Theory of mechano-chemical patterning in biphasic biological tissues (1811.12242v3)

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 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.