Lucie Camut

Barbora Gallova

Lucas Jilli

Mathilde Sirlin-Josserand

Esther Carrera

Lali Sakvarelidze-Achard

Sandrine Ruffel

Gabriel Krouk

Stephen G Thomas

Peter Hedden

Andrew L Phillips

Jean-Michel Davière

Dr Patrick Achard
email: patrick.achard@ibmp-cnrs.unistra.fr

Nitrate signaling promotes plant growth by upregulating gibberellin biosynthesis and destabilization of DELLA proteins

Keywords: Nitrate, gibberellins, hormone biosynthesis, DELLA proteins, growth, plant development, Arabidopsis, wheat

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Nitrogen (N) is one of the most important macronutrients limiting plant growth and yield. [START_REF] O'brien | Nitrate Transport, Sensing, and Responses in Plants[END_REF][START_REF] Fredes | Nitrate signaling and the control of Arabidopsis growth and development[END_REF][START_REF] Jia | Signaling pathways underlying nitrogen-dependent changes in root system architecture : from model to crop species[END_REF] Except for a few plant species that can use atmospheric N 2 gas through symbiotic association with certain soil bacteria, most crops acquire N in the soil from inorganic forms such as nitrate (NO3 -), the main N source for plants in agricultural lands. [START_REF] Dechorgnat | From the soil to the seeds: the long journey of nitrate in plants[END_REF] Nitrate serves as a source of the essential element found in very diverse macromolecules and a signal molecule regulating global gene expression and modulating both root and shoot system architecture. [START_REF] Fredes | Nitrate signaling and the control of Arabidopsis growth and development[END_REF][START_REF] Jia | Signaling pathways underlying nitrogen-dependent changes in root system architecture : from model to crop species[END_REF][START_REF] Wang | Genomic Analysis of the Nitrate Response Using a Nitrate Reductase-Null Mutant of Arabidopsis[END_REF][START_REF] Medici | The Primary Nitrate Response: A multifaceted signalling pathway[END_REF][START_REF] Wang | Nitrate Transport, Signaling, and Use Efficiency[END_REF] The most studied nitrate-related signaling pathway is called the primary nitrate response (PNR). [START_REF] Hu | AtCIPK8, a CBL-interacting protein kinase, regulates the low-affinity phase of the primary nitrate response[END_REF] It is characterized by a fast nitrate specific (manifested in nitrate reductase-null mutant) [START_REF] Wang | Genomic Analysis of the Nitrate Response Using a Nitrate Reductase-Null Mutant of Arabidopsis[END_REF] induction of marker genes (reviewed in [START_REF] Medici | The Primary Nitrate Response: A multifaceted signalling pathway[END_REF] ). These markers include the nitrate transporter families such as the transceptor NITRATE TRANSPORTER 1 (NRT1)/PEPTIDE TRANSPORTER (PTR) FAMILY 6.3 (NPF6.3, also known as CHLORATE RESISTANT 1, CHL1 or NRT1.1), NRT2.1 and NRT2.2, the nitrate assimilation genes NITRITE REDUCTASE (NiR) and NITRATE REDUCTASE (NIA1 and NIA2) and a multitude of transcription factors functioning in diverse signaling pathways. [START_REF] Fredes | Nitrate signaling and the control of Arabidopsis growth and development[END_REF][START_REF] Wang | Nitrate Transport, Signaling, and Use Efficiency[END_REF][START_REF] Canales | Systems analysis of transcriptiome data provides new hypotheses about Arabidopsis root response to nitrate treatments[END_REF][START_REF] Marchive | Nuclear retention of the transcription factor NLP7 orchestrates the early response to nitrate in plants[END_REF][START_REF] Brooks | Network walking charts transcriptional dynamics of nitrogen signaling by integrating validated and predicted genome-wide interactions[END_REF][START_REF] Vidal | Nitrate in 2020 : Thirty years from transport to signaling networks[END_REF] According to the current model of PNR, NRT1.1 perceives nitrate triggering changes in cytoplasmic Ca 2+ levels, [START_REF] Riveras | The calcium ion is a second messenger in the nitrate signaling pathway of Arabidopsis[END_REF] which activate several members of calcium-sensor protein kinases (CPK10/30/32) [START_REF] Liu | Discovery of nitrate-CPK-NLP signalling in central nutrient-growth networks[END_REF] that phosphorylate conserved NIN-LIKE PROTEIN (NLP) transcription factors (NLP6/7) [START_REF] Alvarez | Transient genome-wide interactions of the master transcription factor NLP7 initiate a rapid nitrogen-response cascade[END_REF] to reprogram nitrateregulated genes ensuring adaptive growth to nitrate availability. [START_REF] Liu | Discovery of nitrate-CPK-NLP signalling in central nutrient-growth networks[END_REF][START_REF] Krouk | Nitrate signaling : calcium bridges the nitrate gap[END_REF] Despite sophisticated nitrate uptake, storage and assimilation mechanisms, [START_REF] Vidal | Nitrate in 2020 : Thirty years from transport to signaling networks[END_REF] the fluctuation of nitrate concentration in both time and space, in part due to its high solubility and predisposition to leaching, requires farmers to supply soil with N-fertilizers to ensure optimal crop yield. Hence, since the 1960s, the application of N-fertilizers associated with mechanization and the adoption of high-yielding semi-dwarf varieties led to substantial yield increases, an intensive agricultural practice known as the "Green Revolution". [START_REF] Hedden | The genes of the Green Revolution[END_REF] The resulting semi-dwarf stature prevents lodging and thus enables higher N-fertilizer applications. The semi-dwarfing genes of the rice (semidwarf1, sd1) and wheat (Reduced height 1, Rht-1) varieties were characterized and shown to inhibit the synthesis and action, respectively, of gibberellin (GA) growth hormones. [START_REF] Hedden | The genes of the Green Revolution[END_REF] Strikingly, despite that more than 70% of wheat cultivated worldwide carry a GA-insensitive Rht-1 dwarfing allele, [START_REF] Thomas | Novel Rht-1 dwarfing genes: tools for wheat breeding and dissecting the function of DELLA proteins[END_REF] little is known about whether and how GA contributes to nitrate-regulated growth processes.

GAs constitute a class of diterpenoid molecules controlling major aspects of plant growth and development. Mutants deficient in GA biosynthesis or responses are dwarfs and late flowering, while elevated GA signaling results in taller plants and early flowering. Bioactive GA promotes growth by opposing the functions of DELLA growth repressing proteins (DELLAs), members of the GRAS family of transcriptional regulators. [START_REF] Davière | Gibberellin signaling in plants[END_REF] While cereals usually harbor a single DELLA paralogue, such as SLENDER RICE 1 (SLR1) in rice and REDUCED HEIGHT 1 (RHT-1) in wheat, [START_REF] Peng | Green revolution' genes encode mutant gibberellin response modulators[END_REF] the Arabidopsis genome encodes five DELLAs, GA-INSENSITIVE (GAI), REPRESSOR of ga1-3 (RGA), RGA-LIKE1 (RGL1), RGL2 and RGL3. [START_REF] Davière | Gibberellin signaling in plants[END_REF] GA-mediated physiological responses are activated by the binding of bioactive GA to the GA receptors GIBBERELLIN INSENSITIVE 1 (GID1) that trigger the destruction of DELLAs through the ubiquitin-dependent 26S proteasome pathway. [START_REF] Davière | Gibberellin signaling in plants[END_REF] DELLAs repress GA responses by interacting with and modulating the activity of DELLA-interacting partners (DIP) such as transcription factors or regulators, and chromatin-remodeling complexes.

Thereby, DELLAs regulate the expression of a broad array of genes involved in various pathways.

Similar to other phytohormones, GAs act as mediators of environmental signals, allowing plants to respond, often rapidly, to changes in light conditions, temperature, water and nutrient status. [START_REF] Achard | Integration of plant responses to environmentally activated phytohormonal signals[END_REF][START_REF] Jiang | Phosphate Starvation Root Architecture and Anthocyanin Accumulation Responses Are Modulated by the Gibberellin-DELLA Signaling Pathway in Arabidopsis[END_REF][START_REF] De Lucas | A molecular framework for light and gibberellin control of cell elongation[END_REF][START_REF] Achard | The Cold-Inducible CBF1 Factor-Dependent Signaling Pathway Modulates the Accumulation of the Growth-Repressing DELLA Proteins via Its Effect on Gibberellin Metabolism[END_REF][START_REF] Wild | Tissue-Specific Regulation of Gibberellin Signaling Fine-Tunes Arabidopsis Iron-Deficiency Responses[END_REF] Usually, DELLA accumulation reduces growth to prioritize resources to defense mechanisms, whereas GA-mediated DELLA degradation stimulates growth under favorable conditions. [START_REF] Colebrook | The role of gibberellin signalling in plant responses to abiotic stress[END_REF] Hence, it is now accepted that GA signaling enables appropriate growth in adverse environments. [START_REF] Achard | Integration of plant responses to environmentally activated phytohormonal signals[END_REF][START_REF] Colebrook | The role of gibberellin signalling in plant responses to abiotic stress[END_REF] Interestingly, recent experiments have shown that physical interactions between the rice DELLA SLR1 and GROWTH-REGULATOR FACTOR (GRF4) transcription factor co-regulate growth and the metabolism of carbon and nitrogen.

Whereas GRF4 promotes N assimilation, carbon fixation and plant growth, DELLAs repress these processes. Moreover, a recent study has reported that SLR1, and also GID1, are able to interact with NITROGEN-MEDIATED TILLER GROWTH RESPONSE 5 (NGR5), a rice APETALA2-domain transcription factor induced by N. [START_REF] Wu | Enhanced sustainable green revolution yield via nitrogen-responsive chromatin modulation of rice[END_REF] SLR1 accumulation competitively inhibits GID1-NGR5 interaction, which in turn enhances NGR5 stability and thereby shoots branching. [START_REF] Wu | Enhanced sustainable green revolution yield via nitrogen-responsive chromatin modulation of rice[END_REF] Thus, although it is apparent that GA signaling regulates growth and nitrogenuse efficiency, at present, it is currently unclear whether GA is a component of the regulatory pathway controlling the nitrate-dependent growth. Here, we undertook a molecular and genetic approach to evaluate the role of GA metabolism and signaling in nitrate-regulated growth processes in Arabidopsis and wheat. Essentially, we show that nitrate increases bioactive GA levels, thus promoting the degradation of DELLAs. Reduced DELLA accumulation in turn activates cell proliferation, and as a consequence, root and shoot growth.

Plant growth adaptation to fluctuating nutrient environment can be understood as a feedforward cycle, where nutrients promote plant growth through regulating hormones biosynthesis and transport, and in turn, hormonal pathways control nutrient provision to growth rate. [START_REF] Krouk | A framework integrating plant growth with hormones and nutrients[END_REF][START_REF] Krouk | Hormones and nitrate: a two-way connection[END_REF] Our data lead to the proposal that the GA pathway is a major regulator of this feed-forward loop interconnecting plant growth to nitrate availability.

