Fractal analysis of antigen-antibody binding kinetics: 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 estimated fractal dimension increases linearly from 2.28 to 2.75 for the antirabbit IgG (antibody) (Nygren, H.; Stenberg, M. J. Colloid Interface Sci. 1985, 107, 560-566) as the R1S1 antibody concentration in solution increases 28-fold from 6 to 170 micrograms/mL. Similarly, for the binding of ferritin (antigen) in solution by a "sandwich" immunoassay to antiferritin (antibody) immobilized on a surface (Bluestein, B. I.; Craig, M.; Slovacek, R., Stundter, L.; Urciuoli, C.; Walizak, I.; Luderer, A. In Biosensors with Fiberoptics; Wise, D., Wingard, L. B., Jr., Eds.; The Humana Press, Inc.: Clifton, NJ, 1991; pp 181-223), the estimated fractal dimension decreases from 1.33 to 1.02 as the initial concentration of ferritin increases from 20 to 1000 micrograms/mL. The analysis attempts to provide novel physical insights into the reactions occurring on the surface and the structure or nature of the surface. Diffusional limitations inherent in such systems need to be uncoupled from reaction kinetics and complexities, such as heterogeneity, that exist on the surface.