Abdelhak El Amrani

Ivan Couée

Richard Berthomé

Fanny Ramel

Gwenola Gouesbet

Cécile Sulmon

Abdelhak El

Involvement of polyamines in sucrose-induced tolerance to atrazine-mediated chemical stress in Arabidopsis thaliana

Keywords: ADC, Arginine Decarboxylase, AIH, Agmatine Iminohydrolase, ATAO, Amine Oxidase, Atz, atrazine, DAO, Diamine oxidase, DW, dry weight, Man, mannitol, atrazine herbicide, chemical stress, molecular regulations, polyamine dynamics, sucroseinduced tolerance

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Introduction

Adaptation of plants to challenging environments involves complex processes associating plasticity of gene expression, regulation of protein levels and activities, and physiological and developmental modifications. Signaling molecules play a central role in these adaptive mechanisms by converting the perception of environmental or endogenous cues into stress defence and repair processes. In addition to its major roles as carbon metabolite and as carbon transport molecule, sucrose (Suc) is now recognised to have important regulatory and signaling effects on transcriptional and posttranscriptional control of gene expression, not only in the context of plant development [START_REF] León | Sugar and hormone connections[END_REF][START_REF] Lastdrager | Sugar signals and the control of plant growth and development[END_REF], but also in the context of stress responses [START_REF] Loreti | A genome-wide analysis of the effects of sucrose on gene expression in Arabidopsis seedlings under anoxia[END_REF][START_REF] Couée | Involvement of soluble sugars in reactive oxygen species balance and responses to oxidative stress in plants[END_REF].

Most of the sugar signaling pathways studied by forward and reverse genetic approaches are related to general sensing of carbohydrates rather than to specific sensing of sucrose [START_REF] Jang | Hexokinase as a sugar sensor in higher plants[END_REF][START_REF] Ruan | Sucrose metabolism: gateway to diverse carbon use and sugar signaling[END_REF][START_REF] Li | Dynamic and diverse sugar signaling[END_REF]. Sucrose-specific signaling is indeed difficult to apprehend since sucrose is involved in active metabolic exchanges with hexoses, hexose phosphates and trehalose (Tiessen and Padilla-Chacon, 2013). Nevertheless, there is ample evidence that sucrose is perceived as a distinct sugar signal, which cannot be substituted by hexoses. Indeed, the existence of sucrose-specific signaling pathways can thus be indirectly established from several processes where equimolar amounts of glucose and fructose fail to induce the same responses as sucrose itself [START_REF] Li | Dynamic and diverse sugar signaling[END_REF].

Furthermore, when sucrose is externally supplied to aerial tissues, emergence of lateral roots is induced in Arabidopsis [START_REF] Macgregor | Root system architecture in Arabidopsis grown in culture is regulated by sucrose uptake in the aerial tissues[END_REF]. Application of sucrose to somatic embryos of spruce results in higher frequency of embryos without ectopic cell division [START_REF] Iraqi | Sucrose utilization during somatic embryo development in black spruce: involvement of apoplastic invertase in the tissue and of extracellular invertase in the medium[END_REF]. An Arabidopsis bZIP transcription factor gene (bZIP11) in a promoter-GUS reporter gene construct presented an expression specifically affected by sucrose, whereas other sugars, such as glucose and fructose, alone or in combination, are ineffective [START_REF] Rook | Sucrose-specific signalling represses translation of the Arabidopsis ATB2 bZIP transcription factor gene[END_REF]. Whole-genome transcript profiling also reveals that complex metabolisms, such as flavonoid and anthocyanin biosynthetic pathways, are strongly and specifically up-regulated following sucrose treatment (Solfanelli et al. 2006). At a whole plant level, manipulating the rates of synthesis, transport or degradation of sucrose affects plant growth, development and physiology (Wind et al., 2010). Finally, [START_REF] Loreti | A genome-wide analysis of the effects of sucrose on gene expression in Arabidopsis seedlings under anoxia[END_REF] have shown that exogenous sucrose, to a much greater extent than glucose, enhances anoxia tolerance of Arabidopsis seedlings, thus indicating that the specific regulatory effects of sucrose are relevant to environmental stress tolerance.

Soluble sugars have also been shown to confer to Arabidopsis plantlets tolerance to atrazine (Atz)mediated xenobiotic and oxidative stress [START_REF] Sulmon | Sugar-induced tolerance to atrazine in[END_REF][START_REF] Couée | Involvement of soluble sugars in reactive oxygen species balance and responses to oxidative stress in plants[END_REF][START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]. Binding of this widelyused triazine herbicide to the thylakoid D1 protein results in inhibition of photosystem II (PSII), by blocking electron transfer to the plastoquinone pool, thus leading to production of triplet chlorophyll and 1 O2 and therefore to massive oxidative stress, bleaching and plant death [START_REF] Rutherford | Herbicide-induced oxidative stress in photosystem II[END_REF]. In contrast, exogenous sugar treatment or natural variation of endogenous sugars result in a high level of tolerance to atrazine-mediated stress, with maintenance of chlorophylls, carotenoids, and D1 protein, and protection of photosystem II [START_REF] Sulmon | Sugar-induced tolerance to atrazine in[END_REF]Ramel et al., 2009aRamel et al., , 2009b)). The protective effects of sugar treatment could not be ascribed to mere carbon feeding of preexisting pathways or to carbon compensation of photosynthesis, and, as in the case of induction of tolerance to anoxic stress [START_REF] Loreti | A genome-wide analysis of the effects of sucrose on gene expression in Arabidopsis seedlings under anoxia[END_REF], exogenous sucrose was more effective than exogenous glucose [START_REF] Sulmon | Sugar-induced tolerance to atrazine in[END_REF]Ramel et al., 2009aRamel et al., , 2009b)). Moreover, analysis of the impact of natural variation of endogenous sugars showed that sucrose, rather than glucose or fructose, showed the highest correlation with xenobiotic and oxidative stress tolerance (Ramel et al., 2009b).

Induction of tolerance was associated with important modifications of gene expression related to photosynthesis and chloroplast biogenesis, to reactive oxygen species (ROS) defense and repair mechanisms, to cell death protection and to metabolic re-orientation, and seemed to result from complex interactions between sugar and xenobiotic signaling [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF](Ramel et al., , 2009a[START_REF] Ramel | Xenobiotic sensing and signalling in higher plants[END_REF]. The functional categories of these regulatory effects were in accordance with adaptive biochemical processes of atrazine tolerance, including thylakoid reorganization [START_REF] Mattoo | Adaptive reorganization of protein and lipid components in chloroplast membranes as associated with herbicide binding[END_REF] and ROS quenching and scavenging (Ramel et al., 2009a).

In the present work, characterization of sucrose-induced mechanisms of xenobiotic stress tolerance was carried out through a combination of transcriptomic, metabolic, mutant and exogenous treatment approaches under different conditions of atrazine exposure. Exogenous sucrose was thus found to differentially regulate genes involved in polyamine synthesis. Both ARGININE DECARBOXYLASE (ADC) paralogues, ADC1 and ADC2, which encode the rate-limiting enzyme (EC 4.1.1.19) at the beginning of the polyamine biosynthesis pathway [START_REF] Fuell | Polyamine biosynthetic diversity in plants and algae[END_REF], were strongly transcriptionally upregulated, in terms of transcript accumulation and promoter activity, by sucrose treatment in the presence of atrazine. The potential impact of this gene expression pattern was further characterized through the study of the quantitative variations of major polyamines (putrescine, spermidine, spermine), of xenobiotic stress responses of spe1-1 mutant affected in overall ADC enzyme activity [START_REF] Rook | Sucrose-specific signalling represses translation of the Arabidopsis ATB2 bZIP transcription factor gene[END_REF][START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF], and of the effects of exogenous treatments with varying levels of sucrose, putrescine, spermidine and spermine. The adaptive role that can be inferred from this interplay between sucrose, putrescine and spermine is discussed in relation with survival and anti-death mechanisms in the context of chemical stress exposure.

A C C E P T E D M A N U S C R I P T (Watson

Material and Methods

Plant material

Wild-type Arabidopsis thaliana accessions [Columbia (Col-0) and Wassilewskija (Ws) ecotypes] were obtained from the Nottingham Arabidopsis Stock Centre (NASC). Mutant with reduced activity of arginine decarboxylase [spe1-1 (Watson et al., 1998;[START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF]] was a kind gift from Professor Russell Malmberg (University of Georgia, Athens, USA). Arabidopsis pADC1::GUS and pADC2::GUS transgenic lines were previously described by El Amrani et al. (2002) andHummel et al. (2004a). Analysis of the ADC1 and ADC2 promoter activities were carried out on T3 homozygotic lines. Wild-type, mutant and transgenic lines were homogenized by single-seed propagation and were bulk-amplified prior to utilization.

