eprintid: 10186651
rev_number: 6
eprint_status: archive
userid: 699
dir: disk0/10/18/66/51
datestamp: 2024-02-06 14:18:53
lastmod: 2024-02-06 14:18:53
status_changed: 2024-02-06 14:18:53
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Krause, AL
creators_name: Gaffney, EA
creators_name: Jewell, TJ
creators_name: Klika, V
creators_name: Walker, BJ
title: Turing Instabilities are Not Enough to Ensure Pattern Formation
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: Multistability, Pattern formation, Turing instabilities, Ecosystem, Mathematical Concepts, Models, Biological, Diffusion, Gene Regulatory Networks
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abstract: Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing’s reaction–diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.
date: 2024-01-22
date_type: published
publisher: Springer Science and Business Media LLC
official_url: http://dx.doi.org/10.1007/s11538-023-01250-4
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 2222072
doi: 10.1007/s11538-023-01250-4
medium: Electronic
pii: 10.1007/s11538-023-01250-4
lyricists_name: Walker, Benjamin
lyricists_id: BWALK77
actors_name: Walker, Benjamin
actors_id: BWALK77
actors_role: owner
funding_acknowledgements: [Royal Commission for the Exhibition of 1851]
full_text_status: public
publication: Bulletin of Mathematical Biology
volume: 86
article_number: 21
event_location: United States
issn: 0092-8240
citation:        Krause, AL;    Gaffney, EA;    Jewell, TJ;    Klika, V;    Walker, BJ;      (2024)    Turing Instabilities are Not Enough to Ensure Pattern Formation.                   Bulletin of Mathematical Biology , 86     , Article 21.  10.1007/s11538-023-01250-4 <https://doi.org/10.1007/s11538-023-01250-4>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10186651/1/Turing%20Instabilities%20are%20Not%20Enough%20to%20Ensure%20Pattern%20Formation.pdf