Biomedical Engineering Reference
In-Depth Information
1
1.2
1.18
0.9
1.16
0.8
1.14
1.12
0.7
1.1
0.6
1.08
1.06
0.5
1.04
0.4
1.02
2.86
2.88
2.9
2.92
2.94
2.96
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
A
B
Fractal dimension,
D
f2
Fractal dimension ratio,
D
f2
/
D
f1
Figure 11.2
(a) Decrease in the binding rate coefficient, k
2
, with an increase in the fractal dimension, D
f2
.
Increase in the ratio of the binding rate coefficients, k
2
/k
1
, with an increase in the ratio of fractal
dimensions, D
f2
/D
f1
.
dimension,
D
f2
. For the data shown in
Figure 11.2a
, the binding rate coefficient,
k
2
,is
given by:
k
2
¼½
3
:
6
0
:
8
10
12
D
27
:
46
10
:
45
ð
11
:
4a
Þ
f2
The fit is good. Only four 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 degree of heterogeneity on the biosensor surface or the fractal dimension,
D
f2
, as noted
by the negative order close to twenty seven and a half (equal to
27.46) exhibited.
Figure 11.2b
also shows 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 binding of different targets
(400 nM) in solution to a probe immobilized on a DNA chip surface at 32.5
C and for a
dual-fractal analysis. For the data shown in
Figure 11.2b
, the ratio of the binding rate
coefficients,
k
2
/
k
1
, is given by:
0
:
174
0
:
0656
k
2
=k
1
¼ð
1
:
0094
0
:
0362
ÞðD
f2
=D
f1
Þ
ð
11
:
4b
Þ
The fit is reasonable. Only four data points are available. The availability of more date points
would lead to a more reliable fit. The ratio of the binding rate coefficients,
k
2
/
k
1
, exhibit only
a mild order (equal to 0.174) of dependence on the ratio of the fractal dimensions,
D
f2
/
D
f1
.
Michel et al. (2007
) recently reported that microarrays can readily identify DNA sequences
simultaneously, and are rapidly becoming major tools for pharmacogenomics and clinical
pathology. These authors used an optical method to analyze the DNA surface hybridization.
They noted that DNA surface density is a key parameter in microarray hybridization kinetics.
