QUANTITATIVE LAWS
IN
BIOLOGICAL CHEMISTRY
QUANTITATIVE LAWS
IN
BIOLOGICAL CHEMISTRY
BY
SVANTE ARRHENIUS
Ph.D., M.D., LL.D., F.R.S.
NOBEL LAUREATE
DIRECTOR OF THE NOBEL INSTITUTE OF PHYSICAL CHEMISTRY
LONDON
G. BELL AND SONS, Ltd.
1915
PREFACE
The development of chemical science in the last
thirty years shows a steadily increasing tendency to
elucidate the nature and reactions of substances pro-
duced by living organisms. The problem has been
attacked in two different ways, firstly, by the aid of
the highly developed synthetic methods of organic
chemistry — it will be enough to mention the brilliant
work of Emil Fischer, Kossel, and their pupils —
and secondly, by the powerful technical means
afforded by the modern development of physical
chemistry. The studies founded on the methods of
organic chemistry aim at investigating the structural
composition of the molecules of the chief products of
organic origin and subsequently building them up
synthetically. The physico-chemical methods, on
the other hand, give an insight into the nature of the
chemical processes which play an important role in
the living world. The work of organic chemists in
this region has been generally recognized as being
of high scientific interest, but the same cannot be
said regarding the work of physical chemists in the
domain of physiological chemistry. It may be
enough to cite one of the least aggressive utterances,
vi BIOLOGICAL CHEMISTRY
namely that of Friedemann in the Handbuch der
Hygiene (3rd vol. 1st part, p. 777, 19 13). " The one-
sided (ausschliesslick) interest which has been
directed to this problem ' (the neutralization of
antigens and antibodies) " is not justified by its
biological importance." Yet I am convinced that
biological chemistry cannot develop into a real
science without the aid of the exact methods offered
by physical chemistry. The aversion shown by bio-
chemists, who have in most cases a medical education,
to exact methods is very easily understood. They
are not acquainted with such elementary notions as
" experimental errors," "probable errors," and so
forth, which are necessary for drawing valid con-
clusions from experiments. The physical chemists
have found that the biochemical theories, which are
still accepted in medical circles, are founded on an
absolutely unreliable basis and must be replaced by
other notions agreeing with the fundamental laws of
general chemistry.
I was very glad to find on my last visit to
England that interest in an exact treatment of bio-
chemistry is rapidly growing, and therefore I received
with great satisfaction the proposal of Messrs. G.
Bell & Sons to publish a book founded on the
Tyndall lectures given by me in the Royal Institu-
tion in May 19 14. They contain a short resume of
my own work in this field, supplemented by the in-
vestigations of others on neighbouring ground.
The reader who wishes to consult the literature
of the subject will find references in :
PREFACE vii
S. Arrhenius : Immunochemistry, New York, 1907,
The Macmillan Co.
" Anwendungen der physikalischen Chemie in
der Immunitatslehre," Zeitschrift fiir Chemo-
therapie, vol. 3, p. 157, 1914.
Hoppe - Seylers Zeitschrift fiir physiologische
Chemie, vol. 63, p. 324, 1909.
Memoirs published in Meddelanden frdn K.
Svenska Vetenskapsakademiens Nobelinstitut,
vols. 1 and 2.
Harriette Chick: " The Factors conditioning the
Velocity of Disinfection," Eighth Inter-
national Congress of Applied Chemistry, vol.
26, p. 167, 1912.
Harriette Chick and Martin : Memoirs published
in Journal of Physiology, vols. 40, 43, and
45, 1910-1912.
Madsen and his pupils : Memoirs in the Communi-
cations de rinstihit sdrothdrapique de I 'Etat
danois, 1907-19 13.
In the hope that this little book will evoke
interest for the new discipline and stimulate con-
tinued work, I lay the results of my efforts before
the benevolent public.
I must also express my thanks to Dr. E. N. da C.
Andrade for his valuable assistance in the prepara-
tion of this monograph.
SVANTE ARRHENIUS.
Stockholm, May 191 5.
CONTENTS
CHAPTER I
TAGE
Introduction ...... i
Necessity of quantitative methods. Material treated.
Use of the physico-chemical methods. Graphical
methods. Enzymes. Toxins. Antibodies. Specificity.
CHAPTER II
Velocity of Reactions . . . . 19
Historical remarks regarding biochemistry. Reactions
in vivo and in vitro. Spontaneous decompositions.
Coagulation. Disturbing influences. Inversion of cane-
sugar by invertase. Influence of acids and bases. In-
fluence of concentration. The rule of Schiitz and its
generalization. The ^/-law.
CHAPTER III
The Influence of Temperature on the Velocity
of Reactions. Reactions of Cells . . 49
General law, approximate expression of it. Spon-
taneous decompositions. Destruction of cells at high
temperature. Table of /x-values. Optimum tempera-
tures. Fermentation by yeast cells. Haemolysis of red
blood-corpuscles. Agglutination of bacteria. Killing of
micro-organisms. Different sensibilities. Theoretical
explanation.
IX
/ ? 1 0/
BIOLOGICAL CHEMISTRY
CHAPTER IV
PAGE
The Quantitative Laws of Digestion and Re-
sorption . . . . . .81
The school of Pawlow. Khigine's, Lonnquist's, and
London's experiments on digestion of different food-
stuffs. The square-root rule. Secretion of pancreatic
juice (Dolinsky). Digestion of small quantities calcu-
lated as a monomolecular process. Digestion and
resorption of carbohydrates. Secretion of enteric juice
(London and Sandberg).
CHAPTER V
Chemical Equilibria . . . . -99
Equilibria in enzymatic processes. Taylor's, Robin-
son's, and Gay's experiments. Maltose and isomaltose,
lactose and isolactose. Partition of substances between
two phases. Agglutinins and amboceptors. Adsorp-
tion. Neutralization of toxins by their antibodies.
Ehrlich's experiments. Diphtheria poison. Neutraliza-
tion of strong bases by acids. Cobra poison.
Neutralization of ammonia by boracic acid. "Poison
spectra." Tetanolysin. Prototoxoids. Toxons. Syn-
toxoids. Danysz's phenomenon. Neutralization of
monochloracetic acid. The supposed plurality of toxins.
Compound haemolysins. Complement and amboceptor.
Equilibrium between haemolysin, amboceptor, and
complement. Influence of the relationship of the
animals, which have delivered the erythrocytes and
the amboceptor. Isolysins. Lecithin as "sensitizer."
Precipitins. Blood relationship. Equilibrium between
precipitate, precipitin, and precipitinogen. Calculation
of Hamburger's measurements. The relationship between
sheep, goat, and ox. Agglutinins. Diversion of com-
plement. Wassermann's reaction.
CONTENTS
XI
CHAPTER VI
Immunization
Passive immunization. Influence of the method of
injection. Experiments of Bomstein, von Dungern,
and Bulloch. Rapid decrease and subsequent regular
monomolecular decrease. Influence of relationship.
Passive immunization with typhoid agglutinin. Fate of
red blood-corpuscles in a non-related animal. Time of
incubation. Vaccination. Negative phase. Active
immunization. Rapid increase of the antitoxin content
proceeding uniformly with time. Madsen's and
Jorgensen's experiments on active immunization with
cholera and typhoid bacilli. Antibodies in the blood of
patients after a bacterial disease. Persistent immunity.
TAGE
140
INDEX
161
ZJ
f
CHAPTER I
INTRODUCTION
The content of this little book is founded on three
Tyndall Lectures, given in the Royal Institution,
London, on the 14th, 21st, and 28th of May 1914.
The aim of these lectures was to give a short
review of the new chapters in Biochemistry in
which quantitative measurements have been carried
out, and subsequently discussed at some length from
the points of view adopted in Physical Chemistry.
As long as only qualitative methods are used in a
branch of Science, this cannot rise to a higher stage
than the descriptive one. Our knowledge is then
very limited, although it may be very useful. This
was the position of Chemistry in the alchemistic
and phlogistic time before Dalton had intro-
duced and Berzelius carried through the atomic
theory, according to which the quantitative com-
position of chemical compounds might be determined,
and before Lavoisier had proved the quantitative
constancy of mass. It must be confessed that no
real chemical science in the modern sense of the
word existed before quantitative measurements
B
2 INTRODUCTION
were introduced. Chemistry at that time con-
sisted of a large number of descriptions of known
substances and their use in the daily life, their
occurrence and their preparation in accordance with
the most reliable receipts, given by the foremost
masters of the hermetic {i.e. occult) art.
In the same manner Biochemistry up to a quite
recent time consisted of a great number of descrip-
tions of different products accompanying living
organisms, their properties, use, and their composi-
tion, i.e. their content of hydrogen, oxygen, nitrogen,
sulphur, phosphorus or perhaps other elementary
substances. If possible this composition was ex-
pressed by means of a chemical formula.
But even the quantitative element which is con-
tained in an analysis of the composition of a sub-
stance was lacking in cases where the substances
investigated occur in such small proportions that it is
not possible to isolate them in a pure form. We have
no other possibility of describing these substances
than by indication of their occurrence and mode
of preparation in the most concentrated and purest
possible form, with an indication of their character-
istic properties, unless we employ methods other
than those belonging to the old classical science
of Chemistry. Only by the use of the methods
introduced by the modern physical chemistry is it
possible to form an opinion of the manner in which
these substances react, and thereby to get a clear
scientific idea of their nature. The fundamental
fact must here be recalled that these substances
INTRODUCTION 3
are in many cases so unstable, that their solutions
do not permit a heating to 6o° C, that they are in
most cases rapidly destroyed by acids or bases, and
that if one tries to free them from accompanying
albuminous substances by precipitating these,
they are often carried down with the precipitate.
Common chemical methods are therefore of a
very limited value. On the other hand, physical
chemistry allows us to follow quantitatively the
influence of temperature and of foreign substances
upon these interesting organic products, which are
of the greatest importance in industry, in the
physiological processes of daily life, and in diseases
and their therapy.
The quantitative relations between the properties
of these substances and their concentration, temper-
ature, and the concentration of substances exerting
an influence upon them are given by mathematical
formulae. These formulae give a concise descrip-
tion of the phenomenon investigated. From their
form it is in most cases possible to understand the
mode of action of the temperature, concentration,
and of foreign substances, which is the aim of our
investigations. A knowledge of the differences
between the magnitude of the observed quantities
and the corresponding calculated values is useful
in a twofold manner. On the one hand, it allows
us to determine the probable value of the experi-
mental errors and thereby to improve the methods
of investigation. Amongst different methods in
which the experimental conditions are changed we
4 INTRODUCTION
have to choose those which give the smallest values
of the probable errors. In this manner the ex-
actitude of our scientific methods are improved, and
thereby the accuracy of our conclusions. On the
other hand, the experimental laws found and ex-
pressed by our formulae very often are true only for
a limited region of the field examined. By means
of the deviations between the calculated and the
observed values it is possible to form an idea of
the cause of the said deviations — which in this
case ought to exceed the experimental errors — and
thereby to find new laws of a wider application than
the old ones, and even to discover new, i.e. pre-
viously unknown phenomena.
In the following pages I have made extensive
use of a graphical illustration of the mathematical
formulae, representing the laws accepted, as com-
pared with the observed data, marked by crosses
or points. Now there is only one line, for deviations
from which the eye is extremely sensible, so that
it may be used to prove the corresponding law
with a great strictness, and this line is the straight
one. If now a variable quantity y is dependent
upon another quantity x, which we may change as
we wish, for instance temperature or concentration,
so that the formula expressing this dependency
possesses the form
y = a + bx,
where a and b are two experimentally determined
constant values, then the graphical interpretation
INTRODUCTION 5
of this formula is a straight line (Fig. i). Here a
is the value of y, when x = o> i.e. the distance of
the point, in which the straight line cuts the axis
of ordinates, from the axis of abscissae — in Fig. i
#=1-5. If we put x = 1, then y = a + 6, i.e. b is the
distance of the point in which the straight line
y = a + bx cuts a vertical line x = 1 going through
the point 1 of the ^r-axis, from a horizontal line
*
1
0
0
J?
^
}b
1
\
^
3 -2
►
c
1 1
1
; j
\ X
Fig. 1.
y = a running at a distance a above the ;r-axis.
In Fig. 1, ^ = 0-5.
But in most cases this very simple formula does
not represent the phenomenon which we wish to
describe. For instance, if a substance such as
sulphuric acid acts upon cane-sugar, this is trans-
formed into glucose and fructose in such a manner
that if we call the initial quantity of sugar 100, then
after a certain time / (say, one hour) only the quantity
80 remains unchanged ; after the time 2t (2 hours)
6 INTRODUCTION
only 80 per cent of 80, i.e. the quantity 64 per cent,
remains ; after the time 3/ (3 hours) 80 per cent of 64,
i.e. the quantity 51-2, remains of the sugar; after the
time \t (4 hours) 80 per cent of 51-2, i.e. the quantity
40- 96, and so forth. We say then that when time
increases in an arithmetic series, the quantity of
cane-sugar decreases in a geometric series. If the
quantity of cane-sugar is called z and the quantity
at the beginning of the experiment z0 (we have in
this case put z0 = 100), then the said law regarding
the progress of the inversion of the cane-sugar with
time, t, is expressed by means of the formula
log z0 — log z = bt.
For the time ^ = 0, i.e. when the sulphuric acid
is added to the solution of cane-sugar we have
log z0 = \og 2, i.e. z = z0= 100.
Now if we translate the said law into a graphical
expression, we get the ^-curve as a function of the
time t (Fig. 2, the lower curve). This ^-curve is a
so-called exponential curve. Even to an eye ac-
customed to curves it is rather difficult to distinguish
this exponential ^-curve from another curve indicat-
ing a regular decrease of the quantity of cane-sugar,
2, with increasing time, /. The curve does not tell
us very much in its general character ; only if we
measure special points on it, and determine cor-
responding values of z and t, do we get a real
representation of the meaning of the curve. In
this case a table giving the comparison of calculated
INTRODUCTION 7
figures with observed ones is of a greater use and
clearness.
But we can proceed more simply by putting
y = log z, i.e. plotting log ^ as a function of t, in
which case we get a straight line (the continuous
line in Fig. 2), beginning at the point ^/0 = log20 =
log 100= 2 and cutting the ^f-axis in the point log z
Fig. 2.
= 0, i.e. z= 1, and 2-o = bt0, i.e. t0=2/b (in Fig. 2
4=206, 4 lies so far to ^ right that it does not
appear in the figure). Here the value of b is
very simple, namely, b = 2JtQ, b is the so-called
velocity of reaction, it is equal to 2 divided by the
time in which the quantity of cane-sugar has sunk
to one per cent of its original value. Evidently
the shorter the time for decomposing 99 per cent
8 INTRODUCTION
of the cane-sugar, the greater is the velocity of
reaction.1
In this case we get immediately, by means of the
log £-curve, a general view of the progress of the
reaction, and we see at once how well the law,
represented graphically, agrees with experience (the
dots in Fig. 2 represent some experiments of Wil-
helmy carried out in 1850 ; the unit of time is here
72 min.). Another example we find in the repre-
sentation of Schutz's rule, which says that at constant
temperature the digestion of egg-albumen by the
aid of pepsin proceeds so that if the quantity a is
digested in one hour, it takes four hours to digest
the double quantity 2a, nine hours for the threefold
quantity 3^, sixteen hours for the fourfold quantity
4#, and in general n" hours for digesting the ^-fold
quantity na. If we take the time, counted from the
beginning of the experiment as abscissa, and the
digested quantity y as ordinate, we get a curve (a
parabola) expressing that the square of y is pro-
portional to time, i.e. y2 = art. This curve does not
give a good representation to the eye. To begin
with, it rises extremely rapidly — its tangent is vertical
in the point t — oy then it increases more slowly,
and at higher values of t so slowly that it seems
to reach a certain maximum value asymptotically,
which is not true. But if instead of plotting jy as a
1 It would be more exact to use natural logarithms instead of the common
ones. With natural logarithms the value of b (the velocity of reaction) is
2-3 times greater than with common logarithms, which are still generally
used on account of their convenience. In the following we always use common
logarithms.
INTRODUCTION 9
function of t, we plot y2 as a function of t, then the
j^-curve is a straight line, running through the
origin, y = o, t = o, and we easily see that the y2-
value does not approach to a limit. In this case we
might just as well have tabulated jj/asa function of
the square root of t,y = ad~t and have obtained a
straight line. In the figure 7 representing Schutz's
rule, some experiments of E. Schutz are indicated
by points. Here the quantity x digested in a given
time is represented as a function of the square root,
s/q, of the quantity, q, of pepsin used for the
digestion.
In general if we have a formula expressing a
connection between two quantities of which we
change the one u experimentally, while we observe
the corresponding magnitude of the other, zy which
formula may be
f(z) = K . P(u) + 6,
we shall always be able to illustrate this formula
graphically by a straight line by choosing y =f(z)
and x = p(u), for then we have the linear formula
y = K . x + b.
But in most cases it is preferred to plot z as a
function yjr(u) of u and to draw a curve through the
plotted points, indicating the values actually ob-
served by means of points or crosses. This
method is preferred as soon as the functions f(z)
or p{tt) are at all complicated, so that we are not
10 INTRODUCTION
acquainted with them and therefore lose sight of
the relation connecting z with ut which is, however,
presented to the eye by the curve representing
z = ^(u).
In some cases the function f(z) or p(u) within a
certain interval coincides very nearly with a function
which is familiar to us. Thus, for instance, when
we investigate the influence of temperature upon
the velocity of a reaction, we find that the velocity
of reaction, K, increases nearly in a geometrical pro-
gression, when the temperature, t, increases in an
arithmetical one. For small intervals of temperature
this rule is very nearly exactly true. Then we make
use of this circumstance, and as in Fig. 2 we plot
log K as a function of t. When, as below in Fig.
9, the observations fall within an interval of tem-
perature less than io° C, the deviation of the strict
formula from a linear equation is so small, that it
falls wholly within the errors of observation, and we
make use of the rectilinear representation. But if
the said interval exceeds io° C. the divergence
between the strict formula and a linear equation is ,
so great that we cannot use the straight line as a
true expression of the observed data, but make use
of the representation of the strict formula. But even
in this case we use log K, and not K itself, for the
representation, because the curve then has a nearly
rectilinear form, that is, its curvature is very in-
significant, and the smaller the curvature is, the
clearer is the representation given by the curve
to the eye, and correspondingly, the easier it is
INTRODUCTION 11
to use the curve for finding values by means of
interpolation.
Therefore in all the curves which represent the
velocity of reaction as dependent on temperature, I
have taken as the ordinate y = log K, and when the
interval of temperature was relatively great, I have
drawn the curve giving the exact equation (see
Fig. 10). Something similar has been done when
the progress of digestion with time (cf. Fig. 8) has
been graphically represented. In this case the
square root of the time, J~t, has been chosen as
abscissa. If the rule of Schutz were absolutely
strict the representative curves, giving the digested
quantity as ordinate, ought to be straight lines. But
this is only approximately true ; it holds only for
small values of the time t. This is easily verified
by the eye if we follow the curve representing the
exact formula, and drawn in the figure, down to
values in the neighbourhood of the origin.
In the diagrams, indicating the change of the
velocity of reaction, K, with temperature, I have
drawn many lines representing different substances.
This has been done in order to save space and also
to give a more general view of the phenomenon re-
presented. But this concise representation has only
been possible by changing the origin. This is
indicated for each curve by a formula expressing how
many centigrade degrees of temperature have to be
added to that given by the abscissa, in order that
the figures may represent the observations. In one
case the scale is reduced to the half magnitude, which
12 INTRODUCTION
is indicated by putting^ = 2y and T = a + 2x (see Fig.
9, coagulation of haemoglobin). In the next figure
other reductions of the scale have been introduced
which are easily seen from the indications.
In some cases the differences between observed
and calculated values are so small that they cannot
be represented in diagrams if these are not given on
a very large scale. Under such circumstances it is
preferable to give the values observed side by side
with those calculated.
• •••••
Before we consider the laws governing the re-
actions of the substances treated below, which have
not been prepared in a pure state, it will be worth
while to recall their general properties in order
that we may be familiar with them and understand
why so much work has been done on their examina-
tion. It is quite clear that if these substances did
not exert some very obvious and important actions,
they would probably have escaped our observation.
In reality these substances, products of animal pr
vegetal bodies, are found to govern the chemical
processes going on in living bodies. The most
important for animal life are the juices secreted by
the digestive tract. To begin with, the salivary
glands give a juice containing ptyalin, which trans-
forms the insoluble starch of the food into the
soluble sugar maltose. Then glands in the walls of
the stomach secrete the stomachical juice, which con-
tains two active substances, the pepsin, which decom-
poses the albuminous substances of the food into
INTRODUCTION 13
albumoses and peptones, and even coagulates the
casein of milk, and a lipase, i.e. an enzyme decom-
posing fats — in this special case the fats of the milk
are chiefly attacked — into glycerol and fatty acids.
On its way through the intestine the food subse-
quently comes into contact with the pancreatic juice,
containing new enzymes, the trypsin, which decom-
poses the albuminous substances still further —
namely, to amino-acids — than thepepsin, and further
a lipase, decomposing all kinds of fats, and another
enzyme, maltase, which decomposes one molecule of
maltose into two molecules of ^-glucose, whereby
one molecule of water is also taken up. The enteric
juice, with which the food later on is mixed, contains
the enzymes invertase, lactase, and maltase, which
break down the molecules of cane-sugar, milk-sugar,
and maltose into hexoses of simpler composition, and
a very active proteolytic ferment, erepsin, which
decomposes peptones into amino-acids. When the
food-stuffs have been decomposed into their simple
compounds — amino-acids for the proteids, glycerol
and fatty acids for the fats, and hexoses for the
starches and sugars — they are taken up by the
animal body and, by means of new ferments, partly
built up to living substances contained in the
different tissues, partly burnt down or otherwise de-
composed to give the heat necessary to sustain the
temperature of the body or to supply it with energy
for doing work. Cellulose, which enters into the
food of a great number of animals, is partially
rendered useful to these by the aid of micro-organisms
14 INTRODUCTION
introduced by the food or growing in the digestive
tract, and secreting special enzymes.
In the vegetable kingdom, the chlorophyll acts
as an enzyme in the production of carbohydrates
from carbonic acid and water. But chlorophyll
occurs in such large quantities that it has been
possible to subject it to ordinary chemical analysis
(cf. the work of Willstatter and others), and there-
fore it does not belong to the substances with which
we deal in this book. But the vegetable kingdom
produces and uses ferments or enzymes of the same
action as those known from the animal kingdom.
Well known are the very active lipase contained in
castor beans, the proteolytic ferment papayotin from
Carica Papaya, and another proteolytic ferment in
growing seedlings of barley. Further, we know a
great number of katalases, oxydases, and reductases
both from the animal and from the vegetable
kingdom. Of high importance are the enzymes
furnished by the yeast-cells, namely, zymase, which
causes alcoholic fermentation ; invertase, which de-
composes cane - sugar ; and maltase, which splits up
maltose.
In general, micro-organisms produce a large
number of substances of high chemical activity.
Amongst these a great many are of the highest
interest for us, as, for instance, the diphtheria toxin or
the tetanus -poison, which cause the terrible diseases
diphtheria and lock-jaw. Even higher organisms,
as snakes or spiders or insects, produce similar
poisons, as do also some plants, e.g. Abrus praeca-
INTRODUCTION 15
tortus, Ricinus, etc. In general it may be said that
the diseases caused by pathogenic bacteria are
caused not so much by the bacteria themselves as
by the products secreted during their lifetime or set
free after their death.
The human or animal body possesses means of
combating the action of these poisons. If they are
injected into the body, or even if the bacteria them-
selves are injected, the blood after some time con-
tains substances which neutralize the poisons or
act upon the bacteria. Such substances are called
antibodies, whereas the injected poisons or bacteria
are called antigens, i.e. bodies which cause the forma-
tion of antibodies. Later it has been found that
the injection into an animal of albuminous substances,
e.g. milk or egg-white, or serum or corpuscles from
the blood of non-related animals, which seem to be
comparatively harmless for the animal, causes the
production of antibodies. The antigens and the
antibodies are of extreme importance for the welfare
of man, and they have therefore been the object of
very extensive studies, mostly only of a qualitative,
but in recent time also of a quantitative character.
The antibodies are divided into different groups,
according to their mode of action on the antigens,
as lysins (bacteriolysins, which cause the destruction
of the bacteria, or haemolysins, which let the haemo-
globin, the red colouring matter of the blood-cor-
puscles, go out into the surrounding fluid); precipitins,
which produce a precipitate with their antigens, agglu-
tinins, by the influence of which the antigens — in this
16 INTRODUCTION
case bacteria — are gathered together into lumps ;
and antitoxins, which neutralize the injected toxins.
