BIOLOGY LIBRARY G 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, 341163 vi BIOLOGICAL CHEMISTRY namely that of FRIEDEMANN in the Handbuch der Hygiene (3rd vol. ist part, p. 777, 1913). " The one- sided (ausschliesstUK) 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 1914. 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 fur Chemo- therapie, vol. 3, p. 157, 1914. Hoppe - Seylers Zeitschrift fur physiologische Chemie, vol. 63, p. 324, 1909. Memoirs published in Meddelanden fran K. Svenska Vetenskapsakademiens Nobelinstitut, vols. i 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 rinstitut se'rothe'rapique de I'Etat danois, 1907-1913. 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 1915. CONTENTS CHAPTER I PAGE 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 /z-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 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.5' 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. INDEX PAGE I4O 161 CHAPTER I INTRODUCTION THE content of this little book is founded on three TYNDALL Lectures, given in the Royal Institution, London, on the i4th, 2ist, 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 toy 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 60° 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 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 a= 1-5. If we put x= i, then y = a + b, i.e. b is the distance of the point in which the straight line y = a + bx cuts a vertical line x= i going through the point i of the ^-axis, from a horizontal line y 31 ^ ^ ^ ~^ b ^^ i ^ ^ i a 3 -2 C » I FIG. i. 2 ; \ > y = a running at a distance a above the #- In Fig. i, 0 = 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 it (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 ZQ (we have in this case put £0= 100), then the said law regarding the progress of the inversion of the cane-sugar with time, /, is expressed by means of the formula log #0 — log 2 = bt. For the time / = o, i.e. when the sulphuric acid is added to the solution of cane-sugar we have log z0 = log z, 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, z, 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 /, do we get a real representation of the meaning of the curve. In this case a table giving the comparison of calculated INTRODUCTION figures with observed ones is of a greater use and clearness. But we can proceed more simply by putting y = log Zj i.e. plotting log z as a function of A in which case we get a straight line (the continuous line in Fig. 2), beginning at the point jo = log ZQ = log 1 00= 2 and cutting the /-axis in the point log z 100 80 t- z 60 40 20 \ \ 20 16 I Log z 12 08 04 0 I 2 t^ 3 4 5 6 FIG. 2. = o, i.e. z= i, and 2— o = ^/0, i.e. /0=2/^ (in Fig. 2 /0= 20-6, 4 lies so far to the right that it does not appear in the figure). Here the value of b is very simple, namely, <5 = 2//0, 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 2-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 20, nine hours for the threefold quantity 30, sixteen hours for the fourfold quantity 40, and in general 1? hours for digesting the n-fo\d 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. yi — a"t. 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 ^ = o, 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 y 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 /, we plot y* as a function of t, then the y-curve is a straight line, running through the origin, y = o, t = o, and we easily see that the jy2- value does not approach to a limit. In this case we might just as well have tabulated y as a function of the square root of t,y = a*Jt 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, N/^, 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, z, which formula may be 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 But in most cases it is preferred to plot z as a function -^(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(u) are at all complicated, so that we are not 10 INTRODUCTION acquainted with them and therefore lose sight of the relation connecting z with u, 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 10° 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 10° 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, x//, 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 /. 