A model for leaf initiation: determination of phyllotaxis by waves in the generative circle

A biophysical model is proposed for how leaf primordia are positioned on the shoot apical: meristem in both spiral and whorl phyllotaxes. Primordia are initiated by signals that propagate: in the epidermis in both azimuthal directions away from the cotyledons or the most recently: specified primordia. The signals are linear waves as inferred from the spatial periodicity of the: divergence angle and a temporal periodicity. The periods of the waves, which represent actively: transported auxin, are much smaller than the plastochron interval. Where oppositely directed: waves meet at one or more angular positions on the periphery of the generative circle, auxin: concentration builds and as in most models this stimulates local movement of auxin to: underlying cells, where it promotes polarized cell division and expansion. For higher order: spirals the wave model requires asymmetric function of auxin transport; that is, opposite wave: speeds differ. An algorithm for determination of the angular positions of leaves in common leaf: phyllotaxic configurations is proposed. The number of turns in a pattern repeat, number of leaves: per level and per pattern repeat, and divergence angle are related to speed of auxin transport and: radius of the generative circle. The rule for composition of Fibonacci or Lucas numbers: associated with some phyllotaxes is discussed. A subcellular model suggests how the shoot: meristem might specify either symmetric or asymmetric transport of auxin away from the: forming primordia that produce it. Biological tests that could make or break the mathematical: and molecular hypotheses are proposed.