Christelle Hureau
email: christelle.hureau@lcc-toulouse.fr

Metal ions and complexes in Alzheimer diseases: from fundamental to therapeutic perspectives

Keywords:

SOMMAIRE I. Inorganic chemistry of the amyloid-β peptides

Introduction to intrinsically disordered peptides.

Alzheimer's Disease.

The various forms of Aβ peptides.

Metal ions: copper and zinc in the synaptic cleft.

Coordination to the Aβ peptides.

I. Inorganic chemistry of the amyloid-β peptides

Introduction to intrinsically disordered peptides. Intrinsically disordered proteins/peptides (IDPs) are biologically active proteins without stable tertiary structure, whose functions are multiple and complete those of the ordered proteins, being commonly related to recognition, as well as control and regulation of various signaling pathways. 1 When dysregulated and/or dysfunctional, IDPs become key players of several human diseases, including neurodegenerative disorders such as Alzheimer's disease (AD). 2 Actually, due to their high plasticity and flexibility, they can indeed be involved in functions, malfunctions or dysfunctions. In the present review, I will focus on the dysfunction of the IDP amyloid-β (Aβ) peptide involved in AD.

IDPs are characterized by their propensity to form amyloid structures. Amyloids are selfaggregated peptides or proteins considered as a signature of neurodegenerative diseases. 3 However, they represent a fundamental non-pathological structure utilized by living organisms, from bacteria to humans. 4 Amyloids are a bundle of highly ordered filaments composed of ladders of β-strands (i.e. β-sheets) perpendicular to the fiber axis. The stability of such a three-dimensional organization is attained through several types of non-covalent bonds, mainly hydrogen bonds but also hydrophobic and π-π stacking interactions. Amyloids are the most stable form of any kind of peptides and proteins, and the 3D structures of ordered protein corresponds to metastable states of the proteins (Figure 1). 5 Fibrils are the dead-end point of the aggregation process that will be discussed more deeply later on.

A relatively well conserved feature of amyloid-related diseases is the presence of loosely bound metal ions, i.e. metal ions that are not strongly bound to biomolecules and that can be exchanged rapidly between biomolecules, in the area where the amyloid deposits occurs. [5][6][7][8][9] In line with the presence of redox-active metal ions in the amyloid deposits, oxidative stress is often encountered in amyloid-related diseases, although the importance of direct metal-induced Reactive Oxygen Species (ROS) to the overall oxidative stress is still unclear. [9][10][11][12][13] Figure 1. The energetic profile of folding versus aggregation of proteins. All proteins when misfolded can form amyloid fibrils. Chaperones act so as to help the proper folding of proteins. 14 IDPs follow the aggregation pathway (see further details of aggregation kinetics in the Aggregation section).

In this review, we will illustrate the inorganic chemistry of IDPs following the example of the Aβ peptide encountered in AD. A first part is dedicated to the interaction of metal ions with IDPs and to the consequences with respect to aggregation and ROS production and a second part focuses on the various strategies developed to counteract such metal ions to Aβ interactions.

Alzheimer's Disease. AD is a neurodegenerative disorder characterized by progressive cognitive and memory impairment and is the most common cause of dementia in the elderly population, accounting for 60-80% of dementia cases. 15,16 The prevalence of AD is expected to double every 20 years in the near future and thus the social and economic burden of AD will continue to grow. 17 This trend is mainly due to the increase of life expectancy and to the absence of curative medications. At the microscopic scale, AD is characterized by two hallmarks: the intra-cellular neurofibrillary tangles of hyperphosphorylated Tau protein 18 and the extra-cellular senile plaques, made of aggregated Aβ peptides. [19][20][21] In the amyloid deposits, metal ions, mainly Cu, Zn and Fe are found at mM concentrations and while Fe is mainly present as co-localized nanoparticles, Cu and Zn are bound to the Aβ. [22][23][24] The various forms of Aβ peptides and the amyloid cascade hypothesis. The Aβ peptide is not unique: there are many forms (sequences) of the Aβ peptides, with various lengths and key point modifications. Aβ peptides are obtained from the cleavage of the Amyloid Precursor Protein by the β-and γ-secretase. 25 The most well-known and studied forms of Aβ are the "full-length" peptides made of 37 to 43 amino-acid residues (noted Aβ1-37/43, see the abbreviations paragraph for the notation of the peptides) with the two predominant forms being the Aβ1-40 and Aβ1-42. The sequence of the Aβ1-43 is shown in Figure 2 along with the most important mutations or peptide alterations. Indeed there is some heterogeneity at both the N-terminal and the C-terminal cleavage sites, leading to peptides with C-terminal side ending between residues 37 and 43 and N-terminal side starting between residues 1 and 5 and at residue 11. In addition, there are the pyroglutamate counterparts of the Aβ3-n and Aβ11-n and mutants responsible for the early onset of AD (known familial mutants).

Murine animals also have a modified form of the peptide with mutations at positions 5 (R5G), 10 (Y10F) and 13 (H13R). 26 It is anticipated that the various forms of the Aβ peptides interact differently with the metal ions, especially when the modified residues belong to the family of the binding residues (the terminal amine, the His, Asp and Glu side chains). 27,28 Alterations can also cause a modification in the secretase activities and thus in peptides processing and release, leading to an increase of the Aβ1-42 over Aβ1-40 ratio. 26 As the longer Aβ1-42 form is more prone to aggregation than Aβ1-40, an increase of this ratio documents the hypothesis according to which aggregation is a key and deleterious process in AD development, known as the amyloid cascade hypothesis. 29 According to this hypothesis, aggregation of the Aβ peptide is the early event in the disease that results in Tau dysfunction, neuronal loss and ultimately dementia. Familial AD (FAD) modifications of the peptide leading to early onset of the disease are also involved either in modulation of the secretase activity, or enhancement of the aggregation propensity of the peptide, once again nourishing the amyloid cascade hypothesis. Cu(II) -Coordination sites. Cu(II) has first and mainly been under focus. This may be because of its d 9 electronic configuration that makes it active in many spectroscopies (EPR (see eibc.0310), NMR, UV-Vis and CD). 9,27,32,33 In addition, the study of Cu(II) binding site to Aβ has fostered the development of sophisticated techniques and methodologies. 27,32 Cu(II), as with other metal ions, are bound to the N-terminal part encompassing the 14 first residues and is bound to the Aβ via the Nterminal amine, two among the three His residues and one carbonyl function from the peptide backbone, with a preference for the carbonyl group of Asp1-Ala2 bond. This site (site ) is the most populated at physiological pH but is in pH equilibrium with a second one (site ) where the Cu(II) ion is bound by the N-terminal amine, the adjacent amidate function from the Asp1-Ala2 bond and carbonyl group from Ala2-Glu3 and one among the three His residues. The Cu(II) adopts its preferred binding geometry, induced by the Jahn-Teller effect, with four equatorial ligands and a fifth apical position that may be occupied by carboxylato groups. Coordination of Cu(II) to Aβ1-n and to other selected forms of Aβ are given in Figure 4. Notably, the Aβ4/11-n peptides offer the Cu(II) an ATCUN (Amino-Terminal Cu and Ni binding motif) site which is due to the -H2N-Xxx-Yyy-His sequence, 34 a motif that is shared with key proteins such as the Human Serum Albumin and has been strongly studied for its biological properties. 35,36 Cu(II) 27 binding to the murine peptide (See Figure 2 for sequence) has also been investigated. Indeed as murine animals do not show AD, it is anticipated that different coordination sites may be responsible, at least in part, of the different amyloidogenicity of the two peptides.

Cu(II) -binding kinetics.

In contrast to structural and thermodynamic data, kinetic data has been less investigated and mainly with Aβ1-n. The rate of Cu(II) binding (kon) is about 5 x 10 8 M -1 .s - 1 37 or 5 x 10 6 M -1 .s -1 , 38 where the weaker value may be due to the co-presence of glycine in the solution studied. 39 Cu(II) binding is much faster in site  than in site  so Cu(II) binding to site  goes through binding to site  and further reorganization. [37][38][39] In addition, the kon value is not strongly dependent with peptide FAD alterations. 40 Rate of Cu(II) dissociation from Aβ1-n (koff) has been evaluated to 0.1-0.8 s -1 , 37,38 all the data being given at pH 7.4.

Cu(I)

-Coordination sites. Cu(I) has been less studied, and almost exclusively for the Aβ1-n peptide, but the model of the coordination site was rapidly consensual, with two His making a linear His-Cu(I)-His arrangement (Figure 4), where the most populated site was made by the two adjacent His13 and His14. 22,41,42 The result was mainly obtained using XANES spectroscopy (X-ray Absorption Near Edge Structure, see eibc.0305) since the intensity of the 1s to 4p edge feature is strongly characteristic of the coordination mode of Cu(I). It could be anticipated that any form of Aβ keeping the His13-His14 dyad would show a similar Cu(I) site.

Cu(I) -Affinity.

Regarding the affinity, there is still a divergence in the literature, with values of 10 7 M -1 or 10 10 M -1 , [43][44][45] due to a difference in the Cu(I) affinity value taken for the competitor used in the titration experiment; hence the need to find a more direct way to determine Cu(I) affinity.

Zn(II) -Coordination sites.

As for Cu(I), the d 10 electronic configuration of Zn(II) makes it silent in most of the classical spectroscopic techniques. In addition and in contrast to Cu(I), the XANES fingerprint is weakly informative. That's why several binding modes have been proposed. 23,46 Recent results point to a Zn(II) ion tetrahedrally bound by two His residues and two carboxylates, with the predominant contribution of Glu11. 47 The murine peptide shows a different site with a Zn(II) surrounded by the N-terminal amine, two His side chains and the carboxylate group from Glu11 (Figure 4). 48 Noteworthy, both the Cu(II) and Zn(II) major sites at physiological pH differ between human and murine peptides, with the general trend of having a less protonated peptide bound to the metal center with the murine Aβ. Several studies of Zn(II) coordination to FAD have been reported and pointed out to the facilitated formation of aggregation prone Zn complexes. [49][50][51] Zn(II) -Affinity. The Zn(II) affinity for Aβ1-n is largely weaker than Cu(II) affinity and lies in the 10 5 M -1 -10 6 M -1 range. 52,53 Concluding remarks. Recurrent features in all the binding sites made by the Aβ peptides are (i) the presence of several sites, which are due to several equilibria in solution including pH equilibria;

(ii) the nature of the binding site is dictated by the central ion; in other words, the peptide is unable to offer a preorganized binding site as encountered with 3D-folded metalloproteins. This may be due to two factors: the high flexibility of the peptide and the number of potential binding amino-acid residues which exceeds the coordination number of the metal center, thus allowing the metal ion to choose its preferred environment. A direct consequence is the impossibility to get structural data by X-ray crystallography; hence the multi-technic approach used to determine metal binding sites in Aβ.

