Statistical mechanics of supercoiled DNA

The two strands of a closed circular DNA molecule possess as a topological invariant their linking number. This property, combined with an appreciable twist elastic constant, causes the double helix to assume a supercoiled conformation in space when a nonequilibrium twist is imposed. Thermal fluctuations play a crucial role in determining the conformation of supercoils, setting the linking number scale at which a well defined interwound supercoil forms. In addition to equilibrium supercoil structure, we discuss supercoil bending and branching and show how at large scales supercoiled DNA becomes a branched polymer. The characteristic time required for intrasupercoil reactions to occur and the force necessary to extend twisted DNA are also derived.