scholarly journals Quantitative aspects of antigen-antibody reactions. II. Some comparisons between the theory and the experimental results

1946 ◽  
Vol 44 (4) ◽  
pp. 237-242 ◽  
Author(s):  
Torsten Teorell

The quantitative theory for the interaction between antigen and antibody presented in the previous paper has been compared with some experimental precipitin reactions published in the literature. These reactions include Type VIII pneumococcus polysaccharide-homologous (horse) antibody, egg albumin-(rabbit) anti-egg albumin and diphtheria toxin-(horse) antitoxin.1. The general course of the experimental precipitation curves (total amount of precipitate, amounts of precipitated antigen and antibody) corresponded well to the theoretical type curves. Hence it may be concluded that the precipitates may be composed of mixtures of compounds of the types AG, A2G, A3G, …, ANG in accordance with the law of mass action. In the cases with ‘inhibition zones’, however, AG, or ANG, or both (and perhaps several more compounds) retain the same solubility as the free antigen (G) and free antibody (A).2. With regard to the location of the ‘equivalence zones’, experiment and theory also showed a satisfactory agreement.3. A hypothesis on the velocity of flocculation in the precipitin reaction is presented and compared with some recent results. The relation between the immunological concepts ‘equivalence (neutral) point’, ‘optimum point’ and ‘maximum precipitation point’ is also discussed.

1946 ◽  
Vol 44 (4) ◽  
pp. 227-236 ◽  
Author(s):  
Torsten Teorell

1. A quantitative theory has been developed for the reactions between antigens and antibodies, applicable in particular to the precipitin reaction. The theory is equally applicable to unspecific precipitations, for instance the reaction between proteins and protein precipitating agents such as nucleic acids, etc.2. The theory is based on the concept that the antigen-antibody interaction is governed by the same principles as the dissociation of a polybasic acid, HNT, where the antibody corresponds to the hydrogen ion H, and the antigen to the anion T. In their mutual reactions the antigen G is supposed to be polyvalent and the antibody A monovalent: hence the result of the interaction is a mixture of compounds ANG, AN-1G, …, AG.3. A mathematical deduction is performed starting from the law of mass action, which leads to expressions for the amounts of total precipitate and its constituents in terms of the quantities of antigen and antibody which were mixed and the known equilibria constants.4. A numerical example is given for a tetravalent antigen. Three cases are represented in graphical forms: the ‘X case’ without inhibition zones, the ‘Y case’ with one and the ‘Z case’ with two inhibition zones. Certain characteristics are described and the significance of the ‘equivalence point’ is analysed.5. A discussion deals with the irreversibility in relation to the Danysz phenomenon and the dilution effect, and finally the parameters of the theory are more closely considered.


1937 ◽  
Vol 66 (2) ◽  
pp. 229-250 ◽  
Author(s):  
Elvin A. Kabat ◽  
Michael Heidelberger

1. The reaction between crystalline horse serum albumin and homologous antibody in rabbit sera is quantitatively accounted for by expressions similar to those derived from the law of mass action for other immune precipitating systems. 2. The reaction of an azo dye prepared from crystalline serum albumin by coupling with diazotized R-salt-azo benzidine was also studied with homologous antibody and anti-serum albumin. 3. Quantitative data obtained on cross reactions with the two antigens differ markedly from data on the corresponding reactions in the egg albumin system and indicate that tyrosine and perhaps histidine, while important in determining the serological specificity of egg albumin, have little connection with the specificity of serum albumin. 4. Calculations are made of the equivalent composition of the specific precipitate at various reference points in the reaction range.


1937 ◽  
Vol 66 (2) ◽  
pp. 251-272 ◽  
Author(s):  
Herbert E. Stokinger ◽  
Michael Heidelberger

1. Quantitative data for both homologous and heterologous precipitin reactions of human, hog, beef, and sheep thyroglobulins show that these reactions have the same mechanism as other instances of the precipitin reaction and may be expressed quantitatively by the same equations derived from the law of mass action. 2. It is shown that all of the added antigen is precipitated in the region of antibody excess and in the equivalence zone, so that in these portions of the reaction range the composition of the specific precipitate may be calculated from the nitrogen precipitated and the amount of antigen nitrogen added. 3. The thyroglobulin-antibody reaction is characterized by low antibody N to antigen N ratios, as would be expected with an antigen of high molecular weight. Molecular ratios varying from 60:1 to 1:1 were calculated for the extremes of the reaction range, indicating a very large number of immunologically reactive groupings on the thyroglobulin molecule. 4. Failure of thyroxine or diiodotyrosine to inhibit specific precipitation was confirmed, but it is shown that this need not mean that these substances do not occur in thyroglobulin, as has been claimed.


