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
12
:
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 binding curve exhibits convolutions and complexities in its shape due to 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 dissoci-
ation kinetics.
12.3 Results
The fractal analysis will be applied to the binding and dissociation kinetics. In this chapter we
analyze the binding and dissociation kinetics of the binding and dissociation of IgG species to
a porous SiO
2
interferometric biosensor coated with protein A (
Schwartz et al., 2007
), (b)
binding (hybridization) using differential surface plasmon resonance (
Boecker et al., 2007
),
(c) binding of glucose to a One Touch II blood glucose meter and a SERS sensor (
Stuart
et al., 2006
), (d) binding of H9 avian virus to cadmium quantum dots (Yun et al., 2007),
and (e) the binding of sodium ions of Na
0.44
x
MnO
2
to a selective sodium ion sensor
(
Sauvage et al., 2007
).
Schwartz et al. (2007
) recently analyzed the binding kinetics of protein A to immuno-
globulins derived from different species using a porous SiO
2
interferometric biosensor. These
authors emphasize that it is important to develop biosensing methods that are simple to use,
easy to manufacture, are inexpensive, and are portable. Besides, they should readily be
incorporated into high-throughput arrays. They emphasize that porous Si interferometers
meet these requirements, and different authors have used these instruments for label-free
biological sensing (
Starodub et al., 1996; Lin et al., 1997; Dancil et al., 1999; Chan et al.,
2000; Schwartz et al., 2006
). Furthermore,
Schwartz et al. (2007)
indicate that porous Si is
an attractive material for biological sensing due to its compatibility with conventional silicon
microfabrication methods.
Figure 12.1a
shows the binding of 177 nM human IgG to a Protein A-coated porous SiO
2
sur-
face (
Schwartz et al., 2007
). A dual-fractal analysis is required to adequately describe the
binding kinetics. The values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal analysis, and (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal
dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis are given in
Tables 12.1
and
12.2
.
