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Pattern formation in auxin flux

  • Feller, Chrystel Department of Mathematics, University of Fribourg, Switzerland / Swiss Institute of Bioinformatics, Quartier Sorge, Bâtiment Génopode, Lausanne, Switzerland
  • Gabriel, Jean-Pierre Department of Mathematics, University of Fribourg, Switzerland
  • Mazza, Christian Department of Mathematics, University of Fribourg, Switzerland / Swiss Institute of Bioinformatics, Quartier Sorge, Bâtiment Génopode, Lausanne, Switzerland
  • Yerly, Florence Department of Mathematics, University of Fribourg, Switzerland / Swiss Institute of Bioinformatics, Quartier Sorge, Bâtiment Génopode, Lausanne, Switzerland
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    01.03.2014
Published in:
  • Journal of Mathematical Biology. - 2014, vol. 68, no. 4, p. 879–909
Auxin flux
Pattern formation
Reinforced random walks
English 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.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Biological sciences
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/303657
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