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

Abstract

By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100 base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape, that reproduces the exact loop energy up to the fourth significant digit, and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.

SerraNA: a program to determine nucleic acids elasticity from simulation data

“…6), so local bends can couple for building up a significant curvature. Our results are in the same line of others that highlighted the importance of periodicity 32,72,73 for understanding the special mechanical properties of A-tracts 19 or nucleosome-positioning sequences. [74][75][76] Protein-DNA and sequence mismatch SerraNA has the capacity to deal with perturbed DNA molecules caused by a series of factors like sequence mismatch or protein binding.…”

Length-scale-dependent elasticity in DNA from coarse-grained and all-atom models

“…Besides the individual stiffnesses of tilt (A t ), roll (A r ) and twist (C), the model ( 21) is characterized by a non-vanishing twist-roll coupling (G), as expected from the symmetry of the molecule [26]. The effects of this coupling in the conformations of a DNA molecule were discussed recently in [19,21,28].…”

“…The torsional persistence length, on the contrary, does not have a static component as it is defined from the sum of the excess of local twist densities, see Eq. (28).…”

Three-Dimensional Loop Extrusion

“…Ref. [49]). Instead, we have focused on relaxing the assumption of cis extrusion, which may be difficult to justify in (i) entangled conditions and (ii) non-topological models of loop extrusion, i.e.…”