Single- and dual-fractal analysis of hybridization binding kinetics: biosensor applications

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for both the single-fractal and the dual-fractal analysis examples presented. For example, for a single-fractal analysis and for the hybridization of 10 nM 16CFl (oligonucleotide) to 16B immobilized via sulfosuccinimidyl-6-(biotinamido)hexanoate and streptavidin using chemical and thermal regeneration (Abel, A. P.; Weller, M. G.; Duveneck, G. L.; Ehrat, M. Widmer, H. M. Anal. Chem. 1996, 68, 2905-2912), an increase in the fractal dimension, Df from 1.211 (chemical regeneration) to 1.394 (thermal regeneration), leads to an increase in the binding rate coefficient, k, from 86.53 (chemical regeneration) to 100.0 (thermal regeneration). An increase in the degree of heterogeneity on the biosensor surface leads to an increase in the binding rate coefficient. When a dual-fractal analysis was utilized, an increase in the fractal dimension value from Df1 to Df2 leads to an increase in the binding rate coefficient value from k1 to k2. The fractional order of dependence of the binding rate coefficient, k1, on (a) the analyte (rRNA) concentration in solution and (b) on the fractal dimension, Df1, for the hybridization kinetics to detect Listeria species (Fliss, R.; St-Laurent, M.; Emond, E.; Simard, R. E.; Lemieux, R.; Ettriki, A.; Pandian, S. Appl. Microbiol. Biotechnol. 1995, 43, 717-724.) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the analyte concentration in solution and the fractal dimension are of particular value since they provide a means to better control of biosensor or immunosensor performance.