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

## 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

```python
# 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](https://zenodo.org/records/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](https://orcid.org/0009-0006-7495-5039)

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