1969 ◽  
Vol 114 (1) ◽  
pp. 141-144 ◽  
Author(s):  
Krister Hellsing

The precipitin reaction is enhanced in the presence of polysaccharides (Hellsing, 1966). This reaction has now been studied in detail with labelled antigen (125I-labelled human serum albumin) and antibody (131I-labelled rabbit anti-albumin immunoglobulin G). The relative proportions of antigen and antibody in the precipitates are unchanged by the addition of dextran in spite of the increased precipitation. The ratio of antibody to antigen in the soluble immune complexes decreases with increasing polysaccharide concentration. This can be interpreted as a decrease in the aggregate size of the complexes. At the same time the amount of free antigen in the solution increases. The results are consistent with a decrease in solubility, primarily of the large immune aggregates, together with a shift in the equilibrium between small and large complexes. The effect is in accord with a steric-exclusion phenomenon.


1917 ◽  
Vol 25 (6) ◽  
pp. 837-853 ◽  
Author(s):  
Stanhope Bayne-Jones

1. In these studies several phases of the predpitm reactions were investigated by the use of purified proteins as antigens. These preparations were edestin from hemp-seed and crystalline ovalbumin from fresh eggs. The ovalbumin, isolated by the method of Hopkins and Pinkus,.was apparently as pure as is obtainable by chemical means. This albumin, however, produced moderately severe anaphylactic reactions in animals sensitized with ovoglobulin. Anaphylactic tests of the individuality of a protein cannot be any longer regarded as the criterion of the purity of the substance as an antigen. Wells and Osborne have shown that proteins of considerable chemical difference may have a common antigenic group which causes mutual anaphylactic reactions in animals sensitized to these proteins. In particular, as egg globulin is a mixture of proteins, one of which is undoubtedly egg albumin, anaphylaxis produced by injections of albumin into animals sensitized to the so called globulin offers no evidence for or against the purity of the albumin. The character of the curves shown in Text-fig. 1 confirms the assumption, based upon chemical data, that crystalline egg albumin is a single protein. 2. With edestin and crystalline egg albumin as antigens phases in the precipitin reaction were found in which these substances and their specific precipitins could be demonstrated to be coexistent but ununited in the same serum. 3. When edestin or crystalline egg albumin is injected into a rabbit immunized thereto, the antigen may be found in the circulating blood during 48 hours after its injection, while at the same time the animal maintains a high titer of free precipitin in its blood. 4. When the pure protein antigen is mixed in proper proportions with the serum of a specifically immunized rabbit and the resulting precipitate removed by centrifugation, the supernatant fluid contains both antigen and antibody. 5. The serum drawn from a rabbit during the period in which free antigen and antibody are coexistent in the circulation undergoes slow spontaneous precipitation when kept in sterile tubes in the ice box. The curve of this reaction is reproduced as Text-fig. 1. The relationships of the parabola indicate that the interaction of antigen and antibody takes place according to a definite law. When sufficient quantitative data are obtained to allow an analysis of this curve, the formulas for this reaction will undoubtedly throw light upon the chemical or physical nature of the process. 6. The protective action of the solution of egg albumin as a third colloid preventing precipitation in a reaction between human serum and its antibody was readily demonstrated. This observation and the constancy of the long prozone in precipitin test with egg albumin are in accord with the protective action of ovalbumin upon colloidal gold.


1953 ◽  
Vol 98 (5) ◽  
pp. 451-460 ◽  
Author(s):  
L. A. Sternberger ◽  
Frank Maltaner ◽  
Jacob DeWeerdt

Immune sera were subjected to treatment with alkali in the cold to cause dissociation of antigen-antibody complexes. Precipitates and a capacity to fix complement developed in some of these sera subsequent to such treatment. The specific immunologic nature of these phenomena and their observation in relation to disappearance of free antigen and appearance of free antibody in circulation are discussed. The phenomena observed appear to be consistent with the assumption that a circulating antibody-antigen complex is revealed as a result of treatment.


