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Thermodynamic Analysis
for the Non-canonical Nucleic
Acids

3
...
1 Thermodynamic Analysis for the Intramolecular Triplex and
Tetraplex
Upon triplex unfolding the absorbance at 260 nm is known to increase as a
result of decreased base stacking, and the absorbance at 295 nm decreases,
indicating the presence of cytosine: protonated cytosine base pairs (Hoogsteen
base pairs)
...
The thermodynamic parameters for the
intramolecular triplex and tetraplex can be calculated using Eqs
...
3, 3
...
8)
described above if the unfolding processistwo-state[14]
...
5
...
5)
The global triplex unfolding proceeds in a monophasic triplex-to-coil collapse
SW SC SH ⇌ SW +SC +SH

and the equilibrium constant, K T , can be written as
)
(
[SW SC SH ]
1 − aT 9
−𝛥HT + T𝛥ST
=
= exp
KT =
2
3
[SW ][SC ][SH ]
RT
a T CT

(3
...
17)

where SW SC SH represents the Watson–Crick–Hoogsteen triplex; ΔH T and ΔST are
the van’t Hoff enthalpy and entropy of triplex formation, respectively; 𝛼 T is the molar
fraction of the coiled strands in the structured triplex form; and CT is the total species
concentration
...
T), RT should be equal to ∼0
...
65
𝛥HT

(3
...
0–7
...
19)
(3
...
Although the two
transitions may overlap each other in a certain range, this cross-effect can be nearly
neglected at the melting temperatures, and the values of 𝛼 WC and 𝛼 H at which the
derivative absorbance vs
...
42
and ∼0
...
Thus, the van’t Hoff equations can be simplified by
CT
𝛥SH
R
+
ln
=
𝛥HH
10
...
21)
(3
...
0)

The triplex strand is not formed, and the complex unfolding merely includes
a monophasic duplex-to-coil transition
...
23)

where ΔH D and ΔSD are the van’t Hoff enthalpy and entropy of duplex formation in
the 1 : 1 : 1 mixture of the three strands, respectively, and 𝛼 D is the molar fraction of
the coiled strands in the structured duplex form
...
50 [18], and therefore, the van’t Hoff equation
can be written as
CT
𝛥SD
R
−1
TD =
+
ln
(3
...
5
...
11a)
...

Therefore, the unfolding and folding processes often show different sigmoidal curves
(Figure 3
...
Due to the hysteresis of unfolding and folding processes, the
thermodynamic parameters for intermolecular tetraplex using UV

G

G

G

G

G

G

G

G
(a)

G

G

G
G
G

G

G

G

G

G

G

G

G

G

G

G

G

G
G

G

G

G

G

G

Absorbance at 295 nm

1
...
9

0
...
11 (a) The unfolding process for the intermolecular tetraplex
...


melting curves are not estimated
...

For a folding reaction involving intermolecular and intramolecular tetraplexes
(Figure 3
...
25)

Note that this expression for the equilibrium constant for an association reaction
among same sequences is not identical to the corresponding expression for different
sequences
...
5, the general expression for K shown above reduces to
KTm =

0
...
5)n

(3
...
One also can derive a general expression for
calculating the transition enthalpy for self-complementary associations
...
(3
...
(3
...
12 (a–c) Typical examples for intermolecular and intramolecular tetraplexes
described with equation of nA ⇌ An
...


𝛥HVH = RT2

(

d ln K
dT

)

[
or 𝛥HVH = −R

d ln K
d(1∕T)

]
(3

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