2 More recent accounts and analyses include Sachs, 3 Jean, 4 Cummings and Strickland, 5 Green, 6 Kelly and Cooke, 7 King et al., 8 and Newell et al. Histories of phyllotaxis has been given by Richards 1 and by Adler et al. on plants have been reported and analyzed since at least the eighteenth century, and we shall provide only a brief introduction to the subject. The geometric phyllotaxic patterns of leaves, florets, bracts, etc. Secondary influences of stem outgrowth from the shoot apical meristem and of the resultant degree of packing provide interesting geometric and physiologically significant elaborations, but these can distract from our immediate concern. Leaf primordia are initiated in relatively simple patterns within a so-called generative circle, and are moved out radially by growth of the continually dividing cells at their central edges. Here, we focus on the post-embryonic initiation of leaf primordia per se the vegetative phase of development is less intricate than the reproductive phase. It is our purpose to provide a fresh, integrated examination of these two subjects. The way in which plants initiate their leaves and organs such as flower parts at the stem apex has fascinated scientists from early times, but it has proved difficult to describe satisfactorily either the guiding mathematical rules predicting developmental patterning or the molecular mechanisms underlying it. Biological tests that could make or break the mathematical Meristem might specify either symmetric or asymmetric transport of auxin away from theįorming primordia that produce it. A subcellular model suggests how the shoot The rule for composition of Fibonacci or Lucas numbersĪssociated with some phyllotaxes is discussed. Per level and per pattern repeat, and divergence angle are related to speed of auxin transport and The number of turns in a pattern repeat, number of leaves An algorithm for determination of the angular positions of leaves in common leaf Spirals the wave model requires asymmetric function of auxin transport that is, opposite wave Underlying cells, where it promotes polarized cell division and expansion. Waves meet at one or more angular positions on the periphery of the generative circle, auxinĬoncentration builds and as in most models this stimulates local movement of auxin to Transported auxin, are much smaller than the plastochron interval. The periods of the waves, which represent actively The signals are linear waves as inferred from the spatial periodicity of theĭivergence angle and a temporal periodicity. In the epidermis in both azimuthal directions away from the cotyledons or the most recently Primordia are initiated by signals that propagate Meristem in both spiral and whorl phyllotaxes. A biophysical model is proposed for how leaf primordia are positioned on the shoot apical
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