6 - Fractal Analysis of Binding and Dissociation of Autoimmune Disease Markers on Biosensor Surfaces

Abstract

This chapter presents a fractal analysis to analyze the binding and dissociation kinetics of various concentrations of scFv2 and scFv6 (single chain Fv) to F(ab´)2 antibody immobilized on a sensor chip surface, and the binding and dissociation of CCR5 in solution to gp120:CD4 immobilized on a sensor chip surface. The interactions involved in both these cases are involved in autoimmune reactions that lead to intractable diseases, where the first one is involved in arthritis, and the second one is involved in HIV-1. In both these cases either a single- or a dual-fractal analysis is used. The dual-fractal analysis is used only when the single-fractal analysis could not provide an adequate fit and it was done by the regression analysis provided by Corel Quattro Pro 8.0. In accordance with the prefactor analysis for fractal aggregates, quantitative (predictive) expressions are developed for the binding rate coefficient k, as a function of the analyte concentration in solution or the fractal dimension or the degree of heterogeneity in the binding phase Df that exists on the sensor chip surface; the dissociation rate coefficient kd as a function of the analyte concentration in solution or the fractal dimension in the dissociation phase Dfd; the fractal dimension in the binding phase as a function of the analyte concentration in solution; and the affinity K as a function of the analyte concentration in solution and as a function of the ratio of fractal dimensions present in the binding and dissociation phases. The expressions obtained a high sensitivity of binding and the dissociation rate coefficients (or affinities) on their respective fractal dimensions on the sensor chip surface.