F B Favier
email: favier@supagro.inra.fr

F A Britto

D G Freyssenet

X A Bigard

• H Benoit

HIF-1-driven skeletal muscle adaptations to chronic hypoxia: molecular insights into muscle physiology

Keywords: Altitude, Atrophy, Hypoxia inducible factor, Metabolism, Mitochondria, Oxidative stress

Skeletal muscle is a metabolically active tissue and the major body protein reservoir. Drop in ambient oxygen pressure likely results in a decrease in muscle cells oxygenation, reactive oxygen species (ROS) overproduction and stabilization of the oxygen-sensitive hypoxia-inducible factor (HIF)-1a. However, skeletal muscle seems to be quite resistant to hypoxia compared to other organs, probably because it is accustomed to hypoxic episodes during physical exercise. Few studies have observed HIF-1a accumulation in skeletal muscle during ambient hypoxia probably because of its transient stabilization. Nevertheless, skeletal muscle presents adaptations to hypoxia that fit with HIF-1 activation, although the exact contribution of HIF-2, I kappa B kinase and activating transcription factors, all potentially activated by hypoxia, needs to be determined. Metabolic alterations result in the inhibition of fatty acid oxidation, while activation of anaerobic glycolysis is less evident. Hypoxia causes mitochondrial remodeling and enhanced mitophagy that ultimately lead to a decrease in ROS production, and this acclimatization in turn contributes to HIF-1a destabilization. Likewise, hypoxia has structural consequences with muscle fiber atrophy due to mTOR-dependent inhibition of protein synthesis and transient activation of proteolysis. The decrease in muscle fiber area improves oxygen diffusion into muscle cells, while inhibition of protein synthesis, an ATP-consuming process, and reduction in muscle mass decreases energy demand. Amino acids released from muscle cells may also have protective and metabolic effects. Collectively, these results demonstrate that skeletal muscle copes with the energetic challenge imposed by O 2 rarefaction via metabolic optimization.

Introduction

Skeletal muscle is the most voluminous tissue of the body as it represents almost 40 % of body weight and it accounts for a significant part (20-30 %) of basal metabolic rate [1]. Skeletal muscle is a heterogeneous tissue composed of fibers that have distinct contractile and metabolic properties. Type I fibers (also named slow oxidative) are mitochondria-rich cells with high myoglobin content and capillary density responsible for their red colour. Type IIX and IIB fibers (fast glycolytic) have generally larger crosssection area with higher glycolytic machinery and are less perfused, while type IIA (fast oxidative) exhibit an intermediary profile. More than 90 % of the energy produced by muscle cells comes from the aerobic pathway. A reduction in O 2 availability would therefore challenge skeletal muscle homeostasis. This situation will be exacerbated in case of physical exercise, as it will enhance ATP demand.

Reduced O 2 pressure (hypobaric hypoxia) and sustained exercise are experienced by alpinists and mountaineers, and skeletal muscle adaptations in these subjects have been studied for several decades. Pioneering works evidenced the negative effect of hypoxia exposure on skeletal muscle mass. However, hypoxia is not only restricted to mountaineers or high altitude residents, and could result from pathologies such as anemia, vascular abnormalities, heart failure, chronic obstructive pulmonary disease or sleep apnea. Since reduced muscle mass and/or altered metabolism may be associated with enhanced fatigability, sedentary lifestyle and ultimately increased risk of mortality, the fine understanding of molecular responses driven by skeletal muscle hypoxia is of particular interest for athletes, active people, as well as patients. This review attempts to depict the molecular mechanisms underlying skeletal muscle adaptations to chronic hypoxia (i.e. several days) in healthy subjects.

Defining hypoxia and O 2 sensing pathway Intramuscular O 2 pressure

The first question when dealing with hypoxia is to define what hypoxia means for the cells. Hypoxia literally means under/below oxygen that we could translate by ''less oxygen'' or even under oxygenation compared to physiological level. Hypoxic environment can be experimentally reproduced by decreasing the proportion of O 2 available in ambient air (normobaric hypoxia), therefore reducing the inspired O 2 fraction (FIO 2 ) from the normal value of 20.9 %. Another way is to decrease the barometric pressure leading to the reduction in O 2 availability while its proportion into the inspired air remains constant (hypobaric hypoxia). A correspondence between the common altitude levels used in publications, the FIO 2 , the ambient and inspired O 2 pressure is presented in Table 1. The definition of hypoxia raises the issue of a threshold in O 2 pressure (PO 2 ) that will place the cell in hypoxic condition. Data obtained from magnetic resonance spectroscopy experiments (human) [2, 3], via optical method (rat) [4], surface electrode (dog) [5] or microcatheter (human) [6] lead to resting intramuscular PO 2 of &27 mmHg in normoxic conditions. Few data exist on intramuscular PO 2 during hypoxia: Johnson et al. reported a value of &10 mmHg after 1 min of breathing 7 % O 2 (equivalent to 8300 m) in rat cremaster muscle [4], while Richardson's group found more than double (23 mmHg) in humans with an inspired O 2 fraction of 10 % (&5800 m) [2]. During exercise of even slight intensity (unweighted knee extension at 30 % of maximal leg O 2 uptake), PO 2 rapidly drop to &5 mmHg [3]. There are only subtle changes in intramuscular PO 2 between very light and heavy exercise as PO 2 decreases to 3 mmHg at 50 % of maximal leg O 2 uptake and remains constant until maximal work rate. During hypoxic trial (FIO 2 = 12 %), PO 2 still decreases and reaches &2 mmHg. More recently, Masschelein et al. showed that muscle oxygenation, assessed by near-infrared spectroscopy, was modestly but significantly reduced (&5 %) in subjects breathing 10.7 % O 2 [7]. In the same work, tissue oxygenation index was decreased just after a moderate intensity exercise performed in normoxia (&6 %) and this decrement was slightly enhanced in hypoxia (&9 %). Mitochondrion is the final destination of O 2 into muscle cells. In skeletal muscle fiber, the PO 2 at which mitochondrial metabolism becomes inhibited is about 1.25 mmHg [START_REF] Richmond | Oxygen sensitivity of mitochondrial metabolic state in isolated skeletal and cardiac myocytes[END_REF], that is far lower to what it could be encountered in hypoxic resting muscle. Altogether, it can be concluded that exercise per se induces significant reduction of muscle cell PO 2 and this diminution is worsened by hypoxic environment. Secondly, the effect of hypoxic exposure seems less potent than muscle work to decrease cellular oxygenation, although the knowledge on how hypoxia alters muscle PO 2 at rest is minimal. In tumors, it has been proposed that expression of hypoxia-regulated genes increases at PO 2 below 10-15 mmHg. Energy metabolism would be impaired at PO 2 less than 10-8 mmHg, and apoptosis would be stimulated at less than 1 mmHg [START_REF] Span | Biology of hypoxia[END_REF][START_REF] Ho ¨ckel | Tumor hypoxia: definitions and current clinical, biologic, and molecular aspects[END_REF]. Skeletal muscle is probably more resistant to low O 2 levels as ATP production is maintained during exercise and it is currently not possible to set a value that would mark the occurrence of cellular hypoxic state. One can only point that long term residency of humans seems to be critical beyond 5500 m above sea level, suggesting that whole body oxygenation becomes critical for chronic exposure at this altitude.

Hypoxia-inducible factor (HIF) activation

The best way to characterize muscle cell hypoxia is to look at the cellular response. Since the article of Wang and The reduction of PO 2 between ambient and inspired air is due to the saturation with water vapor in the upper airway Semenza in 1992 [START_REF] Semenza | A nuclear factor induced by hypoxia via de novo protein synthesis binds to the human erythropoietin gene enhancer at a site required for transcriptional activation[END_REF], Hypoxia inducible factor (HIF) 1 has been described as the master regulator of hypoxiamediated cellular adaptations. This a/b heterodimeric transcription factor regulates more than 100 genes involved in erythropoiesis/iron metabolism, angiogenesis, vascular tone, matrix metabolism, glucose metabolism, cell proliferation/survival or apoptosis [START_REF] Ke | Hypoxia-inducible factor-1 (HIF-1)[END_REF]. Accordingly, Hif1a ?/- heterozygous mice (total deletion is lethal [START_REF] Iyer | Cellular and developmental control of O 2 homeostasis by hypoxia-inducible factor 1 alpha[END_REF]) exhibit impaired physiological responses to chronic hypoxia, including alterations in erythropoiesis, pulmonary vascular remodeling and ventilatory adaptations [START_REF] Kline | Defective carotid body function and impaired ventilatory responses to chronic hypoxia in mice partially deficient for hypoxia-inducible factor 1 alpha[END_REF][START_REF] Yu | Impaired physiological responses to chronic hypoxia in mice partially deficient for hypoxia-inducible factor 1alpha[END_REF]. While HIF-1b (also known as ARNT) is constitutively expressed, HIF-1a protein is quickly degraded in normoxic conditions (half-life \1 min [START_REF] Yu | Temporal, spatial, and oxygen-regulated expression of hypoxia-inducible factor-1 in the lung[END_REF]). This degradation is mediated via hydroxylation of proline residues on HIF-1a by prolyl-hydroxylases (PHD) leading to its binding to the von Hippel-Lindau (pVHL) tumour suppressor, ubiquitinylation and subsequent degradation by the proteasome (Fig. 1). A similar mechanism involving asparagine residue hydroxylation by Factor Inhibiting HIF (FIH) silences HIF-1a transactivation domain through inhibition of the transcription coactivators (p300 and CBP) recruitment in normoxia [START_REF] Lando | Asparagine hydroxylation of the HIF transactivation domain a hypoxic switch[END_REF]. PHD-dependent regulation of HIF-1a implies the presence of O 2 and 2-oxoglutarate as substrates and Fe 2? as co-factor. Under reduced O 2 pressure, PHD are inhibited because of the lower O 2 availability, but also via the conversion of Fe 2? into Fe 3? due to mitochondrial reactive oxygen species (ROS) production from the complex III of the electron transport chain [START_REF] Chandel | Reactive oxygen species generated at mitochondrial complex III stabilize hypoxia-inducible factor-1alpha during hypoxia: a mechanism of O 2 sensing[END_REF]. Consistently, data from Chaudhary et al. [START_REF] Chaudhary | Chronic hypobaric hypoxia mediated skeletal muscle atrophy: role of ubiquitin-proteasome pathway and calpains[END_REF] show a strong relation between HIF-1a protein content and free radical generation in hypoxic rat muscle (Fig. 2). Inhibition of PHD results both in the stabilization and the dimerization of HIF-1a with the b subunit. Accordingly, hypoxia can be mimicked by iron chelation (e.g. deferoxamine), some transition metals (e.g. cobalt) or 2-oxoglutarate inhibitors (e.g. DMOG), and this property has been widely used to hypoxia preconditioning. While HIF-1a is subjected to other posttranslationnal regulations such as acetylations, phosphorylations or nitrosylations (reviewed in [START_REF] Wei | Hypoxia-inducible factors: crosstalk between their protein stability and protein degradation[END_REF]), inhibition of hydroxylation is the main regulation involved in hypoxiainduced HIF-1a stabilization.

A specificity of muscle cells could reside in HIF-1a nuclear translocation. Inhibition of HIF-1a degradation by CoCl 2 is sufficient to cause its nuclear accumulation in COS-7 cells, whereas this translocation requires low oxygen levels in primary myotubes. The nuclear import of HIF-1a means an ambiant PO 2 of 159 mmHg that is far greater to that of capillaries) and the reduction in O 2 availability is often drastic (1 % O 2 in ambient air equal a PO 2 of 7.6 mmHg and probably less into the cells). Cell line (e.g. cancer vs. non cancer cells) is also of particular importance since it influences O 2 availability into the medium. Some cell lines are thus hypoxic at 20.9 % O 2 because of high cell density and metabolic rate [START_REF] Metzen | Pericellular PO 2 and O 2 consumption in monolayer cell cultures[END_REF]. This may explain why hypoxia exposure results in a modest increase in HIF-1a protein expression in L6 rat myoblasts (0.5 % O 2 ) or primary rabbit myotubes (3 % O 2 ) [START_REF] Kubis | Accumulation and nuclear import of HIF1 alpha during high and low oxygen concentration in skeletal muscle cells in primary culture[END_REF][START_REF] Nimker | Ethyl 3,4-dihydroxy benzoate, a unique preconditioning agent for alleviating hypoxia-mediated oxidative damage in L6 myoblasts cells[END_REF]. Another major limitation is the short half-life of HIF-1a that would theoretically impact (decrease) its protein content during tissue removal or cell harvest since they are generally performed under normoxic conditions. Recent advances have been made on this issue by using live cell imaging under hypoxia. For example, Bagnall et al. demonstrated that HIF-1a protein is only transiently stabilized (3 h pulses) in HeLa cells exposed to 1 % O 2 [START_REF] Bagnall | Tight control of hypoxia-inducible factor-a transient dynamics is essential for cell survival in hypoxia[END_REF]. The authors showed that the short stabilization of HIF-1a is due to the up-regulation of PHD2 (while HIF-2a seems rather regulated by PHD1 [START_REF] Aragone ´s | Deficiency or inhibition of oxygen sensor Phd1 induces hypoxia tolerance by reprogramming basal metabolism[END_REF]). When HIF-1a protein expression is prolonged over this time lapse, cell engaged into a p53-related apoptosis program, although whether the same is true for muscle cells remains to be determined. It would be thus interesting to determine whether or not muscle PHD2 content increases during chronic hypoxia. This mechanism is likely because endurance trained subjects, whose muscles are submitted to intense hypoxic episodes during contractions, have increased PHD2 and FIH protein content in their vastus lateralis muscle [START_REF] Lindholm | Negative regulation of HIF in skeletal muscle of elite endurance athletes: a tentative mechanism promoting oxidative metabolism[END_REF]. Cigarette smoke exposure also increases PHD2 and pVHL protein expression in mouse skeletal muscle, concomitantly with reduced HIF-1a content [START_REF] Basic | Exposure to cigarette smoke induces overexpression of von Hippel-Lindau tumor suppressor in mouse skeletal muscle[END_REF]. One may suppose that muscle HIF-1a expression will return to basal level within a few hours even if the hypoxic environment persists as it has been observed in brain, liver and kidney [START_REF] Stroka | HIF-1 is expressed in normoxic tissue and displays an organ-specific regulation under systemic hypoxia[END_REF]. Cell culture experiments support this assumption, since HIF-1a protein peaked between 4 and 24 h of exposure to hypoxia (1-2 % O 2 ) before returning to modest or undetectable levels in human myoblasts [START_REF] Pirkmajer | HIF-1alpha response to hypoxia is functionally separated from the glucocorticoid stress response in the in vitro regenerating human skeletal muscle[END_REF] and human induced pluripotent stem cells [START_REF] Badger | Hypoxic culture of human pluripotent stem cell lines is permissible using mouse embryonic fibroblasts[END_REF]. This could explain why gastrocnemius HIF-1a level was not increased in erytropoietin-deficient mice with an hematocrit of 30 % or in wild-type animals after 24 h or 14 days at 4500 m [START_REF] Hagstro ¨m | Epo is relevant neither for microvascular formation nor for the new formation and maintenance of mice skeletal muscle fibres in both normoxia and hypoxia[END_REF]. Skeletal muscle may also be low responder to reduced O 2 delivery, as HIF luciferase reporter activity did not increase after acute anemia in skeletal muscle contrary to other organs such as brain, kidney or liver [START_REF] Tsui | Differential HIF and NOS responses to acute anemia: defining organ-specific hemoglobin thresholds for tissue hypoxia[END_REF] and skeletal muscle deoxygenation was half the size of brain in subjects exposed to 12 % O 2 for 4 h [START_REF] Rupp | Tissue deoxygenation kinetics induced by prolonged hypoxic exposure in healthy humans at rest[END_REF]. A last point that affects data about HIF-1a protein expression is the cellular compartment used for western blot analysis. While HIF-1a in muscle cells is concomitant with its dissociation from HSP90, a protein that has been proposed to mask the nuclear localization signal of HIF-1a under normoxia [START_REF] Kubis | Accumulation and nuclear import of HIF1 alpha during high and low oxygen concentration in skeletal muscle cells in primary culture[END_REF]. Nuclear accumulation of pVHL has been observed in C2C12 myotubes exposed to 1 % O 2 and this translocation promotes HIF-1a stabilization and transcriptional activity in 117 and 786-0 cells [START_REF] Mekhail | HIF activation by pH-dependent nucleolar sequestration of VHL[END_REF]. This mechanism was not induced by the decrease in PO 2 per se, but rather results from the acidosis due to the enhancement in anaerobic glycolysis. This is of particular interest as skeletal muscle can experience metabolic acidosis during intense exercise. It should be noted that HIF-1a can also be activated by growth factors or cytokines such as angiotensin II, insulin, Insulin-like growth factor (IGF), interleukin-1 or transforming growth factor a under normoxic conditions (reviewed in [START_REF] Ke | Hypoxia-inducible factor-1 (HIF-1)[END_REF]). Intensive researches are engaged to decipher the cross-talk between HIF-1 and inflammation notably in the fields of cancer, obesity and metabolic disorders. Some works showed normoxic HIF-1a activation through a Tumor Necrosis Factor-a/Nuclear Factor -kappa B axis [START_REF] Van Uden | Regulation of hypoxia-inducible factor-1alpha by NF-kappaB[END_REF], although the few data available in muscle cells do not support such a regulation [START_REF] Basic | TNF stimulation induces VHL overexpression and impairs angiogenic potential in skeletal muscle myocytes[END_REF]. As during hypoxia, ROS seem to play a key role for normoxic HIF-1a activation [START_REF] Ke | Hypoxia-inducible factor-1 (HIF-1)[END_REF].

The HIF family also comprises HIF-2 and HIF-3. HIF-2a protein is subjected to similar regulation by hypoxia than HIF-1a and it is implicated in hypoxic response as it may confer muscle resistance to ischemia [START_REF] Aragone ´s | Deficiency or inhibition of oxygen sensor Phd1 induces hypoxia tolerance by reprogramming basal metabolism[END_REF]. Yet, muscle HIF-2a protein accumulation is low 6 h after ischemia and undetectable after endurance exercise [START_REF] Aragone ´s | Deficiency or inhibition of oxygen sensor Phd1 induces hypoxia tolerance by reprogramming basal metabolism[END_REF][START_REF] Ameln | Physiological activation of hypoxia inducible factor-1 in human skeletal muscle[END_REF]. Moreover, it seems to have opposite effects on muscle phenotype compared to hypoxia and HIF-1a activity (cf. below and [START_REF] Rasbach | PGC-1alpha regulates a HIF2alpha-dependent switch in skeletal muscle fiber types[END_REF]). Very few data exist on HIF-3 function and there are no studies in skeletal muscle. It has been shown that HIF-3a alternative splicing triggers it transcriptional activity on Hypoxia Response Elements [START_REF] Zhang | Hypoxia-inducible factor 3 is an oxygen-dependent transcription activator and regulates a distinct transcriptional response to hypoxia[END_REF] and one splice variant can bind and inhibit HIF-1a activity [START_REF] Makino | Inhibitory PAS domain protein (IPAS) is a hypoxia-inducible splicing variant of the hypoxia-inducible factor-3alpha locus[END_REF]. Collectively, these results suggest that skeletal muscle adaptations consecutive to hypoxic exposure are mainly driven by HIF-1, though others transcription factors could be also activated during hypoxia and thus contribute to the whole adaptative response [START_REF] Cummins | Hypoxia-responsive transcription factors[END_REF]. Microarray on wild-type and HIF-1a knockout mouse embryonic fibroblasts (MEF) supports this hypothesis, since 89 % of the genes induced after exposure to 1 % O 2 were regulated by HIF-1 [START_REF] Greijer | Upregulation of gene expression by hypoxia is mediated predominantly by hypoxia-inducible factor 1 (HIF-1)[END_REF].

Hypoxic stabilization of HIF-1a in skeletal muscle: myth or reality?

The characterization of HIF-1 response to hypoxia in vivo is limited because of technical outcomes. Extrapolation of results obtained from cultured cells to whole body is subjected to caution. Cell culture experiments use extreme conditions, as control cells could be hyperoxic (20.9 % O 2 protein is usually undetectable in total muscle lysate, the nuclear fraction contains high amounts of HIF-1a under normoxia [START_REF] Lunde | Hypoxia inducible factor 1 links fast-patterned muscle activity and fast muscle phenotype in rats[END_REF], notably compared to others tissues [START_REF] Stroka | HIF-1 is expressed in normoxic tissue and displays an organ-specific regulation under systemic hypoxia[END_REF]. Isolating the nuclear fraction would thus be helpful to characterize HIF-1a protein response to reduced O 2 availability.

