A Design Principle for Floral Organ Number and Arrangement in Flowers with Bilateral Symmetry Aiko Nakagawa1,*, Miho S

Home , Acacia adoxa, Acacia celastrifolia, Adoxa moschatellina, Caldcluvia, Knautia, Ruta

RESEARCH ARTICLE A design principle for floral organ number and arrangement in flowers with bilateral symmetry Aiko Nakagawa1,*, Miho S. Kitazawa1,2,*,‡ and Koichi Fujimoto1,‡

ABSTRACT Some flowers have achieved this regulation of pollen attachment The bilateral symmetry of flowers is a striking morphological position by modifying floral organ number, positioning and form. achievement during floral evolution, providing high adaptation In particular, zygomorphic (or bilateral) flowers, which have dorso- potential for pollinators. The symmetry can appear when floral ventral (also called adaxial-abaxial or DV axis) asymmetry that organ primordia developmentally initiate. Primordia initiation at the corresponds to the DV axis of the pollinator (Fig. 1A,B, lateral ventral and dorsal sides of the floral bud is differentially regulated flower; Endress, 1999), have developed in many plant species in by several factors, including external organs of the flower and various clades adapted to a variety of pollinator species, resulting in CYCLOIDEA (CYC) gene homologues, which are expressed the diversification of floral morphologies (Sargent, 2004). asymmetrically on the dorso-ventral axis. It remains unclear how In the early stages of floral development, the first indication of these factors control the diversity in the number and bilateral perianth diversity appears in the number and arrangement of the arrangement of floral organs. Here, we propose a mathematical floral organs, the sepals and the petals. The perianth of a flower model demonstrating that the relative strength of the dorsal-to-ventral typically consists of two circles or whorls of floral organs, and each inhibitions and the size of the floral stem cell region (meristem) whorl contains the same number of floral organs. Merosity determines the number and positions of the sepal and petal describes the common organ number of perianth whorls and is primordia. The simulations reproduced the diversity of monocots usually clade specific (Fig. 1C; Ronse De Craene, 2010; Smyth, and eudicots, including snapdragon Antirrhinum majus and its cyc 2018). In eudicots, the largest clade of flowering plants, the mutant, with respect to organ number, arrangement and initiation common number is usually four or five, whereas in monocots, the patterns, which were dependent on the inhibition strength. These sister clade to eudicots, it is three (Ronse De Craene and theoretical results suggest that diversity in floral symmetry is primarily Brockington, 2013; Endress, 2010; Remizowa et al., 2010). regulated by the dorso-ventral inhibitory field and meristem size Lateral flowers that bloom as the lateral branch of the main stem during developmental evolution. have two types of floral organ arrangements for each organ number with respect to the DV axis of the flower (Fig. 1C, upper panel). The KEY WORDS: CYCLOIDEA, Bilateral symmetry, Flower development, arrangements along the DV axis are recognized by dividing the Floral evolution, Phyllotaxis, Organ positioning floral bud into three regions from the position closest to the main axis: dorsal, lateral and ventral regions (Fig. 1A,B). The model plant INTRODUCTION Arabidopsis thaliana exhibits tetramerous flowers with four sepals Spatial positioning and number of organs (e.g. eyes, ears, nose and and four petals, and the sepal arrangement along the DV axis has mouth in animals; carpels, stamens, petals and sepals in plants) two sepals in the lateral region and one each in the dorsal and ventral represent one of the most fundamental differences among species. regions (type 4A; Fig. 1C; Smyth et al., 1990). The other type of In flowering plants (angiosperms), the forms of flowers exhibit tetramerous arrangement (type 4B) is also found in certain plants, enormous diversity. Floral symmetry is an important example including those in the genus Veronica (Plantaginaceae). Regarding of this diversity, which affects the success of sexual reproduction pentamerous flowers, the majority of eudicot flowers have one via pollination, i.e. pollen transfer from male to female organs dorsal, two lateral and two ventral sepals (type 5A), whereas flowers (Wozniaḱ and Sicard, 2018). Because plants are immobile, these in several clades have reversed arrangements with two dorsal, two organisms entrust the transport of pollen to wind, water or, in the lateral and one ventral sepal (type 5B; e.g. the subfamily majority of flowering plants, to animals. A recent study suggested Papilionoideae or Fabaceae). The trimerous flowers in monocots that approximately 87.5% of flowering plants are pollinated by typically have one inner and two outer tepals (perianth organs) in animals, such as insects and birds (Ollerton et al., 2011); therefore, the dorsal region, and one outer and two inner tepals in the ventral plant floral forms have evolved to attract and control pollinators. region (type 3B; Rudall and Bateman, 2004). On the other hand, the One mechanism to ensure the success of pollination is to fix reversed arrangement is a representative phenotype in several orders the position of pollen attachment on the body of the pollinator. of monocots (type 3A; Ronse De Craene, 2010; Tobe et al., 2018). Additionally, dimerous flowers appear in several families in

1Department of Biological Sciences, Graduate School of Science, Osaka monocots and eudicots, and have two lateral sepals (outer tepals; University, Toyonaka, 560-0043, Japan. 2Center for Education in Liberal Arts and type 2B). The developmental mechanisms that produce the clade- Sciences, Osaka University, Toyonaka, 560-0043, Japan. specific diversity of organ number and positioning along the DV *These authors contributed equally to this work axis have not been thoroughly elucidated. ‡Authors for correspondence ([email protected]; The number and positioning of floral organs are mainly [email protected]) determined when the floral organ primordia initiate (Endress, M.S.K., 0000-0001-9468-8018; K.F., 0000-0001-6473-7990 1999; Tucker, 1999; Spencer and Kim, 2018). The simplest case occurs when several primordia that make up a whorl (i.e. organs,

Received 22 July 2019; Accepted 7 January 2020 such as petals, with the same identity) in a concentric circle initiate DEVELOPMENT

