The writhing of circular cross–section rods: undersea cables to DNA supercoils

Abstract

The large deflection theory of circular cross-section elastic rods is used to consider the writhing of long straight rods subjected to tension and torque, such as undersea cables, and to closed loops with inserted twist, such as DNA supercoils.The writhed shape of the long straight rod under tension and torque is easily generated by twisting a piece of string with the fingers and consists of three separate parts: a balanced-ply region, a free end loop, and two tail regions. The solution for the rod shape in each of the regions is found. The results are then joined together to ensure continuity of the position and tangent vectors of the strand centreline through the introduction of point forces and moments at the points where the strands enter and exit the balanced ply. The results of the model are consistent with simple experiments on long braided rope.The writhed shape of the closed loop with twist inserted between the ends prior to closure is modelled as a balanced ply joined to two end loops. The analysis combines the mechanics solution with the conservation of topological link to provide a simple formula which quantitatively predicts the approximate shape and helix angle of the supercoil. The results are in good agreement with simple experiments on rope and with available data on DNA supercoils.

Competition between curls and plectonemes near the buckling transition of stretched supercoiled DNA

“…We carried out numerical calculations of equilibria of macroscopic elastic rods with self-contact, building on previously published material [15, 31–33]. The elastic rod of length L is uniform and has a circular cross-section of radius ρ .…”

Screw Motion of Dna Duplex During Translocation Through Pore I: Introduction of the Coarse-Grained Model

“…In such cases, being applied to the both tails of a linear DNA hairpin (or to the opposite strands of a cyclic DNA duplex) confined within the nanopore, the torques with respect to the relevant Manning clouds ought to promote some specific writhing -and thus refolding -of the DNA tertiary structure, to form a combination of balanced plies with end loops. [59][60][61] It is intuitively clear that, in turn, such compact tertiary superhelical structuresought to be effectively translocated through the nanopore at times much shorter -and will cause much deeper ionic current dips than those of the corresponding completely unfolded DNA tertiary structures, just as observed in experiments. 4 In contrast, linear DNA hairpins folded only partially (or cyclic DNA duplexes), that is, without plies, could in many cases clog the nanopore or even be rejected by the latter -just as revealed by computer simulations.…”

Conserved linking in single- and double-stranded polymers

“…The radius of gyration at Lk = 0 scales robustly as N . 6 ,as in Figure 6. The coefficient a as a function of N is plotted in Figure 13.…”

“…We measured autocorrelation functions for the radius of gyration to determine the relaxation time for link-conserving and non-conserving chains. A link-conserving chain with 64 bonds requires roughly 2x10 6 attempted moves to attain a statistically independent configuration.…”

“…The consequences of conserved linking for DNA and for macroscopic cords are well appreciated. [1][2][3][4][5][6][7] A large imposed linking number leads such a chain to twist upon itself. This is the phenomenon of supercoiling.…”