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SUPPLEMENTARY INFORMATION doi:10.1038/nature12791 Supplementary Figure 1 (1/3) WWW.NATURE.COM/NATURE 1

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 1 (2/3) 2 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 1 (3/3). Expression of the regulators of cytokinin signalling and biosynthesis in the different domains of the shoot apical meristem. Normalized values of expression were calculated from previously published microarray datasets (Yadav et al., 2009; see main text) obtained from the FILAMENTOUS FLOWER (FIL) domain in the lateral organs, and from the CLAVATA3 (CLV3) and WUSCHEL (WUS) domains at the centre of the meristem. The dashed lines represent the background level of expression. Differential expression between the FIL domain and the WUS or the CLV3 domain was systematically tested. The stars indicate when expression is statistically different in the WUS and/or CLV3 domains compared to the FIL domain. The diagram corresponding to AHP6 is outlined by a red square. WWW.NATURE.COM/NATURE 3

RESEARCH SUPPLEMENTARY INFORMATION a b c P1 s s d p St p e P1 f P1 g h P1 P3 P4 P2 Supplementary Figure 2. AHP6 is a regulator of cytokinin signalling that is specifically enriched in lateral organs. (a) Summary of the expression profiles of the regulators of cytokinin signalling deduced from the Yadav dataset (see Supplementary Fig. 1). (b-h) Analysis of AHP6 expression pattern in the inflorescence using RNA in situ hybridization. The arrowheads in (b-d) points at expression in the organ initium (b), the sepal initia (c) and the petals and stamens initia (d). A serial section is shown in (e-h) to illustrate the organ-specific expression. s: sepal; p: petal; st: stamen. Scale bar: 20 μm in (b-d) and 50 μm in (e-h). 4 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH a b c d Col-0 ahp6-1 Col-0 ahp6-1 e ** ***** *** * WT * ahp6-1 * f WT, (10/69) ahp6-1, (13/86) ahp6-3, (12/86) Frequency ahp6-1/3, (12/95) Supplementary Figure 3. AHP6 regulates floral phyllotaxis. (a,b) Electron microscopy of wild-type (a) and ahp6-1 (b) stage 3 flowers showing defects in sepal numbers. (c,d) Mature flowers of wild-type (c) and ahp6-1 (d) showing defects in petal numbers. (e) Quantification of sepal numbers in wild-type and ahp6-1. Error bars represent standard deviations. Differences that are statistically significant are indicated (student t-test: p<5.10-2 (*), p<5.10-3 (**), p<5.10-4 (***). 122 and 166 flowers were analyzed for wild-type and ahp6-1 respectively. (f) Petal numbers in wild-type, ahp6-1, ahp6-3 and ahp6-1/ahp6-3. The number of plants and total flowers analyzed are indicated in parenthesis. Scale bar: 20 μm. WWW.NATURE.COM/NATURE 5

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 4. Analysis of ahp6 defects in divergence angles sequences. (a) Distribution of divergence angles observed in wild-type (82 plants) and ahp6-1 (89 plants). While most angles are close to the canonical angle α=137.5, other frequent angle values are observed close to 2α=275, 360-α=222.5 and 3α=52.5 (red arrowheads), suggesting the existence of permutations. The frequency of these non-canonical angles is specifically increased in ahp6-1 mutant plants. The difference between these two distributions is found highly significant with a Kolmogorov-smirnov test: p-value < 2.2.10-16. (b) Penetrance of the ahp6-1 phenotype shown by the cumulative frequency of plants as a function of increasing phyllotactic defects. For illustration we have shaded an areas below each curves that represent 80% of each population. This highlight the fact that, while 80% of wild-type plants exhibit less than 25% of non-canonical divergence angles, it is the case for only 25% of the ahp6-1 population. A vast majority of the ahp6-1 plants exhibit a proportion of non-canonical angles higher than 25%. (c-f) Significant examples of angle sequences explained by permutation in the order of silique insertions on the stem, for wild type (c-d) and ahp6-1 mutant plants (e-f). The particular sequences of permutations explaining the motifs are indicated in bold on each panel. 6 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 5. Structure of ahp6-1 stem and internodes are regular and not twisted. (a) Stem of an ahp6-1 plant at the level of 2 permuted organs. (b) Magnification of the box region in (a) using electron microscopy. Linear lines of epidermal cells demonstrate the absence of twisting or other obvious microscopic abnormalities in the internode separating permuted organs. Scale bars: 500µm (a) and 50µm. WWW.NATURE.COM/NATURE 7

