has proposed the so-called "two-factor"
hypothesis to account for the observed results (5). The
model attributes the low survival at slow cooling rates to
"solution effects" and at fast cooling rates to the
formation of internal ice. To understand these two types of
damage it is necessary to consider the physical-chemical
events which occur during the freezing of a biological cell '
initially suspended in an isotonic solution (Figure 2).
Figure 2 illustrates the essential features of a model
describing cell water transport during freezing, The system

consists of an extracellular solution, an intracellular

70..

104

 

10"

 

Figure 1.

0
D o HAMSTER /

\. °

16 I61 - -
COOLING wwcm

Cell survival as a function
of cooling rate (76).

Heat Removal Heat Addition
During Freezing During Thawing

'r'=—“—"-f """""" .‘==11

PURE ICE

 

 

Net Water Transfer Net Water Transfer
During Solidification During Melting

INTRACELLULAR
SOLUTION:
/ WATER + SOLUTES

Semi-permeable
Cell Membrane

EXTRACELLULAR
SOLUTION:
WATER + SOLUTES + lCE
I. ___________________________ 1

System Boundary /

 

 

---—----—--_-----q
-—-—-——-——-————-—_-——-—-——-

 

 

 

Figure 2. A model describing cell water
transport during freezing (“3).

solution, and a semipermeable membrane separating the two
solutions. When the cell suspension is cooled below its
equilibrium freezing point, the solution external to the
cell begins to freeze. The cell membrane however, acts as a
barrier to prevent the formation of ice inside the cell.

The formation of ice lowers the chemical potential of water
in the external solution relative to the internal solution.
This is a nonequilibrium condition. Restoration of chemical
equilibrium can occur by one of two paths (shown
schematically in Figure 3). Since the cell membrane is
semipermeable (permeable to water but not to salute) the
chemical potential difference of water will act as a driving
force for the transport of water across the cell membrane
from inside to outside (right path in Figure 3). This
transport results in cell shrinkage and a lower chemical'
potential of the remaining internal water.

Alternatively, equilibrium can be re-established with
minimal cell volume change by the formation of intracellular
ice which also lowers the chemical potential of the internal
water of the cell (left path in Figure 3).

Both of the above processes have been linked to
cellular damage. In the case where water passes osmotically
across the membrane, the loss of internal water causes an
increase in concentration of intracellular solutes which can
lead to damage. This damage is lumped under the term
"solution effects." Several specific mechanisms of this

type of damage have been proposed. Among these are:

M _M
M M
M
M
M

N

 

P’LOW

.MQ M.— \
/ ‘l WATERFLUX
M M M
M M M—
' ".9 mo ...
M
M... M M
B . i M.
M . .

INTRACEIIULAR iCE DEHYDRATION
PAST coouuc . SLOW coouua

M8 M M EXTRACELLULAR
m

 

Figure 3. Alternate methods for a supercooled cell
to achieve equilibrium (20).

1) Freezing produces an increased concentration of
electrolytes which can cause dissolution of the
cell membrane (6).

2) Freezing results in the removal of "bound" water
from vital cellular structures such as membranes
and proteins. This results in death since lattice-
structured water is important for the integrity of
the cella(7)

3) The cell volume decrease accompanying dehydration
reaches a critical minimum resulting in a lethal
increase in permeability for solutesJB)

“) Changes in internal pH accompany the increase in
salt levels and precipitation of some salts can
cause irreversible damage (9).

In the case of intracellular ice formation it has been
proposed that the formation of ice crystals and their
subsequent increase in size during thawing can cause
mechanical damage to cell organelles and cell membranes
(10).

1.2 Thermodynamic Water Transport Model

 

 

A major advance in the understanding of cryobiology
problems came as a result of the introduction of
mathematical modelling and the application of thermodynamics
to study the freezing of biological systems. This approach
was pioneered by Mazur when he published the first thermody-
namic model describing water transport during freezing (5).
The use of such modelling allows quantitative prediction of

the response of a cell during freezing and thawing. For

instance, computer simulations of the changes of cell volume
during freezing can be compared to experimental data. Such
comparison can be used to assess the validity of the model.
Various modelling assumptions can be challenged in the light
of experimental data. This allows refinement of the model.
A valid thermodynamic model could be used to predict the
response of cells in untested experimental situations. In
addition the model yields values for important system
parameters, such as the amount of internal supercooling,
which are not directly measurable. Finally, the use of an
analytical model allows parameter studies to quantify the
importance of various parameters in the model relative to
others.

Since the publication of Mazur's original model a
number of researchers have addressed the validity or
significance of some of the simplifying assumptions used
(12, 13). In addition, similar models based upon Mazur's
original one have been developed and used (1“,15). However,
it is still difficult to assess the validity of the model
since comparatively little research has been published which
allows the direct comparison between model predictions and
experimental results (16, 17, 18).

With the development of the cryomicroscOpe system (19),
quantitative measurements of cell volume during computer-
controlled freezing could be made. However, comparison
between an analytical model and experimental results
requires both accurate determination of cell volumes during

an experiment, and accurate prior determination of the

values of transport parameters needed for use of the
analytical model. In the case of the required tranSport
parameters (iJh, the water permeability and its
concentration and temperature dependence) there are few data
availablerfor most biological cells. Several researchers
have attempted to circumvent this limitation by using
experimental freezing data coupled with a model assumed to
be valid, to deduce values of the transport parameters (18,
20). However, any attempt to assess the validity of the
theoretical model must involve independent, experimental
determination of the transport parameters before comparison
between data and the analytical model can be made.

This is the approach adapted in the present work. A
simple system, the liposome system is used as a model to
study various freezing responses, such as volumetric
response and nucleation temperatures. Using this system, an
attempt is made to assess the validity of the analytical
transport model for describing volumetric response during
freezing. In addition, the general validity of the liposome
model system as a model of biological cells undergoing
freezing is examined.

1.3 The Liposome Model System

The liposome system has been studied for various
purposes as a model membrane system for about seventeen
years. In 1965, Bangham and co-workers (21) demonstrated
that an aqueous phOSpholipid mixture spontaneously formed
closed structures whose permeability to ions was very

similar to that of biological membranes. This discovery

10

opened up the possibility for using the closed structures,
liposomes, as model systems for cells. It is generally
accepted that a typical living cell behaves as an osmotic
system, allowing water to pass across its membrane in
response to concentration differences between the inside and
outside of the cell (22). It is possible in real cells to
have water or selective solute transport in the direction of
decreasing concentration, that is, against the concentration
gradient; this kind of transport requires energy input and
is labelled active transport. In either active or passive
transport, the cell membrane acts as a selective barrier to
the passage of water and solutes.

A biological membrane is composed primarily of lipids
and proteins. A lipid molecule is amphipathic, meaning that
one part of the molecule is hydrophilic and one part is
hydrophobic. This amphipathic nature of lipids results in
the formation of the lipid bilayer as illustrated
schematically in Figure “ (62). In the bilayer the
hydrophilic head groups of the lipids are in contact with
the aqueous solution leaving the hydrophobic hydrocarbon
tails of the lipids in the center region of the bilayer.

Quantitative measurement of water permeability in
biological cells is hampered by geometric complexity and by
secondary diffusion barriers within cells because cells
often have complex intracellular membrane systems. Because
of these difficulties, model systems of lipid bilayers have
been used widely to study the basic aspects of the diffusion

of water and solutes across membranes. The first

HYDROPHIUC HEAD GROUP

HYDROPHOBm TAH.GROUPS

Figure “. Schematic representation of
a lipid bilayer.

12

widely used model system was formed by extending a solution
of lipid in a nonpolar solvent across a hole separating two
compartments (23). After a suitable thinning time a black
single bilayer film is formed: the bilayer lipid membrane
(BLM). The study of the electrical and transport properties
of such membranes has resulted in an extensive literature
(2“,25). There are some limitations however in applying the
results of BLM studies to biological membrane systems. One
of the main limitations stems from the presence of the
nonpolar solvent, used for dissolving the lipid, in the
formed bilayer. The presence of this solvent, even if it
can be limited to a small amount, means that the BLM is
never exactly comparable to the bilayer membrane found in
biological cells.

This problem is avoided in the liposome system first
described by Bangham, et. al (21) since the nonpolar solvent
in which the lipid is dissolved is evaporated before the
liposome is formed. In this respect then, the liposome
membrane more closely resembles a biological membrane.
Further motivation for the use of liposomes as model
membrane systems was largely due to the discovery that
liposomes are closed structures which are relatively
impermeable to trapped ions or selected solutes (21,26).
Other attractive features of liposomes for model membrane
systems are (27):

1) Their morphology, a relatively impermeable membrane

enclosing an aqueous space.

13

2) Their ability to encapsulate various solutes
present in the aqueous phase during their
formation.

3) A degree of flexibility of membrane components from
which they can be formed.

These qualities have led to the use of liposomes in
freezing studies by previous researchers. In 1971,
Siminovitch and Chapman (28) were able to show that freezing
caused a pronounced increase in the release of both ionic
and nonionic markers which had been trapped in the liposome.
This method of measuring damage is the same in principle as
that used to measure the extent of freezing injury in
biological cells“ The work of Siminovitch and Chapman
involved a number of different markers trapped within the
liposomes: K2C20u, KHzPou, glucose and glycine. As part of
the same study they were able to observe osmotic shrinkage
of liposomes in the presence of external ice at slow
freezing rates ULSOC/min). At faster cooling rates
(20°C/min) they detected the formation of liposome internal
ice. The observation of these freezing responses was highly
significant since biological cells undergo analogous
behavior when being frozen.

Siminovitch and Chapman continued their work on
liposomes as part of their effort to understand freezing
damage to plant cells by studying the osmotic damage to
liposomes incurred by rehydration of liposomes previously
dehydrated in hypertonic solutions (29). By measuring the

l”elease of an internal marker from liposomes subjected to

1“

salt solutions of increasing molarity they observed damaging
effects similar to the effects found during slow freezing of
liposomes. They concluded that "the correspondence of the
osmotic stress effects of slow extracellular freezing and
plasmolyis on plant cells can be simulated by pure lipid
membrane systems."

In 1981, Morris and McGrath, using multilamellar
liposomes correlated the freezing response of liposomes as
measured by the release of entrapped glucose, with the
cholesterol content of the membrane (30). Membranes
containing more cholesterol were more sensitive to freezing
injury. The effect of DMSO, a cryoprotective compound, on
the release of glucose was also determined. DMSO was
cryOprotective with the extent of protection dependent upon
the cooling rate.

The above study gave further evidence of the value of
liposomes as a model system since a correlation could be
made between freezing response and membrane composition.
Also the effect of a cryoprotective additive was similar to
the effects observed with some types of biological cells.
An additional significant observation was that of the
distortion and apparent dehydration during freezing and
subsequent rehydration during thawing of the multilamellar
liposomes.

One of the major limitations of the above studies stems
.from the use of multilamellar liposomes. Use of these
Iliposomes prevents the quantitative modelling of water

t:ransport, since the transport occurs over a large (unknown)

15

number of bilayers. This limitation is a serious

one since attempts to understand freezing damage to cells
often involve consideration of the cell as an osmotic system
which includes modelling the kinetics of water transport
across the cell membrane in response to osmotic
perturbation. In addition membrane mechanical effects
differ between multilamellar and unilamellar systems and
cannot be modelled easily for multilamellar systems. The
work reported in this thesis represents the logical next
step: the use of large diameter (10-50 Lml) unilamellar
liposomes as a model system to study cells undergoing
freezing and thawing.

The use of large unilamellar liposomes in studying the
nature of osmotic response has been reported previously
by several workers. In 1970, Reeves and Dowben
(31) used unilamellar or paucilamellar liposomes prepared
from phosphatidylcholine to measure water permeability
coefficients. Using a stop-flow aptical system they
determined water permeability coefficients at two
temperatures, and from these measurements they calculated an
activation energy for water transport.

In 1981, Boroske and coworkers reported a study on the
osmotic shrinkage of large egg-lecithin liposomes (32). In
this study they measured the rate of shrinkage of liposomes
subjected to an osmotic gradient across the liposome

membrane. From these measurements they were able to

calculate a value for the water permeability coefficient at

room temperature. These authors reported liposome membrane

16

instabilities induced by osmotic shrinkage which may be
relevant to "salute effect" freezing damage.

This thesis reports the use of large unilamellar
liposomes for freezing studies. Unilamellar liposomes are
eSpecially attractive since it is expected that measurements
of the freezing response of unilamellar liposomes can be
compared quantitatively to predictions, based upon a
thermodynamic water transport model, of liposome volume
changes which occur during freezing. Such a comparison
would be of value since although such models are used and
cited in cryobiology research, their validity remains
uncertain. To date no one has published results which
confirm the existing thermodynamic tranSport models by
measuring the parameters known to be important in the model
for the system of interest and establishing a quantitative
correlation between prediction and observed volume changes
during freezing. In some cases there remain gross
discrepancies between observed (16) and predicted (5) cell
volume changes. In addition, previous quantitative
correlation studies of this type have not addressed the
problems of experimental uncertainty in detail. These
uncertainties are considered here.

1.“ §222£ 2: the Present Work

In view of the above considerations, the major goals of
this work were the following:

1) Establish experience with manufacturing large
unilamellar liposomes in the Bioengineering Transport

Processes Laboratory.

2)

3)

“)

5)

6)

17

Verify that large unilamellar liposomes demonstrate
the qualitative freezing behavior observed in
biological cells: osmotic shrinkage at slow
cooling rates and internal ice formation at fast
cooling rates.

Determine in our laboratory, wherever possible,
values for transport parameters of our liposomes;
and characterize the internal solution of the
liposomes, by determining the amount of internal
osmotically "bound" water. This information is
required for application ofzatransport model in
the study of freezing response.

Determine quantitative freezing behavior (osmotic
volume shrinkage)cfi‘the large unilamellar
liposomes and compare this to the response
predicted by computer calculations based upon a
water transport model.

Determine thawing behavior of large unilamellar
liposomes and compare the observed response with
the response predicted by the model.

Observe the behavior of liposomes, induced by
freezing/thawing stress, to suggest possible

mechanisms of freezing/thawing damage to membranes.

