Biomedical Engineering Reference
In-Depth Information
It is of interest to note, once again, that as the fractal dimension increases by a factor of 4.375
from a value of
D
f1
equal to 0.458 to
D
f2
equal to 2.004, the binding rate coefficient increases
by a factor of 21.86 from a value of
k
1
equal to 50.75 to
k
2
equal to 1109.57. The changes in
the binding rate coefficient and in the degree of heterogeneity or the fractal dimension on the
biosensor surface are, once again, in the same direction.
þ
þ
Figure 16.2c
shows the binding of 40 nM FAM-SP-2
1mMATP
and 2.50 units of l exonuclease at pH 8.0 to the singly labeled DNA hairpin smart probe
(
Song and Zhao, 2009
). Once again, a dual-fractal analysis is required to adequately
describe the binding kinetics. The values of (a) the binding rate coefficient,
k
,andthe
fractal 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 16.2
.
5.6 nM/s 4T PNK
It is of interest to note, once again, that as the fractal dimension increases by a factor of 3.823
from a value of
D
f1
equal to 0.690 to
D
f2
equal to 2.638, the binding rate coefficient increases
by a factor of 48 from a value of
k
1
equal to 98.96 to
k
2
equal to 4750.65. The changes in the
binding rate coefficient and in the degree of heterogeneity or the fractal dimension on the
biosensor surface are, once again, in the same direction.
Figure 16.3a
and
Table 16.2
show the increase in the binding rate coefficient,
k
1
,with
an increase in the
nuclease units in solution for a dual-fractal analysis. For the data
shown in
Figure 16.3a
the binding rate coefficient,
k
1
,isgivenby:
l
0
:
3494
0
:
2613
k
1
¼ð
64
:
71
12
:
52
Þð
l exonuclease units
Þ
ð
16
:
4a
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The binding rate coefficient,
k
1
, exhibits only a mild
dependence on the
exonuclease units in solution as shown by the close to 0.35 (equal to
0.3494) order of dependence exhibited.
l
Figure 16.3b
and
Table 16.2
show the increase in the binding rate coefficient,
k
2
, with an
increase in the
exonuclease units in solution for a dual-fractal analysis. For the data shown
in
Figure 16.3b
the binding rate coefficient,
k
2
, is given by:
l
2
:
299
0
:
2613
k
2
¼ð
703
:
48
127
:
94
Þð
l
exonuclease units
Þ
ð
16
:
4b
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 binding rate coefficient
k
2
, exhibits an order of depen-
dence between two and two and a half (equal to 2.299) on the
l
exonuclease units in solution.