Plant growth conditions

Seeds were surface-sterilized for 5-10 min in 50 % bayrochlore/50 % ethanol containing 0.05 % Triton X-100, rinsed twice in absolute ethanol and dried overnight prior to plating on Petri dishes under axenic conditions. After sowing, Petri dishes were kept at 4 °C for 48 h to break dormancy and homogenize germination. Germination and growth under controlled conditions in vertical Petri dishes were carried out at 22 °C under a 16 h light period with a light intensity of 85 µmol m -2 s -1 . Standard growth media consisted of 0.8 % agar in 0.5X or 1X Murashige and Skoog (MS) basal salt mix (Sigma, St. Louis, MO, USA), pH 5.8. Sucrose (Suc) treatment medium consisted in standard growth medium containing from 15 to 80 mM sucrose. For transcriptomic analysis, sucrose treatment (80 mM) was compared with a control medium consisting in standard growth medium containing 80 mM mannitol (Man) as osmoticum. Atrazine (Atz) treatment medium consisted in standard, Suc-containing or Man-containing growth medium in the presence of varying concentrations of atrazine, as indicated in the Results section. Prior to addition, atrazine was sterilized by microfiltration through 0.2 µm cellulose acetate filters (Polylabo, Strasbourg, France) and added axenically to the melted MS-agar medium. Polyamine treatments consisted in standard growth medium, in the absence or presence of sucrose, and in the presence of varying concentrations of putrescine (Put), spermidine (Spd) or spermine (Spm), as indicated in the Results section. Prior to addition, polyamines were dissolved in water, sterilized by microfiltration through 0.2 µm cellulose acetate filters (Polylabo, Strasbourg, France) and added axenically to the melted MS-agar medium. Atrazine, Put, Spd and Spm were purchased from Sigma (St. Louis, MO, USA). The various combinations and modalities of exogenous

Growth and photosynthetic parameters

At the end of the experiments, length of primary root and fresh weight of seedlings were measured.

Pigments were extracted by grinding shoots of four pooled seedlings in 80 % (v/v) acetone, and the absorbance of the resulting extracts was measured at three wavelengths: 663, 646, and 470 nm. Levels of chlorophylls in these extracts were determined from the equations given by [START_REF] Lichtenthaler | Determinations of total carotenoids and chlorophylls a and b of leaf extracts in different solvents[END_REF]. Results are given as the mean (±S.E.M.) of these determinations.

Determination of polyamines

Seedlings were harvested, immediately frozen in liquid nitrogen and then lyophilized. Polyamine analyses were performed on pools of whole seedlings, corresponding to at least five individual plants to reach the range of 1 to 10 mg dry weight (DW). Free amines were extracted and analysed, as their dansyl derivatives, by HPLC [column with reverse phase spherisorb ODS-2 (particle size 5 mm, 4.6x250 mm, Waters, Milford, USA), elution with methanol:water solvent gradient from 60 % to 95 % over 23 min, flow rate: 0.8 ml min -1 ] and spectrofluorimetry (365 nm and 510 nm as excitation and emission wavelengths respectively), as described in [START_REF] Hummel | Involvement of polyamines in root development at low temperature in the subantarctic cruciferous species Pringlea antiscorbutica[END_REF]. Amine levels were calculated as mean (±SEM) from measurements on three pools.

Microarray data

Gene expression data were extracted from previous transcriptomic profiling experiments [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF] registered as E-MEXP-411 in Array-Express (http://www.ebi.ac.uk/arrayexpress/). These transcriptomic experiments compared the RNA profiles of 1.02 development stage seedlings [START_REF] Boyes | Growth stage-based phenotypic analysis of Arabidopsis: a model for high throughput functional genomics in plants[END_REF] grown on standard growth medium and then transferred to control and treatment media consisting of various combinations of mannitol, atrazine and sucrose [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]. The transcriptomes of Arabidopsis seedlings transferred to control condition (Man, 80 mM mannitol), to condition of atrazine stress (Man-Atz, 10 µM atrazine in the presence of 80 mM mannitol), to condition of exogenous sucrose feeding (Suc, 80 mM sucrose), and to condition of stress tolerance to atrazine exposure (Suc-Atz, 10 µM atrazine in the presence of 80 mM sucrose) were compared after 24 h of treatment. The four conditions were compared pairwise, so that the complete analysis consisted of six comparisons. Differentially expressed genes were those genes showing a P-value ≤ 0.05 after Bonferroni's correction. Conversely, genes with a Bonferroni's P-value higher than 5 % were considered as being not differentially expressed (nde). Current annotations of genes were updated from The Arabidopsis Information Resource [START_REF] Lamesch | The Arabidopsis Information Resource (TAIR): improved gene annotation and new tools[END_REF].

Expression quantification of polyamine-related genes

Quantitative real-time reverse transcription-polymerase chain reaction (RT-qPCR) analysis was performed for 5 candidate genes on the same samples as those described in our previous work (Ramel et al., 2007). Each sample, corresponding to the Man, Man-Atz, Suc, Suc-Atz conditions described above, consisted in a pool of 3 independent biological replicates [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]. Primers were designed with Primer3 (http://fokker.wi.mit.edu/primer3/), with an optimal length of 21 nt, and an optimal temperature of 60 °C, and tested for their PCR efficiency, which ranged between 90 % and 99 % (Supplementary Table A1). Four independent cDNA synthesis reactions were realized. Reverse transcription was performed on 1 µg of total RNA with oligodT primer (18 mer) and the Superscript II Rnase H-reverse transcriptase (Invitrogen, Carlsbad, CA) according to the manufacturer's instruction.

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Three PCR replicates for each of the cDNAs were included in every run. Three template controls were included in every qPCR experiment. Quantitative PCR reactions were performed with SYBRGreen PCR master mix (Eurogentec, Seraing, Belgium). All reactions were performed using the ABI PRISM 7900 HT sequence Detection System (Applied Biosystem, Pleasanton, CA) as follows: 95 °C, 10 min; 40x (95 °C, 15 s; 60 °C, 1 min) and a dissociation step to discriminate primer dimers from the PCR product. Data were then analysed by using the SDS software provided by the manufacturer. Gene expression was quantified relative to the level of expression of the housekeeping genes ACTIN2 and RPN7 (Supplementary Table A1).

Histochemical analysis

Histochemical GUS staining was performed as described previously by [START_REF] Jefferson | GUS fusions: beta-glucuronidase as a sensitive and versatile gene fusion marker in higher plants[END_REF].

Transgenic pADC1::GUS and pADC2::GUS homozygous plants [START_REF] El Amrani | Genome-wide distribution and potential regulatory functions of AtATE, a novel family of miniature inverted-repeat transposable elements in Arabidopsis thaliana[END_REF] were grown as described above and stained for GUS activity at 37 °C during eight hours, in 50 mM potassium phosphate buffer, pH 7, containing 0.1 % Triton X-100, 10 mM K3Fe(CN)6 and 10 mM K4Fe(CN)6 to avoid diffusion of the intermediary reaction product. Plantlets were washed with 50 mM sodium phosphate buffer (pH 7) and then left in 70 % ethanol overnight.

Statistics

All results were given as the mean (±SEM). Statistical analysis was carried out with the Minitab version 17 software. Pairwise comparisons of means used Student's t-test and Mann-Whitney test.

Results

Genome-wide analysis reveals regulatory effects of exogenous sucrose on polyamine metabolism genes under conditions of atrazine xenobiotic stress

As previously characterised [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF](Ramel et al., , 2009a)), 10 µM atrazine treatment in the absence of sucrose induced complete bleaching of seedlings after 6-7 days of stress application, thus leading to seedling death within 8 days. In contrast, addition of exogenous sucrose during atrazine treatment allowed seedlings to maintain growth and development beyond 8 days of transfer [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF](Ramel et al., , 2009a)). Genome-wide analysis of gene expression through a CATMA approach was therefore carried out after 24 h atrazine treatment in the presence of exogenous Suc or Man as control. In this

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microarray experiment, atrazine and Suc showed important effects on transcriptome dynamics [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF](Ramel et al., , 2009a)), while global development and photosynthetic activity were slightly affected. The atrazine treatment that led to injury and plant death was associated with the repression of genes involved in protein translation and ROS defence. Conversely, the situation of sucrose protection against atrazine stress and injury was associated with activation of genes involved in transcription processes, cellular repair and protection, signal transduction, cellular communication, photosynthesis, and anti-ROS defence. Closer analysis of differentially-expressed genes reveals that, surprisingly, expression of genes involved in polyamine biosynthesis pathway showed differential patterns of response to Suc-Atz, Suc, and to Man-Atz treatments (Fig. 1A), specifically highlighting the contrasted patterns of expression of ADC genes. Indeed, the two ADC1 and ADC2 paralogues that encode the ADC enzymes at the start of the biosynthesis pathway were highly activated by exogenous sucrose in the absence or presence of atrazine, whereas atrazine in absence of Suc either induced or repressed significantly ADC genes. In particular, focusing on combined sucrose and atrazine treatment, ADC2 gene exhibited the strongest induction of expression, which was also confirmed by RT-qPCR (Fig. 1B). In contrast, expression of AGMATINE IMINOHYDROLASE (AIH) and N-CARBAMOYLPUTRESCINE AMIDASE (NLP1), as well as of SPERMIDINE SYNTHASE (SPDS) and SPERMINE SYNTHASE (SPMS) genes, which encode the enzymes involved in subsequent steps of, respectively, Put, and Spd and Spm synthesis, showed no significant variation, whether under conditions leading to injury and plant death or under conditions of sucrose protection (Fig. 1).