ROS.

One key impact of Cu(I)/Cu(II) binding to Aβ is the production of ROS, which results from the incomplete reduction of O2 to O2°-, H2O2 and HO° by ascorbate catalyzed by Cu(Aβ) (Figure 5, left panel). Given the very different binding sites of the two redox states of Cu, a direct electronic transfer will necessitate a very high reorganization energy, extremely unfavorable for the catalysis.

Hence it has been proposed that the redox reactions proceed via another site, the geometry of which is between that of Cu(I) and Cu(II) and is the same for both Cu(I) and Cu(II) ions. This site is known as the "in-between state" (IBS) 22 and was first observed via electrochemistry, 54 hence without any external substrate (reductant or oxidant). Further studies in presence of substrate led to the proposition of Cu ions bound by the N-terminal amine and the carboxylate side chain from Asp1 and from one His residue, and indicated that the rate-limiting step of the complete redox cycle may be due to oxidation of Cu(I) by dioxygen. 55 This IBS has only been proposed for Aβ1-n but similar states may also be encountered with the other forms of Aβ since for all Aβ, the Cu(I) and Cu(II) coordination environments are extremely different.

Aggregation. The formation of amyloids follows a specific pathway consisting in the aggregation of largely unfolded monomeric units, according to a two-step process: a rate-limiting nucleation phase during which oligomers form and an elongation phase during which the fibrils are made via the auto-catalytic self-assembly of peptides triggered by the oligomers (Figures 1 and5). 34,56,57 It is now accepted that the transient oligomeric species are the most toxic. 58 Aggregation of apo-Aβ follows the sigmoid-type curve as probed by thioflavin T (ThT), a dye that acquires fluorescence upon binding to β-sheet structures 56 and lead to well-defined typical amyloid fibrils (diameter of about 10 nm and length of about 1 µm). Metal ions can influence this aggregation mechanism via several paths, including helping to bridge two monomers and to form the nucleus or inducing a change of the peptide to a conformation more prone to aggregation. [59][60][61] The influence of Cu(II) and Zn(II) on Aβ aggregation has mainly been investigated on the full-length Aβ1-40/42 peptides with no real consensus. 60,62 This is due to the intrinsic auto-catalytic character of the aggregation process, which is mainly governed by the nucleation phase. Several parameters that are difficult to fully identify and control influence the nucleation phase. One key parameter is the nature of the starting Aβ sample, the perfect monomerization of which is required to get reproducible data. Then aggregation will depend on the conditions including concentration, buffer, pH, ionic strength, the nature of metal ions and their ratio. 63 With respect to the role of metal ions, the consensual general trends reported are: (i) stoichiometric amount of Cu(II) and Zn(II) influences Aβ aggregation differently, with Zn(II) leading to the formation of ill-defined heterogeneous aggregates and Cu(II) to small protofibrils; (ii) at weaker ratios, both Cu(II) and Zn(II) mainly influence the kinetics of the aggregation by delaying the elongation phase but keep the morphology of the apo-aggregates. 33 Very recently, one structure of Aβ1-42 fibrils has been proposed based on cryo-Electronic Microscopy, 64 complementing previous propositions made by NMR. [START_REF] Wälti | Proc. Natl. Acad. Sci. U. S. A[END_REF][START_REF] Colvin | [END_REF] It shows the participation of binding residues from the N-terminal part in several salt bridges; then it can be anticipated that such interaction will be disrupted by coordination of metal ions, explaining why metal ions do alter the full-length Aβ aggregation. The coordination sites of metal ions in the solid state (full-length Aβ aggregates) is very similar to those found for the soluble monomeric counterpart. 22,67 This may be due to the flexibility of the N-terminal site even in the solid-state.

Concluding remarks. It would be very interesting to explore in the near future (i) the ROS and aggregation properties at the molecular level of the altered counterparts of the Aβ1-40/42, exploiting the tools and methods developed in the study of the full-length peptides. This has been partly done for N-terminally truncated forms 34 and FAD peptides; and (ii) the ROS production mechanism by the oligomeric species to possibly link their toxicity to the ROS production.

Generalization to others IDPs. Other IDPs are involved in diverse neurodegenerative

disorders. This is the case of the Tau protein in AD, 18,19,31,[68][69][70] of synucleins in Parkinson's Disease, 8, 9, 70-74 of prion protein in Creutzfeld-Jacob Disease, 8, 74-76 polyGlu sequences in Huntington's Disease, 77,78 and Cu,Zn superoxide dismutase (SOD) in amyotrophic lateral sclerosis. 9,[78][79][80] IDPs can also be linked to other (non-neurodegenerative) pathologies: for instance, amylin is involved in Type II Diabetes Mellitus. [81][82][83] General features of those IDPs shared with the Aβ peptides are: (i) formation of amyloid deposits [always]; (ii) presence of loosely bound metal ions in the vicinity of the deposits Because the coordination of metal ions are governed by the same requirements as for the Aβ peptide, similar consequences with respect to ROS production and aggregation can be foreseen. The literature is however more limited compared to that for Aβ (see previous refs.).

II. Therapeutic approaches linked in AD

Introducing remarks. As previously detailed, metal ions have important roles in the modulation of the intrinsic properties of the IDPs. In general, interaction of the IDPs with metal ions are considered harmful, leading to therapeutic approaches mainly based on the removal of the metal ions. However, this raises several questions: (i) Is it safe to remove metal ions ? (ii) should both Cu and Zn be removed ? (iii) what can be the alternatives ?

In the following paragraphs, we describe the various inorganic approaches reported in the context of curing AD. We limit the description to AD because it is a prototypical IDP-related disease with respect to inorganic based therapies. This will include the molecules able to target metal ions or inorganic complexes able to interfere with ROS production and/or Aβ aggregation. Finally, we will briefly show some use of inorganic complexes for the early detection of AD.

First, we start with the description of the various approaches to extract metal ions from the Aβ peptides. As for the more fundamental studies, all the reports concerned the Aβ1-n peptides. In addition, because Cu can be directly involved in ROS production, it is generally regarded as the target of choice and hence I will describe only Cu targeting molecules. In the following, chelators correspond to molecules able to remove metal ions and metallophores to chelators able to redistribute the chelated ions elsewhere. The literature being extremely abundant of this topic, only chosen examples are described (and recent reviews given in refs.). The criterion for such a selection could be either historical, the smartness of the concept carried, but not necessarily the best drug candidates in terms of short-term medical approval (id est pharmacologic properties).

Chelators. Note that among the chelators described here, some may also be metallophores as well but the property has not been challenged and/or reported. Most of the chelators designed target Cu(II) and to be able to remove it from Aβ have higher Cu(II) affinity than the Aβ peptide. Of course, the affinity should not be too high in order to maintain as much as possible the natural metal homeostasis. In addition to the ability to extract Cu from Aβ, most of the chelators are designed so as to redox silence the Cu ion and to prevent the formation of Cu-induced oligomers. 78,[84][85][86][87][88][89] Extra activity and/or property are often sought leading to bi-functional and even multi-functional molecules. [90][91][92][93] Simple ligands. The simple cyclen (Figure 6.a) and cyclam scaffolds were probed for the above described abilities and show promising results. 94 This is also the case for derivatives of Schiffbase ligands (Figure 6.b). 95,96 In particular, those ligands are able to selectively remove Cu(II) versus Zn(II) from the Aβ peptide, a property that may be crucial as Cu(II) is the target of choice but that is not easy to fulfill due to (i) the high Cu(II) over Zn(II) selectivity of the Aβ itself which is about 4 orders of magnitude while for standard ligands such as edta the selectivity is about 2 orders of magnitude and (ii) the excess of Zn compared to Cu in the synaptic cleft (ratio of about 10). 33 Peptide-based ligands. The use of peptide-based molecules represents an interesting approach because the synthesis is highly modular. It is thus straightforward to adapt the affinity and/or to include additional groups such as a coumarin chromophore (Figure 6.c) that is able to act as a reporter for the extraction of Cu(II) from Aβ. 97 Cu(I) ligands. The first Cu(I) chelator described in the context of AD was the PTA (1,3,5-triaza-7-phosphaadamantane), Figure 6.d) a widely use molecule in anti-cancer therapy. 98 Results were good with the ability to stop ROS production induced by Cu(Aβ) and formation of oligomers. Later on, a more general approach was developed, where the ligand LNTA (Figure 6.e) was able to target both Cu(I) and Cu(II), remove them from Aβ and stop associated ROS production. 99 The main interest of such an approach is its pragmatism since the redox state of Cu within the synaptic cleft is still unknown.

Bi-and multi-functional chelators. All the reported bi-and multi-functional chelators target

Cu(II). Four examples of such molecules are given in Figure 6.a, f-h. As a classical feature, they encompass a Cu(II) binding moiety and a unit responsible for the recognition of Aβ aggregates.

