Single-Molecule Mechanics of DNA - DNA Nanotechnology: From Structure to Function - page 95

D .C =L/. 0 / 0 is

the equilibrium twist (35 ı per bp). This value is more accurate than previous results
because there is only Tw conformation in dsDNA during measurements.

,where L is the rod length, is the twisting angle, and

6.3 Single-Molecule Mechanics of ssDNA

6.3.1 Stretching Elasticity of ssDNA in Aqueous Solution

ssDNA is the building block of dsDNA. Thus, the single-molecule mechanics of
ssDNA should be simpler than that of dsDNA. However, ssDNA is not the native
state of DNA. Therefore, the preparation of long enough ssDNA without the second
structure is rather difficult. In the earlier studies, the ssDNA was prepared by dialysis
or denaturation from native dsDNA. In a report of 1996 by Bustamante et al.,
ssDNA was prepared by denaturing dsDNA in 20% formaldehyde solution [ 19 ].
Force curves of ssDNA were obtained. The experimental force curve can be well
fitted by a modified FJC model (m-FJC; see Eq. 6.5 ). The single-molecule modulus
( K 0 ) of ssDNA was obtained as 800 pN, and the Kuhn length is 1.5 nm. However,
this model could not fit the experimental data in low ionic strength, possibly due to
the charge repulsion in the ssDNA chain.

R.F / D f coth Œ.F l k /=.k B T/ .k B T/=.F l k / g .L C L F=K 0 / (6.5)

It is noteworthy that the length of a single unit of DNA is 0.59 nm [ 19 ], which
has no remarkable relationship to the fitting parameter of l k D 1.5 nm. This result
implies that the m-FJC model is still an empirical model, which has no clear
correlation to the real primary structure of a polymer chain [ 13 ].
By stretching the DNA chain after the melting stage, Gaub et al. obtained the
stretching modulus of ssDNA in physiological conditions. However, they found that
the m-FJC model and the previous reported fitting parameters were only valid when
force is lower than 100 pN [ 31 ].

6.3.2 Stretching Elasticity of ssDNA in Organic Solvents

By utilizing the quantum-chemical (QM) ab initio calculations, Hugel et al. obtained
the theoretical elasticity of the repeating unit of ssDNA. The result was believed to
be more accurate since a more reasonable force field was utilized in the calculations
[ 32 ]. The calculation results show that the single-chain elasticity of ssDNA was
found to be nonlinear, which could be expressed in a polynomial expansion to
provide the basis for a numerical fit of the measured force curves (see Eq. 6.6 ).