An analysis of analyte-receptor binding kinetics for biosensor applications: influence of the fractal dimension on the binding rate coefficient

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.

Continuous flow displacement immunosensors: a computational study

Numerical modeling has been used to investigate the disparity in performance and sensitivity that has been reported for flow displacement immunosensors based on bead-packed columns, membranes, and capillary tubes. The simulations strongly suggest that the high surface areas in the porous media systems may actually be detrimental to sensor performance because of large numbers of free antibody binding sites. Since the free antibody sites are created during the wash step in which the baseline is established, wash protocols are critical in optimizing the sensitivity for a given displacement sensor.

A single- and a dual-fractal analysis of antigen-antibody binding kinetics for different biosensor applications

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modelled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot, 1993 (Scientific Graphing Software: User's Manual. Jandel Scientific, San Rafael, CA) was utilized to determine if a single-fractal analysis is sufficient, or a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the antigen-antibody systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the antigen-antibody binding systems indicate a high sensitivity of the binding rate coefficient on the fractal dimension when both a single -as well as a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-1(15-21) x BSA (bovine serum albumin) immobilised on a surface plasmon resonance surface, the order of dependence of the binding rate coefficient, k on the fractal dimension, Df is 7.0945. Similarly, for a dual-fractal analysis and for the binding of parasite L. donovani diluted pooled sera in solution to fluorescein isothiocyanate-labeled anti-human immunoglobulin IgG immobilized on an optical fibre, the order of dependence of k1 and k2 on Df1 and Df2 were 6.8018 and -4.393, respectively. Binding rate coefficient expressions are also developed as a function of the analyte (antigen or antibody) concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface, and emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.