Conserved backbone–H-bond coupling angles in secondary structures correlate with pLDDT

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Conserved backbone–H-bond coupling angles in secondary structures replicate on AlphaFold predictions and correlate with pLDDT

Data

We measured the acute angle between the backbone propagation vector and the hydrogen bond vector in secondary structures across 69 PDB structures (discovery/validation split, pre-registered hypotheses, 3/4 passed):

Structure	Mean angle	SD	n
Alpha-helix (CA(i)→CA(i+4) vs N(i+4)→O(i))	22.91°	1.62°	35
Antiparallel beta-sheet (cross-strand CA→CA vs N→O)	12.12°	2.20°	34
Separation	10.79°		p = 9.06e-34

We then tested whether AlphaFold predictions respect these angles, and whether deviations correlate with pLDDT.

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AlphaFold Test Results

65 AlphaFold predictions, 9,669 measurements (7,201 helix + 2,468 sheet).

Canonical angles replicate on predicted structures: helix ≈ 23°, sheet ≈ 13°.

Correlation with pLDDT

	n	Pearson r	p-value
Helix	7,201	-0.062	1.38e-7
Sheet	2,468	-0.037	0.069
Combined	9,669	-0.049	1.33e-6

Higher pLDDT → lower deviation from canonical angles. Sheet trend is in the expected direction but not individually significant (p = 0.069); combined analysis is highly significant.

Threshold violations — helix (most actionable result)

pLDDT group	n	Mean deviation	>5° violations	>10° violations
>90	3,500	2.94°	17.1%	2.8%
70–90	984	3.20°	19.9%	3.5%
<70	323	3.75°	27.2%	5.0%

Low-confidence helices show 79% more >10° violations than high-confidence (Mann-Whitney p = 5.50e-6).

Threshold violations — sheet

pLDDT group	n	Mean deviation	>10° violations
>90	1,599	6.55°	17.9%
70–90	732	5.93°	13.3%
<70	137	7.76°	23.4%

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Potential use as a validation signal

The coupling angle deviation captures a complementary geometric signal to pLDDT. Possible applications:

1. Flagging geometrically inconsistent secondary structures in low-confidence regions
2. Intrinsically disordered proteins — do predicted SS elements in IDP regions deviate from canonical angles?
3. Novel folds without structural homologs in training data

The effect size is small (~0.7% variance explained), so this would complement pLDDT, not replace it.

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What we are NOT claiming

• This is not a replacement or improvement for pLDDT
• The effect size is small; this is a complementary geometric signal
• Sheet correlation is borderline (p = 0.069); sheets have inherently higher angular variability
• Geometric SS detection (no DSSP) adds noise; DSSP-based assignment would likely strengthen results

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Reproducible code

# pip install numpy scipy matplotlib requests
# Core measurement — helix coupling angle
for i in range(helix_start, helix_end - 3):
    ca_vec = CA[i+4] - CA[i]          # backbone propagation
    hb_vec = O[i] - N[i+4]            # H-bond direction
    d_NO = np.linalg.norm(hb_vec)
    if 2.5 <= d_NO <= 3.6:            # confirmed H-bond only
        theta = acute_angle(ca_vec, hb_vec)
        # Helices consistently give theta ~ 23°

Full analysis script (~250 lines, downloads AlphaFold structures automatically) and all data are available under CC BY 4.0: doi:10.5281/zenodo.19391357

Paper: Srivastava, A. (2026). Quantized Angular Coupling of Protein Secondary Structures. Zenodo. doi:10.5281/zenodo.19391357

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Author

Abhishek Srivastava
Independent Researcher, Gurgaon, India
bits.abhi@gmail.com | ORCID: 0009-0006-7495-5039

Sharing this finding in the spirit of open science. Happy to provide additional data or run further analyses if useful.