Alex Baumel
email: alex.baumel@univ-cezanne.fr

Pascal Auda

Franck Torre

Frederic Medail

Morphological polymorphism and rDNA internal transcribed spacer (ITS) sequence variation in Armeria (Plumbaginaceae) from south-eastern France

Keywords:

The Armeria populations (Plumbaginaceae) scattered along the south-eastern French coastline are small and often endangered by habitat destruction. Because their taxonomic status remains unclear, we conducted a molecular and phenetic analysis to test for the existence of different taxa and to set conservation priorities. Multivariate analysis of morphometric data demonstrated that the majority of coastal populations are similar to inland populations of Armeria arenaria subsp. bupleuroides. However, discriminant analysis isolated two distinct populations. One of these has a morphology intermediate between the narrow endemic Armeria belgenciensis and A. arenaria subsp. bupleuroides. However, rDNA internal transcribed spacer (ITS) sequences display no fixed variation, even between highly remote populations. We discuss these results in the light of recurrent hybridization in Armeria, and propose the description of two new subspecies of Armeria arenaria (subsp. pradetensis and subsp. peirescii) located in the Var department.

INTRODUCTION

Hybridization is an important process in plant evolution [START_REF] Stebbins | Variation and evolution in plants[END_REF][START_REF] Grant | Plant speciation[END_REF][START_REF] Arnold | Natural hybridization and evolution[END_REF] and represents a source of genetic variation and speciation as it predisposes colonizing populations to rapid adaptive radiation [START_REF] Seehausen | Hybridization and adaptative radiation[END_REF]. However, hybridization is not randomly distributed among families and genera, but associated with certain characters, such as outcrossing, high phenotypic plasticity or clonality [START_REF] Ellstrand | Distribution of spontaneous plant hybrids[END_REF]. At low systematic levels, crossing between lineages interrupts divergence and produces a reticulate pattern of evolution (e.g. Fuertes Aguilar, Rosselló & Nieto Feliner, 1999b). Reticulate evolution promotes gene flow and the exchange of exclusive characters. The resulting decrease in taxonomic resolution for morphological or molecular characters can lead to poor discrimination and identification of species. In this context, insufficient sampling of the polymorphism resulting from such gene flow can lead to the assignment of diverse taxonomic ranks (species, subspecies or varieties) to individual variants. Several methods exist for the empirical delimitation of species [START_REF] Sites | Delimiting species: a renaissance issue in systematic biology[END_REF][START_REF] Seehausen | Hybridization and adaptative radiation[END_REF], and these frequently require the combined use of morphological characters and DNA markers.

The genus Armeria L. (Plumbaginaceae) is a model issue of the delimitation of species boundaries. Polymorphism in Armeria is high and complicated by frequent hybridization and introgression, without a resulting loss of species diversity (Fuertes Aguilar, Rosselló & Nieto Feliner, 1999a). Armeria currently includes c. 120 small perennial herbaceous species, 92 of which are located in the Mediterranean Basin [START_REF] Greuter | Dicotyledons (Lauraceae-Rhamnaceae). Berlin-Dahlem: Conservatoire et Jardin Botanique de la Ville de Geneve[END_REF]. This diversity is concentrated in the Iberian Peninsula, where seven [START_REF] Bernis | Revisión del género Armeria Willd. con especial referencia a los grupos ibéricos[END_REF][START_REF] Bernis | Revisión del género Armeria Willd. con especial referencia a los grupos ibéricos. Parte segunda (descriptiva de los grupos ibéricos)[END_REF][START_REF] Bernis | Revisión del género Armeria Willd. con especial referencia a los grupos ibéricos. Parte segunda (conclusión)[END_REF] or 54 [START_REF] Feliner | Armeria[END_REF] species have been described, depending on the species concept used.

Within Plumbaginaceae, the genus Armeria is characterized by a rosette vegetative system, capitulate inflorescences and a dimorphic reproductive system [START_REF] Lledó | Systematics of Plumbaginaceae based upon cladistic analysis of rbcL sequence data[END_REF]. Polyploidy is rare in Armeria, and almost all chromosome counts in the genus are diploid with 2n = 18 [START_REF] Donadille | Contribution à l'étude du genre Armeria Willd. (Plumbaginaceae). III. Clé générale des taxons français[END_REF][START_REF] Moore | Flora Europea checklist and chromosome index[END_REF]. Most populations are composed of obligate outcrossers as a result of a self-incompatibility system [START_REF] Baker | The evolution, functioning and breakdown of heteromorphic incompatibility systems. I. The Plumbaginaceae[END_REF][START_REF] Vekemans | The evolution and breakdown of the heteromorphic incompatibility system of Armeria maritima revisited[END_REF], with weak internal reproductive barriers [START_REF] Nieto Feliner | Fine-scale geographical structure, intra-individual polymorphism and recombination in nuclear ribosomal internal transcribed spacers in Armeria (Plumbaginaceae)[END_REF]. Crossing experiments [START_REF] Baker | The evolution, functioning and breakdown of heteromorphic incompatibility systems. I. The Plumbaginaceae[END_REF][START_REF] Feliner | Natural and experimental hybridization in Armeria (Plumbaginaceae): A. salmantica[END_REF] and the structure of rDNA internal transcribed spacer (ITS) sequence variation have demonstrated that extensive introgression has occurred at both coarse (Fuertes [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF] and fine (Fuertes Aguilar et al., 1999a, b;Nieto Feliner, Fuertes Aguilar & Rosselló, 2001a;[START_REF] Nieto Feliner | Fine-scale geographical structure, intra-individual polymorphism and recombination in nuclear ribosomal internal transcribed spacers in Armeria (Plumbaginaceae)[END_REF] geographical scales. Thus, the geographical structure of ITS variation is partly independent of and conflicts with the 'classical' taxonomic approach.

An estimated 21 Armeria taxa have been described for France, 16 of which are located in the Mediterranean region [START_REF] Kerguélen | Index synonymique de la flore de France[END_REF]Médail, ined.). In this study, we present an analysis of morphological and rDNA ITS sequence variation focused on taxa belonging to the A. arenaria (Pers.) Schult. group from Provence (south-eastern France), and especially populations situated along the coastline of the Var department. In the molecular phylogenetic analyses of Fuertes [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF], A. arenaria is one of the seven widely distributed species in the genus which share intraspecific morphological variability and between-clade branching patterns in the rDNA ITS phylogenetic trees. However, the sampling of A. arenaria in south-east France was limited to a single population in the Bouches-du-Rhône department, and the major part of the region of Provence was not considered.

We initiated this study, in part, because of the inadequately described systematic status of several restricted populations, despite the previous morphological investigations of [START_REF] Donadille | Contribution à l'étude du genre Armeria Willd. (Plumbaginaceae). III. Clé générale des taxons français[END_REF]. Several of these populations are extremely small, isolated and threatened by human activities, and, beyond systematics, our research aims to set conservation units as recommended by recent work concerning Evolutionary Significant Units (for a review, see [START_REF] Fraser | Adaptive evolutionary conservation: towards a unified concept or defining conservation units[END_REF].

MATERIAL AND METHODS

MATERIAL

Most of the populations from south-east France considered here are included in the A. arenaria aggregate (= A. plantaginea Willd.), which encompasses several subspecies: (1) subsp. arenaria, located throughout the species range; (2) subsp. bupleuroides (Godron & Gren.) Greuter & Burdet, relatively common on dolomitic and siliceous rocky grasslands in Provence, the southern Maritime Alps and the Drôme department [START_REF] Albert | Catalogue des plantes qui croissent naturellement dans le département du Var[END_REF][START_REF] Molinier | Catalogue des plantes vasculaires des Bouches-du-Rhône[END_REF][START_REF] Charpin | Matériaux pour la Flore des Alpes Maritimes. Catalogue de l'herbier d'Emile Burnat déposé au Conservatoire[END_REF][START_REF] Garraud | Flore de la Drôme. Atlas écologique et floristique[END_REF]; and (3) subsp. praecox (Jordan) Kerguélen, mainly located in xeric alpine valleys of the southern Alps [START_REF]Atlas de la flore des Hautes-Alpes. Gap: Conservatoire Botanique National Alpin de Gap-Charance[END_REF], but also along the coastline of the Maures and Esterel mountain chains in Provence [START_REF] Molinier | Observations sur la végétation de la zone littorale en Provence[END_REF]. Another morphologically distinct taxon, Armeria belgenciensis Donadille ex Kerguélen, has been described as a narrow endemic taxon restricted to dolomitic soils near Solliès-Toucas (Var) [START_REF] Donadille | Contribution à l'étude du genre Armeria Willd. (Plumbaginaceae). III. Clé générale des taxons français[END_REF][START_REF] Donadille | Livre rouge de la flore menacée de France. Tome 1: espèces prioritaires[END_REF]. Armeria belgenciensis is characterized by thin, linear (filiform) leaves and a flowering season from August to September. The taxa of the A. arenaria group differ from A. belgenciensis principally by their lanceolate leaves and spring flowering. However, 100 m away from the A. belgenciensis population, at a mountain pass called 'Baisse du Pas Etroit', there is a spring flowering population with sublinear leaves, designated as A. arenaria subsp. bupleuroides. The systematic status of populations on the Var coastline, where our sampling was concentrated, is no less uncertain. These consist of: (1) a copper mine waste population situated on the Cap Garonne (Le Pradet, western Var, near Toulon), which has been treated as A. bupleuroides [START_REF] Albert | Catalogue des plantes qui croissent naturellement dans le département du Var[END_REF]; and

(2) populations situated along the coastline of the Maures and Estérel mountain chains (eastern Var), which have been treated as A. bupleuroides Gren. & Godr. [START_REF] Albert | Catalogue des plantes qui croissent naturellement dans le département du Var[END_REF][START_REF] Camus | Florule de Saint-Tropez et de ses environs immédiats[END_REF], A. praecox Jord. [START_REF] Molinier | Observations sur la végétation de la zone littorale en Provence[END_REF][START_REF] Géhu | Glanures phytosociologiques sur les côtes de Provence[END_REF] or A. arenaria subsp. arenaria [START_REF] Gandioli | Données floristiques sur les Alpes-Maritimes franco-italiennes: l'herbier de Joseph Rodié (Institut de Botanique de Montpellier, MPU)[END_REF].

In order to resolve these taxonomic discrepancies, we used rDNA ITS sequences and multivariate analysis of morphometric data to assess population differentiation according to geographical origin. The collection localities spanned the range of Armeria in Var, where in-depth studies of nine populations were performed. These populations were also compared with specimens from five populations in the depart-ments of Ardèche, Bouches-du-Rhône, Drôme, Hautes-Alpes and Hérault (Fig. 1). The geography and taxonomic treatment of these 14 populations are indicated in Table 1. Almost all Armeria populations of the Var coastline have been inspected and sampled. The northern localities of the Var were not exhaustively surveyed, but their taxonomic status has been less debated by botanists. Extensive sampling of A. arenaria will be necessary to delimit the distribution of subspp. arenaria, bupleuroides and praecox, which are used here only as standards for comparison.

