Biomedical Engineering Reference
In-Depth Information
The fit is poor. 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 coefficient,
k
2
, exhibits a very high (equal to 6.607) order of dependence on the fractal dimension,
D
f2
,
or the degree of heterogeneity that exists on the biosensor surface.
Figure 12.10h
shows the increase in the dissociation rate coefficient,
k
d
, with an increase in
the fractal dimension for dissociation,
D
fd
. For the data shown in
Figure 12.10h
, the dissoci-
ation rate coefficient,
k
d
, is given by:
10
05
10
05
D
16
:
54
15
:
19
k
d
¼ð
1
:
4
0
:
6
Þ
ð
12
:
5h
Þ
fd
The fit is poor. 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
, is extremely sensitive
to the fractal dimension in the dissociation phase,
D
fd
, noted by the very slightly greater than
sixteen and a half (equal to 16.54) order of dependence exhibited on the fractal dimension in
the dissociation phase,
D
fd
.
Figure 12.10i
shows the decrease in the ratio of the fractal dimensions,
D
f2
/
D
f1
, with an
increase in the Con A concentration in solution in the 1-5 nM concentration range for a
dual-fractal analysis. For the data shown in
Figure 12.10i
, the ratio of the fractal dimensions,
D
f2
/
D
f1
, is given by:
D
f1
¼ð
1
:
815
0
:
099
Þ½
Con A
0
:
139
0
:
0191
D
f2
=
ð
12
:
5i
Þ
The fit is good. Only three data points are available. The availability more data points would
lead to a more reliable fit. The ratio of the fractal dimensions,
D
f2
/
D
f1
, exhibits a slight nega-
tive order (equal to
0.139) of dependence on the Con A concentration in solution.
Figure 12.10j
shows the increase in the ratio of the fractal dimensions,
D
f1
/
D
fd
,withanincrease
in the Con A concentration in solution in the 1-5 nM concentration range for a dual-fractal anal-
ysis. For the data shown in
Figure 12.10j
, the ratio of the fractal dimensions,
D
f1
/
D
fd
,isgivenby:
0
:
142
0
:
0221
D
f1
=
D
fd
¼ð
:
:
Þ½
ð
:
Þ
0
768
0
048
Con A
12
5j
The fit is good. Only three data points are available. The availability more data points would
lead to a more reliable fit. The ratio of the fractal dimensions,
D
f1
/
D
fd
, exhibits a slight order
(equal to 0.142) of dependence on the Con A concentration in solution.
Figure 12.10k
shows the increase in the affinity,
K
1
(
¼
k
1
/
k
d
), with an increase in the ratio of
the fractal dimensions,
D
f1
/
D
fd
,
for a dual-fractal analysis. For
the data shown in
Figure 12.10k
, the ratio of the affinity,
K
1
, is given by:
1
:
17
0
:
074
K
1
¼ð
9
:
907
0
:
296
Þ½
D
f1
=
D
fd
ð
12
:
5k
Þ
