Alice Gilbert

Xabier Elorza Vidal

Raul Estevez

Martine Cohen-Salmon
email: martine.cohen-salmon@college-de-france.fr

Anne-Cécile Boulay

Postnatal development of the astrocyte perivascular MLC1/GlialCAM complex defines a temporal window for the gliovascular unit maturation

Keywords: Astrocyte, Gliovascular unit, Blood-brain barrier, Postnatal development, MLC1, GlialCAM

Astrocytes, the most abundant glial cells of the central nervous system are morphologically complex. They display numerous processes interacting with synapses and blood vessels. At the vascular interface, astrocyte endfeet-terminated processes almost entirely cover the blood vessel surface and participate to the gliovascular unit where important vascular properties of the brain are set such as the blood-brain barrier (BBB) integrity. How specific morphological and functional interactions between astrocytes and the vascular compartment develop has not been fully investigated. Here, we elaborated an original experimental strategy to study the postnatal development of astrocyte perivascular endfeet. Using purified gliovascular units, we focused on the postnatal expression of MLC1 and GlialCAM, two transmembrane proteins forming a complex enriched at the junction between mature astrocyte perivascular endfeet. We showed that MLC1 and GlialCAM were enriched and assembled into mature complexes in astrocyte perivascular endfeet between postnatal days 10 and 15, after the formation of astrocyte perivascular Aquaporin 4 water channels. These events correlated with the increased expression of Claudin-5 and P-gP, two endothelial-specific BBB components. These results illustrate for the first time that astrocyte perivascular endfeet differentiation is a complex and progressive process which correlates with BBB maturation. Moreover, our results suggest that maturation of the astrocyte endfeet MLC1/GlialCAM complex between postnatal days 10 and 15 might be a key event in the gliovascular unit maturation.

Introduction

Astrocytes are glial cells now recognized as key actors of the brain physiology [START_REF] Vasile | Human astrocytes: structure and functions in the healthy brain[END_REF][START_REF] Allen | Cell Biology of Astrocyte-Synapse Interactions[END_REF]. They closely interact with both the neuronal and the vascular compartments, maintaining and modulating synaptic and brain vascular functions. At the vascular interface, astrocytes are involved in the coupling between blood flow and neuronal activity [START_REF] Attwell | Glial and neuronal control of brain blood flow[END_REF]. They maintain blood-brain barrier (BBB) integrity by contributing to the basal lamina composition [START_REF] Menezes | The Extracellular Matrix Protein Laminin α2 Regulates the Maturation and Function of the Blood-Brain Barrier[END_REF] or controlling the expression of endothelial tight junction proteins and transporters [START_REF] Abbott | Astrocyte-endothelial interactions at the blood-brain barrier[END_REF]. They regulate perivascular homeostasis and fluid circulation (Amiry- [START_REF] Amiry-Moghaddam | Anchoring of aquaporin-4 in brain: molecular mechanisms and implications for the physiology and pathophysiology of water transport[END_REF][START_REF] Iliff | A Paravascular Pathway Facilitates CSF Flow Through the Brain Parenchyma and the Clearance of Interstitial Solutes, Including Amyloid β[END_REF]. They play a key role in brain immune quiescence, controlling the recruitment and fate of immune cells and influencing inflammatory processes in the brain [START_REF] Alvarez | Glial influence on the blood brain barrier[END_REF]. Astrocyte regulation of brain vascular functions is sustained by a morphological and molecular polarity. At the vascular interface, they send processes called endfeet which almost entirely cover the brain vasculature and form together with endothelial and mural cells (pericytes or smooth muscle cells) the gliovascular unit (GVU) [START_REF] Mathiisen | The perivascular astroglial sheath provides a complete covering of the brain microvessels: an electron microscopic 3D reconstruction[END_REF]. They are equipped with a molecular repertoire dedicated to the regulation of the vascular system, which includes the gap junction proteins Connexin 30 and 43 (Boulay et al. 2015b, a) and the water channel Aquaporin 4 (Aqp4) (Amiry- [START_REF] Amiry-Moghaddam | Anchoring of aquaporin-4 in brain: molecular mechanisms and implications for the physiology and pathophysiology of water transport[END_REF][START_REF] Hawkes | Perivascular drainage of solutes is impaired in the ageing mouse brain and in the presence of cerebral amyloid angiopathy[END_REF]. How this specialized astrocyte interface with the vascular system is set during development is unknown. Vessels are formed during embryonic development from a perineural vascular plexus. They penetrate the neuroectoderm and form immature blood vessels. Around embryonic day (E) 15 in the mouse, neighboring cells such as pericytes induce a primitive endothelial BBB [START_REF] Ben-Zvi | Mfsd2a is critical for the formation and function of the blood-brain barrier[END_REF][START_REF] Chen | CD146 coordinates brain endothelial cell-pericyte communication for bloodbrain barrier development[END_REF]. At birth, while angiogenesis is mainly completed, acquisition of brain-specific vascular functions continues, in particular BBB maturation [START_REF] Obermeier | Development, maintenance and disruption of the blood-brain barrier[END_REF]) and neurovascular coupling [START_REF] Schmithorst | Evidence that neurovascular coupling underlying the BOLD effect increases with age during childhood[END_REF]. Astrocytes are generated from radial glia around E17 and astrocytogenesis continues in the neonates, mainly by local division [START_REF] Ge | Local generation of glia is a major astrocyte source in postnatal cortex[END_REF][START_REF] Nagao | Zbtb20 promotes astrocytogenesis during neocortical development[END_REF][START_REF] Jiang | Cellular and molecular introduction to brain development[END_REF]. Astrocyte maturation is achieved by integration within their environment in particular through the formation of polarized processes interacting with blood vessels [START_REF] Stogsdill | Astrocytic neuroligins control astrocyte morphogenesis and synaptogenesis[END_REF]. Based on the expression of Aqp4, previous studies suggested that astrocyte endfeet perivascular coverage starts around E18 in the mouse and is complete at P5 in the cortex [START_REF] Ezan | Deletion of astroglial connexins weakens the blood-brain barrier[END_REF]) and around P13 in pial vessels [START_REF] Lunde | Postnatal development of the molecular complex underlying astrocyte polarization[END_REF]. However, a precise description of how and when astrocyte endfeet acquire their molecular repertoire and their specific functions is still lacking.

To address this question, we focused here on MLC1 and GlialCAM, two membrane proteins forming a junctional complex enriched between astrocyte perivascular endfeet in the adult brain [START_REF] Teijido | Expression patterns of MLC1 protein in the central and peripheral nervous systems[END_REF][START_REF] Hoegg-Beiler | Disrupting MLC1 and GlialCAM and ClC-2 interactions in leukodystrophy entails glial chloride channel dysfunction[END_REF]). Mutations in their associated genes are linked to Megalencephalic Leukoencephalopathy with subcortical Cysts (MLC), a rare type of leukodystrophy characterized by progressive macrocephaly, that leads to the degradation of motor functions and mental retardation (van der [START_REF] Van Der Knaap | Megalencephalic leukoencephalopathy with subcortical cysts: chronic white matter oedema due to a defect in brain ion and water homoeostasis[END_REF]). In the brain, MLC1 is exclusively expressed by astrocytes and enriched in perivascular endfeet. It has been shown to play a role in osmotic regulations either directly or indirectly through its interaction with other proteins such as the chloride channel CLC-2 [START_REF] Sirisi | Megalencephalic leukoencephalopathy with subcortical cysts protein 1 regulates glial surface localization of GLIALCAM from fish to humans[END_REF]. Despite MLC1 similarity with ion channels and transporters, its function is yet unknown. GlialCAM is a member of the immunoglobulin superfamily of cellular adhesion proteins and is expressed in the brain by astrocytes and oligodendrocytes (Chung [START_REF] Moh | Cloning and characterization of hepaCAM, a novel Ig-like cell adhesion molecule suppressed in human hepatocellular carcinoma[END_REF][START_REF] Favre-Kontula | GlialCAM, an immunoglobulin-like cell adhesion molecule is expressed in glial cells of the central nervous system[END_REF]. It interacts directly with MLC1 and is crucial for its compartmentalization at the astrocyte membrane (López-Hernández et al. 2011b;[START_REF] Jeworutzki | GlialCAM, a Protein Defective in a Leukodystrophy, Serves as a ClC-2 Cl-Channel Auxiliary Subunit[END_REF]. It also protects MLC1 from degradation by acting as a chaperone (Capdevila-Nortes et al. 2013a). Previous reports showed that MLC1 expression starts around E16 in the mouse brain, mainly in progenitor cells from the ventricular zone, and increases specifically in astrocytes until 3 weeks postnatal [START_REF] Schmitt | The brain-specific protein MLC1 implicated in megalencephalic leukoencephalopathy with subcortical cysts is expressed in glial cells in the murine brain[END_REF], while GlialCAM expression increases from birth [START_REF] Bugiani | Megalencephalic leukoencephalopathy with cysts: the Glialcamnull mouse model[END_REF].

Here, taking advantage of our recently described GVU purification technique (Boulay et al. 2015c[START_REF] Boulay | Translation in astrocyte distal processes sets molecular heterogeneity at the gliovascular interface[END_REF], we characterized the astrocyte perivascular endfeet MLC1 and GlialCAM expression during postnatal development.

We show that GlialCAM precedes MLC1 expression and that both proteins increase in already formed Aqp4expressing astrocyte perivascular endfeet between P10 and P15, in parallel to the BBB maturation. Our results provide the first evidence that astrocyte endfeet development is a stepwise process with sequential acquisition of a polarized molecular repertoire.

