Phyllotactic Patterning of Gerbera Flower Heads

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Fibonacci cur- cf. of of phyllotaxis, prevalence base the the explaining at theories to lies gradually rent observation according organs This progress sequence. added will Fibonacci the parastichies the of of of number size circumference lattice the the the increases, spiral if to that, a compared showed lattice of (19) (7, this boundary Iterson stacking distal van iterative or the 1A). 17) (Fig. an at (16, elements as accretion new abstracted as 18)—of commonly to referred is meristem. addition—also process apical space growing resulting as the soon within The primordia as them inserted hypothesis for the are this available primordia refined becomes from new 15) that distant (14, postulating Snow by sufficiently and emerge Snow are primordia earlier. new formed that that locations proposed who at (13), Hofmeister to understood. patterns fully much these been of not with development has the As patterns (11). 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Dominique by Edited Canada 1N4, T2N AB Calgary, Calgary, of University eateto giutrlSine,Vik ln cec ete nvriyo esni 01 esni iln;and Finland; Helsinki, 00014 Helsinki, of University Centre, Science Plant Viikki Sciences, Agricultural of Department h eia dabhn xlntoso hloai sdue is phyllotaxis of explanations behind idea seminal The sub- the been has patterns phyllotactic of development The sosre costepatkndmfo la to algae from kingdom plant the phyllotaxis— across phyllotaxis—spiral observed of type is common most he 01Vl 1 o 3e2016304118 13 No. 118 Vol. 2021 | ueia canalization numerical n oao(,9.I hs lns ra primordia organ plants, these In 9). (8, tomato and a,1 Arabidopsis eso htpyltci pattern- phyllotactic that show We hybrida. Gerbera a,2 ioa Cieslak Mikolaj , Arabidopsis n reylwPrusinkiewicz Przemyslaw and , 1) ncnrs,flrt nteheads the in florets contrast, In (10). n oaodw otemolecular the to down tomato and | oe eddevelopment head flower b,1 nrwOwens Andrew , b,2 | auxin b egWang Feng , doi:10.1073/pnas.2016304118/-/DCSupplemental at online information supporting contains article This 2 1 microcomputed X-ray high-resolution obtained we emerges, Development. Head Results as gerbera phyllotaxis. of studying the usefulness for and the system plant to model the a add of parastichies part of sep- vegetative number The the large novo. from de head case, the develops that latter of heads suggests aration the the which in In axis, pattern growth S1). phyllotactic whole the Fig. the lateral , Appendix constitutes or (SI scape terminal the shoot a in the a appear in by may position supported which is (scape), head to The stem bracts up rim. leafless with involucral head 1D), the (Fig. leaflike near spirals parastichies in 90 34/55 arranged to are florets 80 The ( 1C). by receptacle (Fig. large florets surrounded a individual diameter) to 700 attached in to types, transformation. 600 different genetic three comprises of to head susceptibility gerbera its mature A to due plant model ulse ac 6 2021. 26, March Published BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This interest.y competing no declare authors The A.O., M.C., T.Z., paper.y T.Z., and the results; models; wrote P.P. modeling and mathematical and P.E., data and experimental computational P.P. analyzed and the constructed P.E., P.P. exper-M.C., cloned and other F.W. all A.O., out construct; carried P.P. M.C., T.Z. DR5 hybridization; and iments; situ the P.E., in T.H.T., cloned the T.H.T. conducted T.Z., and and project; construct GhCLV3 S.K.B. the experiments; designed P.P. the and designed P.E., T.Z., contributions: Author how of question arise. the patterns open observed leaving the (26), spirals than produced diver- rather or golden (23–25) whorls the primordia of consecutive between assumption angle priori gence a capture a an to required attempts of process Previous context this 1B). (Fig. the lattice outside built-up emerge gradually high numbers relatively with parastichy patterns Fibonacci however, family, Aster the in species owo orsodnemyb drse.Eal w@clayc rpaula. or [email protected] Email: addressed. be may elomaa@helsinki.fi. correspondence whom To work.y this to equally contributed M.C. and T.Z. h xesvl tde hloatcptenn ntemodel the from in different patterning is plants phyllotactic growth, studied extensively the head florets. of the during and contraction and and zone bracts expansion order organogenetic subsequent by specific the controlled a process, of This in placement early emerge the the which is guide process bracts, critical of The understand patterning develop. to patterns combined techniques these and modeling how gerbera and of microscopy lines right- diverse numbers. reporter and Fibonacci auxin left- examined consecutive of We typically organized numbers are are the spirals mathemati- example, winding They intriguing For florets. with properties: com- patterns cal and sunflower, spiral or bracts conspicuous gerbera into of of hundreds those as prise such heads, Flower Significance okn o nepaain eselected we explanation, an for Looking a uiK Broholm K. 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PLANT BIOLOGY Fig. 1. Problem position and the model system. (A) Example of a spiral phyllotactic lattice. Bracts in the flower head of Cirsium vulgare (common thistle) are arranged into a circular lattice that originates at the stem, possibly continuing the pattern of leaves, and extends by the addition of new elements at its distal boundary. The development of such patterns is largely understood. Image credit: Jouko Rikkinen, University of Helsinki/Finnish Biodiversity Information Facility, licensed under CC BY-NC 4.0 (B) The arrangement of bracts in gerbera. A pattern with a relatively high Fibonacci number of visible parastichies (13) is not preceded by a lattice. The development of such patterns has remained an open problem. (C and D) Gerbera head morphology. (C) Longitudinal section of the head. The head resembles a solitary flower, but comprises three types of florets (ray, trans, and disk) attached to a receptacle and surrounded by bracts. (D) The disk florets are arranged in a spiral phyllotactic pattern, with parastichies (representatives highlighted) occurring in Fibonacci numbers. (Scale bars: 1 cm.)