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 6. The size of the meristem and of the stem cell niche are not affected by the ahp6 mutation. (a-c) meristems are not significantly larger in ahp6-1 plants. Meristem width (white bar) was measured from FM4-64 stained meristems imaged by confocal microscopy, as shown for a wild-type (a) and a ahp6-1 plant (b). Organs with approximatively the same size are indicated with the same color. (c) Quantification over 12 wild-type and 11 mutant apices did not reveal significant differences in meristem width (p=0.3; student t-test). (d,e) The size of the expression domain of the CLV3 stem cell marker is identical in wild-type (d) and ahp6-1 (e). CLV3 expression was analyzed by RNA in situ hybridization. Representative median sections are shown. (f-h) The expression of pwus::gfp is not affected by the ahp6-1 mutation. A representative confocal image (projection) for wild-type (f) and ahp61 (g) is shown. (h) The area of the WUS domain was quantified using images from 3 wild-type and 9 ahp6-1 meristems (p=0.78; student t-test). (i-k) The size of the central area not expressing pdr5::gfp is not affected by the ahp6-1 mutation. A representative confocal image (projection) for wild-type (i) and ahp6-1 (j) is shown. (k) The area of the peripheral GFP domain and of the central non-gfp domain was quantified using images from 9 wild-type and 5 ahp6-1 meristems. This area is not affected by the mutation (p=0.2; student t-test), further suggesting that the size of the central zone is not affected by the ahp6 mutation. Error bars indicate standard deviations. Scale bars: 50 μm. 8 W W W. N A T U R E. C O M / N A T U R E

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 7: Monitoring organ initiation in the SAM using the synthetic auxin-inducible DR5 reporter. Expression pattern of DR5::VENUS (red-white intensity LUT) in living meristems of a wild-type (a-d) and an ahp6 mutant (e-h) plant, observed by confocal microscopy. (a,e) maximum projections of top views; (b-d) and (f-h), maximum projection of longitudinal sections through organs. We considered as initia organs where DR5 expression is restricted to the epidermis (b, f and g), while we staged as primordia organs where DR5 expression extend to deeper inner cells, probably in the nascent provascular strands (white arrowhead, c, d and h). While in WT plants only one initium is typically present (b), two initia can frequently be observed in ahp6 mutant plants (f,g). Autofluorescence is in gray. Scale bars: 50 µm. WWW.NATURE.COM/NATURE 9

RESEARCH SUPPLEMENTARY INFORMATION Initiation Rate WT: 10h40 ahp6-1: 9h30 Supplementary Figure 8. AHP6 does not affect the mean rate of organ initiation Cumulative number of initia produced over time as counted from live imaging of DR5::VENUS in the meristem. Values obtained from 2 replicate experiments out of 3 are represented. One experiment was not used due to slight differences in the timing of acquisition. The mean rate or plastochrone over the 72h period was calculated from these curves using a linear regression and is indicated on the figure. 10 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 9. AHP6 regulates the temporal sequence of DR5::VENUS activation at the shoot apical meristem. Live meristems expressing DR5::VENUS were followed over 72 h. Representative time-courses are shown. (a,b) Wild-type meristems. (a) corresponds to the time-course shown in part in Fig. 2e. (c-e) ahp6-1 meristems. (c) corresponds to the time-course shown in part in Fig. 2f. The co-initiated organ initia are indicated with a star. The double stars in (d,e) indicate initia that arise in a non-canonical order (permutations). Gray: autofluorescence. i: initium; P: primordium. Scale bar: 20 μm. W W W. N A T U R E. C O M / N A T U R E 1 1

