Theoretical and experimental evidence indicates that there is no detectable auxin gradient in the angiosperm female gametophyte

The life cycle of plants alternates between a diploid sporophytic and a haploid gametophytic generation. In flowering plants, the sporophytic generation is the dominant form of the plant life cycle, whereas the gametophytic generation is highly reduced and short lived, and develops within the sexual organs of the flower.

In most flowering plants (70%), including Arabidopsis thaliana and Zea mays (maize), a postmeiotic female reproductive cell termed the functional megaspore (FM) undergoes three mitoses to form a female gametophyte (FG) comprising seven cells of four distinct cell types (Fig. 1).

In FG mutants with abnormally positioned or extra nuclei in maize (Evans, 2007; Srilunchang et al., 2010) and Arabidopsis (Gross-Hardt et al., 2007; Johnston et al., 2010; Moll et al., 2008; Pagnussat et al., 2007), the nuclei acquire their fate according to their spatial positioning along the micropylar-chalazal axis, suggesting that cell specification in the FG is driven by positional information. This hypothesis was strengthened by a microscopy study showing a graded activity of the auxin-sensitive reporter DR5 (Ottenschläger et al., 2003) along the micropylar-chalazal axis of the FG (Pagnussat et al., 2009). Furthermore, overexpression of the auxin biosynthesis enzyme YUC1 and the artificial microRNA (amiRNA)-based knockdown of a group of auxin-dependent transcription factors (auxin response factors, ARFs) leads to the mis-specification of gametophytic cells (Pagnussat et al., 2009). Therefore, it was proposed that the phytohormone auxin is distributed in a gradient and serves as the morphogen driving cell specification in the Arabidopsis FG (Fig. 1) (Pagnussat et al., 2009; Sundaresan and Alandete-Saez, 2010).

Here, we attempted to reproduce the mechanisms of auxin gradient formation in silico for maize and Arabidopsis in order to verify whether the processes proposed previously, i.e. polar auxin influx at early stages and localised auxin synthesis at later stages (Pagnussat et al., 2009), are sufficient for the auxin gradient to be sustained, or whether additional factors should be considered. Using auxin degradation rates and diffusion coefficients from the literature, we found that only a very shallow auxin gradient can be maintained in Arabidopsis and a moderate one in maize, even if additional factors, such as background efflux or localised degradation, are incorporated into the model. Moreover, we showed that the steepness of the gradient obtained in our models does not allow a sufficiently robust cell fate acquisition, especially in the small Arabidopsis FG. Thus, we reanalysed the auxin response within ovules to refine our model. Surprisingly, we could not detect auxin-dependent DR5 activity inside the FGs of either maize or Arabidopsis at any developmental stage. However, in both species we observed an auxin maximum in sporophytic nucellar cells at the micropylar pole of young ovules. As development progressed, DR5 activity migrated towards the chalazal pole in the sporophytic tissues surrounding the FG. We propose a model involving non-cell-autonomous effects of auxin in the sporophytic tissues of the ovule, in which auxin overproduction in the FG can explain the cell fate changes observed by Pagnussat and colleagues (Pagnussat et al., 2009). Thus, auxin may affect cell specification indirectly through a function in sporophytic tissues rather than via a gradient in the FG.

In order to elucidate potential mechanisms underlying the formation of an auxin gradient in angiosperm FGs, we developed a series of reaction-diffusion models based on the following assumptions: (1) auxin is produced or imported in the micropylar region of the FG; (2) auxin is degraded with first-order kinetics; and (3) diffusion of auxin is isotropic and homogenous throughout the cytoplasm.

We tested the contribution of different factor combinations (hereafter referred to as ‘regimes’) as described in Table 1. We included processes such as localised influx, both uniform and localised synthesis and degradation, as well as background efflux at the chalazal pole. As preliminary inspection showed that most parameter values produced only a very shallow gradient, we used parameter values that resulted in the steepest gradient, whenever alternative values were available from the literature (supplementary material Table S1).