Ten herbarium specimens were collected in the field for each population. For each one, one capitulum was conserved in 70% alcohol in order to measure the reproductive characters on fresh material. Most of the collected samples were used for morphological measurements and one sample per population was used for DNA extraction and ITS sequencing. Samples from the Morières-la-Tourne, Cap Dramont, Avinière and Eteize populations were used only for molecular analysis because herbarium specimens were too few to allow a robust morphometric analysis. Populations of less than six specimens were excluded, and the final analysis matrix consisted of 106 individuals for morphometric analysis and 12 for rDNA ITS sequencing. Holotypes for new taxa are conserved at the Muséum d'Histoire Naturelle d'Aix-en-Provence (AIX), and other herbaria vouchers are conserved at the Université Paul Cézanne, Mediterranean Institute of Ecology and Palaeoecology (IMEP, Aix-en-Provence, F. Médail herbarium).

MORPHOMETRY

Vegetative characters were measured on herbarium specimens after at least one week of drying. Vegetative material of Armeria is naturally dry and does not change after a few days in a herbarium press. The 21 characters included in the analysis were derived from the measurements of an initial set of 34 selected characters according to previous systematic studies [START_REF] Bernis | Revisión del género Armeria Willd. con especial referencia a los grupos ibéricos[END_REF][START_REF] Donadille | Contribution à l'étude du genre Armeria Willd. (Plumbaginaceae). III. Clé générale des taxons français[END_REF]Nieto Feliner, Fuertes Aguilar & Rosselló et al., 2001b). By selecting only variable and clearly measurable characters, 18 quantitative and three qualitative characters were retained (Table 2). When possible, three replicates of quantitative measures were taken per specimen and averaged for use in statistical analyses.

DATA ANALYSIS

Multivariate methods were performed according to the principles of phenetic analysis describing morphometric variation. In the first method, principal component analysis on a correlation matrix was conducted to detect specimen groups on the basis of the 21 morphological characters. To investigate the discriminant power of a priori grouping treatments, discriminant analysis was conducted using the ADE4 package of R statistical software [START_REF] Thioulouse | ADE-4: a multivariate analysis and graphical display software[END_REF]R Development Core Team, 2006). The objective of discriminant analysis is to find a linear combination of variables (the discriminant function) that best discriminates among a priori defined groups. Two classification factors were tested by discriminant analysis: 'population' and 'taxonomy'. The factor 'population' represents the geographical location of the population corresponding to each specimen. The factor 'taxonomy' questions the hypothetical existence of well-differentiated morpho- Both principal component analysis and discriminant analysis results were presented as scatter plots using the function 's.class' of the ADE4 package, with ovals drawn around at least 67% of the points belonging to the same class. Each point is connected to its class baricentre (in multidimensional space) by a line. Principal component analysis and discriminant analysis were performed using the ADE4 package of R statistical software. In order to check for cohesiveness of the four putative taxa, according to the taxonomy factor, a Kruskal-Wallis rank sum test of the most discriminant variables in discriminant analysis was performed using R software, considering each taxon versus the rest.

DNA ISOLATION, POLYMERASE CHAIN REACTION (PCR) AMPLIFICATION AND SEQUENCING OF RDNA ITS

Total DNA was isolated from leaves stored in silica gel following a slightly modified 2 ¥ CTAB method [START_REF] Doyle | A rapid DNA isolation procedure for small quantities of fresh leaf tissue[END_REF]. For all sequences, each amplification reaction (100 mL final volume) contained 50 ng of template DNA, 1 ¥ incubation buffer (Q-biogen), 7.5 mM MgCl2, 10 mM of each primer and 5 units of Taq polymerase (Q-biogen). Amplification of the ITS region was performed using primers ITS-4 and ITS-7, as described by Fuertes Aguilar et al. (1999a). The PCR cycling regime involved 30 cycles of 1 min denaturation at 94 °C, 1 min annealing at 48 °C and 2 min extension at 72 °C. PCR products were checked on 1.5% agarose gels before sequencing. As band heterogeneity was never observed on agarose, PCR products were purified using the Qiaquick PCR purification kit (Qiagen) and shipped for direct sequencing (MWG Biotech Company). All fragments were sequenced with ITS-4 and ITS-7 in order to check the quality of the sequences by alignment of the two strands. Sequences were manually aligned with MEGA 3.1 software [START_REF] Kumar | MEGA3: integrated software for molecular evolutionary genetics analysis and sequence alignment[END_REF]. The method of Fuertes [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF] was used to search for polymorphic sites in the electropherograms which could display an additive pattern with respect to Armeria ITS diversity found in GenBank. Additive polymorphic sites (APSs) were determined by two conditions: (1) if a polymorphic site has two peaks at one nucleotide position, the weakest signal must represent at least 25% of the strongest signal; and (2) two nucleotides involved in a polymorphic site must be found separately in the data set or in previous records in GenBank. APSs can be the mark of past reticulation events.

RESULTS

MORPHOLOGICAL ANALYSIS

The main results of the principal component analysis based on 18 quantitative and three qualitative characters are presented in wide calyx spurs. The third component is, to a large extent, determined by one character, calyx hairiness, which is diffuse in the Cap Garonne populations (CapG), and linearized to diffuse in the other populations. All populations overlap, except for the 'Baisse du Pas Etroit' (Bais) population. Discriminant analysis was based on 14 quantitative characters that were visually checked for normality. Two grouping criteria were tested: population origin and taxonomic hypothesis.

Population origin as a grouping criterion

Discriminant components (DCs) 1, 2 and 3 explain 22, 20 and 16% of the variance in the matrix, respectively. Three characters have a high canonical weight on DC1: LoC (-0.46), LaPf (0.37) and LaF (0.30). DC2 is mainly explained by Losc (-0.56), LotC (0.45) and LoC (-0.44). A DC1 vs. DC2 scattergram (Fig. 3) indicates that discriminant analysis fails to distinguish populations, but rather organizes them along a morphological gradient, ranging from the Guisane population in the Hautes-Alpes (Guis) to the population of Baisse du Pas Etroit (Bais).

Taxonomic hypothesis as a grouping criterion

DCs 1, 2 and 3 explain 45, 38 and 17% of the variance, respectively. The highest variable weights on DC1 are those for LaPf (0.42), Dsc (-0.31) and Laf (-0.30). For DC2, Losc (-0.62), LoC (-0.43) and LotC (0.35) are the principal characters. The taxonomic criterion leads to a better discriminant function as shown by the DC1 vs. DC2 scattergram (Fig. 3). The groups 'prae' and 'bup' are well individualized, the groups 'prad' and 'peir' are partly overlapping, and 'prae' and 'bup' or 'prad' and 'bup' are close and overlapping for some individuals. Thus, as for the population criterion, no group is completely discrete in the multivariate analysis. However, the Kruskal-Wallis rank test gives evidence for cohesiveness of the four taxa when the most discriminant variables are considered alone (Table 3).

ITS DIVERSITY

Sequencing of the rDNA ITS genes was conducted on one individual from 12 populations: Sainte-Anne (StAn), Rougiers (Roug), Guisane valley (Guis), Estérel (Est), Cap Lardier (CapL), Cap Garonne (CapG), Morières (A. belgenciensis), Baisse du Pas Etroit (Bais), Eteize (Etei), Avinière (Avin), Cap Taillat (CapT), and Tourtour (Tour). The complete sequences containing the ITS1, 5.8S gene and ITS2 are 620 bp long. Fixed nucleotide or indel variations are absent. Therefore, the 12 samples analysed share the same ITS sequence. Nevertheless, following the method of Fuertes [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF], we found five APSs in all but two sequences (from Avinière and col Ste-Anne); these APSs are summarized and compared with a set of GenBank sequences representative of Armeria ITS diversity (Table 4).

DISCUSSION

In order to delimit morphological groups among Armeria populations in Var, we developed a phenetic analysis and rDNA ITS sequencing. As morphological data are mostly continuous and highly variable, we did not apply species delimitation methods, such as population aggregation analysis [START_REF] Davis | Populations, genetic variation, and the delimitation of phylogenetic species[END_REF][START_REF] Sites | Delimiting species: a renaissance issue in systematic biology[END_REF]. We preferred to use non-specialized methods more suitable for different kinds and quality of data.

Principal component analysis results reveal a pattern of differentiation between populations, but, in parallel, the variation remains high within populations and overlaps between them, forming a continuous morphological gradient. As an illustration, the A. arenaria subsp. praecox population (Guis), sampled near Briançon (Hautes-Alpes), characterized by large and lanceolate leaves, a long scape, a long calyx and pink flowers, encompasses some individuals that are morphologically close to some plants from the Var coastline (Fig. 2). This similar leaf morphology could explain why the coastal and halophilous populations of the Maures and Esterel massifs have often been considered as subsp. praecox [START_REF] Molinier | Observations sur la végétation de la zone littorale en Provence[END_REF][START_REF] Géhu | Glanures phytosociologiques sur les côtes de Provence[END_REF]. Nevertheless, other characters distinguish these alpine and maritime populations, which are also well dif- ferentiated from an ecological point of view. The maritime populations of Armeria in Var should thus be included in subsp. bupleuroides (see below), as proposed initially by local botanists [START_REF] Albert | Catalogue des plantes qui croissent naturellement dans le département du Var[END_REF][START_REF] Camus | Florule de Saint-Tropez et de ses environs immédiats[END_REF]. These results show that the delimitation of groups of specimens in Armeria is not easy and must be based on statistical sampling.

Discriminant analysis was used to confirm the relevance of the a priori treatment of specimen groups. Discriminant analysis using the population criterion produces results similar to those of principal component analysis, and most populations in Var are weakly differentiated, except for the Bais population. populations. The Bais population is situated less than 1 km away from the rare and highly vulnerable A. belgenciensis, which is characterized by thin, linear leaves and a late flowering season (end of summer), whereas all the other taxa analysed flower during the spring. We did not sample this endemic species for the morphological analysis because of its highly endangered status. Although the flowering times of A. belgenciensis and the Bais population do not overlap, the shared ITS sequence and their morphological similarities suggest the potential existence of gene flow between them in the past. To a lesser extent, the vegetative and floral similarities between Bais and CapG populations, as well as their geographical closeness (16 km between them), suggest that their distributions overlapped during the past, promoting gene flow.

Discriminant analysis using the taxonomic criterion groups populations from the Maures and Esterel coastline with inland populations. The latter form a group, called 'bup'; 'bup' is characterized by lanceolate leaves of intermediate width, long outer involucral bracts, long corolla tubes and thin flower bracts. This result confirms that the coastal Armeria spp. in Var fit the delimitation of subsp. bupleuroides. As expected, the population from the Guisane valley near Briançon is well differentiated and corresponds to A. arenaria subsp. praecox ('prae'). It has wide, lanceolate leaves, a long scape with the largest diameter and a long flower calyx. Finally, the a priori treatment did not clearly delimit the hypothetical taxa 'prad' and 'peir', as they both include individuals characterized by sublinear leaves. However, the diffuse hairiness of the calyx appeared to be specific to the 'prad' group. In spite of the important variation found within each taxon, the polymorphism appears to be rather well structured by different characters. The robustness of these characters should be tested in the future by common garden experiments, but we have confidence in our data, which are in accordance with similar results in Armeria [START_REF] Lefèbvre | A numerical taxonomic study of Armeria maritima (Plumbaginaceae) in North America and Greenland[END_REF]Nieto Feliner et al., 2001b).

