**Derek T. A. Lamport 1,\*, Li Tan 2, Michael Held <sup>3</sup> and Marcia J. Kieliszewski <sup>3</sup>**


Received: 1 November 2019; Accepted: 5 February 2020; Published: 9 February 2020

**Abstract:** Phyllotaxis describes the periodic arrangement of plant organs most conspicuously floral. Oscillators generally underlie periodic phenomena. A hypothetical algorithm generates phyllotaxis regulated by the Hechtian growth oscillator of the stem apical meristem (SAM) protoderm. The oscillator integrates biochemical and mechanical force that regulate morphogenetic gradients of three ionic species, auxin, protons and Ca2<sup>+</sup>. Hechtian adhesion between cell wall and plasma membrane transduces wall stress that opens Ca2<sup>+</sup> channels and reorients auxin efflux "PIN" proteins; they control the auxin-activated proton pump that dissociates Ca2<sup>+</sup> bound by periplasmic arabinogalactan proteins (AGP-Ca2+) hence the source of cytosolic Ca2<sup>+</sup> waves that activate exocytosis of wall precursors, AGPs and PIN proteins essential for morphogenesis. This novel approach identifies the critical determinants of an algorithm that generates phyllotaxis spiral and Fibonaccian symmetry: these determinants in order of their relative contribution are: (1) size of the apical meristem and the AGP-Ca2<sup>+</sup> capacitor; (2) proton pump activity; (3) auxin efflux proteins; (4) Ca2<sup>+</sup> channel activity; (5) Hechtian adhesion that mediates the cell wall stress vector. Arguably, AGPs and the AGP-Ca2<sup>+</sup> capacitor plays a decisive role in phyllotaxis periodicity and its evolutionary origins.

**Keywords:** Phyllotaxis; arabinogalactan proteins; auxin; calcium signaling; acid growth; Hechtian oscillator; plasma membrane ion fluxes
