Biomedical Engineering Reference
In-Depth Information
Table 13.7: Fractal dimensions for the binding and dissociation rate coefficients for different
concentrations of rabbit IgG in solution engineered recombinant antibody A10B single chain
variable (ScFv) (
Tang et al., 2006
).
Rabbit Concentration,
Micromole/Antibody
A10B
D
f
D
f1
D
f2
D
fd
1.3
2.758
0.1992
1.8664
0.4990
2.903
0.0136 2.1522
0.0734
0.53
2.3314
0.1434
1.8558
0.4716 2.5784
0.0580 2.1032
0.0442
0.20
2.4164
0.0958
na
na
0.744
0.1226
0.067
2.1882 0.08976
na
na
0.688 0.00326
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 for dissociation
D
fd
for a sin-
gle-fractal analysis are given in
Tables 13.6
and
13.7
.
Figure 13.8c
shows the binding and dissociation of 0.20
m
M rabbit IgG in solution to
engineered recombinant A10B ScFv immobilized on a high-density biosensor. A single-
fractal analysis is adequate to 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,
and (b) the dissociation rate coefficient
k
d
and the fractal dimension for dissociation
D
fd
for a
single-fractal analysis are given in
Tables 13.6
and
13.7
.
Figure 13.8d
shows the binding and dissociation of 0.067
m
M rabbit IgG in solution
to engineered recombinant A10B ScFv immobilized on a high-density biosensor.
Once again, a single-fractal analysis is adequate to describe the binding and the dissocia-
tion kinetics. The values of (a) the binding rate coefficient
k
and the fractal dimension
D
f
for a single-fractal analysis, and (b) the dissociation rate coefficient
k
d
and the
fractal dimension for dissociation
D
fd
for a single-fractal analysis are given in
Tables 13.6
and
13.7
.
Figure 13.9a
and
Table 13.6
show the increase in the dissociation rate coefficient
k
d
with an
increase in the rabbit IgG concentration in solution in the
m
M range. For the data shown in
Figure 13.9a
, the dissociation rate coefficient
k
d
is given by:
1
:
374
0
:
336
k
d
¼ð
1
:
244
þ
1
:
367
Þ½
rabbit IgG concentration,
m
M
ð
13
:
6a
Þ
The fit is reasonable. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The dissociation rate coefficient
k
d
is sensitive to the rabbit
IgG concentration in solution as noted by the order of dependence between the first and one
and a half (equal to 1.374) exhibited.
