Luc Desseyn

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Valérie Gouyer

Frédéric Gottrand

PhD Jean-Luc Desseyn
email: jean-luc.desseyn@inserm.fr

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Ocular mucins in dry eye disease

Keywords: Dry eye, Mouse model, Mucin, Mucus ADDE, aqueous deficient dry eye, BAK, benzalkonium chloride, BTX, botulinic toxin, EDE, evaporative dry eye, MAM, membrane-associated mucin

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Ocular mucins in dry eye disease.

Introduction

Mucus gel is the first defense barrier at the ocular surface. This hydrogel traps bacteria, dust, and pollen, and removes them by eye blinking. Mucus also lubricates the underlying tissue and is crucial to dissipate the energy generated from eye blinking, preventing desiccation of the ocular surface. Dry eye disease (DED) is a common and multifactorial disease. All forms of DED are due to water loss. In aqueous deficient dry eye (ADDE), water loss is due to a deficient lacrimal secretion but a normal rate of evaporation of the tear film, whereas evaporative dry eye (EDE) is due to an excessive evaporation of tears in the presence of normal lacrimal secretion. Regardless, every kind of dry eye enters a self-perpetuating detrimental cycle where the tear film hyperosmolarity induces an inflammatory response that leads to a reduced expression of glycocalyx mucins, apoptotic death of surface epithelial cells, and a loss of goblet cells that secrete gel-forming mucins [START_REF] Bron | TFOS DEWS II pathophysiology report[END_REF]. This decreased goblet cell density is proportional to the disease severity [START_REF] Murube | Impression cytology on conjunctiva and cornea in dry eye patients establishes a correlation between squamous metaplasia and dry eye clinical severity[END_REF]. The aim of this comprehensive review is to summarize current knowledge of mucin production and its role at the ocular surface during health and DED, and to overview the mouse models available for the study of mucins during dry eye.

Mucins

Mucus is a hydrogel that covers secretory epithelium. Its primary functions are the protection, lubrication, and hydration of mucosal tissues. It also constitutes a semipermeable protective barrier between the environment and underlying epithelial cells. Mucus gels are composed mainly of water (> 95%) and mucins (MUCs) represent their major organic component.

Mucins are high molecular weight proteins characterized by long amino acid sequences enriched in Ser, Thr, and Pro that are O-glycosylated. O-glycosylation is a posttranslational modification that consists on the addition of lateral sugars on the mucin backbone, also called apomucin. Apomucins are heavily O-glycosylated, giving them their specific "bottle brush" structure (Fig. 1). O-glycosylation is essential for the gelation process and the mucus rheological properties, to maintain the mucin tertiary structure (linear instead of globular) and to modulate the interactions between mucins with foreign particles (bacteria, dust…) [START_REF] Corfield | Mucins: A biologically relevant glycan barrier in mucosal protection[END_REF][START_REF] Demouveaux | Gel-forming mucin interactome drives mucus viscoelasticity[END_REF].

Human MUC genes and rodent Muc genes encode human MUC and mouse Muc products that can be classified into two families: membrane-associated mucins (MAMs) and secreted mucins (Fig. 1). MUC3A/B, MUC4, MUC11/12, MUC16, and MUC17, are part of large human MAMs found at the apex of epithelial cells of the secretory mucosa [START_REF] Desseyn | Architecture of the large membrane-bound mucins[END_REF] and may to a lower extent contribute to the mucus gel. Several small MAMs are nonspecific to secretory mucosal tissues, such as MUC1, MUC13, MUC15, MUC18, and MUC20-22 [START_REF] Pallesen | Isolation and characterization of MUC15, a novel cell membrane-associated mucin[END_REF][START_REF] Shih | A new Mel-CAM (CD146)-specific monoclonal antibody, MN-4, on paraffin-embedded tissue[END_REF][START_REF] Uhlén | Tissue-based map of the human proteome[END_REF][START_REF] Woodward | Expression analysis of the transmembrane mucin MUC20 in human corneal and conjunctival epithelia[END_REF]. Because these MAMs are not "mucus molecules", they should not be classified as mucins but mucin-like molecules. Among the secreted human mucins, MUC7 and MUC8 are small mucins that do not form oligomers while the five others MUC2, MUC5AC, MUC5B, MUC6 and MUC19 are truly gel-forming. These mucins are macromolecules synthesized and secreted as polymers by specialized cells that are mainly goblet cells. They are highly conserved between human and mouse [START_REF] Culp | The gene encoding mouse Muc19: cDNA, genomic organization and relationship to Smgc[END_REF][START_REF] Desseyn | Characterization of mouse muc6 and evidence of conservation of the gel-forming mucin gene cluster between human and mouse[END_REF] and impart rheological properties to mucus gels [START_REF] Demouveaux | Gel-forming mucin interactome drives mucus viscoelasticity[END_REF][START_REF] Thornton | Structure and function of the polymeric mucins in airways mucus[END_REF].

3.Mucus of the ocular surface

Tear film

The tear film thickness ranges from 2 to 5.5 μm and covers the ocular surface exposed to the external environment. The most simple and logical representation of tear film is the three-layered model: a mucin layer in contact with the corneal epithelium, an aqueous internal layer, and a lipid external layer that prevents evaporation (Fig. 2a). However, it is increasingly considered that the mucins and aqueous layers are actually a single layer, termed the mucoaqueous layer, with a mucin gradient toward the ocular surface (Fig. 2b) [START_REF] Willcox | TFOS DEWS II Tear Film Report[END_REF]. The exact structure of the tear film is continually debated but there are clinical observations suggesting that "the fluid drawn into the menisci from the nascent tear film, in the upstroke of the blink, is more watery than the precorneal film itself and it seems likely that an aqueous layer is retained between TFLL [tear film lipid layer] and the subjacent mucoaqueous layer behavior is distinctly gel-like" [START_REF] Bron | TFOS DEWS II pathophysiology report[END_REF].

The tear film lipid layer, with a mean thickness of 42 nm, is produced by the Meibomian glands and is spread onto the tear film with each blink. The main role of this layer is to stabilize the tear film [START_REF] Willcox | TFOS DEWS II Tear Film Report[END_REF]. The aqueous layer is secreted at the conjunctival fornix by the lacrimal gland [START_REF] Treuting | Special Senses[END_REF]. The mucin layer, formed by MAMs and gel-forming mucins, is produced by corneal and conjunctival epithelia and lacrimal glands.

Mucin expression at the ocular surface

Mucins contribute to the epithelial barrier, prevent binding of debris and pathogens to the ocular surface, maintain hydration of the ocular surface and stabilize the tear film [START_REF] Willcox | TFOS DEWS II Tear Film Report[END_REF]. The production of ocular mucins starts very early during human embryonic development.

Indeed, goblet cells containing sialylated mucins are visible in the fornix of the conjunctiva as soon as the 9 th week of amenorrhea [START_REF] Miyashita | Morphological and histochemical studies of goblet cells in developing human conjunctiva[END_REF]. In BALB/c mice, conjunctival goblet cells producing Muc5ac are visible 21 days after birth by immunohistochemistry using the 45M1 antibody, which is directed against the human MUC5AC counterpart [START_REF] Pajoohesh-Ganji | K14 + compound niches are present on the mouse cornea early after birth and expand after debridement wounds[END_REF].

The three major human ocular MAMs are MUC1, MUC4, and MUC16 (Muc1, Muc4, and Muc16 in the mouse). In humans, MUC1, MUC4, and MUC16 are produced in both the cornea and the conjunctiva [START_REF] Gipson | Distribution of mucins at the ocular surface[END_REF][START_REF] Pflugfelder | Detection of sialomucin complex (MUC4) in human ocular surface epithelium and tear fluid[END_REF], whereas only Muc1 and Muc4 are produced in both the mouse cornea and conjunctiva [START_REF] Kim | Topical application of apricot kernel extract improves dry eye symptoms in a unilateral exorbital lacrimal gland excision mouse[END_REF][START_REF] Marko | The ocular surface phenotype of Muc5ac and Muc5b null mice[END_REF][START_REF] Menon | Suppression of Toll-like receptor-mediated innate immune responses at the ocular surface by the membrane-associated mucins MUC1 and MUC16[END_REF] (Fig. 3). In mice, Muc16 is produced in the conjunctiva but not in the cornea [START_REF] Gipson | Human conjunctival goblet cells express the membrane associated mucin MUC16: Localization to mucin granules[END_REF]. Interestingly, MUC4 is found mainly at the surface of conjunctival epithelial cells and its expression decreases from the edge of the corneal epithelium to the center of the cornea [START_REF] Gipson | Distribution of mucins at the ocular surface[END_REF][START_REF] Pflugfelder | Detection of sialomucin complex (MUC4) in human ocular surface epithelium and tear fluid[END_REF]. To our knowledge, the gradient location of Muc4 has not been verified in mouse ocular surface. In mouse, it has been shown that, in addition to conjunctival and corneal epithelial cells, Muc1 is also produced by the conjunctival goblet cells, and is more produced in the conjunctiva than in the cornea [START_REF] Kardon | Bacterial conjunctivitis in Muc1 null mice[END_REF]. In both humans and mice, MUC16/Muc16 is produced by epithelial cells and goblet cells in the conjunctiva [START_REF] Gipson | Human conjunctival goblet cells express the membrane associated mucin MUC16: Localization to mucin granules[END_REF]. MUC16 is a remarkable MAM since it has been shown that it locates in the mucin granules in the goblet cells [START_REF] Gipson | Human conjunctival goblet cells express the membrane associated mucin MUC16: Localization to mucin granules[END_REF]. The authors suggested that one of the roles of MUC16 could be the facilitation of gel-forming mucin release by preventing the gel-forming mucins to attach to the mucin granule membrane. Soluble forms of MUC1, MUC4 and MUC16 have also been detected in human tear film, in addition to the gel-forming mucins MUC5AC and MUC2 [START_REF] Spurr-Michaud | Assay of mucins in human tear fluid[END_REF]. Human conjunctival and corneal epithelial cells also produce MUC20 [START_REF] Woodward | Expression analysis of the transmembrane mucin MUC20 in human corneal and conjunctival epithelia[END_REF]. In mouse, Muc20 gene is expressed in the conjunctiva (Gupta et al., 2011), however its expression in the cornea has not been studied. Low expression of MUC11 and MUC15 at the mRNA level has been also reported at the human ocular surface [START_REF] Gipson | Distribution of mucins at the ocular surface[END_REF].

