IMMUNOCHEMISTRY THE MACMILLAN COMPANY NEW YORK • BOSTON • CHICAGO ATLANTA • SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON • BOMBAY • CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO IMMUNOCHEMISTRY THE APPLICATION OF THE PRINCIPLES OF PHYSICAL CHEMISTRY TO THE STUDY OF THE BIOLOGICAL ANTIBODIES BY SVANTE AR'RHENIUS ^ Ntto go* THE MACMILLAN COMPANY 1907 All rights reserved ~ COPYRIGHT, 1907, BY THE MACMILLAN COMPANY. Set up and electrotyped. Published October, 1907. Nortoootf J. S. Cashing Co. — Berwick & Smith Co. Norwood, Mass., U.S.A. PREFACE THE following pages contain a summary of six lectures on the Immunity Reactions delivered at the University of California, in Berkeley, California, during the summer session of 1904. The object of the lectures was to illus- trate the application of the methods of physical chemistry to the study of the theory of toxins and antitoxins. The idea that the reciprocal action of toxin and antitoxin is of the same nature as a chemical reaction is nearly as old as the study of these phenomena, which was inaugurated by the discovery of the diphtheria antitoxin by Behring and Kitasato in 1890. The German school, led by Ehrlich, the renowned Director of the Prussian Serum Institute in Frankfort-on-the-Main, has in particular done much work in support of the opinion that the interaction of toxin and antitoxin is of the nature of a chemical reaction ; whereas the French school, led by Metschnikoff, tried to show that the effect of an antitoxin is chiefly of physiological order, an antitoxin was supposed to stimulate in some way the organic tissues in their struggle against the attack of the poison.1 When Ehrlich succeeded in showing that the agglutinat- ing action of ricin upon red corpuscles (erythrocytes) sus- pended in a physiological salt-solution (0.9% NaCl) is inhibited by the antibody, — the antiricin, — the notion that a physiological effect is executed by the antibody was 1 The first studies in this direction were carried out by Buchner (1893) and Roux and Vaillard (1894). Cf. Chapter II. Vi PREFACE abandoned by most scientists. Although I adhere to the chemical school, I cannot say that the proof of Ehrlich is quite convincing, since the erythrocytes may well be regarded as " living " even after their separation from the blood of an animal. The further fact stated by Ehrlich, namely, that approximately the #-fold quantity of a toxin requires the n-fo\d quantity of antitoxin for its neutralisa- tion, may be regarded as a more convincing proof against the physiological hypothesis. The chemical hypothesis is now generally accepted, and has been adopted recently by Bordet, who originally expressed ideas similar to those held by Metschnikoff. Nevertheless, many difficulties to the chemical hypothe- sis remained. Nothing was more natural, therefore, than that the further elucidation of the problem should be sought through the aid of the modern theories of solution. To this end Madsen and Ehrlich invited me to join in their work. My work with Madsen in the Copenhagen Insti- tute enabled us to fix upon a simple explanation of the chief difficulty exhibited by the so-called phenomenon of Ehrlich. The Chief of the Frankfort Institute was so deeply interested in the progress of these studies that he invited me to work in his Institute on the chemical be- haviour of compound haemolysis. In this case, also, it was determined that the laws of equilibrium found their appli- cation. It would seem, therefore, that the adherents of the chemical hypothesis should have felt wholly satisfied with the results. However, one of the strange incidents with which the history of science is replete occurred. In our explanation of the investigated phenomena, especially regarding the diphtheria toxin, Madsen and I, in accord- ance with the usual rule in the exact sciences, tried to employ as few hypotheses as possible, and in this we fol- PREFACE vii lowed the example of Bordet. We tried to show that the phenomena observed might be explained on the supposition that diphtheria toxin is a simple substance which slowly decomposes into an innocuous material that still neutralises antitoxin. In his explanation Ehrlich had previously assumed the presence in the diphtheria poison of a large number of poisonous substances of different strength. Now Ehrlich did not wish to yield this explanation, which he regards as the principal point in his doctrine; and therefore he and his numerous pupils raised a number of objections to the treatment of this branch of science in accordance with the modern theories of chemistry. There- upon Biltz, encouraged by Ehrlich, took up and elaborated the old idea of Bordet, which had been abandoned by this prominent savant in favour of the chemical hypothesis, and suggested that antitoxin does not react chemically with toxin, but behaves about in the same manner as a dye when it becomes fixed in a fibre. Some of these recent objections to the ideas brought forward in the lectures have been taken here into consid- eration, notwithstanding that they have appeared since the lectures were delivered. In the same way, much recent work, especially by Madsen and his pupils (in large part as yet unpublished), bearing upon the velocity of reactions, has been given consideration in the following pages. And the recent work of Hamburger on precipitins has been made use of in the final chapter. I have given to these lectures the title " Immuno-chem- istry," and wish with this word to indicate that the chemical reactions of the substances that are produced by the injec- tion of foreign substances into the blood of animals, i.e. by immunisation, are under discussion in these pages. From this it follows also that the substances with which these viii PREFACE products react, as proteins and ferments, are to be here considered with respect to their chemical properties. And for the purpose of a clarification of ideas, other substances that behave in an analogous manner will be given a con- sideration in the discussion. It is evident that the objection recently raised by Ehrlich and Sachs to this manner of investigation, namely, that it does not enter upon the mode by which the living body produces these so-called antibodies, is quite true. An investigation of the chemical relations of toxin and antitoxin need not carry with it an elucidation of the synthesis of the antitoxin. But I fancy that there are many who are so deeply interested in the chemical be- haviour of these substances that they will find an investi- gation of this question well worthy of study. And for myself, furthermore, I believe that the physiological side of the problem, alluded to by Ehrlich, will not find a satis- factory solution until the more simple chemical aspect is elucidated. The chief purpose of theoretical considerations is to afford clear and concise ideas of the observed facts. They thereby stimulate scientific research to a high degree. I venture to hope that the reader of the following pages will find that the theoretical views advanced by myself in this branch of science have fulfilled their role in a most satis- factory manner during the few years that they have been employed. I am glad to say that during these few years a large experimental material has been produced, which shows that the chief lines pointed out by theory are closely congruent with the facts ; and this material has been pro- duced almost exclusively in order to verify the said theo- retical considerations. These have, therefore, already been of great scientific use, and yet this is only a small part of PREFACE ix what may be expected. The reader will have frequent opportunities to compare the different scientific points of view that are connected with the theoretical views here exposed with those founded on other theoretical consid- erations. I am deeply indebted to my friend Professor Alonzo Engelbert Taylor of Berkeley, California, for his great kindness in the revision of the manuscript and for the cor- rection of some errors. To my many friends in California, these lines will, I hope, recall the pleasant period of time during which I had the good fortune to live with them in their agreeable country. SVANTE ARRHENIUS. STOCKHOLM, SWEDEN, October, 1906. CONTENTS CHAPTER PAGE I. INTRODUCTION i II. REVERSIBILITY OF REACTIONS BETWEEN ANTIBODIES . 18 III. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS . 37 IV. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS . 100 V. EQUILIBRIA IN ABSORPTION PROCESSES . . .144 VI. NEUTRALISATION OF THE H^EMOLYTIC PROPERTIES OF BASES AND OF LYSINS OF BACTERIAL ORIGIN . .167 VII. NEUTRALISATION OF DIPHTHERIA-TOXIN, RICIN, SA- PONIN, AND SNAKE-VENOMS 196 VIII. THE COMPOUND H^MOLYSINS 218 IX. THE PRECIPITINS AND THEIR ANTIBODIES . . . 263 INDEX OF AUTHORS 301 INDEX OF MATTER 305 LECTURES ON THE GENERAL PROPERTIES OF IMMUNITY CHAPTER I INTRODUCTION RECENTLY the so-called antibodies that are produced in animals after the injection of certain more or less poison- ous substances have acquired a very great importance, and the chemical behaviour of these antibodies has been the object of a large number of investigations. Some of these have led to the idea that the reactions of these substances are incomplete and follow the law of Guldberg and Waage. It is of these researches, carried out chiefly by the Direc- tor of the Danish State Serum Institute, Dr. Thorwald Madsen, and myself, that I wish to give a short review in the following lectures. For only a few poisons have the corresponding anti- bodies been prepared. These poisons are termed toxins. They are all of organic derivation. Bashf ord l and Bes- redka2 have tried in vain to prepare antitoxins to solanin and saponin by the injection of these substances into rab- bits and guinea-pigs. And the so-called antimorphine has proved to be a failure.3 Solanin, saponin, and morphin 1 Bashford: "Uber Blutimmunitat," Arch, intern, dc pharmacodynamie et de therapie, T. 8. 101 et 9. 451 (1901). 2 Metschnikoff : " L'immunite," Paris, 1901, p. 410. 8 Morgenroth: Berl. klin. Wochenschrift, 1903, No. 21. 2 LECTURES ON IMMUNITY are therefore not toxins. On the other hand, extracts from the seeds of Ricinus communis contain a toxin called ricin, against which we possess an antitoxin called antiricin. In the same way antitoxins are known corresponding to abrin and robin, extracted from the seeds of Abrus prcecatorius and of Robinia pseudacacia. It is not only against poisons, but also against wholly or nearly inoffensive bodies, that animals produce antibodies. Furthermore it seems that if we introduce nearly any type of cell into the veins of an animal, its blood will contain after a time an antibody which destroys the particular variety of cell. Even after the injection of rennet, the ferment of the coagulation of milk, we obtain an antibody called antirennet, which hinders the coagulative power of rennet.1 It is very diffi- cult to draw a distinction between enzymes or ferments and toxins. Like rennet, many others of these substances are found to yield antibodies after injection into the blood of different animals. Thus, for instance, v. Dungern2 pre- pared in this way antibodies against proteolytic enzymes from pathogenic microbes. Hildebrand 3 obtained in a simi- lar way an antibody against the ferment emulsin. Gessard 4 found it possible to prepare an antibody against tyrosi- nase, an oxydase extracted from mushrooms ; and Sachs 6 showed that the serum from a goose which had been in- jected with pepsin contained antipepsin. A. Schutze prepared " antilactase " by injection of "lac- tase from kefir" into rabbits or hens; other antibodies 1 Morgenroth : Centralblatt f. Bakteriologie, Abt. I, Vols. 26 and 27. 2 v. Dungern: Centralblatt f. Bakteriologie, Thl. I, Vol. 24 (1898). 8 Hildebrand: Virchovfs Archiv, Vol. 131 (1893). 4 Gessard: Annales de Vinstitut Pasteur, 15. 607 (1901). 6 H. Sachs: Fortschritte d. medicin, 20. 425 (1902). INTRODUCTION 3 have been prepared against cynarase, fibrin ferment, pan- creatic ferment, zymase, and urease.1 It therefore seems to be only a question of time when we shall be able to prepare antibodies against ferments and enzymes in general. An antibody to rennet is contained in the so-called normal serum of the horse ; that is, horse blood freed of fibrin by being shaken with small solid bodies such as glass beads or pieces of iron wire, and separated from the red blood corpuscles by centrifugation. (This was first shown by Hammarsten and Roden.2) In the same manner fresh serum and even egg-white contain antibodies against many other substances, as for instance against trypsin and tetanolysin. By natural or normal blood serum is meant that obtained from fresh animals that have not been inocu- lated in any manner. If before the preparation of the blood serum foreign bodies have been injected into the veins of the animal, we obtain generally not normal serum but serum containing an antibody, which is " specific " to the injected body (i.e. immune-serum). In order to render this peculiar subject clearer I will give a short review of the mode in which these antibodies appear in the serum and how they afterwards disappear from it. The next curve shows the concentration of cholera- agglutinin in the blood of a goat, which had some time before the experiment been immunised with cultures of Vibrio cholera, so that the concentration of agglutinin in it 1 Compare A. Schiitze : Zeitschr. f. Hygiene, 48 (1904). 2 Roden: Upsala L'dkarefdrenings Forhandlingar, 22. 546 (1887); Maly's Jahresbericht, 17. 160 (1887). 4 LECTURES ON IMMUNITY was at the commencement four arbitrary units. If we inject a culture of the bacillus (e.g. Vibrio cholera*) into the blood of a goat, it produces antibodies specific to just the injected bacilli. Amongst these antibodies is one called agglutinin, because it causes cholera bacilli to clump together and sink to the bottom of the liquid in which they are suspended. We may measure the concentration of agglutinin in a liquid by a method to be described below. The experiments, the results of which are given in the curve, were carried out by Madsen and Jorgensen,1 follow- ing the subcutaneous injection of 40 c.c. of a culture of chol- era bacilli into a goat. From the jugular vein of the goat small amounts of blood were taken every day and exam- ined as to their content of agglutinin. In the first two days no increase in the quantity of agglutinin in the blood serum was observed, but later on it rose rapidly till it reached a maximum, " acme," on the eighth day, after which it sank at first rapidly, then more slowly. The continuation of the curve illustrates an experiment with the same goat, in which an injection of 5 c.c. of a culture of cholera bacilli was made daily during the whole period of research. Here the first period, in which no agglutinin was produced, lasted four days, and the second period, where the agglutinin increased, eleven days. Madsen has found that the decrease after the maximum follows closely the equation for the velocity of a chemical reaction : 1 A. Jorgensen and Thorwald Madsen : "The Fate of Typhoid and Cholera Agglutinins," Festskrift oed indviclscn af statens scrum-institut,'V\, 12, 1902, Copenhagen. cc-o UJ- u.0 05 oo Hit Q — 8 INTRODUCTION Rate of decrease = const, (concentration), which gives the integrated formula (concentration) — = const.! + const.2 /, where t represents the time (after the maximum) that cor- responds to the concentration in the formula. For the case with cholera agglutinin produced by goats, Madsen found n = 3.5, const.j = 0.082 and 0.32 resp., and const.2 = o.i3 and 0.032 resp. for the first and the second part of the curve represented above. As example we give the figures of the second part, together with the results of the calculation. T (DAYS) C°NC-OBS. CONC'CALC. T (DAYS) C°NC-OB3. C°NC-CALC. 0 250 250 8 43 43 I 91 96 IO 40 40 2 77 74 12 38 37 3 63 63 14 36 35 4 56 57 16 34 33 5 52 52 18 32 3i 6 49 48 20 30 3° 7 46 45 22 28 29 In this case the exponent n was rather high, higher than in other cases examined by Madsen.1 For goats with typhoid agglutinin he found n = 1.3 and #=1.5. This last figure was also found for typhoid agglutinin in the blood of rabbits. The figures of Bomstein for the quan- tity of diphtheria-antitoxin in the blood of dogs and guinea- 1 Th. Madsen : " The Decrease of Antibodies in the Organism," Festskrift, VIII, Copenhagen, 1902. LECTURES ON IMMUNITY pigs after direct injection l of this antibody in the blood of these animals gave #=1.2. In this case the constant const.2 is nearly of the same magnitude for different dogs, as one might expect (it is in three cases 0.15, 0.18, and 0.19). For the destruction of antibodies in the human body, Madsen has found n = 2 in many cases. Of course this formula is only an empirical one. Its physical mean- ing is easily understood. The examples calculated by Madsen show a very good agreement with the experiment. As further instances may be cited the following figures for the decomposition of typhoid agglutinin in the blood of a passively immunised goat (according to Jorgensen and Madsen) and in that pf a man who had suffered from typhoid fever (according to Jorgensen).2 x = concentration. DESTRUCTION OF TYPHOID AGGLTJTININ IN A DESTRUCTION OF TYPHOID AGGLUTININ IN THE PASSIVELY IMMUNISED GOAT BLOOD OF A MAN AFTER TYPHOID FEVER T (Days) '°4x©obs. Io4x(l)calc. T (Days) <°Oob, Io3x©calc. 0 II II 0 17 17 0-3 18 19 2 20 2O I 30 3° 6 28 28 3 48 5° 10 40 37 5 60 64 15 60 53 8 80 81 20 85 74 n 100 94 27 IOO "3 15 no no 35 15° 1 68 42 250 255 = 8 X io-6. n = 1.2. const. 2 = 0.0302. 1 So-called passive immunisation: "Active immunisation " is produced by injection of the toxins or cells themselves, as is described above. 2 Madsen : " Lecture Held at the Meeting of Brit. Med. Ass., Oxford, July, 1904," British Medical Journal, Sept. io, 1904. INTRODUCTION 7 The use of formulae represents a great step forwards in the study of this portion of the science of immunisation. Formerly investigators were content to state that the quantity of antitoxin in the blood decreases gradually, and in the first stages more rapidly than later on. The application of the formula of Madsen teaches us much more. It shows that the phenomenon is a regular one, and we are impelled to seek for a cause for the differences of the values of the constants n and const2. For instance, the different values of const.2 for the three days in the experi- ments of Bomstein — are they really different or do the observed differences depend only upon experimental errors? This and other questions suggest themselves after the use of such an equation, and they lead to improvement in the experimental methods, and to very sharp and well-defined ideas of the natural phenomena themselves. With the help of formulas, which may be empiric or rational, scien- tific progress will be much more rapid than without them; and as the experimental material increases, the empiric formulae will probably be converted into rational ones, i.e. we shall detect new laws of nature. It is therefore very much to be regretted that efforts have been made, espe- cially recently, to reject the use of formulae in the treat- ment of questions of serum-therapy. These efforts may be regarded as a last desperate struggle against the strin- gent conclusions that may be reached by means of the application of mathematical treatment — a struggle that cannot be greatly prolonged. The injection of toxins or cells into the blood of an ani- mal can be done in different ways. Perhaps the most used of them is the "intravenous injection" directly into the 8 LECTURES ON IMMUNITY veins of the animal ; as a special case may be regarded the " intracardial injection" directly into the heart of the ani- mal. More slowly acts the " intraperitoneal injection " into the peritoneum, and still more so the "intramuscular injec- tion," or the "subcutaneous injection," under the skin of the animal. This last method is very much used. In these cases the injected body reaches the blood very slowly, in which fluid it produces antibodies. The anti- bodies may be divided into two great groups according to the nature of the injected fluid, whether it is a homogene- ous solution or an emulsion of cells, e.g. bacteria or red blood corpuscles. These suspensions of, e.g., erythrocytes are secured by centrifugating blood freed of fibrin. Be- tween the centrifugalized blood corpuscles there still remains a noticeable quantity of normal serum. This serum contains a very effective reagent for most of the re- actions which we wish to study. It is therefore necessary to wash it away. For this purpose we use a so-called physiological solution, in most cases of sodium chloride (0.8-0.9 %)• Suspended in this solution blood corpuscles and most bacilli remain unaltered. In stronger solutions the corpuscles or bacilli contract; in weaker solutions the erythrocytes give up their red colouring matter and remain colourless (" stromata "). The bacilli are injured by plasmolysis or imbibition of water. To be washed, the blood corpuscles are shaken with the physiological solu- tion, centrifugalized, separated, and this operation repeated until the serum is washed away as much as necessary. Usually two or three washings with five times the amount of solution are sufficient. The antibodies produced after the injection of a homo- INTRODUCTION 9 geneous solution of a substance, e.g. a toxin, combine in most cases with the injected body to form more innocuous compounds. If these compounds are soluble in the mix- ture, we call the antibodies antitoxins (at least if the injected body is poisonous). If, on the contrary, the compound is insoluble, the antibody is called a precipitin. Such pre- cipitins are produced after the injection of different albuminoid substances. If the injection is a suspension of cells, the antibody formed sometimes dissolves these cells ; in this case it is called a lysin. Thus after the injection of bacteria there are formed bacteriolysins, which under proper conditions dissolve the bacteria of the injected variety. After the injection of erythrocytes so-called haemolysins are formed, which produce haemolysis, i.e. cause the red colouring matter (the haemoglobin) of the injected erythrocytes to leave them and to diffuse into the surrounding liquid. In other cases, other antibodies are formed, often simul- taneously with lysins, so-called agglutinins, which produce an agglutination of the injected cells. In this case the presence of salts plays an important role. The normal serum often contains a certain quantity of anti- bodies. Thus, for instance, in the normal serum of horses re markable quantities of diphtheria-antitoxin and of antirennet are often found. This peculiarity is so frequently observed, that Ehrlich supposes that all possible antibodies exist in normal sera, though in most cases the amount is not suffi- cient to be shown experimentally. In the blood of many animals we find two organic substances, cholesterin and lecithin, which react with many of the injected poisons and therefore play an important r61e as antitoxins or even as IO LECTURES ON IMMUNITY constituents of toxins. Thus, for example, the haemolytic poison tetanolysin that is produced by the Bacillus tetani may be interfered with in its haemolytic power by choles- terin. The researches of Madsen and Walbum seem to prove that the compound of these two bodies is quite innoc- uous, so that the cholesterin may be used as an antibody against tetanolysin. Now it is not specific against tetanol- ysin, as is the antitetanolysin, but it is effective also against other lysins ; namely, saponin, cobralysin, cobralecithid, and olive oil, but not against staphylolysin and arachnolysin.1 The lecithin, on the other hand, combines with the poison of cobra, so that a haemolysin cobralecithid is formed, that also in exceedingly minute quantities exerts an haemo- lytic influence upon erythrocytes. The cobra-poison itself displays such a property, but to a much less degree.2 These different bodies are often rather unstable, so that they are spontaneously decomposed. This decomposition proceeds much more rapidly at higher than at lower tem- peratures. They are therefore in most cases conserved at very low temperatures, sometimes in a frozen form. Ransom 3 has made a very interesting observation regard- 1 Kyes and Sachs: Berl. klin. Wochenschrift, 1903, Nos. 2-4. 2 Overton has expressed the opinion that the action of lecithin and of cholesterin are associated to their lipoidal properties. With respect to lecithin, it seems that this idea may be applied to much of the experimental material. The lecithin seems, namely, to become dissolved in the membranes of the cells (e.g. the erythrocytes) and thereby facilitates the passage of some poisonous substances (e.g. mercuric chloride) into the cell or of haemoglobin outwards through the cell membrane (cf. p. 158). The action of cholesterin seems to be quite different, and of a neutralizing character (cf. Chap. VIII). On the interesting investigations of Overton regarding the permeability of cellular membranes cf. Rud. Hoeber : " Physikalische Chemie der Zelle und Gewebe," 2d ed., Leipzig, 1906, pp. 163-197. 3 Deutsche med, Wochenschrift, 1901, No. 13. INTRODUCTION 1 1 ing the action of cholesterin. Saponin is a powerful haemolytic agent. Its action is conditional upon the pres- ence of cholesterin in the blood corpuscles. On the other hand, cholesterin in the blood serum protects the blood corpuscles from being attacked by saponin. Weigert1 compared the cholesterin with a lightning conductor, which has its proper place on the outside of the protected house. From a chemical point of view we explain the observation in the following manner. The membranes of the red blood corpuscles are permeable to saponin, but not to cho- lesterin or to the haemolytic compound of this substance with saponin. Therefore the saponin is divided between the blood corpuscles and the serum practically in propor- tion to their content of cholesterin. If the content of saponin-cholesterm in the blood corpuscles reaches a certain amount, these are haemolysed, otherwise not. It is the poison dissolved in the blood corpuscles that exerts an action; the poison on their outside is without effect on them. The first step in the development of sero-therapy into an exact science consisted in devising methods for measur- ing the quantities of the different substances employed. In this regard Ehrlich enjoys great distinction in having been the first who with sufficient exactitude measured the strength of diphtheria-poison. To estimate justly the great progress that was due to the introduction of measure- ment methods by Ehrlich, it must be borne in mind that, at the time that Ehrlich did his work, nearly all of the leading men believed it impossible to measure toxins and anti- 1 C. Weigert : " Einige neuere Arbeiten zur Theorie der Antitoxinimmuni- tat," Wiesbaden, 1899. 12 LECTURES ON IMMUNITY toxins. This belief was due to the very different effects which the same quantity of poison exerted on two different individuals of the same species, e.g., diphtheria-poison on guinea-pigs. It was only the practical necessity of having measurements of the force of poisons that led Ehrlich to overcome the great difficulties.1 The chief investigations of Ehrlich concern the diphthe- ria-poison and its antitoxin. He wished to determine the lethal dose of this poison for guinea-pigs. For this purpose he injected a great number of guinea-pigs with different doses ; they lay in the neighbourhood of the lethal doses. It may be here mentioned that large guinea-pigs in general endure a greater quantity of poison than do small ones. Ehrlich supposed that the resistency of different individ- uals was proportional to their weight, and on this assump- tion he calculated the dose corresponding to a " normal " guinea-pig of 250 grammes weight. To obtain uniform results he found it necessary to use animals of nearly the same weight, age, and race. In the summer the animals are more resistent and give more uniform results than at other seasons, when they evidently surfer from the changes of temperature and other climatic conditions. The lethal dose of diphtheria-toxin was defined by Ehrlich as the quantity which injected subcutaneously into a great number of guinea-pigs causes the death of the larger fraction of the animals in three to four days, the rest of the animals dying about as many before as after this time. According to this method of measurement a great deal of JP. Ehrlich: "Wertbestimmung des Diphtheriheilserums," Jena, 1897; "Constitution des Diphtheriegiftes," Deutsche med. Wochenschrift, 1898, No. 38; Ehrlich, Kossel, and Wassermann : Deutsche med. Wochenschrift^ 1894. INTRODUCTION the material (namely, the animals killed in shorter or longer times) is left unconsidered. As now the exactness of the measurements increases sensibly with the material, it is of importance to use the whole material. This may be done in the following manner. The observations con- tain many cases, in which doses larger or smaller than the lethal dose have been injected. These observations offer a statistical material of how many days " normal " guinea- pigs live after injection of 1.5, 1.4, 1.3, 1.2, 1.1,0.9, °-8> 0.7, etc., lethal doses. By means of this statistical material the reduction table given below was constructed, by the aid of which all the data regarding the killed guinea-pigs may be taken into consideration.1 DEATH AFTER DAYS INJECTED LETHAL DOSES DEATH AFTER DAYS INJECTED LETHAL DOSES I 1.6 5 0.80 i«S 1.4 6 0.7I 2 1.25 7 0.64 2-5 I-I5 8 0-59 3 1.05 9 0-55 3-3 I.O 10 0.51 3-5 0.97 12 045 4 0.91 H 0.4 In order to increase the statistical material, Madsen proposed to consider the decrease of weight of the animals in determining the lethal dose.2 In this manner an in- dependent determination was given for each series of measurements. 1 Arrhenius and Madsen : " Le poison diphterique," Oversigt danskc Vid- sthkforh., Copenhagen, p. 269 (1904). 2 Arrhenius and Madsen : I.e., p. 274. 14 LECTURES ON IMMUNITY By the aid of all these different measurements it is possible to determine the probable error of every measure- ment. This was omitted in all previous considerations of this question. Under these circumstances an overestima- tion of the exactitude of the measurements resulted, which often led to conclusions without any solid foundation. The lethal dose of the toxin having been determined, the next step was to standardise the solution of antitoxin. For this purpose Ehrlich determined the quantities of the solution in question that were necessary to neutralise a certain number (e.g., 100) of lethal doses of the poison. As experience has taught that the antitoxin is destroyed much more slowly than the toxin, especially if it is con- served with certain precautions, a given preparation of diphtheria-antitoxin is assumed as " standard serum," and the properties of all poisons and antitoxins to be examined are compared with this standard unit. Ehrlich in his measurements used the assumption that injections of the same quantities of free poison have the same effect, independently of the quantities of "neutralized poison " present. The correctness of this assumption has recently been subjected to question, to which we will return later. The diphtheria-poison can be measured as far as we know only by the aid of experiments on living animals. But there are many other poisons which may be studied outside of the living body, as for instance the hasmolysins, the precipitins, and the agglutinins. Experiments "in vitro " have already long been used in physiological researches, e.g. in digestion, to study processes outside of the living body. Ehrlich adopted this method to study INTRODUCTION 15 the agglutinating power of ricin on erythrocytes in the presence of its antibody.1 In this case it is possible to discriminate between different degrees of agglutination and thereby to measure the quantity of free ricin present. This method has been developed chiefly in the Danish serum institute.2 The most fruitful application of these researches "in vitro " has been in the study of the haemolysins.3 The lysin to be investigated is added in different quantities to circa 8 c.c. of a suspension of 2 c.c. erythrocytes in 98 c.c. of physiological salt solution. Before the admixture of lysin, water was added to the lysin-solution until its total quantity became 10 c.c. The best method is to add the suspension in an energetic manner so that a well-mixed fluid immediately results. Otherwise the lysin is con- centrated in some parts and is absorbed by the erythrocytes in the proximity, and other erythrocytes remain nearly intact if the shaking takes place even a few seconds (30 to 60) after the mixing. Therefore the usual result is that the haemolysis is less the longer the time intervening between mixing and shaking. (Variations of 50 per cent frequently occur for this reason.) To develop the haemol- ysis, the test-tubes are placed during a certain time, gener- ally one or two hours, in a water-bath or other thermostat at the desired temperature (in most cases 37° C). The haemolysis increases with time and seems to tend to a limit which is reached the more rapidly the more active 1 Ehrlich : Fortschritte der Medicin, 1897, No- 2- 2 Compare Jorgensen and Madsen : Festskrift, VI, 6, Copenhagen, 1902. 8 Madsen: "Uber Tetanolysin," Zeitschr. f. Hygiene, 32. p. 214 (1899); Arrhenius, Madsen: Festskrift, III, 9, Copenhagen, 1902. !6 LECTURES ON IMMUNITY the poison (at 37° C. it is reached in about 40 minutes with sodium hydrate, in about 100 minutes with ammonia, and not fully in 200 minutes with tetanolysin as the haemolytic agent). After this time the tubes are placed on ice during about twenty-four hours, when the unattacked erythrocytes fall to the bottom, leaving over them a clear haemoglobin- coloured fluid. Generally the intensity of the colour is pro- portional to the quantity of poison added. The strength of the haemolysis and the colour proportional to it is measured by common colorimetric methods. It is supposed that the haemolysis is dependent (under similar external conditions) only on the quantity of free lysin present, and not to a sensible degree on the quantity of bound lysin or antitoxin present in the mixture. By an operation analogous to that described under the measurement of diphtheria-toxin, it is possible when the haemolysis lies between certain limits (below total haemolysis and above a certain observ- able minimum), to use not only a certain strength of colour, but the whole material of research, for the comparison. The experiments "in vitro" may be carried out through quite definite intervals of time and at any fixed temperature (between o° and 1 00° C. ). Further, to the fluid examined, we may add large quantities of any foreign body and, for in- stance, investigate the influence of different salts by using a physiological solution of cane-sugar (about 7.2 per cent) for the suspension. It is evident how much more diversified knowledge we may obtain by these researches " in vitro " than by those on living animals, which are also expensive, and hence can only be carried out in a relatively small number and at the uncommon institutions equipped with well-filled quarters for animals. INTRODUCTION 1 7 The strengths of the agglutinins are measured by the addition of physiological salt solution until the mixture is unable to produce a certain sharply observable agglutina- tion of a given suspension of cells in a given time and at a definite temperature. The dilution of this mixture is a measure of its content of agglutinin as displayed toward the given type of cells.1 Madsen and Jorgensen2 prefer to measure the agglutinins according to their power of clarifying a bacterial suspension. Even for precipitins (e.g. rennet) such a degree of pre- cipitation or coagulation may be found which is rather sharply defined from higher or lower degrees. By inclin- ing the tubes containing the solutions to be investigated we get an impression of the consistency of the contents after treatment during a given time at a definite tem- perature. In a similar way as for the agglutinins it is possible to determine the strength of the precipitating or coagulating preparations. The bacteriolysins have not been examined quantita- tively. Their effects are studied in mixtures of suspensions of bacilli which are injected intraperitoneally into animals (e.g. guinea-pigs) and examined in specimens taken out after a time. The method of observation makes it very difficult to collect a material fit for quantitative treatment. 1 Eisenbergand Volk: Zeitschr.f. Hygiene, 40. 155 (1902). 2 Jorgensen and Madsen : Fcstskrift, I.e. COLLEGE OF DENTISTRY UNIVERSITY OF CALIFORNIA CHAPTER II REVERSIBILITY OF REACTIONS BETWEEN ANTIBODIES As has been stated, many of the substances with which we deal in sero-therapy are rather unstable. This insta- bility is very different in different cases. Sometimes (e.g. for snake-venom) the toxin is more stable than the anti- toxin ; in other cases (e.g. for diphtheria and tetanus poison) the converse holds true. The snake-venom resists, as Calmette showed, an elevation of the temperature to 68° C., which, however, destroys its antitoxin, the antivenin, in aqueous solution. This circumstance was used by Calmette l to separate the poison from the antivenin; after heat- ing a mixture of the two a poisonous solution remained. According to more recent investigations of Martin and Cherry2 this experiment is not successful if the mixture is held at the temperature of the room for more than thirty minutes before the heating is done. As Martin and Cherry intimate, the simplest explanation of this behaviour is that the snake-poison and the anti- venin require a certain time to react with each other. Hence if the mixture is heated to 68° for ten minutes before the reaction has practically reached the end-value, the free antivenin is destroyed and after the heating the mixture contains some free poison. 1 Calmette : Ann. de rinst. Pasteur, 8. 275 (1894); Compt. Rend, de VAc. de Sc. 134, No. 24 (1902). 2 Martin and Cherry : Proc. Roy. Soc., 63. 420 (1898). 18 REACTIONS BETWEEN ANTIBODIES 19 The experiments of Calmette yield therefore no evidence for his conclusion that the binding of snake-venom by antivenin is a reversible process, whereby as soon as the free antivenin is destroyed, its compound with the poison is dissociated with the production of new quantities of poison and antivenin. The same comment may be made regarding the decomposition, by boiling, of the innocuous mixture of a poison generated by the Bacillus pyocyaneus and its antitoxin. After the boiling, the poison, which is stable at that temperature, remains in the solution, while the more unstable antitoxin is destroyed, as Wassermann * has shown. But there are many other cases that demonstrate rever- sible processes between analogous substances against which no such objections can be upheld. One of the most remarkable of these processes is used for the production of the so-called immune bodies. (Ehrlich terms them "amboceptors.") If we inject a suspension of the ery- throcytes of an ox into the vein of a rabbit, this animal after a certain time presents in its blood a hasmolytic substance, which haemolyses the erythrocytes of the blood employed; i.e. erythrocytes of the ox and perhaps of some nearly related species. If we heat blood-serum containing this haemolysin to 55° C. for about thirty minutes, we find that it loses its haemolytic power. It is said to be "inactivated." The hsemolysin is evidently decomposed, but a fraction of it remains intact, as may be shown by adding the normal serum of a guinea-pig. After the addition of this in- 1 Wassermann : Zeitschr. f. Hygiene u. Infedionskrankhtiten, 22. 263 (1896). 20 LECTURES ON IMMUNITY nocuous serum, the inactivated serum has regained its power of haemolysing bovine erythrocytes. (The guinea- pig serum has in reality a slight haemolytic action on foreign erythrocytes, but in the experiment it need be used in such small dosage as to provoke in itself no visible haemolytic action.) Border.,1 who discovered this interesting phenomenon, concluded from his investigations that the agglutinating and haemolytic power, on erythrocytes from a rabbit, of the serum from a guinea-pig which had been treated with five or six injections of erythrocytes (10 c.c. of defibrinated blood) of a rabbit, is due to the presence of two substances, of which the one, the "immune-body," resists an elevation of the temperature for thirty minutes to 55° C., whereas the other, the "alexin" (Ehrlich's "complement"), is destroyed at that temperature, but may be replaced by normal serum from a guinea-pig or even from a rabbit. Bordet expressed the opinion that the " alexin " serves as a sensibilitator, and renders the erythrocytes susceptible to the " immune- body," which they are supposed not to be in their natural state. Ehrlich,2 on the other hand, tried to demonstrate that the haemolysin is a compound of the "immune-body" and the alexin, which compound is partially dissociated. The "immune-body" is stable at higher temperatures, the alexin not. The alexin may be replaced by a similar substance, an alexin contained in many normal sera. As will be seen in the following pages (Chapter VIII), the added alexin is really consumed in the formation of the haemolysin, and 1 Bordet : Amun. de I'Inst. Pasteur, 12. 692 (1898). 2 Ehrlich and Morgenroth: Berl. klin. Wochenschrift, No. I (1899). REACTIONS BETWEEN ANTIBODIES 21 acts therefore not as a sensibilitator, but is chemically bound, as Ehrlich insists. This is certainly true for the alexin and " immune-body" absorbed by the erythrocytes; but the phenomenon of Neisser and Wechsberg indicates that these two substances are combined to a certain degree even outside the erythrocytes (compare Chapter VIII). Here we have evidently before us a reversible chemical process. Similar reversible processes are found for all the different haemolysins which are formed after the in- jection of a suspension of erythrocytes from one animal into the veins of an animal of another species. In a similar manner, according to Ehrlich, behave the bacteriolysins, which are formed analogously to the haemolysins. A similar experiment was made by Madsen, Famulener, and Walbum on innocuous mixtures of the haemolytic agent produced by staphylococcus, called staphylolysin, and its antitoxin. Here the innocuousness of the mixture shows that the haemolysin is really bound, for during the time of the reaction, as long as there is some haemolysin free, it is, on being mixed with a suspension of erythrocytes, rapidly absorbed by these, which thereafter lose their haemoglobin. The staphylolysin behaves in a very peculiar manner. If it is heated to 70° C, it loses a great deal of its haemolytic power, which, curiously enough, returns almost completely after heating for five minutes to 100° C. Its antitoxin is destroyed by such a heating. On heating the innocuous mixture of staphylolysin and its antitoxin for five minutes to 100° C., the mixture gains haemolytic properties. The binding of staphylolysin with its antitoxin is therefore a reversible chemical process. Bordet injected the milk of one animal into another 22 LECTURES ON IMMUNITY animal of another species and found that the serum from this second animal contained a substance, called lacto- serum, which gave a precipitate with the casein of the injected milk. P. T. M tiller,1 who investigated the prop- erties of this lactoserum, found that it entered into a com- pound with the casein of the milk, which compound was precipitated in the presence of calcium-salts. Now the lactoserum is decomposed by heating to a temperature of 70 to 71° for thirty minutes. By heating the precipitate which contained the lactoserum combined with casein, in a solution of NaCl, to 100° C, Miiller succeeded in recov- ering the casein without loss. Evidently the precipitate is a little soluble, and the Dissolved precipitate is partially dissociated into its components. Through the high tem- perature the free lactoserum is destroyed, then new quantities of the precipitate are dissolved, and the process goes on until all the lactoserum is decomposed and the casein dissolved and recovered. There are other methods of destroying one of the com- ponents in an innocuous mixture of a toxin and its anti- body. Different chemical agents may destroy the one of these substances more rapidly than the other. Thus ricin is digested by proteolytic ferment, but to a much smaller extent than its antibody. This behaviour was used by Danysz2 for restoring the poisonous effect of ricin which had been mixed with so much antiricin that the resulting fluid was innocuous. This fluid was mixed with a solution of ferment and left for a sufficient time (e.g. twenty-four 1 P. T. Miiller: Archiv f. Hygiene, 44. 150 (1902). 2 Danysz : " Melanges des toxines avec les antitoxines," Ann. de Vlnst. Pas- teur, 16. 311 (1902). REACTIONS BETWEEN ANTIBODIES 23 hours) and then found to behave like a solution of ricin. In this case the process goes on so slowly that the ricin and antiricin will have had sufficient time to combine before their destruction has reached a noticeable degree. It is possible to separate partially the two neutralised sub- stances by much less vigorous means ; namely, by shaking their solutions with other solvents. Thus, for instance, Mad- sen and Noguchi treated an innocuous mixture of saponin and cholesterin, which unite so rapidly that their velocity of reaction can scarcely be measured, in the following manner. The mixture was evaporated to dryness and thereafter ground to a powder, which was extracted with chloroform or ethyl ether. These fluids possess a great dissolving power for cholesterin. The residue of the powder was dissolved in 0.9 per cent solution of sodium chloride. The solution so prepared displayed the prop- erties of a solution of saponin, especially in regard to its haemolytic activity.1 Another experiment of the same nature was carried on by Madsen and Walbum.2 They prepared a mixture of ricin and antiricin, which, after having been exposed for two hours to 37° C., showed no toxic effect when injected into guinea-pigs. This mixture was shaken for a time at 37° C. with an equal quantity of a 10 per cent suspension of erythrocytes from a rabbit in physiological salt solution, and then centrif ugated. The liquid was then shown to con- tain an excess of antiricin by its attenuation of the aggluti- 1 Madsen and Noguchi : Oversigt Ac. of Sc. of Copenhagen, No. 6, p. 461 (1904). '2 Madsen and Walbum : " De la ricine et de 1'antitoxin," Centralblatt f. Bakteriologie, 36. 253 (1904). 24 LECTURES ON IMMUNITY nating power of ricin on erythrocytes. On the other hand, the centrifugated rabbit-erythrocytes contained an excess of the nerve poison in ricin; for when they were haemolysed by the addition of pure water they gave a poisonous solu- tion, which injected into guinea-pigs produced death. In this case we have two different poisons, — the haemolytic and the nerve poison in the ricin and the corresponding two antibodies in the antiricin. The experiment shows us that both of these poisons are bound to their respective anti- bodies by means of reversible chemical processes. Another experiment of Wassermann and Bruck 1 may be explained in a similar way. They injected an innocuous mixture of the nerve poison tetanospasmin (which together with the haemolytic tetanolysin is produced by the Bacillus tetani in bouillon medium) and its antitoxin into the hind limb of a guinea-pig. This animal showed no symptoms of tetanus. But if the animal had previously received a local injection of adrenalin, it was killed by the injection. As H. Meyer and Ransom have shown, the antitoxin is chiefly absorbed by the vascular system, the tetanospasmin by the nerves. The adrenalin contracts the vessels and thus hinders the absorption of the antitoxin, but it has no effect on the nervous system, so that the tetanospasmin may execute its disastrous effect. Hence the experiment showed that the innocuous mixture contained free toxin, but we are not quite certain in this case that the poison and its antidote had had sufficient time to fully combine. The simplest way to separate toxins from antitoxins in mixtures is by the aid of diffusion. Toxins as well as anti- toxins diffuse in water or in gel, but the toxins generally 1 Wassermann and Bruck: Deutsche med. Wochenschrift, No. 2 (1904). REACTIONS BETWEEN ANTIBODIES 25 much more rapidly than the antitoxins, which are often said not to diffuse. Madsen and I have made an investigation of this phenomenon. In common test-tubes a 5 per cent solution of gelatine was poured to a height of about 10 cm. This solution solidified in a refrigerator. After this a solu- tion of toxin or antitoxin was added to a height of 1.3 cm. above the column of gel, and the test-tube placed on ice (mean temperature 6° C.), where it remained for sometime, (from one to four or more weeks) according to the diffu- sibility of the substance. After this the fluid solution and the different layers of the column of gel were analysed for their content of the different substances. By the aid of these determinations it is possible to calculate the diffusion constant of the substances examined. In this way we found the following constants, valid for 12° C. and expressed in days and centimeters : — Sodium chloride 0.94 Diphtheria-toxin 0.014 Diphtheria-antitoxin .... 0.0015 Tetanolysin 0.037 Antitetanolysin 0.0021 To the theoretical meaning of these figures we shall return later. The very slow diffusion of the other substances as com- pared with that of sodium chloride is evidently connected with their high molecular weight. This is probably of the same order of magnitude as that found by E. W. Reid1 1 E. W. Reid : Journ, of Physiology, 33. 13 (1905). The molecular weight was calculated from the osmotic pressure of a I per cent solution. This pres- sure was found to be 3.85 mm. at 15° C 26 LECTURES ON IMMUNITY for haemoglobin, viz. 48,000. For the antitoxins it may be still some ten or one hundred times higher. As the antitoxins diffuse about ten times more slowly than the toxins, it seems theoretically possible to separate them by diffusion. The first experiment in this direction was done by Martin and Cherry.1 They prepared 60 c.c. of an innocuous mixture of diphtheria- toxin, containing three hundred lethal doses and its antitoxin, and heated it for two hours at 30° C. This mixture was allowed to filter under pressure (50 atm.) through a film of gelatine sup- ported by a Pasteur-Chamberland filter. The filtrate con- tained chiefly water, which passes through the filtrum very much more rapidly than the toxin or the antitoxin. This fil- trate was examined and found to contain per cubic centi- meter less than 3 and 5 per cent respectively of the poison in one cubic centimeter of the original mixture, the poison being supposed to be entirely free. Now water passes more rapidly than sodium chloride through gelatine, and sodium chloride about sixty-seven times more rapidly than diph- theria-toxin. Hence we should expect that even if no poison at all were bound, the first filtrate would contain per cubic centimeter only 1.5 percent of the quantity of poison in the original mixture. Later on as the original mixture by the extraction of water became more concentrated, as seems to have been the case in these experiments, a higher percent- age might have been expected. But the conclusion which has been drawn from them, that but a small part, say 5 per cent, of the toxin was actually free, may not be regarded as warranted by the facts. A similar experiment has been carried out by Craw in 1 Martin and Cherry: Proc. Roy. Soc., 63. 420 (1898). REACTIONS BETWEEN ANTIBODIES 27 the Lister Institute on mixtures of a lysin from the Bacillus megatherium and its antitoxin.1 He found that the poison from innocuous mixtures was concentrated in the gelatin- film, whereas the residue of the fluid exhibited antitoxic properties. He therefore concludes that the binding of this poison to its antibody is due to a " partially " revers- ible process. This proof seems the more conclusive, as Craw evidently worked under theoretical premises which led him to seek for proof against the reversibility of the process. The experiments resulted in the same manner, even if a great excess of antilysin, one to three times the " neutral- ising " quantity, were added. Craw had taken the precau- tion to heat his mixtures for three hours at 37° C. and then to let them stand one hour at 10° C., so that there is every reason to believe that the reaction, which probably is very similar to that of tetanolysin, had practically reached its end. In the filtrate, Craw did not find a trace of the poison when he worked with " neutral " or " over-neu- tralised " solutions. Let us for a moment consider the ideas which led Craw to suppose that the processes of binding between toxin and antitoxin are not reversible. Toxins, and specially antitoxins, are said to be colloids. Craw therefore supposes the so-called solutions of antitoxins and the products of their reactions with toxins to be in reality fine suspensions. For this statement no evidence is adduced, but it seems as if Craw regarded the lack of diffusibility as characteristic of suspensions, and this may be conceded as being correct. But since Craw supposes antitoxins to be non-diffusible, he 1 T. A. Craw : Proc, Roy. Soc.t 76. 179 (1905). 28 LECTURES ON IMMUNITY seems not to have known the results of Madsen's and my investigations on this point; instead he drew untenable conclusions from Brodie's1 experiments, which indicate that diphtheria-antitoxin does not in an appreciable degree pass through a gelatin filter in a very short time. We may therefore leave the theoretical considerations of Craw, which he furthermore himself considered not to be appli- cable to certain of his own experiments. Others say, with Nernst,2 that the laws of van 't Hoff are not applicable to colloids, i.e. to toxins and antitoxins. Nernst has himself shown that diffusion is caused by and is proportional to the osmotic pressure. As now toxins and antitoxins diffuse just as other known substances, we may conclude that they obey van 't Hoff's law of osmotic pres- sure. In Madsen's and my experiments these substances showed themselves to be distributed in the different layers of gel just as these laws demand. And if van 't Hoff's law is found to be valid for the osmotic pressure of these substances, then also the laws of chemical mass-action (Guldberg and Waage's law) must hold good for their reactions. And even if we did not know that these sub- stances behaved in this regard as do other substances, we would be entitled to work with this quite natural hypothe- sis, until it was shown with great accuracy that the hypoth- esis was wrong. Otherwise we would proceed in a manner wholly different from that used in the other disciplines of science. There has been very much discussion of this question 1 T. G. Brodie : Journ. of Pathology and Bacteriology, 97. 460-464 (1896). 3 Nernst : "Uber die Amvendbarkeit der Gesetze des chemischen Gleich- gewichts," Zeitschr.f. EUktrochemie, 10, No. 22 (1904). REACTIONS BETWEEN ANTIBODIES 2Q in recent times. When Madsen and I calculated for the first time the action of tetanolysin and antilysin upon each other under the supposition that this action comprehended a reversible process, we knew also very well that the teta- nolysin was simultaneously subject to another reaction, which destroyed it slowly. But in this circumstance there was no reason for not employing the known laws for re- versible processes. We ascertained for ourselves that the influence of this secondary process may, with the given method of experimentation, be disregarded. Had this not been the case, a correction for the disturbing effect would have been applied. Recently Sachs 1 has shown that an- other reaction than that investigated by Madsen and myself takes place between tetanolysin and its antitoxin, which may to a certain extent interfere with the chief reaction studied by us. The simple relations found by us seem to indicate that in this case also the perturbations caused by the new factor do not exceed a certain value, of such a magnitude that may be neglected in ordinary experiments on the neutralisation of tetanolysin. We shall later on return to this question. The incompleteness of the chemical binding process between toxins and antitoxins has aided in retarding the idea that real chemical compounds are formed in the union of these substances. The only chemical reactions which were familiar to the scientists who studied the neutralisa- tion of toxins were the complete reactions. Behring,2 who was the first in this field, expressed the opinion that 1 H. Sachs: "tiber die Constitution des Tetanolysins," Berl. klin. Wochen- schrift, No. 16 (1904). 2 Behring and Kitasato : Deutsche med. Wochcnschrift, No. 49 (1890). 