Math Biology Seminar: David Holloway

The growth regulator auxin plays a central role in development across plants. Auxin spatial patterning is critical in the phyllotactic arrangement of leaves along a stem, the shapes of the leaves themselves, and venation within leaves. These patterns depend on polar auxin transport (PAT) at the cellular level, particularly the preferential allocation of PIN efflux proteins to certain areas of the plasma membrane. Two general mechanisms have been studied: an up-the-gradient (UTG) allocation dependent on neighbouring-cell auxin concentrations, and a with-the-flux (WTF) allocation dependent on the flow of auxin across walls. We developed a combined UTG+WTF model for leaf venation. The model simulates intracellular and membrane kinetics and intercellular transport, and is solved for a 2D leaf of several hundred cells. We find that vein initiation in the leaf margin and cell polarization towards new veins is UTG-driven, while WTF is critical for vein extension. UTG is important for joining veins to form a network structure. The model produces the experimentally observed succession of effects when PAT is increasingly inhibited by NPA treatment. Venation patterns are highly correlated with leaf shape; this model enables the investigation of how PAT dynamics contribute to the diversity of leaf shapes across plants.