The Two Helices

Helices are everywhere in biology — alpha helices in proteins, the double helix of DNA, helical filaments in the cytoskeleton. The standard explanation credits biochemical specificity: hydrogen bonding patterns in the peptide backbone, Watson-Crick base pairing, tubulin-tubulin interfaces. The molecular details select the helical geometry. Remove the specific chemistry and the structure should collapse into a featureless globule.

Bagchi (arXiv:2603.27485, March 2026) shows that helices can form through purely physical mechanisms, without biochemical specificity, through two distinct routes — and that helices are special precisely because they require one of these routes to be active.

The context: when a polymer collapses from an extended chain into a compact state, the generic outcome is a globule or a rod. Most collapsed configurations are not helical. Helices are non-generic — they occupy a small region of the conformational landscape. Any theory of helix formation must explain not just how helices are stable but why they are selected over the overwhelmingly more numerous non-helical compact states.

Route A is geometric. Give the polymer backbone a tube-like excluded-volume constraint — the chain cannot pass through itself, and it occupies a finite thickness. Add generic attractive interactions and bending elasticity. The tube-packing constraint, combined with the preference for bending over kinking, selects an ideal helical geometry that maximizes the packing density of the tube within the collapsed volume. Left-handed and right-handed helices are exactly degenerate in free energy — there is no energetic preference for either chirality. Handedness emerges spontaneously, selected by fluctuation and then propagated by the packing geometry. The helix forms because it is the densest way to pack a tube.

Route B is energetic. Place periodic “sticker” interactions along the backbone — attractive sites separated by a fixed number of monomers. When the chain collapses, the stickers seek each other, and the fixed spacing enforces a registry: monomer n interacts with monomer n+k, which interacts with n+2k, and so on. This periodic registry wraps the chain into a helix whose pitch and radius are determined by the sticker spacing and the chain stiffness. The helix is selected not by geometry but by commensurability — the spacing of the interactions is commensurate with a helical arrangement.

The two routes produce helices through different mechanisms and respond differently to perturbation. Route A helices are geometry-dominated: change the tube thickness and the helix parameters shift continuously. Route B helices are registry-dominated: change the sticker spacing and the helix either adjusts discretely to a new commensurability or vanishes entirely.

The structural observation: biology uses both routes simultaneously. The alpha helix in proteins is stabilized by Route B — hydrogen bonds between residues separated by four backbone positions create the 3.6-residue-per-turn registry. But the backbone’s excluded volume and stiffness provide Route A’s geometric selection, preventing the chain from collapsing into a non-helical globule. The biological helix is not one mechanism. It is two mechanisms operating on the same polymer, each insufficient alone but sufficient together. The chemistry provides the registry. The geometry provides the non-generic selection. Neither created the helix. Both maintain it.