EF370060 Y Y Y Y Y CapT EF370059 C Y Y Y Y Est EF370062 Y Y Y Y Y Tour EF370067 Y Y Y Y Y Roug EF370058 C C T Y Y StAn EF370061 C C T T T CapG EF370063 Y Y Y Y T Bais EF370057 C C T Y T Guis EF370064 C Y T Y Y Avin EF370065 C C T T T Etei EF370066 Y Y Y Y Y Mori (A. belgenciensis) EF370056 C C T Y T GENBANK A. alliacea AJ225578 C C T T T A. beirana AY179762 C C T T C A. hirta AJ225568 C C T T C A. pungens AY179810 C C T T C A. arenaria confusa AY179757 C C C C C A. arenaria arenaria AY179756 C C T T T A. villosa bernisii AY444134 C C C C C A. filicaulis filicaulis AY179756 C C T T C A. leucocephala AY179788 C C C C C A. fontqueri AY179783 C C C C C A. trachyphylla AY179818 C C C C C A. maderensis AY179796 C C C C C A. alpina AJ225576 T T C C C A. maritima maritima AY179801 T T C C C A. nebrodensis AY179806 C C C C C
Despite the observation of phenotypic polymorphism, the 12 ITS sequences sampled across a wide range of plants did not display fixed variation. We propose two non-exclusive hypotheses to explain this absence of fixed variation at a coarse geographical scale. First, the range of Armeria in south-eastern France could be the result of a recent expansion of populations from the Iberian Peninsula, in parallel with rapid adaptive and morphological diversification, but, by contrast, a slow drift within neutral DNA sequences. To support this hypothesis, the phylogenetic tree based on ITS sequences of 71 Armeria taxa performed by Fuertes [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF] indicates that the A. arenaria group is included in the Western Mediterranean Clade, together with several Iberian Armeria. According to the second hypothesis, the lack of ITS variation could be a result of recent breeding events occurring between formerly differentiated genetic entities, followed by ribotype homogenization during concerted evolution, a not unusual process in the genus (Fuertes Aguilar et al., 1999a). The second hypothesis supports the compilospecies concept formulated by [START_REF] Harlan | The compilospecies concept[END_REF], and adapted for Armeria by Fuertes Aguilar et al. (1999b) when they discovered the strong geographical structure of rDNA ITS sequence variation in southern Spain; here, different species from the same location have the same ribotype. Compilospecies are widely distributed, polyphyletic taxa which breed with welladapted endemics (Fuertes Aguilar et al., 1999b); they form a system in which free gene exchange is possible and, at the same time, confuses the phylogenetic signal of molecular markers. In the present study, we looked for APSs which could support the second hypothesis. We found that 10 of the 12 ITS sequences included five APSs. Two APSs (positions 377 and 386) support a reticulation event between the A. maritima/ alpina and A. arenaria clades. Three samples (CapL, Est, Tour) from the coastline of Var have the Y state, pointing to a potential and ancient link between the alpine and Mediterranean populations. The three other APSs (387, 388 and 556) also indicate the possibility of between-clade gene flow, but are less informative because the two states (C and T) have a wider distribution in the genus; therefore, the APS 'Y' may indicate different reticulation events. Another pattern supporting the 'reticulation' hypothesis is that A. belgenciensis has the A. arenaria ribotype, whereas it is phonologically and morphologically the most differentiated taxon, with a different flowering time and filiform leaves. Moreover, the morphological intermediacy and APS of the Bais population support the possibility of former gene flow, as this population is located less than 1 km distant from A. belgenciensis.

In the light of the frequent hybridization in Armeria, Nieto [START_REF] Feliner | El género Armeria (Plumbaginaceae) en la Península Ibérica: aclaraciones y novedades para una síntesis[END_REF][START_REF] Feliner | Armeria[END_REF] proposed that, instead of the biological species concept, a combination of morphological characters, geographical range and ecological preferences should be used as criteria to delimit species-level taxa. In fact, morphologically and ecologically differentiated groups exist in this genus, despite extensive reticulation [START_REF] Aguilar | Additive polymorphism and reticulation in an ITS phylogeny of thrifts (Armeria, Plumbaginaceae)[END_REF]. What seems important is that the delimitation of taxa is not arbitrary. Thus, the 'eco-morpho-geo' criterion offers the possibility to label well-separated and localized groups of populations for conservation purposes. This is in agreement with the concept of Evolutionary Significant Units, in which populations with distinct adaptations to different habitats take on importance from a conservation genetics perspective [START_REF] Moritz | Defining evolutionary significant units for conservation[END_REF][START_REF] Crandall | Considering evolutionary processes in conservation biology[END_REF].

In conclusion, we propose the following taxonomy for the Armeria populations living along or near the Var coastline. First, A. belgenciensis is undoubtedly well differentiated and must conserve its species rank. Only one population of less than 200 individuals exists according to a census performed in 2003 (A. Baumel, pers. observ.), and it is one of the most threatened plants in France [START_REF] Donadille | Livre rouge de la flore menacée de France. Tome 1: espèces prioritaires[END_REF]. In addition to its small population size, A. belgenciensis is also endangered by its proximity to a road; furthermore, a great deal of sheep grazing, with a large impact on the local vegetation, was observed in 2004, together with destruction of an important part of the population in 2005 as a result of road alteration work. At present, the future of this narrow endemic is seriously jeopardized, with the persistence of less than 50 individuals in 2005 (A. Aboucaya and A. Baumel, pers. observ.). Secondly, Armeria populations from the Maures and Esterel mountain chains should be included in A. arenaria subsp. bupleuroides, as they are similar to the inland populations sampled in Var, Bouches-du-Rhône and Drôme. The subspecies bupleuroides is therefore a widely distributed endemic taxon of south-eastern France, present from the coastline to the southern parts of the Alps, as populations from the northern part of Var also belong to this taxon (A. Baumel, unpubl. data). A more in-depth sampling should be performed in the Alpesde-Haute-Provence and Hautes-Alpes departments to explore the relationship between subsp. bupleuroides and subsp. praecox, as we have sampled only one locality of the latter. Finally, considering that two populations of Armeria in the Var department need taxonomic recognition, we decided to apply the operational criterion developed by Nieto Feliner et al. (2001b). We propose the recognition of the uniqueness of the 'Bais' and 'Prad' populations, despite some similarities shared with both A. arenaria subsp. bupleuroides and A. belgenciensis. This could be another mark of reticulate evolution that should be recognised by botanists, and we propose to describe them as two new subspecies.

DESCRIPTION OF TWO NEW SUBSPECIES OF ARMERIA FROM THE VAR DEPARTMENT

The Cap Garonne population, growing on copper mine wastes, should be distinguished as a different subspecies with respect to its sublanceolate leaves, unique calyx hairiness and particular ecology on a metalliferous (copper) substrate. We propose that it should be named as follows.

ARMERIA ARENARIA (PERS.) SCHULT. Description: Scapes 17-47 cm. Leaves 50-165 ¥ 1.5-5.2 mm, monomorphic, sublinear to sublanceolate, three-veined, the point mostly acute but sometimes obtuse. Outer involucral bracts 2-6, length 4.2-8.3 mm with an awn easily visible. Middle involucral bracts 1-4, length 3.4-5.5 mm. Inner involucral bracts 3-6, length 4.8-6.6 mm. Spikelet bracts 5.3-7.2 mm long and 4.1-6.9 mm wide. Flower number by spikelet 1-4. Calyx 4.7-6.2 mm long with diffuse pubescence, tube 2.2-3.3 mm long and 1.2-1.6 mm wide. Corolla white.

Derivation:

The name A. arenaria subsp. pradetensis (Pradet thrift) is given in reference to the village of Le Pradet, the municipality in which it grows.

The population of Baisse du Pas Etroit, south of Belgentier (Bais), must be differentiated from A. arenaria subsp. bupleuroides, notably by its linear to sublinear leaves. We propose that this population should be described as follows. Description: Scapes 23-59 cm. Leaves 56-103 ¥ 0.4-1.6 mm, linear to sublinear, one-veined, the apex acute. Three outer involucral bracts, length 2.4-4.1 mm with a short awn. Three to four middle involucral bracts, length 2.7-4 mm. Five inner involucral bracts, length 5.2-7.3 mm. Spikelet bracts 5.2-7.1 mm long and 5.6-6.7 mm wide. Flower number by spikelet 2-3. Calyx 4.6-5.3 mm long with linear pubescence, tube 2.3-2.7 mm long and 1.4-1.8 mm wide. Corolla white. This population occurs at the location called 'Baisse du Pas Etroit', near the village of Sollies-Toucas, but in the Belgentier municipality, and contains no more than a few hundred individuals. We consider its linear leaves as potential proof of gene flow with A. belgenciensis. Derivation: The name A. arenaria subsp. peirescii (Peiresc thrift) is given in reference to Nicolas-Claude Fabri de Peiresc (1580-1637), a famous humanist, jurist, philosopher, astronomer and botanist, who lived for several years in his country house at Belgentier.

CONCLUSION

This work suggests that an increased number of diverse molecular markers must be used in Armeria to refine the taxonomic definition. It provides valuable data to understand how phenotypic diversity evolved despite weak reproductive barriers between the taxa. For the time being, future conservation units should be considered only on the basis of multivariate morphometric analysis. steps of this work, Carey Suehs for checking of the English, and Gonzalo Nieto Feliner and an anonymous reviewer for their helpful comments on the manuscript.

Figure 1 .

 1 Figure 1. Geographical location of the study. A, Departments in which Armeria arenaria subsp. bupleuroides occurs in France are shaded in grey; the box corresponds to the area of study. B, Sampling sites for the study. SeeTable 1 for abbreviations.

Figure 2 .BaisFigure 2 .

 22 Figure 2. Principal component 1 versus 2, explaining 26% and 17% of the variance, respectively. A, Ovals are labelled according to the population origin of the specimens and encompass at least 67% of the samples. B, Correlations and variable weights.

Figure 3 .

 3 Figure 3. Discriminant analysis results. Scatter plots of canonical discriminant function 1 versus canonical discriminant function 2. Ovals are labelled according to: A, population origin; B, taxonomic hypothesis. C, D, Correlations and variable weights for the population and taxonomic hypothesis criteria, respectively.

  ARMERIA ARENARIA(PERS.) SCHULT. SUBSP. PEIRESCII BAUMEL, AUDA & MEDAIL SUBSP. NOV. Diagnosis: Ab subsp. bupleuroide (Godron & Gren.) Greuter & Burdet, differt: foliis linearibus vel sublinearibus (1.2 ± 0.4 mm non 5.1 ± 1.7 mm), involucri phyllis brevioribus (3.48 ± 0.51 mm non 6.92 ± 1.75 mm). Holotype: France, Var department (83), Belgentier, massif de Morières, Baisse du Pas Etroit, alt. 360 m; dolomitic rocks. A. Baumel & P. Auda, Bais5, 27.v.2004, AIX. Isotype: A. Baumel & P. Auda, Bais5, 27.v.2004, Herbarium F. Médail, s.n. (IMEP, Université Paul Cézanne, Aix-Marseille III, Aix-en-Provence).

