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Effect of obstructions on growing Turing patterns
Milos Dolnik1, Christopher Konow1, Noah H Somberg1
1Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02453, USA.
Chaos (Woodbury, N.Y.)
|July 30, 2022
Summary
Obstructions in growing domains alter Turing pattern formation, creating new shapes and disrupting growth. This research offers a flexible simulation framework for studying pattern development in complex environments.
Area of Science:
- Mathematical Biology
- Chemical Physics
- Pattern Formation
Background:
- Turing pattern formation is crucial for biological development.
- Growing domains present unique challenges for pattern stability.
- Discrete domain discontinuities can significantly influence pattern dynamics.
Purpose of the Study:
- To investigate the impact of domain discontinuities on Turing pattern formation.
- To explore how various obstruction geometries affect pattern morphology and growth.
- To develop a customizable simulation framework for heterogeneous growing domains.
Main Methods:
- Numerical simulations using the Lengyel-Epstein reaction-diffusion model.
- Simulating pattern formation on radially expanding circular domains.
- Incorporating diverse obstruction geometries (walls, slits, blocks).
Main Results:
- Obstructions significantly alter Turing pattern formation, leading to novel morphologies.
- Obstructions can induce growth mode switching and disrupt local pattern formation.
- The effects of obstructions depend on their shape, placement, and domain growth rate.
Conclusions:
- Domain discontinuities are critical factors in Turing pattern formation on growing substrates.
- The findings provide insights into biological pattern formation in non-idealized environments.
- The developed framework facilitates further numerical and experimental investigations.
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