Geraldine Sarret
email: gsarret@ujf-grenoble.fr

Emiko Harada

Yong-Eui Choi
email: yechoi@kangwon.ac.kr

M.-P Isaure

Nicolas Geoffroy

Sirine Fakra

Matthew A Marcus

Mandy Birschwilks

Stephan Clemens

Alain Manceau

Géraldine Sarret

Géraldine Sarret

Marie-Pierre Isaure

Trichomes of tobacco excrete zinc as Zn-substituted calcium carbonate and other Zn-containing compounds

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Smoking of tobacco leaves is one of the principal routes of exposure to heavy metals. Metals contained in tobacco leaves originate from root uptake and transfer to the shoots and also from deposition of aerosol particles on the leaves [START_REF] Fleisher | Aerosol particles on tobacco trichomes[END_REF]. Efforts have been made to minimize toxic metal contents in the leaves [START_REF] Moulin | Critical review of the science and options for reducing cadmium in tobacco (Nicotiana tabacum L.) and other plants[END_REF]. However, this is not the case for counterfeit tobacco products, which contain higher concentrations of metals than their genuine equivalents [START_REF] Stephens | Source and health implications of high toxic metal concentrations in illicit tobacco products[END_REF]. Besides its primary application for leaf production, tobacco is also a candidate for phytoextraction.

Although this plant species is not a hyperaccumulator, it has several advantages, including a high biomass, moderate soil requirements, fast growth rate, and ease of harvesting. For this particular application, research is conducted with the aim of enhancing metal accumulation in the shoots [START_REF] Song | Engineering tolerance and accumulation of lead and cadmium in transgenic plants[END_REF].

Little is known about the mechanisms of metals accumulation and detoxification in tobacco.

The exposure of plants to high concentrations of metals generally induces a stress, whose visible symptoms include an inhibition of root elongation, a decrease in shoot growth, leaf chlorosis, and necrosis of the tissues. This stress is generated by the perturbation of cell metabolism by metals, mostly due to the inactivation of proteins by adventitious binding.

Plants have developed various mechanisms to tolerate heavy metals in their tissues [START_REF] Küpper | Heavy Metal Uptake by Plants and Cyanobacteria[END_REF]. One of the most important mechanisms is the sequestration of heavy metals in specific subcellular compartments of particular tissues, whose nature depends on the plant species. Recently, we showed that the trichomes of tobacco exposed to Cd 2+ and Ca 2+ produced Ca/Cd-containing grains [START_REF] Choi | Detoxification of cadmium in tobacco plants: formation and active excretion of crystals containing cadmium and calcium through trichomes[END_REF][START_REF] Choi | Distribution of elements on tobacco trichomes and leaves under cadmium and sodium stresses[END_REF][START_REF] Choi | Roles of calcium and cadmium on Cd-containing intra-and extracellular formation of Ca crystals in tobacco[END_REF]. Other effects of Cd exposure were a retardation of plant growth and a two-fold increase of the number of trichomes in comparison with untreated plants. Also, an increased concentration of Ca in the nutrient medium had a protective effect towards Cd toxicity, and enhanced the production of the grains.

Trichomes are specialized unicellular or multicellular structures derived from the epidermal cell layer, which may have various functions depending on the plant species and organ (Rodriguez et al., 1983;[START_REF] Wagner | New approaches for studying and exploiting an old protuberance, the plant trichome[END_REF]. Tobacco has multicellular glandular trichomes of two types, the so-called long and short trichomes. The long trichomes are known to excrete various alkaloids including nicotine, whereas the short ones excrete terpenoids (resins; (Hallahan et al., 2000) and defensive proteins [START_REF] Shepherd | Phylloplanins of tobacco are defensive proteins deployed on aerial surface by short glandular trichomes[END_REF]. The Ca/Cd-containing grains were 20 to 150 µm in diameter, and formed on head cells of both the short and long trichomes. They consisted in aggregates of micrometer-sized particles. Scanning electron microscopy coupled with energy dispersive X-ray fluorescence (SEM-EDX) analysis indicated the presence of minor amounts of Mg, P, S, and Mn, in addition to major amounts of Ca and Cd. Thus, these studies revealed a new function of tobacco trichomes, the excretion of Cd in the form of particles.

Other epidermal structures, the salt glands of Armeria maritima [START_REF] Neumann | EXAFS study of the nature of zinc complexation sites in humic substances as a function of Zn concentration[END_REF], Avicennia marina [START_REF] Macfarlane | Zinc distribution and excretion in the leaves of the grey mangrove, Avicennia marina (Forsk.) Vierh[END_REF], and Silene vulgaris [START_REF] Bringezu | Heavy metal tolerance of Silene vulgaris[END_REF] have been shown to excrete Ca/metal-containing grains. In contrast, non-glandular trichomes of several hyperaccumulating plants, including Arabidopsis halleri [START_REF] Küpper | Cellular compartmentation of cadmium and zinc in relation to other elements in the hyperaccumulator Arabidopsis halleri[END_REF][START_REF] Zhao | Zinc hyperaccumulation and cellular[END_REF][START_REF] Sarret | Forms of zinc accumulated in the hyperaccumulator Arabidopsis halleri[END_REF] and Alyssum [START_REF] Broadhurst | Simultaneous hyperaccumulation of nickel, manganese, and calcium in Alyssum leaf trichomes[END_REF], and nonhyperaccumulating plants, including Brassica juncea (Salt et al., 1995), Arabidopsis thaliana [START_REF] Ager | Nuclear micro-probe analysis of Arabidopsis thaliana leaves[END_REF][START_REF] Solis | Increased cysteine availability is essential for cadmium tolerance and accumulation in Arabidopsis thaliana[END_REF], pumpkin [START_REF] Iwasaki | Effect of silicon on alleviation of manganese toxicity in pumpkin (Cucurbita moschata Duch cv. Shintosa)[END_REF], and waterlily [START_REF] Lavid | Accumulation of heavy metals in epidermal glands of the waterlily (Nymphaeaceae)[END_REF], have been shown to sequester metals without apparent excretion. Trichomes of calcicolous plants also store large amounts of calcium. DeSilva et al. (deSilva et al.) suggested that this could be a strategy to avoid the interference with stomatal functioning.

The mechanism of metal accumulation and excretion by trichomes, and the binding environment of metals in these structures and their exudates are largely unknown. The aim of the present work is to clarify several open questions arose from our previous studies on tobacco and to extend it to zinc. The cation Cd 2+ is frequently associated with Ca 2+ in the environment because of their similar ionic radii. Does the production of Ca/metal grains occur for a cationic metal of different size from Cd 2+ , such as Zn 2+ ? If so, what is the influence of Ca 2+ supply on the metal uptake, translocation and formation of the grains? Then, what is the mineralogical nature of the excreted Zn-containing grains, and what is the binding environment of Zn in the grains? This information is important because the chemical form of metals (inner or outer sphere complexes, coprecipitates with other metals, …) determines their mobility and their possible release in the environment. The most common biomineral formed by plants is calcium oxalate. However, various forms of calcium carbonate including amorphous CaCO 3 , calcite, aragonite and vaterite are also synthesized by plants [START_REF] Arnott | Calcification in plants[END_REF][START_REF] Setoguchi | Calcification in higher plants with special reference to cystoliths[END_REF]. Another unknown is the mechanism of formation of the grains, which are generally larger than the trichome cells themselves. And finally, what is the relative importance of metal excretion and accumulation in the leaf tissues?

To address these questions, tobacco plants were grown in hydroponics and in vitro in the presence of various concentrations of Ca and Zn. The effect of Ca on the short term (24h) and long term (2 and 5 weeks) accumulation of Zn and on the production of the grains were studied. The endogenous accumulation of Zn in the top cells of trichomes was visualized under confocal laser scanning microscopy (CLSM) after labeling with Zinquin. The density of the trichomes was estimated by examining fresh leaves by variable pressure scanning electron microscopy (VP-SEM), and isolated grains were examined by variable pressure and standard scanning electron microscopy coupled with microanalysis (VP-SEM-EDX and SEM-EDX), and by a combination of three synchrotron-based techniques with a lateral resolution of a few micrometers. Specifically, the distribution of Ca and Zn in the grains was imaged by micro Xray fluorescence (µXRF), crystalline phases were identified by micro X-ray diffraction (µXRD), and the binding environment of Zn was determined by Zn K-edge micro extended X-ray absorption fine structure (µEXAFS) spectroscopy.

RESULTS

Growth retardation and Zn accumulation in tobacco plants treated with toxic level of Zn in hydroponic culture

Seed-derived tobacco plants were grown on hydroponic culture containing high level of Zn (0.25 mM) and with and without supplement of 3 mM of Ca (Table I, Fig. 1), and the Zn toxicity was monitored by the growth of shoots and roots, and chlorophyll contents (Table II).

After 2 and 5 weeks of toxic Zn treatment, both shoot and root growth were severely affected, and the chlorophyll content was markedly reduced. The growth inhibition was more severe for roots than for shoots, especially after 5 weeks of exposure. The supplementation with 3 mM Ca suppressed the growth inhibition effect, but did not restore chlorophyll level. These results suggest that Ca alleviates some (but not all) of the toxic effects of Zn.

The analysis of total Zn content showed that the Ca supplement reduced the Zn accumulation in shoots after 24 hours of Zn treatment (Table II). At the opposite, Zn accumulation was increased after 2 to 5 weeks of the same Zn + Ca treatment. Consequently, the protective effect of Ca cannot be explained by a competition between Ca and Zn resulting in a reduced Zn uptake.

Growth and trichome density and grain production in tobacco plants cultured in vitro

Growth retardation of tobacco plants cultured in vitro was similar to ex vitro culture in hydroponic medium. However, Zn accumulation of in vitro plants was lower (Table II andIII) although the in vitro growing medium contained a 4-fold higher Zn concentration than the hydroponic medium. This difference may result from a lower Zn bioavailability, lower respiration and transpiration rates in vitro.

In vitro plants were used for counting the number of trichomes and isolating the grains because leaves of tobacco plants cultured ex vitro were more easily subjected to bacterial attack and contamination from aerosol particles. Leaves of the plants treated with or without Zn for 3 weeks were observed under VP-SEM (Table III, Fig. 2). There was no difference in trichome density for the mature leaves. At the opposite, the young leaves of plants exposed to Zn and Zn + Ca showed a more than two-fold increase of the density of long and short trichome relative to the control (Fig. 2A-C). No difference of leaf size was observed between the various treatments, so this increase was real. This suggests a possible role of Zn in the trichome development. Figure 2B showed that the length and the volume of the trichomes were increased upon Zn treatment although epidermal cells and stomatal opening were rather smaller that those of control. A number of grains were observed on the top of both short and long trichomes, as seen in Fig. 2C (arrows). For each treatment, the grains were collected and observed by VP-SEM (Table III, Fig. 2D-F). Their number and their mean size increased in the order: in vitro-control > in vitro-Zn > in vitro-Zn + Ca treatment (Table III, Fig. 2 D-F).

