Biomedical Engineering Reference
In-Depth Information
Once again, the fit is good. Only four data points are available. The availability of more data
points would lead to a more reliable fit. The affinity,
K
2
, is very sensitive to the ratio of the
fractal dimensions,
D
f2
/
D
fd
, as noted by the close to four and a half (equal to 4.408) order of
dependence exhibited.
Only four data points were available and plotted in
Figures 4.4i
and
Figure 4.4j
for the affin-
ity values,
K
1
and
K
2
, respectively. It is perhaps instructive to plot them together since so few
data points were available for
K
1
and
K
2
separately.
Figure 4.2k
shows the plot for
K
1
and
K
2
versus
D
f1
/
D
fd
and
D
f2
/
D
fd
, respectively. For the combined (
K
1
and
K
2
) data shown in
Figure 4.4k
, the affinity,
K
1
or
K
2
is given by:
3
:
444
0
:
1818
K
1
or
K
2
¼ð
1
:
849
0
:
283
Þ½ð
D
f1
=
D
fd
Þ
or
ð
D
f2
=
D
fd
Þ
ð
4
:
5k
Þ
Considering that two different sets of data for
K
1
and
K
2
are plotted together the fit is very
good. In this case now eight data points are available. The affinity,
K
1
or
K
2
is sensitive to
the ratio of fractal dimensions,
D
f1
/
D
fd
or
D
f2
/
D
fd
, respectively as noted by the close to three
and a half (equal to 3.444) order of dependence exhibited. It is of interest to note that the
order of dependence exhibited (equal to 3.444) when
K
1
and
K
2
are plotted together is very
close to the order of dependence exhibited (equal to 3.441) when
K
1
is plotted alone. The dif-
ference is only in the fourth decimal place. This would indicate that in some way the affinity,
K
1
dominates the affinity,
K
2
at least in this case as far as the heterogeneities on the biosensor
chip are concerned.
reactions. These authors indicate that protein phosphatases are involved in the control of
the phosphorylation state of many proteins. Furthermore, the authors state that the measure-
ment of P
i
is an important target for the understanding of cellular activities involving such
proteins.
Webb (2003)
has summarized the various kinetic analyses of phosphatases.
Okoh
et al. (2006)
have developed a fluorescence-based biosensor based on PBP. This PBP was
obtained from
Escherichia coli
(
Brune et al., 1994
). They (
Okoh et al., 2006
) report that
the PBP has two domains that are hinged. These close around the phosphate that binds in
the cleft between them (
Luecke and Quiocho, 1990
). They (
Okoh et al., 2006
) point out that
this conformational change provides a mechanism for the development of a biosensor. Fur-
thermore, these authors indicate that the PBP is very specific to inorganic phosphate and
binds phosphate esters and anhydrides very weakly.
Figure 4.5a
shows the binding of a 0.63 micromole inorganic phosphate ion (P
i
) in solution to
a rhodamine-PBP phosphate biosensor (
Okoh et al., 2006
). 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
