Biomedical Engineering Reference
In-Depth Information
11
5
10
4
9
3
8
2
7
1
6
0
5
1
1.2
1.4 1.6
Fractal dimension, D fd
1.8
2
2.2
1
1.2
1.4 1.6
Fractal dimension, D f
1.8
2
2.2
B
A
Figure 8.13
(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 .
or the degree of heterogeneity on the SPR biosensor chip surface leads to a decrease in the
binding rate coefficient in the same direction.
Figure 8.13a shows the increase in the binding rate coefficient, k , with an increase in the fractal
dimension, D f , on the SPR biosensor chip surface for the binding of 0-150 m M oxazaborolidine
derivative, BNO4 in solution to the FTF immobilized on the SPR sensor chip surface. For the
data presented in Figure 8.13a , the binding rate coefficient, k is given by:
D 0 : 7432 0 : 582
k
¼ð
5
:
511
1
:
804
Þ
ð
8
:
6a
Þ
f
The fit is reasonable. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The binding rate coefficient, k , exhibits less than a first
(equal to 0.732) order of dependence on the fractal dimension, D f , or the degree of heterogeneity
that exists on the SPR biosensor surface. This indicates that the binding rate coefficient is
sensitive to the degree of heterogeneity that exists on the SPR biosensor chip surface.
Figure 8.13b shows the increase in the dissociation rate coefficient, k d , for a single-fractal
analysis with an increase in the fractal dimension, D fd , for the dissociation of 0-30 nM
oxazaborolidine, BNO4 in solution to the FTF immobilized on a SPR biosensor chip surface.
The dissociation rate coefficient, k d , is given by:
2 : 611 0 : 987
k d
¼ð
0
:
4368
0
:
319
Þð
D fd
Þ
ð
8
:
6b
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. There is scatter in the data. The dissociation rate
coefficient, k d , exhibits between two and a half and three (equal to 2.611) order of depen-
dence on the fractal dimensions, D fd , in the dissociation phase or the degree of heterogeneity
that exists on the SPR biosensor chip surface.
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