lll3l|”I"!lllfllflflfllllfllflllzlflljll ffllfllfllfll 1

LIBRARY ’
MiChigan: Sm ‘
Univcrfity 5' 7’

This is to certify that the

thesis entitled

KINETIC AND THERMODYNAMIC MEASUREMENTS
IN AN AGING MODEL
BASED ON THE MAMMALIAN ERYTHROCYTE

presented by

David Anthony Juckett

has been accepted towards fulfillment
of the requirements for

MUS degree in Bto‘pkgfiLCj

% (Hum 909% beg
J

Major professor

Date //’//-//’7

0-7 639

\W’a.

 

 

 

KINETIC AND THERMODYNAMIC MEASUREMENTS
IN AN AGING MODEL
BASED ON THE MAMMALIAN ERYTHROCYTE

By

David Anthony Juckett

A THESIS

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

MASTER OF SCIENCE

Department of Biophysics

1976

ABSTRACT

KINETIC AND THERMODYNAMIC MEASUREMENTS
IN AN AGING MODEL
BASED ON THE MAMMALIAN ERYTHROCYTE

By

David Anthony Juckett

The kinetics and thermodynamics for thermal lysis in red
blood cells was studied. This cell is used as a model system for
unicellular aging without repair mechanisms. RBC's were separated
according to age on a Ficoll density gradient. Younger and older
populations of cells were taken off the gradient and their kinetics
of thermally induced lysis examined over the temperature range
42—56°C. The kinetics differ between the populations; they are
not exponential in form but are best described by Gompertz and
power law kinetics. Use of Arrhenius plots give both activation
enthalpies and entropies for the young and old populations. These
values indicate that protein denaturation is the cause of the
lysis event. Use of the Weibull distribution indicates that this
event consists of three steps each with the same value for the
activation enthalpy. The correlation of the results and

implications to other aging systems is discussed.

ACKNOWLEDGMENTS

Thanks to Barnett Rosenberg, Loretta VanCamp, Jim Evans,

two sheep and hundreds of billions of red blood cells.

ii

INTRODUCTION

CHAPTER I

Aging ..................................................

CHAPTER II

Kinetics

Temperature ..........................................
Energetics

Rate Functions

CHAPTER III

 

TABLE OF CONTENTS

and Thermodynamics

The Experimental

The Experimental Model ...............................

The Experiment ........................... . ...........

I.

Separation & Verification Methods ..............

 

II.

(1) 59Fe Incorporation into Erythrocytes .....

 

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

(2) Blood Preparation ........ . ........... ......

 

(3) Ficoll Gradient Preparation ..............

 

(4) Measurement of the 59Fe Radioactivity ....

 

Kinetic Studies of Population Decline ........

 

(1) Blood Preparation . .......................

 

(2) Separation of Young and Old Populations

 

iii

l7

19

21

29

32

32

32

32

33

33

33

33

34

TABLE OF CONTENTS (cont'd.)

 

 

 

 

 

 

 

Page

(3) Determining Population Lysis Kinetics ...... 34
(4) Computer Fitting ........................... 35

RESULTS
I Age Separation and Gradient Reliability ............. 36
II Lysis Kinetics ...................................... 38
III Relationshipiof Lifespan to Activation Energy» ....... 55
IV Derivation of n - AH+ ............................... 57
V The Activation Entropy and Protein Denaturation ..... 60
DISCUSSION AND CONCLUSIONS ................................. 61
I Kinetics ..... . ...................................... 61
II Activation Enthalpy and Entropy ..................... 63
III Young vs Old ........... . ..... . ..................... . 65
IV Comparison to Normal Lifespan ....................... 68
SUMMARY ....................... . ........................... 71
FURTHER WORK .............................................. 73
BIBLIOGRAPHY .............................................. 75

iv

 

Table

LIST OF TABLES

Gompertz parameters R0 and a .........................

Standard deviations of the residuals for Gompertz and
Weibull distributions ................................

Weibull parameters A, l/T, and n .....................

The values of AH+ computed by the shift in life expec—

tancies tL(l) and t%(2) at the temperatures T1 and T2
2

Page

45

49

SO

54

 

LIST OF FIGURES

Figure Page
1 Percent human survivors versus age .................. 23
2 Percent Drosophila survivors versus age for four

different temperatures .............................. 24
3 Relayering experiment (see text for details) ........ 37
4 Location of radioactively labeled cells at day l and
day 7 .............. . ................................ 39
5 Continuation of figure 4 at days 14, 30, and 57 ..... 4O
6 Log of the percent survivors plotted versus time in the
water bath for young cells .......................... 42
7 Solid curves repeated from figure 6, dashed curves
represent old cells at the respective temperatures .. 43
8 Gompertz representation of young cells .............. 44
9 Weibull representation of young cells ............... 47
10 Weibull representation of old cells ................. 48
11 The Arrhenius plot for the young cells using the A
parameter of the Weibull distribution ............... 51

12 The Arrhenius plot for the old cells using the A

parameter of the Weibull distribution ............... 52
13 The Arrhenius plot for both young and old using the
l/T parameter ....................................... 56

vi

INTRODUCTION

One of the first phenomena that is noticed in the study of living
matter is that a living system does not remain the same with the pas—
sage of time. There are, in fact, dramatic changes involved in the
spawning of life, rapid changes during the growth of an organism and
slow but noticeable changes as the organism increases in age. These
changes are the manifestations of the living system's monumentus task
of organizing atoms and molecules from its unorganized surroundings
into complex systems. Systems capable of localizing and transferring
information, and capable of rebuilding and renewing the organism while
constantly battling the surrounding forces which fight this localiza-
tion and ordering of matter and energy.

The growth of an organism is awesome in its complexity, in its
ability to fight the increase of entropy within its boundries and in
the rate at which it increases in size. It battles these forces so
successfully that when it ceases to grow, when less energy is required
to be handled and organized by the organism, it would seem that it
would be very easy to continue at a steady state of no growth forever.
This is not the case, however, when an organism ceases to grow, it
begins to age, to lose capacity to function, and eventually to die.
This has bothered mankind longer than the enigma of growth and much
time has been spent studying this process of aging and death. The
purpose of this thesis is to present one more piece of information in
this study of aging and death.

There have been many theories presented over the years on many

different aspects of the aging phenomena. A brief review of some of

them will be given later. No new theories will be given here, but
some insight into the interrelation of the current ones may be forth-
coming.

The original impetus for the following experiment was as a pilot
study to investigate the possibility of using the Red Blood Cell as
a model for an aging system. This is made possible by the apparent
aging of the RBC in vivo over a period of about five months in large
mammals. Cells are continually produced in the bone marrow to re-
place old red cells thus providing constant relative populations of
young and old cells. Unlike epithelial cells, which are also present
in young through old cell populations in layers of the epithelium,
the red cells are easy to obtain and separate. As red cells grow old
they become more dense and therefore can be successfully separated on
a density gradient.

The model was used to determine if the rate of lysis of the red
cell followed first order kinetics or kinetics similar to that of
dying organisms such as the Weibull distribution or the Gompertz dis—
tribution. It was also used to test the differences in activation
enthalpies for lysis of the RBC's between young and old populations
of cells.

The death rates of bacteria have been believed to be first order
processes because they follow reasonable exponential kinetics. The
denaturation of protein at high temperatures also exhibits this. The
death rates of the multicellular organisms however have not shown first
order kinetics but have been described by the Gompertz function which

reasonably represents the sigmoid shape of these mortality kinetics.

 

Another function, the Weibull distribution, also represents the
data equally well. This has been shown on death rates in humans
and Drosophilal. This distribution was originally introduced by
W. Weibull in 1938 to describe fatigue failure in solids and was
applied to biological systems by Armitale and Doll (1954)2 and
Rosenberg (l97l)3. Preliminary work on red cell lysis showed that
a sigmoid curve described the process and not a simple exponetial.
Therefore, both the Gompertz and Weibull distributions were fitted
to the data and their parameters examined for useful characteristics
to see if one of the distributions had only one temperature dependent
parameter so that a possible activation enthalpy could be determined.
It has been shown that there exists a high activation enthalpy
for the death event in fibroblast cells and in drosophi1a3’l. Both
of these were obtained by studying the rate of population decline or
death over a range of temperatures and then using the Arrhenius rela-
tion to obtain an activation enthalpy of the rate limiting step that
leads to death. In using a range of elevated temperatures, the
aging phenomena is artificially accelerated in these systems implying
that they went through a "sped up aging" process taking them from
their young state to an old state and finally to death at a faster
rate than normal. The activation enthalpy measured is that of the
rate limiting step in this process, but it is not known when during
the course of the lifespan this step occurs. In the above experiments
only young organisms were used. If older organisms were also treated,
a difference in activation enthalpy might be apparent if the rate

limiting step occurred appreciably before death or if it is composed

z.

of several steps, one or more of which occurred before old age and
death. If the rate limiting step or steps occur immediately before
the death of the organism then the activation energy for the older
organism would be identical to the young.

In order to determine if there is more than one step for death in
the RBC model and if there is, whether these steps are spread out or
are close together at the end, young and old cells were both treated
in the same manner at the high temperature range; the kinetics that
best fit them determined; and their respective activation enthalpies
obtained.

In brief, the results show that whatever process is occurring
occurs shortly before death. The kinetics show a sigmoid shape for
both young and old cells and are describable by the Gompertz and the
Weibull distributions. The Weibull distribution has only one tem—
perature dependent parameter which allows the use of the Arrhenius
equation to determine an activation enthalpy for each age. The
activation enthalpies obtained appeared to be identical for young and
old and were of a very high value. The other parameter of the two
parameter Weibull function suggests a 3 step process is occurring
and the activation enthalpy of each step for both young and old are
the same. If one assumes that each step in this process is a first
order reaction then an activation entropy can be calculated. The
corresponding activation enthalpy and entropy for each step resembles
those that are associated with protein denaturation suggesting that
alterations of macromolecules are involved in the process. This

could be the breakage of covalent bonds or one of more hydrogen bonds.

In the following discussion, I will give some background into
the aging phenomena and some of the theories dealing with aging and
death. This will lead into a description of the influence of
temperature on aging, the usefulness of the activation enthalpy, and
a discussion of Gompertz and Weibull kinetics. Then the RBC model
will be presented and the experiment performed on the model followed

by detailed conclusions and discussion.

