Modeling and Theory - Biosensors and Biosensor Kinetics - page 23

value of the fractal dimension, since the system is embedded in a three-dimensional system.
k and k bind , and D f , and D f,bind are used interchangeably in this chapter and in the topic.

It should be noted that different laboratories use different technologies or different experi-
mental designs to analyze the binding affinity of ligands to target proteins (or analytes) of
interest (or to determine the rate coefficients for association and dissociation kinetics for
binding). The comparison of data between different technologies and experimental designs
and conclusions thereof should be made with great caution. The fractal analysis is of value
in that it provides the pros and cons of different in vitro technologies (or more precisely,
in this case, analysis procedures). It makes the user of the technology aware of the quality
of data generated and what can be done to improve the analysis.

One might very reasonably question the utility of the approach, considering the different
dimensions, and subsequently the units one may obtain even for the same interactions. It
would be difficult to compare this technique with other approaches for different interactions.
Nevertheless, the inclusion of the surface effects is essential, albeit difficult. This is espe-
cially true, if the rate coefficients for association and dissociation for binding are very signif-
icantly dependent on the nature of the surface. Unless a simpler alternative approach that
includes the surface effects is suggested, it is reasonable, for now, to follow this approach.
Hopefully, modifications to this approach may be suggested that permit comparison for
different interactions as well as with other approaches.

It would be useful to specify the carrier of fractal properties. It could either be the analyte
surface, the receptor surface, or the immobilizing (in our case, the biosensor) surface. There
is a considerable body of work on fractal surface properties of proteins ( Li et al., 1990;
Dewey and Bann, 1992; Le Brecque, 1992; Federov et al., 1999 ). Le Brecque (1992) points
out that the active sites (in our case, the receptors on the biosensor surface) may themselves
form a fractal surface. Furthermore, the inclusion of nonspecific association sites on the
surface would increase the degree of heterogeneity on the surface, thereby leading to an
increase in the fractal dimension of the surface. At present, we are unable to specify what
the carrier of the fractal properties is. This is exacerbated by our reanalysis of kinetic data
available in the literature. Presumably, it is due to a composite of some or all of the factors
mentioned above. No evidence of fractality is presented.

Dissociation Rate Coefficient

The diffusion of the dissociated particle (receptor or analyte) from the solid surface (e.g.,
analyte-receptor complex coated surface) into the solution may be given as a first approxi-
mation by:

ð Analyte Receptor Þt ð 3 D f , diss Þ= 2
¼

ð 2 : 5b Þ

k diss t ð 3 D f , diss Þ= 2 ,

t > t diss