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 yl = 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 or 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, \he 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 \hepepsin, 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 torius, 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 antianaphylactogens, 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. tNow 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.J 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, yln 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.V ^ 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 ibe 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), of indigo by BAEYER (1878), and still more of the fats by PE"LOUZE and GE"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 01 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^surpas^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 Jri^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 very difficult 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 jyqyo/^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 igher 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 mins. Quantity q of Lysin. t obs. calc. 2 IOO IOO 20 80 80-6 40 6l-I 64-8 60 52-1 52-3 80 46-3 42-1 I2O 26-8 26-7 180 17-6 14-3 K = 0-00474 Decomposition of a Haemolysin at 51* C. Time in mins. Quantity q of Haemolysin. t obs. calc. O IOO IOO 5 74-3 73-4 IO 58-3 62-5 15 48-8 53-3 20 44.9 45-4 25 40-0 38-7 3° 33-7 33'° 35 28-4 28-1 40 25-2 24-0 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 z-u; 1-9 1-8 *a 1-6 a o|5 •00 3u K \ \ \ fO \ 1 s* * O 1 c \ t \ \% \ \ \ N n> 1-3 12 II \ N \ \ \ 0 20 40 60 80 100 120 140 160 18 Time in minutes FIG. 3. 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 = 0-145. 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 2-0OO 464 539 110 1.95 0-80 482 534 130 -0-55 -1-49 511 559 150 - 2-20 -2-40 522 533 00 -7-47 -7-47 I 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 0-0000372. Influence of Acidity on Velocity of Reaction. Inversion of Cane-Sugar (at 30° C.). Cone, of H-ions . . 3-icr4 io~4 3-io~5 io~5 3-io~6 io~6 3-10-* Vel. of Reaction -i o4 . 77 82 83 81 78 73 64 Decomposition of Tetanolysin (at 50° C.). Normality NaOH . . . 0-02 o-oi 0-005 o-o-oi -0-02 : H2SO4 Velocity of Reaction -i o4 .112 97 85 ^7 71 435 Digestion by means of Pepsin (at 52° C.). Cone, of H-ions . . 0-17 iQ-1 6-io~2 2-io~2 5-io~3 8-io~5 Digested quantity/ i hour 8-5 9-3 12-3 15*2 15-0 10-8 in mgms. after \49hours ... 30-3 j/-j 30-9 28-1 16-1 50 per cent Decomposition of Hydrogen Peroxide with Colloidal Platinum (at 25° C.). Cone, of NaOH . . o 0-002 0-008 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 (H2SO4, 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 52° C. The maximum occurs at a concentration of the hydrogen-ions equal to about ooi normal, when the time of digestion is short (i hour). If this time increases, the maximum moves to higher concentrations and lies at about 0-06 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 25° 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. ^ C = Q-Q\ 0'025 0-05 0-1 0'25 0-5 I 1-5 2 _« = 0'58 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 i 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^) 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 . icA IfLc. io«. O-OI 704 704 O-02 375 750 0-04 219 876 0-06 143 858 0-08 105 840 O'lO 87 870 0-12 62 744 0-14 56 722 The velocity of reaction is nearly inversely pro- portional to the concentration, so that the product Kr, 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 IUVVS ^ 1 1 5 —7 3 J > tooo X ^ ^^ <0 0 9nn EUU 0 002 004 0-06 008 01 012 Concentration of vibriolysin — » FIG. 6. 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 : 9- i. 4- 9- 16. 25- 36. io4 x (observed) 212 471 652 799 935 1031 io4* (calculated) 2I3 426 639 852 1065 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 37° 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 cxj 3 FIG. 7. which fell from an initial value of 188-4 (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 188-4 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. 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 O-2 0-4 0-8 1-6 3'2 4-8 6-4 9-6 Q — OO2C, A — 11*1 I7-3 23-Q ^2'O 4.2*2 C-2.A °*°5 IO-2 i.S-6 23-7 32-9 43-2 SS-3 67-0 74-0 OI 9'2 14-2 22-5 33-6 4V2 57-5 69-0 75-3 79'3 86-6 02 ... 