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Fig. 1. Structure and symmetry of flowers. (A) Schematic diagram of an inflorescence. Each lateral flower has a DV axis with respect to the main axis and a bract. (B) DV axis in an Antirrhinum majus lateral flower, corresponding to the DV axis of the pollinators. (C) Upper: typical arrangements of the outermost floral organs (sepals or outer tepals) with respect to the DV axis. Bottom: clade-specific number and arrangement of the outer organs (sepals and petals) with respect to the main axis (black circle) in a phylogenetic tree modified from APG IV (The Angiosperm Phylogeny Group, 2016). Monocots exhibit either dimery or trimery. Most trimerous species show the same arrangement (3B), although their initiating orders are not identical. For example, in Orchidaceae, the outer perianth initiates from the dorsal side (Pabón-Mora and González, 2008). The exceptionally opposite positioning of the trimerous perianth organs along the DV axis (3A) is found specifically in the order Dioscoreales and the family Smilacaceae (Liliales; Ronse De Craene, 2010), which exhibit sequential initiation for both inner and outer perianth organs. A dimerous arrangement with two lateral external tepals, one ventral tepal and one dorsal internal tepal, is found in several clades, including the genus Paepalanthus (Eriocaulaceae and Poales; de Lima Silva et al., 2016), but rarely in orchids [a few Japanese Dendrobium cultivars, abnormal flowers in Cattleya (Harshberger, 1907) and Cypripedium (Masters, 1887)]. The pentamerous and tetramerous flowers co-exist in many eudicot families, such as Plantaginaceae (e.g. 5A in A. majus and 4B in Veronica) and Fabaceae (e.g. 5A, 5B and 4A).

at once; however, this is not the case in many flowering plants, as Floral symmetry depends on the position in the inflorescence early floral development is associated with non-synchronous (Fig. 1A). The lateral flowers are zygomorphic, whereas terminal initiation of the sepal primordia. The initiating order in the sepal flowers are actinomorphic (radially symmetric) in some peloria whorl differs among species. The zygomorphic initiation patterns, mutants of Lamiaceae (Rudall and Bateman, 2003). The merosity of such as unidirectional initiation along the DV axis and bidirectional lateral and terminal flowers can also be different with pentamery and initiation (Tucker, 2003), are unique to floral organ initiation in tetramery, respectively, occurring in Adoxa (Adoxaceae, asterids; contrast to the spiral initiation sequence, which is also observed Roels and Smets, 1994) or the opposite case for Ruta (Rutaceae, in phyllotaxis (the arrangement of leaves along the stem) as rosids; Wei et al., 2012), where the organ initiation is zygomorphic well as floral organs. Although the developmental mechanisms in lateral flowers. Such differences between lateral and terminal underlying the diversity of the initiation sequence, as well as the flowers suggest that lateral floral bud polarity (Thoma and number and positioning of the floral organs, have been proposed for Chandler, 2015) affects zygomorphy. The relative position to the radially symmetric flowers (Kitazawa and Fujimoto, 2015); those inflorescence meristem of the main axis (Fig. 1C) provides an that occur along the DV axis remain largely unknown for bilaterally asymmetric polarity field for floral organ initiation along the symmetric flowers. DV axis via signaling molecules and the polar transport of DEVELOPMENT

2 RESEARCH ARTICLE Development (2020) 147, dev182907. doi:10.1242/dev.182907 phytohormone auxin (Bowman et al., 2002; Wang and Jiao, 2018). from the dorsal and/or ventral side of the floral meristem into the This idea is similar to the inhibitory field theory that pre-existing phyllotaxis model, which originally incorporated the inhibitory organs regulate the initiation position of new organs, as this theory is field from the pre-existing organ primordia (Douady and Couder, widely accepted to explain phyllotaxis (Hofmeister, 1868; Snow 1996a,b) and was recently applied to floral development (Kitazawa and Snow, 1952, 1962; Adler et al., 1997; Dourdy and Couder, and Fujimoto, 2015). The numerical simulation accounted for most 1996a,b; Traas, 2013; Refahi et al., 2016; Kuhlemeier, 2017; of the observed floral organ positioning and numbers in a unified Yonekura et al., 2019). Therefore, the inhibitory field may be key manner, and these positions and numbers depended not only on the for understanding bilaterally symmetric floral organ arrangements. inhibition strength of the dorsal and/or ventral sides but also on the Several genes that affect organ number and position along the DV meristem size. These results suggest that clade-dependent axis have been identified. While wild-type flowers of the differences in DV inhibition lead to the diversification of organ snapdragon Antirrhinum majus (Plantaginaceae; Fig. 1C) have number and positioning in angiosperms. one sepal at the dorsal side, two at the lateral side and two at the ventral side, a loss-of-function mutant of the CYCLOIDEA (CYC) RESULTS gene (cyc mutant) exhibits two sepals via formation of an extra sepal Organ number and arrangement depend on the strength of at the dorsal side without reduction in the number of sepals on the DV inhibition other sides (type 6B; Fig. 1C; Luo et al., 1996). As the CYC gene is First, we examined the simplest condition of the inhibitory field expressed on the dorsal side of the floral bud in wild-type flowers, model without dorsal and ventral factors affecting the floral organ this gene is thought to repress the initiation of dorsal sepal primordia patterning, assuming the primordia as points and a floral meristem (Luo et al., 1996). Although recent studies have suggested that as a disc with radius R0 (Fig. 2; Materials and Methods). The the CYC/TB1 clade of class II TCP transcription factors, which angular position of the new primordium is determined by the include CYC, is involved in regulating shoot branching, floral transition, organ identity and growth (Dhaka et al., 2017), the precise mechanisms that affect organ number and arrangement still remains elusive. Generally, in the angiosperm species with zygomorphic flowers, the CYC gene is expressed on the dorsal side of the floral bud and is considered to be the central regulator of zygomorphy (Spencer and Kim, 2018). The generality of this CYC gene expression pattern, main axis positioning (Fig. 1A) and the suggested function on dorsal primordium initiation prompted us to investigate the contribution of the strength of the dorsal inhibitory field to the clade-specific diversity of organ number and positioning along the DV axis. In addition, the genetic regulation of organ number and positioning at the ventral side has been identified. The double mutation of bop1 and bop2 in A. thaliana converted the arrangement from tetramerous (4A) to pentamerous (5A) via formation of extra sepals and bracts, which are specialized leaves surrounding a flower (Fig. 1A), at the abaxial (ventral) side (Hepworth et al., 2005; Khan et al., 2014; Norberg, 2005). The bract and sepal compete for ventral positioning via regulation of the genes LEAFY and PUCHI (Chandler and Werr, 2014), resulting in an alternate arrangement of sepals and a bract, as seen in many clades (e.g. type 4B flowers in Rutaceae, including Ruta, or rosids; type 4B and 5A flowers in Plantaginaceae, including Veronica and Antirrhinum, or asterids; Endress, 1999; Ronse De Craene, 2007, 2010). This suggests a ventral side inhibitory field by which the pre-existing bract inhibits sepal initiation. PERIANTHIA (PAN) may also be a related candidate, as this transcription factor interacts with BOP1 and BOP2 (Hepworth et al., 2005). The pan mutant of A. thaliana consistently yields arrangement type 5A with an extra ventral sepal (Fig. 1C; Running and Meyerowitz, 1996). PAN is expressed in the apical meristem, floral meristem and each whorl of the organ primordia during A. thaliana wild-type flower development (Maier et al., 2009). The floral meristem adaxial/abaxial (DV) polarity, which is Fig. 2. Extension of the inhibitory field model to floral development. controlled by the genes CYC, PAN and BOP, and external organs (A) Model settings. The edge of the meristematic region is represented by a (bract and main axis), is indispensable for determination of the circle (green), and primordia are represented by points (red) in a 2D plane. numbers and positions of floral organs (Thoma and Chandler, 2015) (B) Inhibitory field of primordium initiation by the pre-existing primordia. The and is a candidate for the DV inhibitory field. inhibition decays with an increase in the distance from the pre-existing In this report, we present a design principle for diverse organ primordium. (C) Snapshots of inhibitory field energy U in a 2D plane for cases of one (top), two (middle) and four (bottom) pre-existing primordia. (D) External positioning and initiation sequence along the DV axis using inhibitory fields at the dorsal (blue) and ventral (orange) sides. Inhibition numerical simulations of a mathematical model for phyllotaxis. strength was controlled by changing the distance (rdorsal and rventral) between

