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Spiral phyllotaxis in flax. Left: 11 days after germination, the phyllotactic pattern is characterized by 3 counter-clockwise parastichies (one represented in red) and 5 clockwise parastichies (3:5 phyllotaxis). 11 days later, as a result of the increase in the size of the apex, the phyllotactic pattern has shifted to 5:8. However, the original 3 parastichies are still evident (one represented in red). (modified from Williams, 1974). 

Spiral phyllotaxis in flax. Left: 11 days after germination, the phyllotactic pattern is characterized by 3 counter-clockwise parastichies (one represented in red) and 5 clockwise parastichies (3:5 phyllotaxis). 11 days later, as a result of the increase in the size of the apex, the phyllotactic pattern has shifted to 5:8. However, the original 3 parastichies are still evident (one represented in red). (modified from Williams, 1974). 

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Plant architecture is characterized by a high degree of regularity. Leaves, flowers and floral organs are arranged in regular patterns, a phenomenon referred to as phyllotaxis. Regular phyllotaxis is found in virtually all higher plants, from mosses, over ferns, to gymnosperms and angiosperms. Due to its remarkable precision, its beauty and its acc...

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Context 1
... spiral phyllotaxis, organs are formed with a constant diver- gence angle, usually 137.5°, resulting in an ontogenetic spiral which runs in clockwise or counter-clockwise direction (Fig. 1B). In addition, secondary spirals, the contact parastichies, can be dis- cerned which run in both directions (Fig. 3). Curiously, the number of parastichies in each direction represents consecutive terms in the Fibonacci series (Steeves and Sussex, 1989). This series consists of terms that represent the sum of the previous two numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.). The number of contact parastichies depends on the relative size of the ...
Context 2
... to the large flower disc, the numbers can be as high as 34:55. In many plants, the diameter of the meristem increases during development. This results in a gradual shift from lower to higher phyllotactic numbers, for example in flax, the phyllotactic pattern of the seedling starts with 3:5 and undergoes a gradual shift to 5:8 phyllotaxis ( Fig. 3; Williams, 1975). Interestingly, the 3:5 pattern remains recognizable for some time, even after the 5:8 spirals are already clearly prominent (Fig. ...
Context 3
... results in a gradual shift from lower to higher phyllotactic numbers, for example in flax, the phyllotactic pattern of the seedling starts with 3:5 and undergoes a gradual shift to 5:8 phyllotaxis ( Fig. 3; Williams, 1975). Interestingly, the 3:5 pattern remains recognizable for some time, even after the 5:8 spirals are already clearly prominent (Fig. ...

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... Background Auxin, a pivotal phytohormone, plays a central role in orchestrating fundamental processes throughout plant development. Its multifaceted influence spans various developmental stages across the entirety of the plant life cycle [1][2][3][4][5][6]. The key players in the intricate pathway of auxin signaling are the auxin/indole-3-acetic acid (Aux/ IAA) genes. ...
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... For the past 25 years, many articles have been proposed supporting the biochemical research direction and stating that auxin (growth hormone) plays a dominant role in the morphogenesis of spiral patterns of phyllotaxis (Reinhardt, 2005;Jönsson et al., 2006). The observation of (Jean, 1994). ...
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... The regularity of plant architecture and morphology is a striking and mysterious phenomenon. The lateral organs, such as leaves, flowers, and floral organs, are arranged in regular patterns around a central axis (Reinhardt, 2005;Traas, 2013;Bartlett and Thompson, 2014). Leaves and flowers arise from the meristem in stereotypical patterns, known as phyllotaxis, which are related to the divergence angle between successive organs, most commonly approximating 137.5° (Smith et al., 2006;Okabe, 2012). ...
... Leaves and flowers arise from the meristem in stereotypical patterns, known as phyllotaxis, which are related to the divergence angle between successive organs, most commonly approximating 137.5° (Smith et al., 2006;Okabe, 2012). The floral organs also exhibit a characteristically symmetrical arrangement, with their number, position, and shape being precisely regulated (Reinhardt, 2005;Thomson and Wellmer, 2019). arf3 mutants exhibit obvious abnormalities in phyllotactic patterning, floral organ patterning, floral organ number, the patterning of abaxial tissues, and the establishment of apical and basal boundaries in primordia (Figures 3A, B, G-J; see section 4 for details). ...
... Although many mathematical, physical, and chemical models have been proposed to explain the mechanism of phyllotactic pattern formation, the regular initiation of organs and their spatial and temporal positioning is the basis for the formation of phyllotactic patterns from a developmental biology perspective (Reinhardt, 2005;Smith et al., 2006;Traas, 2013;Bergeron and Reutenauer, 2019). The phytohormone auxin plays a critical role in establishing phyllotactic patterns by promoting organ initiation (Prasad et al., 2011;Bhatia et al., 2016). ...
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... These zones are generated by asymmetric distribution of PIN1, such that PIN1 is preferentially located to membranes adjacent to cells with the highest auxin concentration, moving auxin up the concentration gradient to produce auxin maxima and deplete surrounding cells of auxin (Vernoux et al., 2000;Benková et al., 2003;Heisler et al., 2005;Vernoux et al., 2011;O'Connor et al., 2014). Thus, in this model, a lack of auxin is the inhibitory signal and prevents formation of primordia directly adja-cent to one another (Reinhardt et al., 2003;Reinhardt, 2005). The control of this PIN1 distribution is dependent on an ARF, MONOPTEROS (MP), with PIN1 polarity tracking MP activity, which is in turn determined by auxin distribution, suggesting a feedback loop in which high levels of auxin induce MP-mediated auxin signalling leading to increased transport of auxin towards those cells (Hardtke and Berleth, 1998;Bhatia et al., 2016). ...
Thesis
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... The phenomenon of regular and periodic patterning of leaves (or other lateral organs) is called phyllotaxis and has drawn the attention of researchers for centuries (e.g., Jean, 1994;Adler, Barabé & Jean, 1997;Reinhardt, 2005;Kuhlemeier, 2007). In the plant kingdom, two major types of leaf arrangements, whorled and spiral (helical) (Zagórska-Marek, 1985;Zagórska-Marek, 1994), are recognised. ...
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Exploration of developmental mechanisms classically relies on analysis of pattern regularities. Whether disorders induced by biological noise may carry information on building principles of developmental systems is an important debated question. Here, we addressed theoretically this question using phyllotaxis, the geometric arrangement of plant aerial organs, as a model system. Phyllotaxis arises from reiterative organogenesis driven by lateral inhibitions at the shoot apex. Motivated by recurrent observations of disorders in phyllotaxis patterns, we revisited in depth the classical deterministic view of phyllotaxis. We developed a stochastic model of primordia initiation at the shoot apex, integrating locality and stochasticity in the patterning system. This stochastic model recapitulates phyllotactic patterns, both regular and irregular, and makes quantitative predictions on the nature of disorders arising from noise. We further show that disorders in phyllotaxis instruct us on the parameters governing phyllotaxis dynamics, thus that disorders can reveal biological watermarks of developmental systems.
... Recently, developments in molecular biology have revealed that auxin plays a crucial role in primordium formation [4,8,[13][14][15]17]. It has been shown in biological experiments that auxin induces leaf and flower primordia in the stem tip, thereby indicating that auxin acts as an activator for primordium formation in stem tip. ...
... Here we will explain the behavior of auxin in a shoot apex from the papers [4,8,[13][14][15]17]. Two distinct types of auxin transport are observed in a shoot apex. ...
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Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram.