Biomedical Engineering Reference
In-Depth Information
9.3 Results
The fractal analysis will be applied to the binding and dissociation of bradykinin con-
centrations (in nM) in solution to bradykinin B
2
receptors immobilized on a RWG biosensor
(
Fang et al., 2006
), binding and dissociation of 20 nM m
b
CD-cholesterol cells exposed to
two cycles of cholesterol enrichment (
Ziblat et al., 2006
), and to the binding and dissociation
on a calcium
รพ
FRET-based calcium biosensor employing troponin C (
Mank et al., 2006
).
At the outset it should be pointed out that alternative expressions for fitting the binding and
dissociation data are available that include saturation, first-order reaction, and no diffusional
limitations, but these expressions are deficient in describing the heterogeneity that inherently
exists on the surface. It is this heterogeneity on the biosensor surface that one is attempting to
relate to the different biosensor performance parameters. More specifically the question we
wish to answer is how may one change the heterogeneity or the fractal dimension,
D
f
on
the biosensor chip surface in order that one may be able to enhance the different biosensor
performance parameters.
Other modeling attempts also need to be mentioned. One might justifiably argue that
appropriate modeling may be achieved by using a Langmuirian or other approach. The
Langmuirian approach may be used to model the data presented if one assumes the presence
of discrete classes of sites, for example double exponential analysis as compared with the
single-fractal analysis.
Lee and Lee (1995)
report that the fractal approach has been applied
to surface science, for example, adsorption and reaction processes. These authors point out
that the fractal approach provides a convenient means to represent the different structures
and the morphology at the reaction surface. They also draw attention to using the fractal
approach to develop optimal structures and as a predictive approach. Another advantage of
the fractal technique is that the analyte-receptor association is a complex reaction, and the
fractal analysis via the fractal dimension and the rate coefficient provide a useful lumped
parameter analysis of the diffusion-limited reaction occurring on a heterogeneous surface.
In a classical situation, to demonstrate fractality, one should make a log-log plot, and one
should definitely have a large amount of data. It may be useful to compare the fit to some other
forms, such as exponential form, or one involving saturation, etc. At present, no independent
proof or physical evidence of fractals in the examples is presented. Nevertheless, fractals
and the degree of heterogeneity on the biosensor surface are still used to gain insights into
enhancing the different biosensor performance parameters. The fractal approach is a conve-
nient means (since it is a lumped parameter) to make the degree of heterogeneity that exists
on the surface more quantitative. Thus, there is some arbitrariness in the fractal approach to
be presented. The fractal approach provides additional information about interactions that
may not be obtained by a conventional analysis of biosensor data. In this chapter as mentioned
above, an attempt is made to relate the fractal dimension,
D
f
, or the degree of heterogeneity on