2.0 Water Transport Model

 

2.1 Introduction

 

The first thermodynamic model describing cell water
transport during freezing was published by Mazur (5) in
1963. Since that time a number of similar models have been
published (1“, 15, 33). Figure 2 shows the basic features
of these models. The system consists of a cell suspended in
a water/solute solution. Heat is removed from the system
during freezing and added to the system during thawing. The
extracellular solution contains solutes as well as liquid
and solid water, while the intracellular solution contains
solutes and liquid water (unless intracellular freezing
occurs.) The boundary of the cell is modelled as a
semipermeable membrane. Quantitative use of the
thermodynamic model requires specification of the system
more completely; First, the extracellular solution must be
modelled since its composition changes as heat is being
removed from the system once extracellular ice is formed.
Second, the intracellular solution must also be modelled.
In general, the exact nature of the internal solution of a
cell is not known. However, it is often possible to
determine experimentally the macroscopic behavior of a cell
as an osmotic system. This information is relevant to the
description of a cell during freezing.

Finally, in addition to modelling the internal and

external solution of a cell it is necessary to specify
18

19

information concerning the kinetics of water transport
across the cell membrane. The effect of temperature and
solution composition on the water permeability also must be
known or assumed.

2.2 The Extracellular Solution

 

The calculation of the activity of the water in the
extracellular solution is derived from consideration of the
equilibrium properties of a solid/liquid solution (3“). For
the case of a two-phase equilibrium of solid and liquid

water:
u (T p X) = u (T F) (2-1)
w ’ ’ w ’

where Di(T,p,x) is the chemical potential of the water in
solution and A: (T,p) is the chemical potential of the pure

solid water. For an ideal solution:

1 1 *
1%(T,p,x) = uw’ (T,p) + RT lnxw (2-2)

x
where ui’ (T,p) is a reference chemical potential,
generally chosen to be that of pure liquid solvent (water),

and x is the mole fraction of solvent (water) in solution.

W

Combination and rearrangement of equations (2-1) and (2-2)

yields:

. , fl
“3(T,p/ " Ui’ (T,p)
1n Xw = " RT (2-3)

 

20

This can be written as:

-AGfus
1“ Xw = “'12?— (24*)

where AGfus = NW S(T,p)- Iuw *(T,p) and is the molar free
energy of fusion of the pure solvent at the temperature T
(3“).

By differentiating equation (2-“) with respect to x,

holding p constant:

 

 

l = -l 3(AGfus/T) (E3) (2 5)
x R 3T ax ’
p p
Making use of the Gibbs - Helmholtz equation (3“):
8(AG/T) _ AH
___§T__ - ”—2 (2'6)
p T
equation (2-5) becomes:
1 = _AHfus 8T (2 7)
x 2 3x '
RT p

Equation (2-7) is rewritten in differential form and

integrated:

J{? flj{ Hfus dT (2-8)

The lower limit corresponds to the case of pure water:

x:xw=1 and T=To, the freezing point of pure solvent.

If AHqu, the heat of fusion of pure water at temperature T,

is assumed constant over the temperature range of interest

21

the integration of equation (2-8) results in:
In X = -—§——(T— - T) (2-9)

Equation (2-9) is an expression for the activity of water in
the (ideal) external solution as a function of temperature.

It is because the external solution is assumed ideal that

x = a (2-10)

where the superscript (o=outside) is now used to explicitly
denote the extracellular solution. In addition to the ideal
- solution assumption the other major assumptions required in

the derivation were:

1) Solid/liquid water are in equilibrium
2) No solutes are frozen into the solid phase, i.e”

the solid phase is pure water

3) AH the heat of fusion of pure water, is

fus

constant over the temperature range of interest.
Note, however, that equation (2-8) can be

integrated for non-constant AHqu if the functional

relationship between AHfus and T is known.

2.3 The Intracellular Solution

 

The intracellular solution is typically modelled asaui

ideal solution so that the activity of the internal water is
equal to the mole fraction of water (5, 15):

1_1 _
aw — xw (2 ll)

22

The ideal solution assumption is adopted in this thesis.
(Several authors have included non-ideal effects and they
appear to be negligible [13, 63, 6H1). In equation (2-11)

the mole fraction of internal water is given as:

 

(2—12)

where the summation is over all the solute molecules in the

solution, Vi

jth solute species.

being the dissociation coefficient of the

In many cases, a refinement of equation (2-12) is
needed. Levin et. a1 (1“) have pointed out the importance
of interpreting intracellular mole fractions on a "bound
water" basis. In this interpretation a distinction is made
between intracellular water which is free to move across the
membrane in response to an osmotic gradient and "bound"
water which is not free to do so. Levin determined the
amount of bound water from a fundamental calculation of the
amount of water hydrated to the molecules of his
hypothetical intracellular solution. This type of
calculation requires detailed knowledge of the internal
constituents of the system of interest including hydration
numbers. In general, this information is not available so
that the fundamental calculation of bound water is not
possible. It should be noted that even if detailed
knowledge of the internal components of a cell is known, a
fundamental calculation of the amount of bound water will

not necessarily be possible. This is due to the ambiguity

23

concerning how "bound" water should be defined. Different
experimental techniques yield different amounts of "bound"
water, and the distinction between bulk water and bound
water cannot be made clearly. Nevertheless, in many
instances the distinction is useful in interpreting
experimental results. One standard method used to determine
amounts of "bound" water is that of Boyle - van't Hoff plots
(35). This method results from consideration of the cell as
an osmotic system and application of the Boyle-van't Hoff
law which states that the osmotic pressure of a solution
various inversely with the volume of solvent in which a
definite quantity of the solute is dissolved (22). Appendix
A gives a thermodynamic derivation of the general osmotic
pressure equations and their use in determining amounts of
bound water.

In the computer model used here the initial mole
fraction of internal water is calculated from the osmolarity
of the solution in which the liposomes are prepared. The
transport equations allow calculation of the amount of water
passing across the membrane as the temperature of the system
is lowered in small incremental steps. If it assumed that
the membrane is perfectly semi-permeable, allowing no passage
of solutes, then the mole fraction of the water inside the
liposome can always be calculated from the initial mole
fraction and the amount of water which has passed across the
membrane. If it is further assumed that the internal

solution is ideal, the mole fraction of internal water is

2“

equal to the activity of the internal water:

81 i

w = xw (2-13)

2.” Water Transport Kinetics

 

The water mole flux across a cell membrane as a result
of the osmotic disequilibrium occurring during freezing can
be described in terms of the chemical potential gradient

across the membrane (33):

dni
Jw)i E % ——% = -k(u% - U3) (2-1“)
n
where n; = number of internal water moles

u: : internal water chemical potential

pa = external water chemical potential

A = membrane surface area
t = time
k = phenomenological coefficient

Equation (2-1“) is a phenomenological equation which
describes a water mole flux into the cell (Jw) in terms of a
chemical potential difference acting as the driving force
for water transport. The flux and the driving force are
related through the phenomenological coefficient, k.

The chemical potential of water can be written:

* —
“w = uw(T) + va + RT lnaw (2-15)

where ‘7“ is the partial molar volume of water, p is the

a
pressure and uw(T) is the chemical potential of a reference

25

state (usually specified to be that of pure water at the
temperature of the solution.) Combining equations (2-1“)
and (2-15), assuming that there is no pressure gradient

across the membrane, leads to (15):

w _,KA ,1 0
—Et - :f(lnaw - lnaw) (2-16)
VW
where K is the water permeability expressed as cm/sec; K=§$k
v

A is the surface area (cm2) w

Vw is the molar volume of water (cm3/mole)
The cooling rate ,8, is constant for all cases

considered here and is given by:
B = —— ’ (2—17)

Combining equations (2-16) and (2-17) results in the

water transport equation:

__ ... —-—(lnavlq - inag) (2-18)

Equation (2-18) is the water transport equation applied

in this thesis. In order to use the equation it is

i o

necessary to specify values for aw, aW and K. The

values ofa1 and 80
w w

are determined, as shown above,
from the intracellular and extracellular models; a brief
description of the information needed to specify K follows.

2.5 Water Permeability

Previous workers (5, 33) have noted that the water

permeability is a strong function of temperature. Mazur (S)

26

described this temperature dependence in exponential form:

K = Kr exp[b(T - Tr)] (2-20)

relating K, the water permeability at temperature T, to the
water permeability Kr at a reference temperature Tr' It is,
however, more common to eXpress the temperature dependence
of water permeability in terms of an activation energy Ea

(2u,33):
-E
_ a 1 l
K - Kr exp['§—(T - T—0] (2—21)

Equation (2-21) is equivalent to equation (2-20) over the
limited temperature range where data exist to define the two
relationships. Both equations indicate that the water
permeability is an exponential function of temperature.
Experimental results for liposomes and BLM's verify this
exponential relationship over moderate temperature ranges
(36, 37, 38).

Mazur's thermodynamic model (5) revealed that both
the values of Kr and Ea play significant roles in the
expected water transport. Unfortunately, not many data have
been reported defining the values of Ea for cells or
liposomes. Using 0.5 - 10pm diameter egg lecithin
liposomes, Reeves and Dowben (31) obtained water
permeability values of approximately an um/s at 25° and 70
pm/s at 37°C. From these values the calculated activation

energy, using equation (2-21) is 8~25 kcal/mole. Blok, et.

27

a1. (37) using egg lecithin liposomes determined an
activation energy value of 10.6 :_o.u kcal/mole in the
temperature range 8°C to 25°C. These same workers,
investigating the effect of varying amounts of cholesterol
in dipalmitoylphosphatidylcholine liposomes obtained
activation energy values ranging from 12 kcal/mole (0 mole %
cholesterol) to 22 kcal/mole (15-50 mole S cholesterol). In
this thesis the activation energy determined by Reeves and
Dowben (31) for egg lecithin liposomes (8.25 kcal/mole) is
used in the thermodynamic water transport model since the
temperature dependence of the water permeability was not
experimentally determined as part of this work. The effects
’ of osmolarity on the water permeability of biological cells
remains a disputed topic (39,“0) and these effects are not
included in the present work. The value for the reference
permeability was experimentally determined as part of this

work; the value used is H11nn/s.

3.0 Experimental Procedures

 

3.1 Preparation of Liposomes

 

The unilamellar liposomes were prepared using the
technique of Boroske, et. a1 (32). The preparation method
consisted of spreading a thin smear of lyophilizid, l-alpha-
egg lecithin (Leon Laboratories, St. Louis, Missouri) on
several glass cover slips (approximately 10 mg lipid/cover
slip) and placing the cover slips into a 0.2 M solution of
sucrose in water or distilled water. The solutions were
covered (to prevent evaporation) and left undisturbed at
room temperature. Liposomes were observed to form in the
solutions after about one hour; however, it appeared that a
larger quantity of satisfactory liposomes were produced from
solutions left undisturbed for one or two days. Typically,
a drop of sample preparation consisted of both unilamellar
and multilamellar liposomes as well as an amount of lipid
debris“ The observed unilamellar liposomes usually ranged
in diameter from 5 to 50 microns with an average diameter of
about 20 microns. The liposomes used for experimentation
generally measured about 20 microns in diameter. It should
be noted that it was not possible to unequivocally ascertain
that the liposomes used for experimentation were
unilamellar. The liposomes were assumed to be unilamellar
if they appeared to be surrounded by a single membrane when
viewed microscOpically. This method, though subjective, is

not unreasonable. Attempts to definitively establish the
28

29

unilamellarity of liposomes have been published UH“ H5) but
these methods are indirect and leave room for doubt. A
convenient non-destructive method to quickly determine the
lamellarity of an individual liposome prior to an experiment
would be valuable. In addition, improved liposome
preparation techniques are desirable. Appendix B lists
several liposome preparation techniques which have been used
in the Bioengineering Transport Processes Laboratory.

3.2 The Cryomicroscope §ystem

 

The cryomicroscope system is based on the designs of
Diller and Cravalho (19) and McGrath et. al (60). The
system consists of a commercial light microscope with a
specially designed heat transfer stage coupled to a computer
controller allowing for the freezing of samples at a desired
cooling rate. The response of the sample can be monitored
visually in real-time, and can be recorded simultaneously
using a video camera system or a 35 mm camera.

Figure 5 shows a schematic of the microscope system.

The basic system consists of:

1) a microscope with a conduction heat transfer stage

2) a programmable digital counter

3) an analog comparator with power amplifier and
heater

u) a refrigeration source, in this case saturated N2
vapor at approximately -196°C.

5) color video recording equipment .

6) a strip chart recorder

3O

 

COLOR VIDEO
CASSETTE RECORDER

 

  

 

 

Q‘O

MOI
TELEVISION
“HERA

 

D

COL" ”ITO.

 

Inca" O D D D 3332333333

LAIP .
‘ ll Hume munch

INOCULAI
EYEHECES

 

EFF-ILLUMINATION
“WRESCEICE ”NCO

 

 

 

 

 

 

 

, I

.3... [T "....m [El
film... W. 3*
=: mun

TRANSFER “ICIOSCOPE fllOE

$33.33.... \ME]

WHSTEN HIP

 

 

 

 

Figure 5. Cryomicroscope system schematic (30).

31

The following is a brief description of the operating
characteristics of the Bioengineering Transport Processes
(BTP) laboratory cryomicroscope system.

Vaporized liquid nitrogen is used as a refrigerant and
is passed through the cryomicroscope stage. Figure 6 shows
a schematic representation of the conduction stage
components. In addition, Appendix C describes modifications
which were made on the stage during the course of
eXperimental work. The stage operates as a thermal sink for
the conduction of heat from the sample. The sample is
placed on the tOp of a glass coverslip which is glued to a
quartz disc. Sandwiched in the epoxy glue (5 minute epoxy,
Devcon Corporation, Danvers, MA) between the coverslip and
the quartz disc is a thin (Sum) copper-constantan
thermocouple (No. 20108-1, Rdf Corporation, Hudson, NH)
which is used to monitor the sample temperature. The bottom
of the quartz disc is coated with a thin layer of
tin/antimony oxide (typical resistance: 60 ohm/square)
which serves as an electrical resistance heater. By
regulating the voltage across the quartz disc, electrical
power is dissipated to counteract the continual heat
transfer from the quartz disc to the thermal heat sink
(Figure 7 shows a schematic diagram of the electronics used
in the thermal controller.) The amount of electrical power
being dissipated is controlled by the Operation of the
programmable digital counter and the analog comparator and
heater. The temperature of the sample is measured by the

thermocouple and the voltage from the thermocouple is

32

THERMOCOUPLE TO POWER SUPPLY

\‘L //

 

 

'1’ ”a
r ’1
g a ; ALUMINUM FOIL
.2 z
59. Q

 

 

...—COPPER BLOCK

 

 

 

QUARTZ DISC

THIN FILM

RESISTOR QUARTZ DISC
SILVER PAINT
ALUMINUM FOIL

 

 

 

 

‘ : \INSULATING TAPE
I 3 .——-— COPPER BLOCK

 

 

/

VIEWING HOLE

 

[Tm TO SCALE ]

 

Figure 6. Schematic of conduction heat transfer
stage.

