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Coarse-grained models have emerged as valuable tools to simulate long DNA molecules while maintaining computational efficiency. These models aim at preserving interactions among coarse-grained variables in a manner that mirrors the underlying atomistic description. We explore here a method for testing coarse-grained vs. all-atom models using stiffness matrices in Fourier space ($q$-stiffnesses), which are particularly suited to probe DNA elasticity at different length scales. We focus on a class of coarse-grained rigid base DNA models known as cgDNA and its most recent version cgDNA+. Our analysis shows that while cgDNA+ follows closely the $q$-stiffnesses of the all-atom model, the original cgDNA shows some deviations for twist and bending variables which are rather strong in the $q \to 0$ (long length scale) limit. The consequence is that while both cgDNA and cgDNA+ give a suitable description of local elastic behavior, the former misses some effects which manifest themselves at longer length scales. In particular, cgDNA performs poorly on the twist stiffness with a value much lower than expected for long DNA molecules. Conversely, the all-atom and cgDNA+ twist is strongly length scale dependent: DNA is torsionally soft at a few base pair distances, but becomes more rigid at distances of a few dozens base pairs. Our analysis shows that the bending persistence length in all-atom and cgDNA+ is somewhat overestimated., Comment: 9 pages, 6 figures

Proteins often regulate their activities via allostery - or action at a distance - in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalpy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

All-atom simulations have become increasingly popular to study conformational and dynamical properties of nucleic acids as they are accurate and provide high spatial and time resolutions. This high resolution however comes at a heavy computational cost and within the time scales of simulations nucleic acids weakly fluctuate around their ideal structure exploring a limited set of conformations. We introduce the RBB-NA algorithm which is capable of controlling rigid base parameters in all-atom simulations of Nucleic Acids. With suitable biasing potentials this algorithm can "force" a DNA or RNA molecule to assume specific values of the six rotational (tilt, roll, twist, buckle, propeller, opening) and/or the six translational parameters (shift, slide, rise, shear, stretch, stagger). The algorithm enables the use of advanced sampling techniques to probe the structure and dynamics of locally strongly deformed Nucleic Acids. We illustrate its performance showing some examples in which DNA is strongly twisted, bent or locally buckled. In these examples RBB-NA reproduces well the unconstrained simulations data and other known features of DNA mechanics, but it also allows one to explore the anharmonic behavior characterizing the mechanics of nucleic acids in the high deformation regime., Comment: 12 pages, 6 figures

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., Comment: 3 pages, 1 Figure

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., Comment: 16 pages, 9 figures; video abstract at https://youtu.be/8FUdFw8IbuY