Pauline Duminil
email: pauline.duminil@uni-goettingen.de

Marlène Davanture
email: marlene.davanture@inrae.fr

Céline Oury
email: celine.oury@universite-paris-saclay.fr

Edouard Boex-Fontvieille
email: edouard.boex-fontvieille@interieur.gouv.fr

Guillaume Tcherkez
email: guillaume.tcherkez@anu.edu.au

Michel Zivy
email: michel.zivy@inrae.fr

Michael Hodges
email: michael.hodges@cnrs.fr

Nathalie Glab
email: nathalie.glab@universite-paris-saclay.fr

Arabidopsis thaliana 2,3-bisphosphoglycerate-independent phosphoglycerate mutase 2 activity requires serine 82 phosphorylation

Keywords: 2, 3-bisphosphoglycerate-independent phosphoglycerate mutase, glycolysis, transient phosphorylation, catalytic mechanism, phosphopeptide, Arabidopsis thaliana

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Introduction

Phosphoglycerate mutase (PGAM) catalyzes the reversible isomerization of 3phosphoglycerate (3-PGA) and 2-phosphoglycerate (2-PGA), and it is involved in glycolysis and gluconeogenesis. There are two evolutionary unrelated PGAM groups, based on their requirement of a cofactor, 2,3-bisphosphoglycerate. Cofactor-dependent PGAM (dPGAM, E.C. 5.4.2.11) is present in vertebrates, some fungi and bacteria where it is often the only type of PGAM, like in humans [START_REF] Fothergill-Gilmore | The phosphoglycerate mutases[END_REF]. Cofactor-independent PGAM (iPGAM, E.C. 5.4.2.12) is found in higher plants, algae, some invertebrates including Nematodes, Trypanosomatideae, some fungi and bacteria (mainly Gram-positive) and requires a divalent cation for catalysis. These two groups of PGAMs show few similarities and can be distinguished by their protein sequence, their protein structure and their catalytic mechanism [START_REF] Jedrzejas | Structure, function, and evolution of phosphoglycerate mutases: Comparison with fructose-2,6-bisphosphatase, acid phosphatase, and alkaline phosphatase[END_REF]. Furthermore, iPGAM proteins can be classified into two families according to their amino acid sequence and cation dependence: family 1 is composed of enzymes found in Trypanosomatideae and plants and use Mg 2+ /Zn 2+ , while family 2 members can be found in Prokaryotes and require Mn 2+ to be active [START_REF] Fuad | Phosphoglycerate mutase from Trypanosoma brucei is hyperactivated by cobalt in vitro, but not in vivo[END_REF][START_REF] Blackburn | Trypanosomatid phosphoglycerate mutases have multiple conformational and oligomeric states[END_REF]. The 3D structure of family 1 iPGAM from the parasitic protozoans Leishmania mexicana (LmiPGAM) and Trypanosoma brucei (TpiPGAM), and family 2 enzymes from Geobacillus stearothermophilus (GsiPGAM), Staphylococcus aureus (SaiPGAM) and Bacillus anthracis (BaiPGAM) have been determined. Such crystallographic data revealed that the monomeric, globular enzyme is composed of two domains: phosphatase (domain A) which comprises the substrate binding site, and the transferase (domain B). The two domains are linked by a flexible junction necessary to allow conformational changes leading to either an open or a closed state required for catalysis [START_REF] Jedrzejas | Mechanism of catalysis of the cofactor-independent phosphoglycerate mutase from Bacillus stearothermophilus: Crystal structure of the complex with 2-phosphoglycerate[END_REF]. Essential amino acids for catalysis have been identified and it was shown that phosphate group transfer during the isomerization reaction involved a transient phospho-serine [START_REF] Jedrzejas | Mechanism of catalysis of the cofactor-independent phosphoglycerate mutase from Bacillus stearothermophilus: Crystal structure of the complex with 2-phosphoglycerate[END_REF][START_REF] Nukui | Structure and molecular mechanism of Bacillus anthracis cofactor-independent phosphoglycerate mutase: a crucial enzyme for spores and growing cells of Bacillus species[END_REF][START_REF] Nowicki | Crystal structures of Leishmania mexicana phosphoglycerate mutase suggest a one-metal mechanism and a new enzyme subclass[END_REF][START_REF] Mercaldi | Structural role of the active-site metal in the conformation of Trypanosoma brucei phosphoglycerate mutase[END_REF][START_REF] Roychowdhury | Complete catalytic cycle of cofactor-independent phosphoglycerate mutase involves a spring-loaded mechanism[END_REF].

In plants, there has been a controversy as to whether both dPGAM and iPGAM exist and whether PGAM is located to both the cytosol and plastids. Pea (Pisum sativum) leaf chloroplasts do not contain any detectable PGAM activity [START_REF] Stitt | Pathways of carbohydrate oxidation in leaves of Pisum sativum and Triticum aestivum[END_REF].

Contradictory observations have been reported in castor bean (Ricinus communis)

endosperm: on the one hand, a very low PGAM activity was found in leucoplasts in addition to a high cytosolic PGAM activity [START_REF] Miernyk | Isozymes of the glycolytic enzymes in endosperm from developing castor oil seeds[END_REF][START_REF] Botha | Isozymes of phosphoglyceromutase from the developing endosperm of Ricinus communis: Isolation and kinetic properties[END_REF] while on the other hand, only cytosolic iPGAM was found by [START_REF] Huang | Higher-plant cofactor-independent phosphoglyceromutase: purification, molecular characterization and expression[END_REF]. To date, iPGAM purified from castor bean endosperm [START_REF] Botha | Isozymes of phosphoglyceromutase from the developing endosperm of Ricinus communis: Isolation and kinetic properties[END_REF], wheat germ [START_REF] Smith | Wheat germ phosphoglycerate mutase: Purification, polymorphism, and inhibition[END_REF] and maize seeds [START_REF] Grana | Purification, characterization and immunological properties of 2,3-bisphosphoglycerate-independent phosphoglycerate mutase from maize (Zea mays) seeds[END_REF] has been associated with a 60-74 kDa monomeric protein with a cofactor-independent activity and a Michaelis constant (K m ) for 3-PGA between 0.33 mM and 0.43 mM.

In Arabidopsis thaliana, TAIR and KEGG databases, along with several publications suggest the presence of several putative PGAM-encoding genes [START_REF] Mazarei | Expression of an Arabidopsis phosphoglycerate mutase homologue is localized to apical meristems, regulated by hormones, and induced by sedentary plant-parasitic nematodes[END_REF][START_REF] Andriotis | Plastidial glycolysis in developing Arabidopsis embryos[END_REF][START_REF] Stein | Cross-species analysis of the glycolytic pathway by comparison of molecular interaction fields[END_REF]. Amongst them, At1g22170 was annotated as a dPGAM and shown to be localised to plastids; nevertheless, a mutant affected in that gene (pglym1) did not exhibit any phenotype and seed lipid content remained unaltered [START_REF] Andriotis | Plastidial glycolysis in developing Arabidopsis embryos[END_REF]. Two Arabidopsis genes, At1g09780 and At3g08590, encoding 61 kDa proteins sharing 90% identity and high similarities with other known higher plant iPGAMs were annotated iPGAM1 and iPGAM2, respectively (Zhao and Assmann, 2011). They appear to have redundant functions since single ipgam mutants with a moderately reduced leaf iPGAM activity are indistinguishable from wild-type plants. However, ipgam1 ipgam2 double mutants where leaf iPGAM activity is undetectable, displayed severely stunted growth, altered stomatal movements and an absence of pollen production thus leading to male sterility (Zhao and Assmann, 2011). In potato (Solanum tuberosum) lines where iPGAM activity had been reduced to 25% of the wild-type level using an anti-sense strategy, a slower growth leading to smaller plants and lower tuber yields were observed [START_REF] Westram | Increases of 3phosphoglyceric acid in potato plants through antisense reduction of cytoplasmic phosphoglycerate mutase impairs photosynthesis and growth, but does not increase starch contents[END_REF].

Taken as a whole, genetics-based results point out the importance of iPGAM in plant development. Such an effect is expected considering its involvement in glycolysis, and the pivotal role of 3-PGA in plant metabolism. Glycolysis is a ubiquitous metabolic pathway occurring in the cytosol of all cell types where it can transform glucose to pyruvate, allowing the generation of reducing power and energy as NADH and ATP, respectively. The oxidation of pyruvate to acetyl-CoA can feed the mitochondrial tricarboxylic acid cycle (TCA cycle). It has been found that several glycolytic enzymes including iPGAM are attached to the cytosolic side of mitochondrial envelope [START_REF] Giegé | Enzymes of glycolysis are functionally associated with the mitochondrion in Arabidopsis cells[END_REF]. Glycolytic enzymes can be found also in plastids where they contribute to lipid metabolism but not all types of plastid contain PGAM [START_REF] Plaxton | The organization and regulation of plant glycolysis[END_REF][START_REF] Givan | Evolving concepts in plant glycolysis: two centuries of progress[END_REF]. The fixation of atmospheric CO 2 and O 2 by ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) produces large amounts of 3-PGA used to fuel the Calvin cycle and starch biosynthesis in chloroplasts. Triose-phosphate molecules generated in chloroplasts from 3-PGA are transported to the cytosol via the triose-phosphate transporter (TPT) (for a review see [START_REF] Facchinelli | The metabolite transporters of the plastid envelope: an update[END_REF] and used to synthesize sucrose, organic and amino acids as well as precursors for secondary metabolism and fatty acid biosynthesis. Interactions between metabolic pathways, such as the competition between triose phosphate utilization for sucrose synthesis versus catabolism, are tightly regulated and several glycolytic enzymes undergo post-translational redox modifications and/or protein phosphorylation while others have their activity modulated by metabolites (for a recent review see O' Leary and Plaxton, 2020). While a posttranslational regulation of plant iPGAM activity has not been reported, the PhosPhAt (http://phosphat.uni-hohenheim.de) and Athena (http://athena.proteomics.wzw.tum.de/) databases contain an Arabidopsis thaliana iPGAM phosphopeptide where serine 80 (S80) and serine 82 (S82) is phosphorylated in iPGAM1 and iPGAM2, respectively. Surprisingly, despite the crucial role of iPGAM, the potential impact of serine phosphorylation in modulating enzyme activity and participating in catalysis has never been examined.

Here, we looked at the role of serine 82 phosphorylation in Arabidopsis iPGAM2.

Based on protein sequence comparisons and in silico structural modelling with non-plant iPGAM proteins, a strategy using recombinant Arabidopsis iPGAM2 and site-directed mutagenesis was adopted to test the hypothesis that S82 phosphorylation was part of the catalytic mechanism of plant iPGAMs. Since our in vitro studies suggest that the amount of detectable S82-phosphopeptide reflects iPGAM2 steady-state catalysis, the metabolic consequences of a higher in planta iPGAM activity in light-treated compared to light/darktreated Arabidopsis thaliana rosette leaves were analyzed.

