Fractal Analysis of Binding and Dissociation of Analytes Related to Human Health on Biosensor Surfaces

Ajit Sadana and Atul M. Doke. Chemical Engineering, University of Mississippi, 134 Rebel Drive, University, MS 38677-1848

A fractal analysis for the binding of riboflavin binding protein (RBP) in solution to riboflavin (Rf) derivative immobilized on a sensor chip (Caelen et al., 2004) provides values of the binding rate coefficient, k and the degree of heterogeneity made quantitative by the fractal dimension, Df on the sensor chip surface. The fractal analysis is an alternate and convenient means to provide a kinetic analysis of the diffusional-limited reactions occuring on heterogeneous or structured surfaces. The fractal analysis is also applied to the binding of (a) glucose in solution to glucose oxidase immobilized on a microcantilever surface (Pei et al., 2004), (b) endogeneous acetylcholine and choline to an acetylcholine and choline sensor, respectively (Mitchell, 2004), and Pb++ to a DNAzyme biosensor (Liu and Lu, 2004). The binding rate coefficient, k is linked to the degree of heterogeneity of fractal dimension, Df that exists on the sensor chip surface. Both single- as well as dual-fractal analysis are used to adequately model the binding kinetics. The dual-fractal analysis is used only when the single-fractal analysis did not provide an adeuqate fit (sum of least squares less than 0.97). This was done by the regression analysis provided by Corel Quatrro Pro 8.0 (1997). The binding mechanisms for the choline (Ch) sensor and the acetylcholine (ACh) sensor are different since a single-fractal analysis is adequate to model the binding kinetics observed with a Ch sensor whereas a dual-fractal analysis is required for the ACh sensor (Mitchell, 2004). On comparing the binding and dissociation rate coefficients for the un-stimulated and K+ -evoked increase for the endogeneous ACh case, one notes that the K+ affects the dissociation rate coefficient more than it does the binding rate coefficient. For the binding of different concentrations of glucose in solution to glucose oxidase immobilized on the microcantilever surface (Pei et al., 2004), one notes that (a) the binding rate coefficients, k1 and k2 exhibit higher than second-order dependence on the fractal dimension or the degree of heterogeneity on the microcantilever surface. The monitoring of glucose for the control of diabetes is and will continue to be an important application of biosensor technology. This is especially true since the occurrence of diabetes amongst the general population is on the increase. Finally, it is suggested that the fractal surface (rougness) leads to turbulence, which enhances mixing, decreases diffusional limitations, and leads to an increase in the binding rate coefficient (Martin et al., 1993). For this to occur the characteristic length of the turbulent boundary layer may have to extend a few monolayers above the sensor chip surface to affect bulk diffusion to and from the surface. The sensor chip surface is characterized by grooves and ridges, and this surface morphology may lead to eddy diffusion. This eddy diffusion can then help to enhance the mixing and extend the characteristic length of the boundary layer to affect the bulk diffusion to and from the surface.