The distribution of auxin within plant tissues largely depends on polar auxin transport across membranes (reviewed by Garnett et al., 2010; Petrásek and Friml, 2009). Pagnussat and colleagues (Pagnussat et al., 2009) examined the expression of members of the PIN-FORMED (PIN) family of auxin transporters encoded by the PIN1-4 and PIN7 genes in the ovules and detected only PIN1 in the micropylar nucellar cells prior to the FG2 stage [all stages of FG development are given according to Christensen et al. (Christensen et al., 1997)]. Here, we further examined the expression of all other known auxin transporters in the FG. According to our RNA-Seq data, neither PIN5 nor PIN6 transcripts are detected in developing ovules (M. Schmid and U.G., unpublished). The PIN8 protein is not detected in ovules either (supplementary material Fig. S1), which is consistent with the fact that the pin8-1 mutant is completely fertile (Dal Bosco et al., 2012).

In maize, we found ZmPIN1a-mRFP expression in sporophytic nucellar cells but not in the FG before the eight-nucleate stage (FG5), similar to previous findings in Arabidopsis (supplementary material Fig. S2; see also Fig. 7). In contrast to Arabidopsis, however, ZmPIN1a is expressed in the antipodal cells during FG maturation (stages FG6 and FG7). Because ZmPIN1a is expressed only at stages when the fate of the FG cells has already been determined, we did not consider this in our model.

The PGP1 (ABCB1) and PGP19 (ABCB19) efflux transporters are also known to participate in polar auxin transport (Geisler et al., 2005). Only PGP19 was found to be expressed in the Arabidopsis FG (supplementary material Figs S3, S4). The rates of PGP19-dependent and background auxin efflux used in our models were thus estimated based on earlier work by Geisler and colleagues (Geisler et al., 2005).

The AUXIN1/LIKE-AUX1 (AUX/LAX) family of transporters are known to facilitate auxin influx in Arabidopsis (Swarup and Péret, 2012). We found AUX1 to be expressed in the Arabidopsis FG starting at the four-nucleate stage (FG4). Moreover, the protein accumulated in the micropylar part (supplementary material Fig. S5). Active auxin influx has been estimated to contribute up to 75% (Delbarre et al., 1996) of total auxin influx, with AUX1 contributing ∼50% (Marchant et al., 1999), which was considered in our models. Close paralogs of AUX1 with similar characteristics are either not detectable in the FG (LAX3) or are expressed at negligibly low levels (LAX1 and LAX2 at 2.2% and 1.0% of AUX1 levels, respectively; M. Schmid and U.G., unpublished).

Based on previous data indicating that the greatest variation in auxin concentration is observed along the micropylar-chalazal axis (Pagnussat et al., 2009), we studied a simplified one-dimensional model featuring spatial inhomogeneity of the processes along this axis. The spatial coordinate representing position along the micropylar-chalazal axis has its origin in the micropylar-most point (denoted as x=0) and spans the cytoplasm until the chalazal-most point (x=1) (Fig. 1). A numerical study of regime 1 (Table 1) in one dimension showed that the rate of auxin reaction-diffusion was much faster than the rate of FG growth, which allowed us to apply the quasi-steady state assumption with regard to reaction-diffusion (for details, see supplementary material Appendix S1). The absolute value of the error due to this simplification did not exceed 0.002% after 45 minutes of initial equilibration (supplementary material Fig. S6). Therefore, we focused on the eight-nucleate stage of FG development (FG5), when cell specification is believed to occur. At this stage, the FG of Arabidopsis reaches a length of up to 70 μm, whereas the maize FG is between 100 and 130 μm in the inbred line A188 (supplementary material Fig. S7).

The GS achieved under different regimes with parameter values obtained from the literature is shown in Fig. 2 and Table 2. Using regime 1 (localised influx and uniform degradation), a rather low GS of 0.78% was obtained for Arabidopsis; in maize, the GS reaches 2.66%. If we included local production of auxin at the micropylar pole instead of localised influx, as was suggested for late stages of FG development (Pagnussat et al., 2009), the simulation resulted in gradients that were even flatter than in the case of localised influx (Fig. 2, Table 2). By contrast, if we considered either localised degradation or background efflux of auxin, the steepness of the gradient increased (Figs 2, 4). Taken together, the simulations based on this one-dimensional model identified two factors capable of increasing GS compared with a result obtained with the simplest model (regime 1): background efflux producing a GS of 0.91% and 2.89% (regime 4) and localised degradation increasing the GS up to 1.36% and 4.55% (regime 3) in Arabidopsis and maize, respectively.

