Biomedical Engineering Reference
In-Depth Information
Similarly, an increase in the degree of heterogeneity or the fractal dimension on the RWG
biosensor surface in the dissociation phase from a value of
D
d1
equal to zero to
D
fd2
equal
to 2.1960 leads to an increase in the dissociation rate coefficient by a factor of 3312 from
a value of
k
d1
equal to 6.9
10
5
to
k
d2
equal to 0.2285.
Figure 9.3c
shows the binding and the dissociation of 32 nM Bradykinin in solution to
the internalized receptor immobilized on a RWG biosensor surface. Adual-fractal analysis is once
again required to adequately describe the binding and 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 anal-
ysis, (c) the dissociation rate coefficient,
k
d
, and the fractal dimension for the dissociation phase,
D
fd
, for a single-fractal analysis and (d) 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 9.3
and
9.4
.
It is of interest to note that for a dual-fractal analysis as the fractal dimension increases from
a value of
D
f1
equal to 0 to
D
f2
equal to 1.7420, the binding rate coefficient increases by a
factor of 108.8 from a value of
k
1
equal to 0.000643 to
k
2
equal to 0.06998. An increase in
the degree of heterogeneity or the fractal dimension on the RWG biosensor surface, once
again, leads to an increase in the binding rate coefficient.
Similarly, an increase in the degree of heterogeneity or the fractal dimension on the RWG
biosensor surface in the dissociation phase from a value of
D
d1
equal to zero to
D
fd2
equal
to 1.7582 leads to an increase in the dissociation rate coefficient by a factor of 867.7 from
a value of
k
d1
equal to 5.2
10
5
to
k
d2
equal to 0.04512.
Figure 9.3d
shows the binding and the dissociation of 16 nM Bradykinin in solution to the
internalized receptor immobilized on a RWG biosensor surface. A dual-fractal analysis is
once again required to adequately describe the binding and 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, (c) the dissociation rate coefficient,
k
d
, and the fractal dimension
for the dissociation phase,
D
fd
, for a single-fractal analysis and (d) 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 9.3
and
9.4
.
It is of interest to note that for a dual-fractal analysis as the fractal dimension increases by a
factor of 3.10 from a value of
D
f1
equal to 0.5376 to
D
f2
equal to 1.6696, the binding rate
coefficient increases by a factor of 24.2 from a value of
k
1
equal to 0.00148 to
k
2
equal to
0.03584. An increase in the degree of heterogeneity or the fractal dimension on the RWG
biosensor surface, once again, leads to an increase in the binding rate coefficient.
Similarly, an increase in the degree of heterogeneity or the fractal dimension on the RWG
biosensor surface in the dissociation phase from a value of
D
d1
equal to zero to
D
fd2
equal