12-4 20- 6 30-3 43-7 55-4 66-8 73-^ 78-6 86-1 Mean value of A = 10 2 14-9 22-7 32-2 43-8 55-4 67-6 74-3 79-0 86.4 49-2 \Jqt = II 15-6 22 3i-i 44 62-2 88 124-4 From this we observe that the rule of SCHUTZ VELOCITY OF REACTIONS 41 is very nearly right till qt reaches the value 0-8, 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 A 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 g the quantity of the ester. The jr-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= x/K. A.^.A which is the rule of SCHUTZ, according to which x is proportional to the square root of A/ 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). *-Obs. %. .r-Calc. 17.3 A// (Schiitz's rule). I 17-5 19.4 17-3 2 25-5 25-2 24.5 3 30-7 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 10 51.2 5i-3 54-7 15 59-6 59-7 67-0 22 67-5 68-0 81-1 30 74-5 74-7 94-7 40 80-7 80-7 109.4 60 88-2 88-2 134-0 . from A \oge [A : (A-x)]-x=K> 18 • 0032 •058 20 •0027 •054 22 •0025 •055 24 •0022 •053 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). r- ft, / (minutes). f- 9* 4 8 32 50 •5 25 6 5 30 70 •4 28 9 3-3 30 80 •32 26 12 1-9 23 100 • 28 28 20 i-3 26 120 •25 30 30 •7 21 180 • 185 33 35 •7 25 240 •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 DIGESTION OF THYMOL-GELATINE BY MEANS OF PYOCYANEUS CULTURE AT 34-5° C. t (hours). f« qt. t (hours). q- qt. 0-5 1-6 •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 •I65 •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 ^-law 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 JBoletus 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 (/ 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 t 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 : KATALYSIS OF H2O2 AT iS*C t. t- K. o 8-0 6 6-9 0-0107 12 5-8 o-oi 16 19 5-0 0-0107 55 2-5 0-0 1 00 Mean 0-0107 SAPONIFICATION OF ETHYL BUTYRATE AT 35° C. /. q- K. 0 2'70 ... 2 2-40 0-0256 6 1.95 0-0235 9 1-65 0-0237 16 1-05 0-0250 Mean 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 where T0 and T1 are two temperatures reckoned from the absolute zero. K0 is the velocity of reaction at the temperature T0, and Kj that at Tl ; /*, is a con- stant. The greater //, is the more rapidly the velocity of reaction increases with temperature. For radio- active substances //. is zero. If T0 and Tx are not too far from each other, the value of T0T1 does not change very much in the interval from T0 to Tx and then the formula may be written : l-To) or logK1-logK. = *(TI-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 5i°C. for haemolysin, 45-15° C. for vibriolysin and 60° C. for haemoglobin. In the last case the scale is reduced 14 12 r *°8 bo o _i '_ 6 x 00 5.4 2 3# x — - FIG. 9. to half size by putting yl = 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 ^1=1-57 and 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 Kt — 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 o 5 _^ T= Tern oera lure m°C FIG. 10. 9° C. or less. In the next diagram (Fig. 10) the range of temperature is greater, 2O°-3O° 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 /I = 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 ^=64,200. The logarithms of these times are plotted in the following diagram (Fig. n), 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 3 49 51 53 55 57 Temperature — - FIG. ii. 59 61 rather small, 10° 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 /*-value = 48,6oo found for disinfection of Bacillus par atyphosus by means of phenol (between 6° and 36° 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 ; /JL= 25,000 to jj, = 30,000). Cf. p. 66. In the following table we give the results of the determinations of //, in this field together with some few figures taken for comparison from general chemistry : Spontaneous 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 . f . 26,300 Lipase from castor-beans, heterogeneous . 26,000 Invertase from yeast .... 72,000 Digestions. Casein by trypsin . . . 3 7, 500 Coli-agglutinin by trypsin . . . 16,500 Gelatin by trypsin . . . .10,570 „ pepsin . . . 10,750 Egg-white by pepsin .... 15,57° Powdered casein by trypsin . . . 7,400 Saponifications. Ethyl acetate by bases . . . 11,150 „ „ acids . 17,40° Cotton oil by powdered castor-beans . . 7, 5 40 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 . . . 11,000 „ precipitin from rabbits . . 6,300 Agglutination of coli-bacilli . . j 30,100 „ typhoid-bacilli . '. , 37,200 Different Processes. Hydrolysis of cane-sugar by acids . . 25,600 „ „ invertase . . 11,000 „ starch by amylase . , 12,300 Destruction of H2O2 by catalase . . 6,200 Alcoholic fermentation by yeast-cells . . 