Nathalie Leblanc

Camille Roux

Jean-Marc Pradier

Catherine Perrot-Rechenmann

Characterization of two cDNAs encoding auxin-binding proteins in Nicotiana tabacum

Keywords: Auxin-binding proteins, Nicotiana tabacum, RT-PCR analysis, organ-specific expression, recombinant Nt-ERabp 1

The isolation and the characterization of two tobacco cDNAs, Nt-ERabp1 and Nt-ERabp2, homologous to Zm-ERabp1, encoding the major auxin-binding protein from maize coleoptiles, are described. Their predicted amino acid sequences correspond to proteins of ca. 21 kDa, in which the characteristic regions common to ABP1-related polypeptides are well-conserved. Southern analysis indicates that the genes corresponding to Nt-ERabp1 cDNA and Nt-ERabp2 cDNA derive respectively from Nicotiana tomentosiformis and Nicotiana sylvestris, the diploid progenitors of Nicotiana tabacum. Analysis of mRNA distribution in tobacco plants indicates that these two genes are preferentially expressed in flowers and growing seedlings. Whatever the tissue tested, Nt-ERabp1 mRNA is more abundant than Nt-ERabp2 mRNA. Furthermore, RT-PCR reveals developmental and organ-specific expression of these two genes in flower parts of tobacco plants. In particular, regulation of Nt-ERabp1 mRNA accumulation appears to be correlated with elongation growth of each floral organ. Recombinant Nt-ERabp1, produced in Escherichia coli, is recognized by antibodies raised against Zm-ERabp1.

Introduction

The plant hormone auxin has been shown to be involved in the regulation of a wide range of responses in the growth and development of plants (for review, see [START_REF] Davies | Plant hormone and their role in plant growth and development[END_REF]). In an attempt to better understand mechanisms by which the auxin signal is perceived by cells, several laboratories have isolated different auxin-binding proteins (for reviews, see [START_REF] Jones | Auxin-binding proteins[END_REF][START_REF] Venis | Auxin receptors and auxin binding proteins[END_REF]). Among these proteins, the auxin-binding protein Zm-ERabp1 purified from maize coleoptiles [START_REF] Löbler | Auxin-binding protein from coleoptile membranes of corn (Zea mays L.). I. Purification by immunological methods and characterization[END_REF][START_REF] Napier | Preparation and characterization of monoclonal and polyclonal antibodies to maize membrane auxin-binding proteins[END_REF][START_REF] Shimomura | Purification and properties of an auxin-binding protein from maize shoot membranes[END_REF] is now well characterized. The primary translation product deduced from the isolated cDNAs [START_REF] Hesse | Molecular cloning and structural analysis of a gene from Zea mays (L.) coding for a putative receptor for the plant hormone auxin[END_REF][START_REF] Inohara | Auxin-binding protein located in the endoplasmic reticulum of maize shoots: molecular cloning and complete primary structure[END_REF][START_REF] Tillman | cDNA clones of the auxin-binding protein from corn coleoptiles (Zea mays L.): isolation and characterization by immunological methods[END_REF] was calculated to be ca. 22 kDa (201AA). This sequence contained a 38 residue N-terminal signal sequence, which was cleaved to produce the mature protein, and a KDEL tetrapeptide localized at the C-terminal end of the protein, which is known to be a retention signal for proteins in the lumen of the endoplasmic reticulum. Using the electrical membrane response to auxin of tobacco mesophyll pro-toplasts as a functional assay, Barbier-Brygoo et al. [START_REF] Barbier-Brygoo | Perception of the auxin signal at the plasma membrane of tobacco mesophyll protoplasts[END_REF] have shown that antibodies raised against Zm-ERabp1 were able to inhibit the auxin-induced hyperpolarization of tobacco protoplasts, suggesting that a protein immunologically related to Zm-ERabp1 was involved in auxin perception. The incubation of tobacco protoplasts with exogenous Zm-ERabp1 increased the sensitivity to auxin of the electrical membrane response. Antibodies raised against a synthetic peptide (D16), corresponding to a putative binding site for auxin within the Zm-ERabp1 protein, were shown to have an auxin-agonist activity on this electrical response [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF]. These results have been recently reinforced by patchclamp analysis performed on maize coleoptile protoplasts. These experiments have demonstrated that auxin induced an increase of H + current at the plasma membrane, current which is thought to reflect activation of the PM-localized H + -ATPase. Whereas this H + current is abolished with polyclonal anti-Zm-ERabp1, D16 polyclonal antibodies enhanced this current in an auxin-like manner [START_REF] Rück | Patchclamp analysis establishes a role for an auxin binding protein in the auxin stimulation of plasma membrane current in Zea mays protoplasts[END_REF]. Furthermore, voltage-clamp analyses of guard cells of Vicia faba have shown that a synthetic peptide corresponding to the C-terminal part of Zm-ERabp1 is able to inactivate the inward K + channels of plasma membrane, mimicking in this way the effects of high concentrations of auxin [START_REF] Thiel | Modulation of K + channels in Vicia stomatal guard cells by peptide homologs to the auxin-binding protein C terminus[END_REF]. Finally, even if the biochemical characteristics of Zm-ERabp1 suggested a localization of the protein in the ER, recent experiments performed on maize coleoptile protoplasts have indicated that a fraction of the protein could be detected at the external face of the protoplasts [START_REF] Diekmann | Auxins induce clustering of the auxin-binding protein at the surface of maize coleoptiles protoplasts[END_REF]. All these data are in favour of a possible involvement of Zm-ERabp1 in the auxin perception at the plasma membrane level.

Immunologically related ABP1 proteins have been detected in other plant species such as pea, mung bean and barnyard grass [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF]. Whereas both genomic sequences and cDNAs, homologous to Zm-ERabp1, have been reported for different dicotyledonous plants such as Arabidopsis [START_REF] Palme | Molecular analysis of an auxin-binding protein gene located on chromosome 4 of Arabidopsis[END_REF] or strawberry [START_REF] Jones | Auxin-binding proteins[END_REF][START_REF] Lazarus | Characterization of a strawberry gene for auxin-binding protein, and its expression in insect cells[END_REF], the function of the corresponding proteins has been poorly studied. In tobacco plants, D16 antibodies were shown to cross-react with a protein of ca. 22 kDa in partly purified microsomal protein fractions of tobacco leaves [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF]. Until now, no molecular tools have been developed from this plant material to further study the auxin electrical response and gain insight into the auxin perception system at the plasma membrane on tobacco.

As a first step towards a better understanding of auxin perception in tobacco plants, we have isolated two cDNAs sharing homology with the Zm-ERabp1 gene using a RT-PCR procedure. These PCR fragments were used to obtain full-length cDNAs from a tobacco seedling cDNA library. The ABP1 gene family in the tobacco genome was characterized by Southern blot analysis and we have studied the specific expression of these two genes in various organs of tobacco plants and in floral organs during flower development. The production of recombinant Nt-ERabp1 protein in E. coli is also reported.

Materials and methods

Plant material

Tobacco plants (Nicotiana tabacum cv. Xanthi, wildtype clone XHFD8 and its progenitor species Nicotiana sylvestris and Nicotiana tomentosiformis)weregrown from seeds in a greenhouse (22 C, 9 h of light per day or 16 h of light per day for flowering).

Nt-ERabp cDNAs isolation

To synthesize first-strand cDNA, 1 g poly(A) + RNA extracted from tobacco leaves and previously treated with DNaseRQ1 (Promega), was incubated in presence of 0.5 g of oligo(dT) 12,18 in buffer contain- i n g8 0m MT r i s -H C lp H8 . 3 ,3 0m MK C l , 6m M MgCl 2 ,8m MD T T ,8 0g/ml BSA (RNase-free), 0.5 mM of each dNTP and 40 U RNasin (Promega). After addition of 200 U of M-ML V reverse transcriptase (Gibco-BRL) and 10 U of AMV reverse transcriptase (Promega), samples were incubated for 90 min at 42 C. One third of the reaction volume was used to perform the amplification procedure. To amplify the two Nt-ERabp cDNAs, 3 oligonucleotides were synthesized. The 25-mer primers 85A (5 0 -TCGCCATGTTCTCGTAGTGGTAGCT-3 0 ) and 92A (5 0 -CCCGCCACATCATCATACTAGTTGC- 3 0 ) correspond specifically to the 5 0 end of the ORF of each Nt-ERabp cDNA, as predicted by sequence analysis of genomic clones Ntt85A and Ntt92A registered in the gene bank [START_REF] Shimomura | EMBL data library accession numbers X70902 and X[END_REF]. The third primer END (5 0 -GCTCATCTTTCCACGAAGTTGTCTG-3 0 ) which matches the 3 0 end of the ORF of Ntt85A and differs only in one nucleotide in Ntt92A, was used as antisense primer in the two reactions. Amplification procedure was performed with 1 U of Taq polymerase (Promega) in the presence of 2 M of the primers and 200 M of each dNTP. PCR conditions were 94 Cfor 3 min, followed by 30 cycles (94 C for 30 s, 65 Cfor 2min,72 C for 2 min), and finished by 5 min at 72 C. The PCR fragments were subcloned into pBlueScript vector and sequenced using T7DNAPol sequencing kit (Pharmacia).

To obtain full-length cDNAs, an auxin-induced tobacco seedling cDNA library constructed in the laboratory (Dargeviciute, unpublished results) using the Stratagene Zap-cDNA GigapackII gold cloning kit was screened with one of the RT-PCR fragment probe. Hybridization was done at 65 C in the hybridization buffer (HB) containing 4 SSC, 10 Denhardt's solution, 20 mM sodium phosphate buffer pH 7, 7% SDS, and 100 g/ml salmon sperm DNA. Three positive clones were selected from 800 000 recombinant plaques obtained from one-time amplified Zap library. After further purification through 3 successive rounds of screening, the Zap clones were excised in vivo following the manufacturer's instructions (Stratagene). Clones were then sequenced by using the Pharmacia kit.

Southern blot analysis

Plant DNA was purified from leaves of different tobacco plant species as described by [START_REF] Dellaporta | A plant DNA minipreparation: Version II[END_REF]. Genomic DNA (5 g) was digested to completion with the restriction enzymes indicated in Fig. 4. DNA fragments were analyzed by electrophoresis in 0.6% Seakem agarose gel (FMC) at 40 V for 16 h in 1 TBE. After HCl treatment, the gel was capillary blotted onto Hybond-N + membrane in alkaline conditions (0.5 M NaOH). Membrane was hybridized with , 32 P]-dCTP-labelled Nt-ERabp1 PCR fragment at 60 Cin buffer HB. Filter was then washed in low-stringency conditions (1 SSC, 0.1% SDS) at 60 C.

Northern blot analysis

Total RNA was prepared from tobacco plant tissues as described [START_REF] Lütcke | Selection of AUG initiation codons differs in plants and animals[END_REF]. Poly(A) + RNA were selected by chromatography on oligo(dT) cellulose (Pharmacia) according to the standard method [START_REF] Aviv | Purification of biologically active globin messager RNA by chromatography on oligothymidylic acidcellulose[END_REF]. 4 g of poly(A) + RNA was electrophoresed through 1% agarose gels containing 50% formaldehyde [START_REF] Sambrook | Molecular Cloning: A Laboratory Manual[END_REF]. The gel was capillary blotted onto Hybond-N membrane (Amersham) in 10 SSC. RNA was subsequently UV cross-linked to the membrane. To increase the radioactive signal, Nt-ERabp1 PCR fragments were labelled using both -[ 32 P]-dCTP and -[ 32 P]-dATP by the random priming Megaprime. Kit (Amersham). Hybridization was performed at 65 C in buffer HB. The membrane was then washed at 65 C in high-stringency conditions up to 0:5 SSC, 0.1% SDS, and exposed to a film between intensifying sheets for times varying between 5 days and 2 weeks or quantified using a phosphor-imager equipment (Molecular Dynamics).

RT-PCR analysis

To visualize the differential expression of the two Nt-ERabp genes, first-strand cDNA was synthesized from 0.5 g of poly(A) + RNA purified from the different plant tissues as previously described. One fourth of each cDNA sample was amplified either with the pair of primers 85A-END to specifically amplify the Nt-ERabp1 cDNA, or with the pair 92A-END for Nt-ERabp2. After a first cycle with heating denaturation for 3 min at 94 C, a PCR of 20 cycles (94 C, 1 min; 68 C, 2 min; 70 C, 2 min) was performed. This number of cycles was determined so as to stay in the exponential phase of PCR. PCR products were subjected to electrophoresis on 1% agarose gel (Appligene) and blotted onto Hybond-N + membrane (Amersham) in alkaline conditions. Membranes were hybridized in standard conditions at 65 C with , 32 P]-dCTPlabelled Nt-ERabp1 probe obtained using the random priming Megaprime kit (Amersham). In the case of experiments shown in Fig. 5C, a PCR of 30 cycles was performed to allow the visualization of Nt-ERabp2 expression in all organs tested. These conditions are no longer quantitative for Nt-ERabp1 transcripts which are more abundant.

Expression of Nt-ERabp1 in Escherichia coli

The expression of recombinant Nt-ERabp1 in E. coli was performed by using the pQE30 expression vector which contains an affinity tag consisting of 6 consecutive histidine residues (6His tag) (Qiaexpress expression system, Qiagen). One BamH1 restriction site was added at each end of the sequence Nt-ERabp1, and the ATG codon was deleted to use the initiator codon included in the vector. These modifications were introduced by amplification of the Nt-ERabp1 fragment with the two primers 5 0 - ATACGGATCCGCTCGCCATGTTCTCGTAGTGGT AG-3 0 for the amino terminal side, and 5 0 - CGCGGATCCTTAAAGCTCATCTTTCCACGAAGT TGT-3 0 for the carboxyl terminal side. PCR conditions were 94 C for 3 min, followed by 25 cycles (94 Cfor 30 s, 65 Cfor2min,72 C for 2 min). After sequencing of these PCR fragments sub-cloned in pBS vector with T7DNAPol kit (Pharmacia), these sequences were inserted in the BamHI cloning site of pQE30, located downstream the 6His affinity tag. E. coli cells (M15) transformed with the recombinant plasmid pQE30-Nt-ERabp1 were grown to 0.7 O.D. Cells were harvested 3 h after induction with 2 mM IPTG and collected by centrifugation at 1000 g for 10 min. The pellet was resuspended in sonication buffer (50 mM sodium phosphate pH 7.8, 300 mM NaCl, 5 mM EDTA, 2 mM DTT), subjected to one cycle of freeze-thaw, sonicated and centrifuged at 10 000 g for 20 min. The supernatant containing soluble proteins was kept at ,20 C with 10% glycerol until further analysis. The pellet was resuspended in the sonication buffer and vortexed for 30 min in the presence of DNaseI (10 g/ml). Samples were submitted to SDS-PAGE on a 12.5% acrylamide gel [START_REF] Laemmli | Cleavage of structural proteins during the assembly of the head of bacteriophage T4[END_REF]. After staining with a cold solution containing 250 mM KCl and 1 mM DTT, the band of correct size was cut out, and grounded with a Potter in PBS (120 mM NaCl, 2.7 mM KCl, 10 mM phosphate buffer pH 7.4). Acrylamide was pelleted by centrifugation at 18 000 g for 20 min. The supernatant was concentrated by filtration on Centricon-3 concentrators (Amicon). Proteins contained in the concentrate were analysed by western blotting and stored at ,20 C with 10% glycerol until further use.

Results

Isolation of two Nt-ERabp cDNAs

The primary objective of this work was to clone fulllength tobacco cDNAs encoding ABP1-like proteins in tobacco plants. After analysis of the maize and Arabidopsis ABP1 sequences [START_REF] Hesse | Molecular cloning and structural analysis of a gene from Zea mays (L.) coding for a putative receptor for the plant hormone auxin[END_REF][START_REF] Palme | Molecular analysis of an auxin-binding protein gene located on chromosome 4 of Arabidopsis[END_REF], oligonucleotides corresponding to well conserved domains (boxes A and B) were first used to isolate partial cDNA sequences (data not shown). Then, as two tobacco genomic clones (Ntt85 and Ntt92), showing high homology with Zm-ERabp genes, were registered in GenBank database [START_REF] Shimomura | EMBL data library accession numbers X70902 and X[END_REF], we designed 3 specific oligonucleotides (85A, 92A, END) allowing to isolate longer cDNA frag-ments. The two primer pairs (85A-END) and (92A-END) were used in a reverse transcription polymerase chain reaction procedure (RT-PCR) to amplify specific cDNAs, synthesized from tobacco leaf poly(A) + RNA.

A single PCR product of 564 bp was obtained for each primer pair. Sequence analysis of these clones demonstrated that Nt-ERabp1, the fragment amplified with 85A-END primers, corresponded exactly to the predicted sequence of the open reading frame of Ntt85a genomic clone, whereas Nt-ERabp2 matches that of the Ntt92a genomic clone. This result reveals that the two Ntt85 and Ntt92 genes are effectively expressed in tobacco leaf tissues.

Sequence analysis of Nt-ERabp2 cDNA

To isolate full-length clones, the PCR fragment corresponding to Nt-ERabp1 was used as hybridization probe to screen a Zap cDNA library constructed from IAA-induced tobacco seedling mRNAs. Among 800 000 recombinant plaques obtained from the amplified cDNA library, only 3 positive clones were detected. After in vivo excision, sequence analysis of each clone demonstrated that two of these clones corresponded to a partial fragment of Nt-ERabp1 sequence. The third one corresponded to the full-length cDNA of Nt-ERabp2 sequence.

The complete nucleotide sequence of the cloned cDNA Nt-ERabp2 and its deduced amino acid sequence are shown in Fig. 1. The cDNA is 957 bp long and contains an open reading frame of 564 bp.

A short 5 0 non coding region of 27 bp precedes the ATG initiation codon. Surrounding the ATG codon, the conserved motif ACAATGGCC is consistent with the initiator consensus sequences described for plant [START_REF] Löbler | Auxin-binding protein from coleoptile membranes of corn (Zea mays L.). I. Purification by immunological methods and characterization[END_REF]. The long 3"-untranslated region of 366 bp contains a potential polyadenylation site at position 844 but no poly(A) tail has been detected. The absence of the extensive 3 0 -terminal poly(A) results probably from cloning artefacts since first-strand cDNA was synthetized using an oligo(dT) 12,18 primer.

The primary protein of Nt-ERabp2 was calculated to be 21.4 kDa (187AA). A putative site for signal peptidase activity is located between the Ala-19 and Ser-20 residues of the amino acid sequence. The deduced mature protein would then be 19.3 kDa (pI 6.3).

Comparison of amino acid sequences of Nt-ERabp1 and Nt-ERabp2 presented in Fig. 2 shows clearly a high degree of homology between these two proteins. The predicted amino acid sequence of Nt-ERabp1 also encodes a mature protein of 19 kDa (pI 6.3). Only 7 amino acids differ from one protein to the other, 5 of them corresponding to conservative substitutions. These results are in accordance with the high degree of homology (95%) observed at the nucleic acid level between these two cDNAs.

The particular regions typifying ABP1 proteins are very well conserved in the tobacco proteins: the 3 cysteine residues (C-22, C-82, C-177), the Cterminal KDEL tetrapeptide, box A and peptide 11 regions potentially involved in auxin binding [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF][START_REF] Brown | Mapping the auxin-binding site of auxinbinding protein 1[END_REF] and the box B region for which no function has yet been assigned (see Fig. 2). In common with ABP1 sequence from Arabidopsis, two potential Nglycosylation sites are present at position N-40 and N-132 within the tobacco sequences. These two potential N-glycosylation sites were also described in the Arabidopsis and strawberry sequences (the latter sequence showing an additional site) while only one site was observed in the maize sequences. All of these data indicate that the two Nt-ERabp sequences encode proteins homologous to Zm-ERabp1.

Southern blot analysis

To better characterize the Nt-ERabp gene family in N. tabacum, genomic DNA was digested with BamHI, HindIII and EcoRI and probed under low stringency conditions with a fragment corresponding to the entire ORF of Nt-ERabp1. In the BamHI restriction lane of N. tabacum genome, three fragments are detected: two bands of high molecular weight ( 7 kb) and one band of ca. 600 bp (Fig. 3). However, when total genomic DNA was amplified with oligonucleotide couples (85A-END) and (92A-END), the 3 kb PCR fragments, corresponding to the region localized between exon 1 and exon 5 of each gene, were not digested by BamH1 restriction enzyme (data not shown). These results suggested that the two fragments larger than 7 kb corresponded to the Ntt85A and Ntt92A genes previously described. The fragment of about 600 bp demonstrated the presence of a third genomic sequence sharing homology with Nt-ERabp genes.

Comparison of the two cDNAs Nt-ERabp1 and Nt-ERabp2 showed 95% homology at the nucleic acid level. As the N. tabacum genome is amphidiploid, it was of particular interest to determine whether these two genes are present or not in its diploid progenit-ors N. tomentosiformis and N. sylvestris. Among the two bands of high molecular weight observed after BamHI digestion of N. tabacum genomic DNA, the upper one is observed in N. sylvestris and the lower one in N. tomentosiformis. Digestion of genomic clones Ntt85A and Ntt92A with EcoRI was expected to give three restriction fragments in the case of Ntt85A gene, including one band of 1100 bp, whereas only two bands of unknown molecular size were expected for Ntt92A. Southern blot analysis showed clearly that the 1100 bp band is detected in N. tomentosiformis and in N. tabacum, but not in N. sylvestris (Fig. 3). These data indicated that Ntt85A gene derived from N. tomentosiformis genome and Ntt92A gene from N. sylvestris. Therefore, the genes Ntt85A and Ntt92A correspond to homeogenes, and encode proteins of similar function. PCR data using 85A-END and 92A-END specific primers for the amplification of genomic DNA from the three tobacco species also reinforced this analysis (data not shown). Whereas all bands detected in N. tomentosiformis are present in N. tabacum,s o m e fragments present in EcoRI and HindIII restriction patterns of N. sylvestris are not observed in N. tabacum ones. Therefore, we cannot exclude that some modifications have occurred after the crossing between the two species.

The 600 bp fragment observed in restriction pattern of N. tabacum is present in both N. tomentosiformis and N. sylvestris.

Organ-specific expression of tobacco Nt-ERabp genes

To perform RNA blot analysis, the PCR fragment corresponding to the coding sequence of Nt-ERabp1 was used as probe, with hybridization and washing conditions that did not allow us to distinguish between the two different Nt-ERabp transcripts. As shown in Fig. 4A, only one transcript of ca. 1 kb is detected in mRNA isolated from young tobacco seedlings, treated or not by using 10 M of NAA. In both conditions, the level of Nt-ERabp mRNA is identical.