Results

Nitrate promotes plant growth in a DELLA-dependent manner

In response to nitrate availability, the root and shoot system architecture undergoes important developmental changes. Thus, while adequate nitrate availability increases the length of both primary and lateral roots, low and high nitrate supplies inhibit their growth. [START_REF] Araya | Statistical modeling of nitrogendependent modulation of root system architecture in Arabidopsis thaliana[END_REF] Similarly, nitrate limitation reduces shoot growth and delays axillary bud activation and therefore shoot branching. [START_REF] De Jong | Auxin and Strigolactone Signaling Are Required for Modulation of Arabidopsis Shoot Branching by Nitrogen Supply[END_REF] Although well described as growth regulators preventing excessive elongation in response to high N fertilizer supply, it is still unclear whether the GA-regulated DELLA proteins inhibit growth under low N regimes. [START_REF] Hedden | The genes of the Green Revolution[END_REF][START_REF] Thomas | Novel Rht-1 dwarfing genes: tools for wheat breeding and dissecting the function of DELLA proteins[END_REF] To assess this point, we first investigated the involvement of DELLAs in the regulation of primary root growth in the absence of nitrate (or 0.5 mM glutamine, an alternative N source) and in response to increasing amounts of nitrate. For this purpose, we compared the primary root length of Arabidopsis wild-type and global-DELLA mutant seedlings (lacking all five Arabidopsis DELLAs) grown with nitrate supply ranging from 0 to 50 mM (Figures 1A and1B). As previously reported, [START_REF] Araya | Statistical modeling of nitrogendependent modulation of root system architecture in Arabidopsis thaliana[END_REF] the growth of the primary roots was proportionally correlated with the amount of nitrate, from low to adequate concentrations (10 mM NO 3 -in our growth conditions), and then inversely correlated under high nitrate supply (50 mM NO 3 -). Interestingly, we observed that the primary root growth of 7-d-old global DELLA mutant seedlings was less affected by low and high nitrate supply than that of the wild-type (Figure 1B). Whereas the length of global-DELLA mutant seedling roots grown on 0.25, 0.5, 1 and 50 mM NO 3 -was significantly longer than wild-type roots, their differences decreased on adequate nitrate supply (10 mM NO 3 -).

Thus, DELLA function inhibits root growth in response to low and high nitrate availability, but becomes less critical on optimal nitrate supply (Figures 1A and1B).

Next, to examine the contribution of DELLAs to nitrate-mediated growth processes during shoot development, we grew Arabidopsis wild-type, global DELLA and ga20ox1 mutants (a weak GA biosynthesis mutant) [START_REF] Xu | The GA5 locus of Arabidopsis thaliana encodes a multifunctional gibberellin 20-oxidase -molecular cloning and functional expression[END_REF][START_REF] Rieu | The gibberellin biosynthetic genes AtGA20ox1 and AtGA20ox2 act, partially redundantly, to promote growth and development throughout the Arabidopsis life cycle[END_REF][START_REF] Hedden | Gibberellin biosynthesis and its regulation[END_REF] on a perlite vermiculite soil supplemented with increasing amounts of nitrate (ranging from 2 to 50 mM NO 3 -). It is noteworthy that nitrate concentrations used for in vitro experiments (Figures 1A and1B) may not be directly comparable to those applied in soil. Nevertheless, in a similar way to the above growth responses, we found that whereas the height of 7-week-old wild-type plants increased with the concentration of nitrate present in the soil, the growth response was attenuated in mutants altered in GA pathway (Figures 1C and1D). Furthermore, while the diameter of wild-type rosettes became larger when nitrate supply was increased, the global-DELLA mutant rosettes were insensitive to a change from 10 to 50 mM NO 3 -(Figure 1E). Taken together, these results demonstrate that nitrate promotes growth in part via a DELLA-dependent mechanism.

There is considerable evidence suggesting that nitrate-dependent regulation of bud activation and elongation are triggered by changes in hormone action. [START_REF] De Jong | Auxin and Strigolactone Signaling Are Required for Modulation of Arabidopsis Shoot Branching by Nitrogen Supply[END_REF] GA has long been known to repress shoot branching; GA-deficient mutants display a high degree of branching. [START_REF] Rameau | Multiple pathways regulate shoot branching[END_REF] We found that nitrate supply increased the number of primary branches of wild-type and ga20ox1 mutant plants in contrast to global-DELLA mutant plants (Figure 1F). Thus, similar to the above results, nitrate enhances bud outgrowth in a DELLA-dependent manner. At this stage, it remains unclear whether the NGR5-GID1-DELLA competitive binding mechanism controlling shoot branching in rice also operates in Arabidopsis. [START_REF] Wu | Enhanced sustainable green revolution yield via nitrogen-responsive chromatin modulation of rice[END_REF]

Nitrate promotes root meristem growth via DELLA-dependent action on cell proliferation

Plant growth is regulated through the activity of apical and intercalary meristems in which the cells divide before elongating and differentiating. Moreover, GA promotes growth through cell proliferation and cell elongation by stimulating the degradation of nuclear DELLAs. [START_REF] Davière | Gibberellin signaling in plants[END_REF][START_REF] Ubeda-Tomás | Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis[END_REF] Previous works reported a key role for DELLAs in controlling root apical meristem (RAM) activity. [START_REF] Ubeda-Tomás | Gibberellin Signaling in the Endodermis Controls Arabidopsis Root Meristem Size[END_REF][START_REF] Achard | Gibberellin Signaling Controls Cell Proliferation Rate in Arabidopsis[END_REF] To investigate whether DELLAs play an essential function in regulating RAM activity in response to nitrate availability, we measured the size of the RAM of Arabidopsis wild-type and global-DELLA mutant seedlings throughout their development (from 3 to 7-dold) on low (0.5 mM) and adequate (10 mM) NO 3 -conditions. Root meristem length was represented as the number of cortical cells between the quiescent center (QC) and the first elongated cell. [START_REF] Achard | Gibberellin Signaling Controls Cell Proliferation Rate in Arabidopsis[END_REF] We found that whereas the size of the root meristem of wild-type seedlings grown on 10 mM NO 3 -was significantly increased compared to those grown on 0.5 mM NO 3 -, the global-DELLA mutant root meristem was less sensitive to the effect of nitrate (Figure 2A).

To corroborate this finding, we also analyzed the activity of the mitotic CYCLIN B1;2-GUS reporter in wild-type and gai-t6 rga-24 double mutant (a mutant lacking the two main DELLAs restraining growth). [START_REF] Achard | Gibberellin Signaling Controls Cell Proliferation Rate in Arabidopsis[END_REF] We observed that the number of dividing cells significantly decreased in the RAM of wild-type seedlings grown in nitrate deficient condition compared with those grown on 10 mM NO 3 -(Figures 2B and2C). In contrast, the number of dividing cells in the gai-t6 rga-24 RAM was less affected by the reduction in nitrate availability.

Taken together, these results indicate that DELLAs contribute to the nitrate-induced cell division activity.

Because root growth is the result of both cell division and cell expansion, we next asked whether nitrate and DELLAs jointly regulate root cell elongation. To this end, we measured the length of differentiated cortical cells in the root differentiation zone of 7-d-old wild-type and global-DELLA mutant seedlings grown on low (0.5 mM) and adequate (10 mM) NO 3 conditions. We found that nitrate increased the length of the cells at a similar level in wildtype and global-DELLA mutant seedling roots (Figure 2D). Thus despite reports that GA/DELLA regulates cell elongation in root, [START_REF] Ubeda-Tomás | Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis[END_REF] adequate nitrate supply (10 mM NO 3 -) enhances cell expansion in a DELLA-independent fashion.

Low nitrate availability enhances DELLA protein accumulation

In a subsequent experiment, we investigated whether the nitrate-regulated growth processes are associated with DELLA protein accumulation. To this end, we used RGA pro :GFP-RGA transgenic seedlings expressing a functional GFP-RGA protein visible in nucleus of root cells. [START_REF] Silverstone | Repressing a repressor: gibberellin-induced rapid reduction of the RGA protein in Arabidopsis[END_REF] We found a significant decrease of the GFP-RGA signal in the RAM of seedlings grown on 1 and 10 mM NO 3 -compared to those grown on low nitrate conditions (Figure 3A).

By contrast, GFP-RGA signal was increased in RAM of seedlings grown on Gln or ammonium chloride (NH 4 Cl), two alternative N sources, thus confirming that this response is specific to nitrate (Figure S1). Remarkably, consistent with the above growth phenotypes, we also observed an increase in GFP-RGA signal in seedling roots grown on high nitrate conditions (50 mM NO 3 -; Figure 3A). Then, we investigated the effect of nitrate supply on GFP-RGA protein accumulation in seedling roots and shoots. Accordingly, we found that nitrate substantially decreases the accumulation levels of GFP-RGA protein in both roots and shoots, but their sensitivity to nitrate was different. Indeed, while 1 mM NO S2F).

Nitrate enhances GA synthesis

An increase in the amount of GA induces a reduction in DELLA abundance, which in turn activates plant growth. [START_REF] Silverstone | Repressing a repressor: gibberellin-induced rapid reduction of the RGA protein in Arabidopsis[END_REF] Moreover, GA metabolism is influenced by various environmental signals including nutrient availability. [START_REF] Jiang | Phosphate Starvation Root Architecture and Anthocyanin Accumulation Responses Are Modulated by the Gibberellin-DELLA Signaling Pathway in Arabidopsis[END_REF][START_REF] Wild | Tissue-Specific Regulation of Gibberellin Signaling Fine-Tunes Arabidopsis Iron-Deficiency Responses[END_REF][START_REF] Colebrook | The role of gibberellin signalling in plant responses to abiotic stress[END_REF] We next examined if nitrate-deficiency-induced DELLA accumulation was attributable to a decrease in GA biosynthesis. To this end, we determined the endogenous GA contents in 7-d-old wild-type seedlings grown on low (0.5 mM) and adequate (10 mM) nitrate conditions, and 48 hr after a transfer from 0.5 to 10 mM NO 3 -. The levels of the major biologically active GA in Arabidopsis, GA 4 , as well as intermediate GAs (GA 12 and GA 24 ) were significantly increased in seedlings grown with 10 mM NO 3 -compared with those of seedlings grown on low nitrate (Figures 4A and4B).

Remarkably, the contents in GA 34 (the inactive 2ß-hydroxylated product of GA 4 ) were also increased in seedlings transferred to 10 mM NO 3 -(Figure 4B). This last result emphasizes that the increase in GA 4 level is not the consequence of a reduction in the activity of the GA 2oxidases, which catalyze the conversion of GA 4 into GA 34 . [START_REF] Rieu | Genetic Analysis Reveals That C19-GA 2-Oxidation Is a Major Gibberellin Inactivation Pathway in Arabidopsis[END_REF] Subsequently, we investigated whether this increase in GA contents correlated with changes in the expression of GA biosynthetic genes. Surprisingly, most of GA biosynthetic genes did not show any obvious expression trend in response to a transfer from nitrate deficiency to adequate nitrate conditions, except a down-regulation for some of the genes, 48 hr after the transfer to 10 mM NO 3 -(Figure S3). However and consistent with the nitrate-induced accumulation of GA 4 and GA 34 , we found that expression of GA3ox1 (which catalyzes the conversion of GA 9 into GA 4 ) and GA2ox2 is substantially up-regulated by nitrate supply (Figure 4C and Figure S3). When examining the expression of GA signaling genes, such as those encoding the DELLAs and GA receptors GID1, most of them did not react in response to nitrate supply, apart from a down-regulation trend 48 hr after transfer, similar to most of GA metabolism genes (Figure S3).