Furthermore, we introduced the inhibitory field of organ initiation the floral center and inhibition sources. DEVELOPMENT

3 RESEARCH ARTICLE Development (2020) 147, dev182907. doi:10.1242/dev.182907 inhibitory energy from the pre-existing primordia [U(θ) in Eqn 2; Next, we introduced external inhibition from the dorsal side Fig. 2B], and the primordia move centrifugally according to tip (Fig. 2D; Eqn 3). The inhibition gradient of the Udorsal produced the growth (Eqn 1). One or more primordia arise at the meristem edge local minima at the ventral side of the meristem edge, thereby taking the local minimum energy below the threshold value generating the first primordium at the ventral side. The angular (Fig. 2C). In silico development began with a quasi-simultaneous positions of subsequent primordia and the primordium number of initiation of four primordia, where the second primordium appeared the first whorl can differ, depending on the distance between the at the opposite side of the first primordium owing to the inhibition dorsal inhibition source and the floral apex (rdorsal). The tetramerous caused by the first primordia, and then simultaneous initiation of the arrangement with one primordium at the dorsal side, two at the two primordia between them followed (Fig. 3A; Fig. 2C), consistent lateral side and one at the ventral side (type 4A; Fig. 1C) appeared at with the previous model for radially symmetric flowers (Kitazawa a certain strength of dorsal inhibition (rdorsal=70; Fig. 3B), which and Fujimoto, 2015). We recognized these four primordia as a was consistent with sepal primordia initiation in A. thaliana whorl, as the first four primordia appeared in successive steps of the (Smyth et al., 1990). Furthermore, the pentamerous whorl with two numerical simulation and at nearly the same distance from the primordia on the dorsal side, two on the lateral side and one on the meristem center (Fig. 3A, right). ventral side, is commonly found in many legume species (type 5B;

Fig. 3. Representative arrangements obtained by numerical simulations. (A) A 2D arrangement (left) and radial coordinates as functions of primordium indices (right) without inhibition from the DV sides. (B-H) The 2D arrangements of primordia under different conditions:

rdorsal=70 without ventral inhibition (Aventral=0.0) (B), rdorsal=50 and Aventral=0.0 (C), rdorsal=60 (D), rdorsal=40 (E), rdorsal=30 (F), rdorsal=60 (G) and rdorsal=40 and a=0.001 (H). The numbers in the red disks indicate the

initiation order of primordia. a=0 (A-G) and rventral=90 (D) and =30 (E-H). (I) Dependency on dorsal and ventral inhibitions. The colors denote the number of primordia within the first whorl, whereas the black frames denote the arrangement along the DV axis (see Fig. 1C). The white characters in the phase diagram correspond to the parameters of Fig. 3B-G. As the model simulations do not include randomness, all results shown in A-I were reproducible once we set the model parameters to values as described above and in the Materials and Methods.