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 10. Positioning of organogenesis and early development of organs is unchanged in ahp6 mutants. Different characteristics of organogenesis were measured from samples used in the DR5::VENUS time-lapse experiment presented in Fig. 2 and Supplementary Figure 9. (a) The distance of new initia to the center of the meristem, estimated from confocal stack projections, was similar for initia appearing sequentially or at the same time, in WT as well as in ahp6-1 plants (p=0.87, ANOVA). These analyses were performed on 14 wild-type meristems and 20 mutant meristems, representing 99 organs and 149 organs, respectively, from 2 independent experiments. (b) The increase in the distance of developing initia to the center of the meristem (calculated on confocal stack projections) was measured using the data of the same time-lapse experiments, from the time initia appeared up to 36 hours (the numbers of organ considered in each time point are indicated in blue for wild-type and in red for ahp6-1). No significant differences in the growth rate away from the center of the meristem was observed. 12 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 11. Geometrical parameters of meristems allows to accurately predict the site of initium i1. 16 plants expressing DR5::VENUS (2 batches of 8 plants, from two independent experiments) were used to measure the accuracy of the prediction of i1, by comparing the actual zone of i1-associated DR5::VENUS expression and the zone predicted by our geometrical model (described indetail in methods). (a) A representative example of the prediction can be seen in this confocal live imaging of a DR5::VENUS expressing plant (maximum orthogonal projection of a top view, red-white intensity LUT: DR5; gray: autofluorescence; scale bar: 50 µm). The red circle surrounds a DR5-expressing nucleus that reveals i1 site while the white dotted circle indicates the predicted i1 site. The star points at the prediction of the center of the meristem. (b) Summary of i1 predictions for the 16 plants. In this scaled, representative cartoon of a meristem, i1 zone and the meristem center (C) are indicated by a red crosshairs and a star (*), respectively. Each black dot represents the center of a predicted i1 zone, for the 16 plants analyzed: their positions indicate absolute errors in distance and in angle relative to i1 and C of the cartoon. Note that all the predictions are at a range equal or smaller than the area choosen for defining i1 zone. (c) Table summarizing the quantification of the error in the prediction of i1 by the geometrical model. This geometrical model is used to predict i1 and i2 positions in Fig. 3h-j and in Supp. Fig. 12. WWW.NATURE.COM/NATURE 13

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 12. AHP6 movement from source primordia generate different levels of AHP6 at the site of i1 and i2. Living plants expressing pahp6::ahp6-gfp in ahp6-1 background were imaged by confocal microscopy. (a, d, h, j) Orthogonal projections (by maximum-intensity) of top-view confocal stacks. (b, e, h, k) Close-up of the previous meristems using a fire intensity LUT. Since i1 forms in the superficial L1 cell layer, we performed summation-intensity projections of only the superficial slices of the stacks (corresponding to a 6- to 12-µm depth from plant to plant) to better assess AHP6 levels at the actual site of i1 and i2. Prediction of i1 and i2 zones by a geometrical model are indicated with white dotted circles, the prediction of the center by a white star (*). (c, f, i, l) Fluorescence distributions along the areas shown in (b), (e), (h), and (k), respectively, with the positions of primordia and initia present in the profile. Scale bars: 50 µm. See also Fig. 3g-j. 1 4 W W W. N A T U R E. C O M / N A T U R E

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 13. AHP6-3xVENUS fusion protein blocks AHP6 movement in the root but complements the loss of protoxylem of ahp6 null mutant. (a-c) Confocal microscopy of roots from plants expressing a pahp6::gfper transcriptional reporter (WT background) (a), and primary transformants expressing a pahp6::ahp6-venus (b) or a pahp6::ahp6-3xvenus transgene (c) in the ahp6-1 background. While AHP6-VENUS location extends outside the cell lines where it is transcribed, this movement is blocked by a larger 3xVENUS tag. (d-e) Normarski microscopy of roots of ahp6-1 plants (d) and of primary transformant ahp6-1 plants transformed with a pahp6::ahp6-venus (e) or a pahp6::ahp6-3xvenus (f) transgene. Black arrowhead: typical protoxylem interruption seen in ahp6-1 mutants. (g) Quantification of the number of protoxylem interruptions scored in the previous plants (n=20 plants for each genotype): both AHP6-VENUS and AHP6-3xVENUS fusion proteins show equal ability to rescue ahp6 loss of function (8 and 9 independent transgenic plants over 20 were fully rescued, respectively). Scale bars= 50 µm. WWW.NATURE.COM/NATURE 15