These substances have been subjected to quantita-
tive studies, especially the haemolysins, which give
an easily measurable colorimetric reaction. Other
antibodies, such as opsonins and ant ianaphy lactogens,
have not yet been investigated in a manner adapted
to quantitative calculations. The agglutinins behave
very similarly to the precipitins, and are therefore
probably only a special kind of precipitins. The so-
called compound haemolysins and the bacteriolysins
also behave nearly in the same manner, except that
the action of the haemolysins is directed against red
blood - corpuscles, that of bacteriolysins against
bacteria.
After the injection of an antigen the serum
generally contains substances giving different actions
of this kind, e.g. an agglutinin and a lysin. Most
investigators regard these substances as different
from each other, and an enormous number of
different substances has in this manner been
recorded. On the other hand, it would be much
more simple to suppose that the same substance
may have many different reactions even on the
same substrate. Thus, for instance, mercuric
chloride agglutinates red blood-corpuscles in less
dilute solutions, but haemolyzes them in very dilute
solutions. Something similar is true of the acids ;
and in this case the presence of a trace of lecitin
hampers the agglutination, and aids the haemolysis.
The presence or absence of a seemingly indifferent
INTRODUCTION 17
substance may exert a great influence on the re-
action. Thus, for instance, agglutination of bacteria
does not occur in absence of salts and is also
prohibited by the presence of salts in higher
concentration. The first circumstance is analogous
to the sedimentation of suspended particles by
salts in solution, the second one is probably due
to the dissolution of the albuminous precipitate,
which causes the agglutination — strong solutions of
salts are good solvents for albuminous precipitates.
Even if we try to avoid new hypotheses regard-
ing the presence of a great number of antibodies
(or antigens) as much as possible, we find that
it is characteristic that every antigen has its
special antibody, which does not react with other
antigens. This so-called specificity is of the
greatest importance, for it is possible to discover
an antigen amongst an immense number of other
organic substances by means of its specific antibody.
The blood of different animals, the secretions of
different bacilli may in this manner be discriminated
from each other with perfect certainty. In this
case ordinary chemical analysis leaves us absolutely
helpless. It may therefore be maintained that this
new department of science opens for us an immense
new field of chemistry of the very highest import-
ance to mankind. This circumstance explains the
exceptional interest of the investigation of this field.
As has been said above, it is physical chemistry
which gives us the mighty instrument for these
investigations. This science itself has been greatly
c
18 INTRODUCTION
enriched by this work. For there is no part of
chemical science which offers such a variety of
examples illustrating the physico-chemical theories
as this new branch of chemistry which has been
called Immuno-chemistry.
CHAPTER II
VELOCITY OF REACTIONS
In the following pages we will treat one of those
problems which have been open to discussion ever
since the beginnings of science. Our special
question is, if living matter obeys the same funda-
mental quantitative laws as those which govern
the reactions of inanimate matter. In other words,
we will look upon the problem of vitalism from a
chemical standpoint. We will limit this investiga-
tion to such laws as are expressed by formulae,
giving the relations between quantities dependent
the one on the other. It is chiefly with laws of
this kind that we are concerned in exact science.
After the discovery of relationships in biological
chemistry, of which we do not know an analogy
in general chemistry, it was naturally maintained
that the general laws are different in these two
domains, and the physiologists have generally had
a tendency in this direction. But a still better
method of working is to seek for an analogy in
general chemistry. If this has been found, it is
in most cases much easier to explain, and after
19
20 VELOCITY OF REACTIONS
a satisfactory explanation has been discovered, it
is natural to apply it to the corresponding bio-
chemical problem, which thereby becomes eluci-
dated. Now it has been found in so many cases
that the laws of general mechanics, those of the
indestructibility of matter and energy and those of
osmotic pressure, are absolutely as valid for living
as for dead matter, that many scientists regard it
as an evident truth that life is in reality only a
form of matter and motion. Therefore it is often
maintained that living matter has developed from
common matter, notwithstanding that no experi-
mental proof has been given for this assertion. It
was a great merit of Tyndall to show experi-
mentally that everywhere where life was observed
to grow up it was caused by germs originating from
living organisms.
It is necessary in this question to keep the
golden middle course, not to assert as self-evident
anything which has not been demonstrated, but
also not to deny the possibility of an agreement
between the laws in the two said domains before
a very earnest effort has been made to reconcile
them.
Biochemistry is of very ancient origin. In
reality we may count as biochemical a great many
of the experiments of the iatro-chemists, who sought
to apply chemical principles to the elucidation of
vital processes. Francis de la Boe Sylvius
discovered that the arterial blood differs from the
venous blood through its content of some of the
VELOCITY OF REACTIONS 21
constituents of air, which gave the arterial blood
its brilliant red colour. Van Helmont described
the carbonic acid, gas sylvestre, which is evolved
in the process of fermentation of wine or beer.
In his famous work, Experiments and Observations
on different Kinds of Air, Priestley described
the action of plants on air deteriorated through the
respiration of animals. He showed that the green
parts of the plants in sunlight decompose carbonic
acid and give off oxygen to the air. In this
way the plants and the animals counteract each
other and help to keep the composition of the air
unchanged. This problem attracted, by its great
practical importance, the chief interest of bio-
chemists for a long time. The most important
investigations in this chapter we owe to Senebier
and Ingenhouss in the eighteenth century, to de
Saussure, Dumas, Liebig, Daubeny, Draper,
Sachs, Baeyer, Pfeffer, Engelmann, and Prings-
heim in the nineteenth century. Baeyer ex-
pounded the prevailing theory that the plant
products from carbonic acid and water are oxygen
and formaldehyde, which through polymerisation
gives the different carbohydrates, such as sugar
or starch or even cellulose. In recent time Daniel
Berthelot, Stoklasa, and others have succeeded
in carrying this process through without the help
of green plants by means of ultra-violet light.
In an analogous manner Duclaux imitated the
chief fermentation process, by which alcohol is pro-
duced from sugar by the agency of yeast-cells, by
22 VELOCITY OF REACTIONS
letting ultra-violet light act upon glucose in the
presence of bases, such as caustic soda, ammonia or
lime water.
Before the nineteenth century it was believed
that some products of animals or plants could not
be prepared without the interaction of life-processes.
Wohler in 1828 was the first to break down this
belief, when he prepared urea from ammonium-
cyanate. The synthesis of alizarin by Graebe and
Liebermann (1869), ofindigo by Baeyer (1878), and
still more of the fats by P£louze and G£lis (1843)
and Berthelot (1854), and of the different sugars
by Emil Fischer (1890), who has even succeeded
in building up polypeptides, giving the reactions
of albuminous substances, and a multitude of other
syntheses, have completed this work in the most
striking manner. It is now generally recognized
that the synthesis of organic products from inorganic
matter will always be possible if we devote sufficient
work to the solution of this question, and even that
the tools of the chemist surpass the living organism
in multiplicity of effects. Ultra-violet light and the
silent discharge of electricity are in this special case
very mighty factors. The enormous success in this
domain has created the conviction that we are
complete masters of these problems, and that in
the course of time we shall be able to prepare
synthetically any product of Nature, living or
inanimated.
But a given compound may be produced in
many different ways, and it is therefore very possible
VELOCITY OF REACTIONS 23
that the method of working in the organism differs
from that used in the chemical laboratory. This
question is of a much more recent date than that
mentioned above, because the progress of chemical
processes has not been thoroughly investigated
before the last great development of physical
chemistry. Therefore our chief task will be to see
if the physico-chemical laws regarding the progress
of chemical processes in general chemistry are also
applicable to biochemical processes, and we shall
especially try to elucidate such biochemical processes
as have been considered exceptions from known
physico-chemical laws.
In this case we have not only to regard the
processes going on in the living organism, for these
are in most cases verydifficult to examine thoroughly,
but also to investigate chemical processes, char-
acteristic of organic products which react upon each
other outside of the living body, or, as it is called,
"in vitro" (in a glass vessel). As far as is known,
biochemical processes develop in the same manner
in the living body, "in vivo," as "in vitro' if the
same reagents are used under the same circum-
stances. Without the aid of experiments " in vitro '
we should really know very little of the much less
accessible reactions " in vivo." The characteristic
feature of these reactions is that they are bound up
with the action of certain organic products, which
have not so far been produced synthetically, because
they occur in such small proportions, and are so
difficult to isolate from other organic products, that
24 VELOCITY OF REACTIONS
we do not know their composition and therefore are>
so far, unable to prepare them. These organic
products have been characterized above.
In most cases these substances are very unstable*
so that they are rapidly decomposed, especially at
higher temperatures* This spontaneous decomposi-
tion has often been regarded as characteristic of these
substances, but closer investigation indicates, as we
will see below, that they behave just in the same
manner in their reactions as do well - defined
substances known from the general chemistry.
Even from inorganic chemistry we know a great
number of products which are stable only at low
temperatures.
As regards the progress with time of this decom-
position it behaves precisely as an ordinary mono-
molecular reaction, as the following figures and
diagrams indicate. They give the rate of destruction
of tetanolysin at 49-8° C. and of a haemolytic anti-
body, found in the serum of a goat after injection of
blood-corpuscles from a rabbit, at 51° C. The law
of monomolecular reactions states that the curves
representing the logarithm of the quantity of the
substance in decomposition, e.g. the tetanolysin or
the haemolytic antibody, as a function of time, is a
straight line (cf. p. 6).
VELOCITY OF REACTIONS
25
Decomposition of Tetanolysin at 49-8° C.
Time in nuns.
Quantity q of Lysin.
t
obs.
calc.
2
IOO
IOO
20
80
8c6
40
6i-i
64.8
60
52-i
52-3
SO
46-3
42-1
I20
26-8
26-7
l8o
17-6
14-3
K = 0-00474
Decomposition of a Haemolysin at 510 C
Time in mins.
Quantity q of Haemolysin*
*
obs.
calc.
O
IOO
IOO
5
74»3
73*4
10 58-3
62.5
15 48-8
53-3
20 44-9
45'4
25 40-0
38-7
30 33-7
33-o
35 28-4
28-1
40 25-2
24-0
K = 0-0154
The curves (Fig. 3) are evidently very nearly
straight lines. This is especially clear for the decom-
position of tetanolysin. The differences between
the observed and the calculated values fall well
within the errors of observation. On the curves
we see that the logarithm of the quantity of haemo-
lysin reaches the value 1-4 in 37 minutes, whereas
the corresponding line for the tetanolysin needs 130
minutes for the same purpose. From that we
conclude that the velocity of decomposition of the
haemolysin (at 51° C.) is 130 : 37 = 3-5 times greater
than that for tetanolysin (at 49-8° C). In this
manner the constant of the velocity of reaction K
is determined.
An analogous case has been investigated by Miss
Chick and Dr. Martin, who determined the rate of
coagulation of haemoglobin and of egg- albumen.
The quantity of protein present in the solution at
a certain time was determined by taking out a small
part of the solution and coagulating it at iooc C.
26
VELOCITY OF REACTIONS
The quantity was measured simply by measuring
the intensity of colour or by weighing the coagulate.
The curves are very nearly straight lines, as is seen
from the diagram, Fig. 4. The coagulation depends
upon a decomposition of the protein. As water
20 40
60 80 100 120
Time in minutes — 3
Fig. 3.
140 160 180
seems necessary for it, it is probably connected
with hydration.
The experiment succeeded at once with haemo-
globin at 70-4° C. The constant was K = oi45.
But with the egg-albumen the investigation gave
at first very irregular results. The rate of decom-
position diminished very rapidly as the coagula-
VELOCITY OF REACTIONS
27
tion process went on. Now it was known from
experiments of different authors that the reaction
of the solution becomes more and more basic
with time during the coagulation, and it was also
known that in many cases the velocity of reaction
20
18
16
£»I4
c
o |2
o
10
0-8
\9*
\
%
8
10
Time in minutes — ►
Fig. 4.
depends in a high degree on the acidity or alkalinity
of the solution. Therefore instead of asserting that
the reaction does not follow the laws known from
general chemistry, as has been done in many similar
cases before, Miss Chick and Dr. Martin tried
if the rate of coagulation was constant at a constant
degree of acidity. This was attained by adding
28 VELOCITY OF REACTIONS
boracic acid to saturation. In this manner these
investigators found the regular values reproduced
in the diagram. In an analogous manner they
obtained regular results by adding powder of
magnesium oxide.
This example is very characteristic and indicates
the special difficulties in experiments with organic
matter. The molecular weight of the organic
preparations is in general very high, so that there
are relatively few molecules present in the solutions
used. These preparations react with other substances
present, such as salts, and especially with acids and
bases. Even when the concentration of these sub-
stances is very low, the number of their molecules
is of the same order of magnitude as that of the
organic molecules, so that these may for a great
part be transformed and give quite unexpected
reactions. Very often the preparations are taken
from a bouillon-culture, which has an alkaline re-
action. In this case the rate of decomposition
generally increases with the alkalinity. Therefore
in such a case, which was investigated by Madsen,
namely, that of the spontaneous decomposition of
a specimen of vibriolysin, the constant of reaction
was double as great for the original solution as for
this solution diluted to half its strength. The alkali
present had been diluted at the same time as the
solution of the lysin.
A very interesting case of this kind has been
observed by Miss Chick and Dr. Martin, when
they examined the coagulation of egg-white (in acid
VELOCITY OF REACTIONS 29
solution). The quantity coagulated in unit time is
proportional to the quantity of egg-white in solution
and, further, nearly proportional to the acidity of
the solution. Now the quantity of acid diminishes
when the egg-white becomes coagulated. Within
certain limits the quantity of acid is nearly pro-
portional to the quantity of egg-white remaining in
the solution during the process. It therefore looks
as if the quantity coagulated in unit time should be
proportional to the square of the concentration of
the egg-white, which is characteristic of a so-called
bimolecular chemical process. If the acidity is
kept constant the process is, as we have seen
above, monomolecular, i.e. the logarithm of the
concentration is a linear function of time.
Even the diluting water itself may interact with
the preparation. It is well known that in most
cases the preparations of organic origin resist de-
composition much better when in a dried state than
when dissolved. On this ground the anti-diphtheric
serum used for standardizing diphtheria-poison is
dried with phosphoric anhydride in a vacuum and
also kept at a low temperature. Very instructive
in this respect are the experiments of Madsen and
Walbum regarding the stability of different solutions
of rennet.
They found the following reaction constants K
at 46-15° C. for different concentrations :
Concentration 7 5 3 2 1 0-25 0-125 0-063
Rate of Decom-
position. . 0-0037 0*0049 0-0154 0-021 0-028 0-039 0-o6o 0-073
30
VELOCITY OF REACTIONS
Dried rennet is extremely slowly decomposed at
that temperature. At 158° C. the constant is K =
004 1. This circumstance recalls the "denaturation"
of egg-albumen at high temperatures, for which also
the presence of water is necessary.
16
14
12
o
o
00 H
o
08
06
Xn
\ X
X N
X. s
*>
N
X
\\o
X. \
\ \
x \
\
\
X N
\_ \
Q \
\ vo
\ \
Q N
\
\
o\\
\\
\\
x
40
with Alkali Time
-without Alkali
80
120
160 min.
Fig. 5.
The enzymatic reaction which has been most
thoroughly investigated is that of invertase on cane-
sugar. The invertase was prepared from yeast-cells.
Victor Henri determined (1902) the velocity of in-
version of sugar with this enzyme and observed that
it behaves in a manner quite different from a mono-
molecular reaction. This experiment was controlled
VELOCITY OF REACTIONS
31
by Hudson, who observed that the glucose formed
during the beginning of the process shows the
phenomenon of mutarotation, and that its quantity
therefore cannot be determined immediately with the
aid of a polarimeter, as Henri had done. In order
to eliminate the mutarotation it is necessary to add
some trace of alkali before the polarimetric deter-
mination. This is made very evident by the
following figures of Hudson, and diagram, Fig. 5.
Time of Inversion
in Minutes.
Rotation at 30° C.
Calculated Velocity of Reaction
K . ioS at 30° C
Without Alkali.
With Alkali.
Without Alkali.
With Alkali.
O
30
60
90
I IO
I30
I50
27-50
16-85
IO-95
4-75
1-95
-o-55
- 2-20
-7-47
27-50
14-27
7-90
3-00
o-8o
- i-49
- 2-40
-7-47
396
399
464
482
511
522
558
530
539
534
559
533
As is easily seen from the figures and Fig. 5 the ex-
periments in which the mutarotation was eliminated
by addition of a trace of alkali give a fairly good
constant (mean value 542- io-5), whereas the figures in
the fourth column, representing the observed rotation
without addition of alkali, give a steadily increasing
value. As early as 1890 O'Sullivan and Tompson
had recognized the error caused through mutarota-
tion, and their measurements, which had fallen into
oblivion, have been verified by Hudson.
Not only the mutarotation exerts an influence on
32 VELOCITY OF REACTIONS
the velocity of reaction in this case, but also the
acidity of the solution, as is seen from the following
figures, borrowed from Sorensen. A series of ex-
periments was carried out with invertase and a small
addition of sulphuric acid at 30° C. As independent
variable is taken the hydrogen -ion concentration.
As is seen from those figures a very flat maximum
is obtained at the hydrogen concentration 000003/z.
Influence of Acidity on Velocity of Reaction.
Inversion of Cane- Sugar (at 30° C).
Cone, of H-ions . . 3-io~4 10-4 3-icr5 io~5 3>io~6 io~6 3-icr7
Vel. of Reaction -io4 . 77 82 83 81 78 73 64
Decomposition of Tetanolysin (at 500 C).
Normality NaOH . . . 0-02 o-oi 0-005 o-O-oi -0-02 : H2S04
Velocity of Reaction • 1 o4 . 112 97 85 47 71 435 *
Digestion by means of Pepsin (at 520 C).
Cone, of H-ions . . 017 io-1 6-io~2 2-io-2 5-io-3 8-io~5
Digested quantity/ 1 hour 8-5 9-3 . 12-3 75-2 15-0 io-8
in mgms. after 1 49 hours ... 30*3 ji'j 30*9 28-1 i6«i
50 per cent Decomposition of Hydrogen Peroxide with Colloidal
Platinum (at 250 C. ).
Cone, of NaOH . . o 0-002 o«oo8 0-031 0-125 0-25 0-5 i-o
Time in mins. . . 255 34 25 22 34 70 162 520
For comparison similar figures for three other
processes are given : the first concerns the influence
of bases (NaOH) or acids (H2S04, indicated by a —
sign) on the rate of decomposition of tetanolysin at
50° C, according to some measurements of my own.
The addition of small quantities of both bases and
of acids increases the decomposition in a marked
degree.
VELOCITY OF REACTIONS 33
The third example is borrowed from Sorensen,
and concerns the well-known influence of acids on
the peptic digestion at 5 2° C. The maximum occurs
at a concentration of the hydrogen-ions equal to about
001 normal, when the time of digestion is short
(1 hour). If this time increases, the maximum moves
to higher concentrations and lies at about 006 normal
for 49 hours.
In order to show that similar effects are known
from general chemistry, I have added an example
dealing with the decomposition of hydrogen peroxide
by means of colloidal platinum at 250 C, according
to measurements by Bredig and v. Berneck. Here
we find a maximum of the velocity of reaction or a
minimum of the time necessary to decompose 50 per
cent (the quantity tabulated) when sodium hydrate
is present to the concentration of about 0-02 normal.
If we investigate the influence of the concentra-
tion on the velocity of reaction we discover a new
discrepancy between these reactions and ordinary
monomolecular reactions. If we use sugar solutions
of moderate concentration (about 10 per cent) and
vary the concentration of the invertase, we find that
the reaction constant remains unchanged, i.e. the
quantity of sugar decomposed in unit of time is
proportional to the concentration of the enzyme.
But if we change the concentration of sugar, keeping
that of invertase constant, we arrive at quite different
results, as is seen from the following figures of
Henri, which indicate the number (n) of milli-
grammes of sugar inverted during the first minute,
D
34 VELOCITY OF REACTIONS
if the concentration of the sugar is ^-normal, c = i
indicates 342 grammes per litre.
<r = 0-OI 0-025 0-05 O-I 0-25 05 I 1*5 2
« = o»58 1-41 2-40 2-96 4*65 5-04 4-45 2-82 1-15
As will be seen from these figures, n is at first
nearly proportional to c, then it slowly reaches a very
flat maximum at c about = 0-5 normal, and subse-
quently falls at very high concentrations, at which
the solvent may be regarded as changed. Adrian
J. Brown has reached similar results.
In general chemistry we are accustomed to find
that the transformed quantity is proportional to the
concentration of the reacting substance, as is the
case in the figures above, when c does not exceed
0-03 normal or about 1 per cent. But this is not at
all true at higher concentrations. It has been found
that this peculiar effect is due to the formation of a
compound of the invertase with the sugar or its
products of decomposition. The compound, into
which the cane-sugar enters, is really the substance
subject to decomposition. With small quantities of
sugar (and not too insignificant quantities of enzyme)
the quantity of the compound is proportional to the
concentration of the sugar ; later on the said quantity
tends to a maximum, dependent on the quantity of
enzyme present. Therefore also the quantity of sugar
decomposed in one minute tends to reach a flat
maximum as is also indicated by the observations.
Michaelis and Menthen have investigated this
question very thoroughly, and found that all observa-
tions are in good agreement with the hypothesis here
VELOCITY OF REACTIONS
35
adopted. We may therefore say, that the observed
discrepancy from the general laws is more seeming
than real.
The compounds of enzyme and reacting substance
seem to play a very important role in this domain,
and there is still much work to be done in order to
elucidate the consequences of this circumstance.
Peculiarly enough some experiments of Madsen and
Teruuchi on the decomposition of vibriolysin by
means of animal charcoal give similar results, namely,
that the decomposed quantity (K.c) in unit of time
is nearly independent of the concentration of the
lysin, as is seen from the following figures obtained
at 12 »5° C. c is the concentration in arbitrary units,
K the velocity of reaction.
Concentration of
Lysin c.
K . i<A
Ke. 106.
OOI
704
704
0-02
375
750
0O4
219
876
0 06
143
858
0-08
105
840
O-IO
87
870
012
62
744
0-14
56
722
The velocity of reaction is nearly inversely pro-
portional to the concentration, so that the product
Kc, which is proportional to the quantity of lysin
decomposed in unit time, is nearly independent of
the concentration. At very small concentrations
we observe an increase of K with the concentration
36
VELOCITY OF REACTIONS
and thereafter a flat maximum. Every particle of
carbon decomposes a certain quantity of lysin in unit
time, independently of its concentration. Here it is
difficult to suppose that the carbon-particles enter
into compounds with the lysin. Probably the ex-
planation is that the decomposed lysin forms a
covering of the particles, and that this covering
1000
800
600
u
CO
O
400
200
002 004 0-06 008 01
Concentration of vibriolysin
Fig. 6.
0 2
014
diffuses away, giving place for new lysin-molecules
at a certain rate nearly independent of the concentra-
tion of the solution. The velocity of decomposition
is proportional to the number of carbon-particles,
which regularity is easily understood. Fig. 6 gives
a graphic representation of the value K^. io6.
The problem of this kind which has attracted
the greatest interest among biochemists is that of
digestion. As is natural, most experiments on that
VELOCITY OF REACTIONS
37
question have been made "in vitro." In 1885
E. Schutz added different amounts of pepsin to
solutions of a given quantity of egg-albumen. The
mixture was then diluted to 100 cc. and kept at
37-5° C. for sixteen hours. After this the albumen
was removed and the quantity of its product of
decomposition, peptone, determined polarimetrically.
Schutz found that this quantity x is proportional
to the square root of the quantity q of pepsin added.
His experiments were repeated by Julius Schutz
in 1900. He determined the quantity of peptone as
proportional to the quantity of nitrogen remaining
in the solution after coagulation of the albumen.
His results are seen from the following table :
<7-
1.
4-
471
426
9-
16.
25-
36.
io4 x (observed)
io4.r (calculated)
212
213
652
639
799
852
935
1065
1031
1278
As is seen from the diagram (Fig. 7) representing
the so-called " Schutz's rule," which says that the
action is proportional to the square root of the
quantity of enzyme, this rule is only approximative^
true. At higher values of q the digested quantity
x falls short of the one calculated in accordance
with the rule.
In 1895 Sjoqvist made a very elaborate in-
vestigation on peptic digestion. He varied both
the quantity of pepsin and the length of time.
The temperature was 370 C, i.e. that of the human
38
VELOCITY OF REACTIONS
body. In 100 cc, which were 0-05 normal with
reference to hydrochloric acid and contained 2-23
grammes of egg-albumen, he dissolved 2-5, 5, 10,
or 20 cc. of a pepsin preparation. He determined
the molecular electric conductivity of the solution
12
10
8
3 6
<o
"GO
■5
>»
5 4
c
re
y °
/ °
o /
D 2_3456
Vq"
Fig. 7.
which fell from an initial value of 188-4 units
(Siemens) to an end-value of about 83-4 units.
