Les hélicènes et les ions métalliques : une combinaison gagnante 1

Résumé : nous décrivons comment, au cours ces dernières années, la chimie des hélicènes combinée à la chimie de coordination et organométallique ont ouvert la voie à un nouveau domaine d'ingénierie moléculaire de ligands hélicoïdaux -conjugués. Des architectures très variées à topologie chirale contrôlée ont été conçues par association à divers éléments du tableau périodique : des hétéroatomes, des métaux, ou encore des lanthanides. Cette ingénierie moléculaire permet de donner une nouvelle dimension aux propriétés dites chiroptiques des structures chirales énantiopures obtenues, étudiées en transmission (pouvoir rotatoire), en absorption (dichroïsme circulaire électronique -ECD) et en émission (émission polarisée circulairement -CPL). Cette stratégie donne aussi accès à des matériaux moléculaires chiraux pour des applications en tant que commutateurs chiroptiques ou émetteurs chiraux dans des diodes électroluminescentes organiques (OLEDs) à émission polarisée circulairement.

Mots-clés : Chiralité, hélicènes, ions métalliques, propriétés chiroptiques, dichroïsme circulaire électronique, luminescence polarisée circulairement

Abstract: herein we describe how, in the recent years, the chemistry of helicenes combined with coordination chemistry and organometallics has paved the way to a new domain of molecular engineering of helical -conjugated ligands. Many architectures with a controlled chiral topology have been prepared from various elements of the periodic table, either heteroatoms, metals or even lanthanide ions. Such a molecular engineering allows the tuning of the chiroptical properties of the resulting enantiopure chiral structures, studied in transmission (optical rotation), absorption (electronic circular dichroism -ECD) and emission (circularly polarized emission -CPL). This strategy gives access to chiral molecular materials for applications as chiroptical switches or chiral emitters in organic light-emitting diodes (OLEDs) with circularly polarized emission.

Keywords: Chirality, helicenes, metallic ions, chiroptical properties, electronic circular dichroism circularly polarized luminescence

Les [n]hélicènes sont l'archétype des molécules organiques à topologie hélicoïdale issues de la fusion en ortho de n cycles aromatiques (Figure 1) [START_REF] Shen | Helicene Chemistry: From Synthesis to Applications[END_REF]. Ces molécules chirales possèdent un système -conjugué étendu ; elles sont configurationnellement stables à partir de 5 ou 6 cycles aromatiques ortho-fusionnés, et présentent des propriétés chiroptiques très intenses, issues de leur interaction avec une lumière polarisée.

Les hélicènes énantioenrichis sont ainsi connus depuis 1956 [START_REF] Newman | The Synthesis and Resolution of Hexahelicene[END_REF] pour présenter des pouvoirs rotatoires extrêmement forts, parmi les plus élevés présentés par des molécules organiques, ainsi que des réponses très intenses en dichroïsme circulaire dans le domaine de l'UV-visible et dans le domaine infra-rouge.

Plus récemment, un engouement s'est développé autour de l'émission polarisée circulairement (notée CPL pour "Circularly Polarized Luminescence"), une propriété chiroptique issue de la combinaison de l'émission de fluorescence ou de phosphorescence avec la chiralité de la molécule (Figure 1

Une diversité structurale foisonnante

Un des grands principes de la chimie de coordination consiste à utiliser un métal de transition pour assembler plusieurs ligands autour de celui-ci. Nous avons pu exploiter cette approche pour organiser des ligands hélicèniques dans un espace contrôlé et créer ainsi de la diversité topologique dans la chimie des hélicènes. Le contrôle de la stéréochimie autour du métal s'avère être un aspect primordial pour organiser l'ensemble de la structure, la plupart du temps grâce à des phénomènes de transfert de chiralité du ligand vers le métal. Par ricochet, de cette stéréochimie contrôlée va surgir une réponse chiroptique claire dépendant directement du métal utilisé et de ses caractéristiques. Par exemple, la coordination de ligands chélates hétéroditopiques N^P de type aza [START_REF] Shen | Straightforward access to mono-and bis-cycloplatinated helicenes that display circularly polarized phosphorescence using crystallization resolution methods[END_REF]hélicène-phosphole à un ion métallique tel que le palladium(II) ou le cuivre(I) a permis d'élaborer des architectures chirales sophistiquées de stéréochimies programmées par les caractéristiques du métal [START_REF] Graule | Metal-bis(helicene) assemblies incorporating -conjugated phosphole-azahelicene ligands: impacting chiroptical properties by metal variation[END_REF]. En effet, dans le complexe Pd1 de la Figure 2, les deux chélates N,P s'arrangent autour de la géométrie plan-carré distordue du palladium(II), en position cis l'un par rapport à l'autre, grâce à l'effet trans entre les atomes N et P. De par la congestion stérique imposée par cette organisation, le métal et les deux atomes de phosphore qui sont des centres stéréogènes adoptent ainsi des stéréochimies fixées et reliées à la configuration absolue de l'hélicène de départ [(P,P,RP,RP,Pd)-(+)-Pd1 et (M,M,SP,SP,Pd)-(-)-Pd1]. Cette stéréochimie contrôlée a de fortes conséquences sur le spectre de dichroïsme circulaire électronique (voir Figure 1) dans lequel apparaissent de nouvelles transitions de type LMLCT ("ligand-metal to ligand charge transfer") caractéristiques de ce nouveau type d'assemblage. Au contraire, dans le complexe Cu1, les deux chélates N^P s'arrangent autour de la géométrie tétraédrique du cuivre(I). Le manque de congestion stérique ne permet pas d'imposer la configuration relative du métal et des atomes de phosphore et la réponse chiroptique n'est pas amplifiée. Une autre manière de créer de la diversité structurale est issue du greffage d'un ou deux ions métalliques (typiquement le ruthénium(II) [START_REF] Anger | Ruthenium-vinylhelicenes: remote metal-based tuning and redox switching of the chiroptical properties of a helicene core[END_REF], ou le fer(II) [START_REF] Shen | Iron-alkynyl-helicenes: redox-triggered chiroptical tuning in the vibrational and telecommunication domain[END_REF]) à la périphérie du coeur hélicènique, via un pont -conjugué (de type éthènyle ou éthynyle), qui jouera le rôle de lien chimique et de connecteur électronique entre le métal et l'hélicène. Les deux complexes Ru1 et Fe1 (Figure 2) en sont deux exemples représentatifs. La présence du pont rend le ligand hélicénique "non-innocent", c'est-à-dire que l'application d'un potentiel rédox aura non seulement un effet sur l'état rédox de métal mais également sur la densité électronique de l'hélice, permettant ainsi de moduler les propriétés électroniques et chiroptiques de l'hélice de façon très efficace (voir ci-dessous).

Enfin, la combinaison des hélicènes avec des dérivés de la 2,2'-bipyridine (bipy) et de la 2,2′:6′,2′′terpyridine (Terpy) et leur chimie de coordination extrêmement riche ouvre un panel très large de complexes chiraux. Nous n'en donnerons que trois exemples ici : les complexes de type (N^N)ReCl(CO)3 (Re1) [START_REF] Saleh | Enantio-enriched CPL-active helicene-bipyridine-rhenium complexes[END_REF], (N^N)Dy(hfac)3 où hfac = hexafluoroacetylacetone (Dy1) [START_REF] Ou-Yang | Improved slow magnetic relaxation in optically pure helicene-based Dy III single molecule magnet[END_REF], et (N^N^N)Zn(OAc)2 (Zn1) [START_REF] Isla | Conformational changes and chiroptical switching of enantiopure bis-helicenic terpyridine upon Zn 2+ binding[END_REF]. Cette stratégie permet d'incorporer dans les structures hélicèniques les propriétés typiques de chaque complexe obtenu : phosphorescence rouge pour les complexes du rhénium, magnétisme moléculaire pour ceux du dysprosium, et commutation de systèmes émissifs par coordination-décoordination avec du zinc.

Des propriétés chiroptiques exaltées et des phénomènes inattendus

Modification des propriétés des hélicènes

Le P-Fe1 préparé à partir du P-2,15-bis-éthynyl-hélicène P-H2 (Figure 4A). Ils sont mis en évidence par 1) la forte diminution des bandes ECD-active typiques des hélicènes vers 280 et 330 nm, et 2) l'apparition de nouvelles bandes ECD-actives autour de 400 et 500 nm. Ces bandes ECD font intervenir des transitions électroniques impliquant les orbitales du métal comme montré dans la HO (orbitale moléculaire la plus haute occupée) qui est centrée sur les ions fer, l'éthynyle et les aromatiques périphériques de l'hélice, tandis que la BV (orbitale moléculaire la plus basse vacante) est centrée sur l'hélice uniquement (Figure 4C). La transition HO-BV centrée autour de 500 nm correspond donc à un transfert de charge de type MLLCT et présente une réponse forte en dichroïsme circulaire ( = 60 M -1 cm -1 ).

Des transferts de charge à travers l'espace ("ligand-to-ligand", LLCT) peuvent également s'établir et influencer les réponses chiroptiques, comme nous l'avons observé dans des complexes d'or [START_REF] El Sayed Moussa | Bimetallic gold(I) complexes with ethynyl-helicene and bis-phosphole ligands: understanding the role of aurophillic interaction in their chiroptical properties[END_REF] ainsi que dans des hélicates à base de cuivre [START_REF] Vreshch | Assembly of helicene-capped N,P,N,P,N-helicands within Cu I -helicates: impacting chiroptical properties by ligand-ligand charge transfer[END_REF]. La présence d'ions métalliques dans ces architectures chirales apporte une nouvelle fonctionnalité qui est la possibilité de commuter leur état d'oxydation et d'accéder ainsi à des commutateurs rédox efficients.

