Biomedical Engineering Reference
In-Depth Information
2.5
1.2
1
2
0.8
1.5
0.6
1
0.4
0.5
0.2
0
0
500
1000
Time (s)
1500
2000
2500
0
500
1000
1500
2000
0
A
B
Time (s)
Figure 16.13
Binding of 50 nM complementary oligonucleotide and one base mismatch to the molecular
beacon (MB) (
Li et al., 2001
): (a) Complementary oligonucleotide, (b) one base
mismatch oligonucleotide. When only a solid line (--) is used then a single-fractal analysis applies.
When both a dashed (- - -) and a solid (--) line are used then the dashed line represents a
single-fractal analysis and the solid line represents a dual-fractal analysis.
coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis are
given in
Table 16.10
and
Table 16.11
.
It is of interest to note that as the fractal dimension increases by a factor of 9.08 from a value
of
D
f1
equal to 0.268 to
D
f2
equal to 2.4330, the binding rate coefficient increases by a factor
of 524.4 from a value of
k
1
equal to 0.00017 to
k
2
equal to 0.08915. The changes in the
degree of heterogeneity or the fractal dimension on the biosensor surface and in the binding
rate coefficient are in the same direction.
Figure 16.14
and
Tables 16.10
and
16.11
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 16.14
, the binding rate coefficient,
k
2
, is given by:
10
7
10
7
D
14
:
92
4
:
08
k
2
¼ð
2
:
6
1
:
5
Þ
ð
16
:
10
Þ
f2
The fit is not good. There is scatter in the data. Only four data points are available. The avail-
ability of more data points would lead to a more reliable fit. Note that owing to the lack of
data points, all the data presented until now are presented together:(a) complementary target
binding to the MB immobilized using streptavidin-biotin on a biosensor, (b) complementary
target binding to immobilized MB using BSA-streptavidin-biotin on a biosensor, (c) comple-
mentary target binding to immobilized MB using BSA-streptavidin-biotin on a biosensor
(repeat), and (d) one base mismatch target binding to immobilized MB using BSA-
streptavidin-biotin on a biosensor. Nevertheless, it is of interest to note that the binding rate
coefficient,
k
2
, is extremely sensitive to the fractal dimension,
D
f2
, or the degree of heteroge-
neity that exists on the biosensor surface as noted by the close to fifteenth (equal to 14.92)
order of dependence exhibited.