The change of conductivity was taken as a measure
of the quantity digested. In the accompanying
diagram (Fig. 8) the square root of the time from
the beginning of the experiment is taken as abscissa,
the change A of conductivity from the original
VELOCITY OF REACTIONS
39
value 1884 as ordinate. The curves drawn are
calculated by means of a formula given below.
The rule of Schutz is given by the tangent at the
origin to the curve ; it is represented by a broken
line and agrees with experiment till about 50 per
cent are digested.
100
80
60
t
20
-7
1
1
^ — '<.
)
$; A
/ 0
So
I/O .
1/ /
So
AQ/yl
3
0 2
! A
^ (
5_ (
J II
3
vr-
Fig. 8.
As is seen from the diagram, the observed values
indicated by circles lie below the theoretical curve
represented by the formula on p. 42 (the line
drawn) for high values of t and above it for low
values of t. The explanation of this behaviour
is obvious. It is supposed that every molecule
of the peptone, formed by the decomposition of
the albumen, binds an equivalent quantity of the
40
VELOCITY OF REACTIONS
hydrochloric acid present and thereby diminishes
the conductivity just as the addition of a base, e.g.
ammonia, would do. Now peptone is a so-called
amphoteric electrolyte, which acts both as an acid
and as a base. But its acid character is much
stronger than the basic one, which is extremely
weak. Therefore, the salts of peptone with acids
are hydrolysed in a very high degree. With a
great excess of acid (HC1), as for the parts of the
peptone first formed, the binding may be nearly
complete, but the salt of the last parts is highly
hydrolysed, and a great deal of them, and therefore
also of the acid, remains in a free state. Con-
sequently, the values of A are lower than those
given by the hypothesis on which the calculation
of the quantity of peptone formed is based. Even
the neutralization of the acid hampers the reaction
(cf. p. 32).
If we now compare the values of A for equal
values of qt in the four different series, we find that
A is equal in the four cases, as is seen from the
following table :
qt=
0-05
o-i
0-2
23-9
237
22.5
20-6
0-4
o-8
i-6 3-2
4-8
6-4
9-6
^ = 0025, A =
0-05
O-I
0-2
Mean value of
A =
49-2 \J qt —
II-I
IO-2
9-2
17-3
15.6
14-2
I2«4
32'0
32-9
33-6
3o-3
42«2
43-2
45*2
43-7
53-4
55-3
57-5
55-4
67.0
69-0
66-8
74-0
75-3
73-6
79-3
78-6
86.6
86-i
1 IO 2
II
14.9
15.6
22-7
22
322
3i*i
43-8
44
55-4
62-2
67.6
88
74-3
79.0
124.4
86-4
From this 'we observe that the rule of Schutz
VELOCITY OF REACTIONS 41
is very nearly right till qt reaches the value 08,
when about 50 per cent of the end-value of A is
reached, as is seen in comparing the last two lines.
We have here a typical example of two laws
of peptic digestion which have long been stated.
The second one, that at constant temperature A is
dependent only on the value of qt, is in perfect
agreement with the general laws of the velocity
of reaction. But the first one, which is represented
by Schutz's rule, before 50 per cent are transformed,
was regarded as absolutely incompatible with those
laws. It was said that the organic ferments behave
in quite a different manner from common catalytic
substances.
In order to show that this assertion is not true
I investigated the case when ammonia acts upon
ethyl acetate in great excess. I found that the rule
of Schutz is valid also in this case until about
50 per cent of the ammonia is used up by the
formation of ammonium acetate. (See the fourth
column in the following table, which is calculated
according to Schutz's rule ; .r-obs. are the observed
values.) I had therefore found a case absolutely
analogous to that of peptic digestion. The cir-
cumstance which causes the deviation from the
common law of a monomolecular reaction is that
the quantity of OH-ions dissociated from the
ammonia is much diminished by the presence of
the ammonium acetate. In reality this quantity
is nearly inversely proportional to the quantity of
ammonium acetate formed, except for the first
42 VELOCITY OF REACTIONS
moments. With help of this regularity it is easy
to deduce the general law for the phenomenon.
It is given by the formula
^^ge^-—-x=Kqt,
where A is the quantity of ammonia at the beginning
of the experiment, x the quantity of ammonia trans-
formed into ammonium acetate at the time /, K the
constant of the reaction and q the quantity of the
ester. The ^-values calculated by means of this
formula are tabulated in the third column and
agree very well with .r-obs. At the commencement,
before x has reached too high values, this equation
gives
x— \/K . A . q . t,
which is the rule of Schutz, according to which x
is proportional to the square root of At for constant
value of the quantity q of ethyl acetate or egg-
albumen.
[Table
VELOCITY OF REACTIONS
43
Inorganic Analogy to Schutz's Rule, NH3 and
Ethyl Acetate
Time, t
(minutes).
.r-Obs. %.
.r-Calc.
17-3,^
(Schutz's rule).
I
17-5
I9.4
17-3
2
25-5
25-2
24.5
3
3o-7
30-4
29-7
4
34-7
34-9
34-6
6
41-5
41-7
42.4
8
47.0
46-9
48-0
IO
51.2
5i-3
54-7
15
59.6
59-7
670
22
67-5
68-o
81. 1
30
74-5
74-7
94-7
40
807
80.7
109.4
60
88-2
88-2
134.0
x-Calc. from A loge [A : (A - x)~\ -x= K<?t.
This deduction not only proves that the rule of
Schutz is the indication of a special case of a
monomolecular process, but it shows also that the
transformed quantity is proportional to the square
root of the quantity q of the substrate. Further,
it gives the general law for the whole process and
not only for its beginning. Whenever we find that
the transformed quantity is a function of Kqt only
this circumstance gives an indication that the pro-
cess studied is of the monomolecular type.
We will in the following find a great number
of very important biochemical processes which
show this characteristic feature. '
As we have seen above, peptic digestion is also,
to a great extent, dependent on the presence of free
44 VELOCITY OF REACTIONS
acid. Its optimum lies at a hydrogen-ion concentra-
tion of about io"2 at the beginning and 6-io"2 after
forty-eight hours. This probably depends upon the
binding of the hydrochloric acid by the formation of
peptone. The action of the acid probably depends
upon the circumstance that the salt of albumen with
an acid is more easily digested than the albumen
itself. A great excess of acid diminishes the activity
of the enzyme, probably by its decomposition. In
this way the presence of an optimum is easily
understood.
Bayliss has investigated the process of tryptic
digestion. In this case an excess of base is
necessary for the reaction. His figures indicate
that digestion by means of trypsin proceeds in a
manner analogous to the peptic one ; the process
is therefore probably a monomolecular one. The
following little table from Madsen's and Walbum's
investigations prove the validity of the ^/-law in
this case as well as for peptic digestion. Here t is
the time which, at a given temperature, is necessary
for reaching a certain degree of digestion, charac-
terized by a corresponding degree of liquefaction of
the gelatinous jelly, when the concentration q of the
enzyme is used.
According to the ^/-rule, the half quantity of
enzyme needs the double time for producing the
same effect as the whole quantity, and so forth.
"Table
VELOCITY OF REACTIONS
45
Digestion of Thymol-gelatine
^ (hours).
<7-
qt.
u
o
2
3
•47
•3
•94
.90
vO
4
6
•26
•i8
1-04
1.08
8
•13
1-04
IO
•095
•95
PL,
0)
12
14
.08
• 07
.96
.98
PQ
20
•o45
.90
24
•038
.91
0.5
.105
• 052
i
.05
• 050
U
o
2
3
• 027
• 02
•o54
.06
CO
4
5
.015
• 01 1
• 06
•055
6
• 009
• 054
.5
8
• 0072
•058
!75
4->
IO
16
• 006
•0037
•060
.059
PQ
18
20
• 0032
• 0027
•058
•054
22
• 0025
.055
24
•0022
•o53
The same is the case with the action of rennet
on milk. The ^/-rule, which indicates that the
action is only dependent on the product qt, is proved
by a great number of experiments of Madsen and
Walbum, as is indicated by the following table.
In this case the liquid slowly loses its fluidity.
Therefore we measure the time needed for pro-
ducing a certain easily observable degree of stiffness
of the milk.
46
VELOCITY OF REACTIONS
Coagulation of Milk by Rennet, 36-55° C.
t (minutes).
?•
7*.
t (minutes).
ۥ
qt.
4
8
32
50
5
25
6
5
30
70
4
28
9
3-3
30
80
32
26
12
1.9
23
IOO
28
28
20
i-3
26
I20
25
30
30
•7
21
l8o
185
33
35
•7
25
24O
167
40
The same rule is valid for the digestion of gelatine
by a substance produced by Bacillus pyocyaneus.
By its action the gelatine is liquefied. The time
of liquefaction t is inversely proportional to the
quantity q of pyocyaneus ferment used. The
figures given in the following table, borrowed
from Madsen and Walbum, give a proof of the
^/-law.
Digestion of Thymol-gelatine by Means of Pyocyaneus
Culture at 34-5° C.
t (hours).
9-
qt.
t (hours).
7-
gt.
0-5
i-6
80
8
• I I
88
I
• 8
80
10
•09
90
2
.46
92
12
•08
96
3
•3
90
16-5
•06
99
4
• 22
88
18
•044
79
4-5
• 2
90
20
•042
84
6
.165
99
25
•035
88
The saponification of fats by the steapsin from
the pancreatic juice is another example of the
VELOCITY OF REACTIONS 47
applicability of Schutz's rule and of the ^/-law. In
this case the fat is suspended in the form of drops in
the liquid. Also, according to Sjoqvist's investiga-
tion, the digestion of coagulated egg-albumen [i.e.
in a solid form) obeys the same laws.
In general we find that the generalization of
Schutz's rule and the qt-\a.vt are valid for a large
number of processes which are of importance for
animal life, such as the action of stomachical or
pancreatic juice on albuminous substances or on
fats.
Even for digestion " in vitro" the simple mono-
molecular formula is sometimes found to hold good,
just as strong bases such as sodium hydrate follow
this law when saponifying a great excess of ester.
Thus, for instance, Euler found this to be the
case in the digestion of glycyl-glycine by means
of erepsin, an enzyme from the intestinal mucous
membrane. The same is true for the saponification
of triacetate of glycerol by means of powdered
castor-beans, whereas higher fats under similar
conditions are subject to Schutz's rule.
In order to illustrate this regularity we give
some figures of Euler. The first table refers to
the katalytic action of a " katalase " contained in
the juice of the mushroom Boletus scaber on the
decomposition of hydrogen peroxide at I5°C. The
quantity q of hydrogen peroxide present in a
solution containing 3 cc. of the mushroom juice
in 200 cc. was determined at different times (t in
minutes) by means of titration with permanganate.
48
VELOCITY OF REACTIONS
The second table gives the results of an experi-
ment on saponification of a concentrated aqueous
solution of ethyl butyrate at 35° C. by means
of a lipase extracted from lard. q indicates the
quantity of non- decomposed ethyl butyrate de-
termined by measuring the butyric acid set free
after a time of / minutes. The acidity was
measured by titration with a solution of barium
hydrate. In both tables K represents the value
of the constant of velocity of reaction calculated by
means of the formula for monomolecular reactions :
t q
Katalysis of H2Oo at
i5°C.
Saponification of Ethyl
Butyrate at 350 C.
t.
q-
K.
0
6
12
19
55
8-o
6.9
5.8
5.0
2-5
0-OI07
O-OI 16
0-0107
O-OIOO
Mean 0-0107
/.
q-
K.
0
2-70
2
2-40
0-0256
6
1.95
0-0235
9
1-65
0-0237
16
1.05
Mean
0-0250
0-0245
The constant K does not in either case vary
more than may be due to experimental errors.
The constancy of K in each case indicates that
the law for monomolecular reactions is really
fulfilled. This is due to the circumstance that the
products of reaction do not chemically interfere
with the reagents.
CHAPTER III
THE INFLUENCE OF TEMPERATURE ON THE
VELOCITY OF REACTIONS REACTIONS OF CELLS
In general reactions proceed very much more rapidly
at higher than at lower temperatures. A very well-
known exception is the breaking down of radio-
active substances, which seems to be wholly in-
dependent of temperature. The influence of the
temperature is given by the formula
M/Ti-T0\
K, = K>A ToTl ;'
where T0 and Tx are two temperatures reckoned from
the absolute zero. K0 is the velocity of reaction at
the temperature T0, and K1 that at T1 ; ^ is a con-
stant. The greater jj, is the more rapidly the velocity
of reaction increases with temperature. For radio-
active substances fi is zero.
If T0 and T± are not too far from each other, the
value of TqTj does not change very much in the
interval from T0 to Tx and then the formula may
be written :
Ki=K0/ 1_ ° or logK1-logK0 = ^(T1 — T0)
49 E
50 INFLUENCE OF TEMPERATURE
with sufficient accuracy, log K is therefore very
nearly a linear function of the temperature, as repre-
sented by the diagrams Figs. 9 and 10.
We may give some few instances showing this
relation. In Fig. 9 the value of T0 is 51° C. for
haemolysin, 45-15° C. for vibriolysin and 6o° C. for
haemoglobin. In the last case the scale is reduced
to half size by putting y1 = iy and T = 60 + 2x.
In Fig. 10 the T0 values are 0-5° C. for vibrio-
lysin with blood-corpuscles, 14-5° C. for egg-white,
3-3° C. for vibriolysin with carbon, and 13-9° C.
for the precipitin. In the third case the scale is
reduced to two-thirds by putting y\ = i-$y and
T =-3-3+ 1-5*.
As is seen from the diagram (Fig. 9), for the spon-
taneous decomposition of a haemolysin from goat's
INFLUENCE OF TEMPERATURE 51
serum, the spontaneous decomposition of vibriolysin
and the coagulation (by heat) of haemoglobin, which
process may also be regarded as due to a spon-
taneous decomposition (with hydration), the value
(log Kx — log K0) as a function of temperature may
be represented by a straight line. In these cases
the observed interval of temperature is only about
■7
o
—I
I
XL
T= Temperature in°C
Fig. io.
9° C. or less. In the next diagram (Fig. io) the
range of temperature is greater, 20°-30° C. Here
the straight line does not fit so well ; the general
formula given above represents the observations
better. The values calculated from this formula
are given by the lines drawn in the diagram. These
are dotted for the heterogeneous systems, which
behave just as the homogeneous ones.
52 INFLUENCE OF TEMPERATURE
Instead of measuring the velocity of reaction by
means of determinations at arbitrary stages of the
reaction, we may also determine it by evaluating
the time which is necessary for reaching a certain
point of the process, for instance that at which 50
per cent of the original substance is transformed. It
is also sometimes possible to decide how long the
process takes to reach practically its end-value, as
is, for instance, done in the measurement on the
time of fermentation by Jodlbauer (cf. p. 60).
This method has also been used in Madsen's ex-
periments on the digestion of gelatine, where he
determined how long it took for a certain quantity
of pepsin or trypsin or another proteolytic ferment
to liquefy the jelly. An analogous case is also the
observation of the time necessary for clotting milk
by means of rennet. In the same manner we
determine the time for total haemolysis or total
bacteriolysis, when all bacteria are killed.
In these cases the velocity of reaction is inversely
proportional to the time necessary for the reaction.
In this manner Gros determined the time necessary
for total haemolysis in hot water at different temper-
atures. His determinations give a value //, = 63,700.
I have repeated these determinations over a greater
interval of temperature. I found the following
values:
Temperature (° C.) . 50-6 54-3 58-2
Time (minutes) . 570 188 57 /x = 64,2oo.
The logarithms of these times are plotted in the
following diagram (Fig. 11), which gives a very
INFLUENCE OF TEMPERATURE 53
good straight line for the haemolysis. In the same
diagram are included some determinations by Miss
H. Chick regarding the time necessary for killing
Bacillus typhosus in hot water at different tempera-
tures. As the observed interval of temperature is
E
bo
o
>Of
%
^
K
>. (
)
<
) \
49
51
53 55
Temperature
Fig. ii.
57
59
61
rather small, io° C. or less, they give a straight line,
within the rather great errors of observation, and
a value of ^ = 92,000. This is about twice as great
as the /rvalue = 48,600 found for disinfection of
Bacillus par atyphosus by means of phenol (between
6° and 360 C). Cf. p. 55. In the same manner
the ^-value for haemolysis by means of hot water
54 INFLUENCE OF TEMPERATURE
(//, = 64,000) is about double that for haemolysis by
means of poisons (acids, bases, lysins ; fi= 25,000 to
fi = 30,000). Cf. p. 66.
In the following table we give the results of the
determinations of n in this field together with
some few figures taken for comparison from general
chemistry :
Sponta7ieons Destructions.
Dibromsuccinic acid
{X= 22,200
Compound haemolysin
198,500
Tetanolysin ....
162,000
Vibriolysin ....
128,000
Rennet, 2 per cent
90,000
Pepsin, 2 per cent
75,600
Trypsin, 2 per cent
62,000
Emulsin, 0-5 per cent .
45,000
„ dry .
26,300
Lipase from castor-beans, heterogeneous
26,000
Invertase from yeast .
72,000
Digestions.
Casein by trypsin
37,5°°
Coli-agglutinin by trypsin
16,500
Gelatin by trypsin
10,570
,, pepsin
10,750
Egg-white by pepsin .
15,570
Powdered casein by trypsin
7,400
Saponifications.
Ethyl acetate by bases
11,150
,, ,, acids
17,400
Cotton oil by powdered castor-beans
7,54o
Triacetin „ ,,
16,700
Emulsion of yolk by pancreatic juice .
13,600
Coagulation, Precipitation.
Egg-white by heat
. 135,600
Haemoglobin by heat .
60,100
Milk by rennet
20,650
INFLUENCE OF TEMPERATURE 55
Egg-white by sulphuric acid
,, precipitin from rabbits
Agglutination of coli-bacilli
typhoid-bacilli
5)
25,000
11,000
6,300
30,100
37,200
25,600
11,000
12,300
6,200
15,600
D tO 30,000
12,000
14,800
I4,IOO
16,060
64,000
92,000
48,600
Different Processes.
Hydrolysis of cane-sugar by acids
,, ,, invertase .
,, starch by amylase
Destruction of H902 by catalase
Alcoholic fermentation by yeast-cells
Haemolysis (by bases, acids, lysins)
Assimilation by plants .
Respiration by plants .
Cell-division in eggs (mean value)
Heart-beats of pacific terrapin .
Haemolysis by means of hot water
Bacteriolysis (B. typhosics) in hot water
„ (B. paratyphosus) in phenol
From the tabulated values of /j, we may conclude
that fi is in general greater for spontaneous decom-
positions, among which we may reckon the coagula-
tions by heat, than for processes in which a substance
acts on another catalytically. The value of ^ for
dry emulsin lies also much below that which holds
for solutions of this enzyme. This behaviour is
probably general. Very remarkable also is the
fact that different vital processes, alcoholic fermenta-
tion by means of yeast, assimilation and respiration
of plants, cell-division in eggs and the heart-beats
of a tortoise possess very nearly the same value of
/x, namely between 12,000 and 16,000, which is of
the same order of magnitude as the corresponding
values for the hydrolysis of cane-sugar by invertase,
or of starch by amylase, or the saponification of
ethyl acetate by bases, or of triacetin by powdered
56 INFLUENCE OF TEMPERATURE
castor-beans, or of yolk of egg by pancreatic juice.
We may therefore say that the vital processes are
in this special case very similar to processes in
general chemistry.
It has often been said that there is a great
difference between vital and ordinary chemical pro-
cesses with respect to the influence of temperature
upon them. It is a very common feature that vital
and even enzymatic processes show an optimum of
temperature. For instance, the assimilation process
in plants goes on with a maximum velocity at about
37° C, as is indicated by the investigations of
Miss Gabrielle Matthaei (see Fig. 12 a). Avery
similar thing holds good for the inversion of cane-
sugar by invertase, according to Kjeldahl (Fig.
12 d), and the coagulation of milk by rennet, accord-
ing to Fuld's experiments (Fig. 12^). The ex-
planation of this fact is in reality very simple. The
spontaneous destruction of, e.g., the saponifying lipase
in castor-beans has a value of /* = 26,000, which is
much greater than the corresponding value 7540
for the saponification of cotton oil by means of
this lipase (according to Nicloux's measurements).
Therefore at sufficiently high temperatures the
enzyme is destroyed during the preliminary heating
to this temperature before it is able to exert a
sensible action on cotton oil. Hence a maximum
effect of the lipase must occur at a temperature
below that given.
Further, the velocity of reaction must in this
special case decrease with time ; at very low
INFLUENCE OF TEMPERATURE 57
temperatures this peculiarity is insensible, but it
o
()
TO
eg
Q.
©
CO
30 40
Temperature
Fig. 12.
70°C
increases rapidly with temperature. This is seen
58 INFLUENCE OF TEMPERATURE
from the diagram (Fig. 12 c), representing observa-
tions of Nicloux, made 30, 90 and 180 minutes after
the mixing of the cotton oil and the lipase. The
mean velocity of reaction calculated from these
figures corresponds to about 60 and 135 minutes.
The optimum falls at about 33° and 30° C. respec-
tively at the two times of observation. From this
observation it is quite clear why different authors
give different values for the optimum temperature.
They have not observed the influence of the time
of heating. If this time were zero (which is im-
possible to realise) we would not observe any
optimum. As is seen from the different curves
of log K or K (this last for Nicloux's figures) the
fall of the K-curve is exceedingly rapid when the
temperature rises above the optimum one.
Regarding vital processes, it may be observed that
the chief substance of living cells, the protoplasm,
generally suffers at temperatures above 40° C. and
in most cases is killed above 55° or 6o° C. Hence it
is obvious that vital processes become hampered
by temperatures above about 40° C. A similar
remark may be made regarding low temperatures.
At about zero the aqueous solutions in the cell
freeze and the life - processes are brought to a
standstill. But even if freezing does not occur
the vital processes are much hindered in the
neighbourhood of zero.
As a general result of our investigation we may
say that the influence of temperature on the velocity
of different processes in which enzymes, organic
INFLUENCE OF TEMPERATURE 59
products such as egg-white, or living cells, such as
blood-corpuscles, bacilli, or even higher organisms
such as eggs or plants are involved, follows the
same law as is found for the influence of tem-
perature on ordinary chemical processes. Atten-
tion may be drawn to the very high values of /jl in
140
120
100
X I
t
; X
1
;
Produd
tqt
J2 80
O
x\
■
" 3
S
<u60
E
40
20
n
(
)
r
>
\ 4
c
i (
r
' I
1
Quantity of yeast in gms.-
Fig. 13.
some cases of spontaneous destruction, coagulation
or destruction of living cells (blood -corpuscles,
bacteria).
The peculiarity that in many cases optimum
temperatures are observed in life-processes or enzy-
matic actions is easily explained by the destructive
influence of high temperatures on living cells or
enzymes. No essential difference exists between
60
REACTION OF CELLS
the processes studied in general chemistry and
those produced by living organisms or enzymes.
We are now in a position to consider some
chemical processes in which simple cells such as
yeast-cells, blood-corpuscles or bacteria act upon or
are treated with chemical reagents, namely, the
fermentation process by yeast-cells, the haemolysis
by means of haemolytic poisons, the agglutination
of bacilli by means of agglutinins or their killing
by poisons (so-called disinfectants).
Jodlbauer determined the time which is necessary
for the fermentation of a certain quantity of sugar
(2 g. in 50 cc.) when different quantities of yeast (in
grammes) were added to the sugar solution. He
found that the time necessary increases when the
quantity of yeast decreases, and in such a manner
that the product of these two quantities is constant,
as is seen from the following table and the accom-
panying diagram (Fig. 13). The ^/-law holds good,
which indicates that the reaction is monomolecular.
Time of Fermentation (Jodlbauer)
Quantity
of Yeast.
Hours of
Fermentation.
Product.
8
5
40
4
10
40
3
15
45
2
20
40
i-5
30
45
1
46
46
•5
90
45
•4
103
41
• 2
240
48
REACTION OF CELLS
61
Rubner has carried out a much more elaborate
series of experiments at 30° C. He took the heat
evolved, determined calorimetrically, as a measure
of the quantity of sugar decomposed. He used
in four different experiments the following quantities
2
O
25
I 20
1=
I 15
E
2
o
TO
o
■&•
c
3
o
■o
2
a.
