1. Pattern formation in auxin flux
- Author
-
Chrystel Feller, Jean-Pierre Gabriel, Christian Mazza, Florence Yerly, University of Zurich, and Mazza, Christian
- Subjects
Lyapunov function ,SX20 Research, Technology and Development Projects ,1101 Agricultural and Biological Sciences (miscellaneous) ,Quantitative Biology::Tissues and Organs ,Pattern formation ,Biology ,Stability (probability) ,Models, Biological ,SX13 Plant Growth ,symbols.namesake ,SX00 SystemsX.ch ,2604 Applied Mathematics ,Auxin ,Botany ,Morphogenesis ,Computer Simulation ,Tissues and Organs (q-bio.TO) ,Equilibrium point ,chemistry.chemical_classification ,Indoleacetic Acids ,Applied Mathematics ,Quantitative Biology - Tissues and Organs ,Biological Transport ,Plants ,biology.organism_classification ,Agricultural and Biological Sciences (miscellaneous) ,Modelling and Simulation ,Coupling (computer programming) ,chemistry ,Modeling and Simulation ,FOS: Biological sciences ,symbols ,570 Life sciences ,biology ,Plant hormone ,Biological system ,Flux (metabolism) ,2611 Modeling and Simulation - Abstract
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 critical configurations., Comment: 27 pages
- Published
- 2019