Biomedical Engineering Reference
In-Depth Information
For a dual-fractal analysis, it is of interest to note that as the fractal dimension increases by a
factor of 1.92 from a value of
D
f1
equal to 1.3724 to
D
f2
equal to 2.6376, the binding rate
coefficient increases by a factor of 50.40 from a value of
k
1
equal to 0.3445 to
k
2
equal to
17.362. Once again, the changes in the degree of heterogeneity or the fractal dimension on
the sensor surface and in the binding rate coefficient are in the same direction.
Figure 16.7c
shows the binding of 500 pM cy3-labelled target (raw data) to a 20-mer
capture probe immobilized on Area 3 on the microarray biosensor (
Schultz et al.,
2008
). It shows, once again, that a dual-fractal analysis is required to adequately describe
the binding kinetics. The values of (a) the binding rate coefficient,
k
,andthefractal
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 16.5
.
For a dual-fractal analysis, it is of interest to note that as the fractal dimension increases
by a factor of 1.50 from a value of
D
f1
equalto1.6406to
D
f2
equal to 2.4670, the bind-
ing rate coefficient increases by a factor of 13.38 from a value of
k
1
equal to 0.9099 to
k
2
equal to 12.179. Once again, the changes in the degree of heterogeneity or the fractal
dimension on the sensor surface and in the binding rate coefficient are in the same
direction.
Figure 16.8a
and
Table 16.6
show the increase in the binding rate coefficient,
k
1
, with an
increase in the fractal dimension,
D
f1
, for a dual-fractal analysis. For the data shown in
Figure 16.8a
, the binding rate coefficient,
k
1
, is given by:
D
5
:
880
0
:
357
k
1
¼ð
0
:
0506
0
:
0037
Þ
ð
16
:
6
Þ
f1
The fit is good. Only three data points are available. The availability of more data points
would lead to better fit. The binding rate coefficient,
k
1
, is very sensitive to the fractal dimen-
sion,
D
f1
, or the degree of heterogeneity that exists on the microarray biosensor surface as
noted by the order of dependence between five and a half and six (equal to 5.880) exhibited.
Figure 16.8b
and
Table 16.6
show the increase in the binding rate coefficient,
k
2
, with an
increase in the fractal dimension,
D
f2
, for a dual-fractal analysis. For the data shown in
Figure 16.8b
, the binding rate coefficient,
k
2
, is given by:
D
10
:
303
3
:
933
k
2
¼ð
0
:
000869
0
:
000305
Þ
ð
16
:
7
Þ
f2
The fit is good. Only three data points are available. The availability of more data points
would lead to better fit. The binding rate coefficient,
k
2
, is extremely sensitive to the fractal
dimension,
D
f2
, or the degree of heterogeneity that exists on the microarray biosensor surface
as noted by the order of dependence between 10 and 10 and one-half (equal to 10.303)
exhibited.
