A fractal analysis is used to model the binding and dissociation kinetics of heparin binding proteins in solution to covalently immobilized heparin on a surface plasmon resonance (SPR) biochip using a preformed albumin-heparin conjugate (Zhang et al., 2002). Heparin is proteoglycan and binds to growth factors. It also influences angiogenesis and other proliferation-dependent processes. The analysis provides physical insights into diffusion-limited heparin protein interactions occurring on biosensor surfaces. Predictive relations are presented for the binding rate coefficients k1 and k2 as a function of the acidic fibroblast growth factor (aFGF) concentration (13.3 to 133 nM) present in solution.

Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness (fractal dimension, Df) present on the biosensor surface. Predictive relations are developed for the binding and the dissociation rate coefficients. The binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity present on the surface. In both of these cases, the order of dependence exhibited by these rate coefficients on their respective fractal dimensions lies between five and six. Affinity, K values are of interest to practicing biosensorists. The affinity value is very sensitive to the ratio of the fractal dimensions in the binding and in the dissociaition phase. An order of dependence higher than fourth order is exhibited.

Practicing biosensorists need to pay more attention to the nature of and the degree of heterogeneity present on the biosensor chip surface. The predictive relationships presented provide one with the flexibility to manipulate experimental conditions to increase biosensor performance parameters such as sensitivity, selectivity, stability, response time, and other parameters of interest.