A Fractal Analysis of Binding and Dissociation Kinetics of Glucose and Related Analytes on Biosensor Surfaces at the Nanoscale Level

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte–receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness (fractal dimension, D_f) present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, as the fractal dimension value increases by a factor of 3.31 from D_f1 equal to 0.5720 to D_f2 equal to 1.891, the binding rate coefficient increases by a factor of 8.88 from k₁ equal to 0.0545 to k₂ equal to 0.4841 for the binding of adipose tissue interstitial glucose. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A single-fractal analysis is adequate to describe the dissociation kinetics. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented.