Biomedical Engineering Reference
In-Depth Information
The fit is poor. This is reflected in the estimates of the error provided. There is scatter in the
data. Only four data points are available. The availability of more data points would lead to a
more reliable and better fit. The dissociation rate coefficient
k
d
for a single-fractal analysis is
extremely sensitive (just like the binding rate coefficient
k
) to the fractal dimension
D
fd
or the
degree of heterogeneity that exists on the aptamer-SA chip surface as it exhibits an order of
dependence slightly higher than seven and a half (equal to 7.56) on the fractal dimension
D
fd
.
Figure 15.10e
and
Table 15.6
show the increase in the fractal dimension
D
f
for a single-fractal
analysis with an increase in the thrombin concentration in solution in the 16-130 nM concentra-
tion range. For the data shown in Figure 15.10e, the fractal dimension
D
f
is given by:
0
:
112
0
:
022
D
f
¼ð
:
:
Þ½
ð
:
Þ
1
589
0
064
thrombin concentration, in nM
15
5e
The fit is good. Only four data points are available. The availability of more data points
would lead to a more reliable and better fit. The fractal dimension
D
f
exhibits a very slight
dependence on the thrombin concentration in solution in the 16-130 nM concentration range
as it exhibits a close to zero (equal to 0.112) order of dependence on the thrombin concentra-
tion in solution.
Figure 15.10f
and
Table 15.6
show the increase in the affinity,
K
(
k
/
k
d
) with an increase in
the ratio of the fractal dimensions,
D
f
/
D
fd
. For the data shown in
Figure 15.10f
, the affinity
K
is given by:
¼
6
:
33
0
:
658
K
¼ð
1
:
367
0
:
205
Þð
D
f
=
D
fd
Þ
ð
15
:
5f
Þ
The fit is very good. Only four data points are available. The availability of more data points
would lead to a more reliable and better fit. The affinity
K
is extremely sensitive to the ratio
of the fractal dimensions as noted by the order of dependence between six and six and a half
(equal to 6.33) exhibited.
15.4 Conclusions
A fractal analysis is presented for the binding and the dissociation (if applicable) kinetics
of protein biomarkers and other medically-oriented analytes on biosensor surfaces. Both a
single- and a dual-fractal analysis were utilized to model the binding and the dissociation
kinetics. The dual-fractal analysis was used only when the single-fractal analysis did not pro-
vide an adequate fit. Corel Quattro Pro 8.0 was used to provide the regression analysis.
The examples analyzed include the following: the binding of CEA (
Gao et al., 2009
), (b) the
binding of TNF-
a
using poly(guanine) functionalized silica nanoparticles (
Wang et al.,
2006
), (c) binding of 400 ppm IgG antithrombin in solution to immobilized biotinylated
thrombin, and binding of 200 nM thrombin in solution to immobilized biotinylated aptamer