Commutation chiroptique rédox

Un des aspects particulièrement intéressants du complexe Fe1 est son oxydation considérablement facilitée par rapport à l'hexahélicène H2, grâce à la présence des ions métalliques qui rendent le coeur aromatique hélicoïdal plus facilement oxydable. Ainsi, les potentiels rédox de première et seconde oxydation de Fe1 sont de -0.64 V et -0.55 V par rapport à la référence ferrocène/ferrocénium (Fc/Fc + ), tandis que l'hexahélicène H2 s'oxyde autour de +1.4 V (vs. Fc + /Fc) [START_REF] Vacek | Anodic deposition of enantiopure hexahelicene layers[END_REF]. Il devient alors aisé d'effectuer la

Modulation de l'émission polarisée circulairement

La CPL est l'équivalent du dichroïsme circulaire électronique (ECD) mais en émission [START_REF] Harada | Comprehensive Chiroptical Spectroscopy[END_REF][START_REF] Collet | Molécules Chirales : Stéréochimie et Propriétés[END_REF] (Figure 2), l'azabora [START_REF] Amouri | Chirality in Transition Metal Chemistry: Molecules, Supramolecular Assemblies and Materials[END_REF]hélicène B1 émettant de la lumière polarisée circulairement bleue (|glum| ~ 1  10 - 3 , Figure 5) [START_REF] Shen | Synthesis and chiroptical properties of hexa-, octa-and deca-azaborahelicenes: influence of the helicene's size and of the number of boron atoms[END_REF] ou encore le complexe d'hélicène-NHC-iridium Ir1 émettant de la phosphorescence verte [START_REF] Hellou | Enantiopure cycloiridiated complexes bearing a pentahelicenic N-heterocyclic carbene and displaying long-lived circularly-polarized phosphorescence[END_REF] avec des temps de vie particulièrement longs (Figure 5). Cette dernière phosphorescence est polarisée circulairement (|glum| ~ 1 à 4  10 -3 ) et son intensité dépend à la fois de la stéréochimie de l'hélice (P/M) et de celle de l'iridium (soit delta (Ir) soit lambda (Ir),) induisant un effet de "match-mismatch" dans les spectres de CPL, ce qui permet ainsi de moduler de façon très efficace les réponses chiroptiques par ingénierie moléculaire.

  et définitions en fin d'article). Les activités développées au sein de l'Institut des Sciences Chimiques de Rennes (UMR 6226 CNRS -Université de Rennes), et notamment dans l'équipe 'Organométalliques: Matériaux et Catalyse' (équipe OMC), s'articulent autour des propriétés des complexes organométalliques sous différents angles, notamment leurs propriétés électroniques, électrochimiques, magnétiques, d'émission, catalytique, ou de commutation. Plus particulièrement, depuis la fin des années 2000, notre groupe étudie comment l'incorporation d'un ion métallique au sein d'une structure de type hélicènique peut donner lieu à de nouvelles découvertes et fonctionnalités issues de la synergie entre les deux mondes inorganique-organique. Quelques exemples représentatifs sont présentés dans cet article, afin de faire découvrir au lecteur le fort potentiel de ce champ pluridisciplinaire.

Figure 1 :

 1 Figure 1: les énantiomères P et M du carbo[6]hélicène (noté H1). Principes du pouvoir rotatoire, du dichroïsme circulaire électronique et de l'émission polarisée circulairement.  est l'angle de rotation de la

Figure 2 :

 2 Figure 2 : diversité des structures hélicèniques préparées à base de métaux de transition ou de lanthanide.

Figure 3 :

 3 Figure 3 : méthode synthétique utilisée au laboratoire pour la construction du squelette hélicoïdal. (A) Cas du carbo[6]hélicène racémique préparé par irradiation avec une lampe à mercure (150W) d'une solution hautement diluée dans du toluène en présence de diode en quantité catalytique [1]. (B) Cas du platina[6]hélicène préparé par la même voie photochimique, suivie d'une réaction de cycloplatination en présence d'une base, d'un précurseur de platine [5]. Les hélicènes sont obtenus sous forme racémique (mélange 50:50 des deux images miroir P/M) et sont ensuite séparés par chromatographie liquide à haute pression (HPLC) sur phase stationnaire chirale.

  spectre ECD d'un hélicène comme P-H2 présente majoritairement deux bandes typiques très intenses, une bande négative ( < -200 M -1 cm -1 ) à 275 nm et une bande positive ( > +300 M -1 cm -1 ) autour de 350 nm tandis que M-H2 présente la signature ECD opposée. Notez que la lecture directe de cette signature en ECD permet de déterminer la configuration absolue (P-(+) et M-(-)) des hélicènes. Par ailleurs, dans les hélicènes substitués, ces deux bandes intenses sont régulièrement accompagnées d'une bande de plus faible intensité à des énergies plus basses.Etablir un lien chimique conjugué entre le métal et le ligand hélicènique permet d'induire des transferts de charge efficaces, de type "metal-to-ligand" (MLCT), "metal-ligand-to-ligand" (MLLCT) ou encore des transferts intra-ligand (IL) ou inter-ligand (LL'CT). Ces transferts de charge influencent très fortement les réponses en dichroïsme circulaire, comme illustré Figure4Bdans le cas du P-hélicène-bis-éthynyl-fer(II)

  double oxydation de P-Fe1 en P-[Fe1] ..2+ et d'observer la variation du spectre ECD et du pouvoir rotatoire (Figures4D et 4E). Nous voyons après cette double oxydation l'apparition d'une bande active en ECD autour de 770-800 nm, c'est-à-dire dans le proche-infrarouge, accompagnée de la forte diminution de la bande intense autour de 330-350 nm. De la même manière, une forte diminution du pouvoir rotatoire spécifique de P-Fe1 a été observée pour la raie D du sodium ([α]23 D variant de +5132 pour l'espèce neutre à +497 pour l'espèce radicalaire bis-oxydée générée par oxydation au diiode); encore plus étonnant, le pouvoir rotatoire mesuré dans le domaine des télécommunications soit à 1.54 microns change de signe ([α] à 1.54 m allant de +260 à -560)! Il faut noter que les deux spins des ions Fe(III) interagissent peu, comme le montrent les potentiels de 1 ère et 2 ème oxydation très proches, ainsi que leur comportement magnétique étudié par la méthode SQUID[START_REF] Shen | Iron-alkynyl-helicenes: redox-triggered chiroptical tuning in the vibrational and telecommunication domain[END_REF]. Par ailleurs, le caractère parfaitement réversible des processus rédox et la très bonne stabilité des espèces radicalaires oxydées ont permis d'accéder à un type original de commutateur chiroptique. L'activité de commutation peut être ici lue de plusieurs façons différentes: par spectroscopie UV-visible (Figure4F), par dichroïsme circulaire électronique (Figure4E), ou par mesure du pouvoir rotatoire (Figure4D). De tels systèmes organométalliques hélicoïdaux constituent de parfaits modèles pour les théoriciens, avec qui nous travaillons de façon très étroite [19],pour développer des calculs numériques précis des propriétés chiroptiques.

Figure 4 :

 4 Figure 4 : (A) Préparation et structure radiocristallographique du complexe de fer-alcynyle P-Fe1 ; (B) comparaison des réponses en ECD de P-H1 et P-Fe1 ; (C) HO et BV de Fe1 ; (D) processus rédox réversible P-Fe1 ↔ P-[Fe1] ..2+ ; (E) variation de la réponse en CD de P-Fe1 en P-[Fe1] ..2+ ; (F) commutateur optique à 767 nm montrant la réversibilité et fatigabilité du processus observée par réponse UV-visible.

  et représente un outil pour l'obtention d'informations structurelles sur les états excités d'édifices chiraux (molécules, polymères, agrégats supramoléculaires, etc..). Moins classique que l'ECD, elle présente néanmoins un potentiel dans de nombreux domaines tels que la compréhension des processus biologiques (sondes sensibles à l'environnement chiral), la cryptographie, l'affichage à trois dimensions (3D), le transport et le stockage d'informations optique. Pour pouvoir utiliser la CPL dans les applications précédemment citées, il est donc nécessaire qu'un édifice chiral génère à la fois une valeur de |glum| la plus élevée possible ainsi qu'un fort rendement quantique de luminescence. Dans les platinahélicènes tels que Pt1, le fort couplage spin-orbite de l'ion Pt(II) leur confère des propriétés de luminescence très originales pour des dérivés hélicèniques, puisque ces hélicènes organométalliques émettent à température ambiante de la phosphorescence rouge efficace (rendement quantique de 10%); cette phosphorescence est polarisée circulairement avec un facteur de dissymétrie de l'ordre de 10 -2 (Figure5), ce qui est correspond à un ordre de grandeur supérieur aux hélicènes organiques classiques (|glum| = 1,2  10 -2 pour P-Pt1 vs. ~ 1  10 -3 pour P-H1). Les bonnes performances du complexe Pt1 ont permis de l'incorporer dans des dispositifs de type diodes organiques luminescentes (OLEDs) et d'obtenir ainsi des OLEDs à émission polarisée circulairement[START_REF] Brandt | Circularly polarized phosphorescent electroluminescence with a high dissymmetry factor from pholeds based on a platinahelicene[END_REF]. Ce type de technologie d'OLEDs chirales permet 1) d'éliminer les réflexions parasites de surface et 2) d'augmenter la quantité de lumière émise, améliorant ainsi les performances de ce type d'éclairage. Nous avons donc poursuivi nos recherches dans ce domaine en explorant de nouvelles structures hétéroatomiques ou organométalliques hélicoïdales inédites, telles que le complexe d'hélicène-bipyridine-rhénium Re1 émetteur de phosphorescence rouge et CPL-actif[START_REF] Saleh | Enantio-enriched CPL-active helicene-bipyridine-rhenium complexes[END_REF]

Figure 5 :

 5 Figure 5 : exemples d'hélicènes organométalliques et hétéroatomiques présentant de la lumière polarisée circulairement.

Figure 6 :

 6 Figure 6 : (A) Coordination réversible d'ions zinc et d'ions H + par le ligand bis-hélicène-bipyridine (P,P)-H3 en, respectivement, (P,P)-Zn1 et (P,P)-H4. (B) Mouvement de type charnière associé au changement conformationnel de H3. (C) Emission de fluorescence et (D) spectres CPL des systèmes énantiopurs en solution dans le dichlorométhane et à température ambiante.

Cet article est dédié à la mémoire de mon mentor, le Professeur André Collet, décédé le

octobre 1999, soit il y a un peu plus de 20 ans.Jeanne CRASSOUS, Directrice de recherche CNRS, Institut des Sciences Chimiques de Rennes (CNRS/Université de Rennes 1/École Nationale Supérieure de Chimie de Rennes/INSA Rennes). * jeanne.crassous@univ-rennes1.fr


Karine Clément
email: karine.clement@aphp.fr

H Mosbah

C Poitou

Rare genetic forms of obesity: from gene to therapy

Keywords: obesity, genetics, leptin-melanocortin pathway, monogenic non-syndromic ! 2

Monogenic non-syndromic obesity is characterized by severe early-onset obesity with abnormal eating behaviour and endocrine disorders. Genes contributing to these rare forms of obesity are mainly located in the leptin/melanocortin pathway, with typically an autosomal additive inheritance of obesity. The normal function of this hypothalamic pathway is essential for the control of energy balance. Genetic variants are involved in 5 to 30 % of severe earlyonset obesity depending on explored populations. Compared to other genes in the pathway especially leptin (LEP), leptin receptor (LEPR), pro-opiomelanocortin (POMC) and prohormone convertase subtilisin/kexin type 1 (PCSK1), Melanocortin 4 receptor (MC4R)linked obesity is characterized by obesity of variable severity with no notable endocrine phenotypes. Managing patients with monogenic non-syndromic obesity is clinically challenging since they display complex phenotypes and the obesity is often morbid and refractory to classical treatments. Until recent years, there has been a lack of effective and targeted pharmaceutical molecules except for leptin therapy that was available for leptin deficiency. The picture has changed and new promising molecules acting on the leptinmelanocortin pathway such as setmelanotide -a new MC4R agonist-are now emerging as novel targeted therapeutic opportunities.