15,600 Haemolysis (by bases, acids, lysins) . 25,000 to 30,000 Assimilation by plants . . . . 12,000 Respiration by plants .... 14,800 Cell-division in eggs (mean value) . . 14,100 Heart-beats of pacific terrapin . . . 16,060 Haemolysis by means of hot water . . 64,000 Bacteriolysis (B. typhosus) in hot water . 92,000 ,, (B. paratyphosus} in phenol . 48,600 From the tabulated values of /JL we may conclude that /x 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 /JL, 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). A very similar thing holds good for the inversion of cane- sugar by invertase, according to KJELDAHL (Fig. 1 2 d\ and the coagulation of milk by rennet, accord- ing to FULD'S experiments (Fig. 126). 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 9'K C. * 1 .3 0 r °- •^ (a) Assimilation in plants ^ ^ 50°C t M! „, 0 30 Ofl / ^\ :S •5 1 ^ .O.2 t i / / 50°C x /"o"""' ^" rAeo nins (C) Saponification of cotton oil ro £ in , 2 ^ SSmins. IU 0 ( ) 10 * Temperature o 4 0 50°C J20 2£ 3 -1 15 0 ^- ^ ^ •> \ 1 ^u ^te g 1 ^ •^ \ ) 0 10 20 30 4 Tempera FIG. 12. 0 50 60 70°C ture — » 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 60° 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 p in 140 120 100 t {280 60 40 20 Produc 34 5678 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. 1 3). 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-S 30 45 I 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 — > Product: Quantity o( yeast in Gramms X Time in ho — Heat evolved - - g - g r Qt Dead yeas lOOOcal. ( ..-^ r- — - \ rl200cal -1000 cal. / 2 1 too c x : -800 cal^ > -D / NP/NA- ( && -*s& Vn 2 hours" ptn-- / / /° / ^ 4 6 8 10 Quantity of yeast in frams — + FIG. 14. of yeast : i 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 product of 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 10-4, which are nearly proportional to the squares of 1 200, 1000 and 800. If we divide the first figures by 1-44, i-oo 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 2-6 20-8 -' 4 5-5 22 u o 2 10-5 21 0 I 21.5 21-5 2 8 2 l6 ~ 4 16 u 2 8 16 8 I 15.5 15.5 2 8 1-2 9-6 _. 4 2-5 10 8 2 5-5 11 8 I II II oo DEAD YEAST (RUBNER) -1000 CALORIES Quantity of Yeast. Hours. Product. 10 2 20 5 2 3-8 8 \l I 20 2O 1 REACTION 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 1000 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 i denotes o-ooi 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 7-5 13(13) 6(57) 26(26) 10(11-5) 5-5(6-o) 35(35) i5(i5-4) 9(8-o) 4(4-7) 44(44) 18(19-4) 12(10-1) 6-2(5.9) 53(53) 23(23-3) 14(12-2) 8(7-1) 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 29° 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 39° 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. / is the temperature, q the necessary quantity in cc. of a 05 normal NH3 solution. The total quantity was 8 cc. containing i 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 /. ?obs. #calc. 21-0 0-60 0-64 25-9 0-30 0-30 29-7 0-17 0-17 34-8 0-085 0-083 39-5 0-04 0-043 The value of ^ used for the calculation, which agrees very well with the observation, is 26,760. F 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 39° C. the values of ^obSM for 60 minutes and for 180 minutes are 0-019 and 0-015 respectively. Instead of being in the proportion 3 to i, these figures are as 1-3 to i. Below 30° C. the proportion is, within the errors of experiment, as 2 to i for the times of action 10 minutes and 20 minutes. In con- sequence of this behaviour the /rvalue seems to sink with increasing time. The right value of //, is the limit-value for the time of action o, which is found by extrapolation from the values observed with different times, 2 (2= 10, £ = 20, £=30, 2 = 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 jj,, 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 p (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 4° C. Cobra poison acts nearly independently of the temperature, and the poison of the water moccasin seems to act 1-5 times more slowly even at 39° C. than at 11° 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 coli 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 37° C. j> 200 40-5 49-6 6-25 6-23 32-5 34-o » » 100 26-5 24-8 4-So 4-42 23-9 24-3 Boiled ,, 2OO 42-1 41-7 5-5 5-65 31-3 26-8 ?» » • 100 20-7 20-7 4-0 4-0 18-9 18-9 Milk, eaten . 600 33-9 5-5 21-8 ,, injected 600 55-8 52-5 6-0 5'4 38-2 » j »> 500 41-4 43-8 4-5 4-9 J> 5 J 200 16-7 17-5 3'° 3'i ... Soup of oats and flesh . 