Supercoiled and braided DNA under tension

Double-helix DNA has a twist persistence length comparable to its bending persistence length, and thus its entropic elasticity depends on how much it is twisted. For low amounts of twist (less than about one turn per twist persistence length) there is linear elasticity for weak forces, while for large forces there is a threshold at which all chirality is expelled from the extended polymer configuration. For larger amounts of twist, plectonemic supercoiling is stabilized and there ceases to be any extension of the polymer for small forces; large forces create a mixed state of plectonemic supercoil and extended molecule. The free energy of two DNAs braided around one another is computed: to insert more than about one braid per persistence length requires expenditure of many ${\mathrm{k}}_{\mathrm{B}}$T per braid. Sufficiently tight braids wrap around themselves to form plectonemic supercoils: the force-distance behavior of braids should thus be similar to that of twisted DNA. Finally, the relevance of the thermodynamics of braiding to the disentanglement of large DNAs in living cells is discussed.