Material and methods

Mice

OF1 mice were purchased from Janvier Labs. (France) and hosted in pathogen free conditions. Male and female were equally included in the study.

Ethical approval

All applicable international, national, and institutional guidelines for the care and use of animals were followed.

All procedures performed were in accordance with the ethical standards of the institution at which the studies were conducted.

Gliovascular unit purification

Gliovascular units (GVU) were isolated from whole brains of OF1 mice as previously described [START_REF] Yousif | Expression of drug transporters at the blood-brain barrier using an optimized isolated rat brain microvessel strategy[END_REF][START_REF] Boulay | Translation in astrocyte distal processes sets molecular heterogeneity at the gliovascular interface[END_REF]. Selective filtration was performed with a negative filtration using a 100 µm nylon mesh filter to remove meninges, choroid plexus and periventricular layers, followed by a positive filtering on a 20 µm nylon mesh filter to retain parenchymal vessels and remove debris from other brain cell types.

Western-blot

Proteins were extracted from purified GVUs (5 brains pooled per sample) or brains (1 hemisphere per sample) in respectively 50 µL and 500 µL of 2 % SDS per sample with EDTA-free Complete Protease Inhibitor (Roche, Mannheim, Germany), sonicated three times at 20 Hz (Vibra cell VCX130, Sonic & Materials, Newtown, USA) and centrifuged 20 min at 10 000 g at 4 °C. Supernatants were heated in Laemmli loading buffer for 5 min at 56 °C. Three independent samples were prepared for each developmental stage (n=3).Protein content was measured using the Pierce 660 nm protein assay reagent (Thermo Scientific, Rockford, IL, USA). 20 µg of proteins were separated by denaturing electrophoresis in 4-12% NuPAGE gradient gel (or 3-8% Tris Acetate for the P-gP) (Thermo Fisher, Waltham, MA, USA) and electrotransferred to nitrocellulose membranes. Membranes were analyzed as previously described [START_REF] Boulay | Translation in astrocyte distal processes sets molecular heterogeneity at the gliovascular interface[END_REF]. HRP activity was visualized by ECL using Western Lightning plus enhanced chemoluminescence system (Perkin Elmer, Waltham, MA, USA) on a LAS4000 (Fujifilm, Tokyo, Japan). β-Actin content was used as a loading reference. Semi-quantitative densitometric analysis was performed with ImageJ software after scanning the bands.

P5 to P15 and P15 and P60 samples were loaded and analyzed separately. Global change in expression was tested using the non parametric test Kruskal-Wallis (indicated as p-value KW ), and between each stage using the Mann-Whitney (indicated as p-value P5/P10 to p-value P15/P60 ). Data are represented as mean ± sd. qPCR mRNAs from mice hemispheres were purified using the RNeasy Lipid tissue kit (Qiagen). cDNA were synthesized from 1 μg RNA using Reverse Transcriptase Superscript III kit with random primers and stored at -20°C. PCR was performed following the droplet PCR procedure (Bio-Rad; Hercules, CA, USA) in 20-μL reactions using ddPCR Supermix for Evagreen (Bio-Rad; Hercules, CA, USA) on 1 μL of cDNA diluted in water 1/6 for Mlc1 and Glialcam (Hepacam) and 1/60 for Gapdh. Droplets were generated following manufacturer's instructions. PCR cycling was 95 °C for 5 min, and 40 cycles of 95 °C for 30 s and 60 °C for 1 min. Primers: Hepacam forward 5′-GACCGCCTAAAATCAGAAGCA -3'; Hepacam reverse 5′-TGGCTCTGTAGCAGGGTTTT-3'; Mlc1 forward 5′-TCAGTGCGATTCCCAACTTTCA-3'; Mlc1 reverse 5′-GGACCGGGCCGAAATGAT-3'; Gapdh forward 5′-AGGTCGGTGTGAACGGATTTG-3'and Gapdh reverse 5′-TGTAGACCATGTAGTTGAGGTCA-3'. Positive droplets were counted on a QX200 ddPCR droplet reader (Bio-Rad; Hercules, CA, USA) and the QuantaSoft Analysis software (Bio-Rad; Hercules, CA, USA). Mlc1 and Hepacam expression were normalized on Gapdh. Change in expression was tested using the Kruskal-Wallis and Mann-Whitney non-parametric tests. Data are represented as mean ± sd.

Immunostaining

Hippocampal slices: mice were anesthetized with Pentobarbital (600 mg/kg, i.p.) and killed by transcardiac perfusion with PBS/PFA 4%. Brain was removed and cut in 30 µm-thick sections using a Leitz (1400) sliding microtome. Three animals were analyzed per developmental stage.

Gliovascular units: GVUs were plated on a glass slide coated with Cell Tak (Corning, Corning, NY, USA) and fixed in PBS/PFA 4% for 15 min at room temperature. Three animals were pooled for each developmental stage.

Hippocampal slices or GVUs were immersed in the blocking solution (PBS/NGS 5%/Triton X-100 0.5%) for 1 h at room temperature and incubated with primary antibodies and Isolectin GS-B4 (IB4) diluted in the blocking solution 12 h at 4°C. After 3 PBS washes, slices or GVUs were incubated 2 h at room temperature with secondary antibodies, rinsed in PBS and finally embedded in Fluormount G. They were analyzed using a 63X objective on a Nikon Eclipse Ti microscope (Nikon Instruments, Melville, NY, USA). Proportions of vessels with MLC1 or GlialCAM were analyzed with the Chi-squared test with Yates' continuity correction. Among GlialCAM-positive vessel segments, the proportion also co-stained for MLC1 were analyzed using an ANOVA/ Bartlett's test and a Student's test. Among MLC1-positive vessel segments, the proportion co-stained for GlialCAM was analyzed similarly. Data are represented as mean ± sd.

Antibodies

Primary: polyclonal rabbit anti-Aqp4 (1:500) (Sigma, St Louis, MO, USA); polyclonal rabbit anti-Claudin-5

(1:250) (Thermo Fisher, Waltham, MA, USA); monoclonal mouse anti-P-gP (1:200) (Enzo Life Sciences, Lausen, Switzerland); monoclonal mouse anti-Connexin 43 (1:500) (BD-Biosciences, Franklin Lakes, NJ, U.S.); horseradish peroxidase (HRP)-coupled β-actin (1:25000) (Abcam, Cambridge, UK); polyclonal rabbit anti- GlialCAM (1:200) andmonoclonal mouse anti-MLC1 (1:500)

Results

In the adult brain, MLC1 and GlialCAM are not only enriched in astrocyte perivascular endfeet but also expressed in perisynaptic astrocyte processes [START_REF] Sakers | Astrocytes locally translate transcripts in their peripheral processes[END_REF] and in oligodendrocytes for GlialCAM [START_REF] Jeworutzki | GlialCAM, a Protein Defective in a Leukodystrophy, Serves as a ClC-2 Cl-Channel Auxiliary Subunit[END_REF]). In addition, during brain development, MLC1 is present in progenitors from the ventricular zone [START_REF] Schmitt | The brain-specific protein MLC1 implicated in megalencephalic leukoencephalopathy with subcortical cysts is expressed in glial cells in the murine brain[END_REF]. In order to specifically focus our study on astrocyte perivascular proteins, we used our recently developed purification technique of the gliovascular unit (GVU), i.e. perivascular endfeet attached to brain vessels (Boulay et al. 2015c[START_REF] Boulay | Translation in astrocyte distal processes sets molecular heterogeneity at the gliovascular interface[END_REF]) (Fig. 1A). As purification of the GVU has been previously obtained only from adult tissues, we first tested if this technique could be developed on early postnatal brains.

We concentrated our study on parenchymal vessels, depleting our samples from pial vessels by differential filtering of the purified vessels (see material and methods) [START_REF] Yousif | Expression of drug transporters at the blood-brain barrier using an optimized isolated rat brain microvessel strategy[END_REF]). To test the presence of astrocyte perivascular endfeet on purified vessels, we performed Aqp4 immunostaining. Blood vessels were labelled by Isolectin GS-B4 (IB4). Immunostaining on postnatal day (P) 5 GVUs revealed a continuous Aqp4 labelling at the surface of most vessels, as observed in adult (P60) GVUs (Fig. 1B). The proportion of Aqp4-positive GVUs was comparable at all stages (Fig. 1C) (P5:83%; P10:88%; P15:96%; P60:93%; p-value=0.45). Performing Western-blot quantification on purified GVU protein extracts, we observed a small, although not significant, increase of Aqp4 between P5 and P10 followed by a stabilization from P10 onwards (P5:1.0±0.2; P10:1.7±0.9; P15:1.8±0.1; P60:1.4±0.1; p-value KW =0.09) (Fig. 1D andE). The same result was obtained using total brain extracts, consistent with the fact that, in the brain, Aqp4 is mostly present in perivascular astrocyte endfeet (P5:1.0±0.1; P10:1.5±0.2; P15:1.4±0.1; P60:1.6±0.2; p-value KW =0.06) (Fig. 1D andE). To further validate our approach, we tested by Western-blot the copurification of the gap junction channel protein Connexin 43 (Cx43) another protein enriched in astrocyte mature endfeet [START_REF] Ezan | Deletion of astroglial connexins weakens the blood-brain barrier[END_REF]). Cx43 was detected in GVU at all stages (Fig. S1). Collectively, these results indicated that intact GVUs can be purified from the brain as early as P5 and that our purification protocol is a valuable tool to explore the molecular composition of astrocyte perivascular endfeet membranes during the postnatal development.