We showed previously that exposure to 30 mM Ca without Zn (Ca treatment) did not enhance the production of the grains but stimulated the formation of intracellular Ca oxalate crystals in leaves [START_REF] Choi | Roles of calcium and cadmium on Cd-containing intra-and extracellular formation of Ca crystals in tobacco[END_REF].

The same general trends in trichome density and grain production were observed on plants grown hydroponically. The amount of Zn excreted per plant was estimated based on the number and size of grains per shoot and their Zn content calculated using the ZAF method [START_REF] Goldstein | Scanning Electron Microscopy and X-ray Microanalysis[END_REF]. We found 4.1 and 11.0 µg of Zn per plant under the in vitro-Zn and in vitro-Zn + Ca treatment, respectively, which corresponds to 9.2 and 16.9 % of total Zn in the leaves, respectively. Note that these values reflect the grains present on the leaves after 3 weeks of exposure, not the total amount of Zn excreted during the experiment.

Confocal imaging of Zn accumulation in trichome cells after Zinquin labeling

Tobacco plants were grown hydroponically with 0.25 mM Zn + 0.28 mM Ca (Zn treatment) and 0.08 mM Zn + 0.28 mM Ca (control) for 2 weeks. Zn distribution on the leaf surfaces was investigated by CLSM after treatment with zinquin (Fig. 3). Zinquin ethyl ester is a liposoluble fluorescence dye which has been used to localize intracellular Zn ions in animal cells (Coyle et al., 1994). This study shows that it can be used on plant cells too. For control plants, a faint fluorescence was detected in the trichomes (Fig. 3A,C). For Zn-treated plants, Zn was preferentially accumulated in head cells of both short and long trichomes (Fig. 3B,D).

Extracellular crystals were not present on the top of the trichomes observed by CLSM because they fell off during the zinquin treatment. Fluorescence was also detected in the epidermal surfaces of the leaves, but was always less dense than in the trichome cells (data not shown).

Zn distribution analysis by micro X-ray fluorescence (µXRF) spectrum

The distribution of Ca and Zn in the leaves of tobacco exposed to 0.25 mM Zn + 3.28 mM Ca (Zn + Ca treatment) was imaged by synchrotron-based X-ray microfluorescence (µXRF, Fig. 4). Zn was systematically more concentrated in veins and trichomes, with the short trichomes being about five times richer than the long trichomes. Short trichomes were also rich in Ca, but in the same proportion as Zn (i.e., the Ca K α /Zn K α ratio equalled about 1 in the two types of trichomes). No grains were observed at the top of the trichomes because they fell off during the sample preparation, such as freeze-drying and mounting and its rastering under the X-ray beam, but some were still detected as Zn hot-spots on the leaf surfaces.

Morphology, chemical composition and solubility of the grains

Some grains present on the surface of a fresh leaf from a Zn-treated plant were studied by VP-SEM-EDX (Fig. 5A), and other grains produced under various conditions (in vitro and hydroponic culture with various Ca and Zn concentrations, Table I) were collected and studied by VP-SEM-EDX and SEM-EDX (Fig. 5B-H). The size of the grains varied from 10 µm to 150 µm in diameter for all treatments. A variety of globular to crystal-like shapes were observed. In most cases, grains consisted in aggregates of small (< 1 µm) particles, as previously observed for Cd 2+ -treated plants [START_REF] Choi | Detoxification of cadmium in tobacco plants: formation and active excretion of crystals containing cadmium and calcium through trichomes[END_REF][START_REF] Choi | Distribution of elements on tobacco trichomes and leaves under cadmium and sodium stresses[END_REF]. The globular grains generally were made of concentric layers. No particular relationship could be established between the grain morphology and the type of treatment.

Ca was always the major element, even for plants grown on 0.28 mM Ca. In contrast, Zn was not detected in the grains when its concentration in the nutrient solution was low (Ca treatment, 0.02 mM Zn + 3 mM Ca). In grains from the Zn + Ca -treated plants (0.25 mM Zn + 3.28 mM Ca), the Zn K α fluorescence peak was small (Zn concentration ranged from 1 to 5 wt. %, as estimated by the ZAF method), and it was occasionally more intense (Zn concentration ranged from 2 to 40 wt. %) in grains from the Zn-treated plants (0.28 mM Ca + 0.25 mM Zn). Minor elements included O, Mg, Si, P, S, Cl, K and Mn (C could not be measured because the grains were coated with carbon). No particular relationship could be established between the concentration of the minor elements and the type of treatment, except for Mn which was not detected in grains from the Zn + Ca treatment. There was no morphological or compositional difference between grains observed directly on the leaves using VP-SEM and grains isolated by water extraction or using toothpicks. The solubility of the grains in water was tested in a wide range of pH. They were insoluble between pH 4 and 12.5, and soluble in acidic conditions: they were dissolved within 10 minutes at pH 3, and within 2 min at pH 2. Therefore, the structure and the composition of the grains are supposed to be preserved during the water extraction.

µXRD analysis of the grains

The grains produced by tobacco plants grown in hydroponics under the three treatments (Ca, Zn, and Zn + Ca) were analyzed also by µXRD (Fig. 6). Five to ten grains per type of treatment were examined. For each grain, µXRD patterns from a 16 × 7 µm 2 spot of the Ca richest region (Ca treatment) or the Zn richest region (Zn and Zn + Ca treatment), and of the whole grain were recorded. The point and average patterns were the same, except that the Debye rings for the second were less intense and longer (i.e., more powder-like). Therefore, either the Ca-and Zn-richest regions are representative of the structural composition of the entire grains, or the other regions contain amorphous material. Figures 6A and6B show the two-dimensional µXRD patterns for two grains produced under the Ca treatment (grains Ca1 and Ca2). The diameter of these grains is about 50 µm. Bragg reflections for grain Ca1 consist of portions of Debye rings, indicating that the grain is composed of sub-micrometric crystals [START_REF] Manceau | Quantitative speciation of heavy metals in soils and sediments by synchrotron X-ray techniques[END_REF]. The intensities along each ring (constant Bragg angle) were integrated to obtain the one-dimensional XRD pattern presented in Figure 6C. The XRD peaks are slightly shifted to higher angles (i.e., smaller d values) relative to those of calcite (CaCO 3 ), indicating smaller unit cell parameters. The refined parameters were a = 4.929 Å and c = 16.754 Å, compared to a = 4.9896 and c = 17.0610 Å for pure calcite (Table S1 in supplemental information). The contraction of the unit cell is likely due to the substitution of smaller cations for Ca. Based on µXRF analyses, Mn is a possible substituent for Ca. This particular grain was not analyzed by SEM-EDX, so the presence of light elements (Z < 20) could not be tested. However, Mg was frequently detected by SEM-EDX in other grains from the same treatment (Fig. 5F and other data not shown). As divalent manganese (0.67 Å) and magnesium (0.72 Å) have a smaller ionic radius than Ca 2+ (1.00 Å; [START_REF] Shannon | Revised effective ionic radius and systematic studies of interatomic distances in halides and chalcogenides[END_REF], these two impurities are good candidate species for substitution at the Ca site. Assuming the presence of only one substitutional atom, the stoichiometry of the Ca1 grain was calculated from the experimental a and c unit cell parameters using the Vegard law [START_REF] West | Solid State Chemistry and its Applications[END_REF]. Briefly, this approach allows the determination of the composition of a binary solid solution from the linear regression between the composition and the unit cell parameters of the two pure endmembers. Two independent calculations were performed with either a or c. The difference in the stoichiometry coefficients obtained by the two calculations was below 0.02 atom for all grains. For the Mg substitution, the end-members were calcite and magnesite (MgCO 3 ), and the calculated formula for grain Ca1 was Ca 0.84 Mg 0.16 CO 3 . For the Mn substitution, the endmembers were calcite and rhodocrosite (MnCO 3 ), and the calculated formula was Ca 0.75 Mn 0.25 CO 3 . As the two impurities may be present in the grain, the proposed formula is Ca (0.84 -0.09X) Mg [0.16(1-X)] Mn (0.25X) CO 3 , with X varying from 0 to 1. Whewellite (calcium oxalate monohydrate, CaC 2 O 4 , H 2 O) was also detected in grain Ca1. This mineral has several XRD peaks at the same position as those from the substituted calcite crystallites, but the peak at Q = 1.058 Å -1 (d = 5.94 Å) is characteristic of this species, thereby allowing its unambiguous identification (Fig. 6C). This peak appears as a spotty feature on the twodimensional pattern (labelled W in Fig. 6A), which indicates that whewellite is coarsely crystalline at the scale of the X-ray probe (16 x 7 µm 2 ). One XRD reflection was attributed to vaterite. This latter mineral was more definitely identified in another experiment, in which tobacco was exposed to Cd 2+ (not shown).

The µXRD pattern for grain Ca2 is spotty (Fig. 6B), which is indicative of coarse crystals [START_REF] Manceau | Quantitative speciation of heavy metals in soils and sediments by synchrotron X-ray techniques[END_REF]. Most of X-ray reflections correspond to substituted calcite, and have an intermediate position between those of pure calcite and grain Ca1 (inset in Fig. 6C for the Bragg reflection 113), which suggests a lower degree of substitution relative to grain Ca1.

The average structural formula of this grain was calculated following the same procedure as for grain Ca1 but, because of the smaller number of diffraction peaks, only the a parameter was refined (Table S1). Calculation yielded Ca (0.91 -0.05X) Mg [0.09(1-X)] Mn (0.14X) CO 3 , with X varying from 0 to 1. Fewer peaks, attributed to whewellite, weddellite (CaC 2 O 4 , 2 H 2 O), and vaterite (CaCO 3 ) also were detected (Fig. 6C).