Introduction

Human obesity is complex and usually results from the interplay between genetic/epigenetic factors [START_REF] Reddon | The importance of gene-environment interactions in human obesity[END_REF] and a myriad of environmental triggers, which in some cases are principal causes of obesity development such as in Japanese SUMO Wrestlers in whom the obesity is caused mainly by high fat diet [START_REF] Nishizawa | Some factors related to obesity in the Japanese sumo wrestler[END_REF]. Whereas polygenic forms of common obesity can explain up to 40% of the heritability for obesity clinical phenotypes [START_REF] Yang | Genetic variance estimation with imputed variants finds negligible missing heritability for human height and body mass index[END_REF][START_REF] Stryjecki | Ethnic and population differences in the genetic predisposition to human obesity[END_REF], monogenic obesity causally relates to early-forms of severe obesity. This so-called "genetic obesity" is mostly due to an alteration in the function of critical neuronal populations of the hypothalamus, the central brain area in regulating energy and weight homeostasis.

Historically, major forms of genetic obesity were classified as: 1) monogenic non syndromic obesity, which includes patients with variants in genes involved in the leptin/melanocortin pathway, and 2) syndromic obesity which includes patients with neurodevelopmental disorders or malformative features such as seen in Prader Willi and Bardet-Biedl syndromes, both being the most frequent observed forms. These syndromic obesity forms also involve genes having molecular cross talks with the leptin/melanocortin pathway such as Single-Minded 1 Transcription Factor (SIM1), brain-derived neurotrophic factor (BDNF), human neurotrophic tyrosine kinase, receptor, type 2 (NTRK2), or SH2B Adaptor Protein 1 (SH2B1) [START_REF] Van Der Klaauw | The hunger genes: pathways to obesity[END_REF]. This review focuses on main genes contributing to monogenic non-syndromic obesity, directly involved in, or regulating the leptin/melanocortin pathway: leptin (LEP), leptin receptor (LEPR), pro-opiomelanocortin (POMC), prohormone convertase subtilisin/kexin type 1 (PCSK1), melanocortin receptor type 3 (MC3R) and type 4 (MC4R) and its regulator

! 3
Melanocortin Receptor Accessory Protein 2 (MRAP2), adenylate cyclase 3 (ADCY3) and more recently Steroid Coreceptor Activator-1 (SRC-1), Semaphorin 3A-G (SEMA3A-G), PlexinA1-4 (PLXNA1-4), Neuropilin1-2 (NRP1-2) and kinase suppressor of ras 2 (KSR2).

Our team and others contributed to the discovery of the genes leading to these rare forms of monogenic obesity as a part of intense research led over the last 20 years [START_REF] Van Der Klaauw | The hunger genes: pathways to obesity[END_REF]. At the end of the 1990s, we identified the first human variants of the leptin (LEPR) and MC4R receptor (6-10).

We further described new variants of genes in these pathways POMC gene [START_REF] Clement | Unexpected endocrine features and normal pigmentation in a young adult patient carrying a novel homozygous mutation in the POMC gene[END_REF], MC3R [START_REF] Mencarelli | Rare melanocortin-3 receptor mutations with in vitro functional consequences are associated with human obesity[END_REF] and LEPR [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF]. Overall, monogenic obesity represents less than 5% of severe early-onset obesity, but it is probably underdiagnosed in some countries and could be more frequent in specific populations and could reach up to 30% [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF][START_REF] Foucan | High Prevalence of Rare Monogenic Forms of Obesity in Obese Guadeloupean Afro-Caribbean Children[END_REF][START_REF] Serra-Juhe | Heterozygous rare genetic variants in non-syndromic early-onset obesity[END_REF], for example in populations with a high level of consanguinity [START_REF] Saeed | Genetic variants in LEP, LEPR, and MC4R explain 30% of severe obesity in children from a consanguineous population[END_REF].

The common phenotype of monogenic non-syndromic obesity includes early-onset (before 5 years of age) severe obesity associated with eating disorders and with a heavy impact on patients' morbidity and mortality. A number of endocrine abnormalities (hypogonadism, growth hormone deficiency, hypothyroidism, corticotropic insufficiency) are often present.

Sometimes neurodevelopmental abnormalities (intellectual deficiency, emotional lability, behavioral problems or even autistic traits) are also present such as in syndromic obesities making clinical management even more complex [START_REF] Huvenne | Rare Genetic Forms of Obesity: Clinical Approach and Current Treatments in 2016[END_REF]. In general, these patients suffer from refractory obesity, meaning that usual standards of care such as life style modification (change in food intake and physical activity) and even bariatric surgery are not efficient in inducing significant weight loss. The discovery of these forms of obesity has not only been critical in the identification of key mechanisms involved in the control of food intake but also led to the discovery of new pharmaceutical drugs. This review provides an updated summary focusing ! 4 on non-syndromic monogenic forms of obesity and their available therapeutic options, with a highlight on innovative therapies.

Gene variants in the leptin/melanocortin pathway: mode of transmission and clinical phenotypes

LEP/LEPR

Patients with homozygous or compound heterozygous variants of LEP or LEPR show a rapid and very early increase in weight gain, as illustrated by the weight curve of LEPR deficient subjects [START_REF] Clement | A mutation in the human leptin receptor gene causes obesity and pituitary dysfunction[END_REF][START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF][START_REF] Montague | Congenital leptin deficiency is associated with severe early-onset obesity in humans[END_REF][START_REF] Krude | Severe early-onset obesity, adrenal insufficiency and red hair pigmentation caused by POMC mutations in humans[END_REF][START_REF] Farooqi | Clinical and molecular genetic spectrum of congenital deficiency of the leptin receptor[END_REF][START_REF] Jackson | Obesity and impaired prohormone processing associated with mutations in the human prohormone convertase 1 gene[END_REF][START_REF] Saeed | Novel LEPR mutations in obese Pakistani children identified by PCR-based enrichment and next generation sequencing[END_REF]. The examination of children's BMI trajectories identified BMI cut-off points with the recommendation of genetic screening of the leptin/melanocortin pathway when BMI values are >27.0 kg/m 2 at the age of 2 years or >33.0 kg/m 2 at the age of 5 years [START_REF] Kohlsdorf | Early childhood BMI trajectories in monogenic obesity due to leptin, leptin receptor, and melanocortin 4 receptor deficiency[END_REF]. Feeding behaviour in these patients is mainly characterized by severe and uncontrolled hyperphagia [START_REF] Licinio | Phenotypic effects of leptin replacement on morbid obesity, diabetes mellitus, hypogonadism, and behavior in leptin-deficient adults[END_REF]. Due to the crucial role of leptin in activating the hypothalamic-gonadal axis [START_REF] Israel | Effects of leptin and melanocortin signaling interactions on pubertal development and reproduction[END_REF], patients carrying variants in the LEP or LEPR gene exhibit hypogonadotropic hypogonadism with in addition to their severe obesity. They can display delayed pubertal development, which suggests a recovery of hormonal functions with time in some individuals.

For example, long term follow-up of a LEPR deficient woman diagnosed at the age of 13 revealed normal pregnancies [START_REF] Nizard | Pregnancy in a woman with a leptin-receptor mutation[END_REF]. Given the general importance of leptin in human physiology, somatotropic insufficiency and thyreotropic insufficiency were also described in some patients with LEPR variants. Impaired T-cell immunity has also been described in leptin-deficient children. Several LEPR variants have been observed in severe obesity with an estimated prevalence of 2-4% [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF][START_REF] Farooqi | Clinical and molecular genetic spectrum of congenital deficiency of the leptin receptor[END_REF]. For example, in the French Reunion Island, a region with high prevalence of obesity, we estimated that the frequency of homozygous LEPR ! 5 variants reaches 4% of severely obese subjects [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF]. Genetic screening is thus recommended in patients with severe obesity and hyperphagia presenting endocrine abnormalities [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF][START_REF] Farooqi | Clinical and molecular genetic spectrum of congenital deficiency of the leptin receptor[END_REF].

Recently, a systematic review found that across 88 patients with LEPR mutations, 100% of the patients had early-onset obesity (<5 years), 96% had hyperphagia and 34% had one or more pituitary hormone deficiencies [START_REF] Kleinendorst | Leptin receptor deficiency: a systematic literature review and prevalence estimation based on population genetics[END_REF].

Measuring serum leptin can sometimes help in leptin deficiency diagnosis [START_REF] Montague | Congenital leptin deficiency is associated with severe early-onset obesity in humans[END_REF]. However, a congenital leptin deficiency, due to biologically inactive leptin, has been described in a young boy with a severe clinical phenotype including extreme early-onset obesity and hyperphagia.

He presented high, but physiological circulating leptin levels in agreement with his obesity level [START_REF] Wabitsch | Biologically inactive leptin and early-onset extreme obesity[END_REF]. In the same line, we previously reported obese patients carrying homozygous LEPR variants with moderately increased serum leptin [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF]. These reports demonstrate that finding serum leptin at physiological levels in relation to a patient's BMI or fat mass does not rule out the presence of LEP or LEPR mutations. Some subjects display LEPR heterozygote variants. However, causally associating these latter genetic variants to propensity to obesity development is complex. Looking at families carrying these variants (for example parents of homozygous carriers) revealed heterogeneity in corpulence and obesity onset. Nevertheless, in a French population of severely obese subjects, we observed that BMI of heterozygous carriers was intermediate between LEPR wild type and homozygous carriers suggesting that carrying a mutated allele in the LEPR favors increased weight [START_REF] Huvenne | Seven novel deleterious LEPR mutations found in early-onset obesity: a DeltaExon6-8 shared by subjects from Reunion Island, France, suggests a founder effect[END_REF].

