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Manufacturing genetically modified crops, regenerating tissues, or cloning sheep and cows … such practices challenge the traditional boundary between the natural and the artificial. It seems that it is the fate of technological progress to gradually blur the ancient dichotomy between nature and artefact. And this erosion of one of the main pillar of Western culture is not without raising societal issues. Undoubtedly a number of people who are protesting against GMO crops, or against medically assisted procreation are doing so because they consider such practices as counter-natural. Symmetrically, for techno-optimists the popular fears about technological innovations are just irrational prejudices due to a kind of fetishism of nature. Thus the dichotomy between nature and technology is the core of a confrontation between two radical attitudes of technophobia and technophobia-phobia,1 which often hinders democratic debates about emerging technologies.

To what extent the distinction between the natural and the artificial can be considered as a popular prejudice, generating technophobia? Is the ancient divide between phusis and technê an obsolete category? The expression of the metaphysical views of a prescientific and premodern era that no longer makes sense in the twenty-first century when our environment, our bodies, our lifestyles are saturated with technology?

In briefly sketching the cultural roots of the distinction between nature and artefact, this paper emphasizes its relativity. Then it proceeds to argue that the notions of nature and artefact are interdependent and continuously reconfigured on the basis of a few historical examples. However, emphasizing the cultural and historical relativity of the notions of nature and artefact does not entail that they are meaningless. Despite its weakness from a rational point of view, this dichotomy has a normative power and plays a key role in the social acceptance of new technologies.

A Greek heritage

First of all, it is important to keep in mind that the dichotomy between nature and artefact as well as the divide between nature and culture are specific to Western culture. As French anthropologist Philippe Descola argues, our view of nature as distinct from human activities is not universal. It is a social and cultural construction, which makes sense only in the Western world. It is only one of the four various ontologies that this expert in Achuar cosmology has identified: totemism, animism, analogism and naturalism.2 Naturalism, according to him, is:

simply the belief that nature exists, in other terms that some entities owe their being and their development to an external principle, which is not an effect of human will. Typical of Western cosmologies since Plato and Aristotle, naturalism generates a specific ontological domain […] As naturalism is the guideline of our own cosmology and impregnates our common sense and our scientific principles, it has become a 'natural' presupposition which structures our epistemology and in particular our perception of other modes of identification. 3 The Ancient Greek roots are clearly visible in Aristotle's Physics Book II. "Technology, Aristotle claimed, imitates nature'. He did not provide explanation, presumably because it sounded like a common sense distinction. The analogy between art and nature turns around the role played by the final cause.

[A]rt partly completes what nature cannot bring to a finish, and partly imitates her. If, therefore, artificial products are for the sake of an end, so clearly also are natural products. The relation of the later to the earlier terms of the series is the same in both. 4 Nevertheless, in another well-known passage from Physics II, where he introduced the distinction between form and matter, Aristotle drew a radical difference between nature and art. Natural beings have an internal principle of motion and rest while artificial objects -a bed or a coat, for example -do not possess any such innate tendency to change. 'Man is born from man, but a bed is not born from a bed.'5 This sentence suggests an essential difference, a difference of kinds.

Based on this passage, a number of medieval scholastics used the distinction between form and matter to argue that there was an ontological difference between natural and technological products. They reinforced the ontological gap by claiming that it was impossible to create an essence by art. Only nature had the capacity to create a 'substantial form'. As a consequence, scholastic thinkers condemned artisans, especially alchemists, for subverting the order of nature. In his comments on Aristotle's Meteorology, the Persian philosopher and physician Avicenna reproved the 'artificers' (Sciant artifices). 6 For him, there is an essential difference between natural gold generated in the mines and its artificial namesake, alchemist's gold. The latter is counterfeit; an imitation of the real thing based on the appearance. For lack of substantial form, the products of human art are necessarily inferior to natural ones. Consequently, alchemists were condemned as charlatans or sorcerers displaying supernatural or demonic power. For Thomas Aquinas, alchemy was neither altogether against nature nor supernatural in the sense of magic, but rather preternatural, from the Latin praeter naturam, meaning beside or outside nature. For Aquinas, the category of the preternatural covered a whole range of anomalies -monsters, marvels, prodigies, and comets -that were not part of the normal course of nature while they could not really be considered against nature either.7

The alchemists replied to scholastic attacks on their art with experimental demonstrations using analysis and synthesis to prove the authenticity of their products. They carefully demonstrated that they could produce artificial bodies identical to natural ones. They also developed rational arguments in favour of artefacts within the then dominant Aristotelian framework. For instance, Paul de Tarente came to alchemy's defence by using the scholastic distinction between primary and secondary qualities. The arts that work with only secondary qualities -colours, odours, etc. -can never hope to act on the nature or the essence of the substances they manipulate. By contrast, certain arts, like medicine, horticulture and alchemy, which work using the primary qualities -hot, cold, wet, dry -have the power to change the very essence or nature of the substance they act on, allowing them to modify natural species whether for better or for worse. The Book of Hermes attributed to Geber (Djabir) features as a staunch defence of alchemical arts. [START_REF]Liber hermetis, attributed to Geber[END_REF] Without challenging the received wisdom that art imitates nature, the author claims that this imitation reproduces the essence of the natural substances in the artificial one. There is no essential difference because art uses the same means and the same processes as nature, and moreover has the advantage of being able to improve upon the natural model. Arts such as alchemy are only possible in so far as man can induce nature to produce the things it normally produces in different circumstances.

Agriculture was cited as the example of an art where humans make use of natural phenomena, the growing and ripening of grain, in a productive context. Similarly alchemists make use of natural raw materials, and of natural reagents (fire) to make artificial products. In Aristotelian terms, the artificial differs from the natural only with respect of one of the four causes, i.e. the efficient cause, i.e. the designer. Thus medieval and Renaissance alchemists raised serious objections against the ontological distinction and featured as early advocates both of experimental methods and of technology.

Seventeen-century natural philosophers -especially Francis Bacon, René Descartes and Robert Boyle -further undermined the radical divide between the natural and the artificial while they promoted laboratory experiments as the optimal way to understand natural phenomena and unveil the laws ruling them. Descartes insisted that the bodies made by art were no different from natural ones:

And it is certain that all the rules of mechanics belong also to physics, of which it is a part or species, [so that all that is artificial is withal natural]: for it is not less natural for a clock, made of the requisite number of wheels, to mark the hours, than for a tree, which has sprung from this or that seed, to produce the fruit peculiar to it. [START_REF] Descartes | [END_REF] As technology is based on natural laws, improving technology and better understanding nature are one and the same objective. Physics will "thereby make ourselves, as it were, the lords and masters of nature". [START_REF] Descartes | Discours de la méthode[END_REF] The rapprochement between the artificial and the natural secured and legitimized the domination of nature by humans. But it also went hand in hand with a reinterpretation of nature as a kind of machine, more precisely a clock designed by a supernatural clockmaker. On the basis of the analogy between automata and animal bodies Descartes developed a mechanistic physiology describing nerves as fountain pipes, muscles and tendons as springs…. 11 . In other terms, human arts became the model for our understanding of nature. While Aristotle described nature as a kind of model that human art had to mimic in order to complement or restore (in the case of medicine) nature, with the emergence of experimental philosophy in the seventh century nature was modelled upon technology.

Trapped in a circle?

Does this mean that we should reverse Aristotle's view and claim that nature imitates art? In his lectures On nature delivered in 1956, French philosopher Maurice Merleau-Ponty noticed the circularity: «We cannot think about nature without realizing that our idea of nature is impregnated with artefacts». [START_REF] Merleau-Ponty | Nous ne pouvons penser la nature sans nous rendre compte que notre idée de nature est imprégnée d'artifice[END_REF] How are we to understand this statement? Merleau Ponty did not just mentioned that nature is always impregnated with technology, that there is no genuine natural space on the Earth: everywhere in artic ice, in deep oceans and in the wild forests we can find traces of the pollution generated by human activities. Merleau Ponty rather argued that our idea of nature is shaped by technology. Each age tends to interpret nature through models and canons derived from one of its most advanced technologies. Nature is not a metaphysical entity that can be defined sub specie aeternitatis. It is continuously redefined according to technological changes. [START_REF] Vincent | The Artificial and the Natural. An Evolving Polarity[END_REF] At the turn of the eighteenth century when skilful artisans such as the French mechanics Jacques Vaucanson or the Swiss clockmaker Jacquet Droz were displaying a collection of clockwork androids, Nature was a viewed as a "blind, deaf and dumb" clockwork automaton. Natural philosophers describing animals as machines also began to view machines as animated bodies, and to design them accordingly [START_REF] Riskin | Eighteenth-century wetware[END_REF] .

