Biomedical Engineering Reference
In-Depth Information
Antibodies may form fractal clusters on biosensor surfaces. These antibodies or receptors on
the biosensor surface may consist of islands of highly organized or disorganized antibodies.
This is similar to the growth of crystalline structures. It is quite possible that a cooperative
effect may arise due to this tightly organized fractal structures. This is one possibility that
could lead to an increase in the binding rate coefficient with an increase in the fractal dimen-
sion or the degree of heterogeneity on the biosensor surface.
The diffusion-limited binding kinetics of antigen (or antibody or analyte or substrate) in
solution to antibody (or antigen, or receptor, or enzyme) immobilized on a biosensor surface
has been analyzed within a fractal framework (
Sadana and Beelaram, 1994; Sadana et al.,
1995
). One of the findings, for example, is that an increase in the surface roughness or fractal
dimension leads to an increase in the binding rate coefficient. Furthermore, experimental data
presented for the binding of HIV virus (antigen) to the antibody immobilized on a surface
displays characteristic ordered “disorder” (
Anderson, 1993
). This indicates the possibility
of a fractal-like surface.
A biosensor system (wherein either the antigen, antibody, analyte, or substrate is attached
to the surface), along with its different complexities, which include heterogeneities on the
surface and in solution, diffusion-coupled reaction, time-varying adsorption, or binding rate
coefficients, etc
.
, can be characterized as a fractal system.
The diffusion of reactants toward fractal surfaces has been analyzed (
De Gennes, 1982;
Pfeifer et al., 1984a,b; Nyikos and Pajkossy, 1986
).
Havlin (1989)
has briefly reviewed
and discussed these results. The diffusion is in the Euclidean space surrounding the fractal
surface (
Giona, 1992
).
Havlin (1989)
presents an equation that may be utilized to describe
the build-up of the analyte-receptor on a biosensor surface during the binding reaction. The
receptor is immobilized on the biosensor surface. This equation is given below. In all fair-
ness, at the outset, it is appropriate to indicate that the biosensor surface is assumed to be
fractal, or possibly so.
Ideally, it is advisable to provide independent proof or physical evidence for the existence of
fractals in the analysis of analyte-receptor reactions occurring on biosensor surfaces. Also,
and as indicated earlier, if the diffusion effects can be separated from the heterogeneity
effects, then one may better understand the effects of each of these on analyte-receptors
reactions occurring on biosensor surfaces. In general, diffusion effects may be minimized
either by increasing flow rates or by immobilizing fewer receptors on the biosensor surface.
In general, to demonstrate fractal-like behavior log-log plots of distribution of molecules
M
(
r
)
as a function of the radial distance (
r
) from a given molecule are required. This plot should
be close to a straight line. The slope of log
M
(
r
)
versus
log(
r
) plot determines the fractal
dimension. In our case, one could try to obtain a log-log plot of two variables,
k
and
time,
t
and perform a least squares fit in this parameter space to find the slope of the curve.