DELLA abundance is regulated by nitrate-dependent signaling

To test how nitrate controls the GA-DELLA pathway, we first examined the effects of nitrate on RGA protein accumulation in a nitrate reductase (NR)-null mutant (nia1 nia2). [START_REF] Wang | Genomic Analysis of the Nitrate Response Using a Nitrate Reductase-Null Mutant of Arabidopsis[END_REF] We found that nitrate decreases substantially the abundance of RGA protein in both wild-type and nia1 nia2 mutant shoots (Figure 5A and Figure S4A). Thus, DELLA accumulation is regulated by nitrate signaling, independent of nitrate reduction and therefore the N status of the plant. In a subsequent experiment, we analyzed the accumulation of RGA protein in nrt2.1 nrt2.2 (nrt2.1-2), which is mutated in two linked genes responsible for high-affinity nitrate uptake in Arabidopsis roots. [START_REF] Cerezo | Major Alterations of the Regulation of Root NO 3 -Uptake Are Associated with the Mutation of Nrt2.1 and Nrt2.2 Genes in Arabidopsis[END_REF] As previously reported, the nrt2.1-2 double mutant displayed a reduction in shoot biomass compared with the wild-type, caused by a decrease of nitrate uptake (Figures S4B andS4C). As expected, RGA accumulated to higher levels in nrt2.1-2 mutant rosettes of 4-week-old plants grown on both low (0.5 mM) and non-limiting (10 mM) nitrate supply, compared with the wild-type (Figure 5B and Figure S4D).

Key components of the nitrate-signaling pathway are the NLP6 and NLP7 transcription factors, which control the expression of a large number of early nitrate response genes. [START_REF] Marchive | Nuclear retention of the transcription factor NLP7 orchestrates the early response to nitrate in plants[END_REF][START_REF] Liu | Discovery of nitrate-CPK-NLP signalling in central nutrient-growth networks[END_REF][START_REF] Alvarez | Transient genome-wide interactions of the master transcription factor NLP7 initiate a rapid nitrogen-response cascade[END_REF][START_REF] Krouk | Nitrate signaling : calcium bridges the nitrate gap[END_REF] To examine the involvement of the NLP in the nitrate-regulated GA-DELLA pathway, we initially took advantage of previously reported genome-wide analyses performed on wild-type and nlp7 mutant during a short-term nitrate resupply kinetics. [START_REF] Marchive | Nuclear retention of the transcription factor NLP7 orchestrates the early response to nitrate in plants[END_REF][START_REF] Alvarez | Transient genome-wide interactions of the master transcription factor NLP7 initiate a rapid nitrogen-response cascade[END_REF] Remarkably, these analyses revealed that even though NLP7 does not bind the genomic region of GA3ox1 in chromatin immunoprecipitation assay, GA3ox1 is among the list of NLP7-dependent nitrate-inducible genes. [START_REF] Marchive | Nuclear retention of the transcription factor NLP7 orchestrates the early response to nitrate in plants[END_REF][START_REF] Alvarez | Transient genome-wide interactions of the master transcription factor NLP7 initiate a rapid nitrogen-response cascade[END_REF] In agreement with these findings, we confirmed that nitrate-NLP7 pathway regulates the expression of GA3ox1 (Figure 5C). Whereas the expression of GA3ox1 was upregulated in wild-type seedlings upon nitrate supply, its expression was only transiently induced in nlp7 mutant. Consistent with this expression pattern, nitrate supply increased the contents of bioactive GA 4 (product of GA3ox activity) in wild-type seedlings, but not in nlp7 mutant (Figure 5D). By contrast, nitrate supply increased the levels of GA 12 and GA 24 in both wild-type and nlp7 mutant, suggesting that nitrate regulates the early GA biosynthetic steps in an NLP7-independent manner (Figure 5D). Finally, we analyzed the accumulation levels of RGA in wild-type and nlp7 mutant seedlings in a time course analysis after a transfer from nitrate deficiency to adequate nitrate conditions. While nitrate supply triggered a reduction of RGA accumulation in wild-type 48 hr after transfer, the amount of RGA was relatively stable in nlp7 mutant, in accordance with the levels of GA3ox1 transcripts and GA 4 contents detected in wild-type and nlp7 mutant (Figure 5E and Figure S4E). Overall, these results

indicate that nitrate-NLP7 signaling decreases DELLA accumulation through the activation of GA 4 synthesis (via up-regulation of GA3ox1 gene expression).

Effect of nitrate on GA metabolism and growth processes in wheat

To examine whether the role of the GA-DELLA pathway in nitrate-mediated growth processes is conserved in diverse angiosperms, we analyzed the effect of nitrate (used as the only N source) on the growth of wheat seedlings (cv. Cadenza) that have altered GA signaling. We compared wild-type (Rht-1 tall) against Rht-D1b (semi-dwarf) and Rht-B1c

(severe-dwarf) gain-of-function mutants that express constitutively active DELLA (Rht-1)

proteins conferring GA-insensitive dwarfism. [START_REF] Peng | Green revolution' genes encode mutant gibberellin response modulators[END_REF][START_REF] Pearce | Molecular Characterization of Rht-1 Dwarfing Genes in Hexaploid Wheat[END_REF] For this experiment, wild-type, Rht-D1b

and Rht-B1c mutants were grown on a perlite vermiculite soil supplemented 3 times per week with the Letcombe nutrient solution containing nitrate (+N; 1.5 mM Ca(NO 3 ) 2 , 5 mM KNO 3 and 2 mM NaNO 3 ) or without N (-N; 1.5 mM CaCl 2 , 5 mM KCl, 2 mM NaCl), and the length of the primary leaf sheath was measured. As previously reported with other semi-dwarf Rht-1 mutant alleles, [START_REF] Hedden | The genes of the Green Revolution[END_REF][START_REF] Thomas | Novel Rht-1 dwarfing genes: tools for wheat breeding and dissecting the function of DELLA proteins[END_REF] the Rht-D1b and Rht-B1c mutant wheat were relatively insensitive to nitrate supply. Whereas the length of the primary leaf sheath was substantially longer in 3week-old wild-type plants grown with nitrate (compared with those grown without N), nitrate supply had respectively little or no effect on the primary leaf sheath length of Rht-D1b and Rht-B1c mutants (Figures 6A and6B). Thus, nitrate enhances wheat growth in part via a DELLA-dependent mechanism.

As a next step, we determined the contents of GA in the first internode of 3-week-old wildtype plants grown with NO 3 -or without N. In wheat, the 13-hydroxylation pathway leading to active GA 1 is the main GA biosynthetic route [START_REF] Hedden | Gibberellin biosynthesis and its regulation[END_REF] (Figure 4A). We found that nitrate supply increases the levels of bioactive GA 1 , GA intermediates (GA 53 , GA 44 and GA 19 ) and inactivation product GA 8 (Figure 6C).

We also investigated the effect of nitrate on growth and GA synthesis at a later stage, in 7week-old wheat cv. Cadenza (Rht-1 tall). In this experiment, the plants were grown with nitrate and then N was sequentially withdrawn week after week, over a time scale of 6 weeks until booting stage. Noteworthy, main tillers were removed from all plants as they appeared, to avoid N resources being redistributed between tillers. In this growth context, we found that the peduncle and first two internodes were gradually shorter as time with N decreases (Figures 6D and6E). By contrast, there was no significant difference in the lengths of the third and fourth internode across treatment groups when compared to control (Figure 6E).

Consistent with these physiological traits, we found that N withdrawal had a gradual effect on endogenous GA contents in the first internode at booting stage. All GA quantified displayed a steady gradual increase with increasing length of time that the plants were supplied with nitrate (Figure 6F). Thus altogether, and as previously shown with Arabidopsis, these results demonstrate that nitrate enhances wheat growth in part through activation of GA pathway.

Discussion

Plants are sessile organisms that must perpetually adapt their growth and development to fluctuating nitrate concentrations in the soil. It is now established that GA signaling plays a critical role in modulating plant growth in response to environmental changes including nutrient availability. [START_REF] Achard | Integration of plant responses to environmentally activated phytohormonal signals[END_REF][START_REF] Jiang | Phosphate Starvation Root Architecture and Anthocyanin Accumulation Responses Are Modulated by the Gibberellin-DELLA Signaling Pathway in Arabidopsis[END_REF][START_REF] De Lucas | A molecular framework for light and gibberellin control of cell elongation[END_REF][START_REF] Achard | The Cold-Inducible CBF1 Factor-Dependent Signaling Pathway Modulates the Accumulation of the Growth-Repressing DELLA Proteins via Its Effect on Gibberellin Metabolism[END_REF][START_REF] Wild | Tissue-Specific Regulation of Gibberellin Signaling Fine-Tunes Arabidopsis Iron-Deficiency Responses[END_REF] While semi-dwarfing genes that interfere with the action or production of GA contributed to substantial yield increases during the green revolution because they prevent excessive stem elongation in response to high nitrogen fertilizer regimes, [START_REF] Hedden | The genes of the Green Revolution[END_REF] the role of GA signaling in adapting plant growth to nitrate availability remained unclear. The experiments described here investigate the connections between the GA pathway and the nitrate-dependent signaling pathway.

Plant root development is strongly influenced by nitrate concentrations in the soil. Whereas limited nitrogen provisions inhibit the primary root length, excess supply of nitrate also leads to a repression of root elongation. [START_REF] Araya | Statistical modeling of nitrogendependent modulation of root system architecture in Arabidopsis thaliana[END_REF][START_REF] Giehl | Root Nutrient Foraging[END_REF] Remarkably, we observed that low (0.5 mM NO 3 -) and high (50 mM NO 3 -) nitrate provisions promoted the accumulation of RGA in roots and that the growth of global-DELLA mutant roots was less affected by these extreme nitrate concentrations than those of wild-type seedlings. Furthermore, the abundance of RGA in wild-type roots and the difference in root growth between wild-type and global-DELLA mutant seedlings decreased progressively with increase in nitrate supply, from low (0.5 mM NO 3 -) to adequate (10 mM NO 3 -) concentrations. Thus, low (and high) nitrate conditions repress root growth in part via a DELLA-dependent pathway. Consistent with our findings, a previous work has reported a similar effect of high nitrate supply on plant growth and GFP-RGA accumulation in RGA pro :GFP-RGA seedlings roots, except that the range of NO 3 concentrations used by the authors was ten-fold less than in our growth conditions. [START_REF] Gras | SMZ/SNZ and gibberellin signaling are required for nitrate-elicited delay of flowering time in Arabidopsis thaliana[END_REF] This difference in effective NO 3 -levels could be attributed to the composition of the N-free medium, which is different between the two works. Interestingly, we also found that seedling shoots had a similar response to roots in terms of RGA accumulation, even though the shoots tend to be less sensitive to nitrate than roots. Consistent with this observation, global gene expression analyses revealed that while roots treated with low nitrate have a much wider response than shoots in term of the number of genes altered, the shoots can be as responsive as roots to adequate nitrate concentrations. [START_REF] Wang | Genomic Analysis of the Nitrate Response Using a Nitrate Reductase-Null Mutant of Arabidopsis[END_REF][START_REF] Wang | Genomic Analysis of a Nutrient Response in Arabidopsis Reveals Diverse Expression Patterns and Novel Metabolic and Potential Regulatory Genes Induced by Nitrate[END_REF] Thus, it is likely that in our growth conditions, 1 mM NO 3 -supply is the minimal concentration to trigger a decrease in RGA abundance in seedling roots, while 10 mM NO 3 -is required to observe the same phenomenon in shoots.

