Boundary effects on Turing pattern formation in a spiral growing domain

Area of Science:

• Chemical kinetics and reaction-diffusion systems
• Mathematical modeling of biological processes
• Pattern formation in complex systems

Background:

• Growth is a fundamental biological process influencing chemical dynamics and pattern formation.
• Previous studies on growth effects on pattern formation primarily used inorganic reactions, lacking biological realism.
• Realistic biological scenarios involve physical boundaries, chemical sources, and varied growth rates.

Purpose of the Study:

• To investigate the influence of physical boundaries and boundary conditions on Turing pattern formation.
• To analyze pattern formation in both linearly and nonlinearly growing spiral domains.
• To explore the role of growth speed and chemical activity in pattern morphology and stability.

Main Methods:

• Utilized the Lengyel-Epstein model for the chlorine dioxide-iodine-malonic acid (CDIMA) reaction.
• Simulated pattern formation in growing spiral domains with varying boundary conditions (e.g., Dirichlet).
• Analyzed pattern morphology, multiplicity, and stability under different linear and nonlinear growth scenarios.

Main Results:

• Dirichlet boundary conditions promoted parallel (activator) and spiral-striped (inhibitor) patterns.
• Inhibitor activity and growth speed determined spiral pattern multiplicity and stability, influenced by internal boundaries.
• Nonlinear growth led to complex spiral patterns with varying local multiplicities.

Conclusions:

• Boundary conditions are critical determinants of pattern variability in reacting growing domains.
• Growth dynamics, chemical activity, and boundary types collectively shape complex spatio-temporal patterns.
• The study provides a framework for understanding pattern formation in biologically relevant, growing systems.