An Analysis of Analyte–Receptor Binding Kinetics for Biosensor Applications: Influence of the Fractal Dimension on the Binding Rate Coefficient

Abstract

The diffusion-limited kinetics of binding of an analyte in solution to a receptor immobilized on a biosensor surface is analyzed within a fractal framework. Antigen–antibody, analyte–receptor, and analyte–receptorless systems are analyzed. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Jandel Scientific, San Rafael, CA, 1993). It is of interest to note that the binding rate coefficient,k, and the fractal dimension,Df, both exhibit changes in the same direction for the antigen–antibody and analyte–receptor systems analyzed. The binding rate coefficient,k, expressed as a function of the fractal dimension,Df, developed for the three types of binding systems indicates the sensitivity ofktoDf. For example, for the antigen–antibody binding of mAb 447/D-II to rgp 120(MN) immobilized on a biosensor surface and for mAb 9205 to rgp (IIIB) (37), the order of dependence onDfwas 10.221 and 9.668, respectively. The fractional order of dependence ofkonDffurther reinforces the fractal nature of the system. For the single example of an analyte–receptorless system (LDL protein adsorption) presented, a more organized biosensor surface (lowerDfvalue) leads to an increased value ofk. Expressions ofkas a function of the fractal dimension,Df, are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface and further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.