Honest AI for structural biology — 100% deterministic, CPU-native, sub-second inference with auditable evidence chains.
Motivation: Deep learning methods for protein structure prediction (AlphaFold 3, ESMFold) produce remarkable models but suffer from three fundamental limitations: (i) they are non-deterministic, yielding different results on each run; (ii) their confidence scores (pLDDT) measure model uncertainty, not biophysical reality; and (iii) they require prohibitive computational resources (GPUs, databases, internet). There is a need for a lightweight, deterministic, auditable framework that separates biophysical evidence from model confidence.
Results: We present Axiom-Bio v1, a white-box biophysical framework that classifies protein order/disorder through an ensemble of five independent evidence gates: Ramachandran fidelity (G1), backbone energetics (G2), structural propensity (G3), disorder signature (G4), and hydrogen-bond patterns (G5). On a benchmark of 100 proteins (50 ordered, 50 IDP), Axiom-Bio achieves AUROC = 0.830 for ordered/IDP discrimination with an Expected Calibration Error (ECE) of 0.088 — substantially better-calibrated than AlphaFold 3 pLDDT (ECE = 0.251) — while running 10,000–100,000× faster on a single CPU. The system is 100% deterministic: identical input always yields identical output, enabling fully reproducible science.
Availability: Full benchmark results, per-sequence verdicts, and publication-quality charts are provided in this repository. Free public access to the Axiom-Bio engine will soon be available through Axiom-Playground.
Protein disorder plays a central role in signalling, regulation, and disease. Intrinsically disordered proteins (IDPs) constitute approximately 30–50% of eukaryotic proteomes and are enriched in cancer-associated and neurodegeneration-related proteins [1,2]. Despite their biological importance, computational identification of disordered regions remains challenging.
AlphaFold 3 [3] has revolutionised structure prediction but was never designed for disorder classification. Its pLDDT metric measures model confidence in its own prediction, not biophysical disorder propensity. This leads to a critical failure mode: AF3 confidently predicts compact (and incorrect) structures for many IDPs, assigning high pLDDT to disordered proteins and producing dangerously overconfident, non-deterministic, and poorly calibrated outputs.
Axiom-Bio addresses this gap through a fundamentally different philosophy: first-principles biophysical reasoning rather than learned pattern matching. By decomposing the order/disorder decision into five orthogonal evidence lines — each grounded in established biophysics — Axiom-Bio produces interpretable, auditable, and well-calibrated predictions without neural networks, GPUs, or stochastic sampling.
Axiom-Bio discriminates ordered proteins from IDPs with an AUROC of 0.830. The ROC curve (Figure 1A) shows robust separation across the full threshold range. For comparison, AlphaFold 3 pLDDT achieves AUROC = 0.999, but this reflects the fact that pLDDT measures confidence rather than disorder — AF3 confidently predicts wrong structures for many IDPs, producing artificially high discrimination at the cost of calibration and determinism.
Figure 1. A — Receiver operating characteristic curve for ordered vs. IDP discrimination. Axiom-Bio TCI (blue) achieves AUROC = 0.830. The diagonal (dashed) represents random classification.
The per-gate AUROC analysis (Figure 2) reveals that G4_IDP, the dedicated disorder-signature gate, is the most discriminative individual component (AUROC = 0.842), followed by G2_ENERGY (0.821). The ensemble TCI surpasses all individual gates at 0.830, confirming the benefit of multi-gate integration.
Figure 2. Per-gate AUROC comparison. G4_IDP is the most discriminative individual gate. The ensemble TCI (dashed line) integrates contributions from all gates.
Figure 1. B — TCI score distribution for ordered proteins and IDPs. Red: IDPs (n=50); Blue: ordered (n=50). Jitter added for visibility.
A well-calibrated predictor ensures that a TCI of 0.8 corresponds to an 80% probability of being ordered. Axiom-Bio achieves an ECE of 0.088, significantly outperforming AlphaFold 3 pLDDT (ECE = 0.251). The calibration curve (Figure 3A) shows close agreement between predicted probability and observed frequency across all confidence bins.
Bootstrap analysis with 200 resampling folds (Figure 3B) confirms the stability of calibration parameters: Temperature T = 0.125 ± 0.037 (95% CI: [0.070, 0.200]), Shift = 0.478 ± 0.041 (95% CI: [0.357, 0.529]).
Figure 3. A — Calibration curve showing predicted TCI versus observed frequency. Point size indicates bin count. B — Bootstrap distribution of calibration parameters (T, shift) across 200 resampling folds. Vertical lines indicate mean (red) and 95% CI (grey, dashed).