30 LECTURES ON IMMUNITY toxin is destroyed by antitoxin without a diminution of the quantity of the latter substance. Chemically speaking, the antitoxin acted as a catalysator. This idea was incom- patible with the measurements of Ehrlich on diphtheria- poison, according to which the double quantity of antitoxin neutralises the double quantity of poison. Ehrlich there- fore held the opinion that a real chemical combination takes place. On the other hand, Buchner1 and Roux2 supposed that this action of antitoxin on toxin takes place only in the susceptible animal. According to their opinion the antitoxin really reacts upon the animal, stimulating it in the struggle against the poison. This idea was supported by such experiments as those of Calmette, according to which toxin and antitoxin coexist in their mixtures. Against this type of explanation, Ehrlich carried out his experi- ments on the neutralisation of toxins "in vitro," outside of the living animal, and Martin and Cherry showed that experi- ments similar to Calmette's might be due to an insufficient time of reaction. The experiments "in vitro" have been mul- tiplied in great number and the influence of the time of reaction has been observed in most cases investigated, so that the idea of the chemical combination between toxins and antitoxins has been generally accepted. But their in- complete knowledge of limited chemical reactions caused Ehrlich and other investigators of these phenomena to suppose that the processes observed are always unlimited; and accordingly they were unable to explain all the phenom- ena indicating the existence of chemical equilibria be- tween the substances examined. To explain some of these 1 Buchner: Deutsche med. VVochenschrift, 480(1903). 2 Roux and Vaillard: Ann, de rinst. Pasteur, 8. 724 (1894). REACTIONS BETWEEN ANTIBODIES 31 phenomena, Ehrlich and his school invented the artificial hypothesis that these poisons consist really of a mixture of a great number of different poisonous and innocuous substances, which combine with antitoxin. The most thoroughly examined poison, that of diphtheria, contains, according to Ehrlich, not less than eight such different substances. Nearly every new phenomenon led him and his school to invoke the presence of a new substance. Owing to this circumstance the theory of Ehrlich has to a great degree lost its credibility. The influence of the time of reaction has also not been considered by Ehrlich as much as it should have been. Thus for instance, Madsen and Dreyer1 had shown that a mix- ture of diphtheria-poison and its antitoxin, which is in- nocuous on subcutaneous injection into guinea-pigs, kills rabbits on intravenous injection- This phenomenon was explained by Ehrlich2 as due to the presence in the diph- theria-poison of a substance which could kill rabbits but not guinea-pigs. The recent investigations of Morgenroth3 show that the whole difference is due to the different modes of injection. A mixture which is innocuous to guinea-pigs when injected subcutaneously may kill them when injected intracardially, i.e. directly into the blood. The reaction between diphtheria-toxin and its antitoxin is not completed in less than a quarter of an hour, as Ehrlich supposed from his subcutaneous injections into guinea-pigs; according to Morgenroth 's experiments, this reaction requires several hours at 20° C. to reach the equilibrium. The experi- 1 Dreyer and Madsen: Zeitschr. f. Hygiene, 37. 250 (1901). 2 Ehrlich: Berl. klin. Wochenschrift, Nos. 35-37 (1903). 8 Morgenroth: Zeitschr. f. Hygiene, 48. 177 (1904). 32 LECTURES ON IMMUNITY ments that gave different results for rabbits and guinea- pigs were carried out with nearly fresh mixtures of poison and antibody. If such a mixture be injected subcutaneously, it diffuses into the blood very slowly during several hours, and in the meantime the antitoxin binds the toxin. It is not necessary, with Morgenroth, to introduce a new hypoth- esis; namely, that the tissues of the guinea-pig contain some catalytic agent reacting on the poison. The relatively high temperature (37° C.) of the animal explains the rela- tively great velocity of the reaction. If, on the other hand, the mixture is injected into the veins, the poison is bound by the tissues of the animal before it has time to react with the antitoxin. There are some other processes common in sero-therapy which are distinguished by a very high velocity of reaction. Thus, for instance, the agglutinins react with bacteria in less than five minutes even at o° C., according to the experi- ments of Eisenberg and Volk.1 (Shorter times of reac- tion were not examined.) Here again we observe a reversible process, since the agglutinin absorbed by the bacteria (or erythrocytes) may be washed out from them with the aid of a physiological salt-solution, as Landsteiner and Eisenberg and Volk showed. It had been supposed by Bordet that this reaction was of the same nature as the adsorption of a dye by a fibre. But the adsorption phe- nomenon is one of slow velocity ; the dyeing of fibres requires some thirty minutes at ioo°C. and demands more than two days at common room's temperature (i7°C). Therefore this theory of Bordet is quite improbable. I have come to the conclusion that the process in question is an absorp- 1 Eisenberg and Volk: Ztschr. f. Hygiene, 40. 155 (1902). REACTIONS BETWEEN ANTIBODIES 33 tion process. If we picture to ourselves bacteria (or other cells) of 5 to 10 /* diameter, shaken with the solution of a substance which enters easily into the cells, we find that even if the diffusion-constant of the substance be so small as o.ooi, as for the least diffusible antitoxins, the process of diffusion may reach its equilibrium in as short a time as less than five minutes. We are led to similar results regarding the velocity of reaction by some experiments of Madsen and Walbum. They added cautiously a little quantity of a solution of tetanolysin to 10 c.c. of a suspension of erythrocytes in a test-tube, so that the solution remained in the uppermost layers of the emulsion, and shook the test-tube after the lapse of thirty seconds. In another experiment they added the suspension precipitously to the poisonous solution, so that the mixing took place immediately. The haemolysis in the second experiment was nearly double that in the first. This is explained by the fact that the tetanolysin has a very much higher solubility in the erythrocytes than in the surrounding medium. During the short time of thirty seconds the uppermost erythrocytes had absorbed about 30 per cent of the poison, so that only about 70 per cent was left for absorption by the larger fraction of the erythrocytes. In consequence of the great absorption-coefficient of the erythrocytes these retain nearly the quantity of poison which they possessed at the moment of shaking, and the final haemolysis was about as marked as if only 70 per cent of the quantity of the poison used had been added in the first experiment, supposing that it had been distributed uniformly in the fluid. Other substances which are ab- sorbed by erythrocytes or other cells seem to behave in 34 LECTURES ON IMMUNITY the same manner. In this category belong the immune- bodies as well as their compound with alexins, which, as will be seen later on, in their absorption behave nearly in the same manner as agglutinins. Bordet J showed that a given quantity of erythrocytes added to a certain quantity of blood-haemolysin gave a greater haemolysis if added simultaneously, than if it was added in two portions, the one after the other. That even in this case the process is a reversible one, is shown by an experiment of Morgenroth.2 He added erythrocytes, which had absorbed immune-body, to other unprepared erythrocytes and mixed the suspension of these with alexin. Not only the originally prepared erythrocytes, but also the others, became haemolysed, which shows that a part of the immune-body had left the prepared erythro- cytes and diffused through the surrounding liquid to the unprepared ones. This experiment would not succeed if a sufficient time (about one hour) was not allotted to the diffusion process before the alexin was added. Similar experiments with analogous results were performed by Joos3 with typhoid-bacilli and their agglutinin. Quite recently Morgenroth4 has done some experiments with cobralysin which indicate in a very conclusive man- ner that this poison is not destroyed but only bound by its antitoxin. He added so much antitoxin to the cobra- poison, that its action was wholly neutralised and a little over. After seven days he added to 5 c.c. of the mixture 1 Bordet : Ann de VInst. Pasteur, 14. No. 5 (1900). 2 Morgenroth: Munch med. Wochenschrift^Q, 2 (1903). 8 Joos: Zeitschr. f. Hygiene, 40. 203 (1902); compare Eisenberg: Cen- tralbl.f. Bakteriologie, 34. 261, 268 (1903). 4 Morgenroth: BerL klin. Wochenschrift, No. 50 (1905). REACTIONS BETWEEN ANTIBODIES 35 0.25 c.c. of normal hydrochloric acid, which caused the binding between the toxin and antitoxin to be dissolved. This was proved by the acid mixture being heated to ioo°C. for thirty minutes, whereby the antitoxin was de- stroyed, whereas the poison itself was not sensibly weak- ened. This could be shown by neutralising the solution after it had cooled down to the room's temperature. The toxicity of the solution was nearly the same as that of the original solution without antitoxin. In this case the peculiarity occurs, as Sachs has first shown, that the pres- ence of acid protects the poison from being destroyed by heat. Morgenroth criticises a theory sketched by Nernst1 and developed by Biltz, Much, and Siebert,2 according to which the toxins are "adsorbed "to the "colloidal" anti-toxins and thereafter destroyed. Morgenroth says rightly that this theory, "which as yet is void of any experimental basis," is completely disproved by his experiments. As will be shown later on, the velocity of reaction of the different toxins changes with temperature according to a law which was deduced from therm odynamical considera- tions, involving the validity of van't Hoff's law for solu- tions. The applicability of this law to the velocities of reaction of toxins may therefore be regarded as a new proof that the general laws bearing on the behaviour of common matter are valid even for the processes going on between the substances studied in the phenomenon of immunity. No single proof has been adduced against the 1 Nernst : Zeitschr.f. Elektrochemie, B. 10, No. 22 (1904). 2 Biltz, Much, and Siebert : Behrings Beitrage (1905). 36 LECTURES ON IMMUNITY validity of these laws, and it seems to me very unphilo- sophical a priori to suppose that other laws should regulate the reaction of toxins and antitoxins, than those which govern the reactions of other substances. CHAPTER III VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS WE have already considered the velocity of the reaction of the most simple kind ; namely, the spontaneous destruc- tion of different antibodies in the veins of animals. If, as seems to be the general case in chemistry, every molecule of a substance is decomposed independently of all other molecules, then the number of molecules decomposed dur- ing a short interval of time is simply proportional to the number of molecules present at this time. If this number at a certain time, which may be regarded as the beginning- time of the process, is called A, and the number of decom- posed molecules at a given time t is called x, then -— - is at the rate of decrease of the active molecules, and we get the well-known equations where t^ corresponds to x^ and /0 to x§. Many such cases are known in chemistry ; for example, the decomposition of hydrogen arsenide (As H3). They are called monomolec- ular reactions. Monochloracetic acid reacts with water, giving glycolic and hydrochloric acid, a so-called bimolec- 37 38 LECTURES ON IMMUNITY ular reaction. If now the initial concentration of the second group of reacting molecules is termed B, we get which, if B is very large compared with x and with A, gives the same solution as the differential equation for the mono- molecular reaction, K^ — KB. In many cases, for instance in the inversion of cane sugar, the one reacting molecule (the hydrogen ion) is reformed by a secondary process so rapidly that its con- centration may be regarded as independent of the progress of the reaction. In this case, belonging to the so-called catalytic processes, we may also apply the formula for the monomolecular reaction, putting K proportional to the concentration of the unchanged molecules (here the //"-ions). If A = B, the differential equation of the bimolecular reaction gives the solution : i i As a special case may be regarded that in which two mole- cules of the same kind react with each other. If n molecules all at the same concentration react with each other (the so-called ;/-molecular reaction), we find which gives the solution : n-l \n-l VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 39 This equation was adopted by Madsen for the spontane- ous decomposition of antibodies, n is in this case no whole number, and the equation may be regarded as a purely empirical rule. Very regular results corresponding to monomolecular reactions were found at an investigation made by Madsen and Famulener. They studied the attenuation of vibrio- lysin at 48° C. The haemolytic power (/) of a solu- tion of vibriolysin, held in a thermostat, was examined at different times (/). The power is inversely proportional to the quantity of the solution which is necessary to pro- duce a certain effect; e.g. the haemolysis of 10 per cent of a 2.5 per cent suspension of erythrocytes within an hour at 37° C. The action evidently follows the law of the mono- molecular reactions, according to the equation : by the aid of which the calculated values /caic., which are to be compared with the observed ones /Obs.> are deduced. The temperature was 46.4° C. .£"=0.0079. / (min.) 4>bs. Ajalc. O 1 00.0 IOO.O IO 78.3 83.2 2O 67.6 69.5 30 59-3 57-9 40 49-8 48.3 50 40.8 40.4 60 344 33-6 70 25.1 28.1 80 23.0 23-3 4o LECTURES ON IMMUNITY The agreement between the observed and calculated values is very satisfactory, so that there is no doubt that the law represented by the differential equation deduced above is really fulfilled. The influence of temperature on the spontaneous de- struction of vibriolysin is very great, as is shown by the following table, taken from a still unpublished work of Madsen and Famulener : — RATE (A*) OF DESTRUCTION OF VIBRIOLYSIN AT DIFFERENT TEMPERATURES TEMP. VELOCITY OF REACTION TEMP. VELOCITY OBS. REACTION CALC. OBS. CALC. 49-975 49-75 0.0778 0.066 0.074I' 0.066 46.4 45-97 0.0079 0.0063 0.0081 0.0062 49 48.15 47-35 0.039 0.023 0.0134 0.041 0.024 0.0128 45-H5 0.0057 0.0036 0.005 l 0.0036 The calculated values are found with help of the formula which has been found to agree with the experiments in reaction velocity in other branches of physical chemistry. ft is 128,000, or about five times as great as for the inversion of cane sugar (2 5, 600). The velocity of reaction increases in the proportion of 10 to i in an interval of 3.8 de- grees. In a similar manner behaves tetanolysin, as is seen from the following table, borrowed from an investigation of Madsen and Famulener: — VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 41 DECOMPOSITION OF TETANOLYSIN AT 53.5° #"!= 0.079 AT 49.8° K0 = 0.0047 t (min.) A>bs. /calc. t (min.) A>bs. /calc. 0 1 00.0 IOO.O 0 IOO.O IOO.O 2 70.9 69.5 20 80.0 80.6 4 43-5 48.6 40 61.1 64.8 6 27.1 33-6 60 52.1 52.3 8 20.4 23-3 80 46.3 42.1 10 14.9 16.2 120 26.8 26.7 12 11.4 II. 2 180 14.6 14.3 Here the influence of temperature is still greater than in the decomposition of vibrio ly sin ; /iis about 162,000. The velocity of reaction corresponds also in this case to that of a monomolecular reaction. DECOMPOSITION OF VIBRIOLYSIN IN THE PRESENCE OF 0.005 N- SODIUM HYDRATE AT 48° ^=0.0313 AT 46.5° A"= 0.012 / (min.) ?obs. ?calc. t (min.) ?obs. ?calc. O.O IOO.O IOO.O O IOO.O IOO.O 2-5 83.0 82.6 15 51-7 48.6 5-o 69.4 69.8 30 32.2 32.2 7-5 60. 1 584 45 21.2 21.2 1 0.0 50.0 48.8 60 I4.I I4.I 12.5 36.5 40.3 75 8.6 9-3 150 32.2 34.2 90 6.2 6.1 17-5 28.2 28.5 i°5 4-4 4.1 The decomposition of lysins, and generally speaking of the substances dealt with in sero-therapy, is increased to 42 LECTURES ON IMMUNITY a very high degree if acids or bases are added to their solutions. Madsen and Famulener have, for instance, investigated the rate of decomposition of a solution of vibriolysin, which contained so little sodium hydrate that it was 0.005 n. in alkalinity. They found the above figures : — The constants of the reaction of this monomolecular process are found to be 0.0313 at 48° and 0.012 at 46.5° C. This gives a value of /x = 128,000, or just the same value as that noted for vibriolysin without the addition of alkali. This correspondence may perhaps not be of so great an interest as it seems at first, since the solution of vibriolysin is in itself a little alkaline. . But it is not probable that its alkalinity is due to sodium hydrate, but chiefly to weaker organic bases, and therefore the coincidence of n in the two different cases is still remarkable. Other substances also exert an influence upon the de- struction of vibriolysin and tetanolysin, although to a much less degree than solutions of the alkalies. Of these, am- monia has a less influence than sodium hydrate, but the dif- ference is by far not so accentuated that it would be possible to invoke the action of the OH ions. Thus, for instance, the reaction-constant of vibriolysin, which at 46.2° reaches the value 0.0066 (per min.) is increased to 0.081 if 3.4 c.c. of I n. NaOH are present in 100 c.c. of the liquid, and to about 0.075 in the presence of the equivalent quantity of ammonia. An addition of hydrochloric acid gave different results according to its quantity. The first addition di- minished the constant of reaction, which reached a mini- mum 0.00052 in the presence of 4.25 c.c. i n. HC1 in 100 c.c. of the liquid. With larger amounts the reaction-constant VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 43 increased again, and reached the value of 0.022 if 6 c.c., and of 0.109 if 6.75 c.c. of i n. HC1 was present in 100 c.c. of the liquid. These circumstances seem to indicate that some alkali present in the original culture was neutralised by the first addition of the hydrochloric acid, which there- after exerted its destructive action. The slight difference between the action of sodium hydrate and ammonia leads to the conclusion that the bases act by setting some alkaline substance in the bacterial culture free. The in- feriority of the ammonia might be explained by its fee- bleness, which allows an equilibrium with the base from the culture to be reached before all the base has been set free. Even the presence of weak acids, e.g. of acetic acid, accelerates the destruction of the vibriolysin. Thus 9 c.c. of i n. CH3 COOH in 100 c.c. of culture gives a reaction- constant 0.064, its action corresponding to that of 6.5 c.c. i n. HC1. The weak acid exerts much less influence than a strong one, which was to be expected, the neutralised base being of less strength than ammonia, so that a noticeable hydrolytic action must occur. The reaction-constant is, considering the great errors of observation, practically proportional to the amount of base added (if the alkalinity exceeds o.oi n.); but for the action of the acids no such regularity is found, even if we calculate from the neutralisation point, which ought to nearly coincide with the point of minimal con- stant of reaction. The content of alkali in the natural solution of vibriolysin explains another fact found by Madsen ; namely, that the constant of reaction depends on the initial concentration 44 LECTURES ON IMMUNITY and is nearly proportional to it. In reality the bouillon in which the vibrions grow is slightly alkaline. Madsen found at 47.8° C. that the original solution of vibriolysin gave K \ =0.0198. The same solution, diluted to the con- centrations 0.5 or 0.25, gave -/T2 = 0.0072 and ./T4= 0.0039 respectively. These three figures are nearly in the pro- portion 4:2:1, or as the corresponding concentrations, which is easily understood if the alkali present exerts a catalytic influence. Much more complicated is the influence which the addi- tion of acids or of bases exerts upon the attenuation of tetanolysin, which is also in itself alkaline. The velocity of reaction K increases with the amount of alkali added, but decreases at first if acid is added until it reaches a very flat minimum, after which it increases again on further addition of acid. This is evident by an inspection of the following figures (valid at 49.83° C.) : — 98 c.c. of tetanolysin solution -f 2c.c. I n. NaOH ^=0.0112 99 c.c. of tetanolysin solution + I c.c. I n. NaOH 0.0097 99.5 c.c. of tetanolysin solution + 0.5 c.c. I n. NaOH 0.0085 100 c.c. of tetanolysin solution 0.0047 99 c.c. of tetanolysin solution + I c.c. I n. ^SO* 0.0071 98 c.c. of tetanolysin solution + 2 c.c. I n. H2SO* 0.0435 This seems to indicate that the acid first added is bound by some weak base in the bouillon ; and that the first trace of alkali added is also bound, probably in setting some weak alkali free in the bouillon. The figures for the reaction velocity in the presence of 2 c.c. i n. H2SO4 in looc.c. are as follows, and indicate a monomolecular process: — VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 45 TIME (min.) STRENGTH (obs.) STRENGTH (calc.) O 100. 0 97-5 5 10 57-3 37-7 59-2 36.0 15 20. o 21.7 20 14.0 13-2 With regard to the decomposition of tetanolysin in the presence of acids or bases, some experiments executed by myself gave the following results : — On addition of equimolecular quantities of hydrochloric, oxalic, citric, and tartaric acid (about 0.003 m°l- normal), the velocity of reaction was increased so much that the decomposition of a i per cent solution of tetanolysin was three-fourths accomplished in ten minutes. Of sulphuric acid half this quantity was sufficient for the same purpose, and for acetic acid a quantity seventy-five times as great. The said concentrations all contain nearly the same quan- tity of hydrogen ions, and it seems, therefore, probable that this catalytic action is caused by the hydrogen ions. Sodium hydroxide acts nearly as strongly as a strong acid of the same molecular concentration ; but an ammonia so- lution of the same concentration had a very little influence. It was necessary to use it in about thirty times as high a concentration as sodium hydrate to obtain the same effect. Both these solutions have also nearly the same concentra- tion of hydroxyl ions. With the aid of these experiences, it is very easy to in- terpret a phenomenon observed by Ritchie.1 He mixed a -solution of tetanolysin with a small quantity of hydrochloric * Ritchie: Jaurn. of Hygiene, 1. 130 ( 46 LECTURES ON IMMUNITY acid at ordinary room temperature. After a certain time he injected this mixture subcutaneously into a guinea- pig. The animal was not killed by the poison; but if before the injection the hydrochloric acid was neutralised by sodium hydrate, the animal was killed. Ritchie inferred that the tetanolysin had been destroyed by the hydro- chloric acid, and was restored by the addition of the base. The simple explanation is the following: The quantity of acid added was not sufficient to cause a rapid destruction of the tetanolysin at the low temperature of the room. But after the subcutaneous injection the temperature of the mixture rose rapidly to about 37° C, and therefore corre- spondingly the destruction of the tetanolysin went on with great speed — according to the figures given above about 200,000 times more rapidly than at 20° C. — before it had time to diffuse into the body of the animal. Therefore the poison was nearly instantaneously destroyed, and had no sensible action on the animal. But if before the injec- tion of the mixture the acid was neutralised (at room temperature) by the addition of an equivalent quantity of sodium hydrate, then the poison was not destroyed after its injection, and could therefore exert its fatal influence. It is not at all necessary to assume such a wonderful pro- cess as a restoration of the destroyed toxin-molecules by the addition of the base. For antitoxins, very few investigations have been car- ried through regarding their destruction in time. Madsen found for antiricin (serum of an injected goat) that its strength fell at room temperature to 40 per cent in forty- seven days and to 19.6 per cent in eighty-nine days, which corresponds rather closely to a monomolecular process ; VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 47 that is, the rate of decrease of strength of the solution was proportional to the strength itself. The greatest increase in the velocity of a reaction with increase in temperature that has ever been found is that of the decomposition of haemolysin contained in normal goat's serum, which dissolves erythrocytes from the rabbit. Madsen and Famulener give for this reaction the follow- ing figures: — DECOMPOSITION OF A HAEMOLYSIN AT 53° AND 5i°C. (MADSEN AND FAMU- LENER) / (min.) ^obs. *calc. t (rain.) ?obs. *calc. 0.0 100.0 100.0 o IOO.O IOO.O 2-5 58.3 58.2 5 74-3 73.4 5-o 44-3 33-4 10 58.3 62.5 7-5 17.9 19-3 15 48.8 53.3 20 44.9 45-4 25 40.0 38.7 30 33-7 33-° 35 28.4 28.1 40 25.2 24.0 fji was for this monomolecular reaction found to be 198,500; with the aid of this figure the following table is calculated : — INFLUENCE OF THE TEMPERATURE ON THE DECOMPOSITION OF A H^MOLYSIN TEMP. VELOCITY OF REACTION TEMP. VELOCITY OF REACTION OBS. CALC. OBS. CALC. 53-o 52.5 52.0 0.095 O.o6o 0.038 0.095 O.O6O 0.038 Sl-S 5I.O 0.025 0.0139 0.024 0.0145 Here we evidently observe two concomitant processes. Probably the process which corresponds to the observed 48 LECTURES ON IMMUNITY figures, is that of the decomposition of haemolysin into immune-body and alexin, and the alexin is destroyed still more rapidly. But the reverse may also be true. The figures indicate that at 60° C. a heating for o.i minute will practically decompose the haemolysin totally and give a solution of immune-body free from alexin. The first reaction of enzymes — namely, the influence of emulsin on salicin, studied by Tammann according to methods used in physical chemistry — seems to be of a complicated nature. The process seems to be monomolec- ular at low temperatures, as is shown by the following figures, indicating the strength (concentration) of a solu- tion containing in the beginning 3.007 g. salicin and 0.08 g. emulsin in 100 c.c. DESTRUCTION OF SALICIN BY EMULSIN AT 25° C. TIME (hours) STRENGTH (obs.) STRENGTH (calc.) 0 too 100 I 87 88 3 68 67 5 42 52 8 35 35 12 24 21 26 9 3 ^=0.057. The last figures seem to indicate that the process is re- tarded at its end. This is still more conspicuous at higher temperatures. Therefore we should not overestimate the accuracy of p calculated from Tammann's figures and giving fi = 3330,1 corresponding to an increase in the proportion of only 1.2 : i in an interval of 10° C. 1 Tammann, Zeitschr. f. ph.. Ch. 18. 436 (1895), gives /* = 2 ^ = 5870, which is evidently due to some misprint or other error. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 49 Tammann investigated also the slow destruction of emul- sin in 0.5 per cent solution and in the form of dry powder. Even in this case the reaction was monomolecular. The content of emulsin in the solution or in the powder at different times was determined by estimating its decom- posing influence on salicin. He found for the solution (between 60° and 75°) /* = 45,000, corresponding to an in- DESTRUCTION OF A 0.5 PER CENT EMULSIN TEMP. ^oba. •K"calc. 40 0.04 O.OII 50 0.18 0.099 60 0.80 0.800 65 2.86 2.180 70 5-90 5.740 75 14.70 14.700 /x = 45,000 crease in the proportion 7:1 in an interval of 10 degrees. For the solid powder /x was only 26,300; that is, 60 per cent of that for the solution (the determination is rather uncertain). Furthermore, the decomposition of the powder at 80.5° C. proceeds about 500 times more slowly than that of the 0.5 per cent solution. As will be seen in the following, rennet behaves in a similar manner, and it seems to be a very common observation that the sub- stances with which we are dealing are much more resist- ing to heat in dried form than in solution. This reminds LECTURES ON IMMUNITY us in a certain sense of the great resistance of dried spores to high temperatures as compared with the pro- nounced destructive influence of higher temperatures on developed bacilli in fluid media. Dr. Euler has collected the experimental data l bearing upon the catalytic action of ferments. In most cases we find that the influence of the time of reaction may be represented as a monomolecular process. Thus, for instance, he finds for the decomposition of hydrogen peroxide (H2O2) by solutions containing 3.4 or 5 c.c. of the juice of the Boletus s caber to the 200 c.c. the following values at 15° C.2 q is the quantity of H2O2, determined by titration with o.oi n. KMn O4 ; n is the concentration of the " catalase," / time in minutes. *=3 «=4 n=s t q K / q K t q K o 8.0 o 8.0 __ O 8.2 . 6 6.9 0.0107 8 6.2 0.0138 2 7-5 0.0193 12 5.8 o.oi 1 6 10 5.6 0.0154 7 6.0 0.0193 19 5-0 0.0107 13 5-i 0.0150 16 4.0 0.0195 55 2-5 O.OIOO 19 4.2 0.0147 22 3.15 0.0190 0.0107 0.0147 0.0193 The constant of reaction K, calculated for a monomo- lecular reaction, increases with the concentration slightly more than proportionally. In the same manner, accord- ing to the investigations of Bredig and M tiller von Berneck, 1 Euler: "Katalyse durch Fermente," Zeitschr. f. ph. Ch. 45. 420 (1905). 2 Euler : " Zur Kenntnis der Katalasen," Beitrage zur chemischen Physi- ologie, 7. h. 1-3 (1905). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 51 behaves the catalytic action of a colloidal solution of plati- num on hydrogen peroxide. In an analogous manner, according to Euler's measure- ments, the catalase extracted from lard saponifies a con- centrated solution of ethyl-butyrate (at 35°C). q is the quantity of butyric acid set free after t minutes, as deter- mined by titration with barium hydrate. t q ?« -q K 0 0.0 2.70 2 0.30 2.40 0.0256 6 0-75 '•95 0.0235 9 1.05 1.65 0.0237 16 1.65 1.05 0.0250 00 2.70 —~ -~ The reaction is clearly monomolecular, as is indicated by the constancy of K. A more complicated formula was found empirically by Henri 1 to be valid for the inversion of cane sugar by means of invertin extracted from yeast cells. Henri's formula is the following : — a — x It differs from the formula for monomolecular reactions by the expression (a -f- x} instead of simply a in the nom- inator after log. As example I quote the reaction of 4c.c. solution of diastase with 0.5 n. sugar at 25° C. '- is the inverted sugar proportional to the initial quantity of cane sugar. 1 V. Henri: Zeitschr. f. ph. Ch. 39. 194 (1901). LECTURES ON IMMUNITY t (rain.) X a i a i a + x /'"6 a- x t * &rt — X 75 0.037 0.000218 0.00022 186 0.103 254 24 499 0.228 28l 25 505 0.292 297 26 557 0.322 303 26 II2O 0.589 345 26 1172 0.6 1 1 350 26 Whereas K increases regularly with time in the propor- tion I : 1.6, KI is nearly constant. The quantity trans- formed in a certain time is proportional to the quantity of diastase present, but no.t to the concentration of the cane sugar in the solution. In a rather large interval (o. 1 5-0.6 n.), the transformed quantity is independent of the concentration of cane sugar, as Duclaux maintained, but at low and high concentrations we get lower values than at mean concentrations. At very low concentra- tions the transformed quantity is proportional to the concentration of cane sugar.1 In some other cases also the formula of Henri has been verified. Still it seems probable that in dilute solutions of sugar the reaction is of the pure monomolecular type. Only at higher concentrations do deviations occur. Bar- endrecht2 has suggested a very singular theory, according to which the deviations might be due to an absorption by the molecules of the sugar of a kind of radiation emanat- ing from the enzyme, which emanation is said to produce 1 Adrian Brown : " Enzyme Action," Journ. Chem. Soc. 81. 387 (1902). 2 Barendrecht : Zeitscr. /. ph. Ch. 49. 456 (1904). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 53 the inversion. This is not the place to enter upon a discus- sion of this peculiar view. Regarding the influence of temperature on the action of invertase on cane sugar we possess some old observations of Kjeldahl.1 They give an optimum at about 52.5° and fji= 9080. They are reproduced in the table: — Temp. o 18 30 40 45 48 50 52.5 55 60 65 70° C. Vel. obs. 17 60 113 179 228 250 260 267 260 179 21 o Vel. calc. 21 (60) 112 181 (228) 261 285 318 353 436 534 651 In a recent memoir2 Henri analyses the hydrolysis of maltose by means of maltase. In this case the reaction- product is glucose, and the constant of reaction increases with the progress of the reaction. Henri's formula 1C = -log— - gives a very nearly constant value for K. t d X This constant decreases as the quantity of maltose in- creases. For the first three hours it is, for instance, for solutions of the following concentration, 2 per cent sol. K= 368 • icr5, 4 per cent sol. K— 164 • io~5, 6 per cent sol. K= 1 06 • icr5. It is nearly inversely proportional to the quantity of maltose present. It would therefore be reason- able to put — where K^ is a new constant, and (a — x) the concentration of the maltose. But as the maltose as well as the glucose has a retarding influence on the process, it would be more rational to put — 1 Kjeldahl: cited from Duclaux, Traite de microbiologie, 2. 177 (1899). 2 Victor Henri: " Recherches physico-chimiques sur les diastases," Archive di Fisiologia, 2. i (Nov. 1904). 54 LECTURES ON IMMUNITY (a— x) + nx dt (a—x)+nx' which, integrated, gives the formula of Bodenstein ; In this case we find a sufficient agreement with the experi- mental results, if we suppose n — ^, as Henri has shown. For invertase acting on saccharose n — 0.5, and for emulsin acting on salicin n — 2. Of course the introduction of a new constant n is favourable to the agreement between the calculation and the observation. Still Henri finds that the agreement for the maltose is not very satisfying (K^ varies between 0.028 and 0.046). - Henri therefore proposes to introduce still a new em- pirical constant in the equation for K^. But it is to be feared that the calculation will not repay the work laid out upon it as long as the experiments are so contradic- tory as now. For instance, I have calculated some obser- vations of Mr. Terroine cited by Henri (I.e. p. 6) according to his formula and found K very nearly constant = 564- io~5, as will be seen from the following figures for a 2 per cent solution of maltose: — t (min. ) *% v- i ,ioo-fjr A = - / — t 100— X V J » I0° / IOO— X 62 0-373 549. io-6 327.IO-6 90 0-5I5 550 349 120 0.656 569 389 150 0.772 593 428 I76 0.832 589 440 210 0.860 535 407 240 0.914 561 444 362 0.965 (483) 402 VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 55 According to the figures of Terroine K does not change more than 10 per cent (the last value, as there are only 3.5 per cent of the matose left, is too unreliable to be used for the calculation). But in the same memoir, on p. 4, Henri gives values for a 2 per cent solution of maltose for which the values of K change between 3i9-io~5 and 489 • io~5 i.e. 53 per cent. The errors of observation must therefore be very great, and the figures should not be ap- plied to delicate calculations. Still greater is the disagree- ment in the figures of Armstrong,1 who finds that the con- MALTOSE 5 % AT 30° (E. F. ARMSTRONG) t (hours) *% V I , 100 Al— .* / 100 — x I 7-3 0.0329 2 13-9 0.0325 4 24.4 0.0304 7.25 3i-7 0.0229 23 35-2 0.0082 stant Kly calculated from the formula for monomolecular reactions, sinks with the progress of the reaction; whereas Henri finds that K, calculated from his formula, is nearly constant; i.e. that K± as is seen in the figures given above, increases very rapidly with the progress of the reaction, and this is valid not only for 2 per cent, but in a still higher de- gree for 4 per cent and 6 per cent solutions.2 Armstrong has communicated additional measurements 1 E. F. Armstrong: Proc. Roy. Soc. 73. 508 (1904). 2 Brown and Glendinning (Journ. Chem. Soc. 81. 388, 1902) find that the formula of Henri's is valid even for the hydrolysis of soluble starch by means of diastase. LECTURES ON IMMUNITY on the inversion of milk sugar by means of lactase or emulsin, which follow a wholly different law from that used in Henri 's formula. The regularity is evident only if the enzyme is present in great quantity. We reproduce only the first two tables (I and VII) illustrating the hydrolytic action of 100 c.c. of lactase-extract or 0.2 g. of emulsin on 2 g. of milk sugar at 36° C. ACTION OF LACTASE ON M:LK SUGAR ACTION OF EMULSIN ON MILK SUGAR / (hours) *% X ^7 t (hours) *% X ^7 I 22.1 22.1 °-5 3-2 4-5 2 31.2 22.O I 4-8 4-8 3 38.9 22.5 2 6.4 4-5 4 45-8 22.9 3 7.6 4-4 5 Sl-5 23.0 4-5 9.0 4.2 6 56.6 23.1 6 1 0.0 4.1 10 69.0 21.8 23 19.7 4.1 17 84.2 20.4 29 22.O 4.1 23 92.4 19.3 48 29.0 4-2 29 95-3 17.7 53 30-7 4.2 38 98.0 15-9 144 62.2 5-2 264 77-5 2.9 Here the quantity transformed is very nearly propor- tional to the square root of the time of action. This cor- responds to the differential equation d* ' dt x x (a—x) or, in other words, the reaction-constant calculated with the common formula for a monomolecular reaction should be inversely proportional to the product of the rest of the milk sugar and of the reaction-products. This will happen, VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 57 provided that the reaction-products are present in sufficient quantity, and that one molecule of the milk sugar and one molecule of the reaction-products unite with one molecule of the enzyme to form a partially dissociable compound. It has been long known that the enzymes differ from chemical catalysors in one very important point. This experiment was done in 1883 by Duclaux,1 with solutions containing 10, 20, and 40 resp. g. of sugar. In 100 c.c. dissolve 20 mg. of invertase and elevate the temperature to 37° C. ; then after four hours we shall find that nearly the same quantity of sugar (about 5 g.) will be hydrolysed in the three cases ; whereas if we had added 20 mg. of an acid, the inverted quantity would have been 2.5 and 5 g. in the two first cases, if it was 10 g. in the last. Arm- strong2 gives some good instances of this regularity, which holds only if the quantity of enzyme is small. The tabulated quantity is the number of grammes of hydrolysed milk sugar in 100 c.c. SOLUTION CONTAINING % MILK SUGAR GRAMMES MILK SUGAR, HYDROLYSED BY A SMALL QUANTITY OF LACTASE IN GRAMMES MILK SUGAR, HYDROLYSED BY A SMALL QUANTITY OF EMULSIN IN 24 h. 46 h. 144 h. 23 h. 48 h. 10 1.42 2.22 3.34 1.97 2.98 20 I.4I 2.18 3.38 2.12 3-06 40 1.44 2.21 3-30 2.10 3.06 On the other hand, if there is present a great quantity of enzyme and a relatively small quantity of sugar, the action is proportional to this latter quantity, just as if an acid acted. 1 Duclaux: Traite de microbiologie, 2. 136 (1899). 2 Armstrong: /. c.t pp. 508-510. 58 LECTURES ON IMMUNITY ACTION OF INVERTASE ON 100 c.c. OF SUGAR SOLUTION (BROWN) l PER CENT SACCHAROSE GRAMMES INVERTED IN i H. 0.25 °-5 i.o 0.060 0.129 0.249 ACTION OF LACTASE ON 100 c.c. OF MILK SUGAR SOLUTION (ARMSTRONG) PER CENT MILK SUGAR AMOUNT CHANGED IN 3 H. 0.2 I.O 0.042 0.098 0.185 If the enzyme is present in small proportion, the trans- formed quantity is proportional to its quantity, as is seen from the following experiments of O'Sullivan and Tomp- son2 and Armstrong. HYDROLYSIS OF CANE SUGAR TO 78 PER CENT BY MEANS OF INVERTASE AT 15.5° (O'SULLIVAN AND TOMPSON) 0.15 g. inv. time 283 min. (calc. 307 ) 0.45 g. inv. time 94.8 min. (calc. 92.1) 1.5 g. inv. time 30.7 min. (calc. 30.7) HYDROLYSIS OF A 5 PER CENT SOLUTION OF MILK SUGAR (looc.c.) SOLUTION CONTAINING AFTER 24 HOURS 0.66 c.c. of lactase 1 c.c. of lactase 2 c.c. of lactase 5 c.c. of lactase OBS. CALC. 2.3 p. C. 2.1 3.2 p. c. 3.1 6.3 p. c. 6.2 15.4 p. c. 15.5 1 Brown: Journ. Chent. Soc. 81. 387 (1902). 2 O'Sullivan and Tompson : Journ. Chem. Soc. 57. 865 (1890). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 59 A very good instance is given by Henri l of the in- version of cane sugar by means of invertase at constant concentration. The following table gives the number (n) of milligrammes inverted during the first minute of solu- tions of cane sugar of the concentration, c. normal ( i normal = 342 g. per liter). c = o.oi 0.025 o<°5 Otl °-25 °-5 l l*S 2 n = 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 reaches a maximum at c = o.5, only later on to sink again at very high concentrations, at which the solvent may be regarded as changed. In good agreement with this experience Terroine found that the quantity of maltose transformed by means of a given quantity of maltase in a 100 c.c. of solution is nearly proportional to the concentration of the maltose until it reaches about 2 per cent and is thereafter independent of the concentration. This regularity may be detected in some experiments executed by Tammann as early as in 1889, on the decomposition of different quantities of amygdalin by means of a constant quantity of emulsin.2 All these DECOMPOSITION OF AMYGDALIN (IN GRAMMES) BY MEANS OF EMULSIN Quantity of amygdalin 2-555 5-11 10.229 Time (min.) = 14 0.61 0.61 0.50 19 0.77 0.85 0.73 23 0.79 0.98 0.86 experiments lead us to the assumption that the substance which really is decomposed into the reaction-products is in 1 Henri: "Lois generals de 1'action les disastases: These," Paris (1899). 2 Tammann : Zeitschr. f. ph. Ch. 3. 33 (1889) ; Hoppe Seylers Ztitschr. 16. 315 (1892). 60 LECTURES ON IMMUNITY these cases a compound of the enzyme and the substrate upon which it acts. If the enzyme is in excess (in the said cases), nearly the whole quantity of the substrate acted upon enters into the compound, the quantity of which is therefore proportional to the quantity of this substrate. If, on the other hand, the substrate is in excess, the quan- tity of compound is nearly proportional to the quantity of enzyme. We may therefore from these experiments draw conclusions as to the quantities of enzyme that are equiva- lent to a certain quantity of, e.g., sugar or milk sugar. These conclusions indicate that the equivalent weights of the enzymes are not so high as is often assumed. The circumstance that enzymes are not in general pure sub- stances hinders the estimation of their true equivalent weights. The formula of Bodenstein and Henri may be deduced in the following manner. The quantity1 of ferment from the beginning may be called F, that of the decomposing substance A. Of this a part, x, may be decomposed so that only A — x remains. The ferment, substance A, and reaction-products may enter into compounds consisting of i molecule of ferment with/* molecules of A and q mole- cules of different reaction-products. Of these compounds z, zlt etc., molecules may be present. Then for every one of these kinds of molecules a formula of the following form is valid : — 2 = klFl(A-x- 2/*)» (x - 2?*)« where F= F1 + 2*. If we suppose ^.z to be small as compared with A and x, we get — z = kFl (A - 1 Cf. Henri : Compt, rwd< 135. 916. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 6 1 Further we have : — In many cases the first term, i, in the denominator is little as compared with the terms under the sign of sum- mation and may therefore be neglected. In this case we get the formula of Bodenstein if we put n — i, and suppose the terms under 2 to be two, one in which /= i and g = o, another in which / = o and q—\. In nearly all cases hitherto investigated the velocity of reaction is nearly pro- portional to the first power of the concentration of enzyme present; therefore the deduction is given only for this case. The more general formula, in which this concentra- tion enters to another power than I, is very complicated. A very common case is that in which only one term with /=o and q= i enters under the sign 2 ; this is the case in the digestion of egg-white by pepsin and trypsin and for the hydrolysis of fat by means of lipases. Here also the term i may be dismissed. This holds good even for the experiments of Armstrong, in which the product of reaction is proportional to the square root of the time of reaction. Here/ = i and 4=1, i.e. the chief influence is due to the formation of a compound between the enzyme, the reaction-product, and the original substance. The for- mula is evidently not valid, if the quantity of substance acted upon by the enzyme or the reaction-product is to a great part bound by the enzyme. Therefore the formula gives no good values for the experiments of Terroine with small quantities of maltose. It will be necessary to carry out a large number of experiments in order to verify this 62 LECTURES ON IMMUNITY view, which seems to be the best expression of our pres- ent knowledge. A very prominent place in this connection is held by the rule of Schiitz, according to which some processes, especially the peptic digestion, proceeds through a certain time nearly proportionally to the square root of the time and thereafter more slowly. To understand the meaning of this rule, we at first examine a very well-known process, the saponification of ethyl-acetate by means of ammonia, on which I have carried out some experiments. A mixture was made of 1 8 c.c. distilled water and I c.c. ( = 0.91 grammes) of ethyl-acetate, in a vessel used for determining conductivi- ties, held at a constant temperature (16° C.). At a certain moment I c.c. of a 0.02 normal solution of ammonia was added and the vessel shaken. Afterwards the resistance was determined. It decreased at first rapidly, then slowly, indicating that the well-conducting acetate of ammonia was formed from the less-conducting ammonia, according to the equation : — NH3 + CH3COO C2H5 + H2O = NH4CH3COO + C2H5OH. By means of the conductivity the progress of the chem- ical process was determined. If we take the quantity of ammonia at the beginning, like 1000, then the following quantities of ammonium-acetate, ;roba., were observed at the given times (t in minutes). The table contains two calculated values of x, viz. ^calc< , found by means of a formula given below, and ;rcalc< 2, deduced by means of Schiitz's rule. At ^=14 the latter quantity exceeds 1000, which is evidently impossible. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 63 PROGRESS OF SAPONIFICATION OF ETHYLACETATE BY MEANS OF AMMONIA AT 1 6° C. t Xobt. .Tcalc.l •Zoslc.2 I 320 352 303 i-5 394 4I2 371 2 453 469 428 3 539 548 525 4 607 608 606 5 657 656 677 6 701 685 742 7 733 728 801 8 764 757 856 10 810 803 958 H 878 864 20 936 923 32 - 980 973 The agreement with Schiitz's rule is rather imperfect, especially for high values of x. This is a general feature of the said rule, and it is quite clear that the rule would give values of x exceeding 1000 for high values of /, which is evidently impossible. In order to deduce a rational formula for this process, we must remember that the saponification is a catalytic process, with a specific velocity of reaction proportional to the concentration of the hydroxyl-ions and of the ethyl- acetate. This latter is here present in such an excess, that only about 0.2 per cent of it is transformed during the process, consequently its concentration may be taken as a constant (P). The concentration y of the hydroxyl- ions is subject to the following formula: — K(A~x\ "'~~ — - — i — '' ky 64 LECTURES ON IMMUNITY where A is the quantity of ammonia present at the time / = o, x the quantity of ammonium-acetate formed, and consequently A—x the quantity of ammonia at a given time, t. The velocity of reaction — is propor- tional to y and to the quantity P of ethyl-acetate, so that the equation dx = K(A-x) dt x + ky is also valid. If x is not too small, ky may be neglected, and we find the integral : — From this formula the values ;rcalc-1 are calculated. A is set as 1000. Here KP is 82. The agreement may be regarded as very satisfying. At low values of t the observed value x is less than the calculated one, due to the neglection of ky, as compared with x, which is not allowed if x is small. If x is very small compared with A, i.e. in the beginning of the experiment, we may as a first approximation put A — x = A and dsc=KAP dt x which gives — x* = KAP, x is proportional to the square root of the time and also to the square root of the concentration of the ammonia at the beginning of the experiment, and to the square root of the concentration of the ethyl-acetate. This is the rule of Schiitz. As is seen from these equations, x is only a function of VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 65 APt, i.e. of the product of the initial concentration of the catalytic agent — here ammonia — of the substrate — here ethyl-acetate — and of time. Evidently here the product KP may be regarded as the constant of the reaction. From the analysis given above we find that the validity of the rule of Schiitz indicates that the active part of the catalysor, ammonia or pepsin, etc., is inversely propor- tional to the products formed. This occurs in the case of ammonia because the product, NH4-ions, gives a com- pound with the active part, the hydroxyl-ions, which is dis- sociated to a very low degree. Probably the case is similar in all the processes in homogeneous media studied below and belonging to this group (peptic or tryptic digestion). In heterogeneous media other circumstances, such as change of solubility, may play a role ; perhaps this occurs in the saponification by means of lipases. One of the most interesting investigations in this line was done as early as 1895 by Sjoqvist.1 He dissolved 2.23 g. of egg-albumen, which by dialysis had been nearly puri- fied from salts, in 100 c.c. of four solutions, which further- more contained 0.005 gramme-molecules (=0.1875 g.) HC1 and 2.5, 5, 10, or 20 c.c. of pepsin. In this homo- geneous system the albumen slowly digested at 37° C. At the same time the conductivity gradually diminished, and this diminution was regarded as a measure of the velocity of digestion. At given intervals samples were taken from the solution and rapidily cooled to 1 8° C., at which tem- perature the velocity of digestion might be practically neglected. The determination of the conductivity was made at this temperature in the ordinary manner. 1 Sjoqvist : Skandinav. Archivf. Physiologie, 5 (1895). F 66 LECTURES ON IMMUNITY He found the following figures : p is the conductivity, A its decrease, Acalc. the corresponding calculated quantity, *J *} ^ fi\ A. and / = -~* , where P is the concentration of pepsin. VP DIGESTION OF EGG-ALBUMEN AT 37° C. BY MEANS OF HCL AND PEPSIN />=0.025 % />=o.os % TIME (hours) A* A *cal. / * A Acal, / 0 188.4 — — — 188.4 — — 0.5 — — 5-3 — — — 7.8 — I — — 7-8 — 178.2 10.2 10.5 120 2 177-3 II. I 10.5 157 172.8 I5.6 I5.6 I56 4 171.1 17-3 15.6 245 164.7 23.7 21.6 237 6 167.4 21. 0 (19.6) 297 159-5 28.9 (26.9) 289 8 164.5 (23.9) 21.6 338 155-5 (32.9) 29.7 329 9 163.1 25-3 (23-0) 358 153-5 34-9 (33-7) 349 12 159-9 28.5 (26.9) 403 149.4 39-o (36-6) 390 16 156.4 (32.0) 29.7 452 145.2 (43-2) 41.6 432 20 152.9 35.5 (34-7) 502 I4I.O 47-4 (46.8) 474 32 146.2 42.2 (41-6) 597 I33-I 55-3 (53-0 553 48 139.8 (48.6) (48.8) 673 126.2 (62.2) (61.2) 622 64 135-0 (53-4) 53.1 755 I2I.4 (67.0) 68.2 670 96 127.9 60.5 (61.2) 856 114.4 74-o (77-o) 740 />=O.I% P=0.2% TIME A . *' A - (hours) ** Acalc. /* calc. •'" 0 188.4 — — — 188.4 — — — °-5 179.2 9.2 10.5 65 176.0 12.4 I5.6 62 i 174.2 14.2 I5.6 100 167.8 20.6 21.6 103 2 165.9 22.5 21.6 1 60 157.9 30.3 29.7 '53 4 154.8 33-6 29.7 237 144-5 43.9 41.6 220 6 148.0 40.4 (36.6) 286 137-2 51.2 49-2 256 8 143.2 (45-2) 41-6 320 133-0 (55-4) 53.1 277 9 140.8 47-6 (44-5) 337 I30.I 58.3 55-7 292 12 136.1 52.3 49.2 370 125.8 62.6 61.1 313 16 130.9 (57-5) 53-1 407 121. 6 (66.8) 68.2 334 20 125.7 62.7 (58.6) 443 117-3 71.1 73-3 356 32 119.4 (69.0) 68.2 488 109.8 78.6 83-7 393 48 113.1 75-3 (77-o) 533 102.3 86.1 91.8 43 * 64 109.1 (79-3) 83-7 561 97-4 (91.0) 96.5 455 96 101.8 86.6 91.8 612 91.2 97.2 101.4 486 VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 67 The figures in brackets are interpolated. KP — 125, if P is expressed in per cent ; and A — 1000. Sjoqvist found that f was nearly constant for constant and small values of t: in other words, the quantity of transformed egg-albumen is proportional to the square root of the acting pepsin. But there is also another rela- tion which holds good even for long times of reaction : the digested quantity of albumen is a function of Pt only, i.e. the quantity n of pepsin digests the same quantity in the time -, as the unit quantity of pepsin in the time t. This is seen from the following table : — / V=o.o5 O.I O.2 0.4 0- 8 1.6 3-2 4.8 6-4 9.6 P=O.O2$ n. i 17-3 23-9 32.0 42. 2 53-4 — — — — 0.05 10.2 I5.6 23-7 32-9 43- 2 55-3 67.0 74.0 — — O.I 9.2 14.2 22.5 33-6 45- 2 57-5 69.0 75-3 79-3 86.6 0.2 — I2.4 20.6 30.3 43- 7 55-4 66.8 73-6 78.6 86.1 Mean IO.2 14.9 22.7 32.2 43- 8 55-4 67.6 74-3 79.0 8M V II I5.6 22 3I.I 44 From this it follows, as is seen in the mean values, that if Pt does not exceed a certain value (i.o) the quantity of digested albumen is nearly proportional to the square root of Pt, as is also seen from the calculated values (F) written below the means. This was already observed by Emil Schiitz l and has been confirmed by Jul. Schiitz,2 who dissolved the quantity, /, of pepsin, 10 c.c. of egg-albumen (containing 1-1.2 g. of co- agulable substance), and 29 c.c. I per cent HC1 in 100 c.c. In a digestion of 15 hours at 38° he found the following digested quantities, d, of egg-albumen, i.e. pepton, which is not coagulable : — 1 Emil Schutz: Zeitschr.f. ph. Ch. 9. 577 (1885). 2 Jul. Schutz: Zeitschr.f. ph. Ch. 30. I (1900). 68 LECTURES ON IMMUNITY g> ^•obs. *cal. I 0.0212 0.0213 4 O.O47I 0.0426 9 0.0652 0.0639 16 0.0799 0.0852 25 0.0935 0.1065 36 O.IO3I 0.1278 Here we have a very nice example of a monomolecular reaction, where the rate of transformation is proportional as well to the quantity of pepsin present as to that of the albumen present, but where, because of the perturbing influence of one of the reaction-products, the simple law of the monomolecular processes is altered. It reminds one in this regard strongly of the monomolecular process of transformation of acetamid studied by Ostwald,1 or of the bimolecular process of saponification of ethyl acetate by ammonia, examined by myself.2 In such cases the experimental fact that x, the trans- formed quantity, is only a function of qt, the product of the quantity of the reacting substance and the time, gives an answer to the question, whether the action is, ceteris paribus, proportional to the quantity, qy of the reacting substance. In an analogous manner if x is only dependent upon (ft or generally upon/(^y, this circumstance indicates that the action of the substance is proportional to its square or in general q to the function/^). By the aid of the integral formula the calculated values are found which are tabulated above beside those found by Sjoqvist. The agreement is very close and 1 Ostwald: Journ. f. prakt. Ck. 27. I (1883). 2 Arrhenius: Ztitschr. f. ph. Ch. 2. 289 (1888). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 69 indicates that the method of Sjoqvist was very useful and even that the theoretical views are rather concordant with the facts. It would have been desirable to have varied the quantity of hydrochloric acid in these experi- ments. Some experiments of Sjoqvist on the digestion in the presence of other acids than HC1, namely, sul- phuric, nitric, and phosphoric acid, seem to indicate that the action of these acids is (about 16, 24, and 37 per cent respectively) less than that of hydrochloric acid ; but more empirical material is desirable before definite conclusions may be induced. E. Schiitz and Huppert l have made a large number of measurements of the digestion of egg-white by means of hydrochloric acid and pepsin. The egg-white was freed of globulins. The influence of the concentration of acid was such that if i g. of egg-white in 100 c.c. was digested, the digested quantity in a given time increased with the quantity of acid, but more slowly than proportionally to this, until its concentration was 0.2 percent; thereafter it was nearly constant, or in some cases, even decreased a little. This agrees with the opinion that the really reacting sub- stance is the albuminat-ion, but further investigations are necessary before this may be stated with certainty. In another series of experiments the temperature was varied. The digested quantity of 0.922 g. egg-white in 100 c.c. of 0.2 per cent HC1 was found to be : — At 30° C. 0.544 g. = 59.0 per cent Calc. 59.0 per cent " 35 " 0.660 " 71.6 " " 71.4 " " 27.5 « 0.713 « 77.3 « « 77.4 « " 40 " 0.775 " 83-° " " 83.0 1 Schutz and Huppert : Pfliiger's Arcbiv. 80. 470 (1900). LECTURES ON IMMUNITY By means of the formula used for the calculation of peptic digestion I have determined /&, which was found to be 15,570, and from this value I have deduced the calcu- lated values given above. The agreement is very satisfac- tory, but additional investigations will be necessary to give a definite value for p. According to Schiitz and Huppert the process has an optimum at about 50° C. On analogous topics many interesting experiments have been carried out in the Danish Serum Institute. Different quantities (q c.c.) of pepsin were added to a solution of 2 c.c. of 7 per cent thymolgelatin, i c.c. 0.4 per cent solu- tion of HC1, and i — q c.c. of i per cent solution of NaCl. The liquid was thereafter well mixed, and the whole was put in a test-tube which was placed in a thermostat at 36.6° C, and held at this temperature during a certain time, /. Then the test-tube was placed on ice until the next day. In this manner different test-tubes with varying q were prepared. The contents of tubes with high q were liquefied. It was noted which value of q was just high enough to produce liquefaction. In this way the following table was found : — DIGESTING INFLUENCE OF PEPSIN ON THYMOLGELATIN t (hours) 9 q.t t (hours) q q.t i-33 0.6 0.8 8 0.13 1.04 2 0.47 0.94 10 0.095 0-95 3 0-3 0.9 12 0.08 0.96 4 0.26 1.04 14 0.07 0.98 6 0.18 1. 08 20 0.045 0.90 24 0.038 0.91 The mean value is q • t = 0.96, and the observed values VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 71 do not vary from it more than may be attributed to the ex- perimental errors. In quite the same manner experiments were done at different temperatures, and the observed values of K =-— compared with the values calculated from the formula above (ji— 10,750). The results are tabulated below : — INFLUENCE OF TEMPERATURE ON THE DIGESTION OF THYMOLGELATIN TEMP. ^obs. •^calc. 2O 0.36 0.36 25 0.45 0.48 29.8 0.62 0.65 36.8 I.OO 0.96 40.7 1. 20 1. 21 Segelcke and Storch * had already stated that a solution of rennet coagulates milk in times which are inversely proportional to the concentration of the solution. Soxhlet confirmed these results by more accurate measurements. On the basis of the proportionality of the digestion and the coagulating power of peptic solutions of different prepara- tion Pawlow concluded that rennet is probably identical with pepsin. Hammarsten objected to Pawlow's opinion, because the pepsin was said to follow the rule of Schiitz, which was not the case with the rennet, according to Soxhlet's experiments. This contradiction is evidently not proved and Saw] alow therefore infers that all experi- ments are in favour of Pawlow's opinion. Recent investi- gations of Bang, Hemmeter, and Schmidt-Nielsen (cf. Chapter IX) seem to indicate that pepsin in acid solution 1 Segelcke and Storch : Ugeskrift for Landmaend (1870). LECTURES ON IMMUNITY coagulates casein, just as rennet in neutral, or even in acid solution. The two coagulating enzymes are therefore not identical. The influence of rennet on the coagulation of milk has been investigated in a manner analogous to that used in the study of pepsin. Thus, for instance, Madsen adds dif- ferent quantities, q, of rennet to a given quantity of milk. Then he places the mixtures in test-tubes and places these during a time, /, in a thermostat at given temperature. After this the tubes are rapidly cooled, and it is deter- mined which is the least quantity, q, sufficing for coagula- tion. The results are quite concordant with those for pepsin, as indicated by the following table : — COAGULATING POWER OF DIFFERENT CONCENTRATIONS OF RENNET IN MILK AT 36.55° C. / (min.) f qt / 9 qt 4 0.08 0.32 35 0.007 0.25 6 0.05 0.30 5° 0.005 0.25 9 0.033 0.30 70 0.004 0.28 ii 0.024 0.26 80 0.0032 0.26 12 0.019 0.23 100 O.OO28 0.28 14 0.0175 0.25 120 O.OO25 0.30 20 O.OI3 0.26 1 80 0.00185 0-33 25 0.01 0.25 240 0.0017 0.41 30 0.007 0.21 The mean value of qt is 0.28 (or if the two last ob- servations are excluded 0.267). The last values display a notable increase of qt, that is, a decrease in the velocity of reaction with increasing time. This agrees well with the other series of observations from Copenhagen, as well VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 73 as with those of other observers, and may perhaps be ascribed to an attenuation of the rennet with time. The influence of temperature on the coagulating power of rennet was investigated by Fuld.1 He found the fol- lowing values of the time of coagulation, /, for the same quantity of rennet : — TEMPERATURE / (sec.) ^obs. •K*calc. 25-05 54 •185 I8S 30 32 312 327 35 17 588 574 140 10.2 980 980 44 9 IIII 1491 5° 14.7 680 2742 fi = 20,650 The values of l£oba, are 10,000 divided by t. They agree quite well with the calculated values up to a temperature of 40° C. ; above this the agreement fails. This evidently depends on the fact that above 40° C. the destruction of the rennet proceeds at such a speed that the observations are disturbed thereby. This explains also the occurrence of an optimum at about 44° C., which optimum therefore must not be regarded as real. The observed effect de- pends upon /z being many times greater (in this case 4.4 times) for the spontaneous destruction than for the pro- cess of fermentation. The same observation may be applied to the other cases in which such optima occur (cf. p. 53). Reichel and Spiro2 have contributed some interesting 1 Fuld : Hofmeisters Beitr'dge, 2. 169 (1902). 2 Reichel and Spiro : Hofmeisters Beitrage, 7. 478 (1905). 74 LECTURES ON IMMUNITY figures regarding the coagulation of milk at different dilutions or with the addition of different quantities of calcium chloride. The most interpretable results were yielded by the additions of calcium chloride. The milk itself contained 0.6 per cent if diluted in the proportion 10 : 8, which was employed in these experiments. Eight c.c. of milk were mixed with i, 0.5, or 0.25 c.c. of a rennet solution, R, and with different amounts of a solution of calcium chloride and water until the total volume was 10 c.c. The authors give the following values: — CACLj IN % TIME OF COAGULATION CONSTANT= (/ + 0.6) t * i c.c. X 0.5 c.c. R 0.25 c.c. R i c.c. R 0.5 c.c. R 0.25 c.c. R 0 95 48 24 57 28.8 14.4 0.05 88.6 45.6 23 57.6 29.6 15.0 O.I 79 41.6 22 55-3 29.1 15-4 0.2 66.4 36 19 53-1 28.8 15.2 0-5 48 26.4 H 52.8 29.0 15-4 1.0 30 1 8.2 10.6 48.0 29.1 17.0 2.O 17 II 6.8 44.2 28.6 17.7 5-o 10 7-4 5-4 56.0 41.4 30.2 10.0 13 9.2 6.2 137-8 97-5 65.7 20.0 22 15 8.6 453-2 309 177.2 As will be seen from these figures, the product (/ + o.6y is nearly constant, if p does not exceed 2%. This relation is quite like that representing the connection between the quantity of rennet and time of coagulation. If the quantity of rennet is called R, the complete equa- tion for the time of action is R(p 4- o.6)/ = const. The value 0.6 which must be added to p to obtain a constant value may be regarded as the quantity of calcium ions VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 75 present if no calcium chloride is added.1 Chlorides of barium and magnesium exert a similar influence to that of calcium ; the less ionised magnesium sulphate has an analogous but weaker action. In another series of experiments the concentration of the casein was changed. The solvent by means of which the attenuation was accomplished was milk freed of casein, i.e. whey. The experimental values are given below ; the quantity of rennet present was always the same, I c.c. of a given solution. MILK WHEY TIME OF COAGULATION obs. calc. c.c. c.c. sec. sec. 0.2 8.8 no no 0.4 8.6 70 64 0.6 8.4 50 49 0.8 8.2 42 42 I.O 8.0 39 374 1.25 7-75 33 33-8 i-5 7-5 31-2 31.5 '•75 7-25 29.6 29.9 2 7 28.6 28.6 2.5 6-5 27 26.8 3 6 26 257 4 5 24 23.2 5-5 3-5 23 23.0 8 i 22 21.8 The calculated values for the time of coagulation (/) are found by means of the empirical formula : — 10 — M t— 21.6= 1.75- M 1 As the authors assert, this supposition assumes that only about 15 per cent of the calcium salts present in milk are in ionic state. f6 LECTURES ON IMMUNITY where M denotes the quantity of milk (in cubic centi- meters) present in the solution. Very complicated results were obtained on dilution with 0.9 per cent solution of sodium chloride, as is seen from the following table, in which M and R respectively desig- nate the number of cubic centimeters of milk and rennet respectively present in 10 c.c. of the solution. (The rennet contained calcium salts.) The rest (10 — M— R ) is the quantity of salt solution added. The tabulated figures give the time of coagulation in seconds. R = 2 1.5 i 0.9 0.8 0.7 0.6 0.5 0.4 0.3 M= 1.25 c.c. 34 9 12 14.5 19 33 50 107 810 3 c.c. 46 10 11.5 '14 18 24 32 45 78 8 c.c. 8 9 ii 12 14 16 19 23 29 42 If R = 0.8 or 0.9 c.c., the time of coagulation is nearly independent of the dilution of the milk ; at lower concen- trations of R the time increases with dilution, at higher concentrations of R the opposite is true. According to the views of Saw] alow the coagulation of milk is only a special case of digestion in which one of the products coagulates. This agrees very well with experi- ments at low temperatures first executed by Morgenroth,1 and then repeated by Fuld. They prepared mixtures of rennet and milk, which were held at low temperatures. Then no coagulation occurred, but the digestion process did occur. After these mixtures had been held for some time at the low temperature and were then heated to 20° or more, they coagulated instantaneously. 1 Morgenroth : Archives Internationales de pharmarcodynamie, 7. 265 (1900). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 77 As we have seen above, the albumose-salts produced in the digestion exert an enormous retarding influence on the velocity of digestion. In the same manner according to Sawjalow the addition of peptone to a mixture of milk and gastric juice increased the time of coagulation to a notable degree. This time, for instance, increased from 29.8 seconds to 791 seconds on the addition of 4 c.c. of peptone solution (i c.c. was equivalent to 5.5 mg. HC1) instead of 4 c.c. of water to a mixture of i c.c. stomachal fluid with 10 c.c. of milk. The action was therefore dimin- ished to about 4 per cent. A like influence is exerted by peptone solution on the velocity of reaction on milk of pancreatic juice or of solution of papayotin. As peptone is very nearly related to albumose, this seems to indicate that the digestive action of pepsin is identical with the coagulating influence of rennet or pan- creatic liquid or papayotin, as Pawlow and Sawjalow have contended. A substance that acts in a similar manner to pepsin on thymolgelatin is trypsin. On the action of dif- ferent quantities (from 0.0022 to 0.3 c.c.) at 47.3° C. the following investigations were carried out by Madsen and Walbum. In this case no acid was added to the liquid in the test-tubes, but only 2 c.c. of thymolgelatin, q c.c. of trypsin solution, and (2 — q) c.c. of I per cent salt solution. These investigations indicate that in this case, as well as in those treated above, the product of the time of reaction and reacting quantity is a constant, if the magnitude of reaction is the same. In the following table the signs / and q denote time and quantity: — 78 LECTURES ON IMMUNITY LIQUEFACTION OF THYMOLGELATIN BY MEANS OF TRYPSIN AT 47.3° C. 9 t (hours) qt 9 / (hours) ft 0-3 0.16 0.048 0.0072 8 0.058 0.105 o-5 0.052 0.006 IO 0.060 0.05 i 0.050 0.0037 16 0.059 0.027 2 0.054 O.OO32 18 0.058 0.02 3 0.06 0.0027 20 0.054 0.015 4 0.06 0.0025 22 o-°55 O.OII 5 o-055 0.0022 24 o-o53 O.OO9 6 0.054 Mean 0.056 With another preparation of trypsin the effect of tem- perature was studied. The inverse value of qt may be regarded as the constant of reaction ; it was found to have the following values : — = -, /*= 10,5/0. INFLUENCE OF TEMPERATURE ON THE DIGESTION OF GELATIN BY MEANS OF TRYPSIN TEMP. *+, *•«*. 22.6 4.18 4.04 24-75 444 4.60 29.2 5.72 5-98 36.5 9.01 9.06 39-8 10.89 10.85 44.96 14.52 14.30 50.2 18.35 18.74 In most of the series of Madsen and Walbum an in- crease of qt with time is observed. This may be explained by the binding of a little of the trypsin or by the weaken- ing of it with time, p is nearly the same as for pepsin. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 79 Bayliss 1 has investigated the progress of the action of trypsin on casein by means of the method of Sjb'qvist. A solution of 8 per cent of the sodium salt of casein was pre- pared and to 6 c.c. of this solution 2 c.c. of 0.5 normal ammonia and 2 c.c. of a 2 per cent solution of trypsin were added. The conductivity was measured at different times and its increase (at 39° C.) plotted in a curve. This curve tends to an upper limit. By measuring the ordinates ( Y) in millimeters of this curve I have found the following values : — PROGRESS OF DIGESTION OF CASEIN WITH TRYPSIN AT 39° C. PROGRESS OF DIGESTION OF EGG- WHITE BY TRYPSIN AT 39° C. TIME (hours) **. n*ie. TIME (hours) *•*.. *".*. 0-3 25.0 29.0 I 10.2 10.2 o-5 35-5 35-7 2 15.0 13-8 0.7 41.0 40.8 4 18.8 I8.5 I.O 48.0 46.4 6 22.0 22.0 i-S 55-5 53-7 8 24.0 24.1 2.O 59-2 584 10 25.5 26.5 2-5 62.2 61.4 '5 29.2 30.3 3-0 64.6 64.2 20 3L8 33-2 3-5 66.0 66.4 25 33-6 35-3 4 67.5 68.1 30 354 36.9 5 70.0 70.8 40 38 394 6 71.4 72.6 5° 4i 41 7 72.7 73-3 00 45 — 8 74.2 74.8 oo (77-0) — The calculated values are found with the aid of the formula KP = 320, adopted for the pepsin action. They 1 Bayliss : Archives des sciences biologiques, II. Suppl. p. 261, St. Peters- burg, 1904. 80 LECTURES ON IMMUNITY agree very closely with the observed ones. The same is the case for the digestion of the solution of egg-white, which had been previously heated to 100° C. in order to destroy its content of antitrypsin. The solution contained 10 c.c. of a mixture of 10 per cent of egg-white and 90 per cent of distilled water, and further i c.c. of a i per cent solution of trypsin. Here KP = 30. The reaction with casein increases (the determination is not very reliable) in the proportion i : 5.3 between 20.7° and 30.7° C. 0 = 29,500) and 1:2.6 between 30.7° and 38.7° and has probably an optimum, due to the instability of trypsin at higher temperature. In this case the increase of conductivity depends prob- ably on the formation of ammonium salts of the reaction- products. These also react with the trypsin, so that the quantity of free trypsin is nearly inversely proportional to the quantity of reaction-products, whereby the reaction progresses proportionally to the square root of the time in its first period. Bayliss showed that the addition of digestion-products, as well as asparagin, glycin (Merck), leucin, and amphopepton (Griibler), retards the action of trypsin to a high degree. Henri and Larguier de Bancels l have used the method of Sjoqvist for the study of digestion by pancreatic juice. They found that this process of tryptic digestion follows the laws for monomolecular reactions and give as an illus- tration the following figures for the changes in the conductivity with time (at 44°, 4 per cent solution of gelatine). 1 Victor Henri and Larguier de Bancels : C. JR. de ta Soc. de Biol. 55. 787, 789, and 866 (1903). VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 8 1 TIME (min.) CHANGE OF CONDUCTIVITY MEAN 7-37 *t IO 27 28 27 27-3 29-3 2O 46 44 42 44 41-5 30 53 55 5i 53 50.0 40 58 60 58 58.7 58.7 55 66 66 65 65.7 68.8 As the end-value was not measured, we may only con- clude that the change of the conductivity is very nearly proportional to the square root of the time of digestion, as is seen in the last column. It might therefore be regarded as probable that these experiments are not in opposition with those made by other observers, who have found that the rule of Schutz1 holds good during the first time of digestion. The same authors have also digested casein dis- solved in a 2 per cent solution of sodium carbonate in the same manner. They found the following changes of the conductivity (at 44° C.) : — TIME CHANGE 5-59 V* 10 24 24 20 36 34 30 41 42 40 42 48 50 44 54 During the first time (30 min.) the change is nearly pro- portional to the square root of the time. Another series of experiments were concerned with the problem of the digestion of different quantities of gelatine or casein, or of both simultaneously, by means of a con- 1 Schiitz and Huppert : Pfluger*s Archiv. 80. 470 (1900). G 82 LECTURES ON IMMUNITY stant quantity of trypsins. The results are given below together with some calculated figures : — TIME G. 3-5 % G.i.75% C.2.5% C. 1.25% obs. calc. obs. calc. obs. calc. obs. calc. 10 17 18 II 13 23 26 20 18 20 30 25 18 18 39 37 26 26 30 37 29 20 22 46 45 28 32 G. 3-5%-!- C. 2.5% G.3.s%+ C.i. 25% G. 1.75% + C. 2.5% G. 1.75 %+C. 1.25% obs. calc. obs. calc. obs. calc. obs. calc. 25 32 28 24 25 29 28 22 50 45 45 34 47 4i 42 32 63 55 55 4i 58 50 47 39 The calculated values a*re obtained on the basis of the assumption that the digested quantities for the gelatin are proportional to 3.05^- A and for the casein to 5.2 V^A where c is the concentration of per cent and t the time in minutes. (In the table above G represents gelatin and C represents casein.) The agreement seems to be within the errors of observation, so that we may well con- clude that the mass digested is, for short times, propor- tional to the square root of the concentration as well as of the time. The calculated values for the mixtures are made under the assumption that I per cent of casein is, so to speak, equivalent to 2.9 per cent of gelatin 2.9 Therefore 3.5 per cent gelatin + 2.5 per cent casein are equivalent to 3.5 -f 7.3 = 10.8 per cent gelatin. The observed effect is in most cases greater than the calculated one for the mixtures ; only for a brief period do they correspond closely. It therefore seems VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 83 probable that the rule for this calculation agrees well with the facts only for short times ; a closer examination of this circumstance can be done only when we know the limit values of the change of conductivity, and even then new observations ought to be carried out and multiplied. The above calculation is carried through on the assump- tion that the products of digestion from casein exert the same binding influence on the reacting bodies (probably the trypsin) as do the corresponding derivatives from gela- tin, since they cause the same change of the conductivity. This, of course, need not necessarily be the case; it is only the simplest hypothesis we may introduce in the present undeveloped state of research on this point. Hence it is not necessary at all to suppose that the trypsin is bound by the gelatin and the casein to explain that the observed effect on digesting gelatin and casein simultane- ously is less than the sum of the effects of the digestion of the two substances separately, as Henri and Larguier suppose. Their hypothesis might be well founded, if we could observe the digestion in such an early period where the quantity digested was proportional to time, or, in other words, when the products of digestion would be much inferior in quantity (according to equivalents) to the quantity of trypsin. But this condition is not ful- filled in these or in any other experiments on tryptic digestion. With the use of a different substratum, however, the action of trypsin exhibits a different behaviour. As deter- mined by Taylor,1 when protamin is digested by trypsin, the acceleration produced by the ferment is directly pro- 1 Taylor, University of California Publications, Pathology, I, 21, 1904. 84 LECTURES ON IMMUNITY portional to its mass. This has been confirmed by Euler,1 who digested glycyl-glycin by means of trypsin. Henri and Lalou2 have also carried out some measure- ments on the decomposition of amygdalin and salicin by means of emulsin at 26° C. The readings were deter- mined by means of a polarimeter. An example may be given : — TIME (min.) SALICIN a % AMYGDALYN z.5% SALICIN 2 % + AMYGDALIN 2.5% SALICIN 4 % AMYGDALIN 1.25% 46 0.67 0.97 1.05 1. 08 0.90 130 I.58 2.38 3-63 2.25 i-57 268 2.32 3.15 4.22 345 1.56 00 3-15 3.17 6.32 6.30 1.59 The decomposition of the mixture is much slower than the sum of the decompositions of the constituents. For comparison the rates of decomposition of 4 per cent salicin and of 1.25 per cent amygdalin under similar conditions are given in parallel. The explanation of the difference is evidently the same as that of the non-proportionality of reaction and concentration, but it offers no more stringent conclusions, regarding the combination of enzyme and sub- strate, than does this latter circumstance. Weis3 has carried out a great number of experiments on the digestion of the protein from wheat by means of tryp- sin or pepsin (extract of malt). A great interest is attached to those experiments in which the quantity of protein was varied. In the experiments on digestion cited above, the 3 Euler: Arkiv fur Kemi, 2. No. 31, p. 8, Stockholm, 1907. 2 Henri and Lalou : C. R. de la Soc. de Biol. 55. 868 (1903). 8 Fr. Weis : Meddelelser fra Carhbtrg-Laboratorict, 5. 127 (1903)- VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 85 protein was always present in constant amount. In the following table the quantity of protein is given in per cent n of the total liquid examined. After this, is tabulated the quantity of protein, in per cent of the whole quantity, which had been digested in 2 or in 5 hours. If, for instance, the digested quantity is 10 per cent of the original quantity of protein, the total quantity of digestion-products is double as great if « = 2, as if n= i. Now the velocity of reac- tion is inversely proportional to the quantity of digestion- products, therefore the point where 10 per cent are digested is reached later if ;z=2, than if n—\. The digested quantity is therefore nearly inversely proportional to the square root of n, as is seen from the following figures, which are compared with figures calculated from the gen- eral formula on p. 64 : — n (per cent) DIGESTED QUANTITY AFTER a HOURS 5 HOURS obs. calc. obs. calc. I 22.0 21.4 36.2 32.4 2 17.0 I5.6 25-9 23.8 3 I3.I 12.9 20.3 19.8 4 9-i II. 2 1 6.0 17-3 5 7-9 1 0.0 13-2 I5.6 The agreement seems to be satisfying considering the rather complex composition of the substrate. It indicates that the quantity of digestible matter enters in the formula in the same manner as the quantity of enzyme. In all cases of digestion or lipolysis which are subject to the formulae given above, p. 64, that is to Schiitz's rule, if the process has not gone too far, the concentration of the sub- 86 LECTURES ON IMMUNITY strate plays the same role as that of the enzyme or as the time, which is also probable on the theoretical grounds. The products from a culture of Bacillus pyocyaneus exert a liquefying action on thymolgelatin, just as do pep- sin or trypsin. This action was investigated by Madsen and Walbum. It was found, as for pepsin and trypsin, that the time necessary for liquefying the gelatin to the stated degree is inversely proportional to the quantity of cul- ture employed. The bouillon in which the B. pyocyaneus had been cultivated for two weeks was filtered through a Chamberland filter and a certain quantity (q c.c.) added to 2 c.c. of 7 per cent thymolgelatin and (2 — q) c.c. of i per cent NaCl solution. The experiments were done at 34.5° C. DIGESTION OF THYMOLGELATIN BY MEANS OF PYOCYANEUS CULTURE f TIME t (hours) it 9 TIME t (hours) 9' 1.6 0-5 0.8 O.I I 8 0.88 0.8 I 0.8 0.09 10 0.90 0.46 2 0.92 0.08 12 0.96 0-3 3 0.9 0.06 I6.5 0.99 0.22 4 0.88 0.044 18 0.79 0.2 4-5 0.9 0.042 20 0.84 O.I7 6 1.02 0.035 25 0.88 Mean 0.89 Madsen and Walbum have investigated the destruction of coli-agglutinin by means of trypsin at 35. 6° C. The strength of the agglutinin was determined by means of its agglutinating power. The observed quantity, q, is that quantity of agglutinin which must be added to a sus- pension of Bacillus coli to obtain a given agglutination in a given time. These values are tabulated below. The strength 5 is the inverse value of q. The reaction is VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 8/ calculated according to the formula for bimolecular reactions. K=6S.io~5. DESTRUCTION OF i c.c. OF COLI-AGGLUTININ SOLUTION BY MEANS OF 5 c.c. OF i% SOLUTION OF TRYPSIN AT 37.5° TIME (hours) •Sobs. •Scale. TIME (hours) •Sobs. •Scale. 0 1000 1000 6 I89 197 o-5 775 763 8 I49 155 i 610 600 10 I40 128 2.25 389 395 12 108 I09 3 280 329 14 88 95 4.17 259 261 23 61 57 5 233 227 25 59 56 The agreement is very satisfactory at the beginning, if we consider that the errors of observation are rather large. This method gives a direct determination of the destruction, and not an indirect one, as do the measure- ments of the electrical conductivity. The destruction of rennet increases very rapidly with increasing temperature, as is shown by the following table : WEAKENING OF RENNET IN 2 % SOLUTION AT 47.55 ° C. WEAKENING OF RENNET (2 % SOL.) AT DIFF. TEMPERATURES / (min.) •Sobs. •Scale. TEMP. -^obs. •A"calc. 0 20 17.9 44-51 O.OI27 O.OII 2-5 14-3 14-3 46.04 0.0231 0.022 5 10.5 II.4 47-55 0.039 0.0414 7-5 8-3 9.1 48.57 0.0646 0.0647 10 7-i 7-i 49.12 0.072 0.0836 12.5 5-9 5-9 49.6 O.IOI O.I O2 15 5-o 4.8 17.5 4.0 3-7 20 3-0 3-0 22.5 2.2 2.2 25 1.8 1.9 K = 0.0386. /* = 89,130. 88 LECTURES ON IMMUNITY The reaction is monomolecular. The influence of tem- perature is characterised by a rather high value of /*. A second series gave /* = 91,000, so that in the mean /A = 90,000. This attenuation is much more marked in weaker than in stronger concentrations, as is indicated by the following figures, valid for the temperature 46.i5°C.: CONCENTRATION VELOCITY OF DESTRUCTION CONCENTRATION VELOCITY OF DESTRUCTION 7 0.00372 I 0.028 6 0.003 °-5 0.032 5 0.0049 0.25 0.039 4 0.0077 0.125 O.o6o 3 0.0154 0.0625 0.073 2 O.O2I2 Dried powder of rennet is very resisting to the influence of temperature ; ^=0.0414 at I58°C. The reaction was monomolecular. The destruction of the rennet is to a high degree accel- erated by the presence of an alkali. To 200 c.c. of a 10 per cent rennet solution Madsen added from 0.5 c.c. to 3 c.c. of i n. NaOH. He found that the velocity of destruction proceeds more slowly than that of a monomolecular re- action. This circumstance is probably due to a retarding influence of the reaction-products. This influence may in the following example, in which 3 c.c. of i n. NaOH acted upon 200 c.c. of a solution of rennet at 46° C, be put proportional to the third root of the quantity of ren- net. ^Ob8 indicates the quantity of rennet which is neces- sary to cause coagulation in ten minutes. q^Cf is the corresponding calculated quantity. VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 89 DESTRUCTION OF RENNET IN PRESENCE OF SODIUM HYDRATE AT 46° C. / (min.) fobs. ^calc. / (min.) ^obs. ^calc. 0 0.040 O.O4O 10 0.50 0.48 2 0.073 0.079 12 0.70 0.66 4 0.130 0.139 14 1. 00 0.88 6 0.20 O.22 16 1-15 «•«$ 8 0-35 0-33 The calculated values are deduced from the formula: — fi* -?o* =0,044 ('i-'o). Madsen has also investigated the destruction of trypsin by means of alkalies and found similar regularities as for the destruction of pepsin. Regarding the spontaneous attenuation of pepsin, Mad- sen and Walbum found that the reaction is monomolecular, which is shown in the following table. The increase of this reaction with temperature gives /*= 75,600, that is, | of the value for rennet (2 per cent solution). As the prepa- rations are not identical and even used in different concen- trations, this difference does not afford any data bearing on the possible identity of rennet and pepsin. The strength of the pepsin was determined by means of its digesting influence on thymolgelatin. WEAKENING OF PEPSIN (5% SOL.) AT 66.8° WEAKENING OF PEPSIN AT DIFFERENT TEMPERATURES t (min.) STRENGTHobg STRENGTHcalCi TEMP. •^obf. •*"calc. 0 17-5 I7.6 57 O.OOII2 O.OOII2 5 II. I 12.8 60 0.0047 0.0036 10 8-33 8.71 63.3 0.0109 0.0098 20 4-35 4.34 64.8 O.OI4I 0.0160 30 2.22 2.25 66.8 0.0305 0.0305 40 I. II 1.06 0.0305. = 75,600. LECTURES ON IMMUNITY Trypsin behaves in a manner very similar to that of rennet and pepsin. The reaction of the spontaneous attenuation is monomolecular and the velocity constant of reaction increases very rapidly with temperature (//. = 62,000). The values are given below: — DESTRUCTION OF TRYPSIN AT 64.03° C. DESTRUCTION OF TRYPSIN AT DIFFER- ENT TEMPERATURES t (min.) STRENGTHobg STRENGTHcajc TEMP. ^oba. /ircalc. O 12.5 I2.I 60.72 0.00127 0.00127 5 1 1.8 11.6 61.95 O.OOlS O.OOlS ii u. i ii. i 63 O.OO24 0.0024 15 10.5 10.8 64.03 O.OO32 0.0032 20 1 0.0 10.4 67.15 0.0073 0.0074 30 9.1 9.6 > 72.15 0.0274 0.0274 40 8.7 9.0 74-35 0.049 0.049 50 8-3 8-3 60 7-7 7-7 80 6.7 6.7 IOO 5-9 5-9 120 5.6 5-0 K = 0.0031 7. (j. = 62,034. The concentration of the trypsin solution exerts no sensible influence on the rate of destruction in this case. Solutions containing 2, 4, 6, 8, or 10 per cent of trypsin all gave satisfying results when calculated with the value K= 0.0073 (at 67.15° C). The strength of the trypsin was measured by means of its property of liquefy- ing thymolgelatin. Trypsin exerts, as we saw, a destructive influence on coli-agglutinin, and this destruction proceeds faster at higher temperature than at lower, as is seen from the following measurements of Madsen and Walbum. At 44.2° C. the calculated values differ for some time rather VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 91 widely from the observed ones, probably because of the spontaneous destruction of the trypsin. DESTRUCTION OF COLI-AGGLUTININ (i c.c.) BY TRYPSIN (5 c.c. i % SOL.) AT DIFFERENT TEMPERATURES AT 33-5° C. AT 37.2° C. AT 44. 2° C. TIME (hours) Strength Strength Strength fobs. obs. rale. ?obs. obi. calc. ?obs. obg. calc. O 0.00 1 1000 IOOO 0.00 1 IOOO IOOO 0.00 1 IOOO IOOO 1-25 0.0017 539 602 0.002 S00 515 0.0025 400 407 3 0.0023 435 386 0.0027 370 308 0.005 200 222 5 0.0038 263 274 0.0047 213 211 0.008 "5 146 8 0.005 200 191 0.008 125 141 0.0095 I°5 96 12 0.008 125 136 O.OI 100 100 O.OII5 87 66 10*^=53 lo5 K = 75 (calc. 70) id^IC— 117 u = 14200 The method used for measuring the potency, i.e. the inverse value of the quantity ^Ob8 necessary for the pro- duction of a certain degree of agglutination, is that described by Madsen and Jorgensen.1 From the observa- tions the values K are calculated, by means of which the calculated values for the potency are deduced according to the formula for bimolecular reactions. The agreement with the observed values is satisfactory. From the two values at 33.5° and 44.2° C. the value p= 14,200 is calcu- lated by means of the general formula. With this value of fM we find 1 0^=70 at 37.2° C. in satisfactory agree- ment with the observed value 75. A peculiar regularity is found for the coagulating power of fibrin ferment on plasma. Here the product of time of reaction and concentration is not nearly constant, as in the coagulation of milk by rennet, but the product of 1 Fcstskriftvtdlndvidscn afStatcns Serum Institut, Copenhagen, 1902, No. 5. LECTURES ON IMMUNITY the concentration to the power f and time of reaction gives a nearly constant value, as indicated by the figures below, found by Madsen and Walbum, as well as by Fuld :l PLASMA AND MUSCLE EXTRACT FROM HORSE (MADSEN AND WALBUM 2) BLOOD PLASMA OF GOOSE (2 c.c.) WITH 6 c.c. OF EXTRACT OF GOOSE MUSCLE (FULD) / (min.) c *(io C)1 /=TlME (min.) CONC. (O tc\ c £=TlME (seconds) /x(io Of 105 0.6 330 80 2 127 0.2 80 127 155 0-3 322 120 I 120 O.I 1 2O 1 20 230 0.15 3OI 1 80 o-5 "3 0.05 1 80 "3 328 O.IO 328 290 0.25 "5 0.025 290 "5 595 0.05 375 The reaction is therefore not proceeding in proportion to the concentration of the fibrinogen, but to the power f of it. Closer investigations seem desirable. Even the process of precipitation is subject to the same influence of temperature as the other reactions studied.2 The precipitating substances were 10 n. sulphuric acid or albumen precipitin, produced by subcutaneous injection of egg-albumen into a rabbit. The following values were observed with a solution of 2 c.c. of egg-albumen in 98 c.c. of physiological salt-solution. 10 N. H2SO4 (90 MIN.) PRECIPITIN (73 MIN.) TEMP. fobs. ?calc. TEMP. ?obs. ?calc. 35-8 O.IO O.I I 36.1 0.25 0.25 29.7 0.16 0.16 3O.I 0.30 0.31 25-4 0.22 0.21 20.0 0-45 0.44 19.9 0.30 0.29 13-9 o-55 o-55 14-5 0.40 0.41 n — 1 1,000. n = 6,300. 1 Fuld: Hofmeistcrs Beitr'dge, 2. 514 (1902). 2 Madsen and Walbum : Oversigt over det kgl. danske Vid-sdsks Fork. (1904), VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 93 The two processes are undoubtedly of a very different nature. Here it is supposed that the precipitins, like ren- net, obey the law that the product of time and reacting mass was constant. Then if, for instance, o.i c.c. of 10 n. H2SO4 acting upon 8 c.c. of egg-albumen solution coagulates it in 90 minutes at 35.8°, we expect that 0.3 c.c. of this acid will give coagulation in 30 minutes. Now this quantity cogulates the egg-white solution in 90 minutes at 19.9°. Therefore we say that the velocity of reaction is three times greater at 35.8° C. than at 19.9° C. In this manner the variation of the velocity of reaction with temperature may be calculated and from that the value of p. In an analogous manner we observe with the precipitin the quantity necessary to give a unit of precipitate in a given time, and from this we calculate the different times in which the same quantity of precipitin will give the same degree of precipitation at the different temperatures. Probably a closer investigation will show that the premises of our calculation are fulfilled. An interesting instance of a bimolecular reaction has been found by Madsen and Walbum1 in the interaction between tetanolysin and pepton. A solution of 2 g. of Witte's pepton in 100 c.c. water and another of 2 per cent tetanolysin in physiological salt-solution were prepared. Mixtures of 4 c.c. of the solution of lysin heated to 36.i°C. with o. 1 5, 0.20, and 0.25 respectively of the solution of pepton (of 36.1°) and so much physiological salt-solution of 36.1°, that the whole equalled 8 c.c. were placed in a water-bath at this temperature and the haemolytic power determined 1 Madsen and Walbum : CentralbLf. Bakteriologie, 40. 409 (1906). . 94 LECTURES ON IMMUNITY at different times. For this purpose a part of the mixture was rapidly cooied in a test-tube surrounded by ice, whereby the destruction of the lysin was practically brought to an end. The quantity of lysin remaining was determined in the ordinary manner by measuring its haemolytic action upon a suspension of erythrocytes. In this manner the following values were obtained : — TIME 0.15 c.c. PEPTON ADDED In hours #) i j Toxicity (obs.) ?calc. ?obs. ?calc. O IOO (55-8) 0.0 1 (0.0179) O.5 47-7 47-7 0.021 0.0210 X 39-7 • 414 O.O252 0.241 2 30.3 33-0 0.0330 0.0303 4 22.3 23-4 0.0448 0.0427 6 18.1 18.1 0.0552 0.0551 8 17 14.8 0.0588 0.0675 0.20 C.C. PEPTON ADDED 0 IOO (60.0) 0.0 1 (O.OI67) o-S 41.6 41.6 0.024 0.024 i 30.3 31.5 0.033 0.0313 2 20 21.5 0.050 0.0460 4 12.2 13-5 0.082 0.0754 6 9.6 9-7 0.105 0.1048 8 8 7-5 0.125 0.1342 0.25 c.c. PEPTON ADDED o IOO (70) 0.0 1 0.0142 o-S 35-2 35-2 0.0284 0.0284 i 22 234 0.0455 0.0426 2 13 14.0 0.0769 O.O7II 4 6.0 7.8 o.i 666 0.128 6 5-3 54 0.1886 0.185 8 3'8 4.1 0.2631 0.242 VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 95 Evidently the reaction follows very nearly the law for a bimolecular reaction, in regard to the quantity of free toxin (q), so that : — and: The observed and calculated values agree within the errors of observation. An exception is evidently displayed by the first value (t = o). Just as in similar chemical processes it is difficult to determine the time zero, since the reaction does not end instantaneously when the mix- ture is removed from the water-bath. We therefore em- ploy the same method that has been applied to similar cases studied before, namely, to reduce the time to that of the first experimental determination of the toxicity, which was made after the mixture had been held at 36.1° C. for half an hour. The constant (K) increases very rapidly with the con- centration of the pepton, as the following table shows : — Concentration of pepton, C . 0.15 0.20 0.25 Constant, K, obs. . . . 0.0062 0.0147 0.0285 Constant, A", calc. = 1.833 C3 • 0.0062 0.0147 0.0286 The velocity of reaction is proportional to g*C3, which may be explained by supposing that at first there is formed a compound of two molecules of tetanoysin with three molecules of peptone, which is decom- posed very rapidly with the destruction of the tetano- lysin. 96 LECTURES ON IMMUNITY Madsen and Walbum have also investigated the influ- ence of the temperature on this process, which in this case is peculiarly low, p being found to be 10,500 only. As a comparison we may cite the saponification of ethyl- acetate, where JJL has a value of the same order of magni- tude, namely 11,160. They investigated the reaction velocity of a solution containing 4 c.c. of the solution of tetanolysin, 0.08 c.c. of a 2 per cent solution of Witte's pepton, and 3.9 c.c. of physiological salt-solution at 37.1, 31.2, 27.5, and 17.8° C. respectively. They found the following figures : — INFLUENCE OF THE TEMPERATURE ON THE DESTRUCTION OF TETANOLYSIN BY PEPTON AT 37.1° AT 31.2° / (hours) *obs. *calc. / (hours) foW fete. O 100 100 0 100 100 0.33 41.5 41.7 o-33 46.7 48.8 I 18.8 18.9 i 26.3 24.2 2 12. 1 10.4 2 13.2 13.8 AT 27.5° AT 17.8° 0 100 100 0 100 100 0-33 48.9 54-9 0-33 69.8 69 I 28.3 28.2 I 46.1 40.8 2 I6.7 16.4 2 21.5 25-7 4 9-5 8.9 4 13 14.8 The agreement between the observed and the calculated values is very satisfying; even at 17.8° C., where the devi- ations are the greatest, they still fall within the possible errors of observation. The calculated constants (K) of reaction, according to the bimolecular formula, are given in the following table O= 10,240): — VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 97 TEMP. •^obs. ^calc. 37-1 0.0431 0.0431 31-2 0.0313 0.0313 27-5 0.0255 0.0255 17.8 0.0144 0.0144 Here the coincidence is nearly exact. In the cases in- vestigated above, where the interval of temperature reached only four degrees, a simple exponential formula would have given just as good results as the more complicated one adopted from physical chemistry ; but in this case the interval of temperature is so great that the exponential formula would have given a markedly inferior agreement with the observations, though still the differences would not have exceeded the errors of observation. It may be remarked that not all peptons exert this weak- ening influence on tetanolysin ; for instance, Chapeautaud's pepton is without influence in this respect. As a general result of these investigations we find that the spontaneous destruction of the substances studied in- creases in solution very rapidly with temperature. In most cases the destruction of these substances by cata- lytic agencies increases much more slowly, about at the same rate as the catalytic processes studied in general chemistry. The observed values of //. are compared in the following table : — Spontaneous destruction of dry emulsin /* = 26,300 (Tammann) Spontaneous destruction of lipase from castor beans in sol. //, — 26,000 (Nicloux, cf. next chapter) Spontaneous destruction of emulsin in 0.5 per cent sol. /* = 45,000 (Tammann) 98 LECTURES ON IMMUNITY Spontaneous destruction Spontaneous destruction Spontaneous destruction Spontaneous destruction Spontaneous destruction Spontaneous destruction Spontaneous destruction of trypsin in 2 per cent sol. of pepsin in 2 per cent sol. of rennet in 2 per cent sol. of vibriolysin in sol. of tetanolysin in sol. of comp. haemolysin in sol. of dibromsuccinic acid M= 62,034 /* At M H M A* Destruction of salicin by emulsin Destruction of cane sugar by invertase Destruction of tetanolysin by pepton Destruction of coli-agglutinin by trypsin Coagulation of milk by rennet Coagulation of digestion of casein-salt by trypsin Precipitation of egg-white by sulphuric acid Precipitation of egg-white by pr^cipitin Digestion of gelatin by means of pepsin Digestion of gelatin by means of trypsin Digestion of egg-white by means of pepsin Hydrolysis of sugar by acids /* = Saponification of cotton oil by lipase from castor beans /x (Nicloux, Saponification of triacetin by lipase from castor beans /A (A. E. Taylor, Saponification of ethyl-acetate by NaOH ju, = 90,000 = 128,000 = 162,000 = 198,500 = 22,220 (van't Hoff = 3,300 ( ? Tammann) 9,080 (Kjeldahl) 10,240 16,500 20,650 29,500 11,000 6,300 10,750 10,570 15,570 25,600 (Spohr) = 7,540 cf. next chapter) = 16,700 cf. next chapter) = 11,15° (Warder) /* = The spontaneous destruction of the different substances investigated by Madsen increases from three to nine times more rapidly with temperature than the corresponding phenomenon . for dibromsuccinic acid (C4H4O4Br2 = C4H3O4Br + HBr). The values of p found by Madsen even exceed those found for emulsin by Tammann. On the other hand, the M for the catalytic actions is of the same order of magnitude as those known heretofore (espe- cially that of Saponification). The similarity of the values VELOCITY OF REACTION. HOMOGENEOUS SYSTEMS 99 of p in the two cases of digestion of gelatin by means of pepsin or of trypsin is very startling. In any case it is not possible to retain the opinion that /-i is of the same order of magnitude for all velocities of reaction, corresponding closely to an increase in the proportion i : 2 for an increase in temperature of ten degrees (fi = 1 1,850 at 20°, p = 14,400 at 50°, and /*= 17,200 at 80° C.). As most of Madsen's determinations were carried out in the proximity of 50°, we may say that /* is between four and fourteen times greater, that is, the increase for 10° C. may be from 28 = 8 to 213 = 8200 times the usual rate. COLLEGE OF DENTISTRY UNIVERSITY OF CALIFORNIA CHAPTER IV VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS MOST of the reactions concerned in sero-therapy occur in heterogeneous systems, and may therefore be regarded as analogous to, e.g., the solution of a metal or a carbonate in an acid. To this category belong, for instance, the haemolytic reactions, which possess such great importance for theoretical researches. Madsen and I l have made some experiments on the velocity of haemolysis by sodium hydrate, ammonia, and tetanolysin. The reagents, solu- tions of the haemolytic substances and suspensions of blood-emulsions, were heated to 37° C., mixed and allowed to act upon each other for a certain time, then the mixture cooled down to o° C. in order to practically check the re- action, and rapidly centrifugalised. The colour of the solution indicates the degree of haemolysis. The velocity of the reaction was calculated under the assumption that the transformed quantity in the unit time is proportional to the number of erythrocytes present. The haemolytic agent was present in such an excess that its quantity was many times greater than that necessary for complete haemolysis. This quantity, being in excess, was therefore regarded as approximately constant during the short time of reaction. Hence the velocity of reaction should be that of monomolecular order in a homogeneous 1 Festskrift, Copenhagen (1902), No. 3. 100 VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS lot system. A series of experiments with 0.5 c.c. o.i n. NH3 mixed with 10 c.c. 2.5 per cent suspensions of blood gave: Time (minutes) o 6 14 23 31 Intact blood (per cent) 100 97 82 60 35 Constant of reaction — 0.00022 0.0062 0.0096 0.0147 The "constant" increases very rapidly as the process advances. This phenomenon depends evidently upon something similar to the "time of induction," observed in reactions in heterogeneous and sometimes also in homoge- neous systems (action of light upon a mixture of chlorine and hydrogen). In this case it is easy to understand that a certain quantity of ammonia must diffuse into the erythro- cytes and act there for some time before the haemoglobin leaves the cells. According to different circumstances, such as varying resisting power of the cells, distance from the molecules of ammonia in the moment of mixing, the different cells are attacked more or less slowly. Still it was possible to prove that the time necessary for haemolysing a given number of erythrocytes is inversely proportional to the strength of the haemolytic agent. Thus, for instance, in experiments with solutions the dilutions (inverse concentrations) of which were proportional to 1:0.44:0.23:0.133 the following times in minutes were necessary for the haemolysis of 3, 10, 20, 30 and 40 per cent respectively of the erythrocytes. In parentheses are printed the calculated values obtained according to the rule mentioned. Haemolysis 310 20 30 40 per cent. Dilution i 13 (13) 26 (26) 35 (35) 44 (44) 53 (53) min. Dilution 0.44 6 (5.7) 10 (11.5) 15 (15.4) 18 (19.4) 23 (23.3) min. Dilution 0.23 5.5(6.0) 9(8.0) 12 (10.1) 14 (12.2) min. Dilution 0.133 i-8 (3.5) 4(4-7) 6.2(5.9) 8(7.1) min. IO2 LECTURES ON IMMUNITY The agreement is very satisfactory. Similar experiments were done with sodium hydrate and tetanolysin. They led to similar results. If different quantities of ammonia are allowed to act upon a unit amount of blood corpuscles during a given time, it fol- lows from the considerations given above that the haemo- lysed quantity increases more rapidly than in proportion to the amount of ammonia. If we consider the quantities a and 2 a, and let the first act during the time -, the second during the time /, the action of the two will be equal. If thereafter the quantity a be allowed to act during the time -, the velocity of reaction will be much greater during this interval than in the first period. There- fore the quantity haemolysed in the time / by the quantity 2 a is more than double that haemolysed in the same time by the quantity a (provided that the total haemolysis is not near completeness, and that we observe in the first stages of the process). It is often found that the quantity haemo- lysed is roughly proportional to the square of the concen- tration of the poison, if this does not act very rapidly as is the case with ammonia and tetanolysis. This rule, which may be of use for many calculations, is illustrated by the following examples (a is the concentration of the poison, b the degree of haemolysis in per cent, c = V# : a). In other cases, generally of rapidly acting haemolytic agents, the rule does not hold, but the value of c sinks rapidly when the degree of haemolysis falls below 10 per cent. Such are the strongly dissociated bases, caustic potash, soda, and lithium, and even solanin. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 103 INFLUENCE OF THE CONCENTRATION OF A POISON ON THE HAEMOLYSIS TETANOLYSIN AMMONIA a b si c= — a a b c- — a O.QI 45 7-4 0.84 65 9.6 0.74 25 6.8 0.67 55 n. i °-57 H 6.6 0.50 37 12.3 0.48 7 5-5 0.40 27 12.0 043 6 5-7 0.36 16 II. I o-38 3-5 5-9 0.31 12 II. I 0.29 2-5 5-5 0.27 6 9.2 0.24 2-5 6.6 0.22 5 10.2 0.20 1-7 6.5 The blood often binds a certain quantity of the poison added, so that under a certain concentration no haemolysis occurs ; this was, e.g., the case with 10 c.c. of a suspension containing 10 per cent of erythrocytes and less than 0.015 milligramme equivalent of caustic soda or ammonia. The quantity bound is very strictly proportional to the quantity of erythrocytes. An analogous case is seen in telanolysin, according to the experiments of Madsen and Henderson-Smith. They added different quantities, q, of telanolysin to 10 c.c. of 2 per cent suspension of erythrocytes from the horse and determined the times which were necessary at 37° C. to produce a certain degree of haemolysis. The results are given below on p. 104. The time oo indicates that the quantity 0.25 telanolysis does not give an appreciable haemolysis. Evidently the product of the reacting quantity (^ — 0.25) and the time of action is constant. IO4 LECTURES ON IMMUNITY H^MOLYSIS BY MEANS OF DIFFERENT QUANTITIES OF TETANOLYSIN AT 37° C. q t (min.) (7-0.25) t q t (min.) (q— 0.25) t 1.0 2 1.50 0.4 11.8 1.77 0.8 2.8 1-54 o-35 13-5 i-35 0.6 4-5 1.48 0-3 28.5 1.42 o-5 6.1 1.52 0.25 oo 0-45 7-i 1.42 The agglutinins display in their general behaviour a very great similarity to the hsemolysins. This was de- termined by experiments in which different quantities, q, of an agglutinin (against Bacillus coli) were allowed to act upon similar suspensions of this bacillus at 37° C. Then the time necessary to produce a given degree of agglutination was found to be inversely proportional to q as will be seen from the following table. Action of different quantities of agglutinin on Bacillus coli atlfC. q t (min.) qt q t (min.) qt 0.08 2O (1.6) 0.008 140 (1,12) 0.035 30 1.05 0.006 150 0.90 0.025 45 I. II 0.0055 I65 0.91 0.017 60 1.02 0.005 1 80 0.90 0.012 90 1.08 0.004 210 0.84 O.OOS 120 0.96 0.0035 240 0.84 O.OO5 1 80 0.90 0.003 300 0.90 O.OO4 240 0.96 O.OO22 420 0.92 0.003 300 0.90 0.002 480 0.96 O.O027 360 0.97 Mean 0.99 Mean 0.90 VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 1 05 The first figures indicate an activity known to be too low (too long time). This may be due to errors in the measuring of the time. It is supposed that the liquids are immediately brought to the temperature of the thermostat in which they are placed. Evidently this is not quite true, and therefore in a more exact calculation a certain time should be subtracted from the observed one. Henri has carried out some interesting experiments on the haemolysis of chicken erythrocytes by means of normal dog-serum. He added different quantities of the serum to 30 c.c. of a 10 per cent suspension of the erythrocytes and so much of 0.9 per cent NaCl solution as to bring the whole volume to 40 c.c. Then he observed that the haemolysis proceeded at first rapidly, later on more slowly, until it reached a limit value. This value was found to be: — Quantity of serum in c.c. ( is given with its limit value as unit. The reaction-constants are calculated from the formula ^ l^ l K =-log . / & i — x Quantity of serum in c.c. o-3 0.4 0-5 0-75 x K x K x K x K Time of reaction, 24 min. 0.33 0.0072 0.35 0.0077 0.33 0.0072 0.50 0.0125 Time of reaction, 63 min. 0.56 0.0057 0.67 0.0076 0.65 0.0072 0.83 0.0122 Time of reaction, 94 min. 0.78 0.0070 0.80 0.0094 0.79 0.0072 0.90 0.0106 Time of reaction, 190 min. 0.96 0.0071 0.94 0.0065 0.96 0.0071 0.98 0.0090 1 Victor Henri: C. r. de la Societe Biologique, 58. 36-39 (Jan. 4, 1605). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS IO/ Another series of experiments seems to indicate that the value of K is independent of the quantity of erythro- cytes, but increases more rapidly than in proportion to the quantity of serum. (It is rather peculiar that this behaviour is not indicated in the figures given above.) Madsen, aided by Walbum and Nugochi, has carried out a large number of experiments on the velocity of reactions of different substances at different temperatures. Their method consisted in determining the qualities of the same agent, e.g. haemolysin, which were necessary to produce a certain effect in a given time, e.g. 10 minutes. The lower the temperature, the greater the quantity of the agent necessary for the effect, generally speaking. Taking ammonia as an illustration, we know that, if the quan- tity exceeds greatly the amount necessary for complete haemolysis in a very long time, the time necessary to secure a certain effect is inversely proportional to the quantity of ammonia used. If therefore, as the experi- ments indicate, the addition of 0.085 c-c- of a solution of ammonia to 8 c.c. of a i per cent suspension of erythro- crytes from horse blood at 34.8° C. will give in 10 minutes the same effect as 0.17 c.c. of the same solution at 29.7° C., the other conditions being the same, we conclude that 0.085 c.c. of the ammonia would require 20 minutes at 29.7° C. to attain the same effect as in 10 minutes at 34.8°; i.e. the velocity of reaction at 34.8° C. is double that at 29.7° C. Generally speaking, the velocity of reaction is in these experiments inversely proportional to the quantity used. Evidently this conclusion is valid only for those cases in which, as for ammonia, the rate of the reaction is propor- tional to the quantity of reacting substance; but this seems io8 LECTURES ON IMMUNITY to be generally the case if a correction be introduced for the first fraction of the poison, which is neutralized in the erythrocytes. This correction, in most cases, seems to be of minor importance. We may again use the formula — where v1 and z/0 indicate the velocities at the absolute tem- peratures 7^ and T0 and p is a characteristic constant. Here we have only to replace the velocity, v, by the inverse value of the concentration necessary to produce the desired effect. Experimentally it was found that the results agreed very well with the formula, as 'shown by the following figures, AMMONIA, 0.5 NORMAL SOLUTION *= 10 Mm. 2=20 MlN. z — 30 MIN. t fobs. ?calc. 39.5 0.04 0.043 34.8 0.085 °-°83 29.7 0.17 0.17 25.9 0.3 0.3 21.0 0.60 0.64 \i.— 26,760 t ?obs. ?calc. 39.2 0.03 0.029 34.8 0.05 0.05 30.2 0.085 °'°81 25.7 0.19 0.17 21. 0 0.3 0.32 15.7 0.55 0.69 /A =24, 360 / fobs. tf'calc. 39-5 0.027 0.023 34.8 0.035 °-°39 29.7 0.07 0.072 25-9 0-13 0.12 21.0 0.25 0.23 15.2 0.5 0.5 /* = 23,020 *=6o Mm. s=iooMm. jz=i8o MIN. t fobs. ?calc. 39.2 0.019 0.014 34.8 0.024 0.022 30.2 0.035 °-°35 25.7 0.050 0.056 15.7 0.17 0.17 12.2 0.26 0.26 At =19,150 / fobs. ^calc. 39.1 0.02 O.OlS 34.6 0.025 0.025 30.7 0.025 0.034 25.9 0.045 O-OS1 21.3 0.060 0.075 16.1 0.115 0.12 12.2 0.17 0.17 /i = 14,920 t ?obs. ?calc. 39.O O.OI5 O.OI5 34.7 0.185 °-l85 30.9 O.O23 O.O23 25.7 0.030 0.029 21.5 0.040 0.037 1 6. i 0.050 0.050 /* = 9»44i VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 1 09 giving the observed concentrations compared with cal- culated values; z gives the time of reaction, t the temper- ature, q the quantity added, i.e. the inverse value of the velocity v. As will be seen from these figures the formula may be well used in this case. We observe also that the magnitude /i increases with decreasing time of reaction. With a pro- longed reaction-time, the quantities of ammonia used do not exceed very much the quantity necessary for total haemolysis and then our premises are not fulfilled. Hence the real value of /<&, corresponding to the theo- retical premises, is that to which the values of ^ converge with decreasing time of reaction. It does not seem to differ very much from that valid for z = 10 min. The appli- cability of the known equation from physical chemistry for even longer times renders it highly probable that it would hold for the limit-value, which would be reached in an ex- ceedingly short time of observation, if it were possible to observe it directly. In heterogeneous systems the direct observation of the velocity of reaction meets in most cases with great difficulties, as has been indicated above, so that the indirect observations such as those executed by Madsen, Noguchi, and Walbum are necessary to obtain a knowledge of these phenomena. I therefore reproduce the values of p found by them for different bases and acids. The interval of temperature was always between about 17 and 39° C. The experiments were arranged in the same manner as those dealing with ammonia. These figures give occasion to remarks similar to those made regarding the behaviour of ammonia. If we could carry out experiments extended through a very long time, 110 LECTURES ON IMMUNITY 0.2 n. SODIUM o 2 n. POTAS- o.i n. FORMIC i n. ACETIC i n. PROPIENIC i n. BUTYRIC HYDRATE SIUM HYDRATE ACID ACID ACID ACID Time Time Time Time Time Time min. ^ min- c- min. min. nun. f- min. ^ 10 15,200 10 11,700 10 8,800 10 23,600 10 24,900 10 21,600 20 9,500 20 9,200 2O 7,600 15 22,2OO 20 1 8, 100 20 19,900 30 9,400 30 8,300 30 4,300 20 18, 100 30 15,900 30 15,200 40 9,200 40 8,000 40 2,600 40 15,500 40 15,100 40 14,000 50 7,400 60 6,100 50 2,900 50 14,200 60 13,700 50 13,200 60 7,200 120 5,200 180 900 60 13,200 90 7,700 80 6,900 180 4,100 90 8,800 120 5,100 loo 6,300 1 20 7,500 180 4,800 180 5,700 2IO 5,IOO i n. MALEINIC ACID i n. CITRACONIC ACID i n. ITACONIC ACID o.i n. OLEINIC ACID Time „ Time „ Time „ Time „ min. min. min. min. 10 12,700 10 13*500. 15 17,000 10 25,800 20 9,100 20 11,700 20 I5,60O 22 23,400 30 8,300 50 4,400 the temperature would probably exert a very minute influ- ence. To attain a certain effect, for instance total haemolysis or the first appreciable trace of haemolysis, a certain amount of acid or base would be necessary, equiv- alent to the quantity of erythrocytes present. Madsen and I found the following values (q) of 0.05 n. NaOH or 0.037 n- NH3 to be the greatest quantities which could NaOH NH3 n ?obs. ?calc. ^obs. ?calc. 20 0.60 0.60 0.82 0.82 10 0.27 O.3O 0.42 0.41 5 0.14 O.I5 O.I9 0.20 2.5 0.09 0.075 O.I I O.IO 1.25 0.047 0.038 0.055 O.O5 0.62 0.018 O.OI9 0.027 0.025 0.31 O.OII O.OIO 0.014 0.013 VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS III be added without producing a sensible effect on 10 c.c. of an n per cent suspension of horse-blood. The calculated values are obtained under the assumption that 0.6 c.c. of the 0.05 n. NaOH solution, which corresponds to 0.082 c.c. of the 0.037 n. NH3 solution, are equivalent to 10 c.c. of a 20 per cent suspension in producing the first trace of haemolysis. This idea of the equivalency is evi- dently true, though the time of reaction was here only one hour at 37° C. To this corresponds indeed the fact found by Madsen and Walbum that equivalent quantities of the four bases investigated (namely, NH3, NaOH, KOH, and Ba(OH)2) must be added to the same quantity of blood to produce the first trace of haemolysis. For 19 different acids the corresponding quantity was in all cases equivalent, but it was double as great as for the bases. The time of reaction was 24 hours at 16.2° C. Here we have evidently not to do with a velocity of reaction, but with a strong chemical binding of the acids or the bases to some sub- stance in the erythrocytes. The same is true according to the experiments of Madsen, Walbum, and Noguchi 1 even for the other reaction which they observed, which was not far from complete haemolysis, if we regard the figures for prolonged times and high temperature (37-39°), where the reaction has nearly come to an end. The three bases yield for this end-value : KOH, 0.008; NaOH, 0.008; and NH3, 0.0075 c.c. respec- tively of i n. solutions; within the errors of observation these quantities are equivalent. For the acids examined we find the following figures (in c.c. of i n. solutions): formic, 0.012; acetic, 0.015 ; propionic, 0.017; butyric, 0.017; 1 Madsen, Noguchi, and Walbum : Oversigtt 1904, No. 6, pp. 425 and 447. 