Figure 7 shows µXRD data for two grains produced under the Zn + Ca treatment (0.25 mM Zn + 3.28 mM Ca). These grains were rich in Ca and Zn, with the two elements being heterogeneously distributed within the grains (average Zn/Ca K α ratio = 7.5 and 1 for grain ZnCa1 and ZnCa2, respectively. The µXRD pattern for grain ZnCa1 exhibits discontinuous rings as well as isolated spots (Fig. 7C). As for grains Ca1 and Ca2, the incomplete rings correspond to substituted calcite. Zn is a likely substitute atom but not Mn because it was not detected in this grain (Fig. 7B). The presence of Mg was not tested by SEM-EDX, but is possible. The chemical formula of this grain calculated with smithsonite (ZnCO 3 ) as Zn endmember and magnesite as Mg end-member is Ca 0.84 (Mg,Zn) 0.16 CO 3 (Table S1). Mg 2+ and Zn 2+ have similar ionic radii (0.72 and 0.75 Å, [START_REF] Shannon | Revised effective ionic radius and systematic studies of interatomic distances in halides and chalcogenides[END_REF] and, consequently, undergo similar reduction of the crystal lattice parameters. The isolated spots were attributed to whewellite. The µXRD pattern for grain ZnCa2 exhibited also incomplete Debye rings (not shown). All peaks were attributed to Ca 0.92 (Mg, Zn) 0.08 CO 3 crystals. The lower degree of substitution of calcite in grain ZnCa2 compared to grain ZnCa1 is reflected in the µXRD pattern by a smaller shift of its peaks relative to calcite (inset in Fig. 7D for the Bragg reflections 110 and 113).

Another form of calcium carbonate, aragonite, was identified in grain ZnCa3 from the Zn + Ca treatment (Fig. 8). This grain also contained Zn-substituted calcite (Ca 0.93 Zn 0.07 CO 3 ). The continuous Debye rings observed in Figure 8A correspond to aragonite, and the incomplete rings and speckles correspond to substituted calcite. Thus, aragonite occurs as nanoparticles, whereas substituted calcite occurs as sub-micrometric crystals. Another grain (ZnCa4) contained Ca 0.87 Zn 0.13 CO 3 (Table S1 and Fig. S1 in supplemental information). For ZnCa3 and ZnCa4, Zn was the only substitute atom because neither Mg nor Mn was detected by µXRF and SEM-EDX (Fig. 8B and Fig. 5G for the EDX spectra, µXRF spectra not shown).

Several grains produced under the Zn treatment contained (Mg,Zn)-substituted calcite (e.g., grain Zn1, Table S1 and Fig. S2 in supplemental information), and other grains (e.g., grain Zn2, Fig. 5H) did not produce hkl reflections, although they contained also Zn and Ca. The amorphous nature of these grains was confirmed by Zn-EXAFS (see below), and by Ca-XANES spectroscopy (not shown).

In conclusion, sub-micrometer-sized calcite crystals substituted by Zn, Mg and Mn were the most frequent mineral species. Other minerals identified include, by decreasing order of abundance, whewellite (always coarsely crystalline), weddellite, aragonite, and vaterite. Zn oxalate never was detected. Zn-containing grains were analyzed also by Zn K-edge µEXAFS spectroscopy in order to confirm the presence of Zn-substituted calcite, to gain more insight on the nature of the amorphous or poorly crystallized Zn species, and to determine the proportions of all Zn phases in case of mixture.

Zn K-edge µEXAFS analysis of the grains

Figure 9 shows the Zn µEXAFS spectra of the Zn-richest regions for the grains. Spectra with several frequencies (e.g., ZnCa1 and ZnCa2) are indicative of a long range ordered Zn binding environment, such as that in a mineral structure, whereas spectra dominated by a single frequency (e.g., Zn2) are indicative of a short range ordered Zn environment. Spectra ZnCa3, ZnCa4 and Zn1 are somehow intermediate between the two previous sets of spectra, suggesting a mixture of Zn species. Data analysis was done by linear combination fits using an extended database of Zn reference compounds containing Zn-bearing and Zn-sorbed minerals, Zn precipitates, and Zn complexed to simple organic acids and complex biopolymers (Sarret et al., 2004;[START_REF] Guiné | Zinc sorption to three gram-negative bacteria: Combined titration, modeling and EXAFS study[END_REF]. One to three-component simulations were tested. All spectra were reproduced correctly with two components (Fig. 9, Table IV).

Adding a third one did not improve the fit quality significantly, as indicated by the normalized sum-squares residual parameter (NSS) since its value decreased by less than 10 % upon adding a third component. Spectra ZnCa1 and ZnCa2 show a marked similarity to that of Zn-substituted calcite, the major difference being a smaller amplitude of the unknowns. Accordingly, the best onecomponent fits for these two samples were obtained with Zn-substituted calcite (Table IV and dashed lines for ZnCa1 in Figure 9). The wave frequencies and overall shapes of the unknowns were satisfactorily reproduced by this model compound, but not the amplitude at low k. Adding a second component greatly improved the simulations. Fits of equivalent quality were obtained with either Zn-humic acid complex ("Zn-organic acids" in Table IV) or Zn-sorbed phosphate (Zn-sorbed hydroxylapatite) as second component. Zn complexes with simple organic acids (oxalate, citrate, malate, etc…) were tested also, but did not provide satisfactory fits. The Zn-humic acid complex reference was used as a proxy for Zn bonded to multiple functional groups, including carboxyl, alcohol and phenol groups. This component species may correspond to organic compounds excreted by the trichomes. Crystalline Zn phosphate compounds, including Zn phosphate tetrahydrate (hopeite and parahopeite) and Zn phosphate dihydrate, did not provide good fits to the data. For technical reasons, grains ZnCa1 and ZnCa2 were not analyzed by SEM-EDX, consequently, the presence of phosphorus could not be verified by chemical analysis. However, this element was frequently detected in grains from the three treatments, as shown for the Ca treatment in Figure 5F.

Therefore, Zn-organics and Zn phosphate forms are equally probable species in grains ZnCa1 and ZnCa2. The presence of Zn in calcite is consistent with µXRD results for the two grains.

Note that calcite grains may also contain Mg, since this element was often detected by SEM-EDX. Spectra ZnCa3, ZnCa4 and Zn1 were simulated correctly by a mixture of Zn-substituted calcite and Zn-organic acids (NSS = 7.2, 7.9 and 4.8, respectively, Table IV). The fractional amount of Zn-substituted calcite (15-23 %) is lower than that in grains ZnCa1 and ZnCa2 (40-53 %), in agreement with the spectral differences of the two sets of grains (see above).

Simulations with Zn-sorbed phosphate instead of Zn-organic acids were much weaker (NSS = 0.136, 0.120 and 0.098, respectively). This result is consistent with the absence of P in ZnCa4 and Zn1 (Fig. 5G and Fig. S2B), and its trace amounts in ZnCa3 (Fig. 8B). Again, the occurrence of Zn-substituted calcite in grains ZnCa3, ZnCa4 and Zn1 is consistent with µXRD results.

The incorporation of Zn in the aragonite crystallites from grain ZnCa3 was not tested because of the lack of Zn-substituted aragonite reference. However, this species is unlikely, or at most minor, for two reasons: first, µXRD data showed that this carbonate species is not substituted, in contrast to calcite, second, the spectrum of Zn-substituted aragonite would be different from that of Zn-substituted calcite because these two carbonate polymorphs do not have the same structure. The fact that the sum of the contributions from individual reference spectra to all sample spectra, but ZnCa4, is 100 ± 10 %, adds further credibility to the determined speciation. The lower sum for ZnCa4 (i.e., 80 %) probably results from an over-absorption effect [START_REF] Manceau | Quantitative speciation of heavy metals in soils and sediments by synchrotron X-ray techniques[END_REF]. This effect decreases the amplitude of the measured signal, without modifying the relative contributions of the component spectra. Spectrum Zn2 was reproduced best with a combination of Zn-sorbed silica and Zn-organic acids. The presence of Si was confirmed by SEM-EDX (Fig. 5H). Zn-sorbed phosphate also provided a good fit to the data (NSS = 2.9), but this model was rejected because the grain did not contain P. The absence of Zn-substituted calcite in this grain is consistent with the lack of diffraction peaks on the µXRD pattern.

In conclusion, the EXAFS analysis engenders confidence in the presence of Zn-substituted calcite thanks to the unique spectral signature of this species and to the consistency in the interpretations of the spectroscopic and diffraction data. In addition, this species is logically more abundant in the Zn + Ca treatment than in the Zn treatment. EXAFS spectroscopy is less sensitive to Zn-sorbed silica, Zn-sorbed phosphate and Zn-organic acids, as a result of the short range order of Zn, multiplicity of Zn binding environments, and presence of light elements (C, Si, P) in the second coordination sphere of Zn in these species. Despite these difficulties, their occurrence suggested by EXAFS data is supported by the detection of Si and P by SEM-EDX, and by the fact that tobacco trichomes excrete organic compounds.

DISCUSSION

The positive effect of Ca on metal tolerance shown here has been observed in other plant species [START_REF] Chen | The effects of chemical remediation treatments on the extractability and speciation of cadmium and lead in contamination soils[END_REF]Samecka-Cymerman and Kempers, 2001). Generally, this effect is attributed to a modification of the speciation of the metal in the nutrient solution, and its competition with Ca for the plant uptake. In this study, increasing the Ca supply inhibited the Zn uptake after 24 hours, but not after 2 and 5 weeks of exposure. Consequently the positive effect of Ca on Zn tolerance results from a cooperative and not an inhibition mechanism between the two elements. Ca and Zn supplements increased the density of the trichomes and led to the production of Ca/Zn-containing grains (Fig. 3F), suggesting that this excretion is a way to eliminate the excess of Zn from the plant tissues.

The mineralogical analysis of the grains showed that they contained calcium carbonates (primarily Zn-substituted calcite and, secondarily, vaterite and aragonite), and calcium oxalate mono-and dihydrate. Calcium oxalate is a rather common mineral in higher plants. In tobacco, it has been found in the vacuoles of specialized leaf cells, called idioblasts [START_REF] Bouropoulos | Calcium oxalate crystals in tomato and tobacco plants: Morphology and in vitro interactions of crystal-associated macromolecules[END_REF], and its presence in the trichome cells has been suggested (Wagner, 2004). This mineral has been shown to sequester heavy metals in some higher plants ( [START_REF] Mazen | Calcium oxalate deposits in leaves of Corchorus olitotius as related to accumulation of toxic metals[END_REF]) and references therein) and lichens (Sarret et al., 1998) and references therein). This study shows that this is not the case in the grains excreted by tobacco trichomes. Calcium carbonate is less usual in plants. Cystoliths, which are calcified bodies formed in specialized cells called lithocysts, have been described in some plants [START_REF] Setoguchi | Calcification in higher plants with special reference to cystoliths[END_REF]. These structures consist predominantly of amorphous calcium carbonate, along with subordinate amounts of calcite and vaterite, and their function is unclear. This study reports for the first time the formation of several types of calcium carbonate by tobacco, and the sequestration of Zn specifically in calcite. Other chemical forms of Zn found in the grains were Zn-organic acids, Zn-sorbed silica and Zn-sorbed phosphate. Silicon is not a component of the nutrient solution. This element might come from glass vessels used to prepare the solutions. The proportion of Zn-substituted calcite relative to the other forms increased with Ca concentration in the nutrient medium.

