Linear coupling of patterning systems can have nonlinear effects

Mahashri, N., Woolley, Thomas E. ORCID: https://orcid.org/0000-0001-6225-5365 and Muthusamy, Chandru 2025. Linear coupling of patterning systems can have nonlinear effects. Physical Review E 111 (1) , 014224. 10.1103/physreve.111.014224

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Abstract

Isolated patterning systems have been repeatedly investigated. However, biological systems rarely work on their own. This paper presents a theoretical and quantitative analysis of a two-domain interconnected geometry, or bilayer, coupling two two-species reaction-diffusion systems mimicking interlayer communication, such as in mammary organoids. Each layer has identical kinetics and parameters, but differing diffusion coefficients. Critically, we show that despite a linear coupling between the layers, the model demonstrates nonlinear behaviour; the coupling can lead to pattern suppression or pattern enhancement. Using the Routh-Hurwitz stability criterion multiple times we investigate the pattern forming capabilities of the uncoupled system, the weakly coupled system and the strongly coupled system, using numerical simulations to back up the analysis. We show that although the dispersion relation of the entire system is a non-trivial octic polynomial the patterning wave modes in the strongly coupled case can be approximated by a quartic polynomial, whose features are easier to understand.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	American Physical Society
ISSN:	2470-0045
Date of First Compliant Deposit:	8 January 2025
Date of Acceptance:	8 January 2025
Last Modified:	03 Feb 2025 12:00
URI:	https://orca.cardiff.ac.uk/id/eprint/175095

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