Binding of the Same Analyte (Glucose) to Different Biosensor Surfaces: A Fractal Analysis of the Kinetics - Biosensors and Biosensor Kinetics - page 174

0.005
0.0048
0.0046
0.0044
0.0042
0.004

0.32

0.315

0.31

0.305

0.3

0.0038

0.295 0.0036

0.92 0.94 0.96

Fractal dimension, D f

0.98 1 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

B

A

Fractal dimension, D fd

85

80

75

70

65

60

1 1.1 1.2

D f / D fd

1.3 1.4

C

Figure 7.2
(a) Increase in the binding rate coefficient, k with an increase in the fractal dimension, D f.
(b) Increase in the dissociation rate coefficient, k d with an increase in the fractal dimension, D fd.
(c) Increase in the affinity, K( k/k d ) with an increase in the ratio of fractal dimensions in the

binding and in the dissociation phases (D f /D fd ).

¼

Figure 7.2b shows the increase in the dissociation rate coefficient, k d , with an increase in the
fractal dimension, D fd , for a single-fractal analysis. For the data shown in Figure 7.2b , the
dissociation rate coefficient, k d , is given by:

D 0 : 465 0 : 474 k d ¼ð 0 : 004472 0 : 000764 Þ ð 7 : 4b Þ

fd

There is scatter in the data. The fit is not good. Only three data points are available. The
availability of more data points would lead to a more reliable fit. The dissociation rate coef-
ficient, k d , for a single-fractal analysis exhibits less than one-half (equal to 0.465) order of
dependence on the fractal dimension, D fd , in the dissociation phase.