🧬 Stem Cell Differentiation: Numerical vs Machine Learning Approaches

Modeling Gene Regulatory Networks in Hematopoietic Stem Cell Fate Decisions

Comparing Classical Numerical Solvers with Physics-Informed Neural Networks

📘Report • 📘 Extended Report • 🚀 Quick Start • 📊 Results • 🤝 Contributing

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🎯 Project Overview

This repository investigates stem cell differentiation through the lens of computational modeling, specifically focusing on the PU.1-GATA-1 toggle switch that controls blood cell fate decisions. We compare traditional numerical methods with modern machine learning approaches to solve complex biological ODEs.

🔬 The Biological Question

How do stem cells make irreversible fate decisions? We model the mutual inhibition between transcription factors PU.1 (myeloid commitment) and GATA-1 (erythroid commitment) that determines whether a hematopoietic stem cell becomes a white or red blood cell.

🧮 The Mathematical Challenge

dG/dt = a₂P²/(1+P²) - G     (GATA-1 dynamics)
dP/dt = a₁G²/(1+G²) - P     (PU.1 dynamics)

A bistable system with nonlinear mutual inhibition

🤖 The Computational Approach

• Classical Methods: LSODA, Radau, Trapezoidal Rule
• Modern ML: Physics-Informed Neural Networks (PINNs)
• Benchmark Analysis: 13 visualizations, 9 performance tables

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✨ Key Features

🎯 Biological Relevance Real hematopoietic stem cell model Clinically relevant to leukemia research Parameters based on experimental data Bistable dynamics reproduction	🔧 Technical Excellence 4 different numerical solvers PyTorch-based PINN implementation Comprehensive benchmarking suite Reproducible scientific workflow
📊 Rich Analytics 13 comparative visualizations Multiple accuracy metrics (MSE, R², MAPE) Performance profiling & timing Statistical significance testing	🚀 Production Ready Modular, reusable code architecture Extensive documentation Cross-platform compatibility Easy parameter customization

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📂 Repository Structure

📦 stem-cell-pinns-project/
│
├── 🔬 notebooks and codes/           # Core implementations
│   ├── 🐍 LSODA.py                  # Adaptive step-size solver
│   ├── 📊 LSODES.r                  # R-based implementation  
│   ├── 🤖 PINNS.ipynb               # Neural network training
│   ├── ⚖️  PINNS_VS_Numerical.ipynb # Method comparison
│   ├── 🔢 Radau.py                  # Implicit Runge-Kutta
│   └── 📐 Trapzoidal.py             # Classical explicit method
│
├── 📚 report/                        # Project documentation
│   ├── 🎤 presentation/             # Slides and visuals for presentation
│   │   ├── Course_Project_Presentation.pdf   # Project presentation (PDF)
│   │   └── Course_Project_Presentation.pptx  # Project presentation (PowerPoint)
│   ├── 📖 Full_Extended_version.md   # Complete analysis (pages)
│   ├── 📖 Numerical_Report_Team_4.pdf   # Main report (4 pages)
│   └── 📖 Numerical_Report_Team_4(Latex_Version).tex   # Main report (Latex-Code)
│
├── 📊 results/                       # Generated visualizations
│   ├── 🔄 both/                     # Cross-method comparisons
│   ├── 📈 case1/                    # Symmetric scenario (a₁=a₂=1)
│   └── 📉 case2/                    # Asymmetric scenario (a₁=5,a₂=10)
│
└── 📋 README.md                      # This file

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🚀 Quick Start

1️⃣ Environment Setup

# Clone repository
git clone https://github.com/SiefEldinSameh/stem-cell-pinns-project.git
cd stem-cell-pinns-project

# Install dependencies
pip install -r requirements.txt

# Optional: R dependencies
Rscript -e "install.packages(c('deSolve', 'ggplot2', 'dplyr'))"

2️⃣ Run Numerical Simulations

# Individual solver execution
python "notebooks and codes/LSODA.py"      # Fastest, adaptive
python "notebooks and codes/Radau.py"      # Most accurate
python "notebooks and codes/Trapzoidal.py" # Educational baseline

3️⃣ Train Neural Networks

# Launch PINN training interface
jupyter notebook "notebooks and codes/PINNS.ipynb"

4️⃣ Compare Methods

# Comprehensive benchmarking
jupyter notebook "notebooks and codes/PINNS_VS_Numerical.ipynb"

5️⃣ View Results

Results automatically save to results/ with organized subdirectories:

• case1/ → Symmetric parameter analysis
• case2/ → Asymmetric parameter analysis
• both/ → Cross-method comparisons

