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28.02.19 Extending Turing's reaction-diffusion model with mechanics, for robust tissue patterning during development

last modified Mar 01, 2019 12:16 PM
The Simons lab, with colleagues in France and Austria, devise a new model for tissue patterning, proposing that mechanical forces work in combination with chemical gradients to generate spatial patterns
28.02.19 Extending Turing's reaction-diffusion model with mechanics, for robust tissue patterning during development

The 'daisy ring' diagram made by Alan Turing in connection with work on morphogenesis

Theory of mechanochemical patterning in biphasic biological tissues

Recho P, Hallou A & Hannezo E (2019)

 

Significance

Pattern formation is a central question in developmental biology. Alan Turing proposed that this could be achieved by a diffusion-driven instability in a monophasic system consisting of two reacting chemicals.

In this paper, we extend Turing’s work to a more realistic mechano-chemical model of multicellular tissue, modelling also its biphasic and mechanical properties. Overcoming limitations of conventional reaction-diffusion models, we show that mechano-chemical couplings between morphogen concentrations and extracellular fluid flows provide alternative, non-Turing, mechanisms by which tissues can form robust spatial patterns.

 

Abstract

The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking.

Here, we propose a minimal model combining tissue mechanics with morphogen turnover and transport in order to explore new routes to patterning. Our active description couples morphogen reaction-diffusion, which impact on cell differentiation and tissue mechanics, to a two-phase poroelastic rheology, where one tissue phase consists of a poroelastic cell network and the other of a permeating extracellular fluid, which provides a feedback by actively transporting morphogens.

While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction-diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics thanks to mechanically induced cross-diffusion flows.

Moreover, we describe a qualitatively different advection-driven Keller-Segel instability which allows for the formation of patterns with a single morphogen, and whose fundamental mode pattern robustly scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

 

Image AMT/K3.3 reproduced from the Turing Digital Archive, with kind permission of King's College Cambridge: "Unpublished writings of A.M. Turing copyright The Provost and Scholars of King's College Cambridge 2019."

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