R0=16.0 (A-I). DEVELOPMENT

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Fig. 1C), and appeared with increased dorsal inhibition (rdorsal=50; primordia in total within the first whorl (Fig. 3G). This finding was Fig. 3C). Thus, two different arrangements typically found in consistent with that in Veronica (type 4B; Fig. 1C), which belongs different species were continuously induced by changing the to the same family as A. majus. The in silico development started strength of dorsal inhibition. with the initiation of two primordia in the dorsal region, followed by We next introduced ventral inhibition (Fig. 2D; Eqn 4), and weak the initiation of two primordia in the ventral region. In these three inhibition reproduced the conversion from type 4A to the 5A arrangements, several primordia appeared at alternative positions to pentamerous sepal arrangement via formation of an extra ventral organ the first whorl, forming the second whorl upon the temporal decay (Fig. 3B,D), which was consistent with findings in the pan mutant of dorsal and ventral inhibitions (a non-zero value of a in Eqns 3 and (Running and Meyerowitz, 1996) and the bop1 bop2 double mutant 4; Fig. 3H). This positioning occurred because the inhibition from (Hepworth et al., 2005) of A. thaliana. The initiation order was also the first whorl on primordia initiation was stronger than that from the consistent with the pan mutant, as the ventral and dorsal sepal dorsal and ventral sides. These three arrangements and initiation primordia appeared first, followed by the two lateral sepal primordia. sequences were observed in the family Plantaginaceae and were Stronger ventral inhibition than dorsal inhibition reproduced continuously altered by changing the degree of dorsal inhibition another initiation order of the 5B arrangement (rdorsal=40, relative to the ventral inhibition (Fig. 3E-G,I). rventral=30; Fig. 3E) in other eudicot species, including wild-type The trimerous and dimerous arrangements observed in monocots A. majus and a few mimosoid legumes (type 5A; Fig. 1C). In these (Fig. 1C) appeared in a small radius of the meristem (R0=8; cases, the two lateral sepal primordia appeared first, followed by Fig. 4A-D). The trimerous whorl with two dorsal and one ventral nearly simultaneous appearance of the remaining three (one dorsal primordia, as observed in the external tepal whorl of most monocots and two ventral) sepal primordia (Luo et al., 1996; Ramírez- (type 3B; Fig. 1C), appeared in two separate parameter regions. In Domenech and Tucker, 1990). The number of organs within the first these two regions, the initiation patterns were different, initiating from whorl was controlled by changing the dorsal inhibition, while fixing either the ventral (Fig. 4A) or the dorsal side (Fig. 4B). The former the other parameters. Increasing the dorsal inhibition to the same appeared with stronger dorsal inhibition than ventral inhibition level as the ventral inhibition (rdorsal=30, rventral=30; Fig. 3F) added a (rdorsal=20 and rventral=50), whereas the latter appeared with a dorsal ventral organ to the first whorl, resulting in the sepal arrangement of inhibition that was weaker than the ventral inhibition (rdorsal=70 the cyc mutant of A. majus (type 6B; Fig. 1C). The resultant and rventral=60), consistent with the initiation pattern of orchids arrangement exhibited two primordia in the dorsal, lateral and (Pabón-Mora and González, 2008). A dimerous arrangement was ventral regions. In addition to these arrangements, the bidirectional obtained in the close parameters (type 2B; Figs 1C and 4C), as for initiation order of these six primordia in the first whorl was several abnormal orchid flowers (Harshberger, 1907; Masters, 1887) consistent with the cyc mutant of A. majus, wherein two lateral sepal and other order Poales (genus Paepalanthus; de Lima Silva et al., primordia initiated first, followed by the appearance of the 2016). As an intermediate of the two separate parameter regions of remaining four sepal primordia (Luo et al., 1996). A decrease in type 3B, a reversed trimerous arrangement with one dorsal the dorsal inhibition (rdorsal=60, rventral=30) led to a decrease in the primordium appeared (type 3A; Figs 1C and 4D). This arrangement number of dorsal primordia from two to one, resulting in four is found in Dioscoreales (monocots) tepals (Fig. 1C). Transition from

Fig. 4. Dependency of number and

arrangement on meristem size R0. (A-D) 2D arrangements of primordia at

a=0.002, R0=8.0. rdorsal=20 and rventral=50 (A), rdorsal=70 and rventral=60 (B), rdorsal=20 and rventral=20 (C), and rdorsal=60 and rventral=70 (D). (E) Dependency on dorsal and ventral

inhibitions at R0=8. The white characters in the phase diagram correspond to the parameters of Fig. 4A-D. (F) Dependency on dorsal inhibition and size of meristematic

region R0.rdorsal=40. The colors indicate the arrangements along the DV axis (Fig. 1C) or the merosities (2 or >6) described in the diagram. As the simulations do not include randomness, all results presented in A-F are reproducible once we set the model parameters as described above, and in the Materials and Methods. DEVELOPMENT

5 RESEARCH ARTICLE Development (2020) 147, dev182907. doi:10.1242/dev.182907 type 3A to type 2B via loss of a dorsal primordium (Fig. 4C,D) was this notion is consistent with the model for radially symmetric also consistent with a previous notion about the evolutionary whorls (Douady and Couder, 1996b) because the geometry of transition of Paepalanthus to dimery (de Lima Silva et al., 2016; meristem and inhibitory field is scale invariant in the present model Fig. 1C). Therefore, the monocot diversity of organ number and (see Materials and Methods). In addition, the parameter range of R0 arrangement appears even under conditions of constant meristem size. for an arrangement type (e.g. type 5B) is wider in the presence of The current model reproduced both floral organ arrangements and ventral inhibition (at rventral=60-70 in Fig. 4F) than in its absence (at initiation sequences in different clades of angiosperms, including the Av=0 in Fig. 4F), suggesting that the robustness of positional two largest clades eudicots and monocots as well as smaller clades arrangement to meristem size variation is promoted by the ventral within a family. A wide range of floral organ arrangements was inhibitory field. Therefore rdorsal/λ (Fig. 3I, Fig. S1A) and R0/λ reproduced by changing three parameters (rdorsal,rventral and R0), (Fig. 4F) synergistically regulate organ arrangements. which were resistant to differences in energy functions (Eqns 2-4) and The non-monotonic changes of organ numbers were found to be angle precision at the meristem edge (0.1 to 5°; Materials and associated with rdorsal and rventral,whenR0 was constant (Figs 3I and Methods) in the inhibitory field model, while the functional form 4E). In addition, some of the arrangements occurred independently in affected the parameter value of dorsal and ventral inhibition for each several regions in the parameter space, yielding different orders of arrangement (Fig. S1B). These results suggest that the changes in DV primordium initiation. For example, in one of the pentamerous inhibition as well as meristem size are potential primary regulators of arrangements (type 5B), unidirectional initiation from the dorsal side the evolutionary changes of floral organ arrangement in angiosperms. (rdorsal=10, rventral=80, R0=20), bidirectional initiation from the lateral side (rdorsal=30, rventral=40, R0=16 in Fig. 3I) and other bidirectional Comprehensive analysis of the model parameters initiation events in the sequence of dorsal, ventral and lateral The dependence of floral organ arrangement on rdorsal,rventral and R0 (rdorsal=40, rventral=80, R0=16 in Fig. 3I) were segregated depending further revealed changes in organ numbers within the first whorl on rdorsal,rventral and R0. As such different initiation orders that lead to (Figs 3I and 4E,F). An increase in R0 accompanied the monotonic the 5B arrangement were observed in legume flowers in different increase in primordium number in the first whorl, as observed in clades (Prenner, 2004), this model may predict the evolutionary path previous phyllotaxis models without DV inhibition (Douady and of Fabaceae; however, some issues, such as the observation that the Couder, 1996b; Kitazawa and Fujimoto, 2015; van Mourik et al., change in these initiation orders did not occur with a continuous 2012). For example, when the dorsal inhibition was slightly weaker change of parameters in simulations, remain to be explored. than the ventral inhibition (rdorsal=40, rventral=30), the organ number in the first whorl was increased to four (type 4B at R0=12), five Design principle of organ arrangement and initiation order (type 5A at R0=16) and six (type 6B at R0≥20; dashed rectangle; along the DV axis Fig. 4F). This diversity of arrangements accounted for those in In our model framework, the position of the first primordia was Plantaginaceae. In general, meristem size, and dorsal and ventral determined by the positional relationship between the meristematic inhibitions normalized by the characteristic length of the inhibitory region with a radius R0 and two inhibitory sources rdorsal and rventral. field from DV sources and pre-existing organs (R0/λ,rdorsal/λ, and The inhibition energy along the DV axis reaches a local minimum at rventral/λ) are the parameters that control organ number (Fig. S1A); the middle of the two inhibitory sources (Voronoi edge; Fig. 5A,

