Twist-bend coupling and the statistical mechanics of DNA: perturbation theory and beyond
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 Ceff 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 nonperturbative 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.