173 research outputs found

    Noise and Robustness in Phyllotaxis

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    A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis – the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles – and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background

    A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis

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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

    Phyllotactic regularity requires the Paf1 complex in Arabidopsis

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    In plants, aerial organs are initiated at stereotyped intervals, both spatially (every 137° in a pattern called phyllotaxis) and temporally (at prescribed time intervals called plastochrons). To investigate the molecular basis of such regularity, mutants with altered architecture have been isolated. However, most of them only exhibit plastochron defects and/or produce a new, albeit equally reproducible, phyllotactic pattern. This leaves open the question of a molecular control of phyllotaxis regularity. Here, we show that phyllotaxis regularity depends on the function of VIP proteins, components of the RNA polymerase II-associated factor 1 complex (Paf1c). Divergence angles between successive organs along the stem exhibited increased variance in vip3-1 and vip3-2 compared with the wild type, in two different growth conditions. Similar results were obtained with the weak vip3-6 allele and in vip6, a mutant for another Paf1c subunit. Mathematical analysis confirmed that these defects could not be explained solely by plastochron defects. Instead, increased variance in phyllotaxis in vip3 was observed at the meristem and related to defects in spatial patterns of auxin activity. Thus, the regularity of spatial, auxin-dependent, patterning at the meristem requires Paf1c

    ハナキカンスウ ノ ガンケンセイ ト バラツキ ヲ ウミダス ハッセイ キバン ノ リロンテキ タンキュウ

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    本論文第3章の内容はOxford University Press のAnnals of Botany 誌に掲載される予定である( DOI: 10.1093/aob/mcw034

    Phyllotaxis and related topics

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    Turing's theory of morphogenesis

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    Magnetism, FeS colloids, and Origins of Life

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    A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via physicalphysical interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201
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