CHAPTER I

AGING

The theories of aging can be broken down into a series of four
hierarchical steps: systematic aging, cellular aging, molecular
mechanisms of aging, and the fundamental processes dictating these
mechanisms.

Systematic aging deals with the gross changes in the organism with
time. such as the physiological decline in the organs and tissues,
the susceptibility to diseases and their permanent impairing effect
on the organism, and the rate of mortality and survival in a popula-
tion. Cellular aging attempts to explain some of the above by
examining the different types of cellular aging and death. The cells
of organisms are basically divided into those cells which do not
divide at all, those which divide for a number of divisions and then
stop and those which appear to divide indefinitely. Degradative
processes affect the first two by decreasing the performance capability
of the cells and reducing their numbers in the organs which results
in a loss of physiological potency characterized by systematic aging.
Theories of molecular mechanisms have been postulated to explain
these observed cellular changes. These are divided into two areas,
the deterioration theories and the pleiotropic theories. The deter—
ioration theories are those that consider somatic mutations, the ever
increasing accumulation of error in protein synthesis, and the spontan—

eous denaturation of macromolecules as the major causes of dysfunction

 

and death of cells. The pleiotropic theories hypothesize that the
genomic expression is advantageous to the organism during develop-
ment but these same genes produce harmful products in the later

stages of life, leading to the death of the organism. This means

that the cells are preprogrammed to die and this is how these theories
explain the cell death and loss of function. The fundamental processes
that underlie these mechanisms seem to fall in two general areas; the
intrinsic inability of a living system to function in a steady state
situation forever because of the laws of nature and the extrinsic,
environmental factors that bombard the organism resulting in damage.
Very little work has been done on learning more about these funda-
mental processes, but the correct perspective of the whole aging
phenomena depends on determining the general underlying causes of the
mechanisms involved.

Systemic theories in multicellular organisms usually consider
generalizations of how combined cellular behavior can result in aging
and death. They site such changes as the loss of cells in organs,
the decrease in proliferative capacity of germ lines, the transfor-
mation of cells, and the susceptibility to disease. These are changes
that are characterized by a decrease in physiological function and
this is assumed to result in the eventual death of the organism.

This loss of vitality follows a linear rate of decline and has been
shown to exist for many organs and their function (eg. basal meta—
bolic rate, cardiac index, vital capacity, standard renal plasma flow,
maximal breathing capacity)5. These different systems show varied

changes with time and it is hard to suggest which system is more

8
important, if any, or how they all fit together to result in the
total aging picture. Models have been proposed that deal with this
on a theoretical level. They correlate this linear decline in
function to the mortality rate which is an easily measurable quantity
and a direct consequence of the total aging phenomena.

Strehler6 gives a good review of the theories of Brody-Failla7,
Simms-Jones8, Simms-Sacherg, and Strehler-Mildvanlo. These theories
analytically attempt to derive the Gompertz function of mortality for
human beings assuming different aspects of physiological decline and
the effects of environment. (More will be discussed about the
Gompertz relation in Chapter Two.) Other theories have correlated
the onset of diseases to the observed mortality. Multiple factor
theories of disease and aging have been formulated by Armitage and
D0112, Burchlo, Burnetll, and Curtislz. They suggest that degenera—
tive diseases are caused by'a sequence of n steps (usually 6) and
that these lead to death. This predicts a power relation for the
mortality kinetics which is related to the Weibull distribution (also
to be discussed in Chapter Two).

These theories do not suggest any mechanisms that might be
responsible for the degeneration of cells and tissues but they only
try to reproduce observed kinetics of mortality.

The theories of cellular aging are very closely allied to those
dealing with the molecular mechanisms. There has literally been an
ad nauseum cataloging of every cell and system and macromolecule in
living organisms of a wide variety to see if they are affected by

aging. What this has shown on the cellular level is that there are

 

9

three basic modes that cells can be in, one in which they do not
divide at all, one in which they divide for a specific length of
time, and one in which they appear to divide indefinitelle. The
cells that do not divide and those with limited proliferative
capacities are believed by almost everyone in the field to be the
cause of systemic breakdown. They are the ones that collect damage
and if not replaced permanently impair the tissue. Disagreement
enters the field when investigators try to explain why there are
these three types of cellular behavior and why degradation has the
affect it does in two of the cases.

Many theories of specific mechanisms have emerged. The most
important ones are the somatic mutation theory, the Orgel error
hypothesis, and preprogrammed senescence.

The somatic mutation theory postulates that spontaneous mutations
occur in the somatic cells, causing them and their progeny to perform
a different function or no function at all. This results in diseases
of dysfunction and malfunction in the tissues which then leads to
death. Only cells which are dividing at fast enough rates to always
allow for cellular selection are unaffected. Cells which do not
divide build up damage and cells which are dividing slowly collect
sufficient damage in every cell and cellular selection cannot occur.
These cells become impaired and diela.

Orgel first proposed that errors in protein synthesis, once having
started, can be an escalating process which leads to cell deathls.

He proposed that random errors in proteins begin to build up and cause

the formation of faulty protein synthesizing machinery which then leads

 

10

to proteins that contain more faults. Holliday and Tarrantl6 gave
evidence to support this. They have found that diploid human fibro-
blasts accumulate heat labile enzymes as they age. That there is
an increasing fraction of these enzymes that show this with age and
a decreasing fraction that appear to be normal. Orgel concluded that
if cells were dividing fast enough damage to proteins could be small
enough and diffuse enough to allow somewhat damaged protein to
synthesize protein with less damage. This would explain the ability
of some cell lines to undergo divisions indefinitely. If the rate
was too slow the cell line would eventually build up lethal amounts
of damage. If the cell was not dividing at all, then the rate of
protein synthesis would be the determining factor, but even that could
not protect the DNA from damage if it wasn't being replicated and so
the cell must have a finite lifetimel7

Programmed cell death was first suggested by Hayflick18, when
he showed the limited number of divisions in fibroblasts. It has
been adopted by many others to explain the phenomena of cellular aging.
Some cells live for only a matter of hours while others live for
years, this follows directly from an idea of programmed lifespan.
Franks13 argued that the short lifespan of certain cells is due to
the fact that they are the product of the last division of a
differentiating cell line. They exist for a while and then they
die (white blood cell for example). Cells such as nerve cells are
thought to be caught in an intermediate state in the cell division
sequence. They live a long time because they have not been able to

divide the necessary number of times.

11

Work done by Dell'Orco supports this hypothesislg. He took
several diploid cell strains and showed that they can be arrested
by alterations in their medium for as long as three or four times
their normal lifespan and then returned to normal growth. When they
finally die they attain or surpass the controls in the total number
of population doublings. This indicates that in yitrg it is not the
length of time the cells are alive that determine their lifespan but
the number of divisions.

All of these theories have many supporting experiments and this
is probably because they all have some truth and value. They don't
seem to answer the question of the underlying cause of aging, however.
They do not deal with what caused the mutations, the original protein
error, or the molecular basis of the programmed death mechanism.

Of all the possible intrinsic and extrinsic factors that could be
responsible for these it is possible the one stands out and is truly
the one that must be dealt with and is the one that ties all these
theories together.

Intuition suggest that either there is an intrinsic inability of
a living system to function forever due to the laws of nature, or an
inability to fight the environmental insults indefinitely, or perhaps
both. The answer to this inquiry lies in the physical laws of the
universe and this then would give the fundamental processes involved
in aging and death.

The empirical laws of thermodynamics describe a living system as
an energy-entropy system far from equilibrium with respect to the

environment. Living matter has two functions, therefore, one is to

 

12
perform the required metabolic processes and the other is to fight
the increase in entropy to maintain structure and organization. In
order to do this it must manipulate both matter and energy. Matter,
even in its quantum mechanical sense, is localized and hence more
easily controlled than energy which has many forms and is not easily
contained or directed. The statistical distribution of energies, for
which the measurement of temperature only represents the mean,
continually contains high energy fluctuations in the extremes of
the distribution. These are always a nuisance to the living system's
organization and functioning tasks. These energies are high enough
to break bonds or denature macromolecules. There is no way to
control this intrinsic nature of energy, so organisms have relied
on replacement of damaged parts and elaborate removal of their
deteriorated components. Even this is only a respite and so the
process of reproduction has evolved to continue where the individual
organism fails.

Extrinsic insults are also thrown at living systems. These come
in many forms but the two most dangerous are UV light of the sun and
the chemical poisons in the environment. Since UV light has been
present through all of evolution, organisms have successfully dealt
with its damage at normal levels of intensity. Higher exposures to
this radiation, however, are quite lethal. The potential number of
chemicals that can poison the organism are almost limitless. The
enzymes of the cell, although very specific, can be permanently
blocked by substrate analogs or can be induced into action on

foreign substrates resulting in products that are even more harmful

13
or in the excess build-up of extraneous material in the cell. Here
again, there seems to be no escaping the continual attack of these
poisons because every system of the organism is vulnerable to one
degree or another.

The effects of extrinsic insults upon aging are not examined
in this study. Rather, the intrinsic factors of the mean temperature
and the fluctuations around this temperature are of main concern
to determine their influences on the aging process.

Temperature has long been known to be important in the optimal
performance of biological systems. In single cell organisms, tissue
cultures, and poikilotherms the alteration in temperature is known
to affect the aging rate and the total lifespan. In homeotherms the
temperature is held constant to within a few degrees. Increases
in this optimal temperature can lead rapidly to death of the organism,
while decreases can be tolerated much more by the homeotherm.

Since the average body temperature is constant except for cases of
disease and dysfunction, changes in the mean temperature are not
important in the aging phenomena in homeotherms. Localized changes
in temperature within the organism, however, may play a role in this
phenomena.

Within organisms there exists the possibility that the temperature
varies from organ to organ and tissue to tissue depending on the
metabolic rates of these tissues. Sacher21 suggested that the
organisms ability to distribute heat evenly throughout its whole
system is directly related to the lifespan of the animal. He men—

tioned the correlation of lifespan of different animals to their

l4

brainsize, this being the important difference that dictates the
ability of an organism to control its internal environment to minimize
the unequal distributions of temperatures. The cebus monkey and the
opossum are the same body weight so their heat dissipation to body
ratio is the same and hence they would expect to metabolize at about
the same rate, and yet the cebus monkey lives eight times longer than
the opossum. The fact that the cubus monkey has a brain which is
70g. as compared to the 6g. brain of the opossum suggests that it
has very highly developed methods for dealing with temperature
regulation. The quick and efficient equalization of heat within the
organism keeps highly active cell groups or organs from operating
at unusually high temperatures which would lead to their deter—
ioration at an accelerated rate.

