On universal aspects of the left-handed helix region

TL;DR

This paper investigates the geometry of protein backbones, revealing a residue-independent, highly localized orientation pattern in the left-handed helix region that involves at least seven amino acids.

Contribution

It introduces a geometric analysis of protein backbones using framed polygons, uncovering universal orientation patterns in the left-handed helix region across multiple residues.

Findings

Localization of $C_β$ carbons in the left-handed helix region

Persistence of localization to $C_γ$ and $C_δ$ carbons

Residue-independent collective behavior over at least seven amino acids

Abstract

We inspect the geometry of proteins by identifying their backbones as framed polygons. We find that the left-handed helix region of the Ramachandran map for non-glycyl residues corresponds to an isolated and highly localized sector in the orientation of the $C_\beta$ carbons, when viewed in a Frenet frame that is centered at the corresponding $C_\alpha$ carbons. We show that this localization in the orientation persists to $C_\gamma$ and $C_\delta$ carbons. Furthermore, when we extend our analysis to the neighboring residues we conclude that the left-handed helix region reflects a very regular and apparently residue independent collective interplay of at least seven consecutive amino acids.