tomography (micro-CT), scanning electron microscopy (SEM), ima in images with the same number of maxima are similar. This and confocal microscopy images of gerbera heads at differ- indicates that the early patterning of gerbera heads is stereotyp- ent stages of development. The growing receptacle can be ical, and the developmental sequence can be reconstructed from divided into the outer zone, in which bract and floret primordia superimposed (SI Appendix, Fig. S3B) or representative (Fig. 4A) have already differentiated, and the still-undifferentiated central images of different heads. zone. The boundary between the two zones is the pattern front Within the set of 56 heads, the distribution of initia numbers (Fig. 2A). Initially, the receptacle is “naked,” with no visible pri- was highly nonuniform: 45 out of the 56 observed heads had a mordia (Fig. 2 A and B, stage I). Up to 13 bract primordia then Fibonacci number of initia (SI Appendix, Fig. S3A). The proba- emerge approximately simultaneously∗ near the receptacle rim bility that they were drawn from a set with uniformly distributed (stage II). As the head grows, subsequent primordia are inserted initia numbers is less than 0.001, according to the χ2 goodness- between those initiated earlier, positioned slightly inward with of-fit test. These data indicate that early initia in gerbera tend to respect to their older neighbors (stages III to V). The pattern emerge in discrete steps, jumping from one Fibonacci number front then gradually moves away from the head rim, initiating a to the next through bursts of concurrent meristematic activ- lattice with visible parastichies (stage VI), and eventually con- ity. The intermediate stages with non-Fibonacci numbers occur tracts, extending the lattice to the head center (stages VII to transiently. IX). The number of parastichies decreases in discrete steps, fol- Up to the 13-initium stage, the initia are arranged near the lowing the reversed Fibonacci sequence. Near the center, the head rim in an approximately circular pattern: The differences pattern becomes chaotic (stage IX). With the entire head sur- in their radial positions are small (Fig. 4A). In contrast, gaps face consumed by primordia, the pattern front and the central between neighboring initia have a bimodal distribution and can zone disappear. Beginning at stage III, the receptacle changes be categorized as short (S) or long (L) at every developmental shape from a dome to a flattened form overhanging the stem. stage (Fig. 4 B and C). The progression of the pattern of gaps This change carries bracts from the upper to the lower side of the over time is summarized by the lineage tree in Fig. 4D. In each receptacle. The overall dynamics of gerbera head development step of development, a new initium emerges in every gap L, divid- and patterning is thus similar to that of sunflower (11, 27), except ing it into a new pair of gaps L and S. Meanwhile, short gaps S that the sunflower receptacle is concave rather than convex. elongate and become long gaps L. From these observations we infer the following: Pattern Initiation. An intriguing element of the developmental sequence is the approximately simultaneous emergence of up • Gap numbers progress in discrete steps (bursts) consisting of to 13 primordia at the receptacle rim in stage II. To analyze concurrent events of type S → L and L → L + S. This progres- processes leading to this emergence, we focused on the plant hor- sion is analogous to the archetypal example of the Fibonacci mone auxin, which plays a key patterning role in Arabidopsis and sequence—the growth of an idealized rabbit population— tomato (8, 28–31). Hypothesizing that this role is conserved in and thus explains the progression of gap and initia numbers Asteraceae, we created transgenic gerbera plants expressing the according to this sequence. DR5rev::3XVENUS-N7 auxin reporter (28) and confirmed that it • The spatiotemporal pattern of gaps coincides with the ideal- is responsive to auxin in gerbera (SI Appendix, Fig. S2). As in Ara- ized pattern of long and short cells resulting from the asym- bidopsis and tomato, the DR5 signal localizes to incipient organ metric cell division in vegetative filaments of cyanobacterium primordia (initia) in gerbera before their outgrowth (Fig. 3). To Anabaena catenula (32); consequently, the early patterning of investigate how the DR5 pattern develops, we analyzed confocal bract initia in gerbera is characterized by the same set of rules images of 56 randomly chosen heads with up to 34 DR5 maxima [L-system (33, 34); Fig. 4E], which adds a spatial component to (SI Appendix, Fig. S3A). Our data show that, setting differences Fibonacci’s population-level model. Arrows above the symbols, in the chirality of heads aside, relative positions of DR5 max- referred to as polarities, point to the older neighbor within each interval (created in an earlier burst)† and control the order of gaps resulting from the insertion of a new initium: LS or SL.

*Throughout this paper, we describe events that take place at the same time as syn- chronous; those that take place within a short time interval, in an order that is not evident in observations, as approximately simultaneous; and those that can occur in †Except for initium 1, which has no neighbors, and 2, which has the same neighbor on any order without affecting the outcome as concurrent. both sides (initium 1).