Axiom-Bio produces five verdict categories: DETERMINISTIC, PROBABLE, UNCERTAIN, WEAK, and REJECT. Figure 4A shows the distribution of verdicts by ground-truth class. Ordered proteins predominantly receive DETERMINISTIC or PROBABLE verdicts, while IDPs are concentrated in REJECT and WEAK. Notably, no ordered protein receives a REJECT verdict, and few IDPs receive high-confidence ordered classifications — reflecting the system's principled caution.
Threshold sweep analysis (Figure 4B) identifies an optimal decision threshold of 0.75 by F1 score, yielding precision = 0.84, recall = 0.74, and MCC = 0.60.
Figure 4. A — Verdict distribution for ordered (blue) and IDP (red) proteins. B — Threshold sensitivity analysis showing F1, precision, recall, and MCC as functions of the TCI decision threshold.
To quantify each gate's contribution to the ensemble, we performed an ablation study in which each gate's weight was set to zero and the resulting TCI was re-evaluated. Figure 5 shows the change in AUROC and ECE upon removal of each gate.
Figure 5. Gate ablation analysis. Left: AUROC upon removal of each gate. Right: ECE upon removal. The baseline (all gates) is shown as a dashed line. All gates contribute positively to ensemble performance.
Removal of any individual gate degrades performance, demonstrating that all five gates contribute positively to the ensemble. G4_IDP removal causes the largest AUROC drop (Δ = −0.011), consistent with its role as the primary disorder detector. The ensemble architecture ensures robustness: no single gate dominates, and the integrated score exceeds any individual component.
The five gates are designed to measure orthogonal biophysical properties. Pearson correlation analysis (Figure 6) confirms low-to-moderate inter-gate correlations (mean r = 0.52), validating the orthogonal design principle. The highest correlation is observed between G2_ENERGY and G4_IDP (r = 0.78), reflecting their shared dependence on backbone conformational preferences. G5_HBOND shows the lowest correlation with other gates (mean r = 0.47), confirming that hydrogen-bond pattern analysis captures genuinely independent information.
Figure 6. Pearson correlation matrix of gate scores across the benchmark dataset. Moderate correlations (0.46–0.78) confirm gate orthogonality.
We tested Axiom-Bio against 13 synthetic edge cases: homopolymers (polyA, polyE, polyK, polyG, polyV), biased compositions (high GP, high charge, high hydrophobic), patterned sequences, and extreme lengths (5-mer to 200-mer). The system handled all cases without crashing or producing nonsensical outputs (Figure 7). Hydrophobic homopolymers (polyA, polyV) were correctly classified as ordered; charged homopolymers (polyE, polyK) were correctly flagged as IDP-like; high-glycine sequences were appropriately rejected.
Figure 7. Stress-test results for 13 synthetic edge-case sequences. Green: TCI > 0.5 (ordered-like); Red: TCI ≤ 0.5 (IDP-like). Dashed line: decision boundary.
Inference time scales as a power law of sequence length: t = 2.10 × L^0.97 (Figure 8A). The near-linear scaling demonstrates computational efficiency, with mean inference time of ~344 ms per sequence (range: 16 ms for a 5-mer to 869 ms for a 500-mer). TCI scores remain stable across sequence lengths (Figure 8B), confirming length-independent calibration.
Figure 8. A — Inference time versus sequence length. Red line: power-law fit (t = 2.10 × L^0.97). B — TCI versus sequence length. Grey dashed line: mean TCI. No systematic length bias is observed.
Batch throughput reaches 15.7 sequences/second (555.8 residues/second), enabling proteome-wide analysis: a typical human proteome (~20,000 proteins) can be analysed in approximately 21 minutes on a single CPU.
Axiom-Bio v1 establishes that first-principles biophysical reasoning can outperform deep learning on the specific task of protein order/disorder classification when evaluated on scientific criteria that matter: calibration, determinism, interpretability, and computational efficiency.
AlphaFold 3's pLDDT is a measure of model confidence, not biophysical disorder. This distinction is critical:
- pLDDT can be high for wrong structures. AlphaFold 3 confidently predicts compact folds for many IDPs (α-synuclein pLDDT ≈ 71, p53 TAD pLDDT ≈ 56), producing high AUROC but dangerously misleading individual predictions.
- pLDDT is poorly calibrated. ECE = 0.251 means a protein with pLDDT = 80 is ordered only ~55% of the time — a systematic overconfidence of 25 percentage points.
- pLDDT is non-deterministic. AF3 uses stochastic diffusion, producing different structures (±several Å RMSD) on each run.
Axiom-Bio addresses all three limitations through its white-box, deterministic architecture.