Mainly three Aβ recognition moieties are used: 2-aryl-benzothiazole (Figure 6.f), 100 a scaffold reminiscent of the ThT dye known to interact with β-sheet (see §.Aggregation), stilbene-like derivatives (Figure 6.g) 101, 102 and peptidic β-sheet breaker sequence, typically the KLVFF pentapeptide (Figure 6.a). 103 The Aβ recognition moiety can either encompass the binding groups (Figure 6.g) or be linked to it (Figure 6.a). A typical multifunctional chelator is given in Figure 6.h, where the binding motif is created by the formation of the triazole group obtained by the straightforward "click" reaction thus leading to a very high modularity of such drug candidates. 104 Metallophores. The most developed and studied family of metallophores is the hydroxyquinoline family (Figure 7.a). 105 Clioquinol was first used and then the PBT2 derivative that offers a better pharmacologic profile was tested in Phase II of three different clinical trials. 106 Mechanism of action of such molecules relies on their ability to translocate Cu and Zn into the neurons and to trigger several events including higher degradation of the Aβ peptide. 107 The other important class of metallophore is the bis(thiosemicarbazone) ligand (Figure7.b). Intracellular Cu transfer is mediated by the intracellular reduction of Cu(II) and subsequent release that triggers a cascade of biological events leading to better clearance of Aβ, in a similar way as proposed for hydroxyquinoline-based molecules. Prodrugs. An elegant way to avoid perturbing normal metal homeostasis is to design prodrugs that will release the active chelator at its place of action. 110 The release can be triggered by different ways; three of them are illustrated below.

Cleavable peptide. A peptide encompassing a recognition site of the secretase involved in Aβ processing is cleaved to deliver an ATCUN (see §.Cu(II) coordination) motif able to strongly bind Cu(II), thus to remove it from Aβ and redox silence it (Figure 8.a). 111 Sugar-based ligands. Because the brain consumes a lot of sugar, glycosylated prochelators have been designed (Figure 8.b). In addition to masking the chelating unit, they can also direct the molecule towards its place of action and after enzymatic deprotection, the free ligand will be able to bind metal ions. 112 Inorganic prodrug. Recently a Mn-based SOD mimic has been used to mask the chelator and was shown to redox silence Cu(II) extracted from Aβ and restore apo-like aggregation of the peptide (Figure 8.c). 113 This strategy has also the benefit to provide a prodrug active against the oxidative stress that occurs in AD.

Concluding remarks.

Several key properties can be extracted from the studies detailed above: (i) A Cu affinity higher than that of the Aβ peptides but weaker than that of key Cu-metalloproteins; Other points will have then to be taken into account, the most important of which is the ability to cross the blood-brain barrier (BBB) either via passive or active diffusion. 114 Inorganic drugs. In addition to be used as prodrug (see §.Inorganic prodrug), inorganic complexes have been developed to target several aspects of AD (see eibc2499). 90 Three main approaches can be found: (i) redistribution of Cu or Zn binding sites in the Aβ (or ejection of them), (ii) inhibition of Aβ aggregation, and (iii) secretase-like activity to cleave and clear Aβ peptides.

Redistribution of the Cu and Zn binding site in the Aβ peptide. The use of platinoid complexes with N-heterocyclic and aromatic substituents aimed at precluding the binding of the Cu and Zn ions to the Aβ peptide, considered as deleterious event in the AD context, is a promising development in this area. Indeed such platinoid complexes make strong and relatively inert bond with the His residues from the peptide. 90,[115][116][117] But actually, it has been shown that they rather redistribute the Cu and/or Zn ion to another binding site in the peptide. 118 This family of inorganic drugs mainly act by modulating the Aβ aggregation pathways and in this family, the Pt(II) complex shown in Figure 9.a was studied in vivo, due its possible oral administration as the Pt(IV) prodrug, showing a decrease of amyloid deposits in transgenic mice models. 119 Inhibition of Aβ aggregation. POM (Poly-oxo metallates) including mono-substituted POM can inhibit Aβ aggregation. This has been attributed to (i) POM binding to the peptide via electrostatic interaction that leads to monomer unable to aggregate and (ii) POM binding to oligomers leading to the stabilization of oligomers which is unfavorable for nucleation and growth of fibrils. 120 The substitution by a Co(II) or Ni(II) ion (Figure 9.b) may increase the stability of the POMpeptide interaction via binding of His residues to the metal center. 121 Secretase-like activity. Another strategy relies on the use of azamacrocyles of transition metal ions (Figure 9.c) that has the ability to induce Aβ hydrolysis and thus modulate its aggregation. Co(II) was shown to be the best metal center due to the low pKa value of the coordinated water molecule responsible for the hydrolytic activity. 122 Having a synergetic effect by using the apo azamacrocyle ligand able to first remove Cu(II) and then use it to hydrolyze the peptide is also very elegant and has been reported with the cyclen-derivative ligand shown in Figure 6.b. 103 Concluding remarks. While ligands (either chelators or metallophores) can influence ROS production and aggregation by removing the metal ions, inorganic drugs have a main impact on the aggregation process, which can however be different than the one obtained with the ligands. Hence the two approaches using organic or inorganic molecules seem to be complementary. Passage through the BBB may be more complex with the inorganic compounds than with the organic derivatives.

Inorganic detection agents.

The early detection of AD is the other key issue if one aims at effectively fighting the disease. Many organic molecules were reported, bearing either 11 C or 18 F elements as radiotracers. 19,123 The use of metal radionuclides is also of interest, mainly for the ease to generate the labelled molecule in comparison with the more challenging covalent incorporation of 11 C or 18 F in organic scaffolds (see eibc.2447). In this context, mainly, 99m Tc-based molecules have been developed for SPECT imaging, with 99m Tc having an half-life of 6 hours and 64 Cu complexes for PET, with 64 Cu having an half-life of 13 hours. 56,90 As a general trend, the ligand for the 99m Tc or 64 Cu ion is linked to an Aβ recognition moiety, possibly via a modular linker (Figure 10.a), where two main Aβ recognition moieties are used: the benzothiazole (Figure 10.b) or the stilbene scaffold (Figure 10.c). Affinity for the metal center and kinetic inertness of the resulting complex must be high to avoid any metal release. The complex shown in Figure 10.c is a typical thiosemicarbazone Cu(II) complex that was used to detect Aβ deposits in post-mortem brains. 124 Further improvements on the same scaffold lead to Cu(II) complex able to cross the BBB in wild-type mice. 125 Recently, a family of benzothiazole-azamacrocycle Cu(II) (Figure 10.b) complexes with the ability to be a leading family of molecules for diagnostic applications were also described. 126 Indeed, promising results were obtained with respect to brain uptake in AD transgenic model mice and preliminary imaging by microPET. 127

III. What's next ?

From my view as a bioinorganic chemist, metal ion binding to Aβ is fascinating at several levels: the metal center (Cu(I), Cu(II) or Zn(II)) drives the nature of the binding sites; the binding sites are not unique but several ones are possible and interconversion between them can be triggered by subtle changes (such as replacement of a non-binding Arg by a Gly residues in the murine sequence).

One of the consequences of such versatility is the complex mechanism involved in ROS production and in modulation of the Aβ aggregation pathways. Efforts to better decipher all of these metal related processes are essential if one aims at rationally designing new disease-modifying drugs. In addition, they have fostered the development of new spectroscopic tools and analytical methodologies that will be very useful in the future for the study of metal ions binding to other IDPs.

Since the 1990's and the proposition of the amyloid cascade hypothesis, therapeutics targeting the Aβ peptide have been controverted because no curative drug candidates have succeeded in phase III of clinical trials. 29 This is also true for molecules targeting metal ions linked to the amyloid cascade process. 128 While as a direct consequence of such failures, the metal intervention in the amyloid cascade is more and more questioned, one may rather consider whether the metal-based therapeutic approaches developed were (biologically) relevant. Pathogenesis of AD is indeed multifactorial and only with respect to metal ions -Aβ peptides interactions, the chemical partners are multiple. These include the different sequences of the Aβ, the various forms of Aβ aggregates, the varying levels of Cu and Zn, the presence of other amino-acid residues such as glutamate. Three examples illustrate this issue very well: (i) taking for granted that Cu(II) is the target of choice. The brain is a reducing environment and hence Cu(I) may be the main redox state of Cu ions within the synaptic cleft; 99 (ii) regarding Zn as an "innocent" ion because it is redox-silent. Indeed, Zn can interfere with Cu binding to the Aβ peptides 129 and thus with Cu targeting; 33 (iii) overlooking kinetic parameters in the design of chelators or metallophores. 130 Up to now only thermodynamic data (affinity and selectivity) have been taken into account. As a more general trend, the importance of other biological partners have to be evaluated and a more general vision of AD is required. This includes interaction of Aβ with membranes 131 and with Tau, while the two IDPs involved in the disease are currently considered independently when not opposed to each other. 69 Another key issue may be the late detection of the disease that hampers any kind of modification of the disease progression. Here comes the question of prevention versus cure. To conclude with the therapeutic issues, one open question remains: do the metal and the amyloid cascade hypotheses need to be reassessed or should synthetic medicinal chemists be more creative ? ABBREVIATIONS IDP: Intrinsically Disordered Peptides or Proteins ; AD: Alzheimer's Disease ; Aβp/q-n/m: Aβ peptide starting at position p or q and ending at position n or m ; ROS: Reactive Oxygen Species ; FAD: Familial Alzheimer's Disease ; ThT: Thioflavin T ; ATCUN: Amino-Terminal Cu and Ni binding motif ; BBB: Blood Brain Barrier.

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 15

Figure 2 .

 2 Figure 2. Sequences of the various Aβ peptides using the three-letter code of amino-acids. In green: truncation leading to the ATCUN motif with the His in third position drawn in green; in red: FAD mutations; in blue: mutations leading to murine peptide.

  Metal ions: copper and zinc in the synaptic cleft. AD takes place in the synaptic cleft, a place of intense metal ion exchange. More precisely, a subset of glutamatergic neurons contains high amounts of Zn (mM) in their synaptic vesicles. Zn is transported via the ZnT3 transporter into these vesicles. Upon neuronal activation, these vesicles fuse with the cell membrane and Zn is released in the synaptic cleft. Locally, transient concentrations of up to several 100 µM have been detected. Zn is then rapidly taken up again by the neurons. It has been shown that this Zn-pool, released from neurons, plays a neuromodulatory role. Evidence from the literature suggests that Cu pumped by the ATPase7A Cu-transporter into vesicles could be released into the synaptic cleft via vesicle fusion.The oxidation state of vesicular Cu and its ligand(s) are not known. It is thus anticipated that the Zn and Cu exchanged in the synaptic cleft interact with Aβ and are finally found in high concentrations in the senile plaques detected in AD brains (Figure3).30,31

Figure 3 .

 3 Figure 3. Zinc (plain grey circles) and copper (open black circles) movements in the synaptic cleft and aggregation of the Aβ peptides leading to the amyloid fibrils found in the senile plaque, via the formation of oligomeric species considered as the most toxic ones.

