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The simplest model of DNA mechanics describes the double helix as acontinuous rod with twist and bend elasticity. Recent work has discussed therelevance of a little-studied coupling $G$ between twisting and bending, knownto 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 appliedforces and torques is investigated. We present a perturbative calculation ofthe effective torsional stiffness $C_\text{eff}$ for small twist-bend coupling.We find that the "bare" $G$ is "screened" by thermal fluctuations, in the sensethat 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 areshifted by $G$-dependent amounts. Using results for torsional and bendingrigidities for freely-fluctuating DNA, we show how our perturbative results canbe extended to a non-perturbative regime. These results are in excellentagreement with numerical calculations for Monte Carlo "triad" and moleculardynamics "oxDNA" models, characterized by different degrees of coarse-graining,validating the perturbative and non-perturbative analyses. While our theory isin generally-good quantitative agreement with experiment, the predictedtorsional stiffness does systematically deviate from experimental data,suggesting that there are as-yet-uncharacterized aspects of DNAtwisting-stretching mechanics relevant to low-force, long-molecule mechanicalresponse, which are not captured by widely-used coarse-grained models.

Twist-bend coupling and the statistical mechanics of the twistable worm-like chain model of DNA: perturbation theory and beyond