At the two-nucleate stage (FG2), a large vacuole begins to form in the centre of the FG (Christensen et al., 1997; Schneitz et al., 1995; Huang and Sheridan, 1994). We investigated whether this vacuole can contribute to the maintenance of an auxin gradient in the FG by impeding the diffusion of auxin. To test this hypothesis, we set up a two-dimensional reaction-diffusion model with regimes 1 and 4, and solved it with the finite element method.

The results of this simulation showed that the large central vacuole will indeed impede diffusion, making the gradient steeper (Fig. 3, Table 2). This effect depends on the width of the cytoplasmic isthmus between the vacuolar and plasma membranes. Without the vacuole, two-dimensional models result in a GS that deviates less than 1% from that obtained with a one-dimensional model. However, with a width of the cytoplasmic isthmus of 1 μm, which is characteristic for Arabidopsis (supplementary material Fig. S8), the GS increases approximately two- to threefold in the two-dimensional model as compared with the model without a vacuole: from 1.33% to 3.21% in Arabidopsis and from 3.65% to 6.95% in maize (Fig. 4). In addition, taking localised AUX1-dependent influx into account, the GS decreases slightly by some thousandth of a percentage point (Fig. 4).

Thus, our simulations identify the effect of a vacuole together with carrier-dependent fluxes of auxin (by PGP19 and AUX1) as the most effective mechanisms that increase the steepness of a potential auxin gradient in the FG, leading to a GS of 3.21% and 6.95% in Arabidopsis and maize, respectively.

The morphogenetic signal providing positional information for cell specification can be corrupted by noise at different levels, both in its generation and perception (Lander et al., 2009). Perturbations of morphogen gradients can thus cause severe developmental aberrations and result in embryo lethality. Therefore, robustness is regarded as a major evolutionary constraint and is often used as an argument for or against the feasibility of theoretical models for morphogenetic gradients (e.g. Lander et al., 2009).

In order to theoretically assess the robustness of cell specification, we analysed the sensitivity of the theoretically achievable auxin gradient to perturbations in auxin concentration (for details see supplementary material Fig. S9 and Appendix S1). The auxin gradient obtained with physiological parameters is very shallow and makes the threshold position demarcating any two cell fate zones highly sensitive to perturbations in auxin concentration. A moderate perturbation of the auxin source by 3.5% leads to a positional shift of a given local auxin threshold throughout the entire length of the FG. Even a very small change of 0.5% in the auxin source leads to a shift of the threshold of at least 20%, which, for instance, is sufficient to disrupt cell specification in the micropylar part of the FG (Fig. 5; supplementary material Table S2). By contrast, a perturbation of the Drosophila Bicoid (Bcd) gradient by 5% results in changes in the perceived position of less than 5% in the region where the positional information is read out under all parameters tested (de Lachapelle and Bergmann, 2010). Therefore, the theoretical auxin gradient in the FG is extremely sensitive to perturbations compared with the well-studied Drosophila Bcd gradient and is thus highly unlikely to provide the stable positional information required for cell specification.

In summary, the auxin gradient obtained with known, realistic parameters is very sensitive to variation in the auxin source and thus would make cell specification highly unreliable. This result can be interpreted as follows: (1) the rate of auxin diffusion or background efflux in the FG is drastically different from that in all other known cases, which is very unlikely; (2) additional factors, for instance efflux mediated by as yet unknown transporters, contribute to the maintenance of the gradient; or (3) the auxin gradient achieved under these realistic conditions is not sufficient, or provides only part of the positional information needed, for cell fate determination; for instance, auxin might be a trigger of polarisation but not provide the positional information required for cell specification.

Our modelling results predicted only very shallow auxin gradients using known, realistic parameters in Arabidopsis and, to a lesser extent, in maize. To test this prediction, we aimed to characterise auxin activity in the ovule and FG experimentally in both Arabidopsis and maize using the classical DR5 auxin-sensitive promoter (Ulmasov et al., 1997) and novel reporters based on auxin-dependent protein degradation.

