Biomedical Engineering Reference
In-Depth Information
due to other reasons, such as nonspecific binding, inherent irregularities on the sensing
surface, mixture of receptors on the surface, and mixture of analytes in solution which
includes the analyte of interest.
Two factors need to be addressed while analyzing the analyte-receptor binding and dissocia-
tion kinetics. The system by its design is heterogeneous. For example, as indicated above,
the receptors immobilized on the biosensor surface may exhibit some heterogeneity, that
is, surface roughness. No matter how careful one is in immobilizing the receptors on the
biosensor surface, there will be some degree of heterogeneity on the surface.
Henke et al. (2002)
have used the atomic force microscopy (AFM) technique to determine
the effects of cleaning fused silica and glass on surface roughness. This is for biosensor
use. Note that prior to the immobilization of receptors on the surface, the surface needs to
be cleaned to remove contaminants, and to create surface attachment sites for example, for
hydroxyl groups. For the analyte-receptor binding (and dissociation) to take place the analyte,
by the diffusion process, must come within the “proximity” of the active site on the receptor.
Mass transport limitations may be minimized or eliminated if the system is either properly
designed or properly operated or both. In most cases, however, both diffusional effects and
heterogeneity aspects will be present in biosensor systems, and their influence on binding
and dissociation kinetics need to be determined. Ideally, one would like to determine the
influence of each of these separately on the binding and dissociation kinetics. In the theoreti-
cal analysis to be presented below (the
Havlin, 1989
, analysis) the effects of diffusion and of
heterogeneity are presented coupled together. One possible way of accounting for the pres-
ence of diffusional limitations and the heterogeneity that exists on the surface is by using
fractals. Ideally, and as indicated above, one would prefer to decouple the influence of diffu-
sion and heterogeneity. Presumably, an approach other than fractal analysis is required to
decouple these two effects.
A characteristic feature of fractals is self-similarity at different levels of the scale. Fractals
exhibit dilatational symmetry. Fractals are disordered systems, and the disorder is described
by nonintegral dimensions (
Pfeifer and Obert, 1989
). Fractals have nonintegral dimensions,
and are smaller than the dimension they are embedded in. In other words, the highest value
that a fractal can have is three. In our case, an increase in the degree of heterogeneity on the
biosensor surface would lead to an increase in the value of the fractal dimension. Another
way of looking at the fractal dimension is its “space filling” capacity. The more the space
a surface fills, the higher is its fractal dimension. The fractal dimension cannot have a nega-
tive value, and very low values of the fractal dimension on the surface indicate that the
surface exists as a Cantor like dust.
Kopelman (1988)
points out that surface diffusion-controlled reactions that occur on clusters
or islands are expected to exhibit anomalous and fractal-like kinetics. These kinetics exhibit
anomalous reaction orders and time-dependent (e.g., binding) rate coefficients. As long as
