Stochastic occurrence of trimery from pentamery in floral phyllotaxis of Anemone (Ranunculaceae)

Merosity, indicating the basic number of floral organs such as sepals and petals, has been constrained to specific and stable numbers during the evolution of angiosperms. The ancestral flower is considered to have a spiral arrangement of perianth organs, as in phyllotaxis, the arrangement of leaves. How has the ancestral spiral evolved into flowers with specific merosities? To address this question, we studied perianth organ arrangement in the Anemone genus of the basal eudicot family Ranunculaceae, because various merosities are found in this genus. In three species, A. flaccida, A. scabiosa, and A. nikoensis that are normally pentamerous, we found positional arrangement of the excessive sixth perianth organ indicating the possibility of a transition from pentamerous to trimerous arrangement. Arrangement was intraspecifically stochastic, but constrained to three of five types, where trimerous arrangement was the most frequent in all species except for a form of A. scabiosa. The rank of frequency of the other two types was species-dependent. We connect these observations with classical theories of spiral phyllotaxis. The phyllotaxis model for initiation of the sixth organ showed that the three arrangements occur at a divergence angle <144°, indicating the spiral nature of floral phyllotaxis rather than a perfect penta-radial symmetry of 144°. The model further showed that selective occurrence of trimerous arrangement is mainly regulated by the organ growth rate. Differential organ growth as well as divergence angle may regulate transitions between pentamerous and trimerous flowers in intraspecific variation as well as in species evolution

Size-correlated polymorphisms in phyllotaxis-like periodic and symmetric tentacle arrangements in hydrozoan Coryne uchidai

Introduction: Periodic organ arrangements occur during growth and development and are widespread in animals and plants. In bilaterian animals, repetitive organs can be interpreted as being periodically arranged along the two-dimensional space and defined by two body axes; on the other hand, in radially symmetrical animals and plants, organs are arranged in the three-dimensional space around the body axis and around plant stems, respectively. The principles of periodic organ arrangement have primarily been investigated in bilaterians; however, studies on this phenomenon in radially symmetrical animals are scarce.Methods: In the present study, we combined live imaging, quantitative analysis, and mathematical modeling to elucidate periodic organ arrangement in a radially symmetrical animal, Coryne uchidai (Cnidaria, Hydrozoa).Results: The polyps of C. uchidai simultaneously formed multiple tentacles to establish a regularly angled, ring-like arrangement with radial symmetry. Multiple rings periodically appeared throughout the body and mostly maintained symmetry. Furthermore, we observed polymorphisms in symmetry type, including tri-, tetra-, and pentaradial symmetries, as individual variations. Notably, the types of radial symmetry were positively correlated with polyp diameter, with a larger diameter in pentaradial polyps than in tetra- and triradial ones. Our mathematical model suggested the selection of size-correlated radial symmetry based on the activation-inhibition and positional information from the mouth of tentacle initiation.Discussion: Our established quantification methods and mathematical model for tentacle arrangements are applicable to other radially symmetrical animals, and will reveal the widespread association between size-correlated symmetry and periodic arrangement principles

A dynamical phyllotaxis model to determine floral organ number.

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

Stochastic occurrence of trimery from pentamery in floral phyllotaxis of Anemone (Ranunculaceae)

Merosity, indicating the basic number of floral organs such as sepals and petals, has been constrained to specific and stable numbers during the evolution of angiosperms. The ancestral flower is considered to have a spiral arrangement of perianth organs, as in phyllotaxis, the arrangement of leaves. How has the ancestral spiral evolved into flowers with specific merosities? To address this question, we studied perianth organ arrangement in the Anemone genus of the basal eudicot family Ranunculaceae, because various merosities are found in this genus. In three species, A. flaccida, A. scabiosa, and A. nikoensis that are normally pentamerous, we found positional arrangement of the excessive sixth perianth organ indicating the possibility of a transition from pentamerous to trimerous arrangement. Arrangement was intraspecifically stochastic, but constrained to three of five types, where trimerous arrangement was the most frequent in all species except for a form of A. scabiosa. The rank of frequency of the other two types was species-dependent. We connect these observations with classical theories of spiral phyllotaxis. The phyllotaxis model for initiation of the sixth organ showed that the three arrangements occur at a divergence angle <144°, indicating the spiral nature of floral phyllotaxis rather than a perfect penta-radial symmetry of 144°. The model further showed that selective occurrence of trimerous arrangement is mainly regulated by the organ growth rate. Differential organ growth as well as divergence angle may regulate transitions between pentamerous and trimerous flowers in intraspecific variation as well as in species evolution

The potential landscape captures pentamerous whorl formation.