Three different DR5 lines were studied, each harbouring a different fluorescent protein: an endoplasmic reticulum (ER)-targeted GFP (Ottenschläger et al., 2003), a nuclear-targeted triple GFP (Weijers et al., 2006), and a nuclear localised tandem Tomato (tdTomato) fluorescent protein; the latter line additionally carried a nuclear YFP expressed under the gametophyte-specific AKV promoter (Rotman et al., 2005), marking all gametophytic nuclei. All three lines displayed the same pattern of DR5 activity. At the megaspore mother cell (MMC) stage (Fig. 6A,F,K), DR5 activity was observed in cells of the L1 and sometimes L2 layer of the nucellus surrounding the MMC, mostly at the future micropylar pole. Later, at the FM stage (FG1, Fig. 6B,G,L), the highest DR5 activity was observed in the micropylar region of the nucellus in cells of the L1 and L2 layer, with some activity in the L2 cells surrounding the FM laterally. At the early two-nucleate stage of FG development (FG2, Fig. 6C,H,M), the pattern remained largely the same; however, the FG begins to displace the nucellar tissue (Schneitz et al., 1995) and, in the late two-nucleate stage (FG3, Fig. 6D,I,N), at its micropylar pole the FG comes into contact with the inner integuments, which lack DR5 expression. At the four-nucleate stage (FG4, Fig. 6E,J,O), most of the nucellar tissue in the micropylar and medial part has degenerated and DR5 activity is concentrated in the nucellar tissue adjacent to the chalazal pole of the FG. Later, at the final developmental stages (FG5 and FG6), some sporophytic cells adjacent to the chalazal pole of the FG were found to express DR5 (supplementary material Fig. S10). From the four-nucleate until the final stages, a single DR5-expressing cell can be seen at the micropylar tip of the inner integument in fewer than a quarter of the ovules.

To obtain an alternative auxin signalling readout, we developed transgenic plants carrying a novel degron-GFP sensor, which exploits the auxin-dependent degradation of AUX/IAA proteins. Auxin binding to the ubiquitin ligase TRANSPORT INHIBITOR RESPONSE1 (TIR1) causes the degradation of AUX/IAA proteins via their domain II (Ramos et al., 2001). We used the six amino acid domain II core VGWPPV peptide, which is common to more than 70% of AUX/IAA isoforms (Ramos et al., 2001), as a C-terminal fusion to GFP6. An analogous reporter, DII-Venus, was developed in parallel (Vernoux et al., 2011) but is driven by the 35S promoter, which is thought to be inactive in the FG (Desfeux et al., 2000) (U.G., unpublished) and was not detected in the FG (supplementary material Fig. S11). By contrast, a bright signal of degron-GFP driven by the ubiquitin 10 (UBQ10) promoter (pUBQ10) is visible throughout FG development (Fig. 6P-T), indicating that there is not a sufficiently high auxin concentration to cause degradation of the reporter. Although degron-GFP levels during the initial stages of ovule development are lower in sporophytic tissues than in the developing FG, an even lower level was detected in nucellar cells that express DR5 (Fig. 6P,Q). Thus, the pattern of auxin activity inferred from degron-GFP is complementary to the pattern displayed by the DR5 promoter. Thus, even though the dynamic range of degron-GFP activity apparently lies in a lower range of concentrations than that of DR5-driven fluorescent proteins, the qualitative patterns displayed by both are consistent.

We observed lower levels of degron-GFP in many sporophytic cells than in the FG, even though neither displayed DR5 activity. This prompted us to test whether pUBQ10 showed differential activity in these cells and to use a control pUBQ10::GFP line to estimate relative auxin levels. A comparison of fluorescence intensities between pUBQ10::degron-GFP and control pUBQ10::GFP lines allowed us to correct for inhomogeneities in the protein levels due to differences in promoter activity. Accounting for these corrections, degradation of degron-GFP is significantly higher in the nucellar cells surrounding the FG than in the FG at both the FM (FG1) and late two-nucleate (FG3) stages (supplementary material Fig. S12, Table S3), which is in agreement with the pattern displayed by the DR5 promoter.

In conclusion, we could not detect any auxin activity inside the Arabidopsis FG experimentally. On the contrary, we found that until the late two-nucleate stage (FG3) the ovule’s minimum auxin activity is localised in the FG. Moreover, the pattern of auxin activity in the sporophytic nucellus tissue is highly dynamic and exhibits the following features: (1) an auxin maximum usually in the two epidermal cells (L1 layer) at the tip of the ovule as the MMC differentiates in the L2 layer; (2) migration of the DR5 activity maximum from the micropylar towards the chalazal pole; and (3) degeneration of DR5-expressing cells in the micropylar region of the nucellus.