Goblet cell distribution within the conjunctiva differs between humans and mice. Gelforming mucins are produced by goblet cells, which occur as single cells in humans, whereas they are usually associated in clusters forming basket like structures in mice [START_REF] Gipson | Visualization of conjunctival goblet cell actin cytoskeleton and mucin content in tissue whole mounts[END_REF] (Fig. 3). Human conjunctival goblet cells secrete the two gel-forming mucins MUC5AC and MUC19 [START_REF] Yu | MUC19 expression in human ocular surface and lacrimal gland and its alteration in Sjögren syndrome patients[END_REF]. Low expression of MUC2 and MUC5B at the RNA level have been reported at the ocular surface [START_REF] Gipson | Distribution of mucins at the ocular surface[END_REF]. Unlike in humans, Muc19 gene seems not to be expressed in the mouse eye [START_REF] Das | Tissue distibution of murine Muc19/smgc gene products[END_REF]. As in humans, mouse conjunctival goblet cells express high levels of Muc5ac while low levels of Muc5b have been reported [START_REF] Marko | The ocular surface phenotype of Muc5ac and Muc5b null mice[END_REF].

Nevertheless, it appears that Muc5b production has been greatly underestimated according to our data using a reporter transgenic fluorescently-tagged Muc5b mouse engineered by homologous recombination (Portal et al., 2017b). This study revealed that almost half of the conjunctival goblet cells produced Muc5b. Furthermore, it demonstrated that Muc5b+ goblet cells represent a good mouse biomarker in an experimental model of dry eye.

Mucins are also produced by ocular glands. Lacrimal gland and Meibomian gland secretions contribute to the mucin content of the tear film. Mucins MUC1, MUC5AC, MUC5B, MUC7, and MUC19 are produced by human lacrimal glands [START_REF] Paulsen | Human lacrimal gland mucins[END_REF][START_REF] Yu | MUC19 expression in human ocular surface and lacrimal gland and its alteration in Sjögren syndrome patients[END_REF]. MUC1 is also produced by human Meibomian glands [START_REF] Tektaş | Characterization of the mucocutaneous junction of the human eyelid margin and meibomian glands with different biomarkers[END_REF]. Transcriptome analysis have shown that Muc1, Muc2,Muc3,Muc4,Muc5ac,Muc5b,Muc6,Muc10,Muc13,endomucin (Muc14), Muc15, Muc16, Muc19 and Muc20 genes are expressed in mouse Meibomian glands [START_REF] Chen | Are BALB/c mice relevant models for understanding sex-related differences in gene expression in the human Meibomian gland?[END_REF][START_REF] Parfitt | Transcriptome analysis of aging mouse meibomian glands[END_REF]. To our knowledge, mucin production by mouse ocular glands has not yet been analyzed at the protein level.

Mucins in dry eye

Dry eye disease

As stated by the Definition and Classification Subcommittee of the TFOS DEWS II, "Dry eye is a multifactorial disease of the ocular surface characterized by a loss of homeostasis of the tear film, and accompanied by ocular symptoms, in which tear film instability and hyperosmolarity, ocular surface inflammation and damage, and neurosensory abnormalities play etiological roles" [START_REF] Craig | TFOS DEWS II Definition and Classification Report[END_REF].

The global prevalence of DED ranges from 5% to 50% worldwide, with a higher prevalence of dry eye for women than for men, and a higher prevalence in Asian than in Caucasian populations [START_REF] Stapleton | TFOS DEWS II Epidemiology Report[END_REF]. For example, in France, the prevalence of dry eye is 21.9% in the elderly (> 73 years), with a higher prevalence in women (27.1% compared with 13.6% for men) [START_REF] Malet | Dry eye disease in French elderly subjects: the Alienor Study[END_REF]. Thirty-five percent of French patients with dry eye suffer from a mild form, 47% from a moderate form, and 18% from a severe form [START_REF] Clegg | The annual cost of dry eye syndrome in France, Germany, Italy, Spain, Sweden and the United Kingdom among patients managed by ophthalmologists[END_REF]. In China, the prevalence of dry eye by symptoms is higher than 50% in the elderly (≥ 70 years) and is 38.9% in the general population (from 5 to 89 years) [START_REF] Song | Variations of dry eye disease prevalence by age, sex and geographic characteristics in China: a systematic review and meta-analysis[END_REF]. In Japan, the dry eye prevalence is 66.2% (30-65 years), with a higher prevalence in women (76.5% compared with 60.2% for men) [START_REF] Uchino | Prevalence of dry eye disease and its risk factors in visual display terminal users: The Osaka study[END_REF].

The etiopathogenic classification of dry eye distinguishes ADDE and EDE, even if they are not exclusive [START_REF] Craig | TFOS DEWS II Definition and Classification Report[END_REF]. However, whatever the etiology of DED, they enter a final common pathway creating a self-perpetuating detrimental cycle: tear hyperosmolarity stimulates ocular surface inflammation, that decreases glycocalyx mucin expression and goblet cell density, and induces surface epithelial cell death that increases ocular surface hyperosmolarity [START_REF] Bron | TFOS DEWS II pathophysiology report[END_REF].

Alteration of mucins in dry eye

A common feature of all forms of DED is goblet cell loss [START_REF] Bron | TFOS DEWS II pathophysiology report[END_REF]. The decrease of goblet cell density, related to the severity of the disease, is accompanied by a decrease of the gelforming mucin MUC5AC production. It has been shown a decreased concentration of MUC5AC in the tears of patients with DED [START_REF] Uchino | Alteration of tear mucin 5AC in office workers using visual display terminals: The Osaka study[END_REF]. Depending on the studies, the level of expression of MUC5AC gene remains unchanged [START_REF] Uchino | Alteration of tear mucin 5AC in office workers using visual display terminals: The Osaka study[END_REF] or is decreased (Corrales et al., 2011b;[START_REF] Machida | Two patients with dry eye disease followed up using an expression assay of ocular surface mucin[END_REF][START_REF] Shimazaki-Den | Symptoms, visual function, and mucin expression of eyes with tear film instability[END_REF] in the conjunctiva of patients with DED compared to healthy subjects. This discrepancy is likely due to different severity of the DED.

A decreased expression of MUC2 gene has also been described (Corrales et al., 2011b). Moreover, it is believed that changes of mucin glycosylation can occur during DED [START_REF] Mantelli | The cellular mechanisms of dry eye: from pathogenesis to treatment[END_REF].

Changes in MUC2 and MUC5AC glycosylation have been described in patients with symptoms but no sign of dry eye [START_REF] Berry | Human preocular mucins reflect changes in surface physiology[END_REF]. The two gel-forming mucins MUC2 and MUC5AC play a pivotal role in the rheological properties of the tear film. Changing in their amount or degree of glycosylation could affect the amount of water retained in the tear film, so the wettability of the ocular surface and its lubrication.

In patients with DED, it has also been reported a decreased expression of the MAM genes MUC1, MUC4 and MUC16 (Corrales et al., 2011b;[START_REF] Machida | Two patients with dry eye disease followed up using an expression assay of ocular surface mucin[END_REF][START_REF] Shimazaki-Den | Symptoms, visual function, and mucin expression of eyes with tear film instability[END_REF]. Disrupted expression of these mucins that are members of the glycocalyx, can lead to an impaired protection of the ocular surface, as well as a less effective lubrication of the ocular surface.

Changes in MUC1 glycosylation has been described in patients with DED, with an increase of MUC1 sialylation in mild to moderate cases and a decrease in severe cases [START_REF] Hayashi | Expression patterns of sialylated epitope recognized by KL-6 monoclonal antibody in ocular surface epithelium of normals and dry eye patients[END_REF].