2 of 11 | PNAS Zhang et al. https://doi.org/10.1073/pnas.2016304118 Phyllotactic patterning of gerbera flower heads Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 hloatcptenn fgreaflwrheads flower gerbera of patterning Phyllotactic al. et Zhang (C staining. in PI box using white The highlighted zone). J are (central walls meristem µm ( cell inflorescence surface undifferentiated meristem The IM, the maxima. of (F DR5 curvature outgrowth. eight Gaussian primordia of and shows absence (D) stage epidermis developmental meristem the same (B in the meristem intensity in of meristem section head optical the The of image Confocal (B) 3. Fig. • 500 (A); mm 1 bars: [Scale IX). (stage center head the near distributed (B head. the within zones different 2. Fig. hw htmrhlgclcagsaesgicnl eae ihrsett h atrigo ui aia sin as maxima, auxin of patterning the to respect with delayed significantly are changes morphological that shows huddvd h pc ewe t egbr codn othe to according neighbors ratio. equa- its golden between the space satisfy the divide lengths should gap the this if rate, tion satisfied same the be at will grow gaps condition all that Assuming initium. length new threshold the reach will L l gap which over time same burst, the each length within of insertion S gap initia a of synchrony full achieve To + s l E mg faha na al eeomna tg hw ovsbeognprimordia. organ visible no shows stage developmental early an in head a of image SEM (A) outgrowth. their precedes primordia of Patterning ir-Tcosscin.Arw n oosindicate colors and Arrows cross-sections. Micro-CT (A) stage. (IX) patterned fully the to (I) early an from heads flower gerbera of Development n udvd nogp n hog h neto fa of insertion the through S and L gaps into subdivide and /s (l = + s )/l s utgo olength to grow must hc mle htanwyisre initium inserted newly a that implies which , E mgs lc ie nrdbcgon ihih aatcis(tgsV oVI) lc osmr rmri chaotically primordia mark dots black VIII); to VI (stages parastichies highlight background red on lines Black images. SEM ) ofim h bec fpiodaotrwhadtepeec fD5mxm.(D maxima. DR5 of presence the and outgrowth primordia of absence the confirms ) –J h mgscrepnigto corresponding images The ) l eoigagpL in L, gap a becoming , A–E (B).] µm taltrdvlpetlsae p ue oewt ifrnitdflrtprimordia; floret differentiated with zone outer Fp, stage. developmental later a at F niae h anfidae iulzdin visualized area magnified the indicates a rpgto fteD5sga nbt ailadlateral and radial both in such signal which DR5 the at of grad- stage a propagation showed developmental images ual The earliest individ- feasible. five experimentally the was of 4H imaging in images (Fig. the heads time-lapse expands obtained initia ual toward we of extends hypothesis, ring the this subsequently as but neighbor older neighbors, halfway approximately its emerges initium between an 4 that (Fig. suggests signal streaks DR5 the of nlzn h pcn fiii ute,w osdrdstreaks considered we further, initia of spacing the Analyzing − 2 (E ) ute eosrtstepeec fD5mxm nthe in maxima DR5 of presence the demonstrates further ) F and D https://doi.org/10.1073/pnas.2016304118 and .Teoinaino these of orientation The G). oprsno images of comparison A G–J. and Saebr:100 bars: (Scale E. E iulzto fD5signal DR5 of Visualization ) PNAS µm.) .T test To ). | f11 of 3 I and )

PLANT BIOLOGY Fig. 4. Analysis and model of early patterning in gerbera heads. (A) Confocal images of representative heads with up to 34 DR5 maxima indicating incipient primordia (initia). An expanding ring of maxima developing near the head rim reveals pattern progression not observed in SEM images (Fig. 2). Individual cells are stained by using PI. The initia are numbered by following the golden divergence angle; the numbers do not imply the exact order of emergence. (B–E) Analysis of pattern progression up to 13 initia. (B) Angular positions (mean values and standard deviations) of the initia in heads with Fibonacci initia numbers (SI Appendix, Fig. S3A). The angles are measured counterclockwise with respect to initium 1. Arrows indicate initia inserted in consecutive steps. (C) Normalized Gaussian kernel plots of the density of gap sizes between initia. (D) The developmental pattern represented as a lineage tree of short and long gaps between the initia. Arrows above the symbols point to the older neighboring initium. (E) The rules of pattern development represented as an L-system. (F) Details of DR5 pattern in the 13-initium stage. The newest initia tend toward their older neighbors. (G) Visualization of DR5 signal intensity in the meristem epidermis for initium P9 (boxed in F). Colors in the dashed wedge indicate the strength of the DR5 signal. (H) Schematic representation of the propagation of the DR5 signal toward the older neighbor. (I) Simulated distribution of the initia generated on the head rim, overlaid on superimposed DR5 images (as in SI Appendix, Fig. S3B). Color gradients on the rim (orange to red) relate the initia to their older neighbors, toward which they propagate. [Scale bars: 500 µm (A); 200 µm (F and G).]

directions, tending toward the older neighbor (Fig. 5). We veri- the rim expands, initia numbers would increase in a geometric ﬁed that the actual outgrowth occurs near the distal (farther from progression: 1, 2, 4, 8, 16... (SI Appendix, Fig. S5A). How- the head center) streak end (SI Appendix, Fig. S4). Although ever, with a lateral displacement toward the older neighbor, the initial DR5 signal is too weak and amorphous to be located initia numbers tend to the Fibonacci sequence for a range of precisely, our observations indicate that the lateral displace- displacement values (over 80% of simulation time for the dis- ment of initia is either the sole or a contributing factor induc- placement rates within the ±20% range of the optimum value; ing the asymmetric position of primordia with respect to their SI Appendix, Fig. S5 B–D). The adherence to the Fibonacci neighbors. sequence thus does not critically depend on any speciﬁc param- To better understand the role of the lateral displacement of eter value, such as the golden ratio. This property is conserved initia, we constructed a computational model operating on the whether the threshold distance at which new initia emerge receptacle rim approximated as a growing circle (SI Appendix, according to the Hofmeister/Snow and Snow rule is constant SI Text, Model 1). If each initium was inserted symmetrically or changes over time. With the threshold distance decreasing between its neighbors and remained equidistant from them as by 85% in the course of a simulation from the 0- to 34-initium