20
15
10
>
©
>
V
a>
/O
fe^
Dead yea si 1000 cal
-v-l200cal
****
in 2 hours
-1000 cal
-800 cal
10
CO
too
-4>500t)al
250c€
6 8 10
Quantity of yeast in grams — >
Fig. 14.
of yeast : 1 gramme, 2 grammes, 4 grammes and
8 grammes for a given quantity of cane sugar (50
grammes in 250 cc. solution), and found, as indi-
cated by the figures below and the accompanying
diagram (Fig. 14), that for a certain degree of de-
composition, corresponding to an evolution of 800 or
1000 or 1 200 gramme-calories, the productof quantity
62
REACTION OF CELLS
of yeast and time is nearly constant. According to
these figures the rule of Schutz nearly corresponds
to reality. For if we take the mean values of the
products in the three cases they are 21-3, 15-9 and
1 0-4, which are nearly proportional to the squares
of 1200, 1000 and 800. If we divide the first
figures by 1-44, 100 and 0-64 we find 14-8, 15-9
and 1 6- 2, which lie very near to each other. In
other experiments this regularity is less evident.
Living Yeast-cells (Rubner)
Quantity
of Yeast.
Hours.
Product.
8
4
2
1
8
4
2
1
8
4
2
1
2-6
5-5
105
21.5
20-8 ~
TO
22 u
21 8
21-5 M
2
4
8
15-5
16 "d
16 <->
16 8
15-5 2
i'2
2-5
5-5
1 1
9-6 _.
IO u
11 8
I I <*>
Dead Yeast (Rubner) -iooo Calories
Quantity
of Yeast.
Hours.
Product.
IO
5
2
1
2
3-8
8
20
20
16
20
11EACTION OF CELLS 63
For dead yeast (killed by means of toluol) the
figures are rather irregular, as is seen from the
diagram giving the product qt corresponding to
the evolution of iooo gramme-calories, but still we
might conclude that the ^/-rule is valid. The lowest
curve represents the heat evolved during the lapse
of two hours, when different quantities of dead yeast
(i, 2, 5 or 10 grammes) act upon the same quantity
of sugar-solution (50 g. in 250 cc. solution). Here
there is no indication that the rule of Schutz might
be applicable.
Another vital phenomenon has been investigated
by Madsen and myself, namely the decomposition of
red blood-corpuscles by means of haemolytic poisons
such as ammonia, sodium hydrate or tetanolysin.
The experiments were carried out at o° C. As
example I give the figures for ammonia.
The longer the process goes on the greater is the
number of the blood-corpuscles killed ; they give
up their red colouring matter, the haemoglobin, to
the surrounding solution, which is in most cases
the so-called physiological salt solution, i.e. 09 per
cent NaCl-solution in water. The said number is
reckoned in per cent of the total number of blood-
corpuscles and called the degree of haemolysis. The
solutions contained 5 per cent of blood-corpuscles, and
different concentrations of ammonia were used ; the
concentration 1 denotes 0001 normal NH3. The
following figures giving the time necessary for
reaching a certain given degree of haemolysis were
obtained. Immediately after the observed figures,
64
REACTION OF CELLS
representing the time in minutes, calculated figures
are given in brackets, which were obtained by
dividing the observed figures for the concentration i
by the concentration used, which is indicated in the
first column.
Concentration.
Degree of Haemolysis in Per Cent.
3-
10.
20.
30.
40.
I
2'27
4-35
75
13(13)
6(5-7)
26(26)
10(11.5)
5-5(6-o)
35(35)
i5(i5-4)
9(8-0)
4(4-7)
44(44)
18(19.4)
12(101)
6-2(5-9)
53(53)
23(23-3)
14(12-2)
8(7-i)
If the calculated values agree with the observed
ones — as is really the case within the somewhat
large errors of experiment in these very difficult
investigations — this indicates that the ^/-rule is
applicable, i.e. that the reaction is monomolecular.
If we try to follow the progress of this reaction, we
find a rather irregular result, which is partly caused
by the circumstance that during the first period no
reaction is visible, which is due to the so-called time
of incubation. This phenomenon is very common
with life-processes, but is also observed in some
cases in general chemistry, for instance in the action
of light on a mixture of hydrogen and chlorine
(Bunsen and Roscoe).
Now, when we know that the ^/-rule holds good
for the haemolysis by means of ammonia, we may
investigate the effect of temperature on this process
by determining the quantities of ammonia which are
necessary to produce the same degree of haemolysis
REACTION OF CELLS
65
in a given time, e.g. 10 minutes. If, for instance, we
find that the fourfold quantity is necessary for
reaching the same haemolytic effect at 290 C. as at
39° C, we may say that — according to the ^-rule —
the same quantity of ammonia would occupy a time
four times as long to produce the same effect at 29°
C. as at 390 C.
Such determinations have been carried out on a
very large scale with different haemolytic agents by
Madsen and his co-workers Walbum and Noguchi.
As an instance, I give a series for ammonia with a
time of action of 10 minutes, t is the temperature, q
the necessary quantity in cc. of a 0-5 normal NH3
solution. The total quantity was 8 cc. containing 1
per cent of red blood -corpuscles from a horse.
^obs> is the observed, ^calc#> a calculated quantity
evaluated by means of the general formula for the
influence of temperature on the velocity of reactions.
The degree of haemolysis was 1 7 per cent.
Haemolysis by means of Ammonia at different
Temperatures
t.
£obs.
^calc.
210
060
0-64
25.9
0-30
0-30
29-7
0-I7
o- 17
34-8
0-085
0-083
39-5
004
OO43
The value of fi used for the calculation, which
agrees very well with the observation, is 26,760.
66 REACTION OF CELLS
Now it ought to be observed that with increasing
time the effect tends to a limiting value, and this the
more rapidly the higher the temperature. Thus, for
instance, at 390 C. the values of ^obSj for 60 minutes
and for 180 minutes are 001 9 and 0-015 respectively.
Instead of being in the proportion 3 to 1, these
figures are as 13 to 1. Below 300 C. the proportion
is, within the errors of experiment, as 2 to 1 for the
times of action 10 minutes and 20 minutes. In con-
sequence of this behaviour the //,-value seems to sink
with increasing time. The right value of \x is the
limit-value for the time of action o, which is found
by extrapolation from the values observed with
different times, z (z= 10, £ = 20, £=30, £ = 60, etc.).
It is about 29,000. For acetic, propionic, and
butyric acid we find in the same manner values lying
round about 26,000. The same figure is given by
vibriolysin. It seems as if weak acids or bases, and
lysins of bacterial origin give nearly the same value
for fi} for very short time of action. Strong acids
and bases give too low values of /^, probably because
their attack is too rapid.
Sodium oleate behaves in quite a different manner.
Here ^ (10 minutes of action) does not reach a
value higher than 3800, so that the velocity of re-
action is only double as great at 36-3° C. as at 40 C.
Cobra poison acts nearly independently of the
temperature, and the poison of the water moccasin
seems to act 15 times more slowly even at 39° C.
than at n° C. These apparent anomalies seem to
merit a closer investigation.
REACTION OF CELLS
67
The agglutinins in their action on bacteria seem
to behave very nearly in the same manner as the
haemolysins in regard to red blood-corpuscles. The
following figures of Madsen, who observed the time
t which was necessary for producing a given degree
of agglutination of Bacillus colt at 37° C. when a
given quantity q of coli-agglutinin acted upon this
bacillus, show that the ^-rule is very nearly obeyed.
Agglutinating Action of different Quantities of
Coli-agglutinin at 370 C.
7-
t (Min.)-
qt.
3-5
30
I05
2-5
45
I I I
i-7
60
I02
1-2
90
I08
08
120
96
05
180
90
0.4
240
96
»3
300
90
0-27
360
97
Mean 99
The value of qt decreases a little with decreasing
quantity. But on the whole the qt-m\e holds pretty
well.
The dependence of the action of this agglutinin
on temperature is shown by the following table. It
gives the quantity, qohs., of agglutinin, necessary for
producing a given degree of agglutination in 10
minutes at the temperature written in the first
column. The calculated values, ^calc,, are found by
means of the formula on p. 49.
68
REACTION OF CELLS
Action of Coli-agglutinin during io Minutes at
different temperatures.
Temp. ° C.
?obs.
^calc.
12-9
30
30
21-2
6.5
6-8
24-9
4-5
4.2
3o-9
i-5
1-4
34-9
055
0-72
38-6
0.5
o-43
The experiments and the calculations are carried
out by Madsen in the same manner as those for the
action of temperature on the velocity of reaction of
haemolysins ; /ju is put equal to 30,000.
For typhoid-agglutinin (10 minutes' action)
Madsen and Walbum found a value of fi = 37,200, i.e.
of the same order of magnitude as for coli-agglutinin
but 24 per cent higher.
Generally speaking, we may say that the action of
agglutinins on bacteria proceeds very nearly in the
same manner as that of haemolysins on red blood-
corpuscles.
A certain similarity to this investigation is ex-
hibited by the disinfecting action, practically so im-
portant, of certain poisons or hot water on bacteria,
which are thereby killed. Kronig and Paul in
1897 investigated the disinfecting action of different
mercuric salts on anthrax bacilli and found that the
chief acting substance is probably the mercuric ion,
for the different salts at the same concentration were
effective according to their degree of electrolytic
REACTION OF CELLS 69
dissociation. The same is true for the hydrogen
ion of acids or the hydroxyl ion of bases. They
also determined the progress of the disinfection with
time. Madsen and Nyman found that this progress
corresponds to a monomolecular reaction, and showed
that this is also the case when hot water acts on
anthrax spores (1907). At about the same time
(1908 and 1910) Miss Harriette Chick carried out
a very elaborate research on this question and came to
similar results when different poisons were used, such
as phenol, mercuric chloride, hot water, and normal
rabbit's serum. Even when bacteria are killed by
drying, the monomolecular law is followed, as Paul
found when he kept dried staphylococci at ordinary
room temperature. In contrast with this the bacteria
remained alive for months at the temperature of
boiling liquid air. Miss Chick has also calculated
some figures given by Clark and Gage (1903) re-
garding the killing of bacteria in sunlight, and even
there found the law of monomolecular reactions to
hold good.
In order to prove this I borrow some diagrams
from Miss Chick's paper delivered to the Eighth
International Congress of Applied Chemistry (vol.
xxvi. p. 167, 19 1 2). These diagrams concern the
killing of anthrax spores with 5 per cent phenol at
333° C. (Miss H. Chick, Fig. 15), or with on per
cent mercuric chloride at 180 C. (Kronig and Paul,
Fig. 16), the killing of Bacillus typhosus with 06 per
cent phenol at 20° C. (Miss H. Chick, Fig. 17), the
killing of this bacterium by means of hot water at
70 REACTION OF CELLS
3r
bo
o
100
200 300
Time — *
Fig. 15.
400 500
20 40
Time — ►
Fig. 16.
REACTION OF CELLS
71
10 20
Time - — ►
Fig. 17.
15 T. 20
Time
Fig. 18.
72
REACTION OF CELLS
48-9° C. and at 5270 C. (Miss H. Chick, Fig. 18),
and the killing of Bacterium coli commune by sunlight
(Clark and Gage, Fig. 19). In all these figures
the time in minutes (/) is taken as abscissa ; the
ordinates represent log n, where n is the number of
surviving bacteria in one drop of the culture.
These results are very interesting. In the case
of yeast-cells the approximative validity of Schutz's
5<
c
N^
1
c
\
too
0
J 3
2
15 30
Time — ►
45
60
Fig. 19.
rule indicates that the products of the fermentation
in some way hinder the process. Now it is true
that the alcohol produced diminishes the activity of
the yeast-cell, but not with such regularity that we
might expect Schutz's rule to hold good. There
are also other disturbing agents in this case which
act in an opposite direction, for instance the incuba-
tion phenomenon. But still both in this complicated
case and in that of the killing of red blood-corpuscles
REACTION OF CELLS
73
by different haemolytic agents the ^/-rule is followed,
that is, if we diminish the quantity of the acting
substance in a certain proportion to reach the given
effect, we must increase the time of action in the
<
I
3
^S^<^
1
c
V
)
xso
2 2
°\
I
(
\
I
3 1
0
1
5
Time — ►
Fig. 20.
same proportion. This rule indicates that the re-
action is of the monomolecular kind.
The figures concerning bacteria show this in a
much more pronounced manner. In some cases,
for instance regarding Staphylococcias pyogenes
aureus (Fig. 20) or Bacillus paratyphosus, Miss
Chick found some irregularities at the commence-
ment of the process. For the staphylococcus the
74 REACTION OF CELLS
velocity is less in the first four minutes than later
on, which probably depends on a kind of incubation ;
for the paratyphosus bacillus the irregularity seems
to indicate some accidental irregular influence. But
on the whole these reactions show such a regular
progress with time, that their monomolecular nature
is obvious. This circumstance indicates that every
bacterium or yeast-cell or red blood-corpuscle acts
as if it were a single molecule in regard to the sub-
stance reacting upon them. This seems from a
biological point of view extremely difficult to under-
stand. We will come back to this question later on.
According to investigations by Harvey, not only
bacteria, but even higher organisms, such as Chlamy-
domonas, are subject to the same regularity. He
determined the number of moving Chlamydomonas
at certain times, 5 to 25 minutes after he had added
hydrochloric acid in the small quantity of 0-009 Per
cent to the water in which the monads swam round.
At the beginning of the experiment this number was
113, after five minutes it had sunk to 67, after further
five minutes to 30, at the next observation five
minutes later to 14, and still hv& minutes later to 6.
The logarithm of this number as a function of the
time of observation is represented by a straight line
as the figure (Fig. 21) indicates.
According to a quotation given by Miss H.
Chick, even seeds of barley are killed by poisons
or hot water according to the law for monomolecular
processes, as shown by experiments of Miss Darwin
and Professor Blackman.
REACTION OF CELLS
75
The explanation of this peculiarity is the same
as that which I have given for the rapid change of
velocity of reaction with increase of temperature, in
which case I specially considered the inversion of
cane-sugar. Only a very small number of the cane-
20
.....
X.
16
I M
X(
>
c
o
-J
08
N^
>
04
0
0
5 1
0 1
5 2
0 2
5
Time in minutes — *-
Fig. 2i.
sugar molecules are at a given time in such a modi-
fied state that they are liable to be decomposed, and
every molecule of sugar enters at some time into
this state, so that at constant temperature molecules
of the said " active ' kind are always present in the
same fraction of the total number. Therefore the
number of molecules decomposed per second is pro-
portional to the total number of sugar-molecules
present.
76 REACTION OF CELLS
The radio-active substances decompose according
to the same law. This law is evidently of very far-
reaching importance.
There is no doubt that the different cells in a sample
of bacteria or red blood-corpuscles possess a different
power of resistance to deleterious substances. We
may, as an instance, take the red blood-corpuscles,
which have been most closely examined. If we
add different quantities of a poison, e.g. vibriolysin,
to an emulsion of i-6 per cent horse erythrocytes in
10 cc. of physiological salt-solution (0-9 per cent
NaCl) and keep the mixture at 2>7° C. for two hours,
we find that no action is observed until more than 5
cubic millimeters of the poison is added. With the
doses indicated we obtain the degree of haemolysis
given below :
Cubic mm. of poison : 5 10 20 30 40 50 60 70 80 90 100 no
Degree of haemolysis : o 06 4 16 34 52 67 78 86 93 98 100
This table gives the sensibility of the erythrocytes,
25 per cent are killed by 35 c.mm., 50 per cent by
49 c.mm., 75 per cent by 67 c.mm. and no cell
resists 1 10 c.mm.
From two different series I have calculated the
relative number of erythrocytes of a certain sensi-
bility and constructed a curve giving the frequency
of the erythrocytes of a certain sensibility, where
the maximum is placed above the value 4 of the
abscissa. The zero-point is placed on the ordinate
10 (upper curve on Fig. 22). Below this curve
the ordinary curve of probabilities (e.g. for the fre-
REACTION OF CELLS
77
quency of a certain velocity amongst gas-molecules,
according to Maxwell) is drawn with the same
height of the maximum ordinate. The two curves
run nearly parallel to each other at a distance of
ten units. Only at high values of the abscissa,
where the probable error of a determination is very
great in the case of haemolysis, is there a little
80
60
If
t
1*40
V \
20
\
)
0
4 6
Sensibility
Fig. 22.
8
10
deviation from parallelism. The parallelism, within
the errors of observation, indicates that the sensi-
bility of the erythrocytes is distributed in accordance
with the law of probabilities, which is the most
regular distribution we could expect.
Even for erythrocytes some observers have
found that their destruction by means of haemolytic
** agents goes on according to the monomolecular law
with progress of time. This law is proved with a
78
REACTION OF CELLS
very high degree of accuracy by experiments on the
killing of bacteria by means of different disinfectants.
Without doubt the bacteria behave in this case
just as the erythrocytes at haemolysis. If now the
different time necessary for killing the different
bacteria was due to their natural resistance, we might
expect that the velocity of reaction would be zero
1
c
o
— 1
Time — ►
Fig. 22A.
to begin with, to increase subsequently and run
through a maximum when about 50 per cent were
killed, and after that to fall again to zero when
nearly all bacteria were dead. The characteristic
line would be expressed by a curved line with an
inflexion-point as in Fig. 22A. Instead of this we
find the straight line in this figure representing the
phenomenon, The different lifetime of the different
REACTION OF CELLS 79
bacteria does not, therefore, depend in a sensible
degree on their different ability to resist the de-
structive action of the poison. Instead of this a
certain fraction of the bacilli still living dies in one
second, independent of the time during which they
have been in contact with the poison.
In order to understand this we make the follow-
ing observation. In a i per cent solution of acetic
acid only i per cent of the molecules are in a
dissociated state (at 250 C). It is not the same
molecules which remain constantly in the dissociated
state, but every molecule is dissociated during one
unit of time and undissociated during ninety-nine
units. The reactivity of the ions is much greater
than that of the whole molecules. We suppose for
simplicity that the ions alone react. Then at any
moment only 1 per cent of the acetic acid
molecules are in state to react. The proteids con-
tained in the living protoplasm are amphoteric
electrolytes. Only a thousandth part (we suppose
this figure for simplicity) of the proteid molecules
has split off its H-ions, and perhaps only a millionth
part its OH -ions. Then probably one part in a
thousand millions has split off both its H-ions and
its O H-ions. Perhaps it is only living protoplasm
containing one or two such ions which is able to
react with the poison. At every moment only this
small fraction is open to attack, and at this moment
a molecule of poison must be present for the cell
proteid to be destroyed. Probably the cell only
dies after a certain number of its proteid molecules
80 REACTION OF CELLS
have entered in reaction with the poison. In this
way we may represent to ourselves the manner in
which it happens that in every second a certain
fraction of the cells is killed by the poison, and that
this fraction is independent of the time of action of
the poison.
It may here be worth while to make a little
reservation. It is a fact very often observed that
immediately after it has been added to the cell-
emulsion the poison has a very small action, or
none at all. This is easily understood, for it is
necessary for the poison to diffuse through the cellular
membrane before it is able to act upon the cell.
This takes a certain time, which is called the time
of incubation. Different bacteria may possess mem-
branes which are rather different in regard to their
permeability for the poison, and it may also be
different for different poisons. It is probably for
this cause that the time of incubation is insensible
in many of Miss Chick's experiments. Only in the
case of phenol acting on staphylococci a clear in-
dication of the incubation phenomenon may be
observed (Fig. 20). But even here the action of
the poison is not zero during the four minutes of
incubation, but only very small. During this time
the cells with the weakest membranes are attacked,
and in this manner the small action of the poison is
understood. With red blood -corpuscles the said
effect is very pronounced, as the experiments of
Madsen and myself indicate.
tf-
CHAPTER IV
THE QUANTITATIVE LAWS OF DIGESTION AND
RESORPTION
We now proceed to consider life-processes, in which
not simple cells but higher organisms are involved.
The question which has been investigated in this
field because of its extreme importance is the
digestion of food in higher animals. For the ex-
periments dogs have been usually examined.
When we consider digestion in the stomach of an
animal, wefind the circumstances rather different from
those for digestion in vitro. Our chief knowledge
we owe to the investigations of Pawlow in Petro-
grad and his school, especially Professor London.
He gave me his figures for calculation, and I found
some very pronounced regularities in them, which
also occur in the observations of Khigine and other
pupils of Pawlow. A short review of the chief
results which may be expressed by quantitative laws
may not be out of place here.
The observations were made in the following
manner. Fistulae were opened to different parts of
the digestive canal of the observed animal. After
the introduction of food into the stomach — which
81 G
82 DIGESTION AND RESORPTION
could be done in two different ways, either by giving
the food to the animal, generally a dog, to eat, or by
putting the food into the stomach direct, by a tube
ending in the stomach — the different juices, gastric,
pancreatic or enteric, are secreted by the animal.
These different juices may be collected by tubes
introduced into the different fistulae.
The production of gastric juice begins about ten
minutes after the introduction of food. The total
time of secretion is observed and the quantity of juice
secreted during this time. Very often the quantity
of juice secreted during a certain time, e.g. one hour
or three hours, reckoned from the beginning of the
process, is also given. The quantity of undigested
food may in the same manner be taken out from the
stomach after a given time and analysed, in which
case a correction is applied for the quantity of ac-
companying gastric juice, determined from the acidity
of the content in the stomach. In order to study
the stomachical secretion free from the food taken,
another method has been used. A small part of
the stomach is separated from the rest of the stomach
by sewing, whereby a tube is formed, which is open
so that its secretions may be collected in calibrated
tubes. Special experiments have shown that the
juice secreted from the "small stomach," or portion
thus separated off, is of the same composition as that
secreted from the corresponding part — the fundus
part or the pyloric one of the stomach — and that it
is always the same fraction of the total secretion.
This method has been used by Lonnquist and
DIGESTION AND RESORPTION 83
Khigine. The "small stomach' of the dog used
by Lonnouist secreted about 4 per cent of the total
secretion.
Professor London and Dr. Lonnquist have
investigated the content of gastric juice in the
stomach after a meal or after introduction of food
through a tube. In the first case the content is
nearly constant during four hours, and subsequently,
when digestion is nearly completed, sinks rapidly.
In the second case the content of juice and pepsin is
at first very small, but increases rapidly afterwards.
For the calculations I have made the simplified
hypothesis that the concentration of pepsin is pro-
portional to the time of digestion, which agrees
fairly well with the experiments of Khigine and
LOBASOFF.
After these preliminary remarks we will consider
the interesting results of Khigine's experiments
given in the table below. Different quantities of
the commonest food -stuffs (recorded in the first
column) were given the dog to eat, or introduced
into the stomach by means of a tube. It is very
obvious that the total quantity of gastric juice
(tabulated in the third column) is proportional to the
quantity of food (tabulated in the second column), if
this is of the same kind. Khigine has also drawn
this conclusion, according to which the calculated
values in the fourth column are evaluated. The
good agreement between these figures and the
corresponding observed values gives a proof of the
said proportionality.
84 DIGESTION AND RESORPTION
Khigine's Experiments on Digestion by a Dog
Quantity
Quantity of
Time of Diges-
Gastric Juice
of Food.
Gastric Juice.
tion—
lours.
after3hrs. — cc.
grammes.
obs.
calc.
obs.
calc.
obs.
calc.
Raw flesh .
4OO
106-3
99.2
875
8-84
51-6
48-6
5> 55
200
40-5
49.6
6-25
6-23
32-5
34-o
55 55 • '
IOO
26-5
24-8
4-50
4.42
23-9
24-3
Boiled ,,
200
42-1
417
5-5
5-65
3i-3
26-8
55 55
IOO
20«7
207
4»o
4-0
1 8-9
18.9
Milk, eaten .
600
33-9
5-5
. . .
21-8
,, injected
600
55-8
52-5
6-o
5-4
38-2
...
5 5 55
500
41.4
43-8
4-5
4.9
...
55 55
200
167
17-5
3-o
3'i
...
Soup of oats and flesh .
600
42-8
41-4
5-8
5.6
...
...
55 55 55 55 55
30O
197
207
3-8
3'9
...
Bread of wheat
200
33-6
■ ■ ■
8.5
20-0
Mixed food 1
SOO
83-2
90-0
9-75
9«o
46-1
44.9
5 5 55 •
4OO
4i-3
45-o
6-25
6-37
3O.6
3i-8
White of egg boiled
IOO
45-7
. . .
6-3
Tallow of ox
IOO
12-9
...
4-5
...
1 100 grammes boiled flesh, ioo grammes bread of wheat, and 600 grammes milk.
