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Pattern formation in auxin flux

Feller, C. ; Gabriel, J. ; Mazza, C. ; Yerly, F.

In: Journal of Mathematical Biology, 2014, vol. 68, no. 4, p. 879-909

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    Titre
    • Pattern formation in auxin flux
    Auteur
    • Feller, C.. Department of Mathematics, University of Fribourg, Ch. du Musée 23, 1700, Fribourg, Switzerland
    • Gabriel, J.. Department of Mathematics, University of Fribourg, Ch. du Musée 23, 1700, Fribourg, Switzerland
    • Mazza, C.. Swiss Institute of Bioinformatics, Quartier Sorge, Bâtiment Génopode, 1015, Lausanne, Switzerland
    • Yerly, F.. Department of Mathematics, University of Fribourg, Ch. du Musée 23, 1700, Fribourg, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Mathematical Biology, 2014, vol. 68, no. 4, p. 879-909. Springer Berlin Heidelberg
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:325776
    Summary
    The plant hormone auxin is fundamental for plant growth, and its spatial distribution in plant tissues is critical for plant morphogenesis. We consider a leading model of the polar auxin flux, and study in full detail the stability of the possible equilibrium configurations. We show that the critical states of the auxin transport process are composed of basic building blocks, which are isolated in a background of auxin depleted cells, and are not geometrically regular in general. The same model was considered recently through a continuous limit and a coupling to the von Karman equations, to model the interplay of biochemistry and mechanics during plant growth. Our conclusions might be of interest in this setting, since, for example, we establish the existence of Lyapunov functions for the auxin flux, proving in this way the convergence of pure transport processes toward the set of equilibrium points.