To study the distribution of Nt-ERabp mRNAs in various organs of tobacco plants, poly(A) + RNA isolated from seedlings, flowers, flower buds, young leaves, stems, and young roots were subjected to RNA gel blot analysis. Whatever the organ tested, no signal could be detected on total RNA, and even using poly(A) + RNA, a long exposure time was required to detect a signal. This result reveals low expression levels of these genes in tobacco plants, in agreement with the low number of cDNA clones isolated from the cDNA library. As shown in Fig. 4B, the transcripts are detected in all organs tested. Nt-ERabp genes are predominantly expressed in developing flowers and young leaves while lower amounts are detected in young roots. The relative amount of these transcripts is significantly reduced in developed organs as the leaves and the roots (data not shown).

To study the specific expression of each Nt-ERabp gene in the same samples and according to the low expression level of these genes in tobacco plants, RT-PCR analysis was also performed (Fig. 4C). This study was carried out by using the two oligonucleotide pairs (85A-END) and (92A-END) to amplify specifically the corresponding cDNAs obtained from mRNAs of the different organs. After blotting of the PCR products onto nylon membrane, the blots were hybridized with a radiolabelled Nt-ERabp1 probe. As a control, PCR fragments were digested in parallel with BsmI, a restriction enzyme specific to the Nt-ERabp1 cDNA sequence. Results have indicated that in our conditions, each oligonucleotide pair is specific to the corresponding Nt-ERabp (data not shown). In all organs tested, Nt-ERabp1 transcripts are much more abundant than Nt-ERabp2. Thus, to visualize the expression of Nt-ERabp2 in all organs tested, a PCR of 30 cycles was performed (Fig. 5C). Under these conditions, PCR products corresponding to Nt-ERabp1 accumulated in a non-quantitative manner due to the higher abundance of this transcript. This means that direct comparison between these results and northern blot analysis is not relevant. However, these data suggested that hybridizing signals observed with northern blot analysis corresponded mainly to Nt-ERabp1 transcripts. This analysis demonstrates that both genes are predominantly expressed in flowers buds. Slight differences in the expression patterns could be detected between the two genes. For instance, Nt-ERabp1 is also well expressed in stems whereas Nt-ERabp2 mRNA is relatively more abundant in young roots than in stems.

Nt-ERabp-specific expression in developing flowers

We have further studied the distribution of Nt-ERabp transcripts in flowers by determining the level of both messengers in floral organs at different stages of development (Fig. 5A). At stage O, all floral organs are already differentiated and then are essentially subjected to cell elongation until stage 4 when the flower opens.

To distinguish the two Nt-ERabp transcripts, this analysis was carried out with a RT-PCR procedure under semi-quantitative conditions for both transcripts (20 cycles). As shown in Fig. 5B, differences are observed between the expression patterns of the two genes. For instance, whereas the steady-state level of Nt-ERabp2 mRNA is constant during stamen development, the Nt-ERabp1 mRNA level decreases from stage 0 to stage 4. The same cDNA samples were used for the amplification reactions of the two fragments. These experiments were performed several times from two independent syntheses of cDNAs. In addition, we have confirmed that the two couples of primers amplified the corresponding Nt-ERabp sequence with the same efficiency (data not shown). Therefore, the variations observed for one gene in comparison with the other reflected significant differential expression in the various floral parts. Nt-ERabp1 appeared to be more highly expressed than Nt-ERabp2 in all samples.

To better analyse the regulation of the expression during flower development, hybridization signals were quantified for each organ as a function of flower development stage. As shown in Fig. 6, high expression levels of Nt-ERabp1 were observed in pistils and stamens of flower buds. The levels decreased slowly until stage 4 where 3-4-fold less mRNA was detected. Nt-ERabp1 mRNA accumulated continuously from stage 0 to stage 4 in ovaries which can be correlated with the unceasing growth of this organ along fruit development. As shown in Fig. 6A, sepal development seems to be already completed at first stage. Interestingly, sepals are the organs where the levels of Nt-ERabp1 are the lowest from stage 2 of flower development (Fig. 6). In petals, Nt-ERabp1 mRNA accumulates and reaches a maximum at stage 2, where the petals are subjected to rapid elongation (Fig. 6A). The mRNA level then rapidly decreases between stage 2 and stage 4 when the flower opens. These differences of Nt-ERabp1 mRNA accumulation were not observed for Nt-ERabp2 which showed less variation during flower development.

Expression of Nt-ERabp1 in E. coli

The low abundance of ABP1-related proteins in tobacco did not allowed their purification from plant material. Therefore, the Nt-ERabp1 protein was produced in E. coli using the 6His tag pQE-30 expression vector. As shown on the silver-staining profile in Fig. 7, one polypeptide of ca. 22.5 kDa is accumulated in inclusion bodies after 3 h of IPTG induction. This protein represents about 40% of the total proteins contained in insoluble fractions. Western blot analysis showed that two polypeptides of 21 kDa and 22.5 kDa share immunological homology with Zm-ERabp1 since they are recognized by polyclonal antibodies raised against this protein (Fig. 7). These two polypeptides are also recognized by D16, a polyclonal antibody raised against a synthetic peptide corresponding to a putative auxin-binding site of Zm-ERabp1 [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF]. The 22.5 kDa form corresponds to the expected size, by adding the 6His tag (900 Da) to the molecular mass predicted by the amino acid sequence of Nt-ERabp1 (21.3 kDa).

The molecular mass of the 21 kDa polypeptide is lower than predicted. The monoclonal antibody 2E7, directed against a synthetic peptide HDEL (His-Asp-Glu-Lys) recognized specifically the two polypeptides. According to these results, the 21 kDa form, which contains the C-terminus KDEL tetrapeptide, corresponds probably to a partial Nt-ERabp1 which could have lost part of the N-terminus region of the pro-tein, including the 6His tag. Analysis of the enriched product (P) using SDS-PAGE showed that one major band of 22.5 kDa is detected after silver staining, and cross-reacts with both the anti-Zm-ERabp1 polyclonal and the anti-HDEL monoclonal antibody (Fig. 7). Such procedure has allowed the production of 20 mg of purified Nt-ERabp1 per litre of bacterial culture.

Discussion

Among the various auxin-binding proteins already identified, the maize ABP1 was proposed to be involved in the auxin perception at the plasma membrane. In particular, experimental evidence has been provided by the study of the electrical membrane response to auxin of tobacco mesophyll protoplasts [START_REF] Barbier-Brygoo | Perception of the auxin signal at the plasma membrane of tobacco mesophyll protoplasts[END_REF]. To go further in the characterization of the auxin perception system involved in this early auxin response, we have developed molecular tools on tobacco.

In this paper, we describe the molecular cloning of two cDNAs from tobacco plants, Nt-ERabp1 and Nt-ERabp2, thus demonstrating the expression of the two genes Ntt85A and NTT92A previously introduced in Gene data bank [START_REF] Shimomura | EMBL data library accession numbers X70902 and X[END_REF]. The encoded proteins share 62% homology with the maize protein Zm-ERabp1. The characteristic regions of ABP1-like proteins (Fig. 2) such as the box A and peptide 11 regions supposed to be involved in auxin binding, the box B and the KDEL tetrapeptide are all present in the amino acid sequences of both tobacco proteins.

The two mature proteins Nt-ERabp1 and Nt-ERabp2 have calculated sizes of 19 kDa and 19.3 kDa respectively. Taking the two potential N-glycosylation sites into account, this molecular mass fits well with the tobacco protein of 22 kDa which cross-react with polyclonal anti-Zm-ERabp1 and with D16 polyclonal antibodies raised to a synthetic peptide corresponding to box A of the maize protein [START_REF] Venis | Antibodies to a peptide from the maize auxin-binding protein have auxin agonist activity[END_REF].

Southern blot analysis indicated clearly that the two genomic sequences Ntt85A and Ntt92A identified in the N. tabacum genome derived from its ancestral diploid progenitors N. tomentosiformis and N. sylvestris, respectively. Therefore, we suggest that these two genes correspond to homeogenes, encoding proteins of similar function. These results are in accordance with the high degree of homology (95%) observed between the two cDNAs and their predicted amino acid sequences. In Arabidopsis also, only one Abp1related gene was isolated [START_REF] Palme | Molecular analysis of an auxin-binding protein gene located on chromosome 4 of Arabidopsis[END_REF]. In maize, at least four genomic sequences have already been identified [START_REF] Hesse | Molecular cloning and structural analysis of a gene from Zea mays (L.) coding for a putative receptor for the plant hormone auxin[END_REF][START_REF] Hesse | Two members of the ER abp gene family are expressed differently in reproductive organs but to similar levels in the coleoptile of maize[END_REF][START_REF] Schwob | Molecular analysis of three maize 22 kDa auxin-binding protein genes: transient promoter expression and regulatory regions[END_REF]. The Zn-ERabp1 and Zm-ERabp4 genes exhibit differential organ-specific expression and the two genes Zm-ERabp4 and Zm-ERabp5, which share 95% identity, have similar pattern of expression and differ only in their expression levels.

As observed in the BamH1 restriction patterns, a third genomic sequence visualized in the three tobacco species shares homology with Nt-ERabp genes. In northern-blot analysis, only one transcript of ca. 1 kb was detected under standard hybridization conditions. At this time, we could not determine whether this third sequence corresponds to a pseudogene related to the ABP1 family or to another sequence sharing homology with Nt-ERabp sequences.

Analysis of Nt-ERabp gene expression in floral organs during floral development is well informative about their regulation. First Nt-ERabp1 was shown to be more expressed than Nt-ERabp2 and the two genes exhibit differential regulation during floral development. As it is well described in Drews et al. [START_REF] Drews | Regional and cellspecific gene expression patterns during petal development[END_REF], even if steps of flower development are identical in the three species. N. tomentosiformis, N. sylvestris and N. tabacum, the flower sizes of these three plants are clearly different. Therefore, we could consider that regulation of the two homeogenes has diverged in the two ancestral species before crossing them to obtain N. tabacum plants. However, the shape and pigmentation of N. tabacum corolla more closely resemble to N. tomentosiformis corolla, whereas the size of corolla is intermediate between the two progenitors species. With these observations, Drews et al. [START_REF] Drews | Regional and cellspecific gene expression patterns during petal development[END_REF] proposed that genes controlling N. tomentosiformis corolla pigmentation pattern and shape are dominant to those specifying these characteristics in N. sylvestris. Interestingly, the Nt-ERabp1 gene, which arose from N. tomentosiformis, is more highly expressed in all tobacco organs tested and is submitted to regulation during flower development. Further experiments such as the study of expression levels of these genes in ancestral species, would permit determination of whether Nt-ERabp2 expression is somehow selectively repressed in the N. tabacum genome in comparison to Nt-ERabp1.

It has been previously suggested that flowers are sites of auxin production in plants and auxin has been shown to influence development of flower parts and fruit setting [START_REF]Auxins in flowering[END_REF]. In particular, it seems that, in several plants, anthers are one of the sources of auxin in the young flower buds since their removal reduces or completely stops the growth of the bud [START_REF]Auxins in flowering[END_REF]. Sepals are the first organs to develop and elongate fully, followed by petals, stamens, and pistils. The enlargement of ovaries which continues after fertilization is essentially due to cell expansion. Interestingly, the expression of Nt-ERabp1 appeared to be regulated during floral development. For instance, higher expression levels are observed in stamens, stigmas, petals and sepals at the first stages of flower development than in mature flowers when the auxin-requiring growth phase of these flower parts is expected to have been completed. In addition, mRNA accumulation increases continuously in the ovary during its development. In mature flowers, the Nt-ERabp1 gene is essentially expressed in this organ. These data reinforce the hypothesis of an important role of ABP1-like proteins in flower development.