Digestion of bread
(Quantity of bread given, grammes: 40 43 100
-! Gastric juice during 3 hours, obs. : 273 280 416
London and PolowzowaJ ^ ^ J ** ^ calc# . ^ 2yg ^
This circumstance may at the first glance seem
very peculiar, for we know from the experiments in
vitro that a small quantity of pepsin (together with
hydrochloric acid) is able to digest a great quantity
of food. Why does not Nature make use of this
property of peptic digestion ? It is easy to see that,
according to the rule of Schutz for peptic digestion,
the length of time necessary for digesting a certain
quantity would increase nearly proportionally to the
square of this quantity. Therefore if 4-42 hours are
necessary for the digestion of 100 grammes of raw
flesh, a time about 16 times longer, i.e. 70 hours,
would be necessary for the digestion of 400 grammes,
and a meal of 1000 grammes would take 442 hours
DIGESTION AND RESORPTION 85
or 1 8 days. This would be not at all favourable for
the animal. Then Nature would proceed in a much
more advantageous manner if it digested the food
in portions successively. This is in fact the case.
If an animal takes a certain quantity of solid food,
e.g. flesh, it is spread over the interior of the
stomach in layers, so that the food first taken forms
the layer nearest to the walls of the stomach and the
innermost layer contains the food eaten at the end.
This is shown in experiments by Ellenberger and
Grutzner. The gastric juice, secreted from glands
in the stomachical walls, diffuses extremely slowly
into the interior parts of the food. Therefore at
first the outermost layer is digested and carried away
through the pylorus, after which the digestion of
the second layer is carried to an end and its
digestion products carried away, and so forth until
the innermost layer is also ready. After this the
secretion of the gastric juice, which has gone on
during this whole time, comes to an abrupt end. In
this process also a part of undigested food is carried
away and without doubt digested later on in the
digestive tract. Therefore when the calculation in-
dicates that only a small quantity of food is left
undigested in the stomach, the experiment shows
that the stomach is really empty. This occurs, for
instance, in the experiments of London with dogs of
25 kilogrammes when less than 3 grammes of flesh
are left.
From an inspection of column 5 in the table
giving Khigine's experiments we find that the time
86 DIGESTION AND RESORPTION
of digestion is very nearly proportional to the
square root of the quantity of food. How well this
law agrees with reality is seen from a comparison
of the fifth and sixth columns, which latter is
calculated according to the said law. In practice
it is rather difficult to observe when the secretion
of juice is at an end. The square root regularity
might not be expected if the secretion of gastric
juice or, better, of pepsin and hydrochloric acid were
independent of the quantity of food. But if the
secretion during a given time increased nearly
proportionally to the square root of the quantity
of food itself, the said regularity would look natural.
That this condition is very nearly fulfilled we see
from the two last columns. The calculated figures
are proportional to the square root of the quantity
of food, and agree very well with the quantity of
gastric juice collected during the lapse of three
hours from the beginning of the secretion. We
must therefore conclude that the food in the mouth
and in the stomach acts upon the nerves of the
secreting glands in such a manner that their activity
is nearly proportional to the square root of the
quantity of food in question. The time for the
digestion of mixed food is in accordance with the
square-root rule calculated from the formula :
/ = v t\ +4 +4
where ^ is the time for the flesh, t2 that for the
bread, and tz the time of digestion for the given
quantity of milk.
DIGESTION AND RESORPTION 87
The acidity of the gastric juice is about 05 per
cent of hydrochloric acid, and varies, according to
Khigine, from 0-56 for the soup given to 047 for
bread — for ox-tallow an abnormously low value of
0-4 was found ; the fats, except milk-fat, remain
nearly unchanged in the stomach. The strength
of pepsin in the gastric juice is very different,
about half as great for milk as for flesh or soup, and
a fifth of that for bread.
The longer the time of digestion of a food-stuff
the more indigestible is it. Boiled flesh is about
10 per cent more easily digestible than raw flesh
(for dogs). If regard is paid to its great content
of water, which is indifferent to the digestion, milk
seems to be less digestible than flesh, and soup of
oats and flesh less digestible than milk. With milk
we observe the influence of eating as compared
with introduction through a tube. This depends
upon the slow secretion of gastric juice in the
beginning in this latter case. The difference is still
more pronounced in the figures for the quantity of
gastric juice, which runs nearly parallel to the time
of digestion. The slow digestion of coagulated
(boiled) egg-white is very pronounced. Boldyreff
has shown that fish needs about 30 per cent more
stomachical juice than horse-flesh.
For bread Khigine has only one figure. London
and Polowzowa have varied the quantity of bread
given to their dog. The quantity of juice secreted
during the first three hours follows the square-
root rule. The high value of this quantity in their
88 DIGESTION AND RESORPTION
experiments depends upon the circumstance that
they have considered the whole quantity secreted
to the stomach, whereas Khigine has observed
the quantity delivered by a " small stomach," which
is only a small fraction of that given to the chief
part of the stomach.
London has carried out a great many experi-
ments regarding the quantity of undigested flesh
in a dog's stomach three hours after the food had
been given. The quantity of flesh given varied
between iooand iooo grammes. The dog's weight
was 25-2 kilogrammes. When I calculated these
figures, I observed that the whole progress of diges-
tion might be expressed by the following formula :
dx\dt= 125(1 -e-o-oo6^
in which x is the quantity of undigested flesh in
grammes, dx : dt gives the quantity digested in
one hour.
This formula is graphically represented in the
following diagram (Fig. 23). The uppermost curve
refers to the digestion of 1000 grammes flesh. The
curve for 800 grammes is obtained from that for
1000 grammes simply by transposing the zero-point
of time by i-6 hours, i.e. to the point where the
1000 grammes-curve cuts a horizontal line, jy = 8oo,
and so on for smaller quantities of food — in the dia-
gram the curves for 600, 400, 200 and 100 grammes
are drawn. The dotted curve is found with the same
dog some time later. Its digestive power was then
diminished in the proportion 1 :o-8, so that the 600
DIGESTION AND RESORPTION 89
grammes of flesh given were digested at the same
rate as 750 grammes according to the drawn curves.
The values calculated according to this assumption
agree very closely with the observed ones. This
observation shows that the same dog at different
stages of health digests in a different manner. A
Time in hours
Fig. 23.
dog of 126 kilogrammes weight will probably digest
500 grammes at the same rate as the observed dog,
weighing 25-2 kilogrammes, digests 1000 grammes.
It is probable that by changing the value of the
ordinates in a certain proportion the diagram will
be applicable for representing the rate of digestion
of flesh for any dog. The figures representing this
diagram are given in the following table :
90 DIGESTION AND RESORPTION
Digestion of Flesh by a Dog (London)
Time
(hours).
Undigested.
A.
Time
(hours).
Undigested.
A.
O
iooo grs.
6
275 grs.
I 12
I
875 „
125
7
178 „
97
2
75° „
125
8
102 „
76
3
627 „
123
9
51 »
5i
4
506 „
121
10
23 »
28
5
387 „
119
1 1
12 „
1 1
It indicates that the rate of digestion, if 1000 grammes
are given, is very nearly constant till about 250
grammes are left. Then it diminishes very rapidly,
as is seen from the figures given in the third
column, representing the quantity A digested during
one hour. If we regard the digestion as ended,
when all but 3 grammes have been digested in the
stomach, we find the following times necessary
for digesting different quantities of flesh written
in the fourth column. If we compare them with
Progress of Digestion with Time (London)
Quantity of flesh
Digested Quantity after three
Hours.
Time of Digestion (Hours).
Obs.
Calc.
Obs.
Calc.
100 grs.
92-2
93-3
3-5
34
200 „
I68-I
174,1
4-7
4-8
3°° »
226o
239- 5
5-7
59
400 ,,
288.5
288.7
66
6-8
500 ,,
317-3
3232
7-4
7-6
600 ,,
357-8
345-8
8-3
8.4
800 „
366-8
367-4
9.9
9-7
IOOO ,,
369- 5
373-4
115
io-8
DIGESTION AND RESORPTION 91
figures calculated according to the square-root rule
(fifth column) we find an excellent agreement.
There is an indication that with great quantities
of food the digestion proceeds a little slower than
is given by the square-root rule. This is a sign
of incipient overstrain which London observed with
still larger meals given to the dog. How well the
formula agrees with the observations of London
regarding the quantity digested after three hours
is seen from a comparison of the second and third
columns of the last table. The differences between
the observed and the calculated values all fall
within the limits of accidental deviations from the
mean value. It must be conceded that the pro-
cess of digestion goes on in a much more regular
way than might have been expected, i.e. that un-
controlled influences — e.g. the psychical state of the
dog, which is very important according to the
highly interesting studies of Pawlow — exert a
much smaller perturbing influence than generally
presumed.
As we have seen above, the digestion proceeds
very much slower if the flesh is introduced directly
into the stomach than when the dog has chewed it.
London gives two series of observations regarding
digestion of food without chewing, and for com-
parison one with chewing, for all of which the same
dog was used. In the first series (i.) the eyes and
the nose of the dog were tightly covered, in the
second (n.) they were uncovered. No sensible
difference, due to the psychical influence of the
92 DIGESTION AND RESORPTION
sight or smell of the food was observed. The figures
are given in the table below, in which the mean
Digestion of Flesh introduced per fistulam, 600 grammes
Time of
Digestion.
Undigested Quantity per Cent.
hours.
I.
11.
Mean.
calc.
O
IOO
IOO
IOO
100 (100)
2
84
84
84
84 (67)
4
56
53
54
50 (36)
6
20
18
19
2 1 (IO)
8
7
5
6
6 (0)
9
0
0
0
3
values from series 1. and 11. are compared with values
calculated from the hypothesis that the concentration
of pepsin in the content of the stomach, in accord-
ance with some experiments of Khigine and Loba-
soff, is proportional to the lapse of time from the
beginning of the digestion. The agreement is nearly
perfect, and gives a strong support to the said assump-
tion. The figures for chewed flesh are written in
brackets. It is easily seen how much more rapidly
the digestion proceeds in this case. This depends
upon the secretion of gastric juice caused by the
psychical influence induced by the chewing. The
secretion begins about ten minutes after the food
has been given to the dog.
The secretion of pancreatic juice shows the same
regularity as that of gastric juice. Dolinsky intro-
duced 250 cc. of hydrochloric acid of different con-
centrations into the stomach of a dog and found that
DIGESTION AND RESORPTION 93
the pancreatic juice secreted in forty minutes was
nearly proportional to the square root of the con-
centration of the hydrochloric acid, as is seen from
the following table, where the calculated values are
found by means of the square-root rule. The time
Secreted Pancreatic Juice in 40 mins. after introduc-
tion of 250 cc. Diluted Hydrochloric Acid
Concentration of the acid . 0-5 o-i 0-05 per cent.
Pancreatic juice, obs. . 80-5 28-3 20-5 cc.
„ „ calc. . 70.7 31-6 22.4 „
of secretion was also nearly proportional to the same
quantity.
For very small quantities of chewed flesh (below
200 grammes) the digestion proceeds nearly accord-
ing to a monomolecular formula, i.e. the curve given
above does not diverge very much from an exponen-
tial curve. The same was found by London for the
digestion of 200 grammes coagulated egg-white.
When the undigested quantity sinks below 20
grammes, the digestion proceeds very much more
rapidly than the formula demands. This probably
depends on the carrying away of a part of the undi-
gested food with the digestion products.
London has carried out some experiments re-
garding the resorption of dextrose, which is not
subject to any digestion before its assimilation. He
introduced a solution of this sugar — generally 200
cc, in some experiments 100, 500 or 800 cc. were
used, heated to 38° C. in doses of about 20 cc, with
intervals of about twelve seconds — in a fistula in the
94 DIGESTION AND RESORPTION
duodenum. The fluid moved down by the peris-
taltic movement to a fistula in the jejunum, 15 metre
distant from the first one, and was collected through
it. After ten to fifteen minutes the whole fluid had
passed and was introduced again through the duo-
denal fistula. The whole experiment lasted in most
cases two hours. At the end the concentration had
decreased, from which the resorbed quantity was
<HJN
O /
/ O
O y
tin
1 oU
CO
Resorbed
— r
0 c
0/
/c
)
n
0
? 4
\ (
>Vc" — ►
Fig. 24.
calculated. For the calculation of the regularities
the mean concentration has been used. As is seen
from the diagram, Fig. 24, in which the square root
of the mean concentration is taken as abscissa
and the resorbed quantity as ordinate, these two
quantities are nearly proportional to each other.
The few experiments with 500 and 800 cc. seem
to indicate that at constant concentration the re-
sorbed quantity is proportional to the volume of the
DIGESTION AND RESORPTION 95
solution. This is not true for the quantity ioo cc.
from which a quantity greater by about 20 per cent
is taken up than the proportionality demands.
The proportionality of the resorbed quantity to
the square root of the concentration indicates that
the process is not a question of a simple diffusion,
but that the resorbing action of the intestinal wall
is excited by the food-stuffs in the moistening fluid.
It seems very noteworthy that the exciting influence,
just as in the case of the secretion of stomachical or
pancreatic juice, is proportional to the square root
of the quantity of the exciting substance. Even the
quantity of enteric juice secreted is nearly propor-
tional to this square root.
Another experiment of London concerns a carbo-
hydrate, amylodextrin, which must be digested
before its resorption. A solution containing 4-8
grammes of amylodextrin was introduced through an
upper fistula and carried through to a lower fistula in
a certain time, from 8 to 240 minutes. The longer
the time the solution remained in the intestine, the
smaller the part of it remaining undigested and
consequently unresorbed. The quantity of amylo-
dextrin remaining undigested and also unresorbed
was determined. The undigested amylodextrin
does not reduce a Fehling solution as the digested
parts of this carbohydrate do. As is generally true
for the digestion of small quantities, that of amylo-
dextrin obeys the monomolecular formula. This is
seen from the diagram, Fig. 25 (the lower curve),
in which the logarithm of the undigested quantity
96 DIGESTION AND RESORPTION
(log n) is plotted as ordinate against the time as
abscissa. Probably the resorption goes on accord-
ing to the square-root rule. But the unresorbed
quantity follows the undigested quantity rather
closely, so that the difference — except for the shortest
time, 8 minutes, in which case it is 5 per cent — is
nearly constant, sinking from the value 16 per cent
0L_
0
120 180
Time in minutes — -
Fig. 25.
240
at 15 minutes down to 11 per cent at 200 minutes.
Therefore even the unresorbed quantity nearly
follows the square-root rule, as is seen from the
upper curve in Fig. 25, in which its logarithm is
given as a function of the time of digestion.
The square- root rule finds also its application
for the digestion of gliadin, a proteid contained in
gluten. This substance was used because its
quantity may be determined as glutaminic acid.
DIGESTION AND RESORPTION 97
Different quantities of gliadin were given to a dog
to eat and the intestinal juice was collected through
a fistula about one metre before the caecum. The
time of secretion and the quantity of nitrogen in the
secreted juice, from which a correction for the nitro-
gen-content of the gliadin was subtracted, were deter-
mined. As is seen from the table below, both the
Secretion of Enteric Juice at Digestion of Gliadin
(London and Sandberg).
Quantity
given — grs.
Time of Secretion — min.
Nitrogen in the Juice — grammes.
Obs.
Calc.
Obs.
Calc.
Diff. Smoothed.
12-5
125
I08
...
25
160
152
•6l
.41
+ -2ol
r + -09
- -OI J
50
205
215
.58
•59
IOO
275
304
LOS
.82
+ •261
ISO
350
372
•74
I-OO
-•26/
200
415
430
...
1. 16
...
300
400
520
630
527
608
101
2-02
1-42
1-64
-■40
0 > -ol
+ •38/
time of secretion and the secreted quantity follow
the law of proportionality to the square root of the
quantity of gliadin eaten. The determinations are
very difficult, because the secretion goes on discon-
tinuously with rather long intervals. For the
secreted nitrogen it is necessary to take the mean
values of two consecutive observations in order to
see the regularity. The sixth observation, (for 200
grammes) is excluded, because this observation, ac-
cording to the authors London and Sandberg, is
rather unreliable.
H
98 DIGESTION AND RESORPTION
I have entered at some length upon these circum-
stances, partly because they are of the greatest
practical interest, — the digestion seems to proceed
in a similar way in the stomach of a dog and of a
man — but also in order to show that the differences
observed in experiments "in vitro" and "in vivo"
are very easily explicable from the different experi-
mental conditions and in some cases do not exist.
On the other hand, a closer inspection of the ex-
perimental data regarding digestion, secretion, and
resorption in an animal's body shows a great number
of very simple regularities, the existence of which
in such "vital" processes, which depend to a very
high degree on psychical effects, was deemed im-
possible. It is precisely the negation of the possi-
bility of applying for the study of vital processes
quantitative methods in the same manner as in
exact science, which is the chief argument of the
vitalists. According to this opinion, forces which
are unknown to us from physics and chemistry
ought to interfere with the measurements and spoil
their value.
CHAPTER V
CHEMICAL EQUILIBRIA
We have now to investigate the equilibria of enzy-
matic processes and to compare them with the
equilibria in physical chemistry. Van 't Hoff ex-
pressed in 1898 the opinion that it might be possible
by the aid of enzymes, which decompose certain
substances, to synthesise these substances from
their products of decomposition. This opinion pre-
supposes that an equilibrium exists between these
products and their compound just as between an
ester (with water) and its products of decomposition,
acid and alcohol ; in this case the equilibrium is
reached when about § of the ester are decomposed.
On the other hand, if we invert cane-sugar by the
aid of an acid, the equilibrium lies so very near to
the end, where the sugar is totally decomposed, that
we have no hope of synthesising the sugar from its
products, dextrose and laevulose. As a matter of
fact it has been repeatedly maintained that this
synthesis has met with success, both by means of
acids and by means of invertase, but Hudson has
proved that these assertions depend upon errors of
observation.
99
100 CHEMICAL EQUILIBRIA
Chemists have succeeded in producing esters,
such as ethyl butyrate, glyceryl butyrate, glyceryl
triacetate, and fats from their alcohols and acids
in presence of lipases from pancreatic juice or
castor beans. Even glucosides, such as amygdalin,
and carbohydrates, e.g. amylose, have been syn-
thesised in an analogous manner. Perhaps the
most interesting case is the synthesis of proteins.
Danilewski and his pupils precipitated so-called
plasteins from concentrated solutions of peptones or
albumoses, to which rennet or pepsin had been
added. The plasteins exhibit the reactions of
proteins, but contain less nitrogen.
A. E. Taylor hydrolysed protamine sulphate by
means of trypsin, and after having separated the
products, he synthesised them again with the aid
of trypsin. In such cases it is not certain that the
original substance is restored, e.g. such is not the
case in the plastein formation from the products of
casein. But in one very important case this has
succeeded, namely, with the paranuclein which was
prepared by T. B. Robertson by the action of
pepsin on the hydrolytic products of casein. The
hydrolytic products into which paranuclein may be
split up do not bind the antibody which F. P. Gay
and Robertson obtained by injection of paranuclein
or casein into guinea-pigs. But if these hydrolytic
products were synthesised by pepsin the product
bound anti-paranuclein, i.e. it was paranuclein. In
other words, the authors used the strict specificity
of the antibody to discover the presence of its
CHEMICAL EQUILIBRIA 101
antigen (see p. 17). The specificity is not absolute
as we see in this case, for the antibody reacts both
against paranuclein and against casein, notwith-
standing that these substances are not identical.
The first observation in this direction was made by
Croft Hill in 1898, who found that maltase from
yeast, acting for a month on a 40 per cent solution of
glucose, gives a substance similar to maltose, which
latter may itself be decomposed by maltase into
glucose. This was regarded as a synthesis of
maltose due to an equilibrium. But later on it
was proved that the substance obtained by Croft
Hill was not maltose, but isomaltose, which is
itself not decomposed by maltase. In an analogous
manner Emil Fischer and E. F. Armstrong syn-
thesised, with the aid of lactase from kephir, from
galactose and glucose, the hydrolytic products of
lactose, not lactose but isolactose, which in contra-
distinction to lactose is not attacked by lactase.
And Armstrong found that emulsin has the opposite
effect to maltase ; it hydrolyzes isomaltose and builds
up maltose from glucose. It is therefore clear that
here we are not dealing with syntheses of substances
in equilibrium with their products of decomposition,
as was at first believed. The observed peculiarity
is probably due to a binding of the different sub-
stances to the enzymes, whereby different equilibria
are produced by different enzymes.
A real equilibrium of a very instructive kind, in
which enzymes are acting, has been investigated by
Bourquelot and B ridel {Journal de Pharmacie et
102 CHEMICAL EQUILIBRIA
de Chimie, y ser., 9, pp. 104, 155, and 230, 1914).
They investigated two different glucosides of methyl
or ethyl, called a-glucosides and /3-glucosides. The
first are decomposed by a glucosidase contained in
air-dried under-yeast, the second by emulsin (from
almonds). The equilibrium was reached from both
sides, when 76-6 per cent of the a-glucoside or 67-4
per cent of the /3-glucoside were decomposed into
glucose and alcohol (in this case ethyl alcohol). The
progress of the decomposition or synthesis may be
followed by means of a polarimeter (a0 is for a-
glucoside + 150-6°, for /3-glucoside — 35*8°, and for
glucose 52-5° at 20° C).
Here we have a quite regular and characteristic
case. Each glucoside is only attacked or synthe-
sised by its specific ferment. The degree of decom-
position is different in the two cases, but does not,
as in most cases investigated, lie so near to 100 per
cent that the equilibrium cannot be determined.
And further, just as with common katalysers, the
equilibrium may be reached from both sides, whether
we let the ferment act upon the glucoside or upon
a mixture of alcohol and glucose. The authors let
the equilibrium be reached at room temperature —
one month was sufficient for it — and then disturbed
it by adding one of the acting substances. The end
result always agreed with the calculations according
to the figures given above.
By far the simplest equilibrium occurs in the
partition of a substance between two phases. If
the. substance retains the same molecular weight in
CHEMICAL EQUILIBRIA 103
both phases, for instance a blood-corpuscle and the
surrounding fluid, then the concentration in the one
phase shall be in a constant proportion to that in
the other phase. This is even true if the substance
enters into compounds which contain or correspond
to just one molecule of the substance. For instance
a lysin, e.g. tetanolysin or vibriolysin, probably enters
into a compound with some proteid in the red blood-
corpuscles. If for the production of one molecule
of this compound precisely one molecule of the lysin
in the surrounding fluid is used up, then the concen-
tration of the lysin in the surrounding fluid and in
the red blood-corpuscle shall be in a constant pro-
portion. This occurs for vibriolysin according to
the following figures for solutions containing 9 84 cc.
of 09 per cent NaCl-solution, and 016 cc. of red
blood-corpuscles in emulsion. Different quantities
of vibriolysin were added (but always so that the
total volume was 10 cc), and by haemolytic experi-
ments it was determined how much was taken up
by the red blood-corpuscles and how much remained
in the solution. The experiments carried out by
Madsen and Teruuchi and calculated by myself
gave the following results :
[Table
104
CHEMICAL EQUILIBRIA
Lysin in Corpuscles.
Quantity of Lysin
added, in cc.
Lysin in
Solution.
Difference.
Observed.
Calculated.
0-2
0-032
0-I68
O165
+ 0-003
0-4
0-075
0-325
0-329
- 0-004
06
o- 103
0-497
O.494
+ 0-003
08
0-137
0-663
0-658
+ 0-005
IO
o- 180
0-820
0-823
- 0-003
i-5
0.255
1-245
1-235
+ O-OIO
2-0
o-395
1-605
1-644
-0-039
The figures for the two highest concentrations
are more uncertain than the others. The agree-
ment between the observed figures and the calculated
ones, which are evaluated on the assumption that
the concentration of the lysin is 286 times greater
in the blood -corpuscles than in the surrounding
salt -solution, may be regarded as extremely satis-
factory.
I have determined the partition coefficient of
different substances between red blood-corpuscles
and an isotonic aqueous solution, in most cases 0-9
per cent NaCl-solution, but for the experiments with
silver nitrate 7-5 per cent cane-sugar solution. The
surrounding solution must be isotonic with, that is
possess the same osmotic pressure as, the red blood-
corpuscles, otherwise they may be haemolyzed by the
solution. The red blood-corpuscles take up more
of the investigated substances, all of which possess
haemolytic properties, than the surrounding solution,
therefore the partition coefficient, that is the propor-
tion of the concentration of the investigated substance
CHEMICAL EQUILIBRIA
105
in the blood-corpuscles to the concentration in the
solution, is greater than i.
The following figures were obtained :
Acetone .
2.9
Methyl alcohol
Ethyl alcohol
Ethyl ether
Isoamyl alcohol
3
33
3-3
5-5
Saponin
Vibriolysin
120
286
Silver nitrate
450
Acetic acid
590
Sodium hydrate
Ammonia
750
780
Mercuric chloride
i
more than 2,000
Evidently the substances may be divided in two
groups, of which the latter (from saponin) show a
strong affinity for the proteids contained in the
corpuscles. Without doubt they enter into com-
binations with them, which are the less dissociated,
the higher the value of the partition coefficient is.