Moreover, one

Effects of exogenous sucrose on the regulation of ADC1 and ADC2 promoter activities in the presence of atrazine

The increase of ADC gene expression under conditions of sucrose-induced protection against atrazine injury was further analysed by a promoter::reporter gene approach. Promoter activities were studied in stable homozygous transformants harboring promoter::reporter gene fusions. Homozygous plants expressing GUS as reporter gene, under the control of ADC1 or ADC2 promoters, including the transcribed 5'UTR, were generated by El Amrani et al. (2002). Exogenous sucrose alone was found to induce significantly both ADC1 and ADC2 promoter activities (Fig. 2). In the presence of atrazine alone, promoter activities of both ADC1 and ADC2 were either not detected or at very low level. In Suc-Atz treatments, promoter activities were found to be positively correlated with the level of sucrose in a dose-dependent manner, as shown in Fig. 2. Particularly, ADC2 promoter exhibited, in such conditions, a stronger response than ADC1 promoter. Moreover, comparing ADC promoter responses

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observed under similar Suc treatment (25 mM) but in the absence and presence of atrazine, highlighted, as found in gene expression results (Fig. 1), a repressive effect of atrazine on ADC1 promoter activity, which was not observed for ADC2. These results strongly suggested that the ADC2 paralogue gene may play a major role under conditions of Suc-induced protection against atrazine injury. This was reinforced by the pattern of transcriptional activity of ADC2, which was more pronounced and generalized in both roots and shoots, whereas GUS staining was localized only in the aerial parts in pADC1::GUS transgenic lines. This important and specific regulatory effect of exogenous sucrose on ADC1 and ADC2 gene expression suggested that the dynamics of polyamine metabolism may be significantly affected under conditions of sucrose-induced protection against atrazine injury.

Impact of mutation affecting ADC enzyme activity on sucrose-induced atrazine tolerance

To analyse the physiological role of ADC activity in atrazine sensitivity and sucrose-induced atrazine tolerance, we determined the effects of reduced ADC activity on atrazine and sucrose responses in Arabidopsis spe1-1 mutant. This mutant, which has been previously described (Watson et al., 1998, Kasinathan and[START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF], exhibits decreased ADC activity. Leaves of spe1-1 have been shown to contain about one quarter of wild-type ADC activity (Watson et al., 1998) and reduced levels of both ADC1 and ADC2 proteins [START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF]. Whole plants of spe1-1 mutant also show perturbations of polyamine dynamics under salt stress conditions in comparison with wild-type plants ( [START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF]. spe1-1 mutant phenotype was analysed after 15 days of growth on atrazine and sucrose treatments. Under conditions of atrazine sensitivity (atrazine alone), spe1-1 seedlings exhibited the expected growth inhibition resulting from atrazine exposure (Fig. 3).

Moreover, growth in the presence of sucrose similarly led to the expected enhancement of root growth for this mutant. However, spe1-1 mutant exhibited contrasted phenotype in comparison to WT, under conditions of sucrose-induced protection against atrazine. Indeed, spe1-1 failed to develop atrazine tolerance despite the presence of exogenous sucrose (Fig. 3). Thus, the atrazine sensitivity of the spe1-1 mutant under conditions of sucrose treatment agreed with the involvement of ADC induction in sucrose-induced protection against atrazine.

Role of polyamine dynamics in atrazine sensitivity and sucrose-induced atrazine tolerance

In order to compare the differential dynamics of polyamines under conditions of atrazine sensitivity and sucrose-induced atrazine tolerance, Arabidopsis seedlings were exposed, during 15 days starting from germination, to a sublethal concentration of atrazine (0.5 µM) in the absence or presence of sucrose. Under conditions of sensitivity, Arabidopsis responses to atrazine were restricted to a strong increase of Spd levels (Fig. 4). In contrast, all the polyamines analysed were found to be highly responsive to exogenous sucrose, with Put, Spm, and Spd levels being significantly increased.

However, in the situation of sucrose-induced atrazine tolerance, atrazine specifically modulated

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sucrose-response patterns of the three polyamines. Whereas Spm levels were strongly decreased under atrazine tolerance in comparison to sucrose treatment, Put levels were found to be significantly increased. In contrast, endogenous concentrations of Spd remained unchanged. Sucrose-induced atrazine tolerance could thus be directly linked to differential regulatory effects of sucrose on the different steps of polyamine synthesis leading to increased level of Put and decreased level of Spm, and to induction of stress-tolerance and survival processes. In other words, it was tempting to hypothesise that sucrose-induced differential dynamics of polyamines may play a major role in alleviation, by sucrose addition, of the deleterious effects of atrazine.

Antagonistic effects of exogenously-applied putrescine and spermine on the responses to atrazine xenobiotic stress in the absence or presence of sucrose

Given the involvement of polyamine dynamics in atrazine sensitivity and sucrose-induced atrazine stress tolerance, we tested whether exogenous treatments with different polyamines (putrescine, spermidine, spermine) could have differential impacts on atrazine responses in the absence or presence of sucrose.

The effects of exogenous Put, Spm, and Spd on Arabidopsis atrazine sensitivity in the absence of sucrose were analysed under conditions of sublethal (0.5 µM) and lethal (1 µM) atrazine treatments (Fig. 5A). Considering primary root growth, Put and Spd exogenous treatments conferred, in the absence of sucrose, and after 15 days of growth, atrazine tolerance at least for the sublethal concentration. In contrast, Spm exposure increased atrazine sensitivity, with seedlings exhibiting at 0.5 µM atrazine the same length of primary root as that of 1 µM atrazine treatment (Fig. 5A). Such differential impacts resulting from exogenous polyamine treatments were associated with modifications of endogenous polyamine levels (Supplementary Figure A1). Indeed, Put, Spd, and Spm exogenous treatments were found to strongly induce their corresponding polyamine endogenous level in seedlings. Moreover, Spd and Spm treatments were also found to similarly increase endogenous levels of Put in comparison to control condition. Nevertheless, these increases remained lower than that observed under exogenous Put treatment. In the same way, Spm slightly increased endogenous Spd content.

The effects of exogenous polyamines on sucrose-induced atrazine protection were also tested by applying an additional step of 20 h of 1 mM polyamine pre-incubation treatment, in order to maximize polyamine-related regulations. After 5 days of treatment, plant growth and development were determined. In the presence of sucrose, roots (Fig. 5B), cotyledons and shoot meristem escaped atrazine injury and the first leaves appeared and underwent normal development (Supplementary Figure A2). Exogenous treatments with the three different polyamines resulted in strikingly different effects on sucrose-induced atrazine protection, in the same way as those observed under atrazine sensitivity conditions (Fig. 5). Thus, whereas exogenous Spd did not show any significant effect, exogenous Spm was found to prevent sucrose-induced atrazine tolerance and even enhanced atrazine-

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related stress with cotyledon bleaching after 5 days of treatment (Supplementary Figure A2). In contrast, exogenous Put significantly increased sucrose-induced root development in the presence of atrazine, with as much as a 25 % increase in comparison with sucrose plus atrazine treatment (Fig. 5B).

The specific effect of Put was further investigated under conditions of strong Put chemical priming.

Chemical priming was performed by pre-incubating 4 day-old seedlings for 20 h in standard growth medium containing 6 mM Put, whereas unprimed seedlings were pre-incubated in standard growth medium. Seedlings were then transferred on treatment media corresponding to 1 µM atrazine in the presence or absence of sucrose and Put, and were analysed after 18 days of growth (Fig. 6). Under conditions of atrazine exposure, high level of Put, in combination with sucrose, positively modulated several markers of sucrose-induced atrazine tolerance (fresh biomass, shoot chlorophyll contents, primary root growth; Fig. 6). Moreover, exogenous Put also activated lateral root formation in comparison with plantlets grown in the presence of sucrose without additional Put (Fig. 6C). Lateral roots are derived from the deep pericycle layer within parent root tissues [START_REF] Malamy | Organization and cell differentiation in lateral roots of Arabidopsis thaliana[END_REF], and the first stages of Lateral Root Primordia (LRP) are therefore an inconspicuous process.

