Vincent Zoma

Yassiya Sawadogo

Main characteristics of African cities

Keywords: Cities, urbanization, Africa

Africa, which entered late in the urbanization process, is the most rural continent, but one that is urbanizing rapidly. This poorly controlled urban growth leads to disproportionate growth of cities because the increase in the number of African millionaire cities raises increasingly acute social questions, questions of planning and management of spaces. This article, based on documentary research, therefore aims to study the main characteristics of large African cities. Overall, it emerges from this theoretical study that African cities are characterized in addition to rapid urbanization, migration increasingly linked to poverty in rural areas; informality, colonial heritage and especially urban macrocephaly and bicephaly.

I-Introduction

Urbanization is an irreversible and universal phenomenon on a global scale. In 2007, for the first time in human history, the urban population exceeded the rural population. More than one in two men live in the city, whereas in 1900 there was only one in ten [START_REF] Veron | Half the population lives in the world[END_REF]. This situation has significant social, economic, environmental and cultural consequences for societies. Africa, which entered the urbanization process late, is the most rural continent, but one that is urbanizing rapidly [START_REF] Labrecque | Urban studies in Africa, In Urban studies in the world, Collection of capsules[END_REF]. From 14.5% in 1950, the urbanization rate rose to 25.7% in 1975, then to 38.7% in 2007 [START_REF]The State of African Cities 2010, Governance, Inequalities and Urban Land Markets[END_REF]. According to the [START_REF]Organization for Economic Co-operation and Development (OECD)[END_REF], by 2050, Africa is expected to experience the fastest urban growth rate in the world. By this time, African cities should be home to an additional 950 million people. It is estimated that 50% of the African population will live in cities in 2035 and 58% in 2050 [START_REF]The State of African Cities 2014[END_REF]. This poorly controlled urban growth results in disproportionate growth of cities [START_REF] Manirakiza | Urbanization process of the city of Kigali, Rwanda: relationship between spatial and demographic dynamics[END_REF]. Indeed, the increase in the number of African millionaire cities raises increasingly acute social issues, planning and space management issues [START_REF] Fournet | une urbanisation différenciée, Collection petit atlas urbain[END_REF]. Thus, the present article based on desk research aims to study the main characteristics of large African cities.

II-Rapid urbanization and its implications

Rapid urbanization is one of the major characteristics of Third World countries [START_REF] Antoine | Urban growth and integration of migrants in African cities[END_REF]. Compared to the other continents of the world, Africa is the most rural continent, but one that is rapidly urbanizing [START_REF] Labrecque | Urban studies in Africa, In Urban studies in the world, Collection of capsules[END_REF]. According to the UN-Habitat report entitled, The State of the World's Cities 2008/2009, the rate of increase of the urban population in Africa is the highest in the world (3.3% per year) and the continent is home to 17 of the 100 fastest growing cities. If current trends are maintained, by 2050 more than half of the population in Africa will be urban and African cities will be home to almost a quarter of the world's urban population, i.e. approximately 1.2 billion people [START_REF]Bank Group Urban Development Strategies, Transforming African Cities and Towns into Engines of Economic Growth and Social Development, Report of the African Development Bank Group[END_REF]. However, urbanization in Africa is not homogeneous. Admittedly, Southern Africa is the most urbanized region of the continent (58.9% in 2011). Central Africa and North Africa are also at 58.53% and 51.5% respectively. On the other hand, West Africa and East Africa recorded the lowest rates on the continent (respectively 44.9% and 21.7%). These two regions are also the part of the world whose population is urbanizing the fastest [START_REF]The State of African Cities 2014[END_REF].

