Binding and Dissociation Kinetics of Different Analytes on Novel Biosensing Surfaces: A Fractal Analysis - Biosensors and Biosensor Kinetics - page 334

resonance imaging microarray ( Ha et al., 2007 ), (b) affinity-based chromatographic
assays for thrombin ( Zhao et al., 2008 ), (c) a new platform technology for DNA extraction
and fast detection of gram positive bacteria ( Aslan et al., 2008 ), and (d) a highly-
selective electrogenerated chemiluminescence (ECL) biosensor for the detection of target
single-strand DNA (ss-DNA) using hairpin DNA as the recognition element ( Zhang
et al., 2008 ).

12.2 Theory

Havlin (1989) has reviewed and analyzed the diffusion of reactants towards fractal surfaces.
The details of the theory and the equations involved for the binding and the dissociation
phases for analyte-receptor binding are available in the literature ( Sadana, 2001 ). The details
are not repeated here except that the equations are given to permit an easier reading. These
equations have been applied to other biosensor systems ( Ramakrishnan and Sadana, 2001 ;
Sadana, 2001, 2005 ). For most applications, a single- or a dual-fractal analysis is often ade-
quate to describe the binding and the dissociation kinetics. Peculiarities in the values of the
binding and the dissociation rate coefficients, as well as in the values of the fractal
dimensions with regard to the dilute analyte systems being analyzed will be carefully noted,
if applicable.

In this chapter we analyze the binding and dissociation kinetics of the binding and dissocia-
tion of IgG species to a porous SiO 2 interferometric biosensor coated with protein A
( Schwartz et al., 2007 ), (b) binding (hybridization) using differential surface plasmon reso-
nance ( Boecker et al., 2007 ), (c) binding of glucose to a One Touch II blood glucose meter
and a SERS sensor ( Stuart et al., 2006 ), (d) binding of H9 avian virus to cadmium quantum
dots (Yun et al., 2007), and (e) the binding of sodium ions of Na 0.44 x MnO 2 to a selective
sodium ion sensor ( Sauvage et al., 2007 ).

12.2.1 Single-Fractal Analysis

Binding Rate Coefficient

Havlin (1989) points out that the diffusion of a particle (analyte [Ag]) from a homogeneous
solution to a solid surface (e.g., receptor [Ab]-coated surface) on which it reacts to form a
product (analyte-receptor complex; Ab Ag) is given by:

t ð 3 D f , bind Þ= 2 t p , ¼ t < t c

ð Ab Ag Þ ð 12 : 1 Þ

t 1 = 2 ,

t > t c

Here D f,bind or D f (used later on in the manuscript) is the fractal dimension of the surface dur-
ing the binding step. t c is the cross-over value. Havlin (1989) points out that the cross-over