At the turn of the nineteenth century, while steam engines were driving the industrial revolution, a number of chemists described animals as combustion engines. For Lavoisier, respiration was a kind of combustion, a combination with oxygen from atmospheric air releasing heat (caloric). [START_REF] Holmes | Lavoisier and the Chemistry of Life : An Exploration in Scientific Creativity[END_REF] Lavoisier approached animal respiration in a famous memoir "On heat" where he focused on the measurement of the amount of heat released by combustion and respiration with an apparatus the ice calorimeter. [START_REF] Lavoisier | Mémoire sur la chaleur[END_REF] Combustion also provided the model for understanding animal nutrition. For Jean Baptiste Dumas and Jean Baptiste Boussingault, animals like engines consume fuel through their nutrition and release carbon dioxide into the atmosphere, while plants 'fix' carbon dioxide and release oxygen. The analogy between animals and with enabled scientists to describe the circulation of carbon through the three realms of nature -mineral, plant and animal.

In the twentieth century synthetic chemistry prompted a deep revision of the images and values attached to the natural and the artificial. The manufacturers of the earliest chemical substitutes -such as celluloid and Bakelite -which were meant to be cheap, flexible and multifunctional, struggled with the dominant view of nature as a rigid economy. [START_REF] Friedel | Pioneer Plastic: The Making and Selling of Celluloid[END_REF] Every natural material was praised for a unique function -wood for construction, cotton for clothing, for instance -, whereas the plasticity of synthetic polymers was depreciated. A few decades later, following the mass consumption of nylon and synthetic polymers, flexibility, plasticity, lightness became positive values, markers of the 'plastic era". And nature came to be considered as a strictly limited stock of resources in stark contrast to the promise of wealth out of the chemical laboratory. The emphasis was on the limitations of nature viewed as a finite collection of products rather than as a continuous process of generation (natura naturata rather than natura naturans).

At the turn of this century nanotechnology and converging technologies once again reshaped the polarity between nature and artefact. While nature is investigated at the molecular level it is more and more described as a collection of molecular machines. At the nanoscale (10 -9 metres) all boundaries between nature and artefact, between living and non-living seem to be blurred. Most natural systems are described as devices or machines; they are identified by what they do (functionalities) rather than by for what they are (structure and composition).

They are praised for their performances and operations. Organisms are reconceptualised in terms of the dominant computer technology, as machines operated by a program or software. This common metaphor underlies the research agenda of synthetic biology, which aims at redesigning life through changes in the program. Thus for the first time, "natural" and "living" cease to be synonymous: organisms are high-tech and all-purpose machines as Harvard synthetic biologist George Church claims: biological organisms could be viewed as a kind of high technology, as nature's own versatile engines of creation. Just as computers were universal machines in the sense that given the appropriate programming they could simulate the activities of any other machine, so biological organisms approached the condition of being universal constructors in the sense that with appropriate changes to their genetic programming, they could be made to produce practically any imaginable artefact. A living organism, after all, was a ready-made, prefabricated production system that, like a computer, was governed by a program, its genome. Synthetic biology and synthetic genomics, the large-scale remaking of a genome, were attempts to capitalize on the facts that biological organisms are programmable manufacturing systems , and by making small changes in their genetic software a bioengineer can effect big changes in their output. 18 This brief historical overview clearly demonstrates the relativity of the art/nature divide. Not only nature and artefacts are ethnocentric notions limited to Western culture, but their representations are also mutually constructed entities. Like prey and predator defining their own identities though their relation, nature and artefact are continuously reconfigured through their changing relations.

Acknowledging the historical relativity of the divide between nature and artefact does not mean that the art/nature divide would be obsolete and has to be overthrown. We do not lose the memory of past notions. The public debates raised by emerging technologies suggest that pre-modern views of nature and artefacts are remarkably resilient and do not suddenly become obsolete or meaningless. In particular, many people express a fear of messing with nature while the view of organisms as reprogrammable computers is shared only by a few biologists. There is a multitude of images of the natural and the artificial co-existing in our societies. For instance, a global survey of the narratives of nature in articles about nanotechology identified a wide spectrum of view: nature as an optimal engineer, nature as a source of inspiration of design principles, nature as a source of physical limits and constraints, as an order to be destroyed, as an environment to be conserved, nature as threatening the fragile human condition, nature as a fragile planet to be protected…. [START_REF] Wickson | Narratives of nature and nanotechnology[END_REF] . Given the tensions and contradictions surrounding the notions of nature and artefact, it seems difficult to get rid of them because of their obsolescence. Are we to consider them as an ideological prejudice, a "vue de l'esprit", which is confounded by human activities?

A non-robust and still powerful dichotomy Indeed, the distinction lacks a rational foundation. Admittedly, the dualism between nature and artefact refers to the temporal distinction between a primordial order and later transformations. Natural is a forest or a piece of land, which has not been used by humans for dwelling or agriculture or mining. Nature is perceived as kind of sanctuary where one can experience direct contact with so-called "primitive" nature, in Yellowstone or Yosemite natural parks. But this romantic view promoted by the advocates of the Wilderness movement has been easily debunked as a mythology, which has occasionally been imposed against native Indian cultures. [START_REF]The Great New Wilderness Debate[END_REF] From a rational point of view, it is also easy to realize that the distinction between natural (extracted from nature) and synthetic (man-made) materials is equally ill-founded. We say that wood, cotton, and wool, are natural whereas plastics are artificial or synthetic. To be sure, wood, which is the archetype of all materials (etymologically materies meant the core-wood used by the carpenter) is the result of life processes achieved by plants according to natural laws. It did not grow out of human purposes out of man's design like the synthetic fibres of nylon for instance. However, the intuitive distinction between extracted from nature and designed by human art is far from clear. It's a weak dichotomy that does not resist any close examination. Many items that we consider 'natural' such as cotton, wool, or wine, are in fact the result of a long manufacturing process. If the boundary between natural and artificial were strictly and exclusively based on the distinction between extraction and man-made product, then it would a quantitative difference, a matter of degree not of kind.

The elusive character of all references to nature is by no means a recent discovery. In the eighteenth-century, Jean-Jacques Rousseau quickly understood that wild nature was out of reach. [START_REF] Rousseau | Rêveries du promeneur solitaire, 7th promenade, OEuvres complètes[END_REF] He nevertheless promoted the state of nature as an intellectual construction, an indispensable fiction for ascertaining the foundations of political order. [START_REF] Rousseau | Discours sur l'origine et les fondements de l'inégalité parmi les hommes[END_REF] In thus emphasizing the strong normative power of the divide between nature and artefact despite its weakness at the descriptive level, Rousseau provides a sure guideline for getting out of the 'vicious circle' of fuzzy notions. We have to shift from the descriptive to the prescriptive, from factual evidence to norms.

For this purpose, a third concept has to appear on stage. In addition to the contrast between phusis and technê, Ancient Greek philosophers used the distinction between phusis and nomos, the social conventions or norms in order to fight against the Sophists. The power relations based on natural inequalities in strength and might do not rule the social world. They give way to laws and rules resulting from collective decisions taken in the agora. Remarkably while Descartes firmly rejected the distinction between nature and artefact he promoted the "great divide" between nature and society. This second dichotomy is a chief characteristic of modernity according to Bruno Latour. 23 It disconnected the social contract, ethics and politics, from nature, and prompted the institution of humanities and social sciences as an independent culture. 24 Thus the divide between nature and artefact has been socially constructed and it is repeatedly reconstructed for normative purposes, for providing a criterion of action and of judgement. To be sure, the cursor arrow locating the boundary between natural and artificial products, or between natural and artificial procreations has significantly shifted over the centuries. However delineating a boundary is vital for several reasons.

The boundary matters not only for archaeologists who have to sort out chopping tools from rocks or stones eroded by nature. It matters not only for legal issues of intellectual property since patents rely on the distinction between discovery and invention. Today it matters above all for regulating technological innovations and achieving what is commonly referred to as "sustainable development".

In the course of the twentieth century the distinction between nature and artefact gained a new normative power when a number of critics of technology -Lewis Mumford, Jacques Ellul for instance -claimed that there was no limit to technological development. On the other hand, environmental activists claimed that such development would quickly bring the death of nature, or in less emphatic terms, irreversibly destroy nature's ecology. In this context, nature has been once again reconfigured. The image of the Earth as the fragile and vulnerable house (oikos) of humans has gained traction, along with the widespread fear that the pace of technological innovations threatens the future of mankind. Techno-optimists keep arguing that technological fixes to the damages caused by previous technologies will soon be available, for instance that geo-engineering will regulate climate changes. However more and more people around the world realize that there is no technological solution to the issues raised by technology, and that political measures, societal changes, are badly needed.

