Auxin transport model for leaf venation
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.
Used in syntheses
Questions this source addresses
- How can chemicals that react and spread create a pattern?
- How do cells know where they are in a growing body?
- How does a living thing know what shape to grow into?
- How does auxin shape a growing plant?
- How can a graph-based model of auxin transport, with non-polar (undirected) membrane edges, still produce directional vein patterns in a leaf?
- How does modeling cells as graph nodes and intercellular membranes as unoriented edges allow branching vein patterns to emerge from a single auxin source-sink pair?
- In what sense does the steady-state behavior of this discrete auxin transport model satisfy Murray's Law for branching transport networks?
- What is the role of positive feedback between auxin flux and transport capacity in stabilizing vein channels during leaf venation?