Experimental study and mathematical modeling of the interaction between antibodies and antigens on the surface of liposomes.

Unilamellar liposomes with incorporated hapten-phospholipid conjugates were proposed as models of polyvalent antigens with migrating determinants for quantitative analysis of their interaction with antibodies. The monovalent pesticide atrazine was used as a model antigen. For its incorporation into the lipid bilayer, the atrazine carboxylated derivative was conjugated with dimyristoylphosphatidylethanolamine (DMPE). Unilamellar liposomes were prepared with dimyristoylphosphatidylcholine/atrazine-DMPE at molar ratios of 90:10, 95:5, 98:2, 99:1 and 99.5:0.5. Their interaction with the peroxidase-labeled anti-atrazine antibodies was studied by enzyme immunoassay and polarization fluoroimmunoassay techniques. It was shown that the increase in hapten content in the liposomes from 0.5 to 10 mol% led to an increase in the equilibrium constants of the interaction with antibodies from 0.093 x 10(8) to 0.303 x 10(8)M-1. The association rate constants varied from 1.45 x 10(5) to 15.5 x 10(5)M-1 s-1 depending on the antigen content in liposomes and experimental conditions. The measured constants were applied for a mathematical model describing multi-step interaction between antibodies and polyvalent liposomal antigens. The model adequately describes the quantitative regularities of the influence of antigen content and the affinity of immunochemical interaction on the quantity and the dynamics of the immune complexes forming.