In maize, we studied the expression pattern of DR5 driving an ER-targeted red fluorescent protein (mRFP:ER) (Gallavotti et al., 2008). As shown in Fig. 7A, a strong DR5 signal was visible at the tip of an ovule primordium in a few epidermal cells of the L1 layer in immediate proximity to a subepidermal cell of the L2 layer that differentiates into the MMC. The auxin response expanded around this cell, which enlarges at its micropylar pole and elongates longitudinally, and which appears smaller towards its chalazal pole (Fig. 7B,C). The nucleus of the emerging, highly polarised MMC moved towards the micropylar pole close to the auxin maximum, and initiated meiosis. After completion of meiosis, the three micropylar-most megaspores degenerated and the FM (FG1) became more deeply embedded into the L3 layer of the developing ovule (Fig. 7D-F).

Although the cells showing DR5 activity at the tip of the ovule expanded to the L2 layer, these sporophytic auxin-responsive cells were no longer neighbouring the FG after the FG1 stage. During FG development, DR5 activity decreased, beginning at stage FG2 (Fig. 7G-I), and was no longer detectable in micropylar nucellar cells from stage FG5 onwards (Fig. 7J). In mature ovules, DR5 activity was entirely absent from this region at stage FG7 (Fig. 7K,L; supplementary material Fig. S13). By contrast, a strong DR5 signal became visible in the tips of the inner and outer integuments (Fig. 7J; supplementary material Fig. S13A,B), as well in the gametophytic antipodal cells, with the strongest signals in the antipodal cells located furthest from the central cell (Fig. 7K,L; supplementary material Fig. S13C,D).

In conclusion, DR5 activity, and thus a nuclear auxin response gradient, was not observed inside the developing FG of maize before the completion of cellularisation at stage FG6, by which time cell specification has presumably already taken place. The only gametophytic DR5 signal was observed in the antipodal cells, after cellularisation and during their proliferation.

Our theoretical results suggested that, with known parameters, an auxin gradient cannot be maintained in the FG, and our experimental data showed that indeed no auxin activity can be detected inside the FGs of Arabidopsis and maize. However, earlier experiments had shown that auxin overproduction in the Arabidopsis FG can lead to changes in the fate of gametophytic nuclei (Pagnussat et al., 2009). Based on the results presented here, this change in cell fate does not come about by altering the auxin gradient inside the FG as previously interpreted. Here, we suggest an alternative hypothesis that can explain such changes through effects of auxin overproduction in the FG on the surrounding sporophytic tissues. Given that there is no detectable auxin gradient in the FG but that (1) there is polarised auxin activity in the sporophyte and (2) there are effects of auxin overproduction on gametophytic cell specification, it is likely that auxin has some effect in sporophytic tissues that indirectly affects cell fate decisions in the FG, namely via a non-cell-autonomous signal (NCAS).

To examine whether such a scenario could explain the experimental observations made by Pagnussat and colleagues (Pagnussat et al., 2009), we used as a basis the two-dimensional steady state model with a vacuole described above. We developed a mathematical model that is based on the assumption that the promoter of NCAS is responsive to auxin in sporophytic cells. Auxin leads to its activation in an all-or-none manner, i.e. the promoter becomes active if the concentration of auxin exceeds a certain threshold concentration c_thr. This serves as a good approximation for a more realistic scenario using a Hill activation function (e.g. Alon, 2007). The NCAS diffuses throughout the domain and is degraded inside the cells with the rate a_NCAS. For simplicity, we assumed that its diffusion coefficient in the membrane has the same value as in the cytoplasm (D_NCAS) (see supplementary material Table S4 for the values of parameters used).

Using this model, we studied the impact of auxin overproduction inside the FG on the spatial distribution of the NCAS. The concentration of auxin, the activity of the NCAS promoter, and the concentration of NCAS itself are visualised in Fig. 8 under different levels of auxin synthesis. It is obvious that, depending on the level of auxin production in the FG (and the promoter activation threshold; data not shown), different spatial distributions of the NCAS can be achieved. In fact, high levels of auxin production lead to a complete loss of polarity in the spatial distribution of NCAS (Fig. 8), which is expected to result in cell fate changes.

In summary, the changes in nuclear fate observed upon auxin overproduction inside the FG can be explained by auxin flux into the surrounding sporophytic tissues. This will lead to an expansion of the auxin response beyond the area seen in wild-type ovules at the chalazal pole and may have indirect effects on cell specification inside the FG.

