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Turing Instabilities are Not Enough to Ensure Pattern Formation.
Krause, Andrew L; Gaffney, Eamonn A; Jewell, Thomas Jun; Klika, Václav; Walker, Benjamin J.
Afiliação
  • Krause AL; Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Road, Durham, DH1 3LE, UK. andrew.krause@durham.ac.uk.
  • Gaffney EA; Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
  • Jewell TJ; Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
  • Klika V; Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic.
  • Walker BJ; Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK.
Bull Math Biol ; 86(2): 21, 2024 01 22.
Article em En | MEDLINE | ID: mdl-38253936
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.
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Texto completo: 1 Base de dados: MEDLINE Assunto principal: Ecossistema / Conceitos Matemáticos Tipo de estudo: Prognostic_studies Idioma: En Ano de publicação: 2024 Tipo de documento: Article

Texto completo: 1 Base de dados: MEDLINE Assunto principal: Ecossistema / Conceitos Matemáticos Tipo de estudo: Prognostic_studies Idioma: En Ano de publicação: 2024 Tipo de documento: Article