alphadynamics 0.3.5

Compact sequence-only neural propagator for protein torsion dynamics — 2.39× lower JSD than Microsoft Timewarp at 3000× fewer parameters.

AlphaDynamics

Compact phase-flow neural propagator for protein torsion dynamics.

This repository ships two complementary releases of AlphaDynamics:

Release	Type	What it gives you	Status
v0.3.0 (latest, 2026-05-01)	sequence-only product	pip install alphadynamics → predict torsion ensembles from a sequence string, no MD seed required	Beta product release
v2.0-preprint (2026-04-29)	per-system paper	per-protein surrogate trained from seed MD; full reviewer-hardening audit, Zenodo DOI	Published preprint (paper)

Both releases share the same phase-flow architecture; v0.3.0 focuses on broad usability (one model, any sequence) and v2 focuses on per-protein fidelity (one model per protein, audited against MD).

---

v0.3.0 — sequence-only product (2026-05-01)

2.39× lower JSD than Microsoft Timewarp · 3000× fewer parameters · 64 phase oscillators · pip install alphadynamics

A tiny (~123K parameter) neural propagator that, given only a protein sequence, predicts an ensemble of torsion-angle (φ, ψ) trajectories matching the marginal Ramachandran density of long-timescale molecular dynamics simulations. On the canonical 4AA benchmark it produces densities that are 2.39× closer to ground-truth MD than Microsoft Research's Timewarp model (396M parameters), at roughly 3000× fewer parameters.

This is a free and open contribution to the protein-dynamics community.

Quickstart

pip install alphadynamics

That installs the code. Pretrained weights (a few MB) are downloaded automatically on first use into ~/.cache/alphadynamics/weights/.

Interactive mode (easiest, since v0.3.1)

Just type the command alone:

alphadynamics

It prompts you for the sequence, ensemble size, timesteps, and output path (all with sensible defaults), runs the prediction, and prints the Ramachandran basin populations on the spot. Good for first-time users and quick exploration.

Predict from the command line (power users)

alphadynamics predict --sequence AAAY --n-ensemble 16 --rollout-steps 2500 -o aaay.npz

Output aaay.npz has shape (16, 2500, 4, 2) — ensemble × time × residues × [phi, psi] in radians.

Predict from Python

from alphadynamics import predict_torsion_ensemble

traj = predict_torsion_ensemble(
    "AAAY",
    n_ensemble=16,
    rollout_steps=2500,
    seed=42,          # deterministic
)
print(traj.shape)     # (16, 2500, 4, 2)

Other CLI commands

alphadynamics            # interactive prompt (NEW in v0.3.1)
alphadynamics info       # banner, headline metric, credits
alphadynamics models     # list available pretrained weights
alphadynamics version
alphadynamics --help     # full subcommand reference

Use from Claude Code (natural language)

If you use Claude Code, you can install the AlphaDynamics plugin and then drive predictions in natural language:

/plugin marketplace add krisss0mecom/AlphaDynamics
/plugin install alphadynamics@alphadynamics-skills

Then in any Claude Code session you can say things like:

"predict torsions for KLVFFAE"

"what conformations does GNNQQNY adopt?"

"compare AAAY vs AAAW alpha-helix populations"

"Ramachandran for FVNQHLCGSHLVEALYLVCGE" (insulin B chain, 20 aa)

Claude Code will run the right alphadynamics predict command, parse the output, report basin populations, and (optionally) plot the Ramachandran map for you. Everything stays local; the plugin just orchestrates the already-installed alphadynamics pip package.

Plugin source lives in this repo under plugins/alphadynamics/.

Headline result (v0.3.0)

Canonical Ramachandran Jensen-Shannon divergence (36 bins, no smoothing, held-out validation as ground truth) on the canonical 4AA test set, averaged over three peptides AAAY, AACE, AAEW:

Model	Params	Mean JSD	4AA wins	Notes
Microsoft Timewarp	396 M	0.468	0 / 3	published baseline (research)
AlphaDynamics v0.3	123 K	0.196	3 / 3	2.39× lower, 3000× smaller

On longer peptides the improvement narrows but the model remains competitive at a tiny fraction of the parameter count:

Test set	Mean JSD
4AA (3 peps)	0.196
mdCATH N≈48	0.276
mdCATH N≈98	0.389

Honest caveats. The headline metric is density match — the model captures the marginal Ramachandran distribution well but its kinetic fingerprints (autocorrelation, dwell-time distribution, transition matrix) do not yet reproduce MD at the same level of precision. v0.3.0 is best read today as a density surrogate, not a kinetics surrogate.

