🧬 Resonance-Flow: Differentiable Protein Structure Prediction with NMR Self-Correction

Resonance-Flow is a JAX-native protein structure prediction framework that integrates differentiable biophysics with experimental NMR constraints. It allows models to "self-correct" by propagating gradients from physical violations (atomic clashes, bad geometry) and NMR observables (RDCs, NOE distances) back into the neural network architecture — end-to-end, with no manual refinement step.

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🚀 Key Features

• JAX-Native Gradient Flow — End-to-end differentiability from experimental constraints to model weights via jax.grad.
• Saupe Tensor RDC Loss — Differentiable least-squares fitting of the alignment tensor at every forward pass (Bax & Tjandra 1997; Cornilescu et al. 1998).
• NOE Distance Restraints — Flat-bottomed harmonic penalty on upper-bound violations, the primary 3D information source in protein NMR (Wüthrich 1986; Güntert et al. 1997).
• Biophysically Correct Geometry — Bond length loss calibrated to the canonical Cα–Cα distance of 3.80 Å (Engh & Huber 1991).
• Differentiable Steric Clash — Harmonic atom-overlap penalty with optional AMBER/CHARMM-style 1-2/1-3 bonded exclusions, powered by jax-md.
• RDC Quality Metric — Built-in Q-factor and Q_free cross-validation (Cornilescu et al. 1998; Clore & Garrett 1999) for structural validation without additional tooling.
• Backbone Conformational Checks — Pseudo-torsion angle calculation (Oldfield & Hubbard 1994) to verify secondary structure plausibility in Cα-only models.
• PBC Support — Periodic boundary conditions for simulation-box contexts.
• Transformer-to-Coords — A pre-LN Transformer architecture that maps amino acid sequences directly to physical 3D Cα coordinates.

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🧠 The Concept: "Self-Correction"

Traditional folding models are trained on static PDB snapshots. Resonance-Flow instead teaches a model to listen to physical laws and NMR data during training itself:

  Sequence  →  [Transformer]  →  Cα Coordinates
                                       │
                  ┌────────────────────┼──────────────────────┐
                  ▼                    ▼                       ▼
           Steric Clash          Bond Length              RDC / NOE
             Penalty               Loss                  Mismatch
                  └────────────────────┼──────────────────────┘
                                       │  ∇θ L_total
                                       ▼
                              [Optimizer Step]

Gradients from every constraint flow back simultaneously into the model weights — the model learns not just from data, but from physics.

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🛠️ Installation

pip install resonance-flow

For development (includes linting, type-checking, testing, and docs):

git clone https://github.com/elkins-lab/resonance-flow.git
cd resonance-flow
pip install -e ".[dev]"

Requirements: Python 3.10+, JAX ≥ 0.4, Flax, Optax, jax-md, NumPy.

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🧪 Quick Start

Run the self-correction demo

from resonance_flow.train import main

state = main(num_steps=100)
# Step   0 | Total Loss: 12.3421 | Steric: 0.0012 | Bond: 1.2034 | RDC: 0.0087
# Step  10 | Total Loss:  4.1823 | ...
# Step 100 | Total Loss:  0.0031 | ...

Use individual loss functions

import jax.numpy as jnp
from resonance_flow import (
    get_steric_clash_loss,
    get_bond_length_loss,
    rdc_loss,
    rdc_q_factor,
    noe_upper_bound_loss,
    estimate_nh_proxy_vectors,
)

# ── Steric clash (AMBER-style 1-2 bonded exclusion) ──────────────────────────
clash_fn   = get_steric_clash_loss(exclude_bonded_range=1)
positions  = jnp.array([[0.0, 0.0, 0.0], [4.0, 0.0, 0.0]])
atom_radii = jnp.array([1.5, 1.5])
clash_fn(positions, atom_radii)          # → 0.0  (no overlap)

# ── Bond length (Cα–Cα virtual bond, Engh & Huber 1991) ─────────────────────
bond_fn  = get_bond_length_loss()        # default target = 3.8 Å
ca_chain = jnp.array([[0.0,0.0,0.0],[3.8,0.0,0.0],[7.6,0.0,0.0]])
bond_fn(ca_chain)                        # → ~0.0

# ── RDC loss (Saupe tensor fitting) ─────────────────────────────────────────
nh_vecs      = jnp.array([[1.,0.,0.],[0.,1.,0.],[0.,0.,1.],
                           [0.7,0.7,0.],[0.7,0.,0.7],[0.,0.7,0.7]])
measured_rdc = jnp.array([10., -5., 2., 0., 4., 8.])
rdc_loss(nh_vecs, measured_rdc)          # → scalar MSE