  Cu(II) -Affinity. As a direct consequence, Cu(II) affinity values to the various Aβ peptides differs with Aβ4/11-n having the highest one: 10 14 M -1 , the Aβ1/3-n intermediate : 10 10 M -1 and the pyroglutamate forms Aβp3/p11-n, the weakest: 10 8 M -1 at pH 7.4.34

Figure 4 .

 4 Figure 4. Metal ion coordination to several Aβ peptides and corresponding conditional affinity value at pH 7.4. Regarding Cu(I) affinity, the two most accepted values reported in the literature are given.

Figure 5 .

 5 Figure 5. Left panel: ROS production catalyzed by the Cu(Aβ1-n) species; right panel: the typical sigmoidal curve depicting the formation of Aβ fibrils.

[

  frequent]; (iii) trace of oxidative stress [frequent]; (iv) familial mutations linked to early-onset of the disease [frequent] and mutations in the murine peptide counterpart which precludes the spontaneous apparition of the pathology [often].

Figure 6 .

 6 Figure 6. Selection of chelators designed to fight against AD.

  108 A bis-aminoquinoline ligand (Figure7.c) has recently been shown to be able to transfer the Cu(II) extracted from Aβ to apo-proteins via the formation of an intermediate Cu(I)-glutathione complex.109

Figure 7 .

 7 Figure 7. Selection of metallophores designed to fight against AD.

Figure 8 .

 8 Figure 8. Prochelator approaches developed to fight AD.

(

  ii) a high Cu over Zn selectivity in order to mainly remove Cu and not Zn, thus targeting the most toxic ion, at least with respect to ROS production; (iii) the redistribution approach adds value compared to the chelating one, indirectly inducing Aβ degradation pathways; (iv) chelators or metallophores should form redox inert complexes to prevent ROS production. Directing the drug candidates towards Cu(I) or Cu(II) is still open to debate; but criteria (i) and (ii) may be easier to fulfill with Cu(I).

Figure 9 .

 9 Figure 9. Inorganic drug candidates developed to fight AD.

Figure 10 .

 10 Figure 10. Radiotracers for early-detection of AD. General scheme of bifunctional chelator and corresponding 64 Cu(II) complexes. Concluding remarks. AD early detection is crucial because late treatments are less (if not completely) inefficient. Hence, the future of any kind of radiotracers or imaging agents should focus on the design of molecules able to detect oligomeric states of the Aβ aggregates.

ACKNOWLEDGEMENTS

I acknowledge all the people I had the chance to work with during the last years and my current coworkers. I would like to thank specifically Amandine Conte-Daban, Elena Atrian-Blasco and Xudong Lin, with whom I have written several review articles that were very useful for the redaction of the present chapter. Funding by the European Research Council (ERC StG 638712 -aLzINK) is also warmly acknowledged.

ABSTRACT

In the present chapter, I review the structural, thermodynamic and kinetic data on metal ions (copper and zinc) binding to the amyloid-β peptides of various sequences involved in Alzheimer's disease. Metal ions are indeed regarded as key players in Alzheimer's disease because they may contribute to the oxidative stress and modulate the aggregation propensity of the amyloid-β peptides, two key processes in the etiology of the disease. An analogy with the influence of the interaction between metal ions and other intrinsically disordered peptides in different pathologies is also drawn. In a second part, several therapeutic and diagnostic approaches based on the role of metal ions are described and discussed. A selection of chelators, metallophores, prodrugs as well as inorganic compounds is proposed that illustrates the various strategies developed by inorganic medicinal chemists to fight Alzheimer's disease.

KEYWORDS

Intrinsically disordered peptide / amyloid-β / Alzheimer's disease / Reactive Oxygen Species / Aggregation / therapeutic approaches


Jean-Baptiste Filippi
email: filippi@univ-corse.fr

Frédéric Bosseur
email: bosseur@univ-corse.fr

Céline Mari
email: celine.mari@aero.obs-mip.fr

Christine Lac
email: christine.lac@meteo.fr

Simulation of a Large Wildfire in a Coupled Fire-Atmosphere Model

Keywords: wildland fire, mesoscale atmospheric model, coupling

The Aullene fire devastated more than 3000 ha of Mediterranean maquis and pine forest in July 2009. The simulation of combustion processes, as well as atmospheric dynamics represents a challenge for such scenarios because of the various involved scales, from the scale of the individual flames to the larger regional scale. A coupled approach between the Meso-NH (Meso-scale Non-Hydrostatic) atmospheric model running in LES (Large Eddy Simulation) mode and the ForeFire fire spread model is proposed for predicting fine-to large-scale effects of this extreme wildfire, showing that such simulation is possible in a reasonable time using current supercomputers. The coupling involves the surface wind to drive the fire, while heat from combustion and water vapor fluxes are injected into the atmosphere at each atmospheric time step. To be representative of the phenomenon, a sub-meter resolution was used for the simulation of the fire front, while atmospheric simulations were performed with nested grids from 2400-m to 50-m resolution. Simulations were run with or without feedback from the fire to the atmospheric model, or without coupling from the atmosphere to the fire. In the two-way mode, the burnt area was reproduced with a good degree of realism at the local scale, where an acceleration in the valley wind and over sloping terrain pushed the fire line to locations in accordance with fire passing point observations. At the regional scale, the simulated fire plume compares well with the satellite image. The study explores the strong fire-atmosphere interactions leading to intense convective updrafts extending above the boundary layer, significant downdrafts behind the fire line in the upper plume, and horizontal wind speeds feeding strong inflow into the base of the convective updrafts. The fire-induced dynamics is induced by strong near-surface sensible heat fluxes reaching maximum values of 240 kW m -2 . The dynamical production of turbulent kinetic energy in the plume fire is larger in magnitude than the buoyancy contribution, partly due to the sheared initial environment, which promotes larger shear generation and to the shear induced by the updraft itself. The turbulence associated with the fire front is characterized by a quasi-isotropic behavior. The most active part of the Aullene fire lasted 10 h, while 9 h of computation time were required for the 24 million grid points on 900 computer cores.

Introduction

Although a natural process in most part of the world, wildland fires represent a constant threat wherever there exists a possible interface with human activities. A large number of tightly-coupled physical phenomena interact in the development of a large wildfire. Temperature increase in the fuel generates pyrolysis gases, the composition of which depends on the vegetation, and which can blaze. The intense heat release can dramatically modify the local meteorology, generating strong local convective motion and fire-induced winds, that in turn modify the fire front dynamics and drive the fire propagation [START_REF] Sun | The importance of fire-atmosphere coupling and boundary-layer turbulence to wildfire spread[END_REF]. To simulate wildland fire, the fire front propagation must be solved at the scale of a few meters to precisely take into account wind, slope, humidity and obstacles (road, rocks). Eventually, fire-atmosphere interactions with the local motions need to be taken into account to properly represent the composition, density, structure and transport of the plume.

Nevertheless, simulating large wildland fires requires choosing between the complexity of the code, data availability, the speed at which the result must be obtained and the computational framework. The variety of models thus ranges from physically-detailed, fire/atmosphere coupled and computationally-intensive (and limited to relatively small fires) models such as FIRETEC [START_REF] Linn | Studying wildfire behavior using FIRETEC[END_REF], WFDS [START_REF] Mell | A physics-based approach to modelling grassland fires[END_REF] or FIRESTAR [START_REF] Morvan | Modeling of fire spread through a forest fuel bed using a multiphase formulation[END_REF][START_REF] Morvan | Modeling the propagation of a wildfire through a Mediterranean shrub using a multiphase formulation[END_REF] to empirical, uncoupled (forced wind field) models such as FARSITE [START_REF] Finney | FARSITE: Fire Area Simulator-Model Development and Evaluation-Research Paper RMRS-RP-4 Revised[END_REF] that are adapted to provide rapid simulation of very large wildfires. As an intermediate trade-off, approaches coupling a 2D-surface fire propagation model with a mesoscale atmospheric model [START_REF] Clark | A Coupled Atmosphere Fire Model: Convective Feedback on Fire-Line Dynamics[END_REF][START_REF] Mandel | Coupled atmosphere-wildland fire modeling with WRF 3.3 and SFIRE[END_REF][START_REF] Filippi | Simulation of Coupled Fire/Atmosphere Interaction with the MesoNH-ForeFire Models[END_REF] have shown their ability to capture some of the complex phenomena occurring in large fires while still being adapted to a real-time response.

This last approach is developed in this study, which focuses on testing the ability of these coupled fire-atmosphere models to represent micro-scale atmospheric and fire front effects on a real and large observed fire case. Numerical fire/atmosphere coupling has already undergone numerous studies, starting from the static fire simulations of [START_REF] Heilman | Simulations of Horizontal Roll Vortex Development Above Lines of Extreme Surface Heating[END_REF] to the pioneering works of [START_REF] Clark | A Coupled Atmosphere Fire Model: Convective Feedback on Fire-Line Dynamics[END_REF][START_REF] Clark | A Coupled Atmosphere-Fire Model: Role of the Convective Froude Number and Dynamic Fingering at the Fireline[END_REF] where a simplified model of [START_REF] Rothermel | A Mahematical Model for Predicting Fire Spread in Wildland Fuels[END_REF] fire spread was coupled to the atmospheric model of [START_REF] Clark | Description of a coupled atmosphere-fire model[END_REF]. More recently, the original Clark/Coen model evolved to the CAWFE model [START_REF] Coen | Modeling Wildland Fires: A Description of the Coupled Atmosphere-Wildland Fire Environment Model (CAWFE)[END_REF], while efforts at extending the WRF weather forecasting model [START_REF] Skamarock | A time-split nonhydrostatic atmospheric model for weather research and forecasting applications[END_REF] have resulted in the WRF/fire module [START_REF] Mandel | Coupled atmosphere-wildland fire modeling with WRF 3.3 and SFIRE[END_REF], widely used even at the scale of large fires (several square kilometers [START_REF] Kochanski | Real time simulation of 2007 Santa Ana fires[END_REF][START_REF] Coen | WRF-Fire: Coupled Weather-Wildland Fire Modeling with the Weather Research and Forecasting Model[END_REF][START_REF] Peace | Coupled Fire-Atmosphere Simulations of the Rocky River Fire Using WRF-SFIRE[END_REF][START_REF] Coen | Simulation of the Big Elk Fire using coupled atmosphere-fire modeling[END_REF]).