Results

S82 of iPGAM2 is phosphorylated in Arabidopsis phosphoproteome

Phosphoproteomics analyses were carried out on Arabidopsis rosettes after either 4 h light or 4 h light followed by 2 h dark in a gas exchange system (and sampled by snap freezing with liquid nitrogen). A phosphopeptide associated with AtiPGAM1 and AtiPGAM2 was found, with the sequence AHGTAVGLPSEDDMGN(pS)EVGHNALGAGR, containing a phosphorylated serine at position 82 of AtiPGAM2 (position 80 of AtiPGAM1). Its abundance was significantly reduced by 30% in darkened leaves compared to illuminated leaves (Figure 1). Data mining in published phosphoproteomes and the literature showed that Arabidopsis iPGAM phosphorylation at this site is a common phenomenon (Table S1). In fact, many phosphoproteomics analyses have already identified this iPGAM phosphopeptide despite contrasting growth conditions: cell cultures [START_REF] Carroll | Analysis of the Arabidopsis cytosolic ribosome proteome provides detailed insights into its components and their posttranslational modification[END_REF][START_REF] Ito | A survey of the Arabidopsis thaliana mitochondrial phosphoproteome[END_REF], cell suspensions [START_REF] Nakagami | Large-scale comparative phosphoproteomics identifies conserved phosphorylation sites in plants[END_REF][START_REF] Lin | Integrating phosphoproteomics and bioinformatics to study brassinosteroid-regulated phosphorylation dynamics in Arabidopsis[END_REF], seedlings grown in liquid media (Wang et al., 2013a,b;[START_REF] Hoehenwarter | Identification of novel in vivo MAP kinase substrates in Arabidopsis thaliana through use of tandem metal oxide affinity chromatography[END_REF][START_REF] Xue | Quantitative measurement of phosphoproteome response to osmotic stress in Arabidopsis based on library-assisted extracted ion chromatogram (LAXIC)[END_REF][START_REF] Rayapuram | Identification of novel PAMP-triggered phosphorylation and dephosphorylation events in Arabidopsis thaliana by quantitative phosphoproteomic analysis[END_REF][START_REF] Rayapuram | Quantitative phosphoproteomic analysis reveals shared and specific targets of Arabidopsis mitogen-activated protein kinases (MAPKs) MPK3, MPK4, and MPK6[END_REF], in vitro seedlings [START_REF] Lan | Quantitative phosphoproteome profiling of irondeficient Arabidopsis roots[END_REF][START_REF] Umezawa | Genetics and phosphoproteomics reveal a protein phosphorylation network in the abscisic acid signaling pathway in Arabidopsis thaliana[END_REF][START_REF] Yang | Stable isotope metabolic labeling-based quantitative phosphoproteomic analysis of Arabidopsis mutants reveals ethylene-regulated time-dependent phosphoproteins and putative substrates of constitutive triple response 1 kinase[END_REF][START_REF] Choudhary | Quantitative circadian phosphoproteomic analysis of Arabidopsis reveals extensive clock control of key components in physiological, metabolic, and signaling pathways[END_REF], hydroponically grown plants (Zhang et al., 2013), and adult plants grown in pots [START_REF] Roitinger | Quantitative phosphoproteomics of the ataxia telangiectasia-mutated (ATM) and ataxia telangiectasia-mutated and rad3-related (ATR) dependent DNA damage response in Arabidopsis thaliana[END_REF] (see Table S1). More recently, it has been identified in each of the 30 matching tissues from Arabidopsis thaliana (Col-0) of the Athena database.

Arabidopsis iPGAM structure and function

iPGAM catalysis involves a transitory phosphorylated serine residue to allow phosphate transfer from the C3 position of phosphoglycerate to the C2 position to form 2phosphoglycerate. However, there is no information about the identity of the catalytic serine in iPGAM from plants. Protein sequence alignment of Arabidopsis iPGAM2 with iPGAM from Trypanosoma brucei and Leshmania mexicana (family 1) and Staphylococcus aureus, Bacillus anthracis, Geobacillus stearothermophilus (family 2) were carried out to identify a putative catalytic serine in the Arabidopsis enzyme (Figure S1). First, AtiPGAM was found to share higher sequence identity with family 1 iPGAM proteins (57.8% with T. brucei and 56.3% with L. mexicana) than with family 2 proteins (35.9-37.5%). Second, sequence alignments clearly indicated that S82 of AtiPGAM2 corresponded to S62 of SaiPGAM and GsiPGAM, S74 of TbiPGAM and S75 of LmiPGAM [START_REF] Blackburn | Trypanosomatid phosphoglycerate mutases have multiple conformational and oligomeric states[END_REF], which have been demonstrated to undergo a transient phosphorylation as part of the catalytic reaction mechanism. Third, it was apparent that residues known to be involved in non-plant iPGAM catalysis (e.g. see [START_REF] Nowicki | Crystal structures of Leishmania mexicana phosphoglycerate mutase suggest a one-metal mechanism and a new enzyme subclass[END_REF] were conserved in the AtiPGAM2 protein (Figure S1).

The relationship between conserved residues and AtiPGAM function was further investigated using an in-silico predicted 3D structural model of AtiPGAM2 constructed with SWISS MODEL (https://swissmodel.expasy.org/) and identified in the Swiss Model Repository (SMR; https://swissmodel.expasy.org/repository), a database of annotated 3D protein structure models generated by the SWISS-MODEL homology-modelling pipeline [START_REF] Bienert | The SWISS-MODEL repository-new features and functionality[END_REF]. The SMR proposed 3 templates to model AtiPGAM2 structure (see A0A384KAQ5 at the SMR database), 3nvl.1.A (T. brucei), 3igy.1.A (L. mexicana) and 5kgl.1.A (C. elegans) (Figure S2). Although T. brucei iPGAM gave a slightly better Qualitative Model Energy ANalysis (QMEAN) score, it was decided to use L. mexicana iPGAM as the template in this study since the structure had been solved to a 2Å resolution, and crystallized in the presence of 3-PGA and two divalent cations (here Co 2+ ) and therefore it was in the active closed conformation. It can be seen that AtiPGAM2 secondary structure predictions based on the chosen template indicated conserved α-helix and β-sheet domains with few differences (Figure 2a) and the AtiPGAM2 3D-predicted structure allowed a clear identification of the phosphatase domain A composed of amino-and carboxy-termini regions connected via two inter-domain loops to the transferase domain B (Figure 2b). A focus on the active site provided information on conserved amino acids involved in the catalysis and how they interact with the substrate and divalent cations (Figure 2c). The model confirmed S82 of AtiPGAM2 as the putative catalytic serine interacting with both 3-PGA and a cobalt cation (Figure 2c). It also indicated the roles of conserved catalytic residues including the interaction of D431, H435 and H505 with one of the two metal ions (Co1) (Figure S3a), the interaction of D29, S82, D472 and H473 with the other divalent cation (Co2) (Figure S3b), 3 H-bonds between 3-PGA and S82 and R207 (Figure S3c) and 14 salt bridges between 3-PGA and S82, H141, R171, R207, R214, R290, R287, K362, H365, H435, H473 and H502 (Figure S3d). Thus, both the sequence comparison (Figure S1) and the 3D structure prediction of AtiPGAM2 (Figure 2 and Figure S3) strongly suggested a central role for S82 in the catalytic mechanism of plant iPGAM. Therefore, it was decided to investigate this further by a site directed mutagenesis approach using recombinant AtiPGAM2.

Characterisation of recombinant AtiPGAM kinetic parameters

Recombinant His-tagged AtiPGAM2 was produced in E. coli cells and purified from the soluble fraction using affinity chromatography (Figure S4). It was then used to measure AtiPGAM2 activity with a coupled enzymatic assay (Figure S5) previously used to measure iPGAM activity in Arabidopsis leaf extracts (Zhao and Assmann, 2011). The calculation of AtiPGAM kinetic parameters showed the K m for 3-PGA was 0.467±0.032 mM. This value is similar to those reported for other plant iPGAM proteins; recombinant castor bean iPGAM (0.43 mM; [START_REF] Huang | Histidine residues 139, 363 and 500 are essential for catalytic activity of cofactor-independent phosphoglyceromutase from developing endosperm of the castor plant[END_REF], and iPGAM purified from either castor bean endosperm (0.33 mM and 0.4 mM; [START_REF] Botha | Isozymes of phosphoglyceromutase from the developing endosperm of Ricinus communis: Isolation and kinetic properties[END_REF] or maize seed (0.324 mM; [START_REF] Grana | Purification, characterization and immunological properties of 2,3-bisphosphoglycerate-independent phosphoglycerate mutase from maize (Zea mays) seeds[END_REF]. Specific activity (k cat ) was found to be 51.3±3.5 s -1 with 3-PGA as substrate in the presence of 5 mM Mg 2+ . The presence of an N-terminal His-tag did not appear to interfere with its correct functioning and therefore our recombinant AtiPGAM2 was used to investigate the role of S82.

Significance of the phosphorylated S82-containing peptide

To confirm the hypothesis that S82 of AtiPGAM was indeed required by the enzyme to carry out the isomerization reaction, it was decided to produce and purify recombinant AtiPGAM2 where S82 had been replaced either by alanine (AtiPGAM2 S82A ) or aspartate (AtiPGAM2 S82D ) (Figure S4). The 3-PGA-dependent activity was abolished in both cases (Figure S6), thus highlighting the cardinal role of S82 in the catalytic mechanism of AtiPGAM2.

To demonstrate that S82 phosphorylation was associated with AtiPGAM2 activity, the amount of S82-phosphopeptide was measured at varying substrate concentration using recombinant AtiPGAM2 WT (Figure 3). Importantly, even in the absence of 3-PGA, the phosphopeptide was identified, showing that AtiPGAM2 produced from E. coli cells was phosphorylated and functional within the bacterium and that the phosphorylated serine residue was stable, at least to some extent, during protein purification. When recombinant AtiPGAM2 was incubated for 10 min with either 2.5 mM, or 5 mM or 10 mM 3-PGA, there was a significant 3-PGA-dependent increase in the amount of detectable phosphopeptide.

Accordingly, the level of the phosphopeptide was lower when 3-PGA-dependent AtiPGAM2 activity was assayed in the absence of added Mg 2+ , however it was still higher than in the absence of 3-PGA probably due to the presence of cation still bound to a fraction of the purified, desalted protein (Figure 3).

We then used our protein sequence alignment (Figure S1) and structural model of AtiPGAM2 (Figure 2c and Figure S3) and chose two conserved amino acids known to participate in catalysis in non-plant PGAMs. Structural studies of iPGAM from other species have demonstrated that an aspartate residue found in the N-terminus region is involved in the phospho-transferase reaction. This aspartate residue located in domain A corresponded to D29 in AtiPGAM2, as it aligned with D11/12 of family 2 iPGAMs, and D22/23 of TbiPGAM and LmiPGAM family 1 enzymes, respectively (Figure S1). It was expected that the absence of D29 would stabilize S82 phosphorylation in the absence of the transferase reaction. On the other hand, R290 in AtiPGAM2 domain B was identified as being equivalent to R284 (TbiPGAM), R285 (LmiPGAM) and R260/R264 (SaiPGAM/GsiPGAM), an arginine residue required for 3-PGA binding to the active site via stabilization of negative charges carried by the phosphate group [START_REF] Jedrzejas | Mechanism of catalysis of the cofactor-independent phosphoglycerate mutase from Bacillus stearothermophilus: Crystal structure of the complex with 2-phosphoglycerate[END_REF][START_REF] Nukui | Structure and molecular mechanism of Bacillus anthracis cofactor-independent phosphoglycerate mutase: a crucial enzyme for spores and growing cells of Bacillus species[END_REF][START_REF] Nowicki | Crystal structures of Leishmania mexicana phosphoglycerate mutase suggest a one-metal mechanism and a new enzyme subclass[END_REF][START_REF] Mercaldi | Structural role of the active-site metal in the conformation of Trypanosoma brucei phosphoglycerate mutase[END_REF][START_REF] Roychowdhury | Complete catalytic cycle of cofactor-independent phosphoglycerate mutase involves a spring-loaded mechanism[END_REF]. Therefore, the absence of R290 was expected to inhibit the phosphorylation of S82.