600 42-8 41-4 5-8 5-6 ... 300 19-7 20-7 3-8 3-9 Bread of wheat 200 33-6 8-5 3 s 20- o Mixed food l 800 83-2 90-0 9-75 9-0 46-1 44-9 » » 400 4i-3 45-o 6-25 6-37 30-6 3i-8 White of egg boiled 100 45'7 6-3 Tallow of ox 100 12-9 4. e 1 ioo grammes boiled flesh, 100 grammes bread of wheat, and 600 grammes milk. Quanti grammes: 40 hours obs.: 273 » caic. . ^09 43 i °o 280 416 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 ioo 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 : where ^ is the time for the flesh, /2 that for the bread, and /3 the time of digestion for the given quantity of milk. DIGESTION AND RESORPTION 87 The acidity of the gastric juice is about 0-5 per cent of hydrochloric acid, and varies, according to KHIGINE, from 0-56 for the soup given to 0-47 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 icoand 1000 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 : 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 1-6 hours, i.e. to the point where the 1000 grammes-curve cuts a horizontal line, y = 800, 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 i :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 10 12 FIG. 23. dog of 12-6 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. 0 1000 grs. 6 275 grs. I 12 I 875 „ 125 7 178 , 97 2 750 n 125 8 102 , 76 3 627 „ 123 9 51 > 5i 4 506 „ 121 10 23 , 28 5 387 „ 119 1 1 12 , ii 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. ioo grs. 92-2 93-3 3-5 3-4 200 „ 168-1 174-1 4-7 4-8 3oo „ 226-O 239-5 5-7 5-9 288-5 288-7 6-6 6-8 500 „ 3I7-3 323-2 7-4 7-6 600 „ 357-8 345-8 8-3 8-4 800 „ 366-8 367-4 9-9 9-7 1000 „ 369-5 373-4 11-5 10-8 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. L ii. Mean. calc. O IOO IOO IOO IOO (IOO) 2 84 84 84 84 (67) 4 56 53 54 50 (36) 6 2O 18 19 21 (10) 8 7 5 6 6 (o) 9 0 0 0 3 values from series i. and n. 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 RESORPT1ON 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, 1-5 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 40 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 100 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 120 180 Time in minutes — - FIG. 25. at 15 minutes down to n 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. 12.5 125 108 ... 25 160 152 • 61 •41 + '20\J_.™ 50 205 2I5 .58 •59 - -OlJ 100 275 304 1-08 • 82 + -26| 150 350 372 •74 I- 00 -«26/ 200 415 430 ... 1-16 ... 300 520 527 I-OI 1-42 — •411 400 630 608 2-02 1-64 + -38J 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 sepretion 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 f 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 Upases 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. 1 7). 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 BRIDEL {Journal de Pharmacie et 102 CHEMICAL EQUILIBRIA de Chimie, 7 ser., 9, pp. 104, 155, and 230, 1914). They investigated two different glucosides of methyl or ethyl, called a-glucosides and ^-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 0-9 per cent NaCl-solution, and 0-16 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 0-168 0-165 + 0-003 0-4 0-075 0-325 0-329 - 0-004 0-6 0-103 o-497 0-494 + 0-003 0-8 0-137 0-663 0-658 + 0-005 I-O 0-180 0-820 0-823 -0-003 i-5 0-255 1-245 1-235 + 0-010 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 . Methyl alcohol Ethyl alcohol Ethyl ether Isoamyl alcohol Saponin Vibriolysin Silver nitrate Acetic acid Sodium hydrate Ammonia Mercuric chloride 2-9 3 3-3 3-3 5-5 120 286 450 590 750 780 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 f 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 I CO too 3 Log C — * FIG. 26. 2 FIG. 27. 3 LogC CHEMICAL EQUILIBRIA 107 t 00 bo o LogC FIG. 28. 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 c0 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 — cl the corresponding concentra- tion in the egg-white. As the content of poison in the standard solution is very small, the value of ^ may naturally be expressed by a very large number. For comparison the square-root \/c0 of CQ and the ratio ^ : ^~ are tabulated : CD- Ci. Vco. _£!_. Vqj' 7 6,200 2-64 2343 16 8,930 4-00 2233 26 1 1, 600 5-10 2275 51 16,670 7-14 2333 73 21,900 8-54 2563 89 27,500 9-43 2915 Average 2444 i As we see from the values tabulated in the last CHEMICAL EQUILIBRIA 109 column, c is very nearly proportional to \/c0. This points to the circumstance that we here observe a phenomenon of adsorption, for, when the concentra- tions cQ 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, 1914). 