A further question involving a macroscopic thermal phenomena
is the heat flux through tissues and individual cells. The ratio of
surface area to volume in an organism and the temperature gradient
from inside to outside determine the flow of heat through the
tissues of the organism. This heat flow in small organisms would be
greater than in larger organisms even though the temperatures would
be close to the same. Similarly, when the external temperature is
low the gradient is high and the heat flux increases because
metabolism increases to counteract heat loss from the skin. The
effect of changes of heat flux under constant temperatures as related
to aging is an area that needs to be studied.

Another intrinsic factor which the organism has no control over

is the microscopic distribution of energies around the temperature

15
mean. This is a distribution in both space and time and hence at
any microscopic point in the system fluctuations occur in the
energies with time. An experiment of Johnson20 showed that the
fluctuations in the thermal bath can explain the observed rate of
death in fibroblast cells at physiological temperatures. This
suggests strongly that the most important factor is the living or—
ganism's fight against the inherent noise in the thermal energy
distribution of its own constituent parts. This distribution of
energy is the Boltzmann's distribution representing the frequency
of energy states above and below the mean energy level which is
defined as temperature. The high energy fluctuations inherent in
the upper regions of the distribution are microscopic localizations
of high energy states distributed randomly in space and time within
a homogeneous system. This suggests that at the right time such a
fluctuation could occur at such a location within a macromolecule that
a covalent bond is broken. This could lead to the denaturation of
the molecule and its inactivation. The denatured macromolecules can
lead to mutations, they can lead to protein synthesis error, and they
could lead to the expression of masked genes. Due to the rarity of
the coincidence of these low probability high energy states occurring
at the right place and at the right time the denaturation of macro—
molecules would be a slow but still significant process as shown by
Johnson. It is even possible, as he suggests, that they account for
the majority of the age related deterioration that is observed in
cells.

To obtain a comprehensive view of aging and death, therefore,

l6
metabolic processes must be examined, the effects of temperature and
heat flux must be determined, and theories that deal with temperature
fluctuations need to be formulated and tested. Chapter II shows
some of the work done already in the area of temperature and high

energy fluctuations.

CHAPTER II

KINETICS AND THERMODYNAMICS

TEMPERATURE

Temperature is an extremely important factor in the process
of life on this planet. A small change in the temperature can
cause drastic changes in organisms and whole eco-systems. It was
said once that if the mean daily temperature of the earth was
changed by 20°C either up or down, all life would perish. The
chemical reactions contained in organisms are very temperature
specific and speed up or slow with increases and decreases in temper—
ature. Consequently, in lower organisms, their metabolic rates
vary up and down with the temperature. This seems to be an
acceptable condition for lower forms of life, but most higher
forms of life seem to need a stable temperature for the proper
functioning of the many, many interreactions of their parts. They
have evolved separate temperature control mechanisms to keep their
bodies at a constant temperature level. Not surprisingly, this has
allowed these organisms to be more versatile in terms of habitable
climates and total activity. This has given mammals a tremendous
advantage in the development of the world animal population. It
is probably through this homeostasis that hemo sapiens was able to
evolve to its present level. An excellent review of temperature,
its affects in biologv, and temperature optima is given by Johnson,
Eyring, and Pollisarzz,

The point of interest in this discussion is how does temperature

affect aging and more importantly, how can this be used to learn more

17

18
about the aging process. As was discussed in the last chapter, the
one factor that seems to link the whole aging process together is
the idea of localized "temperatures" being so high as to damage the
cells and the organism. It has been known that changing the tempera-
ture of poikilotherms changes their lifespan. This has two effects:
the first is that as the mean thermal level changes the high energy
fluctuations that are always present in a distribution of energies
also change in number. These fluctuations are responsible for the
denaturation of macromolecules. The second effect is the increase
in the metabolic rate which increases the number of hot spots in
the organism. These are different from the normal high energy
fluctuations that are present in an assumed uniform distribution.
It is the combination of these two processes that result in shortened
lifespan when the temperature is increased.

In order to give evidence to all this, it needs to be shown that
improbable fluctuations can lead to observed mortality rates, that
temperature changes are tied to changes in rates, and that macro—
molecular denaturation can be linked to death or similar catastrophic
events associated with aging in the cell or organism.

In order to accomplish this I will present some work that has
been done along these lines in the area of energetics and in relating
mortality rates to improbable events through the theory of extreme
values. In the next chapter I will present the red blood cell model
and the experiments which show that the catastrophic process of cell
lysis resembles mortality in multicellular organisms and that the

energetics suggest protein denaturation.

l9
ENERGETICS
The absolute rate theory establishes a relation between the

rate of a chemical reaction and temperature. This is given by:

fasl} i-Anl F

v-—_— ' ———-—~.— I

K = kT e R A el RT i. (I)

Where K is the rate, k is Boltzman's constant, h is Plank's constant,
R is the gas constant, ASI is the activation entropy, AH+ is the
activation enthalpy, and T is temperature. AS+ and AH+ represent
constants of the system which determine the rate of the system.
These are important to determine because they represent a connection
to the mechanism involved in the reaction. In an aging system,
these constants can give a clue to what processes are responsible
for aging. The problem with the aging system is that it is a very
complicated system and absolute rate theory was derived for simple
systems.

Crozier and collaborators22 methodically applied eqn (1) to many
biological phenomena and determined that the relation held almost
invariably. They determined the constants AH+ and AS+ for such
processes as heart beat, cricket chirping, luminescence of bacteria,
oxygen consumption in the clam, division rate of the sea urchin,
the hydrolysis of sugar, the alpha rhythm in the cortex of humans,
and a multitude of other complicated processes. The activation
enthalpies determined were usually between 10 — 30 Kcal/mole.
Equation (1) has also been applied by others to the death rates of
fibroblasts, yeasts, bacteria, Drosophila, and other poikilotherms.

In all cases, an activation enthalpy was determined, ranging from

20
23

25 Kcal/mole to 200 Kcal/mole

These high activation enthalpies for the death rates indicate
that a very low probability reaction is occurring. They are rare
with respect to the normal processes of an organism, such as those
measured by Crozier, which have activation enthalpies much lower,
around 10 - 12 Kcal/mole. It also suggests that a denaturation
process is occurring, such as the denaturation of protein.

Rosenberg et al. gave further evidence to the idea of protein

, 23 . .

denaturation as a cause of death . They showed that the activation
enthalpies and activation entropies of both the rates of protein
denaturation and mortality followed a simple compensation relation,
given by:

AS+ - AH+ + b . (2)

t—ilr—I

C

Where b and TC are constants equal to approximately —65 cal/mole/K°,
and 330°k respectively. This is the first quantitative evidence
relating the normal death of an organism to a molecular process. An
improbable event like death follows well from an improbable event

like macromolecular denaturation.

21

RATE FUNCTIONS

Use of eqn (1) for relating the mortality rates of organisms
to temperature is good only if the measured rate is a constant with
time, more explicitly, a first order rate constant. Unfortunately,
there are many mortality rates that vary with time. In fact, most
multicellular organisms and what now appears to be some unicellular
organisms show mortality rates that vary with time. In 1825,
Gompertz presented a new function to describe human mortality curves,
which has been used widely since then to describe mortality rates
for a variety of organisms. The Gompertz function24 relates the
mortality rate, u(t) to an exponential function of time. It is

given by:

O.

—“ = Re“ . (3)

Mt) = t O

2|»-I

where R0 and a are constants. The parameter a has the dimensions of
a rate constant and hence would be the logical choice for eqn (1).
This does not prove satisfactory, because the parameter R0 is also
temperature dependent and also has the dimensions of a rate constant.

Another equation has been used (25, 26) which is basically an
alteration of simple first order kinetics. The simplest way to
derive it is to consider the probability of an operational site being
incapacitated, call it q. Therefore, q=l — exp (at), if simple first
order kinetics are assumed. If n sites need to be incapacitated
before death, then the fraction of survivors, f, is:

octn

f = 1- (l—e_ )

This equation has the benefit of attempting to describe a multistep

22
reaction and it contains a rate constant, a, directly relatable to
a first order rate constant and only it would be temperature depen-
dent. However, this formulation only seems to fit death rates of
simple organisms. At large t the function approaches an exponential
of slope -an. This is not seen in the mortality curves for multi—
cellular organisms. Figure 1 shows the survival curve for human
beingsZ6. Here, the log of the fraction of survivors is plotted
versus time. It is obvious that no portion of this curve at large
times is a reasonable straight line. Figure 2 shows similar plots
for Drosophila27. Here again, as time increases, the rate constant
(slope) continues to increase.

There is a subtle problem with the formulation of eqn (4). It
assumes an exponential distribution for a reaction as if it was a
separate reaction, a common reaction in the cell. But what is
actually occurring is an aberent reaction, a low probability case
of a larger group of possible ones. The deactivation of a site is
the result of a very high energy fluctuation of an improbable nature
causing a "normal" reaction to occur out of place and out of time.
The study of this kind of phenomena is called the statistics of
extremes or the theory of extreme values. It is used to describe those
phenomena which do occur but only very, very seldom. The theory
describes the distribution of rare events in an ensemble. A
population of organisms is a set of almost exact copies of a single
system, it is an ensemble. The distribution of rare events in the
population, resulting in death, is thus a distribution of extreme

values in an ensemble. It is this theory that must be considered

% SURVIVORS

23

 

'00

80*-

60'-

20

 

r l 1 ‘ 1

I

 

 

IO
20

Figure l.

30 4o 50 60 70
Time (yrs)

Percent human survivors versus age

80

90

% SURVIVORS

24

 

 

 

 

 

IO0.0. e
T3,. 0
ck. 0
q
Q
‘0‘ '
IN}
\
O
\
\
\
' C)
37° 34' \33" '31::
I
I:
.I
I
L()flr LJ 1 In 1 .1 1 n I 1 n
2 4 6 8 IOIZI4I6I82 22
TimeIdOYSI
Figure 2. Percent Drosophila survivors versus age for four

different temperatures

 

25

in describing aging and death.

