Statistical Mechanics of Supercoiled DNA

The conformation of long supercoiled DNA loops under near physiological conditions has been the subject of a long series of laboratory and Monte Carlo experiments, and impressive agreement between theory and experiment has been achieved [1–2]. A closed unnicked DNA loop has fixed linking number: this constraint leads to a competition between twisting and bending (writhing) elastic energy which drives plectonemic supercoiling. However, entropy, as manifest through a fluctuation induced repulsive force, overwhelms this elastic effect for fractional linking number perturbations ∣σ∣ < 0.02, causing a chiral random-coil conformation. For ∣σ∣ > 0.02, plectonemic supercoils are stable, but thermal fluctuations continue to play an important role, competing with bending and twisting elastic energy to set the superhelical radius. We have constructed an analytic theory for this effect that agrees well with experiment [3], using methods from polymer statistical mechanics.