The authors suggested a compensatory mechanism of the MAM in response to the decrease of MUC5AC in milder DED to reduce DED symptoms, that is not maintained as the severity of the disease increase.

Moreover, a decreased expression of the MUC5AC gene in the conjunctiva and a decreased concentration of MUC5AC product in the tears in patients with Sjögren's syndrome, a systemic autoimmune disease characterized in particular by severe dry eye, has been reported [START_REF] Argüeso | Decreased levels of the goblet cell mucin MUC5AC in tears of patients with Sjögren syndrome[END_REF]. Furthermore, it has been shown a decrease of the expression and production of MUC19 in patients with Sjögren's syndrome [START_REF] Yu | MUC19 expression in human ocular surface and lacrimal gland and its alteration in Sjögren syndrome patients[END_REF]. Concerning the MAM, the concentration of soluble MUC16 is increased in the tear film of patients with Sjögren's syndrome, but the level of membrane bound MUC16 in the conjunctiva remained the same than control subjects [START_REF] Caffery | MUC16 expression in Sjogren's syndrome, KCS, and control subjects[END_REF]. It has also been reported an increased concentration of the soluble MUC1 in the tear film of patients with Sjögren's syndrome, as well as an increased level of membrane bound MUC1 in their conjunctiva [START_REF] Caffery | MUC1 expression in Sjogren's syndrome, KCS, and control subjects[END_REF]. The authors suggested that this increased production of MUC1 and MUC16 is a compensatory response of the conjunctival epithelium during Sjögren's syndrome dry eye in order to protect the ocular surface and to maintain a healthy ocular surface.

How does DED affect the mucin pattern expression in specific areas of the ocular surface in patients with Sjögren's syndrome or dry eye patients without Sjögren's syndrome has not been studied. Mucin levels of expression/production are usually determined from tear and/or impression cytology samples, giving only a global vision on how the mucin expression/production is affected at the ocular surface during DED. In addition to modifications in mucin levels of expression/production, O-glycosylation changes appear to be a main feature of DED. This affects directly the rheological properties of the tear film and then its properties to trap and to clear foreign particles, as well as to retain water and so provide hydration and lubrication to the ocular surface [START_REF] Chaudhury | Reduced mucin-7 (Muc7) sialylation and altered saliva rheology in Sjögren's Syndrome associated oral dryness[END_REF][START_REF] Ricciuto | Cell surface O-glycans limit Staphylococcus aureus adherence to corneal epithelial cells[END_REF].

Mouse models for the study of mucins in dry eye

Many animal models are used to study DED, and the mouse appears to be a good model.

Mice are less expensive than bigger animals, and are widely used to study absorption, distribution, metabolism, and excretion and toxicity tests. Numerous genetic and spontaneous mutant models are now available.

Dry eye mouse models

Numerous mouse models have been developed over the past 20 years for the study of ADDE or EDE. For ADDE, a wide variety of mouse models have been developed, including surgical models with excision of the extraorbital lacrimal gland [START_REF] Stevenson | Extraorbital lacrimal gland excision: a reproducible model of severe aqueous tear-deficient dry eye disease[END_REF] and/or cauterization of the lacrimal duct [START_REF] Flores | Smallmolecule CFTR activators increase tear secretion and prevent experimental dry eye disease[END_REF], and physical models by placing mice in a desiccating environment with or without scopolamine transdermic application [START_REF] Barabino | The controlledenvironment chamber: a new mouse model of dry eye[END_REF][START_REF] Dursun | A mouse model of keratoconjunctivitis sicca[END_REF] or by submitting mice to a therapeutic dose of radiation [START_REF] Rocha | Recovery of radiation-induced dry eye and corneal damage by pretreatment with adenoviral vectormediated transfer of erythropoietin to the salivary glands in mice[END_REF]. Chemical models by topical application of benzalkonium chloride (BAK) [START_REF] Lin | A mouse dry eye model induced by topical administration of benzalkonium chloride[END_REF], injection of botulinic toxin (BTX)-B [START_REF] Suwan-Apichon | Botulinum toxin B-induced mouse model of keratoconjunctivitis sicca[END_REF] or BTX-A [START_REF] Kim | Transduced PEP-1-FK506BP ameliorates corneal injury in Botulinum toxin A-induced dry eye mouse model[END_REF], or human recombinant interleukin-1 [START_REF] Zoukhri | A single injection of interleukin-1 induces reversible aqueous-tear deficiency, lacrimal gland inflammation, and acinar and ductal cell proliferation[END_REF] into the lacrimal gland, or injection of concanavalin A intraorbitally or into the lacrimal glands (Lee et al., 2015b(Lee et al., , 2015a) ) are models allowing the use of one eye as a model of dry eye and the other as an internal control. A plethora of genetic mouse models with dry eye have been also reported including NRTN -/- [START_REF] Song | Neurturin-deficient mice develop dry eye and keratoconjunctivitis sicca[END_REF], Klf4CN [START_REF] Swamynathan | Conditional deletion of the mouse Klf4 gene results in corneal epithelial fragility, stromal edema, and loss of conjunctival goblet cells[END_REF], Tet-mev-1 [START_REF] Uchino | A new mouse model of dry eye disease: oxidative stress affects functional decline in the lacrimal gland[END_REF], Sod1 -/- [START_REF] Kojima | Age-related dysfunction of the lacrimal gland and oxidative stress: evidence from the Cu,Zn-superoxide dismutase-1 (Sod1) knockout mice[END_REF], [START_REF] Marko | Spdef null mice lack conjunctival goblet cells and provide a model of dry eye[END_REF], Itpr2 -/-;Itpr3 -/-double-KO [START_REF] Inaba | Mice lacking inositol 1,4,5-trisphosphate receptors exhibit dry eye[END_REF], and NHE8 -/-mice [START_REF] Xu | Loss of NHE8 expression impairs ocular surface function in mice[END_REF]. The nonobese NOD strain known to develop diabetes is a polygenic model for autoimmune diabetes, and male NOD mice have been reported to develop lacrimal lesions leading to a dry eye phenotype [START_REF] Takahashi | High incidence of autoimmune dacryoadenitis in male non-obese diabetic (NOD) mice depending on sex steroid[END_REF].

Spdef -/-
Mouse models for EDE are essentially genetically modified mice that have no, or abnormal, Meibomian glands. These models include the strains ACAT-1 -/- [START_REF] Yagyu | Absence of ACAT-1 attenuates atherosclerosis but causes dry eye and cutaneous xanthomatosis in mice with congenital hyperlipidemia[END_REF], SCD1 -/- [START_REF] Miyazaki | Targeted disruption of stearoyl-CoA desaturase1 gene in mice causes atrophy of sebaceous and meibomian glands and depletion of wax esters in the eyelid[END_REF], TRAF6 -/- [START_REF] Naito | TRAF6-deficient mice display hypohidrotic ectodermal dysplasia[END_REF], K14-Noggin [START_REF] Plikus | Morpho-regulation of ectodermal organs: integument pathology and phenotypic variations in K14-Noggin engineered mice through modulation of bone morphogenic protein pathway[END_REF], Smad4CKO [START_REF] Huang | FGF-regulated BMP signaling is required for eyelid closure and to specify conjunctival epithelial cell fate[END_REF], K14-CreER tam ;C/EBPα ff ;C/EBPβ ff [START_REF] House | C/EBPalpha and C/EBPbeta are required for Sebocyte differentiation and stratified squamous differentiation in adult mouse skin[END_REF], Barx2 -/- [START_REF] Tsau | Barx2 and Fgf10 regulate ocular glands branching morphogenesis by controlling extracellular matrix remodeling[END_REF]), Klf5CN (Kenchegowda et al., 2011), Fatp4 -/- [START_REF] Lin | Requirement of fatty acid transport protein 4 for development, maturation, and function of sebaceous glands in a mouse model of ichthyosis prematurity syndrome[END_REF], Fgfr2CKO mice [START_REF] Reneker | Fibroblast growth factor receptor 2 (FGFR2) is required for meibomian gland homeostasis in the adult mouse[END_REF], and the transgenic lines APOC1 [START_REF] Jong | Hyperlipidemia and cutaneous abnormalities in transgenic mice overexpressing human apolipoprotein C1[END_REF], and Tabby-EDA [START_REF] Cui | X-linked anhidrotic ectodermal dysplasia disruption yields a mouse model for ocular surface disease and resultant blindness[END_REF]. In addition, numerous mouse models of primary and secondary Sjögren's syndrome, which is a long-term autoimmune disease characterized by an extensive dryness of many organs of the body, were developed and reviewed by Lavoie and colleagues [START_REF] Lavoie | Current concepts: mouse models of Sjögren's syndrome[END_REF].

Mucins in dry eye mouse models

Whatever the type of DED, the predominant method of studying mucin as an ocular sensor is periodic acid-Schiff (PAS) staining used to detect all polysaccharides including mucins and which allows assessment of the decrease of goblet cell density (Table 1).

