Comparative analysis of models describing interactions between antibodies and liposomal antigens

Mathematical models of three levels of complexity are proposed that describe the interactions between antibodies and polyvalent liposomal antigens. The models take into account the contribution of high-affinity bivalent complexes and clusters of several antigenic groups to the immunochemical reaction. The models were analyzed numerically at different values of thermodynamic and kinetic parameters of the antigen-antibody reaction. The conditions under which models of different levels of complexity provide a satisfactory description of the antigen-antibody interaction were determined. The adequacy of the results of modeling was confirmed experimentally in liposomal preparations differing from each other by the surface density of a monovalent hapten (atrazine) conjugated with a lipid.