333

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DARLINGTON
TRANSISTOR
PAIR

 

 

 

POWER
SUPPLY
DESIRED TEMPERATURE
SIGNAL CONDITIONING
cmzumn ELECTRONICS THERHOCOUPLB I
I
V (desired
temperature) V (actual
tower: ture)
)1“
museum mun
fl
COMPARATOR

 

 

 

 

HEAT TRANSFER STAGE

 

 

ERROR SIGNAL

Figure 7. Schematic of cryomicroscope temperature

controller.

 

3U

linearized and amplified. This signal is compared to the
voltage being generated by the programmable digital counter.
This generated signal corresponds to the desired
temperature. The difference between the signal generated by
the thermocouple and that from the the programmable counter
is amplified and used to drive a power amplifier which
provides the electrical power dissipated in the quartz disc
heater. The strip chart recorder is used to obtain a
recording of the sample temperature during a freeze/thaw
run. (See Figure 5)

In addition to visual monitoring of the sample being
frozen, a simultaneous videotape recording can be made of
the sample during freezing. A beam splitter in the optical
path of the microsc0pe allows passage of part of the light
to a camera mounted on the microscope. Color videotape
recordings can be made of the experiment for future
reference. Alternatively, a 35mm camera can be mounted on
the microscope.

3.3 Measurement 2: Sample Temperature

 

The temperature measured by the thermocouple represents
the temperature of the sample in the immediate vicinity of
the thermocouple. It should be noted that the sample is
separated from the thermocouple by a thin cover glass and a
small amount of epoxy cement. (See Figure 8) Any
temperature gradient in the vertical (y) direction (through
the cover glass) will lead to error in the temperature
measurement of the sample. This amount of error is assumed

to be negligible Judging by previous work (72). Research is

35

 

 

OBJECTIVE
r? .=-— covensup
. ‘\,___..3AMPLE
Q A). Q
ZC— ' y , covsamJP

 

 

 

 

 

TI'ERMOCOUPLE EMBEDDED
IN EPOXY CEMENT

 

QUARTZ DISC

 

 

 

 

THIN FILM HEATER

a INSULATING TAPE

COPPER BLOCK

 

 

 

 

 

 

 

 

| NOT To SCALE
\ /
LIGHT SOURCE

Figure 8.

Side View diagram of cryomicroscope
heat transfer stage.

36

presently underway, by Mr. Su Ming Tu, graduate student in
the Mechanical Engineering Department to quantify the amount
of error introduced by this temperature gradient using a
numerical heat transfer analysis of the stage (“6). An
additional source of error can arise from temperature
gradients in the horizontal (x) direction. (Figure 8)

Since the thermocouple only measures local temperature, a
sample at a location away from the thermocouple junction
will generally not be at the same temperature as that at the
Junction.

An estimate of the magnitude of the temperature
gradient in the micrOSOOpe viewing field was obtained
eXperimentally. Distilled water was frozen in small
decremental temperature steps. The location of the
ice/water boundary, assumed to represent 0°C, was compared
to the reading of the thermocouple at each temperature step.
Results of this experiment indicated that at points away
from the thermocouple but still within the microscope total
viewing area (16mm2) the steady state temperature could be
as much as 8-9°C different than the temperature measured by
the thermocouple. Such a magnitude of error would be quite
significant for most types of data collection. In addition,
it should be noted that the thermal gradients present in the
field of view are different for different quartz discs.
These differences are probably due to the way in which the
electrical coating is sprayed onto the disc as well as to
the way in which the disc is mounted to the cooling stage.

Non-uniform disc spraying results in unpredictable spatial

37

variations in heating, and the thermal contact between the
quartz disc and copper block can also affect temperature
gradients in the quartz disc. Work is in progress (A6) to
model this effect analytically and to check it
experimentally.

Most researchers who collect data with cryomicrOSOOpes
are careful to choose their sample in the region close to
the thermocouple so that the effect of thermal gradients are
minimized. However, this was not usually possible in the
freezing of liposomes. The yield of "good quality"
liposomes was usually small enough to prevent finding them
close to the thermocouple. In addition, convective movement
I of the liposome sample solution as the ice approached
usually resulted in the movement of liposomes in the field
of view. For this reason, in most cases the sample
temperature was deduced from the videotapes made during a
freezing run. One of the components of the videotape system
was a character generator which allowed the display and
recording of elapsed time on videotape. To obtain
temperature from elapsed time measurement, the time was
noted at which external ice formed around the liposome being
viewed. The temperature at that point in time was assumed
to be the equilibrium freezing temperature of a solution
with an osmolarity the same as that from which the liposomes
were fermed.

Temperatures after that point in time were calculated
from elapsed time measurements and the cooling rate obtained

from the strip chart recording. Two assumptions of this

38

type of approach should be noted: 1) it is assumed that
the concentration of solutes in front of the approaching ice
does not depress the freezing point of the remaining liquid
solution. In other words, the equilibrium freezing
temperature of the sample being viewed is assumed to be the
equilibrium freezing temperature of the bulk solution from
which it was formed even though some of this bulk solution
has already been frozen; 2) it is assumed that the cooling
rate is the same everywhere within the microscope field of
view even though the absolute magnitude of temperature is
known to vary within this region.

It is not easy to quantify the magnitude of
temperature uncertainty resulting from the above method.
Based upon the assumptions made, a reasonable upper bound on
the temperature uncertainty would be 305°C. It should be
remarked that care was taken to keep the thermocouple/
instrumentation calibrated so that the temperature measured
at the thermocouple was an accurate measurement of the true
temperature at that point. Appendix D describes the method
used to calibrate the digital temperature meter (DTM). An
experiment also was devised to verify that the response time
required by the DTM to linearize the input signal from the
thermocouple and provide an analog output for control
purposes did not cause error in temperature measurement.
This experiment is described in Appendix E.

3." Measurement 2: Liposome Volume

 

Volume measurements of liposomes were obtained by

replaying the videotape of a freezing run and tracing the

39

outline of a liposome displayed in 'stOp action' mode on the
television screen. A series of measurements were made of
the liposome diameter at a given time and the volume was
calculated by using a mean diameter to calculate the volume
of a corresponding spherical liposome. Videotapes of
liposomes where the liposome did not shrink in a reasonably
spherical manner were not used. This stipulation resulted
in the rejection of a large number of freezing runs.
Liposomes appeared to be mechanically fragile in the
presence of surrounding external ice and were often squeezed
into channels between dendrites of ice. Many of these
liposomes became very distorted, precluding the possibility
of making reasonable volume measurements.

For the liposomes that appeared to shrink spherically,
it was often difficult to determine precisely the edge of
the liposome membrane boundary. This was partly due to the
use of phase contrast optics for microscope viewing; this
type of optics produces a halo at the boundary of the
liposome. In addition, the presence of external ice often
made the liposome membrane boundary unclear. Because of the
somewhat distorted shape of the liposomes during osmotic
shrinkage, and the difficulty in determining exactly the
boundary of the liposome in the presence of external ice,
the calculated volume of a liposome during a freezing run
can be quite uncertain. This uncertainty is estimated, in
the worst case, to range from 1 15 to 1 20% of the

calculated volume.

MO

 

 

3.5 Measurement 2: Osmotically Inactive 9: "Bound" Water

 

Figure 9 shows the diffusion chamber used to make
equilibrium volume measurements of the liposomes. This
chamber was designed and built by Mr. Russell Ligon,
graduate student in Mechanical Engineering, Michigan State
University. The system consists of a membrane separating
the sample from a lower compartment. A drop of liposome
sample is placed on the underside of the top cover glass
fixture. A small piece of membrane dialysis tubing, cut to
appropriate size and previously soaked for several minutes
in a solution isotonic with the liposome solution is then
placed over the sample drop. To conduct an experimental run
the following procedure is followed. (Refer to Figure 9)

a) Flush and fill the bottom compartment with an
isotonic solution and mount the chamber in place on
the microscope.

b) Locate a liposome appropriate for experimentation
and record its volume from measurement of the
projected area.

0) Rapidly flush the bottom compartment with a
hypertonic or hypotonic solution.

d) Record the size of the liposome after equilibrium
has been established at the new concentration.

The dialysis membrane allows passage of water and
solutes across it but absorbs the shear stresses arising
during the rapid flush. During the flush the liposomes
remain almost stationary. The lower compartment contains a

very large volume compared to the liposome sample drop and

141

w

MICROSCOPE
OBJECTIVE

 

 

 

GLASS\‘
RICIo DIALYSIS
SUPPORT<;:*“ SAMPLE 1 A/r MEMBRANE

 

 

 

 

 

 

 

 

 

 

I I \

I
DIFFUSION
—> BULK FLOW ——>-

 

 

 

- fl l
P ‘ T

\¥——GLASS

\ /
LIGHT SOURCE

Figure 9. Diagram of the diffusion chamber.

“2

acts as an infinite reservoir. The final equilibrium state
attained is thus essentially at the concentration of the
large reservior solution; the concentration of the liposome
sample solution does not affect the final equilibrium
concentration.

At this time, the kinetics of solute and water
transport across the dialysis membrane have not been
measured thoroughly; however, preliminary calculations and
experiments by Russell Ligon indicate that the time constant
for the equilibration of a sodium chloride solution is on
the order of seconds. For the experiments presented here
the kinetics of transport are not an important factor since
measurements were made after equilibrium was established
across the liposome membrane, and thus also across the
dialysis membrane. This equilibrium condition was evidenced
by no further volume changes observed for the liposomes.
When the liposome drop was flushed with a hypertonic or
hypotonic solution the liposome being observed would
typically be observed to shrink (or swell) until a new state
was reached, at which point no further size changes
occurred. The time required to attain this new state was on
the order of several minutes (maximum).

The use of the chamber allowed volume measurements to
be made of a single liposome when placed in solutions of
various concentrations. The analysis of Appendix A shows
that such measurements can be used to obtain a Boyle-van't
Hoff plot from which the amount of "bound" or osmotically

inactive liposome water can be calculated.

“3

3.6 Measurement 9f Water Permeability

 

 

Measurements of water permeability were made using a
method described by Boroske, et. al (32). The diffusion
chamber described in the previous section was not used
because the transport kinetics across the dialysis membrane
are not fully characterized at this time. These kinetics
will affect the response of the liposome volume changes
unless transport across the dialysis membrane is much faster
than the osmotic response of the liposome. The Boroske
method consists of subjecting the liposome to a known
concentration change and measuring the rate of radius
shrinkage for a spherically shrinking liposome. Osmotic

flow of water across the membrane can be described by (32):

J = —KAC (3-1)

where Jw is the molar flux of water; K is the permeability
coefficient having the dimension of velocity; and ACS is
the molar solute concentration difference across the
membrane.

For a spherically shrinking liposome:

dV - 95 3-2)
E? ’ Adt (

uu

Since by definition:

dn
w

*5; (3-3)

DID»
6" <
m
3>II—’

where nw is the number of moles of water, and since the
time rate of change of moles of water is related to the time

rate of volume change by:

(3-“)

I
arm
6* <3

<|P4

W

where V” is the molar volume of water, equation (3-1), (3-

2), (3-3), (3-lI) can be combined to yield:

dB 1

Jw = a? :r = -KACS (3-5)
VW
Ol”
%% = -5“ KACS (3-6)

Equation (3-6) can be used to calculate K from measurements
of dR/dt for a given V" and ACS.

To obtain the required measurement liposomes were
prepared in distilled water and a known volume of liposome
suspension was mixed with an equal volume of sucrose
solution so that the final mixed solution was .01 M or .02M.
A drOp of mixed solution was immediately placed on the

microsc0pe stage and the shrinkage of the liposome was

observed and recorded using the videocamera. Measurements
could then be made from the TV image of the radius as a
function of time. Figure 10 shows representative plots.
Such plots typically revealed a linear relationship as
expected from the analysis of Boroske, et. a1 (32) shown
above.

In a few cases a lower limit of radius was reached.
Since the liposomes were prepared in distilled water this
result is unexpected if only the chemical contribution to
thermodynamic equilibrium is considered. It is likely
however, that as the liposome shrinks, other thermodynamic
variables can play a significant role in the equilibrium
state. Specifically, a pressure increase within the
membrane or bending of the membrane could offset a chemical
potential imbalance across the membrane. This effect could
account for the lower limit of radius shrinkage observed in
some cases. The measurement of water permeability was in
all cases calculated from the initial, linear part of the
radius as a function of time data.

Permeabilities could also be determined for liposomes
made in solution other than distilled water, but when the
intraliposomal compartment solute concentration is non-zero

the analysis becomes substantially more involved (39).

“5

116

.mucoefimoaxm
mpHHHnmmEMma pmpmz wcfipsc mafia mo COApocsm

 

 

 

 

we

to

1.

10.

....

m mm msficmp mEomOQAH mo mpoaa o>fipmpcmmopamm .OH whswfim.
.mvuzz.
cow co... 8.. oo» 08 oo. o
(E... «.33.
‘ O
{5‘ v.3 ...

N.mm NHIOHKN H:HO.I 0 {El Qnuux o

:.:m NHIOHRH. mmoo-| m fill/f4

m.mm waloaxm mmoo.| <

 

Am\Envx Aman\mmaoevmo< Am\E:Vpp\m© cam

 

(W) smovu

”.0 Results and Discussion

 

N.1 Determination pf Liposome Water Permeability

 

 

Table 1 shows the values of water permeability
experimentally determined for egg lecithin liposomes. Each
of the values is the result of an experiment on a single
liposome. Figure 10 shows typical plots of liposome radius
as function of time which were used for calculation of the
water permeability. The slope of the line is obtained from
a least-squares fit through the points in the linear part of
the plot.