How v0.3.0 works (one paragraph)

A residue's torsion state (φ, ψ) is treated as a phase pair. Conditioned on the amino-acid identity, position, and current angles, an MLP emits per-residue oscillator parameters: an intrinsic frequency, a coupling matrix, and an anchor phase. A phase-flow ODE then integrates the joint state of 64 coupled oscillators with classical RK4 over a fixed horizon t_max=4.0 (8 substeps). The integrated phase state is decoded into a mixture of axis-independent von Mises distributions per residue, from which the next torsion frame is sampled. Rolled out autoregressively, this defines a transferable sequence-only propagator over the torsion torus.

The code lives in alphadynamics/. Weights are hosted on the GitHub Releases page and downloaded on demand by alphadynamics.weights.load_pretrained.

---

v2.0-preprint — per-system paper (2026-04-29)

The v2 release is a per-protein surrogate: AlphaDynamics trains a 348K-parameter phase-flow model per protein domain from seed MD and predicts the next-step distribution over backbone torsion angles. In the v2 (2026-04-29) audit it beats:

• a matched MLP baseline on 40/40 domains (paired Wilcoxon $p<10^{-12}$, 6.44× ratio-of-means; 95% bootstrap CI 5.45–7.75×),
• a trivial AR(1) baseline in long rollouts (gap-closure ratio 0.70 vs AR(1)'s 0.00, anchored against the split-trajectory replica floor),
• the 396M-parameter Microsoft Timewarp 4AA model on 3/3 shared tetrapeptides from the public microsoft/timewarp 4AA-large/test split, under a single canonical Ramachandran JSD evaluator applied identically to both models (held-out val GT, 36 bins, no smoothing): mean JSD 0.165 vs 0.468, 2.84× closer to held-out density, using the calibrated κ×1 rollout.

v2 30-second summary

• Task: learn a per-protein molecular-dynamics surrogate in φ/ψ torsion space.
• Model: coupled phase oscillators + neural ODE + mixture-of-von-Mises head.
• One-step NLL: 40/40 wins vs MLP, $p<10^{-12}$. AR(1) is competitive on small systems; AlphaDynamics catches up on N=98 and pulls ahead on rollout.
• Rollout fidelity (load-bearing claim): 70% gap-closure to noise floor, vs MLP rollout 19%, AR(1) -2% (decohered toward uniform), uniform 0%.
• Shared-dataset head-to-head: 3/3 wins vs Microsoft Timewarp 4AA model on out-of-training tetrapeptides under unified canonical JSD; 2.84× closer to held-out density (calibrated κ×1).
• Scope (v2): per-system surrogate trained from seed MD, not a zero-shot sequence-to-dynamics model. (For sequence-only, use v0.3.0.)

Author: Krzysztof Gwozdz Started: 2026-04-14 Preprint DOI (v2, 2026-04-29): 10.5281/zenodo.19877815 Concept DOI (all versions): 10.5281/zenodo.19788564

What v2 does

AlphaDynamics learns a fast surrogate of a specific protein trajectory. Given seed MD data for one folded protein/domain, it trains a compact model that predicts the next-step distribution in backbone torsion space and can generate autoregressive rollouts for analysis.

The v2 release is not a zero-shot sequence-to-dynamics model. For that, use the v0.3.0 sequence-only product above.

• Input: torsion angles (φ, ψ) of all residues at time t
• Output: mixture-of-von-Mises distribution over angles at time t+dt
• Core architecture: phase oscillators coupled via CNOT-style interactions, evolved by torchdiffeq RK4 adjoint ODE solver
• Model size: ~350K parameters per protein/domain for the v1 full-chain model
• Inference speed: ~16 ms per frame on RTX 5090

v2 headline results

Current publication-grade status: the aligned audit is the defensible v1 result: 20 mdCATH domains at N=48, 20 domains at N=98, plus 3+3 aligned rollout/free-energy audits. The converter now aligns φ and ψ by common residue index and stores residue_indices and dihedral_alignment=common_residue_index.

