Theory for the DNA Supercoiling Transition in Extension-Rotation Experiments

Abstract

Extension jumps were recently observed in single-molecule experiments where a DNA molecule (few kbp long) is held under tension while its ends are slowly rotated. For low rotation the molecule is believed to adopt (disordered) straight configurations and when a rotation threshold is reached the molecule jumps into a supercoiled phase: plectonemes arise. The transition is not continuous: the end-to-end extension of the molecule experiences an abrupt decrease.We develop a theory where we compare the free-energies of the straight and supercoiled states. Care is taken with the energy of the supercoiled state where bending and twist energies for the plectonemes tip and the region joining the plectonemes and the ends of the molecules are included.We find that the free energies of the straight and supercoiled states cross for a value n∗ of the imposed rotation. The extension jump is then given by the difference between the extension of the two states. Theoretically computed values compare well with experimental data.View Large Image | View Hi-Res Image | Download PowerPoint Slide