In this context, our western notions of the natural and the artificial may still provide useful conceptual tools, precisely because they are overloaded with layers of historical meanings. The great variety of images and values attached to the natural and the artificial enables us to understand and disentangle the various ways in which technologies relate to nature. Not all technologies aim at subduing nature to the power of a designer. Some of them aim at domesticating nature or operating with nature rather than upon nature. For normative purposes, it is important to go beyond the generic categories of nature and technology and to take into account the nuances between styles of technologies and their various ways to engage with nature.

To conclude, the ancient divide between nature and artefact is more than the vestige of a premodern era that would have been gradually undermined by technological advances. In reality, many claims about the continuum resulting from the increasing artificialisation of our environment are indirect strategies of naturalisation of technological progress. The issue raised by the concepts of nature and artefact is not the dilemma dualism versus monism, which serves to fuel endless confrontations between so-called technophobics and technophilics. The polarity phusis and technê is part of a triangular network of concepts, which involves nomos as a third summit. The boundary between nature and artefact is a matter of nomos, it is a useful guide for decisions about research directions and technological choices. It is an indispensable conceptual tool for regulating technological innovations.

1

  Bernadette Bensaude Vincent Université Paris 1 Panthéon-Sorbonne Nature and art, an ancient divide and still a hot topic. Paper read at the Conference Natural vs Artificial University of Basel, 14 November 2014

Rip A. (2006), "Folk theories of nanotechnologists". Science as Culture 15, pp. 349-365.

Descola, Philippe (2005) Par delà la nature et la culture, (2005). See also Lloyd, Geoffrey, « The invention of Nature » in Methods and Problems in Greek Science Cambridge, Cambridge University Press, 1991, pp. 417-434.

Philippe Descola, "Les cosmologies de Indiens d'Amazonie », La recherche, N° 292, novembre 1996 : 62-67, quot. p. 66 (my transl).

Aristotle, Physics II, Chapter 8.

Ibid., Chapter 1.

Newman, William R. (2004) Promethean Ambitions. Alchemy and the Art-Nature Debate, Chicago, Chicago University Press. See alsoEmerton, Norma (2004), The Scientific Reinterpretation of Form, Ithaca, Cornell University Press.

Daston, Lorraine. "The Nature of Nature in Early Modern Europe," Configurations, 6, 1998 : 149-172

George Church and Ed Regis, Regenesis How Synthetic Biology will Reinvent Nature & Ourselves, New York, Basic Books 2012, p. 4.

Bruno Latour, We Have Never Been Modern, transl. from French by Catherine Porter, Cambridge, Harvard University Press, 1993.

Michel Serres, The Natural Contract, transl. from French by E. MacArthur & W. Paulson, University of Michigan Press, 2012


Stéphane Servais

Dominique Letexier

Roland Favier

Claude Duchamp

Dominique Desplanches
email: desplanc@univ-lyon1fr

Stephane Servais

Prevention of unloading-induced atrophy by vitamin E supplementation : links between oxidative stress and soleus muscle proteolysis ?

Keywords: Muscle atrophy, Vitamin E, Oxidative stress, Uncoupling proteins, Heat shock protein, Caspases, Ubiquitine ligases

Exposure to reduced activity induces skeletal muscle atrophy. Oxidative stress might contribute to muscle wasting via proteolysis activation. This study aimed to test two hypotheses in rats. Firstly, supplementation of the antioxidant vitamin E, prior and during the phase of unloading, would partly counteract unloading-induced soleus muscle atrophy.

Secondly, vitamin E supplementation would decrease the rate of muscle proteolysis by reducing expression of calpains, caspase-3, -9, -12 and E3 ubiquitin ligases (MuRF1 and MAFbx). Soleus muscle atrophy (-49%) induced by fourteen days of hindlimb unloading was reduced to only 32 % under vitamin E. Vitamin E partly prevented the decrease in type I and IIa fiber size. Supplementation increased HSP72 content, suppressed the rise in muscle level of thiobarbituric acid-reactive substance caused by unloading but failed to modify the lower ratio of reduced vs. oxidized glutathione, the higher uncoupling proteins mRNA and the antioxidant enzyme activities (superoxide dismutase, catalase, glutathione peroxidase) observed after unloading. Vitamin E treatment abolished the large upregulation of caspase 9, 12 and MuRF1 transcripts in unloaded muscle and greatly decreased the upregulation of µcalpain, caspase 3 and MAFbx mRNA. In conclusion, the protective effect of vitamin E might be due to modulation of muscle proteolysis-related genes rather than to its antioxidant function.

INTRODUCTION

Exposure to reduced activity induces a disuse atrophy of postural muscles which results in a decrease in muscle volume and strength and in a compromised ability to deal with physical work capacity [START_REF] Desplanches | Structural and functional adaptations of skeletal muscle to weightlessness[END_REF][START_REF] Jackman | The molecular basis of skeletal muscle atrophy[END_REF][START_REF] Mckinnell | Molecular mechanisms of muscle atrophy[END_REF]. Multiple rodent models, including hindlimb unloading, have been developed to better understand the factors involved in muscle wasting [START_REF] Morey-Holton | Hindlimb unloading rodent model : technical aspects[END_REF]. The loss in muscle mass is caused primarily by a rapid decrease in myofibril protein synthesis rate followed by a slower transient increase in myofibril protein degradation rate [START_REF] Thomason | Atrophy of the soleus muscle by hindlimb unweighting[END_REF]. Muscle atrophy is accompanied by a general shift in the contractile and metabolic profiles of a slow-twitch oxidative muscle toward that of a fast-twitch glycolytic muscle [START_REF] Desplanches | Structural and functional responses to prolonged hindlimb suspension in rat muscle[END_REF][START_REF] Wittwer | Prolonged unloading of rat soleus muscle causes distinct adaptations of the gene profile[END_REF]. Among potential triggers and molecular signalling events underlying such skeletal muscle plasticity, oxidative stress might contribute to muscle wasting [START_REF] Jackman | The molecular basis of skeletal muscle atrophy[END_REF][START_REF] Lawler | Hindlimb unloading increases oxidative stress and disrupts antioxidant capacity in skeletal muscle[END_REF][START_REF] Powers | Mechanisms of disuse muscle atrophy : role of oxidative stress[END_REF][START_REF] Kondo | Mechanism of oxidative stress in skeletal muscle atrophied by immobilization[END_REF]. Although early studies in rats suggested that vitamin E (alpha-tocopherol), a potent antioxidative nutrient, decreased skeletal muscle atrophy induced by limb immobilization or plaster cast [START_REF] Appell | Supplementation of Vitamin E may attenuate skeletal muscle immobilization atrophy[END_REF][START_REF] Kondo | Trace element movement and oxidative stress in skeletal muscle atrophied by immobilization[END_REF], Koesterer et al. [START_REF] Koesterer | Increased antioxydant capacity does not attenuate muscle atrophy caused by unweighting[END_REF] demonstrated that antioxidant supplementation failed to attenuate the soleus and gastrocnemius (GS) atrophy or the decrease in Gas force generation induced by hindlimb unloading. Presumably, these discrepancies could be caused by differences in experimental design related to various disuse models and /or potential dose-dependent effects of antioxidant supplementation. More importantly, cellular functions of vitamin E that are independent of its radical-scavenging properties, have been demonstrated in the last years [START_REF] Azzi | Vitamin E mediates cell signalling and regulation of gene expression[END_REF][START_REF] Zingg | Non-antioxidant activities of vitamin E[END_REF]. Azzi et al. [START_REF] Azzi | Vitamin E mediates cell signalling and regulation of gene expression[END_REF][START_REF] Zingg | Non-antioxidant activities of vitamin E[END_REF] reported that alpha-tocopherol mediates cell signalling and regulates the expression of a large number of genes. A protective effect of vitamin E might be due to modulation of muscle proteolysis-related genes rather than to its antioxidant function.

Currently, unresolved questions remain concerning the specific role of reactive oxygen species (ROS) in the regulation of hindlimb unloading-induced muscle atrophy and more specifically which protease system are controlled by ROS [START_REF] Powers | Mechanisms of disuse muscle atrophy : role of oxidative stress[END_REF]. There is evidence that both lysosomal and /or Ca 2+ -activated (i.e. calpains) proteases contribute for a minor part to muscle wasting while the ATP-ubiquitin proteasome pathway is mainly responsible for the unloaded-soleus muscle proteolysis [START_REF] Taillandier | Coordinate activation of lysosomal Ca 2+ -activated and ATP-ubiquitin -dependent proteinases in the unweighted rat soleus muscle[END_REF]. Additionally, a cascade of cystein-dependent proteases called caspases might be involved in the loss of myonuclei by apoptosis in skeletal muscle atrophied fibers [START_REF] Allen | Apoptosis : a mechanism contributing to remodeling of skeletal muscle in response to hindlimb unweighting[END_REF][START_REF] Leeuwenburgh | Agerelated differences in apoptosis with disuse atrophy in soleus muscle[END_REF]. It therefore appeared promising to further explore the therapeutic potential of vitamin E supplementation in muscle atrophy and to advance in the understanding of signaling pathways that control muscle mass following vitamin E supplementation.

