The thermodynamical stability of a set of circular double helical molecules
is analyzed by path integral techniques. The minicircles differ only in
\textit{i)} the radius and \textit{ii)} the number of base pairs (N) arranged
along the molecule axis. Instead, the rise distance is kept constant. For any
molecule size, the computational method simulates a broad ensemble of possible
helicoidal configurations while the partition function is a sum over the path
trajectories describing the base pair fluctuational states. The stablest
helical repeat of every minicircle is determined by free energy minimization.
We find that, for molecules with N larger than 100, the helical repeat
grows linearly with the size and the twist number is constant. On the other
hand, by reducing the size below 100 base pairs, the double helices sharply
unwind and the twist number drops to one for N=20. This is predicted as the
minimum size for the existence of helicoidal molecules in the closed form. The
helix unwinding appears as a strategy to release the bending stress associated
to the circularization of the molecules.Comment: Europhysics Letters (2015