Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulator for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site we suggest a possible resolution to the puzzling occurrence of bipolar cells, such we offer an explanation for the development of closed, looped veins. Employing non-linear analysis we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.Comment: 9 pages, 4 figures, supplemental information included, accepted for publication in Eur. Phys. J.

A GRAMMAR-BASED MODEL OF BARLEY INCLUDING VIRTUAL BREEDING, GENETIC CONTROL AND A HORMONAL METABOLIC NETWORK

Abstract. The incorporation of some genetic and physiological processes in a developmental model of Hordeum vulgare L. (barley) is presented. The model exhibits different hierarchical scales and has been conceived as a Relational Growth Grammar (RGG). RGG is a new formalism that has been developed as an extension of L-Systems and implemented using a new modelling language, eXtended Lsystems (XL). Models written in XL can be executed using the interactive, Java-based modelling platform GroIMP, which has been developed for this purpose. The barley model proper is a set of morphogenetic rules. These are combined with a set of rules representing a metabolic network simulating some key steps of the biosynthesis of gibberellic acid (GA1). The transport of GA1 and GA19 (a metabolic precursor of GA1) along the developing simulated structure has also been foreseen. In the model, the local concentrations of GA1 in a module induce the elongation of internodes. In an extension of this base model, called "BarleyBreeder", individual virtual specimens are chosen interactively from a population, followed by the simulation of reproduction. Both genotype and phenotype of the population are visualized. So far, the model is restricted to a few Mendelian genes, one of which (the dwarfing gene Zeocrithon) is directly interacting with the biosynthesis of GA1