Biomedical Engineering Reference
In-Depth Information
In some cases a single-fractal analysis is adequate to describe the binding and dissociation (if
applicable) kinetics (
Corel Quattro Pro 8.0, 1997
). If the regression analysis indicates that the
fit is not adequate (regression coefficient less than 0.95), only then is a dual-fractal analysis
required.
Predictive relations are presented for the different analyte/receptor systems analyzed on the
different biosensor surfaces. For example, (a) for the binding of 177 nM goat IgG in solution
to a protein A-coated surface (
Schwartz et al., 2007
), the binding rate coefficient,
k
1
, exhibits
a negative (
2.486) order of dependence on the fractal dimension,
D
f1
, or the degree of het-
erogeneity that exists on the protein A-coated porous SiO
2
surface. In this case, the binding
rate coefficient,
k
2
, exhibits a 11.45 order of dependence on the fractal dimension,
D
f2
, or the
degree of heterogeneity that exists on the protein A-coated porous SiO
2
surface, (b) for the
binding of Con A in solution to a gold nanoparticle biosensor (
Guo et al., 2007
), and for a
dual-fractal analysis, the binding rate coefficient,
k
1
, exhibits a slight (equal to 0.322) order
of dependence on the Con A concentration in solution and the binding rate coefficient,
k
2
,
also exhibits a slight (equal to 0.382) order of dependence on the Con A concentration in
solution, in the 0.1-5.0 nM concentration range, (c) and the dissociation rate coefficient,
k
d
,
for a single-fractal analysis exhibits a negligible (equal to 0.153) order of dependence on
the Con A concentration in solution in the 0.1-5.0 nM range.
Similar predictive relations are developed for the fractal dimension,
D
f1
, and the fractal
dimension,
D
fd
, as a function of the Con A concentration in solution. The binding rate co-
efficient,
k
1
, exhibits higher than second (equal to 2.204) order of dependence on the fractal
dimension, D
f1
. The binding rate coefficient,
k
2
, exhibits a higher than six and a half (equal to
6.607) order of dependence on the fractal dimension, D
f2
. The binding rate coefficient,
k
2
,as
noted, is more sensitive (by about three times) to the degree of heterogeneity on the surface
than the binding rate coefficient,
k
1
.
The dissociation rate coefficient,
k
d
, is extremely sensitive to the fractal dimension in the dis-
sociation phase,
D
fd
, as noted by the slightly higher than sixteen and a half (equal to 16.54)
order of dependence on
D
fd
. Finally, predictive relations are presented for the affinities,
K
1
and
K
2
, as a function of the Con A concentration in solution.
Only a few (six exactly) examples are presented where the fractal analysis is effective in
describing the binding and dissociation (if applicable) kinetics of different analytes to receptors
on different sensing surfaces. The analysis provides fresh physical insights into the reactions
occurring on these sensing surfaces. The predictive relations are particularly useful since they
provide a means by which the different parameters such as the binding and the dissociation rate
coefficients, and thereby the corresponding affinities may be manipulated in desired directions.
More examples need to be analyzed for the binding of different analytes to different (and
novel) sensing techniques by the fractal analysis method. This would further validate the
