DNA molecules can form long, closed loops which are mircons in
length (e.g. plasmids) and subject to action by a variety of enzymes
that add or remove turns of twist. When a loop is sufficiently
undertwisted, the circular shape becomes unstable, and the molecule
adopts a more complex conformation known as a supercoil in order
to relieve the internal stresses. A similar process can be visualized
with a circular loop of rope or plastic tubing which is twisted.
The large deflection theory of linear elastic rods is used to model two
canonical supercoiled shapes: interwound and toroidal. The results
correlate reasonably with simple experiments on elastic rod analogues
and available DNA data. The primary purpose of the analysis is to
understand how the solid mechanics drives the process rather than
to obtain a comprehensive catalogue of all possible molecular
conformations.