112 LECTURES ON IMMUNITY maleinic, 0.013; an(i citric acid, 0.012. These figures do not differ very much from each other; they are really a little higher for the weaker than for the stronger acids, perhaps indicating a slightly marked hydrolytic effect. But on the whole they indicate a combination, although of not quite so strong a nature as with the bases. For very long times of reaction we therefore observe no real velocity of reaction, but a binding, and hence we might expect that for these long times of reaction the values of /* converge to zero. This convergence takes place much earlier for the strong acids and bases, which react more rapidly, than for the weak ones. Thus, for instance, a dosage of o.i c.c. normal NH3 needs 210 minutes to yield the same haemolytic effect that the equivalent quantity of the three strong bases exam- ined give in 15 minutes (at 16.2°); and an addition of 0.05 c.c. of dichloracetic acid produces the same hasmolytic effect in 5 minutes as the equivalent quantity of acetic acid in 60 minutes. Therefore even the shortest time (10 minutes) used in these investigations of strong acids or bases seems to be much too long to give a value, ft0, for ft, which approaches that for an infinitely short time, corre- sponding to the real value for the velocity of reaction. On the other hand, the values for the shortest times for weak acids do not differ much from each other, and probably also not from the theoretical limit-value, which seems to be about p= 27,000. A little higher, perhaps, lies the true limit-value for ammonia, p= 29,000. These limit-values are probably valid even for the other acids and bases. The great difference in the speed of reaction between the strong and the weak bases and acids seems to indicate that we have even here to do with an ionic reaction, although the VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 113 differences would be much greater than those observed if the phenomenon were not disturbed by the relatively long time of observation. Oleic acid differs rather widely from the other acids, exhibiting the same effect as about five times larger quan- tities of other weak acids. The haemolytic agent in this acid is therefore probably not only the hydrogen ion, as in other acids, but the undissociated molecules exert also a haemolytic action. The lysins of bacterial origin reach the end-value of their haemolytic effect much more slowly even than ammonia. Hence it is probable that the deduced value of p for these substances does not differ materially from the theoretical value. I reproduce some figures from Madsen and Walbum's series : — INFLUENCE OF TEMPERATURE ON THE ACTION OF LYSINS OF BACTERIAL ORIGIN STREPTOLYSIN (20 MIN.) VlBRIOLYSIN (20 MlN.) TETANOLYSIN (60 MIN.) Temp. fobs. ?calc. Temp. fob*. ftffc. Temp. fobs. *cale. 36.1 3I-I 25.8 22.9 0.08 0.20 0.40 1.30 0.08 0.21 0-54 I.I5 35-3 29.8 26.3 20. 6 0.17 0.25 0.4 I.O 0.10 0.25 0.4 I.O 30.4 25.6 21.9 154 0.40 0.50 0.80 1. 00 o-37 0-53 0.66 I.OO I2.I 1.30 1.27 ju= 31,900 H = 27,300 A* = 10,900 The values of /* for streptolysin and vibriolysin probably do not differ very much from the limit-value, /*0. A com- parison of the observed with the calculated values seem to indicate rather great errors of observation, which make the value of //. relatively uncertain. For vibriolysin, there LECTURES ON IMMUNITY are given four values corresponding to the times, 20, 40, 100, and 180 minutes respectively ; they are 27,300, 24,400, 19,300, and 15,800 respectively. They seem to indicate that the limit-value lies a little above 27,300, but the calcu- lation would give a better agreement if, in the first in- stance, /*> were fixed at 25,000, which value therefore per- haps comes near to the end-value. The only statement that can be made is that these values are of nearly the same magnitude as those for the haemolytic action of (weak) acids and bases, and that a closer investigation might bring them into agreement; this would have a physical meaning, namely, that it is probably a change in the con- dition of the erythrocytes that causes the increase of the reactivity with temperature. Two other haemolytic substances have been investigated by the same authors, namely, the oleate of sodium and triolein. They gave, with the same suspension of erythro- cytes as was used in the other experiments, namely i per cent of red cells from the horse, the following results : — HAEMOLYSIS BY MEANS OF o.oi n. SODIUM OLEATE (10 MIN.) o.oi n. TRIOLEIN (15 MIN.) Temp. ?obs. tfcalc. Temp. fate. (7calc. 36.3 0.125 0.125 38.9 0.17 0.17 31-4 O.I4 O.I4 35-7 0.20 0.20 24.1 0.18 o. 16 30.9 0.32 0.26 15-9 0.19 0.19 24.0 0.40 0.40 12 0.20 0.21 4 0.25 0.25 ^ = 3800 n = 1 3,800 With regard to the magnitude of /*, the oleate and the VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 115 triolein seem to differ from the other lysins. The formula gives the observed results within the limits of the errors of observation. The change of the agglutinating power with temperature was investigated in an analogous manner. The values for mercuric chloride, ricin, coli- and typhoid-agglutinin are given below for the shortest times used : — INFLUENCE OF TEMPERATURE ON AGGLUTINATION BY MEANS OF o.i n. HgClj (45 Mm.) RICIN (30 MIN.) Temp. tfobs. ?calc. Temp. tfobs. tfcalc. 35-8 0.085 0.085 36.2 0.05 0.05 30.9 O.IS 0.15 27.9 0.12 O.I I 25-9 0.25 0.24 I5.6 °-33 § o-37 21.9 o-55 0.36 IO.I 0.70 0.66 16.1 0.60 0.65 0.9 1.30 1.80 12.3 1. 00 0.98 ^=17,900 /t= 17,200 COLI-AGGLUTININ (lO MlN.) TYPHOID-AGGLUTININ (10 MIN.) Temp. ?obi. ftalc. Temp. ?obs. ?calc. 38.6 0.005 0.0043 38.2 0.002 0.002 34-9 0.0055 0.0072 3I.I 0.007 0.0083 30.9 0.015 0.0135 27.4 O.O2 O.OlS 24.9 0.045 0.042 19.2 0.13 0.09 21.2 0.065 0.068 15.9 0.20 0.20 I2.9 0.30 0.30 "•5 0-55 °-55 /i = 3o,ioo /t= 37,200 The two agglutinins acting upon equine erythrocytes give remarkably similar values of /*, although the time of reaction is rather long. The values of /* for longer times seems to indicate that the limit-value of p for the two bacterio-agglutinins Il6 LECTURES ON IMMUNITY probably differs little from that given above. They are for the typhoid-agglutinin, /^40 = 33,000, /-t120 = 18,700, and ^180=8soo (the indices represent the time in minutes). For the coli-agglutinin there are two different series. The one proceeds regularly, so that p sinks with increasing time. In the other series an irregularity occurs ; the /rvalue at first sinks, then passes through a minimum and thereafter through a maximum, and then later on falls toward zero with increasing time. The two series were carried out with the same preparations, so that the differences may be regarded as purely accidental. But the limit-value /^0 seems to be nearly the same in the two series. The phenomenon of agglutination bears a great simi- larity to that of haemolysis in its dependence on time and temperature. We know from Eisenberg and Volk's ex- periments that the absorption of the agglutinins reaches the state of equilibrium in a few minutes (less than 5). But still the agglutination continues through hours, espe- cially at low temperatures. The phenomenon proceeds with time just as does haemolysis, although the haemolytic substance is absorbed before the time of the first observa- tion. The following figures, giving the quantity of coli- agglutinin necessary to reach the observed degree of agglutination at 36.6 and 12.3° C, may illustrate this peculiarity : — Time (min.) 20 30 50 65 80 120 (? obs. at 36.6 4 i 0.5 0.2 0.13 o.i (? obs. at 12.3 85 26 10 2 1.6 0.32 The figures indicate that the limit-value for infinite time is nearly reached in 120 minutes at the higher temperature, but not for the lower one; and that this limit-value is of VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 1 1/ the same order of magnitude (probably equal) in the two instances. The progress of agglutination with time indi- cates that after the agglutinin has been absorbed (in the first five minutes) some change (probably coagulation) takes place slowly within the bacteria, which thereby obtain their agglutinating properties. In the same man- ner, after a haemolysin has been very rapidly taken up by erythrocytes, these are subject to a slow chemical change, which causes them to give up their colouring matter. This circumstance seems rather incompatible with the commonly adopted idea that the agglutination might depend upon some electric charge of the bacteria, due to the absorption of the agglutinin, since the electric charge very likely follows immediately upon the absorp- tion of agglutinin. These far-reaching investigations of Madsen and his pupils have also made us familiar with some substances, the action of which increases with sinking temperature, or has a maximum or minimum at a certain temperature. H^EMOLYTIC ACTION AT DIFFERENT TEMPERATURES POISON OF WATER-MOCCASIN COBRA POISON STAPHYLOLYSIN Time, 5 min. Time, 15 min. Time, 15 min. Time, 15 min. Time, 45 min. Temp. ?obs. Temp. ?obs. Temp. ?obs. Temp. fobs. Temp. ?oba. 39-3 0.38 39-3 0.28 37-3 0.225 36.5 0-35 36.4 0-35 35-2 0.36 35-2 0.28 30.8 0.25 29.1 0.17 28.6 0.08 30-7 0-35 30-7 0-3 24.1 0.30 24-3 0.23 24.4 0.07 28.2 0-35 28.2 0-33 17.7 0.30 19.5 0.33 19.7 0.075 19.2 °-3 19.2 o-3 14.2 0.25 I3.6 1.8 "•3 0.6 14.8 o-3 14.8 0.25 10.8 0.25 10.6 0.25 10.6 0.23 Il8 LECTURES ON IMMUNITY As illustrations may be given the haemolytic action of the snake-venoms of the water-moccasin (Amis trod on piscivorus), and cobra (Naja tripudians) and of staphy- lolysin, produced by staphylococcus. The snake-poisons were tested on horse-blood, the staphylolysin on rabbit-blood. Probably the observed phenomenon is of complex nature. A maximum effect might result if the haemolytic agent were decomposed with increasing temperature. At low temperatures, then, where the decomposition is insignificant, the poisons be- have normally, the velocity of reaction increases with tem- perature. If then at higher temperatures the decompo- sition or dissociation of the^ poisonous substance increases more rapidly with temperature than the velocity of the real reaction, then the quantity of poison necessary for a given haemolytic effect (in a given time) must increase with temperature. A closer investigation of these complicated phenomena will be necessary to show whether an explana- tion analogous to that sketched above may be assumed. The phenomena studied above in this chapter are, gen- erally speaking, due as well to velocities of reaction as to real chemical equilibria. These prevail the more, the longer the time of reaction and the higher the tempera- ture. The observations have great importance because they correspond to the method of working actually used, which is determined by the nature of the material em- ployed. Hence their discussion is useful for the compre- hension of the results of the ordinary method of working, and for the arrangement of similar experiments. There- fore I have discussed them in a rather detailed manner, although their theoretical meaning is not very simple. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 1 19 Rather similar to these haemolytic and agglutinating processes in which the chemical attack is directed against cells suspended in the acting medium, are some other processes in heterogeneous systems, namely, the decom- position of coagulated protein, or of small emulsified fat drops by so-called Upases. These processes are not very different from those in homogeneous systems. The coagulated proteins are introduced in the state of a fine powder and the suspension held in uniform concentration in all its parts by shaking. In this manner the digestion of coagulated egg-white by means of pepsin (Sjoqvist) or for the digestion of casein by means of trypsin (Madsen and Walbum) have been examined. Perhaps the most important of the processes is the diges- tion of coagulated albumen by pepsin (in the presence of acids). Regarding this process Schutz * had found the rule, that the digested quantity of albumen hydrolysed in a given time is proportional to the square root of the time and of the concentration of pepsin. Against the figures of Schutz, which, according to a criticism of Sawjalow,2 give no very accurate results, he quotes the experiment of Sjoqvist3 as indicating that the reaction is proportional to the time, i.e. follows the laws for a monomolecular reaction. In Sjoqvist's experiment the protein was coagu- lated egg-albumen in the state of a powder, which was brought in 100 c.c. of a solution at 37° C. containing 50 c.c. of o.i n. hydrochloric acid, 2.5, 5, 10, or 20 c.c. of a 0.067 per cent solution of pepsin and water to con- 1Schiitz: Zeitschr.f. ph. ch. v. Hoppe-Scyler, 9. 557 (1885). 2 Sawjalow: Zeitschr. / ph. ch. v. Ifoppe-Seyler,$Q. 307 (1905). 3 Sjoqvist: Skand. Archiv. f. Physiologic, 5. (1895). 120 LECTURES ON IMMUNITY stant volumes. After a certain time ( i to 20 hours) a sample of the solution was cooled to o° C., the albumen was cen- trifugalised, and the content of nitrogen in the liquid determined according to the method of Kjeldahl. In this manner the digestion was followed. Sjoqvist found that the same quantity (<2) is digested if the time (/) of digestion is inversely proportional to the concentra- tion (c) of the pepsin, as is shown by the following figures : c t (hours) Q o-5 16 6.90 i 3 6.70 2 4 6.77 4 2 7.00 During the first time there are some deviations. The progress with time is indicated by the following figures t (hours) ?obs. tfcalc.l ?calc.2 o-5 2.25 3-14 2.18 i 3-16 3-47 3.00 2 4.08 4.08 4.04 3 4.72 4.64 4.78 4 5-24 S-'S 5-35 6 6. 10 6.04 6.21 8 6.84 6.77 6.84 10 7-38 7-39 7-35 12 7.84 7.90 7.76 16 8.54 8.67 8-39 20 8.94 9.21 8.83 30 9-39 9-93 9-43 40 9.85 10.21 9.90 oo 10.40 (10.40) (10.40) The calculated figures <2calc>1 are found from the com- mon formula for the monomolecular reaction, those signed £^.2 from the formula given above for the digestion of VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 121 dissolved egg-albumen. As will be seen, the latter formula agrees very closely with the experiments, and much better than the common formula for monomolecular reactions. This indicates that the digestion follows the same laws in both cases. In experiments on digestion there is often used a method of including the coagulated albumen in short capillary tubes, so-called tubes of Mett. By the aid of this method Borissow found the rule of Schiitz to be valid, if a solution of acid and pepsin diffused into the tubes ; whereas Sawjalow, who mixed the pepsin with the albumen, found then that the height of the digested albu- men-pillar was proportional to the quantity of pepsin, and not to the square root of it, as Borissow had found. As is seen above, the results of Sjoqvist agree in the most satisfactory manner with the values <2calc.2, which for short times coincide with values calculated from Schiitz's rule. It should be emphasised that experiments with Mett's tubes ought not to be used in investigating these questions. For in them the rate of diffusion interferes with the chem- ical reaction, and if it is the slower of these processes, it causes the digestion to proceed proportionately to the square root of the time and concentration. An analogous experiment may be made with diffusion of alkali into a Mett's tube filled with an acidulated jelly solution plus phenolphthalein. At a given time (/) the concentration of alkali in the Mett's tube surrounded by a solution of the concentration 2 is at a given point double as great as at the corresponding point in a Mett's tube surrounded by an alkaline solution of the concentration i . Now the height to which the alkali in a given concentration has reached 122 LECTURES ON IMMUNITY after a certain time (/) is proportional to its square root. Therefore at the time — — the distribution of alkali in the V2 first tube is nearly the same as the distribution of alkali in the second tube after the time /. This may be seen in the height of the pink-coloured column of jelly which is the same in the two cases. Experiments with the diffu- sion of pepsin are of quite the same type. The indicator is in this case not the reddening phenolphthalein, but the liquefying solution of albumen. — One measures the length of the liquefied albumen-pillar at a given time. — Therefore Pawlow's and Borissow's experiments, which indicate that the liquefaction of coagulated albumen or gelatin goes on proportionally to the square root of time or of reacting enzyme (pepsin, trypsin, etc.), are not conclusive in favour of Schiitz's rule. A process which is very analogous to the digestion of egg-white is that of the saponification of fats by means of gastric juice or of extracts of gastric tissues (steapsin). Volhard l used glycerine extracts of the pig's stomach and observed that the quotient, q : V/= ^> of the digested quantity q (in per cent), and the square root of the concentration of steapsin, /, is nearly constant. This ob- GLYCERINE EXTRACT (24 HOURS) GASTRIC JUICE (i HOURJ / ? k / ? k i 4-7 4-7 i 4.1 4.1 4 8.5 4-3 4 II. 2 5.6 9 15.0 5-° 9 17-3 5.8 16 19-5 4.9 16 21.3 5-3 25 24-5 4.9 1 Volhard ". Ztitschr.f. klin. Medicin, 42. 414, and 43. 397 (1901). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 123 servation was confirmed by Stade,1 as may be seen from the above figures (temp. 40°). If the digestion proceeds further than 25 per cent the rule of Schiitz is no longer applicable. We then may use the general formula (p. 64) as is seen by the next figures valid for digestion by gastric juice during 16 hours at 40° C. (.AT/* =27): — / fobs. fMfc I 21.6 21.6 4 40.7 39-6 9 50-9 54-6 16 674 66.7 Stade has further done a series of measurements of the progress of saponification of an emulsion of the fat from the yolk of egg by neutralised gastric juice. These measure- ments follow nearly the same formula as those of Sjoqvist, as may be seen from the calculated values. PROGRESS OF SAPONIFICATION OF YOLK OF EGG BY MEANS OF GASTRIC JUICE TIME (hours) fobs. tfcalc. TIME (hours) ?ObB. fcalc. 2 20.4 1 8.6 12 24.1 24.5 4 25.6 257 16 254 27.9 6 29.8 30-8 21* 28.5 314 8 35-3 34-8 37* 39.5 40.0 10 37-6 38.3 39* 39-8 40.9 25* 49-5 55-2 43* 41.7 42.6 29* 5i.5 58.2 46 46.2 43-8 31* 554 59-6 65 53-6 50.2 35* 60.9 62.0 75 77-5 78.4 1 Stade : Hofmtistcrs Beitr'dge, 3. 291 (1902). The dates with an asterisk are the means of two measurements. 124 LECTURES ON IMMUNITY The constants, KP, are respectively 10 and 3. For short times the digested quantity is proportional to the square root of the time, so that if as well time, t, as quantity,/ of steapsin change, the digested quantity is proportional to the square- root of the product of f- 1. Even this rule has been verified by Stade. Stade's work has been repeated by Engel1 for the glycerine extract of " pancreatin Rhenania " as well as for gastric juice, acting on an emulsion of egg-yolk. The following figures reproduce two series of observations, the one at 30°, the other at 40° with 1.24 times as much extract of pancreatin. The time of digestion was 6 and 18 hours respectively. From these observations we may calculate the variation of K with temperature. We so find /JL = 15,600. t= 30° C. / = 40° C. /-I A>bs. = 4-7 Aalc. = 5 ° /= 1.24 A>bs.= 12.8 Aalc.= *4-i 4 IO 9.8 4.96 24.7 26.8 9 15 14.6 ii. 16 39-5 38.2 16 19-5 IQ.O 19.84 51.6 48.2 25 22.3 23.4 31.0 59-5 57-i 36 24.4 27.6 44.64 63.1 64.8 ^ = 1.3:6 JT= 8.9:18 Stade has furnished some measurements on the in- fluence of the concentration (c) of gastric juice at 40° C. on this process, which we reproduce below. The tabu- lated figures concern the hydrolysed quantity in per cent 1 Engel: Hofmeisters Beitrage, 7- 77 (1905), VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 125 TIM EOF ACTION TIME OF ACTION TIME OF ACTION TIME OF ACTION TIME OF ACTION i HOUR 4 HOURS 9 HOURS 16 HOURS 25 HOURS c Abs. Aalc. Abs. Aalc. Abs. Aalc- Abs. Aalc. Abs. Aalc. I 4.1 6.2 13.7 I2.I 19.2 I7.8 21.6 23.2 31-5 28.4 4 II. 2 I2.I 28.0 23.2 39-8 33-3 40.7 42.5 46.0 5°-7 9 17-3 I7.8 38.9 33-3 494 46.7 5°-9 58.0 65.6 67.6 16 21.3 23.2 44.0 42.5 52.9 58.0 57-4 70.3 73-6 79.6 25 23.6 28.4 45-4 50-7 63.3 67.6 68.4 79.6 74.1 88.1 If we calculate the constants for the five series, we find: — 1.8 10.7 21 27 and 41 or 1.1,8 4.2,7 9.2,3 16.1,7 and 25.1,64 or in mean the constant is 2 t. With this constant the calculated figures are obtained. The observed values agree in general as well as might be expected with the calculated ones, and probably the deviation is not greater than might be referred to the experimental errors. (Per- haps real or so-called false equilibria disturb the observa- tions for high values of /.) The seeds of Ricinns communis (castor bean) contain an enzyme which decomposes the oil from these seeds into fatty acid and glycerine. This process seems also to follow the same laws as the decomposition of fats by gastric juice. I reproduce some figures from the article of Connstein, Hoyer, and Wartenberg.1 They prepared an emulsion by grinding 5 g. of Ricinus seeds and 6.5 g. of castor oil, and thereafter adding 4 g. of an acid. The 1 Connstein, Hoyer, and Wartenberg: BerichU d. d. chtm. Gcs., 35. 3988 (1903). 126 LECTURES ON IMMUNITY emulsion was held at constant temperature and at given times samples were removed and titrated for their free acid. (The acid initially added was subtracted.) The first figures concern an emulsion in o. I n. sulphuric acid, the later figures are found for emulsions in o.i and 0.4 n. acetic acid. SULPHURIC ACID o.i N. ACETIC ACID o.i N. ACETIC ACID 0.4 N. Time (min.) A>bs. Aalc. Time (hr.) Abs. Aalc. Time(hr.) A>bs. /calc. 15 12 20 I 50 48.6 I 65 63-9 30 20 27 2 65 62.8 2 86 78.8 45 30 32 3 70 7*-S 3 84 86.5 60 33 36 4 72 77.6 4 84 91.2 90 4i 43 24 8o(?) 99-5 24 9i(?) 99.9 15° 54 53 210 59 59 330 68 69 1620 8i(?) 97 The constants are 1.47 for the first, 180 and 380 respec- tively for the later experiments. The deviation of the figures for the later times seems to indicate that we have here to do with either real equilibria in the presence of lipases acting on ethylic butyrate, mono- glycerid of butyric acid, and triacetin, and known from Kastle and Loewenhart's, Hanriot's, and A. E. Taylor's in- vestigations,1 or some perhaps false equilibrium. These are very common with enzymes, as Tammann (I.e.) found. Even the figures for less than 45 minutes indicate a devia- tion from the premises of the calculation. There are also 1 Kastle and Loewenhart : Amer. Chem. Journ., 24. 491 (1900) ; Hanriot, C. R.t 132. 212 (1901); A. E. Taylor: Journ. Biol. Chemistry, 2. 87 (1906). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 127 some observations regarding the influence of the quantity of enzyme. With 0.5 g. of Ricinus seed were emulsified 5, 10, 15, 20, 25, or 50 g. of Ricinus oil and the same quantities of 2 per cent acetic acid. The results are indicated in the table below. The calculated figures are found under the assumption that the acting mass of the enzyme is proportional to its quantity. The agreement be- tween calculated and observed values is very satisfactory, except for the greatest quantities. The constant for two days is, within the errors of observation, double that for one day. The concentration in the presence of 50 g. oil and 50 g. acid is taken as unit. ACTION OF 0.5 G. RICINUS SEEDS ON DIFFERENT QUANTITIES OF RICINUS OIL AFTER i DAY AFTER 2 DAYS Oil Acid Ab.. >calc. A>b8. Aalc. 50 5° 49 49 49 59 25 25 60 63 74 74 20 2O 7' 69 80 78 15 IS 77 75 87 84 10 10 81 83 86 9i 5 5 89 94 92 98 KP = 186 KP= 300 In this case the presence of a certain quantity of free acid, about 4 c.c. of a 0.2 normal solution, the same quantity for all acids, weak or strong, is necessary. This circumstance resembles very closely the action of acids in peptic digestion. If no acid is added, the acid in the seeds acts, and new acid is procured by the process. A lipolytic process, which probably should be regarded as occurring in a homogeneous system, is that studied by 128 LECTURES ON IMMUNITY Zeller l on the lipolytic agent in the mushroom (Amanita muscarid). An aqueous extract of the powder of this mush- room had no lipolytic action. But if the powder were mixed with olive oil or tallow, they were slowly decomposed. I reproduce some figures for olive oil. In this case the reac- tion is decidedly monomolecular (the constant used for the calculation is 0.00045). The acid from the olive oil evi- dently has no sensible influence on the enzyme. Time (hours) 48 118 160 304 485 631 Decomposition (per cent) 4.8 11.5 14.2 28.5 38.9 46.3 Decomposition (calc.) 4.8 10.9 15.3 27.0 39.5 48.0 Regarding the lipolytic action of the cytoplasma of the seeds of Ricinus commtmis, a large number of experi- ments have been carried out by Nicloux.2 He found that the catalytic agent is not soluble in water, which seems to arrest its action. The conditions of the reaction seem, therefore, to have been nearly the same as in the ex- periments of Zeller. The reaction proceeds (at low tem- peratures) very closely according to the law valid for monomolecular reactions. The cytoplasma was suspended in the oil examined, in most cases cotton oil, and thereafter water containing a small quantity of acetic acid was added. The following figures, valid for 18° C., indicate that the process is monomolecular : — Time (min.) 30 45 60 90 127 150 210 450 Saponification, per cent (.*•) 23.6 33.1 40.4 54.8 67.0 73.2 85.5 94.4 K=— log IOQ _ x 0.388 0.387 0.375 °-382 °-392 0.381 0.399 0-278 1 Zeller : Sitz. ber. d. Ak. d. Wiss, zu Wien (chemical memoirs = Monat- shefte fur Chemie), 36. 727 (1905). 2 M. Nicloux: C. R. de la Soc de. Biol. 56. I. 701, 702, 839, 840, and 868 (1904). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 129 At higher temperatures, above 25° C., the constant K decreases during the period of reaction, as will be seen from the following figures, which give the mean values of K.icr* during the time intervals 30-90 and 90-180 min- utes. From these an extrapolated value for the time o, the beginning of the reaction, is calculated : — Temp. 5 10 15 20 25 30 35 40 45 o min. 7.7 12.5 14.6 20.6 26.6 30.3 40.1 34.4 27.2 30-90 min. 9.0 12.6 13.7 19.3 24.2 26.6 29.7 19.2 10.5 90-180 min. 6.3 12.4 15.4 21.9 21.5 22.6 20.4 9.1 3.2 60 — -.- — — — — — 0.041 0.057 0.130 0*259 0.413 K has a maximum at about 37° C. This evidently depends upon the rapid destruction of the catalytic agent at higher temperatures. Nicloux has found that at 55° C. its action is totally nullified in ten minutes. This destruction is measured by the decrease of log K during the progress of the saponification, if the process is monomolecular, as indicated by the values found at lower temperatures. At temperatures below 2 5° C. this decrease is insensible; at higher temperatures the destruction of the enzyme proceeds at about double the speed with increase of the temper- ature of 5° C. This corresponds to a value of p = 26,000. The extrapolated value of K itself at the time o shows a remarkably small increase with temperature. An increase of about 14° C. is necessary to increase it in the proportion 2 to i. The value of p calculated from the figures for 10° and 30° C. is only 7540. This investigation affords a good insight into the real meaning of optima. If we regard the time o, the optimum 130 LECTURES ON IMMUNITY seems to occur at about 37° C. In the interval, 30-90 min., the optimum seems to lie at about 33° C., and in the interval 90-180 min. at about 29° C. The position of the optimum evidently depends on how rapidly the experi- mental manipulations are done. If it were possible to examine K immediately after mixing the reagents, the optimum would probably be found to lie at a much higher temperature; or there would perhaps be no optimum at all. It is worthy of mention that the dry cytoplasma sus- pended in pure oil resists a temperature of 100° C. for twenty hours ; at 120° C. its activity decreases one-third in a quarter of an hour. Quite recently A. E. Taylor1 has carried out an investi- gation on the action of the lipase from the castor bean on the triglycerid of acetic acid, commonly termed triacetin. This compound is rather soluble in water, so that homoge- neous solutions were prepared containing 0.5, I, or 2 per cent (up to 3 per cent) of triacetin together with i g. of the powder of castor beans, from which the fat had been extracted, in looc.c. of water. The following values were obtained, indicating a monomolecular process. The I A. velocity-constant is K =- log • io4- t ./JL —~ X The agreement between the three values of K indicates that the decomposed quantity is very closely proportional to the quantity of the substrate. The regularity of this process is evidently higher than that of any other ferment- ative action hitherto studied. The velocity of reaction in- creased in the proportion of i to 2.6 if the temperature 1 A. E. Taylor: Journ. Biol. Chemistry, 2. 87 (1906). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS l$t was elevated from 18° C. to 28° C. This corresponds to a value for p of 16,700. SAPONIFICATION OF TRIACETIN BY MEANS OF LIPASE FROM THE CASTOR BEAN AT i8°C. (A. E.TAYLOR) / (hours) 0.5 PER CENT I PER CENT 2 PER CENT A -X K A - X K A - X K O 100 — 100 — 100 — 4 90.4 109 91.7 94 90.2 112 8 83.8 96 82.6 104 82.6 104 16 71-3 92 66.2 112 67.7 1 06 24 58.2 98 58.2 98 56.9 102 28 51-1 104 51.2 104 49.8 108 32 52-3 88 45-8 1 06 51-5 90 40 37-7 106 39-1 102 40.5 98 48 34-8 97 34-5 96 36.4 9i Mean 99 102 101 Taylor thereafter investigated a suspension of triolein (2 per cent) in water containing I g. of castor bean powder in 100 c.c. The liquid was shaken vigorously. He found the following values of A — x for the days, termed t. SAPONIFICATION OF A 2 PER CENT EMULSION OF TRIOLEIN AT i8°C. BY LIPASE FROM THE CASTOR BEAN (TAYLOR) / (days) 012 3457 9111518 A—x loo 97 95 92.5 91 89 84 78.4 72.8 66.9 61.9 x:t — 3 2.5 2.5 2.3 2.2 2.3 2.4 2.5 2.4 2.1 Here evidently the transformed quantity (x) is, as the last line indicates, proportional to the time. This is easily explained. Through the strong shaking the water is a concentrated solution of triolein, its content of triolein is constant, independent of time. Therefore, as the concen- 132 LECTURES ON IMMUNITY tration of the ferment is also unaltered in time, the quan- tity of triolein decomposed in the unit of time is constant, and the total quantity proportional to the time of reaction. We might perhaps at first expect, with Taylor, that the velocity of reaction might increase about in the proportion 1:2.6 for an increase of 10° in temperature; instead of this Taylor found the proportion 1:1.2. This will be easily understood if the solubility of the triolein diminishes in about the proportion i : 2.2 for an elevation of 10° C. The velocity of reaction will then increase in the proportion 2.6 i: — =1:1.2, as found by Taylor. Taylor's conclusion from the low value 1.2 that we do not observe a velocity of reaction but of some other 'process, such as diffusion, seems not very convincing. Kastle and Loewenhart1 had already (1900) found that the velocity of reaction of monobutrinwith animal lipase is proportional to the concentration of the ferment. Here we observe evidently a very simple monomolecular process. New investigations on the different results of Connstein, Hoyer, and Wartenberg seem therefore very desirable. Taylor found that the process is reversible, the ester may be formed from glycerine and fatty acid under the influence of the lipase. The equilibrium is reached very slowly and does not differ sensibly from that attained under the influ- ence of an acid. The following end-values were obtained by means of normal sulphuric acid and lipase (after several months): — 1 Kastle and Loewenhart : Amer. Chem. Journ. 24. 491 (1900), as cited by Taylor. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 133 EQUILIBRIUM IN SOLUTION OF TRIACETIN AT i8°C. (A. E. TAYLOR) CONCENTRATION HYDROLYSIS BY MEANS OF per cent H2S04 Lipase Calc. o-5 88 86 88 I.O 82 79 80. i 2.0 78 70 69.8 The calculated values are found according to the law of Guldberg and Waage, under the assumption that the first figure (88) is correct. As will be seen, the figures found for the action of lipase agree better with the theory than those for the catalytic action of the sulphuric acid. As probably the same end-value is reached, be the catalytic agent sul- phuric acid or lipase, we conclude that the spontaneous hydrolysis of triacetin would reach the same end- value, and that the catalysor only accelerates the process, as is generally assumed and especially set forth by Ostwald. This circumstance, that equilibria are reached under the action of ferments, so that the reaction may be carried in the one or in the other direction, is a direct illustration of the fact that we may apply the laws of physical chemistry to biological science. The first discovery that ferments may synthetise as well as decompose was made by Hill l in 1898 and excited a very great interest. He found that it is possible to synthetise a maltose (according to Emmer- ling,2 it is an isomaltose) from glucose by means of yeast, according to the formula : — 2 C6H1206 C12H22On H20. 1 Hill: Journ. Chem. Soc.t 73. 643 (1898). 2 Taylor: University of California Publications, Pathology, Vol. I., 33 and 65 (1904). For references on literature see this last memoir. 134 LECTURES ON IMMUNITY The sign -^ indicates that the decomposition of the di- saccharide by means of yeast is also possible, and this is the normal process. In a similar manner it is possible to reverse this reaction under the influence of sulphuric acid as the catalysor, as was shown by Musculus, Wohl, and Fischer. Fischer and Armstrong synthetised isolactose by means of kephir yeast (lactase) from //-glucose and ^/-galactose. Kastle and Loewenhart, as well as Hanriot, accomplished the synthesis of ethyl and monoglyceryl butyrate by means of animal lipase ; and Taylor synthetised olein-triglycerid by means of lipase from the castor bean, but he did not suc- ceed in reversing tryptic digestion.1 Emmerling added a maltase from yeast to a mixture of glucose and nitril man- del glucoside and recovered amygdalin after the lapse of three months. As is seen from these illustrations, the reversibility of processes accelerated by ferments is a normal phenomenon. All the experiments cited which give a constant value of qt seem to indicate that even here the reagents dif- fuse into the small particles of the substance examined with such a speed that the time of diffusion may be re- garded as very low compared with the time of reaction. For the erythrocytes and bacteria this may be easily under- stood, because their linear dimensions are very insignifi- cant (cf. p. 25). This may even be the case for the 1 Quite recently experiments on the synthetic action of trypsin or pepsin seem to have been followed by success. Taylor (Univ. of Calif. Publ., Pathol. I, No. 9, 1907, p. 343) synthetised protamin from its products of decomposition by means of trypsin, and T. Brailsford Robertson (Univ. of Calif. Publ., Pathol. Ill, No. 9, 1907, p. 59) synthetised paranuclein from its products of decomposition by subjecting them to the action of pepsin. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 135 finely powdered coagula of egg-white or the emulsified fat drops in Volhard's, Stade's, and Engel's experiments. But with the pillars of coagula this cannot be said to occur. In this case we must suppose that the liquefied part of the column is carried away into the liquid about, so that this is able to attack new portions of the pillar. Here, therefore, the reaction is going on at the surface of the coagulated substrate, and immediately below it, and the constancy of the product qt shows that under constant conditions the number of molecules digested in one second is proportional to the concentration of the ferment in the surrounding liquid (and to the surface, which remains nearly constant). Madsen and Walbum have investigated the progress of dissolution of casein by means of trypsin. Ten g. of casein in the form of the powder were suspended in 100 c.c. of a i per cent solution of trypsin and held at constant tem- perature. In order to prevent the casein from subsiding, the flask containing the mixture was steadily shaken. After different time intervals samples were removed, and the undissolved quantity of casein determined by means of its content of nitrogen — determined according to the method of Kjeldahl. The progress of dissolution is shown by the following table (temperature, 34.1°) : — TIME (hours) NITROGEN (obs.) NITROGEN (calc.) TIME (hours) NITROGEN (obs.) NITROGEN (calc.) 0 O.I I O. II 48 O.o6o 0.058 o-5 0.108 0.109 72 0.0486 0.0464 2-5 O. IO2 0.105 101 0.0374 0.0376 6 O. IOO 0.099 125 0.0329 0.0325 ii 0.096 0.091 1 68 0.0274 0.0269 24 0.076 0.076 192 0.0236 0.0236 33 0.070 0.068 136 LECTURES ON IMMUNITY The nitrogen (calc.) is calculated according to the equa- tion for a bimolecular process, and, as will be seen, the agreement is very satisfying. The relation which, after Bayliss's experiment, is very unexpected, may be regarded as a purely empirical one. The reaction-constant is o. 173. It increases with temperature, as might be expected. At 37° C. it reaches the value 0.194, corresponding to an in- crease in the proportion 1.485 : i in an interval of 10° C. O =7400). Many of the most important processes of normal life occur in heterogeneous systems. As is seen from the fol- lowing examples, they behave as regards the velocity of reaction quite like enzymic processes. All of them pos- sess an optimum at about 4O°-5o° C., and in the vicinity of o° C. the velocity of reaction sinks rapidly with tempera- ture. The most important of these processes are the phenom- ena of assimilation and of respiration of carbonic acid by plants. As van't Hoff1 remarks, the observations of Clausen2 seem to indicate that in the interval of tempera- ture o°-25° C. the quantity of carbonic gas given off by seedlings of wheat, lupins, and flowers of syringa increases with temperature in the proportion 1 12.5 for an increase of 10 degrees (/i= 14,800). The three processes show an optimum at 41,38 and 42° C. respectively. Godlewski3 showed that the assimilation of a leaf of four different plants — the most regular results were those 1 Van't Hoff: Vorlesungen uber theoretischc und physikalische Chemie, 2d ed., 1. 224 (1901); E. Cohen: Vortrage f. Arzte, p. 43 (1901). 2 Claussen: Landwirtsch. Jahrb., 19. 892 (1890). 8 Godlewski : Arbeiten des botanischen Instituts in Wurzburg, 1. 243 (1872), VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 137 of Typka latifolia — increases with the content of carbonic acid in the surrounding air, and nearly proportionally with it, up to about 2 per cent. An optimum occurs at about 6 per cent. At further increase the assimilation decreases, but very slowly. This process was recently studied by Miss Gabrielle Matthaei,1 who found that the assimilation of carbonic acid by a leaf of Pnmus Laurocerasus increases with temperature in the following manner (for a leaf of 50 cm.2 and in one hour) : — TEMP. ASSIMILATION MILLIGRAMMES OF COz obs. calc. o 1-75 i-75 10 20 4.2 8.9 3-79 7.81 30 37 IS-7 23-8 15-3 23-8 The process is in all points analogous to the action of ferments. The chlorophyll may here be regarded as the acting ferment. The value of /* is 11,940. In these figures we observe already a greater increase at lower tem- perature than the formula indicates. If the temperature falls below o°, the assimilation sinks very rapidly, so that at —6° C. the observed figure is only 0.2 mg., correspond- ing to a value of /* between o and —6° C., about ten times greater than between o and 37. Above this latter tem- perature again the assimilation sinks with rising tempera- ture until the leaf dies. This evidently depends on a de- struction of the functions of the chlorophyll at very low or at higher temperatures. 1 Gabrielle Matthaei : Phil. Trans. Roy. Soc., Ser. B, 197. 47 (1904). Cf. Kanitz: Zeitschr.f. Elektroch.^ No. 42 (1905). 138 LECTURES ON IMMUNITY Similar observations may be made regarding the growth of eggs of animals after their fertilisation, as observed by Hertwig and Karl Peter.1 The development of these eggs was followed by means of observations of the cell-division which went on much more rapidly at higher than at lower temperatures. Even chemical influences, especially a small addition of hydroxyl-ions to the sea water, are often very remarkable. The eggs of Arbacia develop a little more rapidly in sea water containing 2 c.c. of o. I n. alkali in 100 c.c. of water than if no alkali has been added. An equivalent amount of HC1 retards the development.2 The increase (/) for increase of the temperature 10° C. and the corresponding value of ft are given below. They are valid for a mean temperature of about 16° C. : — Eggs of Echinus microtuberculatus — First stage /= 2. 29 yu, = 1 3,700 Later stages 2.03 11,700 Eggs of Sphtxr echinus granularis First stage 2.30 13,800 Later stages 2.08 12,100 Eggs of Ranafusca (Hertwig) First stage 2.23 13,300 Later stages 3.34 20,000 As we see, ^ is of quite the same order of magnitude as that for the production or assimilation of carbonic acid by green plants. Further, at low temperatures (3-5° C.) the />& for the eggs of the frog has a very high value — about ten times those given above ; and at the temperatures of over 37° C. the life process is hindered by increase of tem- perature. In a similar manner behaves the heart-beat of 1 Hertwig: Archiv f. mikrosk. Anatomic, 51. 319 (1898); Karl Peter: Archiv f. Entwicklungsmechanik, 20. 130 (1905). 2J. Loeb: Archiv / Entwicklungsmechanik, 7. 631 (1898). Cf. above, the influence of alkalies and acids on the velocity of destruction of lysins. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 139 the Pacific terrapin (Clemmys mamorata), according to ob- servations of Charles Snyder. 1 His observations give the following values for the number of heart-beats in one minute : — Temp. o 2.5 5 10 15 20 25 30 35 37.5 40 Number 0.75 3.2 4.9 7.8 9.7 20.7 27.3 46 48.6 48.2 43.3 Do. calc. 2.4 3.2 4.2 7.0 11.4 18.5 29.3 46 71 87.7 106 /-i is found to be 16,060. As is seen from the figures, the action of the heart has an optimum. This circumstance probably depends upon changes in the protoplasms near o° and 50° ; in the latter case coagulation occurs.2 There- fore the calculated values coincide with the observed ones only within a certain interval, 2.5-30 degrees. The rapid increase in the neighbourhood of the freezing point is very similar to that found for the two other phenomena of life studied above. Another process of great practical importance caused by living cells is the production of alcohol and carbonic acid from glucose by yeast plants. This process has been investigated very thoroughly by Aberson.3 He found that the formula of Henri is valid for this reaction, as will be seen from the following figures, in which the quantity of glucose (A — x) was determined by means of a polarimeter. A is the beginning concentration, A — ^rthe corresponding quantity after / minutes. The temperature was for the first series 17.5°, for the second 27° C. 1 Charles D. Snyder : University of California Publications, Physiology, 2. 125 (1905). 2 Loeb : Vorlesungen uber die Dynamik der Lebenserscheinungen, p. 155 (1906). 8 Aberson: Rec. d, tray. chim. /. Pays-Bas et de la Belgique, 22. 78 (1903), 140 LECTURES ON IMMUNITY PRODUCTION OF ALCOHOL BY MEANS OF YEAST t A - x , io5 , A + x K=TloSA^c t A- x .. io5 , A + jf *-=Tlog — 0 30-7 — o 30.5 43 29.9 26.3 41 28.3 76.5 107 28.7 26.5 86 25.8 78.5 196 27.1 26.1 149 22.6 77-3 269 25-7 26.5 240 18.2 77.2 393 23-5 26.4 300 I5.8 76.1 432 22.8 26.5 357 13.5 76.5 5'2 21.4 26.5 493 II.7 77-5 590 20.5 26.3 5H 9.6 76.5 613 19.7 26.5 529 8.1 78.1 790 I7.I 26.2 752 4.1 76.0 The mean values are 26.85 and 77- From these we cal- culate the value of ^ = 15,607. By means of this value Aberson calculated his other experiments, and found an excellent agreement with the observations. As illustra- tion the following figures may be cited : — TEMP. ^"obs. ^calc. 15-4 31.2 31.2 21.0 55.6 524 27.0 90.0 89.2 32.0 139.8 136.8 In many cases the quantity of yeast was augmented by cellular multiplication during the experiment; in such cases a correction for this circumstance was applied. The quantity of glucose, as well as that of the reaction-products, had an influence upon the constant, whereby the deviation of the velocity of reaction from that valid for monomolecu- lar reactions may be explained. VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 141 The production of alcohol and carbonic acid from glu- cose is, as Buchner showed, not a peculiarity for the living cell, as Pasteur had supposed, but may be performed by dead yeast-cells or an extract from them called zymase. With dead yeast-cells (Herzog)1 and with zymase (Euler)2 experiments have been carried out, — in the latter case the reaction occurs in a homogeneous medium. Euler followed the progress of the reaction by measuring the quantity of carbonic acid developed, or with the polarimeter the destruction of the sugar. The quantity of glucose was 20 c.c. of I n. solution. The quantity of zymase used was 3.6 g. in the first, 1.2 g. in the second series. PRODUCTION OF ALCOHOL FROM GLUCOSE BY MEANS OF ZYMASE OBSERVATIONS OF THE PRODUCED QUAN- TITY OF CO3 OBSERVATIONS WITH THE POLARIMETER Time,/(min.) A - x K 10* A Time,*(min.) A-x .10* A K=TlosA^ K ... bg-— 0 790 — O I075 — I98 709 2-37 81 1018 2.95 237 700 2.21 124 990 2.90 323 672 2.17 224 930 2.81 413 644 2.15 324 877 2.73 355 860 2.73 38i 851 2.67 406 841 2.63 730 700 2.55 Here we find a slow decrease in the values of K and not an increase, in which case the formula of Henri might be applicable. It is therefore probable that the agreement of Henri's formula with the measurements of Aberson is 1 Herzog: Hoppe-Seylers Zeitschr. 37. 149 (1903). 2 Euler: Hoppe-Seylers Zeitschr. 44. 53 (1905). 142 LECTURES ON IMMUNITY due to some perturbation introduced by the life-processes of the yeast-cells. Euler, however, also observed some complications which require additional experimentation before they can be explained. The velocity of reaction increases more rapidly than the concentration of the en- zyme, and not proportionally to a simple power of it. The quantity decomposed does not increase with the concentra- tion of the sugar, but shows on the contrary a relative decrease, if the concentration of sugar is raised. The study of the velocities of reactions in heterogeneous systems indicates that they behave very nearly in the same manner as in homogeneous systems. This observation has often been made concerning the velocity of reactions in heterogeneous systems.1 It depends upon the circum- stance that by means of the experimental arrangements the diffusion goes on so rapidly that it does not perturb the chemical processes. If capillary tubes are employed, this cannot be said to be the case, and therefore Mett's tubes should not be used for quantitative measurements. Even the influence of temperature on these reactions is of the same order of magnitude as for those processes in which different substances react with one another in homogenenous systems. Remarkable is the low value for the haemolysis by means of sodium oleate (/4 = 3800). The agglutination of erythrocytes by means of mercuric chloride and ricin give nearly the same values for //, (17,900 and 17,200) and the values for JJL for the two different bacterio- agglutinins are not of very different order (>i= 30,100 for coli-agglutinin, p= 37,200 for typhoid-agglutin). Near this value also stands that for haemolysins of bacterial 1 Cf . Goldschmidt : Zeitschr. / physikal. CAemig,&l, 235 (1899). VELOCITY OF REACTION. HETEROGENEOUS SYSTEMS 143 origin (streptolysin, //. = 31,900; vibriolysin, /-t = 27,300 ; for tetanolysin the time of reaction has been too long to yield correct value for /A). Close to these values are the highest ones of those for the haemolytic action of acids and bases (ammonia, ^ = 27,000; propionic acid, ^ = 25,000). The values of p for these substances have already been dis- cussed at length above. For comparison I tabulate the other values of JJL given in this chapter : — Digestion of powdered casein by means of trypsin ..../*= 7,400 Saponification of emulsion of yolk by means of pancreatic juice /* = 13,600 Respiration of different plants (mean value) p = 14,800 Production of alcohol by means of yeast-cell /* = 15,600 Assimilation process in plants /A = 12,000 Cell-division in different eggs (mean value) jx — 14,100 Heart-beats of the Pacific terrapin /A = 16,060 The p values are in general of the same order of mag- nitude as in the case of homogeneous reactions. The great similarity of the values of n for the different life- processes would scarcely seem to be accidental. COLLEGE OF DENTISTRY UNIVERSITY OF CALIFORNIA COLLEGE OF DENTISTRY UNIVERSITY OF CALIFORNIA CHAPTER V EQUILIBRIA IN ABSORPTION PROCESSES THE most simple of all processes belonging to this domain seems to be the absorption of agglutinin by the corresponding bacteria. If we add an agglutinin to a sus- pension of bacteria (whether living or dead makes little difference), the bacteria clump together and fall to the bottom of the container. If after the sedimentation of the bacteria, we decant the supernatant fluid and again deter- mine its agglutinating power, we find that it has decreased in large measure. We conclude, therefore, that a large fraction of the agglutinin has been absorbed by the bac- teria. Eisenberg and Volk have studied this phenomenon on a rather large scale. The two following tables give their results with the serum of a horse that had been in- jected with typhoid bacilli, and that of another horse that had been injected with cholera vibrions. Different con- centrations of these agglutinin-holding sera — prepared by dilution with physiological sodium chloride solution — were brought in contact with the same quantities of suspensions of typhoid bacilli or of cholera vibrios. The quantity of agglutinin added is given in the column headed T, the quantity of agglutinin absorbed by the bacteria is found under C\ the quantity remaining in the liquid is called .#ob8. Evidently BQ^ -f- C=T. In the next column is tabulated the figures for J3c&}c.t calculated in a manner to be indicated below. 144 EQUILIBRIA IN ABSORPTION PROCESSES 145 ABSORPTION OF TYPHUS AGGLUTININ BY TYPHOID BACILLI r C *ob, ^calc. K 2 2 o O.O2 — 2O 20 o O.y — 40 40 0 2.1 — 200 1 80 20 19.7 24.4 400 340 60 52.9 22.6 Mean 2,000 10,000 1,500 6,500 500 3>5°o 478 3,890 23.7 28.2 24.7 20,000 11,000 9,000 9, 1 60 25-4 ABSORPTION OF CHOLERA AGGLUTININ BY CHOLERA VIBRIOS T C *obs. ^calc. K 2 2 0 0.03 — 20 2O O I.O — 40 38 2 2.8 24 1 67 60 7 6 16.4 200 120 80? 27 (6.5?) Mean 2,000 1,300 700 620 I6.5 19 11,000 6,500 4,5°° 5,260 23-9 2O,OOO IO,OOO 10,000 10,750 21-5 J As is evident from these figures, on the addition of a small quantity of agglutinin it is absorbed (nearly) totally ; Bobs is found to = o. Indeed, the method of observation does not permit the observation of values of B below B — i. On the further addition of agglutin the absorbed fraction decreases continuously until at the end the absorbed fraction is not greater than the non-absorbed fraction. It has been hitherto often assumed that the agglutinin was chemically bound in the bacteria. To carry out this idea consequentially, we must suppose that the resulting 146 LECTURES ON IMMUNITY compound is a highly dissociable one. For otherwise the oft-observed washing out of the agglutinin from this com- pound in the bacterium would be inexplicable. And, fur- thermore, the absorption of the agglutinin ought to be total until saturation was obtained, and thereafter only a very slight increase (due to the physical absorption) ought to be observed. But even if we suppose the compound to be dissociable to a high degree, we might expect that the bound fraction of agglutinin (C) should increase to a limit value with in- creasing concentration of B (and T). As Eisenberg and Volk remark, no such limit can be observed in the results of their experiments. Even the assumption that the agglutinin contains many different kinds of " agglutinin " of different combining powers does not extricate us from this difficulty. In favour of the hypothesis that the agglutination is the consequence of a chemical combination, Joos has adduced some experiments on the effect of partial additions of agglutinin to a suspension of typhoid bacilli. He deter- mined the least dosage of agglutinin that is able to agglu- tinate all the bacteria in the test. Then he added a part of this quantity to a similar suspension ; the agglutination was incomplete. He centrifugated the solution and in this way segregated the agglutinised bacteria and removed them. Then he added a new portion of agglutinin to the solution, and so forth, until all the bacteria had been agglu- tinated. The total quantity of agglutinin added in the several fractions in this manner was found to be equal to the quantity necessary to agglutinate all the bacteria when added at once. Considering the great experimental errors EQUILIBRIA IN ABSORPTION PROCESSES 147 in such observations, the conclusion does not seem to pos- sess a very high degree of accuracy. And even if this were the case, it is very probable that the quantities of bacteria separated out in the first fractions were rather small, and under such circumstances it was evidently to have been expected that the total quantity of agglutinin in the two experiments would be nearly the same. Now in regard to the figures of Eisenberg and Volk, it is evident that a relation exists between the absorbed quan- tity of agglutinin C and the free quantity B. This rela- tion may be expressed in a very simple mathematical formula, namely: — With the aid of this equation the calculated figures ^calc. are found. They agree very well with the observations, within the errors of observation, as Dr. Eisenberg also has stated. The only observation in the second series which gives an unsatisfactory agreement between the observed and calculated values is where ^Ob8. = 80 and Bc&lCf = 27. Eisenberg and Volk themselves state in their original memoir that this observation must be influenced by some occasional error. The physical interpretation of the above formula is very simple. It states that the agglutinin molecules are divided between two solvents, the bacterial cells and the sur- rounding medium, and that of two molecules of the free agglutinin are formed three molecules of the absorbed agglutinin. In the experiments of Ransom cholesterin is a sol- vent for saponin, and the existence of cholesterin in the red blood-corpuscles causes the entrance of the haemo- 148 LECTURES ON IMMUNITY lytic substance saponin into them, following which the red blood-corpuscles are poisoned, so that they give up their colouring matter, the haemoglobin. Now in a similar man- ner the bacterial cells contain some substance that is a good solvent for the corresponding agglutinin, which is thereby caused to enter the bacteria to a preponderating extent. The molecular weight of the agglutinin in the bacterial solvent is only two-thirds of the molecular weight of the agglutinin in the surrounding fluid, the physiologi- cal salt solution. This behaviour of the agglutinin molecules in two sol- vents recalls vividly the behaviour of benzoic acid in two different solvents, water and benzene. According to determinations of the freezing point of solutions of ben- zoic acid, this has in aqueous solution the molecular weight 122, corresponding to the formula C6H6COOH; but in benzene its molecular weight is double that. Therefore, if we dissolve benzoic acid in water, and shake this solution with benzene, the concentration of the aqueous solution Ca is related to the concentration of the benzene solution Cb as indicated in the following formula : — where K is a constant factor. Nernst verified this equa- tion by experiments on the distribution of benzoic acid between water and benzene. The great velocity of absorption is in good agreement with our interpretation as stated above. A difficult thing to explain is the specificity of the ag- glutinins. The agglutinin produced by injecting typhoid bacilli into the blood of an animal is only absorbed by EQUILIBRIA IN ABSORPTION PROCESSES 149 typhoid bacilli and not by other bacteria, for instance not by cholera vibrios, and vice versa. Probably the cell-- membranes of typhoid bacilli are only permeable to typhoid agglutinins, but not to other agglutinins. Normal sera con- tain different agglutinins against bacteria and red blood- corpuscles; by shaking them with the corresponding bacilli or cells, it is possible to separate the different agglutinins. Thus Malkoff mixed goat-serum, that agglutinates red blood-corpuscles from man, rabbits, and pigeons, with red blood-corpuscles from rabbits. The centrifugalised serum had lost its agglutinating power for rabbit's erythrocytes, but not for the two other varieties.1 The agglutinins lose their agglutinating power spon- taneously, but much more rapidly at high than at low temperatures (cf. pp. 87 and 91). Treatment with different chemical agents, as hydrochloric and other acids, bases, formol, and urea, weakens them. The details of these circumstances have not been closely investigated. Just as agglutinins are absorbed by bacteria and red blood-corpuscles, so in the same manner other different substances are absorbed by these cells, and probably analogous regularities are manifested in these cases. Thus tetanolysin, ricin, and the different immune bodies are absorbed by red blood-corpuscles ; and it seems to be a general law that only such substances as are absorbed by these cells exert an influence upon them. Whether the cells are living or dead, seems, as we observed regarding the absorption of agglutinins, to be quite immaterial if the killing of the cells has been cautiously accomplished, so that no notable chemical changes have occurred. 