Dual-fractal analysis for antigen--antibody binding kinetics for biosensor applications

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor and other surfaces is analyzed within a fractal framework. Often, the binding kinetics may be described by a single-fractal analysis. In some cases, the binding curve exhibits complexities. Then, for these cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This indicates a change in the reaction mechanism on the surface. 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 10 nM insulin growth factor-1 in solution to insulin growth factor binding protein-1 immobilized on a biosensor surface, a 64% increase in the fractal dimension from 1.73 (Df1) to 2.85 (Df2) leads to an increase in the binding rate coefficient by a factor of 31.8 from 3.92 (k1) to 125 (k2). Furthermore, as the IGF-1 concentration in solution increases from 10 to 80 nM in solution, k2 and Df2 exhibit a linear increase. k1 and Df1 exhibit a linear increase with the reciprocal of the IGF-1 concentration in solution. 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 (k1 and k2) and in the fractal dimensions (Df1 and Df2) as different parameters are changed for the different biosensor applications are of particular value, since they provide us with a measure or extent of changes in the binding rate coefficient on changing different experimental parameter values. It is of interest to note the effect of different parameters on the extent or heterogeneity that exists on the surface and how this influences the binding rate coefficients. This may be one method to help manipulate or control the binding rate coefficients on the reaction surface.