Unwinding of circular helicoidal molecules vs. size

The thermodynamical stability of a set of circular double helical molecules is analyzed by path integral techniques. The minicircles differ only in i) the radius and 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 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.