  In mechanical manipulation experiments, a single DNA molecule overwound at
constant force undergoes a discontinuous drop in extension as it buckles and
forms a superhelical loop (a plectoneme). Further overwinding the DNA, we
observe an unanticipated cascade of highly regular discontinuous extension
changes associated with stepwise plectoneme lengthening. This phenomenon is
consistent with a model in which the force-extended DNA forms barriers to
plectoneme lengthening caused by topological writhe. Furthermore, accounting
for writhe in a fluctuating solenoid gives an improved description of the
measured force-dependent effective torsional modulus of DNA, providing a
reliable formula to estimate DNA torque. Our data and model thus provide
context for further measurements and theories that capture the structures and
mechanics of supercoiled biopolymers.
