Unwinding of circular helicoidal molecules versus size

Abstract

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.