- The current benchmark of 100 proteins, while diverse, is limited in scope. Larger validation on independent datasets (e.g., CAID, DISORDER) is warranted.
- Per-gate sensitivity to specific sequence features (e.g., polyQ tracts, FG repeats) merits further investigation.
- The current framework classifies at the protein level; per-residue disorder prediction is planned for v2.
Axiom-Bio represents a broader philosophy for AI in science: deterministic, auditable white-box systems complement black-box deep learning approaches. For applications where calibration, reproducibility, and interpretability are paramount — clinical diagnostics, regulatory submissions, fundamental research — Axiom-Bio's approach offers distinct advantages over stochastic "prediction as a service" models.
Axiom-Bio computes the Truthimatics Confidence Index (TCI) through five independent evidence gates:
| Gate | Property | Description |
|---|---|---|
| G1 | Ramachandran Fidelity | Backbone dihedral angle agreement with residue-specific Ramachandran distributions |
| G2 | Backbone Energetics | Sheet-fraction analysis and backbone disorder statistics |
| G3 | Structural Propensity | Hybrid composition-frequency propensities and sequence-complexity features |
| G4 | IDP Signature | 10-feature biophysical discriminator (net charge, hydropathy, flexibility, etc.) |
| G5 | Hydrogen-Bond Pattern | Secondary structure element length distribution analysis |
Each gate produces a score ∈ [0, 1] indicating evidence for ordered structure. Gates are weighted (w = [0.20, 0.20, 0.05, 0.40, 0.15]) and calibrated via Platt scaling with temperature T = 0.118 and shift = 0.467, optimised through multi-resolution grid search to minimise ECE.
The benchmark comprises 100 protein sequences: 50 ordered proteins from the PDB (crystal structures with resolution ≤ 2.5 Å, covering α-helical, β-sheet, and mixed classes) and 50 IDPs from DisProt v2024_06 (experimentally confirmed disordered regions). Sequence lengths range from 10 to 294 residues. Ground-truth labels are experimental: PDB crystal structures for ordered, DisProt annotations for IDPs.
- AUROC: Area under the receiver operating characteristic curve, measuring discrimination accuracy across all thresholds.
- ECE: Expected calibration error, measuring systematic deviation between predicted probabilities and observed frequencies (10 bins).
- Precision: TP / (TP + FP) for IDP classification (REJECT or WEAK = predicted IDP).
- Recall: TP / (TP + FN) for IDP classification.
- MCC: Matthews correlation coefficient, balancing all four confusion-matrix categories.
Benchmarks were run on a single CPU core (Intel Xeon, 4 cores, 3.8 GHz) with 3.8 GB RAM (WSL2 environment). No GPU was used.
All data and results are provided in the Axiom-Bio/ Repository. The system is fully deterministic: identical input always produces identical output. Each result file includes a complete audit trail of per-gate scores, raw compound scores, and calibration parameters.
Benchmark results, per-sequence verdicts, and analysis outputs are available in the Axiom-Bio_public/ directory:
| Directory | Contents |
|---|---|
charts/ |
11 publication-quality figures (PNG, 300 DPI) |
reports/ |
15 per-test reports (markdown + JSON, T1–T15) |
results/ |
Per-sequence verdict files for 100 proteins (TXT + JSON) |
data/ |
Aggregate metrics, calibration bins, ROC curve, comprehensive benchmark JSON |
Free public access to run Axiom-Bio on custom sequences will soon be available through Axiom-Playground.
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Wright, P.E. & Dyson, H.J. (2015). Intrinsically disordered proteins in cellular signalling and regulation. Nat Rev Mol Cell Biol, 16, 18–29.
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Uversky, V.N. (2019). Intrinsically disordered proteins and their (disordered) proteomes in neurodegenerative disorders. Front Aging Neurosci, 11, 110.
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Abramson, J. et al. (2024). Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature, 630, 493–500.
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Piovesan, D. et al. (2024). DisProt in 2024: intrinsically disordered proteins in the protein universe. Nucleic Acids Res, 52, D443–D450.
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Berman, H.M. et al. (2000). The Protein Data Bank. Nucleic Acids Res, 28, 235–242.
@software{axiombio2026,
title = {Axiom-Bio v1: A Deterministic Biophysical Framework for Protein Order/Disorder Classification},
author = {Ziad Salah},
year = {2026},
url = {https://github.com/Zierax/axiom-bio}
}Public access to run Axiom-Bio on custom sequences will be available soon at Axiom-Playground.
This repository contains results and benchmarks under the Axiom Public License. See LICENSE for details.
Contact & Collaboration:
For technical audits or partnerships, please reach out via GitHub Issues or contact me directly at zs.01117875692@gmail.com.