Histological analysis of stage VI LRPs [START_REF] Malamy | Organization and cell differentiation in lateral roots of Arabidopsis thaliana[END_REF] showed that exogenous Put in combination with the presence of sucrose had therefore an important effect on LRP initiation and development under atrazine exposure, with an 8-fold increase in the number of LRPs per plantlet (Fig. 6C). Put was therefore shown to have specifically strong effects on atrazine responses, reducing atrazine sensitivity in the absence of sucrose (Fig. 5A), and enhancing sucrose-induced atrazine tolerance in the presence of sucrose (Figs. [START_REF] Jefferson | GUS fusions: beta-glucuronidase as a sensitive and versatile gene fusion marker in higher plants[END_REF][6], in sharp contrast with the negative effects of Spm (Fig. 5).

Discussion

Exogenous sucrose modifies polyamine dynamics under conditions of xenobiotic exposure through transcriptional regulation of ADC1 and ADC2 expression

Exposure to abiotic stresses such as drought, cold, heat, and pollutants, including herbicides and heavy metals, generally gives rise to excess accumulation of ROS [START_REF] Price | Plants under drought stress generate activated oxygen[END_REF][START_REF] Bowler | Superoxide dismutase and stress tolerance[END_REF][START_REF] Stohs | Oxidative mechanisms in the toxicity of metal ions[END_REF][START_REF] Schützendübel | Plant responses to abiotic stresses: heavy metal-induced oxidative stress and protection by mycorrhization[END_REF]Ramel et al., 2009a). Previous investigations showed that exposure to atrazine results in a typical situation of abiotic stress with increases of ROS production leading to plant death [START_REF] Rutherford | Herbicide-induced oxidative stress in photosystem II[END_REF]Ramel et al., 2009a). However, when exogenous sucrose is added or when endogenous sucrose increases, ROS accumulation is reduced (Ramel et al., 2009a(Ramel et al., , 2009b)). The molecular mechanisms involved in this process seem to be complex as condition of sucrose-induced atrazine tolerance specifically induced and repressed 1107 and 921 genes, respectively, compared with atrazine condition [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]. Comparison of different sugar feeding conditions, mutant analysis and the dynamics of ROS production show that sucrose enhancement of atrazine tolerance must be ascribed to regulatory and

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signaling effects, rather than to mere nutritional and metabolic effects [START_REF] Sulmon | Sugar-induced tolerance to atrazine in[END_REF][START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]Ramel et al. 2009a). This reflects the idea that sucrose plays pivotal roles as a signaling molecule.

Although no sucrose sensor has been identified yet, accumulating transcriptomic data have shown that sucrose specifically and dramatically affects plant development and stress tolerance by controlling a myriad of genes [START_REF] Loreti | A genome-wide analysis of the effects of sucrose on gene expression in Arabidopsis seedlings under anoxia[END_REF][START_REF] Solfanelli | Sucrose-specific induction of the anthocyanin biosynthetic pathway in Arabidopsis[END_REF][START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF]Ramel et al., , 2009a)).

The present study shows that genes involved in polyamine biosynthesis present a very contrasted pattern of differential expression under conditions of sucrose-induced atrazine tolerance. In particular, genome-wide transcriptomic analysis, gene expression quantification and promoter activity studies (Figs. 12) reveal that ADC1 and ADC2 genes are transcriptionally controlled by exogenous sucrose under conditions of atrazine exposure. The transcripts of ADC1 and ADC2 paralogues were greatly increased under conditions of sucrose-induced atrazine tolerance, and promoter::reporter gene approaches in homozygous transgenic plants expressing pADC1::GUS and pADC2::GUS further showed that this regulation was due to a transcriptional control. The corresponding ADC-catalysed reaction, which produces agmatine from arginine, is placed at the beginning of the polyamine synthesis pathway that leads to Put, Spd and Spm synthesis. In higher plants, Put can be produced by ADC-or Ornithine Decarboxylase(ODC)-catalysed reactions. However, no ODC-encoding gene was found in the sequenced genome of the model plant Arabidopsis thaliana [START_REF] Hanfrey | Arabidopsis polyamine biosynthesis: absence of ornithine decarboxylase and the mechanism of arginine decarboxylase activity[END_REF][START_REF] Liu | Polyamines function in stress tolerance: from synthesis to regulation[END_REF]. This is why, in Arabidopsis, the rate-limiting ADC-catalysed reaction represents the key connection between amino acid metabolism, putrescine production and polyamine metabolism.

On the other hand, in Arabidopsis and in other Brassicaceae species, the two ADC paralogues, generally called ADC1 and ADC2, exhibit complex patterns of differential expression and potential subfunctionalization (Hummel et al., 2004a(Hummel et al., , 2004b)). In Arabidopsis thaliana, induction of ADC2 is associated with osmotic stress, wounding, light, and salinity (Hummel et al., 2004a;[START_REF] Podlešáková | Phytohormones and polyamines regulate plant stress responses by altering GABA pathway[END_REF], whereas ADC1 is particularly responsive to chilling [START_REF] Podlešáková | Phytohormones and polyamines regulate plant stress responses by altering GABA pathway[END_REF]. The present work shows that, under conditions of xenobiotic exposure and potential stress, ADC2 was the most sucrose-responsive of the genes related to polyamine biosynthesis and was therefore likely to play an important role in the sucrose-and atrazine-dependent variations of polyamine levels (Fig. 4).

Moreover, ADC2 was found to be significantly more responsive to exogenous sucrose than ADC1 (Fig. 2), as has been shown to occur under conditions of optimal growth (Hummel et al., 2004a), thus reflecting important differences of regulation [START_REF] El Amrani | Genome-wide distribution and potential regulatory functions of AtATE, a novel family of miniature inverted-repeat transposable elements in Arabidopsis thaliana[END_REF] and suggesting substantial functional differences between ADC1 and ADC2.

At the protein level, analysis of the responses of spe1-1 mutant clearly showed that mutation decreasing both ADC1 and ADC2 protein levels and affecting global ADC activity (Watson et al., 1998;[START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF] led to an impairment of sucrose induction of atrazine tolerance (Fig. 3). This thus confirmed the adaptive importance of ADC gene expression and metabolic impact in such context of atrazine tolerance. In parallel with the regulation of ADC1 and ADC2 expression, carbon status (absence or presence of exogenous sucrose) and exposure to xenobiotic stress resulted in significant and antagonistic changes of polyamine levels in a differential manner, such as the increase of Put and the decrease of Spm (Fig. 4). Such differential dynamics demonstrated that additional regulations were active downstream of the ADC-catalysed step. In the case of atrazine exposure and of sucrose addition in the absence of atrazine, regulations of PAO and/or SAMDC gene expression (Fig. 1A), involved respectively in polyamine catabolism and in DcSAM production, could, at least in part, explain these differential dynamics. However, the weak responsiveness of non-ADC genes, and in particular of SPDS and SPMS genes, to the situation of sucrose-induced atrazine tolerance (Fig. 1) strongly suggested that, besides the transcriptional regulation of ADC1 and ADC2, the differential dynamics of Put, Spd and Spm was likely to depend also on post-transcriptional and post-translational regulations [START_REF] Chang | Characterization and translational regulation of the arginine decarboxylase gene in carnation (Dianthus caryophyllus L.)[END_REF][START_REF] Guerrero-González | uORF, a regulatory mechanism of the Arabidopsis polyamine oxidase 2[END_REF]. Thus, even though sucrose signaling is a complex and poorly understood process, the present work emphasises that sucrose addition can lead to sucrose-dependent regulations modulating polyamine dynamics in parallel with enhanced abiotic stress tolerance.

