Armelle Vigouroux

Magali Aumont-Nicaise

Alain Boussac

Loïc Marty

Lo Léa

Pierre Bello

Karl Legrand

Isabelle J Brillet

Solange Schalk

Moréra

Léa Lo Bello

Pierre Legrand

Karl Brillet

Isabelle J Schalk

Solange Moréra
email: solange.morera@i2bc.paris-saclay.fr

A unique ferrous iron binding mode is associated to large conformational changes for the transport protein FpvC of Pseudomonas aeruginosa

Keywords: iron, solute-binding protein, siderophore, pyoverdine, Pseudomonas aeruginosa PVD, pyoverdine, EPR, electron paramagnetic resonance, SBP, solute-binding protein, RMSD, root mean square deviation, PDB, protein data bank, EDTA, ethylenediaminetetraacetic acid, TCEP, Tris(2-carboxyethyl)phosphine, ITC, isothermal titration microcalorimetry, CD, circular dichroism, DSC, Differential scanning calorimetry

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

Introduction

Under physiological conditions, iron mainly exists in one of two readily interconvertible redox states: the reduced Fe 2+ ferrous form and the oxidized Fe 3+ ferric form. Nonetheless, Fe 2+ is rapidly oxidized into Fe 3+ in the presence of oxygen and precipitates as a polymeric oxyhydroxide. In order to overcome the problem of iron solubility and availability, Gram-negative bacteria produce and secrete siderophores which are high-affinity extracellular chelators of ferric iron. Thus, they scavenge iron in the bacterial environment prior its transport into bacteria and its use as an essential nutrient [START_REF] Lyczak | Establishment of Pseudomonas aeruginosa infection: lessons from a versatile opportunist[END_REF][START_REF] Boukhalfa | Chemical aspects of siderophore mediated iron transport[END_REF]. The recognition and import of siderophore-Fe 3+ complexes across bacterial outer membrane in Gramnegative bacteria involves specific outer membrane transporters [START_REF] Schalk | Structure, function and binding selectivity and stereoselectivity of siderophore-iron outer membrane transporters[END_REF]. Once in the periplasm, some siderophores will release their iron ion in this cell compartment whereas others will cross the inner membrane and deliver it in the cytoplasm [START_REF] Schalk | Fate of ferrisiderophores after import across bacterial outer membranes: different iron release strategies are observed in the cytoplasm or periplasm depending on the siderophore pathways[END_REF]. Mechanisms of iron release from siderophores usually involve an iron reduction step associated sometimes with hydrolysis or chemical modification of the siderophores [START_REF] Schalk | Fate of ferrisiderophores after import across bacterial outer membranes: different iron release strategies are observed in the cytoplasm or periplasm depending on the siderophore pathways[END_REF].

The World Health Organization recently defined a global priority pathogen list of antibiotic-resistant bacteria for prioritization of research and development of new antibiotics (http://www.who.int/medicines/publications/WHO-PPL-Short_Summary_25Feb-ET_NM_WHO.pdf).

Pseudomonas aeruginosa, which is an opportunistic human pathogen, belongs to the first list as a critical pathogen, produces and secretes a major siderophore pyoverdine (PVD) to acquire iron [START_REF] Schalk | Pyoverdine biosynthesis and secretion in Pseudomonas aeruginosa: implications for metal homeostasis[END_REF].

PVD, which is composed of a dihydroxyquinoline-type chromophore linked to an octapeptide chain [START_REF] Schalk | Pyoverdine biosynthesis and secretion in Pseudomonas aeruginosa: implications for metal homeostasis[END_REF], scavenges iron in the bacterial environment, and the formed complex is reabsorbed across the outer membrane by the transporters FpvA and FpvB [START_REF] Poole | Cloning and nucleotide sequence analysis of the ferripyoverdine receptor gene fpvA of Pseudomonas aeruginosa[END_REF][START_REF] Ghysels | FpvB, an alternative type I ferripyoverdine receptor of Pseudomonas aeruginosa[END_REF][START_REF] Brillet | A beta strand lock exchange for signal transduction in TonB-dependent transducers on the basis of a common structural motif[END_REF]. Iron release from this siderophore into the periplasm involves an iron reduction by the inner membrane reductase FpvG and a recycling of the apo PVD into the extracellular medium by the efflux system PvdRT-OpmQ [START_REF] Schalk | Recycling of pyoverdin on the FpvA receptor after ferric pyoverdin uptake and dissociation in Pseudomonas aeruginosa[END_REF][START_REF] Greenwald | Real time fluorescent resonance energy transfer visualization of ferric pyoverdine uptake in Pseudomonas aeruginosa. A role for ferrous iron[END_REF][START_REF] Yeterian | An efflux pump is required for siderophore recycling by Pseudomonas aeruginosa[END_REF][START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF]. Iron acquisition by PVD involves as well a SBP-mediated transport system composed of two SBPs, namely FpvF and FpvC [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF][START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF]. FpvC and FpvF have been shown to bind together and form a FpvF-FpvC-siderophore-iron complex in the periplasm [START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF]. The PVD-Fe 3+ complex is probably first

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scavenged by the FpvF-FpvC complex before iron reduction and dissociation from PVD [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF][START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF].

FpvC, is proposed as the Fe 2+ chelator in the mechanism of iron release from PVD which brings the ferrous iron to the ABC transporter FpvDE for its translocation into the cytoplasm [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF]. Previous primary sequence alignment [START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF] indicated that FpvC (317 amino-acid) belongs to a subgroup of the TroA-like SBPs superfamily [START_REF] Lee | Treponema pallidum TroA is a periplasmic zinc-binding protein with a helical backbone[END_REF]. According to Berntsson and coworkers [START_REF] Berntsson | A structural classification of substrate-binding proteins[END_REF] who established a cluster system of SBPs classification based on both structural and functional properties, these TroAlike SBPs belongs to the cluster A-1. These SBPs are described as binding different metal ions including Mn 2+ , Fe 2+ /Fe 3+ , Cu 2+ and/or Zn 2+ and sharing a similar fold composed of two-domain organization connected by a single long -helix. The canonical binding metal ion site is located at the interface of the two domains and is formed by amino-acids from each domain.

In this study, we investigated the structural and biochemical properties of the SBP FpvC from P. aeruginosa PAO1 to identify the bound iron redox state and its binding mode. We first structurally characterized the metal binding site of FpvC via a fortuitous bound Ni 2+ from two crystal forms at 1.65 Å and 1.92 Å resolution. Indeed, purification of the His-tag FpvC using nickel-affinity chromatography led to a nickel complex. The structure of a bound iron to His-tag FpvC binding site was obtained from a protein expressed under minimal-media with iron supplementation and purified with an ion-exchange chromatography. Electron paramagnetic resonance (EPR) allowed the determination of the redox state of the bound iron after treatment of FpvC-iron complex with ferricyanide. The coordination of the ferrous ion in FpvC with an octahedral geometry involving six histidines is so far unique among SBPs and iron binding proteins, which display a hexahistidine motif via oligomerization. The structure of apo FpvC at 2.1 Å resolution was obtained from the mutant FpvC-H6G where the six chelated histidines were replaced by glycines. This work provides new insights into the mechanism of PVD-Fe dissociation in P. aeruginosa and the large conformational changes that FpvC might undertake under this process. Moreover, it also widens our knowledge on the cluster A-1 SBPs about the canonical metal binding site and protein flexibility.

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Results

FpvC, a SBP from cluster A-1. The mature FpvC expression plasmid is a synthetic gene lacking the first 37 signal sequence residues that serve for the localization to the bacterial periplasm. Nonetheless, the expressed protein contains a C-terminal sequence of 13 residues composed of a TEV cleavage site and a His-tag. The numbering used for the description of residues corresponds to the mature protein of 317 amino acids. Since FpvC shares low sequence identity (less than 26%) with SBPs of known threedimensional structure, we determined the structure of His-tag FpvC by single anomalous dispersion (SAD) at the absorption K-edge of nickel and refined the model up to 1.65 Å resolution (Table 1, Figure 1a). The monomeric FpvC fold consists of a N-terminal domain (residues 41-170) and a Cterminal domain (residues 199-316) with a long helix (residues 171-198) connecting the two domains.

The identity of the fortuitous Ni 2+ ion in the crystal was determined from an X-ray fluorescence spectrum measured at SOLEIL synchrotron beamline PROXIMA 2. The Ni 2+ ion likely came from the nickel-affinity chromatography used to purify FpvC. The FpvC-Ni 2+ complex also crystallized in P2 1 space group with two identical molecules (root mean square deviation (RMSD) of 0.24 Å for all C atoms) in the asymmetric unit using the same crystallisation conditions (Table 1) and its structure was determined by molecular replacement at 1.99 Å resolution using the model determined in the P2 1 2 1 2 1 space group. The three FpvC-Ni 2+ molecules from both crystal forms are very similar as indicates the average RMSD of 0.4 Å for all Cα atoms.

Modifying the purification protocol of His-tag FpvC expressed under minimal-media and iron supplementation allowed us to obtain the structure of an iron-FpvC complex and a manganese-FpvC complex (Table 1, Figures 1b-c). X-ray fluorescence measured at the synchrotron beamline detected only one type of metal per crystal and identified the presence of iron or manganese in the crystal. The structures of FpvC-iron and FpvC-manganese were determined at 2.75 Å and 2.49 Å resolution, respectively, by molecular replacement using the coordinates of the FpvC-Ni 2+ complex obtained at high resolution. The asymmetric unit of FpvC-iron and FpvC-manganese structures contain two and four identical molecules, respectively (RMSD of 0.23 Å and average RMSD of 0.28 Å for all Cα atoms, respectively).

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All metal-FpvC structures are very similar (average RMSD of 0.35 Å for all Cα atoms) with the loop region 132-141 highly flexible and thus not defined in electron density maps, except for one molecule in the FpvC-Mn 2+ structure (molecule A) where the loop main-chain could be almost built in the electron density maps.

