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Image AMT/K3.3 reproduced from the Turing Digital Archive, with kind permission of King's College Cambridge: "Unpublished writings of A.M. Turing copyright The Provost and Scholars of King's College Cambridge 2019."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