Mechanism (biology)

Gene

Quantum mechanics

Biology

Pattern formation

Biochemistry

Computer science

Turing

Cognitive science

Genetics

Thermodynamics

Physics

Psychology

Reaction–diffusion system

Programming language

Biological system

Morphogenesis

Zebrafish

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell–cell interactions have been observed to satisfy the ‘short-range activation and long-range inhibition’ prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction–diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell–cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction–diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue ‘Recent progress and open frontiers in Turing's theory of morphogenesis’.

Studies of Turing pattern formation in zebrafish skin