There are also significant variations between countries. In Burkina Faso, Burundi, Ethiopia, Malawi, Rwanda and Uganda, 10 to 20% of the total population live in urban areas, while this percentage is 50 to 60% for Algeria, Botswana, Congo, Cameroon, Morocco, South Africa and Tunisia. In Libya and the coastal states of Gabon and Djibouti, 75-80% of the population live in cities [START_REF]Bank Group Urban Development Strategies, Transforming African Cities and Towns into Engines of Economic Growth and Social Development, Report of the African Development Bank Group[END_REF]. Cairo (Egypt) remains the largest African city but could be overtaken by Lagos (Nigeria) according to projections [START_REF]The State of African Cities 2014[END_REF]. This trend towards rapid urbanization of African countries is observed from independence with the creation of new States which were to set up both a national civil service, replacing the colonial administration, and a development process including the city, and particularly the metropolis, is the centerpiece. There are many reasons for this growth. We can mainly mention the movement of rural exodus, political instability and above all the natural growth of the population [START_REF] Manirakiza | Urbanization process of the city of Kigali, Rwanda: relationship between spatial and demographic dynamics[END_REF]. However, the share of the rural exodus in the growth of the African urban population has become negligible compared to what it had been in the last two decades of the 20th century [START_REF]The State of African Cities 2014[END_REF]. In addition to this population growth, the cities of these countries are characterized by extension and sprawl. For example, Cairo, which is the most populated metropolis in Africa, was in the years 1999- [START_REF] Denis | Urbanization dynamics, 1950-1920: geo-statistical approach[END_REF]. This rapid growth of African cities imposes challenges to the various municipalities in terms of management, servicing and equipping with basic socio-urban infrastructure [START_REF] Seré | Migration and urban growth[END_REF]. Among the problems inherent in the demographic and spatial growth of African cities, there are, in the field of housing for example, huge slums that have sprung up across the continent. No urban center has been spared by spontaneous housing and slums (even if Tunisia has relatively eliminated this type of housing in these cities from [START_REF]The State of African Cities 2010, Governance, Inequalities and Urban Land Markets[END_REF]). The largest and most impressive slum in Africa is that of Kibera in Nairobi, which is home to between 500,000 to one million people. The International Housing Coalition notes that in several cities in Africa, less than 10% of the population live in viable neighborhoods and decent housing: 74% of city dwellers live in slums in Zambia, 80% in Nigeria, 85.7% in Sudan, 92.1% in Tanzania, 92.9% in Madagascar and 99.4% in Ethiopia [START_REF] Maury | Building housing[END_REF]. This situation of precarious housing remains worrying, even if the rate of slums has fallen relatively from 20 to 13% in North Africa and 5% in sub-Saharan Africa [START_REF]The State of African Cities 2010, Governance, Inequalities and Urban Land Markets[END_REF]. In most Arab countries, urban expansion has been accompanied by a proliferation of clandestine housing: 1,600,000 inhabitants in Cairo (20% of the capital's population) and 346,000 in Morocco [START_REF] Kharoufi | Urbanization and Urban Research in the Arab World[END_REF].

In addition, the phenomenon of climatic hazards supported by the rapid urbanization of the continent exposes African cities to natural and sometimes technological disasters. Indeed, urban poverty, the proliferation of precarious neighborhoods and the weak capacity of communities, households and governments to cope with the risks of flooding and the occurrence of disasters, could exacerbate the situation [START_REF] Soma | Urban vulnerability and resilience: perception and territorial management of flood risks in the city of Ouagadougou[END_REF].

More than one and a half million people are affected each year in African cities by floods following torrential rains. In 2009, Senegal, Burkina Faso, Ghana, Benin, Niger and Sierra Leone were seriously affected by floods which reportedly claimed 200 lives and seriously affected 770,000 victims in the sub-region [START_REF] Soma | Urban vulnerability and resilience: perception and territorial management of flood risks in the city of Ouagadougou[END_REF]. Coastal cities are also affected following the rise in sea level due to climate variability.

In the field of socio-urban infrastructure and services, African countries and cities are victims of their enormous lack of infrastructure and their too limited access to technologies and services. In terms of electrical energy, difficulties in the distribution of electrical current persist, with cuts occurring regularly in no less than 30 countries on the continent [START_REF]The State of African Cities 2014[END_REF]. In Dakar, for example, for lack of being able to supply the entire city, certain districts are in turn deprived of electricity for several hours in a row. About ten companies are equipped with generators, but diesel is expensive [START_REF] Bonkoungou | Social aspects of urban development[END_REF]. Drinking water supply is also very insufficient. Less than 20% of households in Africa benefit from a piped water system and only 40% have access to water within a radius of 200 meters [START_REF]Urban areas[END_REF]. In Guinea-Bissau, urban centers and particularly the city of Bissau, have low drinking water coverage. This situation would be, among other things, due to frequent blackouts and incessant power cuts [START_REF] Compaoré | Urban development policies in Sub-Saharan Africa[END_REF].

In transport, the network is generally deficient at all levels. Public and private public transport is everywhere very insufficient in number and in services. The costs of road transport are very high and the network itself is very insufficient. African cities are regularly congested [START_REF] Thiam | Transport infrastructure in Africa[END_REF]. Finally, rapid urbanization presents health and environmental risks for large African cities [START_REF] Jalle | coord.) Sustainable management of waste and urban sanitation, pS-Eau/PDM Programs[END_REF]. Indeed, the evacuation of urban waste poses a real problem and leads to enormous risks to health and the environment in large African cities (photo n°1).

Photo: [START_REF] Yao-Kouassi | In search of a synergy for the management of household waste in Côte d'Ivoire: case of the district of Abidjan[END_REF].

