Kevin Nay

Maxence Jollet

Benedicte Goustard

Narjes Baati

Barbara Vernus

Maria Pontones

Luz Lefeuvre-Orfila

Claude Bendavid

Olivier Rué

Mahendra Mariadassou

Anne Bonnieu

Vincent Ollendorff

Patricia Lepage

Frédéric Derbré

Christelle Koechlin- Ramonatxo

Christelle Koechlin

Gut bacteria are critical for optimal muscle functiona potential link with glucose homeostasis

Keywords:

INTRODUCTION

About 10 14 bacteria live in our gut in symbiosis. This community is now considered as a central organ due to its tremendous impact on human health [START_REF] Clemente | The Impact of the Gut Microbiota on Human Health: An Integrative View[END_REF][START_REF] Janssen | Potential mediators linking gut bacteria to metabolic health: a critical view[END_REF]. Indeed, gut microbiota dysbiosis is involved, directly or indirectly, in numerous chronic diseases, such as obesity, type 1 and type 2 diabetes, allergy and autism [START_REF] Sekirov | Gut Microbiota in Health and Disease[END_REF]. The impact of gut microbiota in chronic diseases can be explained by its interactions with the host organs, including brain [START_REF] Dinan | Gut instincts: microbiota as a key regulator of brain development, ageing and neurodegeneration[END_REF], liver [START_REF] Boursier | The severity of nonalcoholic fatty liver disease is associated with gut dysbiosis and shift in the metabolic function of the gut microbiota[END_REF] and lung [START_REF] Schuijt | The gut microbiota plays a protective role in the host defence against pneumococcal pneumonia[END_REF].

Recently, the hypothesis of a crosstalk between gut microbiota and skeletal muscle has emerged in the literature [START_REF] Bindels | Muscle wasting: the gut microbiota as a new therapeutic target?[END_REF]. For example, in mouse models of intestinal chronic inflammation, the restoration of commensal E. coli levels efficiently prevents skeletal muscle atrophy [START_REF] Schieber | Disease tolerance mediated by commensal E. coli via inflammasome and IGF-1 signaling[END_REF].

Moreover, the recovery of a "healthy" microbiota by synbiotic treatment prolongs survival and reduces cancer proliferation and cachexia development in mouse models of cancer [START_REF] Bindels | Restoring specific lactobacilli levels decreases inflammation and muscle atrophy markers in an acute leukemia mouse model[END_REF][START_REF] Varian | Beneficial bacteria inhibit cachexia[END_REF]. Gut microbiota may also influence the muscle metabolism and fiber phenotype, and consequently the exercise performance. For instance, after microbiota transplantation from obese or lean pigs, germ-free (GF) mice replicate the fiber characteristics and lipid metabolic profile of the donor's skeletal muscle [START_REF] Yan | Gut microbiota can transfer fiber characteristics and lipid metabolic profiles of skeletal muscle from pigs to germ-free mice[END_REF]. Interestingly, probiotic supplementation in mice also improves muscle mass, promotes the slow and oxidative muscle phenotype associated with increased muscle endurance, and reduces exercise-induced muscle damage [START_REF] Chen | Lactobacillus plantarum TWK10 Supplementation Improves Exercise Performance and Increases Muscle Mass in Mice[END_REF][START_REF] Jäger | Probiotic Bacillus coagulans GBI-30, 6086 reduces exercise-induced muscle damage and increases recovery[END_REF]. More recently, in vitro experiments showed that microbiota-derived phenolic metabolites found in blood promote muscle glucose uptake in differentiated human skeletal muscle myoblast in a dose-dependent manner [START_REF] Houghton | Gut microbiome catabolites as novel modulators of muscle cell glucose metabolism[END_REF].

Considering microbiota as a regulatory element of skeletal muscle function is an innovative idea with significant scientific and socio-economic consequences. Indeed, loss of muscle function and mass is a risk factor of morbidity and mortality in neuromuscular diseases, and also in many chronic diseases (e.g., cancer cachexia, obesity, diabetes) [START_REF] Evans | Skeletal muscle loss: cachexia, sarcopenia, and inactivity[END_REF][START_REF] Levy | Implications of skeletal muscle loss for public health nutrition messages: a brief report[END_REF]. The identification of the role played by gut microbiota in the skeletal muscle dysfunction related to such chronic diseases could clearly improve the management of these patients. However, the in vivo mechanisms underlying the functional link between gut microbiota and skeletal muscle in healthy conditions remain poorly explored. In this context, assessing the effect of microbiota modulation on skeletal muscle function would constitute a significant step forward.

Germ-free mice have been previously used to investigate the functional link between microbiota and different organs [START_REF] Lundberg | Antibiotic-treated versus germ-free rodents for microbiota transplantation studies[END_REF]. However, these mice, have developed compensatory mechanisms to the life-long absence of microbiota [START_REF] Fröhlich | Cognitive impairment by antibiotic-induced gut dysbiosis: Analysis of gut microbiota-brain communication[END_REF]. On the other hand, antibiotic treatment is a recognized procedure to induce short-term gut microbiota depletion for studying its impact on the host organs [START_REF] Reikvam | Depletion of Murine Intestinal Microbiota: Effects on Gut Mucosa and Epithelial Gene Expression[END_REF]. Finally, another advantage of antibiotic treatment is that it allows the subsequent recovery of healthy gut microbiota through natural reseeding.

The aim of this study was to determine in healthy mice whether gut microbiota affects skeletal muscle. To this purpose, we modulated gut microbiota in healthy mice by antibiotic treatment and natural reseeding. We found that antibiotic-mediated gut microbiota depletion induced a decrease of skeletal muscle endurance. Interestingly, this deleterious effect was entirely normalized by natural reseeding. We also investigated putative mechanisms and discovered that glucose homeostasis is modified by gut microbiota as we observed that short fatty acid chain and glucose transporters (Gpr41, Sglt1) expression in ileum and glycogen content in muscle were decreased after gut microbiota depletion and normalized after natural reseeding. In summary, our study strongly suggests that the presence of bacteria in the gut influences the skeletal muscle metabolism and function of the host. C57BL/6 mice. 14-week-old C57BL/6 male mice (Charles River, Saint-Germain-Nuelles) were randomly divided in three experimental groups: control group (CTL, n=10), group treated with antibiotics for 21 days (ATB, n=10), and group treated with antibiotics for 10 days followed by natural reseeding for another 11 days (NAT, n=9). Mice were maintained on a 12:12-h dark-light cycle in a temperature-controlled room in individual cages with filter lids, and ad libitum access to food and water. The diet (3395 Kcal/kg) was standardized and identical for all groups (ref A03, safe diets, Augy, France). It included 69.2% of cereals, 20.2% of vegetal protein, 6.0% of animal protein and 4.6% of mineral and vitamin cocktail. The following is a general description of the macronutrient composition: protein carbohydrates 61.3%, protein 25.2% and lipids 13.5%. This diet is currently used in our animal care facility since the birth of mice. Except for running tests, mice were housed in individual standard cages (not wheel cages), and thus were not subjected to daily exercise.

MATERIAL AND METHODS

Animal

The ATB group received an oral cocktail of broad-spectrum antibiotics (1mg/mL ampicillin, 5mg/mL streptomycin, 1mg/mL colistin, and 45µg/mL vancomycin in drinking water).

To investigate the role of microbiota, not antibiotics per se, has impacts on potential muscle function, we included natural seeding groups (NAT) by allowing antibiotics-treated groups (ATB) to restore microbiota through providing soiled litter from control groups (CTL) after cessation of antibiotics treatment. More precisely, the NAT group received the same antibiotic mixture during the first 10 days of the experiment. Then, antibiotic mixture was removed.

During the following 10-days reseeding period, NAT group received twice soiled litter from CTL group cages. For all groups, bottles were filled with filtered animal care drinking water. All antibiotics bottles were changed every 2 days. Feces were individually collected at D0, D7 and D21. After 21 days and overnight fasting, mice were weighed and euthanized.

Euthanasia and sampling. Mice were euthanized by intraperitoneal injection of ketamine (100 mg/kg) and xylazine (20 mg/kg). The soleus, quadriceps, extensor digitorum longus (EDL), gastrocnemius muscles, white adipose tissue, brown adipose tissue and caecum were isolated and weighed. Muscles, intestinal sections (duodenum, jejunum, ileum, and colon) and caecum content were collected and immediately frozen in liquid nitrogen.