In some few cases, as for the absorption of
agglutinins in their specific bacilli and for the ab-
sorption of so-called amboceptors (see p. 128) in
their specific erythrocytes, I have found, in calculat-
ing the figures observed by Eisenberg and Volk,
that the ratio of the two concentrations in this case
in the bacteria and in the surrounding fluid is not
constant. The result of these calculations is that
the concentration B of the agglutinin in the bacilli
is proportional to the § power of the concentration
in the surrounding fluid. This regularity is indicated
by the diagrams Figs. 26-29 regarding the absorption
of two agglutinins (typhoid, Fig. 26, and cholera,
106 CHEMICAL EQUILIBRIA
4
%
°s^
1
CD
bo
O
-I
3
2
1
I
I
J
4
Log C
Fig. 26.
4
t3
CQ
X>0
ySO
O
-J
2
\
0/
So
1
D
1
\
f
J
4
Fig. 27.
LogC
CHEMICAL EQUILIBRIA 107
100
o
s^O
'Q
o.
1
2
\
*
J
4
LogC
Fig. 28.
00
bo
o
/ °
0
1
/
)
*
\
4
LogC
Fig. 29.
108
CHEMICAL EQUILIBRIA
Fig. 27) and two amboceptors (from rabbit, Fig. 28,
and from goat, Fig. 29). It is evident that, very
nearly, log B = A + f log C.
It may be that this circumstance is due to some
disturbing action, similar to that which obscures
the monomolecular law for coagulating egg-white
(cf. p. 29 above). In reality, agglutination may be
regarded as a kind of coagulation.
Madsen and Teruuchi have investigated the
condensation of vibriolysin on coagulated and finely
divided egg-white suspended in a solution contain-
ing that poison. They found the following figures,
in which cQ indicates the concentration of the poison
in the solution — the concentration is expressed in
cubic millimetres of a standard solution per 10 cc. of
fluid or egg-white — c1 the corresponding concentra-
tion in the egg-white. As the content of poison in
the standard solution is very small, the value of cx
may naturally be expressed by a very large number.
For comparison the square-root \/c0 of c0 and the
ratio c1 : J7Q are tabulated :
c0.
cv
VCQ.
_£l_.
7
6,200
2-64
2343
16
8,930
400
2233
26
1 1,600
5.10
2275
5i
16,670
7-14
2333
73
21,900
8-54
2563
89
27,500
9-43
2915
Average
2444
As we see from the values tabulated in the last
CHEMICAL EQUILIBRIA
109
column, c is very nearly proportional to s/c0. This
points to the circumstance that we here observe a
phenomenon of adsorption, for, when the concentra-
tions c0 are small, such a law as that found above is
found to hold good in similar cases.
As an instance of a case of adsorption, we repro-
duce here some figures of Palme (Hoppe-Seyler's
Zeitschrift f. physiol. Chemie, 92, 184, 19 14). He
added a certain quantity, generally 2 grammes,
of casein to 50 cc. of a solution of ferrocyanic acid
of known concentration. Palme observed that
a quantity of up to 37-8 milligrammes is bound
chemically by the casein. After this further
quantities of the ferrocyanic acid are taken up in the
casein by means of adsorption. The law of adsorp-
tion follows the same formula as the extended rule
of Schutz (see p. 42), if we let t denote the con-
centration and x the adsorbed quantity, which
approaches asymptotically to a maximum A with
increasing t. The following table gives the observed
values of t and x, which latter are compared with
values xcalc. found on the supposition that K^ = 0-0333,
A is just equal to 1 50 milligrammes.
Adsorption of Ferrocyanic Acid on Casein
t
*obs.
x calc.
*• X obs. x calc.
0-0005
0-0164
0*0238
0-1148
16-7
20-6
37-4
2*7
I5'2
i8-i
37-8
0-2746
0-8876
1-8396
57-5
86-i
ii6-i
55-2
87-6
II2-I
The agreement seems to be perfect within the errors
110 CHEMICAL EQUILIBRIA
of observation. The first observed value of xohs,
5 4 is much too high, probably due to the dissociation
of the compound of ferrocyanic acid and casein.
The close coincidence of the xohs. with the ;rcalc
indicates that we really have to do with an adsorption
phenomenon.
In general it is supposed that adsorption pheno-
mena play a very important role in biochemical re-
actions. Without doubt their existence is proved in
many cases, but the predominant influence which is
ascribed by the school of colloidal chemistry to these
phenomena seems to be greatly over-estimated.
The equilibria between highly organized products
similar to the enzymes, namely the toxins, their anti-
bodies and their compounds, have been investigated
at some length, because of the extreme importance
of these substances in therapy. Ehrlich was the
first to subject the neutralization of toxins to a
quantitative study. He was especially interested in
the behaviour of diphtheria poison, when it was
neutralized by adding antidiphtheric serum. He
took a certain quantity of poison containing ioo
lethal doses, i.e. enough for killing ioo guinea-pigs
in between three and four days. He added a
quantity A of antidiphtheric serum which was
sufficient to neutralize 25 per cent of the poison, so
that the mixture contained only 75 lethal doses.
He then added the quantity A again, and repeated
that a certain number of times, say until 6 A were
added. It was in this manner that Julius Thomsen
investigated the evolution of heat on successive
CHEMICAL EQUILIBRIA 111
partial neutralizations of the acids in order to find
out if they were dibasic, tribasic, etc., in which case
the evolution of heat was not constant at the different
measurements, but only as long as the same valency
of the acid was neutralized. For weak acids, such as
silicic or boracic acid, heat is evolved even after
equivalent quantities of bases (generally NaOH)
have been added if still further base is introduced
into the mixture.
Ehrlich observed that the neutralization pro-
ceeded very irregularly, so that sometimes the second
addition of A neutralized more poison than the first
one (this he supposed to correspond to the greater
evolution of heat at neutralizing the second valency
of sulphuric acid as compared with the first). But
the very last portions of antitoxin always neutralized
very little of the toxin. Sometimes even the first
portion of the antitoxin had no neutralizing effect at
all. Different specimens of poison differed in the
highest degree from each other.' In order to
elucidate this question I asked Dr. Madsen to sum
up all his experiments from the Danish States Serum
Institute, which I subjected to calculation, using not
only the data for deaths between 3 and 4 days, as
was done before, but even those in which the death
of the guinea-pigs occurred at other times. The
decrease in weight of the animals was also used for
determining the toxicity of the injected mixture of
toxin and antitoxin. The results are given in the
table below. Two series of observations are given
there for the same poison, the first one (toxicity Tx)
112
CHEMICAL EQUILIBRIA
was carried out in February 1902, the second (toxicity
Tn) 19 months later, i.e. in September 1903. As is
seen, they agree very closely with each other, so that
Neutralization of one equivalent of Diphtheria Poison
by n Equivalents of Antidiphtheric Serum
n.
T,
Tn.
T calc.
O
100
IOO
IOO
•25
73
75
75
•375
58
63
627
•5
5o
48
50.5
•675
32
45
38.4
•75
28
26
27
•875
17-2
17-3
16.5
10
hi
9.6
8-8
1-125
5.6
5-3
4.9
1-25
1-2
3-i
3-i
i-5
16
i-7
2
•9
3
•3
K = o
• 0093
the discrepancy between them is without doubt due
to experimental errors. After the observed values
Tx and Tn are given values calculated according to
the law of Guldberg and Waage, if two molecules
of the compound are formed from one molecule of
the poison and one molecule of the antitoxin. The
formula is :
(Cone, of free toxin) (Cone, of free antitoxin) = K (Cone, of neutralized toxin)2.
As is seen, they agree perfectly with the observed
figures within the errors of observation, which may
be estimated from the differences between the two
CHEMICAL EQUILIBRIA
113
sets of observations. Strangely enough there are
two observations for 72 = 0-675 which differ from
each other by not less than a third of the value, but
the mean value is in perfect accordance with the
calculated value. If we now take # = 025 as the
value of A, we find that the first addition of A
neutralizes 25 lethal doses (obs. 26), the second 24-5
(obs. 25), the third 23-5 (obs. 22), the fourth 182
(obs. 167), the fifth 57 (obs. 8-2), and the sixth only
3 Quantity of Antitoxin
in equivalents
Fig. 30.
14 (obs. 06) lethal doses. This different action of
the different quantities of antitoxin is termed
Ehrlich's phenomenon. This peculiarity is just
what we might expect if the bond is rather weak, so
that a part of the compound is dissociated. The
progress of neutralization is represented by the
undermost curve in the diagram, Fig. 30.
These figures were not the first calculated in the
said manner. There were some experiments on
tetanolysin, a poison produced by the lock-jaw
114 CHEMICAL EQUILIBRIA
bacillus. This poison has the not uncommon pro-
perty of killing the red blood-corpuscles in such a
way that the haemoglobin leaves them and enters
into the surrounding solution. The experiments
are made in test-tubes, containing red blood -cor-
puscles, to which the mixtures of lysin and antilysin
are added in given quantities (the total volume being
iocc. filled up with 0-9 per cent NaCl solution),
and the blood is haemolyzed in the higher degree
the more free toxin is present. Now every test-tube
contains hundreds of thousands of red blood-cor-
puscles, so that every observation gives a statistical
mean value for so many individuals, of which
specimens with very different sensibilities in regard
to the lysin occur (see p. 76 above). With guinea-
pigs each figure is the mean of only some ten
observations on as many individual animals — the
method commonly used is content with only one or
two observations for each figure. Therefore the
haemolytic experiments give in general much better
values than experiments with living animals. Con-
sequently the agreement with calculation is in the
case of haemolysins better, therefore they play an
important role in the doctrine of immunity. When
I worked in Dr. Madsen's institute I observed the
very pronounced similarity between the partial
neutralization of a weak acid by a weak basis, and
the neutralization of tetanolysin by its antilysin
according to Madsen's experiments (represented in
Fig. 30, middle curve) made in Ehrlich's institute.
Now the bases are lysins ; I therefore proposed that
CHEMICAL EQUILIBRIA 115
we should investigate the neutralization of ammonia
regarded as a lysin, i.e. measured by its haemolytic
activity, by means of boracic acid, and of sodium
hydrate by hydrochloric acid.
The result of the experiments was in perfect
accordance with what I expected. The simplest
case is the neutralization of one equivalent of
sodium hydrate by hydrochloric acid. The salt
formed is absolutely innocuous. Say that we have
oi normal solutions of NaOH and HC1 ; if we add
o-i cc. of the alkali to 10 cc. of a 2-5 per cent
emulsion of red blood-corpuscles, this dose gives a
certain degree of haemolysis (after 2 hours at 370 C).
Now we mix 05 cc. HC1 with 1 cc. NaOH and
investigate which quantity of this mixture gives the
same degree of haemolysis. Evidently in 1-5 cc. of
the mixture there is as much free sodium hydrate
as in 05 cc. of the original solution. We must
therefore now take 03 cc. of the mixture for ob-
taining the said effect, and so forth. The diagram
(Fig. 31) representing this behaviour is a straight
line, which cuts the ^-axis at 1 corresponding to
addition of a quantity of acid equivalent to the
quantity of base used. In reality the line of
neutralization cuts the ^-axis a little before, because
the corpuscles sustain a certain minimal quantity
of free alkali before any haemolysis is observed.
If we add more acid we observe a similar small
region of acidity which does not attack the corpuscles,
and then haemolysis occurs again and the haemolytic
power of the solution is proportional to the excess
116 CHEMICAL EQUILIBRIA
of added acid over this point of first acid action.
The smaller angle between the line marked Acid
and the ^r-axis indicates that acids have about half
as great haemolytic power as bases.
The neutralization of cobra lysin (poison from
the cobra) by its antibody, the so-called antivenin,
behaves in nearly the same manner (see Fig. 31,
upper line). But there is really a small degree of
75
o
52
o
Q.
I'5
75
©•25
N&
\ 0
k
w9
^Ca
/\n
^°
Acid or z
ntivenin
2
Fig. 31.
dissociation, for when an equivalent quantity of
antivenin is added to the venom still 3-3 per cent
of its toxicity remains, according to the observations
of Madsen and Noguchi, from which we may
calculate the dissociation constant to be K = 00014
or the seventh part of that for diphtheria poison.
Another snake venom from the water- moccasin
(Ancistrodon piscivorus) gives the value K = o-oo6,
and that from Crotalus only K = 00006. Their
CHEMICAL EQUILIBRIA
117
neutralization products (with their specific anti-
toxins) are consequently less dissociated than the
corresponding products of diphtheria toxin.
If we now consider the neutralization of ammonia
with boracic acid, which is tabulated below, we
find that the toxicity, when equivalent quantities are
mixed, has been reduced to only about 50 per cent,
and, even if the double quantity of boracic acid has
Neutralization of the Haemolytic Action (T) of i Mol.
NH3 through n Equivalents of H303B
ft.
Tobs.
T
calc.
AT
Aw obs.
AT
An ,
calc.
0
IOO
IOO
• • •
o-333
82
75
•54
•75
0-667
63
60-3
•57
•44
1
47-5
5o-3
•47
•30
1-333
43-7
43-2
• 1 1
• 21
1-667
36-0
37-6
•23
•17
2
33-5
33-5
.08
12
3
25
...
.09
5
17
.04
10
9
• 016
5o
...
2
• 002
K= 1-02 (1-04 Lunden).
been used, still 33-5 per cent of the ammonia is not
neutralized(compareFig. 30,uppermostcurve). From
the figures observed we calculate K = 1 02 or about
no times as much as for diphtheria serum. Here
Ehrlich's phenomenon is extremely pronounced.
If we now represent AT : Az/ from the observations,
as Ehrlich did in his so-called " poison spectra,"
118
CHEMICAL EQUILIBRIA
we find that one equivalent of the first dose
(°'333 equivalents) neutralizes 54 ( = 3-18) per cent.
A T
AT = i-oo- -82 = -18 and Au= -333; hence-— = -54.
The second dose corresponds to 57 per cent, and so
forth. The poison spectrum of ammonia should
therefore be represented as in the diagram, Fig. 32,
and we ought therefrom to conclude that ammonia
contains not less than six different "partial poisons,"
Q.uaat ity of H30jB added
Fig. 32.
if we used the same reasoning as Ehrlich regarding
the diphtheria poison, which he and Sachs have in
this manner divided up in not less than ten different
" toxins " and " toxoids." Of course this is not true
for ammonia, and, after all, not more for the diphtheria
toxin ; the conclusion is based only on the relatively-
great errors of observation. This is easily seen
from the figures for ammonia, which agree with the
calculated figures within the possible errors of
observation.
After the determination of K = 1 02 from the
CHEMICAL EQUILIBRIA 119
experiments of Madsen and myself regarding the
haemolytic action of mixtures of NH3 with H303B,
LundilN measured it according to the methods used
in physical chemistry and found it to be K = i 04
at the same temperature (37° C), which is an ex-
tremely good control on the validity of the theory
adopted.
According to the same method and formula I
calculated the figures of Madsen for tetanolysin
and found K = 01 15 at $7° C. At 160 C. it is 1-91
times smaller, from which we may calculate that at
the binding of one gram-molecule tetanolysin to
one gram-molecule antilysin there are formed two
molecules of their compound with an evolution of
5480 calories. The curve representing the neutral-
ization falls between that characteristic for ammonia
with boracic acid, and that for diphtheria toxin with
its antiserum. The agreement between observation
and calculation is very good and wholly within the
errors of observation (see Fig. 30, middle curve,
and the following table).
[Table
120
CHEMICAL EQUILIBRIA
Toxicity q of 004 cc. Tetanolysin after Addition
of n cc. (nY Equivalents) of Antilysin (Madsen)
Quantity of Antilysin.
Toxicity (Free Poison in Per Cent).
n cc.
n\ Equiv.
^ obs.
^ calc.
O
0-05
O. 1
CI5
0-2
o-3
0.4
0.5
0.7
10
1-3
1.6
2-0
O
0-l8
0-36
O.54
0-72
I 09
1-45
I- 8l
2-54
3.26
4-35
5-44
6-52
IOO
82
70
52
36
22
14-2
1 OI
6-1
4-0
2-7
2-0
1.8
IOO
82
66
52
38
23
13-9
10-4
6-3
4.0
2-9
2-5
1.9
K = oii5 at 370 C.
It is quite clear that it is impossible to determine
the quantity of antidiphtheric serum which is equiva-
lent to a given quantity of diphtheria poison by
looking for how much serum must be added to the
said quantity of poison in order that the mixture
shall be innocuous, as is usually done. In medical
practice it is of course necessary to give a moderate
excess of antiserum in order to be certain of the
innocuity. Even if we mix the double equivalent
quantity of antidiphtheric serum with 100 lethal doses
of diphtheria poison, still 9 lethal doses are free, and
with the five-fold quantity of antitoxin (in equiva-
lents) 27 lethal doses are not bound. The only
CHEMICAL EQUILIBRIA 121
method of determining the equivalent proportions
is to draw the tangent to the neutralization curve
(Fig. 30) at its highest point. The point of inter-
section of this tangent with the ;t:-axis gives the
quantity of serum equivalent to the quantity of
poison used (in this special case 02 76 cc. of anti-
toxin are equivalent to 004 cc. of toxin).
In many cases it is said to have been observed that
the first dose of antitoxin exerts no neutralizing action
upon the poison examined. From the theory we
might conclude that it should exert a greater action
than the following equal doses. The diphtheria
poison spoken of above, when it was first examined
by Madsen in the usual manner, seemed to show the
phenomenon that the first parts of antitoxin added
did not act as a neutralizer. In this case only those
observations were taken into account in which the
guinea-pigs examined were killed in three to four
days. When I made the recalculation I used all the
observations in which the animals died in less than a
fortnight and also the observed decrease in weight of
the animals. In this way I had a material about ten
times greater than that used by Madsen, and then
the first admixtures of antitoxin showed themselves
to be of a stronger neutralizing action than the follow-
ing (see table, p. 1 1 2), when the same quantity of anti-
toxin was used. In order to explain the old obser-
vations Madsen supposed, as Ehrlich had done
before, that the diphtheria toxin contains an in-
nocuous substance called prototoxoid, which binds
the antitoxin with stronger forces than the toxin itself,
122 CHEMICAL EQUILIBRIA
and therefore takes away the first part of antitoxin
added and hinders it from neutralizing the poison.
It is quite clear that, in Madsen's case, the errors
of observation caused the spurious effect. Ehrlich
has also found " prototoxoids " only in some of his
diphtheria poisons, which differ rather much from
each other, and I have no doubt that the errors of
observation have caused the observed anomalies.
The only poison for which Madsen, in his exten-
sive investigations on the neutralization of poisons,
has stated the presence of a prototoxoid is ricin.
This poison gives with its antitoxin a flocculent
precipitate of the compound, so that in Guldberg-
Waage's formula the concentration of this compound
enters in the form of a constant. The calculation
gives very concordant results with the observation,
if this peculiarity is observed. But before a pre-
cipitate is formed the compound remains in a
dissolved state and is probably nearly wholly dis-
sociated. Therefore the toxicity does not diminish
until enough antiricin is added to give a precipi-
tate. This limit is not very constant according to
Madsen's experiments, which may be due to super-
saturation or to the presence of foreign substances,
e.g. hydrogen ions, in different quantities.
Even at the end of the neutralization Ehrlich
observed that the mixtures had lost their lethal effect
but were not innocuous and gave different symptoms
from the pure poison. It seems to me not very
strange that a poison gives different symptoms
according to its strength, for similar cases are
CHEMICAL EQUILIBRIA 123
observed with inorganic poisons. But Ehrlich
concluded that the diphtheric poison contains a
substance, called epitoxoid or toxon, which has a
less avidity for the antidiphtheric serum than the
chief poison, the toxin, and therefore remains un-
neutralized, after the toxin has been made innocuous.
Madsen and Dreyer have pointed to the absence
of these " toxons " in some of his diphtheria poisons.
After all we should not accept their existence without
more convincing proofs.
In his investigation of the diphtheria poison
mentioned on p. 1 1 1 Madsen observed that it was
only half as violent in September 1903 as in February
1902. The poison had lost half its toxicity during
the lapse of nineteen months, but still it neutralized
the same quantity of antitoxin and the dissociation
constant had remained unchanged. Similar obser-
vations had been made before by Ehrlich. In
order to explain this peculiarity it seems necessary
to suppose that the half number of the molecules of
the poison had been transformed in an innocuous
modification, which retained the properties of the
poison in regard to the antitoxin. Such an in-
nocuous substance may be called " syntoxoid ' in
accordance with Ehrlich's nomenclature.
Quite recently Calmette and Massol described
a cobra poison (Comptes Rendus, 159, 152, Paris, 1914),
which had lost five-sixths of its toxicity from 1907
till 191 3 and still retained its property of binding
the specific antivenin un weakened. It had been
kept in darkness and in a closed tube. Powdered
124 CHEMICAL EQUILIBRIA
poison is more rapidly weakened than poison ivjj
larger lumps. The antivenin had not changed its
power sensibly during the six years. The innocuous
precipitate which is formed by the combination of
cobra poison with antivenin gave back the whole
quantity of its toxin content unweakened when
heated to 72° with a small quantity of hydrochloric
acid, even after storage for five years.
The adherents of the old Ehrlich theory objeci
to the use of the laws of equilibria on the bindings
of toxins, that the processes in this case are not
reversible, because the compound of toxin and
antitoxin changes with time, so that it becomes
less dissociable. This last assertion is not true
in some cases, as that told of by Calmette,
but in other cases it is true, as we shall soon
see. But on the same ground we might oppose
the use of reversible processes for the calcula-
tions in thermo-dynamics, because ideal reversible
processes are in general not realized in nature.
Every physicist knows that such opposition is
unjustified. Such an irreversible process was
discovered by Danysz in the so-called Danysz
phenomenon. Danysz found in experiments with
ricin or with diphtheria poison that if we have a
certain quantity of poison and a (not too small)
quantity of its antibody and mix them at once, the
mixture possesses a less degree of toxicity than the
mixture which results if we take only a part, say
50 per cent, of the poison and mix it with the
total quantity of antitoxin and after a time add
CHEMICAL EQUILIBRIA 125
the rest of the poison. This phenomenon was
said to be without analogy in general chemistry,
and was therefore said to overthrow all calculations
based on the existence of an equilibrium between
the said reagents.
Thephenomenon recalls an observation of Bordet.
We take enough lysin just to haemolyze completely
a certain quantity of red blood-corpuscles ; divide
this quantity in two equal portions and add the
lysin to the one part, adding the remaining part
of the blood -corpuscles later. Then we find that
the haemolysis is far from complete. This effect
depends evidently upon the well-known capacity
of the proteins in the corpuscles to bind a greater
quantity of poison than that just necessary for
complete haemolysis. The second half part of the
corpuscles therefore receive scarcely any lysin and
the haemolysis becomes incomplete.
From general chemistry we are familiar with
a similar phenomenon. Monochloracetic acid may
be regarded as a lysin and NaOH as its antilysin.
If we add i cc. of i w monochloracetic acid to the
same volume of i n NaOH, the haemolytic effect
is wholly neutralized, and if we heat the solution for
a long time to jo° C. the mixture remains innocuous.
But if we add only 05 cc. of the acid to 1 cc. of
NaOH and keep it at 70° C. during a sufficient
time the NaOH at first forms the Na-salt of the
acid and the half part of the base is free. This
free base slowly transforms the Na-salt to Na-
glycolate and gives NaCl with the chlorine from
126 CHEMICAL EQUILIBRIA
the Na-monochloracetate. After a sufficient time
the whole quantity of NaOH is bound, and if we
then add the remaining 0-5 cc. of monochloracetic
acid, the mixture has haemolytic properties. This
is precisely the Danysz effect.
Madsen and Walbum made a very large number
of experiments on the Danysz effect with tetanolysin.
We are here concerned with the difference, often
very small, in toxicity between the two mixtures, and
owing to the difficulties of the experiments it was
necessary to repeat every observation many times
and take the mean values to be certain of the
validity of the observations. For this purpose
thousands of observations were necessary. At 37° C.
about eight hours were necessary for reaching the
end-value. The process was monomolecular and
increased in the proportion i-86 : 1 in an interval of
io° C, corresponding to a value of p= 11 300.
It is quite clear that if we do not add more NaOH
to the first fraction than is necessary for neutralizing
the monochloracetic acid, the effect will be zero.
Subsequently the effect will increase proportionally
to the excess of NaOH over the neutralizing
quantity till double the neutralizing quantity is
reached. This was also found to be the case with
the Danysz effect for tetanolysin, except that the
effect was not limited to the interval between
equivalent and double equivalent quantities of the
antitoxin. The perfect concordance between the
observed and calculated values of the end effect is
shown by the following observations :
CHEMICAL EQUILIBRIA
127
The Danysz Effect for Tetanolysin
(Madsen and Walbum)
First Fraction.