POMC/PCSK1

One major function of leptin is to stimulate hypothalamic POMC neurons via the leptin receptor to stimulate the release of POMC, the precursor of alpha and beta-melanocyte-! 6 stimulating hormone (i.e. αMSH, βMSH) and adrenocorticotropic hormone (ACTH). As such, obese subjects with complete POMC deficiency (homozygous or compound heterozygous variants) have ACTH deficiency and mild central hypothyroidism [START_REF] Krude | Severe early-onset obesity, adrenal insufficiency and red hair pigmentation caused by POMC mutations in humans[END_REF][START_REF] Krude | Obesity due to proopiomelanocortin deficiency: three new cases and treatment trials with thyroid hormone and ACTH4-10[END_REF]. They also sometimes display alterations in the somatotropic and gonadotropic axes or have red hair [START_REF] Clement | Unexpected endocrine features and normal pigmentation in a young adult patient carrying a novel homozygous mutation in the POMC gene[END_REF].

These modifications in hair color, adrenal function, and body weight are consistent with the lack of POMC-derived ligands for the melanocortin receptors MC1R (αMSH), MC2R (ACTH), and MC4R (αMSH) respectively. Beyond complete POMC deficiency seen in homozygous or compound heterozygous carriers, some heterozygous variants as well as changes in POMC gene methylation could also be involved in obesity development [START_REF] Dubern | Mutational analysis of the pro-opiomelanocortin gene in French obese children led to the identification of a novel deleterious heterozygous mutation located in the alpha-melanocyte stimulating hormone domain[END_REF][START_REF] Kuhnen | Interindividual Variation in DNA Methylation at a Putative POMC Metastable Epiallele Is Associated with Obesity[END_REF].

In those cases, POMC variants led to defective α or βMSH molecules [START_REF] Dubern | Mutational analysis of the pro-opiomelanocortin gene in French obese children led to the identification of a novel deleterious heterozygous mutation located in the alpha-melanocyte stimulating hormone domain[END_REF][START_REF] Lee | A POMC variant implicates beta-melanocyte-stimulating hormone in the control of human energy balance[END_REF]. Carriers of these variants had no endocrine abnormalities or pigmentation peculiarities. However, in our cohort of French subjects with early-onset severe obesity, we found 12 subjects with a heterozygous variant of POMC. Among them, two had an hypogonadotropic hypogonadism and a growth hormone (GH) deficiency (personal data). Proconvertase 1 (PC1), encoded by the PCSK1 gene, is an enzyme involved in the processing of POMC, proglucagon and insulin.

Patients carrying homozygous or compound heterozygote variants in the PCSK1 gene (leading to PC1 deficiency), exhibit early-onset severe obesity, postprandial hypoglycemia, hypogonadotrophic hypogonadism, central hypothyroidism and adrenal insufficiency [START_REF] Jackson | Small-intestinal dysfunction accompanies the complex endocrinopathy of human proprotein convertase 1 deficiency[END_REF][START_REF] Stijnen | PCSK1 Mutations and Human Endocrinopathies: From Obesity to Gastrointestinal Disorders[END_REF].

Severe and persistent diarrhea, secondary to a lack in mature GLP-1 (glucagon-like peptide-1), a derivative of proglucagon, is also described in cases of PC1 deficiency [START_REF] Jackson | Small-intestinal dysfunction accompanies the complex endocrinopathy of human proprotein convertase 1 deficiency[END_REF][START_REF] Martin | Congenital proprotein convertase 1/3 deficiency causes malabsorptive diarrhea and other endocrinopathies in a pediatric cohort[END_REF]. Some patients may also present persistent polydipsia and polyuria due to central diabetes insipidus [START_REF] Frank | Severe obesity and diabetes insipidus in a patient with PCSK1 deficiency[END_REF]. Some heterozygous variants were also described in PCSK1 gene. By using next-generation sequencing in 201 participants (71 were obese subjects), Philippe et al described in 2015 the autosomal dominant mode of inheritance of obesity for a null mutation ! 7 in the PCSK1 gene [START_REF] Philippe | A nonsense loss-of-function mutation in PCSK1 contributes to dominantly inherited human obesity[END_REF]. Creemers et al showed positive association between PCSK1 partial deficiency and obesity [START_REF] Creemers | Heterozygous mutations causing partial prohormone convertase 1 deficiency contribute to human obesity[END_REF]. In 845 non-consanguineous extremely obese Europeans, the prevalence of PCSK1 partial deficiency (heterozygous carriers) was found to be 0.83 % of the population [START_REF] Creemers | Heterozygous mutations causing partial prohormone convertase 1 deficiency contribute to human obesity[END_REF]. More recently, Loffler et al described heterozygous variants of PCSK1 associated with obesity and impaired glucose metabolism in children [START_REF] Loffler | Functional and clinical relevance of novel and known PCSK1 variants for childhood obesity and glucose metabolism[END_REF].

Other genes involved in leptin/melanocortin pathway

After the first discoveries of patients with LEP, LEPR, POMC or PCSK1 variants, genetic screening in obese population led to the discovery of new monogenic obesities in different countries. By sequencing 2,101 individuals with severe early-onset obesity and 1,536 controls, Pearce et al identified rare variants of the gene coding for KSR2 in 45 subjects. Unrelated carriers of these variants showed a severe obesity phenotype with hyperphagia in childhood, low heart rate, reduced basal metabolic rate and severe insulin resistance [START_REF] Pearce | KSR2 mutations are associated with obesity, insulin resistance, and impaired cellular fuel oxidation[END_REF]. This protein, almost exclusively expressed in the brain, regulates the activity of AMP kinase which controls cell thermogenesis, fat oxidation and glucose metabolism [START_REF] Turcot | Proteinaltering variants associated with body mass index implicate pathways that control energy intake and expenditure in obesity[END_REF]. KSR2 is supposed to be involved in melanocortin signaling while its precise action on this pathway still needs to be deciphered.

Moreover, variants with loss of function of the MRAP2 gene, a MC4R regulatory protein, have been associated with early obesity, hyperphagia, hypertension and hyperglycemia [START_REF] Baron | Loss-offunction mutations in MRAP2 are pathogenic in hyperphagic obesity with hyperglycemia and hypertension[END_REF].

Two recent studies have also found homozygous variants of ADCY3 in a population with severe obesity and high level of consanguinity [START_REF] Grarup | Loss-offunction variants in ADCY3 increase risk of obesity and type 2 diabetes[END_REF][START_REF] Saeed | Loss-offunction mutations in ADCY3 cause monogenic severe obesity[END_REF]. The ADCY3 gene codes for an adenylyl cyclase 3 protein which is involved in the formation of cyclic AMP. This protein could contribute to the function of the neuronal primary cilium, within the hypothalamus. The ! 8 protein ADCY3 is co-localized with MC4R, within the hypothalamic neurons. In murine models, the inhibition of ADCY3 in the primary cilia of these neurons induced weight gain.

The SRC-1 protein interacts with a target linked to the activation of LEPR, the phosphorylated form of STAT3, in order to potentiate the transcription of POMC. In an exome study performed on more than 2,500 European subjects, 19 new variants of SRC-1 were identified, including 15 in obese subjects presenting severe and early-onset obesity. Tests are still necessary to understand functional alterations associated with SRC-1 variants [START_REF] Yang | Steroid receptor coactivator-1 modulates the function of Pomc neurons and energy homeostasis[END_REF].

Finally, a recent study has described the role of class 3 semaphorins (SEMA3A-G), via their receptors and co-receptors (plexins: PLXNA1-4 and neuropilins NRP1-2), in the possible regulation of weight and / or fat mass. In mice, SEMA3A-G, via the NRP2 receptor, modulates the development of axonal projections of POMC neurons from the arcuate nucleus to the paraventricular nucleus. Van Der Klaauw et al found 40 rare variants in SEMA3A-G, PLXNA1-4 and NRP1-2 genes in 573 severely obese individuals [START_REF] Van Der Klaauw | Human Semaphorin 3 Variants Link Melanocortin Circuit Development and Energy Balance[END_REF]. All together these new discoveries extend the number of subjects presenting with monogenic obesity possibly related to leptin/melanocortin alterations.

MC4R

MC4R variants-linked obesity follows an autosomal additive mode of inheritance with incomplete age-related penetrance. Homozygous or compound heterozygous carriers of MC4R variants are very rare and their phenotype is more severe than in carriers of heterozygous variants [START_REF] Dubern | Homozygous null mutation of the melanocortin-4 receptor and severe early-onset obesity[END_REF][START_REF] Farooqi | Clinical and molecular genetic spectrum of congenital deficiency of the leptin receptor[END_REF][START_REF] Lubrano-Berthelier | Molecular genetics of human obesity-associated MC4R mutations[END_REF]. Heterozygous variants in MC4R are the most common forms resulting in obesity occurring at a later age than in homozygous variants (10, 47., 48-50). This represents approximately 2 to 4% of childhood and adult obesity [START_REF] Hinney | Melanocortin-4 receptor in energy homeostasis and obesity pathogenesis[END_REF][START_REF] Kuhnen | Melanocortin-4 Receptor Signalling: Importance for Weight Regulation and Obesity Treatment[END_REF].

! 9 However, depending on population background, founder effects were also described in Mexicans where a loss-of-function mutation was found in 1% of them [START_REF] Vazquez-Moreno | The melanocortin 4 receptor p.Ile269Asn mutation is associated with childhood and adult obesity in Mexicans[END_REF].

Patients with obesity related to MC4R variants have a more common obesity phenotype with usually no endocrine anomalies compared to patient harboring variants in genes upstream to MC4R. In addition to obesity, children carrying MC4R mutations often have marked hyperphagia improving with age [START_REF] Mackenzie | Obesity-associated mutations in the human melanocortin-4 receptor gene[END_REF]. The association between binge eating disorder (BED) and MC4R variants is not found in all studies [START_REF] Lubrano-Berthelier | Melanocortin 4 receptor mutations in a large cohort of severely obese adults: prevalence, functional classification, genotype-phenotype relationship, and lack of association with binge eating[END_REF][START_REF] Branson | Binge eating as a major phenotype of melanocortin 4 receptor gene mutations[END_REF][START_REF] Bonnefond | Eating Behavior, Low-Frequency Functional Mutations in the Melanocortin-4 Receptor (MC4R) Gene, and Outcomes of Bariatric Operations: A 6-Year Prospective Study[END_REF][START_REF] Valette | Eating behaviour in obese patients with melanocortin-4 receptor mutations: a literature review[END_REF][START_REF] Valette | Association between melanocortin-4 receptor mutations and eating behaviors in obese patients: a case--control study[END_REF]. One explanation of this discordance between studies can be the heterogeneous variant functionality as a recent meta-analysis focused on participants with obesity showed that only MC4R gain-of-function (GOF) variants are associated with BED [START_REF] Qasim | Gainof-function variants in the melanocortin 4 receptor gene confer susceptibility to binge eating disorder in subjects with obesity: a systematic review and meta-analysis[END_REF].