There are three asymptotic distributions in the theory of
extreme value328. The derivation, stability criterion, or detailed
discussion of each of these is beyond the scope of this paper. Two
of these distributions are of interest, however, in describing the

phenomena of aging populations:

A(t) = l - e (5)

and

II
I--'
l
2)

w<c) (6)

Where 1(t) and W(t) represent probabilities, t is time and a is a

constant. The corresponding mortality rates from these are:

OLt

u(t)IA m e (7)

a—l

mold) a at (8)

Skurnick29 showed that a simple model can relate the linear
decline in function to the distribution for death shown in equations
(7) and (8). The model is represented by N linked systems each able
to receive damage randomly. As the damage builds up on each link
the probability increases for the disfunction of that link. The
combination of this increasing probability and the N independent
systems each capable of acting similarly results in the system
following either equation (5) or (6) for the probability of the
disfunction of a link and thus the death of an organism. The build-
up of damage to each link is hypothesized to be a multistep process
with the rate constant for each of these steps equal. When n steps

have occurred the link is highly prone to break. With less than n

26

steps, probability is finite but not as great. These combined n
steps constitute the rate limiting process for the breakage of a link
and the death of the organ or organism. As each link collects
damage randomly this represents the linear decline in physiological
function because the chain of N links is weaker, i.e. less damage
could result in the breakage of a link.

This model is able to imply the observed kinetics (eqn 7 and 8)
through the use of the theory of extreme values, but the converse
is not necessarily true. It cannot be assumed those hypotheses
follow from the fact that the data fits eqn (7) and (8). In
particular, the model suggests that the rate limiting process is
characterized by n steps. It is worthwhile to investigate the data
in such a way as to assume n steps and then see if this assumption
leads to information which correlates to other knowledge. This
would lend support for the model but it would not imply its truth.

Data of mortality rate fit both equation (7) and (8). Equation
(7) is the function used by Gompertz and equation (8) is the Weibull
distribution. The Gompertz distribution has been used for many
years for the description of mortality but the Weibull distribution
has not. It first was used by W. Weibull in 1938 to describe
distributions of breaking strength and life expectancy in mechanical
systems30. It wasn't until many years later that the equation was
used for life expectancy distributions in living organisms. Curtis
as well as others used a modified form of the Weibull function to
describe the effects of radiation on biological systems. He also

suggested a model system of aging which is describable by the Weibull

27

distributionl4. Rosenberg et al. used this distribution to analyze
the mortality rates of humans and Drosophila. They showed that
mortality rates could be described by this function equally as
well as by the Gompertz equation. They also showed that, if the
formulation:

u(t) = Atnfll (9)
is used, the A parameter is the only parameter which is temperature

dependent. This allowed an attempt to relate A to AH+ though an

Arrhenius type equation +
—AH

A = A0 e RT , (10)

where KO contains the first two factors of eqn (1). The results

+

showed that A behaves like K giving a AH constant equal to

190 Kcal/mole for Drosophila. The A parameter does not have the

+

dimensions of rate, however, and so a AS could not be determined.
They also found that the n value which is not temperature

dependent is a low valued constant that could be an integer. This,
unlike the Gompertz function, suggest a tie to the model of Skurnick.
If n is assumed to be representative of the number of steps in the
rate limiting process, then a logical further assumption is that
each step of this process is represented by a first order rate con-
stant. For the combined process to be the rate limiting process
each step must, therefore, be equal or, in other words, each rate
constant must be identical. If l/T is this rate constant, then

equation (6) becomes:

w<t> = 1 — e " T (11)

28

and equation (9) becomes:
n—l

um = (—§—> <12)

r—IlI-J

The A parameter in (9) is thus equal to (l/T)n. l/T is a first

+

order rate constant and can be used to determine a new AH from

+

equation (10) and a corresponding AS from equation (1). These re—
present the activation enthalpy and entropy of each step. Whether

or not these values have any meaning is a question that must be
answered by determining their values for different systems and
evaluating their reasonability.

The experiment described in Chapter III determines these values
for the lysis process of the red blood cell and shows that the
Weibull distribution is a useful method for examining this process
and that the formulation of equation (12) represents a physically
meaningful function to work with.

The discussion of this chapter has shown that there is already
work showing that highly energetic, highly improbable events result
in what appears to be molecular denaturation and that this is respon—
sible for mortality. Also an uncommonly used equation, the Weibull
function, which has its origins in the distributions of extreme
values needs to be examined for possible use in the description of
mortality. It appears to have parameters that are more meaningfully

representative of physically tangible quantities than the more

commonly used Gompertz function.

CHAPTER III

THE EXPERIMENT

THE EXPERIMENTAL MODEL

It was discussed in Chapter I that there are probably many causes
of aging. All of those that have been studied and all of those on
which models have been based are probably real phenomena in the realm
of aging. Some of them appear to be only symptoms and some are truly
causal, but all stem from the problem the organism has in dealing with
environmental energies that are spontaneous, erratic, and from uncon—
trollable causes. These include high energy radiations, low energy
radiations (heat fluctuations) free radicals, highly reacting foreign
molecules, nuclear decays etc. The purpose of this experimental
model is to show that thermal energies can cause a population of
cells which are not reproducing to accumulate damage and to cease
functioning with kinetics that are very similar to death kinetics of
other closed, non-reproducing organisms: to show that increasing
temperature effects the survivor kinetics of the model organisms in
a manner that can be described by the theory of rate processes: more-
over, to show that an activation enthalpy, AHi, exists for the "death"
event in the model implying a molecular event as key to "death" and
is of the same high magnitude as that for poikilothermic organisms.
(Since the temperature must be varied within the organism to determine
the activation enthalpy homeothermic organisms cannot be compared.)

The model system is the mammalian red blood cell. It has been
shown to be an aging system, with a life span of about 5 months in

mammals. It does not divide nor even replace its own molecules if they

29

30

become inactive because it contains no nucleic acid. It is a closed
system that simply decays with time and is replaced when considered
by the organism to be less valuable than the space it occupies. It
makes a good model because it is a continuously decaying system very
much like multicellular organisms and like most multicellular
organisms, it does not divide and lose its identity. It has the
simplicity of a single cell with the general characteristics of an
aging multicellular organism.

In order to follow the rate of death in the RBC a useful charac—
teristic is needed that can be easily measured in a population of
cells. There are many characteristics of the cell which could be
examined for this decline. Since this experiment was designed as a
pilot, the most conveniently measureable one, the lysis of the cell
membrane, is the one chosen. The proteins, lipids, glycoproteins,
etc. in the membrane are undergoing continuous degradation as are
the other components in the cell. Therefore, the ease at which the
membrane will lyse increases with damage and time. This has been

shown by others in measuring the membrane fragility of RBC's.31’32’

33,34

The plan of the experiment is to follow the rate of lysis in a
population of cells over a range of temperatures. The curves that
describe the kinetics at each temperature will give some clue as to
the type of process occurring, eg., whether it is a first order
reaction or a multistep process. Following the change in these
curves over a range of temperatures will give an indication of

whether or not an activation energy exists for the process of cell

31

lysis. This will be done by using the Arrenhius equation relating a
etemperature dependent parameter from the kinetic curves to the inverse
of temperature. This will all be done for two populations of RBC's,
one young and one old, in order to see if there are any differences

in young and old lysis kinetics and if the activation energy changes

for this process.

32

THE EXPERIMENT

The experiment contains two parts: the verification of the
separation of red blood cells according to age on a density gradient,
and the kinetic studies of following the population decline of the
cells at different temperatures.

I. Separation and Verification Methods

 

A Ficoll density gradient was used to separate sheep red blood
cells following the procedure outlined by Rahman et a135. To assure
the technique was producing the desired results, 59Fe-citrate was
used as a measurable parameter for the distribution. This is
selectively taken up in newly formed RBC's and remains with a cell
until it is removed from the blood stream. A pulse was given allowing
for a labeled population of cells that could be followed as they age.
If the gradient is successfully separating cells according to age,

a band of radioactive cells should move from the less dense regions
of the gradient to the more dense region as these pulsed cells age.

5
(1) 9Fe Incorporation into Erythroeytes

 

A one year old sheep was obtained from the Michigan State
University Sheep Barn and was used as source of blood. The sheep
was given a single dose of 59Fe-citrate injected into the jugular
vein. Approximately 0.4 mCi was dissolved in isotonic saline to
produce total injection volume of 1.0 ml.

(2) Blood Preparation

 

The sheep was exsanguinated at regular intervals in the course of
the life span of the erythrocyte. This was also done through the

jugular vein. The blood was collected into a heparinized vacutaner

33

and stored at 4°C until ready for use. The whole blood was diluted
approximately 2:1 with a balanced buffered saline solution (BBS)36
and this was used for the gradient centrifugations.

(3) Ficoll Gradient Preparation

 

Ficoll was dissolved in the same balance buffered saline solution
as above. Non linear gradients were made using the gradient maker
designed by Bock and Ling37. The gradient ranged from 50% Ficoll at
the bottom of the gradient to 28% at the top. The absolute density
ranged from 1.173 - 1.096 g/cm3. A 1.0 ml sample of the blood pre—
paration was layered on the top of the gradient and the gradient was
spun on a Beckman L3-4O ultracentrifuge at 15000 rpm for 90 minutes.
Longer centrifugation time did not change the pattern of banding.
After centrifugation 3 ml fractions were taken from the bottom of each
tube with the use of a narrow aspirator needle lowered to the bottom
of each tube.

(4) Measurement of the 59Fe Radioactivity

 

Each fraction was washed and the blood cells spun down into a
pellet. These were then digested with Protosol and a fluorescent
cocktail was added. This was counted on a Packard Tri-Carb Scin-
tillation Spectrometer for ten minutes with background subtracted
from each sample.

II. Kinetic Studies of Population Decline

 

(1) Blood Preparation

 

A four year old ovine ewe was used as the source of red blood cells.
It was exsanguinated from the jugular whenever blood was needed. The

blood was collected in a 10.0 ml vacuutaner containing 1.4 ml of a

34

whole blood preservation CPD (.016 M citric acid; .016 M monobasic
sodium phosphate; .14 M glucose; .089 M sodium citrate). This was
to preserve the freshness of the cells for future use and also acted
as an anti-coagulant. A sample of this blood was diluted approxi-
mately 2:1 with BBS and layered on gradients ranging in density from
42—24% Ficoll and absolute density 1.145 - 1.082 gm/cm3. The
gradients were fractioned into 12 fractions which were kept at

4°C while they were examined and washed and stored.

