Figure 1

(a) Stretching of a single ssDNA charomid of extension $l_{0,\mathrm{s}\mathrm{s}}=5.7\mu \mathrm{m}$ in 1 mM phosphate buffer (PB) ($+$), 10 mM PB ($♦$), and 0.5 mM ${\mathrm{M}\mathrm{g}}^{++}$ ($\square$) (data obtained upon decreasing the force). The continuous curves are results of MC simulations of Eq. (2) using known values of the Kuhn length $b=1.6\mathrm{n}\mathrm{m}$ and Young modulus $Y=120k_{B}T/{\mathrm{n}\mathrm{m}}^2$ [13] and an estimated value of the pairing energy $V_p=4.6k_{B}T$ [14]. The electrostatic repulsion was computed (no fitting parameters) for each buffer in the Debye-Hückel approximation [Eq. (2)] (for example, in 10 mM PB, $\nu =1.28e/\mathrm{n}\mathrm{m}$ and $l_D=1.87\mathrm{n}\mathrm{m}$ [14]). The dashed line is the analytical result of Montanari and Mézard [16] using a mFJC model with similar $b$ and $Y$ values and a single fit parameter (accounting for both pairing energy and electrostatic repulsion). The grey line is the WLC result for a dsDNA charomid. (b) Hysteretic behavior observed upon increasing ($+$) or decreasing ($♦$) the stretching force on a ssDNA molecule (in 1 mM PB and 1 mM ${\mathrm{M}\mathrm{g}\mathrm{C}\mathrm{l}}_2$).Reuse & Permissions

Figure 2

Stretching of two different DNA molecules: a 50% GC-rich charomid ($◯$) and a 30% GC-rich $pX\Delta \mathrm{I}\mathrm{I}$ ($♦$) in 10 mM Tris buffer, 5 mM ${\mathrm{M}\mathrm{g}}^{++}$, 25 mM KCl (the calculated values of the Debye length and the DNA’s effective charge density are $l_D=1.54\mathrm{n}\mathrm{m}$, $\nu =1.29e/\mathrm{n}\mathrm{m}$ [14]). The continuous curves are results of MC simulations of Eq. (2) with $V_p=4.6k_{B}T$ for the charomid and $V_p=3.8k_{B}T$ for the $pX\Delta \mathrm{I}\mathrm{I}$. The extension of the different ssDNA molecules was normalized to the crystallographic length of the dsDNA (whose WLC model is shown as a black line).Reuse & Permissions

Figure 3

Extension $l$ of a ssDNA single molecule in (a) 30% formamide/70% PB (1 mM) before ($◯$) and after ($+$) addition of 2 mM ${\mathrm{M}\mathrm{g}}^{++}$ and (b) 10 mM PB after treatment with glyoxal before ($◯$) and after ($+$) addition of 2 mM ${\mathrm{M}\mathrm{g}}^{++}$. In contrast with unmodified ssDNA, note the independence of the curves upon salt conditions and the absence of hysteresis.Reuse & Permissions

Figure 4

Extension of different ssDNA molecules normalized by the contour length $l_{\mathrm{d}\mathrm{s}}^0$ of the equivalent dsDNA molecule observed in 10 mM PB [$+$: after treatment with glyoxal; $♦$: by pulling with an AFM at high forces (data from Rief et al. [22])]. The continuous line is the result of a numerical simulation of the model described in the text with $b=1.6\mathrm{n}\mathrm{m}$, $Y=120k_{B}T/{\mathrm{n}\mathrm{m}}^2$, and no pairing energy ($V_p=0$). The electrostatic repulsion was computed in the Debye-Hückel approximation [Eq. (2), with $\nu =1.28e/\mathrm{n}\mathrm{m}$ and $l_D=1.87\mathrm{n}\mathrm{m}$ [14]]. To fit the results at high forces ($F>70\mathrm{p}\mathrm{N}$), a nonlinear (quartic) elastic term with $Y_2=400k_{B}T/{\mathrm{n}\mathrm{m}}^4$ was added. The dashed black line is a fit of the high force data to a WLC model (leading to an unrealistic $\xi =0.21\mathrm{n}\mathrm{m}$). The dashed grey line is the predictions of the mFJC model for ssDNA [13]. Inset: same data, but plotted on a linear scale (often used in fitting the stretching data of proteins) where the WLC model appears to be a good fit. Notice that the abscissa here does not start from zero but from a relative extension $\sim 1$.Reuse & Permissions