Binding of the Same Analyte (Glucose) to Different Biosensor Surfaces: A Fractal Analysis of the Kinetics - Biosensors and Biosensor Kinetics - page 177

Table 7.3: Fractal dimensions for the binding and dissociation phase for
0.1 M glucose to the DMGCuNP (dimethylglycoxime functionalized
copper nanoparticles) ( Xu et al., 2006 ).

Run D f D fd D fd1 D fd2

A 0.982 0.0157 1.110 0.307 0 þ 0.914 2.3604 0.1554

B 1.006 0.0042 1.740 0.260 0.142 þ 0.362 2.502 0.0836

C 1.0 0 1.780 0.206 na na

Influence of repeat runs.

dissociation rate coefficients, k d1 and k d2 , and the fractal dimensions in the dissociation
phase, D fd1 and D fd2 , for a dual-fractal analysis are given in Tables 7.2 and 7.3 . It is of inter-
est to note that as the fractal dimension in the dissociation phase increases by a factor of
17.62 from a value of D fd1 equal to 0.142 to D fd2 equal to 2.3604, the dissociation rate coef-
ficient increases by a factor of 22.1 from a value of k d1 equal to 0.0957 to k d2 equal to 2.116.
Note that the changes in the fractal dimension or the degree of heterogeneity on the biosensor
surface in the dissociation phase and in the dissociation rate coefficient are in the same
direction.

Figure 7.3c shows that the binding and the dissociation may be adequately described, in
this case, by a single-fractal analysis. In this case, k / k d ), value is

equal to 1.19. Figure 7.4 shows the increase in the dissociation rate coefficient, k d or k d2 ,
with an increase in the fractal dimension, D fd or D fd2 . The two different pieces of data

the affinity, K ( ¼

2.2

2

1.8

1.6

1.4

1.2

1

0.8

0.6

1.6 1.8

Fractal dimension, D fd or D fd2

2 2.2 2.4 2.6

Figure 7.4
Increase in the dissociation rate coefficient, k d or k d2 with an increase in the fractal dimension,
D fd or D fd2 ( Xu et al., 2006 ).