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 14. The PIN1 auxin transport network is unaffected by the ahp6 mutation. (a,b) Whole-mount immunolabeling of PIN1 protein in the epidermal L1 layer of WT (a) and ahp6-1 mutant (b). (c,d) Influence zone analysis of the previous meristems (c: WT; d: ahp6-1) calculated for P1 (green), i1 (blue) and i2 (yellow). The influence zone of a primordia is the set of meristematic cells along 16 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH a path of PIN1 pumps oriented towards the reference cells designated by white dots for each primordia. It can be considered as an indirect measure of the auxin inhibitory field of the primordia. The similar influence zones observed in WT and ahp6-1 suggest a similar connectivity in the PIN1 network and a limited impact of the ahp6 mutation on the auxin inhibitory fields. (e-j) PIN1 polarity coherence index in WT and ahp6-1 meristems. This index measures the coherence of PIN1 polarities between a given cell and its neighbors (this index has a value of 1 when all cells have the same polarity, and a low value if polarities are very different). For illustration, it was plotted on the cellular maps of the previous meristems (e for a and f for b). To quantify the index, data from 3 different meristems of each genotype was used to calculate the histograms (g and h respectively). A control coherence index was generated based on the cellular map of the wild-type with a random polarization of PIN1 proteins. Results are given as an histogram (i) or as a map (j) and differ significantly from observations. The fact that both the spatial distribution of the index (e,f) and the histograms (quantitative distributions; g,h) are unaffected by the ahp6 mutation suggests that the local PIN1 polarity properties are independent of AHP6. WWW.NATURE.COM/NATURE 17

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 15: Model for AHP6 action in the shoot apical meristem. The AHP6 field have been visualized by adding noise under Photoshop using a median filter on the image shown Fig. 3h. The position of i1, i2 and P1-P5 as well as the centre of the meristem (star) are indicated. The movement of AHP6 is indicated by the arrows 18 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Table 1. Primers used in this study Supplementary Table 2. Characteristics of von Mises observation distributions (mean direction µ and circular standard deviation ν) estimated within hidden first-order Markov chains (with different or common concentration parameters) and within a hidden variable-order Markov chain. µ σ first order variable order µ ( σ = 18) weight µ ( σ = 18) weight α (137.5) 136.5 18.3 136.5 0.71 136.6 0.7 2α (275) 273.3 18.2 273.4 0.14 273.1 0.15 -α (222.5) 221.9 17.3 222.1 0.1 221.5 0.1 3α (52.5) 50.3 19.5 50.8 0.03 49.7 0.03-2α (85) 80.9 14.1 83 0.02 88.9 0.02 WWW.NATURE.COM/NATURE 19

RESEARCH SUPPLEMENTARY INFORMATION Supplementary Table 3. Transition probabilities of the estimated hidden variable-order Markov chain. α 2α -α 3α -2α count α 0.89 0.09 (α2α) 0 0.01 0.01 3430 α2α 0.08 0 0.91 0.01 0 308 2α2α 0.06 0 0.94 0 0 62 -α2α 0.81 0.18 (2α2α) 0 0.01 0 346-2α2α 0.01 0 0 0.36 0.63 16 -α 0.01 0.72 (-α2α) 0.07 0.18 0.02 476 3α 0.19 0.01 (3α2α) 0.63 0.03 0.14 149-2α 0.25 0.16 (-2α2α) 0.05 0.13 0.41 90 Differences between the rows corresponding to the second-order memories α2α and -α2α deriving from 2α should be noted. This is an a posteriori justification of the selection of these second-order memories. The memory reached by a transition is indicated between brackets after the corresponding probability in the 2α column. The transition counts (last column) were extracted from the optimally labeled divergence angle sequences computed using the estimated hidden variable-order Markov chain. 20 WWW.NATURE.COM/NATURE