A Predictive Approach Using Fractal Analysis for Analyte–Receptor Binding and Dissociation Kinetics for Surface Plasmon Resonance Biosensor Applications

Abstract

A predictive approach using fractal analysis is presented for analyte–receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the binding and the affinity (kdiss/kbind) as a function of the analyte concentration are of particular value since they provide a means by which the binding and the affinity rate coefficients may be manipulated. Relationships are also presented for the binding and the dissociation rate coefficients and for the affinity as a function of their corresponding fractal dimension, Df, or the degree of heterogeneity that exists on the surface. When analyte–receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in Df) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient. The binding and the dissociation rate coefficients are rather sensitive to the degree of heterogeneity, Df,bind (or Df1) and Df,diss, respectively, that exists on the biosensor surface. For example, the order of dependence on Df,bind (or Df1) and Df2 is 6.69 and 6.96 for kbind,1 (or k1) and k2, respectively, for the binding of 0.085 to 0.339 μM Fab fragment 48G7L48G7H in solution to p-nitrophenyl phosphonate (PNP) transition state analogue immobilized on a surface plasmon resonance (SPR) biosensor. The order of dependence on Df,diss (or Df,d) is 3.26 for the dissociation rate coefficient, kdiss, for the dissociation of the 48G7L48G7H–PNP complex from the SPR surface to the solution. The predictive relationships presented for the binding and the affinity as a function of the analyte concentration in solution provide further physical insights into the reactions on the surface and should assist in enhancing SPR biosensor performance. In general, the technique is applicable to other reactions occurring on different types of biosensor surfaces and other surfaces such as cell-surface reactions.