How Maths Explains Animal Spots and Stripes: Turing Patterns Meet Zebrafish Chasing Cells

Short summary

Cardiff University mathematician Thomas Woolley discusses how animal patterns form through mathematics. Building on Alan Turing's 1952 theory that pattern formation arises from interacting diffusing agents, Woolley extends the model to include chasing dynamics between skin cells observed in zebrafish by Shigeru Kondo. The light xanthophores and dark melanophores interact so that contact triggers a chase, producing not only stationary spots or stripes but rotating hexagons, moving spots and evolving stripes. By modeling large cell populations, his work derives conditions under which patterns exist and shows how micro-scale cellular rules dictate tissue-scale patterns. The piece highlights mathematics as a powerful microscope for biology and outlines ongoing work to align theory with experiments. — Thomas Woolley, Cardiff University

Medium summary

From Alan Turing's foundational reaction-diffusion idea to the observed zebrafish patterns, the article by Thomas Woolley of Cardiff University traces how mathematics explains natural markings. It begins with the concept that pattern formation requires two interacting ingredients: diffusing agents and their interactions, a notion Turing introduced in 1952. The real-world twist comes from Shigeru Kondo's 2014 experiments showing that zebrafish skin patterns arise from two cell types, xanthophores (light) and melanophores (dark), that communicate through a chasing mechanism: light cells reach toward darker cells while dark cells retreat, producing spiraling movements rather than straight-line paths. This discovery motivated Woolley to extend Turing's framework to discrete cells and then to a population-level continuum, clarifying when patterns emerge and when they do not.

"Patterns, as Turing saw them, depend on two components: interacting agents and agent diffusion." - Alan Turing

In modeling many cells, Woolley shows that population-level analyses can replace tracking individual cells, enabling a precise description of the conditions under which patterns form. This approach yields a richer catalogue of possible patterns, including rotating hexagons, moving spots, and stripes that oscillate rather than settle, illustrating how changes in micro-scale cell behavior alter the tissue-scale outcome. The work also aligns with Kondo’s observation that mutant zebrafish patterns stem from altered cellular chasing strategies, reinforcing the idea that tissue patterns are dictated by the micro-scale rules of cell interaction.

"No longer does a system have to evolve to a stationary pattern of spots or stripes." - Thomas Woolley

"Mathematics will be providing biologists with a new microscope with which to examine biological problems beyond their current experimental expertise." - Thomas Woolley

Ultimately, Woolley argues that mathematics will continue to illuminate biology by acting as a diagnostic and predictive tool for pattern formation, even as the cellular mechanisms remain more complex than currently understood. The article also notes the collaborative funding that supports this work, linking Cardiff University, St John's College Oxford, and the Mathematical Biosciences Institute at Ohio State University to a broader effort to connect theory and experiment in biological patterning.