Moreover, the kinetics of DELLA disappearance in response to a transfer from nitrate deficiency to adequate nitrate conditions (and reciprocally) is similar in both roots and shoots, and is visible within a few days after transfer.

Our results also demonstrate that nitrate promotes stem elongation and shoot branching in Arabidopsis and leaf sheath elongation in wheat in part through a DELLA-dependent mechanism. Thus nitrate-mediated regulation of DELLA accumulation is a general mechanism that is conserved among flowering plants and throughout plant development.

Consistent with this finding, we found that nitrate enhances the accumulation of bioactive GAs in both Arabidopsis and wheat. At this stage, it remains unclear whether nitrate enhances the accumulation of bioactive GA 1 in wheat through the NLP-dependent signaling pathway, such as in Arabidopsis. Interestingly, not only the bioactive GAs increased in response to nitrate supply, but also GA 12 and GA 53 in Arabidopsis and wheat, respectively, and later intermediate GAs. This implies increased activity of the earlier part of the GA biosynthetic pathway and enhanced metabolic flux through the pathway (Figure 4A). Overexpression of ent-copalyl diphosphate synthase (CPS) and ent-kaurene synthase (KS) in Arabidopsis massively increases the supply of GA 12 but this has almost no effect on the levels of bioactive GAs. [START_REF] Fleet | Overexpression of AtCPS and AtKS in Arabidopsis confers increased ent-kaurene production but no increase in bioactive gibberellins[END_REF] Thus, although it is likely that nitrate regulates the GA pathway at multiple levels, it enhances the production of bioactive GAs via its effect on the final steps of GA biosynthesis.

It is worth noting that while our results in Arabidopsis indicate that nitrate induces the expression of GA3ox1, we cannot exclude the possibility of post-translational regulation of GA biosynthetic enzymes (e.g. protein turnover) and allosteric control of enzyme activity, two important mechanisms largely understudied. [START_REF] Lee | Regulation of gibberellin 20-oxidase1 expression in spinach by photoperiod[END_REF][START_REF] Takehara | A common allostric mechanism regulated homeostatic inactivation of auxin and gibberellin[END_REF] Moreover, it is important to emphasize that various other hormones, including cytokinins, also act as second messengers in response to nitrate, adapting plant growth to fluctuating environments. [START_REF] Krouk | A framework integrating plant growth with hormones and nutrients[END_REF][START_REF] Krouk | Hormones and nitrate: a two-way connection[END_REF] Previous works revealed that bioactive GAs promote root growth through cell division and expansion by stimulating the degradation of DELLAs in endodermal cells of the RAM and root elongation zone, respectively. [START_REF] Ubeda-Tomás | Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis[END_REF][START_REF] Ubeda-Tomás | Gibberellin Signaling in the Endodermis Controls Arabidopsis Root Meristem Size[END_REF][START_REF] Achard | Gibberellin Signaling Controls Cell Proliferation Rate in Arabidopsis[END_REF] In elongating roots, bioactive GAs are translocated in the endodermis by the GA transporter NITRATE TRANSPORTER1/PEPTIDE TRANSPORTER FAMILY 3 (NPF3) localized in the plasma membrane of endodermal cells. [START_REF] Tal | The Arabidopsis NPF3 protein is a GA transporter[END_REF][START_REF] David | N availability modulates the role of NPF3.1, a gibberellin transporter, in GA-mediated phenotypes in Arabidopsis[END_REF] We also observed that adequate nitrate supply enhances primary root growth by activating both cell proliferation and elongation. However, unexpectedly, whereas nitrate increased the number of cortical cells in root meristem via a DELLA-dependent mechanism, it increased cell elongation in a DELLA-independent manner. DELLAs restrain cell cycle activity by enhancing the expression of cell cycle inhibitors. [START_REF] Achard | Gibberellin Signaling Controls Cell Proliferation Rate in Arabidopsis[END_REF] Accordingly, we found that mitotic activity (monitored with the CYCB1;2:Dbox-GUS reporter) was less reduced in the RAM of the DELLA loss of function gai-t6 rga-24 mutant grown on low nitrate conditions than those of wild-type. By contrast, low nitrate restrained cell length of both wild-type and global-DELLA mutant seedling roots. Thus, it is likely that nitrate-induction of cell size is driven by other hormonal pathways. [START_REF] Krouk | Hormones and nitrate: a two-way connection[END_REF] Of note, it has recently been reported that nitrate promotes cell size by increasing ploidy level. [START_REF] Moreno | Nitrate defines shoot size through compensatory roles for endoreplication and cell division in Arabidopsis thaliana[END_REF] It is now well established that the nitrate-signaling pathway activates plant growth by controlling the hormonal status of the plant. [START_REF] Krouk | A framework integrating plant growth with hormones and nutrients[END_REF][START_REF] Krouk | Hormones and nitrate: a two-way connection[END_REF] Reciprocally, hormone-signaling pathways regulate nitrate acquisition and assimilation, constituting a retro-control of growth on N provision. A recent report revealed that Rht-1 dwarfing genes restrain nitrate uptake and assimilation by interacting with and inhibiting the activity of GRF4, a transcription factor that positively regulates N metabolism. [START_REF] Wu | Enhanced sustainable green revolution yield via nitrogen-responsive chromatin modulation of rice[END_REF] We propose that GA-nitrate interplay provides a highly regulated mechanism permitting flexible and appropriate growth in response to N availability. (A) Simplified GA biosynthetic pathway. Biosynthetic enzymes are highlighted in red.

GGDP, geranyl geranyl diphosphate; CDP, ent-copalyl diphosphate; CPS, ent-copalyl diphosphate synthase; KS, ent-kaurene synthase; KO, ent-kaurene oxidase; KAO, entkaurenoic acid oxidase.

(B) Concentration of GAs (pg g -1 dry weight) in 7-day-old wild-type (Ler) seedlings grown on 0.5 or 10 mM NO 3 -, or two days after a transfer from 0.5 to 10 mM NO 3 -. Endogenous of three biological replicates and different letters denote significant differences (p < 0.05) using one-way ANOVA with Tukey's test for multiple comparisons. Expression levels of related GA metabolism and signaling genes are provided (Figure S3). (D) GA contents (ng g -1 dry weight) in 7-day-old wild-type (Col-0) and nlp7-1 mutant seedlings grown on 0 mM NO 3 -or two days after a transfer from 0 to 10 mM NO 3 -. Different letters denote significant differences (p < 0.05) using two-way ANOVA with Tukey's test for multiple comparisons.

(E) RGA protein accumulation in wild-type (Col-0) and nlp7-1 mutant seedlings transferred from nitrate deficient conditions (0 mM) to 10 mM NO 3 -for 24h or 48h. Numbers represent the fold increase in RGA protein levels relative to blue-stained protein signal. Replicate gels are provided (Figure S4E). Rht-D1b allele was transferred from cultivar Avalon. [START_REF] Griffiths | Meta-QTL analysis of the genetic control of ear emergence in elite European winter wheat germplasm[END_REF] The alleles were selected from homozygous progenies after six backcrosses to cultivar Cadenza (which contains the wildtype Rht-1 alleles: Rht-A1a, Rht-B1a and Rht-D1a) with recurrent selection for the dwarfing mutation.

In vitro, Arabidopsis plants were grown in growth chambers (SANYO, MLR-351H) on 1x

Murashige-Skoog (MS) modified medium without nitrogen [START_REF] Castillo | NIN-like protein7 and PROTEOLYSIS6 functional interaction enhances tolerance to sucrose, ABA, and submergence[END_REF]

Gene expression analyses

Total RNA was extracted using RNeasy Plant mini kit (Qiagen) according to manufacturer's instructions and quantified with a spectrophotometer NanoDrop 2000/200c (Thermo Scientific). 1 µg of total RNA were treated first with 2 units of RQ1 RNase-free DNase (Promega) and then reverse transcribed in a total volume of 40 µL with 2 µM oligo(dT) 20 , 0.5 mM deoxynucleotide triphosphate (dNTP), 5 mM DTT, and 200 units of Superscript III reverse transcriptase (Invitrogen). qRT-PCR was performed using gene-specific primers (listed in Table S1) in a total volume of 10 µL SYBR Green Master mix (Roche) on a Lightcycler LC480 apparatus (Roche) according to manufacturer's instructions. The PCR programme was as following: an initial DNA denaturation at 95°C for 5 min; 45 cycles including a denaturation step at 95°C for 10 sec, an annealing step at 60°C for 15 sec and an extension step at 72°C for 15 sec; and a melting curve from 55°C to 95°C. AT4G26410 gene was used as internal reference transcript [START_REF] Wild | Tissue-Specific Regulation of Gibberellin Signaling Fine-Tunes Arabidopsis Iron-Deficiency Responses[END_REF] . The relative expression level of each gene was calculated using Lightcycler 480 software, release 1.5.0 SP3, and averaged over three

