PROPERTIES OF IMMUNE COMPLEX-FORMING SYSTEMS - NEW THEORETICAL APPROACH

  • 1 January 1977
    • journal article
    • research article
    • Vol. 32  (4) , 445-456
Abstract
A new mathematical model for antigen-antibody interactions was developed. The new model is based on the assumption that the formation of complexes between a bivalent antibody and a multivalent antigen is determined thermodynamically by the concentrations and valences of antigen as well as antibody, together with 1 association constant which is common to all mutual interactions. Formulae were derived for calculation of the distributions of compositionally different antigen-antibody complexes from knowledge of equilibrium concentrations of free antigen and antibody, or from knowledge of total amounts of antigen and antibody in the system. A computer program for these calculations is described. The model yields precise predictions of the formation of soluble immune complexes, as studied by zonal centrifugation. Complex formation as such differs in binding characteristics from adsorption, especially for high concentrations of antigens and antibodies. Complex formation implies that association constants estimated through a Sips plot method will vary with antibody concentration, and that certain curvatures of the lines in a Sips plot reflect inherent properties of complex-forming systems.