It can be seen from Table 1 that there is significant
range (2” um/s - 62 um/s) in the values of the water
permeability determined experimentally for egg lecithin
liposomes. This variability is probably a combination of
two factors: experimental error in the measurement of the
water permeability values, and the actual distribution of
water permeability in the population of liposomes. The
average value (110.5 um/s) is in close agreement with the
value obtained for egg lecithin liposomes by Boroske, et. a1
(32), H1 um/s. However, these researchers observed a
smallem range of values for a comparable number of samples
(n=13). ‘The experimental permeability values obtained for
liposomes are also in good agreement with values calculated
by Fettiplace and Haydon (47) from experimental data of
Huang and Thompson (”8) for an egg lecithin bilayer lipid

membrane system. The calculations of Fettiplace and Haydon

“7

“8

Table 1. Experimental water permeability values
(um/s) for egg lecithin liposomes.

1. 36.7
2. 5“.“
3. ““.“
“. 23.9
5. 31.“
6. 39.2
7. “6.9
8. 50.7
9. 29.6
10. “1.3
11. “5.2
12. “0.8
13. 30.“
1“. 61.7
15. 38.9
16. “1.7
17. 39.0
18. 38.8
19. 30-9
20. 38.1
21. “2.3
22. “3.0
23. “2.5

Average: “0.5 um/s
Range: 23.9 um/s — 61.7 um/s
Standard Deviation: 8.“ um/s

“9

yielded room temperature permeability values for BLM's of
36-“8 um/s, assuming an activation energy of 1257
kcal/mole. Recalculations using an activation energy of
8.25 kcal/mole (31) resulted in slightly higher room
temperature permeability values, “8-63 IJM/S. ‘These higher
values are in reasonable agreement with the values obtained
for egg lecithin liposomes. This reasonable agreement
between liposome data and BLM data lends credence to the
claim that the liposomes are unilamellar, or at worst,
pauci-lamellar.

The activation energy, Ea, which describes the
temperature dependence of the water permeability is an
important parameter in any model describing the predicted
freezing response. Unfortunately, at the present time, this
value has not been obtained experimentally in our
laboratory. EXperimental determination of E8 requires
measurement of the water permeability at a variety of
controlled temperatures. The value for E8 used in the
computer model in this research was obtained from egg
lecithin liposome permeability measurements at two
temperatures, 25°C and 37°C (31).

“.2 Determination gf_Liposome Osmotically Inactive Volume

 

Figure 11 shows a normalized Boyle-Van't Hoff plot
which was used to determine the amount of osmotically
inactive or "bound" water in the liposomes. Appendix A
describes the theoretical background for the use of such a
plot. The analysis in Appendix A indicates that the

liposome volume is expected to be a linear function of

50

NORMALIZED BOYLE-VAN’T HOFF PLOT
1.00 —

#5
am:
I
E
8

+4:-

 

9-99 llmIllulnnllnqlnqnHIHHIFIHIHHIIHI]
.5

NORMALIZED INVERSE CONCENTRATION

Figure 11. Normalized Boyle-van't Hoff plot.

51

inverse concentration. In Figure 11 normalized volume
(volume/initial volume) is plotted as a function of
normalized inverse concentration (initial concentration/
concentration). The data appear to obey a linear
relationship. The line shown is a least squares fit to the
data points collected from experimental runs on seventeen
individual liposomes. (SlOpe = .95; y-intercept = .06;
correlation coefficient = .98). It can be seen that the
osmotically inactive volume is calculated to be 6% based
upon extrapolation of the volume data to infinite osmotic
pressure. (The y-intercept of the line corresponds to the
normalized osmotically inactive volumeJ The present
computer model accounts for the 6% osmotically "bound"
water.
“.3 Percent (1) Internal Ice Formation as a Function 2: Cooling

EEES

Figure 12 shows the percent internal ice formation in
liposomes as a function of cooling rate. The average
diameter of the liposomes used for experimentation was
approximately 20 pm 1_5 pm. The formation of internal ice
in liposomes is observed microscopically as characteristic
"flashing" or darkening of internal contents; the "flashing"
appearance in liposomes is similar to the appearance in
biological cells. Figure 13 shows a liposome before and
after internal ice formation.

The data presented in Figure 12 indicate that the
percent internal ice formation increases for faster cooling

rates, and for egg lecithin liposomes in 0.2 M sucrose the

52

The numbers in parenthesis denote:
# flashing/total Observations.

 

 

 

(SIS) (hfl) (3l3
Ioo- 4 4- )
o (T/K»
O
.2
‘5 50-
I:
3
E
,3! o (4/I2)
O/II
o v ( ) 1 l L L n J
O IO 20 30 4O 50

Comm; Rate (°C/min)

Figure 12. Liposome percent internal ice as a
function of cooling rate.

53.

 

 

A
B
'Figure 13. Formation of Internal Ice a: onset of
external ice; b: before internal ice nuclea-
tion; 0: after internal ice nucleation; d:

after thaw.

5“

.. “JIM...

.

i

«owl/t ...

..ut.’

11*
.IDGIJ r4

.7. I fang“ .

MM}

A.

 

(Figure 13)

55

probability is 100% for cooling rates greater than 20°C/min.
For cooling rates less than 2°C/min no visible internal ice
is expected to be observed as "flashingJ' Figure 12 should
be compared with Figure 1“ which shows similar information
for several biological cells. A comparison indicates that
the liposomes exhibit the same qualitative behavior as that
of the biological cells. The two figures are best
interpreted in terms of a competition occurring between heat
transfer and mass transfer as the system is cooled. The
liposome (or cell) system remains in thermal and chemical
equilibrium as the temperature is lowered until the onset of
external ice. The formation of the external ice lowers the
chemical potential of water in the external solution
relative to the internal solution. The membrane acts as a

barrier to ice penetration so that the chemical potential

difference across the membrane acts as a driving force for
mass transfer from the inside to the outside. Whether the
liposome or cell system re-achieves equilibrium without
internal ice nucleation depends on how fast the mass
transfer occurs relative to the rate at which the
temperature is being lowered as heat is removed from the
system. At very slow cooling rates the chemical potential
difference across the membrane remains small as the
temperature is being lowered since the mass transfer rate is
sufficient to prevent the buildup of supercooled water
inside the liposome. The transport of water is evidenced at
slow cooling rate by the shrinkage of the liposome being

frozen. Figure 15 shows the shrinkage of a liposome at a

56

Wu) 3231 BV'IRTIBDVHINI —

.mHHmo
HMOAonOfin Hmpm>mm mow mama wcflaooo mo

 

 

m mm Amfixm pnwfimv OOH Hmcmmpcfi ucmopmm .2H mmswfim
:58; BE 02:08
000.. Ome— o__ w No
0 QI‘I \Q\<IO/ O
I‘/ Q // 0
ON 1 I— . / \C /tu\ ION
’ .‘l‘\ \ 00/
, /
0v 1 , Lo 0, 10V
.. a D . Q 0 I.
I
om .. 09.7 3...: \ «>0 .8
z. o
00 .1 I /l low
11.1. d
00— 1 o <\ 0 Foo—

 

 

(°/o) 'IVAIABRS --

57

 

  
   

II. in . -'
m I. 1,
‘\n~

...-

” 7311 1mm.“

      

L." 1

5|.

.53

2°C/min;

Figure 15. Osmotic shrinkage for cooling r =
i thaw.

a-d: duirng freeze; e—h: dur

A—
a.

58

 

(Figure 15)

59

 

(Figure 15)

IIIIIIIIIIIIIIIIIIIIIlllll---_______

6O

 

 

(Figure 15)

61

slow cooling rate.

At faster coOling rates water transport across the
membrane is insufficient to prevent the accumulation of
supercooled water inside the liposome as the temperature is
lowered. The presence of supercooled water inside the
liposome is accompanied by an increased likelihood of
internal ice formation.

As first indicated by Mazur (5), the system parameters
having the largest influence on the likelihood of
intraliposomal or intracellular freezing are: the cell
surface area to volume ratio, and the permeability of the
cell plasma membrane to water. The above considerations
indicate the important role of the membrane permeability.
The surface area to volume ratio is important since it is a
measure of the area across which water transport can occur
relative to the volume of water which must be transported to
achieve equilibrium. Small systems which have a high
surface area to volume ratio can respond to non-equilibrium
conditions faster than larger systems. The data for
biological cells” Figure 1“, is consistant with Mazur's two
considerations. A small, very permeable cell such as the
red blood cell requires very fast cooling rates before the
formation of internal ice is observed, whereas a large,
relatively impermeable cell such as mouse ova exhibits the
formation of internal ice at much slower cooling rates.

“.“ Nucleation Temperature fig 3 Function 22 Coolipg Rate

 

Figure 16 shows a plot of nucleation temperature as a

function of cooling rate. Table 2 is a compilation of the

62

Bars represent standard deviation.

I 'n' denotes the number of observations.

 

 

0‘1
E3 { { n-3

- -‘ O
2 '0 111-6
2 n=7 “'10 "=1
O
3
3 20‘
,2
c:
.2
S
5 -30"
2

1 1 l lllJlL 1 1 1. nlLu
I I0 I00

Cooling Rots (“C/min)

I Figure 16. Nucleation temperature as a function
of cooling rate for liposomes.

Table 2. Nucleation temperature data for liposomes.

 

Cooling Rate °C/min

 

 

 

 

 

 

 

7 -ll, -7, -5, -6, -9, -5
13 -11, —12, -5, -7, -l“, -“, -“
20 -11, -1“, -13, -9, -7, —7, -8, -7, -8
3“ -12
f ““ -10, -10, -10
Average nucleation temperature (for all cooling rate) = -8.8°C.

Standard Deviation 3.0°C.

63

raw data for Figure 16. Internal ice nucleation is
Observed microscopically as a characteristic "flash"; the
appearance of a liposome after nucleation is shown in Figure
13. The average temperature for "flashing" in egg lecithin
liposomes is approximately - 8°C, and, as can be seen from
Figure 16, the nucleation temperature appears to be
independent of the freezing rate. (Appendix F presents the
statistical calculations demonstrating the lack of
dependence of nucleation temperature on cooling rate). The
magnitude of the nucleation temperature is similar to that
observed for several types of biological cells in the
absence of cryOprotective agents: Hela S-3 (73),
Chlamydomonas (7“), and Spirogyra (51). Figures 17,

18, and 19 reproduce the data for comparison. It should be
noted that all of the systems, including liposomes, have a
fairly wide range of nucleation temperatures at a given
cooling rate. The reason for this range is not known.

The mechanism by which ice is nucleated inside a cell
is still an unanswered question. Theoretically, ice
nucleation inside the cell can occur by homogeneous or
heterogeneous mechanisms. Experimental evidence on this
subject is not conclusive. A study by Rasmussen, et. a1
(50) indicated that yeast and red blood cells could be
cooled down to -“0°C when the surrounding water was kept
supercooled. 0n the other hand, Mazur (78) has summarized
evidence which indicates that the mechanism for internal ice
nucleation is not homogeneous nucleation since for a number

of biological systems the temperature at which internal ice

Nucleation temperature(°C)

 

6“

 

 

 

 

 

° F
-5 P
E
u "0 '-
S
5
2
3 -15-- §
..
-20 —
l L l l l 1 I ll 1 l l l J l 1 ll
10' lo2 103
COOLING RATE (“C/min)
Figure 17. Nucleation temperature as a function
of cooling rate for HeLa cells (73).
O .
-5 __
.1
l
0
-IO»
1
II.
-15 .t . 3
O 5 IO
Cooling rate (°C min")
Figure 18. Nucleation temperature as a function

of cooling rate for Chlamydomonas (7“).

Nucleation temperature(°C)

65

 

 

 

 

0.-
...5L I
I I)
-|O L I I
.1
—l5 '1 J n
0 IO 20

Cooling rate (°C min")

Figure 19. Nucleation temperature as a function
of cooling rate for Spirogyra (51).

66

nucleation occurs is higher than the homogeneous nucleation
temperature both in the presence of external ice or when
being frozen in a non-aqueous solution where external ice is
presumably absent.

If the nucleating mechanism is heterogeneous
nucleation, the question arises whether the internal ice is
nucleated by internal solution components, the cell
membrane, or the external ice. Mathias and Franks (65) have
presented data indicating that internal ice nucleation is
independent of ice nucleation in the surrounding medium.
However, other work implies that external ice is important
for internal ice nucleation. A study of Morris and McGrath
(51) on the algae Spirogyra indicated that in the presence
of external ice the mean internal nucleation temperature was;
approximately -8°C. If suspensions of Spirogyra were
carefully supercooled, a mean nucleation temperature of
-12°C could be attained without the formation of
intracellular ice. The difference was statistically
significant (P=JKH). Intracellular ice was then observed
to form immediately after the spontaneous nucleation of
external ice. These considerations indicate that external
ice plays a crucial role in the formation of intracellular
ice since internal freezing occurs only in the presence of
extracellular ice.

Attempts have been made to estimate probabilities of
intracellular ice formation based upon an assumed critical
nucleation temperature. For instance, Mazur (10) proposed

that in order for intracellular ice to occur:

67

1) the cell must contain freezable water

2) the water must be supercooled

3) the temperature must be below a critical

nucleation temperature
By applying his water transport model he was able to
estimate probabilities of intracellular ice formation as a
function of cooling rate. In order to do this he had to
assume a value for the amount of critical supercooling
required to nucleate a cell. The calculations indicated
that the estimated probabilities were fairly insensitive to
the amount of supercooling required but were quite sensitive
to the value assumed for the nucleation temperature.

The concept of a critical amount of supercooling has
also been prOposed as a conceptual tool for the
investigation of internal ice formation (15). Cosman
defines a locus of critical states for the formation of
internal ice and compares this with the equilibrium state of
the cell being frozen. Figure 20 reproduced from (15) shows
a representation of the locus of critical states for the
internal solution in terms of the non-dimensional
chemical potential of water. In Cosman's model the critical
supercooling is determined by the nucleating characteristics
of the internal solution. In both Mazur's and Cosman's
models the likelihood of internal ice nucleation is linked
to an assumed critical degree of supercooling allowable
within the cell. The mechanism by which the external ice
causes the nucleation of internal ice is still unknown. An

early hypothesis by Mazur (52) prOposed that the external

TEMPERATURE. 'r (°C)

68

 

 

P

 

   
  
 

3’ CRITICAL
1’ SUPERCOOLING

‘ Locus OI= HETEROGENEOUS

NUCLEATION TEMPERATURES
FOR INTRACELLULAR SOLUTION /
‘;5ySKHJNflCAL (E2222;

JJILL‘ L lLlLllll

 

 

In; -uw)/RT.I-Imwl

.Figure 20. Safe internal thermodynamic states with
respect to ice formation for a hypotheti—
cal cell (15).