We next addressed perivascular endfeet expression of MLC1 and GlialCAM during the postnatal development from P5. Western-blot of purified GVU protein extracts showed that GlialCAM expression was already detectable at P5 (Fig. 2A). Its quantity significantly increased between P10 and P15 and remained stable onwards (Fig. 2A andB) (P5:1.0±0.2; P10:1.0±0.03; P15:2.1±0.2; P60:2.6±0.4; p-value KW =0.002; pvalue P5/P10 =0.4; p-value P10/P15 =0.05; p-value P15/P60 =0.25). In contrast to GVUs, GlialCAM detected in total brain extracts was stable between P10 and P15 (WB, P5:1.0±0.1; P10:1.9±0.2; P15:1.9±0.1; P60:2.2±0.1; pvalue KW =0.02; p-value P5/P10 =0.05; p-value P10/P15 =0.5; p-value P15/P60 =0.2). The same was observed at the mRNA level. We noticed however an increase from P15 to P60 (qPCR, P5:1.0±0.2; P10:1.2±0.2; P15:0.9±0.2; P60:1.8±0.6; p-value KW =0.003; p-value P5/P10 =0.2; p-value P10/P15 =0.06; p-value P15/P60 =0.03) (Fig. 2B). These results suggested a distinct temporal regulation of GlialCAM expression between the GVU and the rest of the brain between P10 and P15. We previously found that Aqp4-containing astrocyte endfeet were similarly purified at P10 and P15 (Fig. 1). The increase of GlialCAM level in the GVU between P10 and P15 could thus reflect an increased expression in endfeet or an increased number of GlialCAM-expressing endfeet. To solve this question, we evaluated the proportion of vessels surrounded by GlialCAM-immunolabeled astrocyte endfeet on P10 and P15 hippocampal slices. Blood vessels were labeled by IB4 (Fig. 2C andD). The proportion of IB4-positive vessels showing a perivascular GlialCAM labeling was similar at P10, P15 and P60 (P5:77%; P10:85%; P15:92%; p-value P10/P15 =0.4; p-value P15/P60 =0.9). Since this observation was performed on a restricted part of the brain while GVU protein extracts used for Western-blot were obtained from whole brains, we further excluded the possibility of regional variation by quantifying the proportion of GlialCAM-positive purified GVU. The same proportion was found than on brain sections (Fig. 2E andF) (P5:86%; P10:90%; P15:83%; pvalue P5/P10 =0.8; p-value P10/P15 =0.2). Thus, GlialCAM is expressed around most brain vessels at P10 and its expression increases in the GVU between P10 and P15. In addition, while at P10, GlialCAM immunostaining was mainly dispersed, it formed clear meshworks surrounding the vessels from P15, suggesting a maturation of its subcellular localization (Fig. 2E).

In contrast to GlialCAM, Western-blot analysis of MLC1 expression in purified GVUs showed a very weak signal at P5 and P10, which significantly increased at P15 and was stable onwards (Fig. 3A andB) (P5:1.0±0.1; P10:1.6±0.2; P15:9.4±1.4; P60:9.5±1.6; p-value KW =0.002; p-value P5/P10 =0.4; p-value P10/P15 =0.02; pvalue P15/P60 =0.9). This increase was not detected in total brain extracts both by Western Blot and qPCR suggesting that it is an astrocyte endfeet-specific event (WB, P5:1.0±0.06; P10:1.3±0.2; P15:1.6±0.1; P60:2.1±0.4; p-value KW =0.03; p-value P5/P10 =0.7; p-value P10/P15 =0.4; p-value P15/P60 =0.3) (qPCR, P5:1.0±0.4; P10:0.9±0.1; P15:0.6±0.2; P60:0.9±0.1; p-value KW =0.15; p-value P5/P10 =0.9; p-value P10/P15 =0.06; pvalue P15/P60 =0.06) (Fig. 3B). On hippocampal slices, perivascular MLC1 immunostaining was barely detectable at P10, while highly present in the astrocyte perivascular endfeet at P15 and P60 (P10:20%; P15:90%; P60:100%; p-value P10/P15 =10 -6 ; p-value P15/P60 =0.5) (Fig. 3C andD). We further investigated the developmental expression of MLC1 on purified GVUs. Astrocyte endfeet perivascular membranes were co-immunostained for Aqp4 and showed a continuous staining as previously observed (Fig. 1B). Interestingly, compared to brain slices, more MLC1-immunostained GVUs were observed at P10, and their number still increased between P10, P15 and P60 (P10:62%; P15:80%; P60:96%; p-value P10/P15 =0.03; p-value P15/P60 =0.01) (Fig. 3E andF). This difference between GVUs and slices was probably due to the fact that, even more strikingly than for GlialCAM, the shape of MLC1 staining evolved from isolated puncta on sections at P10 to clear meshworks at P15 (Fig. 3C andE).

Overall, MLC1 is expressed in astrocyte perivascular endfeet after GlialCAM. It is only weakly detected before P10 and significantly increases between P10 and P15.

In the adult mouse brain, MLC1 and GlialCAM form a protein complex at the perivascular membrane [START_REF] Hoegg-Beiler | Disrupting MLC1 and GlialCAM and ClC-2 interactions in leukodystrophy entails glial chloride channel dysfunction[END_REF]. We addressed the development of this complex in the GVU , analyzing the colocalization of both proteins at the gliovascular interface on hippocampal slices (Fig. 4). Since at P10 GlialCAM was more widely expressed than MLC1, we first quantified the proportion of perivascular GlialCAMpositive for MLC1 (Fig. 4). Co-localization of both proteins significantly increased after P10 (ANOVA and Bartlett's test, p-value=0.003) and between all stages (p-value P10/P15 =0.03; p-value P15/P60 =0.002). While 67% of GlialCAM staining at P10 was also positive for MLC1, it represented 81% at P15 and 97% at P60 (Fig. 4B). These results suggested the existence of two pools of GlialCAM in the developing GVUs, associated or not with MLC1, the later progressively disappearing after P10. GlialCAM was almost entirely co-localized with MLC1 at P60 as shown on GVUs (Fig. 4C). In contrast, MLC1 was systematically colocalized with GlialCAM at all stages.

Altogether, our results indicate that the P10-P15 time window corresponds to a maturation step of the MLC1/GlialCAM complex in astrocyte perivascular endfeet.

We finally asked if this P10-P15 developmental window might correspond to the parallel maturation of specific brain vascular functions. The BBB is an impermeable vascular barrier, which regulates the passage of molecules between the blood and the brain. It is induced in the immature endothelium around E15 but still matures during late embryonic and postnatal development. BBB integrity depends on the expression of endothelial tight junction molecules restricting endothelial paracellular permeability and transporters [START_REF] Armulik | Pericytes regulate the blood-brain barrier[END_REF][START_REF] Daneman | Pericytes are required for blood-brain barrier integrity during embryogenesis[END_REF][START_REF] Tam | Death Receptors DR6 and TROY Regulate Brain Vascular Development[END_REF][START_REF] Qosa | Regulation of ABC efflux transporters at blood-brain barrier in health and neurological disorders[END_REF]. Here, we characterized the expression of the tight junction protein Claudin-5 [START_REF] Nitta | Size-selective loosening of the blood-brain barrier in claudin-5-deficient mice[END_REF], and the endothelial luminal ATP-Binding Cassette (ABC) transporter Pglycoprotein (P-gP) which effluxes xenobiotics to the blood [START_REF] Schinkel | Disruption of the mouse mdr1a P-glycoprotein gene leads to a deficiency in the blood-brain barrier and to increased sensitivity to drugs[END_REF][START_REF] Schinkel | P-glycoprotein in the blood-brain barrier of mice influences the brain penetration and pharmacological activity of many drugs[END_REF]. Strikingly, as observed for MLC1 and GlialCAM, Claudin-5 and P-gP levels detected on Western-blots of proteins extracted from purified GVUs significantly increased between P10 and P15 (Claudin-5; P5:1.0±0.2; P10:0.8±0.2; P15:2.8±0.3; P60:3.3±0.7; p-value KW =0.0004; p-value P5/P10 =0.7; p-value P10/P15 =0.01; p-value P15/P60 =0.9) (P-gP; P5:1.0±0.1; P10:1.3±0.05; P15:6.0±0.5; P60:10.2±0.7; p-value KW >0.0001; p-value P5/P10 =0.1; p-value P10/P15 =0.02; pvalue P15/P60 =0.02) (Fig. 5A andB). P-gP level continued to increase after P15. This increased expression was however not associated with a change in protein distribution within the GVU as both proteins were restricted to endothelial cells and present in all vessels (Fig. 5C). Claudin-5 signal lined endothelial cells showing the location of tight junctions. P-gP was uniformly detected in the endothelium. These results suggested a parallel maturation of the BBB and the astrocyte perivascular endfeet MLC1/GlialCAM complex between P10 and P15.

Discussion

Our results provide the first description of the developmentally regulated perivascular expression of the MLC1/GlialCAM complex (summarized in Fig. 5C). We show that GlialCAM precedes MLC1 in the GVU and that both proteins increase within the GVU between P10 and P15, thus suggesting a progressive maturation of the MLC1/GlialCAM complex after P10. This developmental process is posterior to the formation of Aqp4 water channels in astrocyte perivascular endfeet, and parallels the maturation of the BBB characterized here by the increased expression of some key endothelial BBB components, Claudin-5 and P-gP.

We previously reported that isolating the GVU allows the characterization of the molecular properties of astrocyte endfeet and the other cellular components of the GVU, endothelial cells, pericytes and smooth muscles cells (Boulay et al. 2015a, b, c;[START_REF] Mazaré | Connexin 30 is expressed in a subtype of mouse brain pericytes[END_REF]. Here, we provide the first evidence that this strategy can also be applied to characterize the GVU during brain development. In particular we determined the evolution of perivascular pool of astrocyte proteins within the GVU, which were either stable from P5 for Aqp4, or increasing between P10 and P15 for the MLC1/GlialCAM complex. Finally, the GVU purification allows to distinguish and compare the perivascular and parenchymal counterparts of astrocyte proteins as evidenced here for MLC1 which was highly enriched between P10 and P15 in the GVU fraction while constant in the brain (Fig. 3). Altogether, GVU purification is therefore a valuable tool to study astrocyte perivascular molecular properties during development.

Knowledge of astrocyte perivascular endfeet development is elusive. This question has been almost exclusively studied through the prism of Aqp4 [START_REF] Lunde | Postnatal development of the molecular complex underlying astrocyte polarization[END_REF]. Here, we found that most P5-vessels were covered with Aqp4-containing endfeet (Fig. 1), which confirms previous results based on brain slices showing that coverage of the brain vascular compartment by astrocyte endfeet is complete at P5 [START_REF] Ezan | Deletion of astroglial connexins weakens the blood-brain barrier[END_REF]. Alike Aqp4, GlialCAM, but not MLC1, appears to be another constituent of these early endfeet. Between P10 and P15, a strong increase in GlialCAM and MLC1 occurs, associated with the formation of the MLC1/GlialCAM complex detected by the colocalization of both proteins. Intriguingly, Mlc1 and Glialcam mRNA levels were stable from P5 to P15 suggesting thus that the increase of MLC1 and GlialCAM in the GVU is probably regulated by mechanisms involving post-transcriptional regulations. To further address the importance of this postnatal period in the GVU development, we examined the expression of Cx43, another astrocyte endfeet-enriched protein [START_REF] Ezan | Deletion of astroglial connexins weakens the blood-brain barrier[END_REF]) (Fig. S1). Corroborating previous observations obtained on cortical slices [START_REF] Ezan | Deletion of astroglial connexins weakens the blood-brain barrier[END_REF] we found an increase between P10 and P15 both in GVUs (P5:1.0±0.2; P10:1.5±0.4; P15:3.9±0.2; P60:3.4±0.6; p-value KW =0.001; p-value P5/P10 =0.7; p-value P10/P15 =0.02; p-value P15/P60 =0.4) and in brain extracts (P5:1.0±0.07; P10:1.3±0.2; P15:2.0±0.2; P60:1.8±0.2; p-value KW =0.006; p-value P5/P10 =0.2; p-value P10/P15 =0.05; pvalue P15/P60 =0.7). Altogether, these results indicated that despite the extensive Aqp4 perivascular expression at P5, astrocyte perivascular endfeet are not mature at this stage and that the P10 to P15 postnatal period could represent an important step of astrocyte endfeet maturation with the expression of Cx43 and the formation of the MLC1/GlialCAM complex at the junctions of astrocyte endfeet. A recent report identified a two-step maturation of astrocyte perisynaptic processes, with the formation of major branches at P7 and of finer processes ensheathing synapses at P21 [START_REF] Stogsdill | Astrocytic neuroligins control astrocyte morphogenesis and synaptogenesis[END_REF]. A similar mechanism could apply to perivascular processes during postnatal development.

Our colocalization study suggested that two pools of GlialCAM might exist during the astrocyte perivascular endfeet development, with or without MLC1 (Fig. 4). Since GlialCAM has been implicated in cell-matrix adhesion and cell motility processes [START_REF] Moh | Cloning and characterization of hepaCAM, a novel Ig-like cell adhesion molecule suppressed in human hepatocellular carcinoma[END_REF][START_REF] Favre-Kontula | GlialCAM, an immunoglobulin-like cell adhesion molecule is expressed in glial cells of the central nervous system[END_REF], it might participate to the formation of astrocyte perivascular processes at P5. In contrast, from P10, GlialCAM increasingly colocalized with MLC1. In vitro and in vivo observations have shown that GlialCAM is essential for the localization of MLC1 in astrocyte membranes (López-Hernández et al. 2011b;[START_REF] Hoegg-Beiler | Disrupting MLC1 and GlialCAM and ClC-2 interactions in leukodystrophy entails glial chloride channel dysfunction[END_REF]).

Similarly, Cx43 has been shown to interact with GlialCAM and to depend on GlialCAM to be correctly targeted to the membrane [START_REF] Wu | HepaCAM associates with connexin 43 and enhances its localization in cellular junctions[END_REF]. Thus, between P10 and P15, GlialCAM might be necessary to drive the polarized localization of several astrocyte perivascular endfeet proteins.

Astrocytes are known to maintain the brain vascular properties such as BBB functions [START_REF] Alvarez | Glial influence on the blood brain barrier[END_REF][START_REF] Obermeier | Development, maintenance and disruption of the blood-brain barrier[END_REF]. However, astrocyte contribution during their postnatal maturation has never been documented. Our results provide evidence that the maturation of the MLC1/GlialCAM complex coincides with an increased expression of Claudin-5 and P-gP which are key endothelial proteins for BBB integrity. Thus, postnatal astrocyte endfeet and BBB maturation might be coordinated events. Interestingly, MLC patients as well as MLC mouse models with overexpression of MLC1 [START_REF] Sugio | Astrocyte-mediated infantile-onset leukoencephalopathy mouse model[END_REF], or deletion of MLC1 [START_REF] Dubey | Mice with megalencephalic leukoencephalopathy with cysts: A developmental angle: MLC in Mouse and Man[END_REF] or GlialCAM [START_REF] Bugiani | Megalencephalic leukoencephalopathy with cysts: the Glialcamnull mouse model[END_REF]) display cerebral oedema and macrocephaly during the first year of life in patients and around 3 weeks postnatal in mouse models. These data suggest that an abnormal development of the MLC1/GlialCAM complex may affect the postnatal development of the GVU resulting in impaired BBB maturation and oedema formation contributing to the MLC pathological process. MLC1/GlialCAM complex has also been shown to play a role in maintaining brain ion-water homeostasis [START_REF] Ridder | Megalencephalic leucoencephalopathy with cysts: defect in chloride currents and cell volume regulation[END_REF]Capdevila-Nortes et al. 2013b). Thus, MLC brain oedema could also be linked to an abnormal parenchymal water circulation in parallel to the Aqp4-mediated glymphatic system recently discussed [START_REF] Iliff | A Paravascular Pathway Facilitates CSF Flow Through the Brain Parenchyma and the Clearance of Interstitial Solutes, Including Amyloid β[END_REF][START_REF] Iliff | Impairment of glymphatic pathway function promotes tau pathology after traumatic brain injury[END_REF][START_REF] Xie | Sleep Drives Metabolite Clearance from the Adult Brain[END_REF].

Altogether, our results shed new light on the gliovascular unit postnatal development. Through the study of the MLC1/GlialCAM complex, we demonstrate the existence of a progressive postnatal astrocyte endfeet molecular maturation and polarization, which might participate to the functional maturation of the gliovascular unit. Western-blot analysis (D) and quantification (E) of whole brain-and GVU-purified proteins between P5 and P60. β-actin is used as a loading control. The level of Aqp4 in purified GVUs and brain remains constant during postnatal development. ns, p>0.05. GVU, gliovascular unit; IB4, Isolectin GS-B4. Representative projection image of P10, P15 and P60-purified GVU immunolabelled for P-gP (green) and . Nuclei are labelled with Hoechst (blue) and blood vessel wall with IB4 (grey). D. Visual abstract of the results outlining the changes observed between P10, P15 and P60 within the GVU. At P10, Aqp4 (dark blue) is present in all endfeet, GlialCAM (red) in almost all endfeet, while MLC1 (green) is restricted to some endfeet. Both MLC1 and GlialCAM increase significantly within GVU between P10 and P15. This increase is associated with a progressive colocalization of both proteins (yellow), indicating a maturation of the MLC1/GlialCAM complex at the junctions between endfeet. This maturation of MLC1/GlialCAM correlates with an increased expression of endothelial proteins Claudin-5 (light blue) and P-gP (black) which participate to the BBB formation. *, p<0.05; ns, p>0.05. GVU, gliovascular unit.

Figure legends

  (López-Hernández et al. 2011a); Alexaconjugated Isolectin GS-B4 (IB4) was used to label the blood vessel walls (1:100) (Thermo Fisher, Waltham, MA, USA).Secondary: Alexa-conjugated goat anti-mouse and anti-rabbit IgG (1:1000) (Molecular Probes, Eugene, OR, USA), HRP-conjugated goat anti-mouse or anti-rabbit IgG (1:2000) (Santa Cruz Biotechnology, Santa Cruz, CA, USA).

Figure 1 :

 1 Figure 1: Purification of gliovascular units from postnatal developing brains A. Schematic representation of the gliovascular unit (GVU) purification process indicating its cellular components. A, astrocyte; AE, astrocyte endfeet; E, endothelial cell; M, mural cell; L, vessel lumen;. An astrocyte is shown in red. B. Confocal projection images of purified GVUs from P5 and P60 brains immunolabelled for Aqp4 (red) showing that astrocyte perivascular membranes are co-purified with brain vessels as early as P5. Nuclei are labelled with Hoechst (blue) and blood vessel walls with IB4 (grey). C. Quantification of the proportion of Aqp4-positive GVU segments between P5 and P60. Most purified GVUs contain astrocyte Aqp4-positive perivascular membranes. This proportion does not change after P5. D, E.