CPS-F TCCATTCCAAGTACAACCTTTCT

CPS-R TCTCTAGCGACATTGAGAGGAGA

KS-F GAAAAAGAGATCTGGATCTTAAATGTG

KS-R TTGTCCCCTCTAAAACATAGGC

KO-F AAATCGGAGGCTATCATGTCC

KO-R GCTTCTTATCCATGTTGCATCC

KAO1-F CTTATCGCAGGTTGTCGATG

KAO1-R TTCCAACCTTTTGGGATCAA

KAO2-F CTAGAGGATACAAGAGGTGGTC

KAO2-R CCGTCATAGCTTCAGTCG

GA20ox1-F CATGGGTTTCAGCCATTG

GA20ox1-R CTCTAAAGTAGTCCCGTTTTACGC

GA20ox2-F CGATCTCTCAAGCCAAGACTCG

GA20ox2-R TCGCTGACGCCATGATTG

GA20ox3-F ATGGCTCTAACGAATGGAAG

GA20ox3-R CTTTCTCTCTCGCTGTTCAC

GA3ox1-F TCGCGATGATCTTGGTTG

GA3ox1-R GAGGTCACCAACGTTAACCAC

GA3ox2-F GCCACCACCTCAAATACTGTG

GA3ox2-R GGCCCATTGTATGTCCTTTTC

GA2ox1-F ACGTTGGTGACTCTCTCC

GA2ox1-R CGATTCTCTGAGTCAATGAAGG

GA2ox2-F AGGTCGTAAACCACGGAGTC

GA2ox2-R CAAGCCGAAGAAGCCAATAG

GA2ox3-F CCAAAAGAGTAGACCATGGTAATTG

GA2ox3-R CATTTTGGATTAACATAGAGGTTGC

GAI-F CACCTCGGCTTGGAAACTCTCTC

GAI-R TGACAAAGGGAAAAACAGTAGGATTT

RGA-F AATAGTGGCCAAGGTTATCGTG

RGA-R AGTGTGCCAACCCAACATG

RGL1-F CAAGCATGTTGTTGGCACTT

RGL1-R GCAACAAACAACCTTCATTCTCT RGL2-F CTGCGTTTCCAAAGGAAGAG RGL2-R GTCGGATCCTCTTGCTGCTA RGL3-F CGTCGAATTTACCGGATTCA RGL3-R AATCTCTTCGAAGGAAGGATCA GID1A-F GCTGCGAGCGATGAAGTTA GID1A-R AGTGTCGGTTAAAGGTTCCATC GID1B-F TTTGCTGGGTTTTGGAGACT GID1B-R AGGACCCATGTGTTGAGTGG GID1C-F GAACGGCGTTTAACTACTACCG GID1C-R TTTGGACGGTTCACAAACG AT4G26410-F GAGCTGAAGTGGCTTCAATGAC AT4G26410-R GGTCCGACATACCCATGATCC
Table S1. List of primers used for RT-qPCR, related to STAR methods.

  roots were analyzed for each box plot. Similar results were obtained in independent experiments. (B-C) Effect of NO 3 -treatment on CYCB1;2:Dbox-GUS cell-division marker in wild-type (Col-0) and gai-t6 rga-24 mutant (lines #7 and #18) roots. (B) Photographs show representative 5-day-old root seedlings grown without nitrate (0 mM) or with 0.25 or 10 mM NO 3 -. White arrows indicate the distance between the first and last dividing cells in the longitudinal axis of the root meristem as shown by ß-glucuronidase staining. Scale bars represent 100 µm. (C) Number of CYCB1;2:Dbox-GUS expressing cells in root meristems of 5-d-old seedlings, as in B. Different letters denote significant differences (p < 0.05) using one-way ANOVA with Tukey's test for multiple comparisons. 10 ≤ n ≤ 21 roots were analyzed for each box plot. (D) Length of differentiated cortical cells of 7-day-old wild-type (Ler) and global DELLA mutant seedlings grown without nitrate (0 mM) or with 0.5 or 10 mM NO 3 -. Different letters denote significant differences (p < 0.05) using two-way ANOVA with Tukey's test for multiple comparisons. 51 ≤ n ≤ 66 differentiated cortical cells were analyzed for each box plot. Similar results were obtained in independent experiments.

Figure 3 .

 3 Figure 3. NO 3 --regulated growth processes are associated with DELLA accumulation. (A) GFP fluorescence in root meristem of 7-day-old RGA pro :GFP-RGA seedlings grown on media containing increasing concentration of nitrate (NO 3 -), as indicated. All images were obtained with the same parameters. Gln, glutamine. Scale bars represent 100 µm. More representative images are provided (Figure S1). (B-C) Immunodetection of GFP-RGA (with an antibody to GFP) in roots (B) and shoots (C) of 7-day-old RGA pro :GFP-RGA seedlings grown on media containing increasing concentration of NO 3 -, such as in A. PSTAIR serves as sample loading control. Numbers represent the fold increase in GFP-RGA protein levels relative to PSTAIR levels. Replicate gels are provided (Figures S2A and S2B). (D-G) Immunodetection of RGA (with an antibody to RGA) in shoots (D, E) and roots (F, G) of 7-day-old wild-type (Ler) seedlings transferred from nitrate-deficient conditions to 10 mM NO 3 -(D, F) or inversely (E, G), for the time indicated. Numbers represent the fold increase in RGA protein levels relative to blue-stained protein signal. Replicate gels are provided (Figures S2C, S2D, S2E, and S2F).

Figure 4 .

 4 Figure 4. Nitrate promotes GA synthesis.

GA 9

 9 was analyzed but not detected. The values are means ± s.d. of four biological replicates. Asterisks indicate significant differences (*p < 0.05; ** p < 0.01) for 10 mM versus 0.5 mM NO 3 -growth conditions by Student's t test. (C) Time-course of GA3ox1 transcript accumulation in 7-day-old wild-type (Col-0) seedlings that have been transferred from 0 to 10 mM NO 3 -for the time indicated. Data are means ± s.d.

Figure 5 .

 5 Figure 5. DELLA accumulation is regulated by NO 3 --dependent signaling pathway. (A) Immunodetection of RGA in shoots of 7-day-old wild-type (Col-0) and nia1 nia2 mutant seedlings transferred from nitrate deficient conditions (0 mM) to 10 mM NO 3 -for the time indicated. Replicate gels are provided (Figure S4A). (B) Immunodetection of RGA in 4-week-old wild-type (Col-0) and nrt2.1-2 double mutant plants grown on 0.5 or 5 mM NO 3 -. Replicate gels are provided (Figure S4D). (C) Relative GA3ox1 expression in 7-day-old wild-type (Col-0) and nlp7-1 mutant seedlings that have been transferred from nitrate deficient conditions (0 mM) to 10 mM NO 3 -for 24h or 48h. Asterisks indicate significant differences (*p < 0.05) for Col-0 versus nlp7-1 by Student's t test.

Figure 6 .

 6 Figure 6. Effects of nitrate on GA metabolism and growth in wheat. (A) Leaf sheath length (mean ± s.d. of three biological replicates) of 3-week-old wild-type (cv. Cadenza), Rht-D1b and Rht-B1c mutant wheat grown on perlite vermiculite soil supplemented 3 times per week with a nutritive solution without nitrogen (-N) or containing NO 3 -(+N). Different letters denote significant differences (p < 0.05) using two-way ANOVA with Tukey's test for multiple comparisons. 15 ≤ n ≤ 20 plants were analyzed for each biological replicate. (B) Representative 3-week-old wild-type (cv. Cadenza), Rht-D1b and Rht-B1c mutant wheat grown as in A. The arrows indicate the length of the first leaf sheath. Scale bars represent 1 cm. (C) Concentration of GAs (ng g -1 dry weight) in the first internode of 3-week-old wild-type (cv. Cadenza) wheat grown as in A. The values are means ± s.d. of three biological replicates. Asterisks indicate significant differences (*p < 0.05; ** p < 0.01) for +N versus -N by Student's t test. (D-F) Effect of nitrogen withdrawal on internode elongation and GA contents in wheat. (D) Sections of elongated stem at anthesis. P-1, second internode; P-2, third internode; P-3, P-4 further internodes. (E) Internode length (mean ± s.e.; n=15) of 7-week-old wild-type wheat (cv. Cadenza) growing on different nitrogen (N) status. Plants were grown on sand perlite soil supplemented three times in the first week with a nutritive solution containing NO 3 -(+N). The plants were then divided into six treatment groups for which N was sequentially withdrawn from the watering solution week by week, as indicated. Asterisks indicate significant difference (p < 0.05) for comparisons within internodes for treatments 1-5 weeks with N compared to control, according to two-way ANOVA followed by least significant difference (LSD) test. (F) Concentration of GAs (ng g -1 dry weight) in peduncle and peduncle nodes of 7-week-old wild-type wheat grown on different N status, as in A. Asterisks indicate significant difference (p < 0.05) for comparisons within treatments (1-5 weeks with N compared to control) for each GA, according to residual maximum likelihood (REML) followed by LSD test.

  biological replicates.Observation of GFP fluorescence GFP-RGA fluorescence was determined on 7 day-old RGA pro :GFP-RGA root tip, with a Zeiss LSM780 inverted confocal laser microscope with x20 objective. The GFP excitation and with the same modifications and intensity parameters. Root cell walls were stained with propidium iodide (10 µg/mL, Sigma).GUS analysesHistochemical detection of GUS activity was carried out on roots of 5-d-old CYCB1.2 pro :Dbox-GUS and gai-t6 rga-24 CYCB1.2 pro :Dbox-GUS seedlings grown in Ndeficient or nitrate conditions as indicated. Plant material was infiltrated in GUS solution (250 µg/ml 5-bromo-4-chloro-3-indolyl-ß-D-glucuronide (X-Gluc); 50 mM sodium phosphate pH 7; 1 mM potassium ferricyanide; 1 mM potassium ferrocyanide; 10 mM EDTA; 0.01% triton X-100) for 15 min and incubated at 37°C overnight. Then, the GUS solution was replaced with 100% (v/v) ethanol during 6 h at room temperature and kept in 70% (v/v) ethanol at 4°C. For root observations, 70% (v/v) ethanol was replaced with 0,24N HCl in 20% methanol during 15 min at 57°C. Then, this solution was replaced by 7% NaOH in 60% ethanol during 15 min at room temperature. Finally, seedlings were rehydrated with successive bath of 40%, 20% and 10% ethanol during 5 min each and kept in 5% ethanol 25% glycerol. Roots were observed in 50% glycerol using AxioImager Z1 (Zeiss) microscope.Root length, root meristem size and cell length analysesSeeds of wild-type (Ler) and global-DELLA mutant were surface sterilized in 70% ethanol for 10 min and plated on 1x MS modified medium without nitrogen[START_REF] Castillo | NIN-like protein7 and PROTEOLYSIS6 functional interaction enhances tolerance to sucrose, ABA, and submergence[END_REF] (Ref 30630200; bioWORLD plant media) supplemented with nitrate at the concentration indicated, and placed at 4°C at least 2 days to synchronize germination. Plates were then placed vertically in a growth chamber (22°C; 16h photoperiod). As global-DELLA mutant seeds germinate earlier than wild-type, the plates containing wild-type seeds were disposed in the growth chamber 8h before those containing global-DELLA mutant seeds. Seeds that have germinated synchronously (protrusion of the radicle) were marked (the other seeds were discarded) and root length was measured 7 days post-germination (DPG). Meristem size was expressed as the number of cells in cortex files from the QC to the first elongated cell exhibiting vacuolization. Measurements were performed at 3, 5 and 7 DPG by microscopy (AxioImager Z1, Zeiss) on at least 50 roots for each genotype. Length of differentiated root cortical cells was measured with Image J software version 1.48v (www.imageJ.nih.gov).[START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF] Name Sequence 5'-3'