A decrease in the expression of the secreted gel-forming mucins Muc5ac and Muc5b has been shown at the RNA level in Spdef -/-mice, which lack conjunctival goblet cells [START_REF] Marko | Spdef null mice lack conjunctival goblet cells and provide a model of dry eye[END_REF]. By contrast, in EDE Tabby mice, the absence of Meibomian glands induced an increase of Muc5ac and Muc5b expression, suggesting a different response of goblet cells according to the dry eye model [START_REF] Wang | Meibomian gland absence related dry eye in ectodysplasin a mutant mice[END_REF]. Nevertheless, the genetically ablation of the gel-forming mucins genes Muc5b or Muc5ac alone seemed insufficient to induce dry eye [START_REF] Marko | The ocular surface phenotype of Muc5ac and Muc5b null mice[END_REF], even if modifications of the ocular surface have been shown in several Muc5ac -/-mice [START_REF] Floyd | Mucin deficiency causes functional and structural changes of the ocular surface[END_REF].

The absence of Muc5ac was compensated for by an increase of Muc5b production, which can explain in part why there are only few symptoms observed in Muc5ac -/-mice [START_REF] Marko | The ocular surface phenotype of Muc5ac and Muc5b null mice[END_REF].

In MUC5AC-Tox176 mice, for which the toxicity of diphtheria toxin A was driven by the human mucin MUC5AC promoter, the conditional loss of conjunctival goblet cells was accompanied by a compensatory upregulation of the MAM Muc4 [START_REF] Wang | Alteration of ocular surface mucins in MUC5AC-DTA transgenic mice[END_REF]. Using the ADDE model produced by topical applications BAK twice a day for ten days, we showed that the Muc5b+ conjunctival goblet cell density decreased and reflected the entire goblet cell density. Importantly, this decrease of conjunctival goblet cell density was compensated for by an increased expression of both Muc5ac and Muc5b at the RNA levels and Muc5b production at the peptide level in the remaining conjunctival goblet cells (Portal et al., 2017a).

A decrease of the MAM Muc4 in an ADDE mouse model induced by excision of the exorbital lacrimal gland [START_REF] Kim | Topical application of apricot kernel extract improves dry eye symptoms in a unilateral exorbital lacrimal gland excision mouse[END_REF] and a reduced expression of the two MAMs Muc1 and Muc4 in NRTN -/-mice, which have a defective parasympathetic innervation of the lacrimal gland, have been reported [START_REF] Song | Neurturin-deficient mice develop dry eye and keratoconjunctivitis sicca[END_REF]. However, the genetic ablation of Muc1 seems to not be enough to induce DED. No ocular phenotype was described in Muc1 null mice (C57BL/6 background) and the absence of Muc1 was not compensated by an increase of Muc4 expression [START_REF] Danjo | C57BL/6 mice lacking Muc1 show no ocular surface phenotype[END_REF]. Conjunctivitis and blepharitis, accompanied with a goblet cell hyperplasia, were observed in another Muc1 null mouse line in the C57BL/6 X SVJ129 genetic background only when mice are housed in a conventional facility [START_REF] Kardon | Bacterial conjunctivitis in Muc1 null mice[END_REF]. The authors suggested that Muc1 plays an important role in maintaining resistance to bacterial infection. Muc4 -/-mouse line has also been obtained, and does not have obvious abnormal phenotype [START_REF] Das | Mice deficient in Muc4 are resistant to experimental colitis and colitis-associated colorectal cancer[END_REF]. To our knowledge, the ocular phenotype of Muc4 -/-mice has not been studied in details yet.

Moreover, in Aire -/-mice, a mouse model of ADDE associated with Sjögren's syndrome, an increased acidification of goblet cell mucins and an increased sialylation of terminal galactose residues in goblet cell mucins were observed [START_REF] Stephens | Altered mucin and glycoprotein expression in dry eye disease[END_REF].

Conclusion

MAMs and gel-forming mucins are a key component of the ocular barrier, as they both contribute to the epithelial barrier, prevent binding of debris and pathogens to the ocular surface, maintain hydration of the ocular surface and stabilize the tear film. Clinical evidence of mucin production disruption has been reported during DED. Despite a wide variety of well characterized mouse models of DED, mucins are still poorly studied and well-characterized molecular tools are missing. A better understanding of the role of ocular mucin in health and disease remains elusive due mainly to the technical limitations of observing in vivo or ex vivo how mucins are organized and interact in the tear film. Additionally, mucins are difficult to study, primarily because of their high level of glycosylation, which restricts specific antibody development. This has led to underestimated levels of mucin production.

The development of transgenic mouse strains has allowed better characterization of mucin abnormalities during DED, especially in fluorescently-tagged mice. It would be interesting to develop other fluorescently-tagged mice, with different fluorescent reporter, to allow simultaneous visualization of either both gel-forming mucins Muc5ac and Muc5b or a combination of gelforming and MAMs. The development of knock-out models has revealed that a specific deficiency in one mucin is not sufficient to induce dry eye (no significant ocular phenotype observed in Muc1 -/-, Muc5ac -/-and Muc5b -/-mice). The development of mice genetically deficient for both Muc5b and Muc5ac genes should be considered while interconnection between ocular MAMs and gel-forming mucins should be investigated. Compensatory mechanisms of mucin production and glycosylation were reported in patients, especially in those with mild to moderate dry eye. The loss of goblet cells seems to appear later as the disease progresses or in more severe cases. More attention should be given to mucin glycosylation changes in the different dry eye mouse models.

The pertinence of several mouse models to study the role of the mucins in DED remains to be shown as most of them only evaluated the goblet cell density by PAS staining. Despite the technical limitations to study mucins, mice are a good model to study dry eye since it is possible to mimic ADDE and EDE. Physical models using a desiccating environment are widely used and robust.

Chemical models have the advantage to reduce the number of animal used by experiment since one eye can be used as a control while the other one is treated. Moreover, the variety of transgenic mice can bring insights of the molecular mechanisms of the disease.

Table 1. Evaluation of goblet cell density and mucin expression or production in mouse models of dry eye. Only methods allowing to study goblet cell density and mucins are listed. See references for additional methods to assess dryness used by the authors.

Mouse model Methods to study mucins and goblet cell density Ref

DS with scopolamine PAS (↓ GC density) [START_REF] Dursun | A mouse model of keratoconjunctivitis sicca[END_REF] Ovariectomized mice PAS (ns) / Muc4 (expressed in corneal and conjunctival epithelia) and Muc5ac [START_REF] Lange | Mucin gene expression is not regulated by estrogen and/or progesterone in the ocular surface epithelia of mice[END_REF]) (expressed in conjunctival goblet cells) in situ hybridization / Muc4 (ns) and Muc5ac (ns) expression / Muc4 (ns) and Muc5ac (ns) staining NRTN -/-mice PAS (↓ GC density) / Muc4 (↓) and Muc5ac (↓) staining / Muc1 (↓) [START_REF] Song | Neurturin-deficient mice develop dry eye and keratoconjunctivitis sicca[END_REF] and Muc4 (↓) expression . The expression of MUC1 at the surface of human conjunctival goblet cells has never been reported, contrary to mice. Contrary to humans, Muc16 is not produced by the mouse corneal epithelial cells. Regarding the gel-forming mucins, MUC5AC/Muc5ac is the main one in humans and mice. Gel-forming mucins are produced and secreted by specialized cells, the goblet cells. Goblet cells occur as single cells in human conjunctiva, whereas they form basket like clusters in mouse conjunctiva. In humans, conjunctival goblet cells produce MUC19, while Muc19 gene seems not expressed in the mouse conjunctiva. Very low levels of MUC5B expression have been reported in humans, whereas Muc5b seems more expressed in mice for which half of the conjunctival goblet cells produce the mucin.

Fig. 1 .

 1 Fig. 1. Schematic representation of the human membrane-associated and secreted mucins. The secreted gel-forming mucins MUC2, MUC5AC, MUC5B, MUC6, and MUC19 form oligomers and are responsible for the rheological properties of the mucus gels. By contrast with the other secreted mucins, MUC7 and MUC8 do not form oligomers. Large MAMs MUC3A/B, MUC4, MUC11/12, MUC16 and MUC17 may also contribute to the mucus gels to a lesser extent. Small MAMs are not specific to secretory mucosal tissues.

Fig. 2 .

 2 Fig. 2. Schematic representation of the tear film. (a) The classic representation of the tear film is the three-layer model composed of a mucin layer covering the corneal epithelium, an aqueous internal layer, and a lipid layer preventing evaporation. (b) Because the boundary between the mucin and the aqueous layers is not clear, increasingly considered that these two layers actually form a single mucoaqueous layer.

Fig. 3 .

