A fractal analysis of the influence of non-specific binding on antigen-antibody binding kinetics for biosensor...

A fractal analysis of the influence of non-specific binding on the specific binding of antigen in solution to antibody immobilized on a biosensor surface is presented for first-, one and a half-, second, and other-order reactions occurring under external diffusion-limited conditions. Both single-step and dual-step binding of antigen in solution to antibody immobilized on the surface is considered. For a first-order reaction, an increase in the fractal parameters, b, leads to a decrease in the amount of antigen in solution bound specifically to the antibody on the surface when non-specific binding is either absent or present. The presence of non-specific binding leads to a decrease in the amount of antigen bound to the antibody on the surface. For a one and a half- and for second-order reactions and when non-specific binding is either absent or present to a small degree (alpha = 0.01), an increase in the fractal parameter, b, leads to a decrease in the amount of antigen bound specifically to the antibody immobilized on the biosensor surface. However, for an alpha value of 0.1, the maximum rate and the amount of antigen bound specifically to the antibody immobilized on the biosensor surface is obtained for fractal parameter values of 0.2 and 0.4, and 0.4 for the one and a half- and for second-order reactions, respectively. Apparently, some amount of heterogeneity is helpful in obtaining the optimum amount and rate of antigen in solution bound specifically to the antibody on the surface for reaction orders higher than one. The applicability of the approach to real antibody surfaces is demonstrated.