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Mechanical properties of nucleic acids play an important role in many biological processes which often involve physical deformations of these molecules. At sufficiently long length scales (say above $\sim 20-30$ base pairs) the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites gets coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model which clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables which describe the twist and bending of the molecule. Differently from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior which matches experimental data., Comment: 14 pages, 12 figures

While analyzing the persistence length of DNA atomistic simulations Wu et al. [J. Chem. Phys. 142, 125103 (2015)] introduced an empirical formula to account for the observed length-dependence. In particular they found that the persistence length increases with the distance. Here, we derive the formula by Wu et al. using a non-local twistable wormlike chain which introduces couplings between distal sites. Finally, we show that the same formula can account for the length-scale dependence of the torsional persistence length and is, in fact, applicable to any kind of polymer model with non-local couplings.

The mechanical properties of DNA are typically described by elastic theories with purely local couplings (on-site models). We discuss and analyze coarse-grained (oxDNA) and all-atom simulations, which indicate that in DNA distal sites are coupled. Hence, off-site models provide a more realistic description of the mechanics of the double helix. We show that off-site interactions are responsible for a length scale dependence of the elasticity, and we develop an analytical framework to estimate bending and torsional persistence lengths in models including these interactions. Our simulations indicate that off-site couplings are particularly strong for certain degrees of freedom, while they are very weak for others. If stiffness parameters obtained from DNA data are used, the theory predicts large length scale dependent effects for torsional fluctuations and a modest effect in bending fluctuations, which is in agreement with experiments., 16 pages, 9 figures; video abstract at https://youtu.be/8FUdFw8IbuY