In summary, hypoxia may be defined as a condition of low O 2 pressure sufficient to promote HIF-1a accumulation in the cells. A key signal for stabilizing HIF-1a is the increase in ROS production, even more than the decrease in O 2 pressure per se. Marked increase in HIF-1a protein content has been observed in skeletal muscle during endurance exercise and/or blood restriction [START_REF] Ameln | Physiological activation of hypoxia inducible factor-1 in human skeletal muscle[END_REF]. However, the stabilization of HIF-1a after systemic hypoxia (e.g. altitude exposure) has not been systematically reported [START_REF] Hagstro ¨m | Epo is relevant neither for microvascular formation nor for the new formation and maintenance of mice skeletal muscle fibres in both normoxia and hypoxia[END_REF][START_REF] Vigano | Proteins modulation in human skeletal muscle in the early phase of adaptation to hypobaric hypoxia[END_REF] and seems rather modest (reviewed in [START_REF] Lundby | The response of human skeletal muscle tissue to hypoxia[END_REF]), except for severe hypoxia: FIO 2 of 6 % [START_REF] Stroka | HIF-1 is expressed in normoxic tissue and displays an organ-specific regulation under systemic hypoxia[END_REF] or simulated altitude of 5800 m [START_REF] Palma | Metabolic modulation induced by chronic hypoxia in rats using a comparative proteomic analysis of skeletal muscle tissue[END_REF] and 7620 m [START_REF] Chaudhary | Chronic hypobaric hypoxia mediated skeletal muscle atrophy: role of ubiquitin-proteasome pathway and calpains[END_REF]. Skeletal muscle HIF-1a accumulation likely reflects severe impairment of whole body oxygenation and it would be of clinical interest to measure HIF-1a accumulation in skeletal muscle of patients suffering from pathologies associated with hypoxemia (reduction in arterial O 2 ) or decreased blood flow. Another explanation for the lack of muscle HIF-1a accumulation under hypoxia is the transient nature of its stabilization. This raises an intriguing issue: how such a short up-regulation could have so durable consequences on muscle phenotype?

Skeletal muscle metabolic adaptations in response to chronic hypoxia

Pioneering work from Reynafarje in 1962 reported an increase in myoblogin content and higher cytochrome c reductase activity in skeletal muscle of highlanders, suggesting that prolonged hypoxia resulted in an enhancement of skeletal muscle oxidative capacity. However, further works that studied the effect of hypoxia independently from other factors, such as cold or exercise, showed that hypoxia per se promoted oxidative-to-glycolytic metabolic shift (see Table 2). Accordingly, expression of HIF-1a is higher in glycolytic vs. oxidative muscles [START_REF] Pisani | Skeletal muscle HIF-1alpha expression is dependent on muscle fiber type[END_REF] and subjects carrying a mutation that leads to increased HIF-1a stability have higher distribution of type II fibers [START_REF] Ahmetov | Effect of HIF1A gene polymorphism on human muscle performance[END_REF]. This effect is related to the role of HIF-1 on muscle metabolism through several coordinated mechanisms.

Hypoxia-mediated regulation of metabolic pathways

HIF-1 up-regulates the expression of 11 glycolytic enzymes (aldolase A, aldolase C, enolase 1, glyceraldehyde-3-phosphate dehydrogenase, hexokinase 1, hexokinase 2, lactate dehydrogenase A, phosphofructokinase L, phosphoglycerate kinase 1, pyruvate kinase M, and triosephosphate isomerase) contributing to enhance the glycolytic capacity of cells [START_REF] Semenza | HIF-1, O(2), and the 3 PHDs: how animal cells signal hypoxia to the nucleus[END_REF]. Although these targets have often been identified in nonmuscle cells, significant up-regulation of lactate dehydrogenase and hexokinase activity has been observed in skeletal muscle after hypoxia exposure (Table 2). Further analysis of the literature reveals that most activities of muscle glycolytic enzymes remain unchanged by hypoxia as recently reviewed [START_REF] Horscroft | Skeletal muscle energy metabolism in environmental hypoxia: climbing towards consensus[END_REF]. Given that the glycolytic machinery can support strong increase in glycolysis at exercise in normoxia, one may suppose that there is no need to further upgrade the maximal capacity of this system under hypoxia (at least at rest). Muscle glycolytic capacity (assessed by lactate production under anoxia) was not enhanced after 1, 16 or 90 days at 5500 m [START_REF] Ou | Effects of exposure to a simulated altitude of 5500 m on energy metabolic pathways in rats[END_REF], confirming the marginal effect of chronic hypoxia on the anaerobic pathway in skeletal muscles of sedentary rats.

Besides, HIF-1 inhibits oxidative metabolism by restricting the entry of pyruvate into the tricarboxylic acid cycle [START_REF] Kim | HIF-1mediated expression of pyruvate dehydrogenase kinase: a metabolic switch required for cellular adaptation to hypoxia[END_REF], through the induction of the pyruvate dehydrogenase kinase (PDK) 1. PDK1 phosphorylates and inactivates the pyruvate dehydrogenase enzyme complex that converts pyruvate to acetyl-coenzyme A in the mitochondria. In muscle cells, PDK1 up-regulation has been reported in rats exposed to 10 % O 2 for 2 weeks [START_REF] Palma | Metabolic modulation induced by chronic hypoxia in rats using a comparative proteomic analysis of skeletal muscle tissue[END_REF] and in human satellite cells treated with PHD inhibitor [START_REF] Lindholm | Negative regulation of HIF in skeletal muscle of elite endurance athletes: a tentative mechanism promoting oxidative metabolism[END_REF], but not in humans after 7-9 days at 4560 m [START_REF] Vigano | Proteins modulation in human skeletal muscle in the early phase of adaptation to hypobaric hypoxia[END_REF]. This could be related to the kinetics of gene expression since 24 h of exposure to 4300 m was associated with increased PDK1 protein content while it returned to basal level after 1 week [START_REF] Moine | Changes in HIF-1a protein, pyruvate dehydrogenase phosphorylation, and activity with exercise in acute and chronic hypoxia[END_REF].

As a consequence of these regulations, muscle lactate production would be increased by hypoxia exposure. Yet, lactate concentration and lactate-to-pyruvate ratio were not elevated in the vastus lateralis of subjects exposed for either 4 h or 3 weeks at 4300 m [START_REF] Brooks | Poor relationship between arterial [lactate] and leg net release during exercise at 4300 m altitude[END_REF][START_REF] Green | Altitude acclimatization and energy metabolic adaptations in skeletal muscle during exercise[END_REF], while lactate accumulation was increased in the media of C2C12 myotubes 96 h after treatment with PHD inhibitor [START_REF] Lindholm | Negative regulation of HIF in skeletal muscle of elite endurance athletes: a tentative mechanism promoting oxidative metabolism[END_REF]. Skeletal muscle lactate efflux is notably mediated by MCT4, a monocarboxylate transporter that is upregulated during in vitro hypoxia in a HIF-1-dependent manner [START_REF] Ullah | The plasma membrane lactate transporter MCT4, but not MCT1, is up-regulated by hypoxia through a HIF-1alpha-dependent mechanism[END_REF]. However, in vivo studies provided equivocal data with no change, increase or decrease in MCT4 expression [START_REF] Juel | Human skeletal muscle and erythrocyte proteins involved in acid-base homeostasis: adaptations to chronic hypoxia[END_REF][START_REF] Mcclelland | Changes in MCT 1, MCT 4, and LDH expression are tissue specific in rats after long-term hypobaric hypoxia[END_REF][START_REF] Py | Role of hypoxiainduced anorexia and right ventricular hypertrophy on lactate transport and MCT expression in rat muscle[END_REF].

Although extensively studied at exercise, regulation of lactate metabolism under reduced O 2 availability is not yet fully elucidated.

HIF-1 also triggers oxidative metabolism by impairing fatty acid oxidation and mice lacking skeletal muscle HIF-1a display increased lipid oxidation [START_REF] Mason | HIF-1alpha in endurance training: suppression of oxidative metabolism[END_REF]. HIF-1 reduces the DNA binding activity of peroxisome proliferator-activated receptor a (PPARa)/retinoid X receptor complex, a major regulator of lipid oxidation [START_REF] Belanger | Hypoxia-inducible factor 1 mediates hypoxia-induced cardiomyocyte lipid accumulation by reducing the DNA binding activity of peroxisome proliferator-activated receptor alpha/retinoid X receptor[END_REF][START_REF] Huss | Hypoxia inhibits the peroxisome proliferator-activated receptor alpha/retinoid X receptor gene regulatory pathway in cardiac myocytes: a mechanism for O 2 -dependent modulation of mitochondrial fatty acid oxidation[END_REF][START_REF] Regnault | Peroxisome proliferator-activated receptor -b/d, -c agonists and resveratrol modulate hypoxia induced changes in nuclear receptor activators of muscle oxidative metabolism[END_REF]. Hypoxia also inhibits the PPARc coactivator 1a (PGC-1a) pathway in a HIF-1-dependent way in C2C12 myotubes [START_REF] Slot | Hypoxia differentially regulates muscle oxidative fiber type and metabolism in a HIF-1a-dependent manner[END_REF]. Along with the reduction in the transcriptional activity of the expression (e.g. protein vs. mRNA levels [START_REF] Chaillou | Effect of hypoxia exposure on the phenotypic adaptation in remodelling skeletal muscle submitted to functional overload[END_REF]). Since PPARa and PGC-1a are major regulators of fatty acid metabolism, hypoxia leads to a decrease in mitochondrial PPAR/PGC-1a complex, hypoxia can also result in a decrease in PPARa and PGC-1a protein content [START_REF] Regnault | Peroxisome proliferator-activated receptor -b/d, -c agonists and resveratrol modulate hypoxia induced changes in nuclear receptor activators of muscle oxidative metabolism[END_REF][START_REF] Chaillou | Effect of hypoxia exposure on the phenotypic adaptation in remodelling skeletal muscle submitted to functional overload[END_REF], although there are some discrepancies regarding PGC-1a import and b-oxidation of fatty acids. This is notably illustrated by a decrease in carnitine palmitoyl transferase and hydroxyacyl-coenzyme A dehydrogenase activity that has frequently been reported (Table 2). The overall effect of hypoxia logically resulted in a marked reduction of fatty acid oxidation after 1 week in hypoxic environment [START_REF] Dutta | Impairment of mitochondrial beta-oxidation in rats under cold-hypoxic environment[END_REF][START_REF] Morash | Tissue-specific changes in fatty acid oxidation in hypoxic heart and skeletal muscle[END_REF].

