Biomedical Engineering Reference
In-Depth Information
Table 11.10: Fractal dimensions in the binding and in the dissociation phase for (a) RNA
synthesized on a 42 nM and a 420 nM template (
Blair et al., 2007
).
Template
Concentration (nM)
D
f
D
f1
D
f2
D
fd
420
1.9086 0.04988
1.6862 0.07340
2.2812 0.06678
0.2438 0.1439
42
1.0136
0.04822
na
na
na
Figure 11.16b
shows the binding and dissociation of RNA synthesized on a 42 nM tem-
plate. A single-fractal analysis is adequate to describe the binding kinetics. The values of
the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis
are given in
Tables 11.9
and
11.10
. Note that for the lower 42 nM template concentration
a single-fractal analysis is adequate to describe the binding kinetics, whereas for the higher
420 nM template concentration a dual-fractal analysis is required to adequately describe the
binding kinetics. This would seem to indicate that there is a change in the binding mecha-
nism as one goes from the lower (42 nM template) to the higher (420 nM template)
concentration.
Blair et al. (2007
) analyzed the kinetics of displacement as a function of target concentration.
These authors incubated the pre-hybridized 22-nt FQ (fluorophore quencher) complex with
varying concentrations of the ss DNA target at 37
C for 90 min.
Figure 11.17a
shows the
binding of the 500 nM target ss DNAS (T) in solution in a “broken beacon” assay.
It is of interest to note that as the fractal dimension increases by a factor of 1.352 from a
value of
D
f1
equal to 1.6862 to
D
f2
equal to 2.2812, the binding rate coefficient increases
by a factor of 2.79 from a value of
k
1
equal to 0.1909 to
k
2
equal to 0.5324. The changes
in the binding rate coefficient and in the fractal dimension or the degree of heterogeneity
on the sensor chip surface are in the same direction.
Figure 11.17b
shows the binding of the 250 nM target ss DNA (T) in solution in a “broken
beacon” assay (
Blair et al., 2007
). A dual-fractal analysis is required to adequately describe
the binding kinetics. The values of (a) the binding rate coefficient,
k
, and the 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
Tables 11.11
and
11.12
.
Once again, it is of interest to note that as the fractal dimension increases by a factor of 1.129
from a value of
D
f1
equal to 2.5368 to
D
f2
equal to 2.9659, the binding rate coefficient
increases by a factor of 1.60 from a value of
k
1
equal to 17311.23 to
k
2
equal to 27699.83.
Once again, it is seen that changes in the binding rate coefficient and in the fractal dimension
or the degree of heterogeneity on the sensor chip surface are in the same direction.