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 / 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 ^;calc< found on the supposition that Kg = 0-0333, A is just equal to 1 50 milligrammes. ADSORPTION OF FERROCYANIC ACID ON CASEIN t. *obs. *calc. t. •^obs. *calc. 0-0005 0-0164 0-0238 5-4 16-7 20' 6 2-7 15-2 18-1 0-2746 0-8876 1-8396 £5 116-1 55-2 87-6 II2-I 0-1148 37-4 37-8 The agreement seems to be perfect within the errors 110 CHEMICAL EQUILIBRIA of observation. The first observed value of ^obs 5-4 is much too high, probably due to the dissociation of the compound of ferrocyanic acid and casein. The close coincidence of the #obs> with the ^calc> 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 100 lethal doses, i.e. enough for killing 100 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. Ti. Tn- T calc. 0 100 100 IOO •25 -»v 73 75 75 •375 58 63 62-7 •5 50 48 50-5 • 675 32 45 38-4 •75 28 26 27 •875 17-2 17-3 16-5 I-O n-i 9-6 8-8 1-125 5-6 5-3 4-9 1-25 1-2 3'1 3-1 1-5 1-6 1-7 2 ... ... •9 3 ... ... •3 K = 0-0093 the discrepancy between them is without doubt due to experimental errors. After the observed values T! 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 n = 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 18-2 (obs. 16-7), the fifth 5-7 (obs. 8-2), and the sixth only 3 Quantity of Antitoxin J in equivalents FIG. 30. 1-4 (obs. 0-6) 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 10 cc. 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 o-i normal solutions of NaOH and HC1 ; if we add 01 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 37° C.). Now we mix 0-5 cc. HC1 with i 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 0-5 cc. of the original solution. We must therefore now take 0-3 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 ^r-axis at i corresponding to addition of a quantity of acid equivalent to the quantity of base used. In reality the line of neutralization cuts the ^r-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 #-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 Acid or antivenin — > 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 = 0-0014 or the seventh part of that for diphtheria poison. Another snake venom from the water- moccasin (Ancistrodon piscivorus] gives the value K — 0-006, and that from Crotalus only K = 0-0006. 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 H3O3B n. Tobs. Tcalc. AT A« obs. AT A« calc. 0 100 IOO o-333 82 75 •54 •75 0-667 63 60-3 •57 •44 I 47-5 50-3 •47 •30 1-333 43-7 43-2 • i i •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, uppermost curve). From the figures observed we calculate K = i -02 or about no times as much as for diphtheria serum. Here EHRLICH'S phenomenon is extremely pronounced. If we now represent AT : A^ 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 A^= -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," £-4 o I.. Z/Z Quantity of H30,B 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 = i -02 from the CHEMICAL EQUILIBRIA 119 experiments of MADSEN and myself regarding the haemolytic action of mixtures of NH3 with H3O3B, LUNDE"N 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 37° C. At 16° 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 0-04 cc. TETANOLYSIN AFTER ADDITION OF n cc. (^ EQUIVALENTS) OF ANTILYSIN (MADSEN) Quantity of Antilysin. Toxicity (Free Poison in Per Cent). « cc. #1 Equiv. 9 obs. 9 calc. 0 O 100 100 0-05 0-1 018 0-36 82 70 82 66 0-15 0-2 0-54 0-72 52 36 52 38 0-3 1-09 22 23 0-4 0-5 o-7 I-O 1.45 1-81 2-54 3-26 14-2 10- 1 6-1 4.0 13-9 10-4 6-3 4-0 1-3 4-35 2-7 2-9 2-0 5-44 6-52 2-0 1-8 2-5 1-9 K = 0-115 at 37° 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) 2-7 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 jr-axis gives the quantity of serum equivalent to the quantity of poison used (in this special case 0-276 cc. of anti- toxin are equivalent to 0-04 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 (ComptesRendus, 159, 152, Paris, 1914), which had lost five-sixths of its toxicity from 1907 till 1913 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 in 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 object to the use of the laws of equilibria on the binding 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 n 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 70° C. the mixture remains innocuous. But if we add only 0-5 cc. of the acid to i 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 1-86 : i in an interval of 10° C., corresponding to a value of //,= 11300. 