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PLANT BIOLOGY Fig. 6. Dynamics of the morphogenetically competent zone. (A–C) Relation of the competent zone to the pattern front. (A) SEM image of a head with mock treatment, showing a normal phyllotactic pattern. (B) Head that underwent a 2-wk NPA treatment. The initiation of floret primordia has stopped at a circular pattern front (white circle). (C) Head of a plant that underwent a 2-wk NPA treatment followed by a 1-wk period without applied NPA. Production of primordia (marked with white dots) resumed at a distance from the previously formed pattern front. (D–H) Expansion (D–G) and contraction (H) of the GhCLV3 expression domain. (D) Vegetative shoot meristem. Lf, leaf primordium. (E) Naked head stage. (F) Bract (Br) patterning stage. (G) First floret primordium (Fp) stage. (H) Disk floret patterning stage. All images are light-microscopic sections of in situ hybridization. Black dotted lines accentuate the GhCLV3 expression domain; their endpoints indicate the presumptive position of the active ring. [Scale bars: 1 mm (A–C); 100 µm (D–H).]

and the rate of changes in the threshold distance for inserting ing the receptacle shape and active-ring position in the course new primordia. of head development, and compared it with patterning data. To As the active ring propagates further, extending parastichies model the receptacle, we analyzed proﬁles of heads in a sequence toward the head center, parastichy numbers decrease in reversed of developmental stages scanned using X-ray micro-CT (Fig. 2A; Fibonacci sequence (Fig. 7F). This phase of patterning is well two earliest developmental stages not shown), as well as the described by van Iterson’s model (19). Near the center, the positions of the pattern front (Fig. 8A and Movie S3; for details, pattern becomes disorganized due to the scarcity of available see SI Appendix, Fig. S9 and SI Text, Model 3). By interpolat- space. ing these data, we constructed a three-dimensional (3D) model of receptacle development using the keyframe method with B- The Integrative Model. Investigating whether the described pro- splines (38) (Fig. 8B). Consistent with Fig. 3 I and J, we assumed cesses encompass the entire phyllotaxis of gerbera heads, we that the active ring is positioned ahead of the observed pat- constructed a model driven by experimental data characteriz- tern front. Given this input, we simulated the insertion of new

Fig. 7. Model of the emergence and development of parastichies. (A and B) The active ring (red) gradually separates from the receptacle rim (gray), positioning younger initia (green) closer to the receptacle center than their older neighbors (red; color scheme as in Fig. 4I). (C) Differences in the radial position of initia result in a zigzag pattern front (yellow). The in and out positions of the initia are deﬁned by polarities of gaps S and L. (D and E) A lattice of primordia develops on the zigzag template as the active ring continues to contract. Adjacent primordia delineate two families of spiral parastichies. (F) The ﬁnal pattern. Colored lines highlight select parastichies. The red circle indicates the disorganized pattern at the center.

6 of 11 | PNAS Zhang et al. https://doi.org/10.1073/pnas.2016304118 Phyllotactic patterning of gerbera flower heads Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 aatcynmesuigbt iclradtasetynoncir- 9 transiently (Fig. and rings circular active both cular Fibonacci using with numbers patterns phyllotactic parastichy regular generate front can model pattern the zigzag in differences the the forming and primordia 9B). 9A) (Fig. (Fig. of rim position the radial along pat- gaps the of both includes tern expression agreement DR5 The This of predictions. experimentally. maxima model’s observed matched the closely with positions patterning predicted of phase early the 2B). (Fig. (Fig. head images resulting representation The and (39). 3D S10 data 8D reported Fig. realistic on Appendix, based a (SI 3) Model with primordia floret it growing enhanced of we model, the ohcrua n rninl ocrua ciernsotnoccur often rings 9 active which (Fig. noncircular in transiently heads, and real circular of observations both the with consistent is feature (Fig. occur it for conditions 8C when hypoth- displacement Snow lateral and with Hofmeister/Snow esis, the to (red). ring according active primordia the and (white), zone the floret the of (green), trajectory zone the bract the is (yellow), curve receptacle red the and The stem points. the (C between material zone of transitional trajectories the indicate the 2A Colors (Fig. show primordium 3 curves youngest (Fig. Yellow the changes of receptacle. morphological positions the the of from estimated growth ring the active characterize to curves) (green 8. Fig. hloatcptenn fgreaflwrheads flower gerbera of patterning Phyllotactic al. et Zhang iuae eeomn fagreahead. gerbera a of development Simulated (D) model. receptacle the on generated pattern Phyllotactic ) u olclitrcinbtenicpetpioda the primordia, incipient between interaction local to Due in signal DR5 the compared first we model, the validate To and and hloatcptenn fgreahas (A heads. gerbera of patterning Phyllotactic D lsl ac h E mg fagerbera a of image SEM the match closely S7) Movie .T aiiaetevsa vlainof evaluation visual the facilitate To S4–S6). Movies and F ). C I and and J npht ftercpal oe bandb oaigtepol uvsaon h eetcessmer axis. symmetry receptacle’s the around curves profile the rotating by obtained model receptacle the of Snapshots (B) ). E and oisS5 Movies and rfie ftercpal r rcd(ht uvs n interpolated and curves) (white traced are receptacle the of Profiles (A) construction. Model B) and S6 IText, SI .This ). and ntecneto eaaepatseis eosre that observed We species. plant separate of context phyllotaxis the of Bull-Here by and modes in Classen-Bockhoff emerges Distinct by recognized process. pattern first relatively basic were the same a which the as iterating during described process, commonly homogeneous is patterning Phyllotactic those matched closely Discussion center, the disorgani- near eventual 9 (Fig. the pattern experimentally parastichy observed and the of center, of reduction head zation The the heads. toward typ- gerbera range numbers in the within observed primordia) 84 floret ically rim, 634 the and near primordia, parastichies bract (34/55 characteristics with patterns 9I 9J (Fig. (Fig. center data stem the from head from the 9 at (Fig. bract looking bottom early when the the visible of become the position which nonuni- amplifies radial primordia, the the expansion to in This due differences receptacle. small head initially the the of of side expansion lower form the to upper the from ,tkn noacutta R aiaeeg before emerge maxima DR5 that account into taking S9 ), Fig. Appendix, SI yteedo h iuain h oe erdcdspiral reproduced model the simulation, the of end the By primordia bract of propagation the captures also model The ). G and H .Tedsrbto fbatdistances bract of distribution The ). scnitn ihexperimental with consistent is ) K https://doi.org/10.1073/pnas.2016304118 and L). PNAS | u(40) nu ˜ f11 of 7