Metal binding site of FpvC. Electron density maps could not discriminate the redox status of the bound iron (Fe 2+ or Fe 3+ ). Because X-ray photoreduction occurs during data collection [START_REF] Sigfridsson | Rapid X-ray photoreduction of dimetal-oxygen cofactors in ribonucleotide reductase[END_REF], the ferrous ion is the form present in the structure, bringing no information on the Fe redox state before X-ray exposure. Therefore, an EPR control was realized to determine the redox state of the iron bound to FpvC in solution. EPR measurements were performed at 4.2 K at both pH 6.5 and 8, corresponding to the protein crystallisation and protein purification buffers, respectively. Spectrum a in Figure 2 shows the EPR spectrum recorded on the purified His-Tag FpvC-iron complex (60 µM) at pH 8. The spectrum was identical for His-Tag FpvC-iron complex at pH 6.5 (data not shown). Signals were detected at g = 9.5 (710 gauss) and g = 4.28 (1585 gauss). The amplitude of these two signals increased upon the addition of 30 µM potassium ferricyanide (spectrum b) and further increased upon the addition of 60 µM potassium ferricyanide (spectrum c). The broad signal at 2500 gauss originated from the ferricyanide in excess, which was not reduced in the presence of the protein. These data showed that FpvC binds the ferrous iron form and that this iron is oxidable by ferricyanide. The detection of a ferricyanide signal at concentrations half and similar to that of the protein indicates that the redox potential of the iron is close to 400 (± 60) mV vs NHE. From the shape of the EPR spectrum, the zero field splitting parameter E/D of Fe 3+ was in an almost completely rhombic environment [START_REF] Peisach | An analysis of the electron paramagnetic resonance spectrum of pseudomonas oleovorans rubredoxin. A method for determination of the liganids of ferric iron in completely rhombic sites[END_REF]. The same experiment was performed on the crystals of FpvC-iron complex before X-ray exposure leading to the same result (data not shown).

The bound Ni 2+ , Fe 2+ and Mn 2+ ions are located at the same positions in the cleft between the two domains of FpvC. Their near-perfect octahedral geometry involves six histidines (His77, His102 and His147 from the N-terminal domain and His213, His235 and His286 from the C-terminal domain)

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FpvC presents a distinct metal-binding site compared to all other metal-binding SBPs described so far.

Previous structures of cluster A-1 SBPs showed four metal-coordinating amino-acids, either 2 His and 2 carboxylates (Glu/Asp) or 3 His and 1 carboxylate (Asp) leading to a tetrahedral or a highly distorted octahedral geometry [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF][START_REF] Zheng | Insight into the interaction of metal ions with TroA from Streptococcus suis[END_REF]. FpvC is the first example with a hexahistidine metal site among SBPs. The comparison of its metal binding site with its closest homologue YfeA from Yersinia pestis (His76, His141, Glu207 and Asp 282; PDB 5UYE [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF]) shows that only one conserved histidine superimposed (His147 in FpvC and His141 in YfeA) (Figure 1h). The other conserved histidine (His77 in FpvC) is separated from 3.2 Å from His76 in YfeA. His213 in FpvC corresponds to Glu207 in YfeA. The three remaining histidines in FpvC (His102, His235, His286) have no structural equivalent amino-acid within cluster A-1 SBPs and the conserved aspartate (Asp282 in YfeA) of cluster A-1 SBPs has no structural equivalence in FpvC (Figure 1h).

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FpvC displays large conformational changes. All attempts to crystallize FpvC in its apo form were unsuccessful. Thus, we circumvented the issue by using FpvC-H6G, a mutant in which the six metalliganded histidines were replaced by glycine residues to mimic the metal-free SBP. Indeed, FpvC-H6G is no longer able to bind a metal ion [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF]. All of the six histidines belong to loop regions connecting secondary structural elements, therefore mutating them will likely not affect the secondary structure of the protein.

To check this, we determined and compared the secondary structure of apo FpvC and FpvC-H6G mutant by circular dichroïsm. Both proteins share the same secondary structure content in line with what is observed in the crystal structure of FpvC-H6G (Figures 3 and4 and Table 3). The 2.1 Å structure of FpvC-H6G contains two very similar molecules in the asymmetric unit as indicates the average RMSD of 0.66 Å for all Cα atoms. The structure reveals an open conformation with the site including the 6 Gly residues exposed to the solvent. In contrast to the metal-liganded structures, the full protein is defined in the electron density maps and the flexible loop (residues 132-141) is now very well defined and includes an extra helix (residues 135-139) (Figure 4a).

Superposition of the overall structures of the metal-free FpvC-H6G (apo) and metal-bound FpvC

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terminal domain are unchanged (Figure 4b), because they are deeply buried at the back of the metal cleft. This is not the case for His77, His213 and His235, which are close to the opening of the cleft and thus exposed to solvent in the free-metal form. As it may be expected, these three histidines can move to form the metal binding site upon metal binding.

FpvC can bind a broad range of divalent metals. Using thermal denaturation experiments by differential scanning calorimetry (DSC), a Tm of 58.96 ± 0.002°C was measured with the purified mature FpvC (30 M) devoid of any tag and endogenous metal (Figure 5a, Table 4). Indeed, this Tm was very similar to that (58.97 ± 0.002°C) of FpvC treated with 1 mM EDTA, a strong chelating agent (Figure 5a, Table 4). FpvC and the reductant agent TCEP led to the same Tm showing that TCEP had no effect on the protein (Figure 5a, Table 4). Although glycine can access a greater range of backbone conformations and allows more flexibility on main chain protein, the FpvC-H6G mutant is more stable than the wild-type apo FpvC with a Tm of 62.23 ± 0.002°C (Figure 5a, Table 4).

DCS analyses revealed that Fe 3+ did not alter the Tm of apo FpvC whereas a significant shift by ~5°C was observed with Fe 2+ and was more pronounced ~7°C with Fe 2+ and TCEP (Figure 5b, Table 4).

The presence of Fe 3+ and TCEP induced two peaks, one corresponding to the Tm of the apo FpvC and the second to that of FpvC in the presence of Fe 2+ meaning that TCEP, as expected, can reduce Fe 3+ into Fe 2+ (Figure 5b, Table 4) and that FpvC binds only Fe 2+ and not Fe 3+ . Larger very similar shifts (> 25°C) were observed for Zn 2+ , Mn 2+ , Ni 2+ and an intermediate shift (< 15°C) was present with Mg 2+ and Ca 2+ . Adding Co 2+ , Cu 2+ and Ca 2+ to FpvC showed two similar peaks, one corresponding roughly to the intermediate shift and the other one to the larger shift (Figure 5c, Table 4). Addition of EDTA to any FpvC-metal ions complex resulted in an apo FpvC behaviour. Therefore, EDTA can remove each metal including those responsible for the highest Tm able to strongly stabilize FpvC.

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Binding of Ni 2+ , Zn 2+ and Fe 2+ with TCEP to FpvC was explored using ITC (Figure 6). Similar dissociation constant K D values of 0.19 ± 0.02 M, 0.29 ± 0.07 M and 0.39 ± 0.11 M were measured with Ni 2+ , Zn 2+ and Mn 2+ , respectively, in agreement with the DSC results where a similar Tm values were observed. As expected from the DSC data, the affinity of FpvC for Fe 2+ (K D of 6.3 ± 2 M) is lower than those for Ni 2+ , Zn 2+ and Mn 2+ (Figure 6). The microcalorimetry data confirmed the 1:1 binding stoichiometry and revealed a negative enthalpy change. No interaction could be measured between FpvC and PVD or PVD-Fe 3+ compounds, confirming that FpvC is unable to bind this siderophore [START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF].

Discussion

A hexahistidine metal ion binding site for the SBP FpvC

This work reveals the structural basis of the SBP FpvC, showing that FpvC belongs to the cluster A-1

of SBPs and displays a canonical metal binding site referred as site 1 for all orthologues. In contrast to the closest structural orthologue Yfea from Y. pestis [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF] and its related ZnuA from E.coli [START_REF] Yatsunyk | Structure and metal binding properties of ZnuA, a periplasmic zinc transporter from Escherichia coli[END_REF] or MtsA from S. pyogenes [START_REF] Sun | Crystal structure and metal binding properties of the lipoprotein MtsA, responsible for iron transport in Streptococcus pyogenes[END_REF], FpvC does not possess other metal binding sites. The presence of the fortuitous nickel in FpvC was unexpected and FpvC likely grabbed the nickel ion during the first step of protein purification. The presence of the iron ion in FpvC was not obvious because the purified protein and the crystals did not show any colour or any unusual spectroscopic properties in the UV-Vis spectrum:

iron ions often absorb in visible light wavelength ranges, giving rise to a red colour for hemes and a brownish colour for Fe-S clusters. However, X-ray fluorescence emission scan on each metal crystal showed the presence of either a nickel or an iron. The presence of Fe 2+ bound to FpvC in solution and in the crystals prior to X-ray exposure was confirmed by EPR experiments. EPR detects ferric iron in complex with proteins and not ferrous iron. In the case of purified FpvC-Fe, no iron was observed by EPR, but only after iron oxidation by potassium ferricyanide, proving that the purified FpvC-Fe complex contains the metal under its ferrous form. According to the EPR spectrum of FpvC-Fe (spectrum a in Figure 2), the purified FpvC molecules were loaded with ferrous iron although the

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overall purification process was done under aerobic conditions. This indicates that the hexahistidine site of FpvC has a remarkable ability to stabilize Fe 2+ and protect it from natural oxidation.