Hundreds of MC4R variants have been identified leading to many functional alterations [START_REF] Collet | Evaluation of a melanocortin-4 receptor (MC4R) agonist (Setmelanotide) in MC4R deficiency[END_REF] that are not always consistent across variant subtypes. The functional consequences of these variants have been described in vitro, finding mostly loss of protein expression, impaired αmelanocyte-stimulating hormone binding, alterations in receptor trafficking or coupling to the stimulatory G-protein, Gαs [START_REF] Lubrano-Berthelier | Melanocortin 4 receptor mutations in a large cohort of severely obese adults: prevalence, functional classification, genotype-phenotype relationship, and lack of association with binge eating[END_REF][START_REF] Collet | Evaluation of a melanocortin-4 receptor (MC4R) agonist (Setmelanotide) in MC4R deficiency[END_REF][START_REF] Farooqi | Clinical spectrum of obesity and mutations in the melanocortin 4 receptor gene[END_REF][START_REF] Challis | Mice lacking pro-opiomelanocortin are sensitive to high-fat feeding but respond normally to the acute anorectic effects of peptide-YY(3-36)[END_REF]. However, approximately a quarter of obesityassociated MC4R variants characterized to date do not exhibit such defects. Recent work investigated additional MC4R-related pathways such as Gq and signaling bias toward βarrestin recruitment and increased mitogen-activated protein kinase pathway activation (63, 64) (review in ( 52)).

Moreover, some studies of patients with heterozygous variants on several genes in the MC4R pathway also raise the question of a possible cumulative effect of these variants eventually explaining the phenotype severity. However, detailed phenotypic data on combined heterozygotes are still lacking [START_REF] Ayers | Melanocortin 4 Receptor Pathway Dysfunction in Obesity: Patient Stratification Aimed at MC4R Agonist Treatment[END_REF]. Overall, based on recent progress and therapeutic potential, it will be critical to obtain a clearer picture of the functional effects of these variants ! 10 on MC4R function. The involvement of rare variants of MC3R in the development of obesity is less clear than for MC4R. Modification of body composition has been suggested in MC3R variant carriers. Rare variants leading to the receptor functional alterations have been described and the variant T6K+V81I has been, for example, associated with increased adiposity and hyperleptinemia (review in [START_REF] Demidowich | Polymorphisms and mutations in the melanocortin-3 receptor and their relation to human obesity[END_REF]).

Clinical management in patients with leptin/melanocortin pathway variants

In most cases, clinical management of these patients is complex and requires comprehensive, specialized and multidisciplinary management that include dietary advice with supervision of eating behavior, adapted physical activities, psychomotricity, speech therapy, hormone replacement therapy, amongst others. This approach should be implemented in patients with genetic obesity beginning in early childhood and, if possible, in expert centers. In our experience as a reference center for the care of genetic obesities, we observe that these genetic obesity forms are often refractory to usual medical care, meaning that usual standards of care recommending lifestyle modifications are in general inefficient, albeit scarce data are still available on the effect of nutritional/lifestyle interventions on weight loss response in nonsyndromic obesity. This might be different between patients with MC4R variants and those with gene variant upstream MC4R but this needs deep investigation. Implementing a nutritional and physical exercise program for 1 year, investigators found that weight loss in children with MC4R variants was equivalent to non-carriers. However, a recovery of full weight 1 year after the end of the program was observed, which was not the case in nonvariant carriers [START_REF] Reinehr | Lifestyle intervention in obese children with non-alcoholic fatty liver disease: 2-year follow-up study[END_REF]. The failure of standard of care in patients with variants in the leptin/ melanortin pathway might extend to bariatric surgery, which is a well-known long-term efficient treatment for severe obesity using several operative methods especially laparoscopic ! 11 gastric bypass or sleeve gastrectomy. However, variability in the individual weight loss response to bariatric surgery is well described, probably related to lifestyle habits but also individual genetic background. Data in patients with monogenic non-syndromic obesity are limited and controversial. In patients carrying variants in the LEPR gene, we reported that, while these patients initially lose weight after bariatric surgery, the magnitude is clearly less when compared to patients with common obesity [START_REF] Beyec | Homozygous leptin receptor mutation due to uniparental disomy of chromosome 1: response to bariatric surgery[END_REF]. Moreover, monitoring these patients over the long term in our center, we observed they have all regained the weight initially lost (unpublished data). Recently, a Dutch group published weight loss data after bariatric surgery in a cohort of 1014 patients. In this cohort, 30 patients were diagnosed with heterozygous variants in POMC and PCSK1 genes. Total weight loss after gastric bypass was not significantly different from the non-carriers (69) after 2 years of follow-up. Conversely, in a Chinese cohort of 131 obese subjects, they found 8.4% (11 subjects) with a heterozygous variant located in a gene of the leptin / melanocortin pathway. In patients carrying variants in the LEP, LEPR, SIM1 and PCSK1 genes, the magnitude of weight loss obtained after 6 years of follow-up was significantly lower than that of patients without the variants, also associating with less improvement in metabolic comorbidities [START_REF] Li | Monogenic Obesity Mutations Lead to Less Weight Loss After Bariatric Surgery: a 6-Year Follow-Up Study[END_REF].

In patients with heterozygous variants of MC4R, bariatric surgery induced-weight loss is identical to that of MC4R wild type carrier, at least after one year follow-up [START_REF] Valette | Melanocortin-4 receptor mutations and polymorphisms do not affect weight loss after bariatric surgery[END_REF]. However, the presence of a GOF variant is associated with a high risk of BED preoperatively and alters weight loss response with more reoperations and postoperative complications [START_REF] Bonnefond | Eating Behavior, Low-Frequency Functional Mutations in the Melanocortin-4 Receptor (MC4R) Gene, and Outcomes of Bariatric Operations: A 6-Year Prospective Study[END_REF]. In the Dutch cohort, among 11 patients with heterozygous variants, those who had a gastric bypass had a weight loss equivalent to that of the non-mutated patient. However, in those who had a sleeve gastrectomy, the weight loss magnitude was significantly lower, at 2 years after surgery [START_REF] Cooiman | Genetic Obesity and Bariatric Surgery Outcome in 1014 Patients with Morbid Obesity[END_REF]. Thus, carriers of leptin/melanocortin pathway variants experience variable responses to ! 12 bariatric surgery that is probably multifactorial (review in [START_REF] Kuhnen | Melanocortin-4 Receptor Signalling: Importance for Weight Regulation and Obesity Treatment[END_REF]). Additional studies are necessary to decipher the links between functional characteristics of the variants and weight trajectories (initial weight loss then stabilization / weight gain) especially in the long-term after the surgery. Great caution must be taken before performing bariatric surgery in these patients and probably discussed in detail with a medical reference center for genetic obesity.

Regarding obesity drugs, few data exist on drugs tested in non-syndromic obesity.

Sibutramine was tested in a patient carrying a functional variant in the homozygous state of MC4R without convincing results on weight [START_REF] Hainerova | Hypogonadotropic hypogonadism in a homozygous MC4R mutation carrier and the effect of sibutramine treatment on body weight and obesity-related health risks[END_REF]. GLP1 analogs, including liraglutide, have been tested in patients with MC4R variants using Liraglutide 3 mg / day for 16 weeks.

Interestingly, compared to MC4R wild type carriers, the weight loss of MC4R variant carriers, was similar (approximately 6%), suggesting that a pro-satietogenic effect of GLP1 analogs is also present in subjects with MC4R genetic alterations [START_REF] Iepsen | Patients with Obesity Caused by Melanocortin-4 Receptor Mutations Can Be Treated with a Glucagon-like Peptide-1 Receptor Agonist[END_REF].

New therapeutic perspectives in the leptin/melanocortin pathway: from genes to targeted therapy

In recent years, research has developed therapeutic innovations in the leptin/melanocortin pathway upstream of the MC4R receptor. Before that, pharmaceutical action was limited to the case of leptin deficiency where subcutaneous injection of leptin in children and adults results in weight loss, mainly due to fat mass reductions, with a major and rapid effect on reducing food intake [START_REF] Wabitsch | Biologically inactive leptin and early-onset extreme obesity[END_REF][START_REF] Farooqi | Beneficial effects of leptin on obesity, T cell hyporesponsiveness, and neuroendocrine/metabolic dysfunction of human congenital leptin deficiency[END_REF]. Leptin treatment also induces puberty in these individuals, even in adults [START_REF] Licinio | Phenotypic effects of leptin replacement on morbid obesity, diabetes mellitus, hypogonadism, and behavior in leptin-deficient adults[END_REF].

