Biomedical Engineering Reference
In-Depth Information
0
:
153
0
:
099
k
d
¼ð
:
:
Þð
Þ
ð
:
Þ
0
264
0
083
Con A
12
5c
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The dissociation rate coefficient,
k
d
, exhibits a
very low (equal to 0.153) order of dependence on the Con A concentration in solution.
The fractional order of dependence exhibited by the dissociation rate coefficient,
k
d
, on the
Con A concentration in solution lends support to the fractal nature of the system.
Figure 12.10d
and
Table 12.5
show the increase in the fractal dimension,
D
f1
, 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 12.10d
, the fractal dimension,
D
f1
, is given by:
0
:
151
0
:
021
D
f1
¼ð
1
:
391
0
:
083
Þð
Con A
Þ
ð
12
:
5d
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 fractal dimension,
D
f1
, exhibits a very low (equal to
0.151) order of dependence on the Con A concentration in solution.
Figure 12.10e
and
Table 12.5
show the increase in the fractal dimension,
D
fd
, with an
increase in the Con A concentration in the 0.1-5.0 nM range. For the data shown in
Figure 12.10e
, the fractal dimension,
D
fd
, is given by:
0
:
0077
0
:
0012
D
fd
¼ð
1
:
811
0
:
0063
Þð
Con A
Þ
ð
12
:
5e
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 fractal dimension for dissociation,
D
fd
, exhibits a very
low (equal to 0.0077) order of dependence on the Con A concentration in solution.
Figure 12.10f
and
Table 12.5
show the increase in the binding rate coefficient,
k
1
, with an
increase in the fractal dimension,
D
f1
, for a dual-fractal analysis. For the data shown in
Figure 12.10f
the binding rate coefficient,
k
1
, is given by:
k
1
¼ð
0
:
927
0
:
197
ÞD
2
:
204
0
:
458
ð
12
:
5f
Þ
f1
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. For a dual-fractal analysis the binding rate coeffi-
cient,
k
1
, exhibits a slightly higher than second (equal to 2.204) order of dependence on
the fractal dimension,
D
f1
, or the degree of heterogeneity that exists on the biosensor surface.
Figure 12.10g
and
Table 12.5
show the increase in the binding rate coefficient,
k
2
, with an
increase in the fractal dimension,
D
f2
, for a dual-fractal analysis. For the data shown in
Figure 12.10g
the binding rate coefficient,
k
2
, is given by:
D
6
:
607
þ
7
:
80
f2
k
2
¼ð
0
:
0109
þ
0
:
0158
Þ
ð
12
:
5g
Þ