Antigen-antibody binding kinetics for biosensors: the fractal dimension and the binding rate coefficient.

The diffusion-limited binding kinetics of antigen (or antibody or substrate) in solution to antibody (or antigen or enzyme) immobilized on a biosensor surface is analyzed within a fractal framework. The change in the fractal dimension, Df, is in the same direction as that in the forward binding rate coefficient, k1. An increase or decrease in the fractal dimension, Df leads to an increase or decrease in the forward binding rate coefficient, k1, respectively, irrespective of whether the antigen or the antibody is immobilized on the biosensor surface. For example, an increase in the concentration of IgG (MRC OX-19) (antigen) in solution from 1 to 10 micrograms/mL bound to polyclonal sheep anti-mouse IgG (antibody) immobilized on immunomagnetic beads leads to decreases in Df from 1.93 to 0.517 and in k1 from 2.72 to 0.064, respectively. The different examples analyzed and presented together indicate one means by which the forward binding rate coefficient, k1, may be controlled, that is, by changing the fractal dimension or the disorder on the surface. The versatility of the analysis is indicated by applying it to different examples for both types of systems, wherein either the antigen or antibody is immobilized on the surface. The analysis should assist in improving the stability, sensitivity, and response time of biosensors.