Although the mechanism of formation of the grains remains unclear, some speculations can be offered. Considering the diameter of the grains (10 to 150 µm) and the diameter of the trichome plasmodesmata of tobacco [START_REF] Waigmann | Ultrastructural analysis of leaf trichome plasmodesmata reveals major differences from mesophyll plasmodesmata[END_REF], they are obviously formed externally. However, Zn and Ca are bioaccumulated within the trichomes before their exudation as shown by µXRF, and more precisely in the top cells for Zn, as shown by CLSM (Ca not studied by CLSM). The fact that each grain is heterogeneous in chemical composition and consists in an aggregate of sub-micrometer-sized particles might be due to an excretion of Ca, Zn, and the other elements in liquid form, followed by precipitation in contact with air.

The predominance of calcite relative to the other CaCO 3 polymorphs further supports this hypothesis. Indeed, in a supersaturated solution of Ca 2+ and CO 3 2-, amorphous calcium carbonate precipitates first, then transforms to vaterite, and finally to calcite, which is the most thermodynamically stable CaCO 3 polymorph (Ogino et al., 1990). In the presence of Mg 2+ , the formation of aragonite is favored at the expense of calcite. Therefore, following the definition of [START_REF] Lowenstam | On Biomineralization[END_REF], the crystallization process seem to be "biologically induced" rather than "biologically controlled".

In the perspective of metal exposure through smoking, an enhanced excretion of metalcontaining grains during the plant growth, and the removal of the grains during the cigarettes manufacturing process might help to decrease the Zn and Cd content in the tobacco products.

Studies on the genetics of trichomes differentiation and excretion (Hallahan et al., 2000;[START_REF] Wagner | New approaches for studying and exploiting an old protuberance, the plant trichome[END_REF] should contribute to better understand, and possibly enhance, metal excretion through the trichomes. In contrast, in the perspective of phytoextraction, the production and the release of metal-containing grains to the soil should be avoided in order to optimize the metal content in the harvested shoots. In this study, Zn sequestered amount in the grains in in vitro plants represented 9.2% and 16.9% in Zn and Zn+Ca treated plants, respectively, as estimated from the number and chemical composition of the grains. To estimate more realistically the proportion of excreted Zn, one should monitor the production and composition of the grains during the whole growth period, and consider the total content of Zn in leaf at the time of the harvest.

Finally, this study illustrates the potential of microfocused X-ray techniques in the fields of biomineralization and bioremediation. When combined with molecular biology and biochemical tools, these techniques should provide key information on the strategies developed by plants to cope with metal toxicity and maintain metals homeostasis.

MATERIALS AND METHODS

Plant cultures

The culture conditions and the experimental techniques are listed in Table I. For the hydroponic cultures, seeds were germinated on solid medium-filled PCR tubes, and transferred after 3 weeks to 1.5 L pots (three plants per pot) filled with 1/10 strength Hoagland medium (Hoagland and Arnon, 1938). Fe was supplied as N,N-di-(2hydroxybenzoyl)-ethylendiamine N,N'-di-acetic acid (Fe-HBED, 5 µM) (Weber et al., 2004).

To avoid insect attack and dust contamination, plants were grown at 22°C in a closed culture box in a growth chamber with 16 hr light /8 hr dark cycle. After 3 weeks in the Hoagland medium, plants were maintained in this medium containing 0.08 mM ZnSO 4 and 0.28 mM CaCl 2 (control medium), or transferred to a medium containing 0.25 mM ZnSO 4 and 0.28 mM CaCl 2 (Zn treatment) or 0.25 mM ZnSO 4 and 3.28 mM CaCl 2 (Zn + Ca treatment, Table I). After 2 or 5 weeks, shoots and roots were harvested separately. The height of the shoots and the root length were measured. Aliquots of shoots were freeze-dried, weighted and digested in 10 mL of 60 % nitric acid by a microwave system (µPREP-A, MLS GmbH, Germany) applying the following gradient program: 2.5 min, 700 W, 75°C, 15 bar; 8 min, 500 W, 130°C, 25 bar; 12 min, 1000 W, 200°C, 45 bar; 24 min, 1000 W, 200°C, 45 bar. Zn concentrations in the digests were measured by inductively coupled plasma-atomic emission spectrometry (ICP-AES) with a Perkin Elmer OPTIMA 300DV. Chlorophyll was extracted with 80% acetone and measured spectrophotometrically as described in Delfine et al. (1999).

Each analysis was done on three replicates.

For the short term (24h) exposure, plants were precultured in the Hoagland medium for 5 weeks, and transferred to the control, Zn and Zn+Ca media (Table I). After 24 hours, plants were harvested and analyzed as describe above.

For in vitro culture, seed-derived plants at about 5 cm height were transferred in 300 ml glass culture bottles containing 1/3 MS medium (Murashige and Skoog, 1962) solidified with 0.7% agar and 1 % sucrose, and exposed to 0.03 mM ZnSO 4 and 3 mM CaCl 2 (in vitro-control), 1 mM ZnSO 4 and 3 mM CaCl 2 (in vitro-Zn treatment), and 1 mM ZnSO 4 and 30 mM Ca (in vitro-Zn + Ca treatment, Table I). Plants were cultivated in a growth room at 25 °C under a 16-h photoperiod (35 µmol m -2 s -1 white fluorescent tubes). Trichome densities were determined under VP-SEM (S-3500N, Hitachi, Japan) by counting the short and long trichomes on the third leaf from the top, and dividing these numbers by the leaf area. To collect the grains, plants were plunged in pure water in 50 mL tubes and vortexed for a few seconds. The supernatant was carefully removed and the grains were collected at the bottom with a pipette. Another isolation procedure was tested: grains were carefully collected using toothpicks under a stereomicroscope (Olympus SZX11-ST, Japan). Thereafter, grains were dried in vacuo (Speed Vac SC100, Instruments Inc, USA), counted under VP-SEM (S-3500N, Hitachi, Japan) and analyzed chemically by EDX. To test the solubility of isolated grains, solutions with wide range of pH (2.0, 3.0, 4.0, 5.0, 7.0, 90, and 12.5) were prepared by adjusting the pH of ultrapure water with HCl or NaOH. Isolated grains were put in water drops on the slide glass and then observed the time-lapse solubility under light microscope. Also, ex vitro hydroponic culture of tobacco plants was undertaken to check that the production of Ca/Zn-containing grains was not an artifact of in vitro conditions, and to obtain grains for morphological, mineralogical, and spectroscopic characterization. After 5 weeks of hydroponic culture in the control, Zn, Zn+Ca and Ca media (Table I), grains were collected using the water extraction procedure, and kept under dry atmosphere prior to analyses. Leaf segments were also harvested and directly observed under VP-SEM-EDX, or plunged in liquid nitrogen and freeze-dried for elemental mapping by µXRF.

VP-SEM-EDX and SEM-EDX

Hydrated leaves and isolated grains from the in vitro and hydroponic cultures cultures were glued on an aluminum stub, then mounted in a chamber stage after cooling to -20 °C, and observed by VP-SEM-EDX using a Hitachi, S-3500N fitted with a Horiba, EMAX-7000 Xray detector ( [START_REF] Kuboki | The variable pressure SEM with the cooling stage[END_REF]. The chamber pressure was 30 Pa and the accelerating voltage 15 kV. Isolated grains from the hydroponic cultures were also analyzed by SEM-EDX using a Jeol JSM 840A microscope fitted with a Kevex Si (Li) X-ray detector. The grains were attached on a carbon stub with carbon tape, and coated with carbon. The analyses were performed under vacuum at an accelerating voltage of 15 kV.

Confocal laser scanning microscopy

For visualization of intracellular Zn, leaf segments of plants grown in hydropony in 0.25 mM Zn + 0.28 mM Ca control (Zn treatment) and 0.08 mM Zn + 0.28 mM Ca (control) for 2 weeks were immersed in 1x PBS buffer (137 mM NaCl, 2.68 mM KCl, 8.1 mM Na 2 HPO 4 , 1.47 mM KH 2 PO 4 , pH 7.4) containing 25 µM Zinquin ethyl ester [ethyl (2-methyl-8-ptoluenesuphonamido-6-quinolyloxy) acetate] (Biotium, USA) for 1 hours at 25°C. Leaf segments were washed once with PBS buffer and mounted on glass slides and examined with a confocal laser scanning microscope (CLSM) system (LSM510 META NLO, Carl Zeiss, Germany) with Plan-Neofluar 10 X (0.3 NA) or 20 X (0.5 NA) water-immersion lens. Zinquin florescence was determined at an excitation wavelength of 368 nm with an UV Ar laser (80 mW) at an emission wavelength of 490 nm. Confocal fluorescence and concurrent differential interference contrast (DIC) images were taken, and digital images were processed using AxioCam HR with LSM 5 images software.

Micro-XRF, µXRD and µEXAFS

The experiments were performed on beamline 10.3.2 of the Advanced Light Source (ALS), Berkeley, CA [START_REF] Marcus | Beamline 10.3.2 at ALS: a hard X-ray microprobe for environmental and materials sciences[END_REF]. For the µXRF and µEXAFS measurements, the beam was focused down to 5 × 5 µm and the X-ray fluorescence was measured with a 7-element Ge detector. For the µXRD measurements, the diffraction patterns were recorded with a 1024 × 1024 pixels CCD camera at 17 keV incident X-ray energy with a 16 x 7 µm 2 beam size. Isolated tobacco grains were mounted at the top of a glass capillary (0.2 mm in diameter), and the capillary fixed on a motorized x -y -z stage. The grains were cooled to 150K with a Cryostream cooler (Oxford 611) during measurements in order to minimize any potential beam damage. First, a µXRD pattern of the whole grain was recorded by scanning it under the beam while acquiring the data. Then, a point µXRD pattern, a µXRF spectrum and a Zn Kedge EXAFS spectrum (if Zn present) were recorded successively on the Ca and Zn richest spot. Micro-XRF elemental maps from the freeze-dried leaf segments were recorded at room temperature in mounting the sample directly on the x -y -z stage.