In maize, Zm-ERabp1 was shown to be predominantly expressed in coleoptiles, elongating stems and flowers, especially in ears and styles, whereas Zm-ERabp4 mRNA are more abundant in tassels [START_REF] Hesse | Molecular cloning and structural analysis of a gene from Zea mays (L.) coding for a putative receptor for the plant hormone auxin[END_REF][START_REF] Hesse | Two members of the ER abp gene family are expressed differently in reproductive organs but to similar levels in the coleoptile of maize[END_REF]. More recently, the highest levels of Zm-ERabp1 protein were detected in the apical mesocotyl and basal coleoptile regions, areas which are subject to rapid cell elongation in the etiolated maize seedlings [START_REF] Harnden | Organ distribution of auxin-binding protein 1 in the etiolated maize seedling[END_REF]. Several groups have suggested that ABP1-like polypeptides could be involved in a regulatory pathway of auxininduced cell elongation [START_REF] Jones | Auxin-binding proteins[END_REF]. Until now, no information was available in dicotyledonous plants and it is of particular interest to observe that in tobacco plants, Nt-ERabp messengers accumulate preferentially in tissues able to respond to the hormonal stimulus such as the developing flowers and the young growing organs.

In conclusion, the analysis of Nt-ERabp gene expression suggests an interesting correlation between cell elongation process and the Nt-ERabp1 mRNA accumulation in tobacco. To gain insight into the role of Nt-ERabp1, the study of the protein is required. With this objective, we have first produced Nt-ERabp1 in E. coli to obtain significant amounts of unglycosylated recombinant protein which will allow us to raise monoclonal antibodies to peptidic domains of the tobacco protein. Such antibodies will be used to further characterize the protein and to study its possible involvement in the auxin perception system by working in homologous conditions.

Figure 1 .

 1 Figure 1. Nucleotide sequence of Nt-ERabp2 cDNA and its deduced amino acid sequence.

Figure 2 .

 2 Figure 2. Comparison of the amino acid sequences of Nt-ERabp2 (upper lane) and Nt-ERabp1 (bottom lane). The two potential Nglycosylation sites are shown by an asterisk. The underlined regions correspond to highly-conserved domains of ABP1-like proteins: Box A and peptide 11 are two regions described in maize to be potentially involved in auxin binding [29, 3], no function has yet been assigned to Box B. Arrows indicate conserved cysteine residues in ABP1-like proteins.

Figure 3 .

 3 Figure 3. Southern analysis of tobacco genomic DNA. Total genomic DNA was isolated from leaves of N. sylvestris (SYL), N. tabacum (TAB) and N. tomentosiformis (TOM) and digested with EcoRI (lane 1), HindIII (lane 2) and BamHI (lane 3). The resulting digests were separated on 0.6% agarose gel, transferred to a nylon membrane and probed with a [ 32 P ]-labelled fragment corresponding to Nt-ERabp1 under low-stringency conditions. Each lane contained 5 gDN A . The molecular weight markers HindIII digested phage a n d1k b ladder (Gibco) are shown in kb at the right and left respectively.

Figure 4 .

 4 Figure 4. Tissue-specific expression of Nt-ERabp1 and Nt-ERabp2 in N. tabacum plants. A. Northern blot of poly(A) + RNA (4 g per lane) extracted from tobacco seedlings grown in liquid medium treated (Sd+) or not (Sd) with 10 M NAA for 2 h. The filter was probed with [ 32 P]-labelled Nt-ERabp1. B. Histogram showing differences in Nt-ERabp mRNA accumulation in tobacco seedlings (Sd), flower buds (FB), flowers (F), young leaves (YL), stems (S) and young roots (YR). The filter was probed with [ 32 P]-labelled Nt-ERabp1. The hybridization signals were quantified by a Bioimage analyser system (Millipore). C. Specific expression of each Nt-ERabp gene determined by RT-PCR experiments. The oligonucleotide pairs (85A-END) and (92A-END) were used to amplify specifically Nt-ERabp1 and Nt-ERabp2 cDNAs, respectively. A PCR of 30 cycles was performed with cDNA samples synthesized from 0.5 g mRNA of each tobacco organs (Sd, FB, F, YL, S, YR). PCR fragments were separated on agarose gels, transferred onto nylon membrane and hybridized with [ 32 P]-labelled Nt-ERabp1.

Figure 5 .

 5 Figure 5. Specific expression of Nt-ERabp genes in flower parts during flower development. A. Photographs of flowers at the different stages (F 0 to F 4 ) of development defined to perform the expression analysis. B. Expression of Nt-ERabp genes in flower parts studied by RT-PCR. The oligonucleotide pairs (85A-END) and (92A-END) were used to amplify specifically Nt-ERabp1 cDNA and Nt-ERabp2 cDNA respectively. First-strand cDNAs were synthesized from 0.5 g mRNA of stamens (St), pistils (Pi), ovaries (Ov), petals (Pe) and sepals (Se) of flowers at the different stages of flower development described in (A). 20 cycles of PCR were performed to be under semi-quantitative conditions. n.d., not determined.

Figure 6 .

 6 Figure 6. Curves showing for each flower organ the level of Nt-ERabp1(--) and Nt-ERabp2 (--) transcripts as a function of developmental stage. The mRNA levels (arbitrary units) were determined by quantification of the hybridization signals shown in Fig. 5B using a Bioimage analyser system (Millipore).

Figure 7 .

 7 Figure 7. Analysis of recombinant Nt-ERabp1 protein produced in E. coli, E. coli produced Nt-ERabp1 was analysed by both silver staining and western blot after electrophoresis on SDSpolyacrylamide gel. The lanes contain 2 g of crude soluble (S) and insoluble (NS) protein fractions or 100 ng of purified Nt-ERabp1 (P) extracted from E. coli cells. The western blot procedure was performed by using polyclonal anti-Zm-ERabp1 antibodies (Poly), D16 polyclonal antibodies directed against a synthetic peptide corresponding to BoxA of Zm-ERabp1 protein (D16), or a monoclonal antibody to the HDEL peptide (2E7). Molecular-weight markers are indicated on the right in kDa.

Acknowledgements

We thank Ausra Dargeviciute for supplying the cDNAs library, Austra Dargeviciute and Dr Jurg Bilang for assistance in flower dissection, and Dr Beate Knauth and Professor Jean Guern for critical reading of the manuscript.


Hao Bai
email: hao.bai@nwpu.edu.cn

Chen Liu
email: chen.liu@zzu.edu.cn

Daniela Chrenko
email: daniela.chrenko@utbm.fr

Alexandre Ravey
email: alexandre.ravey@utbm.fr

Fei Gao
email: fei.gao@utbm.fr

System-Level Modeling and Virtual Testing of Fuel Cell Vehicle Mobypost Using Energetic Macroscopic Representation

Fuel cell vehicle (FCV) has drawn much attention due to its high efficiency, long drive range, and zero emission. The development of FCV involves complex architectures and requires an effective virtual testing methodology to improve R&D efficiency. Energetic Macroscopic Representation (EMR) is a graphical formalism to organize models and controls of multidisciplinary systems. It provides the seamless integrations of multi-level models and interconnections between virtual and real testing, which reduces the total development time of the electrified vehicles. Therefore, in this paper, the system-level model of FCV is designed using EMR for the high-fidelity virtual testing of electrified vehicles. An FCV Mobypost that is used for postal delivery in France is chosen as the studied vehicle. The virtual testing results are compared with the real testing. Good consistency is achieved, which validates the performances of the EMR-based FCV model in the virtual testing environment.

I. INTRODUCTION

Air pollutant emissions from transport are one of the main concerns in controlling the air quality worldwide. Many countries are now searching for the electrified transportation solutions to protect the environment and alleviate air pollution. Fuel cell vehicle (FCV) is one of the promising alternatives of the internal combustion engine-powered vehicles to achieve electrified transportation due to its high efficiency, long drive range, and zero emission. FCV uses the fuel cell system in combination with a battery or a supercapacitor to provide power to the onboard electric drives. It involves multiple sources and multidisciplinary knowledge that requires efficient modeling architecture and high-fidelity virtual testing tools to improve development efficiency and reduce cost. The Energetic Macroscopic Representation (EMR) proposed in [START_REF] Bouscayrol | Graphic Formalisms for the Control of Multi-Physical Energetic Systems[END_REF] is a unified modeling formalism that integrates multi-level models of components and connects virtual testing and real testing. EU H2020 PANDA project has the ambition of reducing the time-to-market of EVs by 20% through the EMRbased digital model architecture [START_REF] Bouscayrol | Power Advanced N-level Digital Architecture for models of electrified vehicles and their components[END_REF]. Therefore, the modeling and virtual testing of FCV using EMR is a viable solution to speed up its R&D and shrink its time-to-market.

Mobypost is an FCV developed in the EU project -Mobility with Hydrogen for Postal Delivery [START_REF]Mobility with Hydrogen for Postal Delivery, EU Project[END_REF]. It is designed for ensuring the last step in the postal delivery process and delivers mails and parcels from local sorting centers to recipients. The hydrogen is locally produced by using the electric energy generated by photovoltaic technology to electrolyze water. Mobypost fulfills postal delivery cleanly and sustainably while providing a larger driving range than pure battery-powered vehicles. With the rapid process of the energy transition, there are growing needs for FCV like Mobypost, which brings mass production for the manufacturer and needs an effective tool to reduce the development and testing time. Therefore, in this paper, a system-level FCV model is developed using EMR formalism for the virtual testing of Mobypost. The modeling methodology and the EMR organization method are presented in detail. The developed Mobypost model is implemented in the Matlab/Simulink and simulated using a typical driving cycle in daily postal delivery. The simulation results are compared with the road testing results and the performances of the Mobypost EMR-based model are thus validated.

This paper is organized as follows. The components and system models of Mobypost in EMR are presented in Section II. The developed model is simulated and the results are compared with the real testing in Section III. The discussions and conclusions of this paper are given in Section IV.

II. MOBYPOST MODELING USING ENERGETIC MACROSCOPIC REPRESENTATION

The basic structure of Mobypost is shown in Fig.

1 [START_REF] Ravey | Energy management of fuel cell electric vehicle with hydrid tanks[END_REF]. The Mobypost powertrain consists of a fuel cell stack followed by a DC-DC converter, a Li-ion battery pack directly connected to the DC link, two electric drives (e-drives) composed of two inverters, and two in-wheel permanent magnet synchronous motors (PMSM). There is no gearbox in Mobypost. The modeling of the Mobypost focuses on the fuel cell stack, the DC-DC converter, the Li-ion battery, the e-drives, and the vehicle's motion model. Besides, an effective energy management strategy is applied to coordinate the operation of the fuel cell stack and battery pack. The essential parameters of fuel cell and battery are given in Table .1.