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 0 02 CC. 5 2 0-4 cc. A+ i cc. L O2 2 CC. 23 22 o- 6 cc. A + i cc. L 042 cc. 39 42 0-8 cc. A + i cc. L 0-62 cc. 60 62 1-2 cc. A+ i cc. L I'O2 CC. 97 102 ! A is the solution of antitoxin used ; L the solution of tetanolysin ; i 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 100. 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 = 900. 60 40 (46) 40 37 (45) 25 38 (42) ... ... ... 15 39 (37) 10 38 (33) 7 1 '(84) 98* (ioo) 100 (100) 6 22 (25) 59 (60) 85 (98) 98(100) 4 20 (20) 45 (44) 75 (66) 82 (73) 2-5 24 (29) 5i (43) 47 (47) i'5 I5(i8) 25 (25) 22 (28) 24 (29) i ... 15(17) IS (19) 18 (20) 0-6 ... ii (10) i3(") 13(12) In brackets are written values calculated from the formula (50 -x) (206 -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 50, i.e. 50 — the observation gives not more than 40. In the same manner if b is small, e.g. 0-6 or i, the quantity of haemolysin does not reach 100 even with the greatest excess of amboceptor (0 = 900). According to the formula x cannot in this case exceed a maximum x=2ob, 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 37° C. for two hours and subsequently for seventeen hours at 2° 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 — .#•) (2 5 <£ — #) = 1 900.2:. The second with red blood - corpuscles from ox 132 CHEMICAL EQUILIBRIA and amboceptor from rabbit with guinea-pig serum corresponded to the formula 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 A certain quantity of lecithin (L), 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 o-io 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 . .- . . 0-21 cc. „ „ orang-utang . . 0-13 cc. „ „ dog ape . 0-09 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 1 6,000 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 — i 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 0-4 cc. were mixed with a variable quantity (A cc.) of the sheep serum diluted in the proportion 1:49 with 0-9 per cent salt solution. The quantity of precipitate P was measured (in the unit 0-0004 cc.). At the side of the observed quantities I have written calculated values obtained from the formula 136 CHEMICAL EQUILIBRIA (4oA-P)(i2o-P)_K_ V V 250. In this case when a precipitate is formed the pro- duct of the concentrations ^ ' of the sheep v , (I20-P) . serum and - — L of the rabbit s serum, in which v v is the total volume of the mixture, should be a constant K, which is found equal to 250. The formula indicates that in i cc. of the diluted sheep serum there is enough material to give 40 units of precipitate and that 0-4 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. Fobs. P calc. A. Pobs. P calc. O-02 I 0-5 5 64 65 0-04 2 i-3 7 58 58 0-1 3 3-5 10 49 46 0-15 6 5-3 15 10? 19 0-2 7 7-2 18 5 3 0-6 21 21.5 20 2 o I 35 34 i + 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. 0-9 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 = 3-75. 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 1 80 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 (0-72) and for that of sheep to cattle (0-29 and 0-36 : mean value 0-33). 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 r61e 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- 5 .S3 25 125 ISO 50 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 1897. He injected, for instance, a dog with in 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 xDog oGuindaPig 5 Time in days - FIG. 34. 13 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) . * "O c 'i H Observed total quantity of antibody. L is SJj d Calculated value. Dog i. Dog 2. 1 Dog 3. Mean. I1 0 I 5 9 13 7 3 06 7 3 I 0-2 7 2-5 0.4 0-2 U I-I7 o-S 0-23 •a? 1-19 0-51 022 7 2-1 0-84 o-35 0-14 007 (2-65) 2-1 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 day, 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-serumwith 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 05 025 30 60 Time in days — > FIG. 35. 90 120 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. L 2 148 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 i cc. of the Serum. Time in Days. Observed. Calculated. 0 0 O 0-O2 2 (n.8) I 16 M. 6 4 II ii 24 7-5 7-6 48 5-5 4.9 60 4-5 3-9 77 3-2 2-8 100 1-3 1-9 126 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) Quantity of Agglutinin per cc. Serum. Observed. Calculated. 