XRD and EXAFS data treatment

The two-dimensional XRD patterns were calibrated using an alumina standard and integrated to one-dimensional patterns for peak assignment with the JCPDS database (http://www.icdd.com). The stoichiometry of the Mg-, Mn-and Zn-substituted crystals was estimated by refining the unit cell parameters a and c over the [10-33] ° 2θ angular range ( [1.3-4.0] Å interval) using the Ufit software (M. Evain, 1992, Nantes, France), and then by applying the Vegard law [START_REF] West | Solid State Chemistry and its Applications[END_REF] using calcite and magnesite (MgCO 3 ) as end-members for the Ca-Mg solid solution, calcite and rhodocrosite (MnCO 3 ) as end-members for the Ca-Mn solid solution, and calcite and smithsonite (ZnCO 3 ) as end-members for the Ca-Zn solid solution.

EXAFS spectra were extracted using the standard procedure, and then simulated by linear combinations of reference spectra from an extended spectral library (Sarret et al., 2004). The spectrum for Zn-substituted calcite was provided by R. J. Reeder (Reeder et al., 1999;[START_REF] Elzinga | X-ray absorption spectroscopy study of Cu 2+ and Zn 2+ adsorption complexes at the calcite surface: Implications for site-specific metal incorporation preferences during calcite crystal growth[END_REF]. Zn-sorbed silica was prepared by adding 40 mg of Zn(NO 3 ) 2 4 H 2 O (2.55 mM Zn) to a suspension containing 0.5 g of silica (aerosil 200, Degussa, Germany) preequilibrated at pH 6.0, stirring the suspension for 2 hours at pH 6.0, centrifugating it, and freeze-drying the solid phase. The final Zn content was 2 wt. %. The Zn-humic acid and and Zn-reacted hydroxylapatite references were described previously [START_REF] Neumann | EXAFS study of the nature of zinc complexation sites in humic substances as a function of Zn concentration[END_REF]Panfili et al., 2005).

FIGURE CAPTIONS Figure 1 .

 CAPTIONS1 FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. VP-SEM observation of the third leaf from the top (A-C) and of isolated grains (D-

Figure 3 .

 3 Figure 3. Distribution of Zn in long (A and B) and short (C and D) trichomes of tobacco

Figure 4 .

 4 Figure 4. Distribution of Ca and Zn determined by µXRF in a freeze-dried leaf of tobacco

Figure 5 .

 5 Figure 5. A, Representative VP-SEM image and EDX spectrum of a grain present at the top

Figure 6 .

 6 Figure 6. A and B, µXRD patterns and µXRF spectra for grains Ca1 (A) and Ca2 (B)

Figure 7 .

 7 Figure 7. A, Ca and Zn distributions for grain ZnCa1 produced by tobacco exposed to 0.25

Figure 5 Figure 8 Figure S2

 58S2 Figure 5

Table I .

 I Culture conditions and investigations

			Total Ca	Total Zn
	Culture conditions	Name of the treatment	concentration in the substrate	concentration in the substrate	Duration of exposure	Investigations	Grain name
			(mM)	(mM)
	hydroponic	control	0.28	0.08	24 hr, 2 and 5	Zn contents in shoots,
					weeks	Root and shoot growth and chlorophyll content (2 and 5 weeks only)
						CLSM (2 weeks only)
	hydroponic	Zn	0.28	0.25	24 hr, 2 and 5	Zn contents in shoots,	Zn1, Zn2
					weeks	Root and shoot growth and chlorophyll content (2 and 5 weeks only)
						CLSM (2 weeks only)
						SEM-EDX, µXRD, µXRF and Zn µEXAFS on isolated grains (5 weeks
						only)
	hydroponic	Zn + Ca	3.28	0.25	24 hr, 2 and 5	Zn contents in shoots,	ZnCa1, ZnCa2,
					weeks	Root and shoot growth and chlorophyll content (2 and 5 weeks only)	ZnCa3, ZnCa4
						SEM-EDX, µXRD, µXRF and Zn µEXAFS on isolated grains (5 weeks
						only)
	hydroponic	Ca	3	0.02	5 weeks	SEM-EDX, µXRD and µXRF on isolated grains	Ca1, Ca2
	in vitro	in vitro-	3	0.03	3 weeks	Shoot growth, Size and number of grains, SEM-EDX on isolated grains,
		control				trichome density
	in vitro	in vitro-Zn	3	1	3 weeks	Shoot growth, Size and number of grains, SEM-EDX on isolated grains,
						trichome density
	in vitro	in vitro-	30	1	3 weeks	Shoot growth, Size and number of grains, SEM-EDX on isolated grains,
		Zn + Ca				trichome density

Table II .

 II Plant growth, leaf chlorophyll contents, and Zn accumulation in shoots of tobacco grown under three conditions (culture conditions detailed in TableI)Each value is the mean of three measurements on three different plants plus or minus the standard deviation.

						Chlorophyll contents (mg g -1 FW)
		Height of shoot (cm)	Root length (cm)				Zn accumulation in shoot (µg g -1 DW)
	Treatment					2 weeks	5 weeks
		2 weeks	5 weeks	2 weeks	5 weeks	Chlorophyll a Chlorophyll b Chlorophyll a Chlorophyll b	24 hr	2 weeks	5 weeks
	Control	7.48 ± 0.46	11.3 ± 1.82	9.6 ± 1.6	20.4 ± 0.9	1.18 ± 0.211 0.34 ± 0.060 0.94 ± 0.049	0.29 ± 0.038	21.5 ± 3.5	36.2 ± 6.4	50.8 ± 9.3
	Zn	2.46 ± 0.23	4.31 ± 0.37	6.2 ± 1.6	6.4 ± 1.0	0.67 ± 0.055 0.22 ± 0.031 0.26 ± 0.028	0.08 ± 0.008	326.4 ± 33.5 1511.73 ± 31.6 2309.0 ± 526.5
	Zn + Ca	4.26 ± 0.37	6.37 ± 0.67	8.9 ± 1.0	10.0 ± 0.7	0.66 ± 0.103 0.21 ± 0.040 0.33 ± 0.063	0.10 ± 0.022	175.7 ± 28.2 2783.9 ± 107.6 2398.4 ± 182.4

Table III .

 III Shoot growth parameters and Zn content, number of trichomes and grain production by the leaves of tobacco plants cultured in vitro for 3 weeks under three conditions (culture conditions given in TableI)Each value is the mean of three individual measurements plus or minus standard deviation. The number of trichomes and grain production were determined by VP-SEM observations. a Excreted Zn was calculated based on the number and size of excreted grains (Zn content was 2% in Zn grain, 1% in Zn+Ca grain, as estimated by ZAF method). b Percentage of excreted Zn was calculated based on Zn amount in shoot.

	Treatment	Height of shoot (cm)	Shoot dry weight (mg)	Zn accumulation in shoot (µg g -1 DW)	Number of trichome per cm 2 of leaf	Grain production and Zn excretion per plant
					Short	Long	Number of	Size of	Excreted	Excreted Zn
					trichome	trichome	grains	grains (µm)	Zn (µg) a	(%) b
	In vitro-Control	8.7 ± 0.56	171 ± 12.3	91.7 ± 12.2	21 ± 3.7	14 ± 2.3	127 ± 34	26 ± 11.2	-	-
	In vitro-Zn	4.4 ± 0.33	80 ± 6.5	564.0 ± 36.2	56 ± 7.3	38 ± 4.2	784 ± 216	57 ± 12.8	4.1	9.2
	In vitro-Zn + Ca	6.4 ± 0.45	97 ± 9.3	675.0 ± 33.5	43 ± 5.7	25 ± 6.3	1223 ± 245 86 ± 13.2	11.0	16.9

ACKNOWLEDGEMENTS E. H. is recipient of a BioGreen 21 Program and fellowships from the Human Frontier for Science Program (HFSP) and from the Alexander von Humboldt Foundation. We thank Delphine Tisserand and Martine Lanson (LGIT, France), Sébastien Pairis (Laboratoire de Cristallographie, France), Sylvia Krüger (Leibniz-Institut für Pflanzenbiochemie, Germany), Han-san, the VPSEM-EDX operator, and the students from the Division of Forestry Resources (Kangwon National University, Korea) for their technical assistance. VP-SEM analyses were performed at Korea Basic Science Institute, Chunchon, South Korea. We acknowledge R. J. Reeder for sharing the Zn-calcite EXAFS spectrum, and Prof. Dierk Scheel and Dr. Dieter Neumann (Leibniz-Institut für Pflanzenbiochemie) for fruitful discussions. The operations of the Advanced Light Source at Lawrence Berkeley National Laboratory are supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials

1 This research was supported by a grant of BioGreen 21 Program, Rural Development Administration in Korea. The operations of the Advanced Light Source at Lawrence Berkeley National Laboratory are supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under Contract No. DEAC03-76SF00098.

tolerate high heavy metal concentrations ? J. Plant Physiol. 146: 704-717 Ogino T, Suzuki T, Sawada K (1990) The rate and mechanism of polymorphic

Ca and Zn concentrations given in Table I. d Simulations shown in Figure 9.

larger is the shift of the XRD peaks toward the low d values (or high Q values) and, thus, the higher is the deviation in peak position relative to pure calcite (inset).

Supplemental information


Florian Toque
email: florian.toque@ifsttar.fr

Etienne Come
email: etienne.come@ifsttar.fr

Latifa Oukhellou
email: latifa.oukhellou@ifsttar.fr

Martin Trepanier
email: mtrepanier@polymtl.ca

Florian Toqué

Etienne Côme

Martin Trépanier

Short-Term Multi-Step Ahead Forecasting of Railway Passenger Flows During Special Events With Machine Learning Methods

Keywords: Big Data, Machine Learning, Smart Card Data, Passenger Demand Forecasting, Public Transport, Forecasting Under Special Events

HAL is a

Introduction

Every day a large amount of digital footprints is generated by citizens during their trips (GPS, WiFi, Bluetooth, smart card, social networks logs, etc.). These data can hold a high descriptive value of the urban mobility that could be helpful to develop innovative tools. Such tools can be useful to improve quality of services and to better organize the mobility of citizens in a city. Public authorities wish to develop sustainable urban mobility practices that aim to increase the use of public transport and reduce the pollution involved by private car use. In order to achieve such challenge, the understanding of urban mobility across public transport network is essential. We focus the study on one of the mainly used digital footprints which is the smart-card data collected by automated fare collection systems.