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📊 Key Results

🏆 Performance Leaderboard

Method	Accuracy	Speed	Stiffness	Best Use Case
🥇 Radau	⭐⭐⭐⭐⭐	⭐⭐⭐	⭐⭐⭐⭐⭐	High-precision requirements
🥈 LSODA	⭐⭐⭐⭐⭐	⭐⭐⭐⭐⭐	⭐⭐⭐⭐	General-purpose solver
🥉 Trapezoidal	⭐⭐⭐⭐	⭐⭐⭐⭐	⭐⭐	Educational/simple cases
🤖 PINN	⭐⭐⭐⭐	⭐⭐*⭐⭐⭐	⭐⭐⭐	Data integration/real-time

*Slow training, fast inference

📈 Quantitative Metrics

📊 Case 1: Symmetric Parameters (a₁=1, a₂=1)

Method	MSE (GATA-1)	MSE (PU.1)	R² Score	Training Time
Radau	2.74×10⁻¹⁴	2.74×10⁻¹⁴	1.0000	0.052s
LSODA	1.20×10⁻¹³	1.20×10⁻¹³	1.0000	0.002s
Trapezoidal	8.00×10⁻¹⁴	8.00×10⁻¹⁴	1.0000	0.004s
PINN	7.26×10⁻¹⁰	9.24×10⁻¹⁰	0.9997	197.7s

📊 Case 2: Asymmetric Parameters (a₁=5, a₂=10)

Method	MSE (GATA-1)	MSE (PU.1)	R² Score	Training Time
Radau	2.32×10⁻¹⁴	1.29×10⁻¹³	1.0000	0.052s
LSODA	1.45×10⁻¹³	2.10×10⁻¹³	1.0000	0.003s
Trapezoidal	1.14×10⁻⁸	4.10×10⁻⁷	1.0000	0.006s
PINN	4.70×10⁻⁸	5.90×10⁻⁷	1.0000	370.6s

🎯 Method Recommendations

graph TD
    A[Choose Your Method] --> B{Primary Goal?}
    B -->|Maximum Accuracy| C[🎯 Radau Method]
    B -->|Fastest Results| D[⚡ LSODA Solver]
    B -->|Learning/Teaching| E[📚 Trapezoidal Rule]
    B -->|Data Integration| F[🤖 PINN Approach]
    
    C --> C1[Machine precision<br/>Stiff systems<br/>Critical applications]
    D --> D1[General purpose<br/>Fast prototyping<br/>Parameter sweeps]
    E --> E1[Educational use<br/>Simple systems<br/>Method comparison]
    F --> F2[Experimental data<br/>Real-time inference<br/>Parameter uncertainty]
    
    style A fill:#e1f5fe
    style C fill:#c8e6c9
    style D fill:#fff3e0
    style E fill:#f3e5f5
    style F fill:#ffebee

Loading

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🔬 Biological Insights

🧬 The PU.1-GATA-1 Toggle Switch

    Hematopoietic Stem Cell
           │
           ▼
    ┌─────────────────┐
    │   Bistable      │
    │  Toggle Switch  │
    └─────┬─────┬─────┘
          │     │
          ▼     ▼
    ┌─────────┐ ┌─────────┐
    │  PU.1↑  │ │ GATA-1↑ │
    │ GATA-1↓ │ │  PU.1↓  │
    └─────────┘ └─────────┘
          │           │
          ▼           ▼
    Myeloid Cells   Erythroid Cells
   (White Blood)    (Red Blood)

📊 Clinical Relevance

Disease	Disrupted Factor	Computational Insight
Acute Myeloid Leukemia	PU.1 overexpression	Asymmetric parameter analysis
Polycythemia Vera	GATA-1 amplification	Bistability breakdown modeling
Aplastic Anemia	Both factors reduced	System stability analysis

🎯 Model Predictions

• Commitment Time: 1.2-2.5 hours (parameter dependent)
• Switch Sensitivity: Higher in asymmetric cases
• Therapeutic Targets: Transcription factor balance restoration

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🎨 13 Comprehensive Visualizations

🔴 GATA-1 Dynamics Time evolution comparison	🔵 PU.1 Dynamics Transcription factor trajectories	📊 MSE Analysis Method accuracy comparison
⏱️ Performance Timing Computational efficiency	📈 R² Correlation Goodness of fit analysis	🎯 MAPE Errors Relative accuracy metrics
🔄 Phase Portraits System dynamics visualization	🤖 PINN Training Neural network convergence	⚡ Speedup Analysis Performance benchmarking

💡 All plots are available in the results/ directory in publication-ready quality

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🔧 Technical Specifications

💻 System Requirements

Minimum Configuration 🖥️ 4GB RAM ⚡ 2-core CPU 💾 500MB storage 🐍 Python 3.8+

Recommended Setup 🖥️ 8GB+ RAM ⚡ 4+ core CPU 🎮 GPU (CUDA compatible) 💾 1GB+ storage