1 Malkoff : Deutsche med. Wochenschrifi, 1900. ISO LECTURES ON IMMUNITY Morgenroth and I examined the absorption of an im- mune-body, prepared by the injection of red corpuscles of ox-blood into the veins of a rabbit. Another series of Morgenroth's experiments was carried out with inactivated (heated) serum from a goat injected with sheep's erythro- cytes. Different solutions of the immune-bodies — their strengths in an arbitrary unit are tabulated under T- were treated with a constant quantity of erythrocytes from ox or sheep for about one hour at low temperature and then centrifugalised. The centrifugated liquid was exam- ined for its concentration, B, of immune-body, by the addition of normal serum of the guinea-pig, and measur- ing the haemolytic power of the haemolysin produced. The difference, C, was absorbed by the red blood-cor- puscles. Beside the observed figures, -#ob8., for the quan- tity of free immune-body, are written figures for -#caic.> calculated by the aid of the same formula as that found to be valid for agglutinins. The constants, K, of the formulae were calculated to be 18.3 and 39.5 respectively. ABSORPTION OF IMMUNE-BODIES BY RED BLOOD-CORPUSCLES SERUM FROM A RABBIT INJECTED WITH SERUM FROM A GOAT INJECTED WITH ERY- BOVINE ERYTHROCYTES THROCYTES FROM SHEEP T c -5ob8. -^calc. T c ^obs. •^calc. 250 226 24 39 200 189.5 10.5 10.5 330 275 55 57 400 374 26 28.8 670 500 170 151 800 723 77 78.4 i,330 850 480 376 1,600 1,384 216 211 2,700 1,710 990 942 3,200 2,400 800 55° 5,000 3.070 i,93o 2,050 6,400 5,230 1,170 1,420 10,000 5,800 4,200 4,800 12,800 9,420 3,38o 3,570 16,700 7,820 8,880 8,870 33,000 13,900 19,100 19,700 EQUILIBRIA IN ABSORPTION PROCESSES 151 As will be seen from the figures, the agreement between the observed and the calculated figures is just as good as for the agglutinins, and wholly within the possible errors of observation. The same physical explanation evidently holds good for both phenomena. In some recent investigations bearing upon the absorp- tion of coli-agglutinin in the bodies of the Bacillus colt com- munis, Dreyer has found that not only the constant K, but also the exponent n in the equation C= KB* may turn out different in different experiments, n always falls near unity, sometimes it exceeds it, e.g. in one case n was found to be 1.25. A closer investigation regarding the cause of this variability seems very desirable. This case has a certain theoretical significance. Quite recently the opinion has often been ventured that the ab- sorption of agglutinin by bacteria might be analogous to the so-called adsorption of dissolved substances by char- coal, or of colouring matter by organic tissues. Bordet was the first to make this assumption, which has recently been upheld by Wilh. Biltz. Biltz now states that in the theo- retically hitherto little elucidated adsorption-process n is always lower than i ; for absorption by charcoal it is 0.25, according to Schmidt. If therefore n is sometimes found to exceed i, as in Dreyer's work, we have to abandon the adsorption hypothesis. Biltz, Much, and Siebert for two hours shook typhoid agglutinin with the following colloidal bodies : silicic acid or hydroxids of iron, zircon, and tho- rium. It was found that silicic acid had a noticeable and the three other substances a much greater destructive action on the agglutinin. This seems to indicate that we have here to deal with a real chemical influence, which is not 152 LECTURES ON IMMUNITY astonishing, as many different substances destroy agglu- tinins. For absorption it is, on the contrary, generally possible to show that the absorbed bodies (e.g. dyes) exist on or in the absorbing substance, from which they may often be washed out. The authors have tried in vain to poison animals by the injection of hydroxid of iron which had been shaken with diphtheria poison or tetanospasmin, which, just as agglutinins, are attenuated by such shaking. If these poisons had been absorbed like agglutinins by the bacteria, i.e. in a reversible way, then a strong poisonous effect should have manifested itself in the injected animals. But not a trace of the expected effect was observed. Biltz, Much, and Siebert were then led to the conclusion that the hypothesis of absorption is not tenable. They have therefore taken up an idea incidentally sug- gested by Nernst for the explanation of the neutralisation of toxins by their antibodies. This idea is not very differ- ent from that of Behring. (Cf. p. 29.) Let us suppose we have finely divided colloidal platinum (Bredig's "an- organic ferment") and hydrogen peroxid. The peroxid condenses upon the fine metal particles and thereafter it is decomposed. This would correspond to the condensation of a toxin, e.g. ricin, on the colloidal particles of its anti- body, antiricin, and its subsequent decomposition. The antiricin itself should be slowly attacked by the ricin, just as the platinum, if it were oxidisable by the hydrogen peroxid. This explanation is incompatible with the fact that the ricin can be recovered after it is "neutralised," therefore the neutralisation cannot depend upon its de- struction. It seems that the advocates and adherents of this idea (the schools of Nernst and of Ehrlich) had an EQUILIBRIA IN ABSORPTION PROCESSES 153 intuition that it would conflict with experience. Evidently it agrees with the experiments in the shaking of poisons with colloidal hydroxids (except in that these substances are not chemically attacked by the poisons), but it does not harmonise with our experience with the reactions of bac- teria to their agglutinins. It may also be emphasised that the solutions of anti- toxins do not behave as suspensions, as is seen in their diffusibility in jelly, which is not observed with suspended particles. There is another phenomenon which we encounter in the use of some kinds of agglutinins, e.g. such as have been weakened by acids, or other chemicals, or by heat. These modified agglutinins display an increase in their agglutinating power until a maximum of agglutination is reached. Thereafter new additions of agglutinin dimin- ish the effect and at a high concentration of the agglu- tinin the agglutination ceases. A similar behaviour is characteristic of many salts. Without the presence of some salts in the solution, no agglutination takes place, and the same is also true for very high concentrations of the salts. With increasing concentration of the salt (above the optimum value) a greater quantity of agglutinin is neces- sary to produce agglutination, and at a concentration of the salt above a certain limit value the agglutination fails. On small additions of salts the agglutinated quantity seems to be proportional to the added quantity, which might be expected on the basis of most of the hypotheses regarding the nature of agglutination, and not only from the chemical one, as Joos supposes. In the theory of immunity we find many analogous 154 LECTURES ON IMMUNITY cases where maxima or minima of a certain effect are observed at a certain concentration of the reacting sub- stance. One of the most startling of these phenomena is observed on injection of a mixture of the botulismus-poison produced by Bacillus botulinus, and its antibody, obtained from the blood-serum of animals that have been injected with this poison. Madsen used, for instance, a mixture of o.i c.c. with 0.0013 c.c. of its antitoxin. The injection of ten such doses in a guinea-pig (of 250 g. weight) had no effect; two doses gave just a trace of illness charac- terised by a peculiar flaccidity of the animal; one dose caused a flaccidity lasting four to seven days. Injections of between 0.013 and 0.5 doses had a lethal effect, and the maximal toxicity was shown by a o.i dose, the animal dying after only two days ; o.oi dose was no longer lethal, but caused flaccidity lasting seven days ; and 0.003 dose only a trace of flaccidity lasting only one day. Another similar instance with a minimum and a maxi- mum of effect is shown in haemolysis by means of sapo- nin (Madsen and Walbum), an extract from the roots of Saponaria; 8 c.c. of a suspension of I per cent of erythro- cytes from horse blood was added to the following quanti- ties of a 0.02 per cent solution of saponin with water up to a total quantity of 10 c.c. This mixture was placed for three hours at 37 ° C. and thereafter cooled on ice and the de- gree of haemolysis in per cent measured on the following day after the unattached erythrocytes had subsided. Quantity of saponin in c.c. = I 0.7 0.5 0.4 0.3 0.25 0.2 0.17 O Haemolysis in per cent = 35 16 18 30 36 36 45 41 o Similar observations were also made with mixtures of sa- EQUILIBRIA IN ABSORPTION PROCESSES 155 ponin and cholesterin, which acts as an antitoxin against saponin. Even tetanolysin sometimes gives such maxima of effect for a certain concentration, if the time of action is rela- tively short. After a prolonged action the maximum dis- appears. This maximum seems therefore to be related to the velocity of the reaction and not to the final equilibrium. Probably the same would occur also with the saponin if its action could be prolonged for a sufficient time. Reactions of this kind are often explained as due to the presence in the mixture of two substances of inverse effect. Thus it is supposed that agglutinin treated with acids, etc., contains, besides the real agglutinin, a substance called agglutinoid, which hinders the agglutination. At higher concentrations the bacilli are supposed to absorb chiefly the agglutinoid and not the agglutinin ; at lower concen- trations both are supposed to be absorbed. This explica- tion seems to me to have no advantage, to mean no more than the relation of the simple fact itself, besides being much more difficult to remember. Furthermore, it seems more simple to suppose that the reacting substance exerts two different actions on the cells, of which the one, appear- ing at higher concentrations, hinders the other, prevailing at lower concentrations. Such a behaviour is not rare in common chemistry. Thus, for instance, the addition of alkali to a solution of aluminium chloride gives a precipi- tate of aluminium hydrate, which is dissolved on further addition of alkali. In a brochure dealing with the properties of colloids Biltz1 1Biltz: Gottinger Nachrichten, math.-phys. Klasse 1904, I, Zeitschr. f. ph. Ch. 48. 615 (1904). 156 LECTURES ON IMMUNITY recalls attention to the oft-observed fact that in gen- eral positive colloids (which wander in the electric field in the same manner as cations) precipitate negative colloids (which wander in the same direction as anions under the influence of the electric current). This reminds one some- what of the specificity of agglutinins. As we shall see later on, Henri accepted this idea, but later he found it dis- proved by experiments on agglutinins. Biltz found, further, that in the precipitation of colloids optima are found. Thus, for instance, the addition of 1.62 mg. oxid of zir- con gave a more abundant precipitate with 1.4 mg. gold in colloidal solution than greater or less quantities; 3.25 mg. ZrO2 gave no precipitate at all. In the same man- ner behaved 4 mg. thorium oxid (as colloidal hydrate) with a colloidal solution containing 5.5 mg. SO2S3. In this point also the colloids present analogies with common dissolved inorganic substances. Analogous effects are observed as especially character- istic of precipitins, and we will return to this special question when we later consider them. Regarding the influence of salts upon agglutination, we possess a thorough investigation of Bechhold. He used typhoid bacilli, which were cultivated in bouillon and thereafter killed with formalin and washed by repeated suspension in distilled water, and followed by subsequent centrifugation. These bacteria were in some experiments used in their natural state. One c.c. of a suspension was mixed together in a test-tube with i c.c. of the salt solu- tion under investigation. The test-tube was placed for 24 hours in an incubator at 37° C. and its content then examined. The degree of agglutination was tested by EQUILIBRIA IN ABSORPTION PROCESSES 157 looking through the tube against a printed paper and expressed corresponding to one of the four following degrees : Liquid completely clear, perfect agglutination ; Most bacteria subsided, but liquid not wholly clear, strong agglutination; Some bacteria subsided and agglomerated, no clearing of the liquid, weak agglutination; No appre- ciable change of the liquid, no agglutination. In other experiments the bacteria used had been treated with serum containing agglutinin, nitrate of lead, ferric-sul- phate, alcohol, acids, or uranium acetate (which all agglu- tinate them), and thereafter thoroughly washed until the wash-water did not show any reaction of the agglutinating substances. The bacteria treated in these different man- ners may be called sero, lead, iron, alcohol, acid, and uranyl bacilli respectively. The bacteria had then been altered so that they behaved in a different way to salt- solutions than did the original bacteria. On the addition of sulphuretted hydrogen to the bacteria treated with lead, these were coloured black, which proves that the bacteria had retained the lead in spite of the washing. For a com- parison Bechhold1 examined the behaviour of suspensions of mastic, prepared by adding some drops of an alcoholic solution of this material to water (so-called "a mastic"), or some drops of water to the alcoholic solution (" (3 mas- tic "). The experiments on the agglutination of this last emulsion were done at ordinary room temperature, as the suspended matter would dissolve at 37°. In the first place an influence of the time of reaction was noted. Suspensions of sero-bacilli mixed with 0.05, 0.025, or 0.012 normal solutions of sodium chloride or 1 Bechhold: Zdtschr . f. ph. ^.,48.385 (1904). iS8 LECTURES ON IMMUNITY sodium iodide were completely agglutinated in 50, 90, and 1 20 minutes respectively; normal bacilli are not agglu- tinated at all by these solutions. On the other hand, sero-bacilli are less affected than normal bacilli by some solutions, for instance 0.0033 n. silver nitrate or 0.005 n- hydrochloric acid. After a time of 15, 50, and 1440 minutes these preparations gave the following results: — NORMAL BACILLI SERO-BACILLI Treatm. with 0.0033 n. AgNO3 Treatm. with 0.005 n- *IC1 15' weak weak 5°' perf. perf 1440' perf. perf. 15' no no so' weak weak 1440' perf. perf. Agglutina- tion These and other similar experiments indicate that the agglutination requires time (cf. p. 116). Further, a certain concentration (limit-value) of the salt-solution is necessary to give an appreciable agglutination. The following table gives the limit value in o.ooi n. of the concentration for different salts. The sign co indicates that even the strongest salt-solutions did not agglutinate. The quanti- ties of salt necessary for the first trace of agglutination have the greatest value for a-mastic, then come /3-mastic and normal bacilli, and after them sero-bacilli, which are the most sensitive to salts. The salts of alkalies, alkaline earths, and magnesia exert little or no influence on common bacteria. The agglutinating power is greater for salts of trivalent metals than for those of divalent metals. A very strong influence is exerted by the acids, especially the strong ones. The anions seem to exert very little influence. EQUILIBRIA IN ABSORPTION PROCESSES 159 PREPARA- TION a MASTIC ft MASTIC NOR- MAL BACILLI SERO- BACILLI PREPARA- TION a MAS- TIC ft MAS- TIC NOR-I MAL BAC- ILLI SERO- BAC- ILLI KOH 00 00 00 MgS04 IOO 00 2-5 bad 1000 10 00 25 Mg(N03)2 100 — — Nal — — 25 CaCl2 5° — 00 4-5 NaNOs — — 25 CaN206 50 — — Na2SO4 — 50 — 50 BaO2H2 5° — 25 25 Pbl — — 25 BaCl2 5° 5 oo 5 HgN03 1.25 — I °-5 BaN206 5° — — — AgNO3 I25 — 25 I ZnS04 IOO — 10 I ZnN2O6 50 — — — HC1 10 1.25 I °-5 CdS04 25 — 10 I H2S04 10 — I 0.25 CoN2O6 50 — — 2.5 CH3C02H 500 — I i NiN206 5° — — 2.5 o-Amidoben zoic acid — — 5 5 Ni(C2H302)2 25 — 25 2.5 A12(S04> o-5 — 0.25 0.25 PbN206 5 — 2.5 O.I A1(N03)8 °-5 — — — CuCl2 10 — 2.5 I Fe2(S04)3 °-5 — 0-5 O.I CuSO4 10 — 2.5 — Fe (N03)3 i — — — CuN2O6 5 — — o-5 FeCl3 i — — — Cu(C2H302)2 5 2-5 — — PtCl4 10 — 2-5 o-5 HgCl2 00 — 2.5 o-5 The salts of (univalent) mercury and silver differ rather widely from those of other univalent ions. Probably they form nearly insoluble chemical compounds with the albuminous matter. In other experiments Bechhold investigated the retard- ing influence of small additions of gelatin, serum, gum arabic, extract of typhoid bacilli or of leeches on mastic emulsion. Gelatin did not exert such an influence on normal bacilli, sero-bacilli, or lead bacilli. The alcohol, acid, or uranyl bacilli display properties lying between those of normal bacilli and of sero-bacilli, but their aggluti- nation was lowered by the addition of gelatin. Probably the addition of gelatin or serum covers the suspended par- 160 LECTURES ON IMMUNITY tides of mastic with a thin film, after which the particles behave as if they consisted of drops of gelatin or serum. Recently there have been many efforts made to place in parallel the properties of egg-white and its derivatives, as peptons or albumoses, with those of inorganic colloids, which after all consist of suspensions of particles of ultra- microscopic magnitude. These are generally precipitated by the solution of very small quantities of salts in the suspending water, and they assume an electric charge on contact with the water, whereby they wander to the one or to the other pole of a battery submerged in the solu- tion. The solutions of egg-white and its derivatives seemed at first to behave in the same manner. But as Bechhold says, the albumoses, etc.", do not behave otherwise than common solutions. The same is evidently true of different albuminous substances, according to the recent investiga- tions of Pauli.1 He subjected ox or horse serum to dialysis for a very long time, six to eight weeks. This serum did not migrate with or against the electric current, and it was not precipitated by weak solutions of alkaline salts, nor of salts of zinc, copper, iron, mercury, or lead. It was coagulated by strong heat, alcohol, and strong solutions of alkali salts or zinc sulphate. These sera contain two different kinds of protein, albumin and globulin. These could not be separated by means of the current, so that neither of these substances was carried by the current. The great difference between the so-called organic colloids and the inorganic or true colloids caused Pauli to express the opinion that we should not attempt to deduce the properties of organic from those of the inorganic colloids, 1 W. Pauli: HofmeisUrs Beitragc, 7. 531 (1906). EQUILIBRIA IN ABSORPTION PROCESSES 161 but to confine our studies to the albuminous substances if we wish to understand the processes going on in living matter.1 One of the properties of albuminous substances which was regarded as proving their colloidal nature was pre- cisely the migration of these substances in the electric field. Dialysed serum, says Pauli, does not migrate, but if we add an acid, the egg-white follows the positive cur- rent ; if we add an alkali to the solution, it travels to the positive side. This circumstance is explained by the adherents of the colloidal theory by the assumption that the egg-white absorbs positive H ions or negative OH ions. As Bredig, Freundlich, and Loeb 2 have remarked, this follows at once from the well-known fact that proteins are amphoteric electrolytes, which form salts as well with acids as with bases, just as do the amido-acids, e,g. glyco- coll, with which substances the albumins are even very closely related according to the recent investigations of Kossel and E. Fischer. It is quite true that, just as ammonia by adding an hydrogen ion forms the ammonium ion, in quite the same manner the amido-group of the albuminous substance adds hydrogen and gives an albumin ion. But there is a very great difference between an ion and the suspended particles (e.g. of kaolin) which obtain a positive change through the influence of dielectric forces. That the albuminous substance really so behaves, that it adds a hydrogen ion and gives an albumin ion, — i.e. that the addition of an acid to it gives rise to a real neutralisa- 1 Pauli : Naturiu. Rundschau, p. 3 (1906). 2 Cf. Loeb : Vorlesungen iiber die Dynamik der Lebenscrschcinungen, pp. 65-67, Leipzig (1906). 1 62 LECTURES ON IMMUNITY tion phenomenon like that of ammonia, — is evident from Pauli's investigations. On the addition of acid the wander- ing of the albumen to the cathode at first increases with the quantity of acid added, and then reaches a maximal value. The stronger hydrochloric acid has a greater action than the weaker acetic acid. Evidently the albuminous substance has the character of a weak base and therefore the formation of salt is greater if we use hydrochloric than if we use acetic acid, and a limit of the wandering is reached when the substance is practically neutralised. In an analogous manner the sera investigated by Pauli behave with alkalies. The wandering to the anode in- creases with the quantity of alkali added, until a limit is reached. In this case evidently no hydroxyl ions are annexed to the albuminous substance, but instead its "acid" carboxyl group gives off a hydrogen ion and is thereby itself charged negatively as an albuminate ion. Pauli found that neutral salts do not give a charge to the serum, but KH2PO4, which has an acid reaction, and Na2HPO4, Na3PO4, NaHCO3, and Na2CO3, which have an alkaline reaction, exert an influence like a weak acid or as weak bases. This is quite clear as long as we regard the albuminous substances as amphoteric electrolytes ; but if we regard them as colloidal particles, we cannot predict anything with respect to the influence of these substances. It is quite incomprehensible how this latter view has been so often preferred. The behaviour of albumose, pepton, and of egg-white as bases has been very thoroughly investigated by Sjoqvist,1 1 Sjoqvist : Skandinavisches Archiv f. physioL Chemie, Bd. V., p. 59 (1895). EQUILIBRIA IN ABSORPTION PROCESSES 163 who employed for this purpose his method of study- ing the conductivity. Sjoqvist stated that these substances behave quite regularly as weak bases. The " mean " equivalent weights of these three substances were found to be about 600, 250, and 800 respectively. The egg-albumen was a base about six times weaker than aspartic acid, but about nine times stronger than urea. The albumose (from Schuchardt) was about 1.6 times as strong a base as the albumin. Sjoqvist investigated the neutralisa- tion of these bases by means of different acids as hydro- chloric, sulphuric, phosphoric, and lactic acid, and found always a good agreement with the theoretical view. The amphoteric properties of these substances have also been the basis for investigations on the action of pepsin and trypsin by Sjoqvist, Bayliss, and others (cf. pp. 65 and 79 above). A property of the antibodies, which recalls the tendency of inorganic colloids to precipitate only (or chiefly) colloids of the opposite electric sign, is their specificity. But whereas the positive colloid ferric hydrate is attacked by all the many negative colloids, the typhoid bacilli are agglu- tinated only by typhoid agglutinin. Victor Henri has, in association with his students, M. Malloizel and Mme. Girard-Mangin,1 carried out some experiments on agglutina- tion from this point of view. He found that red blood- corpuscles and typhoid bacilli are, as most substances suspended in water, charged negatively, and therefore con- cluded that these cells would be agglutinated by ferric hydrate, as Biltz had predicted. He found that this really 1 V. Henri et L. Malloizel : C. R. de la Soc. de BioL, 56. I. 1073 (1904) ; Mme. Girard-Mangin et V. Henri : C. R. de la Soc. de Biol., 56. II. 866, 93L 933, 935. 936, 974 (i9<>4). 1 64 LECTURES ON IMMUNITY occurs, and that normal serum or even dissolved starch has a somewhat protecting influence against the agglutina- tion. But later on M. Henri and Mme. Girard-Mangin investigated the influence of negative colloids, and found that they had precisely the same agglutinating influence as the positive ones. The "colloidal theory," therefore, has proved of little avail. That proteins are able to combine with positive ions, not only hydrogen, but even potassium, sodium, or calcium, has, according to the investigations of Pauli and Loeb,1 an extremely great importance for the physiological functions of the proteins. We have seen in the chapter on the velocity of reaction that this is for agglutinins proportional to the concentra- tion of the agglutinin and increases with temperature. From this we concluded that the agglutination depends on a chemical reaction of the agglutinin with some content of the bacterium. In his excellent work on microbiology Duclaux 2 shows that this chemical action is really a coagu- lation. He cites the experiments of Kraus, which indicate that the filtrate obtained by means of a Chamberland filter from cultures of cholera vibrios, typhoid or pest-plague bacilli, give a coagulum with their specific agglutinins. He cites further the experiments of Nicolle, who subjected a fil- trate from macerated coli bacilli to an agglutinin obtained by injecting these bacilli into the veins of a rabbit. In a mixture of ten drops of the filtrate with one drop of the rabbit's serum there appeared after some hours at 37° a large number of flocculent bodies that resembled to a very 1 J. Loeb : " Studies in General Physiology," Part II, 544, Chicago, 1905. 2 Duclaux : "Traite de microbiologie," T. II, p. 706, Paris, 1899. EQUILIBRIA IN ABSORPTION PROCESSES 165 high degree the flocculation in a culture containing living coli bacilli treated with the same agglutinin. One might replace the bacilli with some fine inert powder, e.g. tal- cum ; this fine powder would then, just like the bacilli, be jammed together by the coagulum in their neighbourhood. Therefore the deposits containing bacilli are more volu- minous than those of the fluids from which the bacilli are removed by filtering. The liquid which is coagulated by the agglutinin is according to Nicolle very resistant to low and high temperatures. It is soluble in alcohol and to a certain degree in ether, so that an extract from the bacilli in one of these fluids yields, after evaporation to dryness and dissolution in a weakly alkaline bouillon, a flocculent deposit on treatment with its agglutinin. This coagulable substance is prepared in the interior of the bacilli which contain it, and it is even partially given up to the surrounding medium, as is indicated by the experiments of Kraus. Agglutinins are contained in normal sera, as for instance in the horse, the blood-serum of which agglutinates cholera vibrios to a high degree, and less effectively cultures of Vibrio Metschnikovi, typhoid bacilli, colon bacilli, and tetanus bacilli as well as strepto- coccus. The normal sera of different animals agglomerate the normal erythrocytes of other animals, as, for instance, the serum from the horse agglutinates erythrocytes from guinea-pigs or rabbits. In these cases, just as with the agglutinins acting upon microbes, it is possible to increase the content of the specific agglutinin in the normal serum by repeated injections of the erythrocytes in question. Even simple chemical reagents cause an agglutination of bacilli, thus, for instance, typhoid bacilli are agglutinated 1 66 LECTURES ON IMMUNITY by formaldehyde, hydrogen peroxid, or strong alcohol. In this case the reagents often display the phenomenon that a greater dosage does not agglutinate, whereas a lesser dose produces the effect. Acetic acid does not agglutinate some cholera vibrios if it be used in a concen- tration of o.i per cent, but has a strong agglutinating effect in solutions of 10 per cent only to lose it again at a strength of 50 per cent, according to the experiments of Bossaert. Mercuric chlorid agglutinates in a concentra- tion of only 0.3 per cent and safranin or vesuvin are active at a concentration of 0.05 per cent. Even in this case different bacilli are sensitive to a different degree; thus, for instance, typhoid bacilli are more than ten times as sensitive to safranin as colon bacilli. If the action of the agglutinin be a coagulation of the contents of the bacilli, it is easy to understand how other coagulating substances, such as alcohol, acids, or ura- nium acetate, may change the properties of the bacilli in nearly the same manner as the specific agglutinin, as results from the experiments of Bechhold cited above. The agglutinins are therefore probably only a special class of precipitins, which they in many cases even resemble in showing optima of action at a certain concentration. CHAPTER VI NEUTRALISATION OF THE H^MOLYTIC PROPERTIES OF BASES AND OF LYSINS OF BACTERIAL ORIGIN THE simplest haemolytic agents are the bases and the acids. Of these the bases exert an action on erythrocytes, which is very similar to that of haemolysins of bacterial origin. It is obvious that if we add an acid to an alkaline solution until it is neutralised, its hasmolytic action will be nullified. In some few cases, as for instance for oleic acid, this is not true, since all the olein derivatives are haemolytic agents, which salts in general are not. This case presents the closest analogy to the neutralisa- tion of a lysin, e.g. tetanolysin, by means of its antilysin. At first sight there seems to be a difference, since any base is neutralised by any acid, whereas the antitetanoly- sin is a perfect specificum against tetanolysin and exerts no neutralising action on other lysins. But this difference is more apparent than real, since we know now that the acids all contain hydrogen ions which bind the hydroxyl ions, common to all bases. It therefore seemed to Madsen and myself to promise much for the elucidation of the phenomenon of neutralisa- tion of lysins by their antilysins to make a comparative study of the common neutralisation of a base, regarded as a haemolytic agent, with that of a lysin and its anti- lysin. For this purpose we made a thorough investign- 167 1 68 LECTURES ON IMMUNITY tion of the action of bases, acids, and salts on erythrocytes and of the haemolytic action of a lysin, namely, tetanoly- sin, in the presence of its antilysin and of different other so-called neutral substances, as salts and different proteins. The tetanolysin was chosen because it shows a great similarity in its neutralisation with that practically most important of all poisons, namely, the diphtheria poison. This investigation convinced us that a complete analogy holds for the two phenomena of neutralisation, that of a base, for instance, ammonia, and that of tetanolysin.1 If we add different bases, for instance, ammonia and sodium hydrate, to red blood-corpuscles, we find that the first traces of alkali are without any haemolytic effect on the cells. This first ineffective quantity seems to be bound by the blood-corpuscles rather strongly, since it is, within the errors of observation, proportional to the quantity of blood used, and the quantities of sodium hydrate and of ammonia bound by the same quantity of blood-corpuscles are chemically equivalent (cf. p. no). On the addition of greater quantities of alkali a very weak haemolysis occurs ; the fluid is only faint yellow. As the quantity of alkali increases, the haemolysed quantity of the red blood-corpus- cles increases very rapidly and often nearly proportion- ally to the square of the unbound quantity of alkali. This proceeds until the haemolysis is total, that is, until all the red blood-corpuscles have given up their haemoglobin to the surrounding medium. After this a further addition of alkali produces no change in the quantity of haemolysis, though the velocity of reaction is increased. The state- 1 Arrhenius and Madsen : Festskrift, Copenhagen, No. 3, 1902 ; Zeitschr* f.ph. a., 44. 7 (1903). NEUTRALISATION OF H^EMOLYSINS 169 ment is valid also for the action of such hsemolysins as tetanolysin. It seems as if also in this case a chemical binding takes place, but the compound seems to be to a higher degree dissociated, so that the limit is not so sharp as for the alkalies. To give an idea of this process I reproduce here some figures for the haemolytic action of taurocholate of so- dium, saponin, potassium hydrate, and solanin. For potas- sium hydrate 2.5 per cent suspensions of bovine corpuscles, for the other haemolysins 2 per cent suspensions of equine erythrocytes, were used. Following the addition of the suspension of cells to the poison, the mixture was shaken and then for one hour placed in an incubator of 37° C. and after this eighteen hours in a refrigerator and then com- pared with the solutions of haemoglobin of different concen- trations prepared by the haemolysis of different quantities of the same blood-corpuscles by pure water. The concen- tration is given for the potassium hydrate in fractions of a normal solution, for the other substances in fractions of the whole fluid (weight of dissolved substance : weight of solution). SAPONIN TAUROCHOLATE OF SODIUM Cone. C ' io6 H K- io-5 Cone. C«io» H K. io-s 40 go 2.35 I40 91 6.81 28 40 2.26 IOO 55 7.41 20 IO 1.58 68 18 6.24 H 5 l.6o 48 4 4.17 10 3 i-73 32 2-5 4-94 7 2 2.02 20 i-3 5.70 LECTURES ON IMMUNITY POTASSIUM HYDRATE SOLANIN Cone. C • io5 H K. 10-3 Cone. C'io8 H K- io-s 62.5 27 8.3I 40 86 2.32 5° 13 7.21 28 70 2.98 37-5 4 5-33 20 4 1. 00 3i-S 3-5 5.98 H 2.4 I. II 25 2 5.66 10 '•5 i-5 As will be seen from these figures, these poisons do not follow nearly as closely as tetanolysin and ammonia the rule that the square root of the degree of haemolysis is proportional to the concentration. The quotient of these two magnitudes is tabulated under K. In general the greater the velocity of reaction the more marked is the deviation from the said rule. At about 10 per cent the haemolysis increases relatively more rapidly with the concentration than at other degrees of haemolysis. There- fore the measurement of the quantity of poison present by means of the haemolytic determination has the greatest exactitude in the neighbourhood of this point. Different strong monovalent bases act in equivalent quantities nearly to the same degree upon the blood- corpuscles. The divalent bases Ca(OH)2 and Ba(OH)2 seem to give some solid precipitate in the erythrocytes, which hinders measurements, at least at higher concentra- tions. The haemolysis observed is then nearly independent of the quantity of base added. Ammonia also has nearly the same strength of action as equivalent quantities of the strong monovalent bases. Sometimes (for low concentra- tions of blood) its action is a little less, in other cases (at NEUTRALISATION OF H^EMOLYSINS 1 7 1 higher concentrations of blood) it is somewhat greater than that of the stronger bases, at least after a prolonged time of reaction (cf. p. in). This seems to indicate that some compound is formed, so that the equivalent quan- tities act to the same degree, but that the ammonia com- pound is to some degree hydrolysed, which causes the deviations. Acids also destroy the red blood-corpuscles, but this phenomenon has an appearance somewhat different from the haemolysis by means of bases. Following the action of the alkalies and also of the lysins of bacterial origin, the fluid surrounding the blood-corpuscles takes up their intensive purple colouring matter and assumes the charac- teristic red colour of blood. The acids, on the other hand, alter the colouring matter, so that the fluid becomes dark brown, and after shaking the foam persists often for forty- eight hours or more. This indicates a coagulating influ- ence. With lower degrees of haemolysis by acids the fluid has, however, also a reddish tint. At the same time a strong agglutination of the blood-corpuscles is perceptible. At higher concentrations large clumps are formed, remind- ing one somewhat of the flocculent precipitates of alumin- ium salts mixed with an alkali. The degree of haemolysis by a strong acid is about as pronounced as that of three to four times the equivalent quantity of a strong base. Equivalent quantities of different acids (hydrochloric, sul- phuric, oxalic, tartaric, citric, and acetic) act nearly to the same degree, the weaker acids (for instance, acetic acid) act a little slower than the stronger ; and extremely weak acids, as boracic acid, exert no appreciable haemolytic action (the same is probably valid for extremely weak 1^2 LECTURES ON IMMUNITY bases), probably because the process goes on with insen- sible velocity. For stronger concentrations of the haemolysins total haemolysis occurs if they are permitted to act through a long enough time. If the time of action be restricted (as by centrifugation), it is possible to follow the development of the reaction, as has been said above (cf. p. 100). The presence of salt J exerts a strong retardative influ- ence upon the hasmolytic power of the alkalies. Probably this effect depends on a diminution of the velocity of re- action. Especially is this true for the influence of ammo- niacal salts upon ammonia. The different salts of the strong bases (KOH, NaOH, and LiOH) are of the same degree of efficacy in equivalent concentrations; the effect is nearly proportional to the cube root of the concentra- tion ; 0.02 n. salt solution lowers the effect in the propor- tions i : 0.4. The salts of ammonia also seem to be very similar to each other in this regard : 0.004 n- NH3 salt lowers the effect in the proportion 1:0.7; o.oi6n. in the proportion 1:0.25 ; and 0.06 n. in the proportion 1:0.14. On the other hand, it is perfectly clear that the addition of the equivalent quantity of hydrochloric acid to a solu- tion of sodium hydrate would completely suspend its hae- molytic power, since in this reaction sodium chloride is formed, which has no haemolytic effect. Of a sodium hydrate solution (neutralised to 50 per cent) it would be necessary to add the double quantity (a slight correction should be introduced for the lowering influence of the salt, and for the quantity of alkali bound that gives no action) to attain the same haemolytic effect. We then say 1 In this case the physiological solution is made of cane sugar. NEUTRALISATION OF H^MOLYSINS 173 that the toxicity of the first solution is half as great as that of the second solution. The effect of the neutralisation of the sodium hydrate by the addition of hydrochloric acid may therefore be graphically represented in the following figure by the line AB. The toxicity is here ordinates, and the quantity of acid added is abscissae. This line would be a straight line if the effect of the salt did not produce a perturbing influence. When we have added the acid necessary to neutralise the free alkali (point B\ we have still to add a small quan- tity to neutralise the alkali bound in the erythrocytes, and then further add a small quantity of acid before the solu- tion is strong enough in acid to give haemolysis again. These portions are represented by the parts BC and CD in the diagram. On the addition of more acid to the solu- u BC D FIG. i. tion its toxicity increases nearly proportionally to the quantity of free acid (neither bound to the alkali, nor in the erythrocytes). This toxicity is represented by the al- most straight line DE. In quite the same manner the toxicity changes on the 174 LECTURES ON IMMUNITY addition of a strong acid to a solution of ammonia. The line AB then deviates a little more, but not very much, from a straight line, according to the relatively strong in- fluence of the ammonium salts. The real curve would lie little below AB. FIG. 2. Now, if we add to the ammonia-solution a very weak acid, such as boracic acid, which has no sensible haemo- lytic action, the phenomenon will behave in a rather differ- ent manner, in consequence of the hydrolytic effect of the water. The hydrolysis results in this, that there always re- mains a certain quantity of free ammonia, even if we add as large quantities of boracic acid as possible (up to satu- ration). Then the curve representing the toxicity de- scends as the quantity of boracic acid added increases, but never reaches zero, as is indicated on Fig. 2. The quantity (q) of free ammonia may be calculated according to the equation : — NEUTRALISATION OF H^MOLYSINS where a is the quantity of ammonia present from the be- ginning, before boracic acid was added, q the quantity of free un-neutralised ammonia, n is the added quantity of this acid, consequently (a — is tabulated the quantity of ammonia which is neutralised with regard to its haemolytic power by the ad- dition of the sixth part of one equivalent of boracic acid. The two first additions lower the toxicity by nearly the same amount (16.7 per cent) as a strong acid. The portions between one and two thirds and between two and three thirds have a noticeably lower influence (about £ and f re- 1 According to a recent investigation by H. Lunden on the hydrolysis of ammonium -borate the constant K is 1.02 in complete agreement with the value given above as results of experiments on hydrolysis. NEUTRALISATION OF H^MOLYSINS 1/7 spectively). The next equivalent of boracic acid added has an effect which equals only about the fifth part of that of the first equivalent. This behaviour is to a high degree similar to that termed Ehrlich's phenomenon, observed in the neutralisation of a toxin with its antitoxin. The first part of the antitoxin added neutralises, generally speaking, a greater portion of the toxin than does the second equal addition, this a greater one than the third, and so forth. To explain this peculiarity (of diphtheria-toxin) Ehrlich supposes that the toxin is a mixture of many different " partial toxins," which possess different degrees of toxicity in equivalent quantities, and have a different affinity for antitoxin. If antitoxin be added, it at first neutralises that part of the poison which has the greatest affinity, and which also is the strongest poison ; thereafter that with the' next greatest affinity, which also is the second in toxic strength, and so forth. At the end the very weakest portions appear for neutralisation. Ehrlich designated these hypothetical " partial poisons " with names coined from the Greek language, as prototoxin, deuterotoxin, tritotoxin, epitoxin, etc. If we apply Ehrlich's views to ammonia, this substance should, according to the experiment of neutralisation by boric acid, be composed of different " partial ammonias," of which the strongest one should be neutralised first, the second strongest next, etc. Of course this compli- cated explanation cannot possibly be used for ammonia, which we know is a very simple chemical compound of high purity, but it was by Ehrlich and his pupils applied to other poisons quite generally, e.g. to diphtheria-poison 178 LECTURES ON IMMUNITY and tetanolysin, which, on neutralisation, as we shall soon see, behave in a manner very similar to ammonia. The following figures, found for the toxicity of tetanolysin after the addition of different quantities of antitoxin, may serve as an example. It is illustrated by Fig. 3. This curve has a tangent at its beginning, which cuts the ^r-axis in the point x =0.276, indicating that if the neutralisation proceeded according to the same laws as hold for the neu- tralisation of strong acids by strong bases, i.e. if the quan- tity neutralised was proportional to the antitoxin added until total neutralisation was reached, then 0.276 parts (c.c.) of the unit of antitoxin used would neutralise com- pletely the quantity of toxin used (2 c.c. of a 2 per cent solution). In other words, these quantities are equivalent. By the aid of this value the quantities (n) of antitoxins are calculated in the following table in equivalents («x) of the toxin present taken as unit : — TOXICITY (?) OF TETANOLYSIN AFTER ADDITION OF n c.c. OF ANTILYSIN n *l fobs. ?calc. 0 0 IOO IOO 0.05 0.18 82 82 O.I 0.36 7° 66 0.15 °-54 52 52 0.2 0.72 36 38 0-3 1.09 22 23 0.4 1-45 14.2 13-9 0.5 1.81 10. 1 10.4 0.7 2-54 6.1 6.3 1.0 3.26 4.0 4.0 1.3 4-35 2.7 2.9 1.6 5-44 2.0 2-5 2.O 6.52 1.8 1.9 NEUTRALISATION OF H^MOLYSINS 1/9 The values calculated are derived with the aid of the same equation as given above for ammonia, with the constant o. 1 1 5. The experiments were so executed that the mixture of toxin and antitoxin were left at 20° C. for two hours ; thereupon they were mixed with the suspension of erythro- cytes (2.5 per cent horse blood) and for one hour held in a thermostat at 37°. The degree of haemolysis was deter- mined as described above (cf. p. 15). The constant 0.115 is therefore valid at 20° C. In these and similar experiments it is assumed that the absorption of the poison in the erythrocytes may be neglected. The antitoxin used was a solution containing 0.0025 per cent (per c.c.) of the content of antitoxin in a standard solution. This fact indicates that the original blood-serum containing the antitoxin derived from a horse injected with tetanus poison contained in one c.c. nearly 5800 times as much antitoxin as that which was equivalent to the quantity of poison contained in one gram of the dried teta- nus preparation prepared by precipitation from a strong tetanus bouillon with ammonium sulphate. From this figure it is easy to see that the injected horse held in its blood (about 50 1.) many (about 1 5) million times the equiva- lent quantity of the injected poison (about 20 g. ; some- times this quantity may be still less). This circumstance deters us from accepting an idea which seemed at first rather probable — it was suggested by Behring — that the antitoxin is a derivative of the injected toxin. To sim- ilar results have led the experiments on the production of diptheria-antitoxin. If the antitoxin produced did not ex- ceed many times the poison used for its production, the prep- aration of antitoxin would evidently have no practical value. I So LECTURES ON IMMUNITY The curve which represents the experiments of Madsen on tetanolysin resembles very much that representing the neutralisation of ammonia by means of boracic acid. It is convex to the ;r-axis, which it never reaches. This prop- erty indicates that the greater the quantity added, the less is also the neutralising power of the same quantity of antitoxin. But there is no reason to explain this peculiarity by the hypothesis of Ehrlich, that in the toxic solution exist side by side a large number of poisons. The equation which we used for the calculation of the results, and which coincides very well with the experiment, has the following form : — (Quantity of free lysin) x (guantity of free antitoxin) -j*~ K (quantity of bound toxin2). According to the laws of physical chemistry this equa- tion indicates that of one molecule of toxin and one molecule of antitoxin there are formed two molecules of the reaction-products. This reaction is therefore rather similar to that of alco- hol and acid to give ester and water, one molecule of each substance entering into the chemical equation of reaction. In this case, if equivalent quantities of the reagents are used, two-thirds of them are transformed to ester and water, when the equilibrium is reached. The constant K is in this case ^=0.25, about the double of that found for tetanolysin. The constant K of the equation of equilibrium is altered with temperature. When Madsen and I investigated this phenomenon for the first time, we found a very great increase in the proportion of i : 4.7 for the interval of tem- perature 20 to 37.3 degrees. Later experiments have NEUTRALISATION OF H^EMOLYSINS l8l given a much smaller value of the increase, which amounts only to the proportion i : 1.91 between 16 and 37° C.1 A great difficulty inherent in the determination of the con- stants of tetanolysin, as well as of other poisons, lies in the circumstance that the constant of equilibrium is rather dif- ferent for different preparations of the poison. Fresh specimens of tetanolysin seem to give lower constants than old ones. In general the constant of fresh teta- nolysin seems to lie rather near to 0.12 at 20° C. (room temperature). From the variation of K with temperature it is possible to calculate the heat of reaction which is developed in the combination of one grammolecule of tetanolysin with one of antitoxin to form two of the reaction-products. A change in the proportion of I : 1.91 in the interval be- tween 1 6 and 37° C. corresponds to a development of 5480 calories. As we have seen above (cf. p. 41), tetanolysin is rap- idly decomposed in temperatures in the neighbourhood of 50°. An elevation of the temperature of 3.7 degrees increases the constant of velocity in the proportion 16.8 : 1. At 49.8° C. the rate of destruction is of such a magnitude that a poisonous solution loses half its strength in 62 min- utes. From these it is easy to calculate that at 20.2 and 5.4 degrees it will require 6.6 xio9 and 5.3 x io14 hours (i.e. 7.5 x io5 and 6.2 x io10 years) respectively to descend to half its strength. Now it is often observed that solutions of tetanolysin weaken very rapidly, thus, for instance, it may lose about five-sixths of its haemolytic power within five days iMadsen and Arrhenius: Medd. fr. Vet.~Ak : s. Nobelinstitut, 1. No. 3, 5 1 82 LECTURES ON IMMUNITY at 20° C. (as Madsen and I observed in 1902); and dried toxin lost in two years on storage in a cold room (of about 6° C.) two-thirds of its haemolytic power. This destruction is evidently of a wholly different nature from that observed at 50° C., which would be entirely imperceptible at 6 and 20° C. respectively. In the solutions at room temperature it is perhaps bacteria (e.g. Bacillus pyocyaneus} or the influence of dissolved glass which cause the rapid destruc- tion ; in the dried tetanolysin other slow chemical processes may be responsible for the loss of haemolytic action. The peculiar observation is here made that during this destruction the power of binding antilysin does not decrease at the same rate as the haemolytic activity. Sometimes no decrease of the antitoxin-binding faculty is observed at all, so that solutions of lysin and antilysin, that were equivalent immediately after their union, also remain equivalent after the deterioration of the poison. On this ground Ehrlich concluded that the lysin is trans- formed into an innocuous, or nearly innocuous, modifica- tion, which retains the properties of neutralisation of the antitoxin characteristic of the original poison. This sub- stance is termed by Ehrlich the toxoid. The toxoid not only seems to be equivalent with the poison, but also to possess nearly the same constant of equilibrium. And even one of the reaction-products of the toxoid with the antitoxin seems to be identical with one of the products of the corresponding reaction of the toxin. Only in this manner is it possible to explain that the neutralisation curve of the attenuated toxin is very similar to that of the original toxin. It may, on the other hand, be recalled that the equilibrium-constant of old tetanolysin preparations NEUTRALISATION OF H^MOLYSINS 183 has been found to have a very high value and to change greatly with temperature, so that evidently here greater transformations take place during the course of time. In order to explain this peculiarity of the toxin, Ehrlich originated his so-called side chain theory, which has played a great role in these matters, especially in the German literature. Organic chemistry teaches us that certain properties of different substances, for instance the property of giving coloured solutions, depend upon the presence in these substances of the same group of atoms ; in this special case this group is called the chromophoric group. The other parts of the molecule may be rather different in the different substances with the same prop- erty, and therefore this function is considered to be, so to speak, located in the common group. Now the poisons possess the two common properties of being poisonous and of binding their antitoxins, and these two properties do not vary with each other ; as we have seen, the poisonous attribute diminishes more rapidly than the other in a solution of tetanolysin, and the same is the case with diphtheria-toxin, the study of which led Ehrlich to his conceptions. Ehrlich therefore expresses this peculiarity in the following manner. The two said properties belong to two different groups, called the toxophoric group, which is poisonous, and the haptophoric group, which binds anti- toxin. In the molecule of the poisonous substance, which we suppose to be composed of very many atoms, the two groups lie rather far from each other, so that chemical changes may take place in the one group — the toxophoric — without influencing sensibly the function of the other group. To express this Ehrlich supposes that the two 1 84 LECTURES ON IMMUNITY groups are bound to the central part of the molecule as side chains, known from the chemistry of the benzene derivatives. If now, as is often observed, no other change of the poison takes place than that its toxicity diminishes in a certain ratio, e.g. to 50 per cent, then to explain this peculiarity, Ehrlich must assume that all the partial poisons are weakened to the same degree, which seems very im- probable. From our point of view we might explain the same fact by saying that the constant of equilibrium in the above equation has not been " sensibly " altered by the change in the toxophoric group. This is quite possible, although experience with the constant of equilibrium, the so-called dissociation-constant, in acids teaches us that it is rather sensible to changes in the molecule. But the great distance between the different groups in the poison- ous molecule may have the effect that such an influence is in this case insensible.1 There is another possible explanation of the phenomenon. As will be seen in Chapter VIII, many poisons are com- pounds of two different substances. It is possible to sup- pose that even the so-called simple poisons are compounds of two substances, of which the one corresponding to the haptophoric group is bound by antitoxin. If this antitoxin binding property of the poison is relatively stable and present in great excess, and if the poisonous compound is formed of one molecule of each constituent, and is a highly dissociable substance, its quantity will be proportional to the concentrations of the two constituents. Then, evi- dently, the constant of equilibrium would remain unaltered if the group that does not bind antitoxin slowly disappears, lCf. Ostwald: Ztitschr.f. ph. Ch., 3. 374 (] NEUTRALISATION OF ILEMOLYSINS 1 8$ and we would expect just the phenomenon actually ob- served. In order to avoid unnecessary changes we may, until future experiments decide the question, employ the hypothesis that the poisonous molecules possess two groups, the one toxophorous and rather labile, the other haptophorous and more stable. It is not necessary that the compound poison should exist to a sensible degree. We have, for instance (cf. p. 74), seen that the velocity of coagulation of casein is pro- portional as well to the rennet present as to the concentra- tion of the calcium ions. As has been made probable by Fuld and Spiro, the " antirennet " contained in normal horse-serum acts so that it binds the calcium ions ; before this research, however, it was supposed that the serum neutralised (bound) the rennet. In this case it is possible to destroy the rennet by heating to 60° C. At lower tem- peratures (30° or so) it weakens slowly ; but the calcium ions, we may suppose, remain unaltered. The rennet evidently corresponds to the toxophorous group, the cal- cium ions to the haptophorous group of a toxin, and the serum to the antitoxin. Evidently the binding of the cal- cium ions by the serum will be independent of the quantity of rennet present. Therefore we may say of the combina- tion, rennet-calcium-ions, that its antitoxin binding property remains unchanged, while its toxic (coagulating) property diminishes with time. Such a point of view has obviously a great advantage over that of Ehrlich ; but in favour of the continuous development of the science, it seems rea- sonable to retain for this case the nomenclature of Ehrlich, provided that no far-reaching theoretical developments are based upon it — at least until the decomposition of toxins 1 86 LECTURES ON IMMUNITY into their two constituents has been proved for more cases than the coagulating action of rennet (and other casein- coagulating substances, lactoserum included, cf. Chapter IX). Just in the same manner as tetanolysin behave other lysins of bacterial origin. For streptolysin produced by streptococcus Madsen and Walbum have found the follow- ing figures of the toxicity (q), after the addition of n c.c. of antitoxin to a given quantity of poison. The calcu- lated figures are obtained under the assumption that i c.c. of the antitoxin solution used is equivalent to 4.8 times the used quantity of lysin. The constant of equilibrium is ^=0.13 at 20° C, very nearly like that for tetanolysin. TOXICITY (q) OF STREPTOLYSIN AFTER ADDITION OF n c.c. OF ITS ANTILYSIN n «i ?obs. ?calc. 0 0 100 ICO 0.025 0. 