Our modelling results show that even under the most beneficial parameters and assumptions, the concentration of auxin drops from one end of the FG to the other only by 3.2% and 6.9% in Arabidopsis and maize, respectively. This is much lower than, for instance, the steepness of the Bcd gradient in Drosophila, which is more than 90% (Gregor et al., 2005; He et al., 2010). We found that such a shallow gradient is highly sensitive to perturbations in the auxin source, and perturbations of 3.5% or more in the auxin source completely disrupted patterning in the FG, whereas for the Bcd gradient such perturbations would lead to a shift of the threshold position of merely 4%. Therefore, such a shallow gradient would compromise the robustness of cell specification with regard to the various fluctuations that are inherent to biological systems, especially in the intensity of the auxin source. We conclude that the factors studied do not allow the production of a sufficiently steep auxin gradient to provide enough positional information for cell specification in the FG. This led us to an attempt to quantify DR5 activity in the FG in order to refine the model.

Unexpectedly, our microscopy studies showed that, in contrast to a previous report (Pagnussat et al., 2009), auxin-dependent activity cannot be detected inside developing FGs in Arabidopsis or maize. Additionally, we found that the pattern of auxin activity in sporophytic cells adjacent to the FG is highly dynamic. The most notable developmental change in the pattern of auxin activity in the Arabidopsis ovule is the progressive movement of auxin maxima in cells adjacent to the developing FG from the micropylar towards the chalazal pole. It is tempting to speculate that this polarised activity could trigger indirect, non-cell-autonomous effects that influence cell specification inside the FG. Similarly, in maize, auxin activity was not observed inside the FG until cellularisation was complete. Instead, auxin activity was detected in adjacent sporophytic nucellar cells of the micropylar pole at early stages and in proliferating antipodal cells during FG maturation. A similar pattern has recently been described in Hieracium pilosella, in which no evidence for DR5 activity inside the FG was found (Tucker et al., 2012).

Taken together, our theoretical and experimental studies are inconsistent with the earlier report of a graded auxin-dependent activity in the FG of Arabidopsis (Pagnussat et al., 2009). This gives us reason to believe that these earlier results were misinterpreted and that the area with DR5 activity assigned to the FG in fact encompassed a larger area including sporophytic cells in the nucellus, which indeed express DR5::GFP-ER. The exact boundary of the FG might not be easily identifiable by epifluorescence microscopy, as used in the previous study (Pagnussat et al., 2009), but is very clear under a confocal laser-scanning microscope and, especially, with nuclear localised reporters (Fig. 6A-J).

However, the experimental manipulations of auxin synthesis (by YUC1 overexpression) and signalling (amiRNA-mediated knockdown of ARFs) in the FG that perturbed gametophytic cell fate seemed consistent with the hypothesis of an auxin gradient (Pagnussat et al., 2009) and warrant an explanation. Here, we propose hypotheses that are consistent with the effects on cell specification observed in these studies. First, changes in the fate of gametophytic nuclei can be explained by sporophytic effects of auxin overproduction in the FG. Using a modelling approach, we showed that auxin overproduction can indeed lead to a breakdown of polarity and loss of positional information inside the FG that results from auxin leakage into sporophytic tissues. In fact, our theoretical results agree with previous observations that showed an expansion of DR5 activity into the surrounding sporophytic tissues upon YUC1 overexpression [figure S5 in Pagnussat et al. (Pagnussat et al., 2009)]. Such an effect would be mediated by a hypothetical auxin-dependent NCAS, which is produced in sporophytic cells and controls cell specification in the FG. For instance, the peptide ZmEAL1 secreted from the egg cell has recently been shown to regulate cell fate within the maize FG in a non-cell-autonomous manner (Krohn et al., 2012). Similarly, peptides controlling cell fate in the FG could be secreted by surrounding nucellar cells.

Second, the effects observed by Pagnussat and colleagues (Pagnussat et al., 2009) could be mediated by some auxin-independent components of auxin signalling in the FG. For example, the transcription factors ARF3 and ARF17 possess auxin-like activity but are uncoupled from auxin signalling (Guilfoyle and Hagen, 2007). Both are transcribed in the central cell (Schmid et al., 2012) and show polarised mRNA expression in FGs at the four-nucleate stage (M. Schmid and U.G., unpublished). Downregulation of one of these factors, such as ARF3 in the experiment described by Pagnussat and colleagues (Pagnussat et al., 2009), would reduce such an auxin-independent auxin-like signal, whereas auxin overproduction would mask effects of ARF3 and/or ARF17 expression. Nevertheless, the activity of ARF3 or ARF17 should theoretically be detectable by the DR5 sensor; the fact that DR5 activity is not observed in the FG could mean that this activity is below the threshold of detection.