 

69

ice penetrated the cell membrane through aqueous pores which
some researchers believe to exist in cell membranes. As the
temperature of the external liquid/solid water solution is
lowered the solid phase is able to penetrate through
increasingly smaller pores in the membrane. The data from
the freezing of liposomes does not appear to support the
idea of ice penetration through pores. It is likely that

liposomes prepared from egg lecithin without proteins have a

reasonably homogeneous membrane in which structural holes
are absent. These liposomes, however, undergo internal
nucleation at temperature similar to those of several
biological cells. For the liposomes at least pores are
probably not present; yet the membrane breaks down as a
barrier to ice at temperatures comparable to those observed
in biological cells.
“.5 Computer Simulations

Unless otherwise noted, the following simulations are
for the nominal condition: initial liposome diameter = 20

initial concentration of sucrose = 0.2M; B = 230°C/min; K

u1 um/s; Ea = 8u25 kcal/mole; osmotically inactive volume
6%; surface area calculated to be that of a shrinking
sphere. ‘The normalized volume is defined as: instantaneous
volume/initial volume.
“.5.1 The Effect of Freezing Rate
Figure 21 shows the effect of the freezing rate,
B, on the predicted volume reduction of liposomes.
As expected, the predicted displacement from

equilibrium is greater for the faster cooling rates.

“.5.2

70

This correlates with the experimental observation of
increased likelihood of nucleation temperature at
faster cooling rates (Figure 12). However, Figure 21
indicates that the maximum displacement from
equilibrium occurs at lower temperatures for faster
cooling rates. The nucleation temperature, though,
(Figure 16) does not appear to depend on the cooling
rate. This lack of dependence is significant. As
mentioned previously, the mechanism of internal ice
nucleation is still unknown.
The Effect of Different Assumptions Regarding Membrane
Surface Area During Freezing

Figure 22 shows the effect of different model-
ling assumptions regarding the surface area change of
the liposome membrane during freezing. The two
limiting cases are depicted: 1) constant surface
area during freezing and; 2) surface area
corresponding to that of a shrinking sphere. The
assumption of constant surface area during shrinkage
was part of Mazur's original water transport model
(5). Mazur stated that the surface area is constant
in mammalian red cells (53), but varies as the two
thirds power of volume (idh, as a shrinking sphere)
for sea urchin eggs (5“). As Mazur points out, for
the shrinking of cells the possibility of membrane
folding is plausible, resulting in constant surface
area. In a later statement on this modelling

assumption (10) he noted that a study of cultural

71

COOLING RATE EFFECT

1.02

WLIZEJ VOLUME
Q
01
Q

 

 

$.00
llITI‘IIIIIIIIIIIIIIIIIIIllIIIIIIIIIITIIIIHIIIITTFI
0.00 - 2.00 - 4.00 - SM -B.00 - 119$

TEFPERATURHC)

Figure 21. Effect of freezing rate on predicted
volume response during freezing.

SURFACE AREA ASSUMPTION EFFECT

1.00

   
    

Lu
1:
3
9
Q am
5 CONSTANT SURFACE AREA
g CHANmNC SURFACE AREA

am

am -2Iaa «as -Sw em ~19.“
TEMPERAIUREtC)

Figure 22. Effect of surface area assumptions
on predicted volume response during
freezing.

72

mammalian cells (55) Showed that isotonic cells
contain folds in the form of microvilli and these
microvilli disappear when the cells swell in
hyposmotic media. This observation could account for
those cells' ability to rapidly increase their volume
without lysis.

Observations of other workers are consistent
with the hypothesis that the cell surface area (or
liposome area) is not constant during osmotic
shrinkage. For example in their experimental
measurements of liposome water permeability, Boroske,
et. a1 (32) occasionally observed the formation of
"daughter vesicles" from liposomes whose initial
radii were above 10 pm. Although Boroske and
coworkers apparently did not always observe the
formation of smaller vesicles they noted that
daughter vesicles could likely have been smaller than
the resolving power of the phase contrast Optics used
on their microscope. In addition, since their
experimental observations on osmotic shrinkage
matched well with an equation derived based on the
assumption of changing surface area (See equation [3-6]
above) they concluded that "a loss of active wall
area takes place during osmosis". Earlier workers
(31) had also noted microscopic extrusions, in
shrunken liposomes, of tiny filaments or spherules of
membrane material. These filaments, however,

remained attached to the membrane surface. The above

“.5.3

“.5.“

73

evidence can be interpreted as evidence for a
changing surface area during freezing.

Inspection of Figure 22 suggests that the
assumption regarding the effect of changing the
surface area is not critical in predicting the
volume. The difference between the constant area
curve and the changing area curve is most significant
only at the intermediate subzero temperatures where
the differences in predicted volume (for a cooling
rate of 2°C/min) using the two assumptions is
approximately 5% of the initial volume. The effect
at higher cooling rates has not been predicted.

The Effect of the Reference Water Permeability

Figure 23 shows the effect of a change in the
reference water permeability (K at 25°C) on the
predicted liposome response. This effect can be
significant. In the intermediate temperatures the
volume predicted for the case of K=23.9 um/s can be
almost twice the volume predicted for the case of
K=61.7 'um/s. The two permeability values shown
correspond to the extremes of the range of
permeability values determined in our laboratory.
Activation Energy Effect

The activation energy has previously been
recognized as an important parameter in the water
transport model (5). Figure 2“ also indicates that
this is so. In the intermediate subzero temperature

ranges the predicted volume for cases of large

7“
REFERENCE PERMEABILITY EFFECT

     

 

 

    
 

 

130
i
9
0.50
3 K- 23.9 fun/s
g K:I 61.7 ,um/s
9“ IIIIIIIIIIIITIIIIIIIIIIIIITIIIIHIIIIITIIIITTFITT]
'2.00 4.00 -6.00 -8.00 -10.00
TBPERATURECC)

Figure 23. Effect of reference permeability
on predicted volume response during
freezing.

ACTIVATION ENERGY EFFECT

130
T
3
9
g 0'50 E¢t8.25 keel/mole

EOIIZJ IIcoI/mole

2

000

000 -200 -+00 -800 -&00 -4000

TEJ'PERATURECC)

Figure 2“. Effect of activation energy on
predicted volume response during
freezing.

“.5.5

75

activation energy, Ea = 12:7 kcal/mole, can be
approximately twice the volume as compared to the
case when the activation energy is smaller, E8 = 8.25
kcal/mole. The lower value is obtained from the work
of Reeves and Dowben (31) on egg lecithin liposomes,
while the larger value, 12.7 kcal/mole, is a value
determined by Huang and Thompson (“8) for lecithin-
cholesterol liposomes. The upper value is assumed to
be a reasonable upper bound of possible values for
the activation energy. Another activation energy
value obtained for egg lecithin liposomes is 10.6 I
0.“ kcal/mole (37). In view of the major effect of
E8 on the water transport model predictions it
appears essential to experimentally determine or
verify the activation energy value in the future.

It should again be noted that while the present
model accounts for the temperature dependence of the
water permeability, it is assumed that the membrane
permeability is independent of the osmolarlity of the
surrounding solution.

Comparison Between Computer Predictions and EXperi-
mental Data for Volume Reduction During Freezing

Figures (25) and (26) show representative plots
of the observed shrinkage of liposome compared to
volumetric response predicted from computer
simulations. The data indicate that in general the
observed volumetric reaponse is consistent with the

thermodynamic water transport model. However,

I‘DRMALIZEJ VOLUME

FORMALIZEJ VOLUME

1.00

1.00

76

MODEL VS DATA, COMPARISON .‘L

 

 

Model
EC
000 -200 -&60 —&00 -&00 -1a00
TBPERATURE(C)
Figure 25. Comparison between experimental
data and computer model.
MODEL VS DATA. COMPARISON 2
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIITIT]
000 —200 -maa -sae -&00 -1006
TEI’PERATURHC)
Figure 26. Comparison between experimental data

and computer model.

77

quantitative comparison is hampered both by the
uncertainty in the experimental measurements of
volume and temperature, as well as the uncertainty in
the parameters used in the water transport model. As
discussed previously, the difficulty in determining
the precise boundary of the liposomes in the presence
of external ice and the mechanical distortion of the
liposomes during freezing results in an estimated
absolute volume uncertainty of It 15 to 20%. In
addition, the uncertainty in the values for the water
permeability and activation energy results in a range
of predicted volumetric responses. 'The combination
of the two sources of uncertainty prevents a precise
quantitative correlation between model predictions
and experimental results at this time.

Further work is required before quantitative
comparison can be made. First, it is necessary to
address the problem of imprecise boundary
determination. It is possible that a different type
of microscope Optics would improve the boundary
resolution. For example, differential interference
contrast (DIC) Optics instead of the phase contrast
Optics presently in use is likely to improve boundary
resolution (75).

The uncertainties in the transport parameters
used in the thermodynamic model are also the result

of eXperimental uncertainty since these parameters

are experimentally determined. The range of water

78

permeability values determined experimentally is
probably also the result of the statistical variation
of this parameter within the liposome population.
Since previous workers (32) did not observe as wide a
range of permeability values for egg lecithin
liposomes, careful collection of more permeability
data, with the aim of minimizing eXperimental
uncertainty seems desirable.

A comparison of computer simulations of liposome
freezing with observed nucleation temperature data
indicates one important lack of correlation. At a
cooling rate of 20°C/min the observed average
nucleation temperature is -9.5°C (n=10); however, as
can be seen in Figure 21 the thermodynamic model
predicts that the liposome should be nearly at
equilibrium before this temperature is reached.

“.6 Thawing Response 2: Liposomes

 

The computer thermodynamic model enables prediction of
liposome response upon thawing in addition to the freezing
response. Since the membrane water permeability is a
function of temperature the liposome does not respond the
same upon thawing as upon freezing even for cases when the
thawing rate is the same as the freezing rate. Figures 27
and 28 show the predicted computer response for two
liposomes, one of 27.5 IJm diameter and one of 25.0 um

diameter. The response is for a cooling rate of 2.0°C/min

and a thawing rate of 20°C/min. Also shown are plots of

experimental data for two liposomes. 'The data show two

NORMALIZED VOLUME

NORMALIZED VOLUME

L0
L
I
0.5 -

I.

I.

o l l l l L I l l l J 41 l I l l L l l l
'10 '5 0 IO 20
TEMPERATURE (°C)

Figure 27. Comparison between experimental data
and computer model for freeze-thaw
response.

raeezmo RATE! -2 °cmm K . 41pm

THAWINO RATE = 20 'c/MIN E08 0.25 keel/mole

'OSNOTICALLY INACTIVE VOLUME: 6% INITIAL DIAMETER: 25.0 ,m

SPHERICAL oeuvonmow, REHYDRATION ASSUME!)

L0
0.5 " /
b A
I. r”
0 A 4 A l l A L A A A A A A l A 4 A A J
-IO -5 O IO 20
TEMPERATURE PC)
Figure 28. Comparison between experimental data

79

FREEZING RATE: '2 °C/min K8 “pm/s

THAWING RATE 3 20 °C/min E. 3 8.25 tool/mole

OSMOTICALLY INACTIVE VOLUME: 6% INITIAL DIAMETER 27.5 fim

.SPHERICAL DEHYDRATION, REHYDRATION ASSUMED

 

 

 

 

 

 

 

 

 

 

 

 

 

and computer model for freeze-thaw
response.

 

80

different types of qualitative response. One of the
liposomes (25 um) appears to be essentially inactive
osmotically upon thaw. The other liposome, upon thaw,
swells faster than the predicted computer response.

“.7 Possible Mechanisms g: Freeze-Thaw Damage

 

 

The existence of an Optimum cooling rate for the

survival of biological cells (Figure 1) implies that the
causes of injury at slow cooling rates are different from

the causes of injury at fast cooling rates. It is possible
that observation of the freezing of liposomes could yield
some insight into the mechanism of freezing damage to cells.

One postulated mechanism for irreversible freezing
damage is the loss of membrane material during freezing
which cannot be reincorporated upon thaw (66). Observation
of liposomes indicated that in a number of cases, although
upon thaw a liposome appeared to be very distorted with
pieces of lipid attached by thin strands, the liposome was
able to re-absorb the lipid and regain a Spherical shape.
However, in most cases the final size of the liposome after
thaw was smaller than the initial size (Figure 27). It
seems likely that some of the lipid was lost from the
membrane and was not able to be reincorporated upon thaw.

For biological cells frozen at fast cooling rates
internal ice formation has been correlated with cell death
(“). This cell death could possibly be the result of

mechanical damage to internal organelles or to the membrane

by ice crystals. During the freezing of liposomes it was

observed that the formation of internal ice sometimes

81

resulted in destruction of the liposome. Upon thaw an
amorphous mass of lipid remained which did not reform into a

liposome.

In other cases, the formation of internal ice did not
appear to destroy the liposome. Sometimes a liposome could
be frozen and thawed several times with the formation of
internal ice each time as detected by "flashing". In these
cases internal "flashing" occurred several degrees below the
temperature at which external ice had formed. Such an
observation indicates that after each freeze/thaw cycle the
liposome was able to reattain membrane structural integrity
in the sense of acting as a barrier to ice penetration.

This suggests the possibility that the damage to biological
cells caused by internal ice formation might not necessarily
be due to destruction of the membrane integrity.

“.8 General Response 2: Liposomes During Freeze-Thaw

 

 

 

A number of interesting and significant observations
were made concerning the freeze-thaw behavior of liposomes.
They include:

1) Apparent lightening of the liposomes as the ice

front approached. (Compare Figures 15a and 15b)
This observation can be explained in terms of the
phase optics used to view the liposomes. ‘This
Optical system is useful when observing systems
having a different refractive index than the
background since the contrast is enhanced in such
cases. For the case of liposomes prepared in 0.2 M

sucrose the refractive index difference between the

2)

82

inside the outside of the liposome is small. As a
result the liposomes are somewhat hard to see under
the microscope. As the ice approaches it is
expected that a front of increased solute
concentration exists at the liquid/solid boundary
(56). This results in a larger refractive index
outside the liposomes than within. Consequently
the liposomes appear "lighter". An explanation of

this effect is given by Barer and Joseph (61). It
is possible that this effect could be quantified in
the future to measure intraliposomal concentrations
for comparison with computer predictions.

