DNA elasticity: topology of self-avoidance

Abstract

We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self-avoiding ribbons and provide an underlying justification for the worm-like rod chain (WLRC) model proposed by Bouchiat and Mezard. Some theoretical points regarding the WLRC model are clarified: the 'local writhe formula' and the use of an adjustable cut-off parameter to 'regularize' the model. Our treatment brings out the precise relation between the worm-like chain (WLC), the paraxial worm-like chain (PWLC) and the WLRC models. We describe the phenomenon of 'topological untwisting' and the resulting collapse of link sectors in the WLC model and note that this leads to a free energy profile periodic in the applied link. This periodicity disappears when one takes into account the topology of self-avoidance or at large stretch forces (paraxial limit). We note that the difficult non-local notion of self-avoidance can be replaced (in an approximation) by the simpler local notion of 'south avoidance'. This gives an explanation for the efficacy of the approach of Bouchiat and Mezard in explaining the 'hat curves' using the WLRC model, which is a south avoiding model. We propose a new class of experiments to probe the continuous transition between the periodic and aperiodic behaviour of the free energy.