Figure 2 :

 2 Figure 2: Postnatal expression of GlialCAM in astrocyte perivascular endfeet A.Western-blot analysis and quantification of whole brain-and GVU-purified proteins between P5 and P60. βactin is used as a loading control. GlialCAM expression significantly increases between P10 and P15 in the purified GVUs and between P5 and P10 in the brain. B. qPCR analysis of whole brain mRNAs between P5 and P60. Gapdh is used as a loading control. GlialCAM expression significantly increases at P60. .. C-F. Projection confocal images and quantification of GlialCAM-immunolabelled vessels (green) in hippocampal slices (C, D)and purified GVUs (E, F) at P10 and P15. Nuclei are labelled with Hoechst (grey) and blood vessel wall with IB4 (red). GlialCAM is present around a majority of brain vessels. *, p<0.05; ns, p>0.05. WB, Western Blot; GVU, gliovascular unit; IB4, Isolectin GS-B4.

Figure 3 :

 3 Figure 3: Postnatal expression of MLC1 in astrocyte perivascular endfeetA.Western-blot analysis and quantification of whole brain-and GVU-purified proteins between P5 and P60. βactin is used as a loading control. MLC1 expression significantly increases between P10 and P15 in the purified GVUs but not in the brain. B. qPCR analysis of whole brain mRNAs between P5 and P60. Gapdh is used as a loading control. MLC1 expression is constant. C-F. Projection images and quantification of MLC1immunolabelled vessels (green) in hippocampal slices (C, D) and purified GVU (E, F) at P10 and P15. Nuclei are labelled with Hoechst (grey), blood vessel wall with IB4 (red) and astrocyte endfeet are immunolabelled for

Figure 4 :

 4 Figure 4: Postnatal maturation of the astrocyte endfeet MLC1/GlialCAM complex A. Representative projection image of P10 brain slices immunolabelled for MLC1 (green) and GlialCAM (red) showing GlialCAM colocalized with MLC1 (arrow) or not (arrowhead). Blood vessel wall are labelled with IB4 (grey). B. Quantification of perivascular GlialCAM colocalized with MLC1 (black) and perivascular MLC1 colocalized with GlialCAM (white). Colocalization of GlialCAM with MLC1 increases significantly after P10 while MLC1 is always colocalized with GlialCAM. C. Projection image of a P60-purified GVU immunolabelled for MLC1 (green) and GlialCAM (red) showing extensive colocalization into networks delimiting astrocyte endfeet. Nuclei are labelled with Hoechst (blue) and blood vessel wall with IB4 (grey).**, p<0.01 *, p<0.05; ns, p>0.05. GVU, gliovascular unit; IB4, Isolectin GS-B4.

Figure 5 :

 5 Figure 5: P10-P15, a temporal window for the GVU maturation.A, B. Western-blot analysis (A) and quantification (B) of the tight junction protein Claudin-5 and the ABC transporter P-Glycoprotein (P-gP), on protein extracts from purified GVUs between P5 and P60. β-actin is used as a loading control. Both proteins increase significantly between P10 and P15 and P60 for P-gP. C.

Figure S1 :

 S1 Figure S1: Postnatal expression of Connexin 43 in astrocyte perivascular endfeetWestern-blot analysis (A) and quantification (B) of Connexin 43 (Cx43) expression in purified GVU and whole brains and between P5 and P60. β-actin is used as a loading control. The variable presence of the two upper Cx43 phosphorylated bands in the P60 samples is linked to the migration protocol. Cx43 increases between P10 and P15 both in GVUs and brain. *, p<0.05; ns, p>0.05. GVU, gliovascular unit.

Figure S2 :

 S2 Figure S2: Detailed Western Blot resultsDetailed Western-Blot analysis presented in the figures. Squared areas indicate the bands analyzed for quantification. Saturated signal present on the MLC1 (GVU) Western-Blot is due to rehybridation of the membrane with β-actin. GVU, gliovascular unit.

Acknowledgments

This work has been financed by FRM "Fondation pour la recherche médicale" (PLP20170939025p60 to AG, AJE20171039094 to MCS and SPF20150934067 to ACB), "Fondation Maladies Rares", the European Leukodystrophies Association (ELA) Research Foundation (ELA2012-014C2B to RE), the Spanish Ministerio de Ciencia e Innovación (MICINN) (SAF2015-70377 to RE), the Generalitat de Catalunya (SGR2014-1178 to


to grid services in order to contribute to the whole grid stability [START_REF] Benidris | Enhancing stability performance of renewable energy generators by utilizing virtual inertia[END_REF][START_REF] Nguyen | An analysis of the effects and dependency of wind power penetration on system frequency regulation[END_REF] despite sources intermittence. Adding energy storage systems with corresponding energy management, which are used to create virtual inertia [START_REF] Beck | Virtual synchronous machine[END_REF][START_REF] Benidris | Enhancing stability performance of renewable energy generators by utilizing virtual inertia[END_REF][START_REF] Zaibi | Smart power management of a hybrid photovoltaic/wind stand-alone system coupling battery storage and hydraulic network[END_REF], is one of the major solution to face intermittent character of RES. A lot of studies have been carried out on this topic [START_REF] Haessig | Energy storage sizing for wind power: impact of the autocorrelation of day-ahead forecast errors[END_REF][START_REF] Maroufmashat | Mixed integer linear programing based approach for optimal planning and operation of a smart urban energy network to support the hydrogen economy[END_REF][START_REF] Rigo-Mariani | Fast power flow scheduling and sensitivity analysis for sizing a microgrid with storage[END_REF][START_REF] Rigo-Mariani | Optimal power dispatching strategies in smart-microgrids with storage[END_REF][START_REF] Sechilariu | Power management and optimization for isolated DC microgrid[END_REF][START_REF] Zaibi | Smart power management of a hybrid photovoltaic/wind stand-alone system coupling battery storage and hydraulic network[END_REF] for which the main points are the sizing and the management of the storage system. The sizing problem will not be the aim of this paper which is focused on the energy management of the storage device. Inside the energy management issue, many studies can be done as absolute optimization [START_REF] Rigo-Mariani | Optimal power dispatching strategies in smart-microgrids with storage[END_REF] or statistical analysis [START_REF] Haessig | Energy storage sizing for wind power: impact of the autocorrelation of day-ahead forecast errors[END_REF] and different kinds of problems can be processed. Among them, two classes of management strategy using optimization problems can be distinguished:

-Firstly, rule based heuristics without "a priori" on future events are often proposed, as for example with fuzzy logic management [START_REF] Courtecuisse | A methodology to design a fuzzy logic based supervision of Hybrid Renewable Energy Systems[END_REF][START_REF] Jeong | Energy management strategies of a fuel cell/battery hybrid system using fuzzy logics[END_REF]. Those methods are clearly applicable in real time. Optimal control based approaches (as the example of Pontryagin's maximization principle) are also used on certain systems with the same characteristics even if actual applicability is often more complex. The first category of problems based on heuristics is clearly the most commonly used especially in the industrial context; -Secondly, "global optimization" management where all database are known: "a priori" knowledge on past, present and future events is here assumed. Genetic algorithms [START_REF] Chen | Optimal allocation and economic analysis of energy storage system in microgrids[END_REF], particle swarm optimization [START_REF] Soares | Distributed energy resource short-term scheduling using Signaled Particle Swarm Optimization[END_REF] or linear programming (LP) [START_REF] Maroufmashat | Mixed integer linear programing based approach for optimal planning and operation of a smart urban energy network to support the hydrogen economy[END_REF][START_REF] Morais | Optimal scheduling of a renewable micro-grid in an isolated load area using mixedinteger linear programming[END_REF][START_REF] Rigo-Mariani | Fast power flow scheduling and sensitivity analysis for sizing a microgrid with storage[END_REF][START_REF] Sechilariu | Power management and optimization for isolated DC microgrid[END_REF], are among the class of methods that can be used which guarantee to reach the global optimum of management performance under modeling assumptions: it gives an "absolute answer" on what should be done at each step. This second class of method is clearly not applicable in real time but may be useful for tuning heuristics or to be used during the sizing process of the system design.

In this article, a linear model for Mixed Integer Linear Programming (MILP) optimization of a smart grid energy management is thus presented. The modeling approach is based on power flow models used to run the energy management of the smart power plant including renewable sources (wind turbines) and a Lithium Ion storage device.

The problem statement will be firstly presented. Then a linear model of the system will be proposed with the associated hypothesis. The results obtained over one year of simulation will be exposed and more specifically the impact on some indicators will be presented. The general behavior of the optimal solution will be studied to improve the heuristic management and to develop a new one.

Problem setting

The problem is simplified with only one power source (wind turbines, WT) and only one storage technology (Li-Ion). Many studies have been performed on this kind of grids [START_REF] Mandic | Lithium-ion capacitor energy storage integrated with variable speed wind turbines for power smoothing[END_REF][START_REF] Miao | Coordinated control strategy of wind turbine generator and energy storage equipment for frequency support[END_REF][START_REF] Nasri | Autonomous hybrid system and coordinated intelligent management approach in power system operation and control using hydrogen storage[END_REF][START_REF] Rodriguez | A new energy management strategy for a grid connected wind turbine-battery storage power plant[END_REF] with different storage technologies but on a shorter time horizons: from a few seconds for the frequency control to a few hours. This paper intends to evaluate the proposed method over one year of simulation for a more global evaluation. The concrete goal of this study is to comply with a grid service consisting in a "day ahead power commitment" issue as can be seen in [START_REF] Matee | Determination of optimum economic power commitment by wind farms equipped with energy storage system[END_REF][START_REF] Wang | Day-ahead unit commitment method considering time sequence feature of wind power forecast error[END_REF].

The commitment is generally related to the wind power production forecast; here, in order to focus on the comparison of management strategies, the choice has been made to assimilate power flows for the day ahead forecast (P for ) with commitment: P for (D-1) = P com (D) as displayed on Fig. 1. A tolerance layer (tol) around the commitment power (P com ) is allowed and the storage device coupled with an energy management strategy (EMS) have to correct forecast errors in real time (for the D day) to keep the grid transferred power inside the tolerance band. The study is done in collaboration with industry and the requirements related to smart windfarms with storage for islanded networks are provided by the CRE (https://www.cre.fr ) [START_REF] Cre | Cahier des charges de l'appel d'offres n • 332689-2010-FR portant sur des installations éoliennes terrestres de production d'électricité en Corse, Guadeloupe, Guyane, Martinique, à la réunion, à Saint-Barthélemy et à Saint-Martin[END_REF]. In the case study, the tolerance (tol) is required to be decreased during the three first years (for a 15 year contract) and this study will deal with the third year which is the hardest in terms of commitment with a tolerance band of 15% of the total sizing power of WT sources.

If the mean power transferred to the grid (P grid ) does not fulfill this commitment during 1 min, a Commitment Failure (CF) is triggered and the energy supplied to the grid is not paid for 10 min. Regarding the complexity of system analysis (number of variables and long period of time) simulations have been run with a 10 min time step. Reducing this time step to 1 min will be the purpose of further studies. Preliminary tests showed a low difference between 1 vs 10 min time steps.

Context of the system

The studied grid connected system is simplified with respect to a real smart grid: both commitment and actually produced powers (P prod ) are not based on physical models: power flow vectors P prod and P com are considered as input data. At each time step, the management strategy has to decide which part of the produced power will be sent to the grid (P grid ) and which power will be charged or discharged by the battery (P st : where P st > 0 stands for discharge and P st < 0 stands for charge). The wind turbine production is normally maximized (MPPT mode) but a power reduction (curtailment mode) is expectable if excessive production with respect to the power commitment (P prod > P com +tol) is obtained and if the battery is not able to charge the power excess. For the simulation, this power flow excess (P excess ) is considered as dissipated and lost for the economic balance. The Fig. 2 displays all corresponding power flows related to the power balance (1) for each time step:

P prod + P st = P excess + P grid (1)

Comparative study between two EMS

Our objective is firstly to use LP for the energy management optimization in order to find the best trajectory for P st knowing the whole trajectory of production and forecast data. P st is the unique unknown variable in (1) that leads to the grid transfer P grid . P prod and P com being known, and by considering the battery limits (state of charge and maximum charge power), P excess can be determined with respect to the tolerance band (tol).

This linear optimization will be compared to a rule-based heuristic method. The heuristic is a management method applicable in real time and which follows rules as shown in Fig. 3 where SOC Li-Ion represents the State Of Charge of the storage system. This strategy is a good compromise between complying with the day-ahead commitment and an efficient use of the storage system. P target is the power targeted to be transferred to the grid (P grid ):

Different heuristics have been tested, but all of them had the same rules when P prod is out of the tolerance band. In the low production case with P prod > P com -tol: P target is set to the bottom value of the tolerance band and the difference is discharged with storage (P st ) if enough energy is available in the battery. A CF penalty is triggered in the opposite case. On the contrary, when the upper limit of the band is exceeded, P target is set to the upper value of the band and the difference is stored in the battery within its limits in energy and power. If the one part of the excess power cannot be charged due to storage limits, an excess power (P excess ) is wasted fulfilling Eq. ( 1) but no CF penalty is triggered assuming that wind power production is reduced. This heuristic is a bit more complex when P prod is inside the tolerance band:

-if P com -tol < P prod < P com the storage is off; -if P com < P prod < P com + tol and if SOC<60% then P target = P com ; P prod -P com is then stored in the battery. This heuristic has been tested with a nonlinear model of the system taking account efficiency of static converters and involving the Tremblay Dessaint model [START_REF] Tremblay | Experimental validation of a battery dynamic model for EV applications[END_REF] for the battery. In order to run linear programming, a linear derivation has been developed from the nonlinear model, but subsequent results will be tested with the non-linear model. Indeed the point is to assess the ability of the LP to find an optimal storage trajectory (P st ) with the linear model and to keep a robust performance for the non-linear and more accurate model.

Linear model of the power plant

In this part, the model used in the linear programming optimization is presented. The linear model of the battery is given in details, especially the constraints imposed by the grid and the objective function linearized vs decision variables. The model is presented for a discrete simulation of N time steps of ∆t, k being the current step. Equations derived in the following part have to be verified for each step k belonging to the whole profile [1..N].

Battery linear model

The modeled storage is a Li-Ion battery but its linear model [START_REF] Al | Management of charging cycles for grid-connected energy storage batteries[END_REF] could be easily transposed to any other technology with a simple rated energy E nom . A simple power flow model with charge (η ch ) and discharge (η dis ) efficiencies has been considered to be enough accurate in view of this comparative analysis of EMS performance. Further analysis made with finer models [START_REF] Mandic | Lithium-ion capacitor energy storage integrated with variable speed wind turbines for power smoothing[END_REF][START_REF] Soares | Distributed energy resource short-term scheduling using Signaled Particle Swarm Optimization[END_REF] have shown that it does not affect the performance ranking of the EMS. In order to get a linear function vs efficiency, the P st variable has to be split into 2 parts:

P st [k] = P st + [k] + P st -[k] (2)
where P st + is the positive part and P st -is the negative part of P st in [START_REF] Al | Management of charging cycles for grid-connected energy storage batteries[END_REF]. With this separation the efficiency can be linearly introduced. The P bat variable is used to express the power effectively extracted (stored) from (into) the battery taking account of the losses:

P bat [k] = η ch .P st -[k] + P st + [k] η dis (3)
Different linear constraints related to efficiencies (3) or saturations ( 4), ( 5) can be assigned for charge or discharge powers and SOC.

P bat [k] ≤ P dis max [k] (4) P bat [k] ≥ P ch max [k] (5)
where η ch and P ch max (respectively η dis , P dis max ) represent the efficiency and power saturation during the charge (respectively the discharge) of the battery (absolutes values). The discrete linear implementation of SOC becomes:

SOC [k + 1] = SOC [k] + P bat [k]∆t E nom (6)
Accordingly to the requirements of the battery provider, the SOC is constrained with saturations to maintain the battery lifespan: SOC min = 30% and SOC max = 90%

The constraints needed to run the optimization with the context described above are detailed in the next part.

Linear constraints

Even with this simplified system, several conditions such as "i f P prod < P com -tol" are not linear and mathematical tricks have been used. Operators "max" and "min" can be processed as long as they do not operate on decision variables. To solve certain problem binary variables have also to be defined. The Mixed Integer Linear Programming (MILP) approach is used [START_REF] Vanderbei | Linear Programming: Fundations and Extensions[END_REF].

The first constraint is related to (1) but with linear variables:

P prod [k] + P st + [k] + P st -[k] = P grid [k] + P excess [k] (7)
All members of this equation are related to decision variables except P prod [k]. Considering P grid as a decision variable with the equality constraint ( 7) is equivalent to defining its value. Variables P + st /P - st seem convenient to define the battery management. But in order to ensure that charge and discharge cannot simultaneously take place, a binary variable D[k] (D[k] = 1 for discharge) is introduced and the following constraints are imposed:

0 ≤ P st + [k] ≤ (η dis P dis max ) × D [k] (8) max ( -
P ch max η ch , -P prod [k] ) × (1 -D[k]) ≤ P - st [k] ≤ 0 (9)
If D = 0, (8) ensures P + st = 0, i.e. a battery charge operating. If D = 1, (9) ensures P - st = 0 imposing the battery to be discharged.

Eq. ( 7) and the following constraint define P excess :

P grid [k] ≤ P com [k] + tol (10)
Indeed, imposing P grid below the upper band P excess fulfills the missing power as explained with [START_REF] Abbes | Life cycle cost, embodied energy and loss of power supply probability for the optimal design of hybrid power systems[END_REF].

P excess [k] ≤ max ( P prod [k] -P com [k] , 0 ) (11)
Eq. ( 11) is an upper bound for P excess in order to reduce the search space of the solver. Saturations of the SOC become for each time step (k ∈[1.

.N]):

-

( k ∑ i=1 P st + (i) η dis + η ch P st -(i) ) ≤ E nom ∆t × (SOC max -SOC init ) (12)
k

∑ i=1 P st + (i) η dis + η ch P st -(i) ≤ E nom ∆t × (SOC init -SOC min ) (13)
with [START_REF] Korprasertsak | Comparative investigation of short-term wind speed forecasting models for airborne wind turbines[END_REF] equivalent to SOC min ≤ SOC[k] and [START_REF] Jeong | Energy management strategies of a fuel cell/battery hybrid system using fuzzy logics[END_REF] to SOC[k] ≤ SOC max .

