Biomedical Engineering Reference
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example, the
value in 1 M KCl is ~50 times as long as that in 1 M NaCl,
suggesting that the K
+
-induced G-quadruplex is much more stable than the one
induced by Na
+
. The lifetime of G-quadruplex
t
corresponds to the unfolding rate
t
constant
k
u
,
k
u
¼
=
t
1
(3.1)
The equilibrium constant
K
f
can be inferred by comparing the frequency of short-
lived blocks produced by the linear form TBA (
f
TBAL
) and a control DNA (
f
Ctrl
)
K
f
¼ f
Ctrl
=f
TBA
L
1
(3.2)
This expression is based on the fact that
f
is proportional to the concentration of
linear form DNA in the solution. For example, it was found a lower percent of linear
TBA molecules or a higher percent of folded ones in K
+
than in Na
+
(Fig.
3.4a
traces). The shift in equilibrium toward the folded structure suggests that K
+
is more
capable of the induction of the G-quadruplex formation than Na
+
. By comparing the
short-lived block occurrences for TBA and the control DNA, we can determine the
concentrations of both the folded and linear TBA in the solution. These concentra-
tion data is then used to obtain the equilibrium constant. Finally, the folding rate
constant,
k
f
, can be determined using
K
f
¼ k
f
=k
u
(3.3)
3.2.5
Ion-Regulated Folding/Unfolding of G-Quadruplex
Aptamer
Aided by this analytical approach, we were enabled to use nanopore to study
distributions and variations of different aptamer conformations as the environmen-
tal conditions change [
100
]. We have uncovered the mechanisms that govern how
metal ions regulate the folding and unfolding of the G-quadruplex (Table
3.1
).
Table 3.1 Equilibrium, folding and unfolding rate constants and free energy for the TBA
G-quadruplex in different cations
MTBA
r
(
˚
)
k
f
(s
1
)
k
u
(s
1
)
DG
(kcal mol
1
)
K
f
(no unit)
Li
+
TBA
0.60
1.5
0.095
0.065
0.23
Na
+
TBA
0.95
2.3
6.5
2.9
0.48
K
+
TBA
1.33
7.0
0.46
0.066
1.1
NH
4
+
TBA
1.45
4.6
1.1
0.25
0.89
Cs
+
TBA
1.69
2.8
0.23
0.082
0.61
Ba
2+
TBA
1.35
4.2
0.25
0.061
0.84
Mg
2+
TBA
0.65
-
-
-
-
Ca
2+
TBA
0.99
-
-
-
-
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