Biomedical Engineering Reference
In-Depth Information
0.4
0.02
0.35
0.3
0.015
0.25
0.01
0.2
0.15
0.1
0.005
0.05
0
0
0
20
40
60
80
100
120
140
2.2
2.3
2.4
2.5
2.6
2.7
2.8
A
B
Fractal dimension,
D
f2
Bradykinin concentration (nM)
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
C
Bradykinin concentration (nM)
Figure 9.2
(a) Increase in the binding rate coefficient, k
1
with an increase in the bradykinin concentration
(in nM) in solution. (b) Increase in the binding rate coefficient, k
2
with an increase in the fractal
dimension, D
f2.
(c) Increase in the affinity, K
2
(k
2
/k
d
) with an increase in the bradykinin
concentration (in nM) in solution.
binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis, (b) the bind-
ing 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 from
a value of
D
f1
equal to zero to
D
f2
equal to 2.4906, the binding rate coefficient increases by a
factor of 552.6 from a value of
k
1
equal to 0.001816 to
k
2
equal to 1.0036. An increase in the
degree of heterogeneity or the fractal dimension on the RWG biosensor surface 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 2.1566 leads to an increase in the dissociation rate coefficient by a factor of 44982 from
a value of
k
d1
equal to 5.6
10
6
to
k
d2
equal to 0.2519.
