Biomedical Engineering Reference
In-Depth Information
to 1.3452 leads to an increase in the dissociation rate coefficient by a factor of 75.9 from a
value of
k
d1
equal to 5.2
10
5
to k
d2
equal to 0.04512.
Figure 9.4a
and
Table 9.3
show the increase in the binding rate coefficient,
k
2
, with an
increase in the Bradykinin concentration (in nM) in solution for a dual-fractal analysis. For
the data shown in
Figure 9.4a
, the binding rate coefficient,
k
2
, is given by:
1
:
656
0
:
163
k
2
¼ð
0
:
000302
0
:
000087
Þ½
Bradykinin, nM
ð
9
:
3a
Þ
The fit is very good. Only four data points are available. The availability of more data points
would lead to a stronger fit. For the dual-fractal analysis the binding rate coefficient,
k
2
, exhibits
an order of dependence slightly greater than one and a half (equal to 1.656) order of dependence
on the Bradykinin concentration in the 16-128 nM concentration range in solution. The nonin-
tegral order of dependence exhibited lends support to the fractal nature of the system.
Figure 9.4b
and
Table 9.3
show the increase in the dissociation rate coefficient,
k
d2
, with an
increase in the Bradykinin concentration (in nM) in solution for a dual-fractal analysis. For
the data shown in
Figure 9.4b
, the dissociation rate coefficient,
k
d2
, is given by:
10
5
1
:
758
0
:
412
k
d2
¼ð
8
:
1
1
:
9
Þ
½
Bradykinin, nM
ð
9
:
3b
Þ
The fit is reasonable. Only four data points are available. The availability of more data points
would lead to a better fit. For the dual-fractal analysis the binding rate coefficient,
k
2
, exhibits
an order of dependence between one and a half and two (equal to 1.758) on the Bradykinin
concentration in the 16-128 nM concentration range in solution. The nonintegral order of
dependence exhibited, once again, lends support to the fractal nature of the system.
Figure 9.4c
and
Table 9.3
show the increase in the binding rate coefficient,
k
2
, with an
increase in the fractal dimension,
D
f2
, in the binding phase for a dual-fractal analysis. For
the data shown in
Figure 9.4c
, the binding rate coefficient,
k
2
, is given by:
D
8
:
00
0
:
516
f2
k
2
¼ð
:
:
Þ
ð
:
Þ
0
000694
0
000125
9
3c
The fit is very good. Only four data points are available. The availability of more data points
would lead to a stronger fit. For the dual-fractal analysis the binding rate coefficient,
k
2
,is
very sensitive to the fractal dimension,
D
f2
, or the degree of heterogeneity that exists on
the sensor surface as noted by the eighth order of dependence exhibited.
Figure 9.4d
and
Tables 9.3
and
9.4
show the increase in the dissociation rate coefficient,
k
d2
,
with an increase in the fractal dimension in the dissociation phase,
D
fd2
, for a dual-fractal
analysis. For the data shown in
Figure 9.4d
, the dissociation rate coefficient,
k
d2
, is given by:
D
7
:
24
0
:
352
k
d2
¼ð
0
:
000836
0
:
000125
Þ
ð
9
:
3d
Þ
fd2
