Biomedical Engineering Reference
In-Depth Information
However, a dual-fractal analysis is required to adequately 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 dissociation rate coefficient
k
d
and the fractal dimension for dissoci-
ation
D
fd
for a single-fractal analysis, and (c) the dissociation rate coefficients
k
d1
and
k
d2
and the fractal dimensions
D
fd1
and
D
fd2
for a dual-fractal analysis are given in
Tables 13.3
and
13.4
.
It is of interest to note that as the fractal dimension increases by a factor of 4.91 from a value
of
D
fd1
equal to 0.594 to
D
fd2
equal to 2.9172, the dissociation rate coefficient increases by a
factor of 26.94 from a value of
k
d1
equal to 0.00546 to
k
d2
equal to 0.1471. Note that changes
in the fractal dimension or the degree of heterogeneity on the sensing surface and in the
dissociation rate coefficient are in the same direction.
Figure 13.3f
shows the binding and dissociation of 25.0
m
g/L of TNT in the aqueous environment
to anti-TNT mAb by a highly sensitive TNT immunosensor with a prototype fluorescence-
based detection system (KinExA Inline Biosensor, Sappidyne Instrument, Inc.;
Bromage
et al., 2007
). In this case, a single-fractal analysis is adequate to describe the binding kinetics.
Once again, a dual-fractal analysis is required to adequately describe the dissociation kinet-
ics. The values of (a) the binding rate coefficient
k
and the fractal dimension
D
f
for a
single-fractal analysis, (b) the dissociation rate coefficient
k
d
and the fractal dimension for
dissociation
D
fd
for a single-fractal analysis, and (c) the dissociation rate coefficients
k
d1
and
k
d2
and the fractal dimensions
D
fd1
and
D
fd2
for a dual-fractal analysis are given in
Tables 13.3
and
13.4
.
Tables 13.3
and
13.4
and
Figure 13.4a
show the increase in the binding rate coefficient
k
with
an increase in the fractal dimension
D
f
for a single-fractal analysis. For the data shown in
Figure 13.4a
, the binding rate coefficient
k
is given by:
D
0
:
492
0
:
147
k
¼ð
0
:
0242
0
:
0032
Þ
ð
13
:
4a
Þ
f
The fit is reasonable. Only six data points are available. The availability of more data points
would lead to a more reliable fit. The binding rate coefficient
k
is only mildly sensitive to the
fractal dimension
D
f
or the degree of heterogeneity that exists on the sensing surface as noted
by the slightly less than one-half (equal to 0.492) order of dependence exhibited.
Tables 13.3
and
13.4
and
Figure 13.4b
show the increase in the dissociation rate coefficient
k
d
with an increase in the fractal dimension
D
fd
for a single-fractal analysis. For the data
shown in
Figure 13.4b
, the dissociation rate coefficient
k
d
is given by:
D
4
:
65
2
:
17
fd
k
d
¼ð
:
:
Þ
ð
:
Þ
0
000914
0
000343
13
4b
The fit is reasonable. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient
k
d
is very sensitive to the
