Biomedical Engineering Reference
In-Depth Information
very dilute nature of the analyte (in some of the cases to be presented) or for some other
reasons. Also, in some cases, a dual-fractal analysis may be required to describe the dissoci-
ation kinetics.
4.3 Results
In this chapter we analyze the binding and dissociation (if applicable) kinetics of (a) different
concentrations (in nM) of C
a
in solution to ARC-704 immobilized on a SPR biosensor sur-
face (
Viht et al., 2007
), (b) binding of different concentrations of inorganic phosphate (P
i
)to
a biosensor surface (
Okoh et al., 2006
), and (c) binding of different concentrations (in mU) of
MET-AMC and methionine in solution in a cSPA (
Forbes et al., 2007
).
The fractal analysis will be applied to the different analyte-receptor reactions mentioned
above with the intent of providing a better understanding of these types of reactions along
with obtaining fresh physical insights into them. At the outset it should be indicated 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 defi-
cient in describing the heterogeneity that inherently exists on the surface. It is this heteroge-
neity 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 appro-
priate 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)
indicate that the fractal approach has been applied
to surface science, for example, adsorption and reaction processes. These authors report that
the fractal approach provides a convenient means to represent the different structures and
morphology at the reaction surface. These authors also suggest 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 anal-
ysis 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 defi-
nitely have a large amount of data. It may be useful to compare the fit to some other forms,
such as exponential, or involving saturation, etc. The authors do not present any independent
proof or physical evidence of fractals in the examples presented here. Nevertheless, the
authors still use fractals and the degree of heterogeneity on the biosensor surface to gain
