A Theoretical Description of DNA Plectonemes under Tension

Abstract

Twisting a DNA molecule held under constant tension is accompanied by a transition from a linear to a plectonemic DNA configuration, in which part of the applied twist is absorbed in a superhelical structure. This is seen as a linear shortening of the DNA length with added turns after the transition. So far no theoretical description exists, which consistently describes the slope of the supercoiling curves as well as the torque in the plectonemic regime and its dependency on the applied force and the monovalent ion concentration in solution. Here, we present a simple model, in which the DNA is treated as a semiflexible rod. The energy of the plectonemic structure is calculated considering DNA bending, applied tension and electrostatic repulsion between the DNA strands but excluding fluctuations. We compare the predictions of our simple static theory with experimental supercoiling data, recorded with magnetic tweezers. We obtain an excellent agreement for the supercoiling slopes and the torque as function of force and monovalent ion concentration only if a reduced DNA charge is taken into account. We verify our theory using Monte-Carlo simulations, in which the same energetic terms are used. Surprisingly, the simple static model describes experimental data much better than more sophisticated models considering fluctuations, which considerably overestimate the torque of the plectonemic phase.