Biomedical Engineering Reference
In-Depth Information
coefficient,
k
d
, and the fractal dimension for dissociation,
D
fd
, are given in
Tables 7.4
and
7.5
. In this case the affinity,
K
(
¼
k
/
k
d
), value is equal to 46.75.
Figure 7.6d
shows the binding of 2 mM glucose in 0.1 M PBS in solution to the Pt-PBHNAE
(
Bai et al., 2008
). 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 7.4
and
7.5
.Itisof
interest to note that as the fractal dimension increases by a factor of 2.42 from a value of
D
f1
equal to 1.2402 to
D
f2
equal to 3.0, the binding rate coefficient increases by a factor of
13.14 from a value of
k
1
equal to 0.00609 to
k
2
equal to 0.08.
Figure 7.6e
shows the binding of 3 mM glucose in 0.1 M PBS in solution to the Pt-PBHNAE
(
Bai et al., 2008
). 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 7.4
and
7.5
.Itisof
interest to note that as the fractal dimension increases by a factor of 1.53 from a value of
D
f1
equal to 1.2084 to
D
f2
equal to 1.8484, the binding rate coefficient increases by a factor
of 13.80 from a value of
k
1
equal to 0.004288 to
k
2
equal to 0.05917.
Figure 7.6f
shows the binding of 4 mM glucose in 0.1 M PBS in solution to the Pt-PBHNAE
(
Bai et al., 2008
). 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
Tables 7.4
and
7.5
.Itisof
interest to note that as the fractal dimension increases by a factor of 1.85 from a value
of
D
f1
equal to 1.6244 to
D
f2
equal to 3.0, the binding rate coefficient increases by a factor
of 10.81 from a value of
k
1
equal to 0.007864 to
k
2
equal to 0.085.
Figure 7.7a
and
Tables 7.4
and
7.5
show the increase in the binding rate coefficient,
k
, with
an increase in the fractal dimension,
D
f
, for a single-fractal analysis. For the data shown in
Figure 7.7a
, the binding rate coefficient,
k
, is given by:
D
1
:
683
k
¼ð
0
:
00359
þ
0
:
00399
Þ
ð
7
:
6a
Þ
f
There is scatter in the data, and this is reflected in the error in the binding rate coefficient.
Only the positive error is presented since the binding rate coefficient cannot be a negative
value. Only three data points are available. The availability of more data points would lead
to a more reliable fit. The binding rate coefficient,
k
, is sensitive to the degree of heterogene-
ity on the biosensor surface or the fractal dimension since it exhibits an order of dependence
between one and a half and two (equal to 1.683) on the fractal dimension on the biosensor
surface.