  ∼70 µmol m -2 s -1 ), except for the analysis of the expression of GA metabolism genes, for which the plants were grown in continuous light at 22°C. The seeds were surface sterilized in 70% ethanol for 10 min and stratified at 4°C for at least 2 days to synchronize germination before sowing. In soil, plants were grown in pots on a mix perlite/vermiculite (1/2 v/v) completed with 5% soil under long day photoperiod (16h light at 21°C / 8h dark at 18°C). The pots were watered once a week with 5 ml of 1x MS modified medium without N supplemented with KNO 3 as indicated (K + were adjusted with KCl).BO 3 , 3.6 mM MnCl 2 4 H 2 O, 16 µM Na 2 MoO 4 2 H 2 O, 5 mM KCl and 770 µM ZnCl 2 . The 1x Letcombe modified solution (+N) is set up as following: 1.5 mM Ca(NO 3 ) 2 4 H 2 O, 5 mM KNO 3 , 2 mM NaNO 3 , 1mM MgSO 4 7 H 2 O, 1 mM KH 2 PO 4 , 25 µM

	or N-solution. N was sequentially withdrawn week after week over a time scale of 6 weeks
	until booting stage.
	Immunoblot analyses
	Seedling roots or shoots were ground in 2x SDS-PAGE sample buffer followed by boiling for
	5 min. After centrifugation, the protein extracts were fractionated on a 8% or 10% SDS-
	(Ref 30630200; bioWORLD PAGE gel and blotted onto membrane. Immunoblots were performed using a 2000-fold
	plant media) supplemented with an adequate KNO 3 concentration or 0.5 mM glutamine (as dilution of anti-RGA (Agrisera) or anti-GFP (Clontech), and a 5000-fold dilution of
	indicated in the figures), 0.5 mM NH 4 -succinate, 1% sucrose and 1% ultrapure agar (Merck) peroxidase-conjugated goat anti-rabbit or mouse IgG (Molecular Probes). Signals were
	or 1% type A agar (Sigma) under long day photoperiod (16h light at 22°C / 8h dark at 22°C, detected with Fusion FX (Vilber) using the Luminata Forte Western HRP Substrate
	(Millipore) or Clarty Max TM Western ECL substrate (Biorad). The blot was subsequently probed with anti-cdc2 (PSTAIRE) antibody (Santa Cruz Biotechnology) for loading control or stained with Coomassie blue. Quantification of the signals was performed using ImageJ irradiance conditions of Wheat Rht-1 tall, Rht-B1c and Rht-D1b seeds were stratified at 4°C for four days and sown in package version 1.48v (www.imageJ.nih.gov). 57
	pots containing a mix perlite/vermiculite (1/2 v/v) supplemented with 5% soil under long day
	photoperiod (16h light at 20°C / 8h dark at 15°C). The pots were watered three times a week
	with 13 ml of 1x Letcombe modified nutrient solution without N (N-deficiency condition) or
	with nitrate (N+ condition; 1.5 mM Ca(NO 3 ) 2 , 5 mM KNO 3 and 2 mM NaNO 3 ). The
	Letcombe micronutrients 1000x solution encompasses 160 µM CuSO 4 5 H 2 O, 160 µM CuCl 2
	2 H 2 O, 9.2 mM H 3 FeNaEDTA, and added with 1 mL/L of Letcombe micronutrients 1000x. Meanwhile, the 1x
	Letcombe modified solution (-N) is set up as following: 1.5 mM CaCl 2 , 5 mM KCl, 2 mM
	NaCl, 1mM MgSO 4 7 H 2 O, 1 mM KH 2 PO 4 , 25 µM FeNaEDTA and completed with 1 mL/L
	of Letcombe micronutrients 1000x.

For N withdrawal experiment, the seeds were sown on sand/perlite pots and watered three times per week. The first week, all plants were watered with N+ solution, then with either N+

Acknowledgments

We thank Tp. Sun for providing seeds of RGA pro :GFP-RGA, J. Leon for nia1 nia2 mutant, A.

Krapp for

nlp7.1 mutant and the NASC for CYCB1;2 pro :Dbox-GUS and nrt2.1-2 mutant. This work was supported by the Centre National de la Recherche Scientifique and the French ministry of research and higher education. B.G. was supported by a studentship from the Lawes Agricultural Trust. A.P. and S.T. were supported by Institute Strategic Programme grant BBS/E/C/000I0220 from the Biotechnology and Biological Sciences Research Council of the UK. PH was supported by The Czech Science Foundation (grant Nos 18-10349S and 20-17984S) and the European Regional Developmental Fund Project "Centre for Experimental Plant Biology" No. CZ.02.1.01/0.0/0.0/16_019/0000738.

Author contributions

All the experimental work, except GA quantifications and Figures 6E and6F, was performed by L.C., L.J., L.S.A, J.M.D and P.A. GA quantifications were performed by B.G., E.C., J.K., D.H., S.G.T., P.H. and A.L.P. Experimental work shown in Figures 6E and6F was performed by B.G., S.G.T., P.H. and A.L.P.

Declaration of interests

The authors declare no competing interests.

STAR Methods

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact Patrick Achard (Patrick.achard@ibmp-cnrs.unistra.fr).

Materials availability

Transgenic plant seeds generated in this study are available from the Lead Contact on request.

Data and Code Availability

• All data reported in this paper will be shared by the lead contact upon request.

• This paper does not report original code.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Experimental model and subject details

Arabidopsis (Arabidopsis thaliana) lines were in the Columbia-0 (Col-0) and Landsberg erecta (Ler) backgrounds, and the wheat near isogenic lines were in the cultivar Cadenza, as detailed in the Key resources table. Arabidopsis and wheat were grown in controlled growth conditions, as described in Method details.

Method details

Plant material and growth conditions

Mutants and transgenic lines in Arabidopsis were derived from Landsberg erecta (global DELLA; ga20ox1 (formerly ga5); gai-t6 rga-24; RGA pro :GFP-RGA) or Columbia-0 (nia1 nia2; nrt2.1-2; nlp7-1; CYCB1,2 pro :Dbox-GUS) ecotypes. To generate gai-t6 rga-24 CYCB1,2 pro :Dbox-GUS, the CYCB1,2 pro :Dbox-GUS (Col-0 ecotype) was crossed to gai-t6 rga-24 (Ler background) to obtain an F1 population. The F3 plant was selected and then backcrossed one time into CYCB1,2 pro :Dbox-GUS Col-0 genetic background. Two independent gai-t6 rga-24 CYCB1,2 pro :Dbox-GUS homozygous lines (#7 and #18) were used in the study. Wheat near isogenic lines (cv Cadenza) containing Rht-D1b and dwarf Rht-B1c

alleles were used in this study. The Rht-B1c allele was introduced from cultivar Mercia. [START_REF] Plackett | Analysis of the developmental roles of the Arabidopsis gibberellin 20-oxidases demonstrates that GA20ox1, -2, and -3 are the dominant paralogs[END_REF] The GA contents in Arabidopsis seedlings grown in liquid MS modified medium without nitrogen and supplemented with indicated nitrate concentrations (Figures 4B and5D) and in the primary internode of 3-week-old wheat grown perlite/vermiculite supplemented with Letcombe modified nutrient solution (Figure 6C) were determined by ultra-high performance liquid chromatography-mass spectrometry (UHPLC-MS) using a Q-Exactive spectrometer (Orbitrap detector; ThermoFisher Scientific). Dry grounded material was suspended in 80% methanol-1% acetic acid including 17-


Edgar Chávez

Nathalie Mitton

Héctor Tejeda

Routing in Wireless Networks with Position Trees

Keywords: Location aware routing, virtual coordinates, wireless sensor networks

Sensor networks are wireless adhoc networks where all the nodes cooperate for routing messages in the absence of a fixed infrastructure. Non-flooding, guaranteed delivery routing protocols are preferred because sensor networks have limited battery life. Location aware routing protocols are good candidates for sensor network applications, nevertheless they need either an external location service like GPS or Galileo (which are bulky, energy consuming devices) or internal location services providing non-unique virtual coordinates leading to low delivery rates. In this paper we introduce Position Trees a collision free, distributed labeling algorithm based on hop counting, which embed a spanning tree of the underlying network . The Routing with Position Trees (RTP) is a guaranteed delivery, non-flooding, efficient implicit routing protocol based on Position Trees. We study experimentally the statistical properties of memory requirements and the routing efficiency of the RPT.

Introduction

Sensor networks are wireless networks where all the nodes cooperate for routing messages in the absence of a fixed infrastructure. Here the nodes are low cost with limited computational resources and limited battery life. A simple distributed routing algorithm with small memory overhead, and a small CPU demand is thus mandatory for such networks [START_REF] Hill | Mica: a wireless platform for deeply embedded networks[END_REF]. Typical applications of sensor networks are environment sampling, monitoring disaster areas, security and inventory management.

A route is a sequence of nodes forwarding messages from the source node to the target node. The deployment of new applications in sensor networks heavily relies on the efficiency of route discovery mechanisms. Some (actually deployed) sensor networks use query distribution and data collection based on a model known as data diffusion [START_REF] Intanagonwiwat | Directed diffusion: a scalable and robust communication paradigm for sensor networks[END_REF]. In this model, a sink node has a permanent connection with an outside network (e.g. the Internet or some wired network) and performs most of the data analysis, while the other nodes are only used for data acquisition or for simpler data processing. Several protocols have been proposed to express queries over the data sensed by the nodes and to aggregate them [START_REF] Madden | TAG: a tiny aggregation service for ad-hoc sensor networks[END_REF]. These concepts require support of efficient and robust routing protocols, more powerful than those used to support data diffusion.

Position awareness in sensor networks has improved the efficiency of route discovery and broadcasting algorithms in both power saving and latency measures. The fundamental idea behind position awareness (referred also as geographic or geometric information) is to provide each node in the network with a label having global information. This information is obtained through devices such GPS or Galileo. Routing protocols based on geographic coordinates of the sensors have revealed to be a very competitive alternative to the classical routing protocols for wireless ad hoc networks, reactive [START_REF] Johnson | Ad Hoc Networking, DSR The dynamic source routing protocol for multihop wireless networks[END_REF][START_REF] Perkins | Ad hoc On-demand Distance Vector Routing[END_REF] or proactive [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF].

Our contribution is a collision-free labeling algorithm based on the uniqueness of a path in a tree. This leads to a non flooding, guaranteed delivery routing protocol (as long as the nodes in the path does not vanish while the packet is in transit). Our routing algorithm presents the same good properties as classical geographical routing, yet it outperforms them, as shown with thorough experimentation, and they don't rely on external location services.

The rest of this paper is organized as follows. Section 2 reports geographic routing over virtual coordinates in literature. Section 3 describes our contribution: the Routing with Position trees (RPT). Simulation results are reported in 4 and Section 5 sketches some conclusions and future work.

