Torque and dynamics of linking number relaxation in stretched supercoiled DNA

In micromechanical studies of DNA, plectonemically supercoiled domains are often used as sources of constant torque. These torques are not easily measured and are instead usually estimated. Here, coexisting extended and supercoiled DNA domains are analyzed, and closed-form expressions for the dependence of extension and torque on force and linking number are presented. When there are coexisting domains of plectonemic and extended DNA, the torque depends only on force, with no dependence on linking number. However, torque depends on force in a manner more complex than a simple power law, involving the free energy of the extended and plectonemic DNA. A simple strategy is described for measurement of the free energies of both extended and plectonemic DNA without reference to specific microscopic polymer models. Applications of the theory to analysis of relaxation of supercoiling by enzymes which permit friction-controlled rotational relaxation of linking number is also presented. Such enzymes must display a breaking of symmetry between relaxations driven by equal magnitude but opposite direction torques.