A constraint on the SOC is added to keep its value at the end of the day equal to the initial value:

SOC (N ) = SOC end = SOC init = 50% (14)
This debatable choice has been made in order to decouple planning cycles (i.e. planned days here) from each other. More reasons related to this choice will be detailed in Section 4. P miss is another variable introduced to help defining the CF condition: CF is a binary variable equal to 1 in case of commitment failure and 0 otherwise.

P grid [k] ≥ P eng [k] -tol -P miss [k] (15) BIGM × C F[k] ≥ P miss [k] ( 16
)
when P grid is not inside the tolerance layer, P miss has to be non-zero to verify [START_REF] Maroufmashat | Mixed integer linear programing based approach for optimal planning and operation of a smart urban energy network to support the hydrogen economy[END_REF]. The value of P miss is not really relevant, a non-zero value triggers CF=1 thanks to Eq. ( 16). This method called "Big M" is classically used in LP: the constant BIGM is the big M used to control the value of a binary variable: here CF.

The last constraint is here to prevent the use of the available power to charge the battery during a CF. Indeed, the producer is not paid for the energy provide during a CF period as explained in the introduction. So, during that time, the available power is wasted from the economic point of view.

P st -[k] ≥ -(1 -C F [k]) × P prod [k] ( 17
)
This behavior is due to the time step of 10 min used for optimization and which does not allow to define CF more accurately, since its real value is based on the mean value on 1 min followed a possible penalty over 10 min. The trick used in ( 17) is from the Big M method too which sets CF=1 to impose P - st ≥ 0 and soP - st = 0. With the modeling tricks used, a total of 7 variables are necessary to fully derive the problem instead of one (P bat ) for a nonlinear optimization. Those 7 decision variables are: P st + , P st -, P miss , P excess , P grid , CF and D. CF and D being binary a MILP solver is run. Simulating 24 h with a 10 min time step (144 steps) involves 1008 (7×144) decision variables to be optimized.

The objective function needed to define the optimal solution is detailed in the following section.

Linear objective function

As explained in introduction, the issue of this linear optimization is to satisfy a grid service for day ahead market and of course to maximize energy producer profits. Multi-objective optimization approaches being sometimes adequate but more complex [START_REF] Hernandez-Torres | Techno-economical optimization of wind power production including Lithium and/or Hydrogen sizing in the context of the day ahead market in island grids[END_REF], the choice has been made to minimize a whole cost gathering the process efficiency and the battery use cost. The fulfillment of the grid service is thus shifted in a monetary cost from the CF penalty consequence. The cost function has been decomposed into 4 parts:

-A first part includes the "deviation cost" due to the CF: the producer is not paid for power to the grid (P grid ) if CF=1, the associated cost being defined as:

Cost dev [k] = FIT × C F[k] × P grid [k]∆t ( 18
)
where FIT denotes the Feed in Tariff in [e/kWh]. However, P grid and CF are both decision variables so this expression is not in accordance with the linear programming. If CF = 1, then P grid is below the lower limit of the tolerance layer so P excess = 0. The constraint [START_REF] Matee | Determination of optimum economic power commitment by wind farms equipped with energy storage system[END_REF] prevents against any charge and there is no interest to discharge the battery if we are not remunerated for the energy provided so P st = 0. P grid = P prod in the case of CF = 1 can be deduced from [START_REF] Abbes | Life cycle cost, embodied energy and loss of power supply probability for the optimal design of hybrid power systems[END_REF], where P prod is an input data of the problem and the expression of Cost dev becomes:

Cost dev [k] = FIT × CF[k] × P prod [k]∆t (19)
-A second part consists in the ''wasting cost" where energy is lost with P excess :

Cost was [k] = FIT × P excess [k]∆t (20)
the third and fourth parts represent the costs due to the battery use, especially related to losses and life cost of this storage device. The third part related to efficiency is similar as previously:

Cost η Li-I on [k] = F I T [ (η ch -1) P st -[k] + 1 -η dis η dis P st + [k] ] ∆t (21)
The importance of separating P st to express this cost linearly with decision variables is shown here. Finally, the fourth part related to the life cost of the battery is based on the maximum exchangeable energy E exc-max [kWh] as detailed in [START_REF] Hernandez-Torres | Techno-economical optimization of wind power production including Lithium and/or Hydrogen sizing in the context of the day ahead market in island grids[END_REF]. This last model calculates a percentage of the lifespan already consumed which is multiplied by the cost of one battery Cost Li-I on to obtain the life cost during battery use. This "lifetime model" is based on the cycle to failure curve [3] provided in datasheets which specifies the battery aging with respect to the DOD. This approach is relevant if thermal operation of the battery shelter is controlled as in our case study. A more accurate model counting cycles during operation is sometimes used but this simplification proposed by [START_REF] Abbes | Life cycle cost, embodied energy and loss of power supply probability for the optimal design of hybrid power systems[END_REF] based on the exchanged energy with the battery during its operation is enough accurate in order to assess the performance of an EMS, especially for comparing performance of several strategies. This model is then considered as enough accurate to show a tendency and will not allow the optimizer to use the battery without affecting the cost function Furthermore, this simplification allows deriving an analytical model which can be linearized as:

Cost life [k] = Cost Li-I on .

(

P st + [k] η dis -η ch P st -[k]
) ∆t

E exc-max (22)
The total cost function is obtained by adding all considered costs:

Cost tot [k] = Cost dev [k] + Cost was [k] + Cost η Li-I on [k] + Cost life [k] (23)
The MILP solver minimizes this total cost and seeks the optimal trajectory for P st . Results obtained are exposed in the following and last part of this paper.

Simulations results

Results are obtained using the following method:

We first used GLPK as a unique solver but then switched to CPLEX which is much faster. One year of simulation nearly take 3 min of CPU time. Once all the results (P bat trajectory) are obtained, the system simulation is performed on the non-linear model and the cost criteria are extracted. Results obtained over a full year with a succession of 365 day MILP optimizations raise several issues. In comparison, one year is also simulated with the heuristic algorithm for energy management. The comparative analysis is based on several criteria:

-Cost: as shown in Section 3.3 (Eq. ( 18) to ( 23)) but calculated with the non-linear model.

-Gain: the complementary function of the cost represents the money earned by the energy producer:

Gain = FIT (1 -C F) P grid .∆t -Cost life (24)
Also expressed as:

Gain = FIT × P prod ∆t -Cost tot (25)
where the complementarity is shown. The Cost indicator allows us to optimize the Gain with a greater sensibility.

-Commitment Failure is a relevant criterion for grid services. Indeed agreements are made to increase the penetration rate of intermittent renewable sources with reliable and stable operation of islanded grids.

Model adaptation

The heuristic management strategy is a step by step algorithm which can be applied over a full year of simulation without any problem. The linear optimization is done day by day to be closer to the real commitment problem. In order to be able to simulate one full year, the SOC continuity between two successive days has to be ensured, which is related to [START_REF] Mandic | Lithium-ion capacitor energy storage integrated with variable speed wind turbines for power smoothing[END_REF]: SOC end = SOC init . But even if this constraint is satisfied with the linear model it may be slightly different with the non-linear. The choice has been to calculate the gain available with a ∆SOC = SOC end -SOC init as if this energy would be sold at the FIT price and then would be added to the global gain:

Gain SOC = FIT (SOC end -SOC init ) E bat tot ( 26
)
This choice is questionable, but differences between the linear vs non-linear models were not important so this way of correction was seen as relevant to our study. If this correction is not done, the complementarity between gain and cost is not respected anymore. The following results presented are obtained with 4 wind turbines of 2MW each and 3 battery shelters (SAFT batteries model Intensium Max 20M) of 580 kWh each (P chmax =600kW and P dismax =1100kW per battery). This represents a total estimated investment of 14 900 ke(used for the economic model). Detailed economic data cannot be provided due to confidential issues.

Cost comparison

The costs related to the use of Lithium Ion storage are gathered:

Cost sto = Cost η Li I on + Cost life ( 27
)
Simulations obtained over one year show the ability of the MILP to provide better results than a heuristic even on the same non-linear model. The MILP uses battery twice as much as the heuristic management to reduce wasted and deviation costs. Fig. 5 well emphasizes this issue.

Underusing the battery causes a significant increase of the other parts of the cost function. If only the deviation and storage costs are analyzed, it seems that the battery just has to be used more in a far-sighted approach. But the fact that the wasted cost is increased with heuristic shows that the battery was more often overloaded than for MILP management.

Other comparison on gain and CF

One goal of the study is to focus on the energy producer point of view for which gain is the most important criterion. Furthermore, the grid point of view is another goal of this study, so that the CF will also be a relevant criterion (see Table 1).

The MILP optimization improves all criteria. The sensitivity of the cost function with regard to the gain is clearly demonstrated here. A significant increase of 28% has been made on the cost but only 3% on the gain. This latter gives the total amount of money theoretically earned during one typical year. This result shows the improvement potential on the gain which cannot be more than 10% "even if the cost would be zero" which would correspond with a perfect production forecast. Results on the CF factor show the MILP capability to also enhance the production forecast of this smart wind power plant, the global CF over one year being almost reduced by 30%. It should be noted that the global CF is reduced, but not on every single simulation step. For some particular days, the LP optimizer is able to reduce the cost by slightly increasing the CF. This particular case occurs because the associated deviation cost is weighted by P grid . This aspect is not absurd even on the grid point of view: indeed CF is all the more problematical when the energy producer does not comply with a high power commitment.

