Figure 1

(Color online) The thermodynamics implied by the S-DNA picture of overstretching for salt concentration $c=150\text{mM}$. (a) Cartoon sketches of phases B, M, U, and S (see text). (b) Equilibrium phase stabilities (see Appendix) in the temperature-pulling force plane for phases U, B, and S. We consider a 40 kbp fragment of $\lambda \text{-DNA}$ (left), a similar length of “averaged” CG-DNA (center; see Appendix for details of sequence averaging), and averaged AT-DNA (right). The model of S-DNA described in the main text is not thermodynamically stable at any temperature or stretching force within the first 40 kbps of $\lambda \text{-DNA}$ as a whole. However, its considerable stability against unpeeling in CG-rich regions suggests the possibility of long-lived metastable pockets of S-DNA during dynamic stretching experiments if nicks are few. Compare these data with the dynamic phase diagram of Fig. 3.Reuse & Permissions

Figure 2

(Color online) Dynamic simulations of a microscopic model accommodating U, M, B, and S forms of DNA [11]. Here we show microscopic configurations (vertical axis) as a function of time (horizontal axis) from an illustrative simulation of a 300-basepair fragment of $\lambda \text{-DNA}$ at $21°\text{C}$ and salt concentration 150 mM, extended at 1000 nm/s. The molecule possesses one free end, permitting unpeeling. White indicates B-DNA, red (light gray) indicates unhybridized DNA (unpeeled or molten), and blue (dark gray) indicates S-DNA. The spatial scale indicates molecular length. The maximum force attained is 90 pN (central dotted line). At forces in excess of about 50 pN, S-form DNA is themodynamically unstable with respect to unpeeled DNA. However, unpeeling takes time to proliferate, and S-DNA is seen to be transiently stable even near forces of about 90 pN. The step-by-step processivity of unpeeling confers upon overstretching an anomalous kinetics that, we argue, rationalizes several nontrivial experimental observations [15, 16, 17] (reprinted with permission).Reuse & Permissions

Figure 3

(Color online) Dynamic phase diagram for 40 kbp fragments of $\lambda \text{-DNA}$ with one free end, at salt concentration $c=150\text{mM}$: compare the thermodynamic phase diagram of Fig. 1. Color code: B-DNA (off-white), U-DNA (red), and S-DNA (blue). Here we use the optical trap protocol described in Ref. [10] (trap stiffness 1 pN/nm) to stretch DNA at fixed temperature $T$ at a rate of 1000 nm/s until a force $f_0$ is achieved. The loading rate is then set to zero, and the composition of the molecule is monitored (both molecular force and extension may vary, and force typically decreases slowly). We show molecular composition (fraction of B-DNA (off-white), U-DNA (red), and S-DNA (blue) denoted by bars on the vertical axis, where maximum height represents 40 kbp) for a molecule at specified temperature $T$ for target force $f_0$ at times 0 and 10 s after setting the loading rate to zero. Two features are apparent. First, S-DNA is sufficiently long lived to be seen after 10 s of waiting at low temperatures. Second, near and above room temperature, S-DNA is short-lived.Reuse & Permissions

Figure 4

(Color online) Dynamic phase diagram for 40 kbp fragments of $\lambda \text{-DNA}$ with one free end, at salt concentration $c=150\text{mM}$. The dynamic stretching protocol is as Fig. 3, except that the molecular stretching rate is 100 nm/s rather than 1000 nm/s. In general, more U-DNA is seen here then in Fig. 3: here, attainment of the target force $f_0$ takes of order hundreds of seconds near 65 pN, and as a result the molecule has more time to unpeel than it does at the smaller stretching rate.Reuse & Permissions

Figure 5

(Color online) Dynamic phase diagram for 40 kbp fragments of $\lambda \text{-DNA}$ with one free end, at salt concentration $c=50\text{mM}$. The dynamic stretching protocol is as Fig. 3: note the smaller fraction of S-DNA seen here. At room temperature, S-DNA is short-lived.Reuse & Permissions

Figure 6

(Color online) Dynamic phase diagram for 40 kbp fragments of $\lambda \text{-DNA}$ with one free end, at salt concentration $c=500\text{mM}$. The dynamic stretching protocol is as Fig. 3: note the larger fraction of S-DNA seen here.Reuse & Permissions

Figure 7

(Color online) Molecular compositions at $20°\text{C}$ as a function of sequence (horizontal axis) for 40 kbp fragments of $\lambda \text{-DNA}$ stretched to two target forces $f_0$ at three salt concentrations $c$. The stretching protocol is as Fig. 3 (force and molecular extension may vary after zeroing the loading rate). Each molecule possesses one free end. low salt conditions and long waiting times favor unpeeling; at high salt conditions and short waiting times one is more likely to observe S-DNA.Reuse & Permissions