Darkened appearance of liposomes upon thawing.
Immediately after thawing many liposomes were
observed to appear darker than the surrounding
solution and these liposomes were often surrounded
by a typical phase contrast halo. (See Figures
15f, g, h) Over the period of about a minute, the
liposomes became lighter until their appearance was
the same as that before freezing. These
observations can also be interpreted in terms of
the phase optics and of the osmotic loss of water
during freezing. This loss of water during
freezing would result in the internal solution of
the liposomes becoming concentrated. Upon thaw
before any water influx could re-Establish chemical
equilibrium across the membrane the greater

internal concentration would be expected to result

3)

“)

83

in a larger refractive index inside the liposomes.
This refractive index difference results in the
dark appearance immediately after thawing (61). As
the liposomes achieve equilibrium due to water
transport across the membrane into the liposome
they would be expected to become lighter.
Distortion of liposomes in the presence of
external ice. Often, as ice formed around them,
the liposomes became quite distorted and were
pushed into channels by the ice. Even so, many of
them continued to act as barriers to internal ice
nucleation. It appears that a lipid membrane,
without proteins, is able to withstand severe
mechanical distortion while maintaining enough
structural integrity to continue to act as a
barrier to ice penetration. Severe distortion
often appeared to produce lipid extrusions of
various forms from the lipid membranes. These
extrusions became most visible upon thawing.
Reincorporation of lipid upon thawing. In several
cases, upon thawing, liposomes were observed to
reincorporate lipid extrusions. Typically the
liposomes would eventually reattain a spherical
shape at a smaller diameter than before freezing.
This could be due to the possible loss of membrane
material during freezing.

In some cases the liposomes appeared to be

osmotically inactive upon thawing. (See Figure 28)

5)

6)

7)

8“

"POpping". In several cases the liposomes
exhibited an interesting membrane instability when
thawed. The membrane, when observed in real-time,
appeared to rupture, eject intraliposomal material,
and then reseal. A single liposome would be
observed to "pop" a number of times during the
first several minutes after thawing. This
phenomenon is similar to behavior observed in
erythrocytes placed in hypotonic solution (57).
The behavior could also be induced in liposomes
exposed to hypotonic solution.

Internal gas formation upon thawing. In several
cases internal bubbles were observed to form in
liposomes during thawing. This behavior is
analogous to that observed in the algae, Spirogyra
(51).

Behavior of liposomes frozen in distilled water.
The behavior of liposomes when prepared and frozen
in distilled water was observed to be different
from liposomes frozen in 0.2M sucrose. Figure 29
shows the freezing of a liposome in distilled
water. When frozen at slow rates in distilled
water the liposomes were invariably observed to
break apart after the formation of external ice at
quite high subzero temperature (approximately
-1°C). The reason for this difference in freezing
behavior is unknown. It is possible that the

presence of external and/or internal solutes has an

85

effect on the membrane during freezing. Other
researchers (39. 58) have noted that solutes have
an effect on the permeability of membranes. If
solutes influence a physical characteristic of the
membrane in changing the membrane permeability to
water, it is possible that their presence can
effect the membrane property as a barrier to ice.
For example, Olien (67, 68) has postulated that
freezing stress can arise in part from an adhesion
energy which develops at the membrane due to a
competition for interfacial liquid water by ice and
hydrophilic substances. This adhesion energy could
be different if solutes are present in the liquid

solution.

I .

"It tinge”
" . .I.

Figure 29.

 

A
I
i
I
x
*3
B
Freezing of liposome in distilled water
a: before external ice; b: onset of ex-
ternal ice; 0: liposome embedded in exter—
after destruction of ipcscme.

nal ice; d:

86

87

 

(Figure 29)

5.0 Conclusions

 

Based upon the results of this work the following

conclusions can be made:

1)

2)

3)

“)

Large unilamellar liposomes demonstrate qualita-
tive freezing behavior similar to that observed in
biological cells. Important similarities include:
osmotic shrinkage at slow cooling rates; internal
ice formation at fast cooling rates; comparable
nucleation temperatures; a variety of comparable
thawing responses, iJL, partial swelling, osmotic
"popping", and occasional internal bubble forma-
tion.

Liposomes represent a good model system for freez-
ing studies of cells because of the analogous
behavior observed and because of the comparative
simplicity of liposomes. Liposomes of known
chemical composition can be prepared.

It is a significant observation of this research
that such a simple membrane system, composed of
lipid only, is able to demonstrate a wide variety
of freezing behavior analogous to much more complex
biological systems.

The observed osmotic shrinkage of liposomes is
consistent with a standard thermodynamic model but
experimental uncertainty must be reduced before

precise quantitative comparison can be made.

88

6.0 Suggestions for Future Work

 

The following suggestions are made for future work

involving the use of liposomes as model systems to study

freezing behavior:

1)

2)

3)

“)

Improve the method of liposome preparation. An
improved yield of large unilamellar liposomes would
markedly decrease the time involved in data
collection.

Devise a method to verify that the liposomes used
are unilamellar. Along these lines, electron
micrographs of the liposome membrane would be of
value.

Determine the transition temperature for the egg
lecithin used. Reported transition temperatures
are in the range -7°C to -13°C (59). The
transition temperature could be relevant to
theories of ice nucleation across the membrane and
to the effects of mechanical distortion and
observed lipid extrusion.

Determine activation energies for water
permeability in liposomes. The cryomicroscope
cooling stage could be used in conjunction with the
method presently used at room temperature to

determine water permeability values at lower

temperatures.

89

5)

6)

7)

8)

9O

Collect more data comparing the observed response
of liposomes during thawing with the response
predicted by the computer model. Such data could
establish whether the observed thawing response is
consistent with the thermodynamic model.

Collect more data on freeze and thaw behavior of
liposomes to try to correlate the different thawing
responses observed such as membrane destruction,
membrane "popping", internal bubble formation with
the different freezing histories, ine., cooling
rates, presence of internal ice, mechanical
distortion.

Improve the membrane boundary resolution of the
liposomes. Differential interference contrast
(DIC) optics should help in this regard.

Use the diffusion chamber presently under
development in the laboratory to determine how much
shrinkage a liposome can reversibly tolerate when
exposed to hypertonic solutions. Such an
experiment would represent an attempt to address
the question of how much area or volume reduction a
liposome can withstand without irreversible loss of
membrane material, or irreversible membrane
failure. The use of fluorescent markers should
prove to be valuable in this study. Appendix 0
describes some preliminary investigations into the

use of fluorescent probes as markers.

91

9) Determine the effect of internal and external
solute concentration on the membrane water
permeability.

10) Investigate the effects of cryoprotective chemicals
on the freezing and thawing response of large

unilamellar liposomes.

APPENDICES

APPENDIX A

Equilibrium Description of Cells as Osmotic Systems

Living cells possess membranes which are crucial to
maintaining the proper chemical environment within the cell.
The membranes of living cells are semipermeable; this
selective permeability is evidenced by the fact that a cell
membrane is typically much more permeable to water than to
solutes. An additional feature of living cells which should
be kept in mind is the potential to allow chemical transport
against concentration gradients. This form of transport
requires energy input and is termed active transport. For
the case of liposomes, active transport is not possible
because no proteins are present in the membrane.

The semipermeable nature of the membrane gives rise to
the description of the cell as an osmotic system (22), and
the characterization of the internal and external
concentration of the cell in terms of "osmotic pressure)‘
The term osmotic pressure can be understood by reference to
Figure 30. This figure shows a glass tube attached to a bag
containing a solution of water and solute. If this bag is
then placed into a solution of pure water, and if the bag is
made of a semipermeable membrane (allowing passage of water
but not of solute) then water will pass into the bag from
the pure water solution. The level of the solution in the
glass tube will rise until equilibrium is eventually

established. At the new equilibrium state the solution in

92

93

 

 

 

 

 

A I
Tr = AP
I“;
/ Water and
Phase 0 A . Solute
Pure Water Phase /—-Semi-permeoble
B Membrane

 

 

 

6 #3
S

emi-permeoble
Cell Membrane

(,qu =,u.3, for equilibrium)

Figure 30. Osmotic pressure schematic (“3).

9“

the bag is at a greater pressure than the external pressure.
This pressure difference is termed the osmotic pres-
sure. Alternatively, the osmotic pressure can be considered
to be the excess pressure that must be applied to a solution
of water and solute to prevent the diffusion of pure water
into it across a perfectly semipermeable membrane. It is
important to note that the osmotic pressure of a solution is
not a hydrostatic pressure exerted by the solution; it
should actually be regarded as one of the thermodynamic
properties of the solution. In fact, the osmotic pressure
can be more easily thought of as a direct measure of a
solution's activity (“1). To see this, consider Figure 30,
' which shows a system consisting of pure solvent separated
from a solution by a membrane permeable to solvent only.
The chemical potential of water for the inner solution,

u; , is:

pi = u*(T) + V p + RT lnai (A-l)
w w w w

where u; is the chemical potential of pure water at the
given temperature.
For an ideal solution a$=x$ so equation (A-I) can

be written as:

vi = u*(T) + V p + RT 1nxi (A-2)
w w w w

95

Then if the pressure difference across the membrane is

assumed zero equation (A-2) becomes:

_ i _ 1
Au - “w - u - RT 1nxW (A-3)
1 A
For the inner solution xw<1 so thatuw < uw.

This chemical potential difference can provide a driving
force for water flow from the outer solution to the inner

solution. As stated earlier this flow can be prevented by
applying a sufficient hydrostatic pressure to the inner
solution.

The relationship between the applied pressure and the
change of chemical potential for a solution of constant

temperature and composition is given by (“2):

Sui _
55— T n ‘ V1 (A—“)
’ J

where P is the total pressure and Vi is the partial molal
volume of the solvent (Species i) in the solution.
Equation (A-“) can be integrated to give the amount
that the chemical potential of the solvent is raised by
increasing the applied pressure by an amount fl , equal to

the osmotic pressure.

p+n _
Vi dp (A-S)
p

TTV

Au

Au

1 (A-6)

96

Equation (A-6) follows from (A—5) if Vi is constant,
iue., if the solvent is incompressible.

At equilibrium the chemical potential of water on both
sides of the semipermeable membrane must be the same, that
is U$=U3 (See Figure 30). This means that the reduction of
chemical potential caused by the addition of the solute to
the inner solution is exactly balanced by the raising of the
chemical potential caused by the application of the external

pressure equal to the osmotic pressure. This can be written

as:
Au(solute) + Au(pressure) = O (A-7)

substituting (A-3) and (A-6) into (A-7) yields:

1 — _
RT 1nxw + nvw — O (A-8)
or
n = 3%: lnxi (A-9)
Vw

where 7“ refers to the partial molar volume of water in the
solution.

From equation (A-9) it can be seen that the osmotic
pressure, n, is a measure of water concentration or
activity expressed in this ideal solution ease as the mole

fraction of water. Equation (A-9) can be further simplified

for the case of dilute solutions. The mole fraction of

97

waterijsexpressed:hTtermSIOFtheImale[Tactionscn‘the

various solutes,£ xj:

J

x = 1 - 2 xi (A-lO)
W J
J
Equation (A-9) becomes:
n = 152-1n(1 - X XI) (A-ll)
V j J
W
n = 53 z x? for small 2 x3 (A-12)
533 33
W
Since
2
.1'1.
x x = i——l. (A-13)
:15 “t

where “t is the total number of moles, solvent and solutes,

equation (A-12) becomes:

 

n = _ RT 2 nJ (A-l“)
Vw nt 3
For dilute solutions 0t is approximatley equal to nw, the

number of moles of solvent (water) so that nti = nwvw : Vw.
Vw is the volume of solvent in the solution. Equation (A-

1“) then can be rewritten as:

an = RT 2 n. (A-lS)

98

EQuation (A-15) is an expression of the Boyle-van't Hoff law.
One refinement often made in the Boyle-van't Hoff law,
equation (A-15), is to account for any osmotically inactive
water. In equation (A-15), Vw represents the volume of
solvent which is free to move under an osmotic gradient. If
there is a significant amount of osmotically inactive volume
then Vw will not correspond to the actual measurable volume
of the cell. An apprOpriate correction for Vw is:

Vw'= Vi =(Vicell -'Vb (A_16)

where Vw denotes the "free" water and Vb the "bound" water.
The modified Boyle-van't Hoff law is then:
"(Veell - Vb) = RT? n3 (A-17)
Originally, the Boyle-van't Hoff law was expressed in

terms of an analogy with the perfect gas law as (22):
WV'= constant (A-18)

Comparison of equations (A-17) and (A-18) show that they are

analogous if V = VC - V and RT: n:j = constant. The above

ell b

derivation of equation (A-19) indicates several conditions
required before the law can be expected to hold for cells
(“3):

1) no hydrostatic pressure gradient exists across the

cell membrane.

99

2) the intracellular solution is an ideal, dilute

solution.

3) the temperature is constant during osmotic changes.

“) the total number of osmotically active solute

molecules, I 111, does not vary during osmotic
changes. This means that no solute molecules can
leak across the membrane.

The experimental determination of the equilibrium
osmotic characteristics of semipermeable cells involves
exposing the cells to solutions of various osmotic
pressures, iue., different concentrations. The cells shrink
(or swell and their equilibrium volume is plotted as a
function of the inverse of the extracellular concentration.
A graph is obtained similar to Figure 11. From such a graph
an estimate of Vb can be obtained by extrapolating the curve

to infinite osmotic pressure.

APPENDIX B

Liposome Preparation Techniques

Since the initial report of liposomes and a method for
preparing them (21), a large number of techniques for
liposome preparation have been reported (see reference 27
for review). ‘Work is still active in this area.

