Biomedical Engineering Reference
In-Depth Information
300
60
50
250
40
200
30
150
20
100
10
0
50
1.2
1.4
1.6
1.8
2
2.2
2.4
2.5
2.6
2.7 2.8
Fractal dimension,
D
f2
2.9
3
A
B
Fractal dimension,
D
f1
9
8
7
6
5
1.2
1.4
1.6
1.8
2
2.2
C
D
f2
/
D
f1
Figure 11.14
(a) Increase in the binding rate coefficient, k
1
, with an increase in the fractal dimension, D
f1
(b) Increase in the binding rate coefficient, k
2
, with an increase in the fractal dimension, D
f2
(c) 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.
analysis. For the data shown in
Figure 11.14c
the ratio of the binding rate coefficients,
k
2
/
k
1
,
is given by:
1
:
043
0
:
306
k
2
=
k
1
¼ð
4
:
063
0
:
486
Þð
D
f2
=
D
f1
Þ
ð
11
:
7c
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 ratio of binding rate coefficients,
k
2
/
k
1
, exhibits close
to a first (equal to 1.043) order of dependence on the ratio of fractal dimensions,
D
f2
/
D
f1
, that
exists on the sensor chip surface.
Figure 11.15a
and
Tables 11.7
and
11.8
show the increase in the fractal dimension,
D
f1
, with
an increase in the target DNA concentration in solution in the 1-5
m
M range. For the data
shown in
Figure 11.15a
the fractal dimension,
D
f1
, is given by:
0
:
349
0
:
221
D
f1
¼ð
1
:
354
0
:
387
Þ½
target DNA, in
m
M
ð
11
:
7d
Þ
