Biomedical Engineering Reference
In-Depth Information
3.1
2
3
1.8
2.9
1.6
2.8
1.4
2.7
1.2
2.6
2.5
1
0
1
2
3
4
5
0
1
2
Pi concentration, micromole
3
4
5
A
B
Pi concentration, micromole
12
11
10
9
8
7
6
5
1.6
1.8
2
2.2
2.4
C
D
f2
/
D
f1
Figure 4.6
(a) Increase in the fractal dimension, D
f1
with an increase in the organic phosphate, P
i
concentration (in micromole) in solution. (b) Increase in the fractal dimension, D
f2
with an increase
in the organic phosphate, P
i
concentration (in micromole) in solution. (c) Increase in the binding
rate coefficient ratio, k
2
/k
1
with an increase in the ratio of the fractal dimensions, D
f2
/D
f1
.
Figure 4.6c
and
Table 4.5
show the increase in the ratio of the binding rate coefficients,
k
2
/
k
1
,
with an increase in the ratio of the fractal dimensions,
D
f2
/
D
f1
, for a dual-fractal analysis. For
the data shown in
Figure 4.6c
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
1
:
979
0
:
450
k
2
=
k
1
¼ð
2
:
115
0
:
271
Þð
D
f2
=
D
f1
Þ
ð
4
:
6c
Þ
The fit is good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The ratio of the binding rate coefficients,
k
2
/
k
1
, exhibits
very close to a second (equal to 1.979) order of dependence on the ratio of the fractal
dimensions, (
D
f2
/
D
f1
) present on the biosensor chip surface.
Figure 4.7a
shows the binding of 0.05 mU of MET-AMC in solution in the cSPA (
Forbes
et al., 2007
). A single-fractal analysis is adequate to describe the binding kinetics. The values