Site-directed mutagenesis of AtiPGAM2 was carried out to produce recombinant AtiPGAM2 D29N and AtiPGAM2 R290L proteins. These two proteins did not display 3-PGA dependent catalytic activity at all (Figure S6), thereby confirming the importance of D29 and R290 of AtiPGAM2 in the reaction mechanism and their requirement for enzyme activity. To investigate further the significance of the AtiPGAM2 S82-containing phosphopeptide, recombinant AtiPGAM2 D29N and AtiPGAM2 R290L proteins were incubated with or without 2.5 mM 3-PGA and the amount of phosphopeptide was estimated by liquid chromatography-tandem mass spectrometry (LC-MS/MS) (Figure 4). As predicted from the role of R290 in substrate binding, the phosphopeptide was barely detectable in AtiPGAM2 R290L , and less abundant that in the WT protein (Figure 4). As expected, AtiPGAM2 D29N produced an increased amount of phosphopeptide (Figure 4) since the reaction was blocked, that is, the transferase activity could not take place in the absence of D29. The significant amount of phosphorylated S82 in the AtiPGAM2 D29N assay carried out in the absence of substrate indicated that the 3-PGA pool in E. coli cells was sufficient to allow the occurrence of some phosphatase activity before the protein was purified. These results show that the reaction mechanism of AtiPGAM2 is similar to that described for non-plant iPGAM enzymes and involves a catalytic serine (S82 of AtiPGAM2) that carries the phosphate during the isomerization reaction.

Metabolite profiling of light-and light/dark-treated Arabidopsis rosette leaves

Gas chromatography-mass spectrometry (GC-MS)-based metabolite profiling (Table 1 andTable S2) of the rosette leaves used for phosphoproteomics was carried out to examine possible changes in leaf metabolism between the 4 h light (light) and 4 h light followed by 2 h dark (light/dark) treatments carried out during the natural 8 h day period of our Arabidopsis plants. Organic acids (malate, citrate, and succinate) were significantly 1.5to 3.5-fold lower in illuminated leaves compared to darkened leaves whereas several saturated fatty acids (lauric acid, palmitic acid and stearic acid) where found to be 2-to 5fold higher (Table 1). Only a small non-significant 20% reduction in leaf pyruvate levels were measured between the light and the light/dark treated leaves (Table 1). Amino acid levels showed variable differences between the two treatments, some of them being significantly lower in the light (Ala, Asp, Cys, GABA, Glu, Ile and Lys), while Pro was significantly higher (by 28%) in the light compared to darkened leaves. Other amino acids including aromatic and several branched-chain amino acids (Table 1) showed no significant changes (Gly, Leu, Met, Phe, Ser, Thr, Tyr and Val) (Table S2). Shikimate content did not change significantly between the two conditions (Table 1). Finally, in the light there was more glucose, glycolate and glycerate (Table S2).

Discussion

PGAM is of paramount importance for plant growth and development [START_REF] Westram | Increases of 3phosphoglyceric acid in potato plants through antisense reduction of cytoplasmic phosphoglycerate mutase impairs photosynthesis and growth, but does not increase starch contents[END_REF]Zhao and Assmann, 2011) due to its involvement in glycolysis. The genome of the plant model Arabidopsis thaliana contains two iPGAM-encoding genes (At1g09780 and At3g08590) producing two proteins iPGAM1 and iPGAM2 that share a sequence identity of 90% and redundant functions (Zhao and Assmann, 2011). Arabidopsis iPGAM1 and iPGAM2 share a common phosphopeptide containing a phosphorylated serine (at position 82 in AtiPGAM2) identified in the literature, the PhosPhAt database (see Table S1), and during our phosphoproteomics analysis (Figure 1). In this work, we chose to determine the significance of iPGAM2 S82 phosphorylation.

iPGAM2 activity involves phosphorylation at serine 82

At a first glance, the phosphorylated serine (S82 of AtiPGAM2) could be interpreted as a post-translational modification regulating iPGAM activity, however this is not the case.

It has been shown previously that non-plant iPGAM catalysis involves a transient phosphoserine carrying the phosphate group during the isomerization reaction [START_REF] Jedrzejas | Structure, function, and evolution of phosphoglycerate mutases: Comparison with fructose-2,6-bisphosphatase, acid phosphatase, and alkaline phosphatase[END_REF][START_REF] Nukui | Structure and molecular mechanism of Bacillus anthracis cofactor-independent phosphoglycerate mutase: a crucial enzyme for spores and growing cells of Bacillus species[END_REF][START_REF] Nowicki | Crystal structures of Leishmania mexicana phosphoglycerate mutase suggest a one-metal mechanism and a new enzyme subclass[END_REF][START_REF] Mercaldi | Structural role of the active-site metal in the conformation of Trypanosoma brucei phosphoglycerate mutase[END_REF][START_REF] Roychowdhury | Complete catalytic cycle of cofactor-independent phosphoglycerate mutase involves a spring-loaded mechanism[END_REF]. Sequence alignments (Figure S1), and a structural model of AtiPGAM2 (Figure 2 and Figure S3) indicated that S82 of AtiPGAM2 corresponds to the catalytic phosphoserine.

Although the transient catalytic phosphoserine was expected be too unstable to allow its detection using standard phosphoproteomics techniques, an associated phosphopeptide was indeed detectable (Table S1; Figure 1). The importance of S82 for AtiPGAM activity was shown by the complete loss of PGA-dependent catalytic activity (Figure S6) when S82 was mutated to either alanine or aspartate. Phosphopeptide analyses of recombinant AtiPGAM2 confirmed the involvement of S82 in phosphate transfer during the isomerization of 3-PGA to 2-PGA. First, the amount of detectable phosphopeptide was dependent on the amount of substrate (Figure 3). Second, the amount of detectable phosphopeptide was dependent on the phosphatase and transferase steps of catalysis. AtiPGAM R290L affected in 3-PGA binding to the active site exhibited an extremely low amount of phosphopeptide with a phosphorylated-to-non-phosphorylated (OP/OH) ratio of only 0.08 (Figure 4). On the other hand, AtiPGAM D29N showed an extremely high amount of phosphopeptide with an OP/OH ratio of almost 6 (Figure 4) since D29 is involved in phosphate group transfer from S82 to form 2-PGA in the 3-PGA-dependent reaction. Taken together, our results clearly show that the AtiPGAM2 phosphopeptide is not related to a post-translational regulatory process but it is a consequence of the isomerization reaction. Due to the transient nature of S82 phosphorylation, the amount of the resulting phosphopeptide in steady-state catalysis is low. Interestingly, a comparative phosphoproteomics study of blast resistant and susceptible rice (Oryza sativa) cultivars in response to salicylic acid showed a positive correlation between iPGAM phosphopeptide amounts and iPGAM activity [START_REF] Sun | Comparative phosphoproteomic analysis of blast resistant and susceptible rice cultivars in response to salicylic acid[END_REF].

In planta iPGAM phosphopeptide levels and leaf metabolism

As seen from Table S1, the AtiPGAM1/2 S80/S82-phosphopeptide has been detected previously in Arabidopsis grown in continuous light, continuous dark, and treated to different stresses (including iron availability, N deprivation, dehydration, ABA, flg22, ionizing radiation) but no differential phosphorylation was reported. However, AtiPGAM1/2 S80/S82-phosphopeptide levels were found to change (by a modest extent) between our light and darkened conditions (Figure 1). Thus the content in phosphorylated catalytic intermediate and therefore steady-state catalysis was associated with a slight but significant light/dark effect. This in turn suggests that 3-PGA concentration and thus isomerization to 2-PGA probably changed, possibly impacting glycolytic production of PEP and pyruvate.

In the light, CO 2 assimilation via Rubisco produces 3-PGA that is converted to triosephosphates in chloroplasts. Some triose-phosphates are then transported to the cytosol and used to make sugars and precursors (e.g. PEP and pyruvate) of biosynthetic pathways producing amino acids, organic acids, fatty acids and isoprenoids (see Figure 5). Since chloroplasts do not contain a complete glycolytic pathway as they lack iPGAM [START_REF] Stitt | Pathways of carbohydrate oxidation in leaves of Pisum sativum and Triticum aestivum[END_REF] and enolase [START_REF] Prabhakar | Molecular and functional characterization of the plastid-localized phosphoenolpyruvate enolase (ENO1) from Arabidopsis thaliana[END_REF][START_REF] Fukayama | Characterization and expression analyses of two plastidic enolase genes in rice[END_REF] they cannot produce PEP and pyruvate directly from triose-phosphates and so they are imported from the cytosol via plastid transporters [START_REF] Streatfield | The phosphoenolpyruvate/phosphate translocator is required for phenolic metabolism, palisade cell development, and plastid-dependent nuclear gene expression[END_REF][START_REF] Lee | Seed-specific overexpression of the pyruvate transporter BASS2 increases oil content in Arabidopsis seeds[END_REF]. In the chloroplast, PEP is required for the biosynthesis of aromatic amino acids (Tyr, Trp, Phe) [START_REF] Maeda | The shikimate pathway and aromatic amino acid biosynthesis in plants[END_REF] while pyruvate is used for the biosynthesis of isoprenoids, branched-chain amino acids and saturated fatty acids (Ohlorgge and Jawarski, 1997;[START_REF] Pulido | New insights into plant Isoprenoid metabolism[END_REF][START_REF] Xing | A regulatory hierarchy of the Arabidopsis branched-chain amino acid metabolic network[END_REF]. Interestingly, chloroplastic saturated fatty acid and isoprenoid biosynthetic pathways are more active in the light compared to the dark. PEP also provides OAA/malate (via the anaplerotic function of PEP carboxylase) and pyruvate also provides acetyl-CoA (via pyruvate dehydrogenase, PDH) to the TCA cycle in mitochondria. In the light, it is believed that the TCA cycle is slowed down and can operate as two disconnected pathways and not as a cycle (see [START_REF] Sweetlove | Not just a circle: Flux modes in the plant TCA cycle[END_REF][START_REF] Tcherkez | Respiratory carbon fluxes in leaves[END_REF]. Indeed, mitochondrial PDH activity is reduced by a post-translational phosphorylation mechanism and product inhibition [START_REF] Tovar-Méndez | Regulation of pyruvate dehydrogenase complex activity in plant cells[END_REF] and TCA cycle decarboxylation reactions are strongly reduced in the light when compared to the dark [START_REF] Tcherkez | Respiratory metabolism of illuminated leaves depends on CO 2 and O 2 conditions[END_REF]. Therefore, it would be important to maintain the activity of the lower end of cytosolic glycolysis in the light and in the dark to provide PEP and pyruvate for these essential metabolic pathways (see Figure 5). In that context, the activity of iPGAM is important both in light (biosynthesis of PEP which is partly transported to the chloroplast) and in the dark (catabolic activity driven by mitochondrial PDH and the TCA cycle). As such, the change in relative phosphopeptide content (Figure 1) which is accompanied by changes in metabolites (Table 1) could reflect either a decrease in the amount of cytosolic 3-PGA in the dark, and/or a quantitative change in the glycolytic flux. It has been shown that triosephosphate and 3-PGA levels decrease rapidly when leaves are transferred from light to the dark [START_REF] Arrivault | Use of reverse-phase liquid chromatography, linked to tandem mass spectrometry, to profile the Calvin cycle and other metabolic intermediates in Arabidopsis rosettes at different carbon dioxide concentrations[END_REF][START_REF] Voll | Antisense inhibition of enolase strongly limits the metabolism of aromatic amino acids, but has only minor effects on respiration in leaves of transgenic tobacco plants[END_REF]. Under our experimental conditions, darkening was accompanied by a decrease in chloroplastic saturated fatty acids and an increase in TCA cycle organic acids while several branched-chain and aromatic amino acid levels remained unaffected (Table 1, see also Figure 5). Thus, it is also possible that iPGAM activity decreased in darkened leaves as a consequence of a lower demand for glycolytic precursors to fuel metabolic processes occurring in the dark. It is difficult to compare metabolite data obtained from different plant species grown in different light and nutrient conditions. In this work, light versus a light/dark treatment during the day period was used and whole rosettes were sampled. Published data often refer to diurnal changes in metabolite levels of a leaf at a specific developmental stage. When compared to the metabolite changes reported in Tables 1 andS2, higher amounts of certain organic acids associated with the TCA cycle were found in the day compared to the night in tobacco (Nicotiana tabacum) (e.g. Schieble et al., 2000;[START_REF] Voll | Antisense inhibition of enolase strongly limits the metabolism of aromatic amino acids, but has only minor effects on respiration in leaves of transgenic tobacco plants[END_REF]. In potato, citrate was lower, malate was higher and fumarate was unchanged between day and night [START_REF] Urbanczyk-Wochniak | Profiling of diurnal patterns of metabolite and transcript abundance in potato (Solanum tuberosum) leaves[END_REF]. That said, when lighttreated Arabidopsis rosettes were darkened for 15 min a number of metabolite changes were similar to those observed in our conditions (Tables 1 andS2). Indeed, citrate, malate, and succinate were all lower in the light compared to after the dark treatment, and shikimate did not change [START_REF] Arrivault | Use of reverse-phase liquid chromatography, linked to tandem mass spectrometry, to profile the Calvin cycle and other metabolic intermediates in Arabidopsis rosettes at different carbon dioxide concentrations[END_REF]. Perhaps such changes in organic acid levels between our light-and light/dark-treated plants (Table 1) could be interpreted as a less active TCA cycle functioning in the dark. In our study, there was a significant decrease in several saturated fatty acids during the 2 h dark period (Table 1). Such an observation could be expected since fatty acid biosynthesis is known to be stimulated in the light [START_REF] Browse | Light control of fatty acid synthesis and diurnal fluctuations of fatty acid composition in leaves[END_REF] due to activation of acetyl-CoA carboxylase activity by thioredoxin [START_REF] Sasaki | Link between light and fatty acid synthesis: Thioredoxin-linked reductive activation of plastidic acetyl-CoA carboxylase[END_REF] and light-induced changes in pH and Mg 2+ levels in the chloroplast stroma. Branchedchain and aromatic amino acid levels that are dependent on either PEP or pyruvate in chloroplasts were not affected by the dark period after the light treatment except for isoleucine (Table 1). These pathways appear to be mainly regulated by allosteric inhibition of key enzymes [START_REF] Maeda | The shikimate pathway and aromatic amino acid biosynthesis in plants[END_REF][START_REF] Xing | A regulatory hierarchy of the Arabidopsis branched-chain amino acid metabolic network[END_REF].

