Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry

Area of Science:

• Mathematical Biology
• Developmental Biology
• Biophysics

Background:

• Turing's mechanism explains self-organization via reaction-diffusion systems.
• Tissue stratification, common in embryonic skin, involves distinct layers with unique biochemical processes.
• The impact of tissue stratification on Turing patterning remains under-explored.

Purpose of the Study:

• To investigate Turing patterning conditions in bilayered reaction-cross-diffusion systems.
• To analyze the role of differential interfacial transport and layer asymmetry.
• To quantify patterning conditions in stratified biological tissues.

Main Methods:

• Theoretical analysis of reaction-cross-diffusion models in bilayered regions.
• Linear stability analysis around homogeneous equilibrium states.
• Numerical simulations to validate theoretical findings.

Main Results:

• Quantitative Turing conditions derived for arbitrary numbers of reacting species.
• Demonstrated how interfacial transport and layer asymmetry influence pattern formation.
• Identified scenarios where layer coupling overrides individual layer patterning states.

Conclusions:

• Tissue stratification significantly impacts Turing patterning dynamics.
• Interfacial coupling can act as a switch for pattern formation or stabilization.
• The study provides a framework for understanding self-organization in complex biological structures.