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A universal route to pattern formation in multicellular systems

Author

Listed:
  • Malbor Asllani

    (MACSI, Department of Mathematics and Statistics, University of Limerick
    Namur Institute for Complex Systems, University of Namur)

  • Timoteo Carletti

    (Namur Institute for Complex Systems, University of Namur)

  • Duccio Fanelli

    (Dipartimento di Fisica e Astronomia, Università di Firenze, INFN and CSDC)

  • Philip K. Maini

    (Mathematical Institute, University of Oxford, Woodstock Rd)

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. Graphical abstract

Suggested Citation

  • Malbor Asllani & Timoteo Carletti & Duccio Fanelli & Philip K. Maini, 2020. "A universal route to pattern formation in multicellular systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(7), pages 1-11, July.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:7:d:10.1140_epjb_e2020-10206-3
    DOI: 10.1140/epjb/e2020-10206-3
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    Cited by:

    1. Muolo, Riccardo & Gallo, Luca & Latora, Vito & Frasca, Mattia & Carletti, Timoteo, 2023. "Turing patterns in systems with high-order interactions," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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    Keywords

    Statistical and Nonlinear Physics;

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