Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable worm-like chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40 ± 10 nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago (Marko and Siggia, Macromolecules 27, 981 (1994)), its effects on the mechanical properties of DNA have been so far largely unexplored. We expect that this coupling plays an important role in several aspects of DNA statics and dynamics.Introduction The mechanical properties of doublestranded DNA (dsDNA) are critical for both its structure and function within the cell. The stretching of ds-DNA under applied forces has been measured by single molecule techniques [1, 2] and is accurately reproduced by a simple polymer model, containing the bending stiffness as the only parameter [1]. Elastic polymer models were also successfully employed to study the torsional properties of dsDNA [4] and compared to single-molecule experiments, such as magnetic tweezers (MT) [2] (Fig. 1, right). The currently accepted elastic model for dsDNA is the twistable worm-like chain (TWLC) [6]. Although the TWLC correctly describes the overall response of ds-DNA to applied forces and torques, it fails to quantitatively explain the force-dependence of the effective torsional stiffness [3, 4]. Here, we show that an alternative elastic model proposed by Marko and Siggia (MS) [5], quantitatively describes the force-dependence of the effective torsional stiffness, by taking into account a direct coupling between twist and bend deformations. Furthermore, we demonstrate that the MS model explains an unresolved discrepancy in the measured intrinsic torsional stiffness, obtained from different techniques. Finally, we show that the MS model provides a better description of the pre-buckling torque response of dsDNA, determined in high-resolution magnetic torque tweezers (MTT) experiments, than the TWLC.TWLC and MS models Both the TWLC and MS models describe dsDNA as a continuous, twistable curve by associating an orthonormal frame { e 1 , e 2 , e 3 } with each base pair (Fig. 1) [5]. We choose e 3 tangent to the helical axis and e 1 and e 2 oriented as in Fig. 1. In the continuum limit these vectors are functions of the arc-length variable s. For the stretching forces considered here (f < 10 pN) dsDNA is inextensible, hence 0 ≤ s ≤ L, with L the contour length. A local dsDNA conformation is given by a vector Ω(s) which describes the infinitesimal rotation connecting { e 1 (s), e 2 (s), e 3 (s)} to { e 1 (s + ds), e 2 (s + ds), e 3 (s + ds)}. The direction of Ω(s) identifies the rotation axis, and |Ω(s)|ds the infinitesimal rotation angle. In particular, if Ω(s) is parallel to e 3...

It is well-established that many physical properties of DNA at sufficiently long length scales can be understood by means of simple polymer models. One of the most widely used elasticity models for DNA is the twistable wormlike chain (TWLC), which describes the double helix as a continuous elastic rod with bending and torsional stiffness. An extension of the TWLC, which has recently received some attention, is the model by Marko and Siggia, who introduced an additional twist-bend coupling, expected to arise from the groove asymmetry. By performing computer simulations of two available versions of oxDNA, a coarsegrained model of nucleic acids, we investigate the microscopic origin of twist-bend coupling. We show that this interaction is negligible in the oxDNA version with symmetric grooves, while it appears in the oxDNA version with asymmetric grooves. Our analysis is based on the calculation of the covariance matrix of equilibrium deformations, from which the stiffness parameters are obtained. The estimated twist-bend coupling coefficient from oxDNA simulations is G = 30 ± 1 nm. The groove asymmetry induces a novel twist length scale and an associated renormalized twist stiffness κ t ≈ 80 nm, which is different from the intrinsic torsional stiffness C ≈ 110 nm. This naturally explains the large variations on experimental estimates of the intrinsic stiffness performed in the past.

Recent work indicates that twist-bend coupling plays an important role in DNA micromechanics. Here we investigate its effect on bent DNA. We provide an analytical solution of the minimum-energy shape of circular DNA, showing that twist-bend coupling induces sinusoidal twist waves. This solution is in excellent agreement with both coarse-grained simulations of minicircles and nucleosomal DNA data, which is bent and wrapped around histone proteins in a superhelical conformation. Our analysis shows that the observed twist oscillation in nucleosomal DNA, so far attributed to the interaction with the histone proteins, is an intrinsic feature of free bent DNA, and should be observable in other protein-DNA complexes.