A fractal analysis of external diffusion limited first-order kinetics for the binding of antigen by immobilized...

A fractal analysis of external diffusion limited first-order kinetics for the binding of antigen in solution by immobilized antibody on a fibre-optic biosensor indicates that as the fractal parameter (measure of "disorder" on the surface) increases the rate of binding and the amount of antigen bound to the antibody on the surface decreases. The fractal analysis and exponential type binding rate coefficients are used to analyze the influence of time-dependent binding rate coefficients on external diffusion limited kinetics. A decrease in the binding rate coefficients with time decreases the Damkohler number (decrease in the mass transfer limitations) leading to an increase in the rate of binding and the amount of antigen bound to the antibody on the surface, as expected. An increase in the (exponential) binding rate coefficient with time leads to unusual shapes of the binding curves. The time-dependent binding rate coefficients provide a more realistic picture of the binding of antigen in solution to the antibody covalently attached to the surface, and should assist in the control and manipulation of these interactions at the surface. A value of the fractal dimension of the surface of 2.96 to 2.97 obtained for our system characterizes the anomalies in the reaction-diffusion system and the heterogeneity of the surface.