Biomedical Engineering Reference
In-Depth Information
140
4
120
3
100
80
2
60
40
1
20
0
0
2.35
2.4
2.45
2.5
2.55
2.6
2.65
0
0.5
1
1.5
2
2.5
A
B
Fractal dimension,
D
fd
Fractal dimension,
D
f
4000
3000
2000
1000
0
0
5
10
15
20
25
30
C
Fractal dimension ratio,
D
f
/
D
fd
Figure 11.11
(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 in the
dissociation phase, D
fd
. (c) Increase in the affinity, K (
k/k
d
), with an increase in the fractal
dimension ratio, D
f
/D
fd
.
ΒΌ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. Only the positive error is shown in
Equation (11.5c
),
since the error is large, and the affinity can only have positive values. The affinity,
K
, exhibits
an order of dependence between one and a half and two (equal to 1.746) on the ratio of fractal
dimensions, (
D
f
/
D
fd
), present on the sensor chip surface.
Uno et al. (2007
) analyzed the SPR biosensor responses to PNA-DNA hybridization. These
authors used CYP2C9*2 as the probe PNA and the target DNA was complementary
CYP2C9*2 (target DNA2). They used target DNA concentrations in the 0.1-5.0
m
M range.
Figure 11.12a
shows the binding and the dissociation of 5
m
M target DNA concentration in
solution to the probe PNA immobilized on the sensor surface. A dual-fractal analysis is
required to adequately describe the binding kinetics. A single-fractal analysis is adequate
to describe the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and
the fractal dimension,
D
f
, for a single-fractal analysis, (b) the binding rate coefficients,