This study was designed to test two hypotheses in rats. Firstly, long-term supplementation of the lipid-soluble antioxidant vitamin E, prior (21 days) and during (14 days) the phase of unloading, would partly counteract unloading-induced soleus muscle atrophy. Secondly, vitamin E supplementation would downregulate genes involved in muscle proteolysis. To address this question, we measured biomarkers of oxidative stress (glutathione vs. glutathione disulfide ratio, level of thiobarbituric acid-reactive substance), antioxidant enzyme activities (superoxide dismutase, catalase and glutathione peroxidase) and other potent antioxidant defense systems (uncoupling proteins, UCP2, UCP3 mRNA and heat shock protein content, HSP72). We assessed muscle proteolysis by measuring the relative abundance of mRNA encoding calpains, caspase-3, -9, -12 and two atrophy-related ubiquitine ligases (Muscle Ring Finger 1, MuRF1 and Muscle Atrophy F-box, MAFbx). Here we show that prevention of muscle atrophy by vitamin E might be due to modulation of muscle proteolysis-related genes rather than to its antioxidant function.

EXPERIMENTAL PROCEDURES

Animal care and protocol

Thirty two pathogen-free male Wistar rats, weighting 350 g from Charles River, were housed in a temperature-controlled room (24 ± 2°C) with a light dark cycle (12:12h). After one week of acclimatation, rats were assigned randomly to one of four experimental conditions. Two groups of eight rats received six intraperitoneal injections of vitamin E at a dose of 60 mg / kg twice a week, for 35 days according to Appell et al. [START_REF] Appell | Supplementation of Vitamin E may attenuate skeletal muscle immobilization atrophy[END_REF]. Vitamin E was given in the form of α tocopherol acetate solubilized in soybean oil (Sigma). After 21 days of treatment, half of them were hindlimb suspended for 14 days in individual cages using Morey's tail-suspension model [START_REF] Morey-Holton | Hindlimb unloading rodent model : technical aspects[END_REF]. Other rats were kept as controls. Two other groups of eight rats received soybean injections during 35 days and half of them were suspended for 14 days. This protocol generated 4 groups of rats : controls rats (C), vitamin E-supplemented control rats (C + VE), hindlimb unloaded rats (HU), vitamin E-supplemented and unloaded rats (HU+VE). The present investigation was performed following the recommendations provided by the European Convention for the protection of Vertebrate Animals used for Experimental and Scientific purposes (Council of Europe N° 123, Strasbourg, 1985). The animals were anaesthetised with halothane. Soleus muscles were excised, weighed, frozen in isopentane chilled with liquid nitrogen and stored at -80°C until analysis.

Myosin ATPase

The midbelly region of each muscle was cut in serial transverse sections (10 µm) on a microtome at -25°C and stained for the myosin adenosine triphosphatase (ATPase) as previously described [START_REF] Desplanches | Structural and functional responses to prolonged hindlimb suspension in rat muscle[END_REF]. Muscle fibers were classified into two major types (I, IIa). The fiber cross-sectional areas were calculated by means of a computerized planimetry coupled to a digitizer and the area of at least 100 fibers were measured.

Glutathione levels

Reduced (GSH) and oxidized glutathione (GSSG) were measured according to the method of Anderson (19) by monitoring the reduction by GSH of 5,5'-dithio-bis-(2nitrobenzoic acid) (DTNB) to 5-thio-2-nitrobenzoate (TNB) at 412 nm (25°C). Proteins were precipitated with ice-cold 5 % metaphosphoric acid and centrifuged at 5000 g for 5 min. For GSH measurements, samples were derivated with 2-vinyl-pyridin. The assay was initiated by the addition of 10 µL of 50 U/mL glutathione reductase. GSH was used as a standard and was assayed in parallel under the same condition as the tissue samples.

Muscle lipid peroxidation

The concentration of lipid peroxide was estimated by the thiobarbituric acid-reactive substances (TBARS) method described by Ohkawa et al. [START_REF] Ohkawa | Assay for lipid peroxides in animal tissues by thiobarbituric acid reaction[END_REF].

Antioxidant enzymes activities

A portion of soleus muscle was homogenised with a potter Elvehjem at 4°C, in buffer containing KH 2 PO 4 (100 mM), DTT (1mM) and EDTA (2 mM), pH 7.4. After centrifugation (3000 g/min, for 5 minutes), the supernatant was used for enzymatic assays. Superoxide dismutase (SOD) activity was assayed by monitoring the rate of acetylated cytochrome c reduction by superoxide radicals generated by the xanthine-xanthine oxidase system [START_REF] Flohe | Superoxide dismutase assays[END_REF]. One activity unit of SOD is defined as the amount of enzyme which inhibits the rate of acetylated cytochrome c reduction by 50 %. To distinguish mangano-SOD (MnSOD), exclusively located in mitochondrial matrix, from cuprozinc-SOD (CuZnSOD), which is primarily located in the cytosol, SOD activity was determined after incubation with NaCN (1 mM). At this concentration, cyanide inhibits the CuZn isoform of the enzyme, but does not affect the Mn isoform [START_REF] Ohkawa | Assay for lipid peroxides in animal tissues by thiobarbituric acid reaction[END_REF]. The total activity of glutathione peroxidase (GPx) activity was assayed with cumene hydroperoxide as a substrate according to Tappel [START_REF] Tappel | Glutathione peroxidase and hydroperoxides[END_REF]. The activity of catalase (CAT) was determined by the method of Aebi (23). This technique used the first-order rate constant of the decomposition of H 2 O 2 by tissue CAT at 20°C. One unit of catalase activity was calculated by using k = (2.3/dt)(log A 1 /A 2 ), where k is CAT activity, dt is change in time, A 1 is initial absorbance, and A 2 is final absorbance. All enzyme activities are expressed in U/ mg of proteins.

HSP 72 content

For HSP quantification, we performed polyacrylamide gel electrophoresis and immunoblotting as previously described [START_REF] Desplanches | Skeletal muscle HSP72 response to mechanical unloading: influence of endurance training[END_REF]. Briefly, 200 µL of muscle homogenate were mixed with 200 µL of buffer containing 40 mM Tris(hydroxymethyl)aminomethane pH 6.8, 1% SDS, 6% glycerol, and 1% ß-mercaptoethanol. This mixture was then heated at 100°C for 10 min, and subjected to one-dimensional sodium dodecyl sulfate (SDS)-PAGE with a 5% stacking and 12.5% resolving gels for 12 hours. After electrophoretic separation, proteins were transferred at a constant voltage to nitrocellulose membranes. After protein transfer, the membranes were blocked for 2h, then incubated 2 h with a monoclonal antibody specific for HSP72 (SPA 810, StressGen, diluted 1:1000) and then exposed to the secondary antibody (goat anti-mouse immunoglobulin G conjugated to horseradish peroxidase, Bio-Rad at a 1:10000 dilution). HSP72 were visualized by the enhanced chemiluminescence detection method (RPN 2106, Amersham). Scanning with a densitometer performed quantification of bands from blots and the data were expressed numerically as integrated optical density arbitrary units.

mRNA concentration in soleus muscle

Total RNA were extracted from muscle samples (50 mg) of rats using Trizol® (Invitrogen). Concentration and purity were verified by measuring optimal density at 260 and 280 nm. Their integrity was checked by 1% agarose gel electrophoresis (Eurobio). mRNA relative abundance was measured by semi-quantitative reverse transcription polymerase chain reaction (RT-PCR) using cyclophilin as reference. Primer sequences are shown in table 1. For each sample, a RT was performed from 1 µg of total RNA with 100 U of M-MLV Reverse Transcriptase (Promega), 5µL of M-MLV RT 5X buffer, 20 U of RNasin Ribonuclease Inhibitor, 15 nmoles of deoxynucleotide triphosphate and 1 µg of oligo dT, in a final volume of 25 µL. The reaction consisted of 5 min at 70°C (RNA and oligo dT), then 90 min at 42°C (all mix) followed by 10 min at 70°C. After chilling, 2.5 µL was used for PCR. The 2.5 µL of RT medium was added to 47.5 µL of PCR mix containing 5 µL of 10X EurobioTaq PCR buffer, 75 nmoles of MgCl 2 , 15 nmoles of deoxynucleoside triphosphate, 2.5 U of EurobioTaq DNA polymerase, 22.5 pmoles of corresponding antisense and sense primers.

