Theory of Handedness Selection in Helices of Chiral Polymers and Biopolymers

Abstract

Helices are among the most common ordered structures in biological and synthetic polymers, but their formation involves more than local conformational preference. A finite helix must nucleate, grow, resist breaking, and maintain a selected handedness against thermal fluctuations. We develop a three-state Ising-like transfer-matrix theory in which each segment is coil-like, right-handed helical, or left-handed helical. This formulation separates ordinary helix--coil cooperativity from the persistence of handedness. The right--left symmetric problem decomposes into symmetric and antisymmetric sectors, giving two characteristic lengths: the helical correlation length $ξ_H$ and the chiral persistence length $ξ_χ$. In the strongly helical rare-wall limit, $ξ_χ\simeq (1/2)\exp[β(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.