PLANT BIOLOGY Fig. 9. Model validation. (A and B) Comparison of predicted and observed positions of DR5 maxima in the early patterning phase. (C–F) Comparison of predicted and observed intermediate patterning stages with circular (C and D) and elliptic (E and F) pattern fronts. Chl, chlorophyll. (G and H) Comparison of predicted (G) and observed (H) positions of the ﬁrst 21 bracts on the lower side of a gerbera head. (I and J) Comparison of predicted (I) and measured (J) distances of bracts from the stem center. For the measured distances, mean values in a set of 12 heads (horizontal lines) and the standard errors (vertical bars) are shown. (K and L) Comparison of the simulated head (K) with the SEM of a real head (L). [Scale bars: 5 mm (H); 1 mm (L).]

patterning of a single structure may also have phases with dis- are not sharp, their differences give them a qualitatively distinct tinct characters. Specifically, in the phyllotactic patterning of character. gerbera, we distinguished three major phases: 1) formation The first phase occurs early in head development, when of a circular pattern of incipient bract primordia on the rim of the active ring expands in concert with the receptacle rim. It the head; 2) emergence of a radial offset between primordia, takes place before the patterning process is clearly reflected producing a zigzag template for a lattice of floret primordia; by morphological structures, and therefore was not analyzed in and 3) elaboration of this lattice into a spiral phyllotactic pat- previous studies. It is evident, however, in the spatiotemporal tern filling the head. The progression through these phases is pattern of auxin maxima, which we revealed using transgenic controlled by the dynamics of head growth and propagation of DR5rev::3XVENUS-N7 reporter lines in gerbera. A crucial ele- the active ring. Although the boundaries between these phases ment of this pattern is the progression of the number of auxin