Photo n°1: An overexploited and dangerous landfill of Akouédo in the commune of Cocody (District of Abidjan)

Populations (adults and minors alike) do not hesitate to rummage, without any protection, in waste of all kinds involving all kinds of health risks. Moreover, one of the characteristics, once very closely linked to the rapid urbanization of African cities, was migration.

III-Migration increasingly linked to poverty in rural areas

Several authors ( [START_REF] Savane | Urbanization and Migration in Africa[END_REF], [START_REF] Moro | The big cities of Africa, Manuel Belin terminale[END_REF], [START_REF] Antoine | Urban growth and integration of migrants in African cities[END_REF], [START_REF] Tabah | Villes d'Afrique[END_REF], [START_REF] Bocquier | Urbanization and migratory development in West Africa[END_REF], [START_REF] Ouédraogo | Beyond the hoe: geographic mobility as a major determinant of upward social mobility in Burkina Faso[END_REF] & [START_REF]The state of the world's cities: harmonious cities, annual report[END_REF]) are unanimous that the primary source of urban growth in Africa has been migration. However, they acknowledge that this source of urban growth is declining [START_REF] Seré | Migration and urban growth[END_REF]. Indeed, migratory flows increased from the 1960s. In the large cities of black Africa, the migratory contribution represented 60% of the numerical growth of the population over the period 1960-1975 to fall to 50% around 1995 [START_REF] Bris | Ouagadougou[END_REF]. The history of migrations and urbanization in Africa south of the Sahara can be divided into three major stages. From the 17th to the 19th century, the slave trade dominated, between 1880 and 1945, colonial penetration increased the need for labor (forced labor) and led to the establishment of a few trading post towns. Also during the colonial era, certain intra-African migrations were favored in order to accelerate the economic development of certain strategic regions (Senegal, Côte d'Ivoire, Ghana and later Nigeria). Since 1945, and especially since independence, spontaneous migrations have accelerated [START_REF] Antoine | Program FAO "Food supply and distribution of cities[END_REF]. In addition, spontaneous migration to African cities (rural exodus) which increased in the aftermath of independence was mainly driven by economic inequality between urban and rural areas, and the search for employment remains a priority. But, with the crisis that African countries have been going through since the beginning of the 1980s, this exodus is tending to slow down, and even to reverse itself in certain countries [START_REF] Antoine | Program FAO "Food supply and distribution of cities[END_REF]. For example, the transformation of the relationship between town and country in the Arab countries during the 1980s led to a slowdown in emigration to the major urban centers. In other words, the large urban centers like Cairo, Casablanca, Tunis, Algiers, which offered integration possibilities to migrants in the 1960s, were no longer able to do so due to a constant increase in a flow of workforce since the end of the 1970s. The slowdown in urban migration is also due to a certain development policy for medium-sized towns and rural areas [START_REF] Seré | Migration and urban growth[END_REF]. This slowdown, which should even regulate the demography of African cities, was unfortunately relayed by the natural growth of city dwellers, which remains high due to still high fertility and the fall in mortality [START_REF] Seré | Migration and urban growth[END_REF].. The main consequence of urban migration is the "bulging" of cities by a poor population that cannot resist the demands of city life. Thus, in the city, integration poses a whole range of problems (access to housing, work, etc.) and the majority of migrants settle on the outskirts, thus engaging in informal activities.