Another remarkable outcome was that FpvC possesses a canonical metal site, which is atypical in residue composition and distinguishes FpvC from all other cluster A-1 SBPs. Indeed, FpvC displays a hexahistidine coordination site instead of the classical tetracoordinate site through either 2 histidines and 2 carboxylates (Glu/Asp) or 3 His and 1 Asp. These latter four amino-acids have been mentioned

as evolutionarily conserved across SBPs from cluster A-1 [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF]. In contrast, similar hexahistidine coordination of metal has been observed so far in few proteins: the human metal-sequestering hostdefence protein calprotectin (PDBs 4GGF [START_REF] Damo | Molecular basis for manganese sequestration by calprotectin and roles in the innate immune response to invading bacterial pathogens[END_REF] and 5W1F [START_REF] Nakashige | Nickel Sequestration by the Host-Defense Protein Human Calprotectin[END_REF]), the -crystallin from M. thermophile (PDB 5HT7) [START_REF] Srivastava | A Transition Metal-Binding, Trimeric betagamma-Crystallin from Methane-Producing Thermophilic Archaea, Methanosaeta thermophila[END_REF], the membrane-piercing proteins gpV (PDB 3QR7) [START_REF] Browning | Phage pierces the host cell membrane with the iron-loaded spike[END_REF] and gp138 (PDB 3PQH) [START_REF] Browning | Phage pierces the host cell membrane with the iron-loaded spike[END_REF] of bacteriophages P2 and 92, respectively, and the receptor-binding domain of phage T4 (PDB 2XGF) [START_REF] Bartual | Structure of the bacteriophage T4 long tail fiber receptor-binding tip[END_REF] and phage 11 (PDB 5EFV) [START_REF] Koc | Structure of the host-recognition device of Staphylococcus aureus phage varphi11[END_REF], all able to chelate iron. It is noteworthy that, unlike the monomeric FpvC, all these proteins are oligomeric and their binding metal site is formed at the oligomeric interface. Indeed, the dimeric human calprotectin brings 2 histidines from a monomer and 4 from the other to create the metal site. The remaining proteins are trimeric and each monomer contains a pair of histidines. Three pairs of these histidines create a nearly perfect octahedral coordination shell for the iron ion positioned along the 3-fold axis of the trimer. It is also noteworthy that these phage proteins and FpvC are all colourless in solution [START_REF] Browning | Phage pierces the host cell membrane with the iron-loaded spike[END_REF][START_REF] Bartual | Structure of the bacteriophage T4 long tail fiber receptor-binding tip[END_REF][START_REF] Koc | Structure of the host-recognition device of Staphylococcus aureus phage varphi11[END_REF] meaning that the metalbinding hexahistidine site does not allow any iron colour observation. In agreement, crystals of [Fe(imidazole) 6 ] 2+ are colourless [START_REF] Carver | Spectroscopic and structural characterization of the [Fe(imidazole)(6)](2+) cation[END_REF].

Large conformational changes upon ligand binding

Here, we also showed that FpvC is a flexible protein. Several attempts to obtain the structure of apo FpvC were unsuccessful. In contrast, crystals of the FpvC-H6G mutant, which mimics the wild-type apo FpvC, led to reproducible crystals with good diffraction. This mutant with the hexahistidine

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involved in iron chelation replaced by hexaglycine is more stable than the wild-type apo FpvC, which may explain its crystallization success. The metal-induced structural rearrangement of the C-terminal domain to close the metal binding site can be illustrated by the comparison of free (mutant) and metalbound structures. Upon metal-binding, FpvC displays a very similar loss of secondary structure of the C-terminus of the inter-domain helix, as described for PsaA [START_REF] Counago | Imperfect coordination chemistry facilitates metal ion release in the Psa permease[END_REF]. This helix initially proposed as rigid was thought to preclude large conformational motion. There are now two examples of cluster A-1

SBPs where a rather large conformational change of this helix can occur leading to a rigid-body movement of 13° of the C-terminal domain of PsaA and to an internal rearrangement of the Cterminal domain up to 12.7 Å in FpvC. Moreover, Radka and co-workers [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF] suggest that structural rearrangement is required for metal loading and unloading in YfeA and its was shown that metal binding in TroA induces distinct conformational changes by circular dichroism and NMR [START_REF] Zheng | Insight into the interaction of metal ions with TroA from Streptococcus suis[END_REF].

Therefore, all characterized SBPs clusters [START_REF] Berntsson | A structural classification of substrate-binding proteins[END_REF] including cluster A are subject to conformational changes induced by ligand binding and present a diversity in conformational and dynamic plasticity [START_REF] De Boer | Conformational and dynamic plasticity in substrate-binding proteins underlies selective transport in ABC importers[END_REF].

The physiological ligand of FpvC

The protein calprotectin has been shown to be a polyspecific metal protein, able to bind Mn 2+ , Ni 2+ , Zn 2+ and Fe 2+ in the hexahistidine site [START_REF] Nakashige | Nickel Sequestration by the Host-Defense Protein Human Calprotectin[END_REF][START_REF] Nakashige | Human calprotectin affects the redox speciation of iron[END_REF]. Its structure with a Ni 2+ bound to the hexahistidine motif was reported as unique in 2017 among structurally characterized nickel proteins [START_REF] Nakashige | Nickel Sequestration by the Host-Defense Protein Human Calprotectin[END_REF]. FpvC is now the second example. Using DSC and ITC, we showed that FpvC like calprotectin is polyspecific and can bind different divalent metal including Fe 2+ , Mn 2+ , Ni 2+ , and Zn 2+ . Unlike calprotectin which has a preference for Ni 2+ over Zn 2 , FpvC displays the same affinity for Ni 2+ , Zn 2+ and Mn 2+ which is higher than that for Fe 2+ . This result seems not in agreement with the Irving-Williams series [START_REF] Nakashige | Nickel Sequestration by the Host-Defense Protein Human Calprotectin[END_REF] (Mg 2+ < Mn 2+ < Fe 2+ < Co 2+ < Ni 2+ < Cu 2+ < Zn 2+ ) showing that in the case of FpvC, Mn 2+ and Ni 2+ are thermodynamically favoured over Zn 2+ for an octahedral coordination site. Nonetheless, Fe 2+ and Co 2+ , which also favour octahedral geometry present a lower affinity compared with Mn 2+ . Therefore, other factors such as coordinating environment in terms of geometry, amino acids composition and

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flexibility offered by the metal-binding site may be important for metal specificity. However, in a biological context, the trend of the Irving-Williams series could break to acquire to true metal ligand [START_REF] Dudev | Metal binding affinity and selectivity in metalloproteins: insights from computational studies[END_REF][START_REF] Waldron | Metalloproteins and metal sensing[END_REF]. Thus, in the context of FpvC, its interaction with other periplasmic proteins such as the SPB FpvF might be a critical control point.

Prior works on cluster A-1 SBPs (PsaA, ZnuA, TroA and the most recent on YfeA) showed that these proteins are also capable of interaction with a broad range of metal ions and thus appear to be polyselective [START_REF] Radka | Crystal structure of Yersinia pestis virulence factor YfeA reveals two polyspecific metal-binding sites[END_REF][START_REF] Zheng | Insight into the interaction of metal ions with TroA from Streptococcus suis[END_REF][START_REF] Yatsunyk | Structure and metal binding properties of ZnuA, a periplasmic zinc transporter from Escherichia coli[END_REF][START_REF] Counago | Imperfect coordination chemistry facilitates metal ion release in the Psa permease[END_REF]. These reported metal binding properties emanate from experiments performed in vitro and often, raise the question: what is (are) the physiological ligand(s) of each SBP?

Although FpvC can bind similarly and preferentially several divalent cations other than Fe 2+ in vitro, it is likely dedicated to iron transport in vivo. Uptake experiments of PVD in complex with metals other than iron showed that these PVD-metal complexes do not accumulate and dissociate in P. aeruginosa cells. In contrast, they are expelled from the periplasm by the efflux system PvdRT-OpmQ [START_REF] Hannauer | The PvdRT-OpmQ efflux pump controls the metal selectivity of the iron uptake pathway mediated by the siderophore pyoverdine in Pseudomonas aeruginosa[END_REF] showing that FpvC has probably access only to ferrous iron in P. aeruginosa periplasm.

fpvC gene and genes involved in iron acquisition by PVD belong to the PVD loci. Their transcription/expression is regulated by the intracellular iron concentration in P. aeruginosa cells and probably not by any other metal (Lopez et al., in Enviromn Microbiol under revision). When iron becomes limited, the sigma factors PvdS and FpvI activate the transcription of the PVD loci genes including fpvC gene in order to produce PVD and express the proteins necessary to get access to iron via this siderophore [START_REF] Visca | Iron transport and regulation, cell signalling and genomics: lessons from Escherichia coli and Pseudomonas[END_REF]. On the opposite, in the presence of iron in excess, the transcriptional regulator Fur in complex with ferrous iron (Fur-Fe 2+ ) represses the expression of all these genes [START_REF] Visca | Iron transport and regulation, cell signalling and genomics: lessons from Escherichia coli and Pseudomonas[END_REF].

Moreover, a deletion of fpvC affects iron acquisition by PVD [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF]. Native mass spectrometry showed that FpvC interacts with the SBP FpvF (a ferrisiderophore SBP) as well as the FpvF-PVD-Fe complex [START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF]. Cross-linking approaches on P. aeruginosa cells incubated in the presence of PVD-Fe 3+ confirmed the existence of such complexes in vivo. At last, in vitro PVD-Fe dissociation assays using DTT as an iron reducer and ferrozine as a ferrous iron chelator indicated that FpvC can like ferrozine chelate ferrous iron [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF]. According to our current knowledge of this biological system, the PVD-Fe 3+

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complex is probably first scavenged by the FpvF-FpvC complex before iron reduction and dissociation from PVD [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF][START_REF] Brillet | An ABC transporter with two periplasmic binding proteins involved in iron acquisition in Pseudomonas aeruginosa[END_REF]. In such a mechanism, only iron can be reduced and transferred from PVD to FpvC.

Taken together, all these data in addition to the present EPR experiment and structural data clearly proof that in the mechanism of iron dissociation from PVD in the bacterial periplasm, ferric iron, after having been reduced by the inner membrane FpvG, is transferred from PVD to FpvC. The SBP FpvC brings then the ferrous ion to its associated ABC transporter for transport across the inner membrane into the cytoplasm. It is noteworthy that Fe 2+ appears as the worst metal in terms of FpvC stability and affinity in vitro, probably to facilitate its release to the ABC transporter. This is in line with PsaA where the more tightly binding Zn 2+ over-stabilises the SBP closed state, preventing transfer of the wrong metal to the transporter [START_REF] Counago | Imperfect coordination chemistry facilitates metal ion release in the Psa permease[END_REF].