Finally, there could be minimal auxin-dependent activity in the FG that is below the detection level of any of our reporter systems with a very shallow gradient. Even though our modelling has shown that this gradient cannot provide positional information that is sufficiently robust for cell specification, it could determine the polarity of another morphogen through so-called wave-pinning (Mori et al., 2008). Such a model depends on two interconverting molecular species, whereby a progressing but eventually decelerating activation wave of one species would be initiated at one pole of the FG, leading to the depletion of the second species in this process. Thus, wave pinning could convert a spatially more or less homogeneous concentration profile into an asymmetric stationary front profile. However, wave pinning crucially depends on very different rates of diffusion of the two species, with the active form having the low diffusion rate. For instance, the interconversion of membrane-bound and a soluble forms of Rho GTPases can polarize cells by wave-pinning (Mori et al., 2008). Auxin is known to activate the ROP2 and ROP6 Rho GTPases in Arabidopsis epidermal cells through a yet poorly understood transcription-independent auxin signalling pathway (Xu et al., 2010). However, it is unknown whether Rho GTPases play a role in FG development or whether any other signaling molecules in the FG fulfil the requirements for wave pinning, i.e. rapid interconversion and highly different diffusion rates.

Although alternative explanations for the outcome of the experiments perturbing auxin production and signalling can be provided, there are currently not enough data to suggest a more precise mechanism. In particular, the most frequent cell fate change observed in both auxin overproduction and ARF amiRNA knockdown experiments was a loss of cell fate marker expression, whereas misexpression of egg and synergid cell markers was rather rare (Pagnussat et al., 2009). Thus, additional experiments that allow a more precise manipulation of auxin and/or other factors within and outside the FG will be required to develop accurate models of cell specification in the FG. In conclusion, neither our theoretical nor experimental evidence supports the hypothesis that a gradient in auxin activity provides the positional information for cell specification in the FG of flowering plants.

One-dimensional solutions were found analytically and were simulated in MATLAB 2011b software (MathWorks, Natick, MA, USA) using the pdepe function. Two-dimensional simulations were carried out with COMSOL Multiphysics 4.3a software (COMSOL Group, Stockholm, Sweden), exploiting the finite element method. To study the robustness of patterning, one-dimensional data or one-dimensional averages of two-dimensional simulations were used. Details are provided in supplementary material Appendix S1 and Tables S1, S4 and S5.

The DR5::NLS:tdTomato plasmid was constructed using a 35Smin:TMVΩ:Dof1a:tdTomato vector (B.M., unpublished), which is derived from a pCB302 binary vector (Xiang et al., 1999), carrying the TMVΩ translational enhancer (Gallie, 2002) and the Dof1a nuclear localisation signal (NLS) (Yanagisawa and Sheen, 1998) translationally fused to the tdTomato fluorescent protein gene (Shaner et al., 2004). The PCR-amplified DR5 synthetic promoter from the DR5::GFP-ER plasmid (Ottenschläger et al., 2003) was inserted into the Ω:Dof1a:tdTomato vector.

The pUBQ10::degron:GFP plasmid was obtained by inserting a sequence encoding the degron consensus core of AUX/IAA proteins (VGWPPV) into the pMDC111 vector (Curtis and Grossniklaus, 2003) with subsequent Gateway insertion of the 2.5 kb Arabidopsis ubiquitin UBQ10 promoter as explained in supplementary material Fig. S14. The control pUBQ10::GFP construct was obtained similarly. The constructs were verified by sequencing.