IV-The Informality

Informality, which translates into the "informal" sector, is one of the most striking and recurrent features of African cities [START_REF]Perspectives on informal activity in large African cities, Ateliers de Cergy[END_REF]. Thus, the economy of most African cities is underdeveloped and essentially based on the informal sector. This leads to a situation of poverty for urban populations [START_REF] Compaoré | Urban development policies in Sub-Saharan Africa[END_REF]. In the largest cities in Africa, industry represents less than 30% of the workforce. This weakness of industrialization explains the rise of the informal sector and the hypertrophy of the tertiary sector [START_REF] Carnat | Terminal Geography with Atlas, Chapter 9: The major cities of Africa[END_REF]. The informal sector occupies an important place in developing countries and particularly in Africa. It represents at least 75% of urban jobs in the Sahelian countries, 80% of job creations of the same nature and about 50% of national wealth [START_REF]Proposals to promote the development of small and medium-sized African enterprises, Report and Draft proposals of the Economy and Development Commission[END_REF]. In Côte d'Ivoire, it is estimated that jobs in the formal sector of the economy occupy only 17.5% of the urban working population. The contribution of the informal sector to GDP is estimated at 20% [START_REF] Todor | The contribution of the informal sector to the supply of public services: case study on informal waste collection and recovery activities[END_REF]. The informal sector in Nairobi produces 60% of jobs. In 2011, this sector was responsible for 86% of job creation in Kenya, and grew by 5.5% in Nairobi with nearly 2.3 million workers. The informal sector is the leading "sector" providing employment in Lomé with approximately 210,000 informal production units in this city. In South Africa, more than a quarter of the labor force is out of work, and a growing number (around 2.3 million) are turning to the informal sector to survive [START_REF]Perspectives on informal activity in large African cities, Ateliers de Cergy[END_REF]. The city of Ouagadougou is characterized by a large informal sector. People's incomes are generally low and they are in a precarious situation. Thus, on average, six out of ten households derive all or part of their income from an informal production unit and 47.3% of jobs in the informal sector are held by women [START_REF]The informal sector in the Ouagadougou agglomeration: performance, integration, prospects, 1-2-3 Survey[END_REF]. The causes of "informalization" in African cities are mainly rural exodus, extremely strong demographic growth and the burden of regulations [START_REF]Proposals to promote the development of small and medium-sized African enterprises, Report and Draft proposals of the Economy and Development Commission[END_REF]. Moreover, even if informality plays a significant role in integration and social regulation [START_REF] Maldonado | Methods and Instruments of Support to the Informal Sector in Francophone Africa, InFocus Program for the Promotion of Employment through the Development of Small Enterprises, Department of Job Creation and Enterprise[END_REF], it remains a characteristic problem of African cities for municipal officials. It escapes state control, "ruralizes" cities, accentuates urban poverty and exposes its agents to very precarious living and working conditions. Moreover, while informality has been catalyzed by structural adjustment programs, it partly derives its existence from the colonial heritage, which is also one of the major characteristics of large African cities.

V-Colonial heritage

The existence of cities is a very old phenomenon in Africa. The African continent had long been dotted with trading towns (Saint-Louis, Gorée, Porto-Novo and Libreville), trade centers, such as Aoudaghost, the capital of Ghana (in present-day Mauritanian territory), Gao, Timbuktu, Djenné, Mopti, Koumbi-Saleh, Kano, Zinder, Mogadishu, Aksum, Malindi and Zanzibar, and on the other hand, Arab-Muslim cities in the north such as Kairouan (Tunisia), Cairo (Egypt) and Marrakech (Morocco). In addition, most of these cities were also historic cities like the pyramids of Meroe and the remains of the Kush empire along the Nile, the ruins of Greater Zimbabwe, the royal palaces of Abomey and Ouagadougou [START_REF] Choplin | Building capital cities between the Arab world and black Africa: Nouakchott (Mauritania) and Khartoum (Sudan), comparative study[END_REF], [START_REF] Vennetier | What to do with the cities of tropical Africa? Or: the problems of galloping urbanization[END_REF]. Furthermore, in Central Africa, pre-colonial towns are few in number and have an ephemeral existence due to its climate and its central position [START_REF] Poinsot | The cities of black Africa: urban planning and housing policies and operations between 1950 and 1960[END_REF]. However, the ancient cities of Africa certainly did not meet the current criteria of urbanization, in particular the demographic and architectural criteria; but they were above all the seat of power and housed important non-rural activities [START_REF]General Population and Housing Census of Burkina Faso: final results[END_REF].

If it is true that the city is not something new for Africa, it is nevertheless colonization which imprinted its current characteristics. The current large cities were founded on sites chosen according to considerations linked to the needs of the colonizer (establishment of military posts, mining, agricultural and forestry development, involving administrative and economic management structures, points of collection of products, export ports, communication routes) [START_REF] Vennetier | What to do with the cities of tropical Africa? Or: the problems of galloping urbanization[END_REF]. Seaports were generally favored. These include Dakar, Abidjan, Lagos, Luanda, etc., and the location of large urban centers remains marked by this extroversion. From that time onwards, investments were concentrated in the capitals where most of the senior executives of the colonial administration resided [START_REF] Antoine | Program FAO "Food supply and distribution of cities[END_REF]. Consequently, the new States do not put an end to the colonial urban planning policy, but are part of its continuity. Heir to the colonial urban model, the African city is "dual". A socio-spatial segregative dualism between the "legal" (or European) city, the one that falls under Western standards and participates in the world-economy, and the "illegal" (or indigenous) city, that of informal settlements, and where a subsistence and survival economy is developing [START_REF] Choplin | Building capital cities between the Arab world and black Africa: Nouakchott (Mauritania) and Khartoum (Sudan), comparative study[END_REF]. Most African cities are confronted with these strong inequalities. At the top of the list is South Africa. This situation partly reflects the legacy of more than a century of institutionalized racial segregation (apartheid) [START_REF]The State of African Cities 2010, Governance, Inequalities and Urban Land Markets[END_REF], [START_REF]The urban question in southern Africa, research perspectives[END_REF]. One can also cite as many examples. First, cities like Abidjan, Dakar, Brazzaville have their "Plateau" (Central Business District or business centers), with airy and drained streets, unlike precarious housing areas for natives (Adjamé, Medina, or Poto-Poto) [START_REF] Choplin | Building capital cities between the Arab world and black Africa: Nouakchott (Mauritania) and Khartoum (Sudan), comparative study[END_REF]. Then, urban informality and slums in Nairobi stem directly from these exclusionary practices in the planning policies of colonial regimes [START_REF]Perspectives on informal activity in large African cities, Ateliers de Cergy[END_REF]. In addition, during the era of colonization, most Arab towns in North Africa became two-headed. Around the medina was built a "European" city, with its avenues, its squares, its buildings symbolizing the power of the colonizers (government palace, barracks, churches). The European city became Arabized, but in general it retained the organs of command, while the medina entered a process of social differentiation, marked by the appearance of renovated blocks, tourist districts and occupied spaces by slums [START_REF] Kharoufi | Urbanization and Urban Research in the Arab World[END_REF]. Also, the choice of Kigali as the capital is reflected first and foremost by the colonizer's desire to place the imperial residence in the center of the country in order to facilitate accessibility to heavy goods arriving from the coast, but also the administration as opposed to the posts. Soldiers who were located on the periphery of the territory [START_REF] Manirakiza | Urbanization process of the city of Kigali, Rwanda: relationship between spatial and demographic dynamics[END_REF]. Finally, in Burkina Faso on the eve of independence, the city of Ouagadougou was made up of 9,500 plots with basic servicing. She was dual. The center housing the settlers corresponds to the planned city with specialized neighborhoods and 50 m wide boulevards grouping together most of the equipment and socio-economic infrastructure. On the other hand, the periphery devoid of facilities where the "African" populations lived [START_REF] Nayaga | Planning and natural disasters: case of the floods of September 1, 2009 in Ouagadougou, Master's thesis[END_REF]. This dichotomy still persists today. Thus, the city center which corresponded to the oldest European district, today brings together most of the administrations and shops, and has the highest percentage of permanent housing (more than 90% according to the 1996 census) [START_REF] Meunier-Nikiema | Older people in the center and young people on the outskirts[END_REF].

If at the city scale, the colonial heritage is mainly reflected in large African cities by a typology of neighborhoods (residential, popular, spontaneous and/or slums), it is translated at the national scale by an urban macrocephaly or primacy.

VI-Urban macrocephaly and bicephaly

Unlike the developed countries of Europe and North America, urban macrocephaly or bicephaly characterize urbanization in Africa. They result in the predominance of one city or two cities (in particular the economic capital and the political capital) in the urban framework of the countries. However, even if polycephalic urban systems, even megalopolises exist, the urban structure of African States remains dominated by a macrocephalic city or bicephaly which monopolize the essential economic and administrative functions.

A macrocephalic system characterizes most African countries, especially the coastal countries. Most of the already highly urbanized coastal countries, such as Gabon, Senegal, Côte d'Ivoire and Benin clearly recognize the preeminence of a city, generally the capital city [START_REF] Antoine | Program FAO "Food supply and distribution of cities[END_REF]. Abidjan in Côte d'Ivoire, for example, concentrates 20% of the population, 50% of domestic production, 50% of industrial jobs, 80% of tertiary jobs in the country. The small towns, Bouaké, Abgoville, Dimbokro, are withering before the macrocephaly of the metropolis which absorbs most of the functions and investments available [START_REF] Carnat | Terminal Geography with Atlas, Chapter 9: The major cities of Africa[END_REF]. However, moving the capital to Yamoussoukro could have a decisive influence on the urban structure of the country in the future. Within the continent there are the cases of Kigali (Rwanda) and Ouagadougou (Burkina Faso). Already in 1990, according to [START_REF] Manirakiza | Urbanization process of the city of Kigali, Rwanda: relationship between spatial and demographic dynamics[END_REF], the city of Kigali alone concentrated 61% of the country's urban population, 30% of civil servants in the public sector, 75% of bank deposits, 60% of cars and trucks, 52% government telephone lines, 76% of private telephones and 60% of industrial enterprises. This pattern of Kigali macrocephaly is steadily increasing. In 2007, Kigali housed 44% of civil servants in the public sector and gathered more than 50% of wholesale trade and almost all industrial activities (more than 70%). In 2008, Kigali was home to 4 of the country's 6 public higher education institutions. Also, Ouagadougou is a macrocephalic city in the urban framework of Burkina Faso. First city of Burkina Faso and state capital, Ouagadougou combines the function of political, economic and service command. It concentrates about half (46.4%) of the country's urban population in 2006. The bicephaly that has long marked the country has now disappeared and Bobo-Dioulasso has ceased to play rivals, leaving Ouagadougou to take first place. Indeed, the population of Ouagadougou is currently about 2.71 times that of Bobo-Dioulasso, the country's second city [START_REF] Prat | Sahelian capital: urban growth and land issues, Mappemonde[END_REF], [START_REF] Ournet | a differentiated urbanization, Small urban atlas collection[END_REF], [START_REF]Ministry of Economy and Finance (MEF). General Census of Population and Housing (RGPH) of 2006, Monograph of the urban commune of Ouagadougou[END_REF].

In addition to macrocephaly, bicephalic systems develop on the continent such as in Morocco, Cameroon and Egypt. Morocco has a two-headed urban network, with a political capital (Rabat) of acceptable size and an economic capital resulting from colonization (Casablanca). But the country also has dynamic inland (Fez, Marrakech) and coastal cities [START_REF] Kharoufi | Urbanization and Urban Research in the Arab World[END_REF]. Then in Cameroon two regions were structured, dominated by Douala (the coast) and Yaoundé (the southern forest). Yaoundé only hosts 25% of state officials, but Douala controls most of industry (2/3 of large companies), head offices (57%), and trade in Cameroon [START_REF] Carnat | Terminal Geography with Atlas, Chapter 9: The major cities of Africa[END_REF]. Finally we have Cairo (largest African city) and Alexandria in Egypt. Moreover, since independence, the governments of African countries have developed strategies to rebalance the urban structure through the creation of new towns and in some cases, the displacement of the capital, such as the cases of Côte d'Ivoire, Nigeria and Tanzania [START_REF] Choplin | Building capital cities between the Arab world and black Africa: Nouakchott (Mauritania) and Khartoum (Sudan), comparative study[END_REF]. The colonial segregative dualism and the massive exodus to the big cities in the aftermath of independence are the main motives for urban macrocephaly or bicephaly in Africa.

VII-Conclusion

In sum, large African cities are characterized by their growth, urban macrocephaly, informality and colonial heritage. Such characters are sources of enormous difficulties in the management of these cities. It is above all the growth of these cities, both demographic and spatial, which is the main characteristic, thus leading to the others. In Africa, it is above all the capital cities that jointly concentrate the political and economic functions of the countries. In the urban framework of African countries, when we exclude the capital cities, we see that Africa remains a more or less rural continent. Urbanization is therefore concentrated only in metropolises, leading to major urban challenges. The management of large African cities must necessarily go through a drastic mastery of the spatial extension of metropolises and their decongestion through the creation of new dynamic cities. This would require real decentralization which involves a certain number of actors.


Angélique Gougelet
email: angelique.gougelet@inserm.fr

Sabine Colnot

Les microARN dans le cancer du foie : à l'orée de nouvelles thérapies ciblées ?

microRNA: new diagnostic and therapeutic tools in liver disease?

Angélique Gougelet, Sabine

Introduction

Alors que pendant longtemps la notion du tout génétique a eu la faveur des scientifiques, l'hypothèse du monde à ARN, proposé par W. Gilbert en 1986, a depuis le vent en poupe. En effet moins de 2% du génome sont traduits en protéines et la découverte du rôle catalytique des ARN en 1989 a conforté l'importance des ARN dans l'expression génique. Depuis 1986, le monde à ARN s'est largement agrandi avec la découverte des ARN non codants, constituant une grande variété de régulateurs physiologiques tels que les petits ARN interférents, les ARN interagissant avec piwi, les petits ARN nucléolaires, et surtout les microARN (miARN). Depuis la découverte de Lin-4 en 1993 chez C. Elegans, l'étude des miARN est un domaine de recherche en pleine expansion, comme en atteste le nombre croissant de publications référencées dans PUBMED (Figure 1). D'après la miRbase version 19, 2042 miARN matures ont été identifiés chez l'homme et ce n'est qu'un début. Les miARN sont de petits ARN, d'environ 22 nucléotides, produits sous forme de précurseurs puis rendus matures par la protéine Dicer (figure 2). Les miARN matures s'apparient avec la région 3' non traduite de leurs ARN messagers (ARNm) cibles grâce à l'intervention du complexe RISC (RNA-induced silencing complex). Les miARN sont des régulateurs négatifs de l'expression génique puisqu'ils provoquent la dégradation des ARNm suite à leur déadénylation et/ou bloquent leur traduction (initiation et élongation) [START_REF] Hutvagner | A microRNA in a multiple-turnover RNAi enzyme complex[END_REF]. Un même miARN peut ainsi cibler plusieurs ARNm, et inversement, un ARNm peut être la cible de différents miARN.