Table 1 .

 1 Sampling description

				Sampling for
				morphometry,
		Location and main physiographical	Taxa studied and correspondence	GenBank
	Site	characteristics	with former taxonomic treatments	accession
	Cap Lardier	La Croix-Valmer, coast of the
		Maures massif, Var (83); alt.
		10 m; gneiss
				(Est)
				EF370062
			arenaria: Gandioli & Salanon,
			2000)
	St Pierre-de-Tourtour Tourtour, Var (83); alt. 680 m	A. arenaria subsp. bupleuroides	6 (Tour)
				EF370067
	Rougiers	Rougiers, massif de la Ste-Baume,	A. arenaria subsp. bupleuroides	(Roug)
		Var (83); alt. 450 m		EF370058
	Col Ste-Anne	Mimet, massif de l'Etoile,	A. arenaria subsp. bupleuroides	10 (StAn)
		Bouches-du-Rhône (13); alt.	(Molinier, 1980)	EF370061
		580 m; dolomitic rocks
	Montagne du Poët	Poët-Laval, Drôme (26); alt. 600 m,	A. arenaria subsp. bupleuroides	10 (Poet)
		dolomitic rock	(Garraud, 2003)
	Cap Garonne	Le Pradet, Colle Noire, Var (83);	A. arenaria subsp. pradetensis	20 (CapG, CapG2)
		alt. 90 m; grès-quartzites	(sub A. bupleuroides: Albert &	EF370063
			Jahandiez, 1908)
	Baisse du Pas Etroit	Belgentier, massif de Morières, Var	A. arenaria subsp. peirescii (sub	10 (Bais)
		(83); alt. 360 m; dolomitic rocks	A. bupleuroides: Albert &	EF370057
			Jahandiez, 1908)
	Vallée de la Guisane	Serre-Chevalier, Hautes-Alpes (05);	A. arenaria subsp. praecox (Chas,	20 (Guis)
		alt. 1600 m	1994)	EF370064
	Avinière	Vallée de la Vis, Hérault (34), alt.	A. arenaria subsp. arenaria	(Avin)
		200 m		EF370065
	Eteize	Suc de Clava, Ardèche (07), alt.	A. arenaria subsp. arenaria	(Etei)
		600 m		EF370066
	Morières la Tourne	Solliès-Toucas, massif de Morières,	A. belgenciensis (Donadille, 1969)	(Mori)
		Var (83); alt. 410 m; dolomitic	(sub A. filicaulis: Albert &	EF370056
		rocks	Jahandiez, 1908)

A. arenaria subsp. bupleuroides (sub A. praecox: Molinier, 1954) 10 (CapL) EF370060 Cap Taillat Ramatuelle, coast of the Maures massif, Var (83); alt. 15 m; phyllades A. arenaria subsp. bupleuroides (sub A. bupleuroides: Camus & Camus, 1912) 10 (CapT) EF370059 Cap de St-Tropez St-Tropez, coast of the Maures massif, Var (83); alt. 10 m; phyllades A. arenaria subsp. bupleuroides (sub A. bupleuroides: Albert & Jahandiez, 1908; Camus & Camus, 1912; A. praecox: Molinier, 1954) 10 (CapS) Cap Dramont St-Raphaël, coast of the Estérel massif, Var (83); alt. 10 m A. arenaria subsp. bupleuroides (sub A. arenaria subsp. praecox: Milano, 1960; A. arenaria subsp.

logical groups that could be allocated to four putative taxa: 'bup' (subsp. bupleuroides) for the populations of Saint-Anne, Poët Laval, Tourtour, Cap Taillat, Cap de Saint Tropez and Cap Lardier; 'prae' (subsp. praecox) for the Guisane population; 'prad' for the two populations of Cap Garonne (Le Pradet); and 'peir' for the population of 'Baisse du Pas Etroit' near Belgentier. To perform discriminant analysis, we selected a subset of 14 quantitative characters that were normally distributed (Lof, Laf, Losc, Log, Dsc, Lobre, Nbbre, Nbbrm, LotC, LatC, LoC, LoPf, LaPf, NbF: see Table

2

for details). As for principal component analysis, all variables were standardized before discriminant analysis.

Table 2 .

 2 Morphological characters

		POLYMORPHISM OF ARMERIA IN SE FRANCE 259
	Character	Description
	Leaf length (Lof)	Continuous from 26 to 176 (mm)
	Leaf width (Laf)	Broadest width of the leaf, continuous from 0.4 to 14.5 (mm)
	Leaf shape (FormF)	Four states: 0, linear; 0.33, sublinear; 0.66, sublanceolate; 1,
		lanceolate
	Number of leaf veins (Ner)	Absolute values from 1 to 3
	Scape length (Losc)	Continuous from 118 to 472 (mm)
	Sheath length (Log)	Continuous from 15 to 54 (mm)
	Scape diameter (Dsc)	Measured at the base, continuous from 0.486 to 2.318 (mm)
	Outer involucral bract length (Lobre)	Continuous from 2.4 to 11.4 (mm)
	Median involucral bract length (Lobrm)	Continuous from 2.7 to 9.5 (mm)
	Inner involucral bract length (Lobri)	Continuous from 4.1 to 7.5 (mm)
	Number of outer involucral bracts (Nbbre)	Absolute values from 1 to 6
	Number of median involucral bracts (Nbbrm)	Absolute values from 1 to 9
	Number of inner involucral bracts (Nbbri)	Absolute values from 2 to 8
	Length of the calyx spur (LotC)	Continuous from 2.13 to 3.56 (mm)
	Width of the calyx spur (LatC)	Continuous from 1.1 to 1.8 (mm)
	Calyx length (LoC)	Continuous from 4 to 7 (mm)
	Calyx hairiness (PubCa)	Three states: 0, diffuse; 0.5, intermediate between linear and
		diffuse; 1, linear
	Flower bract length (LoPf)	Continuous from 3.9 to 7.4 (mm)
	Flower bract width (LaPf)	Continuous from 2.8 to 6.9 (mm)
	Number of flowers in spikelet (NbF)	Absolute values, ranging from 1 to 5
	Flower colour (Coul)	Two states: 0, white; 1, pink

© 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159, 255-267

Table 3 .

 3 Mean and standard deviation for the most discriminant morphological metric characters (see Table2and section on 'Data analysis' for abbreviations)

		Lof	Laf	Losc	Dsc	Lobre	LaPf	LoC	LotC
	prae 108.5 ± 27.5ns 7.5 ± 2.6*** 430.8 ± 82.2*** 1.76 ± 0.24*** 6.94 ± 1.69ns	5 ± 0.4ns 6.3 ± 0.4*** 2.74 ± 0.17****
	bup	82.7 ± 33.5*** 5.1 ± 1.7** 241.9 ± 76.8*** 1.19 ± 0.24ns 6.92 ± 1.75*	4.5 ± 0.6*** 5.4 ± 0.6ns 2.75 ± 0.29ns
	prad 125.6 ± 28.6*** 2.4 ± 0.8*** 335.8 ± 84.6*	1.03 ± 0.24** 6.11 ± 1.27ns 5.6 ± 0.7*** 5.4 ± 0.5ns	2.9 ± 0.35*
	peir	83.6 ± 19ns	1.2 ± 0.4*** 311.3 ± 102.3ns 0.86 ± 0.1*** 3.48 ± 0.51*** 6.2 ± 0.3*** 4.9 ± 0.2** 2.48 ± 0.14***
	Results of the Kruskal-Wallis rank test are indicated as follows: *P < 5%; **P < 1%; ***P < 0.1%; ns, P > 5%.
	All measurements in millimetres.

Table 4 .

 4 Summary of additive polymorphic sites found in the internal transcribed spacer (ITS) region (see Table1for abbreviations), compared with a set of GenBank sequences representative of ITS diversity in the genus Armeria

	377	386	387	388	556
	This study
	CapL

  SUBSP. PRADETENSIS MÉDAIL, BAUMEL & AUDA,

	SUBSP. NOV.
	Diagnosis: Ab subsp. bupleuroide (Godron &
	Gren.) Greuter & Burdet differt: foliis longioribus
	(125.6 ± 28.6 mm non 82.7 ± 33.5 mm), angustiori-
	busque (2.4 ± 0.8 mm non 5.1 ± 1.7 mm) latis; ab
	subsp. bupleuroide quoque differt: calyce pilis sparse
	diffusis vestito et non distincte lineatis.
	Holotype: France, Var department (83), Le Pradet,
	Colle Noire, Cap Garonne, alt. 90 m, gres-quartzites.
	F. Médail, P14., 9.vi.2002, AIX. Isotype: F. Médail,
	P14., 9.vi.2002, Herbarium F. Médail, (IMEP, Univer-
	sité Paul Cézanne, Aix-Marseille III, Aix-en-
	Provence).

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A. BAUMEL ET AL. © 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159, 255-267 Downloaded from https://academic.oup.com/botlinnean/article-abstract/159/2/255/2418394 by Universite D'Aix-Marseille user on 25 April 2018

A. BAUMEL ET AL. © 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159, 255-267 Downloaded from https://academic.oup.com/botlinnean/article-abstract/159/2/255/2418394 by Universite D'Aix-Marseille user on 25 April 2018

A. BAUMEL ET AL. © 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159, 255-267 Downloaded from https://academic.oup.com/botlinnean/article-abstract/159/2/255/2418394 by Universite D'Aix-Marseille user on 25 April 2018

A. BAUMEL ET AL. © 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159, 255-267 Downloaded from https://academic.oup.com/botlinnean/article-abstract/159/2/255/2418394 by Universite D'Aix-Marseille user on 25 April 2018

ACKNOWLEDGEMENTS

The authors would like to thank the following: Laurence Affre, Roger Cruon, INFLOVAR, Pierre Donadille, Marianick Juin, Claude Lefèbvre, Pierre Quézel and Jean-Marc Tison for their help during different


Elise Kaspi

PhD Xavier Heim

PhD Brigitte Granel

PhD Benjamin Guillet

Jimmy Stalin

Marie Nollet

Alexandrine Bertaud-Foucault

PhD Andrée Robaglia-Schlupp

MD Patrice Roll

PhD Pierre Cau

PhD Jimmy Stalin D

PhD Marie Nollet D

PhD Alexandrine Bertaud-Foucault D

PhD Aurélie Leroyer D

PhD Richard Bachelier

PhD Audrey Benyamine

PhD Françoise Dignat- George

PhD Marcel Blot-Chabaud D

PhD Nathalie Bardin
email: nathalie.bardin@ap-hm.fr

PhD Françoise Dignat-George

Identification of CD146 as a novel molecular actor involved in systemic sclerosis

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Short summary :

We highlight for the first time that CD146/sCD146 is involved in fibrotic process during SSc. sCD146 could thus constitute a new biomarker to assess disease activity, and potentially a new target for therapeutic applications. E1). All patients fulfilled the 2013ACR/EULAR Classification Criteria for Scleroderma 5 and were then sub classified according to LeRoy et al criteria. [START_REF] Leroy | Criteria for the classification of early systemic sclerosis[END_REF] All samples came from a declared Biobank (DC 2012-1704) with respect of ethical directives (see Table E1 and Methods section in this article's Online Repository). Soluble CD146 levels were significantly higher in patients with SSc than in healthy controls (867.1 ± 32.3 vs 497.7 ± 16.5; p<0.001) (Fig 1A). Regarding clinical association, we found a significant association between lowest sCD146 levels and digital gangrene (n=5; p=0.03) as well as pulmonary fibrosis (n=20; p=0.04), two severe manifestations of the disease, whereas no significant association was found between sCD146 levels and Raynaud's phenomenon (n=29), digital scars / ulcers (n=16). (Fig 1B,C). Sera available 12 months later for 15 patients showed a significant association

(p=0.03) between the diminution of sCD146 levels and aggravation of the disease attested by digital necrosis, pulmonary arterial hypertension and pericarditis (Fig 1D).