A. Fuel cell model

A generic fuel cell model shown in Fig. 2 (a) is used in this paper [START_REF] Tremblay | A generic fuel cell model for the simulation of fuel cell vehicles[END_REF]. The fuel cell is represented by a controlled voltage source in series with a resistor. 𝐸 𝑜𝑐 is the open circuit voltage, 𝑁 𝑐 is the number of cells, 𝐴 is the Tafel slope, 𝑖 0 is the exchange current, 𝑇 𝑑 is the response time, 𝑅 𝑓𝑐 is the internal resistance, 𝑖 𝑓𝑐 is the fuel cell output current, and 𝑢 𝑓𝑐 is the fuel cell output voltage.

𝐸 = 𝐸 𝑜𝑐 -𝑁 𝑐 • 𝐴 • 𝑙𝑛 ( 𝑖 𝑓𝑐 𝑖 0 ) • 1 1/3•𝑇 𝑑 𝑠+1
(1)

𝑢 𝑓𝑐 = 𝐸 -𝑅 𝑓𝑐 𝑖 𝑓𝑐 (2)
The parameters of (1) and ( 2) can be approximated based on the data extracted from the polarization curve in the fuel cell datasheet [START_REF] Tremblay | A generic fuel cell model for the simulation of fuel cell vehicles[END_REF]. Fig. 2 (b) shows the polarization curves obtained from the developed fuel cell model and the datasheet [START_REF] Mes | DEA 1.0 Fuel Cell system datasheet[END_REF]. The simulated voltage-current relationship of the fuel cell is close to the experimental results, especially in the neighborhood of the nominal operating point.

B. Battery model

The battery model is composed of a controlled voltage source in series with a resistor [START_REF] Tremblay | A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles[END_REF], as shown in Fig. 3. The value of the voltage source depends on the battery SOC and can be represented by [START_REF]Mobility with Hydrogen for Postal Delivery, EU Project[END_REF]. 𝐸 0 is the battery constant voltage, 𝐾 is the polarization voltage, 𝐶 𝑏𝑎𝑡 is the battery capacity (𝐴 • ℎ), 𝐴 is the exponential zone amplitude, and 𝐵 is the inverse of the exponential zone time constant. The battery output voltage 𝑢 𝑏𝑎𝑡 is thus expressed by (4) and SOC is computed by [START_REF] Tremblay | A generic fuel cell model for the simulation of fuel cell vehicles[END_REF]. The parameters are approximated based on the discharge and charge voltage profiles provided in the battery datasheet [START_REF] Tremblay | A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles[END_REF].

𝐸 = 𝐸 0 -𝐾 𝐶 𝑏𝑎𝑡 𝐶 𝑏𝑎𝑡 -𝑖𝑡 + 𝐴𝑒 -𝐵•𝑖𝑡 (3)
𝑢 𝑏𝑎𝑡 = 𝐸 -𝑅 𝑏𝑎𝑡 𝑖 𝑏𝑎𝑡 (4)
𝑆𝑂𝐶 = (1 - ∫ 𝑖 𝑏𝑎𝑡 𝑑𝑡 3600𝐶 𝑏𝑎𝑡 ) × 100% (5)

C. DC-DC converter model

A boost converter shown in Fig. 4 (a) is used between the fuel cell stack and the DC link. A static model is applied to represent its behaviors [START_REF] Delarue | Generic control method of multileg voltage-source-converters for fast practical implementation[END_REF]. The model is described by ( 6) and [START_REF] Tremblay | A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles[END_REF], where 𝐷 is the duty cycle, and 𝜂 𝑐𝑜𝑛𝑣 is the averaged efficiency of the power converter. The EMR of boost converter and its controller is illustrated in Fig. 4 (b).

𝐿 𝑑𝑖 𝑓𝑐 𝑑𝑡 = 𝑢 𝑓𝑐 -𝑢 𝑠𝑤 → 𝑖 𝑓𝑐 = ∫ 1 𝐿 (𝑢 𝑓𝑐 -𝑢 𝑠𝑤 ) 𝑑𝑡 (6)
{ 𝑢 𝑠𝑤 = (1 -𝐷)𝑢 𝑏𝑢𝑠 𝑖 𝑐𝑜𝑛𝑣 = 𝜂 𝑐𝑜𝑛𝑣 (1 -𝐷)𝑖 𝑓𝑐 (7) Boost Converter Inverter 1 fc u bat i conv i b a t u PMSM 1 Inverter 2 PMSM 2 1 inv i Fuel Cell Stack Li-ion Battery Pack x4 f c i 2 i n v i 1 a i 1 b i 1 c i 2 a i 2 b i 2 c i
Fig. 1 FCV Mobypost powertrain structure [START_REF] Ravey | Energy management of fuel cell electric vehicle with hydrid tanks[END_REF].

+ d T s - + oc E E fc R fc u fc i 0 l n fc c i N A i       (a) (b)

D. E-drive model

The e-drive of Mobypost includes a three-phase two-level inverter and an in-wheel PMSM. An averaged switch model is used to develop the inverter model. The averaged modulation function is defined by the ratio of phase-to-phase voltages to the DC link voltage, as given in [START_REF] Delarue | Generic control method of multileg voltage-source-converters for fast practical implementation[END_REF]. Therefore, the output voltages of the inverter are computed by [START_REF] Chen | A High-Fidelity and Computationally Efficient Model for Interior Permanent-Magnet Machines Considering the Magnetic Saturation, Spatial Harmonics, and Iron Loss Effect[END_REF].

𝒎 𝑖𝑛𝑣 = [ 𝑢 𝑎𝑐 𝑢 𝑏𝑢𝑠 𝑢 𝑏𝑐 𝑢 𝑏𝑢𝑠 ] 𝑇 (8) [ 𝑢 𝑎 𝑢 𝑏 𝑢 𝑐 ] = 𝑇 𝑙2𝑝 [ 𝑢 𝑎𝑐 𝑢 𝑏𝑐 ] = 1 3 [ 2 -1 -1 2 -1 -1 ] 𝑢 𝑏𝑢𝑠 𝒎 𝑖𝑛𝑣 (9)
A lumped parameter model in the d-q frame is used where the saturation and the cross-saturation effects are not considered. The Park transformation shown in [START_REF] Morimoto | Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator[END_REF] used in this paper is power-invariant, where 𝜔 𝑒 is the electrical angular velocity, 𝑢 𝑑 , 𝑢 𝑞 are d, q axis voltages. The PMSM voltage equation is given by (11) using d, q axis currents 𝑖 𝑑 , 𝑖 𝑞 as the state variables [START_REF] Chen | A High-Fidelity and Computationally Efficient Model for Interior Permanent-Magnet Machines Considering the Magnetic Saturation, Spatial Harmonics, and Iron Loss Effect[END_REF]. 𝑅 𝑆 is the resistance of stator windings, 𝜆 𝑓 is the stator flux linkage induced by the permanent magnets, and 𝐿 𝑑 , 𝐿 𝑞 are d, q axis inductances. Meanwhile, the electromagnetic torque can be computed by ( 12), where 𝑝 is the number of pole pairs.

[ 𝑢 𝑑 𝑢 𝑞 ] = √ 2 3 [ 𝑐𝑜𝑠(𝜔 𝑒 𝑡) 𝑠𝑖𝑛(𝜔 𝑒 𝑡) -𝑠𝑖𝑛(𝜔 𝑒 𝑡) 𝑐𝑜𝑠(𝜔 𝑒 𝑡) ] [ 1 - 1 2 - 1 2 0 √3 2 - √3 2 ] [ 𝑢 𝑎 𝑢 𝑏 𝑢 𝑐 ] (10)
[ 𝑑𝑖 𝑑 𝑑𝑡 𝑑𝑖 𝑞 𝑑𝑡 ] = [ 𝐿 𝑑 -1 0 0 𝐿 𝑞 -1 ] ([ 𝑢 𝑑 𝑢 𝑞 ] -[ 𝑅 𝑆 0 0 𝑅 𝑆 ] [ 𝑖 𝑑 𝑖 𝑞 ] -[ 𝑒 𝑑 𝑒 𝑞 ])
Where

{ 𝑒 𝑑 = -𝜔 𝑒 𝐿 𝑞 𝑖 𝑞 𝑒 𝑞 = 𝜔 𝑒 (𝐿 𝑑 𝑖 𝑑 + 𝜆 𝑓 ) (11)
𝑇 𝑒 = 𝑝(𝜆 𝑓 𝑖 𝑞 + (𝐿 𝑑 -𝐿 𝑞 )𝑖 𝑞 𝑖 𝑑 )

The e-drive model in EMR formalism is presented in Fig. 5. The PMSM torque control is realized based on the maximum torque-per-amp (MTPA) control algorithm by following the (13) [START_REF] Morimoto | Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator[END_REF], where 𝑖 𝑚 is the magnitude of armature current.

{ 𝑖 𝑑 = 𝜆 𝑓 4(𝐿 𝑞 -𝐿 𝑑 ) -√ 𝜆 𝑓 2 16(𝐿 𝑞 -𝐿 𝑑 ) 2 + 𝑖 𝑚 2 2 𝑖 𝑞 = √𝑖 𝑚 2 -𝑖 𝑑 2 (13)
E. Mobypost vehicle model Due to the in-wheel PMSM used in Mobypost, the electromagnetic torque is directly deployed to the wheel. The traction force and rotating speed of the wheel can be computed by ( 14), where 𝑟 𝑤ℎ is the radius of the wheel. In the model, it is assumed that the wheels are not affected by slips and turns. Two sets of e-drive are used in Mobypost, and the driving forces of two wheels ( 𝐹 𝑤ℎ1 + 𝐹 𝑤ℎ2 ) are coupled with the braking force 𝐹 𝑏𝑟 . The total forces 𝐹 𝑡𝑜𝑡 applied to the vehicle is computed by (15) and represented by a coupling element in EMR formalism.

{ Ω 𝑤ℎ = Ω 𝑚 = 𝑣 𝑣𝑒ℎ 𝑟 𝑤ℎ 𝐹 𝑤ℎ = 𝑇 𝑒𝑚 𝑟 𝑤ℎ (14) 𝐹 𝑡𝑜𝑡 = 𝐹 𝑤ℎ1 + 𝐹 𝑤ℎ2 + 𝐹 𝑏𝑟 (15)
The vehicle velocity is thus obtained by ( 16), in which 𝐹 𝑟𝑒𝑠 is the resistive force to the motion and 𝑀 𝑣𝑒ℎ is the vehicle mass. An accumulation element represents the accumulation of the energy in the chassis.

𝑣 𝑣𝑒ℎ = 1 𝑀 𝑣𝑒ℎ ∫(𝐹 𝑡𝑜𝑡 -𝐹 𝑟𝑒𝑠 )𝑑𝑡 (16)
The road environment represents the resistive force 𝐹 𝑟𝑒𝑠 including the aerodynamic drag 𝐹 𝑎 , the rolling resistance 𝐹 𝑟 and the grading resistance 𝐹 𝑔 , as given in (17). 𝐹 𝑎 can be expressed by (18) where 𝜌 is the air mass density, 𝐴 𝑓 is the equivalent front area of the Mobypost, 𝐶 𝑑 is the aerodynamic drag coefficient, and the 𝑣 𝑤𝑖𝑛𝑑 is the wind speed. 𝐹 𝑔 and 𝐹 𝑟 can be obtained by ( 18), where the 𝜃 is the slope and 𝐶 𝑟 is the rolling resistance coefficient.

