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Theory of antigen-antibody induced particulate aggregation—II theoretical analysis and comparison with experimental results

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Abstract

The roles of the concentrations of the three interacting constituents in the aggregation process (antibodies, antigens and particulates) are analyzed in detail. It is shown that the basic equation derived in Part I is consistent over a broad range of conditions with experimental findings previously reported.

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Literature

  • Barrett, J. T. 1974.Textbook of Immunology, pp. 30–47. C. V. Mosby.

  • Capra, J. D. and A. E. Edmundson. 1977. “The Antibody Binding Site”.Sci. Am.,236 50–59.

    Article  Google Scholar 

  • Collins, F. C. and G. E. Kimball. 1949. “Diffusion-Controlled Reaction Rates”.J. Colloid Sci.,4, 425–437.

    Article  Google Scholar 

  • Dybkjaer, E. 1966. “A New Technique for the Quantitation of Haemagglutination”.Vox Sang.,11, 21–32.

    Google Scholar 

  • Economidou, J., N. C. Hughes-Jones, and B. Gardner. 1967. “The Functional Activities of IgG and IgM Anti-A and Anti-B”.Immunology,13, 501–508.

    Google Scholar 

  • —— and —. 1967a. “Quantitative Measurements Concerning A and B Antigen Sites”,Vox Sang. 12, 231–238.

    Google Scholar 

  • Frommel, D., P. J. Grob, S. P. Masoriredis and H. C. Isliker. 1967. “Studies on the Mechanism of Immunoglobulin Binding to Red Cells”.Immunology,13, 501–508.

    Google Scholar 

  • Goldberg, R. J., 1952. “A Theory of Antibody-Antigen Reactions I.”.Am. Chem. Soc.,74, 5715–5725.

    Article  Google Scholar 

  • Greenburg, C. L., D. H. Moore and A. C. Nunn. 1963. “Reaction of Rabbit Antisera with Human Red Cells”.Immunology,6, 421–433.

    Google Scholar 

  • — and — 1964. “Combination with Red Cells of Immune Rabbit 7S Antibody and its Sub-units”.Nature,203, 1147–1148.

    Article  Google Scholar 

  • —— and —. 1965. “The Reaction with Red Cells of 7S Rabbit Antibody, its Sub-units and their Recombinants”.Immunology,8, 420–431.

    Google Scholar 

  • Greenwalt, T. J. and E. A. Steane. 1970. “Quantitative Haemagglutination. II”.Br. J. Haematol.,19, 691–700.

    Google Scholar 

  • Greendyke, R. M. and S. N. Swisher. 1968. “Quantitative Studies of Hemagglutination”.Vox Sang.,15, 321–337.

    Google Scholar 

  • Hoyer, L. W. and N. C. Trabalt. 1970. “The Significance of Erythrocyte Antigen Site Density”.J. Clin. Invest.,49, 87–95.

    Article  Google Scholar 

  • Hughes-Jones, N. C. 1963. “Nature of the Reaction Between Antigen and Antibody”.Br. Med. Bull.,19, 171–177.

    Google Scholar 

  • Leikola, J. and V. Pasanen. 1970. “The Influence of Antigen Receptor Density on Agglutination of Red Blood Cells”.J. Int. Arch. Allergy,39, 352–359.

    Google Scholar 

  • Ming, T. K., H. S. Goodman and B. Brown. 1965. “Mathematical Model for the Process of Aggregation in Immune Agglutination”.Nature,208, 84–85.

    Article  Google Scholar 

  • Nezlin, R. S., Y. A. Zagyansky and L. A. Tumerman. 1970. “Strong Evidence for the Freedom of Rotation of Immunoglobulin G Sub-units”.J. Molec. Biol.,50, 569–572.

    Article  Google Scholar 

  • —— and —. 1972. “The Flexibility of Antibody Molecule”.Haematologia,6, 313–316.

    Google Scholar 

  • Pollack, W., 1965. “Some Physiochemical Aspects of Hemagglutination”.Ann. N.Y. Acad. Sci.,127, 892–900.

    Google Scholar 

  • —, H. J. Hager, R. Reckel, D. A. Toren and H. O. Singher. 1965. “A Study of the Forces Involved in the Second Stage of Hemagglutination”.Transf,5, 158–183.

    Article  Google Scholar 

  • Reif, F. 1965.Fundamentals of Statistical and Thermal Physics. pp. 269–273. New York: McGraw-Hill.

    Google Scholar 

  • Romano, E. L. and P. L. Mollison, 1973. “Mechanism of Red Cell Agglutination by IgG Antibodies”.Vox Sang.,25, 28–31.

    Google Scholar 

  • Schulthess, G. K., R. J. Cohen, N. Sakato and G. B. Benedek. 1976. “Laser Light Scattering Spectroscopic Immunoassay for Mouse IgA”.Immunochemistry,13, 955–962.

    Article  Google Scholar 

  • Schurr, J. M. 1970. “The Role of Diffusion in Bimolecular Solution Kinetics”.Biophys. J.,10, 700–716.

    Article  Google Scholar 

  • Singer, J. M., F. C. A. Vekemans, J. W. Th. Lichtenbelt, F. Th. Hesselink and P. H. Wiersema. 1973. “Kinetics of Floculation of Latex Particles by Human Gamma Globulin”.J. Colloid Int. Sci.,45, 608–614.

    Article  Google Scholar 

  • Smoluchowski, V. M.. 1916. “Drei Vortage uber Diffusion Brownshe Bewegang und Koagulation von Kolloidteilchen”.Physik Z.,17, 557–571, 585–599.

    Google Scholar 

  • — 1917. “Versuch einer mathematischen Theorie der Koagulations-Kinetik Kolloider Losungen”.Z. Physik Chem.,92, 129–168.

    Google Scholar 

  • Solomon, J. M., M. B. Gibbs and A. J. Bowdler. 1965. “Methods in Quantitative Hemagglutination, I and II”.Vox Sang.,10, 54–72, 133–148.

    Article  Google Scholar 

  • Somers, W. R., R. A. Brown and T. Makinodan. 1966. “The Possibility of Determining the Absolute number of Hemagglutinating Antibody Molecules in Antisera”.Immuno. Chem.,3, 343–345.

    Article  Google Scholar 

  • Sugerman, D., and H. E. Hart. 1973. “Thermal Dissociation of Antigen-Antibody Antigen Like Systems”.Bull. Math. Biol.,35, 219–235.

    Article  Google Scholar 

  • Wilkie, M. H. and E. L. Becker. 1955. “Quantitative Studies in Hemagglutination I and II”.J. Immunol.,74, 192–204.

    Google Scholar 

  • Yguerabide, J., H. F. Epstein and L. Stryer. 1970. “Segmental Flexibility in an Antibody Molecule”.J. Molec. Biol.,51, 573–590.

    Article  Google Scholar 

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Chak, KC., Hart, H. Theory of antigen-antibody induced particulate aggregation—II theoretical analysis and comparison with experimental results. Bltn Mathcal Biology 42, 37–56 (1980). https://doi.org/10.1007/BF02462365

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