On the deformation of fluctuating chiral ribbons

A theoretical analysis of the effect of force and torque on fluctuating chiral ribbons is presented. We find that when a filament with a straight centerline and a spontaneously twisted noncircular cross-section is subjected to a sufficiently strong extensional force, it exhibits an asymmetric response to large degrees of overwinding and unwinding. We construct the stability diagram that describes the buckling transition of such ribbons under the opposing action of force and torque and show that all the observed behaviors can be understood in terms of continuous transformations between straight and spiral states of the ribbon. The relation between our results and experimental observations on DNA is discussed and a new re-entrant spiral-to-rod transition is predicted at intermediate values of twist rigidity and applied force.