The power flow simulation over one year has been extended to a 10 year economical study with the calculation of Levelized Cost Of Energy (LCOE), which represents the minimal price of energy to refund the initial investment, and the Net Present Value (NPV) which shows a measure of the project's profitability. The method used is presented in [START_REF] Short | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies[END_REF] and an example can be seen in [START_REF] O'connor | Techno-economic performance of the Pelamis P1 and Wavestar at different ratings and various locations in Europe[END_REF].

NPV and LCOE are more significant indicators than the cost which is more convenient for the linear optimization. The results over a longer range (10 years) are positive. The linear optimization shows a great improvement with 13% on the NPV and 4% on the LCOE. Data used for those calculations are summarized in Table 3.

Day by day analysis

The cost deviation between the LP optimal planning and the rule-based heuristic is now analyzed for each day of the simulated year. This will show if the optimal LP solver is capable of reducing each day cost or if the difference is due to critical days which concentrate all the improvement. Fig. 6 shows a reconstruction of the probability density and the cumulative density functions associated with this cost deviation by considering a day by day comparison between the heuristic and linear programming optimization. The figure shows that for 70% of the days the improvement is less than 300 e. Indeed, for a lot of days, forecasts are very low which reduces the impact of the energy management in the global cost. If the power forecast is below half the size of the tolerance layer, P com = P for would induce a negative part of the tolerance layer. In this case the tolerance layer is set at the minimum from 0 to 30% of the installed power (tolerance layer being +/-15%) which gives more flexibility than usual and prevent from any CF. For 30% of the days, the improvement is beyond 300 ewhich is quite important compared to the mean total cost per day over the year.

As previously mentioned (Fig. 4), one important difference between both management methods resides in the fact that the heuristics plays the 365 days in a row while the LP separately plays each of the 365 days before being assembled. To ensure the continuity of the SOC in that case, the constraint ( 14) is applied. One of the consequences is that each day of the optimal solution begin with SOC init = 50% while this level depends on what happened the previous day for the heuristic. A study of the impact of SOC init has been realized to analyze the day by day difference between linear programming optimization and heuristic.

Impact of SOC init

Several simulations have been performed with different values on the SOC init constraint. The results are summarized in Table 4.

It should be reminded that 30% and 90% are the low and high limits considered in the energy management for the storage system. Table 2 results show that the impact of SOC init is low. Indeed, except when the constraint is set on a saturation level the difference of costs is negligible which comforts our previous hypothesis.

One particular Day analysis

One particular day (low level of production vs forecast power) where the cost difference is quite important is analyzed. Other typical days studied but not presented showed the same difference of behavior between both strategies. Fig. 7 shows the variations of SOC with both strategies for a 24 h sample and the corresponding grid power flow.

In the first part of the day, the difference between both strategies is due to the SOC init which is favorable to the heuristic. This results in a similar behavior of both management strategies which use the stored energy to prevent CF. After 7 a.m. the heuristic trajectory is locked due to the SOC saturation at the lower limit whereas the LP optimal planning is capable of exploiting the storage over the whole SOC range reducing the commitment failure when the forecast error is higher. It should be noted, contrary to the heuristic management, that LP optimal planning charges the battery even in the low part of the tolerance layer in order to have back up energy and prevent further CF. Table 5 details the different parts of the Cost tot for this particular day:

Those results show that the battery has to be used more intensively than for the current heuristic. The storage cost is a bit higher in the linear optimal solution in order to reduce a lot the C.F. However, knowing the future production during the day allows the MILP to use the battery exactly when necessary. These trends are useful for future heuristic tuning as it will be developed in the next part of this article.

New heuristic deduced from the behavior of the lp optimal planning

The LP optimization has been developed in the scope of two different purposes. It can be firstly used during the design step as an energy management for sizing the smart wind power plant components [START_REF] Rigo-Mariani | Integrated optimal design of a smart microgrid with storage[END_REF]. Secondly, as an "ideal" reference, it can also be exploited for improving rule-based heuristics or optimal control laws without a priori on the future for real time applicability. Fig. 8 shows the new heuristic developed compared with the initial one. The rules outside the tolerance layer are the same for both heuristics but the behavior inside the tolerance layer is completely opposite. Indeed the initial heuristic was based "on common sense" to charge the battery in case of overproduction inside the tolerance layer, and directly transfer the produced power through the grid in case of under production. The analysis of the data set revealed "a bias" between wind forecast and production: in particular, a situation of underproduction is most likely to happen again in the following step times increasing the CF occurrence probability. Therefore, in case of a production lower than the forecast the choice is made to charge the battery with the new heuristic in order to be able to prevent future CF by using this stored power. The threshold on the SOC (SOC Li I on < 50%) is here in order to prevent overusing the battery. The behavior in the upper part of the tolerance layer is symmetrical. In case of overproduction, the storage is not used so as to absorb this overproduction and avoid wasted power. This relation between P prod and P f or could be justified by persistence effects [START_REF] Korprasertsak | Comparative investigation of short-term wind speed forecasting models for airborne wind turbines[END_REF].

One cannot conclude on the optimality of this second heuristic but it clearly outperforms the initial one as shown in Table 4 and Fig. 9. In this figure, the wasted power is expressed as a percentage in relation to the power produced, and the CF probability is calculated over the whole year duration. The LP optimization has also been added as the ideal reference (see Table 6).

The changes implemented in the new heuristic strategy have the desired effect on the costs. First of all, the total cost is reduced by almost 5%. The behavior of the new heuristic is closer to the optimal dispatching resulting from the LP optimization. The battery is more efficiently used with regard to the commitment failure reduction. Even if the wasted cost is not strongly reduced, it remains better with the new heuristic.

Wasted power and CF are complementary quantities and it was easy to find a heuristic which reduce one but increase the other one (by playing with the SOC threshold for example). The power of this new heuristic is to be able to reduce both which shows the fundamental improvement.

Conclusion

İn this paper, a smart wind power plant composed by a wind farm and a Li-ion battery is studied in the context of island networks. A linear model has been developed to be used with a MILP optimization solver. A comparative study has been made with a rule based heuristic method: even if this latter is applicable in real time the comparison shows that heuristic may be significantly improved. The ability of a linear programming to give optimal results on linear model but exploitable on a non-linear and more accurate model has been proven. Those results have been used to improve decision making for heuristic algorithms. A second heuristic algorithm has been developed based on LP behavior showing major improvements in particular by reducing the CF without increasing the wasted power by using the storage system more efficiently. Those results will be used in further studies investigating the co-optimization of component sizing and energy management in the smart wind power plant.

Fig. 1 .

 1 Fig. 1. Commitment assimilated to the forecast power.

Fig. 2 .

 2 Fig. 2. Power flows.

Fig. 3 .

 3 Fig. 3. Heuristic algorithm.

Fig. 4 .

 4 Fig. 4. Simulation method.

Fig. 5 .

 5 Fig. 5. Cost comparison for both optimization approaches of energy management.

Fig. 6 .

 6 Fig. 6. Cost deviation between the optimal LP planning and the Heuristic on the data set.

Fig. 7 .

 7 Fig. 7. Comparison between LP and Heuristic strategy a. SOC b. Power flows.

Fig. 8 .

 8 Fig. 8. New Heuristic algorithm.

Fig. 9 .

 9 Fig. 9. Comparison between initial and new Heuristic.

Table 1

 1 Comparison between linear optimization and heuristic management.

		Heuristic	Linear	Relative
		management	optimization	difference
	Gain	4 018 ke	4 134 ke	3%
	Cost	535 ke	418 ke	28%
	CF	8.3%	5.8%	30%

Table 2

 2 10 years economics results.

		Heuristic	Linear	Relative
		management	optimization	difference
	NPV	7 074 ke	7 964 ke	13%
	LCOE	113 e/MWh	108.5 e/MWh	4%
	Table 3
	Economics data.
	Name		Value
	CAPEX wind turbine	1 700 000 [e/MW]
	OPEX wind turbine	3.5 [% CAPEX]
	CAPEX Li-Ion storage	750 [e/kWh]
	OPEX LI-Ion storage	3.98 [% CAPEX]
	Annual inflation rate	2 [%]
	Nominal actualization rate	7 [%]
	Income taxes	33.3 [%]
	Time of the study	10 [years]
	Depreciation coefficient	2.25/years [-]

Table 4

 4 Linear optimization with different SOC init .

		Linear optimization
	SOC init (%)	30%	40%	50%	60%	70%	80%	90%
	Cost tot (ke)	439	425	418	416	415	416	419
	Cost sto (ke) 122 Cost dev (ke) 157	143	137	135	132	131	131
	Cost was (ke)	160	159	159	159	162	162	165

Table 5

 5 Costs' details for Heuristic and linear optimization.

	Day 133	Storage cost	Wasted Cost	Deviation cost	Total cost
	Heuristic	297 e	0 e	5 235 e	5 532 e
	Linear optimization	659 e	0 e	2 528 e	3 188 e
	Difference	-362 e	0 e	2 707 e	2 344 e

Table 6

 6 Comparison of the costs obtained with the initial and new heuristics for the considered year.

		Storage cost	Wasted cost	Deviation cost	Total cost
	Initial Heuristic	55 ke	227 ke	252 ke	535 ke
	New Heuristic	66 ke	224 ke	221 ke	511 ke
	Difference	-11 ke	3 ke	31 ke	24 ke

Acknowledgment

This research benefited from the support of the Cellule Energy of the CNRS, France.