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Single molecule experiments on B-DNA stretching have revealed one or twostructural transitions, when increasing the external force. They arecharacterized by a sudden increase of DNA contour length and a decrease of thebending rigidity. It has been proposed that the first transition, at forces of60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA,while the second one, at stronger forces, is a strand peeling resulting insingle stranded DNAs (ssDNA), similar to thermal denaturation. But due toexperimental conditions these two transitions can overlap, for instance forpoly(dA-dT). We derive analytical formula using a coupled discrete worm likechain-Ising model. Our model takes into account bending rigidity, discretenessof the chain, linear and non-linear (for ssDNA) bond stretching. In the limitof zero force, this model simplifies into a coupled model already developed byus for studying thermal DNA melting, establishing a connexion with previousfitting parameter values for denaturation profiles. We find that: (i) ssDNA isfitted, using an analytical formula, over a nanoNewton range with only threefree parameters, the contour length, the bending modulus and the monomer size;(ii) a surprisingly good fit on this force range is possible only by choosing amonomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobaselength; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss)transitions; (iv) an analytical formula for fitting B to S transitions isderived in the strong force approximation and for long DNAs, which is inexcellent agreement with exact transfer matrix calculations; (v) this formulafits perfectly well poly(dG-dC) and $\lambda$-DNA force-extension curves withconsistent parameter values; (vi) a coherent picture, where S to ssDNAtransitions are much more sensitive to base-pair sequence than the B to S one,emerges.

Mesoscopic models for DNA stretching under force: new results and comparison to experiments