Biomedical Engineering Reference
In-Depth Information
analysis, (b) the dissociation rate coefficient,
k
d
, and the fractal dimension,
D
fd
, for a single-
fractal analysis, and (c) the dissociation rate coefficient,
k
d1
and
k
d2
, and the fractal dimensions
D
fd1
and
D
fd2
, for a dual-fractal analysis are given in
Tables 14.6
and
14.7
.
Figure 14.8e
shows the binding and dissociation of 1 fM SEB in solution to the antibody-
functionalized microbeads on a sensor chip. A single-fractal analysis is adequate to describe
the binding kinetics. A dual-fractal analysis is required 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 dissociation rate coefficient,
k
d
, and the fractal dimension,
D
fd
, for
a single-fractal analysis, and (c) the dissociation rate coefficient,
k
d1
and
k
d2
, and the fractal
dimensions
D
fd1
and
D
fd2
, for a dual-fractal analysis are given in
Tables 14.6
and
14.7
.
Figure 14.9a
and
Tables 14.6
show the increase in the binding rate coefficient,
k
, with an
increase in the SEB concentration (in fM) in solution for a single-fractal analysis. For the
data shown in
Figure 14.9a
, the binding rate coefficient,
k
, is given by:
0
:
1681
0
:
1575
k ¼ð
0
:
00078
þ
0
:
00149
Þ½
SEB, in fM
ð
14
:
6a
Þ
0.004
0.0035
0.25
0.2
0.003
0.0025
0.15
0.002
0.1
0.0015
0.001
0.05
0.0005
0
0
0
2000 4000 6000
SEB concentration, femtomole
8000
10,000
0
200,000 400,000
SEB concentration, femtomole
600,000 800,000 100,0000
A
B
0.25
0.2
0.15
0.1
0.05
0
0
0.2
0.4 0.6
Fractal dimension,
D
fd1
0.8
1
1.2
C
Figure 14.9
(a) Increase in the binding rate coefficient, k, with an increase in the Staphylococcal enterotoxin B (SEB)
concentration in solution (in fM). (b) Increase in the dissociation rate coefficient, k
d
,withan
increase in the Staphylococcal enterotoxin B (SEB) concentration in solution (in fM). (c) Increase in the
dissociation rate coefficient, k
d1
, with an increase in the fractal dimension, D
fd1
.
