Binding and Dissociation Kinetics During Hybridization on Biosensor Surfaces - Biosensors and Biosensor Kinetics - page 466

a single-fractal analysis, and (b) the binding rate coefficients, k 1 and k 2 , and the fractal
dimensions, D f1 and D f2 , for a dual-fractal analysis are given in Table 16.6 .

For a dual-fractal analysis, it is of interest to note that as the fractal dimension increases by a
factor of 2.08 from a value of D f1 equal to 1.1342 to D f2 equal to 2.3628, the binding rate
coefficient increases by a factor of 41.22 from a value of k 1 equal to 0.1378 to k 2 equal to
5.680. Once again, the changes in the degree of heterogeneity or the fractal dimension on
the sensor surface and in the binding rate coefficient are in the same direction.

Figure 16.9c shows the binding of 500 pM cy3-labelled target (raw data) to a 20-mer capture
probe immobilized on Area 3 on the microarray biosensor ( Schultz et al., 2008 ). It shows,
once again, that a dual-fractal analysis is required to adequately describe the binding kinetics.
The values of (a) the binding rate coefficient, k , and the fractal dimension, D f , for a single-
fractal analysis, and (b) the binding rate coefficients, k 1 and k 2 , and the fractal dimensions,
D f1 and D f2 , for a dual-fractal analysis are given in Table 16.6 .

For a dual-fractal analysis, it is of interest to note that as the fractal dimension increases by a
factor of 1.99 from a value of D f1 equal to 1.1520 to D f2 equal to 2.2946, the binding rate
coefficient increases by a factor of 29.56 from a value of k 1 equal to 0.1923 to k 2 equal to
5.684. Once again, the changes in the degree of heterogeneity or the fractal dimension on
the sensor surface and in the binding rate coefficient are in the same direction.

Figure 16.10 and Table 16.6 show the decrease in the binding rate coefficient, k 1 , with
an increase in the fractal dimension, D f1 , for a dual-fractal analysis. For the data shown in
Figure 16.10 , the binding rate coefficient, k 1 , is given by:

D 3 : 65 8 : 96 k 1 ¼ð 0 : 276 0 : 094 Þ ð 16 : 9 Þ

f1

0.22

0.2

0.18

0.16

0.14

0.12

1.1 1.11 1.12 1.13

Fractal dimension, D f1

1.14 1.15 1.16

Figure 16.10
Decrease in the binding rate coefficient, k 1 , for a dual-fractal analysis with an increase in the fractal
dimension, D f1 .