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In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers

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Published on: July 28, 2018

Reaction and diffusion on growing domains: scenarios for robust pattern formation.

E J Crampin¹, E A Gaffney, P K Maini

¹Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, UK. crampin@maths.ox.ac.uk

Bulletin of Mathematical Biology

|September 21, 2007

Summary

Reaction-diffusion systems on growing domains can exhibit frequency-doubling patterns. Domain growth may enhance pattern formation robustness in one dimension.

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Area of Science:

Complex Systems
Mathematical Biology
Pattern Formation

Background:

Reaction-diffusion systems are fundamental to understanding pattern formation in nature.
The influence of domain growth on these patterns is not fully understood.
Previous models often assumed static domains.

Purpose of the Study:

To investigate pattern sequences in reaction-diffusion systems on growing domains.
To develop a general evolution equation for domain growth in these models.
To explore the impact of different growth forms on pattern stability.

Main Methods:

Derivation of a general evolution equation for reaction-diffusion on growing domains.
Analysis of slow and isotropic domain growth in one spatial dimension.
Numerical simulations to verify theoretical predictions.

Main Results:

A frequency-doubling sequence of patterns is predicted for exponential domain growth.
Numerical results confirm frequency-doubling within a specific range of growth rates.
Domain growth can enhance the robustness of pattern formation in one dimension.

Conclusions:

Domain growth is a significant factor influencing pattern dynamics in reaction-diffusion systems.
Frequency-doubling is a potential emergent behavior under specific growth conditions.
The findings suggest domain growth as a mechanism for robust pattern formation.