Biomedical Engineering Reference
In-Depth Information
Surfaces exhibit roughness, or a degree of heterogeneity at some scale. This degree of
heterogeneity on the surface may be due to fracture or erosion. In our case of biosensors,
this may arise due to (a) the inherent roughness of the biosensor surface, or (b) due to
the immobilization or deposition of the receptors on the biosensor surface. The method
of deposition of the receptors on the surface would also lead to different degrees of het-
erogeneity on the surface. The binding reaction takes place between the analyte in solu-
tion and the receptors on the surface through chemical bond formation and subsequent
molecular association. The geometric nature (or parameter) of the surface will significantly
influence these reactions. The influence of surface morphology and structure has been
analyzed (
Lee and Lee, 1994; Chaudhari et al., 2002, 2003
). It would be of interest to
determine the scale of these roughness heterogeneities. Are these at the Angstrom level
or lower? With the current emphasis on nanotechnology and nanobiotechnology these
types of questions are becoming more and more relevant and of significance. The nature
of surfaces in general, and of biosensors in particular (our case), should exhibit a
fractal nature at the molecular level. Furthermore, one of the reasons for the emphasis
on nanotechnology is that as one goes down in scale, the properties of some substances
change, sometimes for the better. It is these beneficial changes that one wishes to
exploit in nanotechnology and nanobiotechnology. Hopefully, similar parallels can
be drawn on analyzing the fractal nature of biosensor surfaces. Do they exhibit self-
similarity; and if they do what are their limits? In other words, what are their lower and
upper bounds?
Furthermore, each binding event need not result in the formation of an analyte-receptor com-
plex on the biosensor surface. All of the receptors on the biosensor surface are presumably
not the results of binding events, and do not exhibit the same activity. In other words, their
active sites should comprise of presumably a probability distribution in “activity.”
In lieu
of any prior information, it is reasonable to assume a bell-shaped Gaussian (or normal)
distribution of active sites on the surface. A probabilistic approach is more realistic here.
Analyses of this sort have presumably not been performed (at least this author is unaware
of them) for analyte-receptor reactions occurring on biosensor surfaces. Thus the fractal anal-
ysis is a convenient method of providing a lumped parameter analysis of analyte-receptor
reactions occurring on biosensor surfaces.
Note that, at present, the dual-fractal analysis does not have a basis at the molecular level.
This represents two different levels of heterogeneity on the biosensor surface. But, in some
of the examples presented, a single-fractal analysis is clearly inadequate to model the data.
Only in these cases does one resort to a dual-fractal analysis. The binding rate coefficients,
k
1
and
k
2
in the dual-fractal analysis have the same units (pg)(mm)
2
(sec)
(
D
f1,bind
3)/2
and
(pg)(mm)
2
(sec)
(
D
f2,bind
3)/2
, respectively, as the association rate coefficient,
k
,
in the
single-fractal analysis.