To investigate whether sCD146 is active in serum of patients, we examined its effect on endothelial cell proliferation. Results showed a significant correlation between seric suggest that patients producing high and sustained levels of sCD146 may be protected against the disease complications. Up to now, sCD146 has been mainly described in human serum as an endothelial biomarker modulated in inflammatory diseases. In inflammatory bowel diseases, we found an association between sCD146 levels and disease activity. [START_REF] Reumaux | Restoration of soluble CD146 in patients with Crohn's disease treated with the TNF-alpha antagonist infliximab[END_REF] Indeed, low level of sCD146 was associated with the active form of the disease and an upregulation of sCD146 occurred after anti-TNF treatment and a favourable disease evolution. [START_REF] Reumaux | Restoration of soluble CD146 in patients with Crohn's disease treated with the TNF-alpha antagonist infliximab[END_REF] Similarly in the present study, unfavorable evolution of SSc was associated with a decrease of sCD146 levels. In addition, vascular ischemic complication (digital gangrene) and pulmonary fibrosis were associated with low sCD146 levels. Although a prospective study is necessary to confirm our conclusion, high sCD146 levels could constitute a good prognostic marker of the disease. Along this line, we showed that CD146KO mice were strongly sensitive to bleomycin-induced skin fibrosis as compared to WT mice. The proof that this effect is CD146-dependent is given by the absence of fibrosis development after sCD146 injection in this animal model. Fibrosis, the hallmark of SSc, is characterized by the proliferation of fibroblasts, their differentiation in myofibroblasts and an excessive extracellular matrix accumulation. Many cytokines such as TGF-, VEGF, and endothelin-1 are considered as key mediators in this process. [START_REF] Kendall | Fibroblasts in fibrosis: novel roles and mediators[END_REF] Our study underlines for the first time that CD146/sCD146 may also regulate fibrotic process during scleroderma. Further studies will be conducted to analyze the specific role of CD146/sCD146 in the fibrotic process and interactions with the other pathways.

In conclusion, our data led us to propose CD146/sCD146 as a novel biomarker in SSc for the assessment of the disease activity. Mechanistic studies will now be necessary to delineate the precise role of CD146/sCD146 in the fibrotic process and to further investigate the potential interest of the molecule for therapeutic applications.

1

 1 Key words: CD146; soluble CD146; Systemic sclerosis; Fibrosis; Biomarker; Disease activity To the Editor: Systemic sclerosis (SSc) is a fibrosing autoimmune disorder characterized by vascular damage, excessive fibrosis in the skin and internal organs, and immune dysfunction. Pulmonary fibrosis and pulmonary arterial hypertension are the most serious complications and currently constitute the major causes of death. The identification of biomarkers for the presence and progression of clinical complications in SSc helps to clarify pathogenic mechanisms, assess disease activity and offer new hopes for treatment. CD146, an adhesion molecule located essentially in the vascular system, is also present as a soluble form (sCD146) in bloodstream. 2 Because of its role in endothelial integrity and inflammatory response, 3,4 two processes modulated in SSc, we hypothesized that CD146/sCD146 could represent a new molecular actor involved in SSc pathogenesis. Sera from 50 SSc patients admitted to internal medicine departments in Marseille (South of France) were analyzed (Table

  CD146 levels and cell proliferation (p=0.021) and a significant decrease in cell proliferation when sCD146 was immunodepleted (p<0.0001) (Fig E1) (see Fig E1 in this article's Online Repository). Thus, sCD146 present in the sera of patients with SSc is biologically active and may represent a protective biomarker of the disease. To further examine the impact of CD146 we used the bleomycin-induced skin fibrosis model in WT and CD146 deficient mice. In this study, we used 1μg of bleomycin/mouse. At this dose, no modification was obtained in dermal thickness under bleomycin or control conditions in WT mice (p=0.64; Fig 2A, B, G). In contrast in CD146KO mice, dermal thickness was significantly higher after bleomycin treatment than in control conditions (p=0.0002; Fig 2C, D, G) showing that this concentration was sufficient to induce skin fibrosis in CD146KO mice but not in WT mice. In the same way, epidermal thickness was also increased after bleomycin treatment in comparison to control conditions in CD146KO mice (p=0.04), whereas no effect of bleomycin treatment was observed in WT mice (p=0.63; Fig 2H). Altogether results showed a highly susceptibility of CD146KO mice to develop skin fibrosis after bleomycin injection. Interestingly, injection of sCD146 in bleomycin-treated CD146KO mice showed a significant reduction of dermal and epidermal thickness as compared to bleomycin condition (p=0.003 and p<0.0001, respectively; Fig 2E to H). Thus, our results suggest that sCD146 protects bleomycin-treated CD146KO mice from fibrosis development. Up to date, SSc-specific autoantibodies and cutaneous sub-classification are the most useful biomarkers for diagnosis and predicting clinical features. If several biomarkers such as ICAM-1 or E-selectin were proposed with a potential prognostic interest, 7 none of them are used in clinical practice. Our results highlighted the role of CD146/sCD146 in SSc because: (i) sCD146 levels were increased in SSc patients compared to controls, (ii) severe manifestations of the disease, digital gangrene and pulmonary fibrosis, were associated with low sCD146 levels in SSc patients, (iii) mice lacking CD146 were highly susceptible to develop skin fibrosis, (iv) in this KO model, skin fibrosis development can be prevented by sCD146 injection. Altogether our data

FIG 1 .

 1 FIG 1. A high and sustained soluble CD146 level in SSc patients is associated with a favourable evolution of the disease.A: sCD146 levels significantly higher in SSc than in controls (p<0.001).B: Significant association between pulmonary fibrosis and low sCD146 levels (p=0.04).C: Significant association between digital gangrene and low sCD146 levels (p=0.03). D: Significant association between diminution of sCD146 levels and disease aggravation (p=0.03).

FIG 2 .

 2 FIG 2. Mice lacking CD146 are highly susceptible to develop skin fibrosis and soluble CD146 injection prevents bleomycin-induced skin fibrosis in CD146KO mice. A to F: Wild type (A, B) and CD146KO mice (C to F) injected with vehicle (A, C and E), bleomycin (B, D) or bleomycin with sCD146 (F). Arrows illustrate dermal thickness. Scale bar: 100μm.

G

  and H: Significant increase of dermal (G) and epidermal thickness (H) after bleomycin injection in CD146KO mice prevented by sCD146 injection.

Acknowledgments

We thank Joëlle Fiteni, Nathalie Boitano, Corinne Derrien, for their help and continuous support.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Authors:

Elise KASPI a,b , PharmD, PhD, Brigitte GRANEL c,d , MD, PhD, Benjamin


Raji Chada

Amol Gorgile Reddy

Siddique Z Tukaram

Uredi Mohammed

Bathini Dilipkumar

Sumana Nagendra Babu

Dwaipayan Chakravarty

Pranav C Bhattacharya

René Joshi

Grée

Reddy

Amol Gorgile Tukaram

Siddique Z Mohammed

Uredi Dilipkumar

Bathini Nagendra Babu

Sumana Chakravarty

Dwaipayan Bhattacharya

Pranav C Joshi

René Grée

Synthesis and biological evaluation of longanlactone analogues as neurotrophic agents

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Synthesis and biological evaluation of longanlactone analogues as neurotrophic agents

Chada Raji Reddy, *,a Amol Gorgile Tukaram, b Natural products and their analogues play an important role as therapeutic agents in the treatment of many diseases. In this direction, the synthesis of various analogues of a natural product and evaluation of their effectiveness became the key topic of research among the medicinal chemistry research groups. Modern synthetic methodologies have emerged as key steps to strengthen the structure activity relationship (SAR) studies in natural product derivatives to improve their efficacy and therapeutic index. [START_REF]For selected reviews of piperidine alkaloids, see; (a) Kuramochi[END_REF] Longanlactone (natural pyrrole lactone, 1, Figure 1) was isolated by Zhen and co-workers from the longan (Dimocarpus longan) seeds, 2 which was used as a traditional medicine in China. 3 From the literature, it was found that the natural sources producing pyrrole alkaloids such as funebral (2), funebrine (3), were used as local folk medicines to control psychopathic fears. 4 In addition, longan fruit has several health benefits. Recently, the central nervous system (CNS) depressant, analgesic and antidiarrheal effects of the seed extracts of Dimocarpus longan have been studied. 5 Aqueous extract of longan has been reported to reduce the neural pain and swelling as well as to improve memory and learning, 6 principally by upregulating Brain-derived neurotrophic factor (BDNF) and its downstream markers leading to heightened cyclic AMP response element binding (pCREB) expression along with greater number of cells immunoreactive for 5'-bromo-2'-deoxyuridine (BrdU) and Doublecortin (DCX). 7 Amelioration of memory impairment in chemically induced cognitively impaired mice models is well reported using HX106N (a water soluble plant extract), one of Corresponding author. Dr. Chada Raji Reddy, E-mail: rajireddy@iict.res.in, Dr. Sumana Chakravarty, E-mail: sumanachak@iict.res.in whose many components is the extract from Longan. 8 However, the biological activity of natural product 1 has not been evaluated. In 2014, we reported the first asymmetric total synthesis of longanlactone (1), a pyrrole alkaloid, in six steps with 31% yield. 9 substantiate the compound concentrations are non-cytotoxic. In neurite growth assay, 1 showed a considerable increase in neurite length at 0.1µM concentration as compared to control (i.e. 37.01% increase in the neurite length when compared to the control) [Table 1, Figure 3B)]. This preliminary outcome encouraged us to synthesize the derivatives of natural product 1 with an array of substitutions, which may lead us towards an enhancement in neurotrophic activity.

Based on the structure of longanlactone (1), analogues were designed with three-point diversity (Figure 2), such as i) C2acylation of pyrrole, to generate the variations at 'R' group ii) aryl substitution on terminal alkyne (R 1 ) and iii) triazole formation with alkyne functionality using azides (R 2 ). Further, to verify the role of stereochemistry at the C4 centre on biological activity, synthesis of 4-epi-longanlactone (1a) analogues were also planned.