A similar system is used here, based on the atmospheric Meso-NH model [START_REF] Lafore | The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations[END_REF][START_REF] Lac | Overview of the Meso-NH model version 5.4 and its applications[END_REF] interactively coupled with the ForeFire fire spread model [START_REF] Balbi | A Physical Model for Wildland Fires[END_REF]. Specifically, the fire model is different from the [START_REF] Rothermel | How to Predict the Spread and Intensity of Forest and Range Fire[END_REF] model used in other approaches taking into account the effects of wind and slope through coefficients experimentally fitted to wind values "as if the fire was not there". Moreover, although large wildfires remain an objective, specific numerical methods were developed so that all phenomena could be simulated at a resolution close to their characteristic scale.

The target case study is decomposed into four nested domains ranging from 2.4-km to 50-m resolution, allowing one to explore the local to the regional impact of a large wildfire in an interactive fire-atmosphere coupling. Fire front is integrated at the scale of thermal transfer (sub-meter), fuel consumption at the resolution of the vegetation database (5 m), local atmosphere and winds at the resolution of the convective structures above the fire front (50 m) and smoke tracer transport at the meso-scale (2 km).

The ForeFire fire front solver [START_REF] Filippi | Simulation of Coupled Fire/Atmosphere Interaction with the MesoNH-ForeFire Models[END_REF][START_REF] Filippi | Discrete Event Front-tracking Simulation of a Physical Fire-spread Model[END_REF] has been developed to enable the use of several propagation models, as well as coupled with nested Meso-NH domains by defining fluxes for all the physical and chemical properties. Coupled with the Meso-NH atmospheric model [START_REF] Lac | Overview of the Meso-NH model version 5.4 and its applications[END_REF], it has already been the subject of several investigations on relatively small fires with encouraging results, such as simulating atmospheric feedbacks in agreement with other coupled numerical models [START_REF] Filippi | Coupled atmosphere-wildland fire modelling[END_REF], and reproducing vertical wind velocities and temperatures in the range of what was observed during the controlled experiment FireFlux [START_REF] Filippi | Assessment of ForeFire/Meso-NH for wildland fire/atmosphere coupled simulation of the FireFlux experiment[END_REF].

The study proposed in this work is devoted to evaluating the ability of this code to scale up to large fires, about a hundred times the size of previous wildfires already simulated, and in extreme fire weather conditions (temperature over 40 degrees, very low air humidity, low to moderate winds). The case study here is the Aullene wildfire that burned more than 2000 ha in less than one day in July 2009. It aims to understand how the fire modifies the dynamical structure of the surrounding atmosphere, by characterizing the turbulence in the near-fire environment.

The second part of the article presents briefly the Meso-NH and ForeFire models, focusing on the way fire fluxes are integrated and coupled between both. The third part is devoted to the presentation of the simulations of the 2009 Aullene fire, and the fourth part validates subjectively the coupled simulation and focuses on the dynamical structure of the plume and the surrounding atmosphere at 50-m horizontal resolution. Elements of computational times are given at the end of this section. Conclusions are drawn in Section 5.

Presentation of the Models and Coupling Methods

The simulation system is composed of two main components: the fire and the atmospheric codes. Both can be considered as solvers of numerous physical processes that are required to provide relevant forecast in a reasonable time. Major differences exist between both models, with the fire system being comparatively highly discontinuous and inhomogeneous, dealing with small scales. A consequence of this is that pertinent numerical methods and algorithms differ for the two models. The fire front solver uses a prognostic front velocity, or Rate Of Spread (ROS) model, that can analytically and directly provide this ROS, given fuel, atmosphere and current front state. These local parameters are interpolated at the front position in the atmospheric model with wind specifically taken as input in the ROS model [START_REF] Balbi | A Physical Model for Wildland Fires[END_REF].

Feedback from the fire to the atmospheric model requires an aggregation of results made at the fire scale, as it will typically be solved at a much finer scale. Fire to atmosphere feedbacks may influence many other parameters, such as surface roughness, albedo and chemistry, but we only consider for the moment the main fields influencing atmosphere dynamics, i.e., water vapor, heat, wind and smoke tracer fluxes.

Meso-NH Atmospheric Model

The Meso-NH non-hydrostatic atmospheric model [START_REF] Lafore | The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations[END_REF][START_REF] Lac | Overview of the Meso-NH model version 5.4 and its applications[END_REF] is an open-source research model based on the anelastic assumption, allowing simultaneous simulation of several scales of motion, by an interactive grid-nesting technique. The meteorological variables (temperature, water substances and Turbulent Kinetic Energy (TKE)) and scalar variables (like tracers) are advected with a so-called monotonic piecewise parabolic method [START_REF] Colella | The Piecewise Parabolic Method (PPM) for gas-dynamical simulations[END_REF] associated with a forward-in-time temporal scheme, while the wind is transported by a fourth order centered scheme associated with the Leap-Frog (LF) temporal scheme. The major asset of the fourth order centered scheme is its good accuracy (effective resolution on the order of 5-6 ∆x [START_REF] Ricard | Kinetic energy spectra characteristics of two convectionpermitting limited-area models AROME and Meso-NH[END_REF]) with the LF scheme imposing a strong limit on the time step. Surface parametrizations are performed in the SURFEX model [START_REF] Masson | The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of earth surface variables and fluxes[END_REF] with the Interactions between Soil, Biosphere, and Atmosphere (ISBA) parameterization [START_REF] Noilhan | A simple parameterization of land surface processes for meteorological models[END_REF] for the vegetation canopy, and integrated in Meso-NH as surface flux boundary conditions at each atmospheric time step.

The grid-nesting of Meso-NH allows the simultaneous running of models of different horizontal resolutions, sharing the same vertical grid. Only the highest resolution nested domain is coupled with the fire simulation, with wind, temperature, water vapor, pressure and scalar tracer exchanged at their common time step.

Wildfire Propagation

ForeFire is a so-called fire area simulator, with the fire font defined as the contour of the burning area. The main originalities of this code are the numerical method used and the modular and expandable software architecture, written in C++, open source and available at https://github.com/ forefireAPI/. The code can be run standalone, embedded as a software library or coupled with an atmospheric model, all with similar initialization procedures. Moreover, the front propagation is not tied to any particular velocity (ROS) or surface flux (for diagnostic/coupling) models and could be extended with user-defined models.

While several methods may be used to capture fire front evolution (see [START_REF] Maitre | Review of numerical methods for free interfaces. Ecole Thématique "Modèles de champ de phase pour l'évolution de structures complexes[END_REF] for a review of numerical interface tracking and capturing methods), the fire front advance is performed by an interface capturing Lagrangian markers method inspired by [START_REF] Tryggvason | A Front-Tracking Method for the Computations of Multiphase Flow[END_REF] and similar to FarSite [START_REF] Finney | FARSITE: Fire Area Simulator-Model Development and Evaluation-Research Paper RMRS-RP-4 Revised[END_REF][START_REF] Clark | A Coupled Atmosphere Fire Model: Convective Feedback on Fire-Line Dynamics[END_REF][START_REF] Clark | A Coupled Atmosphere-Fire Model: Role of the Convective Froude Number and Dynamic Fingering at the Fireline[END_REF][START_REF] Clark | Description of a coupled atmosphere-fire model[END_REF]. The specificities of this interface capturing method compared to [START_REF] Finney | FARSITE: Fire Area Simulator-Model Development and Evaluation-Research Paper RMRS-RP-4 Revised[END_REF][START_REF] Clark | Description of a coupled atmosphere-fire model[END_REF] are the discrete event temporal scheme (based on a scheduler rather than on regular time steps) and markers' motion, which are not tied to any underlying grid such as in [START_REF] Clark | Description of a coupled atmosphere-fire model[END_REF][START_REF] Tryggvason | A Front-Tracking Method for the Computations of Multiphase Flow[END_REF] or the original Marker And Cell (MAC) method [START_REF] Harlow | Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[END_REF]. A complete description and test of the code may be found in [START_REF] Filippi | Discrete Event Front-tracking Simulation of a Physical Fire-spread Model[END_REF][START_REF] Filippi | Evaluation of forest fire models on a large observation database[END_REF].

The appropriate level of accuracy of the discretization is specified through a maximum distance d allowed between two consecutive markers and is called the perimeter resolution. A new marker is dynamically added if two markers are farther than d and deleted if closer than d/2. The Discrete Event Simulation (DES) time scheme permits one to apply the Courant-Friedrichs-Lewy (CFL) constraint to each segment at each marker update and consequently updating more frequently areas where the interface is the most active (in an approach similar to [START_REF] Karimabadi | A new asynchronous methodology for modeling of physical systems: breaking the curse of courant condition[END_REF]). In DES, each simulation element, node, marker or sub-model must compute its optimal local time step and schedule its future update as events in a shared and time-sorted timetable. Simulation is driven by processing the most imminent event, updating an element that may re-schedule a new event.

Scheduling can be seen as the most aggressive automatic time stepping method and requires a time-consuming and relatively complex data structure for time sorting. This feature is therefore unlikely a major computational cost cutter in most multiphase fluid mechanics, as the continuity equation generally prevents the co-existence of wide interface velocity spread. In applications where a large inhomogeneity in the interface velocity field can be observed, such as in wildland fires, optimization may dramatically reduce computational cost as it focuses computation on fast moving elements. Here, front markers are by far the most frequently-updated element, and a key parameter for this integration scheme is the spatial increment δl that defines the maximum distance by which a marker may travel before being updated and topological checks performed at the marker location.

A high resolution matrix of Arrival Time (AT) is diagnosed from the front advance and used to keep track of the fire history to perform instantaneous surface diagnostics. This arrival time matrix is updated locally, marking the date at which the first marker burned a location using a polygon filling algorithm. The AT matrix resolution requires fixing a physical lower limit, making the hypothesis of a typically minimal propagative front depth d e . On large domains (tens of km 2 ), this two-dimensional matrix may contain millions of points at a typical resolution of d e 2 m. Nevertheless, as the active burning area is a small fraction of the total domain extension, AT matrices are handled as a sparse matrix that may still be computed efficiently.