𝐹 𝑟𝑒𝑠 = 𝐹 𝑎 + 𝐹 𝑟 + 𝐹 𝑔 (17)

{ 𝐹 𝑎 = 1 2
𝜌𝐴 𝑓 𝐶 𝑑 (𝑣 𝑣𝑒ℎ + 𝑣 𝑤𝑖𝑛𝑑 ) 2 𝐹 𝑔 = 𝑀 𝑣𝑒ℎ 𝑔 sin 𝜃 𝐹 𝑟 = 𝐶 𝑟 𝑀 𝑣𝑒ℎ 𝑔 cos 𝜃 (18)

In EMR an inversion-based control scheme is used. Eq. ( 16) is inverted by a closed-loop control shown in (19), where C(t) is a PI controller in this paper.

𝐹 𝑡𝑜𝑡_𝑟𝑒𝑓 = 𝐶(𝑡)(𝑣 𝑣𝑒ℎ_𝑟𝑒𝑓 -𝑣 𝑣𝑒ℎ ) + 𝐹 𝑟𝑒𝑠

Eq. ( 15) is inverted using a distribution input 𝑘 𝑏𝑟 to distribute the forces between the brakes and the wheel, and a distribution input 𝑘 𝑑𝑖 to distribute the driving forces between two wheels.

F. Energy management strategy

Mobypost has two energy sources in the powertrain, i.e., fuel cell and battery, and needs an energy management system (EMS) to coordinate their operations. The EMS controls the start/stop of the fuel cell stack according to the battery SOC and sets the reference output power of the fuel cell stack. The rule-based energy management strategy is adopted in Mobypost and described by the flow chart in Fig. 6. By integrating the models developed in Section II. A to Section II. F., the EMR of Mobypost can be organized by Fig. 7.

III. SIMULATION AND VALIDATION USING MATLAB-SIMULINK

The simulation is organized using the EMR formalism shown in Fig. 7. The driving cycle is collected based on the daily postal delivery track and treated as the input of the simulation. The references of the electromagnetic torque of two e-drives are derived base on the driving cycle. The fuel cell and battery are operating under the control of the energy management system. The EMR of Mobypost is implemented in Simulink environment and simulated with a 1ms time-step for the driving cycle from 0 to 10800s. The operating principles of fuel cell and battery are presented in Fig. 6, in which the energy management is implemented using the rule-based strategy according to the battery SOC. The variations of battery SOC and H2 tank SOC during the whole driving cycle are shown at the top of Fig. 10 (a) and (b), while their errors are plotted at the bottom. The error between the measured and simulated SOC is calculated by (20).

1 inv i 2 inv i 1 wh F 2 wh F v e h v v e h v tot F v e h v v e h v res F EMS Start _ veh ref v 1 _ wh ref F 2 _ wh ref F _ br ref F b r F v e h v SOC (5) b u s u 1 abc u 1 a b c i 1 d q u 1 d q i 1 d q i 1 d q e 1 e m T 2 abc u 2 abc i 2 d q u 2 d q i 2 d q i 2 d q e 2 e m T 1 inv m _ 1 abc ref u _ 1 dq ref u _ 1 dq ref i _ 1 em ref T 1 e  2 inv m _ 2 abc ref u _ 2 dq ref i _ 2 dq ref
In Fig. 10 (a), the simulated battery SOC shows accurate results and presents consistent variations with the measured one. The differences can also be observed. On the one hand, the sampling rate of the measured SOC is too slow, and some information of the Mobypost SOC is missing; on the other hand, the simulation errors of the power demands will be accumulated in the computation of SOC. Fig. 10 (b) depicts the results of the H 2 tank SOC. The simulation also produces accurate results. Errors occur in the period when the fuel cell stack is stopped. This is due to the power consumption of auxiliary devices in the fuel cell system, which is not considered in the simulation when the fuel cell is not working. In general, the SOCs of battery and H 2 tank in the developed model are accurate in the system-level simulation of Mobypost.

Fig. 11 shows the waveforms of fuel cell system output voltage, output current, and output power. The simulation results match the experimental results in the steady-state. The differences occur at the starting and stopping stages of the fuel cell. The start-up or shutdown of the fuel cell is determined by the EMS based on the battery SOC. Therefore, the exact time of the start-up and shutdown can be inaccurate due to the simulation errors of battery SOC. Moreover, the shutdown process of fuel cell involves a complex electrochemistry mechanism which is not considered in the system-level model developed in this paper. Nevertheless, the fuel cell model has satisfied accuracy regarding the system-level performance.

Fig. 12 presents the variations of the battery output power in the tested driving cycle. Due to the errors of SOC estimation, the deviations occur in the fuel cell start-up and shutdown processes. The steady-state simulation results are accorded with the experiments. The developed model follows the real power consumption of the vehicle's acceleration and deceleration. The slight differences can be observed in different driving conditions because the models of the power converters, e-drive, and fuel cell system use the averaged efficiencies to represent the power losses in each component.

IV. CONCLUSIONS

This paper presents the virtual testing of the FCV with validation. The concept of the FCV and the tested FCV Mobypost that is developed for daily postal delivery applications are briefly described. The components in FCV including the fuel cell, the battery, the DC-DC converter, and the e-drive system are modeled and organized using the EMR formalism. These components' models are connected to compose the FCV model to be implemented in the virtual testing of the FCV.

Mobypost was tested in a three-hour driving cycle to cover the most use cases of postal delivery. The simulation was implemented in the Matlab-Simulink environment. The simulation results were compared with the measurements from the tests. The system-level behaviors of the Mobypost were accurately simulated, in terms of the current, the voltage, the power, the SOCs of the H 2 tank and the battery, the power demands of e-drives, and the vehicle's dynamic motion. The developed model is thus validated and proved to be credible in virtual testing.

The EMR modeling architecture enables the developed FCV model to be used in other simulation software. The parameters required in the Mobypost model are available in the vehicle development stages and don't involve complicated identification processes. The developed FCV model in this paper provides an efficient tool for the system/component design and testing, which is very favorable to reduce the development cost using the "W-model" concept proposed in PANDA [START_REF] Bouscayrol | Power Advanced N-level Digital Architecture for models of electrified vehicles and their components[END_REF].

Fig. 2 (Fig. 3 Fig. 4 (

 234 Fig. 2 (a) Generic fuel cell model [5]; (b) Polarisation curve from datasheet and simulation results [6].

Fig. 5 EMR

 5 Fig. 5 EMR of e-drive.

Fig. 8 to

 8 Fig. 12 demonstrate the simulation results of the Mobypost EMR model together with the results of the Mobypost on-road experiments. The dashed line is the simulation result and the solid line is the experimental result. Fig. 8 (a) depicts the vehicle speed curves and Fig. 8 (b) depicts the rotating speed of the in-wheel PMSM of the right wheel, where the magnified curves are plotted at the bottom. The Mobypost model follows the reference speed rapidly. The typical characteristics of the postal delivery driving cycle shown in Fig. 8 (a) contain many pauses, which provide the right time for the fuel cell to charge the battery to prolong the overall driving distance. Compared to the measured data, the simulation produces consistent results. The total power consumption of two e-drives is measured from the DC-link side in both experimental tests and simulation. The results are demonstrated in Fig. 9. The top subfigure is the power consumption during the full tested driving cycle, the middle is the magnified waveforms between 8200 s and 9000 s to evaluate the performance of the developed model, and the bottom is the error between the measured results and SOC < 0.2? Energy management start Mobypost stops; Battery charges using charger; Power converter stops working. Mobypost is in motion; Battery charges / discharges; Power converter works. hysteresis comparator Mobypost is in motion; Battery stops charging; Power converter stops working.

Fig. 6

 6 Fig. 6 Mobypost energy management strategy.

Fig. 7

 7 Fig. 7 EMR of Mobypost.

Fig. 9

 9 Fig. 9 Total power consumption of two e-drives measured in the DC side.(a)

TABLE I FUEL

 I CELL AND BATTERY PARAMETERS

				Fuel cell
	Fuel cell type	PEMFC	Number of cells	40
	Nominal Power	1000 W	Active Area	61 cm 2
	Stack Voltage	24-38 V	Nominal Stack	45 A
	Range			Current
				Batttery
	Battery		Lithium-ion Numbers of	4
	Technology			battery module
	Nominal Module	12.8 V	Energy Density	89 Wh/kg
	Voltage
	Nominal Capacity	110 Ah	Max. Continuous	150 A
				Load
	1
	3	1

ACKNOWLEDGMENT

This work was supported by European Commission H2020 grant PANDA (grant no. H2020-LC-GV-2018), EU grant no. 824256.


Goupille

Denis Mulleman
email: denis.mulleman@univ-tours.fr

Trough infliximab concentration may predict long-term maintenance of infliximab in ankylosing spondylitis

Trough infliximab concentration may predict long-term maintenance of infliximab in ankylosing spondylitis D Chu Miow Lin 1 *, D Mulleman 1,2,3 *, N Azzopardi 1,2 , I Griffoul-Espitalier 1 , J-P Valat 1 , G Paintaud 1,2 , P Goupille 1,2,3 1 Tours University Hospital, Tours, 2 Franc ¸ois Rabelais University of Tours, CNRS UMR 6239, Tours, and 3 Inserm CIC 202, Tours, France

Infliximab is approved for refractory ankylosing spondylitis (AS) but 39% of patients experience no response to treatment after 24 weeks (1). de Vries et al reported that the clinical response was related to infliximab concentration, so exposure to infliximab may account for the variability in response [START_REF] De Vries | Decreased clinical response to infliximab in ankylosing spondylitis is correlated with anti-infliximab formation[END_REF]. However, more recent data have not confirmed that responsiveness is associated with infliximab concentration [START_REF] Krzysiek | Circulating concentration of infliximab and response to treatment in ankylosing spondylitis: results from a randomized control study[END_REF].

We analysed the relationship between trough infliximab concentration and long-term maintenance of infliximab treatment in patients with AS routinely treated in our centre. Patients at initiation of treatment were excluded from the study. On the day of the infusion (baseline), infliximab concentration was measured by enzyme-linked immunosorbent assay as described previously (4), as was positivity for antibodies towards infliximab (ATI). Disease activity was assessed at each infusion, for 52 weeks, by the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI). Infliximab treatment was categorized by comparing infusion dose and dosing interval with those recorded at the baseline infusion.

We considered infliximab dosage stable if both the dose (in mg/kg) and the interval (94 days) were equivalent between baseline and subsequent infusions. Dose modification and discontinuation of infliximab were based on disease activity and tolerance. Patients were divided into two groups on the basis of their staying with the same or lower dosage (group A 0 infliximab success) or switching to another biopharmaceutical or requiring an increase in dosage (group B 0 infliximab failure). Infliximab maintenance in group A at the last follow-up was compared between categories of infliximab concentration at baseline according to median infliximab concentration by KaplanÁMeier curves and a logrank test.

We analysed data for 22 patients with AS; the demographic, clinical, and biological characteristics are presented in Table 1. Patients with an infliximab concentration above the median at baseline showed a low, although not statistically significant, risk of treatment failure (p0 0.14). Three patients were positive for ATI at baseline with no detectable infliximab concentration. During follow-up, one patient switched to etanercept 12 weeks after baseline measurement, one discontinued treatment 30 weeks after baseline measurement, and one remained in group A at 56 weeks after baseline measurement.

