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      A Dynamical Phyllotaxis Model to Determine Floral Organ Number

      1 , 2 , * , 1 , *

      PLoS Computational Biology

      Public Library of Science

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          Abstract

          How organisms determine particular organ numbers is a fundamental key to the development of precise body structures; however, the developmental mechanisms underlying organ-number determination are unclear. In many eudicot plants, the primordia of sepals and petals (the floral organs) first arise sequentially at the edge of a circular, undifferentiated region called the floral meristem, and later transition into a concentric arrangement called a whorl, which includes four or five organs. The properties controlling the transition to whorls comprising particular numbers of organs is little explored. We propose a development-based model of floral organ-number determination, improving upon earlier models of plant phyllotaxis that assumed two developmental processes: the sequential initiation of primordia in the least crowded space around the meristem and the constant growth of the tip of the stem. By introducing mutual repulsion among primordia into the growth process, we numerically and analytically show that the whorled arrangement emerges spontaneously from the sequential initiation of primordia. Moreover, by allowing the strength of the inhibition exerted by each primordium to decrease as the primordium ages, we show that pentamerous whorls, in which the angular and radial positions of the primordia are consistent with those observed in sepal and petal primordia in Silene coeli-rosa, Caryophyllaceae, become the dominant arrangement. The organ number within the outmost whorl, corresponding to the sepals, takes a value of four or five in a much wider parameter space than that in which it takes a value of six or seven. These results suggest that mutual repulsion among primordia during growth and a temporal decrease in the strength of the inhibition during initiation are required for the development of the tetramerous and pentamerous whorls common in eudicots.

          Author Summary

          Why do most eudicot flowers have either four or five petals? This fundamental and attractive problem in botany has been little investigated. Here, we identify the properties responsible for organ-number determination in floral development using mathematical modeling. Earlier experimental and theoretical studies showed that the arrangements of preexisting organs determine where a new organ will arise. Expanding upon those studies, we integrated two interactions between floral organs: (1) spatially and temporally decreased inhibition of new organ initiation by preexisting organs, and (2) mutual repulsion among organs such that they are “pushed around” during floral development. In computer simulations incorporating such initiation inhibition and mutual repulsion, the floral organs spontaneously formed several circles, consistent with the concentric circular arrangement of sepals and petals in eudicot flowers. Each circle tended to contain four or five organs arranged in positions that agreed quantitatively with the organ positions in the pentamerous flower, Silene coeli-rosa, Caryophyllaceae. These results suggest that the temporal decay of initiation inhibition and the mutual repulsion among growing organs determine the particular organ number during eudicot floral development.

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          Most cited references 34

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          Local, efflux-dependent auxin gradients as a common module for plant organ formation.

          Plants, compared to animals, exhibit an amazing adaptability and plasticity in their development. This is largely dependent on the ability of plants to form new organs, such as lateral roots, leaves, and flowers during postembryonic development. Organ primordia develop from founder cell populations into organs by coordinated cell division and differentiation. Here, we show that organ formation in Arabidopsis involves dynamic gradients of the signaling molecule auxin with maxima at the primordia tips. These gradients are mediated by cellular efflux requiring asymmetrically localized PIN proteins, which represent a functionally redundant network for auxin distribution in both aerial and underground organs. PIN1 polar localization undergoes a dynamic rearrangement, which correlates with establishment of auxin gradients and primordium development. Our results suggest that PIN-dependent, local auxin gradients represent a common module for formation of all plant organs, regardless of their mature morphology or developmental origin.
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            The no apical meristem gene of Petunia is required for pattern formation in embryos and flowers and is expressed at meristem and primordia boundaries.

            Petunia embryos carrying the no apical meristem (nam) mutation fail to develop a shoot apical meristem. Occasional shoots on nam- seedlings bear flowers that develop ten instead of five primordia in the second whorl. Double mutants with the homeotic gene green petals show that nam acts independently of organ identify in whorl 2 and now also affects primordium number in whorl 3. The nam gene was isolated by transposon tagging. The encoded protein shares a conserved N-terminal domain with several other proteins of unknown function and thus represents a novel class of proteins. Strikingly, nam mRNA accumulates in cells at the boundaries of meristems and primordia. These data indicate a role for nam in determining positions of meristems and primordia.
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              Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism.

              The formation of repetitive structures (such as stripes) in nature is often consistent with a reaction-diffusion mechanism, or Turing model, of self-organizing systems. We used mouse genetics to analyze how digit patterning (an iterative digit/nondigit pattern) is generated. We showed that the progressive reduction in Hoxa13 and Hoxd11-Hoxd13 genes (hereafter referred to as distal Hox genes) from the Gli3-null background results in progressively more severe polydactyly, displaying thinner and densely packed digits. Combined with computer modeling, our results argue for a Turing-type mechanism underlying digit patterning, in which the dose of distal Hox genes modulates the digit period or wavelength. The phenotypic similarity with fish-fin endoskeleton patterns suggests that the pentadactyl state has been achieved through modification of an ancestral Turing-type mechanism.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                May 2015
                7 May 2015
                : 11
                : 5
                Affiliations
                [1 ]Department of Biological Sciences, Osaka University, Toyonaka, Osaka, Japan
                [2 ]Japan Society for the Promotion of Science, Tokyo, Japan
                University Paris Diderot, FRANCE
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: MSK KF. Performed the experiments: MSK. Analyzed the data: MSK. Contributed reagents/materials/analysis tools: MSK. Wrote the paper: MSK KF.

                [¤]

                Current address: Center for Education in Liberal Arts and Sciences, Osaka University, Toyonaka, Osaka, Japan

                Article
                PCOMPBIOL-D-14-01151
                10.1371/journal.pcbi.1004145
                4423988
                25950739

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

                Page count
                Figures: 7, Tables: 0, Pages: 27
                Product
                Funding
                MSK is a JSPS Research Fellow (24.1243). KF is supported by the Osaka University Life Science Young Independent Researcher Support Program through the Special Coordination Program to Disseminate Tenure Tracking System, and Grant-in-Aid for Scientific Research on Innovative Areas (26113511), MEXT. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

                Quantitative & Systems biology

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