Biomedical Engineering Reference
In-Depth Information
Figure 11.13b
and
Table 11.7
show the increase in the binding rate coefficient,
k
2
, with an
increase in the target DNA concentration in the 1.0-5.0
m
M range in solution for a dual-
fractal analysis. For the data shown in
Figure 11.13b
the binding rate coefficient,
k
2
,is
given by:
0
:
842
0
:
254
k
2
¼ð
82
:
13
27
:
67
Þ½
target DNA
ð
11
:
6b
Þ
The fit is reasonable. There is some scatter in the data. The binding rate coefficient,
k
2
,
exhibits an order of dependence between a half and one (equal to 0.842) on the target
DNA concentration in solution. The nonintegral order of dependence exhibited by the bind-
ing rate coefficient,
k
1
, once again lends support to the fractal nature of the system.
It is seen that the binding rate coefficient,
k
2
, exhibits an order of dependence less than one
(equal to 0.842) on the target DNA concentration in solution., and the binding rate coeffi-
cient,
k
1
, exhibits an order of dependence greater than one (equal to 1.067) on the target
DNA concentration in solution.
Figure 11.14a
and
Tables 11.7
and
11.8
show the increase in the binding rate coefficient,
k
1
,
with an increase in the fractal dimension,
D
f1
for a dual-fractal analysis. For the data shown
in
Figure 11.4a
, the binding rate coefficient,
k
1
, is given by:
D
2
:
944
0
:
1698
k
1
¼ð
4
:
517
0
:
377
Þ
ð
11
:
7a
Þ
f1
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
1
, is sensitive to the fractal
dimension,
D
f1
, or the degree of heterogeneity that exists on the sensor chip surface as noted
by the close to third (equal to 2.944) order of dependence exhibited.
Figure 11.14b
and
Tables 11.7
and
11.8
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 11.4b
, the binding rate coefficient,
k
2
, is given by:
D
9
:
734
0
:
48728
k
2
¼ð
0
:
00754
0
:
00038
Þ
ð
11
:
7b
Þ
f2
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 extremely sensitive to
the fractal dimension,
D
f2
, or the degree of heterogeneity that exists on the sensor chip sur-
face as noted by the order of dependence between nine and a half and ten (equal to 9.734)
exhibited. No explanation is offered at present to help explain this extremely very high order
of dependence exhibited.
Figure 11.14c
and
Tables 11.7
and
11.8
show the increase in the ratio of the binding rate
coefficients,
k
2
/
k
1
, with an increase in the fractal dimension ratio,
D
f2
/
D
f1
, for a dual-fractal