<p><b>A.</b> The angular position of the third primordium as a function of <i>α</i>. <b>B–C.</b> Color-coded growth-potential landscape (top) and the section (bottom) at the angle where the fifth (<b>B</b>) and the sixth (<b>C</b>) primordia arise (white dashed line in the top panel). <i>α</i> = 2.0, <i>Vτ</i> = 6.0, <i>R</i>₀ = 20.0, <i>σ</i>_<i>θ</i> = 0.0, <i>λ</i>_<i>ini</i> = <i>λ</i>_<i>g</i> = 10.0, and <i>P</i>_<i>MP</i> = 0 in <b>A</b>–<b>C</b>.</p

Merosity of the first whorl.

<p><b>A, B.</b> The number of primordia before the first arrest (arrowheads in Fig <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.g002" target="_blank">2C</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.g002" target="_blank">2E</a>) is depicted by colors in the legend. The red region indicates a non-whorled pattern. For simplicity, we set <i>P</i>_<i>MP</i> = 0 (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.e009" target="_blank">Eq 4</a>) so that primordia could not move against the potential gradient <i>U</i>_{<i>g</i>, <i>k</i>}. <i>λ</i>_<i>ini</i> = <i>λ</i>_<i>g</i> = 10.0, <i>σ</i>_<i>r</i> = <i>σ</i>_<i>θ</i> = 0.05. <i>α</i> = 0.0 (<b>A</b>) and <i>α</i> = 2.0 (<b>B</b>). The four panels between <b>A</b> and <b>B</b> are representative examples of each merosity where the arrowhead indicates the third primordium. <b>C.</b> Phase diagram of the first-whorl merosity according to <i>α</i> and <i>R</i>₀/<i>Vτ</i> at </p><p></p><p><mi>V</mi><mi>τ</mi><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>5</mn></p><p><mi>R</mi><mn>0</mn></p><mo>+</mo><mn>50</mn><mo stretchy="false">)</mo><mo>/</mo><p></p><p><mn>2</mn><mi>π</mi></p><p></p><p></p><p></p> (white line in <b>A</b>). The color code is the same as that in <b>A</b> and <b>B</b>. The region of dimerous arrangement (green) increases as <i>α</i> increases, because the previous primordium becomes the most dominant inhibitor so that the new primordium initiates just opposite to the previous one and its growth is arrested by the second previous one.<p></p

Reconstructing pentamerous floral development.

<p><b>A.</b> Flower of <i>Silene coeli-rosa</i> (Caryophyllaceae). <b>B.</b> Reproduction of the <i>S</i>. <i>coeli-rosa</i> floral meristem traced from an SEM image by Lyndon [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.ref034" target="_blank">34</a>]; the colors were modified. Numbers indicate the initiation order. K (sepals), C (petals), St (stamens), AB (axillary bud). <b>C.</b> Average position of the <i>S</i>. <i>coeli-rosa</i> floral primordia reconstructed from the divergence angle and plastochron ratio (<b>E</b>) measured by Lyndon (Table 1 in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.ref034" target="_blank">34</a>]). The number of measured apices is 9 for sepals, 5 for petals, 7 for stamens, and 2 for carpels. The positions of sepals and petals are depicted in large squares, and those of stamens and carpels are depicted in small squares. <b>D.</b> Spatial pattern of the model simulation. The first ten primordia are shown by large circles, and the subsequent ten primordia are shown by small circles. <i>τ</i> = 600, <i>R</i>₀ = 30.0, <i>α</i> = 3.0, <i>σ</i>_<i>r</i> = 0.05, <i>σ</i>_<i>θ</i> = 5.0, <i>λ</i>_<i>ini</i> = <i>λ</i>_<i>g</i> = 20.0, <i>P</i>_<i>MP</i> = 0. <b>E.</b> Divergence angle (top panel) and plastochron ratio (middle) between two succeeding primordia, and the distance from the center of the apex (bottom panel) in <i>S</i>. <i>coeli-rosa</i> (blue squares) and in the model simulation (red circles). The order of petal initiation was estimated from that of the adjacent stamens (St6-St10 in <b>B</b>) following the experimental report [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.ref034" target="_blank">34</a>]. The measurements agree with the model until the ninth primordium (open arrowhead). Error bars for the divergence angle and plastochron ratio of <i>S</i>. <i>coeli-rosa</i> denote the standard errors. Because the absolute values of the <i>S</i>. <i>coeli-rosa</i> primordia radii were not published, the distance from the center is normalized by the radius of the first sepal. The values of the parameters are the same as those in <b>D</b>. The green line (<b>D</b> and <b>E</b> bottom panel) indicates the meristem boundary in the simulation.</p

Effects of <i>λ</i>_<i>ini</i>, <i>λ</i>_<i>g</i>, and <i>α</i> on merosities.