Conclusions and perspectives

Taken as a whole, our results show that the catalytic mechanism of AtiPGAM2 involves the transient phosphorylation of S82. Under the assumption that the content in S82phosphopeptide reflects steady-state catalysis, in planta iPGAM activity would be higher in the light than in the dark. Future studies are warranted to provide more insights into the possible role of iPGAM in the regulation of metabolism, for example using 13 C-labelled 3-PGA to follow its conversion to 2-PGA in planta under contrasting light conditions. Also, in the mechanism of phosphotransfer catalyzed by iPGAM, uncertainty remains as to whether it is accompanied by a 12 C/ 13 C or 16 O/ 18 O isotope effect. Typically, the abstraction of the phosphate group from C-3 of phosphoglycerate or addition of the phosphate group onto C-2 of glycerate could discriminate against 13 C and/or 18 O. If so, it would affect the isotope natural abundance in metabolites. Future studies will take advantage of isotopic compoundspecific analyses to examine these aspects.

Experimental procedures

Plant material

Arabidopsis thaliana ecotype Columbia (Col-0) seeds were sown and germinated on soil for at least one week before plantlets were transplanted to individual pots for growth in controlled rooms under short-day conditions with an 8 h light regime of 100 μmol photons.m -2 .s -1 and 16 h dark, 20 °C day/18 °C night and 65 % humidity. Phosphoproteome and GC-MS analyses were carried out on Arabidopsis rosettes placed in a home-made cuvette system to measure photosynthetic activities and sampled by spraying with liquid nitrogen after either 4 h in a photosynthetic steady-state under 250 µmol photons.m -2 .s -1 of photosynthetically active radiation and 10 % blue light (light-treated) or after 2 h in darkness following the 4 h light-treatment (light/dark-treated) as described in Boex-Fontvieille et al.

(2014).

Plasmid constructions and site-directed mutagenesis

Cloning of wild-type, S82A and S82D mutated AtiPGAM2 open reading frame (ORF) cDNA into pET16b was performed using the Gibson assembly-based method [START_REF] Gibson | Enzymatic assembly of DNA molecules up to several hundred kilobases[END_REF]. For pET16b-AtiPGAM2 WT , two PCR amplified fragments were assembled, one corresponding to the pET16b backbone using primers pET16b-fw and pET16b-rev and native pET16b as template and the other to generate the AtiPGAM2 ORF using primers iPGAM2-fw16b and iPGAM2-rev16b and AtiPGAM2 ORF cDNA in pUNI51 as template obtained from the Arabidopsis Biological Resource Center as clone U10048 [START_REF] Yamada | Empirical analysis of transcriptional activity in the Arabidopsis genome[END_REF]. For pET16b-AtiPGAM2 S82A and pET16b-AtiPGAM2 S82D , the same strategy was applied except that mutated AtiPGAM2 ORFs were obtained through the assembly of two PCR amplified fragments each obtained with the following primer combinations: (i) iPGAM2-fw16b and iPGAM2S82Arev and (ii) iPGAM2S82Afwd and iPGAM2-rev16b for AtiPGAM2 S82A and (i) iPGAM2-fw16b and iPGAM2S82Drev and (ii) iPGAM2S82Dfwd and iPGAM2-rev16b for AtiPGAM2 S82D . To obtain pET16b-AtiPGAM2 D29N and pET16b-AtiPGAM2 R290L , the previously described pET16b-AtiPGAM2 WT was used as a template for site-directed mutagenesis using the QuikChange Lightning Site-Directed Mutagenesis Kit (Agilent, Santa Clara, CA, United States) and primer combinations [563PRO+564TER] and [565PRO+566TER], respectively. All primer sequences are given in Table S3.

Purification of recombinant proteins E. coli BL21 (DE3) cells containing either pET16b-AtiPGAM2 WT , pET16b-AtiPGAM2 D29N , pET16b-AtiPGAM2 S82A , pET16b-AtiPGAM2 S82D or pET16b-AtiPGAM2 R290L were grown in 400 mL of Luria-Bertani broth supplemented with ampicillin (50 mg.L -1 ) at 37 °C until a OD 600nm of 0.8 was reached then AtiPGAM2 expression was induced by the addition of isopropyl-β-1-D-thiogalactopyranoside (IPTG) 500 µM final concentration. After an overnight culture period at 20 °C, cells were centrifuged and resuspended in lysis buffer (3 mL for a 200 mL culture pellet) containing Tris-HCl 50 mM pH 7.5, NaCl 300 mM, imidazole 5 mM and a tablet of protease inhibitor (Complete Mini, EDTA-free, Roche Applied Science, Penzberg, Upper Bavaria, Germany) and broken by 3 repeated passes through a French press at 3.5 MPa. After a 30 min centrifugation at 4 °C and 27 000 g, recombinant proteins were purified on His-Select nickel affinity resin (P6611, Sigma-Aldrich, Saint-Louis, MO, United States) according to the manufacturer's "batch" protocol. Washing and elution were performed with modified lysis buffer containing 20 mM and 250 mM imidazole, respectively. Eluate was desalted using PD-10 filtration columns (GE Healthcare, Chicago, IL, United States) previously equilibrated with Tris-HCl 50 mM at pH 7.5 following the manufacturer's instructions. Protein concentrations were determined using the Pierce TM Coomassie Plus Assay Reagent (B6916, Sigma-Aldrich) and bovine serum albumin (A4503, Sigma-Aldrich) as the protein standard.

Enzymatic assay

iPGAM activity measurements were carried out at 30 °C using a Varian Cary 50 UV-Vis spectrophotometer (Agilent) at 340 nm, with 2.5 µg of recombinant protein in a 1 mL final volume containing Tris-HCl 30 mM pH 7.5, KCl 20 mM, MgSO 4 5 mM, 3-PGA (0-10 mM), and 2.5 U each of enolase (E6126, Sigma-Aldrich; EC 4.2.1.11), pyruvate kinase (P7768, Sigma-Aldrich; EC 2.7.1.40), and lactate dehydrogenase (L2518 Sigma-Aldrich; EC 1.1.1.27) according to the coupled reaction described by [START_REF] Zhang | Cofactor-independent phosphoglycerate mutase has an essential role in Caenorhabditis elegans and is conserved in parasitic nematodes[END_REF] (see Figure S5). Kinetic parameters were calculated using the "Kinetic Enzyme Wizard" of Sigma-Plot (Systat Software Inc., San Jose, CA, United States).

iPGAM2 phosphopeptide analyses

Recombinant iPGAM2 proteins (2.5 µg) were incubated at 30 °C with selected 3-PGA concentrations during 10 min in a 20 µL reaction buffer Tris-HCl 30 mM pH 7.5, KCl 20 mM, and MgSO 4 5 mM. To test the effect of Mg 2+ , iPGAM2 was also incubated in the absence of added cation in the presence of 2.5 mM 3-PGA. The reaction was stopped by the addition of Laemmli buffer 4X (Tris-HCl 240 mM pH 6.8, SDS 8 % (v/v), glycerol 40 % (v/v), bromophenol blue 0.04 % (w/v), β-mercaptoethanol 10 % (v/v)). Proteins were separated according to their molecular mass by SDS-PAGE (10 % acrylamide) [START_REF] Laemmli | Cleavage of structural proteins during the assembly of the head of bacteriophage T4[END_REF]. The protein band corresponding to iPGAM (61 kDa) was cut from the SDS-PAGE gel for phosphopeptide analysis according to [START_REF] Hummel | Proteomic LC-MS analysis of Arabidopsis cytosolic ribosomes: Identification of ribosomal protein paralogs and re-annotation of the ribosomal protein genes[END_REF]. Phosphoproteome experiments carried out using proteins extracted from rosettes of either light-or light/dark-treated Arabidopsis thaliana plants have been previously described in [START_REF] Boex-Fontvieille | Photosynthetic activity influences cellulose biosynthesis and phosphorylation of proteins involved therein in Arabidopsis leaves[END_REF].

GC-MS-based metabolite profiling

Metabolite profiling and data analyses were performed as described in [START_REF] Bathellier | On the resilience of nitrogen assimilation by intact roots under starvation, as revealed by isotopic and metabolomic techniques[END_REF]. Briefly, 20 mg of leaf powder from lyophilized leaf rosette samples was extracted with 2 mL methanol:water (70:30 v/v) to which ribitol 100 µM was added as an internal standard. Supernatants used for GC-MS (Pegasus III system; Leco, France) analyses were chemically derivatized with methoxyamine and MSTFA in pyridine.