Validated aligned local inputs currently exist for 20 N=48 mdCATH domains at 348 K, 20 N=98 mdCATH domains at 348 K, and the matching all-temperature rollout inputs. Smoke tests and short undertrained audits are excluded from the public release; the shipped result tables below are the publication-grade 4000-step audits.

Aligned mdCATH N≈50 audit — 20 domains, 4000 steps

Fresh phi/psi-aligned rerun on the 20 locally available N≈50 mdCATH domains at 348 K:

Domains	N used	Steps	Device	Win rate	Ratio of means	Mean ΔNLL
20	48	4000	CPU	20/20	7.66×	-757.96

All 20 input .npz files have dihedral_alignment=common_residue_index. Full table: results/mdcath_aligned20_4000step_cpu.md.

Aligned rollout free-energy audit — 3 domains, GPU

Fresh aligned 2500-step rollouts with κ×30 on three representative domains:

Domains	Training	Rollout	Mean JSD	Mean EMD	Mean |ΔG_basin|	Mean pop err
3	4000 steps, batch 512, CUDA	2500 steps	0.194	20.6°	1.356 kcal/mol	0.093

Ordered domains are good (1lwjA03, 1kwgA03: JSD ≈ 0.14, population error ≈ 0.07). The disordered domain 1vq8L01 is the honest limitation (JSD 0.300, EMD 35.9°, |ΔG_basin| 1.98 kcal/mol).

Full table: results/ramachandran_aligned3_4000step_gpu.md.

Aligned N=100 scaling audit — 20 domains, GPU

Fresh aligned one-step NLL audit at the larger size class (N=98 common residues, mdCATH 348 K), trained for 4000 steps per model with batch 256 on CUDA:

Domains	Win rate	Mean MLP NLL	Mean PF_t4 NLL	Ratio of means
20	20/20 (100%)	519.5	102.2	5.08×

PhaseFlow $t_\text{max}=4$ wins all 20 domains. Best margins: 4ktyB04 (9.8×), 2dhkA01 and 1w36F02 (8.3×). The full table with per-domain identity, MLP, PF_t1, PF_t4 NLLs is in results/mdcath_aligned20_n100_4000step_gpu.md.

Aligned N=98 rollout free-energy audit — 3 domains, GPU

Fresh aligned 2500-step rollouts with κ×30 on three representative N=98 domains:

Domains	Training	Rollout	Mean JSD	Mean EMD	Mean |ΔG_basin|	Mean pop err
3	4000 steps, batch 128, CUDA	2500 steps	0.172	17.9°	1.403 kcal/mol	0.092

Two ordered domains are good (4ktyB04: JSD 0.127, pop err 0.059; 1w36F02: JSD 0.122, pop err 0.065). The disordered domain 2hoxA01 is the honest limitation (JSD 0.266, EMD 30.1°, |ΔG_basin| 2.19 kcal/mol, pop err 0.151).

Rollout fidelity at N=98 is marginally better than at N=48 (N=48 mean JSD 0.194 vs N=98 mean JSD 0.172), suggesting AlphaDynamics scales to larger proteins without rollout degradation.

Full table: results/ramachandran_aligned3_n98_4000step_gpu.md.

Release/audit documentation:

• docs/AUDIT_MANIFEST_2026_04_25.md
• docs/PREPRINT_PACKAGE_2026_04_25.md

v2 empirical laws observed

Law 1 — Warmup time matches protein scale: Optimum ODE integration time t_max depends on chain length N and data temporal correlations. Historical runs favored t=4 on the N≈50 mdCATH benchmark, but the aligned 100-step audit favored t=1 on the five local domains. Treat t_max as a hyperparameter until the full aligned rerun settles it.