Patients with high concentrations of infliximab at baseline showed sustained maintenance of infliximab treatment, although the results were not statistically significant, possibly because of better control of disease activity (Figure 1). In an open-label study [START_REF] Collantes-Estevez | Effectiveness of reducing infliximab dose interval in non-responder patients with refractory spondyloarthropathies. An open extension of a multicentre study[END_REF] and a randomized controlled trial (1), patients with inadequate response to infliximab were found to benefit from dosage escalation. Systematic treatment was also found to produce a better response than an 'on-demand' regimen [START_REF] Breban | Maintenance of infliximab treatment in ankylosing spondylitis: results of a one-year randomized controlled trial comparing systematic versus on-demand treatment[END_REF]. Our study was based on a single measurement of serum infliximab concentration at baseline. A repeated measurement of infliximab concentration would have allowed us to confirm the status of the patients in terms of their exposure to infliximab, and to analyse the impact of exposure on treatment maintenance more precisely.

Positivity for ATI was shown to influence response to infliximab. The study by de Vries et al found that only one in 11 patients with positivity for ATI (9%) were responders to infliximab at 54 weeks as compared to 20 in 27 patients without ATI positivity (74%) [START_REF] De Vries | Decreased clinical response to infliximab in ankylosing spondylitis is correlated with anti-infliximab formation[END_REF]. Positivity for ATI has an impact on infliximab pharmacokinetics and leads to reduced exposure to infliximab in AS [START_REF] Xu | Population pharmacokinetics of infliximab in patients with ankylosing spondylitis[END_REF]. In the present study, only three patients showed ATI positivity; two discontinued treatment. Because detection of ATI is hampered by the persistence of infliximab in the circulation, we may have underestimated the number of patients with ATI positivity.

In conclusion, infliximab concentration in patients with AS seems to predict sustained efficacy of the same infliximab regimen continued throughout treatment.

Figure 1 .

 1 Figure 1. Probability of maintaining equivalent infliximab dosage or decreasing the dosage over time according to infliximab exposure at baseline. Straight line: patients with infliximab concentration above the median. Dotted line: patients with infliximab concentration below the median. Log rank test: p00.14.

Table 1 .

 1 Characteristics of patients at baseline.

	Age (years)	46.5 (29.0Á72.0)
	Sex (F/M)	12/10
	Positivity for HLA-B27	14 (63.6%)
	Duration of infliximab treatment (months)	30.2 (8.3Á52.3)
	Dose of infliximab infusion (mg/kg)	5.0 (4.2Á7.8)
	Time elapsed since previous infusion (weeks) 6.4 (5.1Á17.4)
	BASDAI	3.3 (0.4Á8.0)
	Infliximab concentration (mg/L)	6.4 (0.0Á20.7)
	F, female; M, male; HLA-B27, human leucocyte antigen B27;
	BASDAI, Bath Ankylosing Spondylitis Disease Activity Index.
	Clinical and biological markers were measured just before
	baseline infliximab infusion. Continuous variables are reported
	as median (range).

Acknowledgements

We thank M.-F. Coudray, F. Gouais, P. Pithaud, and R. Laurent for blood sampling, A.-C. Duveau for technical assistance in measuring infliximab concentrations, T. Lecomte and D. Ternant for statistical analysis advice, and C. Magdelaine-Beuzelin for carrying out the measurement of antibodies towards infliximab serum concentrations.


David Ternant
email: david.ternant@univ-tours.fr

Konstantinos Karmiris

Séverine Vermeire

Celine Desvignes

Nicolas Azzopardi

Theodora Bejan-Angoulvant

Gert Van Assche

Gilles Paintaud

Severine Vermeire

Céline Desvignes

Pharmacokinetics of adalimumab in Crohn's disease

Keywords: Adalimumab, Crohn's disease, Pharmacokinetics, Population compartmental modeling, Monoclonal antibody

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

Adalimumab, an anti-TNF-α monoclonal antibody, is approved for the treatment of rheumatoid arthritis (RA), ankylosing spondylitis, psoriatic arthritis, Crohn's disease (CD), and ulcerative colitis. The pharmacokinetics (PK) of adalimumab in RA patients was investigated using compartmental modeling [START_REF] Ternant | Pharmacokinetics and concentration-effect relationship of adalimumab in rheumatoid arthritis[END_REF][START_REF] Weisman | Efficacy, pharmacokinetic, and safety assessment of adalimumab, a fully human anti-tumor necrosis factor-alpha monoclonal antibody, in adults with rheumatoid arthritis receiving concomitant methotrexate: a pilot study[END_REF], but its characteristics in CD patients has never been reported. Patients may develop antiadalimumab antibodies (AAA) which are responsible for a decrease in adalimumab serum concentration [START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF]a n dal o s s of clinical response [START_REF] Bartelds | Development of antidrug antibodies against adalimumab and association with disease activity and treatment failure during long-term follow-up[END_REF][START_REF] Bartelds | Clinical response to adalimumab: relationship to anti-adalimumab antibodies and serum adalimumab concentrations in rheumatoid arthritis[END_REF][START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF][START_REF] Radstake | Formation of antibodies against infliximab and adalimumab strongly correlates with functional drug levels and clinical responses in rheumatoid arthritis[END_REF][START_REF] West | Immunogenicity negatively influences the outcome of adalimumab treatment in Crohn's disease[END_REF]. Antibodies towards another anti-TNF-α monoclonal antibody, infliximab, were shown to increase its clearance [START_REF] Fasanmade | Population pharmacokinetic analysis of infliximab in patients with ulcerative colitis[END_REF][START_REF] Ternant | Infliximab pharmacokinetics in inflammatory bowel disease patients[END_REF][START_REF] Ternant | Influence of methotrexate on infliximab pharmacokinetics and pharmacodynamics in ankylosing spondylitis[END_REF][START_REF] Xu | Population pharmacokinetics of infliximab in patients with ankylosing spondylitis[END_REF]. The quantitative influence of anti-adalimumab antibodies (AAA) on adalimumab clearance has not been reported yet. We report the first quantitative description of adalimumab pharmacokinetics in Crohn'sd i sease patients. This is a post hoc analysis of a prospective cohort of 65 patients, being part of a larger cohort, who participated in an observational study in the Inflammatory Bowel Disease unit of the University Hospital of Leuven and for whom at least four adalimumab concentrations were available. [3]P a t i e n t s were treated subcutaneously either with 160/80 mg at weeks 0/2, or 80/40 mg as an induction phase. Following this phase, all patients were treated with 40-mg adalimumab every 2 weeks. Median follow-up was 20 months. Median [range] age and body weight were 37 years [17-61] and 68 kg [43-109], and 49 (75 %) were women. For 30 out of 65 patients, dosing regimen was increased to 40 mg every week. A total of 341 adalimumab serum concentrations were available. Antiadalimumab antibodies were detected in nine patients. Adalimumab concentrations were measured using an ELISA technique derived from the one developed for infliximab, [START_REF] Ternant | An enzyme-linked immunosorbent assay for therapeutic drug monitoring of infliximab[END_REF] and AAA were measured using a double-antigen ELISA based on their capture by adalimumab-coated plates. Adalimumab concentrations and AAA detection were performed in Tours University Hospital, France.

Adalimumab pharmacokinetics was studied by a population approach using MONOLIX 4.3.2 (Lixoft, Saclay, France). A one-compartment model with first-order absorption and elimination rates was used. Apparent volume of distribution (V/F), clearance (CL/F), and first-order absorption rate constant (k a ) were estimated. Interindividual and residual models were exponential and mixed additive-proportional, respectively. The presence of AAA was tested as a covariate on V/F and CL/F. All parameters were estimated with satisfactory accuracy, and no obvious model misspecification was observed. Estimated typical parameters (relative standard error) were V/F = 13.5 L (10 %), CL/F = 0.42 L/day (9 %) and k a =0 . 1 5d a y -1 . Interindividual standard deviations for V/F and CL/F (relative standard error) were ω V/F =4 8%( 1 9% )a n dω CL/V =6 5%( 1 0% ) ,r e s p e ctively. Interindividual standard deviation for k a could not be accurately estimated (shrinkage = 94 %) and was therefore fixed to 0. Additive and proportional (relative standard error) standard deviations were σ add =1 . 8m g / L (8 %) and σ prop = 0.15 (16 %), respectively. Apparent clearance was 5.5 times higher in presence of AAA (95 % confidence interval = [2.3-13.5], log-likelihood ratio test = 75.5, p < 0.0001). Elimination half-life in absence and in presence of AAA was 22 and 4.1 days, respectively (Fig. 1). Elimination half-life without AAA was similar to that reported for RA, 21 days [START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF].

Our study has some limitations. First, PK data were scarce. Second, the AAA assay was unable to detect them in the presence of adalimumab concentrations above 2 mg/L, which probably led to an underestimation of the proportion of immunized patients.

Overall, this study is the first to report a quantitative description of adalimumab PK in CD. We strongly believe that these results are a prerequisite for the design of future studies on the therapeutic drug monitoring of adalimumab in CD patients.

Fig. 1 Visual predictive check for adalimumab pharmacokinetics in Crohn's disease patients. Unfilled and solid circles represent adalimumab concentrations in patients with and without antiadalimumab antibodies (AAA), respectively. Dark and light gray surfaces represent 5-95 % prediction intervals for patients with and without AAA, respectively

CHRU de Tours, Laboratoire de Pharmacologie-Toxicologie, 2 boulevard Tonnellé,

Tours Cedex, France 3 Department of Gastroenterology, University Hospital, Leuven, Belgium 4 CHRU de Tours, Service de Pharmacologie, Tours, France

Acknowledgments Measurements of adalimumab serum concentrations were carried out within the CePiBAc platform. CePiBAc was cofinanced by the European Union. Europe is committed to the region Centre with the European Regional Development Fund. This work was partly supported by the French Higher Education and Research ministry under the program 'Investissements d'avenir' Grant Agreement: LabEx MAbImprove ANR-10-LABX-53-01. The authors thank Anne-Claire Duveau and Caroline Brochon for technical assistance with adalimumab assays.

Authors' contribution D. Ternant participated actively in execution of the study, analyzed and interpreted the data, and wrote the manuscript. K. Karmiris, G. Van Assche, and S. Vermeire conceived the ideas and experimental design and participated actively in execution of the study.

C. Desvignes participated actively in execution of the study.

N. Azzopardi participated actively in execution of the study and to the analysis of the data.

T. Bejan-Angoulvant participated to the analysis of the data. G. Paintaud participated to the conception of the ideas and experimental design, and participated actively in execution of the study, to the analysis and interpretation of the data, and to the writing of the manuscript.

Conflict of interest K. Karmiris reports personal fees from Abbvie and MSD outside the submitted work.

S. Vermeire reports grants and personal fees from UCB Pharma, Abbvie, Merck, and J&J and personal fees from Pfizer, Genentech/ Roche, Takeda, Ferring, Celltrion, Mundipharma, Hospira, and Shire during the conduct of the study.

G. van Assche reports reports and Consultancy and/or honoraria from the following: Abbvie, Takeda, MSD, Janssen, and Falk. Research support to University of Leuven was from Abbvie.

G. Paintaud reports grants from Novartis, Roche Pharma, Genzyme, MSD, Servier, and Pfizer outside the submitted work. D. Ternant, C. Desvignes, N. Azzopardi, and T. Bejan-Angoulvant declare that they have no competing interest.


