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arXiv · 2608.03586

Theory of Handedness Selection in Helices of Chiral Polymers and Biopolymers

Biman Bagchi
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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 $\xi_H$ and the chiral persistence length $\xi_\chi$. In the strongly helical rare-wall limit, $\xi_\chi\simeq (1/2)\exp[\beta(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.

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Biman Bagchi. 2026-08-04. Theory of Handedness Selection in Helices of Chiral Polymers and Biopolymers. https://arxiv.org/abs/2608.03586

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