! 13
Through in vitro models, it was initially reported that MC4R receptor agonists IRC-022493 and IRC-022511 could rescue the activity of mutated hMC4R. This was especially the case for MC4R variants with altered cyclic AMP response to the endogenous agonists [START_REF] Roubert | Novel pharmacological MC4R agonists can efficiently activate mutated MC4R from obese patient with impaired endogenous agonist response[END_REF]. Then a series of new pharmacological agonists of MC4R, which restore normal mutated receptor activity, were further tested in vitro [START_REF] Fani | The melanocortin-4 receptor as target for obesity treatment: a systematic review of emerging pharmacological therapeutic options[END_REF]. One study demonstrated that the novel human MC4R antagonist, Ipsen 17, acted as a pharmacological chaperone of human MC4R, increased the cell-surface expression of MC4R mutant and their signaling capacity upon α-MSH stimulation [START_REF] Wang | Rescue of defective MC4R cell-surface expression and signaling by a novel pharmacoperone Ipsen 17[END_REF]. Then highly selective MC4R agonists (BIM-22493 or setmelanotide) were then tested in obese animal models and showed a decrease in food intake and an increase in total energy expenditure leading to significant weight loss. In contrast to other previously tested MC4R agonists, no side effect, especially on blood pressure or heart rate, was observed (78) despite evidence linking central melanocortin signaling to the regulation of blood pressure. Indeed, human MC4R deficiency is associated with lower blood pressure and inversely, a previously tested MC4R agonist (LY2112688) had an impact on cardiovascular parameters (79), probably through activation of the sympathetic nervous system. While the reason why setmelanotide safety is different from other MC4R agonists is not fully understood, several hypotheses have been put forward to explain the differential effects on the cardiovascular system. This includes variability between the different compounds in terms of brain penetration, of specificity (for MC3R or MC4R), of binding affinity but also probably of MC4R-related signaling. These results have stimulated considerable interest in the development of molecules targeting leptin/ melanocortin pathway deficiencies. In humans, treatment with RM-493 increases resting energy expenditure without cardiovascular side effects [START_REF] Chen | RM-493, a melanocortin-4 receptor (MC4R) agonist, increases resting energy expenditure in obese individuals[END_REF]. We have also reported that MC4R receptor agonists activate the mutated MC4R receptor in vitro with an altered response to endogenous agonists. Furthermore, previous work also described MC4R variants with ! 14 functional consequences and the response to agonists specific for this receptor while proposing a predictive score for the response in vitro [START_REF] Collet | Evaluation of a melanocortin-4 receptor (MC4R) agonist (Setmelanotide) in MC4R deficiency[END_REF]. With European colleagues, we have recently shown that setmelanotide, a MC4R agonist, restores melanocortin signaling in the presence of homozygous gene variants upstream of MC4R (i.e POMC or LEPR) while it could also be effective in restoring mutated MC4R activity [START_REF] Kuhnen | Proopiomelanocortin Deficiency Treated with a Melanocortin-4 Receptor Agonist[END_REF][START_REF] Clement | MC4R agonism promotes durable weight loss in patients with leptin receptor deficiency[END_REF]. The treatment of two homozygous POMC mutation patients with setmelanotide led to weight loss (-51.0 kg and -20.5 kg respectively) over 12 weeks for both patients and improved hyperphagia scores (81), effects we have observed as stable three years later. To date, no increase in blood pressure or severe adverse events related to the study drug has been observed. The most frequently reported adverse effects are increased pigmentation. With these promising results, the medium and long-term side effects should be monitored, especially evaluating the consequences of chronic stimulation of melanocytes with RM-493. Indeed, this pharmaceutical agonist also activates the MC1R receptor located on the skin. Trials are now ongoing extending Setmelanotide treatment in patients with homozygous and heterozygous variations of the LEPR and POMC genes but also in syndromic obesities such as Bardet-Biedl and Alstrom syndrome. Setmelanotide can activate MC4R, and rescue its activity when a functional variant is present. Thus, patients with heterozygous variants associated with a loss of function in the leptin/melanocortin pathway might benefit from these innovative treatments in the near future.

Conclusion

Genetic forms of obesity are important to diagnose due to the need for a specific management plan to be set up as soon as possible, and to the multidisciplinary team needed to carry out patient care. In the near future, next generation sequencing (NGS) technologies or whole-! 15 exome sequencing may help physicians to identify new molecular anomalies in patients with early-onset severe obesity in order to improve their care management. Similarly, new treatments have recently emerged that could change the prognosis for these rare severe forms of obesity, giving hope to patients with severe monogenic non-syndromic obesity.

Figure 1 :

 1 Figure 1: The leptin/melanocortin pathway

Conflict of interest

The authors have not declared any conflicts of interest.

Acknowledgement : Tim Swartz is acknowledged for critical reading of the manuscript.


Vu Thi

Thu Nga

Gilbert Teyssedre

Modelling of insulation in DC systems: the challenges for HVDC cables and accessories

Cable technologies have evolved in different ways for applications using high voltage alternating current (HVAC) and high voltage direct current (HVDC) over the last 40 years. Since the 1950s, mass-impregnated paper was progressively replaced by extruded insulation made of polyethylene and then crosslinked polyethylene (XLPE). The switch from paper insulation to extruded cables went on continuously while cables were designed with ever increasing voltage requirements. However, regarding space charge build-up and field redistribution, particularly at polarity reversal stages in thyristors, the behaviour of extruded cables under such DC stress is not fully understood. For this reason, material improvement, characterization, and modelling are still intensively researched for cables, accessories, and power conversion equipment. The weaknesses and methods used to simulate the characteristics of insulation are presented and compared in this work through the simulation results of the macroscopic and fluid model.

Introduction

HVDC technologies remain a growing part of energy transmission systems owing to the new sources of energy being introduced, especially renewable energy, and to the need for strengthening energy networks while focusing on the de-carbonation of energy.

There are converging favourable conditions for the development of HVDC links for energy transmission, notably the development of large electrical power lines over long distances to link production and consumption areas and to interconnect different networks with ever growing size. HVDC can also be used in replacement of HVAC lines for transmitting more power over a spatially constrained infrastructure. The demand for HVDC lines has diverse origins, namely, submarine cables, urban areas, and strong public opposition of overhead lines. The switch from HVAC to HVDC systems has great advantages such as simplification of manufacture (Fig. 1) and virtually no limit on transmission length owing to the fact that compensation of the capacitive current is no longer a necessity. Therefore, materials used for the insulation of HVDC cables require specific properties, notably regarding conductivity behaviour. Aside from that, its space charge behaviour is something that is carefully considered at the material characterization level (as samples), as well as in a full cable configuration. The amount of charges is something that can be relatively well characterized, however, the criteria for the kinetics of charge release and the behaviour of materials at polarity reversal are not so well-defined [START_REF] Vu | Space charge criteria for the assessment of insulation materials for HVDC[END_REF]. A slow relaxation of charges implies that, at polarity reversal, the residual field will add to the applied field. Therefore, the objective of this work is the analysis of the weaknesses and methods used to simulate the characteristics of insulation in cables and accessories under DC electro-thermal stress.

Threats for insulation withstanding in HVDC cables

As mentioned above, one of the threats to insulation under HVDC stress is the build-up of space charges in the insulation and its impact on the field distribution, along with the energy released when charges are redistributed upon fast-varying voltage. The weaknesses of polymers with respect to mass-impregnated paper can be found in their lower thermal conductivity and higher electrical resistivity, such that charge release is slower. For example, in mineral insulated (Mi) cables, trapped space charge accumulation is considered insignificant [START_REF] Huang | Thermalelectric rating method for mass-impregnated paper-insulated HVDC cable circuits[END_REF]. Also, the maximal designed thermal stress is 55°C for Mi-paper while it is 90°C for XLPE, at least under AC stress.

The major difference between HVAC and HVDC stress is the change from a capacitive distribution of the field to a resistive distribution; as even under DC there is a progressive switch from capacitive to resistive field distribution at each stress level. Under operating conditions, the electric field is not homogeneous along the cable radius and a thermal gradient exists along the radius due Joule losses from the circulating current in the conductor. As the resistivity of the insulation is much more dependent on the temperature and electric field than it is the permittivity, the thermal-electric stress rating in an HVDC cable is trickier to achieve. Under steady-state HVDC, the phenomenon of stress inversion occurs; i.e. the electric field becomes higher at the outer semiconducting screen than at the inner one (near the conductor) due to the lower temperature. Hence, lower electrical conductivity is found at the outer screen. An example of such stress inversion is represented in Fig. 2 for a medium voltage cable under a thermal gradient of 30°C as modelled by a realistic law for the electric conductivity of polyethylene insulation [START_REF] Qin | Design considerations for HVDC components[END_REF] given by: redistributed upon fast-varying voltage. The weaknesses of polymers with respect to mass-impregnated paper can be found in their lower thermal conductivity and higher electrical resistivity, such that charge release is slower. For example, in mineral insulated (Mi) cables, trapped space charge accumulation is considered insignificant [START_REF] Huang | Thermalelectric rating method for mass-impregnated paper-insulated HVDC cable circuits[END_REF]. Also, the maximal designed thermal stress is 55°C for Mi-paper while it is 90°C for XLPE, at least under AC stress.

The major difference between HVAC and HVDC stress is the change from a capacitive distribution of the field to a resistive distribution; as even under DC there is a progressive switch from capacitive to resistive field distribution at each stress level. Under operating conditions, the electric field is not homogeneous along the cable radius and a thermal gradient exists along the radius due Joule losses from the circulating current in the conductor. As the resistivity of the insulation is much more dependent on the temperature and electric field than it is the permittivity, the thermalelectric stress rating in an HVDC cable is trickier to achieve. Under steadystate HVDC, the phenomenon of stress inversion occurs; i.e. the electric field becomes higher at the outer semiconducting screen than at the inner one (near the conductor) due to the lower temperature. Hence, lower electrical conductivity is found at the outer screen. An example of such stress inversion is represented in Fig. 2 for a medium voltage cable under a thermal gradient of 30°C as modelled by a realistic law for the electric conductivity of polyethylene insulation [START_REF] Qin | Design considerations for HVDC components[END_REF] given by:

( ) ( ) ( ( ) ) (1)
where A and α are constants, E a is the thermal activation energy, k B is Boltzmann's constant, E is the applied electric field, T is the temperature, and B = aT+b is a temperature-dependent parameter to account for the change in threshold field versus temperature. it can be seen that the field initially exhibits a capacitive distribution; after 1000 s it is relatively homogeneous and after 1 h or so, the field is a maximum at the outer shield.

The switch from capacitive to resistive field distribution is controlled by the dielectric time constant, ε/σ, where ε is the dielectric permittivity. When the polarity is reversed, which is usually done over a time much faster than the [START_REF] Vu | Space charge criteria for the assessment of insulation materials for HVDC[END_REF] where A and α are constants, E a is the thermal activation energy, k B is Boltzmann's constant, E is the applied electric field, T is the temperature, and B = aT+b is a temperaturedependent parameter to account for the change in threshold field versus temperature. It can be seen that the field initially exhibits a capacitive distribution; after 1000 s it is relatively homogeneous and after 1 h or so, the field is a maximum at the outer shield. The switch from capacitive to resistive field distribution is controlled by the dielectric time constant, ε/σ, where ε is the dielectric permittivity. When the polarity is reversed, which is usually done over a time much faster than the dielectric time constant, the residual electric field at the inner conductor constitutes an enhancement to the capacitive field and this local and transient enhancement of the field brings harmfulness to the cables. From the assumption on the temperature dependence of conductivity, using Maxwell's equation, it can be shown that the electric field distribution in the cable insulation, in cylindrical geometry and under steady state condition is given by expression [START_REF] Fabiani | HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF][START_REF] Adi | DC model cable under polarity inversion and thermal gradient: build-up of design-related space charge[END_REF] defined [START_REF] Vu | Space charge criteria for the assessment of insulation materials for HVDC[END_REF]. A slow relaxation of charges implies that, at polarity reversal, the residual field will add to the applied field. Therefore, the objective of this work is the analysis of the weaknesses and methods used to simulate the characteristics of insulation in cables and accessories under DC electrothermal stress.

