Biomedical Engineering Reference
In-Depth Information
the binding rate coefficient increases by a factor of 202.32 from a value of k 1 equal to 0.0215
to k 2 equal to 4.350. Once again, changes in the degree of heterogeneity or the fractal dimen-
sion on the sensing surface and in the binding rate coefficient are in the same direction.
Figure 12.1c shows the binding of 171 nM goat IgG to a Protein A-coated porous SiO 2 sur-
face ( Schwartz et al., 2007 ). A dual-fractal analysis is required to adequately describe the
binding kinetics. The values of (a) the binding rate coefficient, k , and the fractal dimension,
D f , for a single-fractal analysis, and (b) the binding rate coefficients, k 1 and k 2 , and the fractal
dimensions, D f1 and D f2 , for a dual-fractal analysis are given in Tables 12.1 and 12.2 .
Once again, it is of interest to note that for a dual-fractal analysis, as the fractal dimension
increases by a factor of 2.06 from a value of D f1 equal to 0.9260 to D f2 equal to 1.9088,
the binding rate coefficient increases by a factor of 26.58 from a value of k 1 equal to
0.0050 to k 2 equal to 0.1329. Note that, one again, changes in the degree of heterogeneity
or the fractal dimension on the sensing surface and in the binding rate coefficient are in
the same direction.
Figure 12.2a and Table 12.1 show the decrease in the binding rate coefficient, k 1 , with an
increase in the fractal dimension, D f1 , for a dual-fractal analysis. For the data shown in
Figure 12.2a , the binding rate coefficient, k 1 , is given by:
D 2 : 486 2 : 04
k 1 ¼ð 0 : 01241 þ 0 : 03831 Þ
ð 12 : 4a Þ
f1
The fit is reasonable. Only three data points are available. There is scatter in the data, and this
is reflected in the error in the binding rate coefficient. Only the positive error is presented
here since the binding rate coefficient, k 1 , cannot be negative. The binding rate coefficient,
k 1 , is sensitive to the fractal dimension, D f1 , since it exhibits close to a negative two and a
half (equal to 2.486) order of dependence on the fractal dimension, D f1 .
0.1
5
0.08
4
0.06
3
0.04
2
0.02
1
0
0
0.5
0.4
0.6 0.7
Fractal dimension, D f1
0.8
0.9
1
1.1
1.2
1.8
2
2.2
2.4
2.6
2.8
A
B
Figure 12.2
(a) Decrease in the binding rate coefficient, k 1 , with an increase in the fractal dimension, D f1 .
(b) Increase in the binding rate coefficient, k 2 , with an increase in the fractal dimension, D f2 .
Fractal dimension, D f2
Search WWH ::




Custom Search