Related Work

When nodes are aware of their geographic coordinates (for instance by the use of a GPS), a geographic routing based on these coordinates is feasible. The greedy approach is called Most Forward Routing (MFR) [START_REF] Takagi | Optimal transmission ranges for randomly distributed packet radio terminals[END_REF]. In MFR, the source node forwards the message to the node that is closest to the destination. This is a simple localized algorithm that does not guarantee delivery. A package can be trapped in a local minimum and the algorithm fails to find a path to the destination leading to low delivery rates. In dense networks the algorithm performs well. Other geographic approaches have then been proposed in order to minimize the energy consumption [START_REF] Kuruvila | Progress and location based localized power aware routing for ah hoc sensor wireless networks[END_REF] or to guarantee delivery [START_REF] Frey | On delivery guarantees of face and combined greedyface routing in ad hoc and sensor networks[END_REF][START_REF] Li | Hybrid greedy/face routing for ad-hoc sensor network[END_REF]. The face routing algorithm [START_REF] Frey | On delivery guarantees of face and combined greedyface routing in ad hoc and sensor networks[END_REF] is generally used to overcome the local optima trap problem of the greedy approach MFR. This is performed by extracting a planar subgraph of the network and forwarding the package through the faces. This geographic approaches assume that all nodes are equipped with a GPS, which can become energy-costly and expensive. Moreover, GPS work only in out-door environments.

In order to reduce the cost, one can also equip only a subset of the nodes with a GPS and use these special nodes like in [START_REF] Ermel | On selecting nodes improve estimated positions[END_REF][START_REF] Capkun | GPS-free positioning in mobile ad-hoc networks[END_REF] to infer the position of the remaining nodes. In such case it suffices to know the distance relative to the special nodes using techniques such as time difference of arrival [START_REF] Priyantha | The cricket compass for context-aware mobile applications[END_REF], angle of arrival [START_REF] Niculescu | Ad hoc positioning system (APS) using AOA[END_REF], or signal strength [START_REF] Niculescu | Ad hoc positioning system[END_REF]. Once the position of every node in the network in estimated one can use, in theory, any geographic routing algorithm. These approaches introduce, however, drawbacks to the geographic routing. It is possible, for example, that two nodes obtain the same coordinates leading to delivery failures.

Other approaches rely exclusively on the relative distances (or hop counting) to a set of nodes in the network, without the intervention of external location services. The general idea is to define a virtual coordinate system and use it to induce a routing protocol based on the virtual coordinates. We survey some of them below.

The authors of [START_REF] Caruso | GPS free coordinate assignment and routing in wireless sensor networks[END_REF] introduce VCap (Virtual Coordinate assignment protocol ) to support geographic routing. A system of virtual coordinates based on three landmarks is proposed. Nodes are assigned a triplet of coordinates given as the number of hops the node is distant from each landmark. A more accurate coordinate system can be established as the number of landmarks increases [START_REF] Benbadis | Enhanced hop-count positioning in sensor networks using multiple coordinates[END_REF]. Then, nodes use a greedy routing, like in MFR, based on the Hamming distance computed on these coordinates (instead of the Euclidean distance in the original MFR). The storage overhead for each sensor is limited to the storage of its coordinates and the coordinates of its neighbors. If the routing reaches a node v with a local minimum, they give a local detour rule which consist in locally flooding within a finite neighborhood. A similar idea is presented in [START_REF] Fonseca | Beacon vector routing: Scalable point-to-point in wireless sensornets[END_REF] with different tie break and recovery mechanisms. Another approach also based in hop counting is presented in [START_REF] Cao | A scalable logical coordinates framework for routing in wireless sensor networks[END_REF] where loops are avoided recording the moving history, a time to live for dropping packages and elaborate tie break and recovery mechanisms. A different approach is used in [START_REF] Fang | Glider: gradient landmark-based distributed routing for sensor networks[END_REF] where landmarks are selected more carefully after partitioning the nodes into tiles, and elaborate gradient descent procedures are used to route packets, and high communication and storage overhead is required to increase the delivery rate.

All these geographic routings relying on virtual coordinates use landmarks and the number of hops each node is distant from each landmark to compute node coordinates. None of them guarantees delivery, unless significantly increasing the resource consumption (e.g. by flooding the network). The core problem of such routing is the amount of reference points needed to produce a unique reference framework. With hop counting, the labels or identifiers obtained are not unique while the routing algorithms rely on the uniqueness of the labels. The authors of [START_REF] Wattenhofer | Geometric routing without geometry[END_REF] studies the number of these reference points needed to avoid duplicate labels. The main result states that the number of beacons needed to get the set fixed is linear on the number of nodes, hence a logical coordinate system must use O(n) such reference points, and consequently must use O(n) space to store the labels. Our result is in line with the bounds given in [START_REF] Wattenhofer | Geometric routing without geometry[END_REF] for nodes in general position. The key difference is that we encode the labels in a different way, using only O(log n) space to represent each label.

In this paper, we propose a geographic routing algorithm based on virtual coordinates.

We use the uniqueness of a path in a tree to assign labels to nodes and assure the labels uniqueness. As far as we know, this approach using this tree feature has only been used in [START_REF] Mitton | Distributed node location in clustered multi-hop wireless networks[END_REF] but it can be used only over a clustering structure.

3 Routing with Position Trees (RPT)

Position Tree Routing Algorithm

Basic Idea In this paper, we propose a geographic routing algorithm based on virtual coordinates. The objective of a logical coordinate system is to fix all the nodes in a network making it invariant under rigid transformations. This is a theoretical requirement motivated by the observation that a dynamic routing algorithm must handle the packet to the next hop using only local information. If two nodes share the same description, then a local and deterministic decision can lead to only one route (unless the packet is divided, i.e. flooding the network), hence one of the nodes will not receive the packet. In a geographic routing using an external positioning service for each node, the network is fixed in the sense above. Our goal is then to fix the network in the sense above by using an internal positioning service while requesting the smallest amount of memory at each node.

Firstly we select and arbitrary root node and label hierarchically from root to child nodes (child nodes are all the unlabeled neighbors of the current root). Child nodes inherit their parent's label plus an extra number. Hence, the path from the root to each node is encoded in the label. A node's label is built from left to right, and it describes the lineage of the node. The size of the label is proportional to the length of the path from the nodes to the root, and is bounded by the height of the tree (O(log n) on the average if the tree is balanced).

The labeling is hierarchical. The root node arbitrarily enumerates its neighbors, it can even skip a neighbor (following an arbitrary enumeration heuristic optimizing an external goal). As a result of this observation, we can build a virtual topology that can be unrelated to the physical topology of the network, optimizing external goals (e.g. the reliability of the nodes), and the correctness of the algorithm will not be compromised.

Labels are thus used to perform an interval routing over the tree. Interval Routing was introduced in wired networks by Santoro and Khatib in [START_REF] Santoro | Labelling and implicit routing in networks[END_REF] to reduce the size of the routing tables. It is based on representing the routing table stored at each node in a compact manner, by grouping the set of destination addresses that use the same output port into intervals of consecutive addresses. The main advantage of this scheme is the low memory requirements to store the routing on each node u: O(δ(u)). The routing is computed in a distributed fashion with the following algorithm: at each intermediate node x, the routing process ends if the destination y corresponds to x, otherwise, it is forwarded with the message through an edge labeled by a set I such that y ∈ I. The algorithm is shown to be optimal for acyclic graphs, and it exhibits a worst-case complexity which is a factor of two from the optimal solution for an arbitrary topology.

For naming nodes, authors of [START_REF] Santoro | Labelling and implicit routing in networks[END_REF] construct a minimum-distance spanning tree and traverse in depth-first style assigning a distinct integer to each node. In our algorithm, this step is not necessary. For assigning labels to the neighbors, they use the spanning tree, in our case we use all the neighbors that are enabled, and this step is done locally. They gave some limitations when nodes are added o deleted, and with permanent disconnections a new tree must be constructed.

Finally, since we use only the neighborhood relationship both when labeling the nodes and routing packages, without additional hypothesis, it is possible to route in any arbitrary network, in particular in three dimensions.

Assumptions We consider a sensor network composed of nodes uniformly scattered. The nodes are assumed static, or with a very low mobility with respect to the signal propagation speed. We assume that every node has a unique ID.

Once each node is labeled, the routing task can be run. To send a message to a destination node u, a node v needs to know the label of node u. It thus need a locating protocol such that [START_REF] Blazevic | Anchored path discovery in terminode routing[END_REF][START_REF] Mitton | Distributed node location in clustered multi-hop wireless networks[END_REF] which retrieves a node label from its identity. We do not consider this locating part in this paper and assume that there exists such a locating service available in the network. Note that this service is required for any routing protocol.

Labeling the nodes The labeling process is very simple. First, a node of the network is chosen to be the "root". It is labeled as the root R. The root node can be selected randomly, or with some heuristic. The selection of the root is not central to the correctness of our algorithm, although different selections will produce different dilations in a given path.

The root R advertises all its neighbors that they are the root's children. For it, it broadcasts a "Discovery" request. Each neighbor of R answers the root node by sending a "Tag Request" message containing its ID. Since this is the root which instances the labeling process, none of its children has already been labeled. The root sorts the ID of its children and is then able to assign a label to each of them. Labels are of the form Rm where m is a positive integer chosen by R, according to the children sort of R.

Once a node u has received its label, it is ready to name its own children in a similar fashion. Node u broadcasts a "Discovery" request to its neighbors. Only the ones of them which have not been labeled by another node answer with a "Tag Request" message. Parent node u sorts the ID of its non-tagged neighbors which become its children in the labeled tree. Node u assigns them a label. If the parent's label is a string s, its children's labels will be obtained by appending a positive integer to s. Since in wireless environments, a transmission by each node reaches all nodes within radius distance from it, node u can send the labels of all its children in only one message instead of sending one message per neighbor node.

This process is iterated until all the nodes in the network have been labeled. Once this happens, we must tell the root the labeling process is done. When a node becomes "childless", that is, all its neighbors are either been labeled or tagged by other nodes, it sends its parent a message informing it that its descendants have been completely determined. When a parent node has received similar messages from all its children, (e.g all descendants have been determined), it advertises its own parent, until the root gets the message from all its children. At that time, all the nodes of the network have been labeled. Figure 1 illustrates the labeling process over an arbitrary topology. Dark lines represent the links in the tree. Dashed lines are the wireless links which have not been selected to be part of the tree during the labeling process.

Storage requirements Once every node is tagged, the routes are computed and the network is ready for routing. The nodes need to store just their own label. As we will see below, nodes do not even need to store their neighbor's labels.

Sending a Packet Once the labels are in place, sending a packet through the network is almost trivial, because the labels define a canonical a path joining any pair of nodes.

Let's suppose node A wants to send a packet to node B. The packet is forwarded up the tree to find the least common ancestor of A and B and then down the tree until finding node B. All the forwarding decisions are made locally, without flooding. To fix ideas, suppose A is labeled R167895 and B is labeled R16774232, the largest common prefix is R167 which corresponds to the least common ancestor of A and B. By broadcasting the source and destination labels there is only one node, labeled R16789, which will forward the packet. This process is repeated with the sequence A = R167895, R167789, • • •, R167 (being the last one the common ancestor) and from there the packet is forwarded to the nodes with unique labels R1677, R16774, • • • , R16774232 = B to reach node B. The up tree forwarding could be an empty step if the source/destination is the least common ancestor of the destination/source respectively.

The above sketch of the routing protocol is as simple as the actual routing protocol. The actual implementation may rewrite the source in each step. In this case the current node will broadcast the new source, and only the new source node will forward the message rewriting the packet each time.