Fig. 5. Design principle of the arrangement of the first organs to initiate along the DV axis. (A) The energy minima (black solid lines) are located between the dorsal and ventral inhibitory fields, which are indicated by the blue and orange discs, respectively. When the line intersects the meristem edge (green circle), two primordia are formed at the first initiation at the intersection points (B-D). When the line contacts or does not intersect the meristem edge, one primordium is formed on either the dorsal or ventral side, depending on the closest inhibition source (E). DEVELOPMENT

6 RESEARCH ARTICLE Development (2020) 147, dev182907. doi:10.1242/dev.182907 black line). When the Voronoi line crosses the edge of the meristem predicts that CYCLOIDEA expression is stronger on the dorsal (Fig. 5A, green circle), the two primordia first appear at the side and that the dorsal inhibition is weaker (Fig. 3G,I) or the intersection points (Fig. 5B-D). When the Voronoi line contacts or meristem size is smaller in these tetramerous flowers (Fig. 4F). is outside the meristematic region, the global inhibition minimum Loss of a dorsal primordium that results in the 4B arrangement on the edge of the meristem is located at the dorsal or ventral side under these conditions in our model is consistent with the and depends on rdorsal and rventral, as well as the meristem size R0 morphological observation-based hypothesis that the dorsal (Fig. 5E). Thus, the strength of the two inhibitory sources relative to organs of the tetramerous Veronica and Plantago flowers are the meristem size determines the number and position of the first derived from the lateral organs of pentamerous flowers in primordia to appear. Plantaginaceae (Endress, 1999). The initiation of the next primordia to appear was determined by Regarding the inhibitor candidates in the ventral regions, several not only the two inhibitory sources but also by the one or two mutants of PAN and BOP produced an extra sepal on the ventral primordia that initiated first. When the intersection points occur at side, thereby converting from the 4A arrangement to the 5A the middle of the meristem (Fig. 5A,B), the arrangement is arrangement in A. thaliana (Running and Meyerowitz, 1996; symmetric to the DV axis. The number of the energy minima Hepworth et al., 2005). The conversion as well as the initiation order between the two intersection points can be either one or two, (ventral, dorsal and then lateral organs) in these mutants were depending on whether the relative strength of the dorsal and ventral reproduced by increasing the ventral inhibition strength in the inhibition is stronger than the energy of the first primordia. When present model (Fig. 3B,D,I). Therefore, these genes may inhibit the the DV inhibition is strong enough to affect the energy landscape of ventral inhibitory field, resulting in a stronger inhibition in these the inhibitory field, the two minima occur at both the dorsal and mutants and playing an anti-symmetric role of CYC along the DV ventral sides, resulting in arrangement type 6B (Fig. 5B). When the axis (Fig. 5A-C). In addition, the consistency with the alternate intersection points do not occur at the middle of the meristem arrangement between two sepals and an extra bract at the ventral (Fig. 5A), the number of minima at the dorsal and ventral sides side of bop1 bop2 mutant verifies the idea that the bract is a ventral varies from zero to two. For example, when the intersection points inhibitor. The present asymmetric regulation of organ initiation in are close to the dorsal side, the number of minima on the ventral side the dorsal and ventral regions is indispensable for bilateral tends to be larger than that of the dorsal side (Fig. 5C,D). When the symmetry that occurs via determination of the numbers and energy is low enough on the dorsal side, the arrangement becomes positions of floral organs. type 5A (Fig. 5C), but when the energy is not low enough, the An increase or decrease in organ number correlated with an arrangement becomes type 4B (Fig. 5D). For this mechanism, the enlargement or reduction in floral meristem size has been observed in inversion of the organ arrangements of the odd-numbered mutants of genes, such as CLAVATA and WUSCHEL, that function in merosities, trimery (between types 3A and 3B in monocots; the maintenance of the meristem population (Schoof et al., 2000) and Fig. 1C) and pentamery (between types 5A and 5B in legumes), is related genes, such as ULTRAPETALA (Fletcher, 2001). The reproduced by inverting the dorsal and ventral inhibition strengths ultrapetala mutant Arabidopsis exhibits a 6A arrangement with (types 3A and 3B in Fig. 4B,D,E; types 5A and 5B in Fig. 3I). increased meristem size (Fig. 1C, upper panel). While the sepal primordia form correctly on the dorsal and ventral sides, additional DISCUSSION sepal primordia can also initiate with two primordia in the lateral Candidates for dorsal and ventral inhibition positions, where only one forms in the wild type (type 4A; Fletcher, The inhibitory field model reproduced organ arrangements of a 2001). In our model, the transition from 4A to 6A occurred wide range of angiosperms, supporting the notion that DV consistently by increasing the meristem size, resulting in addition of asymmetric inhibition of organ initiation is one of the key a primordium to each lateral side (e.g. R0=16 to R0=20 at rdorsal=80, regulating factors of floral diversification. The primary rventral=70). Our model framework may explain not only the mutant candidates for involvement as DV asymmetric inhibition factors phenotypes that result from the defects in DV polarity but also the at the dorsal region are the CYCLOIDEA gene and its homologues. meristem-size mutants that exhibit the diversity of floral numbers As the arrangement differences between the wild-type and cyc and organ arrangements along the DV axis. Accumulation of mutant of A. majus were dependent on only dorsal inhibition in our experimental evidence about additional mutants, as well as the model, the strength of dorsal inhibition may directly account for external organs (bracts) that alter floral organ arrangement specifically differences in CYCLOIDEA expression. In light of the cyc-mutant at the dorsal, lateral or ventral side, will ultimately clarify the role of phenotype with an extra dorsal sepal, an inhibitory effect on the the DV inhibitory field in bilateral symmetry. dorsal side was suggested as a CYCLOIDEA function. The present model, however, suggests the opposite function, i.e. dorsal Consistency with the clade-specific diversity of DV inhibition may be stronger in the cyc mutant because the stronger patterning dorsal inhibition leads to the division of the energy of the dorsal Our model can be applied to the phylogenetic relationship within side into two local minima, resulting in two primordia (Fig. 5A,B). clades. The co-existence of merosity, especially that of pentamery Therefore, CYC gene homologues may similarly inhibit a dorsal and tetramery, is widely found in the eudicot clades (Smyth, inhibitory field, resulting in stronger dorsal inhibition in these 2018), not only in Plantaginaceae (Lamiales, Fig. 4A) but also in mutants. In addition, our model accounted for the bidirectional Dipsacales (e.g. Caprifoliaceae and Dipsacaceae), Fabales, initiation of Antirrhinum sepals with a lateral, dorsal and ventral Malpighiales (Matthews and Endress, 2013), Saxifragales, sequence, and the alternate arrangement of two sepals and a bract at Ericales (e.g. Sapotaceae), Oxalidales (e.g. Caldcluvia paniculata the ventral side, when both dorsal and ventral inhibition was (Fletcher, 2001; Matthews and Endress, 2002) and Brassicales incorporated (Fig. 3E). Therefore, two inhibition sources are likely (e.g. Tropaeolaceae, Caricaceae and Moringaceae). Different to occur, supporting the idea that the bract is a ventral inhibitor. arrangements of the same number of sepals co-exist in some The family Plantaginaceae also includes tetramerous species, such clades. For example, in legume species, type 5B arrangement exists as Veronica and Plantago (type 4B; Fig. 1C). The present model in the subfamily Papilionoideae, and 5A occurs in other DEVELOPMENT

