Discontinuous growth of DNA plectonemes due to atomic scale friction.

We develop a model to explain discontinuities in the increase of the length of a DNA plectoneme when the DNA filament is continuously twisted under tension. We account for DNA elasticity, electrostatic interactions and entropic effects due to thermal fluctuation. We postulate that a corrugated energy landscape that contains energy barriers is the cause of jumps in the length of the plectoneme as the number of turns is increased. Thus, our model is similar to the Prandtl-Tomlinson model of atomic scale friction. The existence of a corrugated energy landscape can be justified due to the close proximity of the neighboring pieces of DNA in a plectoneme. We assume the corrugated energy landscape to be sinusoidal since the plectoneme has a periodic helical structure and rotation of the bead is a form of periodic motion. We perform calculations with different tensile forces and ionic concentrations, and show that rotation-extension curves manifest stair-step shapes under relatively high ionic concentrations and high forces. We show that the jump in the plectonemic growth is caused by the flattening of the energy barrier in the corrugated landscape.