 3 Fig. 3. Mucin production by corneal and conjunctival epithelia in humans and mice.The main MAM produced on the ocular surface of both humans (MUC) and mice (Muc) are MUC1/Muc1, MUC4/Muc4 and MUC16/Muc16. The expression of MUC1 at the surface of human conjunctival goblet cells has never been reported, contrary to mice. Contrary to humans, Muc16 is not produced by the mouse corneal epithelial cells. Regarding the gel-forming mucins, MUC5AC/Muc5ac is the main one in humans and mice. Gel-forming mucins are produced and secreted by specialized cells, the goblet cells. Goblet cells occur as single cells in human conjunctiva, whereas they form basket like clusters in mouse conjunctiva. In humans, conjunctival goblet cells produce MUC19, while Muc19 gene seems not expressed in the mouse conjunctiva. Very low levels of MUC5B expression have been reported in humans, whereas Muc5b seems more expressed in mice for which half of the conjunctival goblet cells produce the mucin.

DS

PAS (↓ GC density) [START_REF] Barabino | The controlledenvironment chamber: a new mouse model of dry eye[END_REF] Klf4CN mice PAS (absence of GC) / AB (absence of GC) [START_REF] Swamynathan | Conditional deletion of the mouse Klf4 gene results in corneal epithelial fragility, stromal edema, and loss of conjunctival goblet cells[END_REF] MUC5AC-DTA mice AB-PAS (↓ GC density) / mucicarmine staining (↓ GC density) / Muc1 (ns), [START_REF] Wang | Alteration of ocular surface mucins in MUC5AC-DTA transgenic mice[END_REF]) Muc2 (↓), Muc4 (↑) and Muc5ac (↓) staining / Muc1 (ns), Muc2 (↓), Muc4 (↑) and Muc5ac (↓) expression / Muc4 (↑) and Muc5ac (↓) in situ hybridization Aire-deficient mice into the AB (↑ AB + GC = mucin acidification) / PAS (ns) (Chen et al


Gilles Madi-Wamba

Yunbo Li
email: yunbo.li@irisa.fr

Anne-Cécile Orgerie
email: anne-cecile.orgerie@irisa.fr

Nicolas Beldiceanu
email: nicolas.beldiceanu@imt-atlantique.fr

Jean-Marc Menaud
email: jean-marc.menaud@imt-atlantique.fr

Green energy aware scheduling problem in virtualized datacenters

With the generalization of cloud infrastructures usage, energy consumption has become a major issue. Scheduling heuristics have been proposed to optimize the resource usage of data center so as to take down the energy consumption. This paper tackles the problem with a different approach by taking into consideration the availability of renewable energy. First we formalize the green energy aware scheduling problem (GEASP) and propose a global model based on constraint programming as well as a search heuristic to solve it efficiently. The proposed model integrates the various aspects inherent to the dynamic planning in a data center: heterogeneous physical machines, various application types (i.e., active or online applications and batch applications), actions and energetic costs of turning ON/OFF physical machines, interrupting/resuming batch applications, CPU and RAM resource consumption, tasks migration, migration costs, and integration of green energy availability. The model can therefore reduce both the costs related to energy consumption and the carbon footprint of a data center. We evaluate the model against the state-of-the-art framework PIKA on real-world workload and solar power traces.

I. INTRODUCTION AND RELATED WORK

Over the years, energy consumption has become a major concern in the field of information technologies. Amazon reports that the cost related to the energy consumption over a 3-years period is more than 40% of the overall cost of its data center [START_REF] Hamilton | Cooperative expendable micro-slice servers (cems): low cost, low power servers for internet-scale services[END_REF]. Besides, in [START_REF] Barroso | The price of performance[END_REF], Barrosso shows that over the lifetime of a data center, the expenses related to the energy consumption can easily surpass the hardware cost. In the literature, most work that attempts to reduce the energetic cost of a data center proceeds by reducing the overall energy consumption [START_REF]Constraint programming based large neighbourhood search for energy minimisation in data centres[END_REF], [START_REF] Cambazard | Bin packing with linear usage costs-an application to energy management in data centres[END_REF]. Apart from the economic aspect, massive energy consumption also has repercussion on the environment, as the brown energy is produced from polluting sources. In this paper, we propose not only to reduce the brown energy consumption to handle the economic issue, but also to maximize green energy consumption to take care of the environmental issue.

The energy consumption of a system comprises a static and a dynamic part [START_REF] Orgerie | A survey on techniques for improving the energy efficiency of large-scale distributed systems[END_REF]. The static part is linked to the system size and the hardware type, and the dynamic part is linked to resources usage. In [START_REF] Li | Opportunistic scheduling in clouds partially powered by green energy[END_REF] and [START_REF]Towards energy-proportional clouds partially powered by renewable energy[END_REF], Li et al. propose a novel framework, oPportunistic schedullIng broKer infrAstructure (PIKA) that aims at reducing the brown energy consumption of a small/medium-size data center. According to the amount of green energy available at each time slot PIKA turns physical machines ON/OFF, pauses, resumes or migrates jobs. However, this opportunistic scheduling is rather reactive than proactive. In this paper, we first formalize the green energy aware scheduling problem (GEASP). Second, we propose a global constraint programming model as well as a search heuristic and show that our model can significantly optimize the overall energy consumption of a data center. The proposed model simultaneously takes into account each of the following aspects:

• compatibility with both active and batch application types, • applications resources requirements varying over the time,

• migration of applications from one physical server to another, • energetic cost of application migrations, • interruption/resumption of batch applications,

• compatibility with heterogeneous physical servers i.e. the resources are variable from one physical server to another,

• turning ON/OFF the physical servers and resources management, • extra energy consumption to turn a physical server ON/OFF, • green energy integration.

The main advantages of constraints programming include a certain level of flexibility that PIKA lacks. Indeed, thanks to this feature, the proposed model is also compatible with business constraints inherent to data center infrastructure management as well as with user preferences. Figure 1

GEASP Model

Configuration plan (Optimizing the green energy consumption)

Fig. 1: The GEASP model computes a global and pro-active configuration plan that minimizes the brown energy and maximizes the green energy consumption of the data center while satisfying all the constraints. Hardware constraints are related to memory/CPU limitations and turning the servers ON and OFF. The application constraints are related to the interruption, the migration, and the placement of the applications as well as to some business constraints (ban, lonely, spread, . . . ).

The rest of the paper is organized as follows: Section II describes the problem and gives all the necessary definitions and Section III formalizes the GEASP problem and presents our model. In Section IV, we present the search heuristic to find suitable solutions to the GEASP. Finally, we evaluate our contribution using real data center workloads and green energy traces in Section V, and we conclude in Section VI.

II. PROBLEM DESCRIPTION AND DEFINITIONS

We consider the problem of scheduling in a small/medium size data center with limited resources [START_REF] Beldiceanu | The epoc project: Energy proportional and opportunistic computing system[END_REF]. The scheduling should minimize the brown energy consumption and maximize the green energy consumption. We recall that a data center is made up of one or more servers that host the applications. We have two types of applications, the active and the batch. Both types of application are introduced in Section II-A.

A. Definitions

Active Application An active application is an application that is executed throughout the time horizon without being interrupted. Each active application is described by its:

• Memory consumption, i.e. is the constant amount of RAM consumed by the application within the server it is hosted. • CPU Usage, the processing power used by a server to execute the application; it may vary from one time slot to the next throughout the horizon. • Migration cost, i.e. the extra energy consumption needed to migrate an application from one server to another. An active application a i of memory requirement mem i , CPU usage cpu i and migration cost migr i is denoted a i (mem i , cpu i , migr i ).

Batch Application A batch application or batch job is an application that can be interrupted and resumed. A time slot during which a batch job is running is called a runtime. Each batch application is characterized by its :

• Memory consumption: its memory consumption of a batch job is constant.

i (mem i , cpu i , d i , migr i , s i ).
Server We define a server in this problem as a machine that hosts the applications. It is characterized by:

• its Memory limit is the total amount of memory that is shared among the hosted applications. • its CPU limit is the total amount of processing power that can be shared among hosted applications. • its ON (resp. OFF) energy is the constant amount of energy required to turn the server ON (resp. OFF).

• its load/consumption relation, which relates the CPU load of the server to its energy consumption. • its id is a unique integer that identifies each server. A server i of memory MEM i , CPU limit CPU i , ON energy E on i , OFF energy E off i , load/consumption relation r and id id i is denoted s i (MEM i , CPU i , E on i , E off i , r i , id i ).

Our goal is to compute an energy efficient configuration plan for the data center which, while reducing the amount of brown energy used and increasing the proportion of green energy, copes with the operational and the business constraints of different application types. Next definition introduces the notion of Configuration plan.

Configuration plan Given a time horizon, a set of active and batch applications and a data center, a configuration plan is a scheduling that meets the following requirements:

• At any time slot through out the horizon, it specifies for each active application an allocated server. A migration occurs when the host of an active application changes from one time slot to the next. • It specifies when each batch job starts, when it ends, and eventual interruption and resumption times. For any batch job, the configuration plan specifies the hosting server at any timepoint. A migration occurs when the host changes from one time slot to the next. • For each server of the data center, it specifies every time slot when the server is turned ON or OFF.

The configuration plan is energy efficient when it maximizes the green energy consumption of the data center. Indeed, the availability of green energy fluctuates over the time. Typical example is the solar energy.

Section III formalizes this problem into a constraint model.

