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The antigen-antibody reaction. IV. A quantitative theory of antigen-antibody reactions

1963; Elsevier BV; Volume: 5; Issue: 2 Linguagem: Inglês

10.1016/0022-5193(63)90060-2

1095-8541

Michael T. Palmiter, Frederick Aladjem,

Analytical Chemistry and Chromatography

A theory is developed which describes the distribution of antigen-antibody complexes resulting from the reactions between bivalent antibody and f-valent antigen. It is assumed, as in Goldberg's theory (1952), that antigen and antibody are immunochemically homogeneous and that no intra-aggregate reactions occur which yield cyclical complexes. Unlike Goldberg's theory, in which all antigen-antibody bonds are assumed to be equivalent, the present treatment allows independent rate or equilibrium constants for the reactions between each of the f-antigen sites with each of the two antibody sites, i.e. it is developed in terms of 2f equilibrium constants or 4f rate constants. In outline, the procedure involves the calculation of the number of antibody molecules and antigen molecules with any particular number of reacted sites, and the determination of the most probable distribution of complexes by means of a mathematical procedure similar to that used by Stockmayer (1943). As a special case, if the existence of one intrinsic equilibrium constant is assumed, Goldberg's expression for the most probable distribution of complexes is obtained from the expressions derived here. Subject to the stated assumptions, the theory provides a numerical procedure for the computation of equilibrium and rate constants of antigen-antibody reactions, and should be useful for the calculation of the behaviour of model systems.