Conclusion

In conclusion, FpvC binds iron in its ferrous state and the octahedral metal site formed by six histidines stabilizes Fe 2+ under aerobic conditions. Our work highlights, that the canonical metal site in FpvC is distinct from those described yet among cluster A-1 SBPs and that large structural changes can occur in this cluster. FpvC is also the first example of a SBP chelating siderophore free-ferrous iron, being involved in a siderophore-dependent iron uptake pathway. All other SBP previously described in such pathways were ferrisiderophore binding SBP, with a transport of ferrisiderophore complexes into the bacterial cytoplasm by the associated ABC transporter.

Materials and methods

Cloning, expression of mature His-tag FpvC and purification using a nickel column. The synthetic gene (Genscript) coding for the mature FpvC fused to a TEV protease cleavage site and a His-tag was inserted into pET-29a. E. coli BL21 pLysS were transformed by pET-29a-fpvC-tag. Cells

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were grown at 37°C in LB broth supplemented with 0.5 mM isopropyl β-D-1-thiogalactopyranoside to induce protein production. Cells were centrifuged, resuspended in a buffer of 50 mM Tris-HCl, pH 8, 20 mM imidazole and 300 mM NaCl, and disrupted by sonication. After centrifugation at 25,000 g for 30 min at 4°C, the supernatant was loaded onto a 5 ml His-Trap column (GE Healthcare). Protein elution was performed with 50 mM Tris-HCl pH 8, 300 mM imidazole and 300 mM NaCl. Protein fractions were loaded onto a gel filtration column (HiLoad 26/60 Superdex 200 prep grade, GE Healthcare) equilibrated with 50 mM Tris-HCl pH 8 and 150 mM NaCl. The protein fractions were pooled, concentrated at 19 mg/ml and stored at -80°C. This protocole leads to FpvC-Ni 2+ complex.

Cloning, expression and purification of His-tag FpvC-H6G mutant. Cloning, expression and purification of His-tag FpvC mutant (H77G, H102G, H147G, H213G, H235G and H286G) namely

FpvC-H6G was performed as described previously [START_REF] Ganne | Iron Release from the Siderophore Pyoverdine in Pseudomonas aeruginosa Involves Three New Actors: FpvC, FpvG, and FpvH[END_REF].

Expression of mature His-tag FpvC under minimal media supplemented with iron and purification using an ion-exchange chromatography. E. coli BL21 transformed pLysS cells were grown at 37°C in M9 minimal medium supplemented with 4 M FeSO 4 and one hour later with 1 mM isopropyl β-D-1-thiogalactopyranoside to induce protein production. Cells were centrifuged, resuspended in a buffer of 20 mM MES, pH 6.5, and disrupted by sonication. After centrifugation at 25,000 g for 30 min at 4°C, the supernatant was loaded onto a cation-exchange chromatography (HiTrap SP 5ml, GE Healthcare). Protein elution was performed with a linear gradient of 0-1 M NaCl.

Protein fractions were loaded onto a gel filtration column (HiLoad 26/60 Superdex 200 prep grade, GE Healthcare) equilibrated with 50 mM Tris-HCl pH 8 and 150 mM NaCl. The protein fractions were pooled, concentrated at 30 mg/ml and stored at -80°C. This protocole leads to FpvC-Fe 2+ complex.

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Removing of the His-tag and bound metal of FpvC. The C-terminal His-tag of pure mature FpvC was cleaved using recombinant TEV protease, which was incubated with the target protein at a mass ratio of 1:30 at 4°C for 12 h. The protein was purified by applying a second step nickel column. The

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Crystallization and structure determination. Crystallization conditions for metal-bound His-tag FpvC, FpvC-H6G mutant and apo FpvC were screened using QIAGEN kits (Valencia, CA) with a Mosquito nanodrop robot (Genomic solutions). Metal-bound His-tag FpvC and FpvC-H6G crystals were manually optimized (Table 1). Crystals were transferred to a cryo-protectant solution (mother liquor supplemented with 25% PEG 400 or ethylene glycol) and flash-frozen in liquid nitrogen.

Diffraction data were collected at 100 K on PROXIMA 1 and 2 beamlines at SOLEIL synchrotron (Saint-Aubin, France). Data processing was performed using the XDS package [START_REF] Kabsch | Xds[END_REF] (Table 1). The first structure was determined at 2.4 Å resolution by SAD method at the peak absorption energy of nickel. The presence of a fortuitous nickel in crystals was found thanks to an X-ray fluorescence emission scan on the beamline. The steps of nickel ion substructure determination, phases calculation and density modification were performed using CRANK from CCP4 (Collaborative Computational Project, Number 4) and a partial model was built using BUCCANEER (CCP4). This model was then used to calculate the phases of a high resolution dataset at 1.65 Å resolution leading to the complete polypeptide chain model except the loop region 132-141. The other structures were determined by molecular replacement with PHASER [START_REF] Mccoy | Phaser crystallographic software[END_REF] using the first refined structure of FpvC as a search model.

Because of the anisotropy of the diffraction of FpvC-Fe 2+ and FpvC-H6G mutant crystals, the DEBYE and STARANISO programs developed by Global phasing Ltd were applied to the data scaled with AIMLESS using the STARANISO server (http://staraniso.globalphasing.or/). These programs perform an anisotropic cut-off of merge intensity data on the basis of an analysis of local I/(I), compute Bayesian estimates of structures amplitudes, taking into account their anisotropic falloff, and apply an anisotropic correction to the data. The corrected anisotropic amplitudes were used for further refinement. Refinement of each structure was performed with BUSTER-2.10 [START_REF] Blanc | Refinement of severely incomplete structures with maximum likelihood in BUSTER-TNT[END_REF],

employing TLS groups and NCS restraints when more than one molecule was present in the asymmetric unit. Inspection of the density maps and manual rebuilding were performed using COOT [START_REF] Emsley | Coot: model-building tools for molecular graphics[END_REF]. Refinement details of each structure are shown in Table 1. Molecular graphics images were generated using PyMOL (http://www.pymol.org).

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Electron paramagnetic resonance (EPR) measurement. X-band cw-EPR spectra were recorded with a Bruker Elexsys 500 X-band spectrometer equipped with a standard ER 4102 (Bruker) X-band resonator, a Bruker teslameter, an Oxford Instruments cryostat (ESR 900) and an Oxford ITC504 temperature controller. Samples of the purified His-tag FpvC-Fe complex at 50 M in MES pH 6.5 or 60 M in Tris pH 8 ( 150 µL) loaded in EPR tubes were frozen in an ethanol bath cooled down at 198 K with dry ice and then transferred in liquid nitrogen. Potassium ferricyanure was added at 30 and 60 µM.

Circular dichroism experiments (CD).

Circular dichroïsm in the far-UV region was performed using a spectropolarimeter (Jasco J-810) equipped with a water-cooled Peltier unit (Jasco circular dichroïsm spectrometer model J810). Apo FpvC and FpvC-H6G mutant were both concentrated at 250 M in 50 mM Tris pH 8 and 150 mM NaCl. Spectra were recorded in a cell width of 0.01-mm path length (121.QS, Hellma) from 185 to 260 nm at 20°C. Six consecutive scans from each sample were merged to produce an averaged spectrum; the spectra were corrected using buffer baselines measured under the same conditions. Data were recorded in mdeg and converted using the mean residues ellipticity method (deg.cm 2 mol -1 ). Secondary structure estimates were derived from the normalized spectra using the CDSSTR, SELCON3, CONTIN of the DICHROWEB server [START_REF] Sreerama | Estimation of protein secondary structure from circular dichroism spectra: comparison of CONTIN, SELCON, and CDSSTR methods with an expanded reference set[END_REF][START_REF] Whitmore | DICHROWEB, an online server for protein secondary structure analyses from circular dichroism spectroscopic data[END_REF].

Differential scanning calorimetry (DSC).

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heat capacity of the buffer was subtracted from that of the protein sample before analysis.

Thermodynamic parameters were determined by fitting the data to the following equation:

where Kd is the equilibrium constant for a two-state process, ΔHvh is the enthalpy calculated on the basis of a two-state process and ΔHcal is the measured enthalpy.

Isothermal titration microcalorimetry measurements (ITC). Isothermal titration microcalorimetry

experiments were performed with an ITC200 isothermal titration calorimeter from MicroCal (Malvern). The experiments were carried out at 20°C. Protein concentration in the microcalorimeter cell (0.2 ml) was 35 µM. Nineteen injections of 2 µl metal at concentrations ranging from 600 to 750

M were performed at intervals of 180 s while stirring at 500 rpm. The experimental data were fitted to theoretical titration curves with software supplied by MicroCal (ORIGIN ® ). This software uses the relationship between the heat generated by each injection and ΔH (enthalpy change in Kcal/Mol), K a (the association binding constant in M -1 ), n (the number of binding sites), total protein concentration and free and total ligand concentrations [START_REF] Wiseman | Rapid measurement of binding constants and heats of binding using a new titration calorimeter[END_REF].