There is accumulating evidence that polyamines are involved in abiotic stress responses, senescence processes and programmed cell death [START_REF] Handa | Differential and functional interactions emphasize the multiple roles of polyamines in plants[END_REF][START_REF] Moschou | Polyamines and programmed cell death[END_REF][START_REF] Liu | Polyamines function in stress tolerance: from synthesis to regulation[END_REF]. Polyamines can act as general protective molecules as they enhance tolerance to various abiotic stresses such as salt [START_REF] Liu | Polyamines function in stress tolerance: from synthesis to regulation[END_REF], heavy metals [START_REF] Groppa | Polyamines and heavy metal stress: the antioxidant behavior of spermine in cadmium-and copper-treated wheat leaves[END_REF], chilling (Hummel et al., 2004c;[START_REF] Liu | Polyamines function in stress tolerance: from synthesis to regulation[END_REF], and flooding (Yiu et al., 2009), which are all known to generate ROS and oxidative stress. Yiu et al. (2009) reported that exogenous application of Put resulted in reduced superoxide radical (O2 •-) and H2O2 contents, and thereby less oxidative stress in plant cells. Their findings suggested that Put can confer abiotic stress tolerance through inducing the activities of various anti-oxidative systems. Polyamines have also been shown to be free radical scavengers and protectants against ozone damage [START_REF] Bors | Polyamine as radical scavengers and protectants against ozone damage[END_REF]. Moreover, polyamines are interconnected with other metabolic pathways involved in the formation of various signaling molecules and metabolites that are involved in plant stress responses and development [START_REF] Liu | Polyamines function in stress tolerance: from synthesis to regulation[END_REF][START_REF] Podlešáková | Phytohormones and polyamines regulate plant stress responses by altering GABA pathway[END_REF]. Thus, polyamines and ethylene biosynthesis are metabolically connected through S-adenosylmethionine (SAM) which acts as a common precursor (Takahashi and Kakehi, 2010;[START_REF] Podlešáková | Phytohormones and polyamines regulate plant stress responses by altering GABA pathway[END_REF]. Different connections also link polyamines with ROS dynamics [START_REF] Moschou | Polyamines and programmed cell death[END_REF]. Additionally, Put, Spd and Spm are known to have differential impacts on plant metabolism, whether under conditions of optimal development or under conditions of abiotic stress [START_REF] Handa | Differential and functional interactions emphasize the multiple roles of polyamines in plants[END_REF]. Finally, polyamines have been listed as promising naturally-occurring metabolites that can promote chemical priming and hardening against multiple abiotic stresses [START_REF] Savvides | Chemical priming of plants against multiple abiotic stresses: mission possible?[END_REF]. However, the exact mechanisms underlying the roles played by polyamines in stress responses remain to be fully elucidated.

A C C E P T E D

M A N U S C R I P T
The various modalities of exogenous treatments with polyamines (Figs. 56) clearly showed that variations of polyamine levels directly acted on the sensitivity or tolerance responses to atrazine exposure. However, whereas the tolerance response to salt stress has been associated with parallel increases of Put, Spd and Spm [START_REF] Kasinathan | Effect of reduced arginine decarboxylase activity on salt tolerance and on polyamine formation during salt stress in Arabidopsis thaliana[END_REF], the relationship between polyamine dynamics and the responses to atrazine was more complex. Indeed, atrazine tolerance was associated with increase of Put and decrease of Spm, and Spm was associated with enhancement of sensitivity . In contrast, Spm has been shown to exert, in wheat, anti-oxidant and protective effects under conditions of heavy-metal-induced oxidative damage (Groppa et al., and to have, in Arabidopsis, anti-senescence properties under conditions of dark-induced senescence [START_REF] Sequera-Mutiozabal | Global Metabolic Profiling of Arabidopsis Polyamine Oxidase 4 (AtPAO4) Loss-of-Function Mutants Exhibiting Delayed Dark-Induced Senescence[END_REF]. In other words, the polyamine response involved in sucrose-induced atrazine tolerance reflected the general involvement of putrescine in stress tolerance and the versatile relationship of Spm with stress tolerance (Takahashi and Kakehi, 2010), versatility probably related to specific molecular and physiological contexts. Put was thus found to alleviate atrazine-mediated stress and injury, and more particularly under priming experiments (Figs. 56). Indeed, Put preexposure strongly increased the tolerance to atrazine conferred by sucrose treatment (Figs. [START_REF] Jefferson | GUS fusions: beta-glucuronidase as a sensitive and versatile gene fusion marker in higher plants[END_REF][6], thus confirming the interest for chemical priming proposed by [START_REF] Savvides | Chemical priming of plants against multiple abiotic stresses: mission possible?[END_REF]. In line with the impact of soluble sugars on responses to abiotic stresses [START_REF] León | Sugar and hormone connections[END_REF][START_REF] Sulmon | Sugar-induced tolerance to atrazine in[END_REF][START_REF] Loreti | A genome-wide analysis of the effects of sucrose on gene expression in Arabidopsis seedlings under anoxia[END_REF][START_REF] Couée | Involvement of soluble sugars in reactive oxygen species balance and responses to oxidative stress in plants[END_REF][START_REF] Solfanelli | Sucrose-specific induction of the anthocyanin biosynthetic pathway in Arabidopsis[END_REF][START_REF] Li | Dynamic and diverse sugar signaling[END_REF], it was therefore shown that sucrose/polyamines cross-talk was important for the responses to xenobiotic stress, and regulated root growth and development processes (Figs. [START_REF] Jefferson | GUS fusions: beta-glucuronidase as a sensitive and versatile gene fusion marker in higher plants[END_REF][6], in line with the effects of sucrose [START_REF] Macgregor | Root system architecture in Arabidopsis grown in culture is regulated by sucrose uptake in the aerial tissues[END_REF] and polyamines [START_REF] Couée | Involvement of polyamines in root development[END_REF]) on root development.

Importance of sucrose/putrescine/spermine crosstalk in survival and death of the chemicallystressed plant

Molecular and physiological analysis of the effects of atrazine and of exogenous sucrose on Arabidopsis [START_REF] Ramel | Genome-wide interacting effects of sucrose and herbicidemediated stress in Arabidopsis thaliana: novel insights into atrazine toxicity and sucrose-induced tolerance[END_REF](Ramel et al., , 2009a) ) showed that initiation of atrazine-mediated chemical stress and toxicity involved inefficient regulation of singlet oxygen ( 1 O2) quenching and ROS scavenging, thus intensifying 1 O2 and ROS accumulation. This situation was also shown to evolve into disruption of cellular homeostasis, induction of senescence-like processes and activation of cell death programs, in line with the programmed cell death effects of singlet oxygen (Wagner et al., 2004) and of some xenobiotics [START_REF] Ramel | Xenobiotic sensing and signalling in higher plants[END_REF]. The growth arrest and bleaching events that were observed under conditions of atrazine toxicity (Figs. 56) reflected these programmed cell death effects. Conversely, exogenous sucrose, which was associated to more efficient 1 O2 quenching and lower 1 O2 accumulation in plantlets (Ramel et al., 2009a), and also exogenous putrescine, which was found to reduce O2 •-and H2O2 contents, and thus oxidative stress, in plant cells (Yiu et al., 2009), could lift growth arrest effects and activate development. In contrast, Spm enhanced developmental arrest and bleaching in the

A C C E P T E D M A N U S C R I P T
absence, but also, in the presence of sucrose (Figs. 56). Spermidine was found to have an intermediate behaviour in the sense that it did not enhance further sucrose-induced atrazine tolerance (Fig. 5B), but had a slight positive effect on tolerance to low levels of atrazine (Fig. 5A). Since exogenous sucrose and polyamine treatments did not lead to similar trends, and since polyamines could alter positively (Put) or negatively (Spm) the induction of atrazine tolerance by sucrose (Figs. [START_REF] Jefferson | GUS fusions: beta-glucuronidase as a sensitive and versatile gene fusion marker in higher plants[END_REF][6], it was therefore clear that the sucrose/polyamines crosstalk had important effects on programmed cell death and survival, as schematically hypothesized in Fig. 7. The pro-survival and anti-death effects of exogenous sucrose could be ascribed to this mechanism of sucrose/polyamines crosstalk (Fig. 7), through the regulation of polyamine metabolism by sucrose (Figs. 1,4), the context-dependent functions of polyamines in survival or programmed cell death [START_REF] Moschou | Polyamines and programmed cell death[END_REF], the increased antioxidative status of sucrose-treated plants [START_REF] Couée | Involvement of soluble sugars in reactive oxygen species balance and responses to oxidative stress in plants[END_REF], and the potential role of sucrose in preventing programmed cell death (Tognetti et al., 2013). Crosstalk with abscisic acid has also been shown to be important for the effects of polyamines on abiotic stress responses [START_REF] Shi | Improvement of plant abiotic stress tolerance through modulation of the polyamine pathway[END_REF]. The regulatory effects of polyamines and sucrose may thus be connected through abscisic acid [START_REF] Rook | Sugar and ABA response pathways and the control of gene expression[END_REF]. However, the specificities of sucrose/polyamine crosstalk in the present work would require further characterization with mutant studies. Differentially expressed genes were those genes showing a P-value ≤ 0.05 after Bonferroni's correction. Conversely, genes with a Bonferroni's P-value higher than 5 % were considered as being not differentially expressed (nde). The nomenclature of DAO genes is as suggested by [START_REF] Shelp | Hypothesis/review: Contribution of putrescine to 4-aminobutyrate (GABA) production in response to abiotic stress[END_REF]. For RT-qPCR (B), RNAs were reverse-transcribed and cDNAs were used. Three replicates were used for each experimental condition. Man: Mannitol, Atz: Atrazine, Suc: Sucrose.