(2) Separation of Young and Old Populations

 

The index of refraction was determined for each fraction of the
gradient. The fractions were then washed and resuspended in BBS and
the absorption of each determined on a Bausch and Lomb Spectronic
20 at 540 nm. This determined the distribution of the red cells on
the gradient and correlated them to specific densities via the index
of refraction. The peak occurred at an index of refraction of
approximately 1.3800, and the band stretched from about 1.3720 to
1.3880. A fraction was taken with an index of refraction of about
1.3750 for the young fraction and one from about 1.3850 for the
old fraction. These were then washed and stored in BBS at 4°C.

(3) Determining Population Lysis Kinetics

 

A water bath with a Fisher Unitized Bath Control was used to
keep the temperature accurate to within : .01°C. The red cells were
diluted to approximately 1/1000 of normal blood cell concentration
or about 4 x 106 cells/m1. This suspension was placed in a 1 gram
vial with glass beads which were used for stirring purposes and this

was placed in the water bath. The time was monitored and samples were

35

removed at intervals. Approximately 50 pl of the blood cell suspension
was removed at each sampling and was placed on a Bright—Line hemo-
cytometer and counted under a microscope. The experiment continued
until less than 5% of the starting number of cells remained. This

was repeated for both young and old and for each temperature. The
temperature range was from 42°C — 56°C.

(4) Computer Fitting

 

A multipurpose curve fitting program, KINFIT, from the computer
library of Michigan State University was used on a CDC 6500 to
determine the best parameters for the Gompertz, Weibull, and
Arrhenius functions. All results and curves shown are least squares
best fit to the data. The differential forms of the Gompertz and
power law were used (eqns. 7 and 8) and were integrated numerically
by the computer program. For the Arrhenius equation the best fit

of eqn. 10 was given to the data.

36

RESULTS

I. Age Separation and Gradient Reliability

 

In order to determine if the gradients were reliable in separating
cells according to density irregardless of age, cells from two
fractions, one high density and one low, were relayered and respun
on separate gradients to see if they banded at the same densities
from which they came.

Four gradients were used in order to obtain enough cells.
Fractions with indexes of refraction approximately equal to 1.3780
were pooled and washed and another set was taken and pooled with an
approximate index of refraction of 1.3860. These represent fractions
from the top and bottom of the red cell band respectively. These
were then layered on separate gradients and spun as mentioned in methods.
The gradients were then fractionated and the results are shown in
Figure 3.

The solid and dashed lines show the decrease in index of refraction
and density with movement up the gradient. They represent two
gradients and show their reproducibility. The densities of the
pooled fractions from the original gradient are indicated by where the
vertical bars cross these two lines. The two peaks show where those
fractions banded on the second gradients. It is clear that the cells
have returned to their original density and that there is little
overlap between these two populations. Since these two densities are
approximately those used later as young and old respectively, it is
important that they do not overlap markedly.

In order to determine if the gradient is separating cells according

37

 

  
  

 

 

 

 

 

co ‘9 V 0'
0 C2 0 CW
rt - °‘ %
ODI540nm) '2 "
C)
‘N
«IQ
E
.9
.IO
E
/ 2
(J a—Kusuao bugsoaJoul g
o a L J <3
,3 " 8 c :7: "‘ E

Figure 3. Relayering experiment (see text for details)

38

to age the 59Fe activity was monitored. Samples of blood were re-
moved from the sheep one day after injection and then weekly from
that point on. The blood was run on the gradients and fractioned and
these fractions were read on a liquid scintillation counter and the
counts were corrected for changes in cell concentration by using OD
measurements on the fractions. The results are shown in Figures 4
and 5.

The dashed line represents the absorbance peak of the red cell
band on the gradient. The trailing edges to the bottom are the
highest densities and those to the top are the lowest densities.

One day after injection the label is in the high density portion of
the gradient. These are the reticulocytes that have a lifetime of
24—48 hours and are more dense than the average red cell38. By

day 7 after injection the reticulocytes have matured into young
erythrocytes and appear at the very top of the gradient or the area
of lowest density.

Figure 5 shows the progression from day 7 until day 57, by which
time the radioactivity is reaching a point of being evenly distri-
buted. It can be seen that the amount of activity is decreasing
in the low density portion of the gradient and increasing in the high
density portion. Since changing density is only a rough estimate
of the changing age of the red cell, clear cut results are not evident.
This does, however, show that the gradient is separating young and

old cells.

II. Lysis Kinetics

 

The percent survivors of the red cells with time was determined for

ABSORBANCE
Q

39

540 nm

C)

U

 

 

 

 

Bottom

 

Top

 

3K).

Figure 4.

(D
01

IO-

SlNOOO "IVIOJ. %

Location of radioactively labeled

and day 7

cells at day l

 

 

4O

 

 

Eozom
O. m

d

 

m

d

0.

ON

 

 

SlNOOO 'IVlOJ. %

Continuation of figure 4 at days 14, 30, and 57

Figure 5.

41

both young and old and for each temperature. The temperatures used
were 42°, 44°, 46°, 48°, 50°, 52°, 54°, and 56°C.

Figure 6 shows a typical set of data for young cells at five
different temperatures. It is plotted as log survivors versus time.
If there had been large straight line portions in these curves, one
could conclude that a simple first order process is occurring. These
are not straight lines but resemble the curves for human survivors
and fruit fly survivors of figures 1 and 2, suggesting a multistep
process.

To show that this rate of decrease in population changes with
the age of the cells, figure 7 contains young and old curves for two
representative temperatures.

It was described in Chapter II that several functions of population
decrease versus time can represent the kinetics seen in these multi-
step processes. For the reasons given there the Weibull relation is
the one of choice if it proves to represent the data well enough.

The Gompertz and the Weibull functions were both fit to the data.
Figure 8 shows the typical Gompertz plot of the data for young cells.
As can be seen, at large times, the curves tend to be straight lines
with slopes that decrease with decreasing temperature. These slopes
represent a and are changing dramatically with temperature. The
ordinate intercept of these extrapolated lines, which are a function
of Ro/a, are varying non uniformly, and as shown in Table l, the R0
value is not constant with temperature. Although the Gompertz
function does a good job in representing the survivor curves, it is

a poor function to use when temperature is a factor in the study.

 

 

 

42

 

 

 

: . .
= a
- A .
. . X . o
A
1.0.. " .
3 ‘ .
9 A
o
i o
r; 2.0. 56" 52° 0° , 48° 46"
Z a
\‘ a
Z a
E.
. 30. , ~
x
A
4.0 - I
I a j
|.O 2.0 3.0
Time (hr)
Figure 6. Log of the percent survivors plotted versus time

in the water bath for young cells

4.0

“hiIN/No)

LO

2.0

3.0

4.0

43

 

 

 

 

‘6‘
\AL \ \ .
\ \ Q
\ ‘°\ .
\ O\ O
L A ‘ O
\ \ o
I- \ O
I \
I ‘ °
I ‘2?
I.
I - \ . 0
‘ \
. 3 50° \ 46°
I
I I
\ I
A
\ I
‘4: ‘ .
'- \A‘ O
\
I
I
\ A
k
L 4 L___
-I.0 2.0 3.0
TImeIhr.)
Figure 7. Solid curves repeated from figure 6, dashed

curves represent old cells at the respective
temperatures

4.0

44

 

I0.0 1 :

l.0

 

 

 

 

’3
Z
\x
Z
5
I
0.|
0.0l _ I J l J 1
to I!) 2.0 2.5 3.0 . 3.5

TimeIhr)

Figure 8. Gompertz representation of young cells

45

 

 

 

Table l. Gompertz parameters R0 and (1
GOMPERTZ PARAMETERS
R Value
0
42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Young .032 .033 .14 .067 .123 .424 .045 .307
Old .103 .033 .18 .06 .228 .72 .979 1.35
a,Value
42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Young .46 .706 .749 2.48 3.11 3.18 10.13 10.54
Old .46 .976 .87 2.10 3.11 3.45 4.52 8.65

46

Both the a parameter and the Ro parameter are temperature dependent
and that makes it very difficult to determine the effect of
temperature on the system or to obtain any useful information about
the activation enthalpy of the process.

Figures 9 and 10 show the Weibull representation of the data for
young and old cells respectively. The "goodness of fit", as repre—
sented by the standard deviation of the residual, is given in Table 2
for both the Gompertz and the Weibull fit for young and old at each
temperature. The Weibull fit is as good or better in describing the
data as the Gompertz. It is, therefore, reasonable to use the Weibull
function because, as is shown in Table 3, only the A value (or l/T
value) is temperature dependent, and the n value is approximately
constant, and the variations present are fairly random.

Examination of Table 1 shows that the parameters of the Gompertz
are both temperature dependent. This makes it impossible to use the
Arrhenius relation for this analysis. The parameters of the Weibull
relationship, however, as shown in Table 2 are not both temperature
dependent. The n value is a stable value with respect to temperature
and only the A value changes markedly. Therefore, the A value was
tried in the Arrhenius equation to see if it resulted in a constant
value for AH+. Figures 11 and 12 shown the Arrhenius plots for young
and old cell populations respectively. A very good straight line is
noticed in the young cell population; and for the old cells there
appears to be a parallel set of lines with a discontinuity at about
50°C. The A parameter seems, therefore, to be related to the

activation energy of the process of lysis.

47

 

 

 

 

 

I0.0 ~
I.O -
To
Z
\
E
c:
I O.I -
0.0I 9 1 __-_L
0.: Lo
TIme (hr)

Figure 9.

Weibull representation of young cells

I0.0

-In (N/No)

48

 

 

 

 

 

I0.0
x
0.0! :1 .
0.: IO
Time (h r.)

Figure 10.

