Turing pattern formation with two kinds of cells and a diffusive chemical

Area of Science:

• Developmental Biology
• Mathematical Biology
• Chemical Ecology

Background:

• Fish skin patterns, such as those seen in zebrafish, are complex biological phenomena.
• The formation and maintenance of these patterns are thought to involve cell-cell interactions and signaling molecules.
• Understanding the underlying mechanisms is crucial for fields ranging from evolutionary biology to synthetic pattern generation.

Purpose of the Study:

• To investigate the formation and maintenance of multi-pigment cell patterns in fish skin using a computational model.
• To identify the conditions leading to diffusion-driven instability and pattern formation.
• To analyze pattern selection mechanisms, determining how specific patterns like spots or stripes emerge.

Main Methods:

• Utilizing a three-variable Turing system model incorporating two cell types and a diffusive chemical.
• Modeling cell-cell inhibition and chemical-dependent cell maintenance.
• Deriving conditions for diffusion-driven instability and analyzing pattern selection in 1D and 2D spatial models.

Main Results:

• The model predicts that local inhibition between cell types leads to clustering.
• A diffusive chemical produced by one cell type is necessary for the coexistence of both cell types in heterogeneous patterns.
• Conditions for diffusion-driven instability were derived, and parameter-dependent pattern selection (spots, stripes) was analyzed in 1D and 2D.

Conclusions:

• The Turing system effectively models the emergence of complex biological patterns like fish skin coloration.
• Cell-cell inhibition and chemical signaling are key drivers for pattern formation and stability.
• The study provides insights into the mathematical principles governing biological pattern selection.