Mitochondrial remodelling and regulation of ROS production

Mountaineers which participated to expeditions in the Himalayas (Lhotse or Everest) presented diminished mitochondrial content [START_REF] Hoppeler | Morphological adaptations of human skeletal muscle to chronic hypoxia[END_REF], with subsarcolemmal mitochondria being more affected than the intermyofibrillar subpopulation [START_REF] Levett | Acclimatization of skeletal muscle mitochondria to high-altitude hypoxia during an ascent of Everest[END_REF]. People living permanently at high altitude (Tibetans and Quechuans) have also reduced mitochondrial content in skeletal muscle suggesting that this phenotype is conserved with long term adaptation [START_REF] Hoppeler | Muscle tissue adaptations to hypoxia[END_REF]. Cellular models demonstrated that hypoxic exposure causes mitochondrial autophagy in an HIF-1-dependent way [START_REF] Zhang | Mitochondrial autophagy is an HIF-1-dependent adaptive metabolic response to hypoxia[END_REF]. Autophagy is a process involving the formation of autophagosomes and this mechanism is initiated by the dissociation of the Beclin1/Bcl-2 complex. HIF-1 mediates the increase in BNIP3 expression during hypoxia exposure in skeletal muscle [START_REF] Band | Hypoxia-induced BNIP3 expression and mitophagy: in vivo comparison of the rat and the hypoxia-tolerant mole rat, Spalax ehrenbergi[END_REF][START_REF] Gamboa | Chronic hypoxia increases insulin-stimulated glucose uptake in mouse soleus muscle[END_REF][START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]. BNIP3 competes with Beclin1 for binding to Bcl-2 leading to the release of Beclin1 [START_REF] Bellot | Hypoxiainduced autophagy is mediated through hypoxia-inducible factor induction of BNIP3 and BNIP3L via their BH3 domains[END_REF], thus promoting the initiation of autophagy and mitophagy.

This process could also be initiated by activation of the metabolic sensor Sirt1, whose expression is increased during hypoxia in a HIF-dependent manner in Hep3B or HT1080 cells [START_REF] Chen | Hypoxia increases sirtuin 1 expression in a hypoxia-inducible factor-dependent manner[END_REF]. Activation of mitochondrial autophagy through a Sirt1/BNIP3 pathway attenuated hypoxia-associated renal damage [START_REF] Kume | Calorie restriction enhances cell adaptation to hypoxia through Sirt1-dependent mitochondrial autophagy in mouse aged kidney[END_REF]. This suggests that the removal of altered mitochondria is required to limit oxidative damages. A recent study showed that the mitochondrial ubiquitin ligase 1 (Mul1) targeted the mitochondrial fusion protein mitofusin-2 resulting in mitophagy during muscle wasting [START_REF] Lokireddy | The ubiquitin ligase Mul1 induces mitophagy in skeletal muscle in response to muscle-wasting stimuli[END_REF]. Whether or not Mul1 expression is increased during hypoxia remains however to be elucidated. Taken together, all these mechanisms reduce the metabolic contribution of mitochondria and increase the involvement of the glycolytic pathway to energy supply (Fig. 3). In agreement, skeletal muscle specific deletion of HIF-1a results in an increase in oxidative capacity and mitochondrial density, a reduction in serum lactate concentration and enhanced performances during endurance exercise measured by the capillary density, is substantially and consistently increased in skeletal muscles of both humans and rats after exposure to hypobaric hypoxia of long duration [START_REF] Bigard | Effects of chronic hypoxia and endurance training on muscle capillarity in rats[END_REF][START_REF] Green | Operation Everest II: adaptations in human skeletal muscle[END_REF][START_REF] Snyder | Adaptations in skeletal muscle capillarity following changes in oxygen supply and changes in oxygen demands[END_REF]. An increase in muscle capillarity could be explained by the transcription of the Vascular Endothelial Growth Factor (VEGF) by HIF-1a. VEGF has even been characterized as ''the'' gene inducible by hypoxia and/or HIF-1a. Overexpression of both HIF-1a and HIF-2a promotes angiogenesis in mouse heart and rabbit ischemic skeletal muscle [START_REF] Niemi | HIF-1a and HIF-2a induce angiogenesis and improve muscle energy recovery[END_REF]. However, accumulating evidence suggest that VEGF mRNA is not systematically elevated throughout the exposition to hypoxia and may be even decreased after chronic exposure [START_REF] Olfert | Skeletal muscle capillarity and angiogenic mRNA levels after exercise training in normoxia and chronic hypoxia[END_REF]. No study evidenced an increase in the number of capillaries per fiber in sedentary muscles e.g. [START_REF] Hoppeler | Morphological adaptations of human skeletal muscle to chronic hypoxia[END_REF][START_REF] Bigard | Effects of chronic hypoxia and endurance training on muscle capillarity in rats[END_REF][START_REF] Green | Operation Everest II: adaptations in human skeletal muscle[END_REF][START_REF] Snyder | Adaptations in skeletal muscle capillarity following changes in oxygen supply and changes in oxygen demands[END_REF][START_REF] Olfert | Skeletal muscle capillarity and angiogenic mRNA levels after exercise training in normoxia and chronic hypoxia[END_REF][START_REF] Lundby | Acclimatization to 4100 m does not change capillary density or mRNA expression of potential angiogenesis regulatory factors in human skeletal muscle[END_REF][START_REF] Macdougall | Operation Everest II: structural adaptations in skeletal muscle in response to extreme simulated altitude[END_REF][START_REF] Sillau | Chronic hypoxia does not affect guinea pig skeletal muscle capillarity[END_REF] and it is now admitted that ambient hypoxia per se does not promote capillary neoformation [START_REF] Lundby | The response of human skeletal muscle tissue to hypoxia[END_REF][START_REF] Hoppeler | Response of skeletal muscle mitochondria to hypoxia[END_REF]. The reason of the potential higher capillary density resides in the reduction of the fiber crosssectional area, as hypoxia may cause skeletal muscle atrophy, resulting in an enhanced capacity for oxygen diffusion.

Regulation of muscle mass

Structural modifications

The negative effect of altitude on muscle mass has been objectivized since the 80's. While this negative influence was thought to be primarily related to cold exposure, high energy expenditure and especially hypophagia [START_REF] Kayser | Fatigue and exhaustion in chronic hypobaric hypoxia: influence of exercising muscle mass[END_REF], we and others have demonstrated that hypoxia per se accounts for skeletal muscle atrophy [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]100,101]. Although numerous differences exist between studies (altitude level, normobaric vs. hypobaric hypoxia, exposure duration, age of animals and acclimatization duration), analysis of published data clearly shows a significant positive correlation between hypoxia severity and the level of muscle atrophy in rats (Fig. 4a). Of note, muscle atrophy occurs at altitude higher than 5000-5500 m. One may suppose that oxidative muscles would be more affected by hypoxia as they are highly dependent from O 2 delivery, although glycolytic ones are generally more sensitive to atrophy [102-104].

Based on the Fig. 4a, it is however not clear whether muscle typology impacts susceptibility to hypoxia (see also [105]). Analysis of changes in the mean fiber cross-sectional area confirms the worsening of muscle atrophy under severe hypoxia (Fig. 4b). Type II fibers appear to be greatly affected by hypoxia, as recently suggested [106], although this assumption is dampened by the heterogeneity of data. A greater susceptibility of type II fibers to hypoxia may be explained by an already low O 2 diffusion capacity resulting from high cross sectional area and poor capilarization.

formation, and excessive ROS production represents a risk of oxidative damage that could lead to cell death if not corrected. Hypoxia exposure therefore results in cellular adaptations to counteract oxidative stress-induced damages. The importance of regulating ROS production under hypoxia was evidenced by the use of HIF-1a deficient MEFs. These cells died after 72 h in hypoxic environment due to a dramatic increase in ROS levels contrary to control cells that reduced H 2 O 2 production [START_REF] Kim | HIF-1mediated expression of pyruvate dehydrogenase kinase: a metabolic switch required for cellular adaptation to hypoxia[END_REF]. At the mitochondrial level, O 2 is used by the cytochrome c oxidase (COX) complex. HIF-1 has been shown to up-regulate the expression of both COX4-2 subunit and LON, a mitochondrial protease targeting COX4-1 in cultured cells [START_REF] Fukuda | HIF-1 regulates cytochrome oxidase subunits to optimize efficiency of respiration in hypoxic cells[END_REF]. This switch from COX4-1 to COX4-2 leads to the improvement in the electron transfer and thus reduction in O 2 2 production. Increased UCP3 expression has also been reported after hypoxia exposure [START_REF] Bo | Endurance training attenuates the bioenergetics alterations of rat skeletal muscle mitochondria submitted to acute hypoxia: role of ROS and UCP3[END_REF][START_REF] Lu | ATF-1 is a hypoxia-responsive transcriptional activator of skeletal muscle mitochondrialuncoupling protein 3[END_REF], and this also contributes to impair ROS production. The miRNA miR-210 is a direct target of HIF-1 and its deletion enhances ROS production and decreases survival upon H 2 O 2 treatment of C2C12 myotubes [START_REF] Cicchillitti | Hypoxia-inducible factor 1-a induces miR-210 in normoxic differentiating myoblasts[END_REF]. These adaptations together with the degradation of damaged mitochondria by autophagy would thus decrease ROS production. As ROS are involved in HIF-1a stabilization (see above), this reduction would suppress HIF-1a accumulation consistently with its transient up-regulation observed in vitro [START_REF] Bagnall | Tight control of hypoxia-inducible factor-a transient dynamics is essential for cell survival in hypoxia[END_REF]. Muscle proteome of highlanders is characterized by reinforced protection against ROS compared to control subjects permanently residing at low altitude [START_REF] Gelfi | New aspects of altitude adaptation in Tibetans: a proteomic approach[END_REF], and hypoxia preconditioning by CoCl 2 in rats reduced exercise-induced skeletal muscle oxidative damages [START_REF] Saxena | Hypoxia preconditioning by cobalt chloride enhances endurance performance and protects skeletal muscles from exercise-induced oxidative damage in rats[END_REF]. Altogether, this confirms that regulation of redox status under reduced O 2 availability is of key importance.

Mitochondrial function is depreciated in rodents exposed to simulated altitude, even when O 2 consumption was normalized to mitochondrial protein content [START_REF] Galbe `s O | Combined effects of hypoxia and endurance training on lipid metabolism in rat skeletal muscle[END_REF][START_REF] Gamboa | Muscle endurance and mitochondrial function after chronic normobaric hypoxia: contrast of respiratory and limb muscles[END_REF][START_REF] Magalha ˜es | Acute and severe hypobaric hypoxia increases oxidative stress and impairs mitochondrial function in mouse skeletal muscle[END_REF]. Unexpectedly, mitochondrial respiration was only modestly altered in humans exposed to 4550 m with slight reduction in maximal oxidative phosphorylation capacity [START_REF] Jacobs | Mitochondrial function in human skeletal muscle following highaltitude exposure[END_REF]. This result is all the more surprising in that O 2 consumption was expressed per mg of muscle, which therefore does not take into account the potential decrease in mitochondrial density. Another difference between this latter study and the formers is that it was performed on permeabilized fibers and not on isolated mitochondria. Since this in situ approach appears to be more relevant from a physiological view, it would be interesting to confirm this result.

Skeletal muscle vascularization

Oxidative metabolism of muscle cells is tightly related to blood perfusion and muscular capillarity. Capillarization, as Assuming that myofibrillar proteins represent about 85 % of the fiber volume [107], the regulation of skeletal muscle mass is closely related to dynamic balance between protein synthesis and degradation. Cellular experiments reveal that a marked reduction in O 2 availability decreases the rate of protein synthesis in various cell lines including C2C12 myoblasts [108]. In rats, Preedy et al. observed a non-significant decrease in muscle protein synthesis (14-17 %) after 6 h at 10 % O 2 [109]. Data in humans are scarce and are often biased by confounding factors such as cold exposure or increased physical activity (trekking) in the days preceding the analysis [110,111]. Etheridge et al. showed that acute hypoxia had no effect on fractional synthesis rate of myofibrillar proteins at rest, whereas it blunted the anabolic effect of resistance exercise [112]. Interestingly, protein synthesis level was correlated to arterial saturation suggesting that severe hypoxemia would affect muscle anabolism.

O 2 -sensitive signaling in the control of muscle mass Activity of the Akt/mTOR pathway is a critical regulator of muscle mass by regulating protein synthesis (via the mTOR complex 1: TORC1) and proteolysis [113,114]. We reported a down-regulation of Akt/mTOR pathway after hypoxic exposure in rats [101]. One explanation of this inhibition could be a reduction in insulin-like growth factor (IGF) 1 expression, the upstream regulator of Akt/mTOR pathway. Nevertheless, IGF-1 mRNA or protein do not present significant variations under sustained hypoxia [START_REF] Chaudhary | Chronic hypobaric hypoxia mediated skeletal muscle atrophy: role of ubiquitin-proteasome pathway and calpains[END_REF]101]. We recently observed that hypoxia blocked IGF-1mediated activation of the Akt/mTOR pathway in C2C12 myotubes [115]. On the contrary, the expression of myostatin, a muscle-secreted factor which reduces muscle mass through inhibition of the Akt/mTOR pathway [116,117], is increased by hypoxia exposure [106,118,119]. Inhibition of myostatin signaling (antibody administration, receptor inhibition or genetic ablation) partly prevents muscle atrophy under hypoxic conditions, further demonstrating that myostatin contributes to hypoxia-mediated muscle wasting [105,119]. Loss in food intake due to hypoxia could also increase glucocorticoids pathway with the induction of KLF15 expression [106], a glucocorticoid receptor target involved in amino acid degradation to provide carbohydrate backbones for gluconeogenesis. Other circulating factors such as cytokines or adipokines may be released during hypoxia exposure, notably because of the loss of adipose tissue. However, analysis of blood cytokines profile [e.g. Tumor Necrosis Factor-a, Interleukin (IL)-1b, adiponectin, chemokine (C-C motif) ligand 5, monocyte chemoattractant protein-1] did not reveal any marked alteration with hypoxia, with the exception of an increase in IL-6 content [120]. From this study, cytokines do no seems to be implicated in hypoxia-induced muscle atrophy, although further work is required to decipher their influence on muscle phenotype.

The Akt/mTOR pathway is also regulated by AMP-activated kinase (AMPK), which causes TORC1 inhibition [121]. The a catalytic subunit of AMPK is activated when cellular energy levels are low and stimulates processes that generate ATP (fatty acid oxidation), while inhibiting those discordant [START_REF] Chaudhary | Chronic hypobaric hypoxia mediated skeletal muscle atrophy: role of ubiquitin-proteasome pathway and calpains[END_REF]101]. Kinetics is likely of particular importance when studying these markers. Some works reported an increase in MAFbx mRNA [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]119], while this expression in not always observed after prolonged exposure [101,123]. The other well studied E3 ligase MuRF1 presents a similar expression pattern with an increase during the first week of hypoxia exposure [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]123] Autophagy is stimulated via different mechanisms among which the activation of ULK1 resulting from TORC1 inhibition. Hypoxia exposure has been associated with an increase in the expression of autophagic markers such as BNIP3 [START_REF] Band | Hypoxia-induced BNIP3 expression and mitophagy: in vivo comparison of the rat and the hypoxia-tolerant mole rat, Spalax ehrenbergi[END_REF][START_REF] Gamboa | Chronic hypoxia increases insulin-stimulated glucose uptake in mouse soleus muscle[END_REF][START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF] or LC3 [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]. As mentioned above, activation of muscle mitophagy under hypoxic environment seems evident. However, the involvement of autophagy in the control of muscle mass during hypoxia exposure has not been extensively described and remains to be characterized.

ATF4 [131], ATF3 [132] and IjB kinase [133] are directly regulated by PHDs in non-muscle cells and may thus play a role in cellular response to O 2 deprivation independently from the HIFs pathways. ATF4 could be of particular interest since it promotes muscle atrophy [134,135] and its mRNA was increased in the gastrocnemius of mice exposed to severe hypoxia [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]. Activation of IjB kinase in hypoxic muscle would increase Nuclear Factor jB (NF-jB) transcriptional activity, and NF-jB is known to promote muscle wasting through stimulation of UPSmediated protein breakdown [136]. Studying the contribution of these transcription factors to muscle remodeling during hypoxia would thus be helpful to better understand signals that trigger skeletal muscle atrophy.

A transient activation of proteolysis together with a sustained reduction in protein synthesis would be advantageous to cope with the energetic challenge induced by hypoxia. On the one hand, protein synthesis is a highly ATP-consuming process accounting for &25 % of the total metabolic rate [1]. On the other hand, a transient activation of proteolytic systems would promote a rapid decrease in that use ATP (triglyceride and protein synthesis). In subjects exposed to 11.5 % O 2 for 20 min, Wadley et al. did not reported any alteration of skeletal muscle AMPKa1 activity, AMPKa2 activity, AMPKa Thr172 phosphorylation, or ACCb Ser221 phosphorylation (a direct target of AMPK) [122]. While AMPK can be transiently activated by acute hypoxia, this activation does not seem to persist after several days at altitude [START_REF] Gamboa | Chronic hypoxia increases insulin-stimulated glucose uptake in mouse soleus muscle[END_REF]101,118,123]. These observations are consistent with the stability of AMP, ADP and ATP concentrations after 21 days at 4300 m [START_REF] Green | Altitude acclimatization and energy metabolic adaptations in skeletal muscle during exercise[END_REF] and do not support a role for AMPK in Akt/mTOR inhibition during skeletal muscle hypoxia in vivo.

Another negative regulator of TORC1 is the stress response protein REDD1 (for regulated in development and DNA damages). REDD1 has a low level of expression in skeletal muscle under basal conditions, while its expression is strongly induced by glucocorticoid and is required for glucocorticoid-induced muscle atrophy [124]. REDD1 is a direct target of HIF-1 and its expression in skeletal muscle is increased in response to hypoxia [7,101,118,125]. It would therefore be a potential candidate to explain muscle loss at altitude even if REDD1 expression does not always correlate with mTOR inhibition [7,118]. Its biological function is likely not restricted to protein metabolism, since it localizes into the mitochondria and triggers ROS production in cultured cells [126].

BNIP3 has also been proposed to inhibit mTOR through its interaction with Rheb [127]. This mechanism still needs to be confirmed as BNIP3-mediated inhibition of mTOR has never been reproduced in skeletal muscle or during hypoxia. Protein translation could also be down-regulated in a TORC1-independent way via the inhibition of the initiation factor eIF2. While eIF2-related inhibition of protein synthesis has been well characterized in tumorigenic cells [128], the few studies investigating such a mechanism in skeletal muscle do not support this hypothesis [START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]125].

In summary, hypoxia-driven reduction in skeletal muscle protein synthesis mostly results from the de-activation of the Akt/mTOR pathway consequently to upregulation of myostatin or REDD1.

Hypoxia-related regulation of proteolytic systems

Muscle protein breakdown mainly results from activation of the ubiquitin/proteasome system (UPS) and the autophagy/lysosome pathway, both processes being controlled by the Akt/mTOR signaling. The TORC2/Akt axis triggers the expression of the E3-ligases MAFbx and MuRF1 or other components of the UPS through FoxOs cytosolic sequestration. Only few experiments investigated UPS activation under reduced O 2 conditions and results regarding enzymatic activity of the 20S proteasome remain muscle mass and thus in whole body metabolic rate and the release of amino acids during muscle breakdown can also be beneficial to protect from hypoxia since they will act as metabolic fuel as well as metabolic modulator synergistically with ketone bodies [137].

Conclusion and perspectives

Hypoxia effects are primarily thought to be deleterious for skeletal muscle function, especially for mountaineers or active people who have to exercise at altitude. Nevertheless, structural and metabolic regulations that have been characterized result in metabolic optimization (Fig. 5) and are able to minimize the effects of decreased oxygen supply on muscle endurance. These effects are mainly related to HIF-1a, although it may be only transiently stabilized. Prolonged HIF-1a expression could promote apoptosis [START_REF] Bagnall | Tight control of hypoxia-inducible factor-a transient dynamics is essential for cell survival in hypoxia[END_REF] suggesting that successful acclimatization needs destabilization of HIF-1a, notably via reduced ROS production. However, data about HIF-1a expression kinetics in skeletal muscle tissue of healthy subjects or patients with impaired O 2 delivery are still lacking. The exact contribution of HIF-2 in hypoxia-induced adaptations also needs to be clarified, especially as it has been proposed in cancer cells that HIF-2 is more involved in chronic adaptation to hypoxia, while HIF-1 would mediate acute responses [138]. The role of miRNAs in hypoxic response has emerged into the field of cancer research, but this remains an unresolved question concerning muscle adaptations to low O 2 . Among the hypoxia-induced targets, miR-199a and -210 may be relevant candidates since they regulate muscle cell phenotype in a HIF-1-dependent way [START_REF] Cicchillitti | Hypoxia-inducible factor 1-a induces miR-210 in normoxic differentiating myoblasts[END_REF]139]. Concerning experimental designs, it remains to determine whether hypobaric and normobaric hypoxia induce similar effects [140]. In addition, extrapolation of data obtained on small animals to humans requires caution because of differences in O 2 diffusion capacity. Identical PIO 2 could have attenuated effects in rodents compared to patients explaining the use of extreme hypoxia in animal studies [START_REF] Chaudhary | Chronic hypobaric hypoxia mediated skeletal muscle atrophy: role of ubiquitin-proteasome pathway and calpains[END_REF][START_REF] De Theije | Distinct responses of protein turnover regulatory pathways in hypoxiaand semistarvation-induced muscle atrophy[END_REF]. Despite the increasing number of people travelling to high altitude or suffering from pathologies associated with reduced O 2 delivery, the response of human skeletal muscle to hypoxic episodes and its interplay with other organs is still an open challenge.