<p>Superposition of the analytical result (the solid lines are identical to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.g005" target="_blank">Fig 5E</a>: <i>λ</i>_<i>ini</i> = <i>λ</i>_<i>g</i> = 10.0, <i>α</i> = 0.0, <i>P</i>_<i>MP</i> = 0) and the numerical result (<i>σ</i>_<i>r</i> = <i>σ</i>_<i>θ</i> = 0.05; the following parameters are different from the solid line: <b>A.</b><i>λ</i>_<i>ini</i> = 5.0, <b>B.</b><i>λ</i>_<i>ini</i> = 20.0, <b>C.</b><i>α</i> = 2.0 <b>D.</b><i>α</i> = 2.0, <i>λ</i>_<i>ini</i> = 20.0, <b>E.</b><i>λ</i>_<i>g</i> = 5.0, <b>F.</b><i>λ</i>_<i>g</i> = 20.0). The colors follow <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004145#pcbi.1004145.g003" target="_blank">Fig 3</a>. <i>λ</i>_<i>g</i> and <i>α</i> affect the boundary lines between each whorl as well as that between non-whorls and tetramerous whorls (<b>C</b>, <b>E</b> and <b>F</b>), whereas <i>λ</i>_<i>ini</i> hardly affects at <i>α</i> = 0 (<b>A</b> and <b>B</b>). At <i>α</i> ≠ 0, <i>α</i> and <i>λ</i>_<i>ini</i> synergistically affect the phase boundaries (<b>C</b> and <b>D</b>).</p

Schematic diagram for pentamerous flower development.

<p>Sepal initiation (the first row), arrangement of sepal (black) and petal (white) whorls in blooming flower (the second row). Green circle represents a floral meristem (FM). Index numbers indicate the initiation order of five sepals. The radial position of the organs (the third row), namely the distance between the organ and floral apex, is spaced regularly in a spiral arrangement, whereas it has a gap between the fifth and sixth organs in the pentamerous pseudo-whorled and whorled arrangement. Regarding the hypothetical time evolution of the radial position (the fourth row), in all arrangements, the radial position increases with the progression of floral development. In the spiral arrangement, the radial position of the organ is always spaced regularly. In the pseudo-whorled and whorled arrangement subsequent to helical initiation, the radial position of organs within a whorl becomes closer during growth. In the whorled arrangement following simultaneous initiation, the radial position of the organs within a whorl is always identical.</p

Emergence of multiple whorls in model simulations.

<p><b>A.</b> Geometric assumptions of the model. <b>B.</b> The initiation process. A new primordium (<i>i</i>) is initiated at the edge of the floral meristem (FM; green circle) where the initiation potential <i>U</i>_<i>ini</i> takes the minimum value. <i>i</i>, <i>i</i> −1, and <i>i</i> −2 are the primordium indices that denote the initiation order. <i>U</i>_<i>ini</i> exponentially decreases with time (<i>α</i>) and the distance between primordia (<i>λ</i>_<i>ini</i>). <b>C.</b> The growth process. Each primordium (<i>k</i>) moves at the outside of the circular FM, depending on the growth potential <i>U</i>_{<i>g</i>, <i>k</i>}. Primordium <i>k</i> rarely moves against the gradient (grey thin arrow), but mostly follows the gradient (black thick arrow; see the Model section). <b>D–F.</b> Emergence of whorled-type pattern with increasing meristem radius <i>R</i>₀ and temporal decay rate <i>α</i>. Left panels: Spatial pattern after 15 primordia (red circles) initiated in an indexed order at the meristem edge (green circle; <i>r</i> = <i>R</i>₀). Middle panels: Radial distance (black) from the meristem center as a function of the primordium initiation index (left panel) averaged over 400 replicate Monte Carlo simulations. Error bars represent twice the S.D. Red circles are a set of representative samples. Right panels: Time evolution of the radial coordinates of each primordium averaged over 400 replicates. Error bars show 2 S.D. The arrowheads in <b>D</b> and <b>F</b> indicate the growth arrest of the fifth and sixth primordia, respectively. Colors denote the index of the primordia. Green line in the left, middle and right panels denotes the meristem edge. (<i>R</i>₀, <i>α</i>) = (20.0,0.0) in <b>D</b>, (5.0,0.0) in <b>E</b> and (20.0,2.0) in <b>F</b>. <i>β</i> = 1.0 × 10⁴, <i>λ</i>_<i>ini</i> = <i>λ</i>_<i>g</i> = 10.0, <i>τ</i> = 300, and <i>σ</i>_<i>r</i> = <i>σ</i>_<i>θ</i> = 0.05 in <b>D</b>–<b>F</b>.</p