To illustrate this routing scheme, let's take the tree plotted on Figure 1. Let's suppose node R211 wants to send a message to node R11. The message will follow the path R211 -R21 -R2 -R -R1 -R11. But when node R21 forwards the message, nodes R211, R12 and R2 receive it whereas only node R2 needs to forward it. In this case R is the least common ancestor between the destination R211 and R11.

Analysis

Message complexity The total number of messages needed to label the nodes is linear in both the number of nodes and the total number of connections. To label its children, each node broadcasts a "Discovery" message, contacting at the same time all its neighbors. We thus generate N messages where N is the number of nodes in the network. After all unlabeled children reply to their parent, the parent node sends a unique message for the totality of its children giving them their corresponding labels. We thus generate N 1 messages where N 1 is the number of internal nodes in the labeled tree. To finish the labeling process, each node must inform its parents when all its children are tagged or if it is a leaf in the labeled tree. Hence the total number of messages is N -1 (the root node does not need to send this message). Hence the total number of these messages is thus 2N + N 1 -1 Memory complexity Let t be the length of the longest path which starts at the root. The longest possible label has as many entries as t, so the largest possible amount of memory to store a label is t. The length of the path is t = O(n) in worst case and t = O(log(n)) if the tree is balanced. If a balanced tree can be found by e.g. selecting a node in the center, then the size of each label will be O(log(n)).

Enhancements

Improving the routing paths Since there is a single path in the tree from the source to the destination, and since the length of this path can be computed before the actual packet forwarding begins, multiple trees may help to discover more efficient routes. It also provides a simple way to recover from vanishing nodes or congestion problems. A way to improve our routing algorithm is to multiple roots to produce orthogonal labels (a vector of labels) and thus get a robust algorithm.

When running the routing algorithm from node A to B, every nodes' labels are compared and the couple of labels minimizing the path length (e.g. the ones which has the greatest common prefix) is chosen.

Nevertheless, maintaining several trees imply more memory requirements and more computations at each node. Yet, there is a trade-off to study between the number of roots and the node resource requirements.

Shrinking the paths Below the logical path defined by the label tree, there could be many physical connections (dashed links in Figure 1), defining a path shorter than the shortest path in the label tree. For example, in Figure 1, if the source node has label R11 and the target node has label R21, the shortest path in the tree would be R11 -R1 -R -R2 -R21. Since nodes R1 and R2 are neighbors, then we can avoid the upper part of the path.

A simple way to discover this shorter route is by examining the labels. Indeed, by examining the label, a node can compute the length of the path in the tree between itself and the destination. If R is the least common ancestor for nodes R1 and R211, the length of the path in the tree from R1 to R211 is equal to the length of the path from R to R211 more the length of the path from R to R21. Yet, the length of a path from node R and one of its descendant (R1 or R211) is equal to the difference between the size of the labels. R has size 1. R1 has size 2 (R and one integer), R211 has size 4 (R and 3 integers), thus hop distance in the tree from R1 and R211 is 4 ((2 -1) + (4 -1). Hence , a node is able to determine whether the path going through it is smaller than the one following the tree and thus decide whether directly forward the message. This will imply a slight modification of the routing algorithm because the shortcut node need to inform that he will be forwarding the message.

Experimental Results

We used our own C simulator assuming an ideal MAC layer, i.e. no interferences and no packet collisions. The nodes were randomly deployed in a 1 × 1 square using a Poisson Point Process (node positions are independent) with different intensity λ (λ represents the mean number of nodes per surface unit). These nodes have the same transmission range, R, therefore, two nodes are connected by an edge if and only if their Euclidean distance is at most R (assuming a Unit Disk Graph [START_REF] Clark | Unit disk graphs[END_REF]). If there exists a link between nodes u and v, we say that nodes u and v are neighbors. We note δ(u) the degree of node u, i.e. the number of neighbors of node u. With such a Poisson node distribution, we have λπR 2 = δ. All results obtained are within a 95% -confidence interval.

Tree Features

First, we are interested in the intrinsic characteristics of the tree the routing is based on. We regard the mean tree depth. Indeed, the mean tree depth gives the latency needed to build the labeled tree. The labels are computed from the tree building and the deeper the tree, the bigger the maximum label size. Since each node only need to store its own label for routing, the maximum label size gives the memory requirements at each node. Tree depth gives a measure for the latency and for the memory requirements. We also computed the average number of messages sent per node for building the tree. This is proportional to the energy cost for building the tree.

First, we run simulations with fixing R to 0.10 with increasing λ. In this way, we can observe the behavior of the tree when the node degree increases while the network diameter remains constant. Figure 2 clearly shows that the parameters are independent of the node degree. This is a consequence of the building process, where each parent node sends only one message for its whole neighborhood, whatever its size. Furthermore, since a node only stores its own label, the memory requirements neither increase. We can thus deduce that when the number of nodes increases in a bounded environment, our labeling protocol scale well since it neither send more messages nor increase the storage needs. We then consider 2 densities: low (mean node degree 8), and dense (degree 15). For each density, we make λ increase, and consequently the number of nodes increase, as well as the network diameter. Figure 3 shows the results. As expected when the network diameter increases, the tree also growths and thus, more memory is required at each node for storing labels. The number of messages sent remains very low and tends toward a constant asymptote. Simulation results match with the analysis of Section 3.2. The tree depth and the label size are in O(log(n)). Please note that we are using a random root node.

Routing evaluation

We compared our algorithm RPT to other geographic routing protocols. Firstly we compared RPT with MFR [START_REF] Takagi | Optimal transmission ranges for randomly distributed packet radio terminals[END_REF] and VCap [START_REF] Caruso | GPS free coordinate assignment and routing in wireless sensor networks[END_REF]. MFR uses geographic coordinates provided by a satellite receiver like GPS. MFR is thus more expensive than RPT in terms of equipments. Nevertheless, it provides routes with small number of hops and thus gives us a reference point. VCap uses virtual coordinates computed from landmarks nodes. Up to the best of our knowledge, this protocol gives the better results in terms of coordinates computing complexity and success rate among existing routing protocols based on virtual coordinates, Note that RPT requires the smaller amount of memory. On can also notice that RPT needs less message exchanges than VCap.

We run the simulation using the routing algorithms for the same samples of node distribution. We considered 2 densities: low (average node degree 8) and dense (average node degree 15). For each density, we make λ increasing, and hence increasing both, the number of nodes increased and the network diameter.

To implement VCap, we use 5 landmarks selected from shows the success rate of the protocols studied. As expected, our protocol achieves a 100% of success, and far outperforms the other protocol based on labels (VCap) but also the geographic routing protocol MFR. Since we use a spanning tree of the network, routes are not optimal. We are thus interested in how far the routes provided by RTP are from the optimal. Figure 4(b) plots the average path length of RTP and MFR, MFR providing optimal paths. Since VCAP succeeds only for small paths, its average path length is not significant and we do not consider it in this figure. As expected, the average path length increases as the nodes have less neighbors. When comparing our algorithm vs. shortest paths (MFR), we can observe that the stretch factor is constant, which allows our algorithm to scale with an increasing network diameter.

We guess that the average path length provided by RTP could be greatly improved, particularly in dense networks, with the use of shortcuts as explained in Section 3.3. We keep this experimental analysis for future work.

We also compared RPT with other geographic routing algorithms that guaranteed delivery like Greedy Face Greedy (GFG) [START_REF] Frey | On delivery guarantees of face and combined greedyface routing in ad hoc and sensor networks[END_REF][START_REF] Li | Hybrid greedy/face routing for ad-hoc sensor network[END_REF]. Since the path length depends on the planar subgraph extracted, we compared RPT with RNG [START_REF] Toussaint | The relative neighbourhood graph of a finite planar set[END_REF], Gabriel Graph [START_REF] Gabriel | A new statistical approach to geographic variation analysis[END_REF], Morelia Graph [START_REF] Boone | Morelia test: Improving the efficiency of the gabriel test and face routing in ad-hoc networks[END_REF] and the virtual spanner [START_REF] Tejeda | A virtual spanner for efficient face routing in multihop wireless networks[END_REF][START_REF] Tejeda | Energy-efficient face routing on the virtual spanner[END_REF]. Please note that GFG relies on an external location service like GPS. We tested two different network densities for all the algorithms and we show the results in figure 5.

As Figure 5 shows, our RTP protocol outperform the GFG when regarding the length of the providing routes for any planarization method independently of the density.

Conclusions and Future Work

The label trees defined here are very similar to the coordinates reported in [START_REF] Ben-Asher | Ad-hoc routing using virtual coordinates based on rooted trees[END_REF], the key difference is the top-down construction of a single tree in our approach.

Our contribution also includes the investigation of statistical properties of the label trees. We showed our routing algorithm is very competitive when compared with other routing algorithms. It offers a very good trade-off between equipment cost, number of messages sent, stretch factor and memory requirement. In the extended version of this paper we will report a thorough comparison with other tree-based routing protocols. Below we enumerate some of the trends we may follow for future work:

-Assuming the nodes can adjust the transmission range we may try to build a tree that is least expensive in terms of the energy used for transmitting a package. As it is known that an optimal transmission radius can be found locally, we may choose edges that better approximate this radius. -Since the underlying structure for routing is a tree, it is natural to explore broadcasting, optimizing e.g. the energy used or the latency in reaching the entire network. In this case a similar technique can be used as in the above case. -For a fixed tree different root node selections may lead to different label sizes with impact in the amount of memory required for each node. The selection of a core node in a distributed manner is an interesting open problem. -It will be interesting to study the behavior of RTP in a non-ideal MAC layer. -The tree maintenance (i.e. taking care of vanishing nodes and the incorporation of new nodes to the network) is a challenging problem, we foresee some strategies based on the analysis of shortcuts in the tree, and the use of multiple roots where we need to balance the memory usage and the failure recovery (this also applies to the case of a non-ideal MAC layer).

We wish to thank the thorough review and suggestions of the anonymous referees who helped to improve the presentation.

Fig. 1 :

 1 Fig. 1: Labeling process. Dark links are links of the tree, dashed links are the wireless underling links.

Fig. 2 :

 2 Fig. 2: RPT characteristics for R = 0..

Fig. 3 :

 3 Fig. 3: Characteristics of the tree for δ = 8 and δ = 15.

Fig. 4 :

 4 Fig. 4: Routing Characteristics of the tree for δ = 8 and δ = 15.

12 Fig. 5 :

 125 Fig. 5: Average path length (in # of hops) for δ = 8 and δ = 12 for RTP and GFG using several planarization methods, for R = 0.25.

Table 1

 1 sums up the complexity in term of messages and storage overhead for these algorithms. N is the number of nodes in the network. L refers to the number of landmarks used in the VCap protocol.

		MFR	VCap	RPT
	Cost	GPS	N × L msg	2N + N1 msg
	Node memory	own coordinates	own coordinates	own coordinates
		neighbors' coordinates neighbors' coordinates

Table 1 :

 1 Comparative complexity