Weibull representation of old cells

I0.0

49

Table 2. Standard deviations of the residuals for Gompertz and
Weibull distributions

0 (RESID)

Young

 

42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Comp. .065 .042 .11 .07 .089 .055 .105 .10

Weibull .076 .04 .107 .07 .08 .073 .011 .027

Old

 

42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Comp. .037 .047 .089 .055 .050 .075 .105 .109

Weibull .038 .12 .08 .048 .034 .073 .06 .039

50

 

 

 

Table 3. Weibull parameters A, l/T, and n
WEIBULL PARAMETERS
A Value-
42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Young .021 .044 .18 .85 2.9 6.7 32.9 128.4
Old .095 .072 .23 .50 5.2 19.8 28.0 65.0
l/T Value
42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Young .25 .34 .54 .96 1.37 2.08 2.7 4.35
Old .37 .42 .63 .83 1.61 2.22 3.45 4.76
n Value
42°C 44°C 46°C 48°C 50°C 52°C 54°C 56°C
Young 2.8 2.8 2.9 3.9 3.4 2.6 3.5 3.3
Old 2.4 3.0 3.2 3.7 3.5 3.8 2.7 2.7

THERMAL LYSIS RATE CONSTANT'A

 

51

 

I02“-

 

 

I

/ l3l.6 KcoI/mole

 

 

 

I03.
I0"-
:02:-
56° 52° 48° 42°
'06! J I l l
3.00 3.04 3.08 3J2 316 3.20
..'.. xl0°
TIK")

Figure 11. The Arrhenius plot for the young cells using
the A parameter of the Weibull distribution

THERMAL LYSIS RATE CONSTANT ’A

52

 

 

  
 
  

 

 

 

3.20

:03
:02 -
’33.? Kcal/mole
Io' -
/ III.9 KcaI/mole
|0° - I
to" -
10°.
56° 52° 48° 42°
'0'3 l __l l l
300 3.04 3.08 3J2 3J6
.L x I03
TIK")
Figure 12. The Arrhenius plot for the old cells using

the A parameter of the Weibull distribution

53

Table 4 lists the values of n and their corresponding marginal
standard deviations as given by the computer program. These standard
deviations would indicate that there is a significant difference of
n values between certain temperatures. To arrive at these values, the
data of several experiments was pooled at each temperature. In order
to compare this to n values computed from unpooled data the three
temperatures shown in Table 4 were chosen and n values computed for
each experiment within the set and the n values were average and the
standard deviations determined. This shows that there is more variance
when one takes the experiments individually, suggesting that possible
differences in n values are really within the experimental error.

Even if one assumes the n values are different over the temperature
range it is difficult to establish a relation for the n values as a
function of temperature. They seem to vary in an unpredictable
fashion, which also suggests that they are constant within experimental
error.

The high value of the activation enthalpy obtained using the A
value suggests that this might be a multistep process. In order to
examine this possibility the Weibull function in the form of equation
12 can be used, where the value A has been replaced by (1/T)n. Table
2 shows the values of l/T at each temperature and age. Skurnick
suggest that the value of n is an indication of the number of steps
in a multistep process, so using the form of the Weibull in equation
12 effectively divides the value of n out of A. This results in a
parameter which has the dimensions of rate which may possibly repre—

sent the rate constant of one of these steps.

Table 4.

54

The values of AH+ computed by the shift in life
expectancies ty(l) and ty(2) at the temperatures T
2 2

and T

 

2

film a”) T1 T2 3222:5225;

.60 .29 52° 56° 38.9
1.40 .29 48° 56° 41.4
5.2 .29 42° 56° 42.7
5.2 1.40 42° 48° 44.2
5.2 .60 42° 52° 44.2
1.40 .60 48° 52° 44.2

 

55

As would be expected the value of l/T follows the Arrhenius
relation as does the value A, but since the n has been eliminated
from A the parameter l/T is less sensitive to variations in the value
of n. Figure 13 shows the Arrhenius plots for young and old cells
using 1/T as the rate parameter. It follows that the activation
enthalpies would be about one third (three being the average value of
n) of those shown in figures 11 and 12. The activation enthalpies
for the young and old cells are approximately the same in figure 13
suggesting that a similar mechanism is responsible for lysis in both
young and old cells. It is interesting to note that the variations
in the plot for the old cell populations have diminished suggesting
that the discontinuity seen in the plot of the A value is an
artifact of the fluctuations in n.

III. Relationship of Lifespan to Activation Energy

 

When examining figure 6 it is apparent that the average lifespan
for the red blood cell decreases with increasing temperatures. This
directly follows from the Arrhenius equation and it is the value of
AH+ that determines the amount of change in lifespan with change
in temperature. By using the A parameter and the l/T parameter two
different activation enthalpies have been determined.

i

It can be shown that one would expect the AH associated with the

l/T parameter to predict this lifespan shift.
By taking the integrated form the Weibull function

n
% = exp [7% 0%)} (5)
i

and two hypothetic curves at temperatures T1 and T2 respectively, and

56

 

40“
30“

  
    
  

Old
\:
f40.4 KcaI/mole
\
%

Young /

 

 

 

7:?" 42.8 Keel/mole
0.5-
I
O.I “LI T T 77 I l j
304 312 3.20

Figure 13. The Arrhenius plot for both young and old
using the l/T parameter

57

 

 

evaluating at the fractional survivorship N = 50% for both, the
N.
result is 1
n n
.5 =.E = expi- %- t%(l) = exp [f-i t%(2)
Ni T1 T2

where tL(l) and t,(2) are the population lifespans associated with
2 /2

50% survival for each temperature and l/T and l/T2 are the respective

 

 

1
rate constants. This simplifies to
tg(1) tg(2)
2 = 2
T1 T2

Using the theory of rate processes (see equation 7) to substitute in

for l/T this then becomes with rearranging

 

 

+
—AH
t3<1> = C2 exp RTz —AH 1 1
ta”) ¥ 1' exp “REIT ‘ r) (5)
C exp Péfl— 2 l
1 RT1

This then relates lifespan to temperature and defines the constant
AH+. Table 5 gives the value of AH+ for several values of T1 and

T2. It shows clearly that the basic increase or decrease in lifespan
with temperature is related to an activation enthalpy almost identical
to that derived from the l/T parameter of the Weibull distribution.
This parameter, l/T, therefore represents a rate constant for the

rate limiting step involved in cell lysis, and the A parameter must
represent some combination of steps that affects the kinetic behavior

of the population but not the thermodynamic behavior.

IV. Derivation of n°AH+

 

+

Let us look more closely at this AH associated with the A

58

parameter. Evidence we have indicates that this activation enthalpy

+

is equal to n-AH where we are now talking about the activation

enthalpy associated with l/T. The fact that the A parameter follows

+

the Arrhenius equation and gives a AH which is the sum of the
activation enthalpies of n steps possibly separated widely in space
and time is solely the result of the statistics involved. Skurnick
has shown in a general treatment of stochastic distributions of
mortality that the Weibull distribution is one of the asymptotic
distributions in the theory of extreme values of order statistics.
He has proposed a model to show that the n parameter of the Weibull
distribution represents the number of highly improbable, sequential,
random events that lead to the death of one organism in the popula-
tion. A result of this model is that the mortality rate, u, of
the population, as described by the Weibull function, contains the
constant A which is related to n times the activation enthalpy
associated with l/T. The simple derivation which follows shows this.

We assume a model that has M links, where M is very large, and
the breakage of a link is the event that causes death. Damage to the
links is random with time and the build up of n units of damage on
any one link would cause it to fail. We can determine the distri—
bution function of failure for the set of links and from that the
mortality rate among a whole set of similar systems which would
correspond to the mortality kinetics of a population.

Using simple first order kinetics, the distribution of links

receiving no damage with time is given by the solution to

 

59

cm0 M k

a? = 0
where k is the rate constant representing the rate of incidence
of "hits". The solution is MO/Mi=exp(—kt), where M1 is the initial
number of links. For a system receiving 1 unit of damage the
distribution can be arrived at by considering the change in the
number of links with one "hit" already minus those with zero "hits"
receiving one. Therefore,

dM

dt

_ k
7 7(M1 7 Mo)

Using the solution for M0, the solution to this equation is therefore

given by

——- = kt exp (~kt)
M.
1
This can be continued until n units of damage are received at which
point the system ceases to exist. The distribution of links with n

units of damage is

(53)“,

= n' exp (—kt)

3‘53

1

By using a theorem demonstrated by Cox40 we can obtain from
equation (6) the distribution of systems that cease to exist due to
the first link receiving n hits. This is what we want in describing
a population of aging organisms each one dying when an average
threshold of maximum damage is reached. Therefore, it can be derived
from equation (6) that the fraction, N/NO, of the number of systems
surviving with time is given by

$6 2 exp[kt]n

60

The mortality rate, n(t)=dN/th is therefore given by
H(t) N k -n-t
(which is simply the Weibull function with k=1/T) or in taking the
10g,
lnIu(t)I “ n In k + 1n In-tn-l}.
Since k is the only parameter on the right side of the equation that

is a function of temperature we can use the theory of rate processes

to give

as

ln Iu(t)} 3 n°AH + 1n {n-tn—l}

RT
This, therefore, shows that, for fixed time, U(t), and, there—

fore, the parameter A is proportional to exp I—n-AHI/RT} which is
the Arrhenius equation and the observed activation enthalpy is
simple n times that for the process of receiving one unit of damage.

V. The Activation Entropy and Protein Denaturation

 

In order to determine an activation entropy we used the
absolute rate theory equation (equation 1) which relates the rate
of a process to the temperature at which it proceeds and the con—
stants AH+ and AS+:

K = EI- exp(AS+/R — AH+/RT),

where k, h, and R are Boltzman's constant, plank's constant, and the
gas constant respectively. Since l/T appears to be the more relevant
parameter with respect to the thermodynamics, the values of l/T and
their corresponding AH+ and T's were used in equation 1 to determine
the value of the activation entropy. The value of AS+ for young

cells was 57.60 cal/mole/°K and for the old cells was 50.29

cal/mole/°K.

61

DISCUSSION AND CONCLUSIONS
I. Kinetics

The results show that the thermal induced lysis of the red blood
cell does not follows simple first order kinetics but can be described
by the Gompertz function and the Weibull (or power law) distribution.
The Gompertz has been assumed by many authors of theories to be
fundamental to the aging process. They have bent their theories and
have designed their hypotheses such that they can derive the Gompertz
function for the rate in decline in the population. Strehler5 gives
a review of such theories and himself assumes the Gompertz relation
in an attempt to derive a major phenomena associated with aging,
the linear decline in physiological function with age.