Law 2 — Advantage scales with protein ordering: The win ratio (MLP NLL / AlphaDynamics NLL) is inversely proportional to the identity baseline (natural frame-to-frame change). Well-ordered proteins (small step) give the largest advantage. Fast/disordered proteins (large step) give smaller advantage but AlphaDynamics still wins.

v2 architecture

dφ_i/dt = ω_i + Σ_j W_ij · cos(φ_j) · sin(φ_j − φ_i) + a · sin(φ_anchor_i − φ_i)

• ω_i: prime-based natural frequencies [2.11, 1.31, 0.67, 0.31, 0.17] rad/s cycled across N oscillators (incommensurable → no mutual resonance, KAM-friendly)
• W_ij: learnable asymmetric N×N coupling matrix (CNOT-inspired efficient decomposition)
• φ_anchor_i: golden phyllotaxis (2π/φ²·i mod 2π − π) — Weyl equidistribution on S¹, breaks symmetry heterogeneously
• Integrator: torchdiffeq RK4 adjoint, integration horizon t_max (tuned)
• Output head: 8-component mixture of von Mises densities on T^N (axis-independent within each mixture component)

---

Repository layout

AlphaDynamics/
├── README.md                            — this file
├── LICENSE                              — Apache 2.0 (code)
├── LICENSE-MANUSCRIPT.md                — CC BY 4.0 (paper)
├── NOTICE                               — author lineage and attribution
├── CITATION.cff                         — citation metadata
├── pyproject.toml                       — pip install alphadynamics
│
├── alphadynamics/                       — v0.3.0 sequence-only product (NEW)
│   ├── __init__.py                       — public API + banner
│   ├── api.py                            — predict_torsion_ensemble
│   ├── cli.py                            — `alphadynamics` (interactive) / predict / info / models
│   ├── banner.py                         — ASCII logo + author credit
│   ├── weights.py                        — lazy download from GitHub Releases
│   ├── ad_init.py                        — von Mises mixture prior
│   ├── models.py                         — phase-flow ODE propagator
│   ├── rollout.py                        — autoregressive rollout
│   ├── training.py                       — training loops
│   ├── data.py                           — protein trajectory loader
│   ├── metrics.py                        — canonical Ramachandran JSD
│   └── baselines.py                      — AR(1), Gaussian-step, identity
│
├── src/                                 — v2 paper code (per-system)
│   ├── alphadynamics_cli.py               — legacy product CLI
│   ├── chain_model.py                     — ChainMLP + ChainPhaseFlow
│   ├── train_real.py                      — training utilities
│   ├── chain_md.py                        — synthetic Langevin MD generator
│   ├── rollout_eval.py                    — autoregressive rollout + metrics
│   ├── ramachandran_energy_v2.py          — Ramachandran free-energy audit
│   └── ... (additional audit + benchmark scripts)
│
├── paper/
│   ├── main.md                            — manuscript source
│   ├── main.pdf                           — compiled preprint
│   ├── references.bib
│   ├── make_figures.py
│   └── figures/                           — fig1/fig2/fig3 + ramachandran panels
│
├── results/                             — aligned audit artifacts (v2 paper)
├── docs/                                — preprint package & audit notes
└── data/                                — how to obtain mdCATH (raw not committed)

---

Reproducing the v2 paper

pip install -e .[paper]

# 1. Download mdCATH domains into mdcath_raw/data/
# Example shown in data/README.md via huggingface_hub

# 2. Convert HDF5 → aligned dihedrals
python src/mdcath_convert_v3.py \
  --bench_dir mdcath_raw \
  --out_dir mdcath_real_data/mdcath_348K

# 3. Run an audit benchmark without overwriting historical tables
python src/mdcath_benchmark.py \
  --data_dir mdcath_real_data/mdcath_348K \
  --out_prefix mdcath_aligned5_results \
  --device cpu

# Or run the aligned five-domain audit end to end
DEVICE=cpu STEPS=4000 BATCH=512 src/run_aligned5_benchmark.sh

# 4. Ramachandran free-energy rollout audit
python src/ramachandran_energy_v2.py

The legacy v2 CLI (src/alphadynamics_cli.py) is preserved for paper reproducibility. The new pip-installable CLI under alphadynamics.cli is the v0.3.0 sequence-only product surface.

The productization plan and research expansion ladder are documented in docs/PRODUCT_V1_2026_04_28.md. The reviewer hardening checklist is tracked in docs/REVIEWER_RISK_REGISTER_2026_04_28.md.