Threats for insulation withstanding in HVDC cables

As mentioned above, one of the threats to insulation under HVDC stress is the build-up of space charges in the insulation and its impact on the field distribution, along with the energy released when charges are From the assumption on the temperature dependence of conductivity, using Maxwell's equation, it can be shown that the electric field distribution in the cable insulation, in cylindrical geometry and under steady state condition is given by expression [START_REF] Fabiani | HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF][START_REF] Adi | DC model cable under polarity inversion and thermal gradient: build-up of design-related space charge[END_REF]:

( ) ( ) (2)
where E 0 and  0 are, respectively, the electric field and conductivity at the reference position, r 0 . The charge density associated with non-uniform conductivity is of the form:

(3) where is the dielectric permittivity of the material. if the temperature dependence of the conductivity follows the Arrhenius law with activation energy E a , the charge density can be written according to the following equation:

      dr r r r E E div r g           ) ( ) ( (2)
where E 0 and σ 0 are, respectively, the electric field and conductivity at the reference position, r 0 . The charge density associated with non-uniform conductivity is of the form: 4 insulator and a temperature of 80°C at the inner conductor are considered.

From the assumption on the temperature dependence of conductivity, using Maxwell's equation, it can be shown that the electric field distribution in the cable insulation, in cylindrical geometry and under steady state condition is given by expression [START_REF] Fabiani | HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF][START_REF] Adi | DC model cable under polarity inversion and thermal gradient: build-up of design-related space charge[END_REF]:

( ) ( ) (2)
where E 0 and  0 are, respectively, the electric field and conductivity at the reference position, r 0 . The charge density associated with non-uniform conductivity is of the form:

(3) where is the dielectric permittivity of the material. if the temperature dependence of the conductivity follows the Arrhenius law with activation energy E a , the charge density can be written according to the following equation:

      dr r r r E E div r g           ) ( ) ( ( 3
)
where ε is the dielectric permittivity of the material. if the temperature dependence of the conductivity follows the Arrhenius law with activation energy E a , the charge density can be written according to the following equation:

5 ( ) ( ) , ( 4
)
where T is the absolute temperature, which is function of r and time, t [START_REF] Mazzanti | Extruded Cables for HVDC Transmission: Advances in Research and Development[END_REF]. it can be noticed from Eqs. ( 3) and ( 4) that the space charge polarity directly depends on the conductivity gradient d/dr.

The sign of the space charge, ρ g (r), is the same as the polarity of the voltage applied to the conductor. Such space charge is normally detected by experimental techniques that provide the charge distributions. Such a geometric space charge is also detected when dielectrics of different natures become associated, as in joints and terminations of cables. These junctions may correspond to a gradient of permittivity, or more likely, to a gradient of conductivity [START_REF] Delpino | Polymeric HVDC cable design and space charge accumulation. Part 2: insulation interfaces[END_REF][START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. We have shown that such an interfacial charge -or macroscopic Maxwell-Wagner effect -can be probed by the space charge measurement method. Depending on temperature and field values, the field can be a maximum in one or the other dielectric. Also, the kinetics for build-up and release of the interface charge depends on field and temperature [START_REF] Vu | Maxwell-Wagner effect in multi-layered dielectrics: interfacial charge measurement and modelling[END_REF].

Besides these geometric space charge effects there are also processes of charge build up due to charge trapping and internal dissociation phenomena. it was shown that the latter effect is strongly influenced by the presence of crosslinking by-products into cross-linked polyethylene. Progress in material behaviour when going from HVAC grade to HVDC was obtained by lowering the amount of crosslinking by-products or even suppressing them completely. But still, the issue remains where electronic carriers can be deeply trapped in the material and contribute to field distortion. There is a general trend towards using high resistivity materials [START_REF] Englund | Characteristics of candidate material systems for next generation extruded HVDC cables[END_REF] to avoid notable thermal runaway and possible breakdown in the cable [START_REF] Olsson | Modelling of thermal behaviour of polymer insulation at high electric DC field[END_REF]. However, this may be accompanied with slower space charge release. So, a kind of trade off has to be found. Figure 3 provides some desired features for insulations with an aim to avoid stress enhancement and heavy charge redistribution, of which both processes lead to damages. [START_REF] Qin | Design considerations for HVDC components[END_REF] where T is the absolute temperature, which is function of r and time, t [START_REF] Mazzanti | Extruded Cables for HVDC Transmission: Advances in Research and Development[END_REF]. it can be noticed from Eqs. ( 3) and ( 4) that the space charge polarity directly depends on the conductivity gradient dσ/dr.

The sign of the space charge, ρ g (r), is the same as the polarity of the voltage applied to the conductor. Such space charge is normally detected by experimental techniques that provide the charge distributions. Such a geometric space charge is also detected when dielectrics of different natures become associated, as in joints and terminations of cables. These junctions may correspond to a gradient of permittivity, or more likely, to a gradient of conductivity [START_REF] Delpino | Polymeric HVDC cable design and space charge accumulation. Part 2: insulation interfaces[END_REF][START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. We have shown that such an interfacial chargeor macroscopic Maxwell-Wagner effect -can be probed by the space charge measurement method. Depending on temperature and field values, the field can be a maximum in one or the other dielectric. Also, the kinetics for buildup and release of the interface charge depends on field and temperature [START_REF] Vu | Maxwell-Wagner effect in multi-layered dielectrics: interfacial charge measurement and modelling[END_REF].

Besides these geometric space charge effects there are also processes of charge build up due to charge trapping and internal dissociation phenomena. it was shown that the latter effect is strongly influenced by the presence of crosslinking by-products into cross-linked polyethylene. Progress in material behaviour when going from HVAC grade to HVDC was obtained by lowering the amount of crosslinking byproducts or even suppressing them completely. But still, the issue remains where electronic carriers can be deeply trapped in the material and contribute to field distortion. There is a general trend towards using high resistivity materials [START_REF] Englund | Characteristics of candidate material systems for next generation extruded HVDC cables[END_REF] to avoid notable thermal runaway and possible breakdown in the cable [START_REF] Olsson | Modelling of thermal behaviour of polymer insulation at high electric DC field[END_REF]. However, this may be accompanied with slower space charge release. So, a kind of trade off has to be found. Fig 3 provides some desired features for insulations with an aim to avoid stress enhancement and heavy charge redistribution, of which both processes lead to damages. Thermal resistivity should be minimized to limit thermal gradients, the insulation's resistivity should be comparatively insensitive to temperature, and having nonlinear properties is attractive for field homogenization purposes (as with paper-oil insulation). These three conditions should limit field intensification. one way to avoid heavy charge distribution is to prevent charge storage, and another is to increase resistivity. However, a higher resistivity can also favour persistent charge storage. Therefore, at the same time as resistivity is reduced, charge generation processes should be avoided. Last, but not least, the DC breakdown stress should be high, even at high temperature, and the material should be insensitive to polarity reversal.

Modelling of insulations under dc electro-thermal stress

Several models have been proposed in the literature through the years to predict space charge and electric field distribution within an insulating material subjected to DC electro-thermal stress. Among these models, two types have been extensively used for the materials of HVDC systems, namely, macroscopic models and fluid models. These models will be described in the following paragraphs and simulation results will be presented for each model and for relevant cases linked to HVDC cables and accessories.

Macroscopic models

The material is considered as weakly conductive for these models and only a gradient in the applied stress (electric field, temperature, etc.) in the material will induce the appearance of a space charge due to nonhomogeneity of the conductivity. These models have the advantage of Thermal resistivity should be minimized to limit thermal gradients, the insulation's resistivity should be comparatively insensitive to temperature, and having nonlinear properties is attractive for field homogenization purposes (as with paper-oil insulation). These three conditions should limit field intensification. One way to avoid heavy charge distribution is to prevent charge storage, and another is to increase resistivity. However, a higher resistivity can also favour persistent charge storage. Therefore, at the same time as resistivity is reduced, charge generation processes should be avoided. Last, but not least, the DC breakdown stress should be high, even at high temperature, and the material should be insensitive to polarity reversal.

Modelling of insulations under DC electro-thermal stress

Several models have been proposed in the literature through the years to predict space charge and electric field distribution within an insulating material subjected to DC electro-thermal stress. Among these models, two types have been extensively used for the materials of HVDC systems, namely, macroscopic models and fluid models. These models will be described in the following paragraphs and simulation results will be presented for each model and for relevant cases linked to HVDC cables and accessories.

Macroscopic models

The material is considered as weakly conductive for these models and only a gradient in the applied stress (electric field, temperature, etc.) in the material will induce the appearance of a space charge due to non-homogeneity of the conductivity. These models have the advantage of requiring only a few macroscopic parameters, namely, conductivity and permittivity, to simulate the electric field distribution in an insulator. While conductivity is a non-linear function of the electric field and temperature, it is relatively easy to measure experimentally. This has been done for XLPE at different fields and temperatures [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF] and an equation for the conductivity variation as a function of these parameters has also been proposed (Eq. 1) [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF][START_REF] Cable | One-Piece Premolded Joint for Extruded Cables from 63 to 500 kV[END_REF]. With these data, it is possible to simulate the field and space charge dynamics in a loaded cable with a conductivity gradient. An example of such a calculation is proposed in Fig. 4 for an XLPEinsulated medium voltage (MV) cable 4.5 mm thick, under proposed (Eq. 1) [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF][START_REF] Cable | One-Piece Premolded Joint for Extruded Cables from 63 to 500 kV[END_REF]. With these data, it is possible to simulate the field and space charge dynamics in a loaded cable with a conductivity gradient. An example of such a calculation is proposed in Fig. 4 for an XLPE-insulated medium voltage (MV) cable 4.5 mm thick, under an applied voltage of -80 kV, and a temperature gradient of ΔT=16°C (i.e. T in =57°C and T out =41°C) across the insulation. The details concerning the conductivity equation, the protocol, and the numerical calculations are detailed elsewhere [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. The experimental fields calculated from space charge measurements using the pulsed electro acoustic (PEA) method are given in Fig. 4B for comparison (the electric field should start at 0 but this part of the inner conductor is not visible due to the method used). In the simulation, the field distribution quickly deviates from the Laplacian field and achieves a maximum of the electric field at the outer electrode after one hour of polarization. The field distribution stabilizes with time. The maximal electric field values calculated are, respectively, 17 and 18.5 kV/mm at the inner and outer

Radius (mm) 200 s 1 h 2 h 3 h

7 proposed (Eq. 1) [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF][START_REF] Cable | One-Piece Premolded Joint for Extruded Cables from 63 to 500 kV[END_REF]. With these data, it is possible to simulate the field and space charge dynamics in a loaded cable with a conductivity gradient. An example of such a calculation is proposed in Fig. 4 for an XLPE-insulated medium voltage (MV) cable 4.5 mm thick, under an applied voltage of -80 kV, and a temperature gradient of ΔT=16°C (i.e. T in =57°C and T out =41°C) across the insulation. The details concerning the conductivity equation, the protocol, and the numerical calculations are detailed elsewhere [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. The experimental fields calculated from space charge measurements using the pulsed electro acoustic (PEA) method are given in Fig. 4B for comparison (the electric field should start at 0 but this part of the inner conductor is not visible due to the method used). In the simulation, the field distribution quickly deviates from the Laplacian field and achieves a maximum of the electric field at the outer electrode after one hour of polarization. The field distribution stabilizes with time. The maximal electric field values calculated are, respectively, 17 and 18.5 kV/mm at the inner and outer an applied voltage of -80 kV, and a temperature gradient of ΔT=16°C (i.e. T in =57°C and T out =41°C) across the insulation.