The Arabidopsis DR5::GFP:ER line (Ottenschläger et al., 2003) was obtained from Jiří Friml (Flanders Institute of Biotechnology, Belgium), DR5::SV40:3×GFP (Weijers et al., 2006) from Dolf Weijers (Wageningen University, The Netherlands), and the DR5::NLS:tdTomato line is described here for the first time (see above). The PGP1::PGP1:GFP line in a pgp1 homozygous background, the PGP19::PGP19:GFP line in a pgp19 homozygous background (Geisler et al., 2005), and the AUX1::AUX1:YFP line in a aux1-22 homozygous background (Swarup et al.,. 2004) were provided by Markus Geisler (Université de Fribourg, Switzerland); the PIN8::PIN8:GFP line (Dal Bosco et al., 2012) was provided by Cristina Dal Bosco (Albert-Ludwigs-Universität Freiburg, Germany). Unless indicated otherwise, all plants used were Arabidopsis thaliana (L.) Heynh. var. Columbia-0 (Col-0).

DR5::NLS:tdTomato transformants were obtained by Agrobacterium-mediated floral dip transformation (Bent, 2006). Seven independent transformants were recovered from BASTA selection and microscopically screened for tdTomato expression in ovules in the T1 (heterozygous plants) and T3 (homozygous plants) generations; a qualitative variation in expression patterns among the seven independent lines was not observed. A representative DR5::NLS:tdTomato line was crossed with the AKV::H2B:YFP gametophytic fate marker line (Rotman et al., 2005), provided by Wei-Cai Yang (Chinese Academy of Science, Beijing, China), which is in the Landsberg (erecta mutant, Ler) background, and F3 plants homozygous for both constructs were analysed.

Arabidopsis plants were grown as described (Schmid et al., 2012). For DR5::SV40:3×GFP seeds, the plates were supplemented with kanamycin (AppliChem, Darmstadt, Germany) to a final concentration of 50 μg/ml. Glufosinate (Plüss-Staufer, Oftringen, Switzerland) was sprayed onto plants carrying the DR5::NLS:tdTomato transgene on the third and sixth day after transfer to soil at a final concentration of 0.2 g/l.

Maize inbred lines A188 and H99 and transgenic lines (Gallavotti et al., 2008) were grown under standard greenhouse conditions at 26°C with 16 hours of light and a relative air humidity of ∼60%.

Ovules of Arabidopsis plants at various stages were dissected and studied either cleared for 5-15 minutes with 1 M glycine (pH 9.6) solution (as in Fig. 6H-J,M,O) or untreated in water (all other images). The pictures were taken with a Leica SP2 laser-scanning confocal microscope (Leica Microsystems AG, Heerbrugg, Switzerland). The GFP fluorescence was collected at wavelengths of 501-532 nm. For simultaneous YFP and tdTomato imaging, scanning was performed sequentially. Emission light of 503-575 nm and 575-632 nm was collected for the yellow and red channels, respectively. An excitation beam splitter DD 488/543 was used in both cases. Image capture was performed using Leica Confocal Software 2.61 and channel overlay was performed using a custom MATLAB script.

Maize cobs were harvested from greenhouse-grown plants. Whole cobs were treated as described (Srilunchang et al., 2010). For microscopy analyses, ovaries were dissected after clearing, mounted in methyl salicylate, and analysed with an LSM 510-META confocal laser-scanning microscope (Carl Zeiss Microscopy GmbH, Oberkochen, Germany) with 488 nm excitation and a LP 505 filter. For selective ZmPIN1a::PIN1a:YFP visualisation, 514 nm excitation and a BP 530-600 filter were applied, whereas DR5::mRFP:ER fluorescence was observed with 543 nm excitation in combination with a BP 560-615 filter. Image capture and processing were performed using the Zeiss LSM 510 META software and Zeiss LSM Image Browser version 3.5.0.359.

While our manuscript was under revision, Ceccatto and colleages (Ceccatto et al., 2013) also reported the absence of DR5 activity in the Arabidopsis FG.

We thank Dolf Weijers (Wageningen University), Jiří Friml (Flanders Institute of Biotechnology), Wei-Cai Yang (Chinese Academy of Science), Markus Geisler (Université de Fribourg) and Cristina Dal Bosco (Albert-Ludwigs-Universität Freiburg) for seeds; Célia Baroux and Christof Eichenberger (University of Zürich) for advice on confocal microscopy; Marc Schmid (University of Zürich) for allowing us to cite unpublished data; Pierre Barbier de Reuille (University of Berne), Enrico Martinoia (University of Zürich), Leah Edelstein-Keshet (University of British Columbia) and Markus Geisler for discussion; and Lucia Colombo (Universita degli Studi di Milano) for critical comments on the manuscript.