  ,

  xenobiotic and biochemical treatments are described in the Results section and in the Figure legends.

  S-ADENOSYLMETHIONINE DECARBOXYLASE (SAMDC) encoding gene was highly activated by Man-Atz and Suc treatments. Considering Put, Spd, and Spm back-conversion and catabolism, three POLYAMINE OXIDASE (PAO) genes were significantly repressed under atrazine exposure in the absence of exogenous sucrose, and one DIAMINE OXIDASE (DAO) gene was significantly repressed under atrazine treatment in the presence of exogenous sucrose (Fig 1A).

  ., Padilla-Chacon, D., 2013. Subcellular compartmentation of sugar signaling: links among carbon cellular status, route of sucrolysis, sink-source allocation, and metabolic partitioning. Front. Plant Sci. 3, 306. https://doi.org/10.3389/fpls.2012.00306.

Figure 1 :

 1 Figure legendsFigure1: Effects of atrazine and sucrose on transcript levels of genes involved in the metabolic pathway of major polyamines (putrescine, spermidine and spermine). Atz (10 µM) and Suc (80 mM) treatments were carried out as described in material and methods. Man (80 mM) was used as osmotic control. Microarray data are shown as log2 ratio of gene expression under indicated conditions (A).

Figure 2 :

 2 Figure 2: Histochemical staining of ADC promoter::GUS expression in homozygous transgenic Arabidopsis (Ws) plants under atrazine or sucrose+atrazine conditions. Promoter activities of ADC1 and ADC2 were studied in stable homozygotic transformants harboring promoter::GUS reporter gene fusions. Homozygotic lines were grown for 3 days on MS medium, then transferred for 4 days on the indicated medium (black bar represents 1 mm).

Figure 3 :

 3 Figure 3: Responses of spe1-1 mutant and of its isogenic WT (Col-0) to atrazine in the absence and in the presence of sucrose. Seedling morphology (A) and primary root length (mean ± S.E.M.) (B) are shown. Seed germination and seedling growth were carried out under the conditions of the different treatments, which consisted in the different combinations of absence (-) or presence (+) of 1 µM Atz and 80 mM Suc in MS medium. Seedlings were measured and photographed 15 days after germination. Statistical analysis between means was carried out using the Mann-Whitney test. Statistical significance of differences (P ≤ 0.05) between treatments and plant lines is indicated by different letters above bars.

Figure 4 :

 4 Figure 4: Effects of atrazine on polyamine levels in Arabidopsis (Ws) seedlings grown in the absence or presence of sucrose. The levels of putrescine, spermidine, and spermine are shown. Seed germination and seedling growth were carried out under conditions of the different treatments, which consisted in 0.5 µM Atz in the absence (Suc-) or presence (Suc+) of 80 mM Suc in MS medium. Values are the mean (±S.E.M.) of measurements of three independent replicates of pooled 15-day-old plantlets. Statistical analysis between means was carried out using the Mann-Whitney test. Statistical significance of differences (P ≤ 0.05) between treatments is indicated by different letters above bars.

Figure 5 :

 5 Figure 5: Effects of exogenous polyamine treatments on atrazine responses and sucrose-induced atrazine protection of Arabidopsis (Ws) seedlings. Primary root length is shown as means (± S.E.M.). (A) Seed germination and seedling growth were carried out under the conditions of the different treatments, which consisted in the different combinations of absence or presence of 0.5 or 1 µM Atz and of absence (Control) or presence of 0.5 mM of either Put, Spd, or Spm in MS medium. Seedlings were analysed after 15 days of treatment. Mean comparisons were conducted by Mann-Whitney test between atrazine treatments (0; 0.5; 1 µM) independently for each exogenous polyamine treatment. (B) Four-day old plantlets were grown on 0.5X MS medium and transferred either on 0.5X MS medium (Control), or on the same medium containing 1 mM Put, Spd or Spm for 20 h. Plantlets were then transferred on Suc (25 mM) and Atz (1 µM) containing media supplemented with 1 mM of either Put, Spd, or Spm. Seedlings were analysed after 5 days of treatment. Statistical analysis between means was carried out using t-test. Statistical significance of differences (P ≤ 0.05) between compared means is indicated by different letters above bars (A, B).

Figure 6 :

 6 Figure 6: Putrescine-mediated enhancement of the protective effect of sucrose under atrazine exposure. Four-day old seedlings (Ws) were separated in two groups. In the first one, seedlings were transferred onto control medium (0.5X MS medium) for 20 hours, and then further grown in the presence of atrazine (1µM) alone or under atrazine-protected conditions (Suc 80 mM + Atz 1µM). In the second one, seedlings were transferred to the MS medium supplemented with Put (6 mM) for 20 hours, and then further grown in a medium containing either Atz (1 µM) and Put, or Atz (1µM), Put and Suc (80mM). Seedlings were analysed after 18 days of growth. Morphological changes (A), fresh weight and chlorophyll contents (B), and root length and lateral root primordium count (C) are presented. Values correspond to the means of at least 20 measurements and bars represent the standard errors of the means. Statistical analysis between means was carried out using the Mann-Whitney test. Statistical significance of differences (P ≤ 0.05) between treatments is indicated by different letters above bars.

Figure 7 :

 7 Figure 7: Hypothetical scheme of the regulatory effects of sucrose and polyamines on death and survival processes in the chemically-stressed plant.

  Tognetti, J.A., Pontis, H.G., Martínez-Noël, G.M.A., 2013. Sucrose signaling in plants, a world yet to be explored. Plant Signal Behav. 8, e23316. http://dx.doi.org/10.4161/psb.23316. Wagner, D., Przybyla, D., Op den Camp, R., Kim, C., Langraf, F., Lee, K.P., Wursch, M., Laloi, C., Nater, M., Hideg, E., Apel, K., 2004. The genetic basis of singlet oxygen-induced stress responses of Arabidopsis thaliana. Science 306, 1183-1185. DOI: 10.1126/science.1103178. Watson, M.B., Emory, K.K., Piatak, R.M., Malmberg, R.L. 1998. Arginine decarboxylase (polyamine synthesis) mutants of Arabidopsis thaliana exhibit altered root growth. Plant J. 13, 231-239. https://doi.org/10.1046/j.1365-313X.1998.00027.x. Wind, J., Smeekens, S., Hanson, J., 2010. Sucrose: metabolite and signalling molecule. Phytochemistry 71, 1610-1614. https://doi.org/10.1016/j.phytochem.2010.07.007. Yiu, J.C., Juang, L.D., Fang, D.Y.T., Liu, C.W., Wu, S.J., 2009. Exogenous putrescine reduces flooding-induced oxidative damage by increasing the antioxidant properties of Welsh onion. Sci. Hortic. 120, 306-314. https://doi.org/10.1016/j.scienta.2008.11.020.

Acknowledgements

This work was supported by the interdisciplinary program "Ingénierie écologique" (CNRS, France), by Rennes Métropole (France) local council, and by recurrent funding from the Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation (France) and the Centre National de la Recherche Scientifique (France). We gratefully acknowledge the kind gift of spe1-1 mutant seed from Professor Russell Malmberg (University of Georgia, Athens, USA). We also gratefully acknowledge Dr Françoise Hennion (University of Rennes, ECOBIO UMR 6553, Rennes, France) for help in polyamine analysis.


Patrick Maillé
email: patrick.maille@telecom-bretagne.eu

Maurizio Naldi
email: naldi@disp.uniroma2.it

Bruno Tuffin
email: bruno.tuffin@inria.fr

Competition for migrating customers: a game-theoretic analysis in a regulated regime

Migration processes of customers between alternative providers are becoming more and more relevant. Providers competing for migrating customers may adopt a delaying strategy to retain customers who are willing to leave, facing regulatory sanctions for that unfair behaviour. A game-theoretic model is proposed to describe the resulting competition among providers. For that model, both stable and unstable Nash equilibria are shown to exist and the providers' equilibrium strategies can be derived, in general numerically. In the stable equilibrium case the delaying strategy predicted by the model introduces a mean delay that is a strongly nonlinear (decaying) function of the sanction value.