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(

  holo) leads to a RMSD of 1.7 Å and shows large conformational changes (Figure4b). An important change results from a rearrangement in the C-terminal end (residues 198-201) of the interdomain helix, which in the open state forms an extra-helical turn as shown in red color in Figure4a. Superposition of the N-terminal domains only including a part of the interdomain helix (residues41- 190) shows that they are nearly unchanged, RMSD being 0.63 Å for all C atoms. Indeed, metal binding has only a local effect with a rearrangement of the loop 73-83 up to 2.6 Å around the ion chelator His77 (Figure4b). In contrast, metal binding has a drastic effect on the C-terminal domain (residues 191-316) as indicated by the RMSD value of 2.25 Å (Figure4b). His213 can move to 5 Å to interact with the metal ion and a large rearrangement up to 12.7 Å of the long loop region (residues 224-240) allows the metal-coordinating His235 to close the metal binding site (Figure4b). This latter loop adopts a different conformation and position between the closed and open states. The three remaining metal ligands, His102 and His147 of the N-terminal domain and His286 from the C-

  flow-through contained cleaved FpvC. FpvC was then concentrated and treated with 50 mM ethylenediaminetetraacetic acid (EDTA) for 30 min. Protein impurities were removed by gel filtration (HiLoad 26/60 Superdex 200 prep grade, GE Healthcare) equilibrated with 50 mM Tris-HCl pH 8, 20 mM EDTA and 150 mM NaCl. Preliminary data using DSC showed that FpvC was devoid of metal and could no longer bind metal likely due to the presence of EDTA. Because of poor yield of pure apo protein, a new synthetic gene was ordered coding for mature FpvC without any tag or artefact cloning.Cloning, expression and purification of apo FpvC devoid of any tag.The synthetic gene (Genscript) coding for the mature FpvC only was inserted into pET-29a. E. coli BL21 pLysS were transformed by pET-29a-fpvC. Cells were grown at 37°C in LB broth supplemented with 0.5 mM isopropyl β-D-1-thiogalactopyranoside to induce protein production. Cells were centrifuged, resuspended in a buffer of 20 mM MES, pH 6.5 and disrupted by sonication. After centrifugation at 25,000 g for 30 min at 4°C, the supernatant was loaded onto a cation-exchange chromatography (HiTrap SP 5ml, GE Healthcare). Protein elution was performed with a linear gradient of 0-1 M NaCl and treated with 50 mM EDTA for 30 min. Protein impurities were further removed by gel filtration (HiLoad 26/60 Superdex 200 prep grade, GE Healthcare) equilibrated with 50 mM Tris-HCl pH 8, 20 mM EDTA and 150 mM NaCl. A desalting column allowed EDTA removing using 50 mM Tris-HCl pH 8 and 150 mM NaCl. The protein fractions were pooled, concentrated at 15 mg/ml and stored at -80°C. This apo protein was used for CD, DSC, ITC and crystallization assays.

Figure 4 .Figure 1 )

 41 Figure 4. (a) Ribbon representation of metal-free FpvC-H6G mutant structure in two orthogonal

Figure 5 .

 5 Figure 5. DSC thermograms of apo FpvC devoid of any tag without (a) and with different cations (Fe 2+ and Fe 3+ in (b) and Ni 2+ , Zn 2+ , Mn 2+ , Co 2+ ,Cu 2+ , Cd 2+ , Ca 2+ and Mg 2+ in (c)) and thermogram of

Figure 6 .

 6 Figure 6. ITC experiments: K D measurements of apo FpvC devoid of any tag towards Ni 2+ (NiSO 4 ), Zn 2+ (ZnSO 4 ), Mn 2+ (MnCl 2 ) and Fe 2+ (FeSO 4 + TCEP) ions. The top panel shows heat differences upon injection of metal ion and low panel shows integrated heats of injection with the best fit (solid

  Thermal stability of the apo form, bound-metal FpvC as well as the FpvC-H6G mutant was performed by DSC on a MicroCal model VP-DSC in a standard buffer with 30 μM and 300 μM for protein and metal, respectively. Divalent metals used were MgSO 4 , MnCl 2 , CaCl 2 , NiSO 4 , CuCl 2 , CoCl 2 , CdCl 2 , ZnSO 4 , FeSO 4 and 1 mM Tris(2carboxyethyl)phosphine) (TCEP), FeCl 3 , FeCl 3 and 1 mM TCEP; TCEP being a reductant agent. Each measurement was preceded by a baseline scan with the standard buffer. All solutions were degassed just before loading into the calorimeter. Scans were performed at 1 K.min -1 between 20 and 90°C. The

Table 1 .

 1 Crystallographic data and refinement parameters

FpvC-Ni 2+ FpvC-Ni 2+ FpvC-Ni 2+ FpvC-Fe 2+ FpvC-Mn 2+

									FpvC-H6G
									Mutant
	PDB code		SAD	6R3Z	6R44	6R5S	6RU4	6R6K
				phasing
	Crystallization		16-18% PEG 6K, 0.1 M MES pH 6.5			8% MPEG 2K
									MES 0.1 M pH
									6.5
	Number of molecules	1	1	2	2	4	2
	in
	asymmetric unit
	Wavelength (Å)	1.48480	0.98	1.48480	1.73867	0.98	0.98
				P2 1 2 1 2 1	P2 1 2 1 2 1	P2 1	C2	P2 1	C2
	Space group Cell parameters (Å,°)	a = 43.5 b = 63.1 c = 90.4	a = 43.6 b = 62.7 c = 90.5	a = 66.8 b = 41.4 c = 104.5	a = 72 b = 44.2 c = 179.8	a = 44.0 b = 178.3 c = 66.8	a = 155.3 b = 53.6 c = 84.4
						 =96.	 = 95.1	 = 90.6	 = 93.2
	Resolution (Å)		50-2.4	39.2-1.65	43.2-1.99	37.62-2.75	44.57-2.49	43.74-2.1
				(2.46-2.4)	(1.75-1.65)	(2.05-1.99)	(2.88-2.75)	(2.64-2.49)	(2.15-2.1)
	No.	of	observed	593452	306200	227822	96186	243884	284413
	reflections		(44210)	(32265)	(8580)	(11989)	(35930)	(45679)
	No.	of	unique	18809	30063	38967	14604	35191	40831
	reflections		(1377)	(4251)	(2567)	(1849)	(5188)	(6474)
	R sym (%)		17.9 (79.3)	11 (122.9)	16.1 (107.1)	12.2 (130)	17 (128.1)	10.6 (320.6)
	R pim			3.2 (24.6) 5.1 (72)	11.2 (85.5) 7.8 (83)	7 (53.3)	4.3 (141)
	Completeness (%)	100 (99)	97.8 (86.7)	98.8 (88.5)	97.2 (93.7)	98.4 (90.1)	99.7 (98.3)
	I/			21.6 (5.64)	12.8 (1.2)	6.13 (1)	9.35 (1.06)	8.58 (1.35)	9.12 (0.42)
	CC 1/2			99.9	99.7	99.1	99.5	99.6	99.9
				(96.4)	(82.8)	(54.4)	(66.8)	(54.1)	(49.4)
	R cryst (%)			18.4	19.5	18.9	19.6	19.4
	R free (%)			21.9	22.6	24.2	23.8	23.4
	RMSD bond lengths		0.01	0.01	0.01	0.01	0.01
	(Å)
	RMDS bond angles (°)		0.97	1.1	1.17	1.16	1.13
	Average B (Å 2 )
	Protein A/B/C/D		30.5	39.1/44.4	54.8/59.8	59.7/73.8/58/65.1	46/132.1
	Metal A/B/C/D		22.6	24.3/27.1/	53.2/51.6	43/51.4/44.8/49
	solvent				41.0	40.2	43.8	52.1	50.9
	Clashscore a			1.17	2.0	4.58	3.48	4.79
	MolProbity score a		0.89	1.63	2.23	1.87	2
	Ramachandran plot (%)
	Favoured			97.7	97.55	95.3	96.33	96.5
	Allowed			2.3	2.55	4.51	3.29	3.5
	Outliers				0	0.19	0.19	0.38	0

Table 2 .

 2 Distances (Å) between metal ion and histidine (His) in metal-bound FpvC structures

		His77	His102	His147	His213	His235	His286
	Ni 2+ in P2 1 2 1 2 1 2.19	2.27	2.20	2.18	2.15	2.20
	Ni 2+ in P2 1	2.13	2.24	2.17	2.11	2.14	2.25
	(mol A)
	Ni 2+ in P2 1	2.17	2.17	2.17	2.11	2.16	2.24
	(mol B)
	Fe 2+ (mol A)	2.27	2.44	2.22	2.37	2.13	2.27
	Fe 2+ (mol B)	2.26	2.37	2.18	2.39	2.19	2.20
	Mn 2+ (mol A)	2.49	2.42	2.26	2.28	2.21	2.25
	Mn 2+ (mol B)	2.46	2.46	2.36	2.30	2.15	2.29
	Mn 2+ (mol C)	2.42	2.45	2.28	2.30	2.22	2.23
	Mn 2+ (mol D)	2.45	2.47	2.29	2.31	2.14	2.28

Table 3 .

 3 Secondary structure estimations from CD experiments

		Apo FpvC FpvC-H6G mutant
	α-helices	53%	51%
	β-sheets	16%	17%
	Random coil	31%	32%

Acknowledgements. This work benefited from the I2BC crystallization and microcalorimetry platforms supported by FRISBI ANR-10-INSB-05-01. We acknowledge SOLEIL for provision of synchrotron radiation facilities (proposals ID 20130869, 20140774, 20150780 and 20170872) in using PROXIMA 1 and 2 beamlines and we thank all the staff for assistance in using the beamlines. We are grateful to Drs. Davy Martin and Human Rezaei (INRA, VIM-UR0892, Jouy-en-Josas) for access to their CD equipment. We thank Dr. Nadine Assrir (ICSN, Gif sur Yvette) for help in CD data processing.

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Declarations of interest: none

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of His-tag FpvC-Fe 2+ (magenta/pink for amino-acids and orange for iron ion) and YfeA-Fe 2+ (yellow).

Amino-acids are labelled and metal-protein ligands interactions are shown as plain lines (orange in FpvC and black in YfeA).


E Nardon
email: eric.nardon@cea.fr

D Hu

M Hoelzl

D Bonfiglio

Fast plasma dilution in ITER with pure Deuterium Shattered Pellet Injection

JOREK 3D non-linear MagnetoHydroDynamic (MHD) simulations of pure Deuterium Shattered Pellet Injection in ITER are presented. Considering a 15 MA L-mode plasma with a thermal energy content of 36 MJ from the non-activation phase of ITER operation, it is shown that such a scheme could allow diluting the plasma by more than a factor 10 without immediately triggering large MHD activity, provided the background impurity density is low enough. This appears as a promising strategy to reduce the risk of hot tail Runaway Electron (RE) generation and to avoid RE beams altogether in ITER, motivating further studies in this direction.