8 of 11 | PNAS Zhang et al. https://doi.org/10.1073/pnas.2016304118 Phyllotactic patterning of gerbera flower heads Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 hloatcptenn fgreaflwrheads flower gerbera of patterning Phyllotactic al. et Zhang for template a as serve and can Pennybacker line similar and a (36) that al. showed figures (37) et 23, Newell (ref. Hotton line recently, zigzag More a prede- form 17–21). its would primordium to front compared pattern each center the head if cessor, the that toward Modifying offset observed Hirmer. slightly he of was another work construction, is the pattern annular to this related his of model front our emergence between of pattern The element distances the pattern. contracting zigzag transforming radial the a increase, active the into initia with result, newer the concert and a older of in As rim domain. dissociation expression the progressive from the ring by characterized heads. gerbera in maxima of displacement lateral apical al. shoot et the in of Galvan-Ampudia maxima meristem recently, auxin traveling More radially S07). observed (50) movie 49, (ref. of J al. and models Heisler computational by in underly- patterning observed cells, auxin was between displacement, travel neighbors. this to their ing maxima to heads auxin of gerbera respect capability in with The maxima asymmetrically auxin them of hypothe- positions displacement these lateral to geometric contrast the In increased ses, patterns. between an resulting distances was the (46) of equalize result regularity Adler end to The mechanism by primordia. by a prominence adjacent as postulated to (47) was Ridley brought displacement and and Primordia (45) history. Schwendener rich a space has the exactly. ratio partition golden the primordia to according incipient neighbors the their older between when their sequence occurs of Fibonacci toward the only range to primordia adherence large strict a incipient pref- a although neighbors, a of for that occurs rates show numbers displacement simulations Fibonacci Our toward according sequence. numbers erence asymme- primordia Fibonacci this of the progression rim, the head 44, to to gerbera (ref. key the the neighbors of is their context try of the In one 37). only figure to new tangent new which were con- in “the to patterns and primordia phyllotactic gap” that of proposed largest diagrams statement next plausible who the structed the into 91–93), with asymmetrically falls pp. rule member 44, Hofmeister the (ref. extend Church by postulated our make ) S8 and S7 Figs. plausible. mechanistically Appendix, model (SI respect changes with robustness parameter the and to undiffer- head, the the of neigh- across zone central the primordia their entiated to distant opposed to relating as interactions, angle respect these divergence the of with and character local rim initia The expanding bors. of the to on posititoning emergence initia asymmetric its of insertion attribute pattern intercalary between we this the angle Instead, explain divergence we primordia. golden previ- 25), consecutive constant, and (24, a Hirmer ideas assuming his to (ref. without on contrast model based in Hirmer’s pattern- models However, with head ous 12–16). match of figures perfect stages almost early 23, an the reveals in the signal ing of DR5 observations prop- Our was of this (25). (43), progression Prusinkiewicz mathematics of and in proof Battjes theorem by formal three-gap given the A to overlapping. related would start erty, primordia they of divergence number before golden Fibonacci a the fit precisely to ring, according a in placed angle were specific arbi- size in of fixed primordia appear if trary to that numerical geometrically tendency showed the their Hirmer numbers. i.e., with 42), organs, (41, connection of collaborators in canalization and phyllotaxis Battjes investigated by who followed (23), work the Hirmer with e.g., consistent rather of is parastichies extensions, it of However, numbers its primordia. the individual phyl- and on than focus of (19) which 21, model Iterson and used 20 van refs. widely by the of patterning progression terms lotactic This in explained sequence. be Fibonacci cannot the to according maxima h eod ritreit,paeo edptenn is patterning head of phase intermediate, or second, The also initiation after displaced be may primordia that idea The was primordia of placement the in asymmetry Historically, u eut xedterfidn othe to finding their extend results Our Arabidopsis. nsn(8 n isoog et Bilsborough and (48) onsson ¨ GhCLV3 ln Material. Plant Methods and Materials processes whether organs. organ multiple and of with wonder understanding flowers our expansion in improve arrangement we may active-ring paper this of Finally, in described dynamics growth? specific receptacle the by an gerbera mechanism—possibly heads in older patterning—actuated auxin-driven an of it feature gerbera is inherent in or observed Asteraceae, displacement in the lateral evolved common? of also or more mechanism case, process is the singular patterning Has interest a three-phase gerbera described displace- Of Is the and here. model: is proposed emergence all reported the the at of maxima generality to of proteins auxin expect mechanism PIN1 of we the which of ment gerbera, on observation in light process vivo shed patterning phyllotaxis in the of be of stages will studies step experimental plants next the model broaden the beyond to need the receptacle. or ring active their noncircular lose a production on (7)—which concurrent the primordia al. of of et context the Godin in by relevance or review meaning recent also the postulate in angle—a made pattern divergence plastochron, and the used spiral, as commonly generative such center, notions phyllotaxis, many of description of of the change revision in This a events. for of set calls the entire perspective the lin- which on a ordering in imposing temporal without ear (58), primordia, only close are processes spatially char- relations for causal concurrent best determined their and of thus events of is set precedence temporal heads a may in that as ring Phyllotaxis acterized active symmetry. syn- an circular loosely of progression only lack the are by neighbors—but globally emerged chronized previously relation in its locally positioned to are is that primordium processes in incipient produced sequential—each (7, are contexts primordia other fur- resulting in The noted the 57). observable; also 21, to as not relevant S11), Fig. not is , Appendix is (SI pattern it front bounds, pattern refs. some within e.g., the floret thermore, which interest, at in of order emerge exact are the primordia however, it, heads, gerbera from In departures diver- 54–56. symmet- golden and the clearly circularly to angle, adhesion are gence small, strict primordia the a both issued and consecutively distinguishable, within where place meristem, applicable ric taking is processes description Such to primordia. angle divergence consecutive fixed primordia a between new with of spiral, generative addition idealized sequential an the along of result a as described resulting the alter substantially and not 9 necessary, (Fig. do patterns not it front—is from pattern departures the some and meristem symme- the radial of models—the try these however, underlying the highlight, assumption results by an modeling quasicrys- that as of and terms experimental well in Our the zones as tals. characterized transitional 51, in who primordia 53), and of (52, patterns Lawrence 21, and 7, Rivier more of its refs. and analyses (19) e.g., Iterson is refinements, van sequence of recent Fibonacci model stacking reversed the paras- the by of explained to reduction according subsequent The numbers associated center. tichy front, dis- head eventually the pattern that ring at the active appears the at of contraction primordia gradual the new with of stacking the pat- 265–269). zigzag pp. van a 19, rim by (ref. characterized Interestingly, the partially Iterson role. and from reported same already ring the was front fulfill active tern can the head of pattern the dissociation zigzag of the the that from demonstrate resulting simulations parastichy Our Fibonacci with numbers. pattern phyllotactic spiral a generating ape sdfrmcocpcadlv-mgn nlsswr olce from collected were analyses live-imaging and microscopic Flower-head for (59). used conditions samples greenhouse standard under grown were plants h itntv etrso hloai ngreaas e forth set also gerbera in phyllotaxis of features distinctive The typically is patterns phyllotactic of regularity spatial The is factor dominant the patterning, of phase third final, the In idtp n transgenic and Wild-type E and F ). Arabidopsis https://doi.org/10.1073/pnas.2016304118 .hybrida G. rtmt.Teessential The tomato. or utvr‘er Regina’ ‘Terra cultivar PNAS | f11 of 9