As early as 2004, Bagchi and White (2) studied the potential role that smart card data can play for travel behavior analysis and considered their potential to complement existing data collection such as survey methods. Since 2005, a multitude of studies highlighted the potential uses of smart card data in transit planing and transit uses (3; 24; 18; 19). One of the major disadvantage of this type of data, is the lack of information about the destination of passenger travels. In this respect, researches have been oriented to improve this source of data with studies like data completion and enrichment with the aim to estimate origindestination [START_REF] Munizaga | Estimation of a disaggregate multimodal public transport origin-destination matrix from passive smart card data from santiago, chile[END_REF] or to validate travel behavior estimation [START_REF] Munizaga | Validating travel behavior estimated from smartcard data[END_REF] and to perform trip purpose inference [START_REF] Lee | Trip purpose inference using automated fare collection data[END_REF].

In order to encourage the use of public transport, transit planners need to correctly adapt the fare proposed to the passengers. To achieve such challenge, an in-depth understanding of the passenger behavior seems essential. In this context, passenger behavior analysis is a field that has been widely studied, which concerns the clustering of passengers depending on their transportation network activity (1; 13; 28; 21; 9; 14), or the characterization of station pattern [START_REF] Poussevin | Mining ticketing logs for usage characterization with nonnegative matrix factorization[END_REF].

Another parameter that directly impacts the satisfaction and the increase of public transport passengers is a good equilibrium between the offer and the demand of transport services. In this respect, urban mobility researchers recently studied the passenger demand with a focus on the short-term forecasting of railway passenger flows in (7; 8; 22; 23). Thereafter, researchers have oriented their work on the spatio-temporal aspect of the forecasting problem. For this purpose, researchers have worked on traffic forecasting with deep neural network and more precisely with combined convolutional and recurrent neural network in (25; 5) or graph convolutional neural network in [START_REF] Yu | Spatio-temporal graph convolutional neural network: A deep learning framework for traffic forecasting[END_REF]. In the same line of work, authors of [START_REF] Zhang | Deep spatio-temporal residual networks for citywide crowd flows prediction[END_REF] have predicted the Citywide crowd flows with spatio-temporal convolutional neural network, and authors of (29) have designed spatio-temporal neural network to predict different sources of related space-time series.

Recently, studies involving passenger flows forecasting in public transport network have been oriented under atypical event. In [START_REF] Li | Forecasting short-term subway passenger flow under special events scenarios using multiscale radial basis function networks[END_REF], the authors use a multiscale radial basis function networks to perform a short-term multi-step ahead forecasting (t+15min, t+30min) subway passenger flow under special events scenarios without exogenous data about special event. In [START_REF] Ni | Forecasting the subway passenger flow under event occurrences with social media[END_REF], short-term prediction approaches were developed to forecast subway passenger flows for the next 4 hours using social media data. The authors focused on the prediction of the total number of passengers (sum of entry and exit) of one subway station of the New York City network. They proposed a two-step methodology: hashtag-based event detection followed by the combined use of linear regression and a seasonal autoregressive moving average model using the social media event as exogenous features in input of the model.

Urban mobility forecasting in public transport is a very challenging task, since it depends on plethora of external factors such as calendar, weather, events or service breakdown. These factors can be hardly taken into account because of their high temporal and spatial irregularity. In this paper, we mainly focus on the problem of short-term multi-step ahead passenger forecasting demand under special events, in order to be able to face some abnormal behavior in the data caused by temporal factors like days off, Christmas Eve, New Year's Eve and exogenous factors such as service breakdown. We can summarize the main contribution of this study in the three following points:

-Comparison of short-term forecasting model of the state of the art with multi-step ahead horizon. -Comparison between short-term multi-step ahead forecasting models with long-term forecasting models, in order to evaluate until which step ahead, it is useful to perform short-term forecasting against long-term forecasting. -Analyze short-term multi-step ahead forecasting results under special events. With special events corresponding to days with anomalies on the public transport network or specials periods such as public holiday.

2 Short-term forecasting

Context and objective

Passenger demand forecasting performed in a long-term horizon (until one year ahead) can be very useful to transit planners for strategic long-term planning of the network in order to reduce operating costs and optimize vehicle use over the network. Nevertheless, long-term prediction has inherent disadvantages in forecasting passenger demand under special event scenarios. Indeed, these special events can cause disruptive impacts on the transportation system, which are hard to predict because they correspond to abnormal behavior patterns. These special events could be categorized, into two groups (i) Anticipated events which may be known or expected in advance such as weather, cultural or sporting event, etc. Collect such event database could be difficult but nonetheless useful to incorporate in demand prediction models [START_REF] Pereira | Using data from the web to predict public transport arrivals under special events scenarios[END_REF] (ii) Unexpected events particularly those corresponding to service breakdown, or events that are not often or never observed in the historical dataset. Taking into account such type of special event, demand prediction should be formalized as a shortterm forecasting problem, requiring the use of last observations of the time series in the prediction model [START_REF] Li | Forecasting short-term subway passenger flow under special events scenarios using multiscale radial basis function networks[END_REF]. We focus this study on the short-term forecasting of passenger demand by using only passenger demand historical database and calendar information such as Month, Day, Holiday, Public School Holiday, Extended Weekend, Christmas Eve and New Year's Eve. In this paper, a clear emphasis is given to the evaluation of the short-term multistep ahead forecasting performances on an extracted subset of a 2 years smart card dataset, including special events. The main objective of this work is to achieve the more accurate passenger flows forecasting in the case of specific events, by means of dedicated forecasting models able to capture the behavior of passengers in such situations. Accurate forecasting results will help transit operators, to improve the re-routing of passengers and to adapt the supply transport the more precisely to fit the passenger demand, in case of atypical event.

We compare different type of short-term models that forecast the number of passengers entering each station during the next 8 time step of 15 minutes (2 hours). In order to evaluate the models in case of abnormal patterns, we select two subset of data that correspond to abnormal periods:

-Days off, Christmas Eve and New Year's Eve: this period can be known in advance and correspond to days with very specific behavior.

-Days with anomaly on the transportation network system: this period is selected with a database given by the transport organization authority. It corresponds to service breakdown due to different sources, such as, technical problems, fire incident or strike of transit operator.

Forecasting methodology

We work on multi-step short-term forecasting using past historical observation and exogenous features to predict the number of passengers entering the studied railway stations at the 8 next time step (data are aggregated with 15 minutes time step). Both univariate, multivariate and multivariate to univariate models are considered to forecast passenger flows. We compared six different models: a long-term model baseline, a long-term machine learning model, a naive short-term model, a statistical model, a machine learning model and a deep learning model with different variants. Each input and output of short-term models are described in Table 1.

Ŷ A t RF LT time information τ Ŷ A t LOCF Y A t-1 Y A t-1 VAR Y A t-n:t-1 Ŷ A t RF ST UNI Y s t-n:t-1 and time information τ Ŷ s t RF ST MULTI Y A t-n:t-1 and time information τ Ŷ A t GRU UNI Y s t-n:t-1 and time information τ Ŷ s t GRU MULTI Y A t-n:t-1 and time information τ Ŷ A t GRU FUSION Y A t-n:t-1 , Y s t-n:t-1 and time information τ Ŷ A t GRU MULTI-UNI Y A t-n:t-1 and time information τ Ŷ s t
Where τ is the time information defined as time step t, encoded as integer value (1-96) and day encoded as day type dt with the vector of categorical variables described in Section 2.2.4. Ŷ A t represents the predicted number of passengers in all the studied stations and Ŷ s t , the predicted number of passengers in the station s at time step t.

Historical average, HA

This model model predicts the number of passenger in the corresponding time step by averaging the value of the historical observations by day (Monday, Tuesday, ..., Sunday). The prediction at 10:00 am on Monday corresponds to the average of all the historical values for Monday at 10:00 am. This model is the baseline of the long-term forecasting model.

Last observation carried forward, LOCF

It is a naive method used in short-term time series forecasting. It returns the last observed value (observation at the previous time step).

Vector autoregressive, VAR

It is a well known statistical model ( 12) used in time series forecasting. It is a variant of the univariate autoregressive model (AR) which is a time-series regression model that predicts the next value by linearly taking into account a stochastic term and the previous observation.

The VAR method is a multivariate linear forecasting approach that captures the linear interdependencies among the different time series to perform prediction. Each predicted variable can be forecasted by resolving an equation representing its evolution based on its own past observation and the past observation of the other variables.

Random forest, RF

The random forest is a machine learning model that has been used for several real-world applications on problem of regression or classification. This model has been introduced by Breiman (4), it is an ensemble learning algorithm based on the average prediction of different decision trees (forest). The results obtained by the different trees make the RF more accurate and robust than a unique decision tree.

Random forest long-term, RF LT: This model forecast the number of passenger on each station until one year ahead. The inputs of the model are only the information of the time and date defined as day type, encoded with the following features:

-Day of the week (1-7): Monday, Tuesday, ..., Sunday.

-Month (1-12): January, February, ..., December.

-Public holiday (0-1): Public holiday in the studied region (for this study, Paris area).

-Extra day off (0-1): Working day of an extended weekend between public holiday and weekend, e.g., Friday is considered as an extra day off if the day before (Thursday) is a public holiday. -School holiday (0-1): Day in period of school holiday.

-Christmas Eve (0-1): December 24.

-New Year's Eve (0-1): December 31.

Random forest short-term univariate, RF ST UNI: The RF short-term model is a univariate model, in order to forecast all the station one model per station is created. This RF ST UNI takes the n last observed values, often named the lag, the information of time and date defined as day type with the features detailed in Section 2.2.4.

Random forest short-term multivariate, RF ST MULTI: In order to take into account the transport network connection in the forecasting, we create a second type of RF model that is a multivariate variant. The principal objective is to learn information about incoming passenger flow from the predicted station and other stations of the transport network. The model takes the n last observed values of all the predicted stations, the day type defined with the features depicted in Section 2.2.4, and the time step in input.

Gated recurrent unit, GRU

This model is a variant of recurrent neural networks (RNNs) and has been introduced by ( 6). RNNs consider that outputs are dependent on previous computations in contrast with traditional neural networks where inputs (and outputs) are temporarily considered independent of each other. Recurrent neural networks keep a "memory" of previous calculations under the form of a constantly updated hidden state. GRU, as well as long short-term memory (LSTM) [35], are a special type of RNN with a gate mechanism that prevents the vanishing gradient problem [36] associated with the base RNN model in order to be able to learn long-term range dependencies. Unlike the LSTM, GRU are composed of a simpler gate mechanism that allows a faster computation time during the learning and predicting step. Currently, GRU are state-of-the-art models for problems involving time series analysis (e.g., machine translation, music modeling). In this study we propose four different versions of the GRU model: Gated recurrent unit univariate, GRU UNI The first version is an univariate model that uses the past observations of one time series in addition to time step and date information to predict the next value of the same time series. One model per station is created.

