Biomedical Engineering Reference
In-Depth Information
In this case,
the product
(antibody-antigen; or analyte-receptor complex, Ab
Ag or
analyte
receptor) is given by:
<
t
ð
3
D
f1
,
bind
Þ=
2
¼ t
p
1
,
t < t
1
t
ð
3
D
f2
,
bind
Þ=
2
ð
Ab
Ag
Þ
t
p
2
,
ð
13
:
3
Þ
¼
t
1
<
t
<
t
2
¼
t
c
:
t
1
=
2
,
t
>
t
c
In some cases, as mentioned above, a triple-fractal analysis with six parameters (
k
1
,
k
2
,
k
3
,
D
f1
,
D
f2
, and
D
f3
) may be required to adequately model the binding kinetics. This is when the bind-
ing curve exhibits convolutions and complexities in its shape due perhaps to the 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 dissociation kinetics.
13.3 Results
A fractal analysis is applied to the binding and dissociation (if applicable) kinetics of different
analyte-receptor reactions occurring on different biosensor surfaces. Understandably, alternate
expressions for fitting the data that include saturation, first-order reaction, and no diffusion
limitations are available, but these expressions are apparently deficient in describing the
heterogeneity that inherently exists on the surface. Another advantage of this technique is that
the analyte-receptor binding (as well as the dissociation reaction) is a complex reaction, and
the fractal analysis via the fractal dimension and the rate coefficient provide a useful lumped
parameter(s) analysis of the diffusion-limited reaction occurring on a heterogeneous surface.
In the classical situation to demonstrate fractality, one should make a log-log plot, and one
should definitely have a large amount of data. It may be useful to compare the fit to some other
forms, such as an exponential form or one involving saturation. At present, we do not present
any independent proof or physical evidence of fractals in the examples presented. It is a conve-
nient means (since it provides a lumped parameter) to make the degree of heterogeneity that
exists on the surface more quantitative. Thus, there is some arbitrariness in the fractal model
to be presented. One might justifiably argue that appropriate modeling may be achieved by
using a Langmuirian or other approach. The Langmuirian approach has a major drawback
because it does not allow for or accommodate the heterogeneity that exists on the surface.
Wang et al. (2007)
have reported that the detection of DNA and RNA sequences is becoming
important for the diagnosis of diseases (
Nebling et al., 2004
), and for the detection of patho-
genic organisms in samples from the environment (
Baeumner et al., 2003
), food (
Ko and
Grant, 2006
), and clinical (
Mitterer et al., 2004
) areas.
Baeumner et al. (2004)
have noted that
nucleic acid sequences unique to a particular organism may be used to discriminate one self-
replicating organism from another.
Wang (2000)
reports that as the demand for faster, sim-
pler, and cheaper methods for obtaining sequence-specific information increases, increasing
emphasis is being placed on nucleic acid-based biosensors.