The details concerning the conductivity equation, the protocol, and the numerical calculations are detailed elsewhere [START_REF] Vu | Correlating conductivity and space charge measurements in multidielectrics under various electrical and thermal stresses[END_REF]. The experimental fields calculated from space charge measurements using the pulsed electro acoustic (PEA) method are given in Fig. 4B for comparison (the electric field should start at 0 but this part of the inner conductor is not visible due to the method used). in the simulation, the field distribution quickly deviates from the Laplacian field and achieves a maximum of the electric field at the outer electrode after one hour of polarization. The field distribution stabilizes with time. The maximal electric field values calculated are, respectively, 17 and 18.5 kV/mm at the inner and outer semiconductor. This change from capacitive (i.e. Laplacian field) to a resistive field distribution is due to the conductivity gradient that drives charges from the higher conductivity (inner semiconductor) to the lower conductivity (outer semiconductor). When compared to the experimental data, the same trend is observed, i.e. an inversion of the location of the maximal value of the electric field after one hour. However, in the experiment, the value is twice that which has been predicted by the macroscopic model (~20 kV/mm at the outer semiconductor). Hence, the macroscopic model can only predict the field values under the limits fixed by the conductivity variation linked to the thermal and/or electrical gradient. if other physical phenomena are at play in the cable, these types of models are not sufficient to predict the entire field response.

The real advantage of such a macroscopic model is to use it for large systems, where often times complex geometries and a large number of materials are present, to provide the field distribution along the system. This is, for example, the case with HVDC cable joints where different dielectrics are used and where the geometry plays a key role in the field pattern. Fig 5 shows an example of a pre-moulded joint actually used for a 200 kV DC link, where an interface is formed between two insulating polymers, namely XLPE and ethylene propylene diene monomer (EPDM). This geometry has been implemented in the macroscopic model. Under the simulation conditions, a voltage of 200 kV is applied at the inner side of the XLPE and the outer face of the EPDM is grounded. A current of I=1000 A flows in the conductor core. These conditions imply a temperature gradient as well as a field gradient, in the cable joint.

The calculated electric field distribution in the cable joint is presented in Fig. 6, for the proposed geometry of Fig. 5. in the simulations, we consider here that the thermal and electrical conditions have reached stationary states, with a thermal gradient on the order of 40°C between the cable core and the outside of the joint. The maximal values of the electric field are located, respectively, at the triple point of the XLPE, EPDM, semiconductor, and at the XLPE/EPDM interface at the limit of the cable joint. The field distribution in these regions is controlled by stress cones. The design and modelling of these parts actually represent one of the key points for reliable cable accessories [START_REF] Olsson | Modelling of thermal behaviour of polymer insulation at high electric DC field[END_REF][START_REF] Quaggia | Development of joints and terminations for HVDC extruded cables[END_REF][START_REF] Hou | Electric field calculation and analysis of HVDC cable joints with nonlinear materials[END_REF][START_REF] Ye | Review on HVDC cable terminations[END_REF]. This example shows the necessity to optimize the various parameters that play a role in the electric field distribution in cable joints, such as the system geometry (at the triple point but also at the junction boundary) and the material properties. Macroscopic modelling could be used as a design tool to optimize these parameters in regard to temperature and field with the goal of developing new materials with specific properties.

Fluid models

Contrary to macroscopic models, fluid models are based on a microscopic approach, where the physical hypotheses at play should be identified before any model development.

They do not rely on the non-homogeneity of the conductivity, but on the generation and transport/accumulation of charges within the material. instead of considering the conductivity as a macroscopic and homogeneous phenomenon under isotropic conditions, the location where charges are generated is taken into account, as well as their nature and fate during transport. These models can simulate the transient processes that occur when a thermo-electrical stress is applied to an insulating polymer. They account for processes linked to the energy levels located in the band gap, i.e. traps for electrons and holes. They also account for charge generation and extraction at the electrodes. These models are more difficult to implement compared to macroscopic models due to the parameterization of the traps distribution. However, as charge transport is to trapping and detrapping, charge accumulation can take place for reasons that are not linked to the non-homogeneity of the conductivity, for example, as a blocking contact at an interface.

Fluid models have been intensively developed these last 20 years [START_REF] Alison | A model for bipolar charge transport, trapping and recombination in degassed cross-linked polyethylene[END_REF][START_REF] Roy | Description of charge transport in polyethylene using a fluid model with a constant mobility: fitting model and experiments[END_REF][START_REF] Xia | Numerical analysis of packet-like charge behavior in low-density polyethylene by a Gunn effect-like model[END_REF], mostly for low density polyethylene (LDPE), the base resin of XLPE. An example of simulation results using a fluid model for an XLPE cable is proposed in Fig. 7, for the same protocol as the one described for the macroscopic model, i.e. an MV cable of 4.5 mm, an applied voltage of -80 kV, and a temperature gradient of 16°C with same internal and external temperatures as mentioned previously. The charges that are accounted for are electronic charges, i.e. electrons and holes. These charges are generated only at the electrodes and follow the Schottky injection law. Charges can be mobile, having a hopping mobility that is a function of the electric field and temperature, or charges can be trapped into a unique level of deep traps, from which they can escape by a thermally activated process. Recombination is also taken into account in the fluid models. Recombination coefficients between each type of charge are a function of the mobility (i.e. Langevin coefficients). A complete description of the physical hypotheses included in the model, the numerical resolution, and the parameterization are detailed elsewhere for cable geometry [START_REF] Roy | Modelling space charge in a cable geometry[END_REF]. When considering the simulated results at a steady state (i.e. 48 h), the electric field distribution is seen to switch from the Laplace field to its maximal value at the outer semiconductor. Moreover, the maximal field value at the outer electrode is on the order of 22.5 kV/mm, which is what has been measured experimentally. From these results, it is noticeable that the fluid model can predict the main characteristics observed experimentally, particularly the field enhancement at the outer electrode compared to the macroscopic model, which is not only due to a conductivity gradient. However, for these models, different processes are at play, with various characteristic times for each process. in this case, the parameterization is very sensitive and has not reached an optimized point and, in the proposed example, the dynamics for field stabilization is longer (48 h) compared to the experimental case (3 h).

Comparing fluid models to macroscopic models by means of electric field distribution shows the strengths and drawbacks of each model:

-Macroscopic models offer an easy implementation of the conductivity and the possibility to simulate complex systems over short time simulations. They are, however, limited when charge accumulation comes into play.

-Fluid models possess an efficient description of the charge behaviour, but at the cost of complex physics and parameterization. Aside from their direct implementation in real geometries in which parameterization and optimization are tricky, fluid models are interesting and efficient for testing hypotheses of physical processes controlling the charging behaviour. Such models are developed based on focused experiments that can be realized at a lab scale, as with electron beam irradiation.

Conclusions

According to current trends, HVDC cables are gradually replacing HVAC because of their significant benefits. However, due to the build-up of space charge and the consequent distortion electric fields, the challenge of designing insulating materials under DC stress is not straightforward. We have explored various research directions for the development of insulating materials and control of stresses upon DC cables by simulations and modelling using different methods. The simulation results of the macroscopic models and fluid models are compared in this work. The macroscopic models have the ability to simulate complex systems over a short time, however, the model is affected by the formation of space charges in the material. Fluid models are effective in modelling the physical processes that control the charging behaviour, but they are difficult in real geometries due to complex parameterization and optimization.

Fig. 2 .

 2 Fig. 2. Example of field redistribution vs. time and stress inversion under DC stress for a MV cable. Adapted from [5]. parameters of equation (1) are: A=3.68×10 7 S•m/V, E a =0.98 eV, B=1.086×10 -7 S•m/V and α=1. A temperature drop of 30°C across the insulator and a temperature of 80 o C at the inner conductor are considered.

  :

Fig. 1 .

 1 Fig. 1. Examples of structures of HV submarine cables rated for 200 MW. Weight reduced by over 60% [2]. (A) 3-core HVAC 110 kV cable; outer diameter 193 mm; (B) +/-160 kV HVDC cable; outer diameter 111 mm.

Fig. 1 .

 1 Fig. 1. Examples of structures of HV submarine cables rated for 200 MW. Weight reduced by over 60% [2]. (A) 3-core HVAC 110 kV cable; outer diameter 193 mm; (B) +/-160 kV HVDC cable; outer diameter 111 mm.

Fig. 3 .

 3 Fig. 3. Strategies for improving material withstanding in HVDC.

Fig. 3 .

 3 Fig. 3. Strategies for improving material withstanding in HVDC.

Fig. 4 .

 4 Fig. 4. Field distributions at different times for an MV cable under -80 kV and temperature gradient of ΔT=16°C. (A) Calculated (macroscopic model), (B) Measured by pulsed-electro acoustic (PEA) method.

Fig. 4 .

 4 Fig. 4. Field distributions at different times for an MV cable under -80 kV and temperature gradient of ΔT=16°C. (A) Calculated (macroscopic model), (B) Measured by pulsed-electro acoustic (PEA) method.

Fig. 4 .

 4 Fig. 4. Field distributions at different times for an MV cable under -80 kV and temperature gradient of ΔT=16°C. (A) Calculated (macroscopic model), (B) measured by pulsed-electro acoustic (peA) method.

Fig. 5 .

 5 Fig. 5. Schematic representation of a pre-moulded joint for HVDC-extruded cables up to 200 kV [14].

Fig. 6 .

 6 Fig.6. Electric field distribution in a cable joint under V appl =200 kV and I=1000 A. the colour scale implies a high electric field for red colours, and a lower electric field for blue colours.

Fig. 7 .

 7 Fig. 7. Simulated electric field distribution (fluid model) vs. radius at different times for an MV cable of 4.5 mm thick insulation polarized at -80 kV, and a temperature gradient of ΔT=16°C.

ACKNOWLEDGEMENTS

We would like to acknowledge the C.N.R.S. (France) for financial support to the ModHVDC project n° PICS07965.

The authors declare that there is no conflict of interest regarding the publication of this article.