Biomedical Engineering Reference
In-Depth Information
Figure 14.10c
shows the binding of the antibody control 10 ng/mL to the STX sensor chip in
a Biacore Q biosensor. A dual-fractal analysis is, once again, required to adequately describe
the binding kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimen-
sion,
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 14.8
.Itisof
interest to note that, once again, that as the fractal dimension increases by a factor of 2.67
from a value of
D
f1
equal to 1.1222 to
D
f2
equal to 3.0 (maximum value), the binding rate
coefficient increases by a factor of 58.02 from a value of
k
1
equal to 5.601 to
k
2
equal to
325. Once again, an increase in the fractal dimension or the degree of heterogeneity on the
biosensor surface leads to an increase in the binding rate coefficient.
Figure 14.11a
and
Table 14.8
show the decrease in the binding rate coefficient,
k
1
, with an
increase in the STX concentration (in ng/mL) in solution for a dual-fractal analysis. For
the data shown in
Figure 14.11a
, the binding rate coefficient,
k
1
, is given by:
k
1
¼ð
7
:
476
2
:
046
Þ½
STX, in ng
=
mL
0
:
0553
0
:
0449
ð
14
:
7a
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to amore reliable fit. The binding rate coefficient,
k
1
, is only very mildly
sensitive to the STX concentration in solution as noted by the negative 0.0553 order of
dependence exhibited on the STX concentration in solution in the 0-10 ng/mL range.
Figure 14.11b
and
Table 14.8
show the decrease in the binding rate coefficient,
k
2
, with an
increase in the STX concentration (in ng/mL) in solution for a dual-fractal analysis. For
the data shown in
Figure 14.11b
, the binding rate coefficient,
k
2
, is given by:
0
:
072
0
:
036
k
2
¼ð
437
:
05
94
:
44
Þ½
STX, in ng
=
mL
ð
14
:
7b
Þ
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to amore reliable fit. The binding rate coefficient,
k
2
, is only very mildly
sensitive to the STX concentration in solution as noted by the negative 0.072 order of depen-
dence exhibited on the STX concentration in solution in the 0-10 ng/mL range.
Figure 14.11c
and
Table 14.8
show the increase in the fractal dimension,
D
f1
, with an
increase in the STX concentration (in ng/mL) in solution for a dual-fractal analysis. For
the data shown in
Figure 14.11c
, the fractal dimension,
D
f1
, is given by:
:
:
0
0194
0
00768
D
f1
¼ð
1
:
0439
0
:
0441
Þ½
STX, in ng
=
mL
ð
14
:
7c
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 fractal dimension,
D
f1
, exhibits close to a
zero (equal to 0.0194) order of dependence on the STX concentration in solution in the
0-10 ng/mL range.