Free A.
Danysz Effect.
Obs.
Calc.
0-2 CC. A+ I CC. L
002 CC.
5
2
04 cc. A+ I cc. L
0-2 2 CC.
23
22
o-6 cc. A+ i cc. L
04 2 CC.
39
42
o-8 cc. A+ i cc. L
0-62 CC.
60
62
i-2 cc. A+ i cc. L
I 02 CC.
97
I02
A is the solution of antitoxin used ; L the solution of tetanolysin ;
1 cc. L was by means of special experiments on neutralization found
equivalent to o- 1 8 cc. of A. The calculated effect is taken pro-
portional to the free quantity of A.
Experiments have been carried out by von
Dungern on the Danysz effect for diphtheria toxin.
He has, however, not let the toxin and antitoxin
react upon each other for sufficient time to reach the
end effect. His figures are therefore only about
half as great as they would have been if he had used
sufficient time of action.
In order to explain the Danysz effect the Ehrlich
school supposes the presence in the toxins of a new
kind of substances called epitoxonoids, which are
neutralized after the "toxons." Of course the sup-
position of one new substance corresponds to the
introduction of two new hypotheses, the one re-
garding its toxicity, the other regarding its quantity.
Sachs believed he had found at least two " epi-
toxonoids."
In his epoch-making Dialogue regarding the
128 CHEMICAL EQUILIBRIA
Two Greatest Systems of the World Galilei makes
his representative Salviati say that the hypothesis
of a daily motion of the earth is much better than
the many hypotheses regarding the Ptolemaic
epicycles and cite the words of Aristoteles :
" Frustra fit per plura quod potest fieri per pauciora,"
or, freely translated: "We ought to use as few
hypotheses as possible in our explanations." This
principle, which is also adopted by Newton in his
Principia, is fundamental in all scientific work, and it
will also give the decision regarding the "plurality-
hypothesis ' in immuno-chemistry regarding anti-
diphtheric serum.
If we inject the red blood -corpuscles from
an animal into the veins of an animal of another
species, we find after a certain time of incuba-
tion— three days or more (cp. p. 15) — an antibody
which haemolyzes blood -corpuscles of the same
kind as the injected ones in this animal's blood-
serum. If we heat this haemolysin to 55° C. for
some minutes it is "inactivated," i.e. it loses its
haemolytic power. But this inactivated fluid still
contains some active substance, for it regains its
haemolytic power after addition of a normal serum —
in most cases fresh serum from guinea-pigs is used —
which itself possesses a very small haemolytic power.
Some substance in this fresh serum is not specific,
but acts against all kinds of erythrocytes, "completes"
the inactivated serum, and is therefore called the
" complement," whereas the active substance in the
inactivated serum, which is specific against the in-
CHEMICAL EQUILIBRIA 129
jected erythrocytes, is called the " immune body " or
"amboceptor" (Ehrlich).
The amboceptor is absorbed very rapidly and in
great quantity by the red blood-corpuscles against
which it is specific (cf. p. 105). These are not
haemolyzed by it. If they are mixed (in physiological
salt solution) with fresh blood-corpuscles of the same
kind, these slowly take up a part of the amboceptor.
Blood-corpuscles which are loaded with a quantity
of amboceptor not too small become laked when
brought into contact with complement.
Bordet, who was the first investigator of this
field, supposed that the amboceptor acts as a
" sensitiser " of the blood-corpuscles when they are
attacked by the complement. Ehrlich, on the other
hand, supposed that the amboceptor binds the
complement and that the addition product is a so-
called " compound haemolysin." This question
could evidently be decided by quantitative measure-
ments, and Ehrlich invited me to carry out the
necessary determinations in his laboratory. In the
following table I reproduce as example a series of
observations on the haemolysis of erythrocytes of an
ox. The emulsion contained 2 per cent of erythro-
cytes and had a total volume of 2-5 cc. In it were
dissolved a cubic millimetres of the inactivated goat
serum, which contained the amboceptor specific
against blood-corpuscles from oxen, and b cubic
millimetres of the complement, natural serum from
guinea-pigs. The quantity of haemolysin is called
x and is taken to be proportional to the square root
K
130
CHEMICAL EQUILIBRIA
of the observed degree of haemolysis in accordance
with experiments of Manwaring. The quantity of
haemolysin necessary for complete lysis is termed
ioo.
Equilibrium between Amboceptor from Goat, Complement
and Haemolysin for Ox Erythrocytes
The tabulated quantity is the concentration x of haemolysin.
b.
a = 10.
a -30.
a =100.
a = 300.
a — goo.
60
40 (46)
40
37 (45)
• • .
...
25
38 (42)
. . .
15
39 (37)
10
38 (33)
71 (84)
98 (IOO)
100 (100)
6
22 (25)
59 (60)
85 (98)
98 (IOO)
4
20 (20)
45 (44)
75 (66)
82 (73)
2-5
24 (29)
5i (43)
47 (47)
i-5
15(18)
25 (25)
22 (28)
24 (29)
1
I5(i7)
i5(i9)
18 (20)
06
...
11(10)
13(H)
13 (12)
In brackets are written values calculated from the
formula
($a — x) {20b — x) = gox.
The agreement between the observed and the
calculated quantities is quite sufficient, considering
the rather large errors of observation. It is quite
clear that the quantity of haemolysin increases both
with the quantity of amboceptor and with the
quantity of complement used. But even with the
greatest quantity of complement (b = 60) we do not
reach complete haemolysis (x = 100) if there is not
a sufficient quantity of amboceptor (a = 20) present.
In this case x according to the formula cannot ex-
CHEMICAL EQUILIBRIA 131
ceed $a, i.e. 50 — the observation gives not more than
40. In the same manner if b is small, e.g. 06 or 1,
the quantity of haemolysin does not reach 100 even
with the greatest excess of amboceptor (# = 900).
According to the formula x cannot in this case
exceed a maximum x=2oby i.e. 12 or 20, in perfect
accordance with the observation. This circumstance
indicates that neither the amboceptor nor the com-
plement acts as a katalyser or sensitiser. (The
test-tubes containing the mixtures were kept at
$y° C. for two hours and subsequently for seventeen
hours at 20 C, so that the final equilibrium was prob-
ably nearly reached.)
The agreement of the formula with the observa-
tions indicates that a binding really takes place, so
that when 100 units of haemolysin are formed the
quantity of amboceptor in 20 cubic millimetres of the
goat serum and the content of complement in 5 cubic
millimetres of guinea-pig serum are consumed.
The fact that total haemolysis is not reached even
with very great quantities of amboceptor or com-
plement if the other component is not present in a
sufficient degree had been proved by Morgenroth
and Sachs in 1902.
Two other combinations were tried. The one
of them in which amboceptor from goat and guinea-
pig serum acted upon red blood -corpuscles from
sheep gave the formula
(^oa—x)(2$b — x)= iqoox.
The second with red blood - corpuscles from ox
132 CHEMICAL EQUILIBRIA
and amboceptor from rabbit with guinea-pig serum
corresponded to the formula
(100a — x)\iob — x) = I-&T2.
In the first of these two we find amboceptor from
goat and guinea-pig serum just as in the example
given in detail above (p. 1 29). The only difference is
that the red blood-corpuscles were taken from sheep
in the one case and from ox in the other case. The
sheep is much more nearly related to the goat
than the ox is. This relationship finds its ex-
pression in the dissociation constant 1900 for the
combination sheep-goat as compared with the dis-
sociation constant 90 for the combination ox-goat.
The higher the dissociation constant the less is the
tendency to form the compound haemolysin. The
more the animal in which the erythrocytes are in-
jected differs from that which has supplied the
erythrocytes, the easier is the formation of the
haemolysin. The attempt to produce a haemolysin
by injection of red blood-corpuscles of one animal
into the blood of another animal of the same species,
therefore, seldom meets with success. Still there
are some reports that so-called isolysins have been
obtained with such a treatment (Ehrlich and Mor-
genroth, 1900). But in this last case, with goat
serum, it was necessary to use thirty times as much
amboceptor for reaching complete haemolysis of
goat corpuscles as with goat serum against ox
corpuscles, which makes an extremely high dis-
sociation constant probable.
CHEMICAL EQUILIBRIA 133
In the last example with rabbit serum acting on
ox erythrocytes we find that the quantity of ambo-
ceptor enters in the formula to the power f . This
is probably due to the so-called diversion of the
complement, which is observed by myself just for
this special combination. With an excess of ambo-
ceptor this binds the complement so strongly in the
solution that a very small fraction of it remains in a
free state. Therefore the diffusion of complement
into the amboceptor-loaded erythrocytes goes on
very slowly, and the reaction does not reach its end
during the time of action. — It is only the haemolysin
contained in the blood-corpuscles themselves which
acts haemolytically. — The retardation increases with
the quantity a and makes itself apparent in diminish-
ing the power to which the term containing a enters
in the formula. It is therefore quite possible that
this power ought to be i if the said disturbance did
not take place.
Great interest was evoked by the discovery that
cobra poison, which is only slightly haemolytic, is
activated in a very high degree by the presence of
lecithin. The lecithin was regarded as a complement
in this special case. When I investigated this case
I found that the observations were expressed by the
following formula
C(L-i5f = 6-67x2.
A certain quantity of lecithin (Z,), namely 0-015
cubic millimetres, was necessary before any haemolytic
action was observed, but neither the cobra poison,
134 CHEMICAL EQUILIBRIA
C, nor the lecithin, Z, was consumed by the haemo-
lytic agent x. In this case Bordet is right : the
lecithin acts as a sensitiser. It is not only for
cobra poison that lecithin acts in this manner, but
even for other haemolytic agents, such as mercuric
chloride and acids.
A very important group of antibodies from serum
are the precipitins, so called because they form a
precipitate with the substances injected in the veins.
In this manner lactoserum is prepared by the injec-
tion of skimmed milk (casein), and a serum against
egg-white by the injection of egg-white. These two
antibodies precipitate their specific antigens.
The precipitins have evoked a very great interest.
They are used for deciding from which kind of animal
a blood -trace is derived. This method has been
developed especially in Germany by Uhlenhuth,
Wassermann, and others. It is mostly applied for
investigating if blood-spots on clothes or knives are
of human or animal origin, and has rendered great
services to justice. Another employment of pre-
cipitins is for determining the relationship of animals
or plants. The greatest merits in this field belong
to Nuttall, who has written a great monograph
on Blood Immunity and Blood Relationship (Cam-
bridge, 1904).
Nuttall was the first to use a quantitative method
in this field by measuring the quantity of the pre-
cipitate collected in a capillary tube. As example,
the results of some experiments in which 010 cc.
of antiserum against human blood was mixed with
CHEMICAL EQUILIBRIA 135
5 cc. of different blood-sera are given here. The
quantity of the precipitate was with :
Human blood . . . . . 0-31 cc.
Blood from gorilla . . . . o- 2 1 cc.
,, ,, orang-utang . . . 0-13 cc.
„ „ dog ape . . . . 009 cc.
Blood from half- apes (lemurides) gave no pre-
cipitate. These animals have very little relation-
ship with man. In the same manner the whales
{cetaceans) were shown to be in relation with the
hoofed animals (ungulata) and the reptiles with the
birds. About 16,000 measurements were carried out.
In a similar manner the plants have been examined,
especially by Friedenthal and Magnus. Their
experiments indicated, for instance, a relationship
between yeast and truffle.
Hamburger has made some quantitative measure-
ments of the quantity of precipitate formed by cen-
trifuging it in a tube which ended in a very narrow
graduated tube — 1 degree of the scale corresponded
to 0-4 cubic millimetres. These measurements were
given me for calculation.
The simplest case was found with sheep serum
and the precipitin obtained by its injection in the
veins of a rabbit. Of the rabbit's serum containing
the precipitin always 04 cc. were mixed with a
variable quantity (A cc.) of the sheep serum diluted
in the proportion 1:49 with 09 per cent salt solution.
The quantity of precipitate P was measured (in
the unit 00004 cc). At the side of the observed
quantities I have written calculated values obtained
from the formula
136
CHEMICAL EQUILIBRIA
(40A-P)(l20-P)
V
V
= K = 25o.
In this case when a precipitate is formed the pro-
duct of the concentrations ^— ' of the sheep
(120-P)
v
serum and
v
of the rabbit's serum, in which
v is the total volume of the mixture, should be a
constant K, which is found equal to 250. The
formula indicates that in 1 cc. of the diluted sheep
serum there is enough material to give 40 units of
precipitate and that 04 cc. of the rabbit's serum is
enough to give 120 units of precipitate. On the
formation of precipitate equivalent quantities of
sheep serum and of its specific precipitin disappear
from the solution.
The results are embodied in the following table :
A.
P obs.
P calc.
A.
Fobs.
* calc.
0-02
I
O.5
5
64
65
0-04
2
i-3
7
58
58
OI
3
3-5
10
49
46
0-I5
6
5-3
15
10?
19
0-2
7
7.2
18
5
3
o-6
21
21.5
20
2
0
I
35
34
1 + iB
28
25
i-5
39?
48
5 + iB
57
5i
2
60
57
10+ iB
4i
32
3
67
66 max.
B denotes I cc. of physiological, i.e. 09 per cent salt solution. By the
addition of this the dilution of the sheep serum was still more increased.
The agreement between the observed and the
CHEMICAL EQUILIBRIA 137
calculated figures may be regarded as very satis-
factory, if we except two observations (marked with
a ?) which do not fit in at all with their surroundings.
For all the observations in which physiological salt
solution has been added the calculated values are
too low, which perhaps is due to a lower solubility
of the precipitate in salt solution than in serum.
The quantity P has a maximum between A = 3
and A = 5 ; the calculation indicates the maximum
to be 67 at A = 375. The maximum depends upon
the dilution of the precipitin increasing with the in-
creasing addition of diluted sheep serum.
The said precipitin does not only give a precipi-
tate with serum from sheep, but also with serum
from related animals such as goats and cattle. In
these cases the normal sera contain enough pre-
cipitinogen per c.c. to give 40 units of precipitate
just as did the normal sheep serum. But the
rabbit's serum does not contain more precipitin
than is necessary for the formation of 85 (for goat's)
and 35 units (for cattle serum) of precipitate, whereas
the corresponding figure for the sheep serum is 120.
The constant K sinks from 250 for the sheep serum
to 180 for the goat serum and to 90 for the serum
from cattle. These figures give a measure of the
relationship of sheep to sheep, which may be taken
as unit, as compared with that of sheep to goat
(072) and for that of sheep to cattle (0-29 and 036 :
mean value 033).
If we add casein in increasing quantities to
lactoserum a precipitin is formed at first which
138 CHEMICAL EQUILIBRIA
reaches a maximum value when the two substances
are mixed in about equivalent quantities, to be re-
dissolved on further addition of casein. This action
is supposed to be due to a formation of a soluble
compound containing more casein relatively to the
precipitin than the precipitate. This case has not
been thoroughly examined, but a similar case was
observed by Hamburger, when he investigated the
precipitate from a mixture of normal horse serum
with immune serum from a calf. In this case it is
not the increasing dilution on adding increasing
quantities of horse serum which causes the observed
maximum of precipitate, but the calculation indicates
that at first a precipitate is formed from one molecule
of precipitinogen and one molecule of precipitin.
This precipitate gives with one or two molecules of
precipitinogen a new compound which is relatively
soluble. In this case, as in the three others observed
by Hamburger, the calculation gives a very good
agreement with the observation.
In the study of agglutinins similar observations
have been made, namely that in some cases the
agglutination at first increases with the quantity of
agglutinin added, and then subsequently decreases
when the quantity of agglutinin is increased. In
general the agglutinins behave much in the same
way as the precipitins or the precipitinogens, and
it is therefore probable that the agglutination is a
special manifestation of the precipitation.
The formation of precipitates plays an important
role in the modern development of the doctrine of
CHEMICAL EQUILIBRIA 139
immunity because they carry down with them the
complements, as was at first demonstrated by
Bordet and his pupil Gay. This effect is called
diversion of complements, and has been of a very
great use for diagnostic purposes, as in the Wasser-
mann reaction and similar cases.
The formation of precipitates and their redissolu-
tion by addition of greater quantities of the precipi-
tating substance is very common in general chemistry.
Thus for instance salts of aluminium are at first
precipitated and then redissolved by alkalies, and the
same is the case with the salts of a great number of
other metals. In this case the precipitate is the
hydrate of the metal, and the dissolution depends
on the formation of an aluminate or an analogous
salt.
I hope that this short exposition has been sufficient
to prove that the very same laws are valid for the
equilibria in which the antibodies and antigens enter
as for the equilibria studied in general chemistry.
The quantitative determination of these equilibria
leads to the conclusion that the antibodies are
not analogous to enzymes or katalyzers, as was
often maintained before, but really take part in the
equilibrium.
CHAPTER VI
IMMUNIZATION
The antitoxins and other antibodies are of the
greatest importance to the animal body. On them
the so-called serum-therapy is founded. In order to
protect against illnesses antitoxin is injected in the
body — diphtheria, for instance, is treated in this
manner — or micro-organisms, living or dead, or their
products are injected, after which the patient himself
produces antitoxin — this treatment is used against
smallpox, for instance. Ehrlich gave the name
passive immunization to the first kind of treatment,
active immunization to the latter one.
It is of high interest to know the fate of these
foreign substances in the body. For this purpose
animals have been treated in the said manner, and
samples of their blood have been taken at different
times and their content of antibodies investigated.
Some rather remarkable regularities have been
observed which will be spoken of in the following
pages.
To begin with we may consider passive immun-
ization. Antidiphtheric serum, or other antibodies,
140
IMMUNIZATION 141
may be introduced into the body in different ways,
by direct injection into the veins, or under the skin,
so-called subcutaneous injection, or in the muscles,
intramuscular injection. From the point of injection
the antitoxin more or less rapidly finds its way into the
blood — it is therefore said to be haemotropic. After
intravenous injection the blood contains the antibody
from the time of injection onwards. Madsen and
Jorgensen have made a great number of measure-
ments regarding the blood's content of agglutinin im-
mediately after its injection into the veins of goats,
cats, or rabbits. They found that the agglutinin was
rapidly spread in the blood so that the content was
just as great as if the agglutinin had been evenly
distributed in the animal's blood-mass. Only rabbits
made an exception. They behaved as if 23 per cent
of the agglutinin had been lost immediately. As
we will see later on, the antibodies rapidly vanish
from the blood in the time just after the injection,
but such an immediate decrease as in this special
case with rabbits has only been observed with these
animals.
The change of the concentration of diphtheria
antitoxin in a goat's blood after intramuscular or
subcutaneous injection is shown by the diagram (Fig.
33) given by Levin. It indicates that the blood's
content of antitoxin after ten hours is about 25 times
greater when the injection has been intramuscular
than if it has been subcutaneous. After twenty
hours the intramuscular injection still has the four-
fold effect of the subcutaneous one. Only after 60
142
IMMUNIZATION
hours do the two different methods show the same
effect, and after that time the effect of the sub-
cutaneous injection seems to be a little (about 10 per
cent) higher.
Now it is of extreme importance in the case of an
attack of diphtheria that the remedy should act as
rapidly as possible. Therefore the intramuscular in-
e3
x
o
c
ra
o4-
c
to
3>
s
/
/
yJ <
>- ,
X
d
i
i
i
t
>
f
-*& , . .
25
50
125
150
75 100
Time in hours — »>
Intramuscular injection Subcutaneous injection
Fig. 33.
jection should be recommended for therapeutic cases
and not the subcutaneous one, which has hitherto
been used in most cases. Against the most rapidly
acting intravenous injection some objections of
practical signification may be raised.
After a maximum content of antitoxin has been
reached about 75 hours after the injection a regular
slow decrease takes place. This decrease has been
IMMUNIZATION
143
investigated by Bomstein with dogs and guinea-pigs
in 1897. He injected, for instance, a dog with
a certain quantity of antidiphtheric serum — this
quantity he termed 7. The next day he took a
sample of the blood and subsequently every four
days until the content was too small to be measured
with certainty. For the measurement Bomstein
used the method of Ehrlich ; he mixed different
t
c
too
0
-1
x Dog
oGuine
a Pig
C
)
1
c
1
3
Time in days — +
Fig. 34.
quantities of blood serum with a given quantity of
diphtheric poison and investigated how much serum
was necessary to render the poison innocuous to
guinea-pigs. From this he could calculate the total
quantity of antitoxin in the dog's blood, for which
he supposed that the total blood-mass was the
thirteenth part of the dog's weight. The results
found in this manner are contained in the following
table and represented in Fig. 34, where log n is
plotted against time ; n is the content of antitoxin.
144
IMMUNIZATION
According to this evidently log n = a — bt} where t is
the time (in days). In other words the decay of the
antitoxin goes on at the same rate as a monomolecular
reaction. Bomstein also maintained that the quantity
of antitoxin decreased to the same fraction in four
days independently of its absolute quantity. The
decrease goes on so that in 3-25 days for the dogs,
of which three specimens were examined, and in
3 days for the guinea-pig, the quantity of antitoxin
sank to the half quantity. After the observed value
a calculated value is written which, as is easily seen,
agrees very well — and within the errors of observa-
tion— with the observed one. The magnitude of the
errors of observation maybe estimated from the differ-
ences between the observed values for the three dogs.
Passive Immunization with Antidiphtheric Serum
(Bomstein)
u5
a
.5
u
S
H
Observed total quantity of antibody.
-a
Mi
313
0
Antibody
in guinea-pig.
•0
V
Ui V
s.2
"rt >
Dog 1.
Dog 2.
1 Dog 3.
Mean.
O
I
5
9
13
17
7
3
i-5
o-6
o-3
7
3
1
02
7
2-5
I
0.4
02
7
2.83
1.17
o-5
0-23
(3-47)
2-80
1-19
0-51
022
7
2-1
0-84
o-35
0-14
0-07
(2-65)
2« I
0-84
o-34
0-13
0-053
The table is of great interest because it indicates
by a comparison of the observed values for the three
dogs with the calculated ones the great improve-
ment effected by forming the mean values of two or
IMMUNIZATION 145
three observations, as against the results of single
observations.
During the first day after the injection the
decrease goes on abnormally rapidly. Therefore
the calculated values for the first dav, which fit in
with the regularity found for the decrease during the
later period, are written in brackets. Evidently
during the time immediately after the injection
another process is going on simultaneously with the
process which is typical for the following regular de-
crease. This goes on as a monomolecular process,
and the simplest hypothesis would be to suppose a
spontaneous destruction, if it was not known that
the antitoxins are rather stable at the temperature of
the animals investigated. But the formula for mono-
molecular reactions would also give good results if
the antitoxin reacted with some substance present in
great excess or which was secreted by the animal's
body as soon as it was consumed. In the time just
after the injection there must also be some other
action of great effectivity.
It is highly probable that the foreign substances
introduced are eliminated by some substance pro-
duced by the animal in which they have been
injected. This is indicated by some interesting
experiments of Baron von Dungern. He injected
blood-serum of the sea spider (Maja squinado, a
Crustacean) into the veins of a rabbit. After three
hours it had disappeared (in this case sunk below
25 per cent). Then he introduced the same quantity
of Maja serum into the rabbit s blood, and found that
L
146 IMMUNIZATION
it did not sink to 25 per cent until after six hours.
Still more startling results were obtained if the
rabbit had received a moderate dose of serum from
the common cuttlefish, Octopus vulgaris, 2-5 hours
before the injection of the Maja serum, which then
did not sink more than to about 50 per cent during two
days. The substance which neutralizes the Maja
serum must therefore be bound or hampered in its
action by Maja, or still more by Octopus serum, which
has been introduced two to three hours before the
investigated Maja serum was injected.
The circumstances become still more complicated
when we consider that the rabbit at a later stage
secretes in its blood a substance, a precipitin, which
binds and precipitates the Maja serum. But this
substance does not occur in a sensible degree during
the first hours after the injection — there is a consider-
able time of incubation. Von Dungern connects
the rapid disappearance of the Maja serum from the
blood-vessels of the rabbit with its power of secreting
the specific precipitin against the Maja serum. If
we inject Maja serum into the veins of the cuttlefish
Eledone moschata, or into the so-called sea-rabbit,
Aplysia depilans, which do not prepare any precipitin
or other antibody against Maja serum in their veins, we
are able to demonstrate the presence of Maja serum in
the blood of these animals some weeks after the injec-
tion by mixing the blood-serum with precipitin against
Maja serum from rabbits. If we inject Maja serum
into a rabbit which has had sufficient time to secrete
a moderate quantity of the precipitin specific to its
IMMUNIZATION
147
blood, then the Maja serum disappears much more
rapidly than after the injection into a rabbit which
has not been treated with Maja serum before. The
effect of the previous injection of Maja serum is
therefore in this latter case just the opposite of that
observed if only some two or three hours have
elapsed between the first and the second injection.
