Biomedical Engineering Reference
In-Depth Information
Table 4.6: Binding rate coefficients and fractal dimensions for the binding of different
concentrations (0.01-0.05 mU) of (a) methionine-T-amido-4-methylcoumarin (MET-AMC) and
(b) methionine in an aaRS (aminoacyl-tRNA synthetase) competitive scintillation proximity assay
(cSPA) (
Forbes et al.,2007
)
.
Analyte concentration, mU
Binding rate coefficient, k
Fractal dimension, D
f
(a) MET-AMC, 0.05
66.248
2.767
1.4522
0.05528
MET-AMC, 0.025
26.008
2.751
1.2260
0.1357
MET-AMC, 0.01
10.644
0.255
1.1422
0.3206
(b) Methionine, 0.05
44.50
3.44
1.2268
0.100
Methionine, 0.025
7.393
1.264
1.2181
0.1151
Methionine, 0.01
7.230 1.1812
1.2512 0.1572
Figure 4.8a
and
Table 4.6
show for a single-fractal analysis the increase in the binding rate
coefficient,
k
, with an increase in the MET-AMC concentration in solution in the 0.01-0.05
mU range. For the data shown in
Figure 4.8a
, the binding rate coefficient,
k
, is given by:
1
:
127
0
:
105
k
¼ð
1836
:
93
234
:
39
Þ½
MET
AMC
ð
4
:
7a
Þ
The fit is good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The binding rate coefficient,
k
, exhibits an order of depen-
dence between first and one and a half (equal to 1.127) on the MET-AMC concentration in
solution in the 0.01-0.05 mU concentration range. The nonintegral order of dependence
exhibited by the binding rate coefficient,
k
, on the MET-AMC concentration in solution in
the 0.01-0.05 mU range lends support to the fractal nature of the system.
Figure 4.8b
and
Table 4.6
show the increase in the binding rate coefficient,
k
, with an
increase in the fractal dimension,
D
f
, for the MET-AMC concentration in solution in the
0.01-0.05 mU range, for a single-fractal analysis. For the data shown in
Figure 4.8b
, the bind-
ing rate coefficient,
k
, is given by:
D
7
:
232
1
:
613
k
¼ð
4
:
764
1
:
548
Þ
ð
4
:
7b
Þ
f
The fit is very good. Only three data points are available. The availability of more data
points would lead to a more reliable fit. The binding rate coefficient,
k
, is very sensitive to
the fractal dimension,
D
f
, or the degree of heterogeneity that exists on the biosensor
chip surface as noted by the greater than seven (equal to 7.232) order of dependence exhibited.
Figure 4.8c
and
Table 4.6
show the increase in the fractal dimension,
D
f
, with an increase
in the MET-AMC concentration in solution in the 0.01-0.05 mU range for a single-fractal
analysis. For the data shown in
Figure 4.8c
, the fractal dimension,
D
f
, is given by:
0
:
1454
0
:
04698
D
f
¼ð
2
:
190
0
:
120
Þ½
MET
AMC
ð
4
:
7c
Þ