7 RESEARCH ARTICLE Development (2020) 147, dev182907. doi:10.1242/dev.182907 subfamilies: 4A occurs in Acacia [Mimosoideae (Prenner, 2011) in those for patterns 3A and 5B, respectively, in the present model Fig. 1C]; tetramery and pentamery (Matthews and Endress, 2013) of (Figs 3I and 4E). both 5A and 5B (Zhang et al., 2010) co-exist in Malpighiaceae; 5A, The relationship with the helical (spiral) initiation order is 4B and 4A co-exist in Saxifragales (Ronse De Craene, 2010); and another important issue for future analysis. For example, in the 4A, 5A and 6A occur in the family Sapotaceae (Kümpers et al., subfamily Papilionoideae (Fabaceae; type 5B in Fig. 1C), an 2016). The causes of such changes are unclear, but the DV evolutionary path from the ancestral helical initiation, which is asymmetric expression of genes as well as bracts affect these found in other subfamilies of Fabaceae (Tucker, 2003), to arrangements. In Dipsacales, the pentamerous flowers are usually simultaneous initiation via unidirectional initiation, which is zygomorphic, whereas the tetramerous species include both radially typical in the subfamily Papilionoideae (Prenner, 2004), has been symmetric (e.g. Symphorycalpos, Caprifoliaceae) and zygomorphic suggested. Evaluating this hypothesis using a theoretical approach flowers (e.g. Knautia, Caprifoliaceae). The localized expression of and relating helical initiation to zygomorphic initiation will provide CYCLOIDEA has been suggested to be responsible for zygomorphy an effective insight into phylogenetic relationships between species in most of these mentioned clades, including Brassicales, Fabales, through morphogenesis and allow estimation of the evolutionary Dipsacales and Malpighiales (Hileman, 2014). Therefore, we expect history of floral ontogeny. that the clade-specific strength and expression domain of CYCLOIDEA plays a central role in the different floral organ Conclusion numbers and arrangements among these clades, suggesting that the We describe an inhibitory field model along the DV axis, where application of the present model is plausible. In the present model, CYC and the main axis are candidates for dorsal inhibitors, whereas changes in either dorsal or ventral inhibition accounted for the direct PAN, BOP and a ventral bract are candidates for the ventral transition from 4A to 5A (rdorsal=50, rventral=50 to rdorsal=50, inhibitor. The model simulations on the number, positions and rventral=30; Fig. 3I). Such direct transitions among the 4A, 4B, 5A initiation patterns of the organ primordia verified not only cyc and 5B arrangement types occurred as the result of changes in either mutant of Antirrhinum as ventral inhibitor, but also pan and bop the dorsal or ventral inhibition or the meristem size (Figs 3I and 4F, mutants of Arabidopsis and bract as ventral inhibitors. Model Fig. S1). By combining our framework with observed organ simulations further showed that the diversity of monocots and arrangements and initiation orders, we can estimate the eudicots in the bilateral symmetry of the organ positions were developmental parameters (i.e. dorsal or ventral inhibition and dependent on the relative inhibition strength and meristem size, meristem size) that accompany evolutionary changes in floral demonstrating a design principle for floral symmetry during development between clades. developmental evolution.