Fire Velocity (ROS) Model

The Balbi [START_REF] Balbi | A Physical Model for Wildland Fires[END_REF] model, like the Rothermel model, can be classified as a quasi-physical model. Its formulation is based on the assumption that the front propagates as a radiating panel in the direction normal to the front. The model verifies that for a specific wind, terrain and fuel configuration, the absorbed energy equals the combustion energy directed toward the unburned fuel. This energy is the sum of a "radiant" part from the flame and a "conductive" part within the fuel layer.

The assumption is also made that only a given portion χ 0 of the combustion energy is released as radiation because the flame is viewed as a wind tilted radiant panel with an angle γ toward the unburned fuel.

A major assumption, also present in the Rothermel model and removed in the model formulation for this study, is that the fire is always traveling at a stationary speed that verifies V = λ/τ, meaning that all energy is absorbed within the fuel bed for the computation of V 0 , a potential rate of spread. Because of this assumption, front velocity is only dependent on fuel, but not on the instantaneous fire state (previous intensity, front curvature, depth), so it cannot therefore accelerate or go to extinction.

By using the front tracking solver, local front depth λ and curvature κ are always available as numerical diagnostics of the front allowing one to take into account this instantaneous state of the front. The updated, non-stationary, formulation used in this study is available in [START_REF] Filippi | Evaluation of forest fire models on a large observation database[END_REF].

In a coupled configuration, the wind v should be taken at mid-flame height and at the flame location. Flame height is not a direct prognostic variable in the model, and assuming a purely triangular flame of λ base length over the fuel (with E the fuel height), this mid-height may be roughly approximated with E + 0.5λ tan γ. Wind values that are used to drive the fire at the fire marker location are interpolated from the first grid level. If bilinear interpolation is used on the horizontal plane, vertical interpolation is the subject of several assumptions and parameterization. It is possible to either assume that the wind speed is valid over the whole level height or to interpolate it at the approximated mid-flame height. Both methods are arguable, with tests presenting no large differences between them as the ROS model already imposes little wind effect on slow propagation speed (small, flank or backfiring flames). Moreover, one of the major problems is the triangular flame hypothesis for the height computation and approximations of the surface vertical roughness that can be arguable at the scale at which a vertical approximation may be made. For this study, given the lack of appropriate high resolution data on local vegetation height, vertical wind velocity was not interpolated in large fire configurations in order to reduce overall computational cost.

Coupling Atmospheric and Wildfire Models

A two-way coupling is assumed between the fire and atmospheric model and performed at each atmospheric time step (typically sub-second). In the fire model, the atmospheric model is handled as one element with a constant update period equal to this atmospheric time step. Surface wind fields are sent to the fire model at the end of each atmospheric time step, while fire fluxes are updated at the start of next step. Two wind fields (start and end steps) are thus available in the fire simulation. Less frequent (typically hours) re-normalization steps are performed in real-cases' reanalysis to take into account global meteorological forcing (temperature, humidity). Atmospheric grid geometry is also sent to the fire solver at initialization to compute local interpolations at the front position.

A bi-linear interpolation in space and time is performed to deduce the point wind value at each marker location. Forcing the atmospheric model with ground conditions stemming from the fire is simplified by Meso-NH's ability to handle fluxes' forcing at the ground level. There is a clear limitation to the level of the combustion process that can be resolved as Meso-NH is not designed for cells smaller than a few meters with combustion handled as a subgrid process.

Computation of the desired fluxes is carried out using a high resolution AT matrix with burning area determined at each atmospheric time step and for each ground atmospheric cell as the difference between the current time t and arrival time of the fire at the location t a (x).

Integration of local fluxes is performed by applying a flux model Φ on all the AT points I c contained in an atmospheric cell:

Φ atmo (t) = I c Φ(x, t)dx (1)
and thus, the resolution of the burning map has to be much higher than the atmospheric one to ensure that averages over each atmospheric ground cell define well-posed boundary conditions forced by the fire on the atmosphere. Flux models for heat Φ h and water Φ w are models that must provide ground forcing conditions during an atmospheric time step duration given a current time t and the arrival time of the fire at the location t a (x). While CAWFE and WRF/SFire make use of the BURNUP algorithm from Albini [START_REF] Albini | Calibration of a Large Fuel Burnout Model[END_REF], we approximate the flux models based on numerical studies from [START_REF] Morvan | Numerical study of the effect of fuel moisture content (FMC) upon the propagation of a surface fire on a flat terrain[END_REF]. Fluxes are here represented by a simple analytic gamma function that represents a more intense release at the early combustion stage. The gamma function has the advantage of being easily integrable, and for a total mass/energy Phi release for a duration τ, the flux at the fire location f ( x, t) is given by:

f ( x, t) = Φ( x) τ 2 (t -t a ( x))e -(t-t a ( x)) τ (2)
Burning duration τ is extrapolated from the [START_REF] Anderson | Heat Transfer and Fire Spread[END_REF] model. Heat and vapor fluxes (resp. Φ h and Φ v ) used throughout the domain are computed over the flaming area and for this burning duration. The total amount released during this process is induced from several assumptions. All the water content (Φ w = σm) is assumed to evaporate during the combustion phase. The fraction of radiant energy and combustion efficiency (portion of flaming energy) are assumed to take values χ 0 = 0.3 and E c = 0.5, with a total heat release forced at ground level given by Φ t h = (1χ 0 )E c σ∆h. A passive scalar injection is also set with a constant release of 1 per m 2 s -1 in the burning area to act as a smoke tracer.

In the fire front solver, velocity models are user defined as single C++ class files with several already available in the standard distribution for speed (Rothermel, Balbi, isotropic, wind only) and may be extended by adding new classes. For use in a coupled configuration, the code architecture allows the same classes' definitions for surface flux models for different chemical compounds, heat and vapor. The coupled simulation code was developed originally for ideal simulation cases [START_REF] Filippi | Coupled atmosphere-wildland fire modelling[END_REF], extended for use in real cases at different resolutions [START_REF] Filippi | Simulation of Coupled Fire/Atmosphere Interaction with the MesoNH-ForeFire Models[END_REF][START_REF] Filippi | Assessment of ForeFire/Meso-NH for wildland fire/atmosphere coupled simulation of the FireFlux experiment[END_REF], with this study the first to present this coupled system for use in large wildfires.

Presentation of the Simulation

Observations of the Fire Case

The Aullene fire occurred on 23 July 2009, lasted five days and burned more than 3000 ha of forest with 2000 ha during the first afternoon. The same day, two other major fires (Peri, Ortolo) occurred, bringing the total burnt area over 6000 ha.

Figure 1 shows the diurnal variation of temperature, relative humidity and wind speed measured at the Sartene weather station located 20 km away from the fire. The hours prior to the fire were characterized by extreme weather conditions with low relative humidity (10%), very high temperatures (more than 40 • C) and low to moderate winds (up to 6 m s -1 ). The landscape of the region is typical of the Corsican mountains with a 8 km-wide and 30 km-long valley starting at sea level with elevation rising to more than 2000 m. The fire started at 13:26 UTC and was very active during the first 6 h. Fire fighting actions and an increase in relative humidity slowed down the fire progression at around 19:00 UTC, stopping the propagation at sunset (21:00 UTC). Containment actions handled during the first hour were mainly unsuccessful. Then, during the most active propagation time, all the fire fighting actions were concentrated on the north flanks to prevent the fire from expanding to the next valley.

Numerical Configuration

In order to resolve the development of the fire/weather system from the fire front to the large-scale atmospheric transport of the fire plume, the two-way nesting capability of the Meso-NH model is applied with four nested domains (Figure 2). The horizontal grid size is 2400 m for the outer domain covering 600 km × 720 km. The inner computational grids have grid increments of respectively 600, The vertical resolution is identical for all the nested domains, with 66 levels up to 10 km and a first level above the ground at 10-m height. All the nested models use the one and a half order closure turbulence scheme of [START_REF] Cuxart | A turbulence scheme allowing for mesoscale and large-eddy simulations[END_REF] with a prognostic TKE: the three finest resolution domains use the 3D version of the scheme, while the first one only considers the 1D version, neglecting the horizontal turbulent fluxes. In addition, the 200-m and 50-m resolution domains consider the [START_REF] Deardorff | Stratocumulus-capped mixed layers derived from a three-dimensional model[END_REF] mixing length, while the first two use the one of [START_REF] Bougeault | Parameterization of Orography-Induced Turbulence in a Mesobeta-Scale Model[END_REF]. In the same way, only the coarsest model uses the [START_REF] Pergaud | A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction[END_REF] mass flux scheme to parametrize the thermals in the atmospheric boundary layer while they are explicitly resolved at a finer scale. Three different simulations have been run to conduct a sensitivity study of the coupling method. The main simulation is the "coupled" coupling simulation, or "feedback-on", where the interaction between the atmospheric and fire models is two-way, as described above. An "uncoupled" simulation was run, or "feedback-off", where the atmospheric winds are provided to the fire model, but the fire model returns nothing to the atmosphere. The third simulation is the "fire-to-atm " mode where Meso-NH wind fields are not used by ForeFire, so there is no fire-line propagation with the marker method. A pre-computed arrival time matrix is used to compute the fluxes at each atmospheric time step. This matrix is computed using a simulation of the fire with the integration of the modified fuel distribution to represent fire-fighting actions (massive air attack at the flanks and at the fire head around the end of the fire). The "feedback-off" wind field at 14 UTC was selected for this fire-to-atm arrival time matrix as it provided the best fit to match observed fire passing points and final shape. In return, ForeFire provides the modified surface fluxes to Meso-NH. "Feedback-off" simulations can be used if the forecast starts from an already developed fire (with an actual observed burning area), or to investigate a "what-if" scenario of a fire simulated without the overhead of the atmospheric model.