In vivo running performance. Running performance was assessed in the three groups (CTL, ATB and NAT) at the beginning (D0), after one week of antibiotic treatment (D7-D8) and before the end of the experiment (D17-D18). Maximal aerobic velocity (MAV) was determined with a running test in which the speed was gradually increased by 2 m/min from 10 m/min until exhaustion. Exhaustion was defined as the inability to maintain the normal running position and/or after five consecutive seconds in contact with the shock grid (<0.2mA) at the rear of the treadmill. Endurance capacity was estimated by calculating the endurance limit time (Tlim) during a submaximal running test, in which the speed started at 12 m/min for the first 2 min and was individually set to 70% of MAV until exhaustion. All tests were repeated at the same time of the day.

Ex-vivo muscle contractile function Muscle contractile properties were assessed in ex vivo

conditions as previously described [START_REF] Ploquin | Lack of myostatin alters intermyofibrillar mitochondria activity, unbalances redox status, and impairs tolerance to chronic repetitive contractions in muscle[END_REF][START_REF] Ryall | Beta 2-agonist fenoterol has greater effects on contractile function of rat skeletal muscles than clenbuterol[END_REF]. This technique allows evaluating the intrinsic muscle contractile properties. After 15min equilibration in the bath, EDL samples were connected to a force transducer/length servomotor system (model 305B, Cambridge Instruments, Aurora Scientific Inc, Ontario, Canada) and were stimulated along their entire length with platinum wire electrodes. The optimum muscle length (L0; i.e., the muscle length producing maximal twitch tension) was determined. All subsequent measurements were made at L0. The isometric tetanic tension was determined (701B Stimulator, Aurora Scientific Inc, Ontario, Canada) using stimulation trains of 500ms, with pulse duration of 0.5ms at different frequencies, from 1 to 150Hz. Stimulus trains were separated by a 1min interval. The maximum isometric tetanic tension (P0) was determined from the plateau of the frequency-tension curve. Three minutes after the tension-frequency determination, the resistance to fatigue was evaluated using a lowfrequency fatigue protocol of 50Hz trains of 700ms delivered every 2s for 5min [START_REF] Lunde | Contraction and intracellular Ca(2+) handling in isolated skeletal muscle of rats with congestive heart failure[END_REF]. The muscle fatigue index was defined as the time taken to produce a 50% reduction from the initial maximum power output. After all measurements, EDL samples were removed from the bath, trimmed of the connective tissue, blotted dry and weighed.

Composition of fecal microbiota.

DNA extraction from feces. Total cellular DNA was extracted from 0.1 g of animal fecal material using the G'NOME® kit (BIO 101, La Jolla, CA) with modifications [START_REF] Furet | Comparative assessment of human and farm animal faecal microbiota using real-time quantitative PCR[END_REF]. Fecal samples were homogenized in the supplied cell suspension solution. Cell lysis/denaturing solution was then added and samples incubated at 55 °C for 2h. To improve cell lysis, 0.1mm-diameter silica beads (750 μL) were added, and samples mixed at maximum speed in a Beadbeater (Biospec, Bartlesville, OK) for 10min. Polyvinylpolypyrrolidone (15mg) was added to ensure removal of polyphenol contamination that could inhibit the qPCR assays. Samples were vortexed and centrifuged at 20 000 g for 3min and supernatants were recovered. The remaining pellets were washed with 400 μL of TENP [50mM Tris (pH 8), 20mM EDTA (pH 8), 100mM NaCl, 1% polyvinylpolypyrrolidone] and centrifuged at 20 000 g for 3min. The washing step was repeated once more and the resulting supernatants pooled. Nucleic acids were precipitated by addition of one volume of isopropanol, incubation at -20°C for 20min, and centrifugation at 20 000 g for 10min. Pellets were resuspended in 400 μL of distilled water plus 100 μL of salt-out mixture and incubated at 4°C for 10min. Samples were spun at maximum speed for 10min, and DNAcontaining supernatants were transferred to clean 1.5-mL microcentrifuge tubes. DNA was precipitated with two volumes of 100% ethanol at room temperature for 5min followed by centrifugation at 16 000 g for 5min. DNA was resuspended in 150 μL of TE buffer and stored at -20 °C.

Evaluation of total bacteria by real-time qPCR analysis of bacterial 16s rRNA genes. The total bacteria present in the fecal samples of each mouse were evaluated by real-time quantitative PCR (qPCR) targeting "all bacteria" 16S rRNA genes using the universal primers F-bact1369 CGGTGAATACGTTCCCGG and R-prok1492 TACGGCTACCTTGTTACGACTT [START_REF] Furet | Comparative assessment of human and farm animal faecal microbiota using real-time quantitative PCR[END_REF].

Analyses were performed using the StepOne Plus detection system (Applied Biosystems, Courtaboeuf, France) with 10μL of Mastermix (PowerUpSybrGreen Master Mix, ThermoFisher Scientific, Courtaboeuf, France), 500nM of both forward and reverse primers, 5μL of diluted cDNA template and water to a final volume of 15μL. All qPCR assays were performed in duplicate using the following cycling conditions: 50°C for 2min, then 95°C for 2min followed by 40 cycles of 95°C for 3s and 60°C for 30s, with a final melting step to improve the amplification specificity. For the quantification, the E. coli DNA standard curve was generated by plotting the threshold cycles (Ct) vs. bacterial quantity. When qPCR assays were performed using fecal DNA samples, this standard curve was used to quantify the bacterial population. The lower limit of detection for bacterial enumeration with good precision is 10 6 bacteria per gram of stool.

Evaluation of microbiota composition. The V3-V4 region of the 16SrRNA genes was amplified using the bacterial primers 343F (5′-CTT TCC CTA CAC GAC GCT CTT CCG ATC TAC GGR AGG CAG CAG-3′) and 784R (5′-GGA GTT CAG ACG TGT GCT CTT CCG ATC TTA CCA GGG TAT CTA ATC CT-3′) modified to add adaptors during the second PCR amplification. PCR assays were performed using the MolTaq 16S DNA polymerase and the corresponding master mix (Molzym GmbH & Co.KG, Bremen, Germany). The PCR mix contained 10 ng of DNA, 1 µL of dNTPs (10mM), 1.25 µL each of forward and reverse primer (20µM), and 0.5 µL of Taq polymerase in a total volume of 50 µL. The cycling program was: 94°C for 3min, followed by 40 cycles at 94°C for 15s, 60°C for 30s, 72°C for 60s, and a final extension at 72°C for 5min. Sequencing was performed using the MiSeq technology (Illumina) at the Genopole Toulouse Midi-Pyrenees (GeT) genomics facility (http://get.genotoul.fr/). Metagenomics analysis. Sequencing data were demultiplexed at the GeT platform. The Galaxysupported pipeline, called FROGS (Find, Rapidly, Otus with Galaxy Solution), is designed to analyze large sets of amplicon sequences and produce abundance tables of Operational Taxonomic Units (OTUs) and their taxonomic affiliation [START_REF] Escudié | FROGS: Find, Rapidly, OTUs with Galaxy Solution[END_REF]. Briefly, this pipeline includes a preprocessing step where reads are merged with FLASH (45), dereplicated, and filtered according to their length, mismatches in primers with cutadapt [START_REF] Martin | Cutadapt removes adapter sequences from high-throughput sequencing reads[END_REF] and N content. This step is followed by Swarm clustering [START_REF] Mahé | Swarm v2: highly-scalable and highresolution amplicon clustering[END_REF] with an agglomeration distance of d=3. Chimera detection is then performed using Vsearch (59) before applying an OTU abundance filter (OTUs < 0.005% of the total abundance are discarded ( 8)). The most abundant sequences of each OTUs were then affiliated with blastn against the Silva v132 database [START_REF] Quast | The SILVA ribosomal RNA gene database project: improved data processing and web-based tools[END_REF]. Abundance tables and taxonomy files were manually imported into RStudio (v1.1.419) package Phyloseq 1.23.1 [START_REF] Mcmurdie | phyloseq: an R package for reproducible interactive analysis and graphics of microbiome census data[END_REF]. Estimates of bacterial OTU diversity was estimated using the Shannon and Simpson indices, in addition to observed richness and Chao indices. β-diversity analyses were performed on weighted and unweighted Jaccard and Bray-Curtis distances matrix of DNA samples and were then visualized using PCoA (Principal Coordinate Analysis) and the ggplot2 R package.

Bacteriodetes and Firmicutes prevalence in ATB group. We explored the phyla levels in ATB group despite a very low bacteria DNA concentration in these samples. We quantified two main phyla by real-time qPCR analysis using PCR primers specific for the ribosomal gene of two main bacterial phyla (Bacteroidetes and Firmicutes), gathered from the literature: Firm934F, GGAGYATGTGGTTTAATTCGAAGCA, Firm1060R, AGCTGACGACAACCATGCAC for firmicutes [START_REF] Guo | Development of a real-time PCR method for Firmicutes and Bacteroidetes in faeces and its application to quantify intestinal population of obese and lean pigs[END_REF] and MIBF, GGCGACCGGCGCACGGG, MIBR, GRCCTTCCTCTCAGAACCC for bacteroidetes [START_REF] Nakanishi | Increase in Terminal Restriction Fragments of Bacteroidetes-Derived 16S rRNA Genes after Administration of Short-Chain Fructooligosaccharides[END_REF].

Muscle fiber phenotype. The muscle fiber phenotype was determined by assessing the presence of the different myosin heavy chain (MHC) isoforms (slow MHC I and fast MHC IIa, IId/x, IIb isoforms), as previously described [START_REF] Derbré | Single Muscle Immobilization Decreases Single-Fibre Myosin Heavy Chain Polymorphism: Possible Involvement of p38 and JNK MAP Kinases[END_REF][START_REF] Talmadge | Electrophoretic separation of rat skeletal muscle myosin heavy-chain isoforms[END_REF]. To obtain cytosolic protein extracts, gastrocnemius samples were lysed in cold lysis buffer (10mM Tris-HCl, pH 7.4, 0.5M sucrose, 50mM NaCl, 5mM EDTA, 30mM Na4P2O7, 1% NP-40, 0.25% sodium deoxycholate, 50mM NaF, 100µM sodium orthovanadate and proteases inhibitors cocktail (Sigma P8340, 5 µL/ml)). Protein concentration was determined using the Lowry assay. Protein samples (6 µg) were separated on high-glycerol-containing (30%) gels with an acrylamide-to-bis-acrylamide ratio of 50:1 for the separating gel (8% total acrylamide, pH 8.8) and for the stacking gel (4% total acrylamide, pH 6.8) using a Mini-Protean II dual slab cell apparatus (Bio-Rad, Hercules, CA). After electrophoresis (at 140V in a refrigerated room at 4°C for 22h), gels were stained with Coomassie blue (IRDye® Blue Protein Stain, LI-COR Biosciences, Lincoln, NE, USA) and the different MHC isoforms were identified according to their electrophoretic mobility pattern [START_REF] Derbré | Single Muscle Immobilization Decreases Single-Fibre Myosin Heavy Chain Polymorphism: Possible Involvement of p38 and JNK MAP Kinases[END_REF][START_REF] Talmadge | Electrophoretic separation of rat skeletal muscle myosin heavy-chain isoforms[END_REF].

Cross-sectional muscle fiber by immunohistochemistry. Serial transverse sections (10µmthick) from liquid nitrogen-cooled isopentane frozen quadriceps muscle samples were obtained using a cryostat at -25°C, and mounted onto glass microscope slides. Sections were then washed in phosphate buffered saline (PBS), blocked and permeabilized with 0.1% Triton-X100 and 10% horse serum. For fiber cross-sectional area (CSA) determination, sections were stained with an anti-laminin antibody (1/200 in PBS, L9393 -Sigma) at 37°C for 1h, followed by washes in PBS and incubation with the secondary antibody Alexa Fluor 488 goat anti rabbit IgG (1/1000 in PBS, A11034 -Invitrogen) for 1h. Whole histological sections were imaged with a digital slide scanner Hamamatsu NanoZoomer 2.0-HT and analyzed with the ImageJ software package. On average, 1800 fibers per animal were quantified according to Demangel et al. method [START_REF] Demangel | Early structural and functional signature of 3-day human skeletal muscle disuse using the dry immersion model[END_REF].

Transcript and protein expression profiles in ileum and skeletal muscle.

To explore potential mechanisms linking gut microbiota composition and skeletal muscle, we measured markers involved in protein turnover, mitochondrial metabolism [START_REF] Jäger | AMP-activated protein kinase (AMPK) action in skeletal muscle via direct phosphorylation of PGC-1alpha[END_REF], inflammation, and related to lipid and glucose metabolism in both ileum and/or muscle, as described below (Table 1 and2).

Immunoblotting. Frozen gastrocnemius muscle samples were homogenized using an Ultra- (TBST) for 1h, followed by overnight incubation with antibodies against proteins involved in muscle metabolism and proteolysis/synthesis balance (Table 1). After three 5min washes at room temperature with TBST, membranes were incubated with a secondary antibody conjugated with horseradish peroxidase at room temperature for 1h. Blots were washed (three times for 5min/each) with TBST at room temperature, and antibody-bound proteins were revealed using the ECL reagent (Bio-Rad Life Science, Hercules, CA). Films were scanned and analyzed using the Image Lab software. All blots were corrected for loading based on the Ponceau red staining.

RNA isolation and RT-qPCR. Total RNA was isolated from gastrocnemius and ileum samples using 2), and 5µL of diluted cDNA (final volume of 15µL). All PCR assays were performed in duplicate using the following cycling conditions: 50°C for 2min, then 95°C for 2min followed by 40 cycles of 95°C for 3s and 60°C for 30s. The relative mRNA levels were normalized to α-tubulin (α-tub) and acidic ribosomal phosphoprotein P0 (Rplp0), as housekeeping genes unaffected by the experimental conditions. Results were expressed using the comparative cycle threshold (Ct) method to generate ΔΔCt values with template dilutions ranging from 10 1 to 10 6 copies. The PCR overall efficiency (E) was calculated from the slopes of the standard curves according to the equation E = [10 (-1/slope) ] -1 and this value was higher than 95% for all assays. The relative abundance of each sample was then normalized according to the equation: Relative Quantity (RQ) = 2 -ΔΔCt . All the experiments were performed according to the minimum information for publication of quantitative real-time PCR experiments (MIQE)

guidelines [START_REF] Bustin | The MIQE guidelines: minimum information for publication of quantitative real-time PCR experiments[END_REF][START_REF] Schmittgen | Analyzing real-time PCR data by the comparative C(T) method[END_REF].

Mitochondrial DNA (mtDNA) isolation and measurement by RT-qPCR.

Total DNA was extracted from the gastrocnemius muscle using a QIAamp DNA kit (Qiagen).

Genomic (ATP synthase beta) and mitochondrial DNA (means of NADH dehydrogenase subunit 5 and NADH dehydrogenase subunit 2) were quantified by quantitative real-time polymerase chain reaction [START_REF] Britto | Glucocorticoid-dependent REDD1 expression reduces muscle metabolism to enable adaptation under energetic stress[END_REF]. Each sample was run in duplicate. Results were expressed using the comparative cycle threshold (Ct) with genomic DNA as the control. The relative changes in the expression level of mitochondrial DNA were calculated by the ΔΔCt formula.

Muscle glycogen content. The acid-hydrolysis method used for glycogen quantification was adapted from the protocols described by Adamo and Jansson [START_REF] Adamo | Comparison of traditional measurements with macroglycogen and proglycogen analysis of muscle glycogen[END_REF][START_REF] Jansson | Acid soluble and insoluble glycogen in human skeletal muscle[END_REF]. 20-30 mg of frozen gastrocnemius muscle powder was placed in ice-cooled 6% perchloric acid and 1M hydrochloric acid. Samples were then boiled at 100°C for 2h, cooled on ice for 10min and centrifuged (1300 RPM, for 5min). 12 µL of supernatant was removed from each sample, diluted in 200µL of GOD-PAP solution (Biolabo, Maizy, France) and incubated in the dark at 37°C for 20min to determine the glucose concentration. Absorbance was measured at 500nm using a microplate reader. Glycosyl units produced by glycogen hydrolysis were expressed as µmol/mg of wet muscle weight.