The preparation techniques of Bangham et a1. (21)
yielded large amounts of multilamellar vesicles. Other
investigators soon reported that unilamellar liposomes could
. be prepared by sonication of multilamellar liposomes (77).
Unilamellar liposomes prepared in this manner are small,
however, (diameter:.02 um) and cannot be resolved with a
light microscope. The research underway in the
Bioengineering Transport Processes (BTP) Laboratory requires
the use of large unilamellar liposomes (diameter=20 um),
Therefore part of the research effort involves attempts to
prepare suitable quantities of large unilamellar liposomes
using literature techniques or modifications of literature
techniques. Students involved in this effort include John
Bacon, Mark Melkerson, and Amir Fallahi. ‘The following is a
summary of unilamellar liposome preparation methods
attempted in our laboratory.

Boroske et. al. Procedure (32)

 

 

This procedure consists of spreading a thin smear of
egg lecithin on 1-3 glass cover slips and placing the cover

'100

101

slip in approximately 20ml of 0.2M sucrose. The solution is
then covered (to prevent evaporation) and left undisturbed.
Liposomes were observed to have formed after one hour but a
greater quantity of large unilamellar liposomes were
obtained from solutions left standing overnight. The
Boroske technique yields a large amount of lipid debris as
well as a number of liposomes which contain smaller internal
liposomes. These liposomes are unsuitable for
experimentation. Therefore attempts were made to modify the
original method to obtain a greater yield of liposomes
suitable for experimentation. One modification involved
placing the sample in a “5°C water bath for 5-10 minutes and
then leaving undisturbed overnight. This modification
appeared to have a slight positive effect on the yield of
unilamellar liposomes.

It was observed that the lipid which had been smeared
on the glass cover slip typically formed a white wispy cloud
in the sucrose solution. Samples removed directly from the
cloud typically consisted of debris and amorphous material
whereas samples removed from the area around the cloud, but
not directly in the cloud, contained a greater pOpulation of
suitable liposomes. Even so, however, most of the liposomes
were not suitable for experimentation.

Another attempt at improving the yield of good quality
liposomes involved centrifugation. A one milliliter sample
drawn directly from a cloudy region was placed in a one
milliliter plastic Eppendorf centrifuge tube and centrifuged
at 15,000 g for five minutes. Some of the debris appeared

102

to have deposited on the bottom of the tube. Samples drawn
from the middle parts of the centrifuge tube appeared to be
largely free of amorphous material, however a large
percentage of these liposomes (90-95%) either were
multilamellar, or contained smaller internal liposomes.

A final modification of the Boroske technique involved
dissolving the lipid smear in a small amount (5 m1) of 1:2
chloroform/methanol solutionu The chloroform/methonal
solution was then evaporated gently using a stream of dry
nitrogen gas. The advantage of this method is that the
lipid layer is deposited more evenly on the glass surface.
The technique of evaporation from chloroform/methanol was
first reported by Reeves and Dowben (31). They were able to
form large unilamellar liposomes (diameters of 0.5 --10 pm)
using this technique. Early attempts in the BTP laboratory
to make unilamellar liposomes by the Reeves and Dowben
technique met with limited success. However the modified
Boroske technique which involves lipid deposition from the
chlorlform/methanol solution yielded quantities of liposomes
similar to those obtained from the unmodified Boroske. It
should be noted that this modified method is essentially the
same as the Reeves and Dowben procedure except that the
amount of lipid used in the preparation is greater.

Kim and Martin Procedure (70)

Kim and Martin have reported a procedure for
preparation of large quantities of cell-sized unilamellar
liposomes which can be formed to incorporate a number of

internal constituents. This technique involves the

103

formation of a double emulsion of organic and aqueous
phases. Evaporation of the organic phase results in the
formation of the liposomes. One limitation of the
technique, as reported, is that it requires the presence of
particular lipids in certain proportions, reducing to some
extent the flexibility in manufacturing liposomes 'to
order'.

Attempts to use the Kim and Martin technique in our
laboratory have not been successful. It appears that the
evaporation step is a critical step. Work is presently
underway by John Bacon to determine the exact conditions
required for formation of liposomes using this technique.

Oku et.alJ‘Procedure (71)

 

A method has been described recently which allows the
preparation of large unilamellar liposomes which are stable
in electrolyte solution. The procedure which involves the
dialysis of lipid and solute in water-miscible organic
solvent against an aqueous buffer results in the formation
of vesicles with diameters between 10 um and 100 um.

The ability to form liposomes in an electrolyte
solution would be an advance allowing more flexibility in
the use of liposomes as model systems. Attempts to use the
Oku procedure to form liposomes in our laboratory are

underway.

APPENDIX C
Design Modification of Cryostage

In the previous design of the micrOSOOpe cooling stage
the quartz disc was bonded to the insulating tape covering
the copper block with a commercial 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, thinner quartz
discs (.025 inch instead of .075 inch) were used. This
resulted in a problem: frequent breaking of the quartz disc
and/or the breaking of the silver paint-quartz disc bond.
This problem was surmised to be due to the thermal stresses
arising from the differential thermal expansion of the
quartz disc and copper thermal sink. In the steady state
condition prior to an experimental run the center of the
quartz disc is typically held at 25°C while the edges of the
disc are in contact with the thermal sink (typically less
than -100°C). The thermal gradients and stresses within the
quartz disc were evidenced by the bowing out, and frequent
subsequent breakage, of the disc. To circumvent this
problem a design modification was made. The thin quartz
disc was painted onto a thin strip of aluminum foil and this
aluminum foil was painted down on the insulating tape of the
COpper block (See Figure 6). This arrangement solved the

breakage problem. One shortcoming of this arrangement is

10“

105

that it decreases the thermal response time of the quartz
disc since the disc is not in optimal contact with the
thermal sink. For the cooling rates used in the studies of
liposomes the aluminum foil configuration proved

satisfactory.

APPENDIX D
Calibration of the Digital Temperature Meter (DTM)

The digital temperature meter (DTM), used in the
controller was initially calibrated using the procedure
described in the owners manual (Omega Engineering, Inc.
Model 199L. This procedure involved the application of
known voltages to the DTM and adjusting variable resistors
to give specified temperature readings of the analog and
digital output. The voltages were supplied by a
potentiometer and these voltages corresponded to temperature

readings of -2o°c and “00°C.
’ After calibration, however, the DTM displayed a value
of -1°C for a thermocouple at 0°C in an ice bath.
Therefore, it was decided to adjust a variable resistor to
give the correct readings for temperature and analog output
for a thermocouple at 0°C. After this adjustment was made,
the DTM readings were checked for a thermocouple placed in
boiling water and for one placed in an isopropyl alcohol/dry
ice bath at -78°C. The temperature of the alcohol/dry ice
bath was obtained by direct thermocouple measurement using
the potentiometer to obtain voltage readouts to be converted
to temperature using thermocouple tables. It was found that
when the DTM was calibrated to read correctly at 0°C the
reading at T=-78°C was 1 to 2°C too high and the reading at
T=100°C was approximately 1°C too low. ‘This amount of error
was deemed acceptable since the temperature range of primary

interest was 0°C to -10°C.

106

APPENDIX E

Error Due to A/D Conversion Time in the DTM

The control electronics in the temperature controller
relies in part on a digital temperature meter (DTM) to
linearize, the input signal from the thermocouple and
display the temperature as well as provide an analog output
which is used in the temperature controller. Due to the
finite time required by the DTM to digitize the thermocouple
signal the possibility for introduction of error at fast
cooling rates exists. An experiment was therefore devised
to determine the analog-to-digital conversion time of the
DTM in order to verify that insignificant error would be
introduced at the cooling rates used in this thesis. Figure
31 shows the experimental setup. Two thermocouples were
used, and a step temperature change was produced by
simultaneously placing both thermocouples in a dry ice-
iSOpropanol bath at ~78°C. The first thermocouple was
connected to a reference junction placed inan ice bath and
the signal was directly connected to the strip chart
recorder. This thermocouple was used to measure actual
temperature and the actual rate of temperature change due to
the pseudo-step temperature change. Voltages obtained from
this thermocouple were converted to temperatures by use of
standard thermocouple tables.

The second thermocouple was connected to the DTM and

the analog output of the DTM was connected to the recorder.

107

108

The reference junction compensation for this thermocouple is
supplied electronically by the DTM.

Experimental results indicated a maximum temperature
rate of change for this procedure of 187°C/s. The
analog output of the DTM responded in step intervals of
approximately 0.“seconds. This measured time is fairly close
to the .30seconds response time listed in the DTM
specifications as a characteristic time for A/D conversion.
Although this update time can result in a large magnitude of
temperature error at very fast cooling rates (80°C at
187°C/second), the maximum amount of error introduced at the
cooling rates used in this study would be small (o.15°c
at 20°C/min).

The rated response time of the strip chart recorder was
less than 0.3 seconds for full scale travel. Since the
tests conducted here involved approximately'75% of full
scale, the response time of the recorder is adequate for the

experiments performed.

109

ANALOG
OUTPUT

 

 

 

RECORDER DTM

(g; C“ Co

 

 

CU

Cu Co ,

 

 

 

DRYICE/ISOPROPANOL BATH

.ICE BATH
(0 °C)

' Figure 31. Experimental apparatus to determine
response time of the DTM. '

APPENDIX F

Nucleation Temperature as a Function of Cooling Rate,

Statistical Calculation

Due to the wide range of nucleation temperatures
at a given cooling rate it is not clear whether the
nucleation temperature is a function of cooling rate. An
example is therefore presented of a calculation to determine
whether the nucleation temperature is statistically
independent of cooling rate. Chapter 12 of reference 69
details the required procedure.

Table 2 gives the raw data which was obtained. To
determine the confidence limits for the slope the following

quantities are calculated from the raw data

Exi = —“99
Eyi = -237
iny1 = “670
in = 12““1
Eyi = 2311

The slope (b) and the y intercept (a) of the least square
line y=bx+a is obtained by solving the following two

simultaneous equations, where n is the number of total

points
Eyi = a n + b2 xi
_ 2
Xxiyi — aXxi + bei

110

111

Solving the equations yields

a -7.11
b = .09

In order to calculate whether the slope of .09 is signifi-

cantly non-zero the following quantities must be calculated

 

_ 2 2 _
SXX - nE xi - (2 xi) — 86906
_ 2 2 _
Syy — n2 yi - (Z yi) - 6228
Sxy = n2 Xiyi - (Z xi)(Z yi) = 7827
2 1/2
S = Sxxsxy - (Sxy) = 2 86
e n(n - 2WSXX) '

The confidence limits for the slope b are
b : (ta/2)(Se)'n:sxx

At the 95% confidence level for n=27

This means that at the 95% confidence level, zero cannot be

excluded as a possible lepe. Therefore at this confidence

level the nucleation temperature is not dependent on the

cooling rate.

112

However, a calculation for the 90% confidence level

yields:

.0238 i b i .156
This means that zero slope is not included at this con-

fidence level.

APPENDIX G

Incorporation of Fluorescent Probes into the Membrane, or

into the Intraliposomal Compartment

Preliminary investigation was made into the possibility

of placing fluorescent markers into the liposome aqueous

internal compartment, or into the liposome membrane.

Experiments indicated that it is possible to do this.

Intraliposomal compartment

A stock solution of .01M was prepared of either
fluorescein or 6-carboxyfluorescein by dissolving an
appropriate amount of solid powder in acetone. A
working solution of dye concentration 2 x 10’5M was
prepared by diluting the stock solution 1/500 into 0.2M
sucrose. The liposomes were prepared from the working
solution in the manner described above in the Procedure
section. After the liposomes were prepared it was
necessary to remove the fluorescent dye from the
external solution. This was done by transferring the
liposome solution to a dialysis bag and dialyzing the
preparation against several changes of an equiosmolar
solution over a period of about 12 hours. Typically,
the yield of liposomes after dialysis was significantly
smaller than the amount present before dialysis. In
addition, it was found that if the external dialysis

solution was 0.2 M sucrose, insignificant dialysis, as

113

B)

11“

evidenced by the green color of the solution in the
dialysis bag, took place over a period of several days.
For this reason the external dialysis solution was
prepared as a mixture of sucrose (.1M) and NaCl (0.05
M). It is possible that the presence of the NaCl in the
dialysis solution had a detrimental effect on the
liposome preparation; this might account for the small
yields after dialysis. In some instances, no liposomes
could be found after dialysis. It is worth nothing that
both fluorescein and 6-carboxyfluorescein exhibited
photobleaching (flourescence fading). While being
viewed the amount of fluorescence faded significantly.
In this respect 6-carboxyfluorescein was more stable
than fluorescein. The fluorescence of 6-carboxyfluores-
cein typically faded away in approximately one minute as
compared to approximately thirty seconds for fluorescein.
Membrane fluorescent probe

The fluorescent probe used was 25(NBD -
methylamine) -27- noncholesterol, purchased from
Molecular Probes (catalog number N-237). Equimolar
amounts of the probe and egg lecithin were dissolved in
chloroform/methanal (1:2 v/v). The approximate
concentrations were 0.2 mg lipid per ml of solvent. The
chloroform/methanol solution was evaporated under a
stream of nitrogen gas. The liposomes were prepared by
introducing a small amount (approximately 10 ml) of 0.2
M sucrose and leaving undisturbed for about 1 day at

room temperature. This final solution contained

115

approximately 0.3 mg egg lecithin/ml solution. It
should be noted that the fluorescent cholesterol
exhibited significant fading during microscopic

observation, on the order of thirty seconds for complete

fading.

REFERENCES

10.

LIST OF REFERENCES

Smith, A.ILW "Prevention of Haemolysis During Freezing
and Thawing of Red Blood Cells," Lancet, 259,
910-911, (1950).

 

Polge, C., "Freezing of Spermatozoa," in Low Temperature
Preservation i3 Medicine and Biology, ed. by
M. J. Ashwood-Smith and J. Farrant, University
Park Press, Baltimore, “5-6“, (1980).

 

 

 

Whittingham, D.(L, Leibo, S.ih, and Mazur, P.,
"Survival of Mouse Embryos Frozen to - 196°C
and - 269°C," Science 178, “II-“1“, (1972).

 

Farrant, J" "General Observations on Cell Preservationfl'
in: Low Temperature Preservation 12 Medicine
and Biology, ed. by M. J. Ashwood-Smith and
J. Farrant, University Park Press, Baltimore,
1-18, (1980).

 

 

Mazur, P” "Kinetics of Water Loss from Cells at Subzero
Temperature and the Likelihood of Intracellular
Freezing," J; Gen. Physiol, “1, 3“7-369,

(1963).

