🧬 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.
• Hardware Acceleration: GPU-optimized pairwise distance kernels.
• 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.
• Chemical Shifts: Differentiable Ring-Current (Johnson-Bovey) shielding and Karplus J-coupling kernels.
• Use Case: Refining side-chain packing and domain orientations against high-resolution NMR data.

4. diff_biophys.cd (Differentiable Dichroism)

• Matrix-Method Simulation: Differentiable simulation of peptide bond transition dipole coupling.
• Use Case: Predicting secondary structure content and verifying fold stability.

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⚡ Technical Architecture

• Backend: JAX (XLA-compiled).
• Parallelism: Native support for vmap (vectorization across ensembles/trajectories) and pmap (multi-device execution).
• Differentiability: Support for both Forward and Reverse-mode autodiff.
• Interoperability: Seamless integration with PyTorch/TensorFlow (via DLPack) and standard structural formats (mmCIF/BCIF).

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🚀 Roadmap

Phase 1: Foundations (Alpha)

• Differentiable NeRF and Kabsch alignment.
• GPU-accelerated Debye formula for SAXS.
• 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.

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 support for BinaryCIF streaming.

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📂 Repository Structure (Proposed)

diff-biophys/
├── diff_biophys/          # Core package
│   ├── geometry/          # NeRF, Kabsch, Torsions
│   ├── saxs/              # Debye kernels, form factors
│   ├── nmr/               # RDCs, Karplus, Ring Currents
│   ├── cd/                # CD simulation
│   └── utils/             # Constants, JAX-NumPy shims
├── tests/                 # Parity and gradient checks
├── examples/              # Jupyter notebooks (Refinement Lab)
├── docs/                  # API and Theory
├── pyproject.toml         # Modern build config
└── README.md