A universal route to pattern formation in multicellular systems

Malbor ASLLANI, Timoteo Carletti, Duccio Fanelli, Philip K. Maini

Research output: Contribution to journalArticle

Abstract

A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-field like ansatz which corresponds, in the biological setting, to sending to zero the size (or volume) of each individual cell. By relaxing this approximation and, provided a directionality in the flux is allowed for, we demonstrate here that instability leading to spatial pattern formation can always develop if the (discrete) system is large enough, namely, composed of sufficiently many cells, the units of spatial patchiness. The macroscopic patterns that follow the onset of the instability are robust and show oscillatory or steady state behavior.
Original languageEnglish
JournalEuropean Physical Journal B
Volume93
DOIs
Publication statusPublished - 13 Jul 2020

Keywords

  • Turing patterns
  • Reaction diffusion systems
  • asymmetric diffusion

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