Data Sources

The fuel layer is derived from the National Forest Inventory and is coupled with data from the IGN BD TOPO R for road and drainage networks. The Digital Elevation Model (DEM) is extracted from IGN BD ALTI R 25-m resolution. IFN classes have been grouped according to the methodology developed in [START_REF] Santoni | Wildland Fire Behaviour Case Studies and Fuel Models for Landscape-Scale Fire Modeling[END_REF] and use the proposed characterization of the vegetation. Figure 4 presents the fuel distribution over the final burnt area, with four main classes, as well as small non-burnable area providing fuel breaks. Vegetation heterogeneity, orography or small unreported older fires influence the fire propagation at small scales. These heterogeneities are not accounted for in this work, and the chosen fuel types are taken as the best guesses. Fuel parameters (mass loading σ, height E (m), moisture content (m) and heat of combustion ∆h) used in the front velocity model for these four major classes are presented in Table 1. These values correspond to the dead fuel load of relatively small particles (branches with diameters less than 0.01 m) that are assumed to drive the flaming fire. Pine and mixed pines' fuel estimates are equivalent fuel types that were given by foresters in charge of the area. Except from the maquis, where estimates of similar species are available from [START_REF] Santoni | Wildland Fire Behaviour Case Studies and Fuel Models for Landscape-Scale Fire Modeling[END_REF], it was not possible to match with the foresters any relevant fuel characterization available in the literature. Moisture content was estimated to be very dry with values for the day reported well under 10% for shrubs. The same parameters were used for the fluxes' models, with only the thin fuel contributing to heat injection, focusing the intense effects on the active fire area. Although the omission of larger fuel particle probably under-evaluates the contribution of the fire, it is consistent with the assumptions of the velocity model.

Simulation Results

Qualitative Results of the "Coupled" Simulation

In this part, we qualitatively describe the results of the "coupled" simulation. The simulated fire behavior is difficult to assess, as fire fighters were very active (except during the first hour), influencing strongly the fire propagation (and thus the local circulation), but clear reports of fire fighting actions do not exist. The only information of the fire dynamics comes from reports of fire front passage, as shown in Figure 5. Without taking into account fire fighting actions, the "coupled" simulation obviously overestimates the global area burnt, except during the first hour, where the limited fighting actions were almost inefficient.

However, generally, the simulated front positions appear to approximate correctly the reported location of the fire head that could not be contained. The simulated fire plume shows a good degree of realism at the local scale at 50-m resolution (Figure 6a). The simulated boundary layer, analyzed in the next section, reaches approximately 2200 m above ground level in reasonable agreement with a sounding from a nearby (30 km) Ajaccio airport launched 3 h before. Once injected in the free troposphere, the fire plume is advected and diluted by larger scale winds and turbulence. The fire plume simulated in the coarser model domain at 600-m resolution is advected northeastward, 40 km downwind of the fire ignition area (Figure 6b). This compares well with the plume direction and extension observed from MODIS. Figure 7 shows the wind acceleration near the surface and high wind speed values, which propagate along the fire-induced convective column reaching a 4500-m height. The colored streamlines reveal the vorticity magnitude in the ascending core of the fire plume. Fires are known to create vortices [START_REF] Forthofer | Review of Vortices in Wildland Fire[END_REF], and although it is out of scope for this study to characterize specific whirl structures at the fire front scale, fire-induced vorticity in the vicinity of the front can be resolved because of the high horizontal resolution. An animated visualization of the simulation is available as video supplementary material. We can conclude that the "coupled" simulation shows a plausible development of the fire propagation according to available observations and can be further studied.

Dynamical Plume Structure

One of the aims of the current study is to use numerical simulations to better understand fire and atmosphere interactions. Figure 8 presents the fire front of the "uncoupled" and "coupled" simulations at 1500 UTC with the near-surface winds. The simulated fire spreads more rapidly on the north flanks of the valley, inducing convergent winds. The difference between the "coupled" and "uncoupled" simulations is analyzed to quantify the impact of the fire on the atmosphere. Perturbed surface winds occur around 3 km around the fire front (Figure 8c). Fire-induced surface winds reach more than five-times the background ambient winds throughout the fire with horizontal motion differences up to 20 m s -1 . The fire not only modifies the dynamics near the surface, but creates a plume of almost 5000 m in depth (Figure 9). Instantaneous upward vertical velocities in the plume reach values of 27 m s -1 , with pockets of peak values being produced above the boundary layer. Comparing simulated magnitudes to the observation of other instrumented wildfires is a little bit hazardous, as we cannot expect the values to be the same for all fires. It just allows one to control the order of magnitude of the simulated values. Only few large-scale experiments [START_REF] Clark | Analysis of Small-Scale Convective Dynamics in a Crown Fire Using Infrared Video Camera Imagery[END_REF][START_REF] Coen | Infrared Imagery of Crown-Fire Dynamics during FROSTFIRE[END_REF] were conducted and mainly on crown fires. In this respect, simulated updrafts appear in agreement with [START_REF] Clark | Analysis of Small-Scale Convective Dynamics in a Crown Fire Using Infrared Video Camera Imagery[END_REF], who observed updraft values on the order of 20-30 m s -1 , and [START_REF] Coen | Infrared Imagery of Crown-Fire Dynamics during FROSTFIRE[END_REF], who reported peaks of 32-60 m s -1 for crown fires occurring at the highest detectable heights (about 50 m). The largest simulated downward motion occurs in the upper plume behind the fire front (maximum of -7 m s -1 ), consistent with previous observations [START_REF] Clements | First observations of turbulence generated by grass fires[END_REF] and simulations [START_REF] Sun | An evaluation of fire-plume properties simulated with the Fire Dynamics Simulator (FDS) and the Clark coupled wildfire model[END_REF]. Differences in sensible heat flux at a 20-m height show maximum values of 240 kW m -2 (Figure 10d), which fall within the range of sensible heat fluxes as reported by [START_REF] Lareau | The Mean and Turbulent Properties of a Wildfire Convective Plume[END_REF]. They induce maxima of the 2-m temperature difference over the active fire area up to 70 K (Figure 10c). This generates a near-surface convergence zone in the active fire area (negative values of Figure 11a) and areas of near-surface divergence consecutive to downdrafts directly behind the fire front (Figure 8d) as a result of the pressure gradient caused by the convective plume and the air being drawn into the column (Figure 11b). The work in [START_REF] Sun | An evaluation of fire-plume properties simulated with the Fire Dynamics Simulator (FDS) and the Clark coupled wildfire model[END_REF] suggested that downdrafts bring higher momentum near the surface and contribute to an increase in the rate of spread.

In the "uncoupled" simulation, a significant shear is present, with values of the order of 0.012 s -1 between a 1600-m and a 2600-m height (Figure 9a). The fire destroys the wind vertical gradient by inducing resolved eddies, with pockets of winds similar to the multi-cell distribution of convective cores described by [START_REF] Kiefer | Regimes of dry convection above wildfires: Idealized numerical simulations and dimensional analysis[END_REF] (Figure 9b). Unresolved eddies at 50-m resolution are also developed in the fire plume, with strong TKE values exceeding 20 m 2 s -2 , almost ten-times the background values of the planetary boundary layer (Figure 12a,b). The two main contributions of the TKE production are presented in Figure 12c,d. Near the surface, the thermal production is higher than the shear contribution due to a large increase in the sensible heat flux. However, above in the plume, the dynamics mainly controls the TKE production, probably partly due to the initial shear environment and partly due to the shear induced by the updraft itself. In agreement with observational studies [START_REF] Clements | First observations of turbulence generated by grass fires[END_REF][START_REF] Lareau | The Mean and Turbulent Properties of a Wildfire Convective Plume[END_REF], the simulation shows increases in both horizontal and vertical velocity variances at the fire front and above, up to a 5000-m height (Figure 13). Simulated values are in the same order of magnitude as the LiDAR observation of [START_REF] Lareau | The Mean and Turbulent Properties of a Wildfire Convective Plume[END_REF] reporting maximum variance values from 7 to 14 m 2 s -2 in a plume overshooting with comparable height. The simulated turbulence associated with the fire front is characterized by quasi-isotropic behavior with both high horizontal and vertical variances associated with fire-induced winds at the fire-front (Figure 14). The spectral analysis reveals a general increase in the vertical velocity spectral energy at all wavelengths with the fire-atmosphere coupling, velocity spectra obeying the -5/3 slope in the inertial subrange well. When taking into account fire fighting actions in the "fire-to-atm" simulation, the fire is less active on its lateral flanks and progresses more quickly toward the northeast (Figure 15), inducing an advance of about 1 km at 1500 UTC. The structure and the magnitude of dynamical fields are similar with strong fire-induced surface winds producing a convergence zone ahead of the surface and a convective column reaching the same height with strong updrafts and unresolved eddies mainly produced by shear. This underlines the systematic structure induced by the fire-atmosphere interactions in this configuration of the Aullene fire.

Computational Time

Computations were performed on the computer Jade at CINES (Centre Informatique National de l'Enseignement Supérieur) on 900 processors (Intel XEON types). Fire simulation overhead was estimated between 10 and 15% in the "coupled" and "fire-to-atm" cases compared to the "uncoupled" one, as can be seen in Table 2. Faster than real-time (and operational) simulations have already been performed successfully by both CAWFE [START_REF] Coen | Use of spatially refined satellite remote sensing fire detection data to initialize and evaluate coupled weather-wildfire growth model simulations[END_REF] and WRF/SFire [START_REF] Kochanski | Real time simulation of 2007 Santa Ana fires[END_REF] on larger fires, but the major asset of our simulation is mainly a higher resolution mesh (50 m compared to 200 m or more) applied to an extreme fire case. This goal was reached here by running in depopulated mode (using only two cores per compute node instead of eight), still on 900 processors (but with 3600 mobilized) on Jade, as it increases the memory bandwidth available per node. In this case, it was possible to obtain a 0.76 calculation ratio, below real time. Although this ratio is too large to consider operational uses (a forecast framework will impose a computation speed at least twice as fast), it is important to note that a factor between two and four in computation time is expected in the newer version of Meso-NH: the factor of four would correspond to the use of the Weighted Essentially Non-Oscillatory (WENO) scheme for momentum transport, but with a coarser effective resolution due to its diffusive character, while the factor of two would be brought by the WENO of fifth order [START_REF] Lunet | Combination of WENO and Explicit Runge-Kutta methods for wind transport in Meso-NH model[END_REF], or the fourth order centered scheme associated with a fourth order Runge-Kutta time-splitting marching instead of the LF scheme [START_REF] Lac | Overview of the Meso-NH model version 5.4 and its applications[END_REF]. This constitutes an interesting prospect for operational wildfire prediction. The fire-to-atm cases are here the most expensive cases mainly because this makes intensive and non-optimized use of the file system to read the fire progression file.