The PCR conditions were : 2 min at 94 °C followed by n cycles of PCR (1 cycle = 1 min at 94°C, 1 min at 60°C, 1 min at 72°C). The numbers of cycles is indicated in table 1 for each target. PCR was ended by 10 min at 72°C. Products were analysed on 1.5% agarose gel prestained with ethidium bromide. For quantitation of relative bands intensities, pictures were taken with a Camera DC120 (Kodak) and the ratio of each target to cyclophilin was determined for each sample with Kodak Digital Science 1D 2.0 (Kodak Scientific Imaging System).

Statistical analysis

All data reported are means ± SE. A multifactorial analysis of variance was used for intergroup comparisons. The Fisher paired least significant difference was used to identify specific means differences. Values were considered statistically different when P < 0.05.

RESULTS

Muscle mass and fiber size.

Soleus muscle to body mass ratio and cross-sectional areas of type I and IIa fibers are shown in Table 2. Soleus muscle atrophy (-49%) induced by 14 days of hindlimb unloading was reduced to only 32 % under vitamin E. Unloading led to a decrease in type I (-59 %) and IIa (-42 %) fiber size. Vitamin E partly prevented this decrease as type I and IIa fiber crosssectional areas were only reduced by 38 and 32 % respectively.

GSH/GSSG

In control rats, there was no significant change in reduced to oxidized glutathione ratio (GSH / GSSG) after vitamin E supplementation (Fig. 1a). Unloading resulted in a significant decrease (-23 %) of GSH / GSSG in HU rats but vitamin E supplementation failed to modify the lower ratio of reduced vs. oxidized glutathione.

Muscle lipid peroxidation

Thiobarbituric acid reactive substances (TBARS) content, an index of lipid peroxidation, was similar in C and C+VE (34.9 ± 3.6 and 33.8 ± 1.5 nmole MDA/g tissue, respectively, Fig. 1b). Vitamin E supplementation abolished the increase (+ 35 %) in TBARS content caused by unloading.

Antioxidant capacities.

There was no significant difference in cytosolic (ZnCu-SOD), mitochondrial (Mn-SOD), GPx activities between C and C+VE rats (Fig. 2 abc). Hindlimb unloading similarly increased ZnCu-SOD activity (+ 47 %), GPx (+ 43%) and CAT ( + 90 %) activities in HU rats and HU+VE rats (Fig. 2 acd). CAT activity was elevated in the vitamin E supplemented control rats (+48 %) and there was a further significant increase on unloading (Fig. 2d).

Complementary defences : uncoupling proteins, heat shock proteins.

Similar patterns were seen for UCP2 and UCP3 mRNA. Unloading led to higher UCP2 (+30 %) and UCP3 mRNA (+ 400%) in HU and HU+VE rats, but no obvious effect of Vitamin E supplementation abolished the unloading-induced increase in caspase -9 and -12 mRNA (+39 and +50%, respectively , Fig. 4b,c) and decreased the upregulation (+ 114 %) of caspase -3 mRNA by 50 % (Fig. 4a). MAFbx and MuRF1 mRNA were increased in unloaded rats by 50 and 59 % respectively (Fig 5). This effect was significantly prevented by vitamin E supplementation for MuRF1 and at the limit of statistical significance for MAFbx (P = 0.07).

DISCUSSION

Supplementation of Vitamin E prevented soleus muscle atrophy by 20 % after 14 days of hindlimb unloading. The type I and IIa fiber cross-sectional areas were only decreased by 38 and 32 % respectively after Vitamin E treatment (vs 59 and 42 % respectively for the untreated-unloaded rats). Similar results were previously observed in rats submitted to various disuse models : plaster cast [START_REF] Appell | Supplementation of Vitamin E may attenuate skeletal muscle immobilization atrophy[END_REF] or immobilization of the ankle joint of one hindlimb in the extended position [START_REF] Kondo | Mechanism of oxidative stress in skeletal muscle atrophied by immobilization[END_REF]. However, using the same experimental design and the same duration of hindlimb unloading, Koesterer et al [START_REF] Koesterer | Increased antioxydant capacity does not attenuate muscle atrophy caused by unweighting[END_REF] reported that vitamin E supplementation was not an effective countermeasure to soleus muscle disuse, suggesting that the mechanisms of atrophy induced by immobilization and hindlimb unloading might be fundamentally different.

The dose-dependent effects, the potential composition and duration of the pretreatment (three weeks vs one) of supplementation might explain these discrepancies. In the present study, unloading, as expected [START_REF] Koesterer | Increased antioxydant capacity does not attenuate muscle atrophy caused by unweighting[END_REF], resulted in a lower ratio of reduced vs. oxidized glutathione and in an increased TBARS content, two biomarkers of oxidative stress and vitamin E supplementation restored the increased TBARS content caused by unloading. In fact, we have clearly demonstrated, as it was reported with other disuse models [START_REF] Kondo | Mechanism of oxidative stress in skeletal muscle atrophied by immobilization[END_REF][START_REF] Appell | Supplementation of Vitamin E may attenuate skeletal muscle immobilization atrophy[END_REF], that vitamin E supplementation partly prevents soleus atrophy. A complex cytoprotective system that includes antioxidant enzymes is recruited against free radical damage. Unloading significantly increased activities of ZnCu-SOD (primarily localized in the cytosol) as previously observed ( 8) but failed to induce a significant rise (P = 0.11) in Mn-SOD (localized in the mitochondrial matrix) activity.

Unloading induces a rise in GPx and CAT activities contrary to the decrease observed by Lawler et al. [START_REF] Lawler | Hindlimb unloading increases oxidative stress and disrupts antioxidant capacity in skeletal muscle[END_REF]. Vitamin E supplementation did not confer an additionnal protection against oxidative damage through a further increase in antioxidant enzymes activities.

One of the main adaptations of mitochondria to oxidative stress would be a mild uncoupling of oxidative phosphorylation that might reduce the mitochondrial production of ROS by lowering mitochondrial membrane potential [START_REF] Halliwell | Free radical in biology and medicine[END_REF][START_REF] Papa | Reactive oxygen species, mitochondria, apoptosis and aging[END_REF]. The UCPs might attenuate cellular oxidative damage in some pathophysiological states leading to increased oxidative stress such as cancer cachexia [START_REF] Argiles | The role of uncoupling proteins in pathophysiological states[END_REF]. Body weight loss and muscle atrophy are commonly associated with this syndrome. An activation of UCP2 and UCP3 gene expression associated with an increased catalase protein content was reported in atrophied gastrocnemius muscles of tumour-bearing rats [START_REF] Sanchis | Skeletal muscle UCP2 and UCP3 gene expression in a rat cancer cachexia model[END_REF][START_REF] Busquets | Activation of UCPs gene expression in skeletal muscle can be independent on both circulating fatty acids and food intake. Involvement of ROS in a model of a mouse cancer cachexia[END_REF]. Busquet et al. [START_REF] Busquets | Activation of UCPs gene expression in skeletal muscle can be independent on both circulating fatty acids and food intake. Involvement of ROS in a model of a mouse cancer cachexia[END_REF] postulate that UCPs might confers protection against muscle oxidative injury. We have previously shown a marked upregulation of UCP3 gene in unloaded soleus muscle suggesting that the rise in UCP3 expression might contribute to protect less active skeletal myocytes from oxidative damage by stimulating oxygen consumption, depleting the local concentration of oxygen and decreasing the generation of ROS [START_REF] Denjean | Muscle-specific up-regulation of rat UCP3 mRNA expression by long-term hindlimb unloading[END_REF]. The current study is the first to report a similar upregulation of UCP2 and UCP3 mRNA in unloaded soleus muscle following vitamin E supplementation compared to untreated rats. These results clearly show that the effects of unloading and vitamin E treatment were found to be non-additive. Assuming a role of UCP2 as a regulator of ROS production by reducing the mitochondrial proton gradient [START_REF] Arsenijevic | Disruption of the uncoupling protein-2 gene in mice reveals a role in immunity and reactive oxygen species production[END_REF][START_REF] Li | Uncoupling protein-2 participates in cellular defense against oxidative stress in clonal beta-cells[END_REF][START_REF] Negre-Salviayre | A role for uncoupling protein-2 as a regulator of mitochondrial hydrogen peroxide generation[END_REF], overexpression of UCP2 would be also beneficial for preventing unloaded cells from free-radical damage. Supplementation of Vitamin E failed to modify the lower ratio of reduced vs. oxidized glutathione, the increased antioxidant enzyme activities (superoxide dismutase, catalase, glutathione peroxidase) and the higher uncoupling proteins mRNA observed after unloading. Consequently, our data suggest that Vitamin E acts in a non-antioxidant way on the prevention of muscle atrophy which is consistent with the findings of previous studies [START_REF] Azzi | Vitamin E mediates cell signalling and regulation of gene expression[END_REF][START_REF] Zingg | Non-antioxidant activities of vitamin E[END_REF]. Since 15 years, it has been well documented that Vitamin E exerts cellular functions that are independent of its radical-scavenging properties [START_REF] Azzi | Vitamin E mediates cell signalling and regulation of gene expression[END_REF][START_REF] Zingg | Non-antioxidant activities of vitamin E[END_REF].