12 88.7 88.2 0.05 0.24 76.1 76.9 0.075 0.36 64.8 66.3 O.I 0.48 55-9 56.4 0.125 0.60 47-5 47-5 O.I5 0.72 40.2 39-8 0-175 0.84 34-6 33-4 0.2 0.96 28.3 28.2 O.225 1.08 23-6 23-6 0.30 1.44 15.0 15.2 0.338 1.62 "•5 13-1 0-375 i. 80 8 II. 2 °-45 2.16 <6 8.6 The observed figures are mean values from three dif- ferent series of observations. The agreement between the observed and the calculated values is nearly perfect until n^ is about 1.5. At high values of n± the observed toxicity NEUTRALISATION OF H^MOLYSINS 187 is somewhat smaller than the calculated action. This ac- cords with the observations on tetanolysin. The experi- mental method was quite the same in the two cases. In a lecture held before the British Medical Association at Oxford in July, IQO4,1 Madsen has given curves repre- senting the toxicity of vibrio, staphylo and streptolysin on the addition of increasing quantities of their specific anti- toxins. These curves indicate clearly the fact that the Ehrlich phenomenon is quite apparent in all of them, inasmuch as the right branch tends to bend asymptoti- cally to the abscissa. In all experiments with the lysins the temperature, which corresponds to the equilibrium, is that at which the mixed fluids, toxin and antitoxin, are held during I h. to 2 h. before the blood cells are added. In this moment the volume increases to so high a degree that the velocity of reaction may be regarded as practically suspended. Cholesterin displays a neutralising influence upon teta- nolysin, as is seen from the following table, indicating the attenuation of 5 c.c. of a broth of tetanus bacilli on the ad- dition of n c.c. of a io~6 normal solution of cholesterin and so much salt-solution that the total volume was icc.c., which reacted upon each other during 3 hours at 37° C. After this time parts of this mixture were added to 8 c.c. of horse blood suspension (2 per cent), and the action ob- served. The equation of equilibrium indicates that I mole- cule of reaction-products results from i molecule of lysin, and i molecule of cholesterin. Of the cholesterin-solution 1.43 c.c. were equivalent to 5 c.c. of the broth, which there- fore had the concentration 2.86 • io~7 normal. 1 Madsen: British Medical Journal^ Sept. 10, 1904, p. 12. 188 LECTURES ON IMMUNITY NEUTRALISATION OF TETANOLYSIN BY nc.c. io~6 n CHOLESTERIN AT 37° C. (MADSEN AND WALBUM) « ?obs. ?calc. 0 100 100 o-5 67.5 66 o-75 5' 49-5 i 34-5 34 1.2 27 23 I.4 15 14 1.6 8 9 1.8 5-5 6.2 2 3-4 4.2 If we choose a concentration in which 5 c.c. of the tetanus broth are contained in loc.c. as the unit concen- tration, we find a value 0.02*1 for K in the equation : (Cone, of tetanolysin) x (cone, of cholesterin)= K (cone, of compound). Even in this case the observed values of T for high values of n are a little less than the calculated ones. Even some so-called neutral substances exert an influ- ence upon the haemolytic action of tetanolysin. The pres- ence of salts in large doses increases the action. In this case the erythrocytes are suspended in a physiological solution of cane sugar. If to this so much salt is added that the solution is 0.04 normal, the haemolysis (during i hour at 37° C.) increases to about the double value. A o.oi normal solution is without appreciable influence. Different salts in the same concentration seem to exert the same influence. This influence is probably due to an ac- celeration of the velocity of reaction. For this reason solutions of lysin seem to be more poisonous in a physio- logical salt-solution than in one containing cane sugar. NEUTRALISATION OF PLEMOLYSINS 189 The presence of protein, as egg-albumen or normal serum, protects the erythrocytes from the attack of bases and much more still from that of lysins of bacterial origin. Probably this action consists chiefly in a diminution of the velocity of reaction. If great quantities of normal serum are added, they act as an antitoxin. In mixtures containing heavy doses of poison and of antitoxin, the velocity of reaction is very much retarded, probably because of the presence of large quantities of protein which as impurities accompany the preparations of poison and of antitoxin. The antitoxic influence of normal serum was first ob- served by Ehrlich,1 who employed horse-serum against tetanolysin. Neisser and Wechsberg 2 found a similar in- fluence of horse-serum or human serum on staphylolysin. Madsen and I3 observed a similar action of chicken egg- white on tetanolysin ; still greater is the influence of egg- white from duck's eggs, according to P. T. Miiller.4 Marshall and Morgenroth5 made similar observations on the action of different sera on different compound haemo- lysins (cf. Chapter VIII). The normal serum of the horse, rabbit, and man are the most efficient, that of pigeons, mice, and geese less, while that of sheep is nearly insensible. According to P. T. Miiller, the antitoxic ac- tion against tetanolysin is probably due to the presence of cholesterin in the horse-serum or egg-white. Against the generalisation of this view it may be pointed out that, ac- 1 Ehrlich : Berl. Klin. Wochenschrift^v. 12 (1898). 2 Neisser and Wechsberg: Zeitschr.f. Hygeine, 36. 314, etc. (1901). 3 Arrhenius and Madsen : Festskrift, III. 37 and 43 (1902). * P. T. Miiller: Centralbl. / Bakteriologic, I. 34. 567 (1903). 6 Marshall and Morgenroth: Ztitschr. f. klin. Mcdicin, 47. fasc. 3 and 4. ICp LECTURES ON IMMUNITY cording to Kyes and Sachs, staphylolysin is not acted upon by cholesterin.1 Madsen has even found that other constituents, and not the cholesterin alone, protect erythro- cytes against tetanolysin (still unpublished). The action of different anti-bodies on their correspond- ing poisons is supposed to consist in a simple neutralisa- tion, molecule for molecule. That the process is followed by another phenomenon is indicated by the circumstance that at high concentrations of antitoxin, where it is in excess beyond the toxin present, the calculated values are often found to exceed remarkably the observed ones. An- other phenomenon also, discovered by Danysz,2 indicates that an excess of antitoxin exerts a perturbing influence. Danysz investigated the toxicity of mixtures of ricin with antiricin. He observed that a mixture of a parts of ricin with b parts of antiricin is less toxic if the two constituents are mixed at once, than if a fraction of a, say one-half, is added to the b parts of antitoxin, and after a time the rest of the toxin added to the mixture. The same phenomenon was observed in diphtheria poison by von Dungern, and3 with tetanolysin, staphylolysin, and rennet by Sachs.4 On the other hand, the cobra poison does not display this behaviour. To elucidate this remarkable phenomenon, which seems to indicate that the same quantity of poison may bind dif- ferent quantities of antibody, a large number of experi- ments were carried out on tetanolysin by Madsen, and I 1 Kyes and Sachs: Berl. klin. Wochcnschrift, Nos. 2-4 (1903). 2 Danysz: Ann. de PlnsL Pasteur, 1902. 8 V. Dungern: Deutsche med. Wochenschrift, Nos. 8 and 9 (1904). * Sachs : Centrtlbl. /. Baktcriologic, 37. Part II, 251 (1904). NEUTRALISATION OF H^EMOLYSINS IQI afterward calculated the results.1 Preliminary experiments showed that the effect increased with the quantity of anti- toxin present and that the dilution of the reacting sub- stances exerted no influence, so that the prevailing chemical process must be a monomolecular one. One c.c. of a bouillon containing tetanolysin, was added to 0.8 c.c. of a solution containing antilysin of which 0.18 c.c. were equivalent to I c.c. of the solution containing the lysin. This mixture was kept at 37° C. for a certain time, /, and afterward mixed with 3 c.c. of the poison and the whole held at 37° C. during 30 minutes. The toxicity, q, was de- termined in the ordinary way and found to increase with the time, /, so that q converged against a maximum value G^. If q9 valid for the time o is taken as a unit, the dif- ference q— qQ is a measure of the effect investigated. The difference q^ — q indicates the progress of the effect with time. This quantity is treated as corresponding to a mono- molecular process with the constant of reaction K. The results are given in the following table : — THE PROGRESS OF DANYSZ'S EFFECT FOR TETANOLYSIN WITH TIME t (hours) 9 f-fo r,-f log (fa) — q ) K 0 .00 0 0.60 0.778 — — 0.167 .04 0.04 0.56 0.748 — O.lSo 0.5 .14 0.14 0.46 0.663 - 0.230 I .24 0.24 0.36 0.556- O.222 2 •33 o-33 0.27 0.431 - 0.173 4 •47 0.47 0.13 O.II4 ~~ 0.168 6 •57 0-57 0.03 0.477 - 2 0.217 00 .60 0.60 o Mean 0.197 1 Madsen and Arrhenius : Medd. fr. Vet. — Ak : s. Nobelinstitut, 1. No. 3 (1906). 192 LECTURES ON IMMUNITY In the same manner TTwas found at 19.7° to be 0.067 and at 27° C. to be 0.105. This corresponds to an increase of the velocity of reaction in the proportion 1.86: i and 1.87 : i respectively for an elevation of the temperature of 10° C. This reaction belongs, as the constancy of K indi- cates, to the order of monomolecular reactions. In other experiments the quantity of antilysin, A, was varied, and the following values of q^—q§ were found. The quantities of lysin, Z, were always the same, namely, i c.c. in the first and 3 c.c. in the second fraction, and the experiments were otherwise executed as indicated above. THE MAGNITUDE OF THE EFFECT OF DANYSZ AS DEPENDENT UPON THE QUANTITY OF^ ANTITOXIN USED FIRST FRACTION ?oo -ft Observed Calculated 0.2 C.C. A+\ C.C.Z 0.05 0.02 (0.02) 0.4 c.c. A + I c.c. L 0.23 0.21 (0.22) 0.6 c.c. A -f i c.c. L 0-39 0.40 (0.41) 0.8 c.c. A + i c.c.Z 0.60 0.60 (0.63) 1.2 C.C. A + I C.C.Z 0.97 0.99 (0.87) The calculated values are found under the assumption that the effect is proportional to the excess of antitoxin over that (0.18 c.c.) equivalent to the quantity of lysin (i c.c.) present in the first fraction. This proportionality is very striking in the figures above. The effect may also be cal- culated as the quantity of antitoxin bound by the poison, if the experiments are executed as above, minus the cor- responding quantity if the total quantity of poison is added at once. The figures calculated in this manner are written in parentheses. NEUTRALISATION OF H^EMOLYSINS 193 Evidently the effect depends upon some slow molecular change in the antitoxin which is not bound by toxin. This process goes on only in the presence of the neutralisation products of toxin and antitoxin or of free toxin itself, which therefore may be assumed to bind the transformed antitoxin, so that the reaction can proceed further. The circumstance that the effect of Danysz is not observed with cobra poison seems to indicate that it is the poison itself which binds the transformed antitoxin. For in this special case the neutralisation is nearly complete, just as the neutralisation of a strong acid with a strong base ; and therefore, if the antitoxin is present in excess, no sensible quantity of free poison exists in the solution, and hence we should expect that the effect would not be apparent. Because of the inverse reaction of the reaction-products, new quantities of toxin are always free to bind the trans- formed antitoxin. This new reaction of (the modified) anti- toxin and toxin is much nearer a complete one than the chief reaction between these substances which prevails during the first time of reaction, and which therefore corresponds to the equilibrium studied before. Conse- quently we find that the bond between toxin and antitoxin "is strengthened with time." Therefore also the toxicity of solutions containing an excess of antitoxin is found to be inferior to the calculated value. In this way it is explica- ble that mixtures with a very large excess of antitoxin may be practically harmless, although the calculation does not indicate it. This circumstance explains some experiments of Madsen, in which he allowed an "innocuous" mixture of diphtheria-toxin with antitoxin (hence containing a very great excess of free antitoxin) to diffuse into a gelatinous IQ4 LECTURES ON IMMUNITY solution over which the mixture was placed in a test-tube. If the mixture had been conserved for a certain time (about half an hour at room temperature) there was no indication that free toxin diffused ; but if the mixture was used as it was freshly prepared, the toxin diffused downward, so that the lower parts of the solid gelatinous solution contained two lethal doses for guinea-pigs. Such a strengthening of the chemical bonds is very often assumed in the doctrine of immunity, and it corresponds really to the phenomenon of Danysz. Therefore the strongly toxic solutions in which tetanoly- sin has been added in fractions slowly lose their abnormal toxicity, and after a time (about 6 hours at 37° C.) they are no more toxic than the corresponding mixtures which have not been fractionated. The results of the experiments of von Dungern regard- ing diphtheria-toxin correspond in their general features with those for tetanolysin, so that there is every reason to believe that the cause is identical in the two cases. The same may be said of the other cases in which Danysz's phenomenon has been observed, but the experimental data are extremely meagre. Portier and Richet observed a peculiar phenomenon, which at first seems rather inexplicable, but which is very similar to the phenomenon of Danysz, and therefore may be interpreted in an analogous manner. They prepared a solution of the poison contained in the filaments of ccelenterates (Actinia or Physalis), which produces the same effects as the poison of Urtica, by macerating these filaments in glycerin and water. The poison was injected into the veins of pigeons or dogs, and caused a deep sleep, NEUTRALISATION OF H^MOLYSlNS 19$ by virtue of which it was called hypnotoxin. In greater doses death results under symptoms of asphyxia. The experimenters hoped to produce an antitoxin in the usual way by injecting increasing doses into the veins of the animals. But they did not succeed, because " if an animal receives in a first injection a parts of the poison and in a second injection b parts, it is killed almost instantaneously after the second injection ; whereas an animal in which the dose a -f- b is injected at once does not show very grave symptoms of intoxication, from which it soon recovers." 1 1 Portier and Richet : Bulletin du musee oceanographique de Monaco^ 25 Dec., 1905, p. 10, No. 56, CHAPTER VII NEUTRALISATION OF DIPHTHERIA-TOXIN, RICIN, SAPO- NIN, AND SNAKE-VENOMS IN very nearly the same manner as tetanolysin behaves the practically most important of all toxins, namely, diph- theria-toxin. Through the circumstance of its preparation and standardisation upon a large scale, a great number of experiments have been carried out with it. Unfortunately in most of these experiments but a few (4-6) points in the neutralisation curves have been determined, and no indica- tions are given of the magnitude of the experimental errors. This is, of course, due to the circumstance that we are still in the first beginning of the development of the quantitative side of this question. In a memoir in the Centralblatt fur Bakteriologie (1903), p. 630 et seq., Madsen reported a greater number of measurements of several preparations of this toxin than had been generally done. As illustration may be given the values for poison No. 471 in February- March, 1902 (5 months old), and in November of the same year (14 months old). The letters n and q corre- spond, as for tetanolysin above, to the quantity of antitoxin added and toxicity. As will be seen from these figures, the addition of the first quantities of antitoxin seem not to diminish the toxicity of the poison, the observed toxicity remains constant, and a decrease of ^obs- is not apparent until the quantities 0.05 respt. o.i 8 of antitoxin have been added. From this Mad- 196 NEUTRALISATION OF SIMPLE POISONS 197 POISON 471. FEB.-MARCH, 1902 POISON 471. Nov., 1902 n ?obs. fcalc. n $obs. fcalc. O 50 67 0 35 67 0.05 5° 58 0.06 35 56 O.I 45 48 0. 12 35 45 0.15 40 40 0.18 35 36 0.2 30 31 0.24 18 25 0.25 20 23 o-3 H 15 0-3 15 15 0.36 8 8 0-35 io—8 9 0.4 7 5 0.4 6 5 0.48 3 3 0.45 3 3 0.56 i 2 0.6 i I sen concluded — in agreement with Ehrlich l — that a frac- tion of the antitoxin-binding substance is not poisonous, and that it binds antitoxin before the toxin itself. Such a substance is called prototoxoid by Ehrlich. As the quan- tity, n, necessary to determine a decrease of the toxicity is greater with the old than with the fresh poison, the con- clusion was drawn that the quantity of prototoxoid in- creases with time, and perhaps as the preparation was quite fresh it may at first have contained no prototoxoid at all. This was in complete agreement with Ehrlich's ideas, but on another point regarding the existence of so-called toxons or epitoxins Madsen differed from Ehrlich. As will be seen from the preceding table, the phenomenon of Ehr- lich is very prominent, the same quantity of antitoxin pro- ducing a much less marked reduction of the toxicity at the beginning of the neutralisation than later on. This is explained by the chemical equilibrium between toxin and 1 Ehrlich: Deutsche med. Wochenschrift, No. 38 (1898); Aug. 31, Sept. 7 and 14 (1903). 198 LECTURES ON IMMUNITY antitoxin on the one hand and the products of their reaction on the other hand, as the calculated figures show. These are calculated from the equation valid for the neutralisa- tion of tetanolysin, only the constant of equilibrium here is about eight times lower than there ; in other words, the reaction proceeds farther in the binding of diphtheria- toxin than in the binding of tetanolysin. When the toxicity sinks below one, the animals under experiment do not die after the injection of the quantity of poison employed (o. I c.c.). By administering greater doses it is still possible to kill the animals. But if the quantity of antitoxin exceed a certain amount, the animals are not killed (in short time, eight, days), but show other symptoms of the disease ; after an incubation time of more than a week paralysis occurs. Now Madsen and Dreyer l showed that such paralysis is sometimes observed also after the injection of a quantity of pure diphtheria-poison less than the lethal dose. The free poison injected subcutane- ously gives other symptoms, namely, necrosis and alopecia at the site of injection. Ehrlich and his pupils now con- tend that with mixtures of toxin and antitoxin which do not kill the animals but produce paralysis, the local effects at the site of injection are much less than after the injection of the corresponding quantity of free poison, whereas the paralysis is much stronger with the use of the mixture than with the free poison; and therefore the paralytic result is ascribed to a poison, toxon or epitoxin, which remains after the neutralisation of the true toxin. According to Madsen the difference observed depends upon the following circumstances. The greater part of 1 Dreyer and Madsen : Festskrift, Copenhagen, No. 5 (1902). NEUTRALISATION OF SIMPLE POISONS 199 the free poison is bound near the area of injection. The remainder on entering the circulation is therefore relatively harmless. The mixture behaves, however, in a wholly different manner. If the greater part of its free poison is bound near the area of injection, the diffusing mixture on entering the circulation gives off free poison through dissociation of the toxin-antitoxin compound and therefore causes a much stronger paralysis than does the smaller quantity of originally free poison. It must also be con- ceded that if, as in the case of poison No. 471, in the one case less than one lethal dose, and in the other case about forty lethal doses, together with a large quantity of anti- toxin, are injected, the animal will have much more diffi- culty in freeing its body of the poison in the second than in the first case. For in the first case it has only to neutral- ise and eliminate less than one lethal dose ; while in the sec-, ond case, after the neutralisation or elimination of one lethal dose, new quantities of poison are set free to be eliminated from the animal's body. In the meantime large enough quantities of poison to cause a marked paralysis may diffuse to the nervous organs and disturb their functions. From this point of view the long period of incubation is also easily understood. There is therefore no adequate ground to assume the presence of a poison such as the toxon or epi- toxin of Ehrlich, different from the lethal poison in the diphtheria poison. In recent times a great number of in- vestigations have been done to strengthen the probability of the existence of "toxons." Morgenroth1 has made a very elaborate study of the action upon guinea-pigs of pure diphtheria-toxin and of mixtures with antitoxin. He con- 1 Morgenroth: Zeitschr.f. Hygiene, 48. 177 (1904). 200 LECTURES ON IMMUNITY trasted the difference between the action of pure toxin and of a mixture of toxin and antitoxin, so that there is no doubt upon that point. But there is also no doubt that this dif- ference may be as well explained by the presence of re- action-products of toxin and antitoxin in the solution as by the assumption of a different poison in the two cases. There is another experiment by van Calcar,1 which is cited by the many pupils of Ehrlich, who attempt to defend his views, v. Calcar believed he had found that it was possible by the aid of diffusion under pressure to separate diphtheria poison from the accompanying "toxon"; the latter, he reported, was not able to pass through a membrane while the real toxin diffused. Romer2 has repeated the experiment of v. Calcar and found that it was impossible to detect " the least difference in the behaviour of the origi- nal diphtheria poison and of its diffusion-products." Fur- thermore, he subjected the results of v. Calcar to a critical examination and stated that his experiments did not war- rant the conclusion that it is possible to separate toxons from diphtheria-toxin. In the laboratory of Madsen, Wai- bum has made a thorough investigation of v. Calcar's experiment and come to the same conclusion as Romer, so that there seems to be no doubt that "toxon" cannot be separated from diphtheria-toxin by means of diffusion under the conditions employed by v. Calcar. The " prototoxoid " also seems to be unproved, if we subject the experimental material to a closer analysis. On surveying the material published by Madsen, it struck me that it had not been employed as exhaustively for the 1 Van Calcar: Berl. klin. Wochcnschrift, No. 39 (1904). 2 Romer: Bchrings Bcitrage z. exp. Thcrapit (1904). NEUTRALISATION OF SIMPLE POISONS 201 purposes of calculation as might have been. A recalcula- tion in accordance with the rules valid in the exact sciences (cf. page 13) gave a neutralisation curve which did not show the presence of " prototoxoid " in the poison No. 471 in the experiments of November, 1902. I therefore made a recalculation of all the data relative to the poisons exam- ined by Madsen. For the poison No. 471 I obtained the following results : — FOR FEBRUARY, 1902 NOVEMBER, 1902 SEPTEMBER, 1903 • ?obs. ?calc. n ?obs. ?calc. n ?obs. ?calc. 0 100 100 O 100 100 0 IOO IOO 0.05 744 87.5 0.06 79.3 86.5 O.I 7S-i 75-1 O.I 72.8 75-i 0.12 76.0 73-2 0.15 62.6 62.7 0.15 57.6 62.7 0.18 64.7 59-8 0.2 47.6 50.6 O.2 49.8 50.6 0.24 5°-9 46.6 0.25 45-8 38.6 0.25 32.2 38-6 0.3 39-1 34-0 o-3 25-9 27-3 0-3 28.0 27-3 0.36 23.1 22.4 0.35 17-3 17-5 0.35 17.2 17-5 0.4 14.8 iS-7 0.4 9-6 9.9 0.4 ii. i 9-9 0.48 8.3 7.0 0.45 5-3 6.0 0.45 5.6 6.0 0.54 2-5 4-5 0.5 3-' 4.1 o-5 1.2 4.1 0.6 2.6 3-o 0.6 1.6 2.6 Abs. toxicity = 4.1 Abs. toxicity = 2.86 Abs. toxicity = 2.14 The constant of equilibrium remained unchanged ( = 0.012), in the whole time. No traces of prototoxoids may be detected from the new calculation. This is also the case for two other poisons, A and C, examined previ- ously by Madsen, and in which he supposed large quan- tities of prototoxoid to be present. If prototoxoid had been present in the poison No. 471, it would have been most evident in the later researches (of September, 1903), since it was then rather old. But just in this case the 202 LECTURES ON IMMUNITY agreement between observation and the calculation by which no prototoxoid is supposed to exist, is very good for low values of n. The hypothesis of prototoxoids seems therefore untenable. But on the other hand, the poisonous effects of No. 471 had fallen very remarkably in the seventeen months — to very nearly half the original toxicity — without change in the antitoxin-binding property of the poison. For this same reason Ehrlich supposed that the poison is slowly converted into an innocuous or less poisonous substance with the same antitoxin-binding prop- erties as the toxin itself (cf . p. 1 84). This new substance is called syntoxoid by Ehrlich. The several preparations of diphtheria-toxin differ from each other in showmg rather marked differences in their constants of equilibrium: No. 471, JT=o.oi2; poison A, ^=0.03; poison C, K= 0.004. It will be nec- essary to make new experiments on this interesting ques- tion (and similar ones for tetanolysin) before this can be elucidated. The observed peculiarity, that K has rather different values, might be explained by supposing that the poison is loosely combined with or absorbed by some concomitant substance, for instance by albuminous sub- stances contained in the preparations, and that therefore only a certain fraction of the toxin enters into the equi- librium with antitoxin. This fraction is different in differ- ent preparations of the diphtheria poison, according to their different content of the reacting proteins, and the less this fraction the greater would be the constant of the equilibrium. This view is supported by the observa- tion of Madsen that the value of K for another poison, namely crotalus venom, is different when injected into NEUTRALISATION OF SIMPLE POISONS 203 rabbits than with guinea-pigs.1 But perhaps this differ- ence depends only upon the different mode of injection (intra-venous respectively intra-peritoneal). In the same manner behaves, according to the researches of Madsen and Walbum,2 ricin and its antibody, at least in so far as the agglutinating action of ricin on red blood-corpuscles (of rabbits) is concerned. The agglu- tinating power of the ricin was measured by observing the limpidity of 5 c.c. of a one per cent suspension of red blood-corpuscles added to 2 c.c. of the solution and there- after held at 37° C. for 20 minutes. As example may serve the following figures : — n =o 0.025 0.035 °-°45 o-°55 0.065 °-°75 0.087 o-1 ?obs. =6.7 6.7 3.6 2.1 1.5 1.0 0.8 0.64 No. 43 (1903), No. 5 (1904). THE COMPOUND H^EMOLYSINS 221 in the blood-corpuscles to cause a trace of laking. As soon as the alexin is bound, new quantities of it diffuse into the blood-corpuscles. Therefore the haemolysis in- creases if corpuscles loaded with immune-body are treated with fresh alexin. On the other hand Ehrlich and Mor- genroth found that the fluid in which the erythrocytes had been suspended for one or two hours at o° C. contained alexin. In this manner they showed that even the haemo- lysins in normal sera (for instance goat-serum acting upon guinea-pigs' erythrocytes) are formed by the union of an immune-body and an alexin. They also stated that a given immune-body combined with different alexins (nor- mal sera from different animals) gives haemolysins of very different haemolytic power, which eventually may be due to many different circumstances. Ehrlich and Morgenroth supposed that the compound of immune-body and alexin, i.e. the haemolysin, which is pres- ent in the mixture of their solutions, is the active part and that it is chemically bound to the erythrocytes, which are regarded as if they were molecules. To explain the failure of the reaction at o° C. they supposed that the haemolysin is nearly completely dissociated at low temperatures, o° C., but not at 40° C. ; this presupposes that the union of im- mune-body and alexin is accompanied by an extremely great absorption of heat, which is in the highest degree improbable. The membrane of the erythrocytes is evi- dently to a very slight degree permeable to the haemolysin ; and, therefore, it is only the haemolysin formed inside their membranes which exercises a poisonous action on the corpuscles, just as in the case of saponin and cholesterin. These experiments do not teach us anything concerning 222 LECTURES ON IMMUNITY the presence of haemolysin in the mixture of immune-body and alexin. Overton has drawn attention to the fact that the alkaloids are much more toxic to cells of animal or vegetable origin than are their salts. This depends upon the circumstance that the cell membranes are permeable to the alkaloids themselves, but not so to their salts, or, more strictly speak- ing, to their ions. The salts are poisonous at all only be- cause they are to some extent hydrolysed in their watery solutions; and therefore the salts of the weak acids are more poisonous than those of the strong acids. Under these circumstances an excess of acid diminishes the toxic- ity of these salts, even to the point of complete suppres- sion of toxic action. On the other hand, the presence of substances with alkaline reaction sets the alkaloid free, and thus increases the toxicity of the solution of the salt of an alkaloid. (Cf . Hoeber, Physikalische Chemie der Zelle und Gewebe, 2d ed., 1906, p. 165.) In some cases, which seem to be rather rare, the absorp- tion of the immune-body by the erythrocytes is by far not so evident as in the ordinary case represented by the figures above (p. 1 50). Ehrlich and Sachs * describe some experiments on the action of a mixture of inactivated ox- serum and normal horse-serum on guinea-pigs' erythro- cytes. These are at 37° C. laked by the said mixture within one hour. But if the erythrocytes are suspended for one hour at 37° C. in the ox-serum, and then after centrifugation mixed with the horse-serum, no such re- sult is observed. Ehrlich explains this observation as due to the circum- 1 Ehrlich and Sachs: Berl. klint Wochenschrifa No, 31 (1902). THE COMPOUND H^MOLYSINS 223 stance that the corpuscle has no affinity for the immune- body until it is bound to the alexin. Evidently this is only a very artificial circumscription, and no real explanation. Bordet, however, later on proved that even in this case the immune-body is absorbed ; to his investigation on this subject we shall return later (cf. p. 260). The first theoretical view of these phenomena was given by Bordet,1 who regarded the immune-body as a kind of catalytic agent, which " sensibilised " the erythrocytes to the attack of the alexin. The objection that alexin alone does not attack the erythrocytes is evidently untenable. Bordet advanced his experiment on the effect of a fraction- ated addition of haemolytic serum (cf. p. 34) to a given portion of erythrocytes as pleading in favour of his idea. This experiment indicated that the binding to the cells does not take place in constant proportion, as Ehrlich tacitly supposed. But Ehrlich replied that the cells might bind more haemolysin than just the quantity necessary for laking. Since we know now that the immune-body is absorbed by the erythrocytes, this controversy has only an historical interest. In a certain sense we must allow Bordet to have been in the right, the entrance of the immune-body into the erythrocytes is the necessary con- dition for the attack of the alexin, which, as we shall see later, is really bound to equivalent quantities of the im- mune-body dissolved in the erythrocytes. Against Bordet the experiment of Ehrlich and Sachs has been cited, but this is easily explained by the view that the immune-body is absorbed. 1 Bordet: Annales de rinst. Pasteur, 12. 688 (1898), and 14. 257 (1900). 224 LECTURES ON IMMUNITY An experiment of Neisser and Wechsberg1 seems to indicate that immune-body and alexin, when mixed, really enter into a compound, at least partially. They used different bacteriolysins, which like the haemolysins are of a compound nature, so that the presence of two differ- ent substances, an immune-body and an alexin, is neces- sary. They used a constant quantity of bacteria and of alexin, to which they added different quantities of immune- body. At first, as we know, the action increases with the concentration of the immune-body, but finally reaches a maximum ; and, if this quantity exceeds a certain magni- tude the effect then decreases, so that the bacteria may even not be destroyed. This phenomenon has been called the "diversion" (Ablenkung) of the alexin. As the ex- periments with bacteriolysins are not very well adapted to quantitative experiments, the following hsemolytic experiments with ox erythrocytes, immunised rabbit- serum as immune-body, and guinea-pig-serum as alexin, may serve to elucidate the relations. In the following table the quantity of alexin present in 2.5 c.c. of solution is called b, and the corresponding quantity of immune- body is called a. As unit is taken the thousandth part of the quantity contained in I c.c. of the two original prep- arations. The quantity of erythrocytes was I c.c. of a 5 per cent suspension of ox blood. The mixture, which had been kept for thirty minutes at 24° C, was allowed to act on the erythrocytes for two hours at 37° C. In this manner I found the following degrees of haemolysis (com- plete haemolysis = 100) : - 1 Neisser and Wechsberg: Munch, med. Wochenschrift (1901). THE COMPOUND H^MOLYSINS 225 ACTION OF DIFFERENT QUANTITIES OF IMMUNE-BODY ("DIVERSION") a = b = 10 1=6 3 = 4 I 31 — — 10 45 37 30 30 100 Si 71 5° 100 87 65 100 100 92 64 200 100 35 15 300 64 24 7 The effect is very evident. The maximum in the three series occurs at about a = 80, 50, and 30 respectively. This observation seems to agree very well neither with the views of Bordet nor with those of Ehrlich. If the catalytic agent were present in greater quantity, we might expect a stronger action, but the reverse is the case if a is greater than 100. Now according to Ehrlich's view we might expect that the active substance, the hsemolysin which is here preformed in the mixture and thus attacks the corpuscles, should not decrease in quantity with in- creasing concentration of immune-body, and therefore the effect should be just as according to Bordet's theory. Ehr- lich has accepted the following explanation given by Neisser and Wechsberg for their experiment, in which the bacteria were not attacked in the presence of an excess of immune-body. " If a is large, there is a marked excess over the quantity of alexin (b), so that all the alexin is combined as lysin (ab) before the mixture is added. The excess of a is then bound to the bacteria (e) and gives the compound ea. If now the affinity of b for a is greater than for ea, b will remain as lysin (ab) in the solution, and Q 226 LECTURES ON IMMUNITY not pass into ea to give the compound eab which gives bacteriolysis. It is mere chance whether the affinity of b for a is greater than for ea, as in this case, or less, in which case haemolysis would occur." This extremely artificial explanation seems to me quite erroneous. For if we have the compounds ea and ab and the compound eab may be formed, its formation depends wholly upon whether e has a greater affinity for ab than for a.1 If not, then eab is not formed, even if a is not present in excess. Therefore, if Ehrlich's idea were right, no bacteriolysis should occur in Neisser and Wechsberg's experiments, and no haemo- lysis in the experiments cited above. The probable cause is the following. If a is large, it is not totally absorbed by the cells, but a fraction of it remains in the surrounding fluid, and this part increases rapidly with increasing a (cf. p. 150). a forms a com- pound (ab) with b as well outside the cells as within them. This compound is partially dissociated, so that its quantity increases and the quantity of free alexin b decreases with increase of a in the liquid. At very high excess of a, b may become practically wholly bound. This seems to have been the case in Neisser and Wechsberg's experi- ment (the errors of observation are too great to give a final decision). The membranes of the cells are (cf. p. 22 r) practically impermeable to the lysin (ab\ and only the lysin formed from a and b within the cells is active. As there is now very little (or practically no) free b in the 1 It is assumed that the amount of a exceeds the quantity which is neces- sary to bind (produce lysis with) the quantities e and b. This necessary quantity of a is rather unimportant, about 2 in my experiments cited above, and even in Neisser and Wechsberg's experiments this condition has proba- bly been fulfilled long before a gave a maximum. THE COMPOUND ILEMOLYSINS 22? solution, b cannot diffuse into the cells during the given time of the experiment and produce a lysis, whereas a is present there in many times the necessary quantity. If a decreases, but not so much so that the quantity necessary for the lytic action is not absorbed by the cells, then b increases in the surrounding fluid and a greater quantity of it diffuses into the cells within a given time. There- fore the quantity of ab present in the cells may increase with decreasing quantity of a, if this substance be present in great excess in the surrounding fluid. The presence of a maximum is therefore quite easy to understand. The very great flatness of the curve of this maximum indicates that the haemolysin ab is stable only in the presence of a large excess of a and b\ and that a binding of strong affinities with sharp discontinuities, as Ehrlich supposes, is excluded. Our view leads furthermore to the conclu- sion that the effect observed by Neisser and Wechsberg should be more prominent for low values of b than for larger values. The quantity of diffusing free alexin is in the first approximation proportional to b. This quantity is therefore proportional also to the quantity of haemolysin formed in the given time of action (two hours at 37° C. and the time of sedimentation at lower temperature, about 3° C.). With large quantities of alexin (b>2O in the present case), the diffusion transports enough of alexin during the time of action to cause total haemolysis, even at the highest concentrations of a employed. Further, it is evident that as the quantity of free alexin is nearly proportional to b and inversely propor- tional to a, nearly the same effect will be reached if - is a a 228 LECTURES ON IMMUNITY constant. This is actually found to be the case ; for in- stance, the degree of haemolysis 64 corresponds to the fol- lowing values of -: = 0.033, = 0.04, and-^- = 0.04. a 300 150 100 This is evidently true only if the haemolytic action is of such a magnitude as it is possible to reach with the quan- tity of b present ; and this circumstance indicates that the said rule is only a rather rough approximation. The rule stated leads to the consequence that the maximum appears at a lower value of a for a lower value of b, and the values of a at the maximum are nearly proportional to the value of b (80 : 10 = 8 ; 50 : 6 = 8.3 ; 30 : 4 = 7.5). It had been observed in different investigations that the quantity of alexin necessary to produce complete haemolysis is the less the greater the quantity of immune- body that had been used for the " sensibilisation " of the erythrocytes.1 This matter was subjected to a closer investigation by Morgenroth and Sachs.2 They found that in one case (viz. haemolysis of sheep erythrocytes by means of immune-bodies from goat blood and alexin from guinea-pig serum) the quantity (b) of alexin was often nearly inversely proportional to the quantity (a) of immune-body used. In another case (haemolysis of ery- throcytes from ox blood with immune-body from goat- serum and an alexin from serum of guinea-pig or of rabbit or even of sheep) the quantity of alexin necessary for com- plete haemolysis was independent (or nearly so) of the quantity of immune-body used. In other cases the same Jv. Dungern: Munch, med. Wochenschrift, No. 20 (1900); Gruber: Wiener klin. Wochenschrift^Q. 15 (1902). 2 Morgenroth and Sachs: Berl. klin. Wochenschrift, No. 35 (1902). THE COMPOUND H^MOLYSINS was true except when the quantity a was very low. To explain this very different behaviour in different cases the authors have made use of rather complicated hypotheses, to enter in detail upon which would consume too much space. These experiments were the first quantitative measurements, on a large scale, bearing upon the action of compound haemolysins, and they therefore merit a certain interest. Another observation of quantitative nature was made by Morgenroth.1 He determined the least quantity of alexin that had to be added to produce complete haemolysis, and the greatest quantity of alexin which could be added before a perceptible haemolysis occurred. In this case immune- body was present in excess. In other cases alexin was present in excess, and the quantities of immune-body necessary for complete haemolysis and for the first trace of haemolysis were observed. Morgenroth found that the two said quantities of alexin were, as the average of 13 combinations, in the proportion 100 to 13.6; and the cor- responding quantities of immune-body in the proportion 100 to 14.1 (mean of 10 combinations). If, as is rather probable, the quantity of haemolysin found is nearly pro- portional to the quantities of alexin or of immune-body used, and the rule holds that the degree of haemolysis is proportional to the square of acting haemolysin, this would indicate that an haemolysis of 2 per cent is just perceptible, which in some cases may be rather probable. Quite recently Wilfred H. Manwaring2 has given a 1 Morgenroth : Wiener klin. Wochenschrift, No. 5 (1904). '2 Manwaring: Journ. Biol. Chemistry, 1. 213 (1906). No definite indi- cation is given of the nature of the preparations employed. 230 LECTURES ON IMMUNITY curve representing the degree of haemolysis by means of different quantities of immune-body in the presence of a great excess of alexin. It may here even be assumed that the quantity of haemolysin found is proportional to the quantity of immune-body. The following figures are taken from the original curve. H is the degree of haemolysis, A the quantity of immune-body. HAEMOLYSIS BY MEANS OF DIFFERENT QUANTITIES OF IMMUNE-BODY A H Sa SH-.A I °-5 0.71 0.71 2 I i o-5 3 i-S 1.23 0.41 4 2 1.41 o-35 5 2-5 1.58 0.32 6 3 '•73 0.29 7 4 2.0 0.29 8 6 2-45 0.31 9 9 3-o 0-33 10 22 4.69 0.47 ii 35 5-92 0-54 12 47 6.86 o-57 13 58 7.62 o-59 14 68 8.25 o-59 15 79 8.89 o-59 16 84 9.17 0-57 17 86 9.27 0-55 18 90 9-49 0-53 19 93 9.64 0.51 20 97 9.85 0.50 21 99 9-95 0.47 22 IOO 10.0 0-45 Between the degrees of haemolysis 35 and 90, i.e. within two-thirds of the interval examined, a remarkable propor- tionality between the square root of the degree of haemoly- sis and the quantity of immune-body is observed. With THE COMPOUND H^MOLYSINS 231 lesser quantities of immune-body, the haemolysis is not so great as this rule predicts, and this corresponds to the behaviour of other lysins (cf. pp. 103 and 169), except that the deviation from the rule in this case is evident throughout the wide interval from o to 30 per cent, where as for other lysins the deviation is observed only under 10 or 15 per cent. In the memoirs cited Morgenroth and Morgenroth and Sachs employed,1 among other hypotheses to explain their observations, this also, that immune-body and alexin some- times enter into a compound haemolysin or haemolysin united with an erythrocyte, which is stable only in the pres- ence of considerable quantities of the components. These different substances participate, according to the Frankfort school, in a chemical equilibrium. On the other hand, the adherents of Bordet, among whom Metchnikoff, Gruber, and Biltz may be cited, regard the haemolytic action as a phenomenon of absorption. It seemed possible to decide by means of quantitative experiments which of these two ideas corresponds to the facts, and Ehrlich invited me to undertake an investigation of this point in the laboratory of the serum institute in Frankf ort-on-the-Main. These in- vestigations led to the very certain conclusion that a chemi- cal equilibrium governs the reaction of immune-body and alexin, but the important reaction takes place within the erythrocytes. It is very probable also that such an equi- librium exists, even in the mixture of immune-body and alexin, as is indicated by the diminution of the haemolytic effect with increasing immune-body, as noted in some cases 1 Morgenroth: Wiener klin. Wochenschrift, No. 43, p. 5 (1903); Mor- genroth and Sachs: Berl klin. Wochcnschrift, No. 35, p. 8 (1902). 232 LECTURES ON IMMUNITY (cf. p. 225). And it is even probable that the haemolysin enters into combination with the molecules of the proto- plasm inside the erythrocytes, just as tetanolysin or alka- lies do (cf. pp. 103 and no); but concerning this reaction we learned very little or nothing from my experiments. My measurements were founded upon determinations of the degree of haemolysis exerted by a given mixture of immune-body and alexin acting upon a given quantity of erythrocytes. To this end i c.c. of a 5 per cent sus- pension of erythrocytes (from sheep or ox) in physio- logical solution of NaCl was mixed with 1.5 c.c. of a fluid containing the desired quantities of immune-body and alexin and additional physiological salt-solution until the total volume was always 2.5 c.c. All the preparations were kindly supplied by the Institute. After the blood suspension and the haemolytic mixture had been each mixed thoroughly by shaking (for reasons referred to above, cf. p. 15), the cell suspension was poured into the mixture in a rapid manner, the test-tubes containing the mixture were placed in an incubator at 37° C. for 2 hours, after which time the test-tubes were taken out and set into a refrigerator at about 2° C., where they remained until the next morning (about 17 hours), when they were examined and the degree of haemolysis deter- mined by comparison with test-tubes containing different quantities of the same variety of erythrocytes, laked in distilled water. The immune-body and the alexin were left together for about half an hour at room temperature (20-24° C.) before the addition of the cell suspension, but the time of reaction between these two substances seemed not to have a per- THE COMPOUND H^EMOLYSINS 233 ceptible influence, as special experiments indicated. As has been said, probably the chemical reaction takes place, at least chiefly, in the interior of the red blood-corpuscles, and under such circumstances it is easy to understand that the time of reaction between immune-body and alexin prior to the addition of the blood is of little or no conse- quence. Since we know the haemolysed quantity, we wish to calculate from it the quantity of haemolysin. For this purpose we may employ the rule that the hasmolysed quan- tity is nearly proportional to the square of the quantity of acting haemolysin. If this rule for low concentrations of haemolysin does not lead to quite exact results, this result does little harm, for the chief thing is to find instances in which the quantity of haemolysin is the same, and this occurs, evidently, as soon as the degree of haemolysis is the same. Approximately the quantity of haemolysin is proportional to the square root of the known quantity of haemolysis. In reality we make use of this rule only in order to set forth the observations in a simple manner. As illustration I reproduce here a series of experiments with red blood-corpuscles from the ox. The immune-body was prepared by injection of such erythrocytes into the veins of a goat. The alexin was normal serum of guinea- pigs. The arbitrary units employed are o.ooi of a c.c. of the preparations containing immune-body or serum of guinea-pigs. The unit of haemolysin is a hundredth part of the quantity necessary for total haemolysis of the fixed quantity of blood-corpuscles. The first of the following series gives the observed haemolysed quantities, the second the quantities of haemolysin (square root of the foregoing 234 LECTURES ON IMMUNITY multiplied by 100). In parentheses are tabulated the calcu- lated values of the same quantities according to the for- mula : — (5 a — x) (20 b — x) — gox. Where a is the quantity of immune-body added, and b the corresponding quantity of alexin, x is the quantity of haemolysin formed. EQUILIBRIUM BETWEEN IMMUNE-BODY FROM GOAT, ALEXIN FROM GUINEA-PIG, AND H^MOLYSIN FOR Ox ERYTHROCYTES A. HAEMOLYSIS a — 10 30 100 300 900 6=60 16 (21) — — — — 40 14 (20) — — — — 25 I4(l8) — - — — 15 15 (14) — * — — — 10 14 (10) 50 (7°) 96 (100) 100 (100) — 6 5(6) 35 (36) 72 (96) 96 (100) — 4 4(4) 20 (19) 56 (43) 67 (53) — 2-5 — 6(8) 26 (18) 22 (22) — i-5 — 2(3) 6(6) 5(8) 6(9) i — — 2(3) 2(3) 3(4) 0.6 — — 1(0 2(0 2(1) B. QUANTITY OF H^MOLYSIN a — 10 3° TOO 3oo 900 b=6o 40 (46) — — — 40 37 (45) — — — 25 38 (42) — — — 15 39 (37) — — — 10 38 (33) 71 (84) 98 (100) 100 (lOO) — 6 22 (25) 59(60) 85 (98) 98 (100) — 4 20 (20) 45 (44) 75 (66) 82 (73) — 2-5 — 24 (29) 51 (43) 47 (47) — i-5 — 15 08) 25 (25) 22 (28) 24 (29) i — — 15 (17) 15 09) 18 (20) 1.6 — — II (10) I3(n) 13 (12) THE COMPOUND H^MOLYSINS 235 As will be seen from these figures, the agreement be- tween experiment and calculation is very satisfactory and the differences lie within the possible errors of observation. For low values of x, the observed values are generally less than the calculated ones, which may be due to the devia- tion from the rule of square roots. The time of reaction was long enough to yield nearly the limit value of the reaction, so that it was not necessary to measure the time with great exactitude. If, now, the immune-body acted like a catalytic agent, we might expect that the haemolysis, at a constant concen- tration of immune-body, would increase with the quantity of alexin, as it indeed does if the quantity of immune-body is not very low. But if the quantity of alexin is sufficient for total haemolysis(£ > 5), then the reaction should attain total haemolysis more slowly with low quantities of immune- body and more rapidly with higher quantities. For small quantities of immune-body the limit of reaction would therefore not be reached before total haemolysis was attained, as soon as b > 5. This does not agree at all with experience. With small quantities of immune-body the haemolysis shows itself to be nearly independent of the added quantity of alexin as soon as this exceeds a certain quantity (b > 10). This can be explained only by assuming a chemical reaction in which the immune-body contributes material to the formation of haemolysin. With low quan- tities of immune-body there cannot be formed a greater quantity of haemolysin than is equivalent to the available quantity of immune-body; the added quantity of alexin may be of any magnitude. This corresponds very well with the observations and the same reasoning is evidently valid 236 LECTURES ON IMMUNITY for the alexin. If it be added in small quantity, there cannot be formed more than the equivalent quantity of haemolysin. This property is also very evident from the measurements. Much better than all general considerations do the agreements between the values calculated from the for- mula and the observed values indicate the correctness of the view adopted. This formula indicates also that one unit of the haemolysin (that is, the hundredth part of the quantity necessary to haemolyse completely i c.c. of a 5 per cent suspension of bovine red blood-corpuscles) is equivalent to the fifth part of a unit of immune-body and to the twentieth part of a unit of alexin. The cir- cumstance that the quantity of haemolysin is to be sub- tracted from the quantity of added immune-body and alexin, recalculated to equivalent quantities, shows that both substances are consumed in the formation of the haemolysin. The form of the equation indicates also that one molecule of immune-body and one molecule of alexin form one molecule of haemolysin. Another illustration is red corpuscles from sheep blood attacked by a haemolysin formed of an immune-body from a goat injected with sheep blood, and alexin in serum from guinea-pigs. The quantity of haemolysin, x, was cal- culated with the formula : — (40 a — x) (25 b — x)= 1900 x. I give only the series for the observed haemolysis. The agreement between the observed and calculated values is, as in the preceding illustration, as good as could be desired, that is, within the possible experimental errors. THE COMPOUND H^iMOLYSINS 237 HAEMOLYSIS OF ERYTHROCYTES FROM SHEEP BY IMMUNE-BODY FROM GOAT AND ALEXIN FROM GUINEA-PIG a = i 3 10 3° 100 300 1000 b = 6o 5(4) — — — — — 40 5(2) 17 (16) — — — — — 25 2(2) 15(9) 60 (75) — — — — 15 — 5(4) 35 (33) 95 («») — — — 10 1(0-3) 3(2) 20 (16) 80 (85) 95 (I0°) — — 6 — 2(1) 7(6) 35 (30 75 (10°) 100 (100) 100 (lOO) 4 — — 3(3) 1505) 35 (44) 80 (75) 70 (90) 2-5 — — — 7(6) I5(i7) 30 (30) 50 (36) i-5 — — — 4(6) 4(10) 17 (13) i — — — — — 2(4) 3(6) It may perhaps seem strange that greater quantities of alexin have not been used, but the normal serum of guinea- pigs in itself contains a little haemolysin, so that it is nec- essary to introduce a correction for this action ; a simple subtraction was used. For greater concentrations of alexin the corrections would be rather great, and as they are always accompanied by some uncertainty, it seemed best not to use such concentrations. Even in this case the formula indicates that from one molecule of immune-body and one molecule of alexin one molecule of haemolysin is formed. This is not always the case, as will be seen from the following examples. The in- dicator used was bovine red blood-corpuscles ; the immune- body was prepared from the blood of a rabbit injected with bovine corpuscles ; the alexin was normal serum from the guinea-pig. The arrangement of the experimental series was quite the same as in the instances treated above. The values concern the haemolysis. Here we meet with the exponent f , which seems to be common in this domain. The equation indicates that two 238 LECTURES ON IMMUNITY molecules of immune-body with three molecules of alexin yield six molecules of hsemolysin. H^MOLYSIS OF BOVINE ERYTHROCYTES BY IMMUNE-BODY FROM RABBIT AND ALEXIN FROM GUINEA-PIG a = 0.4 i IO 5° IOO 300 = 60 12 (II) 32 (35) — — — — 40 12 (10) 27 (26) IOO (lOO) — — — 25 5 (7) 18 (17) 70 (83) — — — 15 3 (5) 6 (ii) 40 (44) — 90 (loo) — 10 — 5 (7) 27 (27) — 70 (59) 6 — 2 (4) 12 (I3) 40 (22) 22 (26) — 4 — i (3) 4 (7) 10 (10) 3 (12) 10 (I4) 2-5 — — 2 (3) 3 (5) 2 (5) 5 (6) The equation used for the calculation has the form : — (1000 — *)*(iO b — x)= i. a*2. H/EMOLYSIS OF ERYTHROCYTES FROM Ox BY MEANS OF COBRA-LECITHID LECITHIN = 2 3 10 50 IOO Cobra =250 88 (94) — — — — 15° 80 (57) IOO (lOO) — — — IOO 32 (37) 72 (79) — — — 75 32 (28) 64 (59) — — — 50 20 (20) 36 (39) IOO (lOO) — — 35 10 (13) 32 (28) 88 (87) — — 25 8(9) 32 (20) 66 (62) IOO (lOO) — 15 — 8 (12) 36 (38) 72 (84) — 10 — 4 (8) — 60 (56) IOO (IOO) 7-5 — — — 40 (42) 68 (96) 5 — — — 36 (28) 64 (64) 3-5 — — — 4 (20) 40 (45) 2-5 — — — — 40 (32) i-5 — — — — 32 (16) i — — — — 24 (13) In all these cases the immune-body and the alexin are THE COMPOUND H.EMOLYSINS 239 consumed to a sensible degree in the formation of the haemolysin. Therefore in the formulae x is always sub- tracted from the equivalent quantity of immune-body and alexin. In another simikr case, namely, the formation of the haemolytic substance cobra-lecithid from cobra-poison and lecithin, the quantity of haemolysin seems always to be so small that it makes no difference if it be subtracted from the quantities of cobra-poison and lecithin or not. The experiments were carried out with a o. i per cent solu- tion of cobra-poison (i c.c. = 10,000 units) and a i per cent solution of lecithin (i c.c. = 1000 units). The arrange- ment of the table is the same as in the foregoing. The calculated values were obtained with the aid of the formula : — C (L- i. 5)1 = 6.67*2 = 6.67/2, where C represents the quantity of cobra-poison added, L the corresponding quantity of lecithin, x the quantity of haemolysin formed, and h the observed quantity of haemo- lysis tabulated above. As will be seen from the equation, no haemolysis occurs until 1.5 units of lecithin have been added. This quantity was determined by special experi- ments. The experiments with cobra-lecithid indicate that this poison behaves a little differently than the other haemolysins. With these a limit of the reaction was prac- tically reached on standing for two hours in an incubator at 37° C., and afterwards for seventeen hours in a refrig- erator. But in the case of cobralysin, haemolysis continued in the sedimented blood-corpuscles after the observations cited above were ended, so that the result was wholly dif- ferent after an additional twenty-four hours, during the 240 LECTURES ON IMMUNITY chief part of which time the temperature was 2° C. The haemoglobin that had passed out in the last twenty-four hours had not had time to diffuse throughout the liquid, but remained in the lowest strongly coloured stratum. These observations suggest strongly that the haemolytic substance was absorbed by the erythrocytes. The quantity, 1.5, of lecithin must in some manner be bound by a foreign substance in the blood suspension, so that it is not available for the cobra-poison. In this case we cannot see from the formula that cobra- poison and lecithin are consumed for the formation of the cobra-lecithid. This must therefore be dissociated in solu- tion to an extremely high degree, and the least quantities of it must be sufficient to produce haemolytic actions. But precisely for this case Kyes has made it probable that a compound — cobra-lecithid — is formed, that even in very small quantities produces haemolysis.1 The power f for the quantity of lecithin in the last formula is the same which is sometimes found for the immune-body, but never for the alexin. This seems to in- dicate that the lecithin plays the same r61e as the immune- body in the formation of the haemolysin, and that the cobra-poison corresponds to the alexin. This opinion seems corroborated by the fact that the alexin is regarded as the properly poisonous substance of the two, and it seems more natural to suppose that the cobra-poison is the carrier of the poisonous properties, than that the innocuous lecithin acts haemolytically. Quite recently there has been a vivid discussion, if lecithin exerts an influence on the haemolytic action of a 1 Preston Kyes: Berl. klin. Wochenschrift, Nos. 42 and 43 (1903). THE COMPOUND H^MOLYSINS 241 very simple substance, namely, mercuric chloride.1 As this process is rather perspicuous and indicates the mode of action of lecithin, we will take it under consideration for some moments. In weak doses mercuric chloride acts haemolytically ; in greater concentration it agglutinates the erythrocytes and the haemolysis is weak or insensible. At a certain con- centration, therefore, the degree of haemolysis passes through a maximum. The disappearance of the haemo- lytic action at higher concentrations is regarded as due to the hardening of the protoplasma and especially of the membranes of the erythrocytes, whereby the passage of haemoglobin through it is hindered. As Sachs has shown,2 it is possible to provoke the haemolysis of such hardened erythrocytes by treating them with solutions of potassium iodide or hyposulphite of sodium or of albumen, which all take away a deal of the mercuric chloride from the erythrocytes, which have been in contact with a solution of this substance. The observed maximum, therefore, in this case depends upon a double action of the mercuric chloride, one de- structive, whereby the erythrocytes give away their haemo- globin *-to the surrounding fluid, and one hardening, whereby the permeability of the membranes of these cells is checked. It is well possible that other similar cases, in which maxima are observed, as for instance with the botulismus-poison or with mixtures of saponin and 1 Detre and Sellei: Berl. klin. Woe kens chrift, No. 30 (1904); Wiener klin. Wochens chrift, Nos. 45 and 46 (1904); No. 30 (1905). Sachs: Wiener klin. Wochenschrift, No. 35 (1905). 