Chiral symmetry breaking of a double-stranded helical chain through bend-writhe coupling

This paper explores asymmetric elasticity of a double-stranded helical chain, which serves as a minimal model of biopolymers. The model consists of two elastic chains that mutually intertwine in a right-handed manner, forming a double-stranded helix. A simple numerical experiment for structural relaxation, which reduces the total elastic energy of the model monotonically without thermal fluctuations, reveals possible asymmetric elasticity inherent in the helical chain. It is first shown that a short segment of the double-stranded helical chain has a tendency to unwind when it is bent. It is also shown that a short segment of the helical chain has a tendency to writhe in the left direction upon bending. This tendency gives rise to a propensity for a longer segment of the chain to form a left-handed superhelix spontaneously upon bending. Finally, this propensity of the helical chain to form a left-handed superhelix is proposed to be a possible origin of the uniform left-handed wrapping of DNA around nucleosome core particles in nature. The results presented here could provide deeper insights into the roles and significance of helical chirality of biopolymers.