Mathematical Model for the Process of Aggregation in Immune Agglutination

Abstract

IMMUNE haemagglutination is the combination of bivalent antibody molecules with specific antigenic determinants on the surface of red cells and the coincident collision of red cells resulting in the formation of antibody cross-linkages between cells and visible aggregation^1,2. As a means of characterizing immune haemagglutination, rates of red cell aggregation were examined with the aid of a Coulter electronic cell counter³. In the course of this examination it was empirically found that the initial decrease in free cell concentration followed an exponential decay curve. There was no basis, however, for considering aggregation to be a first-order reaction. Subsequent consideration suggested that aggregation involved an orderly sequence which might be expressed mathematically.