As was shown earlier both the Gompertz and the Weibull distri-
butions are derivable from the asymptotic distribution of extremes.
A model was presented by Skurnick which showed that a linear decline
in vitality does result in both the Gompertz and the Weibull distri—
bution in this asymptotic limit29. This appears to be the only way
to derive these functions because the processes involved in aging
and death involve a small number of events of a highly improbable
nature. Choosing distributions for simple reactions and expecting
them to describe these rare phenomena has been a mistake many have
made. The gross phenomena that is observed when measuring the death
rate in large populations is the probablistic result of these extreme
occurrences in nature. Whether the cause of aging and death is the
result of the denaturation of a protein or RNA or DNA or the melting

of lipid, or due to action of a poison, or the build up or debris or

62

the specific action of a "death" related gene, the numbers and
quantities involved make these events small in number and improbable
in occurrence in comparison to the multitude of reactions of the
normal cell processes. The reason that these can be called impro—
bable events in the total number of events and not a whole separate
class of occurrences is that they are simple molecular processes

of the same exact nature as the other ”normal" molecular reactions
of the cell.

The Gompertz and the Weibull functions are the simplified
descriptions of the behavior of extremes of other distributions. If
these other distributions describe the processes of the cell in some
way then the analysis of the extremes seems to be the only logical
way to derive these functions and explain their relation to aging
and death. No more simple method of deriving these functions has
been shown that doesn't either assume the function itself in the
first place or a simplified precursor in an ad hoc derivation.

Since these functions don't appear to be derivable from simple
physical concepts, their parameters do not straight forwardly repre-
sent the physical world. These parameters, however, are the only
possible attachments to reality and they do appear to have physical
significance. The (land R0 parameters of the Gompertz have been
shown by Strehler to be correlated, and different combinations of
the two represent possible influences of the environment on the organ-
ism. ie. good or bad growth conditions. The fact that they are
correlated means that they are both affected by external factors.

This presents a problem when dealing with temperature. The Weibull

63

function on the other hand has only one parameter which depends
heavily on the environment, so that this allows an attempt to
evaluate the phenomena using the theory of rate processes which in-
volves the relation of one parameter to temperature, energy, and
entropy.

There have been no theories that have shown that the parameters
of the Weibull distribution have physical meaning in biology.
Rosenberg et al. have suggested that the parameter n represents the
number of steps involved in a multistep process and that the A para—
meter is related via the Arrhenius relation to the activation enthalpy.
This experiment has shown that both the A value and the l/T value
follow an Arrhenius relation suggesting a tie to the theory of
absolute rate processes, and that n is fairly constant for this
system independent of age. Comparing n with experiments on other
organisms, n increases with increasing complexity of the system as
would be expected if there are more steps responsible for death. Both
of these facts suggest that the Weibull distribution, which can only
be derived from asymptotic limits of order theory, has physically
meaningful parameters describing the reactions rate and the possible
number of processes occurring.

II. Activation Enthalpy and Entropy

 

A further result of this experiment is the activation enthalpies
derived. An activation enthalpy for a lysis phenomena of 130 kcal/
mole suggests a very large reaction involving many steps at once.

The denaturation of protein has been shown to be this high due to

its many hydrogen bonds and crosslinkings that can be broken. If we

 

64

assume a process of three equal steps as indicated by the number n,
then the activation enthalpy of each step was shown from figure 13

to be about 40 Kcal/mole. If we further assume that l/T represents

a first order rate constant then an activation entropy of 57 cal/mole/
°K can be calculated for the young cells. These individual steps are
comparable to most protein denaturation values that have been
measured in the past and, therefore, represent a possible denatura—
tion process or, at the least, a degradative process. The high en—
tropy suggests that it is an irreversible process.

The quantity in the exponential of equation 1 is also known as
the free energy of activation, AF+, and is given by AH+ — TAD+. The
value of this quantity has been shown to be fairly consistantly equal
to 25.0 Kcal/mole for heat induced protein denaturation and enzyme
inactivationzz. AF+ is also temperature dependent but over the range
of this experiment the value is relatively constant. The value of
AF+ for young cells at 50°C is 24.2 Kcal/mole and for old cells is
24.1 Kcal/mole. This directly suggests that the process involved in
the lysis of the red cell is protein denaturation.

Further evidence for a protein denaturation process comes from
the fact that the activation enthalpy and the activation entropy
follow the compensation law. Rosenberg et al. showed that a compen—

sation relation

AS+ = — — b (7)

holds for the denaturation of many proteins and viruses, and the death

of yeasts and bacteria. To is a compensation temperature which is a

65

constant approximately equal to 330°K and b is a constant equal to
64 — 66 cal/mole/°K. If the set AS+ and AH+ for each group of

+ vs. AH+

systems is plotted as AS then a straight line is observed
with intercept b and slope l/TC. Protein denaturation and thermal
death fall along this line suggesting that the rate limiting step in
thermal death is protein denaturation.

In the experiment with the red blood cells, if the values of
TC and b which were derived from death in bacteria are used to deter—

+ +

of 64.3 for AS+ for the young and a value of 56.9 cal/mole/°K for

mine AS using the known values of AH then equation 7 yields a value
AS+ for the old. Both of these are within the error range of the
regression line of AH+ and AS+ given by Rosenberg et al.

This not only points to a possible protein denaturation as a
mechanism in the lysis of the red cell but also gives more evidence
that the parameter l/T in the power law is indeed a first order rate
constant. All the values compiled by Rosenberg et a1. were from
kinetics that showed a first order process. In fact, the way in which

they were able to calculate a AST was by using

KT AST — AHT
=( —_ __._
K ‘R)e R 8 RT

 

from the theory of rate processes knowing that the observed rate
constant was a first order process. In this case, a first order
process was assumed and a AST calculated. A good fit to the compensa—
tion law by this calculated AST suggests that the assumption was valid.

III. Young vs Old

 

One of the main purposes for this experiment was to evaluate the

66

kinetic and the thermodynamic differences between populations of

20’39 has shown that

young and old cells. Work of H. A. Johnson
fluctuations in thermal noise at physiological temperatures can cause
macromolecular denaturation in sufficiently high numbers to explain
the spontaneous mortality seen in cultured cells. He suggests that
increasing the temperature simply speeds up this denaturation process
by increasing the number of high energy fluctuations in the thermal
environment. Therefore, the process of thermal death is not a special
case but a real representation of the mortality process. By per—
forming the high temperature experiments on young and old populations
of cells the remaining portions of their aging process proceeds at
rates fast enough to be observed in short times. The older cells
have a shorter time remaining before deactivation or death than the
younger cells and, therefore, their ip_yi££p_lifespans are shorter.
This is observed in this experiment; the rate constant of lysis,
l/T, is greater for the old cells characteristic of the shortened
lifespan.

The thermodynamic parameters show little change between young
and old populations but this is because small changes in these values
can cause tremendous changes in the rate constants. A change in
AF+ of 2 kcal/mole for example can change l/T by a factor of 10. The
important thermodynamic parameters are AH+ and AS+. The value of
AF+ can remain unchanged while both the activation enthalpy and entropy
vary widely. The values of AH+ and AS+ give the important clues to

the mechanisms involved. High AS+ suggest increase in disorganization

typical of denaturation of tertiary structure, and suggests the

67

breakage of many covalent or hydrogen bonds. Many combinations of
AH+ and AS+ are possible including negative values. In this experi-
ment the values of both of these parameters are reasonably high, but
are approximately equal for both young and old. This implies that
the same process is occurring in the lysis of the young and old cells
and this process is associated with some macromolecular denaturation.
The fact that l/T is measured to be different between the two ages
suggest that the same rate limiting process is occurring but that more
of the degradative steps leading up to this rate limiting process
have occurred in the old cells. The examination of the n value also
supports this idea.

There is no apparent change in the n values of the Weibull
distribution between young and old and this raises the question of
the meaning of the parameter n. Many investigators have postulated
that the shoulder seen in mortality kinetics of humans, fruit flies,
and tissue culture cells is due to a series of steps constituting the
rate limiting process of death2’3’12’29. Skurnick has shown that
the n in the Weibull function represents the number of steps in a
sequential process each with a rate constant l/T. He postulated that
these steps occur during the aging process and thus the value of n
would decrease with the age of the system. If these theories are
assumed then the fact that the n value does not change suggest that
the age differences between these populations of cells is not
significant with respect to the process of lysis. This can be under—
stood by considering that under normal conditions one would not expect

the blood cells to be allowed to deteriorate to the point where they

68

were close to lysing before they were removed. It is to the organism's
advantage to replace the red blood cells before they have reached the
point where the proteins in the membrane are near denaturation in

order to be pumping only highly active, highly efficient cells. So,

in spite of the fact that this experiment has separated the youngest
and oldest cells from the blood stream and has shown that the older
cells have deteriorated somewhat, the analysis indicates that the older
cells have not aged significantly towards the event that was chosen to
represent the death event, or that the death event is unaltered
regardless of age.

IV. Comparison to Normal Lifespan

 

If we extrapolate the line in figure 13 to 37°C to determine l/T
and then plug this into the integrated form of equation 12,

n
-1n(N/N ) = l 5— .
O n T

with n/NO = .50 and n=3, we can determine the lifespan at 50% survival
(th). This results in a t,/2 equal to approximately 30.6 hours. This
is dramatically different than its 5 month lifespan in the organism.
This is not unexpected, however, because it is known that red blood
cells age rapidly in storage even at 2-6°C. Their "shelf life" at

4°C is only 21 days and at this temperature they metabolize glucose
approximately 30 times more slowly than at 37°C41. This could put
their lifespan at 37°C around the one day mark. The reason for this
rapid aging in storage is unknown but is believed due to the highly
foreign environment in which they are placed. This raises the

question of how this ip_vitro deterioration effects the results given

here.

69

This does not change the fact that the kinetics are best
described by the Weibull distribution, that the possible number of
steps involved is 3, that there exists an activation enthalpy for
the process measured, and that this activation enthalpy is the same
for both young and old even though the rate of deterioration is
greater for the older cells. The question to be answered is: what
is the process that is being measured? Most directly we are measuring
the activation enthalpies for red blood cell deterioration ip_yi££p,
Does this invalidate or weaken the experiment?

The inability of the experiment to represent the red cell
survivorship ip_yiyp does not detract from the original idea of using
the red blood cells as an aging medal. The ip>yi££p_aging of the
blood cell still represents a system which exhibits irreversible
deterioration with time. The ip_yi££p_red cell is still an independent
entity which does not reproduce or grow, but simply wears out with
time. The increased rate at which this occurs ip_yi££p_is due to
the environment which should not affect the activation enthalpy but
rather the activation entropy. One would expect the lines given in
figure 13 to be shifted downwards such that the activation enthalpies
would be the same but the activation entropies would be greater. If
one calculated the new activation entropies after shifting the lines
in such a way that the lifespan at 37°C is 5 months, the result is
65.8 and 58.5 cal/mole/°K for the young and old respectively. If

+

this is compared to the AS '3 computed using the compensation law,
one sees that these values are even closer than those derived from

the experiment. (see page 61 and 56) This suggests that the

7O

activation enthalpies still validly represent the energy of activa—

tion for the catastophic, final event in this aging biological system.