III. MODEL OF THE PROBLEM

In this section, we propose a constraint based model to capture the already mentioned aspects of the green energy aware scheduling problem in virtualized data centers. Before detailing different parts of the model, we first shortly recall key notions of constraint programming in the context of virtualized data centers.

A. Background on constraint satisfaction problems

Constraint satisfaction problem A constraint satisfaction problem (CSP) [START_REF] Rossi | Handbook of constraint programming[END_REF] is a triple P = (X, D, C) where :

• X is an tuple of n > 0 variables, X = x 0 , x 1 , . . . , x n-1 . • D is a tuple of n > 0 domains, D = D 0 , D 1 , . . . , D n-1 such that x i ∈ D i . • C is a tuple of k > 0 constraints C = C 0 , C 1 , ..., C k-1 .
We now define the notion of constraint.

Constrain Given a CSP P = (X, D, C), a constraint C i ∈ C is a pair R i , S i where S i is a subset of X, and R i is a relation over S i . The relation R i specifies the tuples of values forbidden among the Cartesian product of the domains of the variables in S i .

Solution of a CSP Given a CSP P = (X, D, C), a solution S of P is a tuple v 0 , v 1 , ..., v n such that v i ∈ D i and for every constraint

C i = R i , S i ∈ C, the relation R i holds.

B. Constraint programming for the green energy aware scheduling problem in virtualized data center

Constraint programming is a suitable solution to solve most scheduling problems [START_REF] Baptiste | Constraint-based scheduling: applying constraint programming to scheduling problems[END_REF]. In the case of a green energy aware scheduling problem, constraint programming is well suited as it has a good expressiveness to precisely model each component of the problem. It also enables to add any new constraint to an existing model. In [START_REF] Hermenier | Bin repacking scheduling in virtualized datacenters[END_REF], Hermenier et al. present four side constraints that may be required by the administrator of a system or by the users to restrict the placement of the applications into servers.

• Ban. At a given time t, the system administrator may want to turn off a server to perform a hardware or a software maintenance. • Spread. In order to achieve tolerance to hardware failures, an application may use replication. For the fault tolerance, the application and its replication should run at any time on different servers. • Lonely. For some reasons, an application may require to run alone in a server. • Capacity. Sometimes, due to some shared resources, it might be useful to limit the number of applications executed in a server. The capacity constraint is used to ensure that the number of applications hosted on a given server is below a given limit. This list of side constraints is not exhaustive. Besides the good expressiveness and the flexibility, the solving process of a constraint satisfaction problem through constraint propagation [START_REF] Rossi | Handbook of constraint programming[END_REF] ensures that all the constraints of the problem are satisfied.

We now formalize the definition of a green energy aware scheduling problem.

Green energy aware scheduling problem A green energy aware scheduling problem (GEASP) is a tuple such that P = {S, A, B, T, E} where:

• S is a set of servers.

• A is a set of active applications.

• B is a set of batch jobs.

• T is the time horizon: an integer specifying the total number of time slots to consider. • E is a time series of length T which specifies the quantity of green energy available at each time slot. In Sections III-C up to III-G, we present how we formalize each aspect of a GEASP into a constraint satisfaction problem. We will use the toy example III.1 to illustrate our model.

Example III.1. Throughout this paper, we use the following toy GEASP. P = {S, A, B, T, E} where:

• S = {s 0 (3, 50, 3, 3, r, 0), s 1 (3, 50, 3, 3, r, 0)} where we have r(cpu load) = 10 + cpu load [START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF][START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF]90,90,[START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF][START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF][START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF]48,43 An energy efficient configuration for the GEASP is given below:

• A = {a o (1, 20, 2)} • B = {b 0 (2, 20, 3, 1, 5), b 1 (2, 20, 3, 1, 5)} • T = 10h • E = 10,
• Slot 0 s 0 is turned ON,
and a 0 is placed on s 0 .

• Slot 1 No change. • Slot 2 No change. • Slot 3 b 0 is launched on s 0 . s 1 is turned ON

C. Turning a server ON or OFF

To model the action of turning a server ON and OFF, we have to consider two aspects. First we need to consider the inherent energetic costs of these actions, and second we need to ensure that no application can be scheduled on a switched off server.

1) Energetic cost: As seen in the definition of a server in Section II-A, each server has a turning ON/OFF cost. Let P = {S, A, B, T, E} be a GEASP. For each server

S i (MEM i , CPU i , E on i , E off i , r i , id i ) ∈ S, a set of T + 1 boolean variables ON (i,t) indicate at each time slot t(t ∈ [-1, T -1]) if the server is ON or OFF. ON (i,-1) = false indicates that server S i is initially off.
Turning a server ON or OFF at a time slot t consumes an extra energy at this time t. For each server S i (MEM i , CPU i , E on i , E off i , r i , id i ), the model of this energetic cost relies on T switch task variables. Before we detail these variables, we first introduce the notion of task.

Task A task i is a tuple task i (s i , d i , e i , < r i >, h i ) where:

• s i is the start time of the task.

• d i is the duration of the task.

• e i is the end of the task.

• < r i > is the list that contains all the resource requirements of the task. A task might consume one or more resources of different types. • h is the server hosting the task. Given a server s i (MEM i , CPU i , E on i , E off i , r i , id i ), the energy consumption of its switch task at time t depends of the server s i being turned ON or OFF at that time t. It is a variable switch energy i,t given by :

switch energy i,t = E oni * (ON (i,t-1) < ON (i,t ) + E of fi * (ON (i,t-1) > ON (i,t) ). (1)
where a term like ON (i,t-1) > ON (i,t) is interpreted as a 0 -1 variable that will be assigned value 1 (resp. 0) if the corresponding conditions holds (resp. doesn't hold).

Example III.2. According to the configuration plan given in Example III.1 we have:

• switch energy 0,0 = 3 Since server s 0 is turned ON at t = 0. • switch energy 1,3 = 3 Since server s 1 is turned ON at t = 3. • switch energy 1,5 = 3 Since server s 1 is turned OFF at t = 5. • switch energy 0,t = 0 for all t = 0 and besides switch energy 1,t = 0 for all t ∈ {0, 1, 2, 4, 6, 7, 8, 9}

2) Availability of a server: The availability of a server is the constraint that makes a server unavailable for scheduling at any time slot during which it is switched off. Since any application consumes a strictly positive amount of memory on the server on which it runs, a server can not host any application if it has no free memory available. Thus to make a server unavailable, we set its available memory to 0. To do so, we create memory tasks whose aim is to fill any server's memory at any time t when the server is off.

In order to avoid creating T extra tasks, we add a memory resource mem i,t to the switch tasks of Section III-C1. The memory consumption m i,t of the switch task switch (i,t) of a server s i (M EM i , CP U i , E oni , E of fi , r i , id i ) at time t is given by :

mem i,t = M EM i * (ON (i,t) = 0). (2)
The switch tasks of the model are therefore indexed by the server index i and the time slot t, they are denoted switch (i,t) (t, 1, t + 1, < energy i,t , mem i,t >, i).

Section III-D here after describes how we model active and batch applications using the notion of task introduced in Definition III-C1.

D. Modeling the applications

The most difficult part of a GEASP is the model of the applications. The model should take into consideration the following requirements:

• [Host]. At any time t any active application and any uninterrupted batch job should be hosted on a server. • [Migration]. Both active and batch applications can be migrated from one server to another one. These migrations have costs that should be taken into consideration. Details on how to model the migration costs are given in Section III-E. • Active applications are never interrupted.

• Batch jobs can be interrupted as long as the corresponding slack constraint is not violated. In order to meet these requirements, we model each active application a i (mem i , cpu i , migr i ) (resp. each batch application b i (mem i , cpu i , d i , migr i , s i )) by a set S ai (resp. S bi ) of tasks.

1) Active applications: As active applications are not interrupted, each active application a i (mem i , cpu i , migr i ) is modeled by a set S ai of T tasks that are denoted sub (a i ,t) (t, 1, t + 1, < mem i,t , cpu i,t , energy i,t >, h i,t ), t from 0 to T -1 where:

• mem i,t (resp. cpu i,t ) is the memory consumption (resp.

the CPU usage) of the task a i (mem i , cpu i , migr i ) at time t. • h i,t is the server that hosts a i (mem i , cpu i , migr i ) at time t. • energy i,t is the amount of extra energy consumed by the server h i,t to host sub (ai,t) . 2) Batch applications: Since the duration of each batch job is fixed, any batch job b i (mem i , cpu i , d i , migr i , s i ) is modeled by a set S bi of d i tasks which are denoted sub (b i ,j) (s (b i ,j) , 1, e (b i ,j) , < mem i,j , cpu i,j , energy i,j >, h i,j ) where j ∈ [0,

d i -1].
The batch applications can be interrupted and resumed. Therefore s (bi,j) and e (bi,j) are variables taking values in [0, T -1] with the following constraints:

∀j ∈ [1, d i -1], s (bi,j) ≤ e (bi,j-1) (3)
The slack constraint is modeled as follows:

e (bi,di-1) -s (bi,0) -d i ≤ slack. (4)
For both active and batch jobs, the variables energy i,t and energy i,j specify how much extra energy is needed by a server to host this given application. Its value varies from one host to another. Details on how this value is set are presented in Section III-G.