In silico analyses 3D structural models of AtiPGAM2 were made using either SWISS MODEL (https://swissmodel.expasy.org/) or identified in the Swiss Model Repository (SMR; https://swissmodel.expasy.org/repository). Multiple sequence alignment of iPGAM proteins was performed using Clustal Omega (1.2.4).

Data statement

The complete metabolomics data sets are not available in a public repository but they are available on request to michael.hodges@cnrs.fr Table S3: Primers used for cloning and site-directed mutagenesis with their corresponding names, sequences, and Tm °C.

All data supporting the findings of this study are available within the paper and within its supporting information published online.

Table legends Table 1: Metabolite levels of organic acids, fatty acids, shikimate and associated aromatic amino acids, and branched-chain amino acids from light-and light/dark-treated

Arabidopsis rosette leaves

Values are mean ± SD metabolite levels (arbitrary units per g DW) from n=3 independent biological replicates of light-and light/dark-treated Arabidopsis plants. Asterisks correspond to significant difference values between the 2 treatments with the following p-values: **≤ 0.01, *≤0.05 (2-tailed Student's t-test). andR290) and their closest neighbors in dark grey (D472, H473, H141 and R207; for others see Figure S3). Purple lines represent the five interactions of each metal ion with both 3-PGA and the chain. Blue and yellow lines represent respectively the three H-bonds and the 14 salt bridges of the 3-PGA with the chain. Each bond is separately detailed in Figure S3.

Arabidopsis rosette leaves

In the light, photosynthetic CO 2 assimilation by Rubisco leads to the production of 3-PGA which is converted to triose phosphates via the Calvin cycle. Triose-phosphates can be used to make RuBP and starch or exported to the cytosol via a triose-phosphate transporter to make sugars and precursors (PEP and pyruvate) for several metabolic pathways including the TCA cycle in mitochondria, and saturated fatty acid, isoprenoids, branched-chain and aromatic amino acids in chloroplasts. Based on the amount of S82-phosphopeptide, iPGAM activity was higher in our light-treated compared to light/dark-treated Arabidopsis rosettes.

Metabolite profiling showed that in our experimental conditions, saturated fatty acids accumulated in the light while organic acids associated with the TCA cycle increased in the dark. Shikimate and aromatic amino acid levels appeared to be insensitive to the treatments while amongst the three branched-chain amino acids only isoleucine (Ile) levels were significantly increased by the additional dark treatment. Colour codes: Metabolites found to be higher in the light (green), lower in the light (red), no significant difference (blue), not measured (black); ** and * indicate significantly different metabolite levels between the light and light/dark treatments with p-values of ≤0.01 and ≤0.05, respectively (2-tailed Student's t-test). Enzymes (boxed)/pathways activated in the light (green), inactivated in the light (red), unchanged in the light (blue). In the light, the TCA cycle operates in both reverse and forward directions (green lines) (see [START_REF] Tcherkez | In folio respiratory fluxomics revealed by 13 C isotopic labeling and H/D isotope effects highlight the noncyclic nature of the tricarboxylic acid 'cycle' in illuminated leaves[END_REF] The diagram represents the coupled reaction used to measure the AtiPGAM activity according to [START_REF] Zhang | Cofactor-independent phosphoglycerate mutase has an essential role in Caenorhabditis elegans and is conserved in parasitic nematodes[END_REF]: 3-PGA: 3-phosphoglycerate; 2-PGA: 2-phosphoglycerate; PEP: phosphoenolpyrvuvate; iPGAM: cofactor independent-phosphoglycerate mutase; ENO: enolase; PK: pyruvate kinase; LDH: lactate dehydrogenase. Since every step is equimolar, recombinant AtiPGAM2 activity can be measured by the disappearance of NADH detected with a spectrophotometer at A 340 nm .

Figure S6: 3-PGA-dependent iPGAM activity of recombinant wild-type and mutated

AtiPGAM2 proteins

Real-time Varian Cary 50 spectrophotometer traces measuring NADH oxidation at A 340nm and showing the requirement of specific residues for in vitro AtiPGAM2 activity, as measured via the coupled reaction described in the Experimental Procedures and Figure S5.

All iPGAM activities were measured after the addition of 1 mM 3-PGA (blue arrow) and 2.5 µg of recombinant protein (AtiPGAM2 WT , AtiPGAM2 S82A, AtiPGAM2 S82D, AtiPGAM2 D29N, AtiPGAM2 R290L ; black arrow). When S82, D29 or R290 was mutated, 3PGA-dependant iPGAM activity was abolished.

PubMed[uid] Aim of the study

Arabidopsis plant material and growth conditions

Light conditions 17934214

To gain proteomics insight into Arabidopsis cytosolic ribosomal composition and its post-translational modifications.

Arabidopsis thaliana cell culture unspecified 19688752

To investigate protein phosphorylation in purified mitochondria from cell suspensions of the model plant Arabidopsis thaliana

An Arabidopsis thaliana (ecotype Lansberg erecta) cell culture established from callus of stem explants weekly subcultured in MS medium at 22 °C. Prior to mitochondrial isolations cell cultures are maintained in the dark for 7 days at 22 °C continuous dark for 7 days prior mitochondrial isolation 20466843

To investigate the conservation of phosphoproteomes between rice and Arabidopsis (Arabidopsis thaliana) using a novel phosphorylation-site evaluation method

Arabidopsis thaliana cell suspensions line (ecotype Landsberg erecta) grown at 22 °C in MS medium adjusted at pH 5.7, containing sucrose 3% (w/v), MES 3 mM, myoinositol 100 mg.L -1 , thiamine-HCl 10 mg.L -1 , pyridoxine-HCl 1 mg.L -1 , nicotinic acid 1 mg.L -1 , 1-naphthaleneacetic acid 0.5 mg.L -1 , and 6-benzylaminopurine 0.05 mg.L -1 16 h light/8 h dark

22438062

To gain insights into adaptive processes to low Fe availability at the posttranslational level using a quantitative analysis of Fe deficiency-induced changes in the phosphoproteome profile of Arabidopsis (Arabidopsis thaliana) roots

Arabidopsis thaliana (ecotype Columbia-0) seeds were kept for 1 day at 4 °C on Petri dishes in the dark, and transferred to a growth chamber and grown at 21 °C under continuous illumination (50 μmol.m -2 .s -1 ; Phillips TL lamps). The growth medium was made of : KNO3 (5 mM), MgSO4 (2 mM), Ca (NO3)2 (2 mM), KH2PO4 (2.5 mM); H3BO3 (70 µM), MnCl2 (14 µM), ZnSO4

(1 µM), CuSO4 (0.5 µM), NaCl (10 µM), Na2MoO4 (0.2 µM), and FeEDTA (40 µM), solidified with Phytagel (Sigma-Aldrich) (0.3 % w/v). Sucrose (43 mM) and MES (4.7 mM) were included, and the pH was adjusted to 5.5. Arabidopsis thaliana (ecotype Columbia-0) seeds were cold-treated at 4 °C for 2 days and germinated seeds were grown around flasks and temperature at 22 °C in an Innova 4340 illuminated shaker (New Brunswick Scientific) at a speed of 90 rpm. After 7 days, the media were changed in all flasks; some received 1/2 MS (+N) media 100 mL as the control while others received N free (-N) media (no KNO3, which was replaced by KCl 5 mM for N deprivation. On day 8 (24 h after N deprivation), the media were renewed in all flasks. On day 9 (48 h after N deprivation), the media in some of the -N flasks were changed into +N media for recovery and the media in other flasks were renewed with N-free media continuous light of 50 μmol. Arabidopsis thaliana (ecotype Columbia-0) seeds were grown in liquid medium (1/2 MS salts and sucrose (1.5 % w/v)) with 24 h light at room temperature with shaking at 30 rpm. For the osmotic stress treatment, seedlings of 12-day-old were transferred to fresh medium or medium containing mannitol 800 mM for 30 min. For the ABA treatment, the 12-day-old seedlings were transferred to fresh medium containing ABA 100 μM for 30 min continuous light 24043427 To address how ethylene alters the cellular protein phosphorylation profile in a time-dependent manner

Arabidopsis thaliana (ecotypes Columbia-0 and ctr1-1 mutant) were mixed with agar solution (0.1 % (w/v)) and sown on agar growth media containing KNO3 (9 mM), Ca5OH(PO4)3 (0.4 mM), MgSO4 (2 mM), H3PO4 (1.3 mM), Fe-EDTA 50 μM, H3BO3

(70 μM), MnCl2 (14 μM), CuSO4 (0.5 μM), ZnSO4 (1 μM), Na2MoO4 (0.2 μM), NaCl (10 μM), CoCl2 (0.01 μM), sucrose (10 g.L -1 ), thiamine-HCl (1 mg.L -1 ), pyridoxine (0.1 mg.L -1 ), nicotinic acid (0.1 mg.L -1 ), myo-inositol (100 mg.L -1 ), and bacteriological agar (0.8 % w/v, pH 5.7). In each growth jar, 13 to 16 rcn1-1 seeds or 18 to 24 of both ACC-treated wild-type and ctr1-1 seeds were sown. Seeds for the normal size plant were sown about 1.5 to 2 cm apart from each other, and dwarf plants were sown 1 to 1.5 cm apart. In each biological replicate, 10 to 20 jars of Arabidopsis plants were routinely grown for each treated or unique genotype plant group. These jars were then transferred to plant growth chambers with a 16 h light/8 h dark cycle with a constant temperature of 22 °C ± 2 °C 16 h light/8 h dark 23328941

To identify and quantify the early signaling events following lateral root auxin-inducible system using combined (15)N-based metabolic labeling and phosphopeptide enrichment and applied a mass spectrometry-based approach Arabidopsis thaliana (ecotype Columbia-0) seeds were liquid-sterilized and sown on agar (0.6 %) in a hydroponic system supplied with single component B5 medium containing [ 14 N] or [ 15 N] ammonium nitrate and potassium nitrate. Seeds were vernalized for 2 days at 4 °C in the darkness and transferred to long day growth conditions (16 h light/8 h dark) 16 h light/8 h dark 24601666

To obtain high confidence substrate phosphorylation sites and assign them to specific kinases and to search for rapidly phosphorylated proteins in Arabidopsis thaliana in response to bacterial flagellin, a pathogen-associated molecular pattern (PAMP)

Arabidopsis thaliana (ecotype Columbia-0) seeds were surface sterilized and stratified for several days at 4 °C. Seedlings were first grown for 5 days in liquid 1/2 MS medium (M6899, Sigma-Aldrich) containing MES (0.5 g.L -1 ) (M8250, Sigma-Aldrich) pH 5.7 and sucrose 1 % (w/v) (S5016, Sigma-Aldrich) in a culture chamber at 24 °C with a 16 h photoperiod. Then, seedlings were transferred to Erlenmeyer flasks and grown under shaking in the same medium, in the dark, at 25 °C for about 1 month. Plants are grown in the dark to avoid high ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) content in the plant tissues as RuBisCO is the most abundant protein in photosynthetic organisms. The culture in liquid medium allowed applying the PAMP flg22 easily and on a large plant surface. )/12 h dark cycles for 10 days on MS medium plates with sucrose 3 % w/v and agar 1 % w/v at 22 °C. The seedlings were then maintained under constant light and temperature for 24 h before harvesting. The tissues were harvested in tubes containing Zirconia beads at serveral time points during the 12 th day of growth and frozen immediately 12 h light 120 μmol.s -1 .m -2 /12 h dark cycles for 10 days and constant light for 24 h 26187819 To conduct a global and dynamic phosphoproteome profiling across five time points of brassinosteroid treatment in the period between 5 min and 12 h

