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.

We investigate the influence of non-local couplings on the torsional and bending elasticities of DNA. Such couplings have been observed in the past by several simulation studies. Here, we use a description of DNA conformations based on the variables tilt, roll and twist. Our analysis of both coarse-grained (oxDNA) and all-atom models indicates that these share strikingly similar features: there are strong off-site couplings for tilt-tilt and twist-twist, while they are much weaker in the roll-roll case. By developing an analytical framework to estimate bending and torsional persistence lengths in non-local DNA models, we show how off-site interactions generate a length scale dependent elasticity. Based on the simulation generated elasticity data the theory predicts a significant length scale dependent effect on torsional fluctuations, but only a modest effect on bending fluctuations. These results are in agreement with experiments probing DNA mechanics from single base pair to kilobase pair scales.

The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling G between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here, the effect of G on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness C eff for small twist-bend coupling. We find that the "bare" G is "screened" by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with G = 0, but with long-wavelength bending and twisting rigidities that are shifted by G-dependent amounts. Using results for torsional and bending rigidities for freely-fluctuating DNA, we show how our perturbative results can be extended to a non-perturbative regime. These results are in excellent agreement with numerical calculations for Monte Carlo "triad" and molecular dynamics "oxDNA" models, characterized by different degrees of coarse-graining, validating the perturbative and non-perturbative analyses. While our theory is in generally-good quantitative agreement with experiment, the predicted torsional stiffness does systematically deviate from experimental data, suggesting that there are as-yet-uncharacterized aspects of DNA twisting-stretching mechanics relevant to low-force, long-molecule mechanical response, which are not captured by widely-used coarse-grained models. arXiv:1809.07050v2 [cond-mat.stat-mech]

By combining analytical results and simulations of various coarse-grained models we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twistbend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternance of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, not the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants. arXiv:1812.03701v2 [cond-mat.soft]