II. MODEL AND SIMULATION DETAILS The model we consider resolves a given basepair (of type A, T, C or G) only to the extent that we assign to it a particular instantaneous state. We consider four possible states, sketched in Fig. 1(a). The first is the helical B-form of DNA. The second is the ‘molten bubble’ form of DNA (M-DNA) in which both strands bear tension but do not interact with each other. The third state is the unpeeled form (U-DNA) in which one strand has frayed and no longer bears tension. It is crucial to distinguish between the two forms of unhybridized DNA: in the presence of nicks, M-DNA is unstable to U-DNA [6]. All three states can be parameterized using thermal and mechanical data [4, 6, 13]. The fourth state is the putative S-form (S-DNA). The model of S-DNA used in Refs. [10, 11] is based on two assumptions: first, that S-DNA has a contour length 70% greater than B-DNA and is stiffer at large forces [6, 14, 15]; and second, that it is in thermal equilibrium with B-DNA, irrespective of sequence composition, at 65 pN. The motivation for the latter assumption is the observation that λ -DNA (about 50% CG content) and poly(dG-dC) DNA both overstretch at about 65 pN [16]. This observation is difficult to reconcile with the assumption that overstretching consists solely of melting of the double helix. The thermodynamics implied by this picture at a salt concentration of 150 mM is summarized in Fig. 1(b) (see Appendix). At low forces B-DNA is stable; at high forces either U-DNA or S-DNA are stable. The assumption that S-B phase coexistence occurs at 65 pN independently of sequence and environmental conditions immediately implies that S-DNA is more stable with respect to U-DNA in CG-rich DNA than in AT-rich DNA, and that increasing temperature favors U-DNA over S-DNA. Further, for the parameters used in Ref. [10], we find that S-DNA is not thermodynamically stable (under the conditions shown) with respect to U-DNA within the first 40 kbp of λ -DNA as a whole. However, as discussed in Ref. [6], this does not mean that S-DNA is never observed in dynamic stretching simulations. U-DNA must emerge in a processive, basepair-by-basepair fashion. It is therefore possible to find thermodynamic conditions such that while complete unpeeling of the molecule is thermodynamically favorable, the passage of U-DNA through CG-rich tracts of the molecule is hindered by free energy barriers in excess of hundreds of k$_{B}$T . Under such conditions, S-DNA can be transiently stable. To illustrate this point, we show in Fig. 2 a microscopic space-versus-time plot of dynamic molecular composition within a 300-basepair fragment of λ -DNA stretched at 1000 nm/s. Unpeeling from the molecule’s free end eventually leads to complete dehybridization, but because the advance of the unpeeled front is processive and slow, S-DNA is transiently stable. To reveal the effect of environmental conditions on the degree of this stability, we plot in Fig. 3 a ‘dynamic phase diagram’ at salt concentration c = 150 mM for 40 kbp fragments of λ -DNA stretched at 1000 nm/s at temperature T to a target force f$_{0}$ . We use the ‘optical trap’ protocol described in detail in Ref. [10]: trap stiffness is 1 pN/nm, and molecules possess one free end and no internal nicks. Once the target force is achieved, the loading rate is set to zero and the molecular composition monitored. We show molecular composition (vertical axis, maximum 3