Future implications for our model MATERIALS AND METHODS Our model does not incorporate some known parameters, such as Model for perianth organ positioning the geometrical shape, fusion and division of primordia, during Numerous theoretical studies have targeted the organ patterning of plant aerial floral development. The shape of the primordium is considered to be parts, especially phyllotaxis. More than a century ago, Hofmeister (1868), who a regular disc in the present model, whereas the actual shape is more described several rules of plant development, noted the periodic initiation of likely to be wider in the ventral dimension than in the dorsal leaf primordia at the least crowded space around the apical meristem. This ‘Hofmeister’srule’ was later modified by Snow and Snow (1962), who dimension in many bilaterally symmetrical flowers (e.g. Luo et al., performed surgical and chemical treatments to alter phyllotaxis and suggested 1996). In some species, a decrease in organ number may occur due that the initiating position of primordium is strongly affected by the to the fusion of primordia (Endress, 1999; Rudall and Bateman, neighboring primordia. These investigators insisted that the primordia 2004; Wozniaḱ and Sicard, 2018). For example, the evolutionary appears when there is enough space to support initiation (Snow and Snow, transition from pentamery (5B) to tetramery (4A) via the fusion of 1952), as opposed to the periodic initiation suggested by Hofmeister. Douady two dorsal sepals has been suggested in Dipsacaceae (Ronse De and Couder (1996a,b) developed two mathematical models that assumed Craene, 2010). Similarly, some flowers, such as Pisum sativum an inhibitory energy imposed on primordium initiation by the existing (Fabaceae), exhibit co-initiation of two or more organs as a common primordia. The first model included periodic initiation following Hofmeister’s ’ primordium and subsequent division (Ferrandiz et al., 1999). observations, while the second model relied on Snow and Snow s Therefore, our model must be carefully compared not only with the modification. The substance responsible for initiation inhibition has been suggested to be related to the polar transport of phytohormone auxin organ arrangement of mature flowers but also with the early floral (Fujita and Kawaguchi, 2018; Jönsson et al., 2006; de Reuille et al., 2006; development. Furthermore, the timing of the termination of the Smith et al., 2006), the mechanical properties of epidermal tissues (e.g. floral meristem by formation of carpel(s) can affect the initiation buckling wavelength) (Green, 1996) or the direction of microtubule alignment order of floral organs, especially that of the inner organs, such as (Heisler et al., 2010). Based on the second phyllotaxis model of Douady and stamens. In some species, zygomorphy is established after an organ Couder (1996b), we considered the organ primordia to be points and the apical initiates and its fate is determined (Jabbour et al., 2009). The meristem to be a disc with radius R0 (Fig. 2A). We denoted the position of the θ regulation of organ growth in later development, in part, by CYC primordium j as (rj, j) in polar coordinates. Owing to the growth of the apex, homologues in the dorsal region, also contributes to zygomorphy the primordia move centrifugally with a constant speed V.Thus, (Chang et al., 2010; Hileman, 2014; Spencer and Kim, 2018). In r ðtÞ¼R þ Vðt T Þ; ð1Þ addition, the bracts, which we considered here as a ventral inhibitor, j 0 j also exist at the dorsal and/or lateral sides (Ronse De Craene, 2010). where Tj represents the time when primordium j appeared. A new primordium Properties such as organ size, shape, growth, timing of termination i arises at the edge of the apical meristem, namely ri=R0. The angular position and zygomorphy establishment, and dorsal/lateral bracts are of the new primordium is determined by the inhibitory energy from the other θ therefore factors that may be incorporated into our model. In primordia, U( ), given by future theoretical studies, these properties may contribute to the Xi1 Xi1 explanation of the observed predominance of patterns 3B and 5A UðuÞ¼ Uj ¼ expðdij=lÞ; ð2Þ among angiosperms, while these parameter ranges are as wide as j¼0 j¼0 DEVELOPMENT

