Biomedical Engineering Reference
In-Depth Information
Compared with the situation in organic solvent, the single-chain elongation of
ssDNA in aqueous solution consumes more energy. The difference between the two
cases can be calculated to be 0.58
k
B
T
/base (1.4 kJ/mol base). We already know that
ssDNA presents “pure” elasticity in organic solvent. Then, why the elongation in
water consumes more energy?
ssDNA is hydrated in water. Due to the limitations in chain conformation, it is
expected that, in the fully stretched state, there are much less bound water molecules
per repeating unit than that in the free coil state. Thus, the ssDNA chain would lose
bound water gradually during the force stretching process. The structured water
molecules around the chain are forced to undergo a rearrangement upon stretching,
which would cost considerable energy in addition to that for the inherent elasticity
(or “pure” modulus) of the chain [
33
]. This energy cost for the water rearrangement
upon stretching is reflected in the deviation (1.4 kJ/mol base) between aqueous
solution and organic solvents.
The self-organization from ssDNA to dsDNA is usually formularized below,
where ssDNA
0
denotes the complimentary chain of ssDNA:
ssDNA
C
ssDNA
0
•
dsDNA
(6.8)
However, the influence of water molecules is not considered in Eq.
6.8
. In fact,
water is involved directly in the process since it is clear that dsDNA has less binding
sites with water than that of the sum of the two free ssDNA chains. Therefore, a
partial dehydration process should occur prior to the self-organization of ssDNA.
Thus, Eq.
6.8
should be revised into a more rigorous form below:
H
2
O
C
ssDNA
0
x
ssDNA
x
H
2
O
•
dsDNA
y
H
2
O
C
.2x
y/
H
2
O
(6.9)
Like other complex reactions, Eq.
6.9
can be separated into the following two
simpler steps:
ssDNA
x
H
2
O
•
ssDNA
y=2
H
2
O
C
.x
y=2/
H
2
O
(6.10)
H
2
O
C
ssDNA
0
y=2
ssDNA
y=2
H
2
O
•
dsDNA
y=2
H
2
O
(6.11)
All the water rearrangement is completed in Eq.
6.10
, whereas all the assembly
between ssDNA chains occurs in Eq.
6.11
. It is clear that
G
9
D
2
G
10
C
G
11
(6.12)
It is reasonable to assume that the partial dehydration (Eq.
6.10
) is a non-
spontaneous process (i.e.,
0). Whether the supramolecular self-organization
described in Eq.
6.9
can occur is hinged on the free energy change (
G
10
>
G
9
)
of the process. A typical value measured by differential scanning calorimetry
is
4.3 kJ/(molbp) [
37
]. However,
G
10
(or
G
11
) is neither a ready data in
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