Arabidopsis thaliana (ecotype Landsberg erecta) cell suspension cultures maintained in MS medium (50 mL) (4.43 g.L -1 ), sucrose (30 g.L -1 ), naphthalene acetic acid (0. mg.L -1 ), kinetin (0.05 mg.L -1 ); adjusted to pH 5.7 with KOH (1 M) at 27 °C under gentle agitation (130 rpm) in the dark. Cells were weekly subcultured in fresh medium at a 1/10 dilutions continuous dark 29167316 To identify substrates of MAPKs likely involved in cell division, growth and development the phosphoproteomes of wild-type and mpk3, mpk4, and mpk6 were compared. To study the function of these MAPKs in innate immunity, their phosphoproteomes were analyzed following microbe-associated molecular pattern (MAMP) treatment

Arabidopsis thaliana (ecotype Columbia-0) was used as wild-type (WT) plant and mpk3-1 (SALK_151594), mpk4-2 (SALK_056245), and mpk6-2 (SALK_073907) as mutants were all grown, treated and harvested as described in [START_REF] Rayapuram | Identification of novel PAMP-triggered phosphorylation and dephosphorylation events in Arabidopsis thaliana by quantitative phosphoproteomic analysis[END_REF], previously described in this table continuous dark during 1 month Supplementary Table S1: List of papers indexed in PhosPhAt 4.0 (http://phosphat.uni-hohenheim.de/), describing phosphoproteomic experiments in which S80/S82 of AtiPGAM1/2 was found phosphorylated

For each occurence of S82-containing phosphopeptide (AHGTAVGLPSEDDMGN(pS)EVGHNALGAGR), PubMed[uid], informations on the aim of the study, the plant material and growth conditions as well as details on light conditions are documented in this table together reference of thecorresponding paper. The last line in yellow describes the paper in which S75 was also annotated as phosphorylated, even if the peptide identified is the same. MS medium: Murashige and Skoog medium; MES: 2-(N-morpholino)ethanesulfonic aci

Metabolite name

Light to Light/Dark ratio p-value 2-hydroxyglutaric acid 0,59 0,03 ± 0,01 0,05 ± 0,02 0,08 ± 0,01 0,28 ± 0,18 0,20 * aspartic acid 0,40 3,30 ± 0,32 8,14 ± 2,04 0,05 ** β alanine 0,63 0,42 ± 0,07 0,66 ± 0,05 0,01 benzoic acid 1,10 0,39 ± 0,04 0,35 ± 0,02 0,29 citramalic acid 0,67 0,12 ± 0,03 0,18 ± 0,03 0,08 ** citric acid 0,45 0,45 ± 0,14 0,99 ± 0,08 0,01 * cysteine 0,53 0,06 ± 0,01 0,10 ± 0,02 0,05 di-galactosylglycerol 1,09 0,16 ± 0,02 0,14 ± 0,03 0,26 ± 0,01 0,28 ± 0,01 0,02 ** threonic acid-1,4-lactone 0,66 0,52 ± 0,04 0,79 ± 0,06 0,00 tyrosine 0,89 0,12 ± 0,01 0,13 ± 0,01 0,11 tyramine 0,58 0,25 ± 0,02 0,43 ± 0,14 0,15 urea 0,77 1,39 ± 0,25 1,80 ± 0,91 0,52 valine 0,85 3,68 ± 0,57 4,31 ± 0,39 0,20 xylose 0,80 0,71 ± 0,11 0,89 ± 0,08 0,08

Figure 1 :

 1 Figure 1: Phosphorylation status of AtiPGAM1/2 phosphopeptide in light-and light/dark-treated ArabidopsisThe histogram shows AtiPGAM1/2 phosphopeptide amounts in rosette leaves from plants initially grown under a short day (8/16 h light/dark) then given either a 4 h light (light) treatment or the same 4 h light followed by a 2 h dark (light/dark) treatment during the natural 8 h day period and further analyzed as previously described by[START_REF] Boex-Fontvieille | Photosynthetic activity influences cellulose biosynthesis and phosphorylation of proteins involved therein in Arabidopsis leaves[END_REF]. Phosphoproteomics analyses were carried with three biological replicates.Statistical significance was determined by a Student's t-test (*p<0.01).

Figure 2 :

 2 Figure 2: AtiPGAM2 3D-structure model Using both modelling and the repository tools of SWISS-MODEL, the 3D structure of AtiPGAM2 was predicted. (a) The protein sequence alignment of AtiPGAM2 (Model_01) and Leshmania mexicana iPGAM (3igy.1.A) (see Figure S2 for its 3D-structure). The two protein sequences share 56.3 % sequence identity. Purple boxes indicate α-helices and green arrows β-sheets. (b) The rainbow-colored 3D-structure of AtiPGAM2 (A0A384KAQ5 from the SWISS-MODEL Repository database) built using 3igy.1 as template with a global model quality estimation (GMQE) of 0.8 (on a scale from 0 to 1). The phosphatase and transferase domains (A and B, respectively) are indicated. This structure includes two metal ions (pink balls) and 3-PGA (see Figure S2 for a Qualitative Model Energy ANalysis (QMEAN) representation). (c) The catalytic core of the enzyme. Insert shows the position of the

Figure 3 :

 3 Figure 3: 3-PGA-dependent S82 phosphorylation of recombinant AtiPGAM2 The effects of 3-PGA concentration and Mg 2+ -dependence on in vitro AtiPGAM2 phosphorylation were analysed. Recombinant AtiPGAM2 WT was incubated for 10 min either in the presence of different 3-PGA concentrations or in the absence of 5 mM Mg 2+ (with 2.5 mM 3-PGA), separated on SDS-PAGE gels before AtiPGAM phosphopeptide amounts were estimated using LC-MS/MS peak areas of phospho-S82 (OP) and non-phosphorylated S82 (OH) containing peptides. The OP/OH ratios were then normalized to those obtained for AtiPGAM2 in the presence of 5 mM 3-PGA. Values are means ± SD (n=4 biological replicates) and statistical significance determined by a Student's t-test (*p<0.01) is shown with respect to 0 mM 3-PGA.

Figure 4 :

 4 Figure 4: S82 phosphorylation of recombinant AtiPGAM2 with altered catalytic mechanism propertiesThe effect of active site-specific mutations that alter either 3-PGA binding (R290L) or phosphate transferase activity (D29N) on the amounts of detected AtiPGAM2 phosphopeptide. Recombinant AtiPGAM2 WT , AtiPGAM2 D29N and AtiPGAM2 R290L were incubated with/without 3-PGA (0 mM and 2.5 mM), and separated on SDS-PAGE gels before AtiPGAM phosphopeptide amounts were estimated using LC-MS/MS peak areas of phospho-S82 (OP) and non-phosphorylated S82 (OH) containing peptides. Value are means ± SD (n=3 biological replicates) and statistical significance was determined by a Student's ttest (*p<0.05).

Figure 5 :

 5 Figure 5: A simplified scheme of PEP and pyruvate-related metabolic pathways and significant changes in metabolite levels observed between light-and light/dark-treated

Figure S1 :

 S1 Figure S1: Duminil et al.

Figure

  Figure S2: Duminil et al.

Figure S5 :

 S5 Figure S5: Duminil et al.

Figure S6 :

 S6 Figure S6: Duminil et al.

Figure S3 :

 S3 Figure S3: AtiPGAM2 structure prediction: catalytic core details. (a-d) are details of the catalytic core in the AtiPGAM2 predicted structure based on 3igy.1 that includes two Co 2+ ions (Co1 and Co2, pink balls) and 3-PGA (C, O, P atoms are grey, red and orange balls, respectively). The catalytic serine 82 (S82) is coloured in green on the chain. All residues involved in the different bonds are licorice represented. (a) Depicts the interactions (purple broken lines) of the first Co 2+ ion (Co1); three interactions with residues D431, H435 and H502 and two with 3-PGA. (b) Depicts the interactions (purple broken lines) of the second Co 2+ ion (Co2); four interactions with residues D29, S82, D472 and H473 and one with 3-PGA. (c) Displays H-bonds (blue broken lines) between the 3-PGA and the chain, one bond with S82 and two with R207. (d) Shows the 14 salt bridges (yellow broken lines) between 3-PGA and the following residues: H141, R171, R207, R214 (2 bonds), R287 (2 bonds), R290, K362, H365, H435 (2 bonds), H473 and H502.

Figure S4 :

 S4 Figure S4: Purification of AtiPGAM2 WT , AtiPGAM2 S82A , AtiPGAM2 S82D , AtiPGAM2 D29N and AtiPGAM2 R290L . SDS-PAGE gels were performed with protein samples collected at different purification steps of AtiPGAM2 WT (His 10 -AtiPGAM2 WT ), AtiPGAM2 S82A (His 10 -AtiPGAM2 S82A ), AtiPGAM2 S82D (His 10 -AtiPGAM2 S82D ), AtiPGAM2 D29N (His 10 -AtiPGAM2 D29N ) and AtiPGAM2 R290L (His 10 -AtiPGAM2 R290L ), and stained with Coomassie blue. Numbers indicate the following purification steps: (1) Proteins from the total bacterial lysate before induction using IPTG; (2) Total proteins from IPTG-induced bacteria collected after the French press; (3) Soluble proteins harvested after centrifugation; (4) Pass-through proteins that did not fix to the Ni 2+affinity resin; (5) Proteins collected after the first washing step; (6) Proteins eluted from the affinity resin using 250 mM imidazole; (7) Desalted proteins. (MM) corresponds to molecular weight markers.

Figure S5 :

 S5 Figure S5: AtiPGAM2 activity measurement with a coupled reaction.

Table 1 : Metabolite levels of organic acids, fatty acids, shikimate and associated aromatic amino acids, and branched-chain amino acids from light-and light/dark-treated Arabidopsis rosette leaves

 1

	. Abbreviations: RuBP,

  Arabidopsis thaliana (ecotype Columbia-0) and srk2dei seeds were sown on germination medium agar plates. After stratification for days at 4 °C, the plates were placed at 22 °C under 16 h light/8 h dark conditions for 2 weeks. After preconditioning plants in water (10 mL) in a plastic plate overnight, 30 to 40 plants were exposed to ABA treatment or dehydration stress as follows. For ABA treatment, plants were placed in (±)-ABA (10 mL of 50 μM) for 0, 15, 30, and 90 min. For dehydration stress, plants were placed on plastic plate without any solution for 0, 15, 30, and 90 min. Plant samples were frozen in liquid nitrogen and stored at -80 °C Arabidopsis thaliana seedlings were grown in half-strength MS medium (40 mL) at 22 °C in continuous light on a rotary shaker set at 100 rpm. Twelve-day-old seedlings were treated with ABA in ethanol (50 μM) or with ethanol as the control for 30 min

					s -1 .m -2
	23172892	To identify and quantify, with high selectivity, site-specific	Arabidopsis thaliana seedlings GVG::FLAG-NtMEK2DD grown in 50 mL 1/2 MS medium at 22 °C in continuous light (70 μmol.s -	continuous light of 70 μmol.s -1 .m -2
		phosphorylation of MPK substrate candidates in the model plant Arabidopsis thaliana	1 .m -2	). Twelve-day-old seedlings were treated with DEX (1 μM) in ethanol or with ethanol as a control and collected 6 h after
	23572148	To identify multiple components of the ABA-responsive protein	treatment	16 h light/8 h dark
		phosphorylation network using the SnRK2 triple mutant
	23111157	To better understand the phosphorylation regulatory network in	Arabidopsis thaliana (ecotype Columbia-0) seedlings hydroponically grown. Briefly, sterilized Arabidopsis seeds were imbibed	continuous light of 50 μmol.s -1 .m -2
		plants	in sterile half-strength MS medium containing MS Vitamin Mixture (Caisson labs, USA), sucrose (0.5 %), MES (3 mM), pH 5.7 at
			a ratio of 10 mg of seeds/100 mL of media. Seeds were cold-treated at 4 °C for 2 days and grown under continuous light of
			50 μmol.s -1 .m -2 at 22 °C in an Innova 4340 illuminated shaker (New Brunswick Scientific) at a 90 rpm speed. After 7 days, the
			media in all flasks were refreshed and after another 2 days, the whole seedlings were harvested and immediately frozen in
			liquid nitrogen
	23776212	To identify additional substrate proteins of the SnRK2s and			continuous light
		provide insight into the molecular actions of ABA using
		quantitative phosphoproteomics to compare the global changes
		in phosphopeptides in WT and snrk2.2/2.3/2.6 triple mutant
		seedlings in response to ABA treatment.
	23660473	To measure phosphoproteome responses to osmotic stress in
		Arabidopsis with a novel mass spectrometry-based label-free
		quantitation method that facilitates systematic profiling plant
		phosphoproteome changes with high efficiency and accuracy

Acknowledgements

This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissement d'Avenir" programme, through the "Lidex-3P" project and a French State Grant (ANR-10-LABX-0040-SPS) funded by the IDEX Paris-Saclay.