To ensure that a server s in which a task is scheduled at time t is ON at that time, we add the following constraint for each active and batch tasks. ∀sub (ai,t) (t, 1, t+1, < mem i,t , cpu i,t , energy i,t >, h i,t ) ∈ S ai , h i,t = s ⇒ ON (s,t) = 1 [START_REF] Beldiceanu | The epoc project: Energy proportional and opportunistic computing system[END_REF] ∀sub (bi,j) (j, 1, j+1, < mem i,j , cpu i,j , energy i,j >, h i,j ) ∈ S bi , h i,j = s ⇒ ON (s,t) = 1 (6)

E. Migration cost

This section models the migration cost of both active and batch applications. For any active application a i (mem i , cpu i , migr i ) and any task sub (a i ,t) (t, 1, t + 1, < mem i,t , cpu i,t , energy i,t >, h (i,t) ) ∈ S ai , we create a migration task migr (a i ,t) (t, 1, t + 1, < migr energy i,t >, h (i,t) ) where migr energy i,t is the energy that is consumed whenever this active task a i is migrated from one server to another at time t. Its value is given by: migr energy i,t = 0 t = 0 migr i * (h (i,t) = h (i,t-1) ) t > 0 Similarly, we create migration tasks migr (b i ,j) for batch applications.

Example III.3. According to the configuration plan given in Example III.1, we have:

• migr energy b1,9 = 1 since batch application b 1 is migrated from server s 1 to server s 0 at slot 9.

F. Memory consumption and CPU usage

Each server has a limited quantity of memory and CPU. An application can be scheduled on a server s i ∈ S at time t if and only if server s i has enough resources to satisfy the application requirements. To take these constraints into consideration, we use a cumulative constraint [START_REF] Arafailova | Global Constraint Catalog, Volume II, Time-Series Constraints[END_REF], [START_REF] Letort | A scalable sweep algorithm for the cumulative constraint[END_REF].

Cumulative constraint Given a set T of single resource tasks, the cumulative constraint ensures that at any time t, the cumulative resource of the set of tasks scheduled at t does not exceed a fixed limit.

The standard definition of the cumulative constraint given above assumes that there is one single host for the tasks. We will instead use the cumulatives constraint [START_REF] Beldiceanu | A new multi-resource cumulatives constraint with negative heights[END_REF], a slightly generalized version of the cumulative constraint which allows more than one host, i.e. more than one server. The cumulatives constraint: cumulatives(Tasks,Machines) where • T asks is a set of single resource tasks of the form task(start, duration, end, resource, host). • M achines is a set of fixed resource hosts of the form machine(id, resource limit).

holds if, for each machine m, at each point t, where at least one task is assigned to machine m, the cumulative resource of the set of tasks assigned to m at t is less than or equal to (respectively greater than or equal to) the capacity associated with machine m.

The host of a task is the id of the server where it is scheduled. Before we detail the use of the cumulatives constraint in the case of memory and CPU usage, we first introduce the notion of restriction of a task to a given resource.

Restriction of a task Given a task t(start, duration, end, < r 1 , r 2 , . . . r n >, host) its restriction to the resource r ∈< r 1 , r 2 , . . . r n > is the task t r(start, duration, end, r, host).

To model the memory consumption and CPU usage of a GEASP, we will use two cumulatives constraint, cumulatives(M emory T asks, M emory M achines) and cumulatives(CP U T asks, CP U M achines) where:

• M emory T asks is the set of active tasks, batch tasks and switch tasks restricted to the memory resource. • CP U T asks is the set of active tasks, batch tasks and switch tasks restricted to the CPU resource plus a set of complementary tasks that we use to compute the energy consumption of each server at each time slot. Details on these complementary tasks are given in Section III-G. • M emory M achines and CP U M achines are the set of machines built in the following way:

1 M emory M achines = {machine mem(id i , M EM i ) such that ∃s i (M EM i , CP U i , E oni , E of fi , r i , id i ) ∈ S} 2 CP U M achines = {machine cpu(id i , CP U i ) such that ∃s i (M EM i , CP U i , E oni , E of fi , r i , id i ) ∈ S} Example III.4.

G. Minimizing the brown energy consumption

Before we detail how to minimize the brown energy consumption of a data center, we first need to specify how to compute the energy consumption of a server. We assume server s i is already turned ON at time t ∈ [0, T -1] and there is no migration scheduled at time t. Then the energy consumption e i,t of s i at time t is obtained from Equation ( 7) by:

e i,t = r(load si,t ) (7)
where load si,t is the CPU load in percent of s i at time t. Therefore to know the energy consumption of a given active (resp. batch) task sub (a i ,t) (t, 1, t + 1, < mem i,t , cpu i,t , energy i,t >, h i,t ) (resp. sub t,1,t+1,<mem i,j ,cpu i,j ,energy i,j >,h i,j ) ) at time t, we first need to know the CPU capacity of the host h i,t (resp. h i,j ) in which it is scheduled at time t. The problem is that h i,t (resp. h i,j ) is not initially fixed, so we have no way to know in advance the CPU capacity of the host. To overcome this issue, we introduce the element constraint [START_REF] Van Hentenryck | Generality versus specificity: An experience with ai and or techniques[END_REF].

element constraint Given a list L of integer values, two integer variables index and V , the element(L, index , V ) constraint ensures that V is the index th element of L i.e V = L index .

Let CP U Capacities be the list of the CPU capacities of the servers. The list is sorted in ascending order of servers id's. For any time t ∈ [0, T -1] and for any active (resp. batch) task sub (a i ,t) (t, 1, t + 1, < mem i,t , cpu i,t , energy i,t >, h i,t ) (resp. sub (b j ,j) (s (b i ,j) , 1, e (b i ,j) , < mem i,j , cpu i,j , energy i,j >, h i,j )) we state:

element(h, CP U Capacities, HostCapacity) (8)
The energy consumption energy of the task is therefore given by:

energy = r( cpu * 100 HostCapacity ) (9)
We now present the energetic model that we used in this paper to characterize the function r for all the servers.

Energetic model: As seen in Section II-A, each server is characterized by a relation r that relates its workload to its energy consumption. In [START_REF] Li | Opportunistic scheduling in clouds partially powered by green energy[END_REF], Li et al. experimented multiple tests on Taurus node at the Lyon site of Grid'5000, a largescale and versatile test-bed for experiment driven research. Each node has 12 cores and each core presents 8.3% overall CPU utilization. They came out with the conclusion that, the overall energy consumption of the node depends on the number of activated cores. Table I Following the idea of the PowerModel of CloudSim [START_REF] Calheiros | Cloudsim: a toolkit for modeling and simulation of cloud computing environments and evaluation of resource provisioning algorithms[END_REF], we use Table I to implement the function getPower() in order to compute the energy consumption of a server. The pseudo code of getPower() is given in Algorithm We thus have :

energy(h, t) = r(load(h, t)) = getP ower(CP U h , cpu used h,t ) (10)
where CP U h is the CPU capacity of host h and cpu used h,t is the amount of CPU used in host h at time t.

Algorithm 1 Procedure getPower() to compute the energy consumption of a server according to its CPU load Require: CPU Capacity The CPU capacity of the server Require: CPU Used CPU usage of the server P ower table ← [97, 128, 150, 158, 165, 171, 177, 185, 195, 200, 204, 212, 220] Step

← 1 12 × CP U Capacity A ← 1 Step+1 × CP U U sed B ← min(A + 1, 13) E A ← P ower table A E B ← P ower table B Energy ← E A + ((E B -E A ) × CP U U sed × 10)/(CP U Capacity × 10) return Energy
The value energy(h, t) only takes into consideration the load of the host h. To obtain the actual consumption of the data center, we need to take into consideration all the extra energy costs resulting from turning the servers ON and OFF, and migrating the tasks over the different hosts.

Equation 11 states the total energy consumption of the data center at a given time slot t.

E t = h energy(h, t) + a migr energy (ai,t) + b migr energy (bi,t) + h,t
switch energy (h,t) [START_REF] Hamilton | Cooperative expendable micro-slice servers (cems): low cost, low power servers for internet-scale services[END_REF] where:

• migr energy (ai,t) (resp. migr energy (bi,t) ) is the extra energy consumed at time t whenever the active task a (respectively batch task b) is migrated from one host to another at time t. • switch energy (h,t) is the extra energy consumed at time t when host h is switched ON or OFF at time t. Equation 12 computes the total amount of brown energy consumed by the data center at time t.

B t = max(0, E t -G t ) (12)
where G t is the amount of green energy available at time slot t. Finally, Equation 13 computes the total amount of brown energy consumed by the data center throughout the time horizon.

B = T -1 t=0 B t (13)
Example III.5. Figure 3 shows the overall energy consumption of the data center with the configuration plan of Example III.1. As we can see from the plot, the batch jobs are run, migration are executed, and servers are turned ON preferably during time slots when the green energy is highly available. This is achieved by our heuristic that we present in Section IV.

