Biomedical Engineering Reference
In-Depth Information
Figure 16.15c
shows the binding of cDNA to the MB immobilized on the biosensor surface
in the presence of 10 mM MgCl
2
. Once again, a dual-fractal analysis is required to
adequately describe the binding kinetics. The values of (a) the binding rate coefficient,
k
,
and the fractal dimension,
D
f
, for a single-fractal analysis, and (b) the binding rate
coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis
are given in
Table 16.12
. It is of interest to note that as the fractal dimension increases
by a factor of 1.71 from a value of
D
f1
equal to 1.3672 to
D
f2
equal to 2.3378, the binding
rate coefficient increases by a factor of 29.4 from a value of
k
1
equal to 0.003359 to
k
2
equal to 0.09877. Note that changes in the degree of heterogeneity or the fractal dimension
on the biosensor surface and in the binding rate coefficient are, once again, in the same
direction.
Figure 16.15d
shows the binding of cDNA to the MB immobilized on the biosensor surface
in the presence of 100 mM MgCl
2
. Once again, a dual-fractal analysis is required to ade-
quately describe the binding kinetics. The values of (a) the binding rate coefficient,
k
, and
the fractal dimension,
D
f
, for a single-fractal analysis, and (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis are given in
Table 16.12
. It is of interest to note that as the fractal dimension increases by a factor of
2.48 from a value of
D
f1
equal to 1.0788 to
D
f2
equal to 2.6728, the binding rate coefficient
increases by a factor of 110.1 from a value of
k
1
equal to 0.003981 to
k
2
equal to 0.4834.
Note that changes in the degree of heterogeneity or the fractal dimension on the biosensor
surface and in the binding rate coefficient are, once again, in the same direction.
Figure 16.15e
shows the binding of cDNA to the MB immobilized on the biosensor surface in
the presence of 500 mM MgCl
2
. Once again, a dual-fractal analysis is required to adequately
describe the binding kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal
dimension,
D
f
, for a single-fractal analysis, and (b) the binding rate coefficients,
k
1
and
k
2
,
and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis are given in
Table 16.12
.
It is of interest to note that as the fractal dimension increases by a factor of 2.058 from a
value of
D
f1
equal to 1.3266 to
D
f2
equal to 2.7308, the binding rate coefficient increases
by a factor of 88.07 from a value of
k
1
equal to 0.007705 to
k
2
equal to 0.46786. The changes
in the degree of heterogeneity or the fractal dimension on the biosensor surface and in the
binding rate coefficient are, once again, in the same direction.
Figure 16.16a
and
Table 16.12
show the increase in the binding rate coefficient,
k
1
, with an
increase in the ion concentration (MgCl
2
) in solution in the 0.1-500 mM range for a dual-fractal
analysis. For the data shown in
Figure 16.16a
, the binding rate coefficient,
k
1
, is given by:
0
:
378
0
:
0694
k
1
¼ð
0
:
000841
0
:
000541
Þ½
ion concentration, mM
ð
16
:
10a
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 binding rate coefficient,
k
1
, for a dual-fractal analysis
