Influence of Different Parameters on a Dual-Fractal Analysis for Antigen–Antibody Binding Kinetics for Biosensor Applications

Abstract

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The fit obtained by a dual-fractal analysis is compared with that obtained from a single-fractal analysis. In some cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (46). It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase as the reaction progresses on the biosensor surface. For example, for the binding of HIV-1 p24 in solution to monoclonal antibody (MAb) 18 covalently attached to a biosensor surface (49), an increase in the fractal dimension by 59% from a value ofDf1equal to 1.91 toDf2equal to 2.95 leads to an increase in the binding rate coefficient by a factor of 15 fromk1equal to 21.1 tok2equal to 339. Also, the binding of MAb 6301 and 6303 in solution to insulin growth factor binding protein-1 (IGFBP-1) covalently attached to the sensor surface is adequately described by a single-fractal analysis (48). The binding of MAb 6302 to IGFBP-1, however, requires dual fractals. This indicates a difference in the binding mechanisms of these MAbs. The different examples analyzed and presented together provide a means by which the antigen–antibody reactions may be better controlled by noting the magnitude of the changes in the fractal dimension and in the binding rate coefficient as the reaction progresses on the biosensor surface. Also, the magnitude of the changes in the binding rate coefficients (k1andk2) and in the fractal dimensions (Df1andDf2) as different parameters are changed for the different biosensor applications are of particular value.