IV. SOLVING THE GEASP

According to the problem size, it might take a long time to find an optimal solution to a constraint satisfaction problem and to prove its optimality. To overcome this issue, it is important to have a dedicated search strategy that speeds up the process of finding a good solution.

We propose a dynamic heuristic that targets the starts of the batch tasks. Once these variables are fixed, the other variables of the problem will be fixed by propagation.

Since the batch tasks are the ones whose start and end variables are flexible, the intuition of the heuristic is to try to schedule them at times when the green energy is highly available. To do so, we proceed as follows.

1) Variables ordering: Let b(mem, cpu, d, migr, slack) be a batch application modeled by the set S b of batch tasks of the form sub (b,i) (s (b,i) , 1, e (b,i) , < mem, cpu, energy >, h). The order in which the start variables of the batch tasks in S b are fixed is s (b,0) , s (b,1) , . . . , s (b,d-1) . The purpose of this order is to take into consideration the precedence constraint stated in Equation 3 through out the search.

2) Values ordering: This part of the search strategies deals with the order in which values are chosen from the domain of each start variable. Let s (b,i) be the start of sub (b,i) . We have dom(s (b,i) ) = [0, T -1]. Following the intuition, the idea is to try to fix s (b,i) to a value t ∈ dom(s (b,i) ) when the green energy availability is maximal. Doing this ensures that we maximize the green energy consumption. We proceed in two steps:

1 Sort step. This is the first step that is performed each time a start variable has to be instantiated. Let E = e 0 e 1 . . . e T -1 be the green energy of a GEASP where

E(t) = e t , t ∈ [0, T -1]
The Sort step and the Update step presented in this Section sketch the general idea of the heuristic to solve the GEASP. It is possible to optimize the Sort step by avoiding a total sorting over all the indices. The advantage of doing a partial sort is that, since some tasks are linked through a precedence relation, it does not delay too much the first tasks of the precedence chain.

V. EVALUATION

To measure how effective is the model when used in a small/medium size data center, we run simulations on real workload traces.

As stated in [START_REF]Towards energy-proportional clouds partially powered by renewable energy[END_REF], finding real traces for data center's activity is very difficult. For this, we studied anonymized traces provided by EasyVirt, a French SME monitoring Cloud data centers. We used 3 real workload data sets. Each data set reports the activity of a Cloud provider with 55 servers over a 12 hours period. The traces reports client requests for virtual machines with specified CPU and RAM needs. In the context of a virtualized data center, the virtual machines are used to encapsulate the applications that are executed on the physical machines. Before we present the results of the evaluation, we first give details on the used data set.

Data set description

Each of the 3 real workload data set is organized as follows:

(1) We have 55 servers, where each server is characterized by a limited amount of CPU and RAM resource. (2) A set of 567 active applications to be encapsulated into virtual machines. As introduced in section III-D, each active application is executed throughout the time horizon. In our case, the time horizon is 12 hours. We see from the traces that the CP U and RAM needs of an active application may vary from one time slot to another. This translates into 6804 = 567 × 12 active tasks to handle. The migration cost in terms of energy consumption is also specified. (3) A set of 2268 batch applications to be encapsulated into virtual machines. Each batch application has a fixed execution time, a slack value, a fixed start time and a migration cost. The requirements of the batch applications also vary from one time slot to another. This translates into more than 6500 batch tasks to handle. (4) The renewable energy availability. Each data set includes a time series of length 12. This time series is the record of the renewable energy available every hour. To evaluate our model and to follow the same protocol as in [START_REF] Li | Opportunistic scheduling in clouds partially powered by green energy[END_REF], we compared the results to those of a baseline first fit algorithm. The first fit algorithm tries to schedule the task as soon as possible when there is enough resources available. Both models were implemented in Prolog with the constraint solver Sicstus Prolog [START_REF] Carlsson | SICStus Prolog User´s Manual[END_REF].

Figures 4a and4b show how the model is able to move a considerable amount of the data center workload to slots where green energy is available. On average compared to baseline, GEASP model reduces by 55% the brown energy consumption of the data center and increases by 50.9% its green energy consumption. Although PIKA [START_REF] Li | Opportunistic scheduling in clouds partially powered by green energy[END_REF] has a much higher green energy consumption as compared to the baseline algorithm, it does so with two major drawbacks. First, unlike PIKA [START_REF] Li | Opportunistic scheduling in clouds partially powered by green energy[END_REF] that uses opportunistic scheduling, our model finishes all the tasks not later than the baseline. This advantage comes from the time horizon that is fixed such that no task is allowed to be scheduled beyond it. If the time horizon constraint is dropped, then there will eventually be room for more optimization. For example, an amount of the workload at slot 11 of Figure 4b could be opportunistically postponed to a later slot where there is more green energy available. But this in turn will result to the tasks being finished later than with the baseline algorithm. Second, while the GEASP model slightly decreases the total energy consumption (Brown + Green), PIKA increases it by up to 31%. Most of this energy consumption increase occurs during slots that have a high green energy availability, therefore the green energy integration ratio is increased.

VI. CONCLUSION

Energy consumption and environmental issues have become major concerns over the recent years in cloud computing. In this paper, we introduced the green energy aware scheduling problem (GEASP) to optimize the energy consumption of a small/medium size data center. Using our model to solve the GEASP, we could optimize the energy consumption of a small/medium size data center in three ways. First, we slightly decrease its overall energy consumption, second we considerably decrease its brown energy consumption and finally we significantly increase its green energy consumption. To achieve these results, our solution relies mostly on batch applications whose execution can sometimes be delayed to periods with high green energy availability. Active applications on the other hand can not be suspended. Future work involves optimizing the energy consumption of active applications, by means of adapting the quality of service (QoS) with respect to the green energy availability [START_REF] Hasan | Enabling green energy awareness in interactive cloud application[END_REF].

and b 1

 1 is launched on it. • Slot 4 No change. • Slot 5 b 0 and b 1 are interrupted and s 1 is turned OFF. • Slot 6 No change. • Slot 7 No change. • Slot 8 b 0 is resumed on s 0 . • Slot 9 b 1 is resumed and migrated from s 1 to s 0 .

Figure 2 ab 0 b 0 b 0 b 1 Timeb 1 b 1 Time RAM usage on server 1 Fig.

 2111 Fig. cumulatives constraint for the RAM resource limits

Fig. 3 :

 3 Fig. 3: Energy consumption of the configuration plan. The red curve is the green energy availability per slot

Fig. 4 :

 4 Fig. 4: Workload scheduling.

  illustrates different aspects of this context.

				Hardware
	applications Active applications Batch	Data center (Physical machines resources) with variables	Constraints	constraints	CP Solver
	Energy Problem instance	Energy consumption	Application constraints

  • CPU Usage: CPU usage of a batch job is constant. • Duration. • Migration cost. • Slack. The total amount of time during which it is interrupted shall not exceed a given slack. A batch job b i of memory mem i , CPU usage cpu i , duration d i , migration cost migr i and slack s i is denoted b

  summarizes these results.

	# cores	0	1	2	3	4	5	6
	Power (W)	97	128 150 158 165 171 177
	# cores	7	8	9	10	11	12
	Power (W)	185 195 200 204 212 220

TABLE I :

 I Experimental energy consumption of a 12 cores node according to the number of activated cores

  is the amount of green energy available at time t. We sort the values e t in descending order and obtain the list SortedE = e (0,t0) , e (1,t1) , . . . , e (T -1,t T -1 ) such that ∀e (i,ti) ∈ SortedE, E(t i ) = e ti = e (i,ti) This gives the order in which values are chosen from dom(s (b,i) ), namely t 0 , t 1 , . . . , t T -1 . 2 Update step. This step is performed immediately after a start variable is fixed. Let a batch task sub (b,i) (s (b,i) , 1, e (b,i) , < mem, cpu, energy >, h) and suppose s (b,i) is fixed to t ∈ [0, T -1]. Since running sub (b,i) consumes energy, this step updates the green energy available at time t. This update is done by decrementing E(t) by energy. The following constraint updates the green energy.E ← e 0 , e 1 , . . . , e t -energy, e t+1 , . . . , e T -1

TABLE II :

 II Energy saving on the first real trace (W).

		Total E.C	Brown E.C.	Green E.C
	Baseline	78309	38699	39610
	GEASP Model	78374	18196	60178
		+0.08%	-51.98%	+51.92%

TABLE III :

 III Energy saving on the second real trace (W).Tables II, III and IV give details on how the GEASP model significantly reduces the brown energy consumption and increases the green energy consumption.

		Total E.C	Brown E.C.	Green E.C
	Baseline	79100	36195	42905
	GEASP Model	78868	14670	64198
		-0.29%	-59.46%	+49.62%

TABLE IV :

 IV Energy saving on the third real trace (W).

ACKNOWLEDGMENTS

This work has received a French state support granted to the CominLabs excellence laboratory and managed by the National Research Agency in the "Investing for the Future" program under reference Nb. ANR-10-LABX-07-01.

The authors would like to thank the EasyVirt company for providing them real workload traces from Cloud providers.