Fractal analysis of binding and dissociation kinetics and interactions of cancer markers on biosensor surfaces

A fractal analysis is presented for the binding and dissociation of different cancer markers on biosensor surfaces. The data analyzed include putrescine in solution to PDDA/APTES/MWCNT/Puo-modified GCE (glassy carbon electrode) (8) and vascular endothelial growth factor (VEGF) in solution to the soluble form of the VEGF receptor (SFlt-1 or VEGF-1) immobilized on a sensor chip (1). Single- and dual-fractal models were used to fit the data. Values of the binding and dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (13). The binding rate coefficients and the affinity values are sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the heterogeneity present on the biosensor chip surface. The analysis presented provides physical insights into these cancer biomarker-receptor reactions occurring on the different biosensor surfaces.