Muscle triglycerides content.

Muscle triglycerides were determined by using DiaSys kit (Diagnostic System, Grabels, France) following a preliminary organic phase extraction according to Bligh & Dyer's method. Briefly, 50 μg of gastrocnemius samples were crushed with 500 μL of 150mM sodium chloride. Then 150 μL of muscle homogenates were extracted with 600 μL of a methanol-chloroform mixture (1:1, v/v). The organic layers were collected after centrifugation (10,000g for 10 min) and dried under nitrogen. Dry samples were reconstituted in 37.5 μL of isopropanol/acetonitrile/water mixture (2:1:1, v:v:v) and 10 μL were analyzed according to the manufacturer recommendations [START_REF] Bligh | A rapid method of total lipid extraction and purification[END_REF].

Statistical analysis.

All data are presented as the mean ± SEM. The normality of each distribution and homogeneity of variance were assessed with the Kolmogorov-Smirnov and Fischer test, respectively. Signifiance between CTL, ATB and NAT data were checked using a one-way analysis of variance (ANOVA). Significant interactions effects were analyzed with the Fischer LSD post-hoc test. For some parameters, the unpaired t-test was used to compare directly CTL vs. NAT or CTL vs ATB. The Mann-Whitney rank sum test was chosen when the normality and/or equal variance tests failed. For running tests, significance between parameters at D0, D7 and D17 were checked using the paired t-test, after checking normality. For all statistical analyses, the significance level was set at 0.05. Data were analyzed using the statistical package GraphPad Prism version 6.02 for Windows (GraphPad Software, La Jolla, California).

RESULTS

Treatment tolerance. During the entire study period, neither diarrhea nor visible adverse side effect was recorded. Consequently, no mouse was excluded from the data analysis. Food intake and hydration were checked daily and no significant change was observed during the entire study period (Table 3).

Antibiotic treatment and natural reseeding efficiently modulate gut microbiota. To confirm gut microbiota depletion induced by the antibiotic treatment, we quantified by Q-PCR allbacteria in feces, as well caecum weight (caecum hypertrophy is a marker of gut microbiota depletion ( 56)). At D0, microbiota DNA content did not differ in the three mouse groups (CTL, ATB and NAT) (Fig. 1A). After 7 days of antibiotic treatment (D7), bacterial DNA content was strongly reduced in the ATB and NAT groups (Fig. 1B). This effect was still present in the ATB group after 21 days of treatment (D21) (Fig. 1C). Despite a very low bacteria DNA concentration in gut samples in the ATB group at D21, we managed to estimate the phyla prevalence by qPCR analysis and found the following: 83% of firmicutes and 17% of bacteriodetes, the other phyla were not detectable (data not shown).

Conversely, natural reseeding restored the bacterial DNA level in the NAT group (Fig. 1C). At D21, alpha diversity (Fig. 1D) and beta diversity analyses (Fig. 1E-F) showed no statistical differences in microbiota between CTL and NAT groups. Neither phyla abundance (Fig. 1G-H), nor levels of main family from Bacteroides and Firmicutes showed statistical differences between CTL and NAT groups (Fig 1I -J). Moreover, caecum weight at D21 was significantly higher in ATB mice than in the CTL group (+456%, p<0.001, SI supplemental Table 1). Caecum weight in the NAT group was significantly lower than in the ATB group (-76%, p=0.003), and did not significantly differ from that of the CTL group (Table 3). All together, these results support that NAT group can be used to assess the effects of gut microbiota per se on skeletal muscle function together with ATB group.

Effects of gut microbiota depletion on the structure of skeletal muscle mass. At the end of the study, the muscle wet weight (Fig. 2A) and mass index calculated as wet weight normalized to the whole-body weight (Fig. 2B) were significantly lower for gastrocnemius and quadriceps, but not for EDL and soleus, in the ATB group compared with the CTL and NAT groups (on average, between 7-10% of reduction). Normalization to the whole-body weight could be misleading because of the caecum hypertrophy in the ATB group (Table 3). Indeed, when the muscle mass index was normalized to body weight without the caecum weight, the weight of gastrocnemius, quadriceps, EDL and soleus were comparable between CTL and ATB mice (Fig. 2C). Moreover, histological analysis on quadriceps muscle samples showed that the fiber crosssectional area (CSA) was comparable between CTL and ATB groups (Fig. 2D-E). Similarly, gene/protein activation of several key factors involved in protein synthesis, proteolysis, inflammation and autophagy (Igf1, Murf1, Trif, Foxo-3a and NfκB, PRAS40, 4EBP1, RPS6 and LC3B) was comparable in the gastrocnemius muscle of CTL and ATB mice (Fig. 2F-G-H).

Gut microbiota depletion induces muscle fatigability that is reversed by natural reseeding.

To determine the impact of gut microbiota depletion/natural reseeding on skeletal muscle function, mice underwent running tests at different time points. Moreover, at the end of the study, we tested ex vivo the contractile properties of EDL muscle samples to identify the specific role of skeletal muscle on the running performance (Fig. 3). MAV, which is dependent on the maximal oxygen consumption, was comparable in the three groups (CTL, ATB and NAT) and at all time points (D0, D7 and D17) (Fig. 3A-B-C). Conversely, performance indicators related to endurance were significantly affected by gut microbiota changes (Fig. 3D-E-F). Specifically, the endurance limit time (Tlim) during the running endurance test was significantly lower at D9 compared with the D0 values in ATB and NAT mice (-27%, in ATB group p=0.015 and -12% in NAT group, p=0.012 respectively, Fig. 3E). At D19, Tlim was still lower than at D0 in the ATB group (-19.3%, p=0.037), whereas it was back to the D0 values in the NAT group (Fig. 3F). Ex vivo contractile tests performed at the end of the protocol showed that EDL maximal strength (sP0) was not affected by the experimental conditions (Fig. 3G), whereas EDL muscle fatigue index was significantly reduced in the ATB group compared with both CTL and NAT groups (-26%, p=0.036 and -37%, p=0.001, respectively (Fig. 3H). EDL muscle fatigue index in the CTL and NAT groups did not differ significantly.

Potential mechanisms linking gut microbiota and skeletal muscle function: focus on glucose homeostasis. Several cellular adaptations, including muscle fiber phenotype, mitochondrial biogenesis and/or substrate availability, affect skeletal muscle endurance [START_REF] Egan | Exercise metabolism and the molecular regulation of skeletal muscle adaptation[END_REF]. Here, we observed that the expression of the different MHC isoforms in gastrocnemius muscle was comparable in CTL and ATB (Fig. 4A-B). Similarly, the protein level of key markers of mitochondrial metabolism (AMPK, PGC1α, COX IV; Fig. 4C-D) or the mRNA expression of Glut4, Cd36, Cpt1, as well Nrf-1 and the mitochondrial DNA content (Fig. 4E-F) did not change after ATB treatment. These results suggest that disruption of gut microbiota composition does not impact the myofiber phenotype or the mitochondrial metabolism.

Gut microbiota depletion leads to major changes in intestinal epithelial cells [START_REF] Yu | Host-microbial interactions and regulation of intestinal epithelial barrier function: From physiology to pathology[END_REF] and the gut microbiome has a profound influence on inflammatory states [START_REF] Steves | Microbiome and Musculoskeletal Conditions of Aging: A Review of Evidence for Impact and Potential Therapeutics: MICROBIOME AND MUSCULOSKELETAL CONDITIONS OF AGING[END_REF]. Here, we reported in ileum that ATB treatment and subsequent natural reseeding did not affect gene expression of myeloid differentiation primary response 88 (Myd88) and Toll Like Receptor 4 (Tlr4), two canonical proteins involved in inflammatory signaling pathways (Fig. 5A).

As shown by others, the lack of some bacteria-derived metabolites could interfere with the metabolism of energetic substrate, such as lipid and glucose metabolism [START_REF] Catoire | Fatty acid-inducible ANGPTL4 governs lipid metabolic response to exercise[END_REF][START_REF] Houghton | Gut microbiome catabolites as novel modulators of muscle cell glucose metabolism[END_REF] and this could play important roles in the gut-skeletal muscle axis. In this context, fasting-induced adipocyte factor, Fiaf also known as angiopoietin like protein 4, is a key protein reducing fatty acids synthesis, adipogenesis and lipogenesis [START_REF] Chang | Role of Angptl4/Fiaf in exercise-induced skeletal muscle AMPK activation[END_REF]. Fiaf expression is known to be negatively regulated by intestinal bacteria [START_REF] Bäckhed | The gut microbiota as an environmental factor that regulates fat storage[END_REF]. In our study, Fiaf gene expression in ileum was indeed significantly higher in ATB group compared to CTL and NAT groups (+164%, p=0.001 and +135%, p=0.002, respectively, Fig. 5A). However, this Fiaf increase was not associated with changes in muscle triglycerides levels in all experimental conditions (Fig. 5C). Finally, gut microbiota modulation did not affect Lat1 expression, suggesting no major effects on branched amino acids transport (Fig. 5A).

Antibiotic treatment and reseeding did not exert any effect on free fatty acid receptor 1 and 4 (Gpr40 and Gpr120 respectively), both receptors being activated by medium to long chain fatty acids. However, Short Chain Fatty Acids (SCFAs) are the most abundant microbial metabolites derived from intestine, and SCFAs activated enteroendocrine cells via the free fatty acid receptor 3 (Gpr41). Interestingly, we reported in ileum samples that Gpr41 gene expression was significantly decreased in the ATB group compared to CTL group (-48%, p=0,007; Fig. 5B).

After natural reseeding, NAT group exhibited higher Gpr41 mRNA levels compared to ATB group (+111%, p<0.001; Fig. 5B). As the activity of these enteroendocrine receptors are linked to glucose metabolism [START_REF] Hansen | The gut microbiome in cardio-metabolic health[END_REF][START_REF] Macdonald | The multiple actions of GLP-1 on the process of glucose-stimulated insulin secretion[END_REF][START_REF] Tolhurst | Short-Chain Fatty Acids Stimulate Glucagon-Like Peptide-1 Secretion via the G-Protein-Coupled Receptor FFAR2[END_REF], we measured additional markers both in ileum and skeletal muscle. It's noteworthy that the gene expression of sodium/glucose cotransporter 1 (Sglt1) followed the same pattern in ileum than Gpr41, i.e significant lower levels in ATB condition (-34%; p=0.001 vs CTL group; Fig. 5B) such effect being reversed by natural reseeding (+44%, p=0.033 vs ATB group; Fig. 5B). However, these gene expression changes were not associated with modification in blood glucose levels (Table . 3). Finally, as glucose stored in glycogen is the one main substrate involved in muscle energy supply during endurance exercise [START_REF] Egan | Exercise metabolism and the molecular regulation of skeletal muscle adaptation[END_REF], we monitored muscle glycogen content. In agreement with results obtained in ileum on Gpr41 and Sglt1, muscle glycogen content was significantly lower in ATB than in CTL mice (Fig. 5D) and this was normalized after natural reseeding (Fig. 5D).

DISCUSSION

The present study is the first one designed to explore the consequences of gut microbiota depletion and reseeding on skeletal muscle structure and metabolism. Using experimental model of gut microbiota modulation, we demonstrated negative impacts on skeletal muscle endurance, reversed by bacterial reseeding. Our ex vivo functional analyses clearly support a role of gut microbiota on muscle intrinsic contractile properties. Gut microbiota appears to play a role in glucose homeostasis, as we observed that short fatty acid chain and glucose transporters (Gpr41, Sglt1) in ileum and muscle glycogen content paralleled the muscle endurance changes observed after ATB treatment and reseeding. Altogether, our results highlight that gut microbiota depletion impact on muscle endurance can be mediated through the modulation of muscle glycogen availability.

Gut microbiota and muscle mass

Researches from the group of Delzenne suggested a link between gut microbiota profile and skeletal muscle mass in pathological conditions [START_REF] Bindels | Restoring specific lactobacilli levels decreases inflammation and muscle atrophy markers in an acute leukemia mouse model[END_REF][START_REF] Bindels | Non Digestible Oligosaccharides Modulate the Gut Microbiota to Control the Development of Leukemia and Associated Cachexia in Mice[END_REF]. Recently, Varian et al. [START_REF] Varian | Beneficial bacteria inhibit cachexia[END_REF] showed that probiotic supplementation partially prevents skeletal muscle atrophy related to cancer cachexia and sarcopenia. Here, in healthy mice, we found lower wet weight and mass index of some muscles in ATB mice. However, the caecum hypertrophy, a widely known phenomenon associated with depleted bacteria condition [START_REF] Linninge | Pre-treatment with antibiotics and Escherichia coli to equalize the gut microbiota in conventional mice[END_REF], could mask a body weight reduction in these mice, as indicated by the absence of difference on muscle mass when normalization was done after subtraction of the caecum weight. This suggests that gut microbiota modulation does not directly cause skeletal muscle atrophy in our experimental conditions. This is emphasized by the absence of changes in muscle strength or changes in protein of factors involved in muscle protein turnover, in quadriceps fiber CSA, and in the ex vivo maximal strength. In view of these data, we suggest that, gut microbiota only slightly influences skeletal muscle mass in healthy conditions.

Gut microbiota and muscle endurance

It has been recently proposed that gut microbiota could affect physical performance [START_REF] Clark | The Crosstalk between the Gut Microbiota and Mitochondria during Exercise[END_REF].

For instance, the diversity of gut microorganisms is higher in professional athletes [START_REF] Clarke | Exercise and associated dietary extremes impact on gut microbial diversity[END_REF]. In addition, endurance performance is enhanced in conventionalized and specific pathogen-free (SPF) mice than in GF mice [START_REF] Hsu | Effect of intestinal microbiota on exercise performance in mice[END_REF]. Several skeletal muscle-independent factors can alter the endurance performance, including cardiovascular deficiency, insufficient muscle capillarity, central fatigue or pain [START_REF] Gonglach | Muscle Pain as a Regulator of Cycling Intensity: Effect of Caffeine Ingestion[END_REF][START_REF] Hermansen | Cardiac output during submaximal and maximal treadmill and bicycle exercise[END_REF][START_REF] Olfert | Musclespecific VEGF deficiency greatly reduces exercise endurance in mice[END_REF][START_REF] Piedimonte | Placebo-induced decrease in fatigue: evidence for a central action on the preparatory phase of movement[END_REF]. To determine the specific impact of gut microbiota modulation on skeletal muscle, we performed in addition to in vivo running tests, ex vivo muscle contractility tests. We observed in both experimental conditions a negative effect of gut microbiota depletion on muscle endurance, fully reversed by natural reseeding. Altogether, the ex-vivo results confirm that gut microbiota specifically and directly affects muscle endurance.

Skeletal muscle endurance can be affected by several muscle alterations, including changes in muscle contractile phenotype, mitochondrial biogenesis and/or reduction in substrate availability [START_REF] Egan | Exercise metabolism and the molecular regulation of skeletal muscle adaptation[END_REF]. Interestingly, after transplantation of gut microbiota from obese or lean pigs to germ-free mice, these mice replicated the skeletal muscle fiber characteristics and lipid metabolic profiles of the donor [START_REF] Yan | Gut microbiota can transfer fiber characteristics and lipid metabolic profiles of skeletal muscle from pigs to germ-free mice[END_REF]. Here, the absence of significant modifications in the proportion of the different MHC isoforms in the ATB group excludes major effects of microbiota changes on the muscle contractile phenotype. Bäckhed et al. [START_REF] Bäckhed | Mechanisms underlying the resistance to diet-induced obesity in germ-free mice[END_REF] observed that in GF mice, AMPK activity is increased in liver and skeletal muscle, and suggested that this adaptation is a key mechanism by which GF mice are better protected from obesity. In our study however, we did not find any modification in skeletal muscles in the activity of AMPK, the expression of PGC-1α and mitochondrial DNA content in skeletal muscle of ATB mice. This suggests that mitochondrial biogenesis remained unchanged in ATB mice and therefore that endurance alteration is probably not due to reduction of the maximal muscle oxygen consumption capacity.

Such muscle metabolic discrepancies between ATB mice and GF mice could be due to differences in the duration of skeletal muscle exposure to a systemic environment with depleted gut microbiota.

Gut microbiota modulation targets muscle glycogen availability

Muscle endurance also depends on metabolic parameters, including substrate availability in skeletal muscle, such as glycogen and triglycerides, two key energetic substrates that regulate muscle capacity during prolonged strenuous exercise [START_REF] Goodpaster | Skeletal muscle lipid content and insulin resistance: evidence for a paradox in endurance-trained athletes[END_REF][START_REF] Hermansen | Muscle Glycogen during Prolonged Severe Exercise[END_REF]. Interestingly, GF mice exhibit higher gut Fiaf expression compared with conventionalized mice, leading among others to a reduction of triglyceride storage in peripheral tissues including liver [START_REF] Bäckhed | The gut microbiota as an environmental factor that regulates fat storage[END_REF]. Fiaf is a glycoprotein recognized to also promote fatty acid oxidation through AMPK activation in skeletal muscle, and to attenuate muscle lipid uptake by inhibiting LPL activity [START_REF] Chang | Role of Angptl4/Fiaf in exercise-induced skeletal muscle AMPK activation[END_REF][START_REF] Robciuc | Angiopoietin-like 4 mediates PPAR delta effect on lipoprotein lipase-dependent fatty acid uptake but not on beta-oxidation in myotubes[END_REF]. Here, we confirmed the data of Bäckhed and colleagues by showing that gut Fiaf gene expression is modulated by the lack/presence of gut bacteria. However, these results were not associated in skeletal muscle with changes in i) FFA transporters gene expression (Cd36, Cpt1), ii) AMPK activation and iii) muscle triglyceride content. Altogether, these findings suggest that muscle lipid metabolism is unlikely to play a major role in alterations of muscle endurance observed after gut microbiota modulation.

Our data on glucose homeostasis both in ileum and skeletal muscle open some interesting hypotheses. Indeed, in ileum, Gpr41 and Sglt1 gene expression patterns followed the skeletal muscle endurance capacity (i.e decrease in bacteria-depleted conditions reversible upon natural reseeding). Dependent to metabolites-derived from gut bacteria, Gpr41 contributes to the enteroendocrine cells activation and, by its action on glucagon-like peptide 1 release, regulates glucose-mediated insulin secretion [START_REF] Hansen | The gut microbiome in cardio-metabolic health[END_REF][START_REF] Tolhurst | Short-Chain Fatty Acids Stimulate Glucagon-Like Peptide-1 Secretion via the G-Protein-Coupled Receptor FFAR2[END_REF]. In the same line, we observed the modulation of expression of Sglt1 gene, encoding a Na + /glucose cotransporter located in enterocytes, which could reflect glucose homeostasis dysregulation in the intestinal tract. Overall, these results are in agreement with previous studies using antibiotic-induced microbiome depletion and showing a modulation of gene expression programs required for glucose homeostasis both in intestine and liver [START_REF] Cresci | Colonic gene expression in conventional and germ-free mice with a focus on the butyrate receptor GPR109A and the butyrate transporter SLC5A8[END_REF][START_REF] Rodrigues | Antibiotic-Induced Alterations in Gut Microbiota Are Associated with Changes in Glucose Metabolism in Healthy Mice[END_REF][START_REF] Zarrinpar | Antibioticinduced microbiome depletion alters metabolic homeostasis by affecting gut signaling and colonic metabolism[END_REF]. Zarrinpar and colleagues also highlighted that antibiotics, by depleting gut bacteria in colon, reduce SCFAs production and deprive colonocytes from butyrate their main fuel source; and this results in lowering serum glucose and improving insulin sensitivity [START_REF] Zarrinpar | Antibioticinduced microbiome depletion alters metabolic homeostasis by affecting gut signaling and colonic metabolism[END_REF].

This potential mechanism may contribute to the reduction of muscle glycogen store reported in the present study, since glycogen storage depends of both carbohydrates availability and uptake [START_REF] Jensen | Regulation of glucose and glycogen metabolism during and after exercise[END_REF] For bacterial DNA content, a one-way ANOVA followed by the LSD Fisher post-hoc test was used. To evaluate the reseeding process, bacterial and families abundance, as well α-diversity was compared in CTL and NAT groups using unpaired non parametric t-test. For -diversity, significance between CTL and ATB was checked using PERMANOVA, as implemented in the 'adonis' function from the R vegan package, with 9999 permutations. ***:p≤0.001 vs CTL, controls (no treatment); ATB, antibiotic treatment for 21 days; NAT, 10-days antibiotic treatment followed by natural reseeding for 11 days. Values are the mean ± SEM. Significance between the 3 groups was checked using a one-way ANOVA followed by

  experiments were approved by the Animal Experimentation Ethics Committee (APAFIS#2551-2015110311365663) in accordance with the recommendations of the Guide for the Care and Use of Laboratory Animals (NIH Publication No. 85-23, Revised 1996) and according to the European directives (86/609 / EEC).

Figure 1 .

 1 Figure 1. Effect of gut microbiota depletion and natural reseeding on bacterial DNA content, α-and  diversity indices, phyla and families abundance. Real-time qPCR quantification of all-bacteria in feces at D0 (A) and D7 (B) and in the caecum at D21 (C) (n=5). Bacterial α-diversity (D) and -diversity (E-F) in caecum at D21 (n=5); Sample denotation: red: CTL, blue: NAT. Bacterial phyla (G-H) and families (I-J) abundance in caecum at D21 (n=5). For bacterial DNA content, a one-way ANOVA followed by the LSD Fisher post-hoc test was used. To evaluate the reseeding process, bacterial and families abundance, as well α-diversity was compared in CTL and NAT groups using unpaired non parametric t-test. For -diversity, significance between CTL and ATB was checked using PERMANOVA, as implemented in the 'adonis' function from the R vegan package, with 9999 permutations. ***:p≤0.001 vs CTL, controls (no treatment); ATB, antibiotic treatment for 21 days; NAT, 10-days antibiotic treatment followed by natural reseeding for 11 days.

Figure 2 .

 2 Figure 2. Effects of gut microbiota depletion and natural reseeding on skeletal muscle structure. In CTL, ATB and/or NAT mice gastrocnemius, quadriceps, soleus and EDL (A) wet weight (B) weight relative to body weight at D21. (C) weight relative to body weight after subtraction of caecum weight at D21. (D) Quadriceps fiber CSA distribution at D21. (E) Representative images of quadriceps muscle sections at D21. (F) RT-qPCR analysis of Igf-1, Murf-1, Trif, Foxo-3a and Nf-κB expression in gastrocnemius muscle at D21. (G) Activation of PRAS40, 4EBP1, RPS6, LC3B in gastrocnemius muscle at D21. (H) Representative blotting images used for the quantification shown in (G).On the blot for RPS6 (G), a line was added to show an arrangement due to an empty well between the samples on the western blot gel. Values are the mean ± SEM. Significance between CTL, ATB and NAT was checked using a one-way ANOVA followed by the LSD Fisher post-hoc. Significance was checked using a one-way ANOVA followed by the LSD Fisher post-hoc test (A-B-C-F-G). The mean muscle fiber cross-sectional area was compared in CTL and NAT groups using unpaired t-test (D). *: p≤0.05; **: p≤0.01; ***: p≤0.001 (n=8-10 for each group).

Figure 3 .

 3 Figure 3. Effects of gut microbiota depletion and natural reseeding on skeletal muscle function. Maximal Aerobic Velocity (MAV) in the CTL (A) ATB (B) NAT groups (C) at D0, D7 and D17. Limit time to exhaustion during a submaximal running test in the CTL (D), ATB (E) and NAT groups (F) at D0, D9 and D19. (G) Ex vivo EDL maximal strength relative to its weight at D21. (H) Ex vivo EDL muscle fatigue index at D21. Values are the mean ± SEM. Significance was checked using the paired t-test (A-B-C-D-E-F) and a one-way ANOVA followed by the LSD Fischer post-hoc test (G-H). *: p≤0.05; ** vs ATB vs CTL and NAT; p≤0.01 ATB vs CTL and NAT: (n=9-10 for each group).

Figure 4 .

 4 Figure 4. Effects of gut microbiota depletion and natural reseeding on skeletal muscle metabolism. (A) Gastrocnemius MHC distribution at D21. (B) Representative images of protein electrophoresis shown in (A). (C) Cd36 and Cpt1 mRNA expression in gastrocnemius samples at D21. (D) Mitochondrial DNA content and Nrf-1 mRNA expression in gastrocnemius samples at D21. (E) AMPK phosphorylation, PGC-1α and COX IV protein content in gastrocnemius muscles at D21. (F) Representative blotting images used for the quantification shown in (E).Values are the mean ± SEM. Significance between groups was checked using a one-way ANOVA followed by the LSD Fisher post-hoc test, except for mt-DNA, a Mann-Whitney were used to compare CTL and ATB groups (n=8-10 for each group).

Figure 5 .

 5 Figure 5. Effects of gut microbiota depletion and natural reseeding on energetic substrates metabolism. (A) RT-qPCR expression of Fiaf, Myd88, Tlr4 and Lat1 in the ileum at D21 (n=8). (B) RT-qPCR expression of Gpr41, Gpr40, Gpr120 and Sglt1 in the ileum at D21 (n=8). (C) Gastrocnemius triglyceride content at D21 (n=9-10). (D) Gastrocnemius glycogen content at D21 (n=9-10).Values are the mean ± SEM. Significance between the 3 groups was checked using a one-way ANOVA followed by

Table 1 . List of primary antibodies used for Western Blotting

 1 . As reduction of glycogen content affects muscle fatigue in both in vivo and ex vivo conditions (51), the muscle glycogen depletion observed in ATB mice could be one of the key mechanisms to explain the muscle endurance reduction in these animals. Furthermore, the restoration of glycogen content to values close to CTL mice after natural reseeding reinforced this hypothesis. Interestingly, we demonstrated the same muscle glycogen levels reduction in Germ-Free mice another recognized model of gut microbiota depletion, in comparison with GF-

	reseeded mice (data not shown). All these findings finally suggest that the reduction of energetic
	substrate availability, especially glucose, due to intestinal microbiota disruption could induce a
	reduction of muscle glycogen storage to maintain glucose homeostasis, translating in skeletal
	muscle endurance impairment.
	To conclude, our results indicate for the first time that gut bacteria are critical for optimal
	muscle function in mice at least in part by altering glucose homeostasis regulation. How could
	we translate these finding in human? The presence of a gut-muscle axis in the pathogenesis of
	age-related sarcopenia in humans has been proposed recently based on very promising results
	(67). The interplay between microbiome and skeletal muscle has been highlighted by Siddhart
	and colleagues (64) who demonstrated that age-related changes of gut microbiome are associated
	with the physiological decline of musculoskeletal function. Future studies will be needed to
	identify the bacterial species and/or the underlying mechanisms and the putative metabolites that

contribute to the functional link between gut microbiota and skeletal muscle. Our work opens promising perspectives to develop new therapeutic strategies based on gut microbiota modulation for muscle-related diseases, muscle disuse and sport training.

TABLES

Table 2 . Gene expression in skeletal muscle and ileum-Sequences of primers (5'-3') Markers Gene Reference Forward Reverse Gene expression in skeletal Muscle Protein Turnover

 2

		Igf-1	XM_006513261.2	AGCAGCCTTCCAACTCAATTAT	GAAGACGACATGATGTGTATCTTTATC
		FoxO3a	XM_006512806.1	GGAAATGGGCAAAGCAGA	AAACGGATCACTGTCCACTTG
		Murf1 (Trim63)	NM_001039048.2	TCCTGCAGAGTGACCAAGG	GGCGTAGAGGGTGTCAAAC
	Inflammation	Trif (Ticam1) Nf-B	NM_174989.4 NM_008689.2	CAGCTCAAGACCCCTACAGC TGAGGACGGGGTATGCAC	CTCCCACACAGCCTCGTC TCACATGAAGTATTCCCAGGTTT
	Lipid transport	CD36	NM_001159557.1	CAGATCCGAACACAGCGTAG	GCGACATGATTAATGGCACA
	Mitochondrial	Cpt1	NM_009948.2	CATCCCAGGCAAAGAGACA	AAGCGACCTTTGTGGTAGACA
	metabolism	Nrf-1	NM_001164226	GGTGGGGGACAGATAGTAGTCT	ATGCTCACAGGGATCTGGAC
	Mitochondrial Content	ATP5b ND2 ND5	NC_000076 NC_005089.1 NC_005089.1	GTTTGCTGAAGCCACACTCA AAGGGATCCCACTGCACATA ATAACCGCATCGGAGACATC	CATGATTCTGCCCAAGGTCT AGTCCTCCTCATGCCCCTAT GAGGCCAAATTGTGCTGATT
			Gene expression in ileum
	Glucose and
	lipid	Fiaf (Angptl4)	NM_020581.2	GGGACCTTAACTGTGCCAAG	GAATGGCTACAGGTACCAAACC
	metabolism
	Inflammation	Myd88 Tlr4	NM_010851.2 NM_021297.3	GCCTTGTTAGACCGTGAGGAT GGACTCTGATCATGGCACTG	CTAAGTATTTCTGGCAGTCCTCCT CTGATCCATGCATTGGTAGGT
	Branched
	Amino Acids	Lat-1	NM_011404.3	ATGTGGCTCCGATTCAAGA	GGAGGGCCAGATTCACCT
	Receptor
	Short-Chain
	Fatty Acids	Gpr40 (Ffar1)	NM_194057.2	AGGCGCTCTCCTCACACTC	CTAGCCACATTGGAGGCATTA
	Receptor
	Mean-Chain
	Fatty Acids	Gpr41 (Ffar3)	NM_001168509.1	TGCTCTGAAGAAGCCAATCA	TTCTCCTCTGGTCCAGTGCT
	Receptor
	Long-Chain
	Fatty Acids	Gpr120 (Ffar4)	NM_181748.2	TTGGTGTTGAGCGTCGTG	CCAGCAGTGAGACGACAAAG
	Receptor
	Glucose transporter	Sglt1	NC_000071.6	CTGGCAGGCCGAAGTATG	TTCCAATGTTACTGGCAAAGAG
	Reference	Arp (Rplp0)	NM_007475.5	ACTGGTCTAGGACCCGAGAAG	TCCCACCTTGTCTCCAGTCT
	Gene	α-Tubulin	NM_011653.2	CTGGAACCCACGGTCATC	GTGGCCACGAGCATAGTTATT

Table 3 . Effects of antibiotic treatment and natural reseeding on body mass, glycemia, caecum liver and adipose tissue weights, as well food intake and hydration.

 3 Values are group mean at D21 for weights, and weekly for food intake and hydration ± SEM. Significance was checked using ANOVA followed by LSD Fisher post hoc test *: p<0.05; **: p≤0.01; ***: p<0.001. vs. CTL group; <0.01 and  p<0.001 vs. ATB group n=9-10 for each group.

Acknowledgements:

We are grateful to the Genotoul bioinformatics facility, Toulouse Midi-Pyrenees (BioinfoGenotoul), for providing help, computing and storage resources. We thank the animal staff from the METAMUS DMEM platform facility, which belongs to the "Montpellier animal facilities network" (RAM). We also acknowledge the MRI imaging facility, which is a part of the national bioimaging infrastructure supported by the French National Research Agency (ANR-10-INBS-04, Investments for the future).

Grants

: The work was supported by INRA, Brittany Council and partially supported by AlimH department grant. This work was also supported by the Centre National d'Etudes Spatiales (CNES).

the LSD Fisher post-hoc test *: p≤0.05 ATB vs CTL and NAT; **: p≤0.01 ATB vs CTL and NAT; ***: p≤0.001 ATB vs CTL and NAT.


Cássio F Dantas

Jérémy E Cohen

Rémi Gribonval

Tensor-structured Dictionaries for Hyperspectral Imaging

Dictionary learning, paired with sparse coding, aims at providing sparse data representations. When dealing with large datasets, the dictionary obtained by applying unstructured dictionary learning methods may be of considerable size, posing both memory and computational complexity issues. We show how a previously proposed structured dictionary learning model, HO-SuKro, can be used to obtain more compact and readily-applicable dictionaries when the targeted data is a collection of multiway arrays. We introduce an alternating optimization learning algorithm and apply it to a hyperspectral image denoising task.

