Biomedical Engineering Reference
In-Depth Information
Figure 9.5c
shows the depletion (only) binding of 10 nM m
b
CD cholesterol to cyclodextrin
modified HeLa cells cultivated on a gold-coated prism. A single-fractal analysis is adequate
to describe the dissociation (depletion) kinetics. The values of the dissociation (depletion)
rate coefficient,
k
d
, and the fractal dimension
D
fd
, for a single-fractal analysis are given in
Tables 9.5
and
9.6
.
Figure 9.5d
shows the binding and dissociation (depletion) of 10 nM m
b
CD cholesterol
followed by inactive analog of 3 nM of m
b
CD to cyclodextrin modified HeLa cells cultivated
on a gold-coated prism. A dual-fractal analysis is, once again, 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 dissociation rate coefficient,
k
d
, and the fractal
dimension
D
fd
, for a single-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 0.0002 to
D
f2
equal
to 2.1936, the binding rate coefficient increases by a factor of 2.39 from a value of
k
1
equal to
1.3086 to
k
2
equal to 3.1336. Once again, 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 9.5e
shows the binding of 10 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 by a factor of 26.24 from a value of
D
f1
equal to 0.1118 to
D
f2
equal to 2.9347, the
binding rate coefficient increases by a factor of 6.17 from a value of
k
1
equal to 0.6715 to
k
2
equal to 4.1405. 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.
Figure 9.5f
shows the dissociation (depletion only) of 3nM inactive analog of m
b
CD,
a
CD
from the cyclodextrin HeLa cells cultivated on a gold-coated prism to the solution. A dual-
fractal analysis is required to adequately describe the dissociation kinetics. The values of
(a) the dissociation rate coefficient,
k
d
, and the fractal dimension in the dissociation phase,
D
fd
, for a single-fractal analysis, and (b) the dissociation rate coefficients,
k
d1
and
k
d2
, and
the fractal dimensions,
D
fd1
and
D
fd2
, for a dual-fractal analysis are given in
Tables 9.5
and
9.6
. It is of interest to note that for a dual-fractal analysis, as the fractal dimension in
the dissociation phase increases by a factor of 6.572 from a value of
D
fd1
equal to 0.4128
to
D
fd2
equal to 2.7130, the dissociation rate coefficient increases by a factor of 10.03 from
a value of
k
d1
equal to 0.9638 to
k
d2
equal to 9.668. Once again, an increase in the degree of
