Elastic model of highly supercoiled DNA

The equilibrium shapes of supercoiled DNA are investigated by employing an elastic model. First, a set of Euler equations is derived to determine the equilibrium shapes under ring‐closure conditions. Two exact solutions that describe circular and figure‐8 shapes are obtained. Using these and their topological properties, the configuration change from the circular to the figure‐8 form is discussed. Second, more intricate structures of supercoiling DNA are studied by a numerical analysis. Among a class of configurations, the shape that has the minimum elastic energy is explicitly determined. Poisson's ratio, the ratio of the self‐avoiding radius to the total length, and the deficit (or excess) of the linking number ΔLk are found to be the important parameters. We conclude that the topology and the elastic theory of looped DNA explain the essential features of the supercoiling phenomena.