Les miARN en tant que marqueurs diagnostic et pronostic

Les miARN sont impliqués dans de nombreux processi physiologiques tels que la croissance, la prolifération ou la différenciation, mais ils sont également impliqués dans de nombreux processi pathologiques tels que le cancer. Durant les phénomènes de cancérisation, les miARN jouent un rôle ambivalent de suppresseurs de tumeurs ou d'oncogènes. L'expression des miARN est en effet soumise aux mêmes régulations qu'un gène "classique" (amplification, hyperméthylation du promoteur, délétion, translocation, polymorphisme d'un nucléotide simple…). De nombreuses études visant à analyser l'expression des miARN dans une grande variété de tumeurs ont mis en évidence l'existence de signatures miARN spécifiques dépendant de l'origine cellulaire et tissulaire de la tumeur [START_REF] Lu | MicroRNA expression profiles classify human cancers[END_REF][START_REF] Volinia | A microRNA expression signature of human solid tumors defines cancer gene targets[END_REF]. Ces miARN constituent donc des marqueurs de tout premier choix non seulement pour le diagnostic mais aussi pour le pronostic de certaines tumeurs. En effet, l'existence d'une population de miARN circulants sous forme de complexes protéiques ou encore encapsulés dans des vésicules appelées exosomes permet d'envisager leur détection dans différents fluides biologiques (sérum, plasma, urine, salive…), et d'offrir ainsi un outil diagnostique non-invasif.

Le cancer du foie

Ces dernières années, de nombreux travaux ont montré l'importance des miARN dans l'organogenèse hépatique mais aussi dans le développement et la progression des tumeurs du foie [START_REF] Ladeiro | MicroRNA profiling in hepatocellular tumors is associated with clinical features and oncogene/tumor suppressor gene mutations[END_REF][START_REF] Murakami | Comprehensive analysis of microRNA expression patterns in hepatocellular carcinoma and non-tumorous tissues[END_REF] (Figure 1). Le cancer du foie constitue la troisième cause mondiale de mortalité liée au cancer dans le monde. Le carcinome hépatocellulaire (CHC) en constitue la forme primitive la plus fréquente avec environ 500 000 nouveaux cas/an. Les principaux facteurs de risque du CHC sont les infections virales B et C (VHB et VHC, respectivement), la cirrhose, l'abus d'alcool ou l'exposition à l'aflatoxine. A la fin des années 2000, l'analyse transcriptomique globale des CHC a permis d'établir une classification moléculaire de ces tumeurs [START_REF] Boyault | Transcriptome classification of HCC is related to gene alterations and to new therapeutic targets[END_REF]. Les voies de signalisation les plus fréquemment touchées dans le CHC sont la voie β-caténine (15-40%), la voie p53 (26%), et la voie Ras (5-10%). De manière générale, les CHC mutés pour la β-caténine, apparaissant dans un contexte d'infection chronique par le virus VHC ou d'abus d'alcool, sont plus stables génétiquement, peu proliférants, bien différenciés, cholestatiques et de pronostic moins sombre ; à l'inverse les autres CHC, apparaissant dans un contexte VHB, présentent une instabilité génétique, sont peu différenciés, stéatosiques et de moins bon pronostic (Figure 3). Bien que de nombreux efforts aient été menés pour la compréhension et le traitement de cette maladie, l'espérance de vie moyenne après diagnostic d'un CHC n'est que de six mois. Il paraît donc essentiel d'identifier de nouveaux acteurs moléculaires oncogéniques. Etant donné le rôle majeur des miARN dans le métabolisme, l'immunité, l'inflammation et le cancer, ces petits ARN apparaissent comme des cibles prometteuses. Dans cette revue, nous traiterons des dernières découvertes concernant les miARN dans le CHC, et surtout des perspectives thérapeutiques qui en sont issues.

