Biomedical Engineering Reference
In-Depth Information
1
20
18
0.8
16
14
0.6
12
0.4
10
8
0.2
6
4
0
2.35
2.4
2.45
2.5
2.55
2.6
2.65
1.2
1.3
1.4 1.5
Fractal dimension,
D
f1
1.6
1.7
B
Fractal dimension,
D
f2
A
60
50
40
30
20
10
1.5
1.6
1.7
1.8
1.9
2
C
D
f2
/
D
f1
Figure 16.8
(a) Increase in the binding rate coefficient, k
1
, for a dual-fractal analysis with an increase in the
fractal dimension, D
f1
. (b). Increase in the binding rate coefficient, k
2
, for a dual-fractal analysis
with an increase in the fractal dimension, D
f2
. (c) Increase in the binding rate coefficient ratio,
k
2
/k
1
, for a dual-fractal analysis with an increase in the fractal dimension ratio, D
f2
/D
f1
.
Figure 16.8c
and
Table 16.6
show 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 16.8c
, the binding rate coefficient ratio,
k
2
/
k
1
, is given by:
4
:
884
2
:
767
D
f2
D
f1
k
2
=
k
1
¼ð
1
:
0494
0
:
133
Þ
ð
16
:
8
Þ
The fit is reasonable. There is scatter in the data. Only three data points are available. The
availability of more data points would lead to better fit. The ratio of the binding rate coefficients,
k
2
/
k
1
, is very sensitive to the ratio of the fractal dimensions,
D
f2
/
D
f1
, as noted by the close to five
(equal to 4.884) order of dependence exhibited for a dual-fractal analysis.
Figure 16.9a
shows the binding of 500 pM cy3-labelled target (raw data) to a 20-mer
capture probe immobilized on Area 1 on the microarray biosensor (
Schultz et al., 2008
).
