Figure 1

Dependence of DNA supercoiling on force and salt concentration. (a) Experimental setup and superhelix parameters. (b) DNA supercoiling curves recorded in buffer containing 170 mM ${\mathrm{Na}}^{+}$ at stretching forces of 0.25, 0.5, 1.0, 2.0, 3.0, and 4.0 pN (gray, light blue, dark blue, red, green, and dark gray lines, respectively) for a 1.9 kbp long DNA molecule. Continuous twisting was carried out at 0.5 Hz. Data were taken at 300 Hz and smoothed to 20 Hz. (c) Slopes after buckling as a function of force obtained from the supercoiling curves (taken in part from previous measurements [16]) for ${\mathrm{Na}}^{+}$ concentrations of 30, 60, 170, and 320 mM (gray, red, black, and blue circles, respectively) together with the prediction from the theoretical model (solid lines) calculated for a charge adaptation factor ${\chi }_{\mathrm{CR}}$ of 0.42. Inset: Slopes for 60 mM ${\mathrm{Na}}^{+}$ (red circles) together with theoretical predictions for different values of ${\chi }_{\mathrm{CR}}$ (lines).Reuse & Permissions

Figure 2

Comparison of the predictions from the theoretical model with data from Ref. 14. (a) Slopes after buckling versus force for different ${\mathrm{Na}}^{+}$ concentrations. Circles represent experimental data and solid lines the theoretical prediction for ${\chi }_{\mathrm{CR}}=0.42$. (b) Torque after buckling as calculated from force-extension data [14]. Colors and symbols are as in (a).Reuse & Permissions

Figure 3

Coarse-grained Monte Carlo simulations of DNA supercoiling. (a) Snapshots of the formed plectoneme at 1 pN and 8 turns in the presence of 30 and 320 mM monovalent ions. (b) Simulated DNA supercoiling curves for 170 mM ${\mathrm{Na}}^{+}$ at stretching forces of 0.25, 0.5, 1.0, 2.0, 3.0, and 4.0 pN for ${\chi }_{\mathrm{CR}}=0.42$ [colors are as in Fig. 1b]. Simulations reproduce the experimentally observed abrupt buckling at the onset of the plectonemic phase, which is accompanied by a torque overshoot [see (d)]. Buckling is followed by a linear DNA length decrease with added turns at constant torque. (c) Slopes after buckling obtained from the simulated curves for ${\mathrm{Na}}^{+}$ concentrations of 30, 60, 170, and 320 mM [circles, colors as in Fig. 1b] and corresponding predictions from the theoretical model for ${\chi }_{\mathrm{CR}}$ of 0.42 (solid lines). Inset: Slopes from simulated curves at 60 mM ${\mathrm{Na}}^{+}$ for ${\chi }_{\mathrm{CR}}=0.42$ (red dots) as well as for ${\chi }_{\mathrm{CR}}=0.32$ and ${\chi }_{\mathrm{CR}}=0.55$ (gray dots with dashed lines). The prediction for ${\chi }_{\mathrm{CR}}=0.42$ is shown as a solid red line. (d) Torque during DNA supercoiling for the curves shown in (b). (e) Torque after buckling as obtained from the simulations (filled circles) and after subtraction of 1.5 pN nm (open squares) together with the corresponding predictions from the theoretical model for ${\chi }_{\mathrm{CR}}$ of 0.42 (solid lines). ${\mathrm{Na}}^{+}$ concentrations and colors are as in (c).Reuse & Permissions

Figure 4

All-atom molecular dynamics simulations of the effective force between double-stranded DNA. (a) All-atom model. The DNA atoms are depicted as red spheres, counter- and coions as blue and purple spheres, respectively, and water as a semitransparent molecular surface. The distance between the DNA molecules was restrained by a harmonic potential, schematically depicted as a spring. (b) Mean force between the DNA molecules from molecular dynamics simulations (circles, solid lines) alongside the theoretical predictions for ${\chi }_{\mathrm{CR}}=0.42$ (dashed lines) and 1.0 (dotted lines) at 60 (red) and 170 mM (black) bulk ion concentrations. Data for 300 mM (blue) are reproduced from previous work [26].Reuse & Permissions