Biomedical Engineering Reference
In-Depth Information
2.526. The changes in the fractal dimension or the degree of heterogeneity on the sensing
surface and in the binding rate coefficient are in the same direction.
Figure 12.9b
shows the binding and dissociation of 1.2 nM Con A in solution to the gold
nanoparticle biosensor (
Guo et al., 2007
). A dual-fractal analysis is required to adequately
describe the binding kinetics. A single-fractal analysis is adequate to describe the dissociation
kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a
single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis and the dissociation rate coefficient,
k
d
and the fractal
dimension,
D
fd
for a single-fractal analysis are given in
Table 12.5
.
It is of interest to note that as the fractal dimension increases by a factor of 1.696 from a
value of
D
f1
equal to 1.3648
D
f2
equal to 2.3138, the binding rate coefficient increases by
a factor of 2.40 from a value of
k
1
equal to 1.5722 to
k
2
equal to 3.7724. The changes in
the fractal dimension or the degree of heterogeneity on the sensing surface and in the binding
rate coefficient are, once again, in the same direction.
Figure 12.9c
shows the binding and dissociation of 4.8 nM Con A in solution to the
gold nanoparticle biosensor (
Guo et al., 2007
). A dual-fractal analysis is required to ade-
quately describe the binding kinetics. A single-fractal analysis is adequate to describe the
dissociation 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 and the dissociation
rate coefficient,
k
d
and the fractal dimension,
D
fd
for a single-fractal analysis are given in
Table 12.5
.
It is of interest to note that as the fractal dimension increase by a factor of 1.498 from a value
of
D
f1
equal to 1.8150 to
D
f2
equal to 2.7190, the binding rate coefficient increases by a fac-
tor of 3.32 from a value of
k
1
equal to 3.745 to
k
2
equal to 12.439. The changes in the fractal
dimension or the degree of heterogeneity on the sensing surface and in the binding rate coef-
ficient are in the same direction.
Figure 12.10a
and
Table 12.5
show the increase in the binding rate coefficient,
k
1
, with an
increase in the Con A concentration in the 0.1-5.0 nM range for a dual-fractal analysis. For
the data shown in
Figure 12.10a
, the binding rate coefficient,
k
1
, is given by:
0
:
322
0
:
115
k
1
¼ð
1
:
916
0
:
718
Þð
Con A
Þ
ð
12
:
5a
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
1
, exhibits a low (equal to
0.322) order of dependence on the Con A concentration in solution. The fractional order of
dependence exhibited by the binding rate coefficient,
k
1
, on the Con A concentration in solu-
tion lends support to the fractal nature of the system.
