Chapter 7 - Fractal Dimension and the Dissociation Rate Coefficient

Abstract

A confirmable fractal analysis only of the binding of antigen (or antibody) in solution to antibody (or antigen) immobilized on the biosensor surface provides a quantitative indication of the state of disorder (fractal dimension bind) and the binding-rate coefficient on the surface. Including the fractal dimensions for the dissociation step and dissociation-rate coefficients provides a more complete picture of the analyte–receptor reactions occurring on the surface. One may also use the numerical values for the rate coefficients for the binding and dissociation steps to classify the analyte–receptor biosensor system. The fractal dimension value provides a quantitative measure of the degree of heterogeneity that exists on the surface for the analyte–receptor systems. The degree of heterogeneity for the binding and dissociation phases is different for the same reaction. This indicates that the same surface exhibits two degrees of heterogeneity: one for the binding and one for the dissociation reaction. In this chapter examples are provided where either a single- or a dual-fractal analysis was required to describe the binding kinetics. The dual-fractal analysis was used only when the single-fractal analysis did not provide an adequate fit. This was determined using the regression analysis provided by Sigma plot. The dissociation step was adequately described by a single-fractal analysis for all the examples presented in the chapter.