Biomedical Engineering Reference
In-Depth Information
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Figure 11.9
Binding (hybridization) of (a) a perfectly matched ODN (ODN-P) and (b) a noncomplementary
ODN (ODN-N) to an electrochemical sensor with a EST2-A34 reporter ( Wang et al., 2007 ). When
a solid line is only used then a single-fractal analysis applies. 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. In
Figure (b) a single- and a triple-fractal analysis is shown.
analysis is required to adequately 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 binding rate 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,
D fd , for a single-fractal analysis are given in Tables 11.4 and 11.5 . It is of interest to note
that for a dual-fractal analysis, as the fractal dimension increases by a factor of 5.766 from
a value of D f1 equal 0.4432 to D f2 equal to 2.556, the binding rate coefficient increases by a
factor of 13.25 from a value of k 1 equal to 2.8403 to k 2 equal to 37.626. Increases in the
degree of heterogeneity or the fractal dimension on the electrochemical biosensor surface
and in the binding rate coefficient are in the same direction.
Figure 11.9b shows the binding of p -aminophenylbutyrate/esterase 2 from Alicyclobacillus
acidocaldarius plus ODN in solution to a site-specific manner ODN-N (mismatch; noncom-
plementary) immobilized on an electrochemical biosensor surface. In this case, a triple-
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,
(b) the binding rate coefficients, k 1 and k 2 , and the fractal dimensions, D f1 and D f2 , for a dual-
fractal analysis, and (c) the binding rate coefficients, k 1 , k 2 , and k 3 , and the fractal dimensions,
D f1 , D f2 and D f3 , for a triple-fractal analysis are given in Tables 11.4 and 11.5 . The binding
kinetics is a bit more complicated in this case (ODN-N; noncomplementary) when compared
to the complementary (ODN-P) case, as for the ODN-N case a triple-fractal analysis is required
to adequately describe the binding kinetics whereas for the complementary (ODN-P) case a
dual-fractal analysis is adequate to describe the binding kinetics. It is of interest to note that
for a triple-fractal analysis, as the fractal dimension increases by a factor of 1.358 from a value
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