Biomedical Engineering Reference
In-Depth Information
Fig. 6.7
The scheme of FJC
model
l
k
R
the entropic contribution. The force law of the FJC model is given by the Langevin
function as Eq.
6.2
:[
13
,
15
]
R.F /
D f
coth
Œ.F
l
k
/=.k
B
T/
.k
B
T/=.F
l
k
/
g
L
(6.2)
In this equation, only
L
and
l
k
are the free parameters. The different chains of
the same species of polymer present identical
l
k
in the same conditions. The fitting
process can be regarded as the process of seeking the approximate solution of
l
k
in
a heuristic way.
The fact that the WLC model fitting result is much better than that of the FJC
model indicates that dsDNA is a semi-flexible macromolecule [
18
-
21
].
Since DNA is a kind of polyelectrolyte, the fine structure of the double helix
can be influenced by the ionic strength of the solution. Bustamante et al. found that
the persistence length of dsDNA is decreased with increasing of the ionic strength,
finally reaching an equilibrium value. For the simple case of monovalent ion, the
relationship between the persistence length of dsDNA and the ionic strength can
be explained by the Poisson-Boltzmann theory, which can be calculated by Eq.
6.3
[
2
,
22
]:
l
p
D
l
p
C
0:0324
I
1
nm
(6.3)
Both of the FJC and WLC models assume that (1) the polymer chain has no fine
structure and (2) the chain has a fixed length. When the chain is being stretched,
the conformational entropy is decreased and the potential increased, leading to a
restoring force. This elasticity is called entropic elasticity [
23
], due to the origin of
conformational entropy. It was shown that the WLC fitting curve can superimpose
with the experimental force curve when the stretching force is less than 5 pN. That
is, the theory of entropic elasticity can explain the results of dsDNA well at the low
force regime.
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