📦 Dependencies

# Core Scientific Computing
numpy >= 1.21.0      # Numerical operations
scipy >= 1.7.0       # Scientific algorithms  
matplotlib >= 3.5.0  # Visualization
pandas >= 1.3.0      # Data manipulation

# Machine Learning
torch >= 1.11.0      # Neural networks
torchvision >= 0.12.0 # Vision utilities

# Interactive Computing
jupyter >= 1.0.0     # Notebook environment
ipykernel >= 6.0.0   # Jupyter kernel

⚡ Performance Optimization

• GPU Acceleration: Enable CUDA for PINN training
• Vectorization: Batch operations for inference
• Parallel Computing: Multi-core parameter sweeps
• Memory Management: Efficient tensor operations

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🎓 Educational Value

👨‍🎓 Learning Objectives

• Systems Biology: Gene regulatory network modeling
• Numerical Methods: ODE solver comparison and selection
• Machine Learning: Physics-informed neural networks
• Scientific Computing: Benchmarking and validation

📚 Pedagogical Features

• Step-by-step Implementation: Well-commented code
• Mathematical Derivations: Complete in extended report
• Biological Context: Real-world relevance
• Comparative Analysis: Method trade-offs discussion

🔬 Research Applications

• Method Development: Template for new solver comparison
• Biological Modeling: Extensible to other toggle switches
• Parameter Studies: Systematic exploration framework
• Clinical Translation: Disease modeling foundation

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🤝 Contributing

🌟 How to Contribute

1. 🍴 Fork the repository
2. 🌿 Create a feature branch (git checkout -b feature/amazing-solver)
3. 📝 Commit your changes (git commit -m 'Add amazing solver')
4. 📤 Push to the branch (git push origin feature/amazing-solver)
5. 🔀 Open a Pull Request

🐛 Reporting Issues

• Use GitHub Issues for bug reports
• Include system information and error traces
• Provide minimal reproducible examples
• Tag with appropriate labels (bug/enhancement/question)

🎯 Areas for Contribution

• New Solvers: Additional numerical methods
• Biological Models: Other gene regulatory networks
• Visualizations: Enhanced plotting and analysis
• Documentation: Improved explanations and examples
• Performance: Optimization and profiling
• Testing: Unit tests and validation suites

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📚 References & Further Reading

🔬 Key Scientific Papers

Foundational Biology

• Chickarmane et al. (2006) - "Transcriptional dynamics of the embryonic stem cell switch" - Computational modeling of PU.1-GATA-1 system
• Orkin & Zon (2008) - "Hematopoiesis: an evolving paradigm for stem cell biology" - Nature Reviews Genetics
• Enver et al. (2009) - "Stem cell states, fates, and the rules of attraction" - Cell Stem Cell

Computational Methods

• Raissi et al. (2019) - "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems" - Journal of Computational Physics
• Hairer & Wanner (1996) - "Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems" - Springer
• Shampine & Gear (1979) - "A user's view of solving stiff ordinary differential equations" - SIAM Review

Systems Biology

• Alon (2006) - "An Introduction to Systems Biology: Design Principles of Biological Circuits" - CRC Press
• Davidson (2010) - "Emerging properties of animal gene regulatory networks" - Nature
• Elowitz & Leibler (2000) - "A synthetic oscillatory network of transcriptional regulators" - Nature

🌐 Useful Resources

• 📖 Full Extended Report - Complete mathematical derivations
• 🔗 SciPy ODE Documentation - Numerical solver details
• 🤖 PyTorch Tutorials - Neural network implementation
• 📊 Systems Biology Resources - Domain knowledge

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📄 License & Citation

📜 License

This project is licensed under the MIT License - see the LICENSE file for details.

📝 Citation

If you use this work in your research, please cite:

@software{stem_cell_pinns_2024,
  title={Stem Cell Differentiation: Numerical and Machine Learning Approaches},
  author={[Your Name]},
  year={2024},
  url={https://github.com/SiefEldinSameh/stem-cell-pinns-project},
  note={Computational modeling of PU.1-GATA-1 toggle switch}
}

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🙏 Acknowledgements

🔬 Scientific Foundation

Built upon decades of research in systems biology and hematopoietic development

🧮 Computational Infrastructure

Powered by the scientific Python ecosystem and PyTorch framework

🌍 Open Science Community

Inspired by principles of reproducible research and collaborative science

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This project bridges computational biology, numerical analysis, and machine learning to understand fundamental processes in stem cell biology. We hope it serves as both a research tool and educational resource for the scientific community.

⭐ Star this repository if you find it useful for your research or learning!