Biomedical Engineering Reference
In-Depth Information
180
24
160
22
140
20
120
18
100
16
80
14
60
12
40
10
20
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.2
1.3
1.4
1.5
1.6
1.7
1.8
B
A
Fractal dimension,
D
f
D
f
/
D
fd
12
10
8
6
4
2
0
0.6
0.8
1
1.2
1.4
1.6
C
Fractal dimension,
D
fd
Figure 8.7
(a) Increase in the binding rate coefficient, k, with an increase in the fractal dimension, D
f
.
(b) Increase in the affinity, K (
k/k
d
), with an increase in the fractal dimension dimension ratio, D
f
/D
fd
.
(c) Increase in the dissociation rate coefficient, k
d
, with an increase in the fractal dimension, D
fd
.
¼
oxazaborolidine, BNO1 in solution to the FTF immobilized on a SPR biosensor chip surface.
The dissociation rate coefficient,
k
d
, is given by:
2
:
516
0
:
957
k
d
¼ð
3
:
155
2
:
732
Þð
D
fd
Þ
ð
8
:
3c
Þ
The fit is reasonable. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient,
k
d
, exhibits very close to
a two and a half (equal to 2.516) order of dependence on the fractal dimension,
D
fd
, in the
dissociation phase or the degree of heterogeneity that exists on the SPR biosensor chip surface.
Figure 8.8a
shows the binding and dissociation of 15 nM oxazaborolidine derivative,
BNO2
þ
2 mM sucrose in solution to FTF immobilized on a SPR sensor chip surface
(
Jabbour et al., 2007
). A single-fractal analysis is adequate to describe the binding and the
dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimen-
sion,
D
f
, for a single-fractal analysis, and (b) the dissociation rate coefficient,
k
d
, and the
