Biomedical Engineering Reference
In-Depth Information
The fit is very good. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient,
k
d2
, is extremely sensitive
to the degree of heterogeneity or the fractal dimension that exists in the dissociation phase,
D
fd2
, as noted by the order of dependence between seven and seven and a half exhibited.
Figure 9.4e
and
Tables 9.3
and
9.4
show the increase in the affinity,
K
2
(
k
2
/
k
d2
), with an
increase in the ratio of fractal dimensions present in the binding and in the dissociation
phases,
D
f2
/
D
fd2
, for a dual-fractal analysis. For the data shown in
Figure 9.4e
, the affinity,
K
2
is given by:
¼
5
:
41
0
:
513
K
2
ð¼
k
2
=
k
d2
Þ¼ð
1
:
6236
0
:
1802
Þð
D
f2
=
D
fd2
Þ
ð
9
:
3e
Þ
The fit is very good. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The affinity,
K
2
, is extremely sensitive to the ratio of the fractal
dimensions present in the binding and in the dissociation phases, respectively,
D
f2
/
D
fd2
, as noted
by the close to five and five and a half (equal to 5.41) order of dependence exhibited.
Ziblat et al. (2006)
have analyzed the binding and dissociation of m
b
CD cholesterol to HeLa
cells cultivated on a gold-coated prism.
Figure 9.5a
shows the binding of 20 nM m
b
CD cho-
lesterol to cyclodextrin-modified HeLa cells cultivated on a gold-coated prism. A dual-fractal
analysis is required to adequately describe the binding kinetics. A single-fractal analysis is
adequate to 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 binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, and (c) the dis-
sociation rate coefficient,
k
d
, and the fractal dimension
D
fd
, for a single-fractal analysis are
given in
Tables 9.3
and
9.4
. It is of interest to note that as the fractal dimension increases
by a factor of 1.50 from a value of
D
f1
equal to 1.892 to
D
f2
equal to 2.8457, the binding rate
coefficient increases by a factor of 1.83 from a value of
k
1
equal to 2.913 to
k
2
equal to
5.3312. An increase in the degree of heterogeneity or the fractal dimension on the sensor chip
surface leads to an increase in the binding rate coefficient.
Figure 9.5b
shows the binding of 20 nM m
b
CD cholesterol to cyclodextrin modified HeLa
cells cultivated on a gold-coated prism (second cycle of binding). A dual-fractal analysis
is, once again, required to adequately describe the binding 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 9.5
and
9.6
. It is of interest to note that as the fractal
dimension increases from a value of
D
f1
equal to zero to
D
f2
equal to 2.8392, the binding rate
coefficient increases by a factor of 6.253 from a value of
k
1
equal to 1.1117 to
k
2
equal to
6.952. An increase in the degree of heterogeneity or the fractal dimension on the sensor chip
surface, once again, leads to an increase in the binding rate coefficient.