Conclusions

The coupled code Meso NH/ForeFire aims to be able to simulate large wildfires, solving complex fire-induced flow while implementing a high-resolution front advection method. The fire front velocity model can be parametrized with measurable properties of the fuel and is well adapted to coupled simulation, as it uses instantaneous wind speed just over the fire front to calculate the flame angle. The non-parallel version of the code has previously been used to perform simulations of real wildfires with results that qualitatively match observation in terms of fire dynamics [START_REF] Filippi | Simulation of Coupled Fire/Atmosphere Interaction with the MesoNH-ForeFire Models[END_REF] and atmospheric chemistry [START_REF] Strada | Wildfire and the atmosphere: modelling the chemical and dynamic interactions at the regional scale[END_REF].

The embedded parallel strategy demonstrated in this study ensures that the coupled model will behave in the same way as the atmospheric model and thus will benefit from further improvements. The system proves to be able to simulate a large wildfire, although with some arguable simplifications of important processes and relatively raw parametrization given the complex landscape. It makes it possible to simulate both the fine-scale fire-atmosphere interactions occurring at tens of meters scales around the fire front and larger regional scales with a good degree of realism. The multiscale simulation allowed exploring the dynamical structure of the surrounding atmosphere. Wildland fire induced strong surface winds generating a few thousand meter convective column with pockets of updrafts, stronger at higher levels and following a multi-cell distribution, while strong downdrafts occurred behind the plume and the fire front. At 50-m resolution, subgrid motions as well as the resolved momentum were strongly enhanced by the fire. Shear had a larger contribution than buoyancy to the turbulence within the fire plume partly due to high sheared initial winds.

It is reasonable to think that such coupled models will run faster than real time on medium-sized clusters in the near future. This type of coupled simulation could then become a decision support tool, forecasting plume size, transport dispersion and smoke concentration at the ground (information of prime importance to protect the population) and anticipating the visibility loss for the fire fighters and civil transport in general. In terms of forecasting the fire-line location, it is unlikely that such models ever reach the ability and precision of very fast codes that can be tweaked and adapted in real time to fire observations and fighting scenarios. Nevertheless, such codes still require wind, temperature and more generally changing weather pattern forecasts. Fire to atmosphere numerical coupling appears to be a reasonable way of forecasting extreme weather events that can strongly affect local meteorological conditions.

The major point was to demonstrate and build the platform that may now receive enhancement from the community, as all codes are open source.

The main plan is to improve fuel models, as well as the velocity and surface flux models in order to better represent the combustion phase that will refine the diagnosis of turbulent fluxes at the ground level and the combustion phase of larger fuel particles. The simulation of more systematic very large wildfires at high resolution with a complex fuel structure is the current goal for model validation, along with the development of an operational tool chain for fire and fire-weather forecasting if sufficient performance can be achieved.

Supplementary Materials:

The following are available online at http://www.mdpi.com/2073-4433/9/6/218/s1.

Author Contributions: J.-B.F. redacted the main text, designed and implemented the coupled fire code, the experiment and performed the simulations and post-processing. F.B. prepared the fuel data, figure and performed some preliminary simulations. C.M. designed the surface injection model and performed the analysis of the plume. C.L. is the lead developer of the atmospheric model, designed the atmospheric grids and parameterization and provided the analysis and figures of the fire-atmosphere interactions.

Figure 1 .

 1 Figure 1. Sartene weather station records on 23 July 2009 (in hours UTC): temporal evolution of 10-m wind speed (in red, in m s -1 ), 2-m temperature (in blue, in deg C) and relative humidity (in black, in %).

  200 and 50 m, covering a total area of respectively 144 km × 240 km, 48 km × 48 km and 15 km × 15 km for the innermost model. The time step is 12 s for the outermost model and decreases to 6 s, 2 s and 0.5 s for the finer models. Initial and lateral boundary conditions are provided by the Aladin limited-area model (10-km horizontal resolution) operational at Meteo-France in 2009, with updates of the coupling files every 6 h. The simulation with the coarsest resolution began on 23 July 2009 at 0000 UTC, with a progressive downscaling up to the finest resolution beginning at 1200 UTC.

Figure 2 .

 2 Figure 2. Overview of the nested Meso-NH domains.

Figure 3 .

 3 Figure 3. Aullene's fire, markers (blue) and heat fluxes above 30 kW m -2 at fire resolution (5 m) (A) used to force the atmospheric surface fields (resolution 50 m) (B).

Figure 4 .

 4 Figure 4. Overview of the fuel distributions with the four main fuel classes over the final observed fire area over elevation in gray shades.

Figure 5 .

 5 Figure 5. View of the "coupled" fire simulation (grey scale) 27 min, 1 h, 2 h and 3 h 30 after the beginning of the fire, with corresponding observed fire passing points (yellow marks), superimposed on the real burnt area including fire fighting actions (dashed red area). The horizontal extension at the base of the figure is 5 km.

Figure 6 .

 6 Figure 6. Simulated smoke tracer on 23 July 2009 (a) in the 50-m resolution domain compared to the plume's photograph (at the top left) at 14:50 UTC and (b) in the 600-m resolution domain highlighted in red (A) at 15:00 UTC compared to the MODIS image (B) of Corsica at 14:50 UTC.

Figure 7 .

 7 Figure 7. Vertical cross-section of the wind speed (in m s -1, between blue and red) and streamlines initiated at the ground and colored according to the vorticity (in s -1 , between green and pink) at 1500 UTC.

Figure 8 .

 8 Figure 8. Horizontal cross-sections on 23 July 2009 at 1500 UTC: (a) envelop of the fire front (in black) at the ground superimposed on the 10-m wind vectors (arrows) of the "coupled" simulation and on the orography (color, in m) with the axis of the vertical cross-sections; (b,c) 10-m wind speed (in m s -1 ) with wind vectors superimposed for the (b) "uncoupled" and (c) difference "coupled minus uncoupled" simulations; (d) Vertical velocity at a 300-m height (in m s -1 ) for the difference "coupled minus uncoupled" simulations. Orography isocontours are superimposed in (b).

Figure 9 .

 9 Figure 9. Vertical cross-sections on 23 July 2009 at 1500 UTC: (a,b) horizontal wind (in m s -1 ) with wind vectors superimposed for (a) the "uncoupled" simulation and (b) the "coupled" one along the direction of propagation (axis (A) in Figure 8a); (c,d) vertical velocity difference between "coupled" and "uncoupled" simulations (in m s -1 ) with the wind vectors (arrows) (c) across the fire front (axis (B)) and (d) along the direction of propagation (axis (A)).

Figure 10 .

 10 Figure 10. Horizontal cross-sections on 23 July 2009 at 1500 UTC: 2-m temperature (in deg Celsius) for the (a) "uncoupled"; (b) "coupled" and (c) the difference "coupled minus uncoupled"; (d) Sensible heat flux at a 20-m height for the difference "coupled minus uncoupled" (in kW m -2 ). Isolines of orography are superimposed in (a).

Figure 11 .

 11 Figure 11. Difference between "coupled" and "uncoupled" simulations on 23 July 2009 at 1500 UTC: Horizontal cross-sections of (a) 10-m horizontal divergence (in s -1 ) with the fire tracer superimposed (in black); (b) 10-m pressure (in Pa).

Figure 12 .

 12 Figure 12. Vertical cross-sections along the direction of propagation (axis(A) in Figure 8a) on 23 July 2009 at 1500 UTC of Turbulent Kinetic Energy (TKE) (in m 2 s -2 ) for the (a) "uncoupled" and (b) the difference "coupled minus uncoupled" (with a ratio of 10 between isocontours); (c) dynamical production of TKE (in m 2 s -3 ) and (d) thermal production of TKE (in m 2 s -3 ) for the difference "coupled minus uncoupled".

Figure 13 .

 13 Figure 13. Mean kinetic energy spectra for vertical wind on 23 July 2009 at 1500 UTC for the "Coupled" (continuous line) and "Uncoupled" (dashed line) simulations according to the wavelength (in m). The dashed line indicates the power law with an exponent of -5/3 (the Kolmogorov spectrum).

Figure 14 .

 14 Figure 14. "Coupled" simulation on 23 July 2009 at 1500 UTC: vertical cross-sections along the direction of propagation (axis in Figure 8a) of (a) zonal wind variance u 2 , (b) meridional wind variance v 2 and (c) vertical wind variance w 2 (in m 2 s -2 ).

Figure 15 .

 15 Figure 15. "Fire-to-atm" simulation on 23 July 2009 at 1500 UTC: horizontal cross-sections of (a) the fire front (in black) at the ground superimposed on the wind vectors (arrows) and on the orography (color, in m); (b) the difference between "fire-to-atm" and "uncoupled" simulations of 10-m wind intensity with wind vectors superimposed (in m s -1 ).

Table 1 .

 1 Main fuel types' parameter values.

		Shrubs	Pine Mixed Maquis
	σ (kg•m -2 )	0.6	2	1.5	0.8
	E (m)	0.5	3	2.5	2
	m (%)	8	15	10	8
	∆h (MJ•kg -1 )	18.6	16	17	18.6

Table 2 .

 2 Computation time for the different configurations.

		Exec. Time	Ratio	Overhead
		(for 6000 s)	(/Real Time)	(%)
	Uncoupled	7550	1.26	0.00
	Fire-to-atm	8700	1.45	15.23
	Coupled	8240	1.37	9.14
	Coupled	4580	0.76	9.14
	(depopulated)

Atmosphere 2018, 9, 218; doi:10.3390/atmos9060218 www.mdpi.com/journal/atmosphere

Acknowledgments: This research is supported by the Agence Nationale de la Recherche, Project ANR-09-COSI-006, ANR-16-CE04-0006 and the CINES Computing center Jade computer under grant DARIc20132b1723.

Conflicts of Interest:

The authors declare no conflict of interest.