PLANT BIOLOGY the plants and dissected under a stereomicroscope (Zeiss Stemi 2000-C). epidermis in selected samples, the meristem surface was isolated and seg- Exogenous treatment with the polar auxin transport inhibitor NPA (Supelco, mented, and the DR5 signal and Gaussian curvature values were projected Sigma-Aldrich) was carried out by applying 1 mL of 100 µM NPA solution with MorphoGraphX (67), as described in the user manual. three times at 2-d intervals to each shoot of the growing gerbera rosettes. We added 0.015% Silwet-L77 (Lehle Seeds) surfactant immediately before Light-Sheet Microscopy. To obtain overviews of auxin distribution corre- the treatment. Flower-head samples were collected for imaging 2 and 3 wk sponding to later stages of head development (Fig. 9 D and F), the entire after the first treatment. flower heads with large physical sizes (>1 mm in diameter) were examined by using a Z.1 light-sheet microscope (Carl Zeiss) equipped with a 5×/0.16 air Isolation and In Situ Hybridization of GhCLV3. The gerbera CLV3 objective. The data were collected by using filter sets designed for VENUS-PI homolog (GhCLV3) was amplified with gene-specific primers: (50- imaging (SP525 for VENUS and LP585 for chlorophyll autofluorescence) and AAAAAGCAGGCTCGATGGTTTTTTCACTCAGATATC-30, 50-AGAAAGCTGGGT- visualized by using the Zeiss ZEN pro software. TTAAGGAGTTCGGGGCTTTTTC-30) and cloned into Gateway entry vector pDONR221 (Invitrogen). The full sequence is available in GenBank In Vitro Culture and Live Imaging of Growing Head Meristem. To observe auxin (accession no. MN793057). For in situ expression analysis, samples were patterning on a growing head meristem using live imaging, we cultured ger- prepared, sectioned, and hybridized as described in ref. 60. The full-length bera head meristems in vitro. The explants were dissected gerbera rosettes coding region of GhCLV3 (327 bp) was designed as the probe, and it was (approximately 3 mm × 3 mm in size) containing the growing head at an early synthesized by using primers containing a T7 overhang as described in ref. developmental stage. They were surface-sterilized with 5% Plant Preservative 61. Sections were examined and photographed with a Leitz Laborlux S Mixtures (PPM; Plant Cell Technologies) and placed on the gerbera multipli- Microscope equipped with a Leica DFC420 C Digital Camera. cation medium (69) supplemented with 1 mg/L gibberellic acid 3 (Duchefa Biochemic B.V.), 0.1% PPM, and 45 g/L sucrose. Growing conditions were as Reporter Construct and Genetic Transformation of Gerbera. The auxin described in ref. 69. The growing head meristems were imaged by LSCM at reporter construct was generated by transferring a NotI fragment contain- three time points (0 h, 48 h, and 96 h) using the same settings as described ing the DR5rev::3XVENUS-N7 sequence (28) into the pRD400 vector with a above. Cell walls were stained with PI applied before each imaging. nos-nptII marker gene encoding kanamycin resistance (62). The binary construct was then electroporated into Agrobacterium strain C58C1 (pGV2260) Measurement and Analysis of the Pattern of Gaps. To quantify gaps between (63). Genetic transformation of gerbera was carried out as described in ref. DR5 maxima on the receptacle rim (Fig. 4B), we estimated angles between 64. The transformation yielded four independent lines (TR3, TR5, TR7, and the maxima with respect to the visually determined head center. Positions TR8) that showed consistent patterns of fluorescence signals. Auxin respon- of individual maxima were annotated by considering the distal (farthest siveness of the reporter construct was tested on dissected involucral bracts from the head center) end of each DR5 streak (SI Appendix, Fig. S3 A, from these lines, treated with 10 µM indole-3-acetic acid (IAA) and 10 µM Inset). The angular gaps were then measured in the counterclockwise direc- 1-naphthaleneacetic acid (NAA) water solutions. Mock treatments without tion by using the Fiji (66) “angle tool” function. The distribution of gaps hormones were made for control. All four lines were used for subsequent (Fig. 4C) was characterized by using an in-house program implementing the microscopic analysis. kernel-density method.