This work was also supported by the ANR-14-CE19-0015 grant Regul3P awarded to MH. PD was supported by a PhD grant from the French Ministry of Higher Education and Research.

We would like to thank Samuel Mainguet, Julie Capitanio and Julie Mignon for their contributions to some of the experiments and Jean Vidal for his help with the manuscript.

Authors declare that they have no conflicts of interest. Supplementary Table S3: List of the primers used for the cloning and site directed mutagenesis with the corresponding names, sequences and Tm °C.

Supporting figures

Supporting tables


Julien Dauchy
email: julien.dauchy@cea.fr

Daniel Chatroux

Comparison between energy battery and power one for electrical vehicle applications

In 2009, a presentation was done in PCIM about the experience feedback on electric vehicles of the French car fleet and about the replacement of the initial NiCd battery of an AX vehicle by an iron phosphate Lithium battery with 1600 small cells [1]. Theses cells are power ones. This presentation is a comparison between this power battery and an energy battery in the same format.

The theoretical capacity gain of the energy battery against the power battery is 39 %. However, the theoretical energy density is only 22 % more important because the mass of the energy battery is higher.

The internal resistor of the energy battery is more important than the power battery (around 50% for the tested batteries). During a C/2 discharge, the real energy delivered is approximately equal to the theoretical one. But during a discharge at 1 C or 2 C, the real energy is not as important as the theoretical one because of the internal resistor.

The use of the energy battery is limited for the systems with a low power corresponding to 1 C maximum. A use with a current inferior to 1 C is better. The efficiency is so acceptable. The energy battery can be envisaged for the vehicle with autonomy around 200 km, or higher, where the discharge current is around C / 2. However their use is outlawed in vehicles needed strong current like the hybrid vehicles. For this kind of vehicles, the power battery is better adapted.

To complete this study, one other study is to do to evaluate the degradations of the performances of the batteries with the temperature. Negative temperature can cause an increase in internal resistor and have an effect in the autonomy and in the life time. The impact should be more important for energy batteries.

I. Introduction

Last year a presentation was done in PCIM about the experience feedback on electric vehicles of the French car fleet. The initial NiCd battery of an AX vehicle was replaced by an iron phosphate Lithium battery with 1600 small cells. These cells are power batteries. This presentation compares one other kind of battery (energy battery) in the same format in order to observe the differences and to conclude on the better battery for this vehicle. The conclusion will be extended to other kinds of vehicles.

II. Description of the two kinds of battery compared

The two kinds of batteries have exactly the same dimensions and the same shape. The energy battery has a superior capacitance of 39 %. But because of the mass 14 % higher, the energy density is only 22% more important.

III. Comparison between the real capacitances for different rates of discharge

The different specifications were checked and compared between these two batteries.

Power battery

Energy battery Gain

Real discharge at 0,5 C The table 2 presents the theoretical gain about the capacitance, the energy and the mass between these batteries.

The energy density decreases when the discharge current increases. This phenomenon is due to the internal resistor which is stronger in the energy battery. For the power battery, the internal losses are low.

For a 2 C rate, the energy density of the energy battery is only 13% higher than the power one.

The figure 1 and 2 presents the real curves of capacity for the energy battery and the power battery respectively.

Voltage against capacity Energy battery

IV. Internal resistors

The internal resistor of a battery is a very important characteristic because it is this parameter which defines a great part of the level of thermal lost energy of the battery. To measure this resistor, we discharge the batteries from the total capacity to the minimal with a fixe current of 3 A, and some brief discharges were done at 20 A. The ratio of the voltage difference by the current difference is the internal resistance value.

This work is done for several points all over the discharge.

The figure 3 shows the points done for the two kinds of battery. The internal resistor is sensibly stable during the discharge. The mean resistor of the energy battery is 27 mOhm and only 12 mOhm for the power battery.

Internal resistor

These resistors include the resistors of the connections which are around 3 mOhm for each battery.

V. Charge and discharge curves

The charge and the discharge curves permit to see the evolution of the voltage during the time and to see the stability of the batteries. In this test, the temperature is also measuring to detect the impact of the current on the temperature.

In order to be exactly in the same condition for the two batteries, they were assembly in series and so the current in the two batteries is strictly the same.

The figure 4 shows the voltage and the temperature of the two batteries for two charge and discharge cycles. The current is 1 C for the energy battery and 1.4 C for the power battery.

Of course, the power battery (red curve) is full before the energy battery (pink curve) because his capacity is only 2.3 Ah against 3.2 Ah for the energy battery. This curve (figure 4) shows that the temperature of the energy battery is more important than the power battery. The maximum elevation of temperature is around 10 °C for the energy battery against only 4 °C for the power battery. Moreover, the voltage of the energy battery is more important during the charge and less important during the discharge than the power battery.

The figure 5 In order to highlight this voltage difference, a curve of hysteresis (figure 6) is done for a current of 1 C for the energy battery and 1.4 C for the power battery.

The red curve is the voltage during the charge of the power battery and the pink curve is the voltage during its discharge. And by the same way, the light blue is the voltage during the charge of the energy battery, and the dark blue is the voltage during his discharge.

The red and pink curves are smaller because of the smaller capacity of the power battery.

The hysteresis effect is small for the power battery and very important for the energy battery.

This hysteresis effect traduces directly the internal energy losses, and the temperature rise. The global mass variation is acceptable and is always less than 900 kg.

VI. Conclusion

In this presentation, to kinds of batteries are tested and compared. The two kinds of battery are power and energy batteries.

The theoretical capacity gain of the energy battery against the power battery is 39 %. But the theoretical energy density is only 22 % because the mass of the energy battery is higher.

During a discharge at C/2, the real gain is around the theoretical gain. However, during a discharge at 1 C or 2 C, the gain is not as important as the theoretical gain because of the internal resistor and additional hysteresis losses.

The use of energy battery is well adapted for systems with a current less than 1 C discharge rate. The efficiency is so acceptable with low current.

For the vehicle with high current, superior at 1 C, the power battery is better.

The power battery is well adapted for electrical vehicles with autonomy less than 100 km which need a continuous discharge current more than C (100 km done at 100 km/h, so total discharge in one hour). The energy battery can be used for vehicles with autonomy like 200 km or more, where the continuous discharge current is around C/2.

All of these tests are done for an ambient temperature. It is necessary to study the degradation of the performances and the autonomy where the temperature is negative because of the internal resistor increase. This impact should be more important on energy battery, because the internal resistance and the hysteresis losses are higher.

VII. References

[

Figure 1 :Figure 2 :

 12 Figure 1 : Energy battery: voltage against capacity for several currents

  Figure 3 : Internal resistor comparison

Figure

  Figure 4 : Voltage and temperature curves comparison for a 1 C and 1.4 C current

Figure 5 :

 5 Figure 5 : Voltage and temperature curve comparison for a 2 C and 2.8 C current

Figure 6 :

 6 Figure 6 : Voltage hysteresis comparison

Table 1

 1

	There

Table 2

 2

Table 3

 3

	Last year, the replacement of the initial NiCd
	battery of an AX vehicle by 1600 small
	LiFePO4 batteries was presented. According
	to the results of this presentation, energy
	batteries are well adapted for 200 km range
	with C/2 discharge rate.
	The table 3 compares the performances for
	1600 and 2200 cells for our AX demonstrator.
	If the 1600 actual power cells are replaced by
	1600 energy cells, the autonomy goes up from
	110 km to 147 km. If we used 2200 energy
	cells, the autonomy is 210 km against 151 km
	for 2200 power cells.


Gabriella Bettonte
email: gabriella.bettonte@cea.fr

Stéphane Louise
email: stephane.louise@cea.fr

Renaud Sirdey
email: renaud.sirdey@cea.fr

Two real-time applications of quantum computing for the evaluation of WCETs

Keywords: Calcul quantique, pire temps d'exécution, préemptions, applications temps réel Compas

While the interest in quantum computing is constantly rising, the design of quantum algorithms suitable for real applications is still in its infancy. We hereby investigate the issues of worst-case execution times (WCETs) which are fundamental for the validation of real-time systems in which all time constraints must be met. Since the cache handling in non-deterministic sequence of memory accesses impacts substantially on the execution time, we use it as a case study to design quantum algorithms meant to improve the static analysis of cache misses on programs performing random accesses to the memory and in programs where preemption is allowed. Cache misses are connected to the execution time of a program : for in-order processors, the worst-case execution time is tied to the path with the highest amount of cache misses.

Introduction

The evaluation of worst-case execution-times (WCETs) on real-time applications plays a important role in the validation of real-time systems. It is a requirement that all time constraints are met to ensure the validity of a system but, at the same time, there exists the risk of building an over-engineered, and thus too expensive, system. In other words, a trade-off between precision and efficiency must be reached in the evaluation of WCETs. Quantum computing could bring benefits for this purpose because of its intrinsic parallelism that can boost computations but this also comes with a caveat : one must identify precisely the problems where quantum computing can bring real advantages. In this paper we show two applications of quantum computing applied in the evaluation of WCETs. The first is an evaluation of WCETs in a sequence of memory accesses with some random accesses where usually a classical approach performs poorly. In the second application, the WCETs are evaluated in a deterministic sequence of memory accesses that can be preempted at any time, representing a difficult problem because of its low predictability.

Background overview

In our discussion we use concepts from quantum computing and cache memories, which we briefly overview in this section.

On quantum computing

Classic computers rely on bits, that are deterministic : they can be either on (in the state 0) or off (in the state 1). In contrast, qubits (short for quantum bits) have the capacity of being in a superposition of |0 and |1 (in Dirac notation 1 ). More precisely,

ψ := α |0 + β |1 , | α | 2 + | β | 2 = 1, with α, β ∈ C (1)
A part of the interest that quantum computing arises, comes from the ability of qubits to generate states of superposition that reflect all the possible outcomes of a given algorithm, up until a measurement is done, which is usually at the end of the algorithm. This property is called "quantum parallelism" and could theoretically give a massive performance boost for quantum algorithms. However the advantages of quantum computing is not without caveats : only some classes of problems can be solved by quantum computing with a significant gain in terms of efficiency with respect to classical computing. Indeed, one important research issue related to quantum computing is defining with precision those kinds of problems [START_REF] Nielsen | Quantum Computation and Quantum Information[END_REF].