To our knowledge this is the first report to demonstrate an increase in the stressinducible form of HSP70 (HSP72) content as a result of Vitamin E supplementation in unloaded rats. In non-supplemented rats, the maintained basal HSP72 level in soleus muscle after two weeks of unloading is in accordance with our previous data [START_REF] Denjean | Muscle-specific up-regulation of rat UCP3 mRNA expression by long-term hindlimb unloading[END_REF] and those of Oishi et al. [START_REF] Oishi | Upregulation of HSP72 in reloading rat soleus muscle after prolonged hindlimb unloading[END_REF]. The induction of HSP72 protein suggests that HSP72 acts as a complementary protective mechanism against muscle atrophy. Given the role of HSP72 as molecular chaperones preventing aggregation and facilitating the refolding of denaturated proteins, increased expression of HSP72 may prevent oxidative damage and assist in repair of damaged proteins [START_REF] Georgopoulos | Role of the major heat shock proteins as molecular chaperones[END_REF][START_REF] Smolka | HSP72 as a complementary protection against oxidative stress induced by exercise in soleus muscle of rats[END_REF]. Moreover stress-inducible form of Hsp70 prevents cell apoptosis by interfering with the ability of cytochrome c and Apaf-1 (apoptosis protease activator protein) to recruit procaspase-9 [START_REF] Beere | Heat-shock protein 70 inhibits apoptosis by preventing recruitment of procaspase-9 to the apaf-1 apoptosome[END_REF][START_REF] Saleh | Negative regulation of the apaf-1 apoptosome by hsp70[END_REF].

In a recent review, Powers et al. [START_REF] Powers | Mechanisms of disuse muscle atrophy : role of oxidative stress[END_REF], raised the interesting question of whether the redox control of protease activity during muscle disuse atrophy occurs by allosteric regulation (ie control of intracellular calcium levels) and /or via increased gene expression of proteases.

The present study characterizes some signaling pathways that control unloading-induced muscle proteolysis following antioxidant supplementation. Vitamin E supplementation was found to prevent the upregulation of µ-calpain mRNA while m-calpain mRNA remained unaffected during muscle wasting. Ubiquitous calpains are non-lysosomal Ca 2+ activated cystein proteases that cleave titin and nebulin at sites near the Z-disk, leading to a progressive disruption of the Z-disk [START_REF] Goll | The calpain system[END_REF][START_REF] Bartoli | Calpains in muscle wasting[END_REF]. They are involved in the initial breakdown of myofibrils, releasing actin and myosin from the sarcomere before they undergo ubiquitination and degradation by the proteasome. The ubiquitous µ and m-calpains (also called 1 and 2) may have different role in the development of soleus atrophy since they have different in vitro calcium sensibility (in the range of 3-50 µM for µ-calpain and 400-800 µm for m-calpain, 36). In parallel to the upregulation of µ-calpain in our study, a 36 % increase in resting intracellular calcium (from 17 to 23 nM) was reported by Ingalls et al. [START_REF] Ingalls | Intracellular Ca 2+ transients in mouse soleus muscle after hindlimb unloading and reloading[END_REF] in mice soleus muscle after 14 days of hindlimb suspension. Goll et al. [START_REF] Goll | The calpain system[END_REF] postulated that the increase in intracellular calcium is not sufficiently large to activate the calpains directly but it seems probable that it alters the regulation of calpain activity by calpastatin, phosphorylation or still unknown mechanisms. Indeed, a previous study reported a sustained activation of m-calpain activity after 9 days of hindlimb suspension [START_REF] Taillandier | Coordinate activation of lysosomal Ca 2+ -activated and ATP-ubiquitin -dependent proteinases in the unweighted rat soleus muscle[END_REF].

Vitamin E partly controls the soleus muscle proteolysis mediated by the ubiquitin proteasome pathway via two muscle-specific ubiquitin ligases (E3) : MAFbx (muscle atrophy Fbox or atrogin-1) and MuRF1, (muscle ring finger, [START_REF] Bodine | Identification of ubiquitin ligases required for skeletal muscle atrophy[END_REF][START_REF] Gomes | Atrogin-1, a muscle specific F-box protein highly expressed during muscle atrophy[END_REF]. MAFbx and MuRF1 are critical regulators in the enhanced proteolysis leading to muscle atrophy in various diseases [START_REF] Jackman | The molecular basis of skeletal muscle atrophy[END_REF][START_REF] Bodine | Identification of ubiquitin ligases required for skeletal muscle atrophy[END_REF].

As Murf1 has been shown to bind titin [START_REF] Centner | Identification of muscle ring finger proteins as potential regulators of the titin kinase domain[END_REF], MurF1 might participate to the disruption of the Z disk in addition to the calpain system. Vitamin E supplementation prevented MurF1 induction whereas MAFbx expression was greatly reduced (P = 0.07). It has been well documented that Vitamin E has important non-antioxidant effects and mediate cell signalling and regulation of gene expression [START_REF] Azzi | Vitamin E mediates cell signalling and regulation of gene expression[END_REF][START_REF] Zingg | Non-antioxidant activities of vitamin E[END_REF]. For example, vitamin E downregulates a number of genes involved in acute inflammation. Given the role played by cytokines such as TNFα (tumor necrosis factor) which activate NF-KB in muscle cells [START_REF] Li | Skeletal muscle myocytes undergo protein loss and reactive oxygen-mediated NF-KB activation in response to tumor necrosis factor α [END_REF] and the pronounced antiinflammatory effects of vitamin E (15), one could possibly explain the prevention of MurF1 upregulation. However, if cytokines are involved in cachexia, Hunter et al. [START_REF] Hunter | Activation of an alternative NF-KB pathway in skeletal muscle during disuse atrophy[END_REF] did not find any change in TNFα -protein levels after a short period of muscle unloading (seven days).

Previous studies have shown that apoptosis contributes to the unloading-induced soleus muscle atrophy [START_REF] Allen | Apoptosis : a mechanism contributing to remodeling of skeletal muscle in response to hindlimb unweighting[END_REF][START_REF] Leeuwenburgh | Agerelated differences in apoptosis with disuse atrophy in soleus muscle[END_REF]. In the present study, vitamin E supplementation prevents the upregulation of caspases-9 and -12 but failed to totally abolished the increased caspase-3 mRNA. Sarcoplasmic reticulum can induce apoptosis through a calpain-mediated activation of caspase-12 and subsequent activation of caspase-9 and the key effector protease caspase-3 [START_REF] Dupont-Vergsteegden | Apoptosis in muscle atrophy : relevance to sarcopenia[END_REF]. A second intrinsic pathway of apoptosis, dependent of mitochondria, is partly initiated by reactive oxygen species [START_REF] Dupont-Vergsteegden | Apoptosis in muscle atrophy : relevance to sarcopenia[END_REF]. Release of cytochrome c into the cytosol induced the formation of an apoptosome complex with Apaf-1, ATP and procaspase-9, leading to the activation of caspase 3. Recently, Leeuwenburgh et al. [START_REF] Leeuwenburgh | Agerelated differences in apoptosis with disuse atrophy in soleus muscle[END_REF] reported an increase in caspase-3 activity in young unloaded muscles suggesting that disuse-induced apoptosis was likely caspase-dependent whereas additional pathways such as the caspase-independent translocation of a proapoptotic endonuclease (EndoG, a mitochondrion endo-specific nuclease) might be involved in old rats. The implication of these different patterns in unloading-induced atrophy and in prevention by vitamin E should be further investigated.

The present study demonstrates that acute dosing of vitamin E, prior and during unloading, partly prevents soleus muscle atrophy. Vitamin E failed to modify markers of oxidative stress (GSH/GSSG, SOD, GPx, CAT, UCPs), suggesting a non-antioxidant mechanism for Vitamin E action. A number of genes involved in muscle proteolysis such as µcalpain, caspases-3,-9,-12 and two atrophy-related ubiquitine ligases (MuRF1 and MAFbx), were downregulated by Vitamin E while HSP72 was upregulated. These results provide an alternative signaling mechanism for understanding the muscle protective effects of Vitamin E during unloading, via muscle proteolysis-related genes regulation. Vitamin E may be regarded as an adjuvant to protect muscle cells from atrophy.

