Biomedical Engineering Reference
In-Depth Information
The fit is reasonable. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The affinity,
K
1
(
¼
k
1
/
k
d
), exhibits close to a negative
one-half (equal to
0.473) order of dependence on the stimulation frequency (in Hz).
Figure 9.8h
and
Tables 9.9
and
9.10
show the increase in the affinity,
K
2
(
k
2
/
k
d
), with an
increase in the fractal dimension ratio,
D
f2
/
D
fd
, for a dual-fractal analysis. For the data shown
in
Figure 9.8h
, the affinity,
K
2
, is given by:
¼
0
:
595
þ
0
:
909
K
2
¼
ð
k
2
=
k
d
Þ ¼
ð
0
:
5581
0
:
1124
Þ
ð
D
f2
=
D
fd
Þ
ð
9
:
5h
Þ
The fit is poor. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The lack of a good fit is clearly reflected in the figure
and in the order of dependence equal to 0.595
0.909 exhibited. Clearly, as the
Figure 9.8h
shows the affinity,
K
2
, increases with the fractal dimension ratio,
D
f2
/
D
fd
. Note that only
the positive error (
þ
0.909) is given in this case to correspond to
Figure 9.8h
.
þ
Figure 9.9a
shows the binding and the dissociation of TN-XL in solution to the sensor chip
surface. The stimulus conditions were AP-frequency 40 Hz for 2.2 s. A single-fractal analysis
is adequate to describe the binding kinetics. A dual-fractal analysis is required to adequately
describe the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and the
fractal dimension,
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
Tables 9.9
and
9.10
.
Figure 9.9b
shows the binding and the dissociation of YC 2.0 in solution to the sensor chip
surface. The stimulus conditions were AP-frequency 40 Hz for 2.2 s. Once again, a single-
fractal analysis is adequate to describe the binding kinetics. A dual-fractal analysis is required
to adequately describe the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis, (b) the dissociation rate coeffi-
cient,
k
d
, and the fractal dimension,
D
fd
, for a single-fractal analysis, and (c) the dissociation
rate coefficients,
k
d1
and
k
d2
, and the fractal dimensions,
D
fd1
and
D
fd2
, for dual-fractal anal-
ysis are given in
Tables 9.9
and
9.10
. It is of interest to note that for the dissociation phase as
the fractal dimension increases by a factor of 9.23 from a value of
D
fd1
equal to 0.254 to
D
fd2
equal to 2.3436 the dissociation rate coefficient increases by a factor of 1.55 from a value of
k
d1
equal to 0.3682 to
k
d2
equal to 0.5697. An increase in the degree of heterogeneity in the
dissociation phase leads to an increase in the dissociation rate coefficient.
Figure 9.9c
shows the binding and the dissociation of GCAMP13.0 in solution to the sensor
chip surface. The stimulus conditions were AP-frequency 40 Hz for 2.2 s. Once again, a
single-fractal analysis is adequate to describe the binding kinetics. A dual-fractal analysis
is required to adequately describe the dissociation kinetics. The values of (a) the binding
rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis, (b) the
