  Using Langevin dynamics simulations, we study elastic response of single
semiflexible polyelectrolytes to an external force pulling on the chain ends,
to mimic the stretching of DNA molecules by optical tweezers. The linear chains
are condensed by multivalent counterions into toroids. The force-extension
curve shows a series of sawtooth-like structure, known as the stick-release
patterns in experiments. We demonstrate that these patterns are a consequence
of the loop-by-loop unfolding of the toroidal structure. Moreover, the
dynamics, how the internal structure of chain varies under tension, is
examined. At the first stage of the stretching, the toroidal condensate
decreases its size until the loss of the first loop in the toroid and then,
oscillates around this size for the rest of the unfolding process. The normal
vector of the toroid is pulled toward the pulling-force direction and swings
back to its early direction repeatedly when the toroidal chain looses a loop.
The results provide new and valuable information concerning the elasticity and
the microscopic structure and dynamic pathway of salt-condensed DNA molecules
being stretched.