2 Sachs: Miinchner medicinische Wochenschrift, No. 5 (1902). 242 LECTURES ON IMMUNITY cholesterin, may be due to a secondary action, whereby the velocity of the process is retarded, concurring with the chief action of the poison. Detre and Sellei had observed that the haemolytic action of mercuric chloride is diminished by the presence of lecithin. Against this Sachs stated that lecithin ac- celerates the action of mercuric chloride. Sachs rightly holds the opinion that no poisonous combination of mer- curic chloride and of lecithin exists, but that we here observe an action of the lecithin on the erythrocytes, whereby these are rendered more accessible to the mer- curic chloride. Here we find that Sachs takes up the opinion of Bordet regarding the sensibilisating action of certain substances on erythrocytes. Evidently the lecithin enters into the cell-membranes and increases their per- meability to the haemoglobin or to the mercuric chloride. According to this observation it seems obvious to sup- pose that the action of lecithin on erythrocytes treated with cobra-poison is due to a similar circumstance. The slowness of the hsemolytic action in this case speaks in favour of this opinion. If the chief part of the lecithin remains in the fluid, the absorbed part in the membranes of the erythrocytes is proportional to the f power of the quantity of lecithin, diminished by the chemically bound part of it. The results given above regarding the action of cobra-poison in presence of lecithin will then be under- stood if we make the very plausible hypothesis that the haemolytic action is proportional to the concentration of the cobra-poison, and further that the permeability of the cell-membranes is proportional to the absorbed quantity of lecithin. THE COMPOUND HJEMOLYSINS 243 As we have seen before, the immune-bodies in the rabbit treated with ox erythrocytes, and in the goat treated with sheep erythrocytes are almost completely absorbed by the red blood-corpuscles (cf. p. 150) in weak solutions. The same is probably the case for the immune-body from a goat treated with ox erythrocytes. The formation of haemolysin is, without doubt, effected only in the red blood-corpuscles themselves, for these absorb the immune- body before a reaction takes place (cf. p. 220). On the other hand, they dissolve very little of the alexin, but this is combined with the immune-body, so that new alexin enters and forms the poisonous haemolysin. The circum- stance that the alexin always enters to the power i would then indicate that the alexin has the same molecular weight in the blood-corpuscle and in the surrounding fluid, so that a constant fraction, probably very little, is always con- tained within the blood corpuscles. In the equation of reaction this fraction should probably be introduced, but if instead of that we, as in the formulae above, write the whole quantity of alexin, that has no other effect than that the constant of equilibrium changes in a certain pro- portion. The haemolysin formed probably remains for the greatest part absorbed in the red blood-corpuscles. As for lecithin, it probably enters very easily into the red blood-corpuscles, and therefore plays the r61e of an immune-body. The action of the compound haemolysins is therefore, like that of the simple haemolysins, based upon their presence in the red blood-corpuscles, which are thereby so changed that the membrane becomes permeable to haemoglobin. As we have seen before, the immune-body at higher 244 LECTURES ON IMMUNITY concentrations is not wholly absorbed by the erythrocytes, and therefore gives a compound with the alexin, even out- side the erythrocytes. Thereby we explain the seeming anomaly that a less degree of haemolysis may be pro- duced by a greater quantity of immune-body (cf. p. 224). It is evident that equations like those given above are not able to reproduce such a phenomenon. The same effect may even exert a diminishing influence, though to a lesser degree, on the action of the immune-body. It would therefore be conceivable that this effect is responsible for the exponent f for the quantity of the immune-body ; and that in reality, if this disturbing effect did not occur, the first power of the said quantity would result from the experiments. This opinion seems confirmed by the fact that the exponent f occurs precisely for the combination of immune-body from the rabbit treated with ox erythrocytes and alexin from guinea-pigs, which in another series of experiments — with different preparations — gave a very pronounced diversion of the alexin. But this explanation is not applicable to the action of lecithin in the experi- ments with cobra-lecithid. My experiments show that even in this case a remark- able regularity governs the binding of immune-body and alexin. Therefore it has not been necessary for me to make use of a large number of different methods of ex- planation, as Morgenroth and Sachs did. To explain the results of their measurements they suppose that the im- mune-body is bound to the erythrocytes in different manners, that the affinity of immune-body for alexin is altered to different degrees by the influence of the erythro- cytes, and that the immunised sera contain a great number THE COMPOUND H^MOLYSINS 245 of different immune-bodies. " We observe that the different phenomena which we have found correspond to relative quantities of immune-bodies and alexins (at complete haemolysis) may have very different causes, but that they, if we regard all these factors related above, may be ex- plained in an unconstrained manner." 1 On the other hand, I have found that the observed phenomena may be explained by assuming that the law of mass action governs the equilibrium of reaction between immune-body and alexin, and that no special hypotheses are necessary for the special cases. It may even be regarded as very prob- able that a closer investigation of the combinations ex- amined by Morgenroth and Sachs would have led them to a more simple explanation than that which they have pro- posed. We have stated above that after repeated injections of a poison, e.g. ricin, into the veins of an animal, e.g. a rabbit, the serum of this animal contains an antitoxin, in this case antiricin. If we inject this antibody into the veins of another animal, e.g. a guinea-pig, this animal is said to be passively immunised against ricin, i.e. its blood-serum contains the injected antiricin, which slowly disappears (cf. p. 4) from the blood. On the other hand, the animal produces an antibody against the antiricin, as may be shown by experiments with mixtures of ricin, antiricin, and the anti-antiricin. Such experiments were executed by Bashford,2 who even says that some of his experiments indicate analogous properties of blood from animals in- jected with diphtheria antitoxin, or with antitetanolysin. 1 Morgenroth and Sachs: Berl. klin. Wochenschrift, No. 35, p. 8 (1902). 2 Bashford: Journ. of Pathology and Bacteriology, 9. 192 (1903). 246 LECTURES ON IMMUNITY The experiments do not succeed if the passively immunised animal is of the same species as that which has produced the antitoxin. Probably the new antibody, the anti-antiricin, binds the antiricin, just as ricin does, so that the antiricin becomes divided between the ricin and the antibody ; and therefore the ricin acts as if a less quantity of antiricin than that used in the experiment had been employed. In the same manner it is possible by intravenous injec- tion of a haemolysin (i.e. an antierythrocytic substance) to produce corresponding antibodies. Thus, for instance, after the injection of immune-body from the blood-serum from a rabbit which had been actively immunised against bovine erythrocytes into the veins of a guinea-pig, this animal presented in its serum an anti-immune-body, specific against the injected immune-body. Such experiments were first carried out by Bordet,1 who called the new antibody " anti-sensibilisatrice." Nearly simultaneously Ehrlich and Morgenroth2 produced what they called "anti-immune-bodies," and later on " anti-amboceptors." Pfeiffer and Friedberger3 prepared anti-immune-bodies against cholera-serum from a goat, by injecting such serum into the veins of a rabbit. Now, a compound haemolysin contains immune-body and alexin and hasmolysin ; it may therefore seem possible to obtain antibodies against these three different sub- stances. To determine if the antibody be anti-immune- 1 Bordet: Ann. de VInst. Pasteur, 14, 270 (1900). 2 Ehrlich and Morgenroth: Berl. klin. Wochenschrift, No. 31 (1900); Nos. 21 and 22 (1901). 8 Pfeiffer and Friedberger : Berl. klin. Wochenschrift, No. I (1902). THE COMPOUND H^EMOLYSINS 247 body or antialexin, Ehrlich and Morgenroth proceeded in the following manner. Immune-body is added to the anti- body, and if this is an antialexin, it leaves the immune-body free, which thereafter may be extracted with erythrocytes, that may afterward be haemolysed through treatment with alexin. If it be an anti-immune-body, it binds the immune- body present, which thereafter cannot be extracted by erythrocytes. Evidently the antihsemolysm, if such an antibody exists, behaves in this case as the antialexin. The specificity is not very prominent. Normal serum contains anti-immune- bodies and antialexins, and after its injection into animals these produce antialexins. According to Ehrlich and Morgenroth, inactivated serum heated to 56° C., which ought not to contain alexin, still gives an antialexin after injection. (The antialexins resist a temperature of 55- 60° C. ; usually they are heated before using in order to free them of perturbations through the presence of alexins.) Another peculiarity was found by Ehrlich and Morgenroth, namely, that serum from a goat previously injected with serum from a rabbit contains an antialexin, not only against the alexin in rabbit-serum, but also against the alexin contained in guinea-pig-serum. The same antialexin is even contained in the serum of a goat treated by injections of horse-serum. The antialexins have been regarded as especially im- portant because they bind the alexins, which are — according to the views of Bordet as well as of Ehrlich — the effective parts of the haemolysins. Therefore the chief part of the work on the antihaemolytic substances has been concerned with investigations of antialexins, 248 LECTURES ON IMMUNITY which were generally prepared simply by the injection of the normal serum of one animal into the veins of another animal. As will be seen from the following accounts of the results of experiments, the sera thus prepared seem to contain anti-immune-bodies as well as antialexins.1 And regarding the relative probability of the production of these two antibodies, it must be said that as the immune- bodies are very much more rare than the alexins, the organism will more easily produce the necessary quantity of anti-immune-bodies than of antialexins. Moreover, the serum of the animal which is exposed to dangers of a haemolytic nature contains in its blood-serum generally an alexin which, united with the proper immune-body, haemolyses its own erythrocytes. Against this alexin the animal evidently produces no antibody, for otherwise the alexin would be of no use against foreign substances which enter the blood. Morgenroth and Sachs2 have carried out an investiga- tion on the quantities of antialexin which are necessary to completely suppress the action of a mixture of immune- body and alexin which is just able to produce complete haemolysis of the erythrocytes used in the experiment. The results are given in the following table, where a denotes the quantity of immune-body (given as number of c.c. of the preparation used), b the corresponding quan- tity of alexin, and c the quantity of antialexin necessary to inhibit the haemolysis. The erythrocytes were present in the amount of i c.c. of a five per cent suspension. The alexin and the antialexin were in contact for thirty minutes 1 This circumstance has been observed already by Bordet (I.e. p. 273). 2 Morgenroth and Sachs: Berl. klin. Wochenschrift, No. 35 (1902). THE COMPOUND H^MOLYSINS 249 at 37° C. before the erythrocytes and the immune-body were added. EXPERIMENTS OF MORGENROTH AND SACHS ON ANTIALEXIN i. SHEEP BLOOD ERYTHROCYTES Immune-body, from goat treated with sheep erythrocytes ; alexin, normal serum of guinea-pigs ; antialexin, immune-serum from goat, treated with rabbit-serum a 6 c c : b c \ a. 0.3 0.006 0.35 58 1.2 0.05 0.006 O.I 17 2 o.oi o.oi o-°75 7-5 7-5 0.005 °-°5 0-015 °-3 I0 2. Like I, but the antialexin is from a rabbit which has been treated with guinea- pig-serum a. b c c : b c : a 0.2 0.0035 0.005 I-4 0.025 o.i 0.025 °-°4 J-6 0.4 3. BOVINE ERYTHROCYTES Immune-body, from rabbit treated with bovine erythrocytes; alexin, normal serum of guinea-pigs ; antialexin, from goat, treated with rabbit-serum a. b c c:b c : a 0.2 0.05 0.75 15 38 0.004 o-1 °-i i.o 25 4. ERYTHROCYTES FROM HUMAN BLOOD Immune-body, from a rabbit, treated with human erythrocytes; alexin, normal serum from a rabbit ; antialexin, from goat, treated with rabbit-serum a b c c '. b c '. a 0.2 0.05 0.075 x-5 °-38 o.i 0.05 °-°35 °-7 0.35 0.05 o.i 0.025 o>25 °-5 Only in the case 2 is there the approximate proportionality between c and b which was expected by the authors. Evi- dently if the alexin is bound by the antialexin without dissociation, the quantity of antialexin necessary for neu- tralisation will be proportional to the quantity of alexin used, just as is the case in this experiment. The authors call attention to the remarkable fact that in this case the 250 LECTURES ON IMMUNITY antialexin was produced by the injection of the alexin used, which was not the case in the other series. It seems quite possible that this method is the only one adapted to yield a specific antialexin with a strong affinity for the injected alexin. If the affinity be not very marked, and therefore the reaction between alexin and antialexin to a high degree incomplete, we would not expect to find a proportionality between the neutralising quantity of antialexin and the quantity of alexin present. (It may be remarked that it is here not a question of an absolute neutralisation, by which the quantity of haemolysin would sink to zero, but only of a reduction of the quantity of haemolysin to about 14 per cent of the value exhibited in the absence of antialexin (cf. p. 229).) What complicated phenomena may be encountered in such cases is evident from the following example, in which it is supposed that the formula valid for the equilibrium has the form, (5 a — ;r)(2O b — x)— 100 x> which quite closely corresponds to the combination of the immune-body (a) from a goat treated with bullock erythrocytes and with guinea-pig serum as alexin (b) to haemolysin (;r). I have supposed that an antialexin of the same affinity for the alexin as that of the immune-body is added, so that the same formula may be used for the two cases of equilibrium. From this it follows that the proportions of alexin bound to immune-body and antialexin are identical with the pro- portions of these two substances themselves. The fol- lowing table corresponds directly to those of Morgenroth and Sachs, b is the quantity of alexin necessary for com- plete haemolysis in the presence of the quantity a of im- THE COMPOUND H^EMOLYSINS 251 mime-body, c is the quantity of antialexin necessary to reduce the quantity of haemolysin to the eighth part of that necessary for total haemolysis, which nearly corre- sponds to the limit of observable haemolysis. INFLUENCE OF ANTIALEXIN ACCORDING TO THE LAW OF MASS-ACTION a b c C'.b c : a 1000 5-i 7130 1400 7-i 300 5-4 2270 45° 7.6 100 6-3 885 141 8.9 70 7.0 690 99 9-9 50 8.4 606 72 12. 1 30 '5 670 45 22-3 25 25 95° 38 38.1 Here we observe that for a certain quantity of immune- body (a =40 ; b = 10), when the immune-body and the alexin are present in equivalent quantities, c passes through a minimum ; for higher values of a, c increases with a and tends to reach proportionality with a as a attains very high values; for lower values of a, c increases with b. In other words, the addition of a given quantity of antialexin has a maximal influence when a — 40, and the haemolytic action is reduced to a lesser degree for values of a above or below 40. The general behaviour will be the same even if the affinity of the immune-body for the alexin is not equal to that of the antialexin for the alexin, only then the minimum of c is displaced. If we now compare this last general table with those of Sachs and Morgenroth, we observe that all of them may very easily, within the errors of observation, be regarded as special cases of the general table ; while they conclude 252 LECTURES ON IMMUNITY that from their observations " it must of necessity (!) be concluded, that the different relations of the affinities can- not give a sufficient explanation." "We must therefore," they say, " make use of another factor, namely, the plu- rality of the alexins and antialexins, for the explanation." This conclusion shows clearly how necessary it is to be cautious in regard to theoretical deductions in this disci- pline of bio-chemistry. The results of similar deductions led Bashf ord * to introduce one of his memoirs with the words: " On immunity, especially, investigation is rendered difficult by the habit of pushing conclusions farther than the facts really warrant; impartial work and judgment too often lead to the conviction that the ' generally accepted facts ' are but flimsily supported hypotheses." The relations are still more complicated by the possi- bility that the velocity of absorption for immune-body and antialexin may be rather different in different cases. In two masterly memoirs Bordet2 has considered the properties of antisera, procured by injection of normal and immune sera into the veins of a non-related animal. Bor- det found that serum from the guinea-pigs which had been treated with erythrocytes from a rabbit caused after injec- tion into a rabbit, the production of substances which counteracted the immune-body contained in the immune- serum of guinea-pigs, as well as the alexin in normal serum from guinea-pigs. This antialexic action not only protected the erythrocytes of rabbit, treated with the said immune- serum, from being haemolysed, but even cholera vibrios, 1 Bashford: Journ. of Pathology and Bacteriology, 8. 52 (1902). 2 Bordet : Ann. de VInst. Pasteur •, 18. 593 (1904) ; Bordet and Gay : ibidem, 20. 467 (1906). THE COMPOUND H^IMOLYSINS 253 treated with bacteriolytic cholera-serum, from being de- stroyed by guinea-pig-serum. This antialexic action was in so far specific that it did not protect against other alexins than that from guinea-pigs. Bordet made a large number of experiments with the following combination : erythro- cytes, from bullock ; immune-body, serum of rabbit injected with erythrocytes from bullock ; alexin, normal serum from a guinea-pig ; antiserum, serum from a guinea-pig treated with normal rabbit-serum. The immune-body and the antiserum were freed of alexin by heating to 55-56° C. for thirty minutes. Bordet separated the active sub- stances from a large number of other substances present in the sera by letting the erythrocytes absorb them, then only those substances that were specific to the erythrocytes were able to act. That the erythrocytes absorb the im- mune-body almost completely if it be not present in great excess, we have seen above; and this method has long been used for the extraction of immune-bodies from sera. Bordet has shown that erythrocytes charged with immune- body also absorb alexins, so that a serum may in this way be freed from its content of alexin, which is indicated by the fact that it has lost its hasmolytic power against ery- throcytes treated with immune-body. The alexin is, on the other hand, not absorbed by normal erythrocytes, those that do not contain immune-body. Further, Bordet in an analogous manner proved that erythrocytes, charged with immune-body, absorb the antiserum and thereafter have lost their power of absorbing alexin. Evidently the im- mune-body is neutralised by the antiserum, which seems to have a stronger affinity for the immune-body than has alexin. This observation is confirmed by the fact that a 254 LECTURES ON IMMUNITY certain quantity of antiserum can bind only a given equiv- alent quantity of immune-body, so that erythrocytes pro- tected from haemolysis by the absorption of a certain quantity of antiserum may yet be haemolysed on the further addition of immune-body and alexin. Normal rabbit-serum heated to 56° C. contains a substance which does not act as an immune-body against bovine erythrocytes, but has the faculty of binding antiserum, so that it can produce the haemolysis of erythrocytes that are loaded with the com- pound of immune-body and antiserum. This haemolytic action is weaker if the compound has lain for a long time in the erythrocytes, than if the preparation is fresh. This peculiarity seems to indicate that the compound, just as the analogous haemolytic substances such as tetanolysin and probably also the compound hoemolysins, is slowly bound by the protein substances in the erythrocytes. The normal rabbit serum evidently contains some substance which com- petes with the immune-body in binding antiserum. Bordet and Gay made an observation confirming a dis- covery of Klein.1 The immune-bodies and alexins con- tained in sera are absorbed to a much higher degree by the erythrocrytes if these are suspended in a physiological salt-solution, than if they are suspended in a natural serum. Thus a mixture of 0.4 c.c. of normal horse-serum and 0.4 c.c. of erythrocytes from the guinea-pig was treated with i c.c. of ox-serum without showing agglutination of the erythrocytes to a notable degree. If, on the other hand, 0.6 c.c. of physiological salt-solution had been present for some time in the said mixture, agglutination was very pronounced. In an analogous manner we may explain an- 1 Klein: Wientr klin. Wochcnschrift, No. 48 (1905). THE COMPOUND H^MOLYSINS 255 other observation of Bordet. 0.2 c.c. of bovine erythrocytes loaded with immune-body were mixed with 0.6 c.c. of antiserum and physiological salt-solution. After a time the erythrocytes were separated from the liquid by centrif ugal- isation. To the erythrocytes was then added a mixture of 0.2 c.c. of alexin from the guinea-pig with 0.6 c.c. of normal guinea-pig-serum heated to 56° C. Another ex- periment was quite similar, but instead of the O.6 c.c. of guinea-pig-serum, 0.6 c.c. of physiological salt-solution was added. In the first experiment no haemolysis was observed, but the second gave haemolysis during the course of one hour. The absorption of the alexin was much greater in the presence of the physiological salt-solution than in the presence of normal serum. The absorbed alexin competes with the antiserum absorbed in the erythro- cytes, so that a certain quantity of compound haemolysin was formed, enough to yield haemolysis. This action of the physiological salt-solution which causes the absorption of, e.g., the immune-body and the alexin from horse-serum in the experiment of Bordet and Gay, speaks very much in favour of the view that an ab- sorption and not a chemical binding of the immune-bodies takes place in the erythrocytes. Through absorption experiments Bordet proved that the same antiserum protects bovine erythrocytes against the immune-body contained in serum from a rabbit treated with bovine erythrocytes, and chicken erythrocytes against rab- bit-serum treated with chicken erythrocytes. The same antiserum may therefore neutralise two entirely different immune-bodies, which are produced by the same species of animal (here rabbits). Therefore Bordet rejects the 256 LECTURES ON IMMUNITY proof given by Ford and Wassermann,1 that the agglutinin to chicken erythrocytes, which is found in normal rabbit- serum, is identical with that contained in serum from rab- bits treated with the said erythrocytes, because both are neutralised by serum from chicken treated with rabbit erythrocytes. Bordet makes some remarks of great theoretical interest bearing upon the results of his experiments. Ehrlich and Morgenroth2 found that in the said combination of erythro- cytes and immune-body it was possible to use alexin from goat-serum, although it had a weaker haemolytic action than that from guinea-pigs. They then made experiments with the neutralising action of an antiserum produced by the injection of serum from rabbits treated with bovine erythrocytes into the veins of a goat. They found that this serum (in a given quantity) hindered the haemolysis by alexins from guinea-pigs, but not by that of goat-serum. But as the alexin from goats is much weaker, they used in this special case a much greater quantity of immune-body. Thereby they introduced not alone the immune-body in great quantity, but also the substances contained in normal rabbit-serum which are able to neutralise the antiserum. Bordet explains in this simple manner that the antiserum Jhad no action in this case, and rejects the explanation of Ehrlich and Morgenroth, who assume that the different effect is due to the presence of two different kinds of im- mune-bodies in the preparation, of which the one gives compounds with the alexin from guinea-pigs and with the JFord: Zeitschr. f. Hygiene, 40. 363 (1902); Wassermann: ibidem, 42. 267 (1903). 2 Ehrlich and Morgenroth: Berl. klin. Wochenschrift, Nos. 21 and 22 (1901). THE COMPOUND H^MOLYSINS 257 antiserum, the other with alexin from goats but not with the antiserum used. Evidently this proof is without validity. This is now conceded by Ehrlich, who believes, however, that other proofs are still valid.1 Another remark of Bordet touches the side-chain theory of Ehrlich. Ehrlich conceives the formation of antibodies in the following manner : If a foreign substance is injected into the body of an animal, it may be " anchored " to some cells in the tissues of the animal. A chemical affinity localised on a " receptor " of this cell is thereafter bound, and hence the cell is hindered in one of its functions. The cell then produces a new "receptor" to fill the place of that seized by the foreign substance. " According to a law of Weigert's, the regeneration does not only compensate the defect, but overcompensates it." (This so-called " law" has no standing whatever.) The excess of recep- tors thus produced is given off to the blood and forms the antitoxin. In our case, therefore, the immune-body, according to Ehrlich, is a receptor which is able to bind an erythrocyte. This receptor is called amboceptor, be- cause it may even bind a molecule of alexin at the same time as the erythrocyte. Now, we have seen that the immune-bodies are probably not bound by the erythro- cytes, but only absorbed by them. Therefore, in its old formulation, the side-chain theory probably has no appli- cation to this special case. Bordet, on the other hand, accepts the theory of a binding process like that by which dyes are bound to fibre. He, therefore, seeks another proof that the theory of Ehrlich, as it is used, cannot be correct. To explain the action of antisera Morgenroth 1 Ehrlich and Sachs: Berl klin. Wochenschrift> Nos. 19 and 20 (1905). s LECTURES ON IMMUNITY supposes that they, as formed by the injection of an im- mune-body, consist of receptors which bind the same affinity of the immune-body that otherwise might bind the erythrocyte. (Evidently it would be much better to sup- pose, as Ehrlich does in his reply to Bordet, that the antisera may replace the alexins, and therefore do not attack the affinity with which an erythrocyte may be bound.) Then, Bordet retorts, every substance capable of binding the antiserum ought to bind erythrocytes. As we have seen, normal rabbit-serum contains a sub- stance which combines with the antiserum, but not with bovine erythrocytes. Even immune-serum from the rabbit treated with bovine erythrocytes, which serum had pre- viously, by being shaken with ox erythrocytes, been de- prived of substances that bind these erythrocytes, showed an affinity for antiserum. Further, the same antiserum binds immune-bodies which are absorbed by different erythrocytes, as bullock's and hen's, and which are specific for them. Hence the attack of Bordet on the side-chain theory in the form of its original application to this phenomenon was quite correct. But this theory possesses a high degree of elasticity, and against the new formulation given by Ehrlich and Sachs in their reply to Bordet, according to which the antiserum competes with the alexin in binding the immune-body, no objection is to be made. We might, perhaps, therefore look for a new method of elucidation of this theoretical question. But, as Bordet remarks, Ehrlich has, in his later publications, modified the side-chain theory to such a degree that the differences between Bordet's and Ehrlich's opinions almost disappear, THE COMPOUND H^EMOLYSINS 259 and are now more of a formal than of a real character. Evidently, if an animal reacts to injection of a foreign fluid substance, the simplest way to explain this is to assume that the injected fluid attacks some cell of the animal chemically. In common language, we say that some sub- stance in the fluid has been bound by the cells. The ani- mal retaliates with the production of some substance, the so-called antibody, which, as we have seen, partially binds the reacting substance in the fluid ; if the reacting substance be a cell, the antibody enters into similar cells, and in many cases causes chemical alterations in the contents. As now the reacting substance is bound chemically by the cells of the inoculated animal, as well as by the antibody produced by it, we may, with Ehrlich, for the sake of simplicity, sup- pose that the antibody consists of just that part of the cells which are attacked by the foreign fluid. But it is not necessary to make this supposition. On a closer inspec- tion, the side-chain theory seems to be little more than a circumscription of the definition of the conception " anti- body," under the further supposition that we are dealing with chemical processes. If, as for the immune-bodies, no proof has been given of their chemical action, the side- chain theory finds, in its present state, no application. Bordet also makes an attack upon Morgenroth's l proof that immune-body and alexin bind each other in solutions containing both. As Morgenroth,2 and likewise Ehrlich and Sachs,3 have later on conceded that the criticism of Bordet is well founded, we will not here enter upon this 1 Morgenroth: Centralbl.f. Baktcriologie, 35. 501 (1904). 2 Morgenroth : Arbeiten aus dem pathologischen Institut zu Berlin, p. 6 (1906). 8 Ehrlich and Sachs : /.<:., p. 1 6. 260 LECTURES ON IMMUNITY criticism. We only remark that the compound is very easily dissociated, so that it was only with the help of quantitative measurements that a proof of its presence could be given (cf. p. 224). As this compound occurs in the erythrocytes, it would seem very improbable that it should not exist also outside of the erythrocytes, although dissociated to a high degree. As we have seen above, Ehrlich and Sachs made experi- ments with erythrocytes from guinea-pigs, normal bovine serum heated to 56° C. (which they regarded as immune- body), and alexin from horse blood. They found that the haemolytic agent from the bovine serum was not absorbed by the erythrocytes, for it did not lose its activity after having been shaken with such erythrocytes. Hence they concluded that not the immune-body, but its compound with alexin, is absorbed by the erythrocytes. This con- clusion is not corroborated by the investigation of Bordet and Gay, for they found that if they used alexin from guinea-pigs instead of alexin from horses, haemolysis oc- curred, but not after the immune-body had been separated from the bovine serum by treatment with erythrocytes from guinea-pigs. There must therefore be another ex- planation of the experiments of Ehrlich and Sachs. After a thorough investigation, Bordet and Gay conclude that the normal horse-serum, used by Ehrlich and Sachs, furnishes not only the alexin, but also the immune- body to the erythrocytes. The compound haemolysin of these two substances is too weak to cause a percep- tible haemolysis, but it is strengthened by the presence of some substance contained in the bovine serum, which they call "colloide de boeuf." This colloid is indeed THE COMPOUND H^EMOLYSINS 26l active in other similar cases. The proof of Ehrlich and Sachs that an immune-body is not itself soluble in (able to be bound by) ery throcytes, but only after combina- tion with alexin, is henceforth untenable. I have made some experiments on the action of anti- alexins and found that cases occur in which the influ- ence of the antialexin has even a minimum value for a medium concentration of the immune-body, and not a maxi- mum, as in the theoretical example cited above. In one case the erythrocytes were from sheep (i c.c. of a 5 per cent suspension) ; the immune-body (a), from a goat, treated with erythrocytes from sheep the alexin (b) was guinea-pig-serum ; and the antialexin (c) was from a goat injected with serum from a rabbit. The quantity of alexin was of such a magnitude that three-fourths of it would be just sufficient to produce complete haemolysis. The quantities are given in centimetres of the preparations used. The experimental method was the same as that used by ACTION OF DIFFERENT QUANTITIES OF ANTIALEXIN SER. i SER. 2 SER. 3 SER. 4 c (c.c.) a = 0.1 c.c. £ = 0.004 c c- «=O.OI C.C. b =0.015 c.c. a = 0.001 c.c. £ = 0.04 c.c. « = 0.0005 c.c. 3=0.1 C.C. 0 IOO IOO IOO IOO 0.025 67 IOO IOO IOO 0.035 48 IOO IOO 90 0.05 22 IOO IOO Si 0.075 H IOO 54 36 O.I 9 90 4(?) 13 0.15 6 28 4 8 0.25 8 12 6 8 0-35 8 7 6 9 o-5 10 8 8 9 262 LECTURES ON IMMUNITY Morgenroth and Sachs. The total quantity was 2.2 c.c. The tabulated quantity is the degree of haemolysis. The action is the least in Ser. 2, after this comes Ser. 3, then Ser. 4, and last Ser. I. It seems difficult to explain this peculiar behaviour, which was controlled by other measurements, so long as we suppose that the "antialexin" entered into combination only with the alexin present. The observations may be understood if we assume that either an anti-immune-body or an antihaemolysin was pres- ent. If we suppose that the preparation c contained anti- immune-body as well as antialexin and their affinities are strong, then small quantities of c may be sufficient for the neutralisation to a remarkable degree if small quantities of either the alexin (Ser. i) or of the immune-body (Ser. 4) are present. The explanation is analogous (the result of the partial dissociation) if we suppose the presence of an antihaemolysin in the solution c. In any case the reactions in the presence of antialexins or anti-immune-bodies are rather complicated and difficult of survey. CHAPTER IX THE PRECIPITINS AND THEIR ANTIBODIES IN many instances the reaction-products of the ferments are solid bodies, and such ferments are called precipitins. Generally these solid substances contain a great deal of water, like albuminous substances in general ; and this cir- cumstance has in recent times led to the opinion that the act of precipitation might consist only of a coalescence and subsidence of the "colloidal" particles of the particular albuminous substance in the system. Thus, for instance, the casein of milk is, according to this theory, present in the state of so-called pseudo-solution. Its smallest parti- cles may be regarded as an extremely fine solid powder of ultramicroscopic magnitude (dimensions less than .0002 millimeter). On the addition of rennet these solid particles coalesce to form larger clumps and subside, just as finely powdered clay sedimentates following the addition of salts or acids to the water in which it is suspended. In corroboration of this view Duclaux l cites the follow- ing observation. "In milk, which is turning sour but which is still quite liquid, we observe with the miscroscope, as I have indicated, a precipitate of fine grains, which at the beginning are seen only with difficulty, and are detected only by a faint disturbance of the visional field, but which later on display quite distinct granulations, charac- terised by the Brownian movement, just as minute particles 1 Duclaux: Microbiologief1omQ 2, pp. 253-339 (1899). 263 264 LECTURES ON IMMUNITY of clay. Shall we suppose now that the coagulation of the casein changes its value rapidly in the same moment that we are able to observe its progress ? From this point of view the phenomenon manifests itself to our eyes as a steadily increasing molecular condensation. It displays the behaviour of clay particles which aggregate and subside. . . . We are therefore led to suppose that this regular con- densation, which causes the coagulation as far as we are able to observe it, begins already before the microscope can detect it. But however well grounded this induction may seem to us, it would remain unfounded if we could not control it by experiment." This experimental proof Duclaux finds in the reaction of Tyndall. Ultramicroscopical powders suspended in an absolutely clear fluid reveal their presence by the produc- tion of a blue colour on illumination by a ray of light, and this blue reflected light is polarised. This phenomenon is displayed, for instance, by a suspension of fine particles of mastic, prepared by adding a few drops of an alcoholic solution of mastic to water. If we add greater quantities of the solution, the light reflected becomes more .pale and white; and at a certain point it is possible by means of the microscope to detect in it small particles that show the Brownian movement. At a still higher concentration of the solution a real precipitate is formed, which is easily observed with the naked eye. To this argument may be added still another fact. Such submicroscopic particles may be observed by means of the ultramicroscope of Siedentopf. Solutions of proteins generally reveal the presence of such submicroscopic granules, and this observation has been interpreted in THE PRECIPITINS AND THEIR ANTIBODIES 265 favour of the view that all solutions of proteins may be regarded as pseudo-solutions, i.e. consisting of suspensions of finely divided particles. Against this view it may, how- ever, be urged that the presence of some submicroscopic particles does not prove at all that the whole of the quan- tity of protein present, or even that a considerable part of it, is in this state of pseudo-solution. Even in this case some salts, especially those of calcium, strontium, and barium, exert a great influence, just as in the case of agglutination, with which the phenomenon of coagulation shows many analogies. (Cf. above, pp. 73 and 159.) Just as salts are of marked influence on the agglom- eration of fine particles, as, e.g., of clay or of mastic (cf. p. 1 59), so in the same way the influence of the salts of Ca, Sr, and Ba on the process of coagulation is so prominent that it is doubtful if coagulation can be realised in their absence. These salts alone, without rennet, give precipi- tates with milk or solutions of casein. The coagulated matter is more flocculent and does not entangle the fat- drops to so high a degree as the coagulum produced under the action of rennet. But this action of the salts of the metals of the calcium group seems to be rather specific. Next to them come the salts of magnesia, which accelerate also the coagulation by rennet if they are present in greater quantity, though according to Lorcher's observations small quantities of MgCl2 retard the action of rennet, whereas even the least traces of Ca, Sr, or Ba salts accelerate the coagulation by rennet. These salts give without ren- net a coagulation with the casein of milk. Salts of the other alkali metals coagulate milk only at high concentra- tions ; they retard the coagulating action of rennet. In 266 LECTURES ON IMMUNITY strong solution even the salts of Ca, Sr, and Ba retard the action of rennet. This action of stronger solutions is probably only due to a change in the solubility, just as the precipitation of casein by means of alcohol, and possesses, therefore, only a secondary interest. Acids precipitate the casein, even in rather minute quan- tity. Salts which have an acid reaction accelerate the action of rennet just as acids do. This may be due to the presence of free acid in these solutions. On the other hand, alkalies hinder or retard the precipitation of the casein, and in the same manner behave salts with an alka- line reaction, as the carbonates or bicarbonates of the alkali metals. These last facts speak very much in favour of the chemical theory first advanced by Hammarsten, who regards the casein as an acid, which is very slightly solu- ble, whereas its salts with alkali metals are soluble in water. Laqueur and Sackur1 have determined its equivalent weight to be 1135. The conductivity of the sodium salt in solution seems to indicate, according to a rule of Ost- wald, that the acid is tetra- or hexavalent, so that its molecular weight is computed to be 4540 or 6710. With this last number agrees very well another (6600), found by Hedin, Blum, and Vaubel2 from a study of the products of the decomposition of casein. By the prolonged action of weakly alkaline solutions on casein, another stronger acid is formed, termed isocasein, possessing the equivalent weight 960. Its molecular weight is four or six times greater. 1 Laqueur and Sackur : Hofmeisters Beitrdge, 3 (1902); Sackur: Zeitschr.f. ph. Ch., 41. 672 (1902). 2 Hedin, Blum, and Vaubel: Journ. /. praktischc CA., 60. 55 (1899). THE PRECIPITINS AND THEIR ANTIBODIES 267 Upon these chemical properties Hammarsten founded his method for the preparation of pure casein. Milk is di- luted with three to four times its volume of water, and a pre- cipitate produced by the addition of o. i per cent of acetic acid. The precipitate is separated from the solution by filtration through linen and then dissolved in a weak solu- tion of caustic soda or better ammonia. The fat-drops carried down by the precipitate separate upon the top of the liquid, which is thereafter again precipitated and redis- solved four or five times. The last traces of fat are removed from the precipitate by extraction with alcohol and ether, and the precipitate is after that dried to a white powder, casein, which is very slightly soluble in water. Its suspensions in water behave as an acid, and it drives the carbonic acid out from the carbonates of alkali metals or calcium, giving clear solutions of its salts with these metals. If a solution of the calcium caseate is neutralised by the addition of a diluted solution of phosphoric acid, a precipitate of calcium phosphate is formed, and a white liquid remains which resembles very much a milk devoid of cream. Probably we have here a pseudo-solution of casein. It behaves like milk in being coagulated through the action of rennet. The adherents of the chemical theory of coagulation by rennet assume that this ferment exerts a decomposing action on the casein, just as pepsin on protein,1 after which 1 According to recent investigations of Bang (Zeitschr. f. ph. Ch., 43. 358, 1905), Hemmeter (Berl. klin. Wochenschrift, E-wald-Nummer, 14, 1905), and Schmidt -Nielsen (Zeitschr. f. physiol C/z., 48. 92, 1906), pepsin and chymosin — the milk-coagulating substance in neutral rennet — are different substances. Pepsin seems to coagulate milk in acid solution, wherein the results of Pawlow and Sawjalow find their explanation (cf. p. 71). 268 LECTURES ON IMMUNITY the digestion-product is precipitated by Ca ions. Some very strong arguments are advanced in favour of this view. The reaction goes on at low temperatures without coagula- tion, which then occurs almost instantaneously upon eleva- tion of the temperature to over 25° C.,1 and small quantities of pepton have a strong retarding influence (cf. p. 77). One of the products of decomposition, called para-casein, is sup- posed to yield the coagulum at higher temperature, whereas other products, for instance serum-albumen, remain in solu- tion. In reality Hammarsten has proved that serum-albumen is an albumos-like substance with characteristic reactions : it is not precipitated by acids (acetic and nitric) nor by diluted solutions of CuSO4, HgCl2, FeCl3, K4(CN)6Fe, nor Pb (CH3CO2)2 J it does not give the reaction of Heller ; but responds to the biuret-reaction and the reaction of Millon ; it is precipitated by tannin in acetic acid and by alcohol. Rennet and casein produce serum-albumen even in absence of calcium or barium salts. Duclaux combats this view, which he says leads to the conclusion that these soluble products ought to pass through a Chamberland filter. Now a Chamberland filter restrains casein, but some of the proteins of milk pass through it. Therefore, according to Duclaux, milk filtered through a Chamberland filter should give a filtrate containing more of the filterable proteids after it had been coagulated by rennet, than before this treatment. This, he showed, was not the case. But the conclusion drawn does not seem to be quite convincing. For, just as the casein does not pass through the filter, so the serum-albumen may be held back by it. That the lrThis was first observed by Morgenroth (Archives Internationales dt pharmacodynamie^ 7. 265, 1900). THE PRECIPITINS AND THEIR ANTIBODIES 269 casein does not pass through is explained by Duclaux as due to its state of pseudo-solution, which is really only a mode of expression and no real explanation ; and the same property may be characteristic of the serum-albumen, especially if the filter is covered by a gel of casein. The addition of a solution of an oxalate or of a fluoride to milk inhibits its coagulation. One might suppose this action to be due to the precipitation of the calcium from the compounds of the milk and of the rennet. Duclaux combats this view and states that the coagulation is not inhibited if the oxalate (or fluoride) is not present in excess. He assumes that the oxalate or fluoride has itself a direct influence upon the milk, lowering its tendency to coagula- tion. From the modern point of view of physical chemistry, it seems quite obvious that for the coagulation a certain degree of concentration of the calcium ion (or barium or strontium ion) is necessary. The more oxalate present, the lower would be this concentration, so that a certain concen- tration of the free oxalate ion (or fluorine ion) is necessary to prevent coagulation. This concentration probably de- pends in part upon the temperature. Another coagulation process of especial interest is the precipitation of blood-plasma by means of fibrin-ferment (cf. p. 91). This process is very similar to the coagula- tion of milk or casein, but seems to be different in the fact that coagulation of the plasma can occur spontaneously. According to Duclaux, this depends upon the action of the leucocytes present in the blood. In their cytolysis they form a coagulating ferment. Coagulating ferments that act upon blood-plasma are very common in the differ- ent tissues, fluids, and organs of the body. Alexander 2/0 LECTURES ON IMMUNITY Schmidt prepared this fibrin-ferment by precipitating blood- serum with 15 to 20 times its volume of alcohol. The precipitate was filtered and dried. This precipitate con- tains a rather large quantity of fibrin-ferment which coagu- lates the fibrin contained in blood-plasma. It is possible to prepare solutions of plasma as well as of fibrin-ferment nearly free of calcium ions, by the addi- tion of oxalates or fluorides to the blood. On mixing these two coagulations occur, although there are oxalate ions present in excess. From this experiment it has been concluded that calcium ions are not necessary in the coagu- lation of fibrin. The conclusion is not quite binding, for there are always calcium ^ions present, although in very minute quantity. A more accurate examination of this question would be profitable. On the other hand, it is cer- tain that the ions of calcium, strontium, and barium accel- erate to a high degree the coagulation of fibrin. On the whole, the different salts seem to exert upon the coagula- tion of fibrin an influence similar to that upon milk. The presence of acids is favourable to the plasmatic coagu- lation. In the coagulation of plasma (as in that of casein, ac- cording to Hammarsten's investigations) two different phases may be observed, according to the opinion of Bor- det and Gengou.1 The one, the transformation of the so- called fibrinogen, contained in the plasma, into fibrin, may proceed as the result of the action of the ferment in the absence of calcium salts ; the second process, the coagula- tion, requires the presence of calcium ions. Hence a perfect analogy exists between the coagulations of plasma 1Bordet and Gengou: Ann, de Plnst. Pasttur, 18. 26 (1904). THE PRECIPITINS AND THEIR ANTIBODIES and of casein. This duality of the processes recalls the action of the compound haemolysins in which at first the immune-body is absorbed in the erythrocytes, following which the formation of haemolysin occurs. According to Bordet's view, the parallelism between haemolysis and co- agulation is still more prominent. Bordet and Gengou 1 suggest that the action of fluorides on blood-plasma interferes not only with the action of the Ca ions, which are precipitated from the solution as CaFl2, but also with that of the fibrin-ferment, which is carried down from the solution by the precipitate. The addition of an oxalate does not interfere sensibly with the action of the ferment. Leo Loeb2 found a certain specificity between fibrin- ferment and plasma, " in so far as the blood of each species of animal used coagulated more rapidly under the influence of the tissues of animals of the same species or of the tissues of related animals than under the influence of the tissues of more distant animals." The addition of serum of the animal producing the fibrin-ferment increases the ac- tion. Even the products of bacteria (especially Strepto- coccus pyogenes aureus) are sometimes favourable to the coagulation. There is a third type of coagulation provoked by a ferment. In certain fruits and even roots of plants occurs a substance called pectin. This substance gives with water solutions of high viscosity; it is precipitated by alcohol. It may be coagulated by means of a ferment called 1 Bordet and Gengou: Ann. de VInst. Pasteur, 18. 98 (1904). 2 Leo Loeb: Hofmeisters Beitrage, 5. 534 (1904) ; Journ. of Medical Re- search, 10. 407 (1903). 2/2 LECTURES ON IMMUNITY pectase, found in the juice of carrots, beets, etc. The co- agulation is hindered by the presence of oxalate ions, i.e. the presence of calcium ions (or ions of barium or stron- tium) seems necessary also in this reaction. Acids retard the coagulation, and strong mineral acids exert a greater influence than weak vegetable acids. Coagulation or precipitation plays a very important r61e in the chemistry of antibodies. We have already spoken of the action of agglutinin as probably associated with a coagulating influence upon the cells (cf. p. 164). The agglutinating power of acids for erythrocytes is fol- lowed by a very obvious coagulation. Corrosive sublimate produces on erythrocytes^both coagulative and an agglu- tinating action in higher concentrations, and a haemolytic action in lower concentrations. Haemolysis and coagula- tion (which makes itself manifest as agglutination) seem to be so often concomitant in the so-called phytalbumoses — toxins of vegetable origin, as, e.g., ricin or crotin — that Ehrlich has assumed that they are in this case inseparable.1 But for the bacteriolysins this is not the case, according to Kraus and Ludwig.2 If toxins and antitoxins are mixed in higher concentra- tions, they often yield a precipitate. Thus, for instance, Jacoby3 observed a flocculent precipitate on mixing ricin and antiricin; and Hausmann4 made a similar observation for abrin and antiabrin. Bashf ord 6 found that blood-serum 1 Ehrlich : " Schlussbetrachtungen " in " NothnagePs spezielle Pathologic und Therapie," Bd. 8, p. 13, Vienna, 1901. 2 Kraus and Ludwig: Witn. klin. Wochenschrift, No. 5 (1902). 8 Jacoby: Hofmeisters Beitrage, 1. 51 (1901). 4 Hausmann : Hofmeisters Beitr'dge, 2. 134 (1902). 6Bashford : Journ. of Pathology, etc., 8. 59 (1902). THE PRECIPITINS AND THEIR ANTIBODIES 2/3 from a rabbit, which had been actively immunised against crotin, gave a very dense precipitate with this substance, a precipitate not produced with normal serum. Myers showed that various albuminous bodies (Witte pepton, crys- tallised egg-albumen, serum globulin) injected into rabbits produced precipitins in their serum which acted upon the corresponding albuminous bodies in experiments in vitro}- "If this reaction in vitro" Bashford continues, "be comparable to the action in the body, then the injection of a solution of Witte pepton into the ear-vein of such an immunised animal should result in death from embolism." " The injection very slowly, however, of 5 c.c. 20 per cent Witte pepton into the ear-vein "of a highly immu- nised rabbit " gave no symptoms." " The reactions in vitro and in corpore are here again different. Also in the case of a rabbit immunised against crotin ; direct injection of my albumin-containing crotin-solution had no consequence which I could observe." As we have seen before (p. 205), the equation of equilibrium for ricin and antiricin is not of the same form, if we investigate the action of this poison on red blood-corpuscles in vitro and in living animals. From this circumstance we must conclude that there are different poisons acting in the two cases. Ehrlich2 and Robert 3 supposed that the two poisons were identical, and used this hypothesis as a basis for theoretical deductions. But now it is well known that this hypothesis is wrong. Even for tetanolysin and corrosive sublimate Bashford found a different action in vitro and in vivo. Haemolysins, 1 Myers : Centralbl.f. Bakteriologie, 28 (1900). 2 Ehrlich: Fortschritte de Medidn, 15. 41 (1897). 3 Robert: Arbeiten des pharmakologischen Instituts zu Dorpat, Tome 8 (cited from Bashford). T 2/4 LECTURES ON IMMUNITY as cyclamin, saponin, digitalin, solanin, cobra-venom, and haemolytic sera, produce, when injected into living animals, haemolysis, which is manifested by haemoglobinuria. " It must, however, be stated that the actions of the haemo- lysins in corpore are in no case limited to the erythro- cytes." At all events, it seems prudent not to assume a priori that the actions of poisons in vitro and in vivo are identical. The best known of all the coagulating substances is ren- net (or chymosin). It seems rather probable that the chief action of rennet is analogous to that of peptic digestion, and that the coagulation is a mere accidental property belonging to the products of the digestion at higher tem- perature (cf. p. 267). Be that as it may, the coagulation is the property employed hitherto for the investigation of the action of rennet. The coagulating power of rennet is diminished by some normal sera, especially serum from horses, as well as by immune-sera produced by the injection of rennet into animals,1 rabbits being especially adapted to this purpose. Madsen and Walbum have investigated the neutralising power of this " antirennet " and found that it behaves just as antitetanolysin does against tetanolysin. The experi- mental method was the following : Mixtures of 4 c.c. of a i per cent solution of rennet and different quantities (0.02-1 c.c.) of the antirennet-containing serum and of physiological salt-solution were prepared so that the total quantity was 5 c.c. These mixtures were held at room 1Morgenroth: {Centralbl. f. Bakteriologie, i. Abth. 26. 