Interactive Tutorial: Parameter Estimation for ODE Models

An interactive Jupyter notebook tutorial for learning parameter estimation in ordinary differential equation (ODE) models using pypesto, AMICI, and PEtab.

📚 Overview

This tutorial teaches you how to:

• Extract quantitative parameters (e.g., mRNA half-life) from noisy experimental data
• Build and fit mechanistic ODE models to time-series measurements
• Use modern tools (pypesto, AMICI, PEtab) for parameter inference
• Interpret results biologically and validate model fits

Case Study: Estimating mRNA degradation rates from single-cell fluorescence measurements after mRNA transfection.

Level: Intermediate (familiarity with Python and basic ODEs helpful)

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🎯 Learning Objectives

By the end of this tutorial, you will:

1. ✅ Understand why mathematical modeling is necessary for biological data analysis
2. ✅ Know how to formulate an ODE model for gene expression dynamics
3. ✅ Be able to use the pypesto + AMICI + PEtab pipeline for parameter estimation
4. ✅ Interpret fitted parameters biologically (e.g., calculate half-lives)
5. ✅ Validate model quality through residual analysis
6. ✅ Know when to extend to hybrid approaches (Universal ODEs, Neural ODEs)

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📊 Dataset

This tutorial uses single-cell fluorescence microscopy data from:

Fröhlich, F., Reiser, A., Fink, L. et al. Multi-experiment nonlinear mixed effect modeling of single-cell translation kinetics after transfection. npj Syst Biol Appl 4, 42 (2018). https://doi.org/10.1038/s41540-018-0079-7

Data description:

• System: mRNA → GFP translation in mammalian cells (HuH7)
• Protein: eGFP (stable fluorescent protein)
• Measurement: Time-lapse fluorescence microscopy (~500 single cells tracked for 30 hours)
• Technology: Micropatterned protein arrays for standardized single-cell environments
• Original data repository: https://doi.org/10.5281/zenodo.1228898

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🚀 Quick Start

Prerequisites

• Python 3.8 or higher
• Jupyter Notebook or JupyterLab
• C++ compiler (for AMICI compilation)
  • macOS: Xcode Command Line Tools (xcode-select --install)
  • Linux: build-essential package
  • Windows: Visual Studio Build Tools

Installation

1. Clone this repository:

   git clone https://github.com/echorliu/ode-simple-demo.git
   cd ode-simple-demo

2. Create a virtual environment (recommended):

   python -m venv tutorial-env
   source tutorial-env/bin/activate  # On Windows: tutorial-env\Scripts\activate

3. Install required packages:

   pip install -r requirements.txt

   Key packages:

   • pypesto - Parameter estimation toolbox
   • amici - Fast ODE simulation (compiled C++)
   • petab - Standardized parameter estimation format
   • pandas, numpy, scipy - Data manipulation
   • matplotlib - Visualization

4. Accept Xcode license (macOS only):

   sudo xcodebuild -license accept

5. Launch Jupyter:

   jupyter notebook pypesto_tutorial_interactive.ipynb

🎓 Exercises

The tutorial includes 5 interactive exercises with progressively increasing difficulty:

Exercise	Topic	Difficulty	Learning Goal
1	Half-life calculation	⭐ Easy	Understand parameter-to-phenotype mapping
2	Data interpretation	⭐ Easy	Recognize biological time delays
3	Parameter bounds	⭐⭐ Medium	Understand optimization search space
4	Biological prediction	⭐⭐ Medium	Apply estimated parameters
5	Model validation	⭐⭐⭐ Hard	Assess model quality via residuals
Challenge	Hypothesis testing	⭐⭐⭐ Hard	Modify and re-fit model

Each exercise includes:

• Clear question or task
• Code cell to complete
• Hints (where helpful)
• Hidden answers (click to reveal)
• Biological interpretation