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    Auxin transport model for leaf venation

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    pin_auxin_Dec18.pdf
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    Description:
    Preprint
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    Type
    Preprint
    Authors
    Haskovec, Jan
    Jönsson, Henrik
    Kreusser, Lisa Maria
    Markowich, Peter A. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2019-01-10
    Permanent link to this record
    http://hdl.handle.net/10754/660007
    
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    Abstract
    The plant hormone auxin controls many aspects of the development of plants. One striking dynamical feature is the self-organisation of leaf venation patterns which is driven by high levels of auxin within vein cells. The auxin transport is mediated by specialised membrane-localised proteins. Many venation models have been based on polarly localised efflux-mediator proteins of the PIN family. Here, we investigate a modeling framework for auxin transport with a positive feedback between auxin fluxes and transport capacities that are not necessarily polar, i.e.\ directional across a cell wall. Our approach is derived from a discrete graph-based model for biological transportation networks, where cells are represented by graph nodes and intercellular membranes by edges. The edges are not a-priori oriented and the direction of auxin flow is determined by its concentration gradient along the edge. We prove global existence of solutions to the model and the validity of Murray's law for its steady states. Moreover, we demonstrate with numerical simulations that the model is able connect an auxin source-sink pair with a mid-vein and that it can also produce branching vein patterns. A significant innovative aspect of our approach is that it allows the passage to a formal macroscopic limit which can be extended to include network growth. We perform mathematical analysis of the macroscopic formulation, showing the global existence of weak solutions for an appropriate parameter range.
    Sponsors
    LMK was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 and the German National Academic Foundation (Studienstiftung des Deutschen Volkes)LMK was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 and the German National Academic Foundation (Studienstiftung des Deutschen Volkes).
    Publisher
    arXiv
    arXiv
    arXiv:1901.03244
    Additional Links
    https://arxiv.org/pdf/1901.03244
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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