Binding and Dissociation Kinetics During Hybridization on Biosensor Surfaces - Biosensors and Biosensor Kinetics - page 478

Figure 16.16c shows the increase in the binding rate coefficient ratio, k 2 / k 1 , with an increase
in the fractal dimension ratio, D f2 / D f1 , for a dual-fractal analysis. For the data shown in
Figure 17.16c, the binding rate coefficient ratio, k 2 / k 1 , is given by:

6 : 156 1 : 498

k 2 = k 1 ¼ð 1 : 0127 0 : 7851 Þð D f2 = D f1 Þ ð 16 : 10c Þ

The fit is reasonable. There is some scatter at the higher values of the D f2 / D f1 presented. The
availability of more data points at the higher D f2 / D f1 ratios would lead to a better fit. The
binding rate coefficient ratio, k 2 / k 1 , exhibits a very high and close to sixth (equal to 6.156)
order of dependence on the ratio of the fractal dimensions, D f2 / D f1 .

16.4 Conclusions

A fractal analysis is presented for the binding of different hybridization reactions occurring
on different biosensor surfaces. Both a single- and a dual-fractal analysis were used to model
the binding kinetics. The dual-fractal analysis was used only when the single-fractal analysis
did not provide an adequate fit (sum of least squares less than 0.97). Corel Quattro Pro 8.0
(1997) was used to model the binding kinetics. The fractal analysis is an alternate and con-
venient means to provide a kinetic analysis of the diffusion-limited reactions occurring on
heterogeneous or structured surfaces.

In accord with the prefactor analysis of fractal aggregates ( Sorenson and Roberts, 1997 ),
quantitative (predictive) expressions are developed for (a) the increase in the binding rate
coefficient, k 1 and k 2 , for a dual-fractal analysis with an increase in the exonuclease units

in solution during the real-time monitoring of the activity and kinetics of T4 PNK by a single
labeled DNA-hairpin smart probe coupled with l exonuclease cleavage ( Song and Zhao,
2009 ), (b) the increase in the fractal dimension, D f2 , for a dual-fractal analysis with an
increase in the l exonuclease units in solution during the real-time monitoring of the activity
and kinetics of the T4 PNK by a single labeled DNA-hairpin smart probe coupled with

l

exo-
nuclease cleavage ( Song and Zhao, 2009 ), (c) the increase in the binding rate coefficient, k 2 ,
and in the ratio of the binding rate coefficients, k 2 / k 1 , with a increase in the fractal dimension,
D f2 , and in the ratio D f2 / D f1 , respectively (d) an increase in the binding rate coefficients, k 2
and k 1 , with an increase in the fractal dimensions, D f2 and D f1 , respectively, during the bind-
ing of 500 pM cy3-labeled target (raw data) to a 20-mer capture probe immobilized on dif-
ferent areas (the vignetting effect-distance from the detector) on a microarray biosensor
( Schultz et al., 2008 ). In some cases these predictive relations indicate that the binding rate
coefficients are very sensitive to the fractal dimension or the degree of heterogeneity that
exists on the biosensor surface. This is explained for other reactions occurring on biosensor
surfaces in chapters elsewhere in this topic. These predictive relationships presented provide
a means by which these binding rate coefficients may be manipulated by changing either the
analyte concentration in solution or the degree of heterogeneity that exists on the biosensor

l