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where dij is the distance between an existing primordium j and the candidate Supplementary information Supplementary information available online at position (R0, θ) for primordium i,andλ denotes the characteristic length of the decay of inhibitory energy (Fig. 2B). The position θ′ is employed as the http://dev.biologists.org/lookup/doi/10.1242/dev.182907.supplemental position of a new primordium, when U(θ′) is below a threshold and has a local minimum of U(θ). Under these conditions, one or more primordia arise References Adler, I., Barabe, D. and Jean, R. V. (1997). A history of the study of phyllotaxis. corresponding to the number of local minima that satisfy these criteria Ann. Bot. 80, 231-244. doi:10.1006/anbo.1997.0422 (Fig. 2C), whereas the apex continues to grow without generating any Bowman, J. L., Eshed, Y. and Baum, S. F. (2002). Establishment of polarity in primordium when a sufficiently low minimum is not achieved. The major angiosperm lateral organs. Trends Genet. 18, 134-141. doi:10.1016/S0168- parameters of this model include the threshold value of U to initiate a 9525(01)02601-4 primordium, decay length of inhibition λ and the size of meristematic Chandler, J. W. and Werr, W. (2014). Arabidopsis floral phytomer development: auxin response relative to biphasic modes of organ initiation. J. Exp. Bot. 65, region R0. Following the suggested inhibitory effect on the initiation of primordia by 3097-3110. doi:10.1093/jxb/eru153 Chang, Y.-Y., Kao, N.-H., Li, J.-Y., Hsu, W.-H., Liang, Y.-L., Wu, J.-W. and Yang, gene expression along the DV axis (Luo et al., 1996), we employed external C.-H. (2010). Characterization of the possible roles for B class MADS box genes in inhibitory sources to our model. The inhibition from the dorsal side of the floral regulation of perianth formation in orchid. Plant Physiol. 152, 837-853. doi:10. meristem, Udorsal, was expressed in the same form as Eqn 2 for simplicity: 1104/pp.109.147116 de Lima Silva, A., Trovó, M. and Coan, A. I. (2016). Floral development and vascularization help to explain merism evolution in (Eriocaulaceae, Poales). Udorsal ¼ AdorsalexpðatÞexpðddorsal=lÞ; ð3Þ PeerJ 4, e2811. doi:10.7717/peerj.2811 where d denotes the distance between the candidate position of the de Reuille, P. B., Bohn-Courseau, I., Ljung, K., Morin, H., Carraro, N., Godin, C. dorsal – initiating primordium and the external inhibitory factorat the dorsal side. A and Traas, J. (2006). Computer simulations reveal properties of the cell cell dorsal signaling network at the shoot apex in Arabidopsis. Proc. Natl. Acad. Sci. USA denotes the strength of inhibition relative to that of the older primordia (Eqn 2). 103, 1627-1632. doi:10.1073/pnas.0510130103 We examined not only the condition when Udorsal was constant throughout Dhaka, N., Bhardwaj, V., Sharma, M. K. and Sharma, R. (2017). Evolving tale of development (a=0) but also the condition when Udorsal decreased with a TCPs: new paradigms and old lacunae. Front. Plant Sci. 8, 479. doi:10.3389/fpls. constant a. The radial and angular positions of the dorsal inhibitory factor were 2017.00479 Douady, S. and Couder, Y. (1996a). Phyllotaxis as a dynamical self organizing given as (rdorsal,0),andanincreaseinrdorsal decreased the inhibitory effect by this factor at the meristem edge (Fig. 2D). Inhibition by an external inhibitory process part I: the spiral modes resulting from time-periodic iterations. J. Theor. Biol. 178, 255-273. doi:10.1006/jtbi.1996.0024 factor at the ventral side at position (rventral, 180°) was formulated similarly: Douady, S. and Couder, Y. (1996b). Phyllotaxis as a dynamical self organizing process part II: the spontaneous formation of a periodicity and the coexistence Uventral ¼ AventralexpðatÞexpðdventral=lÞ; ð4Þ of spiral and whorled patterns. J. Theor. Biol. 178, 275-294. doi:10.1006/jtbi. 1996.0025 where ddorsal denotes the distance between the candidate position of the Endress, P. K. (1999). Symmetry in flowers: diversity and evolution. Int. J. Plant Sci. initiating primordium and the external inhibitory factor at the ventral side. 160, S3-S23. doi:10.1086/314211 Endress, P. K. (2010). Flower structure and trends of evolution in Eudicots and their Aventral denotes the strength of inhibition. When the x-y coordinate in the 2D meristem geometry (Fig. 2) is scaled by x→cx and y→cx (implying d →cd , major subclades. Ann. Mo. Bot. Gard. 97, 541-583. doi:10.3417/2009139 ij ij Ferrandiz, C., Navarro, C., Gomez, M. D., Canas, L. A. and Beltran, J. P. (1999). dventral→cdventral,ddorsal→cddorsal,R0→cR0, λ→cλ,rdorsal→crdorsal and → Flower development in pisum sativum: from the war of the whorls to the battle of rdorsal crdorsal), where c is a constant, the present model (Eqns 2, 3 and 4) the common primordia. Dev. Genet. 25, 280-290. doi:10.1002/(SICI)1520- has the scale invariant property, U(θ)→U(θ), Udorsal→Udorsal and 6408(1999)25:3<280::AID-DVG10>3.0.CO;2-3 Uventral→Uventral. Fletcher, J. C. (2001). The ULTRAPETALA gene controls shoot and floral meristem size in Arabidopsis. Development 128, 1323-1333. Fujita, H. and Kawaguchi, M. (2018). Spatial regularity control of phyllotaxis pattern Numerical simulations generated by the mutual interaction between auxin and PIN1. PLoS Comput. Biol. The potential energy of the initiating primordia was calculated for discrete 14, e1006065. doi:10.1371/journal.pcbi.1006065 angles with an interval of 0.1°. Without the dorsal and ventral inhibition Green, P. (1996). Phyllotactic patterns: a biophysical mechanism for their origin. sources, the potential is uniform over the edge of the meristem upon Ann. Bot. 77, 515-528. doi:10.1006/anbo.1996.0062 initiation of the first primordium/primordia. Therefore, we manually placed Harshberger, J. W. (1907). Teratologic notes. Plant World 10, 186-189. https://www. one primordium on the dorsal side. The whorl in Figs 3 and 4 and Fig. S1 jstor.org/stable/43476599. Heisler, M. G., Hamant, O., Krupinski, P., Uyttewaal, M., Ohno, C., Jönsson, H., was defined when the radial distance between successive organ primordia is Traas, J. and Meyerowitz, E. M. (2010). Alignment between PIN1 polarity and V or less. In other cases, the position of the first primordium/primordia was microtubule orientation in the shoot apical meristem reveals a tight coupling specified according to the potential landscape. All programs were written in between morphogenesis and auxin transport. PLoS Biol. 8, e1000516. doi:10. the C programming language. V=0.01, λ=10 and Adorsal=Aventral=1, and the 1371/journal.pbio.1000516 threshold value of U to initiate a primordium was 0.5 unless specified in the Hepworth, S. R., Zhang, Y., Mckim, S., Li, X. and Haughn, G. W. (2005). BLADE- texts or figure captions. ON-PETIOLE-dependent signaling controls leaf and floral patterning in Arabidopsis. Plant Cell 17, 1434-1448. doi:10.1105/tpc.104.030536 Hileman, L. C. (2014). Bilateral flower symmetry — how, when and why? Curr. Opin. Acknowledgements Plant Biol. 17, 146-152. doi:10.1016/j.pbi.2013.12.002 We thank Kimiko Yoshikawa for related simulations during the early stages of the Hofmeister, W. (1868). Allgemeine morphologie der gewächse. In Handbuch der work, and Akitoshi Iwamoto, Hirokazu Tsukaya and Hiroyuki Hirano for helpful Physiologischen Botanik, Vol. 1 (ed. W. Hofmeister), pp. 405-664. Leipzig: discussions. Engelmann. Jabbour, F., Ronse De Craene, L. P., Nadot, S. and Damerval, C. (2009). Competing interests Establishment of zygomorphy on an ontogenic spiral and evolution of perianth in The authors declare no competing or financial interests. the tribe Delphinieae (Ranunculaceae). Ann. Bot. 104, 809-822. doi:10.1093/aob/ mcp162 ̈ Author contributions Jonsson, H., Heisler, M. G., Shapiro, B. E., Meyerowitz, E. M. and Mjolsness, E. (2006). An auxin-driven polarized transport model for phyllotaxis. Proc. Natl. Conceptualization: A.N., M.S.K., K.F.; Methodology: A.N., M.S.K.; Validation: Acad. Sci. USA 103, 1633-1638. doi:10.1073/pnas.0509839103 M.S.K.; Investigation: A.N., M.S.K.; Data curation: A.N., M.S.K.; Writing - original Khan, M., Xu, H. and Hepworth, S. R. (2014). BLADE-ON-PETIOLE genes: setting draft: A.N., M.S.K., K.F.; Writing - review & editing: M.S.K., K.F.; Supervision: K.F.; boundaries in development and defense. Plant Sci. 215-216, 157-171. doi:10. Project administration: K.F.; Funding acquisition: K.F. 1016/j.plantsci.2013.10.019 Kitazawa, M. S. and Fujimoto, K. (2015). A dynamical phyllotaxis model to Funding determine floral organ number. PLoS Comput. Biol. 11, e1004145. doi:10.1371/ This work was supported by Grants-in-Aid for Scientific Research from the Ministry journal.pcbi.1004145 of Education, Culture, Sports, Science and Technology of Japan (17H06386, Kuhlemeier, C. (2017). Phyllotaxis. Curr. Biol. 27, R882-R887. doi:10.1016/j.cub.

16H01241, 16H06378 to K.F.). 2017.05.069 DEVELOPMENT

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