Gated recurrent unit multivariate, GRU MULTI In order to take into account the spatial information in the prediction model, we created a gated recurrent model with a multivariate shape. This model uses the past observations of all the time series to predict the next values of all the stations. Gated recurrent unit fusion, GRU FUSION As multivariate and univariate models perform differently depending on the observed passenger flows, we created a model that combines the predictions of both multivariate and univariate models. This method is a combined model that links a weight with each of the multivariate and univariate model prediction. These weights are generated by an attention mechanism that captures the importance of each model (multivariate and univariate) at each time step of the prediction. The final output detailed in Equations 1 and 2 corresponds to the weighted sum of the model predictions.

α s (t) = φ (H U s (t)) (1)
Ŷ F s (t) = α s (t) ŶU s + (1 -α s (t)) Ŷ M s (2)
where Ŷ F s (t) is the prediction of the number of passengers at station s at time step t of the GRU FUSION model (M corresponds to the GRU MULTI model and U to the GRU UNI model). The weights α s (t) (one weight per station) are obtained by the attention mechanism represented by the sigmoid function φ over the hidden state (H U s (t)) of the univariate GRU model at time step t.

Gated recurrent unit multivariate to univariate, GRU MULTI-UNI

To account for the spatial information in the prediction model, we compute a multivariate-univariate variant of the gated recurrent model. This model uses the past observations of all the time series to predict the next values of one station. This variant involves the computation of one model per time series.

The univariate and multivariate-univariate approach builds as many models as there are stations, whereas the multivariate approach uses one model to forecast the passenger flows for all stations.

Multi-step ahead forecasting

Short-term multi-step ahead forecasting aims to predict the values of all stations A at time step t + n, with n > 1. In this study, we forecast until 8 step ahead, {Y A t+n |n ∈ 1, 8 }, with 15 minutes aggregated data. Multi-step ahead forecasting is a challenging task because of the lack of updated observation and the accumulated errors of the model. Different methods of multi-step ahead forecasting can be built. Here we have adopted the iterative method meaning that we iteratively use the prediction at time t +1 as input variables for the next step prediction. Thus, we can repeatedly predict step by step until obtaining the target horizon forecasting.

Experiments

Problem case study

To evaluate our models, a real 2 years smart card dataset (2014-2015) with passenger demand aggregated per 15 minutes is used. This dataset is provided by the transport organization authority of Ile-de-France (Ile-de-France Mobilités) and depicts the number of passengers entering the 30 stations of the multimodal transport network of the business district La Défense of Paris in France. The considered stations include different transport modes such as train (suburban railway service), metro, RER (Regional Express Network) and tramway. The considered district includes one tramway line with 13 stops and five metro, RER and train lines with 17 stations. Each day the studied railway stations handle more than 215k passengers while the tramway line transport 35k passengers. In order to highlight the analysis of passenger demand forecasting under special events, the evaluation of the proposed models is performed on the whole dataset as well as on a subset of data which contains only periods with non-regular behaviors.

A weeklong example (Monday, February 23, 2015 to Sunday, March 1, 2015) of the most visited stations of each transportation mode (train and tramway) with data aggregated by 15 minutes is depicted in Figure 1. This figure shows that tram stations has noisy pattern, moreover it reveals for all transport modes, a familiar temporal trends in public transport usage such as the difference between week-end and weekday characterized by activity peaks in the morning the evening and by low passenger flows during the weekend. The greater number of passenger during the evening activity peak than the morning activity peak of the train station "La Défense Grande Arche" is due to the fact that this station is located in the center of the business district.

Evaluation methods

We evaluate the results obtained by the different forecasting models with several well-known metrics. In order to have a better understanding of the errors, two different measures of prediction accuracy were used, namely the Root Mean Square Error (RMSE) and the Mean Average Percentage Error at v (MAPE@v). The errors can be expressed as:

RMSE = ∑ S s=1 ∑ T t=1 ( ŷs (t) -y s (t)) 2 T × S (3
∀y s (t) > v, MAPE@v = 100 T × S × S ∑ s=1 T ∑ t=1 y s (t) -ŷs (t) y s (t) (4)
where ŷs (t) is the forecast value of station s at time step t, y s (t) is the actual value, µ s is the mean of the observed values y s and S is the station number. As explained in Figure 2, four training and test sets were used for the short term prediction. Short-term forecasting errors over the test set have been performed by concatenating the prediction of the 4 test sets. This kind of split better reflects the real situation where the model will be updated every quarter. Days with free transportation because of pollution peaks were removed from the dataset. There were four such days in 2014 and six days in

Results

The results for the two long-term models and the four short-term prediction models detailed in Section 2.2 are summarized in terms of RMSE in Table 2 and MAPE@5 in Table 3. According to the evaluation protocol explained in Section 3.2, the performances for both the global training and test sets are given in this table. The high difference between the train set and the test set in terms of MAPE and RMSE error of the multivariate models (RF ST MULTI and GRU FUSION), demonstrate that these models are overfitted. The univariate models RF ST UNI and GRU UNI perform the best prediction in the test set in terms of RMSE and MAPE errors. Besides these analysis we can also observe that recurrent neural network GRU models perform better multi-step prediction than the others short-term models and seems to be less sensible of error propagation between the different multi-step prediction. In order to better understand how the models work, we focus the analysis of the forecasting results during two specific periods (i) Public holiday and special day period and (ii) transport network anomaly period. Indeed, such special periods are harder to predict and specifically at multi-step ahead. The best results in term of RMSE are obtained by the univariate GRU model until time step t + 3, then it is the long-term model RF that performs the best prediction. These results could be explained by the fact that short-term models give more importance to past observation than exogenous calendar features during the prediction and that RMSE explodes after several multi-step forecast during such special periods. In term of MAPE, multi-step results are less impacted by the exploding error propagation. The best models are the multivariate models GRU, due to his high capability to generalize, the GRU FUSION model is the best prediction model in term of multi-step horizon forecasting.

Forecasting with Transport network anomaly periods

To quantify the robustness of multi-step ahead prediction models under special events, we evaluate their performances within special days periods created with an anomaly database provided by the transport authority of Ile-de-France (Ile-de-France Mobilités). The anomalies of this database can be categorized into the following types: We filtered this database in accordance with the station and period study, resulting in a subset of 45 days during the test set period (2015).

Table 5 depicts the multi-step ahead prediction results of the models, in terms of RMSE and MAPE during the transport anomaly period.

We can observe that long-term models have difficulty to forecast the number of passenger during anomaly periods in terms of RMSE and MAPE. In contrast, short-term univariate model GRU UNI performs equivalent result to the global performance in Table 2 and Table 3. The results in terms of MAPE error show that GRU models are better prediction models for multi-step ahead prediction. The short-term model results on this special period that contains not predictable events, demonstrate that short-term models perform better prediction at multi-step ahead than long-term models.

Conclusion

Passenger demand prediction could be useful for trip planning, transport operation and passenger information. From this perspective, we investigated the short-term multi-step prediction of passenger flows with real smart card dataset. The case study considered in this paper involves several stations of different modes in a major business district in the Paris metropolitan area (La Défense). We compare basic and machine learning long-term models with short-term models under two special periods, in order to understand the results of short-term multi-step forecasting. We considered different variants of short-term models including statistical, machine learning and deep learning models both in univariate and multivariate case. The results have demonstrated that deep learning models performed better forecasting during the special periods containing public holidays and special days. On the other special periods defined by days with transport network anomalies, the univariate models RF and GRU obtained the best results. Besides these results, this study has demonstrated the effectiveness of recurrent neural networks for multistep prediction tasks. These models have shown to be less sensitive to error propagation along the different time step contrary to the other models such as vector autoregressive or random forest.

Future research should investigate different methodologies of multi-step ahead forecasting, in order to better incorporate the spatiotemporal links between the different time series. From this perspective, it could be relevant to investigate other architectures of neural network that could better capture these links within a transport network and thus make better prediction during atypical periods. Future work should also investigate the application of prediction model on other cities and new datasets that involve more information such as event database.

Fig. 1

 1 Fig. 1 Weekly pattern of the number of ticketing logs of the most visited train and tram stations aggregated by 15 minute intervals. The weeklong example extends from Monday, February 23, 2015 to Sunday, March 1, 2015.

  2015 (Friday 14 to Monday 17 March 2014, Saturday 21 to Monday 23 March 2015 and from Sunday 29 to Monday 30 November 2015). The transport was also free on Sunday 11 January 2015 because of the people's march through Paris after the terrorist attack. We also remove from the dataset the period between 23 July and 24 August 2015, because of the renovation work on the principal line of the study (RER A line).

Fig. 2

 2 Fig.2Train sets are colored in blue, test sets are red and unused data is shown in gray. Four training and test sets (TT1, TT2, TT3, TT4) were used to capture real situations (the model is updated every three months) for the short-term forecasting.

Table 1

 1 Inputs and outputs of passenger forecasting models at time step t on day d

	Model	Input	Output
	HA	Day (Monday, .., Sunday) and time step feature

Table 2

 2 Results of the short-term multi-step ahead prediction models for passengers entering railway and tram stations in 15 min intervals on the global training and test set, in term of RMSE. RFs and GRUs are the models described in Section 2.2, and RMSE and MAPE@5 are the measures of prediction defined in Section 3.2.

