Zebrafish Stripe Simulation and Pattern Fitting

ISEF Category: Computational Biology and Bioinformatics

Subcategory: Computational Biomodeling  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

Zebrafish stripes are not painted on. They emerge from simple rules that cells follow while the fish grows. That means you can study a living pattern like a puzzle made of math. If your model matches real images, you are not just making art, you are testing how biology builds order.

What Is It?

Reaction-diffusion models describe how two or more chemicals, or signals, spread and interact to make patterns. Think of a drop of food coloring in water, then add a second process that speeds up in some places and slows down in others. With the right balance, simple local rules can create stripes, spots, and bands.

The Gray-Scott and Turing models are two famous versions of this idea. In a zebrafish project, you build a simulation that makes stripe-like patterns, then compare those patterns to public zebrafish images from ZFIN, the Zebrafish Information Network. A differentiable PDE approach means your simulator is set up so you can change model parameters and see how the predicted pattern changes in a smooth, searchable way. That makes it possible to estimate which parameter values best fit real fish images.

Why This Is a Good Topic

This is a strong science fair topic because you can test a clear claim, whether a reaction-diffusion model can reproduce real zebrafish stripe variants. You also connect math to a real biology problem, how animals form body patterns during growth. You can learn image analysis, simulation, parameter fitting, and model validation. Those are useful skills for computational biology, and they can all be judged with real data.

Research Questions

• How does changing the diffusion ratio alter stripe width and spacing in a zebrafish reaction-diffusion model?
• What is the effect of different reaction rates on whether the simulation produces stripes, spots, or mixed patterns?
• Does a Gray-Scott model or a Turing model fit public ZFIN zebrafish images more closely?
• To what extent can a differentiable PDE fit recover morphogen parameters from stripe variants in different zebrafish strains?
• Which image similarity metric best matches simulated patterns to real zebrafish photos?
• How does adding growth to the model change the match between simulated and observed stripe curvature?
• To what extent does noise in the input image change the inferred parameter values?

Basic Materials

• Computer with enough memory to run Python and simulations.
• Python installation with NumPy, SciPy, Matplotlib, and PyTorch or JAX.
• Public zebrafish images from ZFIN.
• ImageJ for measuring stripe width, spacing, and contrast.
• Spreadsheet software for logging parameter sets and scores.
• External hard drive or cloud storage for simulation outputs.
• Notes file or lab notebook for tracking model choices and image sources.

Advanced Materials

• Workstation or university lab computer with a strong GPU for faster parameter fitting.
• Python with PyTorch, JAX, or another automatic differentiation library.
• Access to a version-controlled code repository.
• Image analysis pipeline for segmentation and alignment.
• Public zebrafish image sets from ZFIN with metadata.
• Statistical software for model comparison and uncertainty estimates.
• Optional plotting package for scientific figures and parameter maps.

Software & Tools

• Python: Runs the simulation, image processing, and parameter fitting code.
• ImageJ: Measures stripe spacing, segment boundaries, and image contrast.
• PyTorch: Supports differentiable modeling and gradient-based parameter search.
• JAX: Speeds up array math and automatic differentiation for PDE fitting.
• PubMed: Helps you find review articles on reaction-diffusion pattern formation and zebrafish pigmentation.

Experiment Steps

1. Define the biological pattern you want to match, such as wild type stripes, stripe breaks, or variant stripe spacing.
2. Choose one simulation family first, then lock its parameter list before you start fitting.
3. Build an image pipeline that turns public zebrafish photos into comparable measurements.
4. Design controls that separate true biological fit from image size, orientation, and contrast effects.
5. Set up a scoring rule that compares simulated patterns to real fish images in a consistent way.
6. Test how stable your inferred parameters stay when you change the starting guess, the image set, or the noise level.

Common Pitfalls

• Trying to fit raw photos without first standardizing scale and orientation, which makes stripe measurements inconsistent.
• Comparing simulations to pretty-looking images instead of a numeric similarity score, which hides weak model fit.
• Changing too many PDE parameters at once, which makes it hard to tell which one caused the pattern shift.
• Using only one zebrafish image, which makes the result fragile and hard to defend.
• Ignoring growth or body shape, which can make a good local pattern model fail on real fish outlines.

What Makes This Competitive

A stronger version of this project goes beyond making a nice animation. You compare at least two model forms, quantify fit with more than one metric, and report uncertainty in the recovered parameters. You also test whether the model generalizes across multiple zebrafish variants, not just one image. That kind of careful validation turns a cool simulation into a serious modeling study.

Project Variations

• Fit the same model to zebrafish fin or trunk pattern regions instead of whole-body stripes.
• Compare juvenile and adult zebrafish images to test whether growth changes the best-fit morphogen parameters.
• Replace Gray-Scott dynamics with another reaction-diffusion system and compare which one matches ZFIN images better.

Learn More

• ZFIN: Search the Zebrafish Information Network for public images, strain records, and pigment pattern references.
• NIH PubMed: Search review articles on reaction-diffusion, Turing patterns, and zebrafish pigmentation.
• MIT OpenCourseWare, Computational Biology: Find free course notes on modeling, fitting, and parameter estimation.
• NOAA and NASA image analysis guides: Read free material on image preprocessing, segmentation, and measurement workflows.
• Journal of Theoretical Biology: Search for peer-reviewed articles on pattern formation and reaction-diffusion models.
• PLOS Computational Biology: Search for open-access papers on biological pattern modeling and image-based inference.