To synthesize the C-2 acylated derivatives, previously reported 9 pyrrole-lactone 4 was treated with different anhydrides such as acetic anhydride, propionic anhydride and trifluoroacetic anhydride in the presence of BF 3 •Et 2 O at 0 °C to afford the corresponding products longanlactone 1 and analogues 5, 6 in good yield. Similarly, 4-epi-longanlactone 1a and analogues 5a, 6a were synthesized from compound 4a, without epimerization.

Scheme 1. Synthesis of acyl derivatives

Towards the arylation of the terminal alkyne, natural longanlactone 1 and its 4-epimer 1a were independently subjected to a Sonogashira coupling reaction 10 with 4-iodonitrobenzene in the presence of palladium-catalyst to give the desired products 7 and 7a in 74% and 72% yields, respectively (Scheme 2).

Scheme 2. Synthesis of 4-nitrophenyl alkynyl analogues of 1 and 1a

Later, triazole analogues 8, 9, 8a and 9a were obtained in 1,4regioselective manner from the reaction of 1 and 1a with benzyl azide and AZT-derived azide in the presence of CuI catalyst in toluene (Scheme 3). 11

Scheme 3: Synthesis of triazole derivatives of 1 and 1a

The synthesized natural product derivatives (1a, 4-9 and 4a-9a) were evaluated for their in vitro cell cytotoxicity against mouse neuroblastoma cells (Neuro 2a) by using 3-(4,5dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay. 12,13 The results of in vitro cytotoxicity revealed that the tested compounds were relatively less cytotoxic as compared to the untreated control (see the supplementary information). This preliminary observation was promising to explore the neurotrophic potential in Neuro2a cells using standard in vitro protocol. 12 Initially, neurite outgrowth assay was performed to investigate the neurotrophic potential of natural product derivatives (1a, 4-9, 4a-9a). In this study, the Neuro 2a Cells were serum starved for 6 hours and were exposed to the synthesized compounds (1a, 4-9, 4a-9a) along with Nerve growth factor (NGF) as a positive control at concentrations of 0.1 µM and 0.01 µM for 48 hours. The results illustrated in Figure 3B revealed that compound 6 having -CF 3 substitution showed significant increase in neurite length at 0.1µM concentration as compared to control and other tested compounds (Figure 3B). Interestingly, compound 6 displayed better neuritogenic potential in neurite outgrowth assay even at 0.01 µM concentration (i.e. 33.74% increase in the neurite length when compared to the control) whereas decreased activity was observed for natural product 1 at lower concentration (0.01 µM, Figure 3A). In addition, compound 1a, 4a, 5 and 9a also showed noticeably increased neurite length as compared to DMSO. Furthermore, the compounds exhibited promising results in neurite outgrowth assay were screened for BDNF gene expression, 14,15 which suggested the mRNA fold change in BDNF after the exposure of compound 1 and 6 at 0.1 µM and 0.01 µM respectively (Figure 3C). These results clearly demonstrated that the involvement of BDNF mediation in this activity. However, no significant mRNA fold change was observed in NT3 (Figure 3D).

In summary, various analogues of a pyrrole-lactone natural product, longanlactone, have been synthesized. In addition, we have studied the neurotrophic effects of the natural product 1 as well as its analogues for the first time. Interestingly, compound 1 and 6 showed considerable neurotrophic activity on neuro2a cells at 0.1 µM and 0.01 µM concentrations, respectively. Further analysis of these compounds on BDNF gene expression demonstrated the mRNA fold change in BDNF. Although more studies are required to discover the target at the molecular level of this molecule, its mode of action is supposedly via the upregulation of BDNF as shown by real time PCR. Thus, we might safely surmise that this compound holds potential as a framework for further development of highly neuroactive compounds that might contribute significantly to CNS therapy.

  epi-Longanlactone (1a) C4 = Evaluation of neurotrophic activity of longanlactone along with its analogues has been achieved for the first time. A total of 12analogues have been prepared including C4-epimers.

Figure 1 .

 1 Figure 1. Structures of pyrrole-lactone based natural alkaloids

Figure 2 .

 2 Figure 2. Structure of designed analogues

  24 h in DMSO (0.1%), Compounds (0.01µM & 0.1 µM). The tabulated data and bar graphs were expressed as mean±SEM where n= 60 and *p<0.01 vs control.

13

 13

Figure 3 .

 3 Figure 3. (A & B): Average neurite outgrowth at 48 hours for control, NGF and test compounds at a concentration of 0.01 µM and 0.1 µM respectively. There was significant increase in neurite length in NGF and compound 6 treated cells after 48 hours compared to control at 0.01µM concentration. Data were analyzed by student's t-test [(Where * p<0.05 and #p<0.1; (n=60)]. (C): Represents the pictorial micrographs (bright field) of different treatment groups taken at 10X magnification using Motic AE31 microscope. (D): Showing mRNA fold change in BDNF and NT3 after 2 h of treatment for control, NGF and test compounds 6 at 0.01 µM and 1 at 0.1 µM concentrations. There was significant increase in BDNF fold change in compound 1 and 6 treated cells as compared to control whereas no significant fold change for NT3 was seen. Data were analyzed by student's t-test. [(Where * p<0.05 (n=60)].

  Siddique Z. Mohammed, a Uredi Dilipkumar, a Bathini Nagendra Babu, b Sumana Chakravarty, *, c Dwaipayan Bhattacharya, c Pranav C. Joshi c and René Grée d a Division of Natural Products Chemistry, CSIR-Indian Institute of Chemical Technology, Hyderabad, 500007, India b National Institute of Pharmaceutical Education and Research, Hyderabad, 500037 India c Centre for Chemical Biology, CSIR-Indian Institute of Chemical Technology, Hyderabad, 500007, India,

d Institut des Sciences Chimiques de Rennes, CNRS UMR 6226, Avenue du Général Leclerc, 35042 Rennes Cedex, France

Table 1 :

 1 Morphometric analysis of neurite outgrowth of differentiated Neuro2a cells a

	Treatment	Average neurite length (µm)	Percent change from
		± SEM	control (%)
	Untreated control	77.29±2.38	-
	DMSO	82.43±3.79	6.65
	NGF (100ng/mL)	151.73±5.47*	96.31
		Treatment	Treatment	Treatment	Treatment
		dose-0.01	dose-0.1 µM	dose-0.01	dose-0.1
	Compound	µM		µM	µM
	1	83.5±3.59	105.90±3.66*	8.03	37.01
	1a	84.28±3.75	93.48±4.03	9.04	20.95
	4	82.36±4.52	85.72±4.91	6.56	10.90
	4a	86.68±3.13	88.55±4.78	12.15	14.56
	5	86.28±4.45	84.62±4.82	11.63	9.47
	5a	80.87±2.76	84.63±4.62	4.63	9.50
	6	103.37±5.56	109±4.41	33.74	41.02
	6a	83.29±3.58	94.47±3.57	7.76	22.22
	7	71.44±3.51	84.33±4.88	-7.58	9.11
	7a	78.39±3.32	87.55±5.01	1.43	13.27
	8	81.48±4.05	89.37±3.57	5.41	15.62
	8a	75.57±3.15	90.45±3.53	-2.23	17.02
	9	80.13±3.07	82.40±4.23	3.67	6.61
	9a	84.65±2.61	88.73±4.48	9.52	14.80

a Neuro2a cells cultured for

Acknowledgments

UD thanks CSIR, New Delhi for research fellowship. CRR and SC are grateful to CSIR, New Delhi for financial support as part of XII-five year plan project under title ORIGIN and SMILE. This research has been performed as part of the Indo-French "Joint Laboratory for Natural Products and Synthesis toward Affordable Health". We thank CNRS, CSIR and University of Rennes 1 for support of this research.

Highlights

• Longanlactone, a natural pyrrole-lactone alkaloid, analogs were synthesized. • Neurotrophic effects of Langanlactone analogs were studied for the first time • mRNA Fold change was observed in BDNF gene expression study of Longanlactone


C Duval
email: duval@cpt.univ-mrs.fr

G W Gibbons
email: g.w.gibbons@damtp.cam.ac.uk

P A Horvathy
email: horvathy@lmpt.univ-tours.fr

P.-M Zhang

Carroll symmetry of plane gravitational waves

Keywords: numbers: 04.20.-q Classical general relativity, 02.20.Sv Lie algebras of Lie groups, 04.30.-w Gravitational waves

The well-known 5-parameter isometry group of plane gravitational waves in 4 dimensions is identified as Lévy-Leblond's Carroll group in 2 + 1 dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.

I. INTRODUCTION

A gravitational plane wave is the 4-manifold, R 4 globally, endowed with the Lorentz metric [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF][START_REF] Bondi | Gravitational waves in general relativity. 3. Exact plane waves[END_REF][START_REF] Ehlers | Exact solutions of the gravitational field equations[END_REF][START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF][START_REF] Kramer | Exact solutions of Einstein's field equations[END_REF][START_REF] Gibbons | Quantized Fields Propagating in Plane Wave Space-Times[END_REF][START_REF] Garriga | Scattering of quantum particles by gravitational plane waves[END_REF][START_REF] Torre | Gravitational waves: Just plane symmetry[END_REF], g = δ ij dX i dX j + 2dU dV + K ij (U )X i X j dU 2 , (I. [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF] where the symmetric and traceless matrix K(U ) = (K ij (U )) characterizes the profile of the wave. Here U and V are light-cone coordinates, whereas X = (X 1 , X 2 ) parametrizes the transverse plane which carries the flat Euclidean metric dX 2 = δ ij dX i dX j . This metric is a Brinkmann pp-wave metric [START_REF] Brinkmann | Einstein spaces which are mapped conformally on each other[END_REF]. Since the only non-vanishing curvature components are

R i U jU = -R V ijU = -K ij ,
it is Ricci-flat. In 3 + 1 dimensions, (I.1) is the general form of a Ricci-flat Brinkmann metric.

In this paper we identify, following [START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], the isometry group of the gravitational wave (I. [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF] we denote here by C, as the Carroll group in 2 + 1 dimensions with broken rotations.

Let us recall that the Carroll group, C(d+1), has originally been introduced as an unusual contraction, c → 0, of the Poincaré group E(d, 1) [START_REF] Lévy-Leblond | Une nouvelle limite non-relativiste du group de Poincaré[END_REF][START_REF] Sen | On an Analogue of the Galileo Group[END_REF][START_REF] Duval | Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time[END_REF]. It acts on (d + 1)-dimensional flat "Carroll space-time", C d+1 , with coordinates (x, v), according to

x → A x + c, v → v -b • A x + f, (I.2)
where A ∈ O(d) and c ∈ R d represent spatial orthogonal transformations and translations;

b ∈ R d and f ∈ R generate "Carrollian boosts" and translations of "Carrollian time", v, respectively. Let us recall that the flat Carroll space-time, C d+1 ∼ = R d+1 , is endowed with the degenerate metric γ = dx 2 with kernel spanned by the constant vector field ξ = ∂ v , and is equipped with its flat affine connection. The Carroll group, C(d + 1), is thus the group of all affine transformations of "space-time" which leave γ and ξ invariant.

