Biomedical Engineering Reference
In-Depth Information
surface as noted by the slightly less than negative eleven and a half (equal to
11.45) order
of dependence exhibited.
Figure 11.18e
and
Tables 11.11 and 11.12
show the increase in the ratio of the binding rate
coefficients,
k
2
/
k
1
, with an increase in the ratio of the fractal dimensions,
D
f2
/
D
f1
. For the
data shown in
Figure 11.18e
the ratio of the binding rate coefficients,
k
2
/
k
1
, is given by:
D
f1
7
:
17
1
:
93
k
2
=
k
1
¼ð
0
:
653
0
:
019
Þ
D
f2
=
ð
11
:
8e
Þ
The fit is good. Only three data points are available. The availability of more data points
would lead to a more reliable fit. The ratio of the binding rate coefficients,
k
2
/
k
1
, is very sen-
sitive to the ratio of fractal dimensions,
D
f2
/
D
f1
, as noted by the order of dependence between
seven and seven and a half (equal to 7.17) exhibited.
11.4 Conclusions
A fractal analysis is presented for the binding and dissociation of different analytes on arrays/
microarrays/DNA chips. The analysis of both the binding as well as the dissociation (wher-
ever applicable) provides a more complete picture of the reaction occurring on the sensor
chip surface, besides providing for values of the affinities wherever applicable. This is the
ratio of the rate coefficients in the binding and in the dissociation steps. The fractal analysis pro-
vides values of the binding rate coefficient,
k
, and the degree of heterogeneity made quantitative
by the fractal dimension,
D
f
, on the sensor chip surface. The fractal analysis is applied to
(a) the binding and dissociation (hybridization) of different targets (400 nM) in solution to a
probe immobilized on a DNA chip surface (
Fiche et al., 2007
), (b) binding (hybridization) of
different concentrations (in nM) of free-DNA in solution to a 22-mer strand (bound DNA)
immobilized via a phenylene-diisocyanate linker molecule on a glass substrate (
Michel et al.,
2007
), (c) binding (hybridization) of SA-HRP in solution to a capture probe on a QCM electrode
along with a detecttion probe (
Feng et al., 2007
), (d) binding (hybridization) of a complementary
and a noncomplementary (three-base mismatch strand) DNA in solution to a 30-mer 3
0
-thiolated
DNA strand immobilized on an electrochemical enzymatic genosensor (
Abad-Valle et al., 2007a,b
),
(e) binding (hybridization) of (i) a ODN-P and (ii) a noncomplementary ODN (ODN-N) to
an electrochemical sensor with a EST2-A34 reporter (
Wang et al., 2007
), (f) binding and
dissociation during PNA-DNA hybridization—binding of different concentrations (in
m
M)
of target DNA complementary to CYP2C9*2 (target DNA2) to CYP2C9*2 as a probe
PNA immobilized on a IS-FET-based biosensor (
Uno et al., 2007
), (g) binding and dissoci-
ation during PNA-DNA hybridization—binding of different concentrations (in
m
M) of target
DNA complementary to CYP2C9*2 (target DNA2) to CYP2C9*2 as a probe PNA immobilized
on an IS-FET-based biosensor (
Uno et al., 2007
), (h) binding and dissociation of RNA synthesized
on a (i) 42 nM template and a (ii) 420 nM template (
Blair et al., 2007
), and (i) binding (hybridization)
of different concentrations of ss DNA in solution pre-incubated with pre-hybridized 22-nt FQ
duplextoa“brokenbeacon”immobilized on a sensor surface (
Blairetal.,2007
).