Lovelock, J. E" "Physical Instability of Humam Red
Blood Cells," Biochem. J., 60, 692-696,
(1955).

Doebler, G. F. and Rinfret, A. P., "The Influence of
Protective Compounds and Cooling and Warming
Conditions on Hemolysis of Erythrocytes by
Freezing and Thawing," Biochim. BiOphys.
Acta., 58, ““9-“58, (1962).

 

 

Meryman, H.‘T" "Modified Model for the Mechanism of
Freezing Injury in Erythrocytes," Nature,
218,333-336,(1968).

Morris, 0. J., Cryopreservation, Institute of
Terrestrial Ecology, Cambridge, (1981).

 

Mazur, P” "The Role of Intracellular Freezing in the
Death of Cells Cooled at Supra-Optimal Rates,"
Cryobiology,_]_“, 251-272, (1977).

 

116

11.

12.

13.

1“.

15.

16.

17.

18.

19.

20.

21.

117

Fujikawa, 8., "Freeze - Fracture and Etching Studies on
Membrane Damage on Human Erythrocytes Caused by
Formation of Intracellular Ice," Cryobiology,

11. 351-362, (1980).

 

Levin, R. L., Cravalho, E. C., and Huggins, C. E., "A
Membrane Model Describing the Effect of
Temperature on the Water Conductivity of

Erythrocyte Membranes at Subzero Temperatures,"
Cryobiology 13, “15-“29, (1976).

Mansoori, G. A., "Kinetics of Water Loss from Cells at
Subzero Centigrade Temperatures," Cryobiology,
1g, 31145. (1975).

Levin, R. L., Cravalho, E. C., and Huggins, C. E.,
"Effect of Hydration on the Water Content of

Human Erythrocytes," Biophys. J,L1§,
1“11-1“26, (1976).

 

 

Cosman, M. D. "Optimal Cooling Protocols for
Cryopreservation of Individual Cellsfl'IL S.
Thesis, Department of Mechanical Engineering,
MIT, (1978).

Watson, W} W., "Volumetric Changes in Human
Erythrocytes During Freezing at Constant Cooling
Velocities," S. M. Thesis, Department of
Mechanical Engineering, MIT, (197“).

Knox, J. M. Schwartz, G. S., and Diller, K. R.,
"Volumetric Changes in Cells During Freezing and
Thawing," Journal of Biomechanical Engineering,

192, 91- 9m 19 07’

Scheiwe, M. W., and Korber, C., "Basic
Investigations on the Freezing of Human Leukocytes,"
manuscript, (1982).

 

 

Diller, K. R. and Cravalho, E. C., "A Cryomicroscope
for the Study of Freezing and Thawing ProcesSes in
Biological Cells," Cryobiology 7, 191-199,
(1970).

 

Ferguson, J. R., "The Thermodynamics of the Freezing and
Thawing of Biological Cells," M. 5% Thesis, Cornell
University, (1980).

Bangham, A. D., Standish, M. M., and Watkins, J. C.,
"Diffusion of Univalent Ions across the Lamellae
of Swollen Phospholipidsfl'J’. Mol. Biol., 13,
238- 252, (1965)

 

22.

23.

2“.

25.

26.

27s

28.

29.

30.

31.

32.

3“.

118

Lucke, B», and McCutcheon, M., WThe Living Cell as an
Osmotic System and its Permeability to Water,"
Physiological Reviews, _1_2_, 68-139, (1932).

 

Mueller, P., Rudin, D.O., Tien, H. T., and Wescott,
W. C., "Reconstitution of Cell Membrane Structure
in vitro and its Transformation into an Excitable
System," Nature, 12“ 979-980, (1962).

Tien, H. T., Bilayer Lipid Membranes (BLM); theor
and practice. Marcel Dekker, New York, (197 ).

 

Jain, M. K., The Bimolecular Lipid Membrane; 2 System,
Van Nostrand Reinhold, New York, (1972).

 

Bangham, A. D., DeGier, J., and Greville, G. D.,
"Osmotic Properties and Water Permeability of
Phospholipid Liquid Crystals," Chem. Phys. Lipids,
l, 225-2“6, (1967).

 

Szoka, Jr., P., and Papahadjopoulos, D., "Comparative
Properties and Methods of Preparation of Lipid
Vesicles (Liposomes)," Ann. Rev. Biophys.
Bioeng., 9, “67-508, (1980).

 

Siminovitch, D., and Chapman, D., "Liposome Bilayer
Model Systems of Freezing Living Cells," FEBS
Letters, 16, 207-212, (1971).

Siminovitch, D., and Chapman, D., WThe Simulation of
Osmotic Stresses of Plant Cells by Lipid
Liposome Membrane Systemsfl'(abstract)
Cryobiology, 11, 552, (197“).

 

Morris,(h J” and McGrath,.L J.,"The Response of
Multilamellar Liposomes to Freezing and Thawingfl'
Cryobiolosx. 1g. 390-398. (1981).

Reeves, J. P., and Dowben, R. M., "Water Permeability of
Phospholipid Vesicles," J; Membrane Biol.,
3, 123-1“1, (1970).

 

Boroske, E., Elwenspoek, M., and Helfrich, W., "Osmotic
Shrinkage of Giant Egg-Lecithin Vesicles,"

Levin, R. L., "Kinetics of Water Transport in

Biomaterials During Freezing," Ph.D. Thesis,
Department of Mechanical Engineering, MIT,(H976).

Castellan G. W. Ph sical Chemistr Addison-Wesley
Reading, Messacfiusetts, (1971): ’

35.

36.

37.

38.

39.

“0.

“1.

“2.

“3.

““.

“5.

“6.

119

Hempling, H.(L, "Permeability of the Ehrlich Ascites
Tumor Cell to Water," J; Gen. Physiol., “3,
365-379. (1960).

Tien, H.13, and Ting,lL P.,"Permeation of‘Water
through Bilayer Lipid Membranes," J. Coll;
Interface Sci., _2_'_7_, 702-713, (19687.

 

 

Blok, M. C., VanDeenen, L. L. M., and DeGier, J., "The
Effect of Cholesterol Incorporation on the
Temperature Dependence of Water Permeation
through Liposomal Membranes Prepared from
Phosphatidylcholines," Biochim. BiOphys. Acta.,
“Q“, 509-518, (1977).

 

Price, H. D., and Thompson, T. E., "Properties of Liquid
Bilayer Membranes separating Two Aqueous Phases:
Temperature Dependence of Water Permeability,"

J; Mol. Biol., “1, ““3-“57, (1969).

 

Terwilliger, T. C., and Solomon, A. K., "Osmotic .Water
Permeability of Human Red Cells," J; Gen. Physiol.,
11. 5“9-570. (1981).

 

Farmer, R. E., and Macey, R. I., "Perturbation of Red
Cell Volume: Rectification of Osmotic Flow,"
Biochim. Biophys. Acta” 126, 53-65,

 

Denbigh, K. R., The Principles pf Chemical Equilibrium,
Cambridge University Press, Cambridge, T1981).

 

 

Dick, D. A. T., "Osmotic Properties of Living Cells," in
International Review pf Cytology eds. Bourne and
Daniel 1i, Academic Press, New York, (1959).

 

McGrath, J. J” "Preservation of Biological Material by
Freezing," in Heat Transfer in Medicine and

Biolo : Analysis and AppITeations,
eds., EberfiarfandSEther, (1983).

 

 

 

Servuss, R. M., and Boroske, EL, "Lamellarity of
Artificial PhOSpolipid Membranes Determined by
Photometric Phase-Contrast MicrOSCOpy," Phys. Lett.,
695, “68-“70. (1979).

Harbich, W. R., Servuss, R. M., and Helfrich, W.,
"Optical Studies of Lecithen - Membrane Melting,"
Phys. Lett., 57A, 29“-296, (1976).

 

 

Tu, S., M. S. Thesis, Michigan State University, in
preparation, (1983).

“7.

“8.

“9.

50.

51.

52.

53.
5“.

55.

56.

570

58.

59.

120

Fettiplace, R., and Haydon, D. A., "Water Permeability
of Lipid Membranes," Physiol. Rev., 60,
510-550, (1980).

 

Huang, E., and Thompson, T. E., "Properties of Lipid
Bilayer Membranes Separating Two Aqueous Phases:
Water Permeability," LI; Mol. Biol., _1_5_,
539-55“, (1966).

 

Mazur, Pu, and Miller, R.IL, "Survival of Supercooled
Yeast," Cryobiology, 13, 365-366, (1967).

 

Rasmussen, D.IL, Macaulay, M.IL, and MacKenzie, A.Ih,
"Supercooling and Nucleation of Ice in Single
Cells," Cryobiology, L2, 328-339. (1975)-

 

Morris, 0. J. and McGrath, J..L, "Intracellular Ice
Nucleation and Gas Bubble Formation in Spirogyra,"
Cryo-Letters, 2, 3“1-352, (1981).

 

Mazur, P" "The Role of Cell Membranes in the Freezing
of Yeast and Other Single Cells," Ann. N_._ L
Acad. Sci. 125, 658-676, (1965).

 

Ponder, ‘En ProtOplasmatologia, 1p, 2, (1955).

 

Lucke, B., Hartline, H. K., and McCutcheon, M., "Further
Studies on the Kinetics of Osmosis in Living
Cells," 9.: Gen. Physiol., _1_“_, “05-“19, (1931).

 

Knutton, S., Jackson, D., Graham, J. M., Micklem, K. J.
and Pasternak, C. A” "Microvilli and Cell
Swelling," Nature (London), 262, 52-53, (1976).

 

Korber, Ch., Scheiwe, M. W.,and Wollhover, K.,
"Solute Polarization During Planar Freezing of
Aqueous Salt Solutions" submitted to, Int. J_._
Heat Mass Transfer.

 

Yee,.L P” and Mel,IL C” "Cell-Membrane and
Rheological Mechanisms: Dynamic Osmotic
Hemolysis of Human Erythrocytes and Repair of
Ghosts, as Studied by Resistive Pulse
Spectroscopy," Biorheology, 15, 321-339,

1978).

Papanek, T.IL "The Water Permeability of the Human
Erythrocyte in the Temperature Range +25°C to
-10°C," Ph.D. Thesis, Department of
Mechanical Engineering, MIT, (1978).

Ladbrooke, B. D., and Chapman, D., ”Thermal Analysis of
Lipids, Proteins, and Biological Membranes. A
Review and Summary of Some Recent Studies," Chem.
Phys. Lipids, _3, 30“-319,(1969).

60.

61.

62.

63.

6“.

65.

66.

67.

68.

69.

70.

71.

121

McGrath, J. J., Cravalho, E. G., and Huggins, C. E., "An
Experimental Comparison of Intracellular Ice

Formation and Freeze - Thaw Survival of Hela S-3
Cells", Cryobiology, 1g, 5“0-550, (1975).

Barer, R., and Joseph, S., "Refractometry of Living
Cells, Part I. Basic Principles," Quart.I J;
micr. Sci., _9__5_, 399-“23, (195“).

Singer, S. J., and Nicolson, G. L., "The Fluid Mosaic
Model of the Structure of Membranes," Science,
175,720-731,(1972).

Silvares, O. M., Cravalho, E. G., Toscano, W. M., and
Huggins, C. E., WThe Thermodynamics of Water
Transport for Biological Cells During Freezing,"
Trans. A.S.M.E., h Heat Transfer, 98, 582-588,
(1975).

Levin, R. L. Cravalho, E. G., and Huggins, C. E.,
"Effect of Solution Non-Ideality on Erythrocyte
Volume Regulation," Biochim. Biophys. Acta.,
592. 179-190. (1977).

Mathias, S. F., and Franks, F., "Freezing Kinetics in
Cells Undercooled to Low Subzero Temperatures
(abstract)," Cryobiology, _1_9, 67“, (1982).

 

 

 

 

'Williams, R. J., and Hope, H. J., "The Relationship
between Cell Injury and Osmotic Volume Reduction.
III Freezing Injury and Frost Resistance in
Winter Wheat," Cryobiology, 18, 133-1“5, (1981).

 

Olien, C. R" "Energies of Freezing and Frost
Dessication," Plant Physiol., 53, 76“-767,
(197“).

Olien, C. R., and Smith, M.N., "Ice Adhesions in
Relation to Freeze Stress," Plant Physiol., 69,

Miller, 1., and Freund, J. E., Probability and
Statistics for Engineers, Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, (1965).

Kim, S" and Martin, G.IL, "Preparation of Cell-Size
Unilamellar Liposomes with High Captured Volume
and Defined Size Distribution," Biochim. Biophys.
Acta” 6“6, 1-9,(1981).

 

 

Oku, N., Scheerer, J. F., and MacDonald, R. C.,
"Preparation of Giant Liposomes," Biochim.
BiOphys.Acta.,692, 38“-388,(1982).

72.

73.
7“.
75.

76.

77.

78.

Diller, K. R”

122

Intracellular Ice Formation in Frozen Human

Erythrocytes," Ph.D. Thesis,

Mechanical Engineering,

Department of

MIT, (1972).

McGrath, J.J., unpublished data.

Morris, G. J.,

Allen, R. D.,

equipment for transmitted- light microsc0py, "

and McGrath, J.

David,(L B”

"A Microscopic Investigation of

J., unpublished data.

and Nomorski, G.,
Zeiss-Nomarski differential interference

"The

Zeitshrift fur wissenshaftliche MikroskOpie und
mikroskopische Technik,

 

 

Mazur, P., Leibo, S. P., Farrant, J.,
Hanna, Jr., M. G., Smith,
_C___e_l__l_, eds., Wolstenholme, G. E. W., and O' Connor,
M. Churchill, London, (1970).

PapahadjOpoulos, D., and Miller, N.,

Model Membranes.

135, 62“-

638, (1967).

g9,193221,<fi9afl.

Chu, E. H. Y.,
L. IL, in The Frozen

 

"Phospholipid

BiOphys.

I. Structural Characteristics of
Hydrated Liquid Crystals," Biochim.

Acta,

 

Mazur, P” "Physical and Chemical Basis of Injury in
Single-celled Micro-organisms Subjected to
and Thawing", in Cryobiology, ed.,

Freezing
Meryman,

Academic Press,

 

New York,

(1966).

H. T.