Spectral analysis of protein backbone geometry reveals abrupt helix-coil boundaries.

Authors

Yiquan Wang

Published in

The European physical journal. E, Soft matter. Volume 49. Issue 8. Aug 07, 2026. Epub Aug 07, 2026.

Abstract

The boundaries of cooperative helix-coil transitions influence protein allostery and conformational dynamics, yet the persistent one-to-two-residue ambiguity in their assignment remains poorly characterized. We apply the discrete Hasimoto map to translate three-dimensional C $_{\alpha }^{}$ backbone geometry into a one-dimensional discrete nonlinear Schrödinger effective potential and analyze its spatial-frequency structure. Helical segments appear as near-integrable, low-entropy states whose spectral power concentrates at the zero-frequency mode, whereas coil regions show broadband fluctuations. A pointwise integrability residual and a windowed spectral entropy separate the two phases with ROC AUC values of 0.783 and 0.715, and their combination reaches 0.803, while combining the residual instead with a low-frequency energy ratio reaches 0.815. Across 1986 proteins and 19,148 of 21,107 fitted helix-coil boundaries the transition is abrupt, with a median sigmoid width of 0.145 residues that measures the steepness of a single-step discrete jump rather than a literal sub-residue distance; the transition is directionally asymmetric, with helix exits sharper than entries. Across the full dataset every C $_{\alpha }^{}$ geometry-based assignment, including DSSP-calibrated P-SEA and both spectral probes, loses agreement with the DSSP hydrogen-bond reference most acutely at these boundaries, indicating that the assignment ambiguity is a general feature of C $_{\alpha }^{}$ geometry rather than any single algorithm. The windowed spectral probe is subject to a Gabor resolution limit and is therefore outperformed by the pointwise probe, which attains the lattice-limited resolution.

PMID:
42566124
Bibliographic data and abstract were imported from PubMed on 07 Aug 2026.

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