# ── RDC Q-factor (structure quality; Q ≤ 0.20 = high quality) ───────────────
rdc_q_factor(nh_vecs, measured_rdc)      # → 0 – 1 (lower is better)
train_mask = jnp.array([True, True, True, False, False, False])
rdc_q_free(nh_vecs, measured_rdc, train_mask)  # → Q-factor on held-out data

# ── N-H proxy vectors from Cα coordinates (Cα-only models) ──────────────────
ca_coords = jax.random.normal(jax.random.PRNGKey(0), (10, 3))
nh_proxy  = estimate_nh_proxy_vectors(ca_coords)   # → (8, 3) unit vectors

# ── NOE upper-bound distance restraints (Wüthrich 1986) ─────────────────────
noe_pairs    = jnp.array([[0, 2], [1, 3]])
upper_bounds = jnp.array([5.0, 4.5])
noe_upper_bound_loss(positions, noe_pairs[:1], upper_bounds[:1])  # → 0.0

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🎓 Interactive Tutorial Catalog

Experience Resonance-Flow directly in your browser via Google Colab. These interactive Jupyter Notebook tutorials cover everything from basic biophysics to advanced structural self-correction.

Tutorial	Difficulty	Time	Action
Self-Correction Demo	⭐ Beginner	15 min
Biophysical Constraints	⭐ Beginner	15 min
Differentiable NMR	⭕ Intermediate	25 min
Transformer-to-Coords	🏔️ Advanced	30 min

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🔬 Scientific Basis

All loss functions and validation metrics are grounded in published, peer-reviewed NMR methodology:

Loss / Metric	Scientific Basis
RDC loss — Saupe tensor	Bax & Tjandra, J. Biomol. NMR 1997; Cornilescu et al., JACS 1998
RDC Q-factor	Cornilescu et al., JACS 1998; Clore & Garrett, JACS 1999
NOE distance restraints	Wüthrich, NMR of Proteins and Nucleic Acids 1986; Güntert et al., J. Mol. Biol. 1997
Cα–Cα bond distance (3.8 Å)	Engh & Huber, Acta Crystallogr. A 1991
N-H proxy vectors	Zweckstetter & Bax, JACS 2000
Bonded exclusion (1-2/1-3)	Cornell et al. (AMBER), JACS 1995; MacKerell et al. (CHARMM), J. Phys. Chem. B 1998
d_max = 21 700 Hz	Ottiger & Bax, JACS 1998

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🧬 Architecture

TransformerCoordinatePredictor
├── Embedding         (vocab_size=21, d_model=128)
├── Positional Embed  (learned, max_len=512)
├── N × Pre-LN Block
│   ├── LayerNorm → MultiHeadDotProductAttention → Residual
│   └── LayerNorm → FFN (4× expand, GELU) → Residual
└── LayerNorm → Linear(3)   # → (batch, seq_len, 3) Cα coordinates

The pre-LN (LayerNorm before attention) layout avoids gradient explosion and follows the convention recommended by Xiong et al. 2020.

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🤝 Contributing

Contributions are welcome! Please open an issue or pull request. The project follows:

• Formatting + Linting: ruff / ruff format
• Type checking: mypy
• Testing: pytest with coverage

# Run the full quality pipeline before submitting a PR
ruff check resonance_flow tests
ruff format resonance_flow tests
mypy resonance_flow tests
pytest --cov=resonance_flow tests

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📚 Documentation

Full theory, API reference, and examples at elkins-lab.github.io/resonance-flow.

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⚖️ License

MIT © George Elkins

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🔗 Related Projects

Resonance-Flow is the most complete end-to-end model in this ecosystem, depending on:

• diff-biophys — Differentiable RDC, NOE, bond-length, and clash kernels
• synth-nmr — NMR parameter libraries (chemical shifts, Karplus, RDC)
• synth-pdb — Protein structure data generation
• torsion-tuner — Single-structure refinement using similar torsion-space kinematics
• diff-ensemble — Ensemble counterpart for IDPs

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📖 Citation

@software{resonance_flow,
  author  = {Elkins, George},
  title   = {Resonance-Flow: Differentiable protein structure prediction with NMR self-correction},
  year    = {2026},
  url     = {https://github.com/elkins-lab/resonance-flow},
  version = {0.1.3}
}