Eur. Phys. J. B 21, 455-462 (2001)
https://doi.org/10.1007/s100510170189

Helix coil mixing in twist-storing polymers

Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK

Corresponding author: ^a emt1000@cam.ac.uk

Received: 16 November 2000
Revised: 6 February 2001
Published online: 15 June 2001

Abstract

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in "ribbons" ) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes.