The formation of URLanized patterns is key to the morphogenesis of URLanisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a biologically realistic and unifying approach to emergent pattern formation. Our biphasic model of multicellular tissues incorporates turnover and transport of morphogens controlling cell differentiation and tissue mechanics in a single framework , where one tissue phase consists of a poroelastic network made of cells and the other is the extracellular fluidpermeating between cells . 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 unravel a qualitatively different advection-driven  instability which allows for the formation of patterns with a single morphogen and which single mode pattern scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.
The formation of URLanized patterns is key to the morphogenesis of URLanisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics to 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.
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biologically realistic and unifying approach to emergent pattern formation. Our biphasic model of multicellular tissues incorporates
minimal model combining tissue mechanics to morphogen
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of morphogens controlling
in order to explore new routes to patterning. Our active description couples morphogen reaction-diffusion, which impact on
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in a single framework
, to a two-phase poroelastic rheology
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network made of cells
cell network
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is the extracellular fluidpermeating between cells
of a permeating extracellular fluid, which provides a feedback by actively transporting morphogens
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unravel
describe
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Keller-Segel
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and which single mode pattern
, and whose fundamental mode pattern robustly