Length Scale Dependence of DNA Mechanical Properties

Although mechanical properties of DNA are well characterized at the kilobase-pair range, a number of recent experiments have suggested that DNA is more flexible at shorter length scales, which correspond to the regime that is crucial for cellular processes such as DNA packaging and gene regulation. Here, we perform a systematic study of the effective elastic properties of DNA at different length scales by probing the conformation and fluctuations of DNA from the single base-pair level up to four helical turns, using trajectories from atomistic simulation. We find evidence that supports cooperative softening of the stretch modulus and identify the essential modes that give rise to this effect. The bend correlation exhibits modulations that reflect the helical periodicity, while it yields a reasonable value for the effective persistence length, and the twist modulus undergoes a smooth crossover—from a relatively smaller value at the single base-pair level to the bulk value—over half a DNA turn.

Figure 1

56-mer (a) and 36-mer averages (c) together with the corresponding end-stretching essential modes (see Movie S1 in the Supplemental Material [23]). (b) Molecular position dependence of the local strain for the end-to-end distance ($\Delta L$) occurred at the 56-mer end-stretching mode using subfragments of 3 bp length. (d) Side view of a regular straight DNA turn made using dimer average values from our simulations ($\mathrm{\text{shift}}=0.0$, $\mathrm{\text{slide}}=-0.5$, and $\mathrm{\text{rise}}=3.3\AA$; $\mathrm{\text{tilt}}=0$, $\mathrm{\text{roll}}=3$, $\mathrm{\text{twist}}=33$ degrees) where end-to-end (black) and contour length (red) are differentiated. (e) Snapshots from the “zigzag” essential mode for the 56-mer central 16 bp (see Movie S2 in the Supplemental Material [23]).

Figure 2

(a) End-to-end $L$ as well as contour-length $L_0$ (inset) raw ($v$) and partial variances ($v_p$) as extracted from the 56-mer trajectory. Stretch modulus $B$ associated with the $L$ (b) and to the $L_0$ (c) from MD trajectories. Values reported here are averages over all possible subfragments with a particular length, and the corresponding standard deviations are given as error bars. (d) End-to-end partial variances extracted from the 56-mer trajectory considering the whole molecule, the central 16 and 20 bp, predictions for a 1500 pN stretch modulus and the fitted curve. (e) $B$ calculated for the 56-mer’s central 16 bp associated with $L$, $L_0$, the corresponding added rise ($Z_0$), added lateral shear (slide $Y_0$ and shift $X_0$), and with $L$ of the trajectory with the “zigzag” essential mode filtered out ($L_z$). Note that $B$ associated with added rise and lateral shear is obtained by full variances instead of partial variances.

Figure 3

(a) Directional decay of the 56-mer (black) and the 36-mer (red) MD trajectories. The inset shows the exact cosine function between base-pairs axial vectors, while the rest of the plots use the quadratic approximation [see Eq. (2)]. (b) Apparent persistence length $A_{\mathrm{app}}$ calculated by a linear fit of the local directional decay (2 parameters, 5 degrees of freedom, all reduced ${\chi }^2$’s were under 0.2) where the asymptotic standard errors of the fitted persistence length are given as error bars. The static (c) and the dynamic (d) contributions to the fluctuations of the bending angle $\theta$ [see Eq. (3)] calculated from the MD trajectories, as well as that of the regular straight B-DNA (in thick blue) for comparison.

Figure 4

Torsion elastic constant $C$ calculated by the inverse covariance matrix [Eq. (1)] using the 56-mer (black) and the 36-mer (red) MD trajectories.