71

SUMMARY

Briefly summarizing the results of the test we have seen that
lysis kinetics of the red blood cell in an ip_yi££p system of heat
induced lysis does not follow simple first order kinetics but rather
kinetics with substantial shoulders. These are describable by the
Gompertz and the Weibull distributions but only the Weibull parameters
are suitable for further use in thermodynamic considerations. The A
parameter of the Weibull follows the Arrhenius relation but this
gives an activation enthalpy which appears to be n times higher than
that which represents the rate limiting step. The l/T parameter,
when used in the Arrhenius relation, results in an activation enthalpy
which correlates to that predicted by the shift in lifespan. This

+

rate, l/T, also results in a AS from the rate theory equation

which follows the compensation law for proteins and thermal death

1

in simple organisms and in a AF which is closely comparable to
those measured for thermal protein denaturation. This strongly
implies that l/T is a rate constant which is directly connected to
the basic processes involved in the thermal lysis. The comparison
of the n parameter and the thermodynamic parameters between the
young and the old suggest that the only difference between the young
and the old is an increased level of deterioration in the older
cells but not a change in the basic process in lysis. Had a para—
meter been chosen which more appropriately describes the timing of
the termination of red blood cell ip_yiyp_then there might have been

a noticeable change in the n parameter.

The connections that we can make to the aging and dying process

72

are that kinetics of mortality in living systems can be reproduced,
in form, in a simple system where the mechanism of action is
associated to protein denaturation. This is consistent with the
mortality of Drosophila and human fibroblasts, which both suggest
high activation energies typical of macromolecular denaturation.
The fact that the red cell does not contain DNA and yet that its
"mortality" is very similar to the mortality of other organisms
and the activation enthalpies are also similar suggests that the
cause of death in other organisms is associated with protein

denaturation resulting from thermal fluctuations in the environment.

 

73

FURTHER WORK

This experiment along with many others has shown that temperature
is a very important parameter in life. Slight changes in it can cause
a speeding up or slowing down in many processes. The thermal bath
regulates the system. I think it is clear that the causes of the
rarely occurring low probability extremes that are assumed in the
derivation of the power law and the Gompertz can be attributed to
high energy fluctuations that occur with low probabilities. This idea
fits well with this derivation of these functions and makes for a
simple answer to the causes of aging. I suggest that the main con—
tribution to these high energy fluctuations are due to the thermal
bath. Others have suggested this39, but so far the only method of
changing the level of fluctuations in order to study it has been
either to use very high energy X-rays or Gamma rays or to raise the
temperature. The first lacks a basis in reality; its energies are
too high. The second is lacking in that the whole thermal bath is
being raised in order to increase the populations of the fluctuations.
When the bath temperature is raised many, many reactions occur that
are not normal either due to their speed or their type. More than
just the affects of the fluctuations are accentuated. The mean heat
level is increased which results in gross physical problems, such as
membrane fluidity, heat dissipation, osmotic changes, etc. These are
changes that are directly due to the mean thermal level and not to
the distribution of the energies around the mean.

An experiment which might get around this problem would use a

culture of bacteria or some other culturable organism that can be

74

suspended in media and followed for rate of proliferation. They would
be treated in a constant temperature bath at physiological temperature
with infrared radiation. This could be monitored for intensity and
frequency resulting in specific quanta on the order of high thermal
fluctuations at a density significant for affect. The bath would
maintain a thermal mean equal to the best growing temperature but
the radiation would be able to increase the probability of high energy
fluctuations. A frequency of 1000 nm results in quanta of energy
30 kcal/mole which is high enough to break bonds. When everything
is considered via quantum mechanics the thermal quanta in the form
of infrared radiation and the thermal quanta being emitted and ab—
sorbed over and over within matter are identical. Therefore, this
type of radiation is much more reasonable than the very high energies
that are involved in X-rays or UV radiation.

The proliferation rate of the cells would be followed to see if

"aging" faster than controls. The number of them unable

they are
to reproduce is a measure of their fight against degradation. If this

increases with IR radiation, then this points to thermal fluctuations

contributing heavily to the eventual death of all organisms.

B IBLIOGRAPHY

 

10.

ll.

12.

13.

BIBLIOGRAPHY

Rosenberg, B. et al. The Kinetics and Thermodynamics of Death
in Multicellular Organisms. Mech. of Aging and Dev, 2 (1973)
275.

 

Armitage, P. and Doll, R. Br. J. Cancer 8 (1954) l.

 

Johnson, H. On the Thermodynamics of Cell Injury. Am. J. Path.
75 (1974) 13.

 

Strehler, B.L. Origin and Comparison of the Effects of Time
and High Energy Radiations on Living Systems. Quart. Res. Biol.
34 (2) (1959) 117.

 

Strehler, B. Time Cells and Aging. Academic Press, New York,
1962.

 

Failla, G. The Aging Process and Carcinogenesis. Proc. N. Y.
Acad. Sci. 71 (1958) 1124.

 

 

Jones, H.B. A Special Consideration of the Aging Process,
Disease and Life Expectancy. Adv. in Biol. and Med. Phys. 4
(1956) 281.

 

Sacher, G. On the Statistical Nature of Mortality with Special
Reference to Chronic Radiation, Radiology 67 (1956) 250.

Strehler, B.L. Fluctuating Energy Demands as Determinants of

the Death Process (a Parsimonious Theory of the Gompertz Function).
Ip_"The Biology of Aging" (B.L. Strehler et al., eds.) pp 306-

314. Publ. No. 6, Am. Inst. Biol. Sci. Washington, 1960.

Burch, P.R.J. "An Inquiry Concerning Growth Disease and Aging"
Oliver and Boyd, Edinburgh, 1968.

Burnet, M. Somatic Mutation and Chronic Diseases. Brit. Med. J.
1 (1965) 338.

 

Curtis, H.J. A Composite Theory of Aging. Gerontologist 6
(1966) 143.

 

Franks, L.M. Aging in Differentiated Cells. Gerontologia 20
(1974) 51.

 

75

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

76

Curtis, H.J. Genetic Factors in Aging. Adv. Genet. 16 (1971) 305.

 

Orgel, L.E. The Maintenance of the Accuracy of Protein Synthesis
and its Relevance to Aging. Biochemistry 49 (1963) 517.

 

Holliday, R., Torrant, G.M. Altered Enzymes in Aging Human
Fibroblasts. Nature 238 (1972) 26.

Orgel, L.E. Aging of Clones of Mammalian Cells. Nature 243 (1973)
441.

Hayflick, L. The Limited in vitro Lifetime of Human Diploid Cell
Strains. Exp. Cell Res. 37 (1965) 614.

Dell'Orco, R.T. The Use of Arrested Populations of Human Diploid
Fibroblasts for the Study of Senescence in vitro. Advances in
Experimental Medicine and Biology 53 (1975) 41.

 

 

Johnson, H. Thermal Injury Due to Normal Body Temperature. Am.
J. Path. 66 (1972) 557.

Sacher, G.A. Molecular Versus Systemic Theories on the Genesis
of Aging. Exp. Geront. 3 (1968) 265.

 

Johnson, F., Eyring, H., Polissar, M. The Kinetic Basis of
Molecular Biology. John Wiley & Sons, New York. 1954.

 

 

Rosenberg, B. et a1. Quantitative Evidence for Protein Denatura-
tion as the Cause of Thermal Death. Nature 232 (1971) 471.

Gompertz, B. On the Nature of the Function Expressive of the Law
of Human Mortality and on a New Mode of Determining Life Contin-
gencies. Pil. Trans R. Soc. (Lond), Series A, 115 (1825) 513.

Erying, H. and Stover, B. The Dynamics of Life, II. The Steady-
State Theory of Mutation Rates. Proc. Nat. Acad. Sci. 66(2)
(1970) 441.

Vital Statistic of the United States, 1967, Vol. 2, Mortality

 

(Part A), U.S. Government Printing Office. Department of Health,
Education, and Welfare, 1969.

Rosenberg, B. Personal Communication.

Gumbel, E.J. Statistics of Extremes. Columbia University Press,
New York, 1958.

 

Skurnick, I.D. Stochastic Studies of Aging and Mortality in
Multicellular Organisms. Ph.D. Thesis, Michigan State University.
(1974).

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

77

Weibull, W. Investigations into Strength Properties of Brittle
Materials. Proc. the Roy. Swedish Inst. for Engr. Res. Nr. 149.
(1938).

 

Detraglia, M. et al. Erythrocyte Fragility in Aging. Biochem.
Biophy. Acta 345 (1974) 213.

 

Rakow A. & Hochmuth R. Effect of Heat Treatment on the Elasticity
of Human Erythrocyte Membrane. Biophy. J. 15, (1975) 1095.

 

Kuiper, P. et al. Changes in Lipid Composition and Osmotic
Fragility of Erythrocytes of Hamster Induced by Heat Exposure.
Biochem. Biophys. Acta. 248 (1971) 300.

 

Danon, Y. et al. The Effect of Heat on Red Cells of Incubated
Human Blood. Israel J. Med. Sci. 8 (1972) 111.

 

Rahman, Y.E. et al. Studies on the Mechanism of Erythrocyte

Aging and Destruction. I Separation of Rat Erythrocytes According
to Age by Ficoll Gradient Centrifugation. Mech. Age. Dev. 2
(1973) 141.

 

Shortman, K. Australian J. Exprl. Biol. Med. Sci. 44 (1966) 271.

 

Bock, R. and Ling, N. Devices for Gradient Elution in Chromoto-
graphy. Analyt. Chem. 26 (1954) 1543.

 

Walter, H. and Selby, F. Counter-Current Distribution of Red Blood
Cells of Slightly Different Ages. Biochem. Biophys. Acta. 112
(1966) 146.

 

Johnson, H. Thermal Noise in Cells. Am. J. Path. 69 (1972) 119.

 

Cox, D.R., Renewal Theory, Methuen & Co. Ltd. London, 1967.

 

Bird, G.W.G. The Red Cell, Brit. Med. J. l (1972) 293.

 

"IIIIIIIIIIIIIIIIIIIIIIIII“