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 Ca 2+ . Hechtian adhesion between cell wall and plasma membrane transduces wall stress that opens Ca 2+ channels and reorients auxin efflux "PIN" proteins; they control the auxin-activated proton pump that dissociates Ca 2+ bound by periplasmic arabinogalactan proteins (AGP-Ca 2+ ) hence the source of cytosolic Ca 2+ 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-Ca 2+ capacitor; (2) proton pump activity; (3) auxin efflux proteins; (4) Ca 2+ channel activity; (5) Hechtian adhesion that mediates the cell wall stress vector. Arguably, AGPs and the AGP-Ca 2+ capacitor plays a decisive role in phyllotaxis periodicity and its evolutionary origins.Int. J. Mol. Sci. 2020, 21, 1145 2 of 15 stress-strain to the plasma membrane where an auxin-activated proton pump dissociates AGP-Ca 2+ . Elevated cytosolic Ca 2+ -activates exocytosis thus regulating plant growth. Discussion of the Hechtian Oscillator vis-a-vis the role of the primary cell wall in plant morphogenesis [2] suggests extrapolating the oscillator to phyllotaxis based on the premise that presence of the oscillator components implies the presence of a functional Hechtian Oscillator. Indeed, recent work suggests the mechanotransduction of stress relocates auxin efflux PIN proteins that generate new protoderm primordia. However, the precise biochemical mechanisms involved in stress transduction and the role of auxin and calcium homeostasis remain to be elucidated. Here, we invoke Hechtian adhesion and AGPs as essential components that lead us to propose a novel biochemical algorithm for floral phyllotaxis and an explanation of its strong tendency towards a periodic series first described by Fibonacci (1170Fibonacci ( -1240. This approach contrasts with many previous studies with an overwhelming mathematical bias. Indeed, many observations in Nature involve periodicity and the probable underlying oscillations Oscillatory plant growth, known since Darwin [3], was subsequently confirmed by rapid tip growth of pollen tubes and root hairs [4]. Plant morphogenesis also involves periodicity strikingly displayed by the pattern of leaves and floral organs [5] that often appear as Fibonacci spirals typified by whorls of 3, 5, 8, 13, 21 and 34 petals [6]. Hypothetically, such periodicity depends on an underlying oscillator such as the recently formulated Hechtian growth oscilla...