LISTE OF ABBREVIATIONS

CAT: catalase

  vitamin E was observed in C rats (Fig 3ab). No change occurred in basal HSP 72 level in various treatments whether supplementation or hindlimb unloading (Fig 3c). However, high levels of HSP 72 (+ 50 %) were found in soleus muscle of HU+VE rats (Fig 3c). Calpains, proapoptotic caspases, E3 ubiquitine ligases. In control rats, the relative abundance of caspases 3, 9, 12, MAFbx and MuRF1 mRNA were not affected by vitamin E supplementation (Fig 4, 5ab). µ-calpain mRNA was increased to 29 % after unloading, an effect that was 93 % prevented by vitamin E supplementation (P = 0.055, Fig 5c). m-calpain mRNA was neither affected by unloading nor by vitamin E supplementation (Fig 5d).

GPx

  heat shock protein of 72 KDa MAFbx: muscle atrophy F-box/ atrogin-1 MuRF1 : muscle ring finger 1 ROS: reactive oxygen species SOD: superoxide dismutase TBARS = thiobarbituric acid-reactive substance UCP : uncoupling protein

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Effect of unloading and vitamin E supplementation on reduced to oxidized glutathione

Fig. 4 .

 4 Fig. 4. Effect of vitamin E on Caspase 3, 9, 12 mRNA in control and unloaded soleus

Fig. 5 .

 5 Fig. 5. Effect of vitamin E on expression of two atrophy-related ubiquitin ligases, MAFbx and

Table 1 : Primer sequences used for RT-PCR

 1

		Sense (5'	3')	Antisense (5'	3')	Size (bp) n cycles
	cyclophilin (NM_017101)	GTG GCA AGT CCA TCT ACG GAG	CCA CAG TCG GAG ATG GTG ATC	265	25
	MAFbx (AY059628)	GCC TGA ACT ACG ATG TTG CAG	GCT GGT CTT CAA GAA CTT TC	323	29
	MuRF1 (AY059627)	AGG TGC CTA CTT GCT CCT TGT	GCT GTT TCC ACA AGC TTG GTC	378	27
	caspase 3 (NM_012922)	CAC TGG AAT GTC AGC TCG CAA	CCA CTG TCT GTC TCA ATA CCG	359	32
	caspase 9 (NM_031632)	GCA GGA TCC AGA AGC TGT TAC	GCC ATA TCT GCA TGT CTC TCG	281	36
	caspase 12 (NM_130422)	CCG ACA AAC AGC TGA GTT TAC	GTC AGT CTC AGC ATC ATC TCT	361	32
	µ-calpaine (NM_019152)	CCG ATA TCC GTG ATT TGG AGG	TCG ACT GTC ATA GTC GTC TGC	478	36
	m-calpaine (NM_017116)	CAT CGC GAT GAA ACT GGC CAA GGA AGC TCT GGT CTA GAG GCA CA	388	36
	UCP2 (NM_019354)	AGC AGT TCT ACA CCA AGG GC	AGC ATG GTC AGG GCA CAG TG	471	28
	UCP3 (NM_013167)	ATG CAT GCC TAC AGA ACC AT	CTG GGC CAC CAT CCT CAG CA	314	28

Table 2 : Soleus muscle to body mass ratio and cross-sectional areas of type I and IIa fibers in soleus muscle

 2

	Fiber Areas
	(µm 2 )

This work was supported by CNES (Centre National de la Recherche Spatiale) Grant 071299 to D. Desplanches. The authors thank Marie-Hélène Sornay-Mayet and Anne Sophie Rouziere for excellent technical assistance and Christiaan Leeuwenburgh for stimulating discussions.


E Sonnendrücker

F Filbet

A Friedman

E Oudet

J.-L Vay

Vlasov simulations of beams with a moving grid

Introduction

Thanks to the rapid increase of computing power in recent years, simulations of plasmas and particle beams based on direct solution of the Vlasov equation on a multi-dimensional phase-space grid are becoming attractive as an alternative to Particle-In-Cell (PIC) simulations. Their strength lies essentially in the fact that they are noiseless and that all parts of phase space, including the tail of the distribution, are equally well resolved. Their major drawback is that, for inhomogeneous systems, many of the grid points (where no particles are present) are wasted. This is especially the case for beam simulations where the beam moves rapidly through the phase space (due to varying alternating-gradient focusing forces, for example). This inefficiency has made such Vlasov simulations unsuitable for those cases.

One of the methods which has proven very efficient for the direct resolution of the Vlasov equation is the semi-Lagrangian method [START_REF] Sonnendrücker | The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations[END_REF][START_REF] Sonnendrücker | Simulation of heavy ion beams with a semi-Lagrangian Vlasov solver[END_REF]. It consists in updating the values of the distribution function at the grid nodes by following the characteristics ending at these nodes backwards and interpolating the value at the bottom of the characteristics from the known values at the previous time step. In general the interpolation grid is fixed, but this is not mandatory.

This paper introduces the concept of a moving grid which is mapped at each time step from a logical uniform grid to the beam, so that it contains the whole beam without needing too many points with vanishing values of the distribution function. In order to implement this new method, we introduce a new time stepping algorithm which does not rely on the time splitting procedure traditionally used in Vlasov solvers.

The model we consider throughout this paper is the nonrelativistic Vlasov equation coupled self-consistently with Poisson's equation. It reads

∂f ∂t + v • ∇ x f + q m (E + v × B) • ∇ v f = 0, (1)
the self electric field E is computed from Poisson's equations

-0 ∇ 2 φ = ρ(x, t) = q f (x, v, t) dv, E = -∇φ.
The magnetic field is external and considered to be known. The paper is organized as follows: We first recall the traditional semi-Lagrangian method. After that, we introduce a new time stepping algorithm that does not require splitting and which is required when the coordinate axes are not aligned with the x and v directions. We then describe the moving grid algorithm in a general setting first and finally present its application to the simulation of beams in transverse phase-space along with some first numerical results.

The semi-Lagrangian method for the Vlasov equation

The semi-Lagrangian method consists in computing a numerical approximation of the solution of the Vlasov equation (1) on a phase space grid by using the property of the equation that the distribution function f is conserved along characteristics. More precisely, for any times s and t we have

f (x, v, t) = f (X(s; x, v, t), V(s; x, v, t), s),
where (X(s; x, v, t), V(s; x, v, t) are the characteristics of the Vlasov equation which are solution of the system of ordinary differential equations

dX ds = V, (2)
dV ds = E(X(s), s) + V(s) × B(X(s), s), (3)
with initial conditions

X(t) = x, V(t) = v.
From this property, f n being known one can induce a numerical method for computing the distribution function f n+1 at the grid points (x i , v j ) consisting of the following two steps:

1. For all i, j, compute the origin of the characteristic ending at x i , v j , i.e. an approximation of X(t n ; x i , v j , t n+1 ), V(t n ; x i , v j , t n+1 ).

2. As f n+1 (x i , v j ) = f n (X(t n ; x i , v j , t n+1 ), V(t n ; x i , v j , t n+1 )), f n+1 can be computed by interpolating f n which is known at the grid points at the points X(t n ; x i , v j , t n+1 ), V(t n ; x i , v j , t n+1 ).

This method can be simplified by performing a time-splitting separating the advection phases in physical space and velocity space, as in this case the characteristics can be solved explicitely.

The semi-Lagrangian method does not require any specific interpolation scheme. However, numerical experience dictates use of a high enough order so that diffusion, which is the most important numerical error in this method, is limited to an acceptable level. The only natural requirement is that the interpolation enables to get a good continuous reconstruction of f (at the lowest possible cost). Hence one could use a different interpolation grid for each time step. This can save a lot of time when the support of the distribution function evolves considerably over time, as is the case for a beam in a periodic focusing channel. In the remainder of this paper, we extend the semi-Lagrangian method to allow use of an interpolation grid which is moving in time.

A second order algorithm for the characteristics

When the grid transformation mixes space and velocity components the traditional splitting method ( [START_REF] Cheng | The integration of the Vlasov equation in configuration space[END_REF]) cannot be performed. Therefore we need to introduce an efficient method for solving the characteristics without splitting. A possible option would be to use the two time-steps method that was introduced in [START_REF] Sonnendrücker | The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations[END_REF]. However, this has the drawback of decoupling even and odd time steps. Let us instead introduce a second order predictor-corrector method to compute the origin of the characteristics based on an isochronous leap-frog algorithm.

