Biomedical Engineering Reference
In-Depth Information
dependence between seven and seven and a half (equal to 7.351) on the fractal dimension,
D
f1
, for the C
a
concentration in solution in the 0-50 nM concentration range.
Figure 4.2g
and
Tables 4.1
and
4.2
show the increase in the binding rate coefficient,
k
2
, with
an increase in the fractal dimension,
D
f1
, for the C
a
concentration (in nM) in the 0-50 nM
range in solution for a dual-fractal analysis. For the data shown in
Figure 4.2g
, the binding
rate coefficient,
k
2
, is given by:
10
7
10
7
D
17
:
86
6
:
105
k
2
¼ð
1
:
5
1
:
1
Þ
ð
4
:
4g
Þ
f2
The fit is very good. Only five data points are available. The availability of more data points
would lead to a more reliable fit. The binding rate coefficient,
k
2
, exhibits an order of depen-
dence between seventeen and a half and eighteen (equal to 17.86) on the fractal dimension,
D
f2
, for the C
a
concentration in solution in the 0-50 nM concentration range.
Figure 4.2h
and
Tables 4.1
and
4.2
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 the
C
a
concentration (in nM) in the 0-50 nM range in solution for a dual fractal analysis. For
the data shown in
Figure 4.2h
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
4
:
01
0
:
728
k
2
=k
1
¼ð
0
:
772
0
:
193
ÞðD
f2
=D
f1
Þ
ð
4
:
4h
Þ
The fit is good. Only five 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
an order of dependence very close to four (equal to 4.01) on the ratio of the fractal
dimensions,
D
f2
/
D
f1
, for the C
a
concentration in solution in the 0-50 nM concentration
range.
Figure 4.2i
and
Tables 4.1 and 4.2
show theincrease in the affinity,
K
1
(
k
1
/
k
d
) with an
increase in the fractal dimension ratio,
D
f1
/
D
fd
. For the data shown in
Figure 4.2i
, the affinity,
K
1
, is given by:
¼
3
:
441
0
:
629
K
1
¼ð
:
:
Þð
D
f1
=
D
fd
Þ
ð
:
Þ
1
856
0
458
4
4i
The fit is good. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The affinity,
K
1
, is sensitive to the ratio of the fractal
dimensions,
D
f1
/
D
fd
, as noted by the close to three and a half (equal to 3.441) order of depen-
dence exhibited. This is one way of changing the affinity,
K
1
, by changing the degree of het-
erogeneity exhibited on the biosensor surface. Of course, some ingenuity is involved here in
that one needs to change the degree of heterogeneity exhibited in the binding and in the dis-
sociation phases differently so that one may change the ratio,
D
f1
/
D
fd
, in the required
direction.