  Fig.1Regulation of HIF-1a under normoxia and hypoxia. HIF-1a associates with HIF-1b and p300/CBP, binds DNA and activates transcription under reduced O 2 . In presence of O 2 and 2-oxoglutarate, prolylhydroxylases (PHD) and factor inhibiting HIF (FIH) hydroxylate HIF-1a on prolines (Pro) 402 and 564 and on asparagine (Asn) 803, respectively. Asparagine hydroxylation (OH) inhibits the association between HIF-1a and p300/CBP, while prolines hydroxylation results in the binding to the E3 ubiquitin ligase Von Hippel-Lindau complex (VHL), leading to its degradation by the proteasome

Fig. 3

 3 Fig. 3 Metabolic adaptations of skeletal muscle cell exposed to hypoxia. HIF-1 coordinately regulates muscle metabolism through (1) enhanced transcription of glycolytic enzymes, (2) repression of lipid oxidation via inhibition of PPAR/PGC-1a axis and (3) reduction in mitochondrial content by induction of the BNIP3-dependent mitophagy. ATG mitochondrial autophagy, BNIP3 BCL2/adenovirus E1B

Fig. 4

 4 Fig. 4 Skeletal muscle atrophy in rats and humans exposed to simulated altitude between 1 and 6 weeks. a muscle weight (rats only) and b fiber cross-sectional area (FCSA) reduction (rats and humans) in function to simulated altitude level (hypobaric and normobaric hypoxia). Type IIX/B fibers measured at 8848 m are indeed undifferentiated type II fibers. c, d representative pictures from hematoxylin-eosin stained cross sections of rat plantaris muscle c in normoxia or d after 12 days at 5500 m (obtained from [118] with permission). Data for muscle weight and FCSA were obtained from [19, 101, 118, 123, 146, 149, 151-155] and [55, 91, 96, 101, 142, 151, 153, 155], respectively

Fig. 5

 5 Fig. 5 Consequences of metabolic and structural adaptations on muscle homeostasis after hypoxia exposure. Reduced muscle size is mainly driven by the inhibition of the Akt/TORC1 pathway. HIF-1 inhibits the PPARa/PGC-1a axis resulting in a decrease in fatty acid

Table 1

 1 Correspondence between the inspired O 2 fraction (FIO 2 ), the altitude level and the ambient O 2 pressure

	FIO 2 (%)	Altitude (m)	Ambient PO 2	Inspired PO 2
			(mmHg)	(mmHg)
	20.9	0	159	149
	15	2700	114	107
	12	4400	91	86
	10	5800	76	71
	8	7400	61	57
	6	9400	46	43
	1	19,500	8	7

Table 2

 2 Effect of hypoxia on the activity of metabolic enzymes in human (H), mouse (M) or rat (R) skeletal muscles Glycolytic enzymes are in bold and enzymes specific from lipid oxidation are underlined. The percent changes (increase or decrease) are indicated when available Muscles: EDL extensor digitorum longus, GAS gastrocnemius, PLA plantaris, QUA quadriceps, SOL soleus, TB triceps brachii, VL vastus lateralis Enzymes: COX cytochrome oxydase, CPT carnitine palmitoyl transferase, CS citrate synthase, GP glycogen phosphorylase, HAD hydroxyacyl-CoA dehydrogenase, HK hexokinase, LDH lactate dehydrogenase (H or M: heart or muscle isoform), MDH malate dehydrogenase, PFK phosphofructokinase, PK pyruvate kinase, SDH succinate dehydrogenase

	Altitude	Duration	Specie Muscle	Enzymatic activity
	(m)	(days)

  1. Rolfe DF, Brown GC (1997) Cellular energy utilization and molecular origin of standard metabolic rate in mammals. Physiol Rev 77:731-758 2. Richardson RS, Duteil S, Wary C et al (2006) Human skeletal muscle intracellular oxygenation: the impact of ambient oxygen availability. J Physiol 571:415-424. doi:10.1113/jphysiol.2005. 102327 3. Richardson RS, Noyszewski EA, Kendrick KF et al (1995) Myoglobin O 2 desaturation during exercise. Evidence of limited O 2 transport. J Clin Invest 96:1916-1926. doi:10.1172/ JCI118237 4. Johnson PC, Vandegriff K, Tsai AG, Intaglietta M (2005) Effect of acute hypoxia on microcirculatory and tissue oxygen levels in rat cremaster muscle. J Appl Physiol Bethesda Md 1985 98:1177-1184. doi:10.1152/japplphysiol.00591.2004 5. Hutter J, Habler O, Kleen M et al (1999) Effect of acute normovolemic hemodilution on distribution of blood flow and tissue oxygenation in dog skeletal muscle. J Appl Physiol Bethesda Md 1985 86:860-866 6. Jung F, Kessler H, Pindur G et al (1999) Intramuscular oxygen partial pressure in the healthy during exercise. Clin Hemorheol Microcirc 21:25-33 7. Masschelein E, Van Thienen R, D'Hulst G et al (2014) Acute environmental hypoxia induces LC3 lipidation in a genotypedependent manner. FASEB J Off Publ Fed Am Soc Exp Biol 28:1022-1034. doi:10.1096/fj.13-239863


Kean Dequeant
email: kean.dequeant@grenoble-inp.fr

Pierre Lemaire
email: pierre.lemaire@grenoble-inp.fr

Marie-Laure Espinouse
email: marie-laure.espinouse@g-scop.grenoble-inp.fr

Philippe Vialletelle
email: philippe.vialletelle@st.com

A study of variability induced by events dependency in microelectronic production

Keywords: variability, cycle time, dependent events, simulation, complex manufacturing, industry 4.0 I. Accurate modelling

Complex manufacturing systems are subject to high levels of variability that decrease productivity, increase cycle times and severely impact the systems tractability. As accurate modelling of the sources of variability is a cornerstone to intelligent decision making, we investigate the consequences of the assumption of independent and identically distributed variables that is often made when modelling sources of variability such as down-times, arrivals, or process-times. We first explain the experiment setting that allows, through simulations and statistical tests, to measure the variability potential stored in a specific sequence of data. We show from industrial data that dependent behaviors might actually be the rule with potentially considerable consequences in terms of cycle time. As complex industries require strong levers to allow their tractability, this work underlines the need for a richer and more accurate modelling of real systems.

Industry 4.0 is said to be the next industrial revolution. The proper use of real-time information in complex manufacturing systems is expected to allow more customization of products in highly flexible production factories. Semiconductor High Mix Low Volume (HMLV) manufacturing facilities (called fabs) are one example of candidates for this transition towards "smart industries". However, because of the high levels of variability, the environment of a HMLV fab is highly stochastic and difficult to manage. The uncontrolled variability limits the predictability of the system and thus the ability to meet delivery requirements in terms of volumes, cycle times and due dates.

Typically, the HMLV STMicroelectronics Crolles 300 fab regularly experiences significant mix changes that result in unanticipated bottlenecks, leading to firefighting to meet commitment to customers. The overarching goal of our strategy is to improve the forecasting of future occurrences of bottlenecks and cycle time issues in order to anticipate them through allocation of the correct attention and resources. Our current finite capacity projection engine can effectively forecast bottlenecks, but it does not include reliable cycle time estimates. In order to enhance our projections, better forecast cycle time losses (queuing times), improve the tractability of our system and reduce our cycle times, we now need accurate dynamic cycle time predictions.

As increased cycle-time is the main reason workflow variability is studied (both by the scientific community and practitioners, see e.g. [START_REF] Delp | The development of the complete X-factor contribution measurement for improving cycle time and cycle time variability[END_REF] and [START_REF] Kim | Measuring cycle time through the use of the queuing theory formula (G/G/M)[END_REF]), what follows concentrates on cycle times. Moreover, the "variability" we account for should be understood as the potential to create higher cycle times, even though "variability" may be understood in a broader meaning. This choice is made for the sake of clarity, but the methodology we propose and the discussion we lead can be applied to any other measurable indicator. Sources of variability have been intensely investigated in both the literature and the industry, and tool down-times, arrivals variability as well as process-time variability are recognized as the major sources of variability in that sense that they create higher cycle times (see [START_REF] Dequeant | A literature review on variability in semiconductor manufacturing: the next forward leap to Industry 4.0[END_REF] for a review and discussion). As a consequence, these factors are widely integrated into queuing formulas and simulation models with the objective to better model the complex reality of manufacturing facilities. One commonly accepted assumption in the development of these models is that the variables (MTBF, MTTR, processing times, time between arrivals, etc.) are independent and identically distributed (i.i.d.) random variables. However, these assumptions might be the reason for models inaccuracies as [START_REF] Shanthikumar | Queueing theory for semiconductor manufacturing systems: a survey and open problems[END_REF] points out in a literature review on queuing theory. Several authors have studied the potential effects of dependencies, such as [START_REF] Ross | Some pitfalls of blackbox queue inference[END_REF] who studied the potential effects of dependencies between arrivals and process-times or [START_REF] Buzacott | The Effect Of Queue Discipline On The Capacity Of Queues With Service Time Dependent On Waiting Times[END_REF] who investigated dependent process times, [START_REF] Shanthikumar | Queueing theory for semiconductor manufacturing systems: a survey and open problems[END_REF] also gives further references for studies on dependencies effects. In a previous work [START_REF] Dequeant | A literature review on variability in semiconductor manufacturing: the next forward leap to Industry 4.0[END_REF], we pinpointed a few elements from industrial data that questioned the viability of this assumption in complex manufacturing systems. For instance, Figure 1.A shows the number of arrivals per week at a toolset from STMicroelectronics Crolles300 fab, while Figure 1.B shows arrivals per week generated using the same inter-arrival rate as in Figure 1.A, but assuming independence of arrivals. The number of arrivals per week appears to be much more variable in reality than with the i.i.d. assumption.

