🧬 DiffBiophys: Differentiable Biophysics for the AI Era

DiffBiophys is a high-performance Python library for differentiable biophysical modeling. Built on JAX, it re-implements core structural biology and spectroscopy observables (SAXS, NMR, CD) as hardware-accelerated, auto-differentiable kernels.

Documentation Website | Use Cases

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🎯 Vision

To bridge the gap between static structural models and experimental solution-state data by providing a "differentiable bridge." This allows researchers to:

1. Optimize protein structures directly against experimental spectra via gradient descent.
2. Train machine learning models using physics-informed loss functions.
3. Accelerate large-scale biophysical simulations on GPUs and TPUs.

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🏗️ Core Components

1. diff_biophys.geometry (Differentiable Structural Engine)

• NeRF (Natural Extension Reference Frame): Differentiable conversion from internal coordinates ($\phi, \psi, \omega$, bond lengths/angles) to Cartesian XYZ.
• Kabsch Alignment: Differentiable optimal superposition using SVD.
• Torsion Analysis: Vectorized calculation of all backbone and side-chain dihedrals.

2. diff_biophys.saxs (Differentiable Scattering)

• Debye Formula: $O(N^2)$ inter-atomic interference summation.
• Hydration Shell Correction: Excluded-volume solvent subtraction (Fraser et al. 1978).
• Hardware Acceleration: GPU-optimized pairwise distance kernels via JAX vmap.
• Use Case: Fitting structure compactness and radius of gyration to solution-state X-ray scattering curves.

3. diff_biophys.nmr (Differentiable Spectroscopy)

• Residual Dipolar Couplings (RDCs): Differentiable Saupe tensor alignment and coupling calculation. Includes SVD-based tensor fitting.
• Chemical Shifts: Differentiable ring-current (Johnson-Bovey) shielding and softmax-weighted secondary structure Cα shift predictor.
• Karplus J-coupling: Parameterizable 3J coupling equation (Vuister & Bax 1993 defaults).
• Use Case: Refining side-chain packing and domain orientations against high-resolution NMR data.

4. diff_biophys.cd (Differentiable Dichroism)

• Matrix-Method Simulation (planned): Differentiable simulation of peptide bond transition dipole coupling via DeVoe theory.
• Status: ⚠️ Not yet implemented — raises NotImplementedError.

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⚡ Technical Architecture

• Backend: JAX (XLA-compiled) — supports CPU, GPU, and TPU.
• Parallelism: Native support for vmap (vectorization across ensembles/trajectories) and pmap (multi-device execution).
• Differentiability: Forward and reverse-mode autodiff through all kernels.
• Interoperability: JAX arrays are compatible with NumPy and can be exchanged with PyTorch via dlpack (user-managed conversion).

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🚀 Roadmap

Phase 1: Foundations (Alpha)

• Differentiable NeRF and Kabsch alignment.
• GPU-accelerated Debye formula for SAXS with hydration shell correction.
• Unit tests verifying parity with synth-pdb NumPy implementations.

Phase 2: NMR & Spectroscopy (Beta)

• Differentiable RDC and Karplus kernels.
• Differentiable Johnson-Bovey ring current model.
• Integration with synth-nmr parameter libraries (optional dependency).

Phase 3: Integration & Optimization (v1.0)

• Example notebooks for structure refinement via gradient descent.
• Plugin for torch-based AI models to use biophysical loss functions.
• Full CD matrix-method implementation (DeVoe theory).
• Full support for BinaryCIF streaming.

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📂 Repository Structure

diff-biophys/
├── diff_biophys/          # Core package
│   ├── geometry/          # NeRF, Kabsch, Torsions
│   ├── saxs/              # Debye kernels, form factors
│   ├── nmr/               # RDCs, Karplus, Ring Currents, Chemical Shifts
│   ├── cd/                # CD simulation (planned)
│   └── ensemble.py        # Ensemble averaging API
├── tests/                 # Parity, gradient, and scientific validation checks
├── examples/              # Jupyter notebooks (Refinement Lab)
├── docs/                  # API and Theory
├── pyproject.toml         # Modern build config
└── README.md

🚀 Installation

pip install diff-biophys

For GPU support (CUDA):

pip install "jax[cuda12]" diff-biophys

🤝 Contributing

Contributions are welcome from both ML and structural biology communities! Please open an issue or pull request on GitHub. Run pre-commit run --all-files before submitting.

🔗 Related Projects

diff-biophys is the differentiable engine powering the higher-level tools in this ecosystem:

• synth-pdb — Synthetic structure generation (uses NumPy implementations)
• synth-nmr — NMR observables (optional dependency)
• synth-saxs — SAXS profile simulator
• diff-ensemble — IDP ensemble VAE (depends on diff-biophys)
• TorsionTuner — GNN refinement (depends on diff-biophys)
• resonance-flow — NMR-guided folding (depends on diff-biophys)

⚖️ License

MIT License — see LICENSE for details.

📖 Citation

@software{diff_biophys,
  author  = {Elkins, George},
  title   = {diff-biophys: Differentiable biophysics kernels for JAX},
  year    = {2024},
  url     = {https://github.com/elkins/diff-biophys},
  version = {0.1.2}
}