---

Related work

• AlphaFold 2/3 (DeepMind) — static structure prediction (different task).
• Timewarp (Klein et al., NeurIPS 2023, Microsoft) — Cartesian normalizing flow for peptide dynamics (396M params).
• AlphaFlow / ESMFlow (Jing et al., MIT, 2024) — flow matching on conformational ensembles (different task).
• MDGen (Jing et al., MIT, 2024) — autoregressive MD in Cartesian.
• AlphaFold-MSA-subsampling (Wayment-Steele et al.) — hack AF2 via reduced MSA to get ensembles (different task: states, not trajectories).
• AlphaFold-Metainference (Vendruscolo lab, Cambridge 2024) — NMR- restrained ensemble from AF2.

AlphaDynamics occupies a distinct niche: continuous temporal propagation of torus dynamics with minimal parameters and ODE-based inductive bias.

---

Status

• v2 preprint (2026-04-29) on Zenodo, DOI 10.5281/zenodo.19877815
• v0.3.0 sequence-only product release (2026-05-01) — pip install alphadynamics
• Aligned mdCATH N≈50 benchmark — 20 domains, 20/20 wins
• Aligned mdCATH N=98 scaling audit — 20 domains, 5.08× ratio
• Aligned N=98 rollout audit — comparable fidelity to N=48
• Head-to-head vs Microsoft Timewarp 4AA — 3/3 wins (per-system, calibrated κ×1)
• Sequence-only head-to-head vs Microsoft Timewarp 4AA — 3/3 wins (transferable, v0.3.0)
• Statistical tests on aligned audit (Wilcoxon, bootstrap CI, AR(1) baseline)
• Anchored JSD reference scale vs floor / uniform / AR(1) / MLP rollout
• K-sweep ablation on mixture components
• Editable package metadata — pip install -e . exposes alphadynamics
• Bivariate von Mises head (Singh et al. 2002)
• Kinetic observables (residence times, MFPT)
• Scaling to N=150, N=200 residues
• Head-to-head vs AlphaFlow, bioEmu, MDGen
• CASP Refinement targets (CASP15 / CASP16)
• arXiv preprint
• NeurIPS ML4Sci / ICLR workshop submission

---

Data

Raw mdCATH trajectories are not committed (3.3 TB total, 200 MB per domain). See data/README.md for download instructions via Hugging Face compsciencelab/mdCATH and for the aligned .npz file format used by the audited benchmarks.

---

License

Source code is licensed under the Apache License 2.0; see LICENSE. Author and lineage attribution is in NOTICE — please preserve it in any redistribution or derivative work, as required by Section 4 of the Apache 2.0 license.

The manuscript, paper figures, result tables, and documentation are licensed under CC BY 4.0; see LICENSE-MANUSCRIPT.md.

---

Citation

If you use AlphaDynamics in academic work, please cite the relevant release. A CITATION.cff file is included so GitHub's "Cite this repository" button generates the right entry automatically.

For the v2 paper (per-system, peer-reviewable preprint):

@misc{gwozdz2026alphadynamics,
  author       = {Gwóźdź, Krzysztof},
  title        = {{AlphaDynamics}: A Per-System Phase-Flow Propagator for
                  Protein Torsion Dynamics with Calibrated Rollout Fidelity},
  year         = {2026},
  publisher    = {Zenodo},
  version      = {v2.0-preprint-2026-04-29},
  doi          = {10.5281/zenodo.19877815},
  url          = {https://doi.org/10.5281/zenodo.19877815}
}

For the v0.3.0 sequence-only product release:

@software{gwozdz2026alphadynamicsproduct,
  author  = {Gwozdz, Krzysztof},
  title   = {AlphaDynamics: Compact sequence-only neural propagator
             for protein torsion dynamics},
  year    = {2026},
  url     = {https://github.com/krisss0mecom/AlphaDynamics},
  license = {Apache-2.0},
  version = {0.3.1}
}

---

Author

Krzysztof Gwozdz — independent researcher, Poland [e-mail]

AlphaDynamics is the protein-dynamics application of a multi-year research program on phase-oscillator computation across hardware (REZON), formal phase computing, and neuroscience. See NOTICE for the full research lineage.

This project is released as a gift to the protein-dynamics community.

---

Acknowledgements

• Microsoft Research's Timewarp paper and codebase, used as the comparison baseline.
• The mdCATH consortium for long-timescale MD trajectories.
• The 4AA-large test set from microsoft/timewarp used in the canonical benchmark.