Algorithm 1: Knowing the final position (X n+1 , V n+1 ) at time step t n+1 , as well as f n , ρ n-1 , E n we can compute the initial position (X n , V n ) using the following algorithm:

1. Predict Ēn+1 using the continuity equation (or directly Ampere's law in 1D)

ρ n+1 = ρ n-1 -2∆t∇•J n , J n = q f n (x, v)v dv, -∇ 2 φ n+1 = ρ n+1 0 , Ēn+1 = -∇φ n+1 . 2. V n+ 1 2 = V n+1 -∆t 2 Ēn+1 (X n+1 ); X n = X n+1 -∆tV n+ 1 2 ; V n = V n+ 1 2 -∆t 2 E n (X n ). 3. f n+1 (X n+1 , V n+1 ) = interpolation(f n )(X n , V n ); ρ n+1 = f n+1 dv, 4. Correct Ēn+1 using -∇ 2 φ n+1 = ρ n+1 0 , Ēn+1 = -∇φ n+1 . 5. If Ēn+1 -Ēn+1
prev > threshold go back to 2. Our first 1D tests show that the error decreases very rapidly: the relative error is of the order of 10 -2 after the predictor step, decreases to around 10 -9 after one corrector step and reaches 10 -15 after two corrector steps. Hence, given the other errors inherent in any discrete algorithm, a single corrector step is sufficient. Therefore the cost of the algorithm, which comes mostly from the interpolation step, is roughly the same as for the split algorithm, where one interpolation at each split step is necessary.

The semi-Lagrangian method on a moving grid

The algorithm for the Vlasov solve

The semi-Lagrangian method consist in two conceptually different steps:

1. An advection step which consists in solving a large number of decoupled ordinary differential equations. This step is completely independent of the grid and is most naturally performed in the physical space,

2. An interpolation step which is necessary to compute the value of the distribution function at the origin of the characteristics which are not on the grid. The interpolation grid is only needed to reconstruct the distribution function at every point in phase space at one given time step and needs not be the same at two different time steps.

In order to optimize step 2 one needs to position the interpolation points so as to be able to reconstruct f with a given acuracy at the lowest possible cost. In beam dynamics simulations the global movement of the beam is mostly determined by the external forces and even if the self forces are important it can be determined by the evolution of the envelope equation. Hence this information should be used to position the grid points.

On the other hand, in order to simplify the interpolation step, we choose to always perform it on a uniform logical grid, the position in the actual phase space of the grid points being given by an invertible mapping ϕ t from the logical grid to the physical grid. We choose ϕ t such that it is continuously differentiable as well as its inverse. The subscript t reminds us that ϕ t can be different for different times.

In order to describe the algorithm, we need to introduce a few notations regarding the logical and physical grids. We shall denote with a * the coordinates in the logical grid. Then for a given point (x, v) in the physical phase space, we have

(x * , v * ) = ϕ -1 t (x, v) or (x, v) = ϕ t (x * , v * ).
Let us also introduce the distribution function on the logical grid defined by

f * (x * , v * , t) = f (ϕ t (x * , v * ), t).
Then, the property that f is conserved along the characteristics translates into the following new conservation property for f * that shall be used in the algorithm:

f * (x * , v * , t) = f (ϕ t (x * , v * ), t), = f (x, v, t), = f (X(s; x, v, t), V (s; x, v, t), s), = f (ϕ s (X * (s; x, v, t), V * (s; x, v, t)), s), = f * (X * (s; x, v, t), V * (s; x, v, t), s),
where s parameterizes motion along the characteristics. Now, f n being known as well as ϕ n (= ϕ tn ) and ϕ n+1 , the following algorithm can be used to compute f n+1 .

Algorithm 2:

1. Compute positions in physical phase-space of grid points where f n+1 is to be computed:

(x n+1 i,j , v n+1 i,j ) = ϕ n+1 (x * i , v * j )
, where (x * i , v * j ) are the nodes of the logical grid. 2. Compute origin of grid points (x n+1 i,j , v n+1 i,j ) using algorithm 1 or similar. We denote by (X n i,j , V n i,j ) these origins. 3. Transform (X n i,j , V n i,j ) back to the logical grid at time t n : (X * n i,j , V * n i,j ) = ϕ -1 n (X n i,j , V n i,j ). 4. Interpolate f * n at origin of characteristics on logical grid to get f n+1 , as

f * (n+1) (x * i , v * j ) = f * n (X * n i,j , V * n i,j ).
Steps 2 and 4 exist in any nonsplit semi-Lagrangian code. Hence the extension of such codes to moving grids can be performed easily by implementing the transform from logical to physical space (step 1) and the back transform from physical to logical space (step 3).

Coupling with the Poisson equation

One of the problems that can arise with the moving grid is that the grid points fail to be aligned along a given position x in physical space. Hence when velocity moments, in particular ρ, need to be computed we need to interpolate f at some specified points for the numerical integration.

In order to minimize these interpolations the numerical integration is performed using an adaptive Gauss quadrature. The grid motion could be constrained to avoid this (forcing points to line up in columns of constant x); but if it is desired that the mesh motion track the phase space flow as closely as possible (so as to minimize numerical diffusion) such measures are needed. The trade-off for real applications has yet to be assessed.

In some systems, the requirement that the mapping from logical to physical mesh remain simple may itself limit the ability of the grid to follow the phase space flow.

Application to beam simulation in transverse phase space

In this kind of simulation the beam envelope can evolve greatly, leaving at any given time an large portion of a fixed grid empty and inducing much unnecessary computation. For this reason, we use a moving grid, and adapt that grid at each time step to the RMS beam envelope. Hence the transform ϕ is a rotation coupled to a dilation following the envelope motion. In the following, we consider x to be a dimensionless quantity, scaled to the size of the physical domain and More precisely, the ellipse defined by its larger dimension a, its smaller dimension b and its angle θ with respect to the (Ox) axis can be defined by the RMS parameters of the beam from the relations

tan 2θ = 2 xx x 2 -x 2 , a = 2(cos 2 θ x 2 + sin 2 θ x 2 + 2 sin θ cos θ xx ), b = 2(sin 2 θ x 2 + cos 2 θ x 2 -2 sin θ cos θ xx ),
where for a function χ(x, x ) we denote by χ(x, x ) = χ(x, x )f (x, x ) dxdx f (x, x ) dxdx .

In this calculation, we consider x to be a dimensionless quantity, scaled to the size of the physical domain and, as usual in beam physics, x = vx vz , where v z is the longitudinal velocity of the beam. The computing box at time t n+1 is determined using a, b and θ obtained from RMS values of the beam computed at time t n .

Numerical results

In order to validate our method and pinpoint its advantages, we applied it in cases where the RMS envelope motion is important, namely first in the case of a mismatched beam in a uniform focusing channel and then in the case of a matched beam in a periodic focusing channel.

We considered the model problem of the transverse axisymmetric Vlasov-Poisson equation with vanishing canonical angular momentum. This problem reads

∂f ∂t + v r ∂f ∂r + (F app + q m E r ) ∂f ∂v r = 0, 1 r d dr (rE r ) = ρ = f dv r .

Mismatched Gaussian beam in a uniform focusing channel

We consider a mismatched Gaussian beam

f 0 (r, v r ) = n 0 e -(r 2 /a 2 +v 2 /v 2 th )
with a linear applied field of the form αr.

We represent snapshots of the beam and the moving computing box in Figure 1. The results are very satisfying as the computing box follows very precisely the global motion of the beam.

Matched Gaussian beam in a periodic focusing channel

We consider here a matched Gaussian beam

f 0 (r, v r ) = n 0 e -(r 2 /a 2 +v 2 /v 2 th )
with a linear applied field of the form α(z)r, where α(z) is a piecewise constant function switching beetween 0 and some fixed value, the pattern repeating periodically (the repetition length is called a lattice period).

We represent snapshots of the beam and the moving computing box in Figure 2. Here as well, although some filaments are generated by the nonlinear forces, the computing box obtained from the RMS envelope of the beam does a good job in helping to determine the region of non vanishing f .

Conclusion

The transform method appears very promising for beam simulations. Use of a very simple transform given by the RMS motion of the beam allows the grid to follow more closely the global motion of the beam, and thus reduces considerably the size of the grid necessary for the simulation. This method has been implemented on a 1D model problem. The next step will be to assess its usefulness in more realistic cases, including 2D transverse simulations and/or 1D longitudinal simulations. Finally, we note that many other applications of such a method outside of beam physics can be envisioned.

Figure 1 :

 1 Figure 1: Snapshots of the motion of a mismatched Gaussian beam in a uniform focusing channel

Figure 2 :

 2 Figure 2: Snapshots of the motion of a matched Gaussian beam in a periodic focusing channel


Edward G Belaga

Daniel Grucker

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