1958 ◽  
Vol 108 (1) ◽  
pp. 139-157 ◽  
Author(s):  
Charles L. Christian

The material in gamma globulin ("reactant") which reacts with rheumatoid sera in the F II precipitin and F II tanned sheep cell agglutination tests was concentrated by precipitation with sodium sulfate. The concentrated "reactant" appeared to consist of polydispersed molecular aggregates of gamma globulin with s20 constants as high as 40, as well as the previously described inhomogeneous aggregated material. Aggregated gamma globulin precipitated readily with most rheumatoid sera regardless of the reaction volume, and in low concentration inhibited the F II tanned sheep cell agglutination reaction and sensitized tanned erythrocytes to the agglutinating action of a positive rheumatoid serum. On the other hand, non-aggregated gamma globulin (7S) did not precipitate with rheumatoid sera and in low concentration did not inhibit the F II tanned sheep cell agglutination reaction, or sensitize tanned erythrocytes. Non-aggregated gamma globulin in large excess inhibited the precipitin reaction of aggregated gamma globulin with "rheumatoid factor," and accounted for the characteristic shape of the whole F II precipitin curves and the volume effect described by Vaughan (relation of increased precipitate yield relative to the reaction volume in whole F II precipitin studies). In serological systems other than the F II tanned sheep cell and F II precipitin reactions, the sensitization involves an antigen-antibody combination; i.e., sheep erythrocyte plus hemolysin in the sensitized sheep cell test, and egg albumin plus anti egg albumin in the absorption experiments with specific precipitates. The aggregation of gamma globulin that was essential for sensitization in the F II tanned sheep cell and F II precipitin tests may have simulated the aggregation of antibody gamma globulin that occurs with antigen-antibody union. The present information has been incorporated into a schematic hypothesis for the basis of the rheumatoid serological reactions.


1937 ◽  
Vol 65 (6) ◽  
pp. 885-902 ◽  
Author(s):  
Michael Heidelberger ◽  
Elvin A. Kabat

1. By the application of an absolute, quantitative microchemical method for the estimation of agglutinins, precise data have been obtained on the course of the agglutination of Type I pneumococcus by homologous anticarbohydrate. 2. Within the limitations imposed by the necessity for the agglutination reaction to take place at the bacterial surface, the reaction is shown to be analogous to the precipitin reaction and subject to the same laws. 3. The entire process of a typical instance of specific bacterial agglutination has been quantitatively accounted for on a purely chemical basis and expressed in the form of equations derived from the law of mass action. 4. Experimental verification of predictions based on the theory has shown a fundamental difference between this instance of specific bacterial agglutination and the commonly adduced analogies, and necessitated a revision of current conceptions regarding the rôle of electrolytes and of physical forces in the reaction.


1940 ◽  
Vol 71 (2) ◽  
pp. 247-262 ◽  
Author(s):  
A. M. Pappenheimer ◽  
H. P. Lundgren ◽  
J. W. Williams

Purified diphtheria antitoxic horse pseudoglobulin has been prepared which is homogeneous by sedimentation, diffusion, and electrophoresis. Immunologically, however, the preparation contains only 43.5 per cent antitoxin specifically precipitable by toxin. The inactive pseudoglobulin remaining after specific precipitation was found to have the same physical and chemical properties as the original antitoxic pseudoglobulin. Although the molecular weight of antitoxin is the same as that of the normal horse serum globulins, the electrophoretic mobility does differ from those normally present. The molecular weight of diphtheria toxin is 70,000 and of antitoxin is 150,000. From ultracentrifuge studies on the two reactants and on mixtures of toxin and antitoxin in the soluble inhibition zones, the average molecular composition of the specific floccules at certain reference points throughout the equivalence zone and the maximum "valence" of toxin and antitoxin with respect to each other have been calculated. The significance of the results has been discussed in relation to antigen-antibody reactions in general and a possible explanation for the exceptional behavior of the toxin-antitoxin reaction in the region of excess antitoxin has been suggested.


Author(s):  
Frederic Alberti

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.


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