From the (variability) modeling point-of-view, the i.i.d assumption means that all the information of many individual similar events (e.g., down-times) is contained within their distribution, and that the actual sequence of the events does not carry any additional information or, here, variability potential. That is why some events can be described by standard statistics, such as the mean and the variance, that completely define the statistical distribution. For simplicity of explanations, we will refer to sequences of i.i.d. random variables as i.i.d. sequences and the events they represent as i.i.d. events. The objective of this article is to investigate the impact that the i.i.d assumption may have on the quality of cycle time models and simulations by testing real world sequences of data. We therefore propose in the rest of our article an experiment framework for testing the variability potential of dependencies and show the results obtained on down-time distributions.

II. An experiment framework for testing the variability potential of dependencies A. Objective: testing sources of variability for "dependency variability potential"

The objective we have is to investigate whether or not some information contained in the sequence of events might contribute to the variability. We therefore wish to investigate if there is any significant variability potential stored in the sequences of industrial data. Note that, from an operational perspective, if the events are not i.i.d but the result in terms of cycle time generated is similar, it can be considered that there is no useful information contained in the sequence and that the assumption is acceptable. What we understand by the "variability potential" of a source of variability is its tendency to generate higher cycle times. For instance, queuing theory proposes using the coefficient of variation (the ratio between the standard deviation and the mean) for measuring the variability potential of arrivals (applied on inter-arrival times) and processing times (see e.g. Factory Physics [START_REF] Hopp | Factory Physics: Foundations of Manufacturing Management[END_REF]). To go further, we propose a framework to test if a specific sequence of data points carries a different variability potential than an i.i.d. sequence from the same data points. We will illustrate this approach by running a simulation model that integrates tool down-times, as they are the main source of variability in semiconductor manufacturing. Figure 1 shows a sequence of down-times and up-times of a specific tool from the Crolles 300 semiconductor fab recorded for a period of 1 year. Crolles 300 tool over a year.

We call 𝑆 0 such a particular (real) sequence of events. Our fundamental question is whether the cycle time induced by the specific sequence 𝑆 0 is significantly different than that of an i.i.d. sequence from the same distribution, which we can create by applying a random permutation to the data points representing 𝑆 0 . To answer this question, we propose an experiment framework that measures through simulations whether the effect of 𝑆 0 is statistically significantly different to that of i.i.d. sequences from the same distribution. The following subsections detail the different components of the proposed framework.

B. Setting the simulation

The framework we propose is quite generic and could be applied to many situations: the simulation model could be any system, as long as one can control its inputs and measure its ouputs according to the hypothesis one wants to test.

In our case, we want to challenge the i.i.d. hypothesis, and test its effects on cycle-times. We therefore settle for a minimalistic simulation model, so as to disregard all potential sources of variability other than the independence (or not) of the down-times. We therefore consider the following system: agents queue in an infinite FIFO queue, waiting to be processed by a single tool with constant process times that treats each agent one after another with no inefficiency whatsoever except for the down-time events. These down-time events are set to follow specific sequences, being on the one hand the reference (real) sequence 𝑆 0 , and on the other hand (as a basis for comparison) many other i.i.d. sequences. We ran all our simulations with Anylogic Professional in an agent based simulation exported as a standalone application: this allowed us to control the simulation model with R, and manage the inputs/ouputs of thousands of simulations in an automated manner.

C. Measuring the effect of 𝑆 0

In our case, the effect of a sequence of down-times is measured as the average cycle-time of the agents in a simulation. This should be evaluated on an infinite horizon, that is until the measure is stable enough, but it is in practice impossible since 𝑆 0 is finite (as it is real, empirical data). As an alternative, to prevent any bias from a particular arrival sequence, we simply evaluate the long term average cycle-time by running many simulations on different scenarios, i.e. on different arrival sequences (following i.i.d. exponentially-distributed inter-arrival times). Thus, let 𝐶𝑇 0,𝑗 be the mean cycle time of agents from the simulation run on sequence 𝑆 0 of down-times and scenario j of arrivals; the effect of 𝑆 0 is then 𝐶𝑇 ̅̅̅̅ 0 , the mean of mean cycle times from simulations that used 𝑆 0 as an input. The number of different scenarios j is an important parameter and will be discussed in section II.F.

D. Measuring the effect of i.i.d. sequences

To measure the effect of i.i.d. sequences, we generate many such sequences from the same distribution; those sequences (𝑆 𝑖,𝑖≠0 ) are generated as random uniform permutations of 𝑆 0 . Using the same procedure as for 𝑆 0 , we compute for each sequence 𝑆 𝑖,𝑖≠0 its effect: 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 . Note that we use the exact same scenarios for arrivals as for 𝑆 0 , this extra requirement insuring that any significant difference between the population 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 and the value 𝐶𝑇 ̅̅̅̅ 0 comes strictly from the difference between 𝑆 𝑖,𝑖≠0 and 𝑆 0 . The effect of a particular i.i.d. sequence is of virtually no interest as we want to measure the effect of any i.i.d. sequence. This could be measured as the mean value of the 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 , but to get a better control on the comparison we prefer measuring the effect as a 95% confidence interval 𝐼 95 .

We compute 𝐼 95 as 𝜇 ∓ 2𝜎 where 𝜇 and 𝜎 are respectively the mean and the standard-deviation of 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 . Doing such calculation, we assume that the 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 follow a Gaussian distribution. We justify this statement both by the central limit theorem as each point of our sample population is a mean and by the fact that the underlying population 𝐶𝑇 𝑖≠0,𝑗 most likely follows a Gaussian distribution (since the cycle time of each distribution comes from the accumulation of many independent random effects).

As for the computation of 𝐶𝑇 ̅̅̅̅ 0 , the right number of sequences and of scenarios must be carefully chosen so as to get good estimates within reasonable running times. This is also discussed in section II.F.

E. Comparing the effects

Once 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 have been computed accurately, they must/can be compared using a standard procedure for a statistical test: if 𝐶𝑇 ̅̅̅̅ 0 falls within 𝐼 , then it cannot be said that 𝑆 0 has an effect significantly different than that of an i.i.d. sequence; In the alternative, it can be assumed that 𝑆 0 has a different effect on cycle-time than an i.i.d. sequence. Figure 3 illustrates the three possible outcomes of the test. If 𝐶𝑇 ̅̅̅̅ 0 is on the left side of 𝐼 95 (Figure 3 A), 𝑆 0 carries a negative variability potential; If 𝐶𝑇 ̅̅̅̅ 0 is within 𝐼 95 (Figure 3.B), it cannot be said that 𝑆 0 carries any significant potential; If 𝐶𝑇 ̅̅̅̅ 0 is on the right side of 𝐼 95 (Figure 3.C), 𝑆 0 carries a positive variability potential.

Note that setting a 95% confidence interval actually means, from a skeptic point-of-view, that there is a 5% chance for any sequence tested that the results will turn out to be positive by pure randomness. It is therefore essential to test different 𝑆 0 sequences, and to compare the number of positives with the probability of getting such results by "luck". For instance, if we test 19 sequences, the chance of getting more than half results positive by luck is less than 10 -5 . Note that a Student's t-test is not directly applicable here as it does not answer the question we are asking: should we perform a t-test between the populations 𝐶𝑇 ̅̅̅̅ 0,𝑗 and 𝐶𝑇 ̅̅̅̅ 𝑖≠0,𝑗 , we would be asking if the mean of both populations are identical or not. With a finite horizon of 1 year (resulting in a significant difference between each 𝑆 𝑖 ), almost all 𝐶𝑇 ̅̅̅̅ 𝑖 are different than the mean of 𝐶𝑇 ̅̅̅̅ 𝑖≠0,𝑗 , thus a significant difference with this test would not bring any particular information on 𝑆 0 .

As a complementary measure, we check, for each arrival scenario j, whether the mean of the population 𝐶𝑇 ̅̅̅̅ 𝑖≠0,𝑗 is statistically different than 𝐶𝑇 ̅̅̅̅ 0,𝑗 . For each scenario j, we can answer this question using a t-test and then count the number of times a scenario j gave 𝐶𝑇 ̅̅̅̅ 0,𝑗 respectively statistically smaller, non-statistically different and statistically higher than the mean of the population 𝐶𝑇 ̅̅̅̅ 𝑖≠0,𝑗 . As the population 𝐶𝑇 ̅̅̅̅ 𝑖≠0,𝑗 represents average cycle times from identical simulation sets and parameters, only with randomness coming from different draws of the parameters, we can assume that they follow a normal distribution and can apply the t-test. These numbers are referred to as the "t-test triplets" in the results section III and are computed as a secondary test, keeping the previously explained methodology as the main measure.

F. Handling uncertainties on 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 As 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 come from a finite population we created through simulation, the values we measure are actually estimates of the true values (that we would get if we had an infinite population) and therefore carry uncertainty. The actual value of 𝐶𝑇 ̅̅̅̅ 0 is contained in a confidence interval around 𝐶𝑇 ̅̅̅̅ 0 , which we call [𝐶𝑇 ̅̅̅̅ 0 ]. The same applies to 𝐼 95 : as we had to estimate 𝐼 95 , we are not certain of the two limits of this interval, however 𝐼 95 is most likely contained within inner/outer limits which we call 𝐼 95 and 𝐼 95 + . + -𝐼 95 -) not to intersect, then whatever the value 𝐶𝑇 ̅̅̅̅ 0 takes within [𝐶𝑇 ̅̅̅̅ 0 ], and whatever the value 𝐼 95 takes within ( 𝐼 95 + -𝐼 95 -), the conclusion is the same (as for Figure 3). The problem arises when the uncertainty areas of [𝐶𝑇 ̅̅̅̅ 0 ] and 𝐼 95 overlap: depending on what true value 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 take inside their intervals, the answer can be different, and we can therefore not be sure of the answer. This is a "we do not know" situation as we cannot say with confidence that there is a difference, nor can we say with confidence that there is no difference.

In order to get definitive answers, these uncertainty areas around 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 need to be reduced to a point where they do not overlap anymore: to this extend, we need to increase the number of simulation runs so as to decrease either [𝐶𝑇 ̅̅̅̅ 0 ] or the gap between 𝐼 95 + and 𝐼 95 -. The appendix gives more details on the computation of these values and the way to minimize the number of simulations in order to get out efficiently of an overlap situation. In any case, there needs to be a minimum amount of simulations in order to start computing the uncertainty intervals. To test one 𝑆 0 sequence, we decided to run simulations on at least 20 i.i.d. sequences and 20 arrivals scenarios. Therefore, one simulation set is composed of at least 400 simulations.

G. Ending simulations

Each simulation needs to be run over the period of time defined by the sequence 𝑆 0 that is tested. However, at the end of this period of time, some agents may have accumulated in the simulation. Cutting the simulation abruptly can either lead to the loss of the cycle time of these agents or an underestimation of their cycle time depending on how the information is recorded in the simulation.

