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Updated: Jul 11, 2026

In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers
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
Abstract:
We investigate the sequence of patterns generated by a reaction-diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction-diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation.
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