  Helically coiled filaments are a frequent motif in nature. In situations
commonly encountered in experiments coiled helices are squeezed flat onto two
dimensional surfaces. Under such 2-D confinement helices form "squeelices" -
peculiar squeezed conformations often resembling looped waves, spirals or
circles. Using theory and Monte-Carlo simulations we illuminate here the
mechanics and the unusual statistical mechanics of confined helices and show
that their fluctuations can be understood in terms of moving and interacting
discrete particle-like entities - the "twist-kinks". We show that confined
filaments can thermally switch between discrete topological twist quantized
states, with some of the states exhibiting dramatically enhanced
circularization probability while others displaying surprising
hyperflexibility.