Introduction

Shattered Pellet Injection (SPI) is the reference concept for the ITER Disruption Mitigation System (DMS) [START_REF] Lehnen | 27th IAEA Fusion Energy Conference[END_REF] [1]. One of the main objectives of the DMS is the avoidance of large Runaway Electron (RE) [START_REF] Breizman | [END_REF] beams. There are two particular concerns regarding RE beam formation during ITER disruptions [4] [9]. The first one is that the hot tail mechanism [5] may be very efficient when a hot plasma disrupts. This is suggested by recent experiments on DIII-D [6] but remains largely an open question due to our limited understanding of the Thermal Quench (TQ) phase of a disruption. The second concern is that, even if the generation of RE seeds (whether by the hot tail mechanism or by other mechanisms such as Dreicer, Tritium β decay or Compton scattering of gamma rays emitted by the activated wall) is small, these seeds may still be converted into a large RE beam via the avalanche mechanism [7] during the current quench phase of the disruption [8]. Suppressing the avalanche would require raising the electron density n e up to the so-called Rosenbluth density, which is in the range of several times 10 22 m -3 [9]. This would require an increase in n e by more than 2 orders of magnitude, which seems to be a difficult task. Even if the Rosenbluth density cannot be reached, increasing n e may still be useful by raising the critical energy for running away and thus reducing seed REs, with the exception of Compton seeds [10] [8]. Modelling studies suggest that, assuming a moderate hot tail seed, large RE beams may be avoided during ITER disruptions if n e could be raised by a factor of 20 to 40 throughout the plasma [10] [11], although more recent work puts this in question [12]. It is imagined that this increase in n e could be achieved by injecting shattered pellets containing a large quantity of Deuterium (D 2 ) mixed with a much smaller quantity of impurities like Argon or Neon, the latter being necessary to mitigate thermal and electromagnetic loads [START_REF] Lehnen | 27th IAEA Fusion Energy Conference[END_REF]. However, it is not established that such large amounts of material could actually be assimilated by the plasma, and even less so in a uniform fashion.

An important point is that the ablation of pellet shards is strongly dependent on the electron temperature T e [16]. With typical ITER SPI parameters, ablation is strong at large (multi-keV) pre-TQ T e , but becomes almost negligible at low (∼ 10 eV or less) post-TQ T e . In order to maximize the amount of ablated material, a late TQ thus appears clearly beneficial.

A problem when using pellets containing impurities is that they typically trigger a TQ while shards are still far away from the plasma center [14]. This effect, which is captured by 3D non-linear MHD modelling [17], is due to the fact that, via radiation, impurities cool the electrons down to T e ∼ 10 eV or below on a timescale which is much shorter than the time it takes for shards to reach the plasma center, τ travel ≡ v s /a, where v s is the shards velocity and a the plasma minor radius. This T e drop increases the plasma resistivity η (which scales like T -3/2 e ) dramatically, which in turn modifies the current density distribution [25], destabilizes MHD modes and leads to the TQ.

On the other hand, pure D 2 SPI may behave differently because Deuterium radiates very little. Electron cooling in this case comes essentially from dilution. If the dilution factor is of the order of, say, 30, and if the initial T e is, say, 3 keV, then the postdilution T e is 100 eV. The effect on η is thus much more limited than in the presence of impurities, such that the current density distribution will evolve on a much slower timescale. As a matter of fact, it has been observed on DIII-D [14] and JET [15] that the cooling time, defined as the duration between the moment when first shards reach the edge of the plasma and the onset of the TQ, is much longer when pure D 2 is used than when the pellet contains impurities. Also, studies on rapid plasma shutdown by massive uniform D 2 delivery in DIII-D and ITER with NIMROD found that the plasma remains stable to n = 1 and n = 2 modes (n being the toroidal mode number) [24].

These considerations suggest that pure D 2 SPI may be much more efficient at raising n e than mixed D 2 -impurities SPI, because the plasma is likely to remain hot for a longer duration, allowing a much more efficient ablation. Also, the longer cooling time will allow shards to penetrate deeper and provide direct core fuelling. As already mentioned above, impurities are necessary to mitigate thermal and electromagnetic loads, but these could be injected in a second step, after the pure D 2 SPI, by means of a second SPI. Results shown in this paper suggest that there would be sufficient time for this.

Preliminary axisymmetric simulations by Akinobu Matsuyama with the 1.5D transport code INDEX [START_REF] Matsuyama | Runaway Electron Meeting[END_REF] support the above considerations by showing that with pure D 2 SPI, the current density profile is weakly affected, at least on a τ travel timescale. In the present work, we use the JOREK 3D non-linear MHD code [21][22] [START_REF] Hoelzl | The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas[END_REF] to further assess the feasibility of this scheme.

The paper is constructed as follows. In Section 2, we introduce the simulation setup. Section 3 presents axisymmetric simulations and discusses the impact of the resistivity used in the simulation and of background impurities. Section 4 describes 3D simulations and addresses in particular the effect of the toroidal localization of the ablation clouds and (again) of background impurities. Finally, Section 5 discusses the results and concludes.

Simulation setup

The simulations presented in this study were performed with the fixed-boundary reduced MHD version of JOREK comprising an extension for neutrals and SPI. The model is described in detail in [20]. The same tool has been used recently to simulate pure D 2 SPI in JET [20] and ASDEX Upgrade [START_REF] Hoelzl | [END_REF].

The target plasma used for this study is taken at time t = 60 s from a CORSICA simulation of an ITER Hydrogen L-mode scenario (Scenario 5 from Table 1 in [26]). The plasma current is 15 MA, the toroidal magnetic field 5.3 T and the thermal energy content 36 MJ. The computational grid in the poloidal plane is shown in Fig. 1. It comprises about 6000 elements. In the toroidal direction, JOREK uses a Fourier decomposition. Axisymmetric simulations shown in Section 3 include only the n = 0 component whereas the 3D simulations of Section 4 include harmonics from n = 0 up to n = 10.

Hydrogen is replaced by Deuterium in JOREK since the model assumes that neutrals and ions are of the same species. This is not expected to have important consequences since the ion mass should not play an important role here. Initial profiles of the safety factor q, electron density n e , electron temperature T e and toroidal current density j φ , as a function of the normalized poloidal magnetic flux ψ N (ψ N = 0 on the magnetic axis and ψ N = 1 at the last closed flux surface), are shown in Fig. 2. Central values of n e and T e are 5.3 × 10 19 m -3 and 5 keV, respectively. It can be noted that q is slightly smaller than 1 near the plasma center. Due to this, the plasma has an intrinsically unstable n = 1 mode localized in the core, which complicates the interpretation of our simulations. We have therefore increased B t by 10 % so as to make q > 1 and have an intrinsically stable target plasma. The corresponding q profile is shown as the dash-dotted blue line in Fig. 2.

The injected pellet is a 'large' pellet from the present ITER DMS design, which is cylindrical with a diameter D = 28 mm and a length over diameter ratio L/D = 2 [START_REF] Lehnen | 27th IAEA Fusion Energy Conference[END_REF]. The total number of Deuterium atoms in the pellet is 2 × 10 24 . We assume, for simplicity, the pellet to be shattered into 1000 shards of equal radius (about 2 mm). All shards originate from the position R = 8.25 m, Z = 0.5 m, φ = 0 (i.e. from the low field side midplane). The velocity vector of each shard has a modulus picked randomly between 100 and 300 m/s, and a direction picked randomly inside a cone of aperture 0.349 radians.

The ablation rate N (i.e. the number of ablated atoms per second) of each shard is calculated according to the neutral gas shielding model (see [27] and references therein):

N = 4.12 × 10 16 • r 1.33 s • n 0.33 e • T 1.64 e (1)
where r s is the shard radius in m, n e is in m -3 and T e in eV. The radius of each shard is evolved in time according to its ablation.

Ablated atoms are deposited in an ablation 'cloud' via a volumetric source term which has the following spatial shape:

S n ∝ exp - (R -R s ) 2 + (Z -Z s ) 2 r 2 cloud exp - (φ -φ s ) 2 ∆φ 2 cloud , (2)
where (R s , Z s , φ s ) corresponds to the shard's position. The poloidal extent of the ablation cloud in our simulations is r cloud = 20 cm and the toroidal extent varies between 1 and 1000 radians (the latter corresponding to a virtually axisymmetric cloud). These dimensions are much larger than those of real ablation clouds [16], but we are constrained by a limited spatial resolution.

For most simulations, we use a realistic resistivity: η = 2 × η Sp = 5.6 × 10 -8 /T 3/2 e , where η Sp is the Spitzer resistivity [START_REF] Spitzer | Transport phenomena in a completely ionized gas[END_REF], η and η Sp are expressed in Ω.m and T e in keV. The factor 2 accounts for the fact that only passing electrons carry current (assuming a trapped fraction of 0.5, which is representative of the plasma edge). This corresponds to a Lundquist number S ≡ µ 0 aV A /η 6 × 10 9 in the center of the plasma (a = 2 m is the minor radius and V A is the Alfvén speed). Note that in some simulations, we include background impurity radiation but for simplicity we do not take impurities into account in the resistivity. We use a realistic Spitzer-Harm parallel heat diffusivity [START_REF] Spitzer | Transport phenomena in a completely ionized gas[END_REF]. The perpendicular heat diffusivity is 10 m 2 /s. The plasma particle perpendicular diffusivity as well as the isotropic neutral diffusivity are 40 m 2 /s. Parallel plasma particle transport is purely convective. The central value of the kinematic viscosity acting on the perpendicular flow is equivalent to a diffusivity of 2 m 2 /s and the viscosity is scaled with temperature in the same way as the resistivity to keep the magnetic Prandtl number approximately constant spatially. The viscosity acting on the parallel flow is constant and equivalent to 200 m 2 /s. In order to avoid numerical issues related to very low temperatures, Deuterium radiation and recombination are turned off and background impurity radiation is turned off below 5 eV, which has a minor impact on simulations. Small hyperdiffusion terms are also included for numerical reasons but do not affect the results significantly.