349, 1899, and 27. 721, 1900) was the first to prepare antirennet. He immunised goats by the subcutaneous injection of rennet. After repeated injections the serum of the goat contained antirennet. THE PRECttTTlNS AND THEIR ANTIBODIES 27§ temperature (in mean 16° C.) during twenty to fifty min- utes. Special experiments seemed to indicate that this time of reaction has no notable influence if it only exceeds five minutes, and after this time different quantities of the mix- ture were added to 10 c.c. of milk and physiological salt- solution added up to 12 c.c. The test-tubes containing these mixtures were placed in a water-bath of constant temperature and the coagulation examined after a given time (two hours). The calculation for the experiment is the same as for tetanolysin. One c.c. of the antirennet was found equivalent to 1.48 times the fixed quantity of rennet. The constant of equilibrium was found to be K = 0.0 1 2. n is the quantity of antirennet used. NEUTRALISATION OF RENNET BY MEANS OF IMMUNE-SERUM FROM RABBIT n = ***. ^calc. A « **•, ^calc. A 0 100 100 0.4 42.6 41.8 ±1-3 0.02 974 97.1 ± 0.6 0-5 30.2 28.2 ± 1.2 0.05 92.3 92.6 ±1.4 0.6 16.5 I6.5 ±0.4 O.I 85.9 85.2 ±i-5 0.7 8.2 8.4 ±0.6 O.2 70.4 7O.6 ±1.8 0.8 4.7 4-7 ±0.3 0-3 54-3 56.0 ±1.9 0.9 2.8 3-i ±0.2 The experiments are rather difficult and therefore a great number of observations have been taken. The observed values of the strength of the rennet in the mixture are mean values of not less than eleven different measure- ments. Thanks to this circumstance, it has been possible to calculate the probable error of each value. This proba- ble error is tabulated under A. As is seen from the comparison of ^calc. with g0^ the difference between the calculated values and the observed ones are in eight cases 276 LECTURES ON IMMUNITY less than the probable error ; only in two do they exceed these, and even then not greatly. The agreement may be regarded as striking, and the whole series, which is the condensed result of about seven hundred and fifty tests, — of every mixture there were taken six to eight different tests in as many test-tubes, — may be regarded as a model for further investigation on these difficult subjects. The concordance of ^-calc. with gobtm may serve as a very strong proof that the equation used for the calculation is the correct expression of the phenomenon. As has already been noted (cf. p. 3), Hammarsten and Roden 1 observed that normal horse-serum contains a sub- stance which is in many respects similar to antirennet. Therefore Madsen and Walbum have examined this anti- body in a similar manner, only the time of reaction between the two antibodies was longer, two to four hours. The results of experiments with two different preparations are abridged in the table on opposite page. This process of neutralisation is not reproduced by the formula valid for the action of rennet upon antirennet, but the equation is the same as that valid for the neutral- isation of tetanolysin by means of cholesterin, which indicates that one molecule of rennet and one of the antibody give only one molecule of the reaction-product. The constants are, if we use as unit concentration that of the unneutralised rennet in the first experiment, for the first preparation K — 0.354, and for the second K — 0.138 ; 1 Roden: Upsala lakareforenings forhandlingar, 22. 546 (1887). Roden observed that serum of swine blood is nearly as active as that of horse blood; sera from cattle or rabbits have a much weaker action. Even ascites-fluid has some action. The active substance is destroyed by heating for some few minutes to 70° C. or even by treatment with alcohol. THE PRECIPITINS AND THEIR ANTIBODIES I c.c. of the first serum was equivalent to 2 times the fixed part of rennet and i c.c. of the second serum corresponded to 2.1 part of the rennet. The observed values in the first series are mean values of three, and in the second of two different series of measurements. NEUTRALISATION OF RENNET BY MEANS OF NORMAL HORSE-SERUM n *ob, ^calc. • *obs. ^calc. 0 100 100 O 100 100 O.I 80.0 80.2 0.02 93-o 96.3 0.2 64-3 62.1 0.05 87.3 90.9 0.4 51-7 52.1 O.I 71.0 82.0 0.8 33.5 28.4 0.2 63.5 65-3 1.0 24.9 22.2 0-3 54-5 49-5 1.2 21.0 18.1 0.4 34-7 38.3 '•35 1 6.0 15.8 0-5 29.4 28.9 J-5 13.5 14.0 0.6 22.0 22.2 i-7 10.0 12.2 0.8 19.2 144 I.O 9.4 10.3 1-3 8.7 7.1 '•7 3.1 5-0 2.0 2.9 4.0 The circumstance that the neutralisation of the antibody rom normal serum follows quite different laws than those alid for the antirennet produced by immunisation, is a ertain indication that these two antibodies are really ifferent substances. This is also probable because the ntirennet is much more easily destroyed by heat than the ntibody from normal serum.* The occurrence of many ntibodies in normal sera led Ehrlich to the supposition 'This criterion gives alone no absolutely certain indication, for the thermo- ihty of a dissolved substance may depend to a rather high degree on e presence of other substances, as salts or proteids (^. pepton), in the >lution. Cf. Biernacki: Zeitschr.f. Biologic, 28 (1891) 278 LECTURES ON IMMUNITY that animals generally produce antibodies against different toxins and that this production is only augmented by the experimental injection of toxins into the blood of the ani- mal. In other words, the antibodies in normal sera ought to be identical with those produced after active immunisa- tion. This is evidently not true for the antirennets. There are also many other considerations which speak against Ehrlich's idea, of which Bashford has given a detailed criticism.1 In one point I cannot agree with Bashford. He assumes that the toxin, i.e. in this case the rennet, is divided between the normal serum and the rest of the fluid. This is quite like the idea held by Biltz. According to Bashford, if for the second serum 0.3 c.c. of the serum takes half of the rennet, then 0.6 c.c. ought to fix two-thirds of it, whereas it actually takes 78 per cent; 0.9 c.c. should fix 75 per cent, whereas the table gives 88; 1.2 c.c. should carry 80 per cent, instead of the 91 per cent observed. This last series may be calculated according to the scheme of Biltz; it gives a nearly constant value of the exponent /, viz. / = 2.3 (cf. p. 216). But the first series for normal horse-serum yields a steadily increasing value of/ with increasing n. Between n = o.i and n — 0.4, / is 0.85 ; between n — 0.4 and n — i.o, we find / = 1.5 ; be- tween n = i.o and n = 1.5, / is 2.4; for higher values of n, p is found to be 3.3. If we apply the idea of Biltz to the fixation of rennet to antirennet, we find that at first the concentration oil rennet in the serum is constant until about n — 0.6, whereas that of the rennet in the fluid sinks in the proportion 6 to i 1 Bashford: Journ. of Pathology, 8. 62 (1902). THE PRECIPITINS AND THEIR ANTIBODIES 279 which is evidently impossible,/ is infinite. Then/ passes through the value 12 between n = 0.6 to 0.7, and sinks to 5.3 between n — 0.8 and n — 0.9. In a very excellent memoir Fuld and Spiro1 have made it probable that the " antirennet " contained in the normal serum of horse blood is a so-called pseudo-globulin 2 which acts in such a manner that it binds a part of the calcium ions and thereby hinders, or better retards, the coagulation. As we have seen before (cf. p. 74), the influence of the quantity of free calcium ions upon the time of coagulation is as large as that of the quantity of rennet. Therefore a binding of the calcium ions in a certain proportion has the same effect as a neutralisation of rennet in the same proportion. In this case the quantity of calcium salt of the para-casein regulates the velocity of coagulation. The salts of calcium with para-casein and with the pseudo- globulin must be dissociated to a very low degree, and for the sake of simplicity we may suppose that the degree of dissociation of the two salts and of the acids in the pres- ence of a given quantity of calcium ions is such that we may make use of the formula of Guldberg and Waage. This may at least be regarded as a preliminary approxima- tion, which we may employ until the properties of the reacting compounds have been better examined. Then if the quantity of para-caseate of calcium in the absence of 1 Fuld and Spiro: Zeitschr. f. ph. Ch., 31. 147 (1900). 2 On precipitation with ammonium sulphate, euglobulin and pseudo-globu- lin separate out. Their aqueous solution is dialysed, then the euglobulin precipitates and the pseudo-globulin remains in solution. The euglobulin has a coagulating influence on casein. The pseudo-globulin retards the coagu- lation, even if caused by papayotin, cynarase or euglobulin, as well as by rennet. 280 LECTURES ON IMMUNITY serum be taken as a unit, this may be regarded as nearly equivalent to the quantity of calcium present,. if it does not exceed a certain limit ; now n equivalents of pseudo-globulin are added, then at equilibrium we have (n — x) equivalents of pseudo-globulin, (i — x) equivalents of calcium para- caseate, x equivalents of calcium salt of the pseudo-globu- lin, and (a + x) equivalents of para-casein, where a is the quantity of free para-casein for n = o. Then the equi- librium follows the equation (n- x)(\- x) = K-x(a+x). If a is high, i.e. in the presence of much casein, we may regard (a + x) as a constant, and we have the equation with the aid of which the calculated values above have been derived. We may therefore say that the opinion of Fuld and Spiro agrees with the experiments, and it is easy to see how these might be controlled to a still higher degree. Even against the coagulation of blood-plasma there exist some natural antibodies, one of which, the hirudin, the extract of leeches, has been known for a long time. Fuld and Spiro l made the following determinations of the quan- tity of "free muscle extract" from goose, of which 0.4 c.c. had been taken, in the presence of n c.c. of an extract of leeches, acting on i c.c. of goose plasma. NEUTRALISATION OF MUSCLE EXTRACT FROM GOOSE BY MEANS OF HIRUDIN n *<*•. ^calc. 0 100 100 0.2 75-0 82.0 0.4 66.7 64.9 0.8 357 36.0 1.6 ii. i II. 2 1 Fuld and Spiro: Hofmcisters Beitrage^ 5. 181 (1904). THE PRECIPITINS AND THEIR ANTIBODIES 281 For the calculation the formula used was that employed before for the calculation of the influence of horse-serum on rennet. Of the solution of hirudin i c.c. is equivalent to the fixed quantity (0.4 c.c.) of the extract, and the con- stant is K = 0.09. The agreement is very satisfying. It therefore seems quite proper to assume that the action of hirudin on the coagulation of blood-plasma is of the same nature as the action of pseudo-globulin on the co- agulation of casein. The circumstance that the substances concerned in bio- chemistry react not only with their specific antibodies, but also with other compounds, specially with such well-known properties as acids, bases, salts, or even lecithin and cholesterin, is a very promising feature. For if there were no reactions except with the specific antibodies, which we have very little hope of obtaining in the pure state adapted to a detailed investigation, we would have very slight prospects of rapid progress. Besides the coagulating ferments there is another group of precipitins which deserve this name to a higher degree, namely, those prepared by injection into living animals of fluids containing proteins. Among these the lacto-serum, which is obtained by the injection of milk into animals, has been investigated very thoroughly by P. T. Miiller.1 Other precipitins produced by the intraperitoneal injection of egg-albumen or normal horse-serum into rabbits were studied by Eisenberg;2 they behaved very like the lacto- serum prepared by the intraperitoneal injection into rabbits and studied by Miiller. JP. T. Miiller: Archiv f. Hygiene, 44. 126 (1902); Centralbl f. Bah- teriologie, etc., 32. 521 (1902), and 34. 48 (1903). 2 Eisenberg: Bull, de VAc. des Sciences de Cracovic, p. 289 (1902). 282 LECTURES ON IMMUNITY Bordet1 early drew attention to the great difference between rennet and lacto-serum, though both coagulate milk (casein). The coagulation with rennet is much more voluminous and gelatinous than that with lacto-serum, which also gives precipitation at lower temperatures (under 20° C.), very different from rennet. Furthermore, lacto-serum is inactivated only by being heated for thirty minutes to over 70° C., whereas a 2 per cent solution of rennet loses its coagulative power in less than five minutes at 50° C. (cf. p. 87). The lacto-serum is, on the other hand, much more easily precipitated by ammonium sul- phate than is rennet. A very important point is that the coagulum of the lacto-serum yields no serum-albumen. A similarity is that in both cases the presence of calcium or barium salts is necessary for the precipitation, so that the reaction is hindered by the presence of oxalates in the milk. M tiller investigated other salts, viz. NaCl, KC1, NH4C1, Na2HP04, NaCH3CO2, NaNO3, KNO3, KI, KBr, KSCN, and MgSO4, but none of them could replace Ca salts. In this point there is a great distinction from the agglutinations, which are rendered possible by the most widely different salts (cf. p. 159) according to Fried- berger.2 The precipitins examined by Eisenberg do not seem to need salts for their action. Many salts diminish the action in even rather weak concentrations, thus, for instance, (NH4)2SO4 in 0.25 normal solution and MgCl2 in 2 normal solution completely check the precipitating action. By heating the milk during some time to 100° C. 1 Bordet: Ann. de VInst. Pasteur, 13. 241 (1899). 2 Frierlberger : Centralbl. f. Bakteriologie, 30. 341(1901). Cf. Bechhold; p. 159 above. THE PRECIPITINS AND THEIR ANTIBODIES 283 or egg-albumen to 78° C. during 60-90 minutes, their precipitability was lost. But M tiller found that the pre- cipitation by lacto-serum could be restored by the addition of Ca salts, or even that it would not disappear if the milk contained naturally much calcium. Concentrated solutions of urea or formalin destroy the precipitability of egg-albumen as well as the agglutinability of bacteria. The precipitate from a mixture of milk and lacto-serum dissolves in a i per cent solution of NaCl. This solution can be precipitated again by rennet or lacto-serum, just as a solution of casein. The treatment with rennet also yielded serum-albumen. Evidently the precipitate is somewhat soluble, and in solution partly dissociated into the two components. At high temperature the free lacto- serum is decomposed and new quantities of lacto-serum are successively formed by the decomposition of the soluble fraction of the precipitate until this is wholly reconverted into casein. M tiller also isolated the lacto-serum from the precipitate through cautious treatment with acetic acid; the liquid obtained by centrifugation of the precipitate, which had been in contact with the acid solution for two hours, contained a noticeable quantity of precipitin. The compound of lacto-serum and casein may be precipitated by the sudden addition of acetic acid. The precipitate dis- solves completely upon neutralisation, but is precipitated by small quantities of a calcium salt. The compound, therefore, probably exists in the solution, but in a partially dissociated state, and gives an insoluble product with calcium or barium salts. Para-casein, prepared by the action of rennet on milk, does not bind the lacto-serum. The lacto-serum heated to 70° C. for thirty minutes 284 LECTURES ON IMMUNITY acquires the peculiar property of hindering the precipita- tion of casein by means of lacto-serum. In the same manner Eisenberg found that his precipitin for egg-albu- men on heating for one hour to 72° C. was transformed into an antiprecipitin. In the same manner the precipi- tins against cholera and typhoid, prepared by injection of cultures of the corresponding bacteria into the veins of a horse, lose their property of coagulating the correspond- ing bacterium on being heated for thirty minutes to about 60° C.,1 and acquire anticoagulating properties on heating to 73° C. (for cholera-serum). Even for the agglutinins, similar observations have been made by Eisenberg and Volk. Through different experiments Miiller was led to the conclusion that the antiprecipitin binds the casein, with which it gives a compound soluble in the presence of calcium salts. Antiprecipitin may even dissolve the pre- cipitate, in the same manner as a carbonate is dissolved by a not too weak acid. This was shown in a simple manner by Eisenberg, by preparing in one test a mixture of pre- cipitin and antiprecipitin with egg-albumen, and in a second test a mixture of antiprecipitin and egg-albumen with precipitin. In the second case no precipitate was formed because the egg-albumen was bound by the anti- precipitin, while in the first case precipitation occurred. (The velocity of reaction is evidently rather slow, otherwise the two experiments would give the same result.) Similar experiments were made by Eisenberg with coagulating serum antagonistic to the bouillon of typhoid cultures. The antiprecipitins are derived from the precipitins, for after these have been precipitated from the serum (for 1 Pick: Hofmeisters Beitragc, 1. 8 1 (1901). THE PRECIPITINS AND THEIR ANTIBODIES 285 instance, from lacto-serum by means of milk), it yields no antiprecipitin on being heated ; normal serum likewise gives no antiprecipitin. The binding of precipitin to casein may be judged, on the basis of the insignificant solubility of the compound, to be nearly complete if the two substances are present in equivalent quantities. If one of them is present in the fluid in excess, it is to a large extent carried down by the precipitate. Especially is this valid for precipitin. With the precipitable substance there is another perturbing influence, which is especially prominent with egg-albumen and which has its analogies in the behaviours of agglu- tinins and serum-precipitins. An excess of egg-albumen dissolves the precipitate, so that it is often observed that a given quantity of precipitin causes a precipitate with a weak but not with a stronger solution of egg-albumen. Even with casein this peculiarity may be observed, as Miiller's later experiments indicate. The quantity of the precipitate produced by a given quantity of lacto-serum therefore increases at first with the quantity of casein added, and reaches a maximum in the neighbourhood of the point where the casein added is equivalent to the quantity of lacto-serum, only to decrease thereafter and fall to zero at a point where the quantity of casein added is nearly double that corresponding to the maximum value; the determinations do not seem to be accurate enough to warrant more than an approximative valuation. Some experiments of Eisenberg afford an idea of the relations between antiprecipitin and precipitin. The quan- tities of the preparations are given in drops. The antiserum was heated precipitin diluted in the proportion I to 5. 286 LECTURES ON IMMUNITY A is the quantity of egg-albumen, B the quantity of pre- cipitin, C that of antiprecipitin, D the rest of the fluid given in quantity of physiological salt-solution. The total quantity was always about sixty drops. ANTAGONISM BETWEEN PRECIPITIN AND ANTIPRECIPITIN A B C D OBS. P 0.6 0 58 Free. 0.6 1.2 i 56 No 0.38 3 i 55 Free. 0.6 12 5 42 No o-55 30 5 24 Trace 0.75 53 5 i Free. 0.84 44 15 o No 0-59 3 3 15 39 No 0.27 10 3 15 32 Free. 0.9 The results may be calculated on the supposition that the antiprecipitin is double as strong as the precipitin, i.e. one drop of the antiprecipitin contains double the number of equivalents as one drop of precipitin, and that the egg- albumen is divided equally between the different equiva- lents. Then the precipitate P formed may be calculated from the formula : — P = 2C -A. I have therefore calculated this expression and tabulated it under P. It will be seen that if P equals 0.6 or is greater, precipitation is observed ; if it is less, not. The precipitate from egg-albumen is soluble in weak solutions of acids or bases, but insoluble even in concen- trated solution of sodium chloride. The acid solution yields precipitation on neutralisation. On heating, it coag- THE PRECIPITINS AND THEIR ANTIBODIES 287 ulates, so that it loses its solubility in weak acids. In this point it differs from the lacto-serum precipitate and from agglutinated bacteria, which lose their agglutination at high temperatures. It is soluble in concentrated solu- tions of urea or magnesium chloride or in formalin. In this point it resembles agglutinated bacteria. A great practical importance is attached to the examina- tion of the properties of serum-precipitins, prepared by the injection of serum from one animal into the veins of another animal. These precipitins are to a high degree specific, and they have therefore been used to determine the origin of blood-flecks for forensic or medico-legal purposes. On this point it may be sufficient here to refer to the investigations of Uhlenhuth,1 Wassermann and Schutze,2 and Hamburger.3 Recently Hamburger4 has executed some quantitative experiments on the action of these precipitins. He meas- ured the precipitate formed in the reaction between a certain quantity of a blood-serum and its antibody pro- duced by the repeated injections of this serum into the veins of another animal. The reacting fluids were mixed in a funnel-shaped vessel which extended into a capillary tube of uniform calibre and graduated in 100 divisions. By vigorous centrifugation of this vessel for 1.5 to 2 hours he packed the precipitate into the capillary tube, where it reached a constant volume and was measured by the read- ing of the divisions. 1 Uhlenhuth: Deutsche med. Wochenschrift, No. 30, p. 499 (1901). 2 Wassermann and Schutze : Berl. klin. Wochenschrift (1901). 8 Hamburger: Deutsche med. Wochenschrift, No. 6 (1905). * Hamburger: Folia hcematologica, Vol. 2, No. 8 (1905). 288 LECTURES ON IMMUNITY One series of experiments was done with serum (A) from horse blood and serum (B) from a calf which had been treated with horse-serum several times. The horse-serum was diluted with 50 times its volume of a i per cent solution of sodium chloride. If to a certain quantity, i c.c., of the calf-serum increasing quantities of horse-serum (A) were added, at first no precipitate ap- peared; then at higher concentrations of A the quantity of precipitate increased nearly proportionally to the quan- tity of A added until a maximum was reached. Thereafter further additions of horse-serum caused the quantity of precipitate to decrease until -at a certain limit the precipi- tate again disappeared. This behaviour, which is very common in reactions between sera and their precipitins, is clearly apparent from the following figures.1 In this case the total volume (100 div.) of the capillary tube was 0.04 c.c. The precipitate is therefore in the fol- lowing table given in units of 0.0x304 c.c., corresponding to one division. One c.c. of calf-serum is fixed as 100 units, corresponding to the fact deduced from the experi- ments that it could yield in maximo 100 units of precipi- tate, P\ and i c.c. of the diluted horse-serum is on analogous grounds fixed as 300, so that i c.c. of A is equivalent to 3 c.c. of B. This seems to indicate that nearly the whole quantity of the albuminous substances in A, but only a very small fraction of those in B, enter into the precipitate. The maximum is reached at A = 100; that is, on the addition of 0.333 c«c- of horse-serum, the quantity equiva- 1 Hamburger and Arrhenius: Proc. of the Meeting of the R. Ac. of Sciences, in Amsterdam, May 26, 1906, p. 33. THE PRECIPITINS AND THEIR ANTIBODIES 289 lent to the quantity of calf-serum present. (This observa- tion has really led to the determination of the equivalent quantities of the two sera.) ACTION OF DIFFERENT QUANTITIES {A} OF HORSE-SERUM ON A GIVEN QUANTITY (100) OF CALF-SERUM A VOL. •^obs. Pc&lc. A VOL. •^obs. -^calc. 4 I.OI3 0 O.2 79 .267 51 53-6 8 1.027 3 3-9 88.3 .294 55 57-1 '5 •°5 10 10.3 90 •3 57 57-5 24 .08 17 17.8 100 •333 59 58.9 30 ,i 21 23.6 "54 •385 55 57-4 39 •13 32 29.7 137 •457 5° 5L3 45 •15 34 34-0 167 •557 43 4i.3 54 .18 43 40.1 214 .713 25 26.8 60 .2 45 43-9 300 2.0 5 5-5 75 1.25 (53 (5i 5i-9 500 2.67 2 o The calculated figures, which within the errors of ob- servation agree with the observed values — the magnitude of the errors of observation may be judged by the differ- ence of the two observations for ^4 = 75 — are found in the following manner : The quantity B of calf-serum (in this case B = 100) may react with A equivalents of horse- serum. Then a certain amount of precipitate, Plt is formed, of which / parts are soluble in i c.c. and the rest, P1 —p V= P, is packed in the capillary tube (y is the volume of the mixture). Then there are remaining in the solution A — Pl equivalents of horse-serum, and B — Pl equivalents of calf-serum. But experience indicates that a further addition of horse-serum dissolves the precipitate. Let us suppose that there are formed Y equivalents of 290 LECTURES ON IMMUNITY soluble compound, such that one equivalent of it contains one equivalent of precipitate and n equivalents of horse- serum (or in other words n + I equivalents of horse-serum and i equivalent of calf-serum). Then there are present in the solution the following quantities in equivalents of the different substances : — (A - P —p V— (n + i) F) of horse-serum, (B-P-p V- Y) of calf-serum ; and the following equations of equilibrium are valid : — \A-P-pV-(n+i)Y\ {B-P-pV-Yl^ If we determine Ffrom the last equation and introduce it into the first one, we obtain : — / is found in the experiments to be 2.5. If we put ^ + « + i = 345 and ATi/"" - ^±i£±0/ = T 30, we find / A2 the calculated values of the total quantity (P) of precipi- tate. The tabulated values of P give this quantity divided with the volume, Vt i.e. the quantity of precipitate in i c.c. J£ jjm, + 1 The last equation gives -~ — -- =130. If we suppose A2 0.29 m = i, i.e. that one molecule of precipitate is formed from one molecule of each of its two components, we obtain K+ . K, 3.08 — i = 3.08 ; if we suppose m = 2,we find — ^ = — — = 0.879. A2 A2 / THE PRECIPITINS AND THEIR ANTIBODIES 29 1 These two assumptions regarding m seem the most prob- able. In the first case the constants of reaction are of the same order of magnitude; in the second case K^ is of the same order of magnitude as K^p. As, further, n = 2.45 — TS- -IS" — -, and — - has a positive value, n can only be I or 2 (if we do not take into consideration fraction numbers). The proba- bility is therefore that the soluble compound of precipitate with the active fraction of the horse-serum is built up of one molecule of the precipitate and one or two molecules of the other reacting substance. In some cases it is not necessary to assume that the precipitate is dissolved on the further addition of the serum which has been injected. A very interesting instance of this behaviour is given by Hamburger in the action of the serum of a rabbit treated with sheep- serum on the sera of three different animals, viz. : sheep, goat, and bullock, which are so closely related to each other that all yield precipitates with the said rabbit-serum. As is natural, the sheep-serum yielded the most voluminous precipitate ; next comes the goat-serum, which animal is the most closely related to the sheep ; and the least quan- tity of precipitate is given by the serum from the bullock, which is less closely related to the sheep than is the goat. The figures are given in the following three tables. The rabbit-serum was always used in the quantity of 0.4 c.c. The quantity of the precipitate is given in scale-divisions of the capillary tube (100 divisions = 0.04 c.c.). The sheep- serum was normal serum diluted with 49 times its volume of i per cent solution of sodium chloride. The sera of goat and bullock used in the following two series of ex- 292 LECTURES ON IMMUNITY ACTION OF SERUM FROM A RABBIT, IMMUNISED WITH SHEEP-SERUM, ON SHEEP-SERUM ^ QUANTITY OF A r. QUANTITY P OF PRECIPITATE c.c. Equiv. obs. calc. 0.02 0.8 0.162 I 0-5 0.04 1.6 0.163 2 !-3 O.I 4 0.25 3 3.5 O.I5 6 0.302 6 5-3 0.2 8 0.36 7 7.2 0.6 24 1. 00 21 21.5 I 40 1.96 35 34 1.5 60 3.61 39 48 2 80 ' 5.76 60 57 3 120 11.56 67 66 5 200 29.2 64 65 7 280 54-8 58 58 IO 400 108.2 49 46 15 600 237 10 19 18 720 338 5 3 20 800 416 2 o i ( + i c.c. aq.) 40 5.76 28 25 5 ( + i c.c. aq.) 200 41 57 51 IO ( -f I c.c. aq.) 4OO 130 41 32 periments were also diluted in the same manner. The experiments were calculated in the following manner, i c.c. of the sheep-serum is equivalent to 40 units of precipi- tate. The number of such equivalents of sheep-serum is given in the second column. In the same manner 0.4 c.c. of rabbit-serum contains 120 such equivalents, i.e. i c.c. contains 300 equivalents. If now the volume is V, con- taining originally A equivalents of sheep-serum and 120 equivalents of rabbit-serum, and P equivalents of precipi- tate have been formed, then the concentrations of the two THE PRECIPITINS AND THEIR ANTIBODIES 293 (A-P) , (I20-P) sera are a — ^ — / and - — — — % and the formula repre- senting the equilibrium is: — where K is a constant, which according to the experiments is 250. With the aid of this equation the calculated values of P have been found and are written beside the observed values. In the three last tests i c.c. of water containing I per cent of sodium chloride has been added to the mix- ture of the sera, which circumstance has been taken ac- count of in the calculation of the volume F(in c.c.). The agreement between the observed and the calculated values may be regarded as very satisfying, especially with respect to the enormous change of A (in the proportion of i : 1000) and of F2 (i : 2500). The simple form of the equation of equilibrium depends upon two circumstances : the extremely low solubility of the precipitate in rabbit-serum (not i in 3000), and in sheep- serum. Probably these two circumstances are connected with each other. The figures obtained with goat-serum were calculated in the same manner and the results are given below. In this case I c.c. of the goat-serum was always equivalent to 40 units of the precipitate, but 0.4 c.c. of the rabbit- serum was equivalent to only 85 units of pre- cipitate. The constant K is set at 200. Here the agreement is not so perfect as in the foregoing series. The agreement would have been much closer for the latter part of this series if we had taken K = 160, but then the first part would have shown greater deviations than it does now; 294 LECTURES ON IMMUNITY ACTION OF SERUM FROM A RABBIT, IMMUNISED WITH SHEEP-SERUM, ON GOAT-SERUM (A) QUANTITY OF A V* QUANTITY P OF PRECIPITATE c.c. Equiv. obs. calc. 0.02 0.8 0.162 I 0.4 0.04 1.6 0.163 2 1.2 O.I 4 0.25 4 3-4 0.15 6 0.30 5 5.2 0.2 8 0.36 6 7 0.6 24 1. 00 16 21 I 40 1.96 26 32 i-5 60 3.61 30 43 2 80 5.76 35 48 3 120 11.56 40 5i 5 200 29.2 50 47 7 280 54-8 52 40 10 400 108.2 34 27 12 480 154 27 18 '5 600 237 9 5 18 720 338 8 0 20 800 416 4 0 I (+i c.c. aq.) 40 5.76 21 22 5 (+i c.c. aq.) 200 41.0 48 35 10 (+i c.c. aq.) 400 130 30 17 perhaps this difficulty depends upon a different solubility of the precipitate in rabbit-serum and in i per cent solu- tion of sodium chloride. Perhaps even a difference of tem- perature in the two parts of the series is responsible for the disagreement; it is really the weak point of these measurements that the temperature cannot be controlled during the centrifugation. But in any case there can be no doubt that the chief part of the phenomenon is repre- sented by the last formula. THE PRECIPITINS AND THEIR ANTIBODIES 295 ACTION OF SERUM FROM A RABBIT, IMMUNISED WITH SHEEP-SERUM, ON BULLOCK-SERUM (A) QUANTITY OF A V* QUANTITY P OF PRECIPITATE c.c. Equiv. obs. calc. 0.02 0.8 0.162 I o-5 0.04 1.6 0.163 2 i-3 O.I 4 0.25 4 3-4 O.I5 6 0.30 5 5-2 0.2 8 0.36 7 6.7 0.6 24 1. 00 16 19 I 40 I.96 20 24 l-J 60 3-61 22 26 2 80 5.76 25 26 3 1 20 II.S6 28 25 5 200 29.2 22 21 7 280 54-8 IO 17 10 400 108.2 7 II 12 480 154 5 7 15 600 237 3 i 18 720 338 2 0 20 800 416 I 0 l(+I c.c. aq.} 40 5.76 16 15 5(+I c.c.aq.} 200 41 13 16 io(+ I c.c. aq.} 400 130 5 7 This is to a still higher degree valid for the experiments with bullock-serum, reproduced above. One c.c. of this serum contained 40 equivalents, 0.4 c.c. of the rabbit-serum only 35 equivalents. KWZLS found to be equal to 85. The agreement is very satisfying. The conclusions which may be drawn from these three series are rather interesting. On injection of sheep- serum into rabbit blood we have obtained an antiserum containing per centimeter cube 300 equivalents of pre- 296 LECTURES ON IMMUNITY cipitin against sheep-serum, 212 equivalents of precipitin against goat-serum, and only 90 equivalents of pre- cipitin against bullock-serum. All of these three normal sera contain 2000 equivalents per centimeter cube. In the same manner and in nearly the same proportion the constant of reaction sinks from 250 for sheep-serum to about 170 for goat- and to 85 for bullock-serum. Probably the sheep-serum contains additional substances which occur also in sera of goats and of bullocks, which after injection into rabbits produce antibodies against these sera, although in lesser proportions than the pre- cipitin against the chief substance in sheep-serum, which gives a precipitate with the serum from the inoculated rabbit. The observations lead to the conclusion that we have a mixture of three different precipitins in the rabbit-serum. Otherwise it is difficult to understand that i c.c. of all the three normal sera, from sheep, goat, and bullock, contain nearly the same number (2000) of equivalents of the precipitate formed. As 100 equivalents pack a volume of 0.04 c.c., the precipitates given by i c.c. of the rabbit-serum would pack a volume of 0.24 c.c., of which probably only a small part is derived from this serum itself, the chief part being derived from the other sera. The experiments with precipitins lead to the conclusion that they are really bound in the precipitates and do not act as catalytic agents. The action of agglutinins dis- plays a very great similarity to that of the precipitins, so that it is reasonable also for this case to assume a real chemical reaction in stoichiometric proportions and not a catalytic action. Further, we have observed that haemo- THE PRECIPITINS AND THEIR ANTIBODIES 297 lytic substances, such as tetanolysin, are bound to the sub- stance acted upon, so that a given quantity of lysin can lake only a given equivalent quantity of erythrocytes (cf. pp. 104, in). Even for the agglutinins such an equivalence has been observed. It is a general feature of the theory of Ehrlich that he assumes that the action of poisons depends upon a binding, or as he often says an "anchoring," of the poison to the substrate upon which it acts. In this regard Ehrlich goes however a little too far, since he, for instance, supposes that all the immune-body absorbed by an ery- throcyte is " anchored " to it. Furthermore, we have found that on neutralising a poison or an analogous substance with its antibody, a real binding takes place according to stoichiometrical propor- tions. It may here be observed that in some cases — and these are perhaps rather common (cf. p. 267), as for in- stance in the coagulation of casein — the reacting substance is really not a single one but two, rennet and calcium ions ; the antibody (e.g. that from normal horse-serum) binds only the one component of the reacting mass (here the calcium ions), probably leaving the rennet intact. In simi- lar cases it is very easily possible that the one component that is not bound by the antibody acts as a catalysor. This seems very probable for rennet, as the time necessary for coagulation is within very wide limits inversely pro- portional to its quantity. Nevertheless, on the whole, we obtain from a closer study of these phenomena the opinion that the catalytic action does not play the chief r61e which has been often assigned to it by different authors. Ehrlich has on re- peated occasions rightly laid stress upon the necessity of an 298 LECTURES ON IMMUNITY investigation of the relations between toxins and antitoxins according to the general principles of physical chemistry.1 In the foregoing pages I have tried to carry through the programme advocated so strongly by Ehrlich. That this has been possible, is due in large part to the great num- ber of quantitative measurements which have been carried out in the last quinquennium, especially by Madsen and his collaborators. This work is still in full progress ; and it may therefore be well regarded as very probable that we are here entitled to use the words with which Dr. Find- lay 2 closed his lectures in the University of Birmingham, " Considering the very brief period during which physical chemical methods have found application to the study of biological problems, the advance which has been made is very remarkable ; and there is every reason to believe that in the future, as the methods become more and more extensively applied, the advance will become more rapid and widespread." Our hope in this direction lies chiefly in the treatment of quantitative experiments on the basis of physical chemistry. It may be confidently expected that the accumulating quantitative work will rapidly give solidity to this discipline of science. I know well that objections have been raised to some of the conclusions that I have here enunciated. But it is clear to me that, if these objections are to deserve a more than momentary 1 Cf. P. Ehrlich : Rapport au 13* Congrh Internationale de medicine, Paris, 2-9 Aoftt, 1900, Section de bacteriologie ; " Schlussbetrachtungen," "Nothna- gel's spezielle Pathologic und Therapie," T. 8, pp. 6-7, Wien, 1901 ; Bericht iiber die Th'dtigkeit des Instituts f. Serumforschungen zu Sieglitz, p. 19, Jena, 1899 (G. Fischer) ; "UeberToxine und Antitoxine" in Therapie der Gegen- wart, 1901. 2 Al. Findlay : " Physical Chemistry and its Applications in Medical and Biological Science," p. 68, Longmans, Green & Co., London, 1905. THE PRECIPITINS AND THEIR ANTIBODIES 299 interest, they must be shown to agree with the quantitative measurements already executed or with other new ones. In the foregoing discussions it has been shown that the available observations conform to the laws deduced by physical chemistry for common chemical compounds. Therefore discussions as to whether toxins and their antitoxins, being defined as colloids, might be held not subject to these general chemical laws, will possess but little interest until the assumed deviations from said laws are measured quantitatively. Any other method of procedure has a very hypothetical value. INDEX OF AUTHORS Aberson, 139, 140. Armstrong, 55, 57, 58, 61, 134. Arrhenius, i, 13, 15, 25, 29, 45, 62, 68, 100, no, 150, 167, 180, 181, 189, 190, 200, 224, 231-239, 250, 261, 288. B Bang, 71, 267. Barendrecht, 52. Bashford, i, 205, 206, 245, 252, 272, 273- Bayliss, 79, 136, 163. Bechhold, 156-160, 166, 282. Behring, 29, 152, 179. Besredka, i. Biernacki, 277. Biltz, 35, 151, 152, 155, 156, 165, 215, 216, 217, 231, 278. Blum, 266. Bodenstein, 54, 60. Bomstein, 5, 7. Bordet, 20, 21, 32, 34, 151, 218, 219, 223, 225, 242, 246, 247, 252-260, 270, 271, 281. Borissow, 121, 122. Bossaert, 166. Bredig, 50, 152, 161. Brodie, 28. Brown, 52, 55, 58. Bruck, 24. Buchner, 30, 141, 218. Calcar, 200. Calmette, 18, 19, 30. Cherry, 18, 26, 30. Clausen, 136. Cohen, 136. Connstein, 125, 132. Craw, 26-28. Danysz, 22, 190, 192, 194. Detre, 241, 242. Dreyer, 31, 151, 198. Duclaux, 52, 57, 164, 194, 263, 268, 269. v. Dungern, 2, 190, 194, 228. Ehrlich, 9, 11-15, r9-2I» 3°. 31. 152, 177, 180, 182-185, X89, 197, 205, 219, 223, 225-227, 231, 246, 247, 256- 261, 272, 273, 277, 278, 282, 297, 298. Eisenberg, 17, 32, 34, 116, I44~i47» 281, 283-285. Emmerling, 133, 134. Engel, 124, 135. Euler, 50, 51, 84, 141, 142. Famulener, 21, 39, 40, 42, 47. Findlay, 298. Fischer, 134. Fischer, E., 134, 161. Ford, 256. Freundlich, 161. Friedberger, 246, 282. Fuld, 73, 76, 97, 185, 278, 280. Gay, 252, 254, 255, 260. Gengou, 270, 271. Gessard, 2. Girard-Mangin, 163, 164. Glendinning, 55. Godlewski, 136. Goldschmidt, 142. Gruber, 220, 228, 231. Guldberg, i, 28, 133, 175, 216, 279. 301 302 INDEX OF AUTHORS H Hamburger, 287-296. Hammarsten, 3, 71, 266-268, 270, 276 Hanriot, 126, 134. Hausmann, 272. Hedin, 266. Hemmeter, 71, 267. Henderson Smith, 103. Henri, 51-56, 59, 60, 80-84, Jo5> IQ6, 139, 156, 163, 164. Hertwig, 138. Herzog, 141. Hildebrand, 2. Hill, 133. Hober, 10, 222. van 't Hoff, 28, 35, 98, 136. Hoyer, 125, 132. Huppert, 69, 70. Jacoby, 272. Joos, 34, 146, 153. Jorgensen, 4, 6, 15, 17, 91. Kanitz, 137. Kastle, 126, 132, 134. Kitasato, 29. Kjeldahl, 53, 98. Klein, 254. Kobert, 273. Kossel, 12, 161. Kraus, 164, 165, 272. Kyes, 10, 190, 209-214, 240. Lalou, 84. Landois, 218. Landsteiner, 32. Laqueur, 266. Larguier de Bancels, 80-83. Loeb, J., 138, 139, 161, 164. Loeb, L., 271. Loercher, 265. Loewenhart, 126, 132, 134. Ludwig, 272. Lunden, 176. M Madsen, i, 4, 5, 6, 7, 10, 13, 15, 17, 21- 23. 25, 29, 31, 33, 39, 40, 42-44, 46, 47. 70. 72, 77. 78, 86, 88-100, 103, 107-117, 135, 154, 167, 180, 181, 186-190, 196-198, 200, 202, 203, 204, 206-213, 274» 298. Malkoff, 149. Malloizel, 163. Manwaring, 229. Marshall, 189. Martin, 18, 26, 30. Matthaei, 137. Metchnikoff, 231. Mett, 121. Meyer, H., 24. Morgenroth, i, 2, 20, 31, 32, 34, 35, 76, 150, 189, 199, 214, 215, 219-221, 228, 229, 231, 244-251, 256, 257, 259, 262, 268, 274. Much, 35, 151, 152. Miiller, P. T., 22, 189, 281-283. Miiller von Berneck, 50. Musculus, 134. Myers, 273. N Neisser, 21, 189, 224-227. Nernst, 28, 35, 148, 152. Nicloux, 97, 98, 128, 129. Nicolle, 164, 165. Noguchi, 23, 107, 109, in, 206-213. Ostwald, 68, 133, 184. O'Sullivan, 58. Overton, 10, 222. Pasteur, 141. Pauli, 160, 161, 162, 164. Pawlow, 71, 77, 122, 267. Peter, 138. Pfeififer, 246. Pick, 284. Portier, 194. R Ransom, 10, 24, 147, 220. Reichel, 73. Reid, 25. Richet, 194. Ritchie, 45, 46. Robertson, 134. INDEX OF AUTHORS 303 Rdde"n, 3, 276. Romer, 200. Roux, 30. S Sachs, 2, 10, 29, 35, 190, 211, 214, 218, 222, 223, 228, 231, 241, 242, 244, 245, 248-251, 257-262. Sackur, 266. Sawjalow, 71, 76, 77, 119, 121, 267. Schmidt, A., 270. Schmidt, G., 151, 216. Schmidt-Nielsen, 71, 267. Schiitz, Emil, 62, 67, 69, 70, 119. Schlitz, Julius, 67. Schiitze, 2, 3, 287. Segelcke, 71. Sellei, 241, 242. Siebert, 35, 151, 152. Siedentopf, 264. Sjoqvist, 65-69, 119-121, 123, 162, 163. Snyder, 139. Soxhlet, 71. Spiro, 73, 185, 278, 280. Spohr, 98. Stade, 123-125, 135. Storch, 71. Tammann, 48, 49, 59, 97, 98, 126. Taylor, A. E., 83, 98, 126, 130-133, 134. Terroine, 54, 55, 59, 61. Tompson, 58. Tyndall, 264. U Uhlenhuth, 287. Vaubel, 266. Volhard, 122, 135. Volk, 17, 32, 116, 144-147, 284. W Waage, i, 28, 133, 175, 216, 279. Walbum, 10, 21, 23, 33, 77, 78, 86, 89, 90, 92-97, 107, 109, in, 113, ii4t 135, 154, 186, 188, 200, 203, 204, 274. Warder, 98. Wartenberg, 125, 132. Wassermann, 12, 19, 24, 256, 287. Wechsberg, 21, 189, 224-227. Weigert, n, 257. Weis, 84. Wohl, 134. Zeller, 128. INDEX OF MATTER Abrin, 2, 272. Absorption, 32, 33, 144-155, 207, 216, 219, 297. Acetic acid, 166, 283. Acids, coagulating action, 266, 270, 272; destroying action, 35, 43, 44, 45, 138; digesting action, 69, 126; haemolytic action, in, 167, 171; neu- tralisation, 35, 222. Active immunisation, 6, 218. Acme, 4. Adrenalin, 24. Adsorption, 32, 35, 151, 152, 215, 216. Agglutination, agglutinins, 4, 9, 14, 17, 32, 115, 116, 144-166, 219, 241, 256, 284, 287. Agglutinoid, 155. Albumen, 65, 92, 119, 189. Albumen precipitin, 273, 281, 285, 286. Albumose, retarding influence of, 77; equivalent weight, 162. Alcoholic fermentation, 139-142. Alexin, 20, 34, 48, 218-262. Alkali, haemolysis through, in, 167- 177; influence on eggs, 138; on toxicity, 222; on coagulation, 266. Alkaloids, toxicity, 222. Alopecia, 198. Amanita muscaria, 128. Amboceptor, cf. Immune-bodies. Ammonia, destroying action, 42; haemolytic action, 101-103, I7It J72J saponification, 62-65. Amphoteric electrolytes, 161-163. Amygdalin, 59, 84. Ancistrodon, see Water-moccasin. Antialexin, 246-252, 261, 262. Anti-antitoxin, 245. Antibodies, formation and decomposi- tion, i, 3-7, 179, 257-259; in normal serum, 3, 9, 165, 185, 274-277. Antihaemolysin, 247, 262. Anti-immune-body, 246-252, 261, 262. Antimorphine, i. Anti-sensibilisator, 246. Antitoxins, 9; decomposition, 4-9, 46; standardisation, 14; cf. corresp. Toxins. Antivenin, 18, 209-214. Arachnolysin, 10, 214; ascites-fluid, 276; asparagin, 80. Assimilation, 137. Attenuation, influence of, 49, 88, loa- 104, 169, 170, 191, 229, 230. B Bacillus botulinus, 154. Bacillus coli, 86, 104, 151, 165, 166. Bacillus megatherium, 27. Bacillus pyocyaneus, 19, 86, 182. Bacillus tetani, 10, 24. Bacteriolysins, 9, 17, 21, 224. Barium salts, 265, 270. Bimolecular reactions, 38, 87, 93, 136. Blood-plasma, 269-271. Boletus scaber, 50. Boracic acid, 171, 175. Botulismus-poison, 154, 241. Brownian movement, 263. Calcium salts, influence of, 74, 185, 265, 268, 269, 270, 279, 282, 297; of casein, 266; of para-casein, 266, 279. Cane-sugar, inversion of, 38, 51-54, 57-58, 98. _ Carbonic acid, assimilation of, 137; respiration of, 136. Casein, 79, 81, 135, 262; coagulation, 72-76, 297; precipitation, 22, 281- 283. Castor beans, see Ricinus seeds. 305 306 INDEX OF MATTER Catalase, 50, 51. Catalysis, catalysator, 30, 57, 133, 223, 235, 296, 297. Chlorophyll, 137. Cholera- agglutinin, 3. Cholera-precipitin, 284. Cholera vibrions, 3, 144, 164, 165. Cholesterin, 9, 10, n, 23, 147, 155, 187, 189, 206, 214, 220, 242. Chymosin, 267, 274. Coagulation, 17, 71, 164-166. Cobra-lecithid, 10, 213, 214, 238-240. Cobra-poison, 10, 34, 117, 190, 210, 212, 242, 274. Coelenterates, 194. Coli- agglutinin, 86, 91, 115, 151. Colloide de boeuf, 260. Colloids, 28, 35, 151-153, 156, 163, 215, 216, 263; retarding influence, 159. Colorimetric methods, 15. , Complement, see Alexin. Crotalus-poison, 202, 209, 212. Crotin, 272, 273. Cyclamin, 274. Cynarase, 3. D Diastase, 51, 55. Dibrom-succinic acid, Diffusion of enzymes, toxins, and anti- toxins, 24-28, 33, 121, 132, 134, 142, i53» 227. Digestion, 61, 65-69, 77-86, 89, 119, 135- Digitalin, 274. Diphtheria-antitoxin, 5, 245. Diphtheria- poison, 11-14, 18, 26, 152, 177, 190, 196-202. Diversion of alexin, 224-228, 244. Dog's serum, 105. Eggs, influence of temperature on de- velopment of, 138. Egg-white, 3, 61, 69, 79, 160, 162. Ehrlich's phenomenon, 177-185, 187. Electric charges, 117, 156, 160, 163. Emulsin, 2, 48, 49, 55, 57, 59, 84. Enzymes, 2, 3, 48, 57-60, 142; com- pounds of, 57, 60-62. Epitoxin, 177, 197-200. Equilibria, 31, 118, 125, 126, 132-134, IS5i l(>9, 180-182, 184, 202, 205, 215, 217, 231-251, 288-293. Equivalency, in, 170, 171, 172, 188, 254, 288-293. Equivalent weights of albumose, 162; casein, 266; pepton, 162; egg-white, 162. Ethyl-butyrate, 51. Euglobulin, 279. Fats, saponification of, 51, 61, 119, 126- 134- Ferments, 2, 3 ; see also Enzymes. Fibrine, 270. Fibrin-ferment, 3, 91, 269, 271. Filtration, 26, 27, 164, 268. Fluorides, 269, 271. Formalin, 166, 283, 287. Formulae, use of, 7. Gelatine, 70, 77, 78, 81, 82, 86. Globuline, 273. Glucose, 53, 133, 139-142. Glycin, 80, 84. Goat's serum, 47, 220, 221, 228, 233, 243, 246, 247, 249, 250, 256, 261, 274, 291, 294, 296. Goose, extract of muscles, 92; plasma of, 92, 280; serum of, 2. Guinea-pig, normal, 12; serum of, 19, 224, 228, 233, 236, 237, 238, 244, 245, 246, 249, 250, 253, 256, 260, 261. H Haemolysis, haemolysins, 9, 15, 16, 47, 105, 117, 167, 189, 206-211, 274; compound, 218-262. Haptophor, 183. Heart-beats (influence of temperature), 139- Hen's serum, 256. Hirudin, 280. Horse-serum, 3, 9, 165, 189, 208, 222, 254, 255, 260, 274-278, 287; plasma, 92. Hydrochloric acid, 35, 43. Hydrogen peroxide, 50, 166. INDEX OF MATTER 307 Hydrolysis, 171, 174, 222, 283. Hypnotoxin, 195. Immune-bodies, 3, 19, 20, 48, 150, 219- 261. Immune-serum, 3, 219-261. Immunisation, 6, 219-261. Inactivation, 19. Incomplete reactions, 29, 30. Injection, i, 2, 7-8; of cells, 2. Intra-cardial, -muscular, -peritoneal, -venous injection, 7-8. Inversion of cane-sugar, 38, 51-54, 57, 58, 59- Invertin, 51-55, 58. "In vitro" and "in vivo" reactions, 14, 15, 16, 30, 205, 273, 274. Isocasein, 266. Lactase, 2, 55, 57, 58. Lactoserum, 22, 281-286. Lecithin, 9, 10, 210, 238-242. Leeches, 280. Lethal dose, 12, 13, 154, 198. Leucin, 80. Leucocytes, 269. Lipase, 65, 119. Lipolysis, see Fats. Lysins, 9. M Magnesium-salts, 265. Malt, extract of, 84. Maltase, 53-55, 59. Maltose, 53-55, 59, 133. Mass action, i, 28, 133, 175, 216, 245, 279. Mastic emulsion, 157-159. Mercuric chloride, 115, 166, 273. Mett's tubes, 121, 142. Migration in electric field, 160-162. Milk, 21 ; coagulation of, 71-76. Milk-sugar, 56, 57, 58. Molecular- weight of casein, 266; toxins and antitoxins, 25; haemoglobin, 26. Monomolecular reactions, 37, 52, 68, 87, 89, 101-106, 120, 130, 191. Morphin, i. Muscles, extract of, 92, 280. Mushroom, 2, 128. N Naja, see Cobra. Neutralisation, 29, 161-163, 167-181, 234-239. Neutralised poison, 14, 21-28, 30, 34, 152, 167-181, 192-217. w-molecular reaction, 38, 95. Oleate of sodium, 114, 142. Oleic acid, 113, 167. Olein, derivatives of, Olive oil, 10. Optimum, 70, 73, 117, 129, 137-139, ^S-iSS, 241, 285. Oxalates, 269-272, 282. Ox-serum, 208, 218, 222, 254, 260, 276, 287, 291, 295, 296. Pancreatic ferment, 3, 124. Pancreatic extract, 77, 80. Papayotin, 77. Para-casein, 268, 283. Paresis, 198, 199. Partial toxins, 177, 183. Passive immunisation, 6, 245. Pectase, 272. Pectin, 271. Pepsin, 2, 61, 71, 89, 119, 134, 163, 267. Pepton, 77, 80, 93, 162, 273. Permeability of membranes, 10, 221, 222, 241, 242, 243, 268. Physiological solution, 8, 15, 172, 254. Plague-bacilli, 164. Plasma, 91, 269-271. Plurality of poisons, 177, 183; of alexins and antialexins, 252. Poisons, calibration of, 11-17. Potassium hydrate, hsemolytic action, 170. Precipitins, 9, 14, 17, 92, 156, 166, 263- 299. Probable error, 14, 196, 215, 275. Protamin, 83. Protein, 84, 164, 189. Proteolytic ferment, 2, 22. 308 INDEX OF MATTER Prototoxoid, 197, 200-204. Pseudo-globulin, 279. Pseudo-solution, 263, 265, 267. Rabbit's serum, 206, 224, 228, 238, 244, 246, 247, 249, 253, 254, 255, 258, 273, 276, 291-296. Reaction, velocity of, 18, 32, 36-143, 155, 189, 242, 252, 284. Receptor, 257. Rennet, 2, 3, 71-76, 87, 88, 185, 190, 265-269, 270, 275, 283, 297. Respiration of plants, 136. Reversibility of reactions, 18-36. Ricin, 2, 15, 22, 23, 24, 115, 149, 190, 203, 272. Ricinus oil, 125-127. Ricinus seeds, 2, 98, 125-127. Robin, 2. Safranin, 166. Salicin, 48, 54, 84. Salts, action of , at agglutination, 9, 153, 156-159, 254; at haemolysis, 172, 188, 255; at coagulation, 265, 266, 279, 282. Saponification of ethyl-acetate, 62-65, 98; see also Fats. Saponin, i, 10, n, 23, 147, 169, 206- 208, 220, 241, 274. Schutz' rule, 62-68, 81, 85, 121-126. Sensibilitator, sensibilisation, 20, 223, 228, 242. Sero-bacilli, 157. Serum, inactivated, 19, 218, 247; nor- mal, 3, 9, 160, 165, 189, 208, 218, 221, 254, 270, 278, 284. Serum-albumen, 268, 283, 285. Serum-precipitin, 273, 287-299. Sheep's serum, 228, 237, 291, 292, 294, 296. Side-chain theory, 31, 177, 180, 182- 185, 257, 258. Snake-poisons, 18, 209-215. Sodium hydrate, hsemolytic action, 102; action on poisons, 41, 44, 88. Solanin, i, 170, 274. Solubility, 132. Specificity of agglutinins, 163; of anti- toxins, 3, 163, 281. Standard serum, 14. Staphylolysin, 10, 21, 107, 187, 189, 190. Starch, 55. Statistical methods, 13. Steapsin, 122-125. Stomachal extract, 122; juice, 77, 122, 123. Strengthening of binding, 192. Streptococcus, 165, 271. Streptolysin, 113, 186, 187. Strontium salts, 265, 270. Subcutaneous injection, 8. Sublimate, see Mercuric chloride. Sub-microscopic granules, 264. Sulphuric acid, 92. Swine-serum, 276. Synthesis, 133. Syntoxoid, 202. Taurocholate, 170. Temperature, influence, 10, 18, 21, 35, 40-42, 46-49. 53, 69, 71, 73, 76, 87, 89, 90, 91, 96-99, 107-117, 180, 268, 277, 283, 284. Terrapin, Pacific, 139. Tetanolysin, 3, 9, 18, 33, 41, 44, 45, 93, 102-104, 113, 149, 155, 178-182, 187, 189, 190, 245, 273. Tetanospasmin, 24, 152. Tetanus bacilli, 24. Thymolgelatine, 70, 77, 78, 86, 89. Time of reaction, 18, 31, 101, 118, 157, Toxicity, estimation of, 11-17, 175. Toxins, i. Toxoid, 182, 211. Toxon, 197-200, 211. Toxophor, 183. Transfusion, 218. Triacetin, 130, 131. Triolein, 114, 131, 132. Trypsin, 3, 61, 77, 78-81, 86, 89, 90, 91, 134, 135, 163. Typhoid agglutinin, 5, 115, 144, 151, 163. Typhoid bacilli, 144, 156, 163-166. Typhoid-precipitin, 284. Tyrosinase, 2. INDEX OF MATTER 309 Urea, 283, 287. Urease, 3. Vesuvin, 166. Vibrio cholerae, see Cholera vibrions. Vibrio Metschnikovi, 165. Vibriolysin, 39, 40, 41-43, 113, 187. Vital processes, 136. W Water-moccasin, 117, 211, 213. Whey, 75. Yeast, 139-141. Yolk, 123. Zymase, 3, 141. The Common Bacterial Infections of the Digestive Tract AND THE INTOXICATIONS ARISING FROM THEM By C. A. HERTER, M.D., Professor of Pharmacology and Therapeutics in Columbia University; Consulting Physician to the City Hospital, New York. Cloth, 8vo, j<5o pages, $1.50 net; by mail, $1.63 " The methods of investigating the digestive tract outlined in this volume will prove valuable to the practitioner who would determine the presence of abnormal bacterial processes before the onset of the clinical signs of incurable or highly refractory states of intoxication — and this is the all-sufficient raison I2mo, $7.50 net " The authors have rendered a distinct service to students of physiological chemistry in preparing this volume, which covers all the essentials of organic chemistry in very simple, easily understood language. The text is, moreover, elucidated by means of a profusion of graphic formulas. It is manifestly im- possible to be exhaustive in a book of 200 pages or so; nevertheless, it is astonishing to note the immense range covered. A chapter devoted to disease and immunity is of particular interest, as it presents the latest phases of Ehrlich's theory of antitoxins, and treats of ptomaines, toxins, leucomains, agglutins, precipitins, etc." — Merck's Archives. Inflammation: AN INTRODUCTION TO THE STUDY OF PATHOLOGY By J. GEORGE ADAMI, M.D. A revised and enlarged reprint of an article in Allbutfs " System of Medicine " by Dr. Adami, who is a Professor of Pathology in McGill University, Montreal. Cloth, gilt top, 8vo, xvi +24.0 pp.; index, illus.; $1.60 The author believes that a knowledge of the inflammatory process is the foundation of all pathology, and has here brought together all the data known to him bearing upon the subject, including some very recent, such as a descrip- tion of Sir A. E. Wright's brilliant researches upon opsonins, and Professor Bier's treatment of inflammation by induced hyperaemia. Studies in the Bacteriology and Etiology of the Oriental Plague By E. KLEIN, M.D,, F.S.S. ; Lecturer on Advanced Bacteriology in Medical School of St. Bartholomew's Hospital, London. With 89 Photograms. Cloth, 8vo, ocv + 301 pp.; $4.00 net THE MACMILLAN COMPANY 64-66 FIFTH AVENTJE, NEW YORK By HARRY C. JONES Professor of Physical Chemistry, Johns Hopkins University The Elements of Physical Chemistry New edition, enlarged and thoroughly revised, 8vo, $4.00 net The wide-reaching significance of the subject would account for its almost unprecedented growth in the last quarter of a century. It has already ex- tended into nearly every field of chemical science until no chemist to-day, scientific or technical, can omit the study of it without missing an essential part of his training. The Theory of Electrolytic Dissociation AND SOME OF ITS APPLICATIONS Cloth, i2tno, $1.60 net " I have tried several of the German works, small and large, and I have no hesitation in saying that Professor Jones's presentation is the simplest, clearest, and most adequate in any language." — Professor S. F. BARKER, Johns Hopkins University. " It is a text-book which will supply a long-felt want to teachers who have to do with students unfamiliar with the German language. . . . The examples chosen are apt, well described, and clearly explained. With this book and Professor Walker's Introduction to Physical Chemistry our students have now a remarkably good presentation of the subject in English." — Professor J. W. WALKER, Me Gill University. THE MACMILLAN COMPANY 64-66 FIFTH AVENUE, NEW YORK A History of Chemistry From the Earliest Times To the Present Day BEING ALSO AN INTRODUCTION TO THE STUDY OF THE SCIENCE By ERNEST VON MEYER, Ph.D., Professor of Chemistry in the Technical High School, Dresden Translated wiih the author's sanction by GEORGE McGOWAN, Ph.D. Third English Edition translated from the Third German Edition, with various additions and alterations xocvii + 6gi pages, $4.25 net " To physicians this work recommends itself strongly for various reasons : First of all is the great value of genuine historical study for the understanding of general chemistry, the increasing and fundamental importance of which to medicine is evident to all. And then the historical relations between medi- cine and chemistry seem to make the history of chemistry attractive on medico-historical grounds as well. Many of the brightest pages in the history of chemistry are written by physicians : Paracelsus, Van Helmont, Stahl, Black, Berzelius, — 'the brilliant model for ages to come,' — and others. Finally von Meyer's work recommends itself because of its style and form. Taking it all in all, it is a book of rare educational value." — American Medical Association. " It is decidedly the most useful history of chemistry." — The Nation. THE MACMILLAN COMPANY 64-66 FIFTH AVENUE, NEW YORK !