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.