Axisymmetric simulations

We begin our study with axisymmetric simulations (and thus also with axisymmetric ablation clouds). We present a set of three simulations. The first one has a realistic resistivity, that is η = 2 × η Sp . This corresponds, in JOREK normalized units, to η 0 = 2 × 10 -9 . The second simulation has a 50 times larger resistivity, that is η 0 = 10 -7 (however, for the Ohmic heating term, the realistic resistivity is kept, so as to avoid spurious Ohmic heating). The third simulation, like the first one, has a realistic resistivity but also includes radiative losses from background impurities with a homogeneous density n imp = 10 17 m -3 and a radiative cooling rate resembling that of Argon at coronal equilibrium (at least in the 1 -100 eV range), as shown in Fig. 3. 4 shows the time evolution of the plasma current I p and internal inductance l i (3), and Fig. 5 shows profiles of n e , T e , j φ and pressure at 2, 4 and 6 ms, for the three simulations. Let us consider first the simulation with a realistic resistivity and no background impurities (blue lines). It can be seen in Fig. 5 that n e increases massively, first near the edge and gradually towards the core, as shards penetrate deeper and deeper into the plasma (compare the blue n e profiles at 2, 4 and 6 ms). Due to dilution, T e decreases accordingly while the pressure profile remains virtually unaffected. In spite of the strong modification of the n e and T e profiles, the j φ profile, and consistently I p and l i (3), barely change over a 10 ms timescale (which corresponds to the typical time needed for shards to reach the plasma center). The second simulation, with the 50 times larger resistivity (red lines), shows virtually the same evolution of the n e , T e and pressure profiles but, in contrast to the first simulation, displays strong changes in j φ , I p and l i (3), demonstrating the key role of the resistivity used in the simulation. It can be seen in the j φ profile evolution shown in Fig. 5 that current is removed from the edge and partly re-induced further into the core, with a skin current progressing towards the core, as described in [25]. Accordingly, I p decreases and l i (3) increases. The third simulation, with the realistic resistivity and background impurities (black lines), shows a similar n e and T e evolution to the other two simulations, with the important difference that T e is reduced to much lower values in the edge region. This is because, in addition to dilution, electrons are now also cooled by background impurity radiation. The evolution of j φ , I p and l i (3) qualitatively resembles that of the second simulation, with current being removed from the edge and re-induced further into the core, but the skin current is sharper and progresses more slowly towards the core, and the evolution of I p and l i (3) is accordingly slower. The behaviour displayed by these three simulations may be understood in light of the following considerations. By depositing material, shards cool down the plasma gradually from the edge to the core. Considering that, at any given time, the cooled region is bounded by still hot plasma on one side and by a highly conducting wall on the other side, the current in the cooled region should decay on a current diffusion timescale τ d = µ 0 δ 2 c /η c , where δ c and η c are respectively the radial thickness and the resistivity (assumed homogeneous in this simple, order of magnitude estimate) of the cooled region. Fig. 6 shows τ d as a function of the electron temperature (assumed homogeneous) in the cooled region T e,c and of δ c , using the Spitzer resistivity. In the above simulations, δ c is obviously increasing in time, but to fix ideas, let us consider that δ c = 0.4 m, which corresponds to 20 % of the minor radius. The condition τ d < τ travel = 10 ms translates to T e,c < 12 eV. This condition is clearly not met in the first simulation (realistic resistivity, no background impurities), in which T e,c remains in the 50 eV range, while it is met in the third simulation, where impurity radiation brings T e,c below 10 eV. This explains why the current profile is not modified in the former case while it is in the latter. In the second simulation, the artifical increase of η by a factor 50 corresponds to a proportional decrease of τ d , such that now T e,c 50 eV is sufficient for a substantial current decay in the cooled region. We have included this simulation because it is common practice in 3D non-linear MHD simulations to use an artifically increased resistivity for numerical reasons. As demonstrated here, this choice may have important consequences, especially in cases where the cold front is 'not very cold'. A safer choice is probably to use the Spitzer resistivity up to a certain T e , and then, if necessary, cut-off the T e dependency of resistivity, i.e. use η = η Sp (min(T e , T e,cut-of f )). In the present work, we however do not use a cut-off. An important question is what background impurity density n imp is needed to affect the dynamics. A rough estimate can be drawn by considering that the radiated power per unit volume is P rad = L rad n e n imp where L rad is the radiative cooling rate. Since the electron thermal energy per unit volume is en e T e , the cooling time is τ cool = eT e /(L rad n imp ), neglecting transport and Ohmic heating and assuming L rad to be a constant. Taking L rad 10 -31 W.m 3 (which is roughly the peak cooling rate for Argon at coronal equilibrium, see Fig. 3) gives τ cool 10 12 × T e /n imp . In the above simulations, dilution cooling takes T e down to ∼ 100 eV. The time it takes for radiation to further reduce T e to 10 eV or below is thus τ cool 10 14 /n imp . The condition τ cool > τ travel = 10 ms then translates to n imp < 10 16 m -3 . JOREK axisymmetric simulations indeed show that n imp ∼ 10 16 m -3 is the level above which impurities start to make a difference.

3D simulations

We now turn to 3D simulations. We consider only cases with a realistic resistivity. From the above results, it may be expected that cases without background impurities will develop little MHD activity, while cases with n imp above a certain value will develop tearing mode activity due to the effect of shards on the current density distribution. However, the above axisymmetric simulations did not take into account the toroidal localization of the ablation clouds, ∆φ cloud . We will first study this aspect by scanning ∆φ cloud at fixed n imp . We will then come back to the role of impurities by scanning n imp at fixed ∆φ cloud .

Effect of the toroidal localization of the ablation clouds

Fig. 7 compares the evolution of the magnetic energy of the n = 1 (blue), 2 (red) and 3 (black) modes for three values of ∆φ cloud (in radians): 1000 i.e. virtually axisymmetric clouds (plain lines), 2 (dashed lines) and 1 (dotted lines), all other parameters being the same. These simulations include background impurity radiation with n imp = 10 17 m -3 . Two phases can be distinguished. Before ∼ 5 ms, modes are many orders of magnitude weaker for the ∆φ cloud = 1000 case than for the other ones. After 5 ms, modes grow strongly for the ∆φ cloud = 1000 case and the mode amplitudes become comparable to the ∆φ cloud = 2 case around 7 ms and then saturate. The n = 1 mode is dominant. The ∆φ cloud = 1 case, although it has comparable n = 1 and larger n = 2 and 3 mode amplitudes to the ∆φ cloud = 2 case in the early phase (and thus a broader n spectrum, consistently with the smaller ∆φ cloud ), has a much smaller n = 1 amplitude after 5 ms (until 10 ms). Thus, it appears that the drive of low n modes decreases (or at least is delayed) as the ablation cloud becomes more strongly toroidally localized.

Fig. 8 helps interpret these results. It presents poloidal cross-sections of the axisymmetric part of the electron temperature, T e,n=0 (top row), and of its deviation from axisymmetry, T e -T e,n=0 (bottom row), for the three simulations at t = 4 ms. It can be seen, not surprisingly, that the effect on T e,n=0 is larger for larger ∆φ cloud while the effect on T e -T e,n=0 is larger for smaller ∆φ cloud . As has been discussed in previous publications [29] [20], there are two main ways through which tearing modes can be driven by a massive material injection: the first one is via a modification of the current density profile leading to a positive ∆ , and the second one is via helical cooling of flux tubes on rational surfaces. Only the first mechanism is present in the ∆φ cloud = 1000 case. In the early phase, mode excitation is dominated by the second mechanism, explaining the much smaller mode amplitude in the ∆φ cloud = 1000 case than in the other ones. From about 5 ms, a fast and large mode growth takes place for the ∆φ cloud = 1000 case as the first mechanism is strongly activated by the skin current passing across the q = 2 surface (note that the early evolution of profiles for this simulation is very similar to that of the third axisymmetric simulation, i.e. to the black profiles in Fig. 5). Fig. 8 shows that decreasing ∆φ cloud reduces the first mechanism and increases the second one. These two changes roughly compensate each other for the ∆φ cloud = 2 case, which has a comparable maximal n = 1 amplitude to the ∆φ cloud = 1000 case. On the other hand, for the ∆φ cloud = 1 case, the much smaller n = 1 amplitude shows that the reduction of the ∆ effect is not compensated by the increase of the helical cooling effect. The detailed reasons why a smaller ∆φ cloud leads to a reduction of the axisymmetric temperature (and current) profile modification would deserve a specific study, but are probably related to the fact that localized ablation clouds promptly generate magnetic islands at rational q surfaces, whose O-points coincide with their position. The cooling then tends to remain localized inside the islands and thus non-axisymmetric, which limits axisymmetric profile modifications. Another contributing factor is that, due to a stronger local reduction of the temperature, the ablation rate decreases with ∆φ cloud . At t = 4 ms, the number of ions in the plasma is 3.5 × 10 23 , 2.9 × 10 23 and 2.2 × 10 23 for ∆φ cloud = 1000, 2 and 1 respectively, showing that this effect is substantial. ). In the top row, the colourscale is saturated at 150 eV so as to highlight differences in the edge, but the core temperature is much higher, around 5 keV.