Expression des miARN dans les pathologies du foie

Le rôle des miARN dans la physiologie et la pathologie du foie a été appuyé par deux travaux de Sekine et coll. montrant que l'invalidation hépatospécifique de Dicer chez la souris conduit à l'apparition de tumeurs [START_REF] Sekine | Disruption of Dicer1 induces dysregulated fetal gene expression and promotes hepatocarcinogenesis[END_REF][START_REF] Sekine | Dicer is required for proper liver zonation[END_REF]. De nombreux travaux ont depuis mis en lumière l'importance d'un panel de miARN dans le développement embryonnaire du foie, dont la plupart sont dérégulés dans les pathologies hépatiques telles que la maladie alcoolique du foie (MAF), les stéatopathies hépatiques non alcooliques, les états de fibrose, autant d'affections prédisposant au développement du CHC, et bien sûr le CHC lui-même (Figure 3) ([9] pour revue). Nous pouvons citer: miR-122 Physiologiquement, miR-122 est le miARN hépatique le plus représenté (70% des miARN). C'est une cible du facteur de transcription HNF-4α, un acteur majeur de la différenciation des hépatocytes; il est impliqué dans le métabolisme des lipides et du fer et la synthèse de cholestérol ( [START_REF] Wen | miR-122 regulates hepatic lipid metabolism and tumor suppression[END_REF][START_REF] Vaulont | miR-122, a microRNA gatekeeper of iron homeostasis[END_REF] pour revue). Ce miARN cible en particulier la cycline G1, impliquée dans l'arrêt du cycle cellulaire en G2/M en réponse aux dommages à l'ADN, et la molécule anti-apoptotique Bcl-w [START_REF] Law | Emerging roles of microRNA in the intracellular signaling networks of hepatocellular carcinoma[END_REF]. miR-122 est, de plus, détourné par le virus de l'hépatite C pour sa réplication. C'est ainsi que la première stratégie thérapeutique basée sur l'inhibition d'un miARN dans le foie fut un anti-miR-122, le Miravirsen, qui s'est avéré efficace dans le traitement des hépatites C chroniques chez les primates [START_REF] Lanford | Therapeutic silencing of microRNA-122 in primates with chronic hepatitis C virus infection[END_REF] et chez l'homme [START_REF] Janssen | Treatment of HCV Infection by Targeting MicroRNA[END_REF]. miR-155 miR-155 est majoritairement exprimé par les macrophages du foie, les cellules de Kupffer. Sa surexpression est à l'origine de la production accrue de TNFα par les cellules de Kupffer observée chez les patients atteints de maladie alcoolique [START_REF] Bala | Up-regulation of microRNA-155 in macrophages contributes to increased tumor necrosis factor {alpha} (TNF{alpha}) production via increased mRNA half-life in alcoholic liver disease[END_REF]. Récemment, une étude du même groupe a montré l'existence d'un enrichissement de ce miARN circulant dans des exosomes dans des modèles murins de MAF [START_REF] Bala | Circulating microRNAs in exosomes indicate hepatocyte injury and inflammation in alcoholic, drug-induced, and inflammatory liver diseases[END_REF]. Ce miARN cible SOCS1, un inhibiteur de la cascade STAT3/MMP9 [START_REF] Yan | Hepatocellular carcinoma-associated mesenchymal stem cells promote hepatocarcinoma progression: Role of the S100A4-miR155-SOCS1-MMP9 axis[END_REF]. miR-29 miR-29, majoritairement exprimé dans les cellules étoilées du foie -cellules dont l'activation est responsable d'une production accrue de matrice extracellulaire induisant une fibrose hépatique -est un régulateur clé de la voie NFkB et TGFβ. Il cible également les molécules anti-apoptotiques bcl-2 et

Mcl-1 [START_REF] Law | Emerging roles of microRNA in the intracellular signaling networks of hepatocellular carcinoma[END_REF]. Son expression est diminuée dans les atteintes chroniques du foie [START_REF] Wang | MicroRNAs in liver disease[END_REF]. miR-199 miR-199 est également exprimé dans les cellules étoilées, mais aussi dans les cellules endothéliales sinusoïdales du foie. Il est augmenté en cas de fibrose [START_REF] Wang | MicroRNAs in liver disease[END_REF]. Il interfère en particulier avec la voie mTOR [START_REF] Hou | Identification of miRNomes in human liver and hepatocellular carcinoma reveals miR-199a/b-3p as therapeutic target for hepatocellular carcinoma[END_REF].

Tous ces miARN dérégulés dans les atteintes hépatiques prédisposant au cancer, le sont également dans les tumeurs du foie, et notamment dans les carcinomes hépatocellulaires. Ils pourraient ainsi constituer à la fois des marqueurs précoces d'initiation et de progression des tumeurs du foie et des cibles pour la prévention ou le traitement des CHC.

miARN et carcinomes hépatocellulaires

Malgré des différences dues à l'échantillonnage, l'analyse globale des miARN exprimés dans les tumeurs du foie a permis d'identifier une signature miRNA commune à tous les types de CHC. Comme nous l'avons mentionné dans le paragraphe précédent, une perte de miR-122 [START_REF] Ladeiro | MicroRNA profiling in hepatocellular tumors is associated with clinical features and oncogene/tumor suppressor gene mutations[END_REF], de miR-29 [START_REF] Xiong | Effects of microRNA-29 on apoptosis, tumorigenicity, and prognosis of hepatocellular carcinoma[END_REF], et de miR-199 [START_REF] Hou | Identification of miRNomes in human liver and hepatocellular carcinoma reveals miR-199a/b-3p as therapeutic target for hepatocellular carcinoma[END_REF] a été identifiée dans les CHC (Figure 3). D'autres miARN suppresseurs de tