Biomedical Engineering Reference
In-Depth Information
Note that an increase in the fractal dimension by a factor of 1.265 from a value of
D
f1
equal
to 1.9482 to
D
f2
equal to 2.465 leads to an increase in the binding rate coefficient by a factor
of 6.67 from a value of
k
1
equal to 0.01789 to
k
2
equal to 0.1193.
Figure 11.3b
shows the binding of 7.5 nM free-DNA in solution to a 22-mer strand (bound
DNA) immobilized via a phenylene-diisocyanate linker molecule on a glass substrate
(
Michel et al., 2007
). 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 11.2
.
Figure 11.3c
shows the binding of 5.0 nM free-DNA in solution to a 22-mer strand (bound
DNA) immobilized via a phenylene-diisocyanate linker molecule on a glass substrate
(
Michel et al., 2007
). 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 11.2
.
Figure 11.3d
shows the binding of 2.0 nM free-DNA in solution to a 22-mer strand (bound
DNA) immobilized via a phenylene-diisocyanate linker molecule on a glass substrate
(
Michel et al., 2007
). 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 11.2
.
Figure 11.4
and
Table 11.2
show for a single-fractal analysis the decrease in the fractal
dimension,
D
f
with an increase in the initial free-DNA concentration in the 2-7.5 nM range
in solution. For this 2-7.5 nM concentration range, the fractal dimension,
D
f
, is given by:
0
:
1298
0
:
0429
D
f
¼ð
2
:
547
0
:
107
Þ½
initial free
DNA, in nM
ð
11
:
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
f
, exhibits a very slight negative order
(equal to
0.1298) of dependence on the initial free-DNA concentration in solution. The fractal
dimension,
D
f
, is based on a log scale. Thus, even very small changes in the fractal dimension
indicate significant changes in the degree of heterogeneity on the biosensor chip surface.
Figure 11.5
shows the binding of 1 nM initial free-DNA concentration in solution at 22 mer
strand (bound DNA) immobilized via a phenylene-diisocyanate linker molecule on a glass
substrate (
Michel et al., 2007
). 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
, are given
in
Table 11.3
.