Long considered as a sort of mathematical curiosity [START_REF] Duval | Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time[END_REF][START_REF] Bergshoeff | Dynamics of Carroll Particles[END_REF][START_REF] Ngendakumana | Group theoretical construction of planar Noncommutative Phase Spaces[END_REF], the Carroll group has reemerged more recently in brane-dynamics [START_REF] Gibbons | Tachyon condensates, Carrollian contractions of the Lorentz group and fundamental strings[END_REF][START_REF] Gibbons | Thoughts on tachyon cosmology[END_REF], for the BMS group [START_REF] Duval | Conformal Carroll groups and BMS symmetry[END_REF], in string theory [START_REF] Duval | Conformal Carroll groups and BMS symmetry[END_REF][START_REF] Cardona | Dynamics of Carroll Strings[END_REF][START_REF] Bagchi | Flat Holography: Aspects of the dual field theory[END_REF], and in non-relativistic gravitation [START_REF] Bergshoeff | Carroll versus Galilei Gravity[END_REF].

We find it useful to record our notations: (X, U, V ) denote "Brinkmann" coordinates which appear in (I.1), whereas (x, u, v) in (III.1) are Baldwin-Jeffery-Rosen (BJR) coordinates [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF][START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], convenient for determining both the isometries and the geodesics [START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF]. In Minkowski space-time, K = 0, both coordinates reduce to the usual light-cone coordinates (r, t, s).

Our clue is that the space-time with metric (I.1) is also a Bargmann manifold [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF] in that it carries a null, covariantly constant, vector field, namely ξ = ∂ V .

Bargmann spaces are convenient tools to study non-relativistic dynamics in one lower dimension [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF][START_REF] Eisenhart | Dynamical trajectories and geodesics[END_REF][START_REF] Cariglia | Hidden Symmetries of Dynamics in Classical and Quantum Physics[END_REF] : the quotient of a (d + 1, 1)-dimensional Bargmann space by the foliation generated by ξ carries a (d + 1)-dimensional Newton-Cartan structure [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF]; U in (I.1), can be viewed as non-relativistic time and -1 2 K ij (U )X i X j as a time dependent quadratic scalar potential. Non-relativistic motions in Newton-Cartan spacetime are projections of null geodesics in extended Bargmann space-time [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF][START_REF] Eisenhart | Dynamical trajectories and geodesics[END_REF]; the ξ-preserving isometries of the latter project to non-relativistic Galilean symmetries.

The metric (I.1) describes, in Bargmann language, the Eisenhart lift of a (possibly anisotropic) planar oscillator with time dependent frequencies [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF][START_REF] Eisenhart | Dynamical trajectories and geodesics[END_REF][START_REF] Cariglia | Hidden Symmetries of Dynamics in Classical and Quantum Physics[END_REF][START_REF] Burdet | Time Dependent Quantum Systems and Chronoprojective Geometry[END_REF]; its ξ-preserving isometries span the [centrally extended] Newton-Hooke group [without rotations in the anisotropic case] [START_REF] Zhang | Newton-Hooke type symmetry of anisotropic oscillators[END_REF]; when K = 0, the latter goes over to the [centrally extended] Galilei group (also referred to as the Bargmann group in (d+1, 1) dimension) [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF]. The latter is conveniently represented by the matrices parametrized by (r, t, s), according to

       A b 0 c 0 1 0 e -b † A -1 2 b 2 1 f 0 0 0 1        , ( II
r → Ar + bt + c, t → t + e, s → s -b • Ar - 1 2 b 2 t + f. (II.2)
Recall that flat Bargmann space is endowed with the metric g = dr 2 +2dt ds, and the null, constant, vector field ξ = ∂ s . The null hyperplane C d+1 t 0 defined by t = t 0 = const. is a Carroll spacetime [START_REF] Duval | Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time[END_REF][START_REF] Duval | Conformal Carroll groups and BMS symmetry[END_REF] as it carries a twice-symmetric, semi-positive "metric", dr

III. ISOMETRIES OF PLANE GRAVITATIONAL WAVES

Our first step in identifying the isometries of the plane wave (I.1) is to recast the metric in a new coordinate system (x, u, v) [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF][START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], which allows us to determine the isometry group in terms of elementary functions, see eqn. (III.6) below. This can be achieved [START_REF] Kramer | Exact solutions of Einstein's field equations[END_REF][START_REF] Gibbons | Quantized Fields Propagating in Plane Wave Space-Times[END_REF][START_REF] Garriga | Scattering of quantum particles by gravitational plane waves[END_REF] with the help of a change of coordinates (X, U, V ) → (x, u, v), namely

X = P (u)x, U = u, V = v - 1 4 x • ȧ(u)x , (III.1)
where a(u) = P (u) † P (u) for some non-singular 2×2 matrix P (u) 1 . The change of coordinates allows us to present the metric (I.1) in the form g = a ij (u) dx i dx j + 2du dv, (III.2)

provided the matrix P (u) is a solution of the joint system

P = KP, P † Ṗ = Ṗ † P. (III.3) Since K = 1 2 P L + 1 2 L 2 P -1 , L = a -1 ȧ, (III.4)
the Ricci flatness of the metric (III.2), namely Tr(K) = 0, is given by the equation [START_REF] Baldwin | The Relativity Theory of Plane Waves[END_REF][START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF],

Tr L + 1 2 L 2 = 0. (III.5)
Isometries. We now claim that the (generic) isometries of (III.2) form a 5-dimensional Lie group. Following Souriau [START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], in terms of the BJR (x, u, v), the latter acts on space-time as,

x → x + H(u)b + c, u → u, v → v -b • x -1 2 b • H(u)b + f, (III.6)
where H is a (symmetric) 2 × 2 matrix verifying Ḣ = a -1 , that is,

H(u) = u u 0 a(t) -1 dt. (III.7)
Manifestly, c ∈ R 2 and f generate transverse-space resp. null translations along the v coordinate [START_REF] Gibbons | Quantized Fields Propagating in Plane Wave Space-Times[END_REF]. Moreover, the group law deduced from (III.6),

(b, c, f ).(b , c , f ) = (b + b , c + c , f + f -b • c ), (III.8)
is precisely that of the Carroll group, (I.2) with no rotations, i.e. A = Id. Thus the isometry group of the above gravitational wave is indeed the group

C ⊂ C(2 + 1) of matrices        1 b 0 c 0 1 0 0 -b † -1 2 b 2 1 f 0 0 0 1        . (III.9)
The vector b ∈ R 2 generates, in particular, a Carroll boost acting as in (III.6), while c ∈ R 2 and f are Carrollian "space-time" translations, as before. Let us note that C is a normal subgroup of the Carroll group of

C(2 + 1), C(2 + 1)/C ∼ = O(2).
It is worth stressing that while the way the Carroll group is implemented on an u = const.

null hypersurface does depend on the (fixed) value of u [START_REF] Torre | Gravitational waves: Just plane symmetry[END_REF], all these actions can be derived from the simple Carroll action at u = u 0 according to (III.6)-(III.7). The coordinate transformation (III.1) followed backwards yields the Carroll action in terms of the Brinkmann coordinates and we recover eqn. # (3) in [START_REF] Torre | Gravitational waves: Just plane symmetry[END_REF].

Geodesic motion. As noted by Souriau [START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], the conserved quantities associated with geodesic motions are then readily determined by Noether's theorem. Choosing, with no restriction, u as parameter, they are

p = a ẋ, k = x -Hp, m = 1, (III.10)
interpreted as linear momentum, boost-momentum and "mass" (unity in our parametrization). In BJR coordinates, the geodesics have then the remarkable explicit expression

x(u) = H(u) p + k, v(u) = - 1 2 p • H(u) p + e u + d, (III.11)
where e = 1 2 g µν ẋµ ẋν is. (This constant is negative/zero/positive for timelike/null/spacelike geodesics). d is an integration constant. The isometry group acts on the above constants of the motion as

(p, k, e, d) → (p + b, k + c, e, d + f -b • k) (III.12)
allowing us, in particular, to carry any geodesic to a geodesic defined by p = k = 0 and d = 0, which then becomes "vertical" [START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF], x = 0, v = c u. Conversely, any geodesic can be obtained by "exporting a vertical one" by an isometry : the only group-invariant property of the trajectory is the sign of e.

IV. CLASSICAL EXAMPLES

Let us illustrate our procedure by simple examples. 2. For a less trivial example, consider, e.g.,

P (u) = χ(u) diag e α(u) , e -α(u) (IV.1)
with α(u) some arbitrarily chosen function. The associated metric

g = χ 2 e 2α (dx 1 ) 2 + e -2α (dx 2 ) 2 + 2du dv (IV.2)
is Ricci-flat if χ + α2 χ = 0, (IV.3) see (III.5). The pp-wave profile is, in this case,

K ij (U )X i X j = 1 2 A(U ) (X 1 ) 2 -(X 2 ) 2 , A = 2 χ 2 d du χ 2 dα du . (IV.4)
From the mechanical point of view, this metric describes two uncoupled timedependent harmonic oscillators, one attractive, the other repulsive, with opposite frequency-squares.

The metric (IV.2) is manifestly invariant against transverse space and advanced timetranslations, x → x + c and v → v + f , respectively, while retarded time, u, is kept fixed. The orthogonal group, O(2), is clearly broken since the spatial metric is not diagonal unless α(u) = 0. Carroll boosts act as in (III.6) with

H(u) = u u 0 P (w) -2 dw,
where P is as in (IV.1).

To have a toy example, let us take, e.g., α(u) = u. Then a Ricci-flat metric which is regular in the neighborhood of u = 0 is given, for example, by χ(u) = -cos u, whose profile is

1 2 K ij (U ) X i X j = tan U (X 2 ) 2 -(X 1 ) 2 . (IV.5)
It describes a saddle-like surface with "time"-dependent scale, depicted on Fig. 1, which

shows the change of the profile when u passes from negative to positive2 . Let us mention that choosing instead of (IV.1):

P (u) = χ(u)   cosh β(u) sinh β(u) sinh β(u) cosh β(u)   (IV.7)
with β(u) an otherwise arbitrary function, we find that the associated metric (III.2)

is Ricci-flat if χ + β2 χ = 0. The pp-wave profile becomes

K(U ) ij X i X j = B(U ) X 1 X 2 , B = 2 χ 2 d du χ 2 dβ du . (IV.8)
The examples (IV.4) and (IV.8) can be combined, keeping α and β independent, to end up with the most general profile.

3. So far, the functions A and B encoding the polarization states of the gravitational wave have been traded as arbitrary. Now in the periodic case the isometry group is actually 6-dimensional [START_REF] Kramer | Exact solutions of Einstein's field equations[END_REF]. In fact, if

K ij (U )X i X j = cos(ωU ) X 1 X 2 + 1 2 sin(ωU ) (X 1 ) 2 -(X 2 ) 2 (IV.9) ⇒ (a) (b)
FIG. 3: The geodesic motion is determined by the conserved quantities. For p = (1, 0) and k = 0, for example, the trajectories remain in the hyperplane x 2 = 0 which can therefore be ignored, yielding 3D pictures for x 1 (u), u, v(u) . All trajectories can be "straightened out" by a suitable action of the Carroll group. We took α(u) = u.

with ω = const., then, putting Z = X 1 + iX 2 , one finds that the advanced time translations

Z → e -1 2 iωe Z, U → U + e, V → V, (IV.10)
act isometrically for all e ∈ R. This subgroup of the Bargmann group (II.1) is however clearly not a subgroup of the Carroll group C(2 + 1) which leaves U fixed, see (III.9).