Effect of background impurities

We now come back to studying the effect of background impurities, but this time with 3D simulations. We choose ∆φ cloud = 2 as a 'pessimistic' value in the sense that, as shown above, low n modes (which are responsible for the TQ triggering [29]) are more strongly driven for this value than for a smaller, more realistic ∆φ cloud . Fig. 9 compares the magnetic energy of the n = 1 mode (top left), the total number of free electrons in the plasma, N e (top right), the central T e (bottom left) and the central n e (bottom right) for simulations with n imp = 0 (blue), 10 17 m -3 (red) and 8 × 10 17 m -3 (black), all other parameters being equal. It can be seen that the n = 1 mode is substantially excited only in the presence of impurities. Fig. 10 shows a series of Poincaré cross-sections at different times for the n imp = 0 simulation, with the position of shards overlayed in black, revealing that shards travel across the plasma without perturbing flux surfaces much. By t = 20 ms, when shards have almost left the plasma, about 10 24 free electrons have been added to the plasma (see the top right plot of Fig. 9). This represents half of the initial pellet content. The other half splits roughly equally between leftover shards and transport losses.

For n imp = 10 17 m -3 , the n = 1 mode is excited from about 6 ms. The series of Poincaré cross-sections shown in Fig. 11 reveal the associated destruction of flux surfaces and growth of a stochastic region from the edge to the core. It can be seen that shards travel faster than the inner boundary of the stochastic region up to about the time when they reach the core, at 10 ms, at which point the magnetic field is fully stochastized. The evolution of the core n e and T e is similar to that observed in the n imp = 0 case until 10 ms, consistently with the persistence of flux surfaces in the core region until this time.

For n imp = 8 × 10 17 m -3 , the n = 1 mode is excited earlier, from about 3 ms. This is because the larger n imp results in a shorter duration for the radiative collapse to take place in the cold front. The series of Poincaré cross-sections shown in Fig. 12 now show that the stochastic region expands faster than the shards velocity. As a result, the magnetic field becomes fully stochastic while the shards are still located around midradius. This stochastization causes a fast drop of the core T e before n e has substantially increased in this region (see the bottom plots of Fig. 9): this is an illustration of a 'premature' TQ, which may be problematic regarding RE generation. The simulation is not pushed further since the purpose of this work is not to study TQ dynamics, but only to investigate whether or not a TQ is triggered.

Discussion and conclusion

The above simulations suggest that for the considered ITER 15 MA L-mode scenario, pure D 2 SPI may be able to substantially fuel the plasma all the way to the core without provoking a major MHD-driven TQ, provided the background impurity density is low enough. It may be speculated that a similar conclusion would have been drawn for an H-mode case since, according to the considerations made in Section 3, hotter plasmas should be harder to destabilize than colder ones (for a given dilution factor). On the other hand, H-mode plasmas could be much more sensitive to edge instabilities, which might change the picture. This question should be addressed by future simulations. Another important point is that, although our simulations strongly exaggerate the size of ablation clouds, results presented in Section 4.1 suggest that more localized ablation clouds would reinforce our conclusion.

Overall, these results motivate the consideration and further exploration of a disruption mitigation strategy based on a pure D 2 SPI followed by impurity-containing SPI. As mentioned in the introduction, this is probably the most efficient way to fuel the plasma and thus to implement the present RE avoidance strategy in ITER [10]. An important additional observation is that the relatively slow dilution cooling could be extremely efficient at suppressing risks of hot tail RE generation during the TQ. Fig. 13 shows how the energy of an electron evolves under pure drag from the bulk electrons. It has been obtained by solving the equation dp/dt = -eE CH c 2 /v 2 where p is the electron momentum and v its velocity, E CH is the Connor-Hastie field and c is the speed of light (see e.g. Appendix A in [28]). A bulk electron density of 10 21 m -3 has been assumed. It can be seen that even at an initial energy of 1 MeV, electrons are braked within 3 ms. Thus, if n e could be increased to above 10 21 m -3 and maintained at this level for at least 3 ms before the TQ takes place, the electron population would remain Maxwellian, and the moderate post-dilution T e would probably remove the risk of hot tail RE generation. The above JOREK simulation results suggest that this is feasible, provided the background impurity density is low enough. The most serious threat to the proposed strategy indeed appears to be the presence of background impurities. In this study, we have considered an Argon-like impurity and have found that for n imp larger than ∼ 10 17 m -3 , there is a risk to trigger a TQ before shards have reached the plasma center. Future work should aim for a more realistic treatment of background impurities. We note that the NIMROD study on uniform D 2 delivery had considered Beryllium as the background impurity with a density of 5 × 10 18 m -3 , and found no n = 1 or n = 2 mode excitation over the simulated duration of 12 ms, in spite of the large dilution factor of 150 [24]. The effect of pre-existing magnetic islands could also represent a threat to the proposed strategy and will be the object of upcoming work.

Yet another point to consider is the fact that a substantial fraction of gas may be produced during the shattering process. As shown in Fig. 6 of [31], above a certain pellet velocity, the mass fraction contained in solid fragments drops sharply from > 70 % to < 10 %. A large gas fraction is clearly not desirable since the gas will not fuel the plasma directly in the core but will instead fuel at the edge [32], with the risk of cooling down the edge too much and triggering MHD modes [29]. This sets a limit on the pellet velocity, which depends on the angle of the shattering tube. Future work should be devoted to optimizing the injector design, taking into account the gas cloud accompanying or preceding the solid shards and a more realistic description of the shard plume characteristics based on existing knowledge [31] [START_REF] Lehnen | The ITER Disruption Mitigation Strategy[END_REF].

Future efforts should also be devoted to the validation of pure D 2 SPI simulations on present experiments, e.g. on DIII-D, JET, KSTAR or ASDEX Upgrade, with however the expected difficulty that the behaviour may be strongly influenced by the presence of background impurities whose properties are difficult to assess.

Finally, it would be useful to test the proposed 2-step SPI scheme experimentally in present machines equipped with multiple (shattered) pellet injection systems, or even using SPI for the first (D 2 ) injection followed by MGI for the second (impurity) injection.

Figure 1 .

 1 Figure 1. Computational grid used in the JOREK simulations

Figure 2 .

 2 Figure 2. Initial profiles for the target ITER plasma used in this study (15 MA Hydrogen L-mode)

Figure 3 .

 3 Figure 3. Radiative cooling rate as a function of the electron temperature

Fig.

  Fig.4shows the time evolution of the plasma current I p and internal inductance l i (3), and Fig.5shows profiles of n e , T e , j φ and pressure at 2, 4 and 6 ms, for the three simulations. Let us consider first the simulation with a realistic resistivity and no background impurities (blue lines). It can be seen in Fig.5that n e increases massively, first near the edge and gradually towards the core, as shards penetrate deeper and deeper into the plasma (compare the blue n e profiles at 2, 4 and 6 ms). Due to dilution, T e decreases accordingly while the pressure profile remains virtually unaffected. In spite of the strong modification of the n e and T e profiles, the j φ profile, and consistently I p and l i (3), barely change over a 10 ms timescale (which corresponds to the typical time needed for shards to reach the plasma center). The second simulation, with the 50 times larger resistivity (red lines), shows virtually the same evolution of the n e , T e and pressure profiles but, in contrast to the first simulation, displays strong changes in j φ , I p and l i (3), demonstrating the key role of the resistivity used in the simulation. It can be seen in the j φ profile evolution shown in Fig.5that current is removed from the edge and partly re-induced further into the core, with a skin current progressing towards the core, as described in[25]. Accordingly, I p decreases and l i (3) increases. The third simulation, with the realistic resistivity and background impurities (black lines), shows a similar n e and T e evolution to the other two simulations, with the important difference that T e is reduced to much lower values in the edge region. This is because, in addition to dilution, electrons are now also cooled by background impurity radiation. The evolution of j φ , I p and l i (3) qualitatively resembles that of the second simulation, with current being removed from the edge and re-induced further into the core, but the skin current

Figure 4 .Figure 5 .

 45 Figure 4. Time evolution of the plasma current I p (left) and internal inductance l i (3) (right) for the three axisymmetric simulations: realistic resistivity (blue), resistivity increased by a factor 50 (red), and realistic resistivity with background impurities (black)

Figure 6 .

 6 Figure 6. Current diffusion time in the cooled region as a function of its electron temperature T e,c and radial thickness δ c . The 10 ms contour (corresponding to the shards travel time to the plasma center) is highlighted by the dashed white line.

Figure 7 .

 7 Figure 7. Evolution of the magnetic energy of the n = 1, 2 and 3 modes for simulations with ∆φ cloud = 1000, 2 and 1 rad (all with realistic resistivity and n imp = 10 17 m -3 )

Figure 8 .

 8 Figure 8. Axisymmetric component (top) and deviation from axisymmetry (bottom) of the electron temperature at t=4 ms for ∆φ cloud = 1000 (left), ∆φ cloud = 2 (middle) and ∆φ cloud = 1 rad (right) (all with realistic resistivity and n imp = 10 17 m -3). In the top row, the colourscale is saturated at 150 eV so as to highlight differences in the edge, but the core temperature is much higher, around 5 keV.

Figure 9 .Figure 10 .

 910 Figure 9. Time evolution of the magnetic energy of the n = 1 mode (top left), the total number of free electrons in the plasma (top right), the central electron temperature (bottom left) and the central electron density (bottom right) for simulations with n imp = 0 (blue), 10 17 m -3 (red) and 8 × 10 17 m -3 (black)

Figure 11 .

 11 Figure 11. Poincaré cross-sections at t=4, 6, 8 and 10 ms (from left to right) for the simulation with n imp = 10 17 m -3 . The shards position is shown in black.

Figure 12 .

 12 Figure 12. Poincaré cross-sections at t=2, 4, 4.5 and 4.7 ms (from left to right) for the simulation with n imp = 8 × 10 17 m -3 . The shards position is shown in black.

Figure 13 .

 13 Figure 13. Electron energy versus time, for different initial energies, for test electrons undergoing only a friction force from bulk electrons

Acknowledgements

Parts of this work have been carried out within the framework of the EUROfusion Consortium and have received funding from the Euratom Research and Training Programme 2014-2018 and 2019-2020 under Grant Agreement No. 633053. Part of this work was carried out using the Marconi-Fusion supercomputer. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Part of this work is supported by the National Natural Science Foundation of China under Grant No. 11905004.