Twist-bend coupling and the statistical mechanics of the twistable wormlike-chain model of DNA: Perturbation theory and beyond

Abstract

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]

Twist-bend coupling, twist waves, and the shape of DNA loops

“…The origin of the observed diffusive behavior stems from the very weak contribution of ∆E(φ) to Eq. (19), as discussed in Section IV, indicating that the phase φ moves on an almost-flat energy landscape.…”

A Primer on the oxDNA Model of DNA: When to Use it, How to Simulate it and How to Interpret the Results

“…This model can be augmented with an extensional modulus ( Odijk, 1995 ) and a representation of twist with associated twist modulus ( Yamakawa, 1977 ). It is also possible to consider coupling between the modes of deformation ( Gore et al, 2006 ; Nomidis et al, 2019 ). As with the nearest-neighbour model of DNA, the influence of these approaches is enormous, particularly within the biophysics community.…”

“…The oxDNA model, first published in 2010 ( Ouldridge et al, 2010a ) (and with a slightly updated potential in 2011 ( Ouldridge et al, 2011 )), has now been extensively applied to problems in nanotechnology ( Ouldridge et al, 2013a ; Doye et al, 2013 ; Srinivas et al, 2013 ; Machinek et al, 2014 ; Snodin et al, 2016 , 2019 ; Henning-Knechtel et al, 2017 ; Hong et al, 2018 ), soft matter ( De Michele et al, 2012 ; Rovigatti et al, 2014 ; Procyk et al, 2020 ; Stoev et al, 2020 ), biophysics ( Matek et al, 2012 ; Romano et al, 2013 ; Matek et al, 2015 ; Mosayebi et al, 2015 ; Harrison et al, 2019 ; Nomidis et al, 2019 ) and biology ( Lee et al, 2015 ; Wang et al, 2015 ; Craggs et al, 2019 ). Numerous tools exist to generate and visualize systems with oxDNA ( Henrich et al, 2018 ; Suma et al, 2019 ), alongside two independent, publicly-available code bases for actually running simulations with at least three qualitatively distinct algorithms for simulating the model ( Ouldridge et al, 2011 ; Snodin et al, 2015 ).…”

A quantitative model of a cooperative two-state equilibrium in DNA: experimental tests, insights, and predictions

“…This is due to the rotational averaging of the properties over several turns. The long-distance torsional rigidity depends upon the local twist–bend coupling and bending anisotropy potential parameters in the derived manner (Nomidis et al ., 2019). However, this new theory is evidently incapable of fitting the experimental data at both low and high forces with a single set of parameters.…”