I. PROBLEM STATEMENT

Let Y ∈ R m 1 ×m 2 ×m 3 ×n be a collection of n tensor data {Y1, . . . , Yn}. The Dictionary Learning problem [START_REF] Rubinstein | Dictionaries for sparse representation modeling[END_REF] is classically formulated for vector input data. Each Yi is thus vectorized, yielding

argmin D∈S D ,x i n i=1 vec(Yi) -Dxi 2 2 + g(xi) (1)
where D ∈ R m 1 m 2 m 3 ×d is the dictionary which is often overcomplete (d ≥ m1m2m3) and belongs to a constraint set SD. Function g is a sparsity-inducing penalty and xi is the sparse vector of coefficients describing the vectorized tensor Yi in the set of atoms D. Most often, SD is the set of matrices with unit 2-norm columns. When tensor data is considered, two main drawbacks emerge in this formulation: i) it ignores the original multidimensional structure of the data; ii) data sizes mj may be relatively large (even more so the product m1m2m3) and both the storage of matrix D and the computation of products such as Dxi may be cumbersome.

One way to tackle the second issue is to restrict the class SD of dictionaries that are sought in problem [START_REF] Rubinstein | Dictionaries for sparse representation modeling[END_REF]. To also tackle the first mentioned issue, we previously proposed the High-Order Sum of Kronecker model (HO-SuKro) [START_REF] Dantas | Learning fast dictionaries for sparse representations using low-rank tensor decompositions[END_REF], [START_REF] Dantas | Learning Dictionaries as a sum of Kronecker products[END_REF], a class of tensor-structured dictionaries which are particularly suited to tensorial input data:

D = r q=1 D1,q D2,q D3,q (2)
where is the Kronecker product [START_REF] Cohen | About notations in multiway array processing[END_REF], Dj,q are matrices in R m j ×d j and d1d2d3 = d. To provide some extra intuition, for a fixed q we can see the terms Dj,q as linear operators acting independently in the j-th mode of the input data Y.

An obvious remark about HO-SuKro is that the number of parameters to represent D using (2), which is r(m1d1 + m2d2 + m3d3), is much smaller than the number of entries m1m2m3d1d2d3 as long as r is small. Moreover, matrix products with the dictionary can be computed markedly faster.

II. PROPOSED ALGORITHM (A GLIMPSE)

As usually done in the literature, problem (1) is tackled by alternating between estimating only D and estimating only the coefficients xi: respectively the dictionary update and sparse coding steps.

The sparse coding problem remains formally unchanged. Therefore, one may apply the usual greedy heuristics such as Orthogonal Matching Pursuit (OMP) [START_REF] Pati | Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition[END_REF] or convex relaxations based algorithms such as FISTA [START_REF] Beck | A fast iterative shrinkage-thresholding algorithm for linear inverse problems[END_REF]. The Kronecker structure can be exploited to positively impact the complexity and running time of these methods. Indeed, any matrix-vector product with the dictionary becomes a sequence of mode products with the smaller matrices Dj,q which involves approximately r( j mj)( j dj) operations instead of ( j mjdj) for a unstructured matrix-vector product (cf. Table I).

Dictionary update, on the other hand, is heavily modified in the HO-SuKro formulation. The partial cost function, with respect to the blocks {Dj,q} j=1,...,3 q=1,...,r , may be written as follows:

f ({Dj,q}) = n i=1 vec(Yi) - r q=1 (D1,q D2,q D3,q) xi 2 2 (3)
In the spirit of Alternating Least Squares algorithms (ALS), it is possible to gather all elementary blocks Dj,q for a fixed mode j and alternate between three macro-blocks (one per mode) ∆j = {Dj,q} q∈[1,r] , 1 ≤ j ≤ 3, obtaining a closed-form solution. For instance, for j = 1 (and similarly for other modes)

∆1 = Y [1] U † , (4)
where

Y [1] ∈ R m 1 ×m 2 m 3 n is the first-mode unfolding [4] of Y, U = [U1; . . . ; Ur] ∈ R rd 1 ×m 2 m 3 n with Uq = X [1] (D2,q D3,q In) T and U † = U T U U T -1 is the right inverse of U .
III. EXPERIMENTS Given a hyperspectral image from San Diego and Houston [START_REF]2013 IEEE GRSS Data Fusion Contest[END_REF] datasets corrupted with random Gaussian noise uniform over all spectral modes, we consider n = 10 5 uniformly-spaced overlapping 3D-patches centralized to zero mean with dimensions {m1, m2, m3} from the noisy image to form our training data.

A dictionary is learned from this data with 20 iterations of alternating optimization. Sparse coding is performed by OMP with an error threshold proportional to the noise level. The learned dictionary is then used to reconstruct patches with a one-pixel step. The recovered patches are averaged in the overlapping pixels along with the noisy image itself to form the final denoised image.

Table II shows the denoising performance of the proposed structured dictionaries compared to K-SVD [START_REF] Aharon | Sparse and redundant modeling of image content using an image-signature-dictionary[END_REF] as an unstructured counterpart. Increasing the patch size improves significantly the performance of HO-SuKro, while that of K-SVD doesn't benefit as much and may even deteriorate, indicating the onset of overfitting.

Table III compares HO-SuKro's performance to that of other techniques from the literature. Both HO-SuKro and K-SVD outperform the wavelet-based approaches (2D and 3D [START_REF] Basuhail | Wavelet-based noise reduction in multispectral imagery[END_REF]), corroborating the interest of learning the sparsifying dictionary from data. HO-SuKro also consistently outperforms FORPDN [START_REF] Rasti | Hyperspectral image denoising using first order spectral roughness penalty in wavelet domain[END_REF] which exploits the correlation within spectral bands. Naturally, for this task, we don't manage to reach state-of-the-art performance (HyRes [START_REF] Rasti | Automatic hyperspectral image restoration using sparse and low-rank modeling[END_REF]) which makes use of a meaningful low-rank prior on the HSI. An example of denoised image is provided in Figure 1.

IV. CONCLUSION

An alternate minimization algorithm was proposed for learning tensor-structured dictionaries designed to tackle the inherent multidimensional structure of the data. The proposed structure proved to be beneficial in terms of performance in Hyperspectral image denoising experiments compared to an completely unstructured dictionary. A closer look reveals that our approach may over-smooth some details.

Fig. 1 :

 1 Fig.1: Example of denoised images (100 th spectral band). A closer look reveals that our approach may over-smooth some details.

TABLE I :

 I Speedups in matrix-vector products

	Dimensions	Theoretical speedup | Empirical speedup
	m	d	r = 1	r = 3	r = 5
	[ 6, 6, 6]	[12, 12, 12] 20.3	0.8	6.8	0.4	4.9	0.3
	[ 8, 8, 8]	[16, 16, 16] 36.6	4.5	12.2	2.0	7.3	1.4
	[10, 10, 10] [20, 20, 20] 57.1	13.2	19.1	5.7	11.4	3.5

TABLE II :

 II Output SNR for various patch sizes -San Diego

	Algorithm	Patch size		Input SNR
		m	d	10	15	20	25
		[ 6, 6, 6]	[12,12,12]	21.77 25.31 29.09 32.68
	K-SVD	[ 8, 8, 8]	[16,16,16]	21.51 25.19	29.2	32.95
		[10,10,10] [20,20,20] 21.52 25.34 29.42 33.24
		[ 6, 6,20]	[12,12,20]	22.49 26.06 29.91 33.21
		[ 6, 6, 6]	[12,12,12]	22.05 25.35	28.9	32.3
	HO-SuKro	[ 8, 8, 8]	[16,16,16]	22.73 25.82 29.22 32.64
	(r = 3)	[10,10,10] [20,20,20] 23.08 26.35 29.73	33.27
		[ 6, 6,20]	[12,12,20]	24.10 27.07 30.09	33.22

TABLE III :

 III Output SNR [dB] comparison with literature .00 21.70 25.92 Wavelet 3D 23.11 26.04 28.91 31.68 San Diego FORPDN 22.23 24.17 26.42 29.00 HyRes 25.38 28.60 31.75 34.70 HO-SuKro 24.10 27.07 30.09 33.22 Wavelet 2D 14.22 17.67 21.43 25.80 Wavelet 3D 22.35 25.54 28.65 31.86 Houston FORPDN 22.80 25.46 28.09 30.74 HyRes 26.00 29.35 33.24 37.05 HO-SuKro 23.29 26.63 29.93 33.20

	Image	Algorithm		Input SNR [dB]
			10	15	20	25
		Wavelet 2D	14.75 18