I. INTRODUCTION

The end of the monopolistic era in telecommunications services has spurred the entry of a number of competing providers in the market arena. Customers can now choose among many different offers for the same service and are allowed to freely migrate from a provider to another. Migration phenomena (often indicated as churn) are particulary relevant for mobile services, where annual churn rates as high as 25% are often observed [START_REF] Wieland | The customer retention challenge[END_REF] and studies have been devoted to ascertain the churn determinants (see e.g. the recent [START_REF] Ahn | Customer churn analysis: Churn determinants and mediation effects of partial defection in the korean mobile telecommunications service industry[END_REF] and [START_REF] Eshghi | Determinants of customer loyalty in the wireless telecommunications industry[END_REF]). In any migration process we can identify four stakeholders: the customer (who initiates the process), the recipient provider, the losing provider, and the regulatory authority (which sets the rules for migration and checks for compliance). Since the customer's migration represents an economic loss for the losing provider, the latter has no interest in accelerating the migration process. Even when that process is led by the recipient provider, the losing provider has the possibility of delaying it, to the extent of reducing the effectiveness of the liberalization process [START_REF] Buehler | Mobile number portability in Europe[END_REF]. In the fight for customer retention the losing provider may often be led to adopt unfair practices, calling for the intervention of the regulatory authority, e.g. through appropriate economic sanctions. The losing provider must therefore evaluate the convenience of its delaying strategy, by taking into account the pros linked to retaining the customer (continuation of the revenue stream associated to that customer) and the cons due to the possibility of incurring the sanctions for the undue delay in migration operations. The analysis reported in [START_REF] Naldi | A simple model for the effectiveness of delaying strategies for telecommunications churn reduction[END_REF] has shown that the losing provider may identify a maximum tolerable sanction value, relating it to the customer lifetime value, i.e. the present value of the future revenue stream generated by the customer. Though the analysis has so far focused on the losing provider, the relative ease with which the customer may change his provider may however lead to a back-and-forth situation, in which competing providers play both roles. In fact a provider may be a losing one as well as a recipient one for a) the same customer at different times; b) different customers at the same time. The resulting competition between providers may be suitably modelled through a game, where each provider has to choose its delaying strategy. In this paper we propose a game-theoretic model with two providers, that takes into account the strategies of both providers competing for a migrating customer as well as the behaviour of the customer and the danger represented by sanctions. The model is then used to study the Nash equilibria of the interaction among providers, and analyze the influence of the sanction level on those equilibria.

II. MARKOV CHAIN MODEL OF USERS' BEHAVIOR

The goal of this section is to model the switching behavior of a customer between two available providers called A and B. We assume that it is represented by the Markov chain1 depicted in Figure 1, the meaning of the four states being defined in Table I to the other provider; the reverse transitions model instead the customer reneging to the migration (due to winback actions by the losing provider or to its delaying strategies). The actual migration rates (from state 2 to state 3, and from state 4 to state 1) depend either on a) the delay introduced by the losing provider in the porting operation, or on b) the impatience of the customer forcing the losing provider to comply with the migration-supporting regulations. The resulting infinitesimal generator is

R :=     -λ 12 λ 12 0 0 λ 21 -(λ 21 + λ 23 ) λ 23 0 0 0 -λ 34 λ 34 λ 41 0 λ 43 -(λ 41 + λ 43 )     .
From standard Markov chain analysis, the steady-state probability for each of the four states given by line vector π = (π i ) i=1,...,4 exists2 and is given by the solution of equations πR = 0,

4 i=1 π i = 1.
If c := λ 34 λ 41 (λ 23 +λ 21 )+λ 12 λ 23 (λ 41 +λ 43 )+λ 12 λ 34 (λ 41 +λ 23 ), it can be readily checked that the solution is

π 1 = λ 34 λ 41 (λ 23 + λ 21 ) c π 2 = λ 34 λ 41 λ 12 c π 3 = λ 12 λ 23 (λ 41 + λ 43 ) c π 4 = λ 12 λ 23 λ 34 c . (1)
The question is now, how do we relate some of the transition rates appearing in the infinitesimal generator to the relevant parameters of the problem? Our goal being to study the retention policy of providers and defining regulation rules, we introduce the average delay imposed by the two providers, respectively T A and T B , and the suing rate µ taking into account the attitude of the customer to force the migration by taking legal actions against the delaying provider. We then express the transition rates that mark the migration to the other provider, i.e. λ 23 and λ 41 , as the sum of two rates, since either the end of the retention period or the legal action taken by the customer leads to a provider change:

λ 23 = 1 T A + µ, λ 41 = 1 T B + µ. (2)
With full generality, it seems also relevant that the other rates depend on T A and T B too. Indeed, a customer could be more inclined to switch (and to renege) depending on the respective retention times of providers. We therefore let them depend on the retention times, i.e., λ 12 = λ 12 (T A , T B ),

λ 21 = λ 21 (T A , T B ), λ 34 = λ 34 (T A , T B ) and λ 43 = λ 43 (T A , T B ).
Note that other parameters such as reputation of the provider, price, etc., can also be included in those rates. Though, not being the purpose of the current study, they are just hidden and kept constant.

III. NON-COOPERATIVE GAME DESCRIPTION AND ALGORITHMIC SOLUTION

The customer behavior having been described, we can now investigate provider strategies. providers have an open interest in keeping the customer, since any delay in the migration allows the losing provider to keep the revenues associated to that customer. On the other hand the legal actions taken by the customer lead to a sanction s 0 . The utility function of each provider, representing here their financial net benefits per time unit at steady-state, is therefore given by the difference between the average net profits associated to the customer (respectively net revenues associated to customers p A or p B times the probability of keeping the customer) and the average sanction (which is levied only if the customer has expressed his intention to leave the provider and has taken a legal action). The resulting expressions of the utility function for the two providers are therefore

U A = p A (π 1 + π 2 ) -s 0 π 2 µ, U B = p B (π 3 + π 4 ) -s 0 π 4 µ. (3)
In this competitive environment, each provider strives to find its best strategy, i.e., its average retention time (assuming here fixed revenues) maximizing its utility. But its utility depends not only upon its own choice (from values of steady-state probabilities π i , i ∈ {1, . . . , 4}), but also upon the strategy choice of the opponent provider. In this situation, the solution concept is that of Nash equilibrium from non-cooperative game theory [START_REF] Osborne | A Course on Game Theory[END_REF]. A Nash equilibrium is here an average retention time profile T * = (T * A , T * B ) from which no provider has any incentive to deviate unilaterally. Formally,

T * A ∈ argmax TA∈S U A (T A , T * B ) and T * B ∈ argmax TB ∈S U B (T * A , T B ), (4)
i.e., the best strategy provider i ∈ {A, B} can use is T * i given that the strategy of the other provider is T * j (with j ∈ {A, B}, j = i). In (4), S is the strategy set of each provider. In general we search our solution in the set of non-negative real numbers S := R + , however we consider that very large values of the retention time (larger than 1 year for example) are not realistic and should not be considered. For the numerical analysis carried out in Section V, we therefore take S = [O, T max ] for a given value of T max , which makes the strategy set of each provider a compact and bounded set.

To determine practically the Nash equilibria (if any) of the game played among providers, we define the best response of each provider as a function S → 2 S of the strategy of its opponent. Those best response functions are

BR A (T B ) := arg max TA∈S U A (T A , T B ) and BR B (T A ) := arg max TB ∈S U B (T A , T B ).
If we define the best response correspondance BR :

S × S → 2 S × 2 S as BR(T A , T B ) := {(t A , t B ) ∈ S × S : t A ∈ BR A (T B ), t B ∈ BR B (T A )}, then a Nash equilibrium is simply a fixed point of the 2-dimensional function BR.
Therefore an exhaustive way to proceed to find Nash equilibria is to follow Algorithm 1 described below.

Alg. 1 Graphically finding the Nash equilibria of the game

Input:

• the transition rates of the Markov chain in Figure 1 Note that when the analytical derivation of the best response is not feasible in step 1 of the algorithm, only a finite number of values can be tried in practice. In the numerical results presented in Section V, we use a given number (say, 500) of equally spaced values in S.

BRA(TB) BRB(TA)

TA TB Nash equilibria Figure 2. Graphical determination of Nash equilibria (here the best response of each user is unique, but this need not be the case in general).

IV. ANALYSIS OF THE GAME IN A SIMPLIFIED SETTING

Consider the special case where

λ 12 = λ λ 34 = λ + ν λ 21 = α λ 43 = α λ 23 = 1 T A + µ λ 41 = 1 T B + µ,
for some fixed nonnegative values λ, ν, α, and µ. That is, only the migration rates depend on retention times: the willingness to leave or the reneging behavior are assumed constant. We take λ 34 > λ 12 to introduce some asymetry into the game; this models the fact that provider A has for instance a better reputation (or could provide a better quality of service) than provider B. To avoid dealing with too many parameters and separating in several different cases, consider an arbitrarily chosen example where λ = ν = 1, α = 2, µ = 4 and p A = p B = 1. After simple computations, we get

U A = 2 (1 + 4T B ) (1 + 7T A -4s 0 T A ) 3 + 18T A + 16T B + 88T B T A U B = (1 + 4T A ) (1 + 8T B -8s 0 T B ) 3 + 18T A + 16T B + 88T B T A .
We now consider the Nash equilibria of the game. Since we manage to carry out an analytical study, we can take S = R + here. Computing the partial derivatives of the utility functions gives

∂U A ∂T A = 2 (1 + 4T B ) (3 -12s 0 + 8(3 -8s 0 )T B ) (3 + 18T A + 16T B + 88T B T A ) 2 ∂U B ∂T B = 8 (1 + 4T A ) (1 -3s 0 + (7 -18s 0 )T A ) (3 + 18T A + 16T B + 88T B T A ) 2 .
We remark here that the numerator of each derivative does not depend on the average retention time of the corresponding provider. It can actually be easily checked that whatever the values of parameters λ, ν, α, µ, p A and p B , this property is verified.