V. CARROLL SYMMETRY OF AN ISOTROPIC OSCILLATOR

When K = -ω 2 Id with ω = const., the metric (I.1) does not solve the vacuum Einstein equations and is therefore not that of a gravitational wave; it describes instead an isotropic harmonic oscillator [START_REF] Duval | Bargmann structures and Newton-Cartan theory[END_REF][START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF]. However the procedure described in Sec. III can be carried out at once : P = cos(ωU ) Id is a solution of (III.3) ; then (III.1) yields (III.2) with g ij (u) = cos 2 (ωu)δ ij . Integrating (III.7) we get,

H(u) = tan(ωu) ω - tan(ωu 0 ) ω Id. (V.1)
Then (III.6) yields the Carroll action on oscillator-Bargmann space. Redefining the time and renaming x and v allows us to recover, moreover, Niederer's transformation [START_REF] Burdet | Time Dependent Quantum Systems and Chronoprojective Geometry[END_REF][START_REF] Niederer | The maximal kinematical invariance group of the harmonic oscillator[END_REF],

t = tan(ωU ) ω , r ≡ x = X cos(ωU ) , s ≡ v = V - ω X 2 2 tan(ωU ), (V.2)
which maps every (half-oscillator-period)×R d+1 conformally onto the Bargmann space, R d+1,1 , of a free particle, dr 2 + 2dt ds = cos -2 (ωU ) dX 2 + 2dU dV -ω 2 X 2 dU 2 . It is worth noting that, in terms of the redefined time, (V.1) is in fact

H(t) = (t -t 0 ) Id, consistently
with what we had found in the flat case.

We mention that the Niederer trick (V.2) could be used for an alternative derivation of the Carroll symmetry. Recall first that the free (Minkowski) metric has the (extended)

Schrödinger group as group of ξ-preserving conformal symmetries [START_REF] Duval | Celestial mechanics, conformal structures and gravitational waves[END_REF]. The latter is in turn exported to the oscillator by (V.2). Now, as said before, the t = 0 slice of flat Bargmann space is a Carroll manifold C d+1 , with the Carroll symmetry group embedded into the Bargmann group by eliminating the time translations (II.1). Moreover, for t = 03 the conformal factor is equal to one. The image is therefore an isometry. However, the Niederer trick fails to work in the anisotropic case (and thus for a gravitational wave), whose Bargmann space is not conformally flat [START_REF] Zhang | Newton-Hooke type symmetry of anisotropic oscillators[END_REF].

VI. SCATTERING OF LIGHT BY A GRAVITATIONAL WAVE

We conclude by some additional comments on the scattering of light by a plane gravitational wave. In [START_REF] Westerberg | Experimental quantum cosmology in time-dependent optical media[END_REF] the analogy between photon production in a medium with a timedependent refractive index and particle production (and its absence) [START_REF] Gibbons | Quantized Fields Propagating in Plane Wave Space-Times[END_REF][START_REF] Rosen | Stability of the Graviton Against Radiative Decay[END_REF][START_REF] Deser | Plane waves do not polarize the vacuum[END_REF][START_REF] Liu | On the Vacuum Propagation of Gravitational Waves[END_REF][START_REF] Jones | Particle production in a gravitational wave background[END_REF] by gravitational waves has been stressed and the prospects for laboratory experiments explored. For this purpose the Baldwin-Jeffery-Rosen form of the metric would seem to be the most useful. In fact one may use the general formulae developed by Tamm, Skrotskii and Plebanski [START_REF] Plebanski | Electromagnetic Waves in Gravitational fields[END_REF][START_REF] Tamm | The electrodynamics of anisotropic media in the special theory of relativity[END_REF][START_REF] Skrotskii | The Influence of Gravitation on the Propagation of Light[END_REF][START_REF] Mccall | Classical gravity does not refract negatively[END_REF] to extract the relevant permittivities ab = ba and permeabilities µ ab = µ ba . We mainly follow the notation of [START_REF] Plebanski | Electromagnetic Waves in Gravitational fields[END_REF] but use the opposite signature convention and a different notation for permittivity and permeability.

We where D a = ab E b , B a = µ ab H b . Since g 00 = -1 and g 0a = 0 in these coordinates, there are no magneto-electric effects, which in turn implies that the medium is "impedance matched", that is, ab = µ ab = √ -g g ab . In detail, one has

define t = x 0 , z = x 3 , u = 1 √ 2 (z -t), v = 1
ij = det a(u) a(u) -1 ij , 33 = det a(u), 3i = 0. (VI.3)
If instead of the Maxwell equations one were to look at the Dirac equation, one might be able to treat the analogue for gravitational waves of the Kapitza-Dirac effect [START_REF] Kapitza | The reflection of electrons from standing lightwaves[END_REF] for electromagnetic waves.

VII. CONCLUSION

Plane gravitational waves have long been known to have a 5-dimensional isometry group.

The first three parameters are readily identified as translations in transverse space, resp.

along one of the light-cone generators. The other two have remained somewhat mysterious, though; here we identify the latter as Carroll boosts. In fact, we show that the isometry group of (I.1) is the Carroll group without rotations. If the matrix a = (a ij (u)) in (III.2) happens to depend on u periodically, then u-translational symmetry is restored and the isometry group is enhanced to a 6-parameter group; see (IV.10). In the isotropic case, as in section V, rotations are also restored and we end up with the 7-parameter centrally extended Newton-Hooke group. In the flat case, K ≡ 0, the latter becomes the Bargmann group, which is a subgroup of the 10-parameter Poincaré group.

The appearance of these typically non-relativistic structures is surprising in that the theory is fully general relativistic. It is also unexpected, since the Carroll group has originally been defined as an ultra-relativistic contraction of the Poincaré group. Moreover, bearing in mind that (conformal) Carroll structures have been shown to dwell in the edge of space-time, e.g., conformal infinity of certain solutions of Einstein's equation [START_REF] Duval | Conformal Carroll groups and BMS symmetry[END_REF], it is remarkable to witness the Carroll group appearance in the bulk of some instances of the latter, namely gravitational plane waves. From our point of view, the key formulae are This fact plays a key rôle in our subsequent applications to the memory effect [START_REF] Zhang | The Memory Effect for Plane Gravitational Waves[END_REF] and thus underlines the importance of Carroll symmetry for the study of gravitational waves.

Our clue is the double role played by "Bargmann space" -which is both a relativistic space-time and a convenient tool to study non-relativistic physics in one lower dimension.

From the group theory point of view, our finding corresponds to the fact that the Bargmann (centrally extended Galilei) and Carroll groups are both subgroups of the Poincaré group in one higher dimension -a way of seeing we find more convenient than the original derivation by group contraction [START_REF] Lévy-Leblond | Une nouvelle limite non-relativiste du group de Poincaré[END_REF][START_REF] Sen | On an Analogue of the Galileo Group[END_REF][START_REF] Duval | Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time[END_REF]. This is the point of view espoused systematically in Sections II, III, and IV to unveil the Carroll structure of the group of isometries of the gravitational waves under study. A similar argument, developed in Section V, sheds some light also on the Niederer trick [START_REF] Niederer | The maximal kinematical invariance group of the harmonic oscillator[END_REF]. Section VI comments about using BJR coordinates in studying the scattering of light by gravitational waves.

In this paper we identified the isometries of plane gravitational waves with the Carroll group with no rotations. Conformal extensions can also be studied, through, with the remarkable outcome that the celebrated BMS group is, in fact, a conformal Carroll group [START_REF] Duval | Conformal Carroll groups and BMS symmetry[END_REF]. It is puzzling to ask what role (if any) the latter could play for gravitational waves.

. 1 )

 1 where A ∈ O(d); b, c ∈ R d ; and e, f ∈ R stand for a Galilei time translation and for a "Carroll time" translation, respectively. The superscript † means transposition. The Bargmann group (II.1) acts affinely by matrix multiplication on Bargmann extended spacetime R d+1,1

1 .

 1 The restriction of flat Minkowski space with metric g = dr 2 + 2dt ds to the constant "time" slice t 0 = 0 is a Carroll manifold with ξ = ∂ s , upon which the restriction e = 0 of the Bargmann group (II.1) acts, consistently with the Carroll action (I.2), via (III.6) with H(t) = (t -t 0 ) Id . The conserved quantities (III.10) take the familiar Galilean form. Shifting the basepoint, t 0 → t 0 , merely shifts the transformation law of v by a constant, namely v → v -b.x -1 2 b 2 (t 0 -t 0 ) + f.

FIG. 1 : 0 cos - 2 0 cos - 2 FIG. 2 :

 102022 FIG. 1: Wave profile (IV.5) for α(u) = u for u = -π/2 + 0.1, u = -π/4, u = 0, u = π/4, u = π/2 -0.1. For u = 0 we get flat Minkowski space, as expected.

√ 2 (

 2 z + t) and write the metric (III.2) asg = -dt 2 + g ab (u)dx a dx b , g ab dx a dx b = a ij (u)dx i dx j + dz 2 , (VI.1)where a, b = 1, 2, 3 and i = 1, 2. Now in the coordinates (t, x), where x = (x a ), Maxwell's equations take the usual flat-space form in a medium curl E = -

1 . 2 . 1 ; 3 .

 1213 The metric in Baldwin-Jeffery-Rosen coordinates, (III.2); The exact equation for the matrix a in (III.5) related to various profiles, cf. Fig.The explicit form of the action of the Carroll group, eqn. (III.6), viewed as a subgroup of the Bargmann group, (III.9); 4. In BJR coordinates the geodesics are expressed in terms of the conserved quantities associated with the Carroll symmetry through Noether's theorem, (III.11), and can be determined explicitly when the matrix H(u) in (III.7) is calculated, yielding Fig.2.

The square root, P , of the matrix a > 0 is not uniquely defined since RP with R(u) ∈ O(2) is another one. However, eqns (III.3) guarantee that Ṙ = 0, i.e., that P is merely defined up to O(2). Conditions (III.3) implies that K = P P -1 in (I.1) is indeed symmetric.

For u = ±π/2 χ = det(a(u)) 1/4 vanishes. This is a general property which indicates a mere coordinate singularity[START_REF] Souriau | Ondes et radiations gravitationnelles[END_REF].

For t = t 0 = const. the conformal factor is constant and can be absorbed by a redefinition of the metric.

Acknowledgments

Enlightening discussions with T. Schücker are warmly acknowledged. GWG would like to thank the Laboratoire de Mathématiques et de Physique Théorique de l'Université de Tours for hospitality and the Région Centre for a "Le Studium" research professorship.

PH is grateful for hospitality at the IMP of the Chinese Academy of Sciences in Lanzhou.

Support by the National Natural Science Foundation of China (Grant No. 11575254) is acknowledged.