Biomedical Engineering Reference
In-Depth Information
fractal dimension,
D
f1
, or the degree of heterogeneity that exists on the biosensor surface as
noted by the order of dependence between three and three and a half (equal to 3.225)
exhibited.
Figure 14.2b
and
Table 14.1
show the increase in the binding rate coefficients,
k
2
or
k
3
, with
an increase in the fractal dimension,
D
f2
or
D
f3
, for a dual- and a triple-fractal analysis. For
the data shown in
Figure 14.2b
, the binding rate coefficient,
k
2
or
k
3
, is given by:
0
:
5639
0
:
2167
k
2
or
k
3
¼ð
0
:
7649
þ
1
:
2720
Þð
D
f2
or
D
f3
Þ
ð
14
:
4b
Þ
The fit is poor. Seven data points are available. However, the data for
k
2
and
k
3
and
D
f2
and
D
f3
are plotted together. This may be the reason for the poor fit. The binding rate coefficients,
k
2
and
k
3
, exhibit a low and close to one half (equal to 0.5638) order of dependence on the
fractal dimension,
D
f2
and
D
f3
. The fractal dimensions,
D
f2
and
D
f3
, and the binding rate
coefficients were plotted together in an attempt to see if there was some sort of continuity
between these binding phases with regard to the surface heterogeneities on the biosensor
surfaces.
Figure 14.2c
and
Table 14.1
show the increase in the ratio of the binding rate coefficients,
k
2
/
k
1
, with an increase in the ratio of the fractal dimensions,
D
f2
/
D
f1
. For the data shown
in
Figure 14.2c
, the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
:
:
0
3722
0
1435
k
2
=
k
1
¼ð
0
:
04367
0
:
03320
Þð
D
f2
=
D
f1
Þ
ð
14
:
4c
Þ
The fit is poor. Only four 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 only
mildly sensitive to the ratio of fractal dimensions,
D
f2
/
D
f1
, as noted by the less than one half
(equal to 0.3722) order of dependence exhibited.
Yoo et al. (2007)
immobilized the bioluminescent bacteria, DK1 to a microcell chip to ana-
lyze the specificity of, for example, an oxidative toxicant.
Figure 14.3
shows binding and dis-
sociation of 0.88
m
M hydrogen peroxide mixed with LB medium to the GC2 immobilized
microcell chips. A 10-fold increase in the bioluminescence was observed when 0.88
m
M
hydrogen peroxide was present in solution compared to when it was absent. This 10-fold
increase in the bioluminescence proved to
Yoo et al. (2007)
that their microbioluminescent
bacteria chip could monitor toxicity.
A single-fractal analysis is adequate to describe the binding and the dissociation kinetics. The
values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal
analysis, and (b) the dissociation rate coefficient,
k
d
, and the fractal dimension,
D
fd
, for the
dissociation phase for a single-fractal analysis are given in
Table 14.2
.