Note also that ∂UA ∂TA can be zero iff 1/4 ≤ s 0 ≤ 3/8. Below, it is always positive and above, always negative. Same thing for ∂UA ∂TA which can be zero iff 1/3 ≤ s 0 ≤ 7/18. Depending on the value of s 0 , we end up with several possible cases.

• If s 0 ≤ 1/3, provider B's only interest is to set T B = ∞,
and therefore, the same strategy applies for provider A.

The unique Nash equilibrium is then (∞, ∞). The reason is that the sanction is too low to prevent the providers from retaining abusively the customers. • Similarly, if s 0 ≥ 3/8, provider A's interest is to set T A = 0. At this value, the derivative of U B with respect to T B is negative, meaning that T B = 0 is the best response.

The resulting unique Nash equilibrium is (0, 0). Here, the sanction is too high for providers, their interest is to let customers leave if they are willing to. • Now, if 1/3 < s 0 < 3/8, we then end up with three possible Nash equilibria: (0, 0), (∞, ∞) and

(T * A , T * B ) = ( 1-3s0 7-18s0 , 3-12s0 8(3-8s0)
). Indeed, in the later case, both derivatives are null and we are at a (individual) maximum for each provider. On the other hand, as soon as a player i ∈ {A, B} plays T i > T * i , the other player has a maximum at ∞, and then i also. The reasoning is similar for T i < T * i , leading to (0,0). This illustrates the interest of the analysis: determining threshold values on the sanction fee in order to prevent providers from retaining customers.

V. NUMERICAL ANALYSIS IN A COMPLEX CASE

In this section, we consider a more complex setting, where all transition rates depend on the relative quality of the two providers (via their mean retention time T ). We use here the following model:

λ 12 = λ • 1 -ω + ω T B -T A T A + T B λ 34 = λ • 1 -ω + ω T A -T B T A + T B + ν λ 21 = α • 1 -ω + ω T A -T B T A + T B λ 43 = α • 1 -ω + ω T B -T A T A + T B λ 23 = 1 T A + µ λ 41 = 1 T B + µ,
where λ, ν, α and µ are constant as in the previous section, and ω is a constant that represents users sensitivity to providers reputation in their churning decisions. This model reflects the fact that a user is less likely to leave a provider that retains customers, and is also more likely to renege because he is reluctant to have to fight to churn. With such a model, providers have an even stronger incentive to use retention policies, because of the direct gain in terms of income during the retention period and the indirect gain due to the fact that users are less willing to leave. Since an analytical study like the one carried out in the previous section is not realizable anymore, we use numerical computation following Algorithm 1 to determine the Nash equilibria of the game and the influence of sanctions. We present next an example where time is expressed in years, with λ = 1/5 (which corresponds to around 20% of customers willing to churn each year if T A = T B ), ν = 1/10, α = 1/6 (mean reneging time of 2 months) and µ = 1/6. We also take T max = 1 year, i.e. S = [0, 1], and p A = p B = p (no price game among providers). Remark that due to the utility functions (3), when both providers get the same revenues p then the outcomes of the game depend only on the ratio s 0 /p. Without sanctions (s 0 = 0), our numerical computations highlight that best response functions BR A and BR B simply consist in choosing the highest possible retention time, i.e. ∀T ∈ S, BR A (T ) = BR B (T ) = T max . Therefore a sanction s 0 needs to be introduced to incentivize providers to reduce their retention times. Figure 3 there are two Nash equilibria, namely (T A , T B ) = (0, 0) and (T A , T B ) = (0.29, 0.35). Notice however that only the latter equilibrium is stable, since a small deviation of any of the two providers from the point (T A , T B ) = (0, 0) leads the best response dynamics to that equilibrium. Notice also that at this equilibrium, the provider that benefits from a better reputation (modelled by the ν parameter) retains his customers less than its opponent.

Increasing more the sanction value gives the same form of best response functions as those presented in Figure 3. We therefore focus now on the stable Nash equilibrium that a given sanction level yields. expected, increasing the sanction level indeed makes providers reduce their mean retention time. However, unlike what was observed in the simplified model of the previous section, it seems that there is no threshold here for the value of s 0 above which the only Nash equilibrium is (0, 0). Therefore the sanction level has to be chosen such that the resulting retention times be sufficiently small (say, less than 0.1 year, which from Figure 4 corresponds to s 0 ≥ 18p).

To compare the providers' perception of both Nash equilibria of the game, we plot in Figure 5 their utilities at those two possible outcomes when the sanction s 0 /p varies. Notice that (T A , T B ) = (0, 0) is not a Nash equilibrium when the sanction is below 5.6p. In that case, the game has only one Nash equilibrium (that is stable). This equilibrium consists in each provider setting the largest possible retention time (here T max = 1). We observe that provider A obtains a larger utility than provider B in all cases due to its advantage ν.

Interestingly, it appears that both players would be better off playing the unstable Nash equilibrium instead of the stable one. Therefore the use of the sanction is justified by its effect on the stable equilibrium: enforcing users to reduce their retention time makes the outcome (T A , T B ) get closer to the more efficient situation (0, 0). Moreover, we also notice in Figure 5 that when the stable equilibrium is different from (T max , T max ), i.e. for s 0 /p ≥ 8 in our example, an increase in the sanction unexpectedly leads to an increase in both providers' utility. This also justifies the use of the sanction. Consequently, we can say that for this model, the sanction improves the user perceived quality of both providers (that is decreasing in their retention times), but can also be beneficial to both providers by enforcing their opponent to reduce its retention time.

VI. CONCLUSIONS

A game-theoretic model has been developed to describe the behaviour of two service providers competing for migrating customers. The model takes into account all the stakeholders, namely the delaying behaviour of the two providers, the sanctions levied by the regulatory authorities, and the impatience of the customer waiting for the completion of the migration process. A simplified setting has been examined to show the use of the model. In that setting it has been shown that both stable and unstable Nash equilibria exist. The stable equilibrium retention strategies, consisting in determining appropriate mean delaying times, have been derived for both providers. The game outcome predicted mean delay of each provider appears to be a strongly non linear function of the sanction imposed by the regulator.

2 . 4 )

 24 , as functions of the decision variables T A and T B (and possibly prices), • the values of prices p A and p B , • the value of the sanction s 0 . 1) For all possible values of T B in S, find the set BR A (T B ) of T A values in S that maximize U A (T A , T B ). 2) For all possible values of T A in S, find the set BR B (T A ) of T B values in S that maximize U B (T A , T B ). 3) On a same graphic, plot the best response functions T A = BR A (T B ) and T B = BR B (T A ), as exemplified in Figure The set of Nash equilibria is then the (possibly empty) set of intersection points of those functions (see Figure 2).

Figure 3 .

 3 Figure 3. Nash equilibria with sanction s 0 = 10p

Figure 4 Figure 4 .

 44 Figure 4. Stable Nash equilibrium strategies when the sanction varies.

Figure 5 .

 5 Figure 5. Providers' utility at stable and unstable (if any) Nash equilibria.

  . The transition from state 1 to state 2 (and

	State	Meaning
	1	Customer staying with provider A and unwilling to leave
	2	Customer staying with provider A and willing to leave
	3	Customer staying with provider B and unwilling to leave
	4	Customer staying with provider B and willing to leave
		Table I
		STATES OF THE MARKOV CHAIN
		2	λ 23	3
		λ 12	λ 21	λ 43	λ 34
		1	λ 41	4
		Figure 1. Markov chain model of the customer's switching behaviour
		from state 3 to state 4) is for the customer willing to migrate

We therefore implicitely assume that all events leading to a state change occur after an exponentially distributed time.

Remark that when a provider i sets T i = 0, the Markov chain described before is degenerate: if T A = 0 for example then states 2 and

are only one state. However the corresponding Markov chain with fewer states remains ergodic as soon as all transmission rates are strictly positive, which will be the case in the examples we consider.

ACKNOWLEDGMENT

The authors would like to acknowledge the support of Euro-FGI Network of Excellence through the specific research project CAP (Competition Among Providers).