SEM. We investigated flower-head growth using SEM images and micro-CT Measurement of Distances between Bracts and the Center of Receptacle. To scans. For the SEM imaging, head meristem samples collected from the wild- examine the positions of the first bracts in a mature gerbera flower head type and NPA-treated gerbera plants were prepared as described in ref. 65. (Fig. 9J), we photographed the base of 12 randomly selected heads. The first The images were acquired by using a Quanta 250 SEM (FEI Corporation). 21 bracts were then labeled in accordance with their positions, assuming an approximately golden divergence angle. The distances of the bract bases to Micro-CT. To investigate flower head growth in 3D, we obtained micro-CT the receptacle center were measured by using the Fiji (66) “measurement” scans of 20 wild-type gerbera flower heads. A developmental series was function. compiled by using 10 samples, selected on the basis of their sizes. Head samples were fixed in 10% formalin, 5% acetic acid, and 50% ethanol for 48 Computational Modeling. All models were written in the L-system-based h; dehydrated through ethanol series (50%, 60%, 70%, 80%, 95%, 100%, plant modeling language L+C (70), and executed by using the lpfg simu- and 100%, each for 2 h); and critical point dried with a Leica EM CPD300 lator incorporated into the Virtual Laboratory (vlab) v4.5.1 plant modeling dryer (Leica Mikrosysteme GmbH). The micro-CT scanning was conducted software (algorithmicbotany.org/virtual laboratory). The models are avail- by a Skyscan 1272 micro-CT scanner (Bruker Micro-CT) for smaller heads able at algorithmicbotany.org/papers/gerbera2021.html. To construct the (with bracts being initiated) or a GE Phoenix Nanotom scanner (GE Sens- data-driven dynamic receptacle model (SI Appendix, Fig. S9), optical sec- ing & Inspection Technologies GmbH) for larger heads (with florets being tions of developing heads were superimposed with Adobe Photoshop and initiated). The 3D reconstruction of the original X-ray images from micro-CT traced by using a custom extension of the vlab contour editor (Fig. 8A). scans was performed by NRecon version (v) 1.7.0.1 (Bruker Micro-CT). The All models were visualized directly by using lpfg, except for the realis- reconstructed image stacks were further analyzed and visualized with Fiji tic head model (Figs. 8D and 9K and Movie S7), which was rendered (66) and MorphoGraphX (67). by using Blender v2.79 (https://blender.org). Voronoi diagrams involved in this model (SI Appendix, Fig. S10 G–I) were constructed by using the Laser-Scanning Confocal Microscopy. Laser-scanning confocal microscopy Advancing Front Surface Reconstruction package from the Computational (LSCM) was used to examine the gerbera auxin reporter lines. To understand Geometry Algorithms Library (CGAL) v4.14.1 (https://cgal.org). All simu- pattern formation during the early stages of head meristem development, lations were performed on MacBook Pro computers under macOS High we obtained images of 56 randomly sampled head meristems smaller than Sierra v10.13.6. See SI Appendix, SI Text for a detailed description of the 700 µm in diameter (SI Appendix, Fig. S3). The samples were prepared models. as described in ref. 68. Special care was taken to remove trichome hairs Data Availability. All data underlying the study are available in the paper and the involucral bracts surrounding the head meristem. Cell walls were or SI Appendix. The full length sequence for gerbera GhCLV3 is available in stained by using 1 mg/mL propidium iodide (PI; Sigma-Aldrich) applied over GenBank (accession no. MN793057). The models are available at Algorithmic an extended period (30 min). The specimens were imaged by a Leica TCS Botany (algorithmicbotany.org/papers/gerbera2021.html). SP5 MP microscope (Leica Mikrosysteme Vertrieb GmbH) equipped with an HCX APO L 20×/1.0 W water-dipping objective. For imaging, the samples ACKNOWLEDGMENTS. We thank Heikki Suhonen and the staff of the micro- were excited by an argon laser at 514 nm, and emission of VENUS fluores- CT laboratory and the Electron Microscopy and Light Microscopy Units at cent protein and PI was recorded at the 519- to 537-nm and 624- to 695-nm the Institute of Biotechnology, University of Helsinki, for assistance; Siobhan wavelengths, respectively. Z-stacks representing head meristems in 3D were Braybrook for information on the capitulum in vitro cultivation method; visualized and analyzed by using MorphoGraphX (67). Top views of each Pascal Ferraro for software support; Johannes Battjes for early inspiration; sample were exported as two-dimensional images for further analysis. To and Jacques Dumais, Lawrence Harder, Yka¨ Helariutta, and Lynn Mercer for discussions. This work was supported by Academy of Finland Grant 1310318 generate the superimposed images of the DR5 signal (SI Appendix, Fig. S3B (to P.E.); Natural Sciences and Engineering Research Council of Canada and Fig. 4I), the top-view images were first manually aligned by rotating the Discovery Grants 2014-05325 and 2019-06279 (to P.P.); the Plant Phenotyp- images. The aligned images with the same number of DR5 maxima were ing and Imaging Research Centre/Canada First Research Excellence Fund combined into image stacks, then composed by using the Fiji (66) “sum- (P.P. and M.C.); the Helsinki University Doctoral Program in Plant Sciences slice” function. To analyze the DR5 signal and the curvatures of meristem (T.Z.); and the Finnish Cultural Foundation (T.Z.).

10 of 11 | PNAS Zhang et al. https://doi.org/10.1073/pnas.2016304118 Phyllotactic patterning of gerbera flower heads Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 5 .Fece,U rn,M unn,R io,E .Myrwt,Sgaigo cell of Signaling Meyerowitz, M. E. Simon, R. Running, M. Brand, U. Fletcher, J. 35. Lindenmayer, A. Prusinkiewicz, P. 34. mech- control interactive versus Lineage algorithms: “Developmental Lindenmayer, A. 33. in division cell governing Rule Wilcox, M. Mitchison, G. 32. Reuille de P. 31. J H. 30. 9 .Smith R. 29. Heisler M. 28. with cope capitulum sunflower of meristem the pro- does a How Turc, O. and Tardieu, F. review Dosio, G. A pattern: 27. produce plants “How Rennich, S. Steele, C. Green, P. 26. flowerheads” Asteracean of phyllotaxis. characters spiral meristic “Modeling of Prusinkiewicz, P. model Battjes, J. collision-based A 25. Battjes, J. Prusinkiewicz, P. Fowler, D. 24. Pflanzenreich. im Schraubenstellungen pattern der Kenntnis phyllotactic Zur Hirmer, for M. fields Inhibition 23. Prusinkiewicz, P. Kuhlemeier, C. Smith, S. R. III. II, 22. I, process. iterative self-organizing a as Phyllotaxis Couder, Y. series. Douady, Fibonacci S. the and 21. Phyllotaxis Mitchison, J. G. 20. Iterson, van G. 19. 8 .Gol C. 18. in growth” and pattern “On Meinhardt, H. 17. biologi- symmetry high of morphogenesis the for models spacing “Uniform Marzec, C. 16. determination. leaf and areas Minimum Snow, primordium. R. a Snow, isolating M. of effect 15. The I. phyllotaxis. in Experiments Snow, R. Snow, M. 14. of expression and pattern vascular Primary Dengler, N. Donnelly, P. Tang, J. Kang, J. 10. 3 .Hfese,“lgmiemrhlgedrGew der morphologie “Allgemeine Hofmeister, W. 13. sun- Phyllotaxis. the Kuhlemeier, in C. initiation floret 12. of site the as area generative The Steer, T. B. Palmer, H. 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