3 - Fractal Analysis of Toxin and Pathogen Detection on Biosensor Surfaces

Abstract

This chapter presents a fractal analysis to analyze the binding kinetics of yessotoxin (YTX) in solution to phosphodiesterase 3´, 5´ - cyclic-nucleotide specific to bovine brain (PDE) immobilized on an aminosilane surface, of Cy3-labeled ricin in solution to gelimmobilized antibodies against ricin Rch 1, and lipopolysaccharide (LPS) in solution to cyclic decapeptide immobilized on a CM5 sensor chip surface. The fractal analysis provides a quantitative indication of the state of disorder (fractal dimension) and the binding (and dissociation) rate coefficients on the sensor chip surface. Quantitative (predictive) relations are developed for the binding rate coefficient, k, as a function of the YTX concentration in solution, and as a function of the fractal dimension, Df ; the binding rate coefficient, k as a function of lipopolysaccharide (LPS) in solution and as a function of the fractal dimension, Df; the dissociation rate coefficient, kd2, as a function of the LPS concentration in solution and as a function of the fractal dimension in the dissociation phase, Dfd2, and the affinities, K1 and K2, as a function of the ratio of the fractal dimensions present in the binding and in the dissociation phases, respectively. The binding rate coefficient, k, for YTX is very sensitive to the fractal dimension, Df, or the degree of heterogeneity present on the chip surface as noted by the slightly higher than sixth (= 6.0359) order of dependence on Df exhibited. Similarly, the binding rate coefficient, k, for LPS exhibits close to a negative second (= –2.1099) order of dependence on the degree of heterogeneity on the sensor chip surface.