Biomedical Engineering Reference
In-Depth Information
Figure 10.4b
and
Table 10.3
show the increase in the dissociation rate coefficient,
k
d
, with
an increase in the reciprocal temperature,
T
in
K
1
. For the data shown in
Figure 10.4b
,
the dissociation rate coefficient,
k
d
, is given by:
10
56
10
56
T
1
,in
K
1
19
:
79
3
:
31
k
d
¼ð
3
:
8
3
:
1
Þð
Þ
ð
10
:
6b
Þ
There is scatter in the data. This is reflected in the fit and in the error in the binding rate co-
efficient,
k
, value. The dissociation rate coefficient,
k
d
, is very sensitive to the reciprocal tem-
perature,
T
1
, as reflected in the 19.79 order of dependence exhibited. In other words, both
the binding rate coefficient,
k
, as well as the dissociation rate coefficient,
k
d
, are both
extremely sensitive to the presintering temperature. Note that the dissociation rate coefficient,
k
d
, exhibits more that twice the order of dependence (equal to 19.79) on temperature, in
K
than the binding rate coefficient,
k
, in the 673-873
K temperature range.
Figure 10.4c
and
Table 10.3
show the increase in the affinity,
K
(
¼
k
/
k
d
), with an increase in the
reciprocal temperature,
T
in
K
1
.Forthedatashownin
Figure 10.4c
, the affinity,
K
, is given by:
10
29
10
29
T, in
K
9
:
99
4
:
53
K
ð¼
k
=
k
d
Þ¼ð
3
:
3
4
:
3
Þð
Þ
ð
10
:
6c
Þ
There is scatter in the data. This is reflected in the fit and in the error in the affinity value
presented. Only the positive value of the affinity,
K
, is presented since the affinity cannot
have a negative value. The affinity,
K
, is extremely sensitive to the temperature,
T
,as
reflected in the close to the tenth (equal to 9.99) order of dependence exhibited.
Figure 10.5a
and
Table 10.3
show the decrease in the fractal dimension,
D
f
, for a single-
fractal analysis with an increase in the temperature,
T
in
K in the 673-873
K temperature
range. For the data shown in
Figure 10.5a
, the fractal dimension,
D
f
, is given by:
Tin
K
Þ
1
:
931
0
:
382
D
f
¼ð
474, 207
:
8
34, 557
:
5
Þð
ð
10
:
6d
Þ
The fit is good. Only three data points are available. The availability of more data points would
lead to a better fit. The fractal dimension,
D
f
, or the degree of heterogeneity on the biosensor chip
surface is sensitive to presintering temperature as it exhibits close to a second (equal to
1.93)
order of dependence. The binding rate coefficient,
k
, exhibits a decrease with an increase in
temperature in the 673-873
K range. For a 200
K change in the presintering temperature from
873to673
K, the binding rate coefficient,
k
, exhibits a 65.9% increase as it goes from a value of
0.9608 to 1.594, respectively. Note that the fractal dimension,
D
f
, is based on a log scale, and thus
this 65.9% change on changing the presintering temperature from 873 to 673
Krepresentsa
very significant change in the degree of heterogeneity on the biosensor surface.
Figure 10.5b
and
Table 10.3
show the decrease in the fractal dimension in the dissociation
phase,
D
fd
, with an increase in the temperature,
T
in
K in the 673-873
K temperature range.
For the data shown in
Figure 10.5b
, the fractal dimension,
D
fd
, is given by:
