  A theoretical analysis of the effect of force and torque on spontaneously
twisted, fluctuating elastic ribbons is presented. We find that when a filament
with a straight center line and a spontaneously twisted noncircular cross
section is subjected to a sufficiently strong extensional force, its average
elongation exhibits an asymmetric response to large over and undertwist. 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
predicted behaviors can be understood in terms of continuous transformations
between straight and spiral/helical states of the ribbon. The relation between
our results and experimental observations on DNA is discussed and a new
reentrant spiral to rod transition is predicted at intermediate values of twist
rigidity and applied force.