0 909 (274) o-3 555 (267) i 333 (250) 3 208 208 5 167 173 8 125 131 1 1 100 100 15 91 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 100 to 65 units, another time from 1 20 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. 0 4 4 Injection. 0-5 I 3 3 4 4 [Negative Phase. Last day of the time of 2 4 4 incubation. 3 10 10 ' 4 25 30 5 6 50 65 50 70 Time of rapid increase. 7 90 90 8 125 IOO , Acme. 10 IOO (60) Rapid decrease between days 9 and 1 1 . ii 59 56 12 5o 53 13 42 49 Slow, regular, monomolecu- 1 8 33 35 lar decrease. 21 28 28 26 20 20 The time of rapid increase, between the time 2-5 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 10 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. 0 I36 136 Injection. I 136 I36 Incubation time at an end after 2-7 days. 3 1 88 186 } 5 268 272 (Time of rapid increase (43 units a 7 367 358 | day). 9 442 444 J Acme. 1 1 323 323 Rapid decrease between the days 9 and 1 1 . 13 286 285 i? 20 225 196 221 183 Slow, regular, monomolecular decrease. 23 J51 151 25 117 133 Here the time of incubation is reduced to 2-4 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 5-5 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. 0 Obs. 60 Calc. 60 2 6 10 50 36 25 51 36 26 15 17 17 20 12 II 27 35 10 6-7 6-2 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 8-4 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 1600 1600 6 1000 I I 60 13 800 810 19 600 602 25 420 456 33 320 325 40 270 250 48 200 195 58 ISO 153 ?i 130 125 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 2-3 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, 110-127 Antivenin, 116, 123, 124 Assimilation, 21, 55-57, 93-95 Atomic theory, i Bacteria, 53-55, 67-74, 105 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, J34 Complement, 128-132 Compound haemolysins, 16, 128-132, !5r 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, 113-123 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- 132, 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. JI5 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, 101 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, i 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, 110-133 Oleate, 66 Opsonin, 16 Optimum, 56-58 Osmotic pressure, 104 Oxydase, 14 Pancreatic juice, 13, 46, 47, 82, 92, 93 Papayotin, 14 Paranuclein, 100, 101 Partial poisons, 118 Partition between two phases, 102-108, 125 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, 59-65, 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, 85-86, 87, 91, 94- 97 Starch, 12 Steapsin, 46 Stomachical juice, 12, 13, 47, 82, 83- 85- 92 Subcutaneous injection, 141, 142, 148, 151, 155, 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> IO2 I 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, i 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 Bunsen, 64 Calmette, 123, 124 Chick, Harnette, 27, 28, 53, 69, 72, 73. 74. 80 Clark, 69, 72 Dalton, i 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, .143 Eisenberg, 105 Ellenberger, 85 Engelmann, 21 Euler, 47 Fischer, Emil, 22, 101 Friedenthal, 135 Fuld, 56 Gage, 69, 72 Galilei, 128 164 INDEX Gay, ioo, 139 Ge~lis, 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, i Levin, 141 Liebermann, 22 Lobasoff, 83, 92 London, 81, 84, 85, 87, 88, 91, 93, 95- 97 Lonnquist, 82, 83 Lund£n, 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 Man waring, 130 Martin, 27, 28 Massol, 123 Matthaei, Gabrielle, 56 Maxwell, 77 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 P£louze, 22 Pfeffer, 21 Polowzowa, 84, 87 Priestley, 21 Pringsheim, 21 Robertson, T. B., ioo Roscoe, 64 Rubner, 61, 62 Sachs, Hans, 118, 126, 131, 150 Sachs, Julius, 21 Salomonsen, 152 Sandberg, 97 de Saussure, 21 Schiitz, E., 8, 9, n, 37, 39, 41, 42, 43, 47, 62, 63, 72, 84, 109 Schiitz, Julius, 37 Senebier, 21 Sjoqvist, 37, 47 Sorensen, 32, 33 Stoklasa, 21 Taylor, A. E., ioo Teruuchi, 35, 103, 108 Thomsen, Julius, no Todd, 150 Tompson, 31 Tyndall, i, 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 Printed by R. & R. CLARK, LIMITED, Edinburgh, RETURN NATURAL RESOURCES LIBRARY TO— ^ 40 Gianinni Hall Tel. No. 642-4493 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS DUE AS STAMPED BELOW ••.'•, t^t 1-jO UNIVERSITY OF CALIFORNIA, BERKELEY FORM NO. DDO, 50m, 1/82 BERKELEY, CA 94720 LD 21A-15m-2,'69 (J6057slO)476 — A-32 University of California Berkeley U.C. BERKELEY LIBRARIES 341163 DlUL UNIVERSITY OF CALIFORNIA LIBRARY