Antigen‐Antibody Binding Kinetics for Biosensors: The Fractal Dimension and the Binding Rate Coefficient

Abstract

The diffusion-limited binding kinetics of antigen (or antibody or substrate) in solution to antibody (or antigen or enzyme) immobilized on a biosensor surface is analyzed within a fractal framework. The change in the fractal dimension, Df, is in the same direction as that in the forward binding rate coefficient, k1. An increase or decrease in the fractal dimension, Df leads to an increase or decrease in the forward binding rate coefficient, k1, respectively, irrespective of whether the antigen or the antibody is immobilized on the biosensor surface. For example, an increase in the concentration of IgG (MRC OX-19) (antigen) in solution from 1 to 10 micrograms/mL bound to polyclonal sheep anti-mouse IgG (antibody) immobilized on immunomagnetic beads leads to decreases in Df from 1.93 to 0.517 and in k1 from 2.72 to 0.064, respectively. The different examples analyzed and presented together indicate one means by which the forward binding rate coefficient, k1, may be controlled, that is, by changing the fractal dimension or the disorder on the surface. The versatility of the analysis is indicated by applying it to different examples for both types of systems, wherein either the antigen or antibody is immobilized on the surface. The analysis should assist in improving the stability, sensitivity, and response time of biosensors.

Tethered-bead, immune sandwich assay

“…More specifically, the fraction, f, of PSA molecules that should be captured at equilibrium can be estimated from the well-known relationship between free ligand and fractional receptor occupancy, f (e.g., see Squires et al, 2008): f=1/(1+K D /[Ab]) =.9, where [Ab] is the concentration of “free” antibody molecules. A characteristic time to reach equilibrium for many antibody-antigen reactions at nM concentration is ~20–60 minutes (Sadana, 1995). The beads were pulled to the side of the tube using a magnet, washed, and incubated with 50μl of 1nM biotinylated detection antibody for 1 hour.…”

A Kinetic Study of Analyte–Receptor Binding and Dissociation, and Dissociation Alone, for Biosensor Applications: A Fractal Analysis

“…It is obvious that the above biosensor system (wherein either the antigen or the antibody is attached to the surface) along with its different complexities, including heterogeneities on the surface and in solution, diffusion-coupled reactions, and time-varying adsorption (or binding), and even dissociation rate coefficients, may be characterized as a fractal system. The diffusion of reactants toward fractal surfaces has been analyzed (43). Havlin (44) briefly reviewed and discussed these results.…”

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

“…It is obvious that the above biosensor system (wherein either the antigen or the antibody is attached to the surface) along with its different complexities, including heterogeneities on the surface and in solution, diffusion-coupled reactions, and time-varying adsorption (or binding), and even dissociation rate coefficients, may be characterized as a fractal system. The diffusion of reactants toward fractal surfaces has been analyzed (44). Havlin (45) has briefly reviewed and discussed these results.…”