			RMSE -Train set (2014) -Global set
		t + 1	t + 2	t + 3	t + 4	t + 5	t + 6	t + 7	t + 8
	HA	87.19	87.19	87.19	87.19	87.19	87.19	87.19	87.19
	RF LT	39.18	39.18	39.18	39.18	39.18	39.18	39.18	39.18
	LOCF	64.28	104.56	145.12	182.33	217.59	248.78	275.92	299.37
	VAR	31.34	38.12	45.74	53.26	61.02	67.74	73.24	77.92
	RF ST UNI	20.63	27.14	31.86	35.64	39.20	42.43	45.35	47.85
	RF ST MULTI	13.02	18.79	23.74	28.17	32.61	36.76	40.68	44.20
	GRU UNI	27.22	29.26	31.71	33.61	35.11	36.45	37.57	38.5
	GRU MULTI	27.77	30.35	32.54	34.27	35.68	36.87	37.93	38.85
	GRU FUSION	25.04	26.99	29.06	30.67	31.95	32.98	33.84	34.55
	GRU MULTI-UNI	26.69	29.79	32.62	34.67	36.38	37.85	39.21	40.43
			RMSE -Test set (2015) -Global set
	HA	88.03	88.03	88.03	88.03	88.03	88.03	88.03	88.03
	RF LT	57.29	57.29	57.29	57.29	57.29	57.29	57.29	57.29
	LOCF	65.72	107.52	149.86	188.23	224.74	256.85	285.08	309.38
	VAR	34.60	42.41	51.35	59.60	68.42	76.18	82.82	88.58
	RF ST UNI	31.34	34.42	38.08	40.84	44.12	46.78	49.50	51.51
	RF ST MULTI	41.00	42.92	45.42	47.57	50.26	52.41	54.43	56.21
	GRU UNI	31.27	33.14	36.02	38.20	40.53	42.44	44.45	46.08
	GRU MULTI	37.74	41.54	44.64	46.83	48.67	50.23	51.61	52.79
	GRU FUSION	32.33	34.74	37.74	40.23	42.52	44.30	45.92	47.28
	GRU MULTI-UNI	34.98	38.70	42.56	45.09	47.08	48.77	50.39	51.91
	HA, LOCF, VAR,

Table 3

 3 Results of the short-term prediction models for passengers entering railway and tram stations in 15 RFs and GRUs are the models described in Section 2.2, and RMSE and MAPE@5 are the measures of prediction defined in Section 3.2.4.1 Public holiday, Christmas Eve and New Year's EvePublic holidays, Christmas Eve and New Year's Eve, are special days during which passenger demand can be considerably different from normal. Here, we analyze the prediction of passengers flows aggregated by 15 minutes computed with the multi-step forecasting models at time step t + n with n in the range[START_REF] Agard | Mining public transport user behaviour from smart card data[END_REF][START_REF] Ding | Predicting short-term subway ridership and prioritizing its influential factors using gradient boosting decision trees[END_REF]. In table4we can observe the RMSE and MAPE errors on the sub-test set corresponding to these special types of days(12 days in 2015).

	min intervals
			MAPE@5 -Train set (2014) -Global set
		t + 1	t + 2	t + 3	t + 4	t + 5	t + 6	t + 7	t + 8
	HA	40.39	40.39	40.39	40.39	40.39	40.39	40.39	40.39
	RF LT	26.32	26.32	26.32	26.32	26.32	26.32	26.32	26.32
	LOCF	41.08	49.24	60.14	71.36	84.52	97.06	109.40	122.01
	VAR	32.09	36.31	41.32	46.11	51.23	55.21	58.42	60.83
	RF ST UNI	17.81	21.23	23.41	24.86	26.07	27.01	27.88	28.77
	RF ST MULTI	10.55	14.50	17.86	20.56	22.94	24.97	26.72	28.24
	GRU UNI	24.16	24.43	24.77	25.07	25.35	25.57	25.80	26.08
	GRU MULTI	24.78	25.36	25.85	26.18	26.45	26.68	26.96	27.21
	GRU FUSION	22.25	22.85	23.38	23.78	24.10	24.36	24.59	24.86
	GRU MULTI-UNI	24.08	24.96	25.68	26.20	26.65	27.04	27.42	27.82
			MAPE@5 -Test set (2015) -Global set
	HA	40.80	40.80	40.80	40.80	40.80	40.80	40.80	40.80
	RF LT	33.89	33.89	33.89	33.89	33.89	33.89	33.89	33.89
	LOCF	40.75	49.00	60.16	71.49	84.58	97.30	110.13	123.2
	VAR	34.29	39.49	45.51	51.18	57.41	62.44	66.62	69.76
	RF ST UNI	27.49	28.11	28.83	29.50	30.04	30.49	30.90	31.4
	RF ST MULTI	30.29	30.82	31.36	31.85	32.40	32.78	33.11	33.43
	GRU UNI	27.58	27.94	28.52	28.98	29.43	29.81	30.19	30.52
	GRU MULTI	28.46	29.21	29.93	30.43	30.87	31.25	31.58	31.88
	GRU FUSION	28.25	28.61	29.14	29.57	29.99	30.29	30.60	30.97
	GRU MULTI-UNI	27.97	28.62	29.32	29.84	30.30	30.73	31.22	31.67
	HA, LOCF, VAR,

Table 4

 4 Results of the long-and short-term prediction models for passengers entering train and tram stations during three special periods: public holidays, Christmas Eve and New Year's Eve, in term of RMSE and MAPE errors. RMSE -Sub test set (2015) -Public holiday, Christmas Eve and New Year's Eve(12 days)

	t + 1	t + 2	t + 3	t + 4	t + 5	t + 6	t + 7	t + 8
	HA

Table 5

 5 Results of the long-and short-term prediction models for passengers entering train and tram stations during special periods: sub-dataset of days with anomalies. , VAR, RF ST UNI and RF ST MULTI are the short-term models described in Section 2.2, and RMSE, MAE and MAPE@5 are the measures of prediction defined in Section 3.2.

		RMSE -Test set (2015) -Sub-dataset transport anomaly
		t + 1	t + 2	t + 3	t + 4	t + 5	t + 6	t + 7	t + 8
	HA	114.76	114.76	114.76	114.76	114.76	114.76	114.76	114.76
	RF LT	97.19	97.19	97.19	97.19	97.19	97.19	97.19	97.19
	LOCF	56.65	90.87	125.85	157.37	187.52	213.98	237.14	257.15
	VAR	37.13	48.66	61.02	71.91	82.76	92.71	100.36	107.20
	RF ST UNI	32.32	38.39	44.93	50.53	55.76	59.54	63.21	66.06
	RF ST MULTI	62.86	66.00	71.52	76.52	82.22	86.15	89.07	91.24
	GRU UNI	32.29	35.63	40.88	45.65	50.67	55.44	60.09	64.10
	GRU MULTI	52.55	59.83	66.37	71.13	75.19	78.83	81.94	84.56
	GRU FUSION	37.60	42.22	48.54	54.17	59.29	63.56	67.49	70.81
	GRU MULTI-UNI	44.22	51.09	58.57	63.72	67.92	71.47	74.82	78.00
		MAPE@5 -Test set (2015) -Sub-dataset transport anomaly
	HA	56.96	56.96	56.96	56.96	56.96	56.96	56.96	56.96
	RF LT	47.71	47.71	47.71	47.71	47.71	47.71	47.71	47.71
	LOCF	41.55	48.24	58.4	68.21	79.17	90.2	101.54	112.44
	VAR	37.83	44.68	52.93	60.70	69.17	76.73	83.27	88.26
	RF ST UNI	29.91	31.21	32.60	34.37	35.60	36.92	38.05	39.18
	RF ST MULTI	39.02	40.55	42.15	43.63	45.14	46.34	47.23	48.46
	GRU UNI	30.67	31.34	32.60	33.81	35.08	36.25	37.46	38.37
	GRU MULTI	35.00	36.63	38.52	39.84	41.15	42.27	43.16	43.83
	GRU FUSION	32.35	33.19	34.76	36.01	37.24	38.05	38.99	40.00
	GRU MULTI-UNI	33.07	34.40	35.99	37.21	38.39	39.63	41.22	42.28

LOCF

Table 6

 6 Informations about the studied stations

	ID	Name	Line Type	Latitude	Longitude Agency
	393	LA DEFENSE-GRANDE ARCHE	A	RER	48.892187 2.237018	RATP
	394	LA DEFENSE-GRANDE ARCHE	L	Transilien 48.892187 2.237018	SNCF
	269	ESPLANADE DE LA DEFENSE	1	Metro	48.888631 2.247932	RATP
	151	CHARLES DE GAULLE ETOILE	A	RER	48.874238 2.294491	RATP
	577	NANTERRE-PREFECTURE	A	RER	48.895745 2.223213	RATP
	414	LA DEFENSE-GRANDE ARCHE	1	Metro	48.892187 2.237018	RATP
	578	NANTERRE-UNIVERSITE	A	RER	48.901550 2.215232	RATP
	357	HOUILLES-CARRIERES-SUR-SEINE	A	RER	48.920379 2.185353	SNCF
	580	NANTERRE-VILLE	A	RER	48.895126 2.195364	RATP
	100	BOULOGNE-PONT DE SAINT CLOUD 10	Metro	48.840745 2.228537	RATP
	812	SAINT-CLOUD	L	Transilien 48.846103 2.217621	SNCF
	843	SURESNES-MONT VALERIEN	L	Transilien 48.871714 2.221030	SNCF
	29	ASNIERES	J	Transilien 48.905706 2.283629	SNCF
	436	LE VAL-D'OR	L	Transilien 48.856420 2.216572	SNCF
	217	COURBEVOIE	L	Transilien 48.898119 2.247943	SNCF
	579	NANTERRE-UNIVERSITE	L	Transilien 48.901746 2.215111	SNCF
	712	PUTEAUX	L	Transilien 48.883384 2.233692	SNCF
	413	LA DEFENSE-GRANDE ARCHE	T2	Tramway	48.892123 2.237214	RATP
	1085 PONT DE BEZONS	T2	Tramway	48.923268 2.217590	RATP
	844	SURESNES-LONGCHAMP	T2	Tramway	48.868239 2.221411	RATP
	1090 VICTOR BASCH	T2	Tramway	48.914048 2.229572	RATP
	1088 CHARLEBOURG	T2	Tramway	48.907665 2.238309	RATP
	623	PARC DE SAINT-CLOUD	T2	Tramway	48.843124 2.221851	RATP
	713	PUTEAUX	T2	Tramway	48.883335 2.233871	RATP
	1086 FAUBOURG DE L ARCHE	T2	Tramway	48.896664 2.240079	RATP
	1087 LES FAUVELLES	T2	Tramway	48.902768 2.239542	RATP
	1089 JACQUELINE AURIOL	T2	Tramway	48.910803 2.233989	RATP
	457	LES COTEAUX	T2	Tramway	48.857471 2.220604	RATP
	1091 PARC PIERRE LAGRAVERE	T2	Tramway	48.917515 2.224812	RATP
	461	LES MILONS	T2	Tramway	48.849850 2.221233	RATP

Acknowledgements

The authors wish to thank the transport organization authority of Ile-de-France (Ile-de-France Mobilités) for graciously providing the smart card data.