To give an idea of the momentum the scientific community gives to quantum computing [START_REF] Bravyi | Quantum advantage with noisy shallow circuits[END_REF], the Quantum Algorithm Zoo [START_REF]The quantum algorithm[END_REF] (at the time of writing) cites 430 papers and counting on quantum algorithms, and enterprises such as Google, IBM or Rigetti Computing are investing a lot of resources on research on quantum technologies. Among all quantum algorithms we can identify two main important blueprints. The first one is defined by quantum algorithms able to reach an exponential speedup over classical algorithms on precisely defined and heavily structured mathematical problems, as e.g. Shor's algorithm for integer factorization. The second one is defined by quantum algorithms with a polynomial speedup over classical ones, as e.g. Grover's algorithm for searching an unstructured array. Still, a lot of questions remain open about the real world applications and benefits of quantum computing [START_REF] Hall | A quantum algorithm for software engineering search[END_REF].

On cache memory and WCETs

Real-time systems are computer systems for which processing outcomes must also meet timing constraints which otherwise would jeopardize the real-time system or its environment, potentially including the life of human beings. With respect to the verification of this kind of systems, the evaluation of a WCET for programs and tasks is an important issue. In this context, the behavior of cache memories has usually the most significant impact on the execution-time of programs and must be taken into consideration while evaluating worst-case performance.

Cache memories are used to address the problem represented by the so-called memory wall : the gap between the speed of processors and the memory latencies increases by an order of magnitude every few years. The solution, largely applied since the '80s, has been to add little amounts of high-speed memory close to the processing parts -the cache memories-to provide faster access to a local copy of often or recently used values in memory, thus speeding up the average access time to memory.

The data accessed -and data close to accessed location, to exploit the principle of locality -are copied into the cache memory. The position of the copy inside the cache memory is decided by several parameters including its so-called associativity A -which determines the number of lines in which a particular copy of the memory can reside-size, and replacement policy.

Compas'2021 : Parallélisme / Architecture/ Système/ Temps Réel MILC -Lyon, France, 5-9 juillet 2021

Applications

In this section we present two applications where quantum computing has the potential to be beneficial for the evaluation of WCETs. It is worth noting that the two patterns of work are not yet fully explored but they are the seeds of our future work.

Sequences of random memory accesses

We consider programs that perform non deterministic accesses to the memory, using the count of cache misses as a first proxy evaluation2 of the WCET (or as the literature calls it, the Cache memory related delay). A"dual" approach has already been explored in the literature, with papers about applying static analysis techniques to quantum algorithms to evaluate their performance [START_REF] Facon | Detecting cache-timing vulnerabilities in post-quantum cryptography algorithms[END_REF][START_REF] Abhari | Scaffcc : a framework for compilation and analysis of quantum computing programs[END_REF]. Instead, the applications of quantum computing to improve the static analysis of cache misses (and more largely to static analysis problems at all) has still, to the best of our knowledge, to be fully explored.

We designed an algorithm that, using a quantum-inspired formalism, builds a superposition of all the possible sequences of memory accesses. The superposition produced by the algorithm is suitable to be used as input for a yet to be determined quantum algorithm that will boost the speed-up, allowing to count the worst number of cache misses with increased efficiency (i.e. using less time) with regards to the classical equivalent.

We consider evaluating the WCET with respect to a simple model of program that considers only a sequential sequence of memory accesses, some of which are deterministic, and others non deterministicly chosen from a given subset of memory addresses. We study in the following the case of a direct mapped cache memory (i.e. a block of the main memory can be mapped only to a specific block/line of the cache memory). Despite its simplicity, this non-deterministic model of program we study in this paper is difficult to statically analyze for the evaluation of WCET with classical algorithms 3 . Indeed, the non-deterministic memory accesses produce a large set of possible execution paths for which a non exhaustive analysis can result in a large overestimation of the WCET.

Our algorithm : an overview

The sequence of memory accesses performed by the program, contains non-deterministic accesses which our quantum algorithm superposes in order to take into account, in one execution, the number of cache misses for each possible paths. Our final goal, which is still beyond the scope of this paper, is to design an algorithm that returns (with non negligible probability) the largest number of cache misses over every paths, which should give important hints about the WCET for in-order processors. Since the program performs some non-deterministic accesses to the memory there exist multiple possible linear sequences. Our goal is to exploit the quantum parallelism for computing a superposition of the total number of cache misses over each possible execution path. It is not difficult to produce a superposition of all the possible elements that can be chosen by means of a small network of Hadamard gates, in the example section we will give an hint on how it is possible in practise. For every access to the memory in each possible sequence of accesses, the algorithm checks if a cache miss or hit occurs and modifies the cache's content accordingly : after a cache miss, the accessed element is added to the cache to its assigned place while after a cache hit the cache state does not change (since it is direct-mapped, As final step, we can use one of the many quantum sum operators in the literature, e.g. [START_REF] Cherkas | Quantum adder of classical numbers[END_REF], to perform the sum of the qubits : the obtained value, plus the cache misses we counted before the first non-deterministic access, is the total number of memory-cache misses of the sequence we are considering. The largest value of the total number of cache misses for each possible path can be tied to an estimation of the (cache-related) WCET for the program considered in the case of in-order processors.

Example

We consider a 1-way associative cache with 2 lines. We suppose to have this sequence of accesses :ABABE * AE * where E * = {E, F}. This means we have four deterministic accesses (A, B, A, B, A) and two non-deterministic accesses (E * can be either E or F). We encode the four possible elements we can access to as α 0 α 1 .

A 00 B 01 E 10 F 11

We need 4 qubits to store the state s of the cache : s = s 00 s 01 s 10 s 11 .

s i = 1 if α is in the cache 0 otherwise .
In our example we have four possible situations that can happen : ABABEAE, ABABEAF, ABABFAE and ABABFAF.

At the beginning there are only deterministic accesses : we have 2 cache misses (A,B) and 2 cache hits (A,B). We apply the Hadamard gate on the second qubits to build a superposition of E and F. We provide some details of the miss operator M for our example to give an insight of our algorithm.

0000
|α | s | b -→ |α | s | b ⊕ miss(α, s) (2)
where α is the access, s the cache state and b the target qubit. In particular :

miss(α, s) = m A ∨ m B ∨ m E ∨ m F (3)
More precisely, m e = 1 if we are accessing to the element e and it is not into the cache.

The number of (non-auxiliary) qubits needed by the operator M for our example is (2 + 4 + 1) :

Deterministic memory accesses sequences with preemption

Preemption is the act of interrupting one task to allow the execution of another task on a machine. The advantage is allowing the operating system to allocate the processor to urgent tasks. In particular, in fully preemptive systems, the running task can be interrupted at any time by another task with higher priority and be resumed to continue when all higher priority tasks have completed [START_REF] Buttazzo | Limited preemptive scheduling for real-time systems[END_REF]. When the task is preempted, a large number of memory blocks belonging to the task are flushed away from the cache memory. When the preempted task resumes its execution, a substantial amount of time is spent to reload the cache with the previously displaced memory blocks, leading to a great increase of the task execution time [START_REF] Lee | Analysis of cache-related preemption delay infixed-priority preemptive scheduling[END_REF].Preemption damages program locality and therefore it causes a degradation of system predictability, making WCETs more difficult to characterize and predict [START_REF] Ramaprasad | Tightening the bounds on feasible pre-emption points. 27[END_REF] [8] [START_REF] Buttazzo | Limited preemptive scheduling for real-time systems[END_REF]. The total increase of the WCETs of a task is also a function of the total number of preemptions experienced. The usual approach to evaluate WCETs in case of preemption relies on the analysis of NP-problems i.e. finding the actual points of preemption. With our algorithm we want to avoid the NP-problem because even if we would obtain a decreased execution time, since it would be an exponential order of magnitude we would obtain again an exponential time, being very useful in real-world application.

Our algorithm : an overview

We take into consideration the example of one task producing a deterministic sequence of accesses preempted a fixed number of times k. The approach in [START_REF] Louise | A first step toward using quantum computing for low-level wcets estimations[END_REF] evaluates the WCETs (that is what interests engineers having to design real-time applications) avoiding to compute the exact point of preemptions and obtaining a speed-up. Following this idea, we are working on building a superposition of all the possible sequences of memory accesses to evaluate their execution time at once, in a similar way as the one described in the first application. In parallel, We are developing another approach with the aim of improving the precision, by finding the point of preemption. Being this a NP-problem, as mentioned before, for now we are considering very simple sequences of memory accesses. We designed a dynamic programming algorithm that given the sequence of memory accesses and the number of preemption K finds the "optimal" solution, i.e. the minimum number of cache hit and thus the worst-case scenario. We are working on a quantum version of this algorithm, building a superposition on the possible numbers of preemption k , where k < K. This dynamic programming algorithm, has a polynomial

Conclusion

This paper aims to show the state of our research project until now, and both the applications we described are still work in progress. In the first application we built the superposition of memory accesses sequences but we still need to find a way to exploit its potential to obtain a valuable speed-up in the execution time. In particular, we need to build an oracle (black box) able to amplify the coefficient of the searched sequence (i.e. the one with the highest number of cache misses). In the second application we proposed two different approaches. In the first one we want to obtain a speed up of the computation of WCETs for the preempted sequence of memory accesses, by avoiding to actually find the points of preemption. In this case we still need to build the superposition, but the operators will probably be similar to the one presented for the first application. The second path privileges precision over efficiency, meaning that, on very simple sequences of memory accesses we want to find the points of preemption. To achieve that, we are building the superposition on the number of preemptions, but then we will have to rely on a quantum searching algorithm, such as Grover's algorithm, to actually isolate the solution with the desired number of preemptions. Both the applications we presented in this paper are paths of works that have the ambition of becoming two fully developed contributions in the next months.

  a unique possible position into the cache). We designed a circuit Q that checks if a cache miss occurred, takes note of it and creates a new cache state that contains the considered element. It is worth noting that we have to create a new cache state instead of updating the previous one to maintain the reversibility of the quantum circuit. The circuit Q is the concatenation of the circuits M and N below. The miss operator M is designed to evaluate if the requested data is available in the cache (cache hit) or the program has to access to the main memory (cache miss). The inputs of the miss operator are the accessed data element, the actual state of the cache and a qubit b to store the result : at the beginning b = |0 , while, after the application of the miss operator, the qubit b will be in the state |1 if a cache miss occurred or be left to the state |0 if a cache hit occurred. The operator "Next" N is built to create a new cache state from the previous one. The inputs of the "Next" operator N are : the accessed data element, the current state of the cache and the new state of the cache. It is required to repeat the Q circuit as many times as the number of accesses the program performs after the first non-deterministic access). The picture in the appendix represents the main flow of the algorithm. In this figure two iterations of the algorithm are represented. The number of qubits required to represent the considered access or cache state is indicated on the right. As result of the previous steps, we have m cache misses wires (i.e. qubits) : the wires associated to a cache miss are in the state |1 while the wires associated to a cache hit are in the state |0 .

	Compas'2021 : Parallélisme / Architecture/ Système/ Temps Réel
	MILC -Lyon, France, 5-9 juillet 2021
	every element has

This is true especially for in-order execution for which the execution-time grows monotonically with the number of memory cache misses.

It is worth noting that despite its apparent simplicity any single-threaded program is amenable to our model, by replacing at relevant points in the execution, accesses on different branches of the control-flow graph by a corresponding number of non-deterministic accesses.