Biomedical Engineering Reference
In-Depth Information
6
6
4
4
2
2
0
0
0
200
400
600
800
1000
1200
200
400
600
800
1000
1200
0
A
B
Time (s)
Time (s)
4
3
2
1
0
0
200
400
600
800
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1200
C
Time (s)
Figure 9.3
Binding and dissociation of DMR signals mediated by different bradykinin concentrations (in nM)
in solution (Fang et al., 2006): (a) 128 (b) 64 (c) 32 (d) 16. When only a solid line (--) is used then
a single-fractal analysis applies. When both a dashed (- - -) and a solid (--) line are used then the
dashed line represents a single-fractal analysis and the solid line represents a dual-fractal analysis.
Figure 9.3b
shows the binding and the dissociation of 64 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 2.15 from a value of
D
f1
equal to 0.992 to
D
f2
equal to 2.1368, the binding rate coef-
ficient increases by a factor of 1.75 from a value of
k
1
equal to 0.1757 to
k
2
equal to 0.3078.
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.