An Information-Cosserat Framework for Spinal Geometry

This repository contains the manuscript, reproducible analysis code, and datasets supporting a theoretical framework that explains how developmental information shapes biological structures against gravity. The work bridges developmental genetics, biomechanics, and differential geometry to understand spinal curvature in normal development, microgravity adaptation, and pathological conditions like scoliosis.

Key Insight: Developmental information acts as biological "countercurvature"—modifying the effective spacetime metric experienced by living structures, enabling them to maintain complex geometries against gravitational loading.

📄 Manuscript: manuscript/main.tex
📊 Figures: figures/main/
🔬 Core Logic: src/spinalmodes/

The repository is organized into clear functional domains:

.
├── theory/                       # Theoretical frameworks, derivations, and living hypotheses
│
├── src/                          # Core Python packages
│   ├── spinalmodes/              # Main IEC model and Cosserat implementation
│   └── afcc/                     # Protein structure utilities
│
├── research/                     # Active research modules (e.g., AlphaFold Countercurvature)
│
├── manuscript/                   # Camera-ready manuscript sources
│   ├── main.tex                  # Main LaTeX file
│   └── references.bib            # Bibliography
│
├── scripts/                      # Reproducible experiment runners
│   ├── experiments/              # Core simulation runners
│
├── docs/                         # Project documentation and admin plans
├── data/                         # Datasets (tracked and external)
└── archive/                      # Legacy code and prior iterations

# Clone repository
git clone https://github.com/sayujks0071/life.git
cd life

# Create virtual environment (Python 3.10+ required)
python3 -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# Install dependencies
pip install -r requirements.txt

To run the minimal Elastica experiment utilizing the Counter-Curvature Rod System:

python scripts/experiment_minimal_elastica.py

For protein structure analysis steps, refer to research/alphafold_countercurvature/README.md (if available) or explore the module directly.

The model demonstrates that the characteristic spinal S-curve emerges as the energetic ground state when developmental information (HOX patterning) couples to mechanical properties via the Information-Elasticity Coupling (IEC).

Three distinct regimes identified in the parameter space:

• Gravity-dominated: Structure follows passive gravitational geodesics.
• Cooperative: Information and gravity balance (normal physiology).
• Information-dominated: Strong geometric distortion (potential pathology).

Model predicts spinal curvature persists in microgravity, identifying a "Stagnant Pool" effect driven by fluid shifts that may drive inflammatory scoliosis.

If you use this work, please cite:

@article{krishnan2025biological_countercurvature,
  title   = {Biological Countercurvature of Spacetime: An Information--Cosserat Framework for Spinal Geometry},
  author  = {Krishnan, Sayuj},
  journal = {preprint},
  year    = {2025},
  url     = {https://github.com/sayujks0071/life}
}

This project adopts a dual-licensing model:

• Source Code: Licensed under the MIT License.
• Manuscript & Documentation: Licensed under CC BY 4.0.

See docs/LICENSING.md for full details on component licensing, including third-party and legacy code in archive/.