The antidiphtheric serum consists of serum from
10
075
t
c 05
too
o
_i
025
o
0
o
o
3
0
6
0
c
0
12
!0
Time in days — »-
Fig. 35.
an animal, generally a horse, which has been treated
with diphtheria toxin. If this horse-serum is injected
into the blood-vessels of another non-related animal,
such as a dog or a guinea-pig, precipitins against
horse-serum are secreted and found in the veins of
this animal. These precipitins may give precipitates
with the injected antidiphtheric horse-serum, which
precipitates show a great tendency to absorb sub-
stances from the blood.
148
IMMUNIZATION
This absorption, for instance, plays a very im-
portant role in the diversion of complement (cf.
p. 138). If we inject antidiphtheric horse-serum into
a nearly related animal such as an ass, we might
expect the antitoxin to disappear more slowly than
if injected into a dog or a guinea-pig. This experi-
ment has been carried through by Bulloch (in 1898).
As the following table and the diagram, Fig. 35,
indicate, the antitoxin required 37-5 days to sink
to the half value, i.e. about twelve times longer than
in Bomstein's experiments. In this case the injec-
tion was subcutaneous, as is seen from the first two
values in the table. If the total quantity of anti-
toxin had spread uniformly in the blood an initial
value 19 per cc. ought to have been observed.
The value 16 after one day reaches nearly this
theoretical value 19.
Passive Immunization of an Ass with Antidiphtheric
Serum from Horse (Bulloch)
Quantity of Antitoxin
in 1 cc. of the Serum.
Time in Days.
Observed.
Calculated.
O
O
O
002
2
(11. 8)
I
16
1 16
4
I I
1 1
24
7-5
7-6
48
5-5
4.9
60
4-5
3-9
77
3-2
2-8
100
i-3
19
126
0.9
1-2
IMMUNIZATION 149
The observation at the time o was made immedi-
ately before the injection. It indicates that the
ass possessed no natural immunity against diphtheric
poison. Half an hour later about 10 per cent of
the antitoxin had spread to the veins. After the
first day the rapid elimination took place. During
the three following days the content sank from 16
to 1 1 units, for which decrease at a later stage 20
days would have been needed.
Behring has also observed that antitoxins remain
longer in the blood of animals of the same kind as
that from which the antitoxic serum is taken.
MADSENand Jorgensen found that typhoid agglutinin
from a rabbit disappeared 2-5 times more slowly
from the veins of a rabbit than from those of a
goat.
As the observations referred to above all con-
cern the fate of antidiphtheric serum it may be of
interest to reproduce the figures of Madsen and
Jorgensen regarding the fate of typhoid agglutinin
in the veins of a goat. •
[Table
150
IMMUNIZATION
Intravenous Injection of Typhoid Agglutinin
in a Goat (Madsen and Jorgensen)
Time in Days.
Quantity of Agglutinin per cc. Serum.
Observed.
Calculated.
O
o-3
i
3
5
8
1 1
i5
909
555
333
208
167
125
100
9i
(274)
(267)
(250)
208
173
131
IOO
69
In the first day we observe a very rapid decrease,
which is about 1 1 times greater than the regular
monomolecular decay which begins about 1-5 days
after the injection (as found by extrapolation from
the regular curve) and gives a fall to the half-value
in 7-5 days.
Red blood-corpuscles from an animal may be
identified by means of a specific haemolysin, obtained
by injection of these corpuscles into the veins of
another animal. Sachs injected erythrocytes from
an ox into the ear vein of a rabbit, and was able
to find traces of them after 41 to 92 (average 57)
hours; after 46 to 116 (average 72) hours they
had disappeared. On the other hand Todd and
White identified similar erythrocytes injected into
an ox after four days.
In his experiments on the injection of ox
erythrocytes into the veins of a rabbit Sachs
IMMUNIZATION 151
looked for the first appearance of the correspond-
ing antibody, a haemolysin against ox erythrocytes.
He demonstrated the presence of this antibody just
after the disappearance of the erythrocytes or
perhaps a little before. The time of incubation had
therefore a mean value of 72 hours, which agrees
completely with an observation of Bulloch. If
the erythrocytes were injected subcutaneously the
time of incubation was much longer, as we might
expect, namely 7 days* An analogous case is found
in infectious diseases, which may be regarded as
a special case of active immunization. In small-
pox the infection generally comes through the
respiratory organs, and the time of incubation lasts
no less than from 10 to 14 days, whereas after
inoculation of genuine small-pox (variolation) or of
weakened virus from cow-pox (vaccination) the time
of incubation is only 3 to 5 days. Still shorter some-
times is the time of incubation after repeated vaccina-
tion. This circumstance makes it possible for a
man, freshly infected with small-pox, to be (partially)
protected by vaccination. The antibodies appear
after the time of incubation, and this is after vac-
cination so short that it may be at an end before
the incubation time of the genuine small-pox is
completed. In this case this latter time of incuba-
tion is shortened, and the patient gets an easy form
of small-pox, the so-called varioloid, as is generally
the case with vaccinated people who are attacked
by the genuine small-pox. Still longer is the time
of incubation in hydrophobia ; in this case it depends
152 IMMUNIZATION
on the distance of the infected wound from the central
nervous system, and may sometimes last for one
month. Owing to this it was possible to Pasteur
to check the illness by inoculation of weakened
rabies virus.
After active immunization of an animal which has
been immunized before against the same bacilli the
time of incubation is sometimes characterized by a
diminution of the content of antibody — this is the
so-called " negative phase." The said decrease is
regularly observed with the immunization of horses
against diphtheric toxin, whereby antidiphtheric
serum is prepared. Thus Salomonsen and Madsen
found that the antitoxin content of a horse went
down one time from ioo to 65 units, another time
from 120 to 105 units, to rise subsequently above its
initial value. A similar decrease was also observed
after every bleeding (at which seven litres of blood
were taken for the preparation of antidiphtheric
serum); in one case the fall was from 120 to 105
units, another time from 85 to 70 units.
After the end of the time of incubation an enor-
mous increase of the quantity of antitoxin takes
place. As an example may be cited the following
table from Madsen's and Jorgensen's investigation,
illustrated by the diagram, Fig. 36. The animal
treated was a goat which had been used for similar
experiments before, so that it contained a little
initial quantity — designated as four units — at the
time of injection. This quantity decreases a little
— one unit — in the first day; this is the "negative
IMMUNIZATION
153
phase." After that comes a slow, and later a rapid
increase.
Agglutinin in a Goat, actively immunized with a Culture
of Cholera Vibrions
Time
in Days.
Quantity of Agglutinin in the Serum.
Remarks.
Obs.
Calc.
O
4
4
Injection.
0-5
I
3
3
4
4
> Negative Phase.
2
4
4
Last day of the time of
incubation.
3
IO
10
>
4
25
30
5
6
50
65
5o
70
►Time of rapid increase.
7
90
90
8
125
100
j Acme.
IO
IOO
(60)
Rapid decrease between
days 9 and 1 1.
1 1
59
56
■<
12
50
53
13
42
49
Slow, regular, monomolecu-
18
33
35
lar decrease.
21
28
28
26
20
20
The time of rapid increase, between the time 25
days and 9 days, is characterized by the fact that the
content of agglutinin increases by nearly the same
quantity, 20 units, every day. The process is some-
what similar to the increase of gastric juice in the
stomach after introduction of food through a tube
(see p. 92). The corresponding stage with increas-
ing illness in small-pox is called the prodromal stage.
This stage ends with a maximum, the so-called
154
IMMUNIZATION
"acme," after which an abrupt decrease of the
agglutinin takes place. From this time (the ninth
day in our case) the content of antibody is very
similar to that after passive immunization. After
a rapid decrease comes the regular slow one, which
30
15
Time in days
Fig. 36.
may be calculated as a monomolecular reaction.
The calculated values for this time agree very well
with the observed ones. The same is the case for
the values calculated on the assumption that the
quantity of agglutinin increases with constant speed
during the time of rapid increase.
In order to corroborate these statements I repro-
IMMUNIZATION
155
duce some figures given by Madsen and Jorgensen
for the content of agglutinin in a goat, which was
strongly immunized before the experiment against
typhoid bacilli. At the time indicated as o, i cc. of a
culture of typhoid bacilli was injected subcutaneously.
Active Immunization of a Goat against Typhoid Bacilli
(Madsen and Jorgensen)
Time
in Days.
Content of Agglutinin.
Remarks.
Obs.
Calc.
O
I36
136
Injection.
I
I36
I36
Incubation time at an end after 2-7
days.
3
188
186
\
5
268
272
Time of rapid increase (43 units a
7
367
353
day).
9
442
444
Acme.
1 1
323
323
Rapid decrease between the days
9 and 1 1.
13
286
285
17
20
23
225
196
151
221
183
151
"Slow, regular, monomolecular
decrease.
25
117
133
Here the time of incubation is reduced to 24
days, which is probably due to the previous strong
immunization, 136 units. The time of rapid increase
(6-6 days) lasts about as long as in the last case (6-5
days). The rapid decrease is not so pronounced
as in the last case. The final regular decrease
causes a sinking of the agglutinin to the half-value
in 1 1 days, whereas in the last case the corresponding
156 IMMUNIZATION
time was 10 days, i.e. about the same. The good
agreement of the calculated figures with the observed
ones during the periods of rapid increase and of
regular decrease are strongly pronounced.
In another experiment Madsen and Jorgensen
injected 20 cc. of a culture of typhoid bacilli sub-
cutaneously into a goat which had not been treated
before. The time of incubation with absence of
agglutinin lasted for 55 days and was much longer
than in the two last cases, when the animals had
been injected with the same bacilli before. The
time of rapid increase for about nine days showed
an enormous production of agglutinin — about 2000
units a day. The observations of the regular
decrease are very few (only three). They seem
to indicate a sinking to the half-value in about five
days, i.e. about double as rapidly as in the goats
which had been immunized before.
A special case of active immunization, in which
till now only the period of regular slow decrease has
been observed, concerns the content of agglutinins
in the blood of persons who have been attacked by
bacterial diseases. In such cases it is often found
that the slow decrease goes on much more slowly in
the latter part of the observed period than in the
first time. As instances I give two series, the one of
Jorgensen regarding the content of typhoid agglutinin
in a patient's blood after typhoid fever, the other of
Sir Almroth Wright regarding agglutinin specific
against the bacillus causing Malta fever.
IMMUNIZATION
157
Agglutinin in the Blood of a Patient in Typhoid
Fever (Jorgensen)
Time
in Days.
Quantity of Agglutinin.
Obs.
Calc.
O
6o
60
2
5o
51
6
36
36
IO
25
26
15
17
17
20
12
I I
27
10
6-2
35
6-7
3-2
42
4
1.8
Till the twentieth day the decrease of the content
of agglutinin in the patient's blood goes on quite
regularly, so that it sinks to its half-value in 84
days. But in the last 15 days the quantity of
agglutinin is rather greater than the calculation
indicates. Perhaps this circumstance is partly due
to errors of observation, but the regularity of the
figures seems to indicate that the decrease goes on
much more slowly than in the former part of the
process. In a similar manner it has often been
found with strongly immunized animals that they
retain the last traces of immunity for a long time
undiminished or falling off very slowly. It seems
as if a part of the antibodies were stored up in parts
of the body, from which it very slowly diffused back
to the veins. Still more pronounced is the second
instance.
158
IMMUNIZATION
Agglutinin in the Blood of a Patient in
Malta Fever (Sir Almroth Wright)
Time
in Days.
Content of Agglutinin.
obs.
calc.
O
l6oO
160O
6
IOOO
I 160
13
800
8lO
19
600
602
25
420
456
33
320
325
40
270
250
48
200
195
58
I50
153
7i
I30
125
In the first period the agglutinin sinks to its half-
quantity in 13 days, at the end 30 days (41 to 71)
are necessary for a diminution to the half-value. In
other words, the rate of sinking is 23 times more
rapid at the beginning than at the end. Of course
it is impossible to calculate these figures in the way
used before. I have therefore supposed that the
agglutinin content sinks to an end-value above
zero, namely 100 units, and treated the excess of
the observed value over 100 in the usual manner.
The agreement with the observations obtained in
this manner is really startling. We may therefore
say that the content of agglutinin behaves as if
it tended to a minimal value of 100 units, which it
would retain for any time. But without doubt this
value also sinks with the progress of time. Sir
Almroth Wright has observed a case, in which
IMMUNIZATION 159
the patient retained a content of agglutinin in his
blood, reaching 20 units seven and a half years
after his illness (Malta fever). Different patients
show in this respect a high degree of individuality.
In most cases the agglutinin has disappeared after
two years or is only present in very small quantities.
The presence of agglutinins in the blood during
and after diseases is of a high diagnostic value
(Reaction of Gruber - Vidal). It is very well
known that after some diseases, such as scarlatina,
measles, and whooping-cough, the immunity against
these diseases lasts for the whole life. It is not
clear whether this peculiarity depends upon a small
content of antibodies remaining for a long time in
the tissues of the patients.
But it seems to me in any case that the study
of the active immunity throws much light on the
progress of illnesses produced by micro-organisms.
It is a very promising feature that we are able to
treat the content of antibodies during and after
the illness in a strictly quantitative manner, and that
we have succeeded in subjecting this extremely
important phenomenon to calculations which agree
as well with the observed facts as with ideas
conceived for the explanation of other parts of
chemical science.
INDEX OF SUBJECTS
Acids, 16, 27-29, 32, 40, 66-68, 82, 115
Acme, 153
Active immunization, 140, 151-158
Active molecules or cells, 75-80
Adsorption, 108-110
Alcoholic fermentation, 21, 52, 55, 60-
63
Alkalinity, 27, 28, 32, 33
Amboceptor, 105, 108, 128-133
Ammonia, 43, 44, 63, 64
Amphoteric electrolytes, 40, 79
Amylodextrin, 95
Amianaphylactogen, 16
Antibodies, 15, 139-159
Antigen, 15
Antitoxins, 16, 1 10-127
Antivenin, 116, 123, 124
Assimilation, 21, 55-57, 93"95
Atomic theory, 1
Bacteria, 53-55. 67-74- io5
Bacteriolysin, 15
Bacteriolysis, 52
Bases, 66, 115-116 ; see also Alkalinity
Biochemistry, 2
Bleeding, 152
Blood, 20, 21 ; content of antibodies,
140-159
Blood - corpuscles, 76-78, 103, 114,
125, 150
Blood relationship, 134, 135, 137, 148,
149
Boracic acid, with ammonia, 117-119
Carbohydrates, 21
Casein, 100, 101, 109, 137
Castor-beans, 47, 56
Cell reactions, 60-80
Charcoal, 35, 50, 51
Chewing, 91
Chlamydomonas, 74
Chlorophyll, 14
Cholera, 108, 153
Coagulation, 25-29, 45, 46, 54, 55,
108
Cobra poison, 66, 116, 123, 124, 133,
134
Complement, 128-132
Compound haemolysins, 16, 128-132,
Concentration, influence of, 33-41
Condensation, 108
Conductivity, electric, 38
Crotalus poison, 116
Danysz's phenomenon, 124-127
Destruction, spontaneous, 24-30, 54
Dextrose, 93, 94
Diagnostic sera, 134, 139, 159
Digestion, 33, 37-47, 54, 81-98
Dilution, 29
Diphtheria toxin, 14, 111-113, 117,
120, 127, 140, 143, 147
Dissociation, 79, 116, 119, 130-132
Diversion of complement, 133, 139,
148
Egg-albumen, 25-29, 37-41, 47, 50,
51, 93, 108, 134
Ehrlich's phenomenon, 1 13-123
Enteric juice, 13, 82, 97
Enzymes, 34, 35, 37, 58-60, 99-102
Epitoxoid, 123, 127
Equilibria, chemical, 99-139
Equivalents, 120, 121
Erepsin, 13, 47
Ethyl acetate, 41-43
Ethyl butyrate, 48
Experimental errors, 3
Fats, 13, 47, 87, 100
Ferrocyanic acid, 109
Fistulae, 81, 92, 94, 95
Food-stuffs, 83-94
Foreign substances, elimination of,
145-147, 150
161
162
INDEX
Gelatine, 45, 46, 52
Gliadin, 96, 97
Glucosides, 100-102
Graphical methods, 4-12
Guldberg-Waage's law, 112-122
Haemoglobin, 25, 26, 50, 51, 63
Haemolysin, 15, 24, 25, 50, 51, 127-
i32. 151
Haemolysis, 52-55, 63-66, 73, 104,
114-120, 125, 130
Haemotropism, 141
Heat, evolution of, 119
Hydrochloric acid, 38-40, 82, 86, 87,
93- IX5
Hydrogen ion, concentration of, 32, 69
Hydrolysis, 40, 55, 100, 101
Hydroxyl ion, 69
Immune body, 129
Immunization, 141-159
Inactivation, 128
Incubation, 64, 74, 80, 82, 128, 151-
156
Instability of organic products, 24
Intramuscular injection, 141, 142
Intravenous injection, 141, 142, 151
Inversion of cane-sugar, 20, 30-34, 56
Invertase, 13, 14, 99
"In vitro" and "in vivo" reactions,
23. 98
Irreversible processes, 124-127
Isolactose, 101
Isolysin, 132
Isomaltose, 101
Isotonic solutions, 104
Katalase, 14, 47, 48
Katalyzer, 131, 139 %
Lactase, 13, 101
Lactose, 10 1
Lactoserum, 134, 137, 138
Layers of food-stuffs in the stomach, 85
Lecithin, 16, 133, 134
Lifetime, 78
Lipase, 12, 14, 48, 56
Liquid air, "69
Malta fever, 158
Maltase, 13, 14, 101
Maltose, 12, 13, 101
Mass, constancy of, 1
Mechanistic view on life, 20
Mercuric chloride, 16
Mercuric ion, 68
Milk, 45, 46, 56, 87
Monochloracetic acid, 125, 126
Mutarotation, 31
Natural immunity, 149
Negative phase, 152-154
Neutralization phenomena, 1 10-133
Oleate, 66
Opsonin, 16
Optimum, 56-58
Osmotic pressure, 104
Oxydase, 14
Pancreatic juice, 13, 46, 47, 82, 92, 93
Papayotin, 14
Paranuclein, 100, 10 1
Partial poisons, 118
Partition between two phases, 102-108,
I25
Passive immunization, 140-150, 154
Pepsin, 12, 32, 37-40, 45, 52, 83, 84, 100
Peptone, 39, 40
Peroxide of hydrogen, 32, 33, 47, 48
Phenol, 69
Plastein, 100
Platinum, colloidal, 32, 33
Plurality of poisons, 128
Poison spectrum, 117, 118
Precipitation, 54, 55, 122, 134-139
Precipitin, 15, 16, 50, 51, 134-138,
146-148
Probability, 76, 77
Prodromal stage, 153
Protamine, 100
Proteolytic ferments, 13, 52
Protoplasm, 58, 79
Prototoxoid, 121, 122
Ptyalin, 12
Pyocyaneus ferment, 46
(#-law, 40-47. 59-°5. 67, 73
Rabies, 151, 152
Redissolution of precipitates, 137-139
Reductase, 14
Relationship, 134, 135, 137
Rennet, 29, 45, 46, 52, 56, 100
'Resorption, 95, 96
Respiration, 21, 55
Reversible processes, 124, 125
Ricin, 122
Saponification, 46-48, 54-58
INDEX
163
Salivary glands, 12
Schiitz's rule, 37-47, 72, 109
Sedimentation, 17
Seeds of barley, 74
Sensibility, 76-79
Sensitiser, 129, 131, 133
Serum-therapy, 140, 142
Specificity, 17, 100, 128, 136, 137
Small-pox, 146, 151, 153
"Small stomach," 82, 83, 88
Square- root rule, 83-86, 87, 91, 94-
97
Starch, 12
Steapsin, 46
Stomachical juice, 12, 13, 47, 82, 83-
85, 92
Subcutaneous injection, 141, 142, 148,
isi> j55. 156
Sunlight, 69, 72
Synthesis of organic products, 22, 98-
102
Syntoxoid, 123
Temperature, influence of, 49-60
Tetanus-poison, 14, 24, 25, 32, 103,
113, 114, 119, 120, 126, 127
Toxins, 14-17, 110-127
Toxoids, 118
Toxon, 123, 127
Trypsin, 13, 44, 45, 52
Typhoid bacilli, 53, 69, 93, 108, 154-157
Vaccination, 140, 151
Variolation, 151
Varioloid, 151
Velocity of reactions, 19-59
Vibriolysin, 28, 35, 50, 51, 103, 108
Vitalism, 19, 98
Vital processes, 55, 57-60, 64, 81-98
Water-moccasin, 66, 116
Weakening of poisons, 123, 124
Yeast, 14, 30, 60-63, 72> I02
Zymase, 14
INDEX OF AUTHORS
Aristoteles, 128
Arrhenius, 32, 41, 52, 63, 75, 88, 104,
105, in, 114, 115, 129, 135
Armstrong, E. F. , 101
Baeyer, 21, 22
Bayliss, 44
v. Berneck, 33
Berthelot, D., 21
Berthelot, M. , 22
Berzelius, 1
Blackman, 74
Boldyreff, 87
Bomstein, 143, 144, 148
Bordet, 125, 129, 134, 139
Bourquelot, 101
Bredig, 33
Bridel, 101
Brown, Adrian, 34
Bulloch, 148, 151
Bun sen, 64
Calmette, 123, 124
Chick, Harriette, 27, 28, 53, 69, 72,
73- 74. 80
Clark, 69, 72
Dalton, 1
Danilewski, 100
Danysz, 124, 125, 126
Darwin, 74
Daubeny, 21
De la Boe Sylvius, 20
Dolinsky, 92
Draper, 21
Duclaux, 21
Dumas, 21
v. Dungern, 127, 145, 146
Ehrlich, no, in, 113, 114, 117, 118,
121, 122, 123, 124, 126, 129, 132,
J43
Eisenberg, 105
Ellenberger, 85
Engelmann, 21
Euler, 47
Fischer, Emil, 22, 10 1
Friedenthal, 135
Fuld, 56
Gage, 69, 72
Galilei, 128
164
INDEX
Gay, ioo, 139
Gelis, 22
Graebe, 22
Gros, 52
Gruber, 159
Griitzner, 85
Guldberg, 112, 122
•
Hamburger, 135, 138
Harvey, 74
van Helmont, 21
Henri, 30, 31, 33
Hill, 101
Hudson, 31, 99
Jodlbauer, 52, 60
Jorgensen, 141, 149, 154, 155, 156,
157
Khigine, 81, 83, 84, 85, 87, 88, 92
Kjeldahl, 56
Kronig, 68, 69
*
Lavoisier, 1
Levin, 141
Liebermann, 22
Lobasoff, 83, 92
London, 81, 84, 85, 87, 88, 91, 93,
95- 97
Lonnquist, 82, 83
Lunderi, 117, 119
Madsen, 28, 29, 35, 44, 45, 46, 52,
63. 65, 67, 68, 69, 80, 103, 108,
in, 114, 115, 119-123, 126, 141,
149, 152, 154, 155, 156
Magnus, 135
Manwaring, 130
Martin, 27, 28
Massol, 123
Matthaei, Gabrielle, 56
Maxwell, jj
Menthen, 34
Michaelis, 34
Morgenroth, 131, 132
Newton, 128
Nicloux, 56, 58
Noguchi, 65, 115
Nuttall, 134
Nyman, 69
O'Sullivan, 31
Palme, 109
Paul, 68, 69
Pawlow, 81, 91
Pelouze, 22
Pfeffer, 21
Polowzowa, 84, 87
Priestley, 21
Pringsheim, 21
Robertson, T. B. , 100
Roscoe, 64
Rubner, 61, 62
Sachs, Hans, 118, 126, 131, 150
Sachs, Julius, 21
Salomonsen, 152
Sandberg, 97
de Saussure, 21
Schutz, E., 8, 9, 11, 37, 39, 41, 42,
43, 47, 62, 63, 72, 84, 109
Schutz, Julius, 37
Senebier, 21
Sjoqvist, 37, 47
Sorensen, 32, 33
Stoklasa, 21
Taylor, A. E. , 100
Teruuchi, 35, 103, 108
Thomsen, Julius, no
Todd, 150
Tompson, 31
Tyndall, 1, 20
Uhlenhuth, 134
Van 't Hoff, 99
Vidal, 159
Volk, 105
Waage, 112, 122
Walbum, 29, 44, 45, 46, 65, 68, 126
Wassermann, 134, 139
White, 150
Wilhelmy, 8
Willstatter, 14
Wohler, 22
Wright, 156, 158
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