Philippe Helluy

Pierre Gerhard

Victor Michel-Dansac

Bruno Weber

QUASI-EXPLICIT, UNCONDITIONALLY STABLE, DISCONTINUOUS GALERKIN SOLVERS FOR CONSERVATION LAWS

 a parallel and quasi-explicit Discontinuous Galerkin (DG) kinetic scheme for solving hyperbolic systems of conservation laws. The solver is unconditionally stable (i.e., the CFL number can be arbitrary), has the complexity of an explicit scheme. It can be applied to any hyperbolic system of balance laws. In this work, we improve the parallel scaling of the method thanks to an implicit-explicit subdomain decomposition strategy.

Kinetic approximation of first order conservations laws

In this work, we are interested in the numerical approximation of a hyperbolic system of m conservation laws in dimension d

(1)

∂ t W + d i=1 ∂ i Q i (W ) = 0,
where the unknown is a vector W (X, t) ∈ R m depending on the space variable: X = (x 1 . . . x d ) and the time variable: t. For the partial derivatives, we use the notation ∂ i = ∂ ∂xi , ∂ t = ∂ ∂t . This kind of system is generally difficult to approximate numerically. One of the difficulties is that explicit schemes are subject to restrictive time steps conditions. Implicit schemes do not suffer from time step conditions but require solving large sets of linear equations. In previous works (see [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF] and included references), we have proposed a method, based on a kinetic approach, for avoiding this constraint. We first recall the principles of the kinetic representation.

We consider a set of d + 1 (or more) kinetic velocities V k , k = 0 . . . d, associated to vectorial kinetic functions F k (W ) ∈ R m . We also define "Maxwellian" equilibrium functions M k (W ) ∈ R m . The kinetic BGK representation is given by transport equations with relaxation source terms [START_REF] Bouchut | Construction of BGK models with a family of kinetic entropies for a given system of conservation laws[END_REF][START_REF] Aregba | Discrete kinetic schemes for multidimensional systems of conservation laws[END_REF] (2)

∂ t F k + V k • ∇ X F k = 1 τ (M k (W ) -F k ) .
When the relaxation time τ → 0 + , the kinetic model ( 2) is formally equivalent to the initial system of conservation laws (1) provided that

(3) W = k M k (W ), k V i k M k (W ) = Q i (W ), i = 1, . . . , d.
Conditions (3) constitute a set of m(d + 1) equations with m(d + 1) unknowns for finding the Maxwellian. It possesses a unique solution. Theoretical arguments show that the formal limit is a true limit, under a so-called sub-characteristic condition [START_REF] Bouchut | Construction of BGK models with a family of kinetic entropies for a given system of conservation laws[END_REF][START_REF] Aregba | Discrete kinetic schemes for multidimensional systems of conservation laws[END_REF]. This condition states that the kinetic velocities have to be greater than the wave speeds λ r of the underlying hyperbolic system:

∀k, |V k | > max r |λ r | .
In practice it is difficult to solve directly the BGK system (2). It is better to split the equations into transport and a collision steps. This leads to the following kinetic algorithm for advancing one time step:

(1) Solve, for a duration ∆t , the free transport equation

∂ t F k + V k • ∇ X F k = 0.
(2) Solve, for the same duration, the relaxation (or collision) step

∂ t F k = 1 τ (M k (W ) -F k ) .
This algorithm is iterated in order to compute an approximation of W = k F k . The presented splitting algorithm is only first order accurate in time. But it is possible to improve its order, for instance by using an over-relaxation algorithm [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF]. It has been observed, since a long time that these kinds of kinetic schemes are free of CFL conditions. See for instance [START_REF] Brenier | Averaged multivalued solutions for scalar conservation laws[END_REF]. However, this interesting property is rarely exploited in practical applications.

This work was supported by: IRMIA++ https://irmiapp.unistra.fr/ and France Relance. We also thank the Mathematisches Forschungsinstitut of Oberwolfach where it was first presented.

Unconditionally stable DG approximations

The kinetic algorithm presented in Section 1 relies on transport steps and relaxation steps. The relaxation step is generally easy to implement at each interpolation point of the approximation. In addition, it is embarrassingly parallel. The most complicated part of the kinetic algorithm requires solving transport equations of the form (4)

∂ t f + V • ∇f = 0.
If the computational domain has a simple shape and if the solution is computed on a structured Cartesian grid, it is natural to solve this transport equation by the characteristic method. With well-chosen time step ∆t and kinetic velocities V k , this approach leads to the so-called Lattice Boltzmann method.

In a domain Ω with a complex geometry and for unstructured grid, the characteristic method is no more a good choice because it leads to difficulties such as instabilities or loss of conservation. In addition, the treatment of boundary conditions is not natural in this framework. In the unstructured case, we prefer to rely on a DG approximation of (4).

We consider an unstructured mesh of the computational domain Ω made of tetrahedral cells. The transported function f is approximated in cell L by a linear expansion on basis functions

f (x, t) ≃ f L (x, t) = j f L,j (t)ψ L j (x), x ∈ L.
The unknowns are the coefficients f L,j (t) of the linear expansion. After a DG in space approximation of (4), the DG scheme read as follows [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF] (5)

KF ′ (t) = 0,
where F(t) is a large vector containing all the coefficients f L,j (t), and K is the large matrix arising from the DG approximation of the transport equation. We then have to solve a large set of linear Ordinary Differential Equations (ODE). Explicit-in-time approximations of this set of ODEs suffer from constraining stability conditions on the time step ∆t. In order to suppress the stability condition, we can use an implicit time scheme for solving (5) for going from time step n -1 to time step n. For simplicity, we describe the case of an implicit first order Euler method. The strategy can be extended to other more accurate schemes, such as the Crank-Nicolson scheme (that we use) or DIRK (Diagonally implicit Runge--Kutta) approaches. With F n ≃ F(n∆t), the implicit Euler scheme reads (6)

(I + ∆tK)F n+1 = F n
It seems that one would need to assembly and solve a large linear system for computing F n+1 from F n . But when the numerical flux of the DG solver is the upwind flux, then the matrix K is block-triangular. In practice there is thus an explicit algorithm, the downwind algorithm, for solving the system (6) efficiently. See [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF].

Subdomain parallelism

We have implemented the downwind and the kinetic algorithms in a parallel software based on a work stealing strategy [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF]. We have observed a decreasing efficiency of the method when the number of threads increases. This is because the parallel scaling of the downwind algorithm is limited, at a given point, by the dependencies in the computations.

In order to increase the parallel scaling, we now describe a subdomain strategy that relaxes the computational dependencies. The main idea is to apply the above time-implicit downwind algorithm in each subdomain, but with a time-explicit coupling between the subdomains, for suppressing some dependencies. Because of the explicit coupling, it will be necessary to apply an iterative algorithm for computing the exact solution in a stable way. The algorithm can be proved to converge in a finite number of iterations. In most configurations three iterations are sufficient. Let us now describe the principles of this subdomain iterative algorithm. As in Section 2, the main task is the resolution of the transport equation in Ω × [0, ∆t], with initial data:

∂ t f + V • ∇f = 0, f (X, 0) = f 0 (X).
We assume that Ω is decomposed into a finite number of subdomains Ω i , i = 1 . . . n d . For the simplicity of the presentation, we assume that Ω is a periodic domain or the whole space, in order to avoid the description of the boundary conditions. However the approach is also valid when ∂Ω ̸ = ∅.

We then denote by f i the restriction of f to subdomain Ω i , by N i (X) the outward normal vector on ∂Ω i , and by ∂Ω - i the upwind part of the boundary of Ω i defined by Left: subdomains structure, Middle: 2 iterations scheme, Right: 3 iterations scheme. We observe that the iterative algorithm is stable, even with large time step, but that three iterations seem to be necessary.

∂Ω - i = {X ∈ ∂Ω i , N i (X) • V < 0} .
We initialize the algorithm by setting f 0 i (X, t) = f 0 i (X). Thus, the initial iteration does not depend on time. We then consider an iterative algorithm for computing successive time-dependent approximations f p i of f i in subdomain Ω i for p ≥ 1. For computing f p i from f p-1 i we solve the following time-dependent boundary value problem

∂ t f p i + V • ∇f p i = 0, in Ω i , (7)
f p i (X, 0) = f 0 i (X), X ∈ Ω i , (8)
f p i (X, t) = f p-1 j (X, t), X ∈ ∂Ω - i ∩ ∂Ω j . (9)
In other words, the f p i in subdomain Ω i are computed from the f p-1 j in the neighboring subdomains Ω j . We can prove the following result.

Proposition let L be the diameter of the smallest subdomain. Under the condition

∆t ≤ L |V | ,
in the generic case, the above algorithm (7)-( 9) converges to the exact solution in at most three iterations:

f 3 i = f i .
The proof relies on the characteristic method. It is briefly sketched in Figure 1. 3.1. Stability. We have implemented the above iterative algorithm. The parallelism within each subdomain is managed, as before, through the work stealing strategy. The communications between the subdomains are managed through calls to the MPI (Message Passing Interface) library. In our first experiments, we have verified the stability properties of the transport solver. They indicate that the number of iterations of the iterative algorithm is indeed important for the stability of the method. For a general domain decomposition obtained with an automatic partitioner, and with large time steps, the algorithm is stable provided that three iterations are done for advancing one time step. An illustration is given in Figure 2.

The objective of the subdomain algorithm was to relax the computational dependencies and to achieve a better parallel (strong) scaling of the method.

We compare the time spent in the iterative algorithm with a varying number of threads and subdomains. We define the efficiency e of the acceleration as the ratio of the elapsed time of the algorithm with the time that we would get with an ideal perfect scaling. The efficiency is perfect if e = 1. We observe, for instance, that with a single subdomain the efficiency with 64 threads

Figure 1 .

 1 Figure 1. Subdomain algorithm, in a generic subdomain decomposition, with corners shared by several subdomains. In this case, the iterative algorithm reaches the exact solution in at most three iterations. First iteration: the boundary value on ∂Ω - 2 is updated. Second iteration: the boundary value on ∂Ω - 3 is updated. Third iteration: the correct value is transported.

Figure 2 .

 2 Figure2. Stability of the subdomain iterative algorithm. Left: subdomains structure, Middle: 2 iterations scheme, Right: 3 iterations scheme. We observe that the iterative algorithm is stable, even with large time step, but that three iterations seem to be necessary.

Université de Strasbourg,

IRMA UMR CNRS 7501,

Inria Tonus,

AxesSim Illkirch

 1. Multithread and MPI scaling. For a computation done with 64 threads, we observe that it is better to split the domain into 8 subdomains instead of affecting all the threads to one single subdomain.

drops to e = 0.39, while with 8 subdomains and 8 threads per subdomain the efficiency is better e = 0.72. We have thus validated the efficiency of this approach. Of course, the whole algorithm is impacted by a slowdown factor imposed by the additional iterations. However the weak scaling of the method on a supercomputer for very large computations is now certainly ensured. Indeed, explicit subdomain decomposition methods are known to be well adapted to the architecture of supercomputers. More measurements are given in Table 1.

Conclusion

We presented an adaptation of the kinetic DG method introduced in [START_REF] Gerhard | Unconditionally stable and parallel discontinuous galerkin solver[END_REF]. The method can handle arbitrary conservation laws and complex unstructured meshes. It is explicit in time but CFL-free. The method has good parallelization features, for both shared memory and distributed memory computers. For improving the parallel scaling on distributed memory computers, we have proposed a subdomain decomposition method that relaxes the task dependencies of the kinetic scheme but keeps the possibility to use large time steps.