Biomedical Engineering Reference
In-Depth Information
Figure 16.3c
and
Table 16.2
show the increase in the fractal dimension,
D
f2
, with an increase
in the l nuclease units in solution for a dual-fractal analysis. For the data shown in
Figure 16.3c
the fractal dimension,
D
f2
, is given by:
0
:
475
0
:
119
D
f
2
¼ð
1
:
791
0
:
260
Þð
l
exonuclease units
Þ
ð
16
:
4c
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 fractal dimension,
D
f2
, exhibits only a mild dependence
on the
exonuclease units in solution as shown by the less than one-half (equal to 0.475)
order of dependence exhibited.
l
Figure 16.3d
and
Table 16.2
show the increase in the binding rate coefficient,
k
2
, with an
increase in the fractal dimension,
D
f2
, for a dual-fractal analysis. For the data shown in
Figure 16.3d
the binding rate coefficient,
k
2
, is given by:
4
:
816
0
:
164
k
2
¼ð
42
:
399
4
:
055
Þð
D
f2
Þ
ð
16
:
4d
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 binding rate coefficient,
k
2
, is very sensitive to the frac-
tal dimension,
D
f2
, as noted by the close to fifth (equal to 4.816) order of dependence
exhibited.
Figure 16.3e
and
Table 16.2
show the increase in the binding rate coefficient ratio,
k
2
/
k
1
, with
an increase in the fractal dimension ratio,
D
f2
/
D
f1
, for a dual-fractal analysis. For the data
shown in
Figure 16.3e
the binding rate coefficient ratio,
k
2
/
k
1
, is given by:
:
:
2
668
0
970
k
2
=
k
1
¼ð
0
:
729
þ
0
:
918
Þð
D
f2
=
D
f1
Þ
ð
16
:
4e
Þ
There is scatter in the data. This is reflected in the error for the ratio of the binding rate
coefficients,
k
2
/
k
1
. 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
, is sensitive
to the fractal dimension ratio, (
D
f2
/
D
f1
) as noted by the order of dependence between two and
a half and third (equal to 2.668) exhibited.
Figure 16.4a
shows the binding of 20 nM FAM-SP-2 to T4 PNK immobilized on the sensor
surface. A single-fractal analysis is adequate to describe the binding kinetics. The values of
the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis is
given in
Table 16.3
.
Figure
16.4b
shows the binding of 30 nM FAM-SP-2 to T4 PNK immobilized on the sensor
surface. A single-fractal analysis is adequate to describe the binding kinetics. The values of
the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis is
given in
Table 16.3
.