In order to prevent from such effects, we decided to stop the arrivals after the time duration defined by 𝑆 0 , and continue the simulation until all agents have exited the simulation. We also chose to leave the tool up after the end of the given up/down sequence. This was first motivated by the fact that any other decision could introduce uncontrolled biases to the results. Secondly, by having a similar end to all simulations, we actually slightly underestimated the difference between the historical sequence and its i.i.d. counterparts: this only strengthens any significant results.

III. Results and implications

A. Down-times of C300 tools

Using the method described in section II, we tested 19 tools from the C300 fab. For each tool, we extracted the empirical sequence of up-times/down-times over a year. We then applied the procedure described in section II. One implicit parameter for all simulations is the utilization rate of the tool: in our simulation this utilization rate is fixed by adjusting the mean inter-arrival time of the scenarios. Since this utilization rate influences the cycle times, we set it as the same value across all simulations: 80%, as this is both a high and common, realistic level. Table 1 summarizes the results of our experiments. The results are normalized so that the average cycle time for the sample i.i.d. sequences (𝜇) is equal to 100. Therefore, the values of 𝐶𝑇 ̅̅̅̅ 0 can be compared straightforwardly between them and relative to the central cycle time for i.i.d. sequences 𝜇. We also provide the confidence interval [𝐶𝑇 ̅̅̅̅ 0 ] and the 𝐼 95 * value, which correspond to 𝐼 95 + if 𝐶𝑇 ̅̅̅̅ 0 is outside 𝐼 95 + or 𝐼 95 -otherwise. The column "s" shows the result of our test: YES if there is a significant different, NO if there is no significant different, and NA if we were not able to get a definitive answer. We also add the "t-triplets" described in section II.E. Tools with same letters are from the same tool type.

Table 1: Results of the experiment framework tested on 19 tools from STMicroelectronics

As Table 1 shows, out of the 19 historical sequences we tested, 3 did not show any significant difference in the variability potential they carried compared to their i.i.d. counterparts, 13 showed an increase, 2 showed a decrease, and 1 could not draw a definitive answer after 10000 simulation runs. The t-test triplets confirm the results and bring additional information on the impact of the arrival scenarios, but are not enough to assert a significant difference (e.g. see tools E6 and L18).

The differences between 𝐶𝑇 ̅̅̅̅ 0 and 𝜇 in Table 1 first show that the empirical sequences of down-times we tested are statistically different than i.i.d sequences in terms of variability potential. Secondly, it should be noticed that the historical sequences added non negligible cycle time: the average increase in cycle time when the variability potential is positive is +174%, the median increase being +64%. This means that, for the majority of cases we tested, more than one third of the cycle time came from the actual sequence and not from the statistical distribution.

An interesting result is that the sequence of down-times can actually carry negative variability potential. The probability of false-positive is here ruled out by the fact that both tools that showed a sequence of down-times with a negative variability potential are from the same tool type. We explain this as being the result of "regular" down events amongst "irregular" down events. Indeed, these tools need regular changes of an important resource which create down-time events. However, even though the time between these special events are somewhat constant, there are many other down-time events that happen more or less randomly. Therefore the regularity of these events is lost in the statistics, and when running a simulation with i.i.d. down-time events, this regularity is broken and more variability occurs. The results from table 1 were obtained at a utilization rate of 80%. However, it is also interesting to run distinct experiments for the same sequences, but at different utilization rates. For each empirical sequence, we actually ran experiments on 9 different utilization rates ranging from 10% to 90% for a total number of 180 experiments, each requiring a minimum of 400 simulations. The blue curves of Figures 5 are the average cycle times for the sample populations 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 along with its 95% confidence interval. They represent the outputs of the simulations run on the i.i.d down-times sequences. The red curves represent the values 𝐶𝑇 ̅̅̅̅ 0 , i.e. the average cycle times generated by the simulation runs that used the historical down-times sequences. These curves display the expected exponential behavior of cycle time when it comes to utilization rates. The cycle times added (or removed) by the dependencies seem to be proportional to the original cycle times and the utilization rate does not seem to impact whether 𝑆 0 is significantly different or not.

B. Results from an operational point-of-view

The results we show indicate that a large part of the cycle time generated by down-time events from historical data in the case of i.i.d. arrivals is unaccounted for in most queuing and simulations. However, the difference in cycle times between most current models (using queuing theory or simulation) and reality is not in the order of magnitude that we pointed out. How can it be that we see a significant difference that does not happen in reality?

We believe this difference comes from another dependency phenomenon that is still mostly unaccounted for: the dependency between the arrivals and the tool behaviors. Indeed, in the complex reality of manufacturing, decisions are made dynamically based on the flow of products. For instance, maintenances might be pushed back in the case of temporary over-saturations, more maintenance staff is also affected to tools that are forecasted to be highly used in the near future, etc.

IV. Perspectives and conclusion

A. Quantifying other sources of variability

The results we give in this article show strong evidence that tool down-times actually do not follow i.i.d. distributions and that this difference has a huge impact on the variability potential of down-times. As Fig. 1 shows, there is strong evidence that other sources of variability such as arrivals and processing-times also do not follow i.i.d. sequences. The next step is therefore to apply the same procedure on historical arrivals sequences as well as historical processing-times sequences.

B. Quantifying intra-sources relations

As we previously mentioned, there is strong evidence for a relation between the different sources of variability both from the shop-floor experience and from our quantification of the variability potential of down-time events. Further research should focus on quantifying this relation. Indeed, better modelling this relation could help both making models more accurate and reduce the overall variability fabs experience, as measuring is always the first step to reducing.

C. Conclusion

Accurate modelling of sources of variability (i.e. root causes for the generation of queuing time inefficiencies) is a key element of the manufacturing strategies put forward with industry 4.0 and High Mix Low Volume production. Previous works had questioned the viability of the assumption of independent and identically distributed random variables when it comes to the modelling of sources of variability such as tool down-times, arrivals, process times… In this article, we proposed an experiment framework based on the repetition of many simulation runs that allows testing on historical sequences of data if this assumption has any implication in the modelling of variability. The experiment framework was built around the specific scenario of testing down-times, but can be applied to any sequence of data as long as a simulation is able to integrate the source of variability that is tested.

We then tested 19 different industrial down-time sequences of 1 year taken from tools from the Crolles 300 semiconductor fab. The results show that not only do the sequences of downtimes carry significant variability potential, they actually contain an important part of the variability potential for most tools. We also showed that, quite interestingly, the sequence of downtimes can actually carry negative variability potential and generate less cycle time than if they were sequences of independent and identically distributed variables.

Our results suggest that there is a strong relation between the arrivals and the behaviors of the tools in the reality of complex manufacturing. A next essential step is therefore to measure, quantify and understand the interactions that happen in the real world of complex manufacturing in order to better model these interactions and give industrials the levers they need to follow their transition to industry 4.0.

Appendix

We mentioned in section II.G that the uncertainties on [𝐶𝑇 ̅̅̅̅ 0 ] and 𝐼 95 might be too high to draw a definitive conclusion. As the uncertainties on [𝐶𝑇 ̅̅̅̅ 0 ] and 𝐼 95 come from the estimators, they reduce with the number of simulation runs. Both uncertainty areas can be estimated straightforwardly: the standard deviation of the estimator for the mean 𝜇 and the standard deviation 𝜎 are respectively where n is the sample size [START_REF] Ahn | Standard errors of mean, variance, and standard deviation estimators[END_REF]. Once again, we use these formulas as we make the assumption that the underlying populations follow normal distributions. Thus, we ).

After the initial 400 simulations, the condition to either increase the number of sequences 𝑆 𝑖 or the number of arrivals scenarios is actually the same: an overlap between the red area and either of the grey areas of Figure 5. The decision of which to do first should be taken in order to minimize the computation time required. Drawing another arrival sequence will reduce [𝐶𝑇 ̅̅̅̅ 0 ] whereas drawing another 𝑆 𝑖 sequence will reduce the gap between 𝐼 95 -and 𝐼 95 + . We therefore need to compute the decrease in the uncertainty area per simulation for either case of making a new draw of arrivals or of down-times, knowing that any new draw of arrivals needs to be run on all existing 𝑆 𝑖 sequences and vice-versa.

Figure 1 :

 1 Figure 1: Number of arrivals per week from real data (A) and generated by removing dependencies (B)

Figure 2 :

 2 Figure 2: Historical down-times/up-times from a specific Crolles 300 tool over a year.

Figure 3 :

 3 Figure 3: Three possible outcomes when comparing 𝐶𝑇 ̅̅̅̅ 0 to the sample population 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0

Figure 4 :

 4 Figure 4: uncertainty areas around 𝐶𝑇 ̅̅̅̅ 0 and 𝐼 95 These limits are represented on Figure 4 along with two greyed areas ( 𝐼 95 + -𝐼 95 -) and the interval [𝐶𝑇 ̅̅̅̅ 0 ]. If 𝐶𝑇 ̅̅̅̅ 0 is far away enough from 𝐼 95 as for [𝐶𝑇 ̅̅̅̅ 0 ] and ( 𝐼 95+ -𝐼 95 -) not to intersect, then whatever the value 𝐶𝑇 ̅̅̅̅ 0 takes within [𝐶𝑇 ̅̅̅̅ 0 ], and whatever the value 𝐼 95 takes within ( 𝐼 95 + -𝐼 95 -), the conclusion is the same (as for Figure3). The problem arises when the uncertainty areas of [𝐶𝑇 ̅̅̅̅ 0 ] and 𝐼 95 overlap: depending on what

Figures 5

 5 shows operational curves (representing cycle time versus utilization rate) for tools showing respectively an increase in variability potential, no significant change in the variability potential, and a decrease in the variability potential.

Figure 5 :

 5 Figure 5: operational curve showing 𝐶𝑇 ̅̅̅̅ 0 (statistically) higher (A), non-different (B), and lower (C) than 𝜇

)

  where 𝜎 0 and σ are respectively the standard deviation of 𝐶𝑇 ̅̅̅̅ 0,𝑗 and 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 ; n and m are respectively the number of different i.i.d. sequences and of arrival scenarios; And μ is the mean of all 𝐶𝑇 ̅̅̅̅ 𝑖,𝑖≠0 . To derive the formulas on 𝐼 95 -and 𝐼 95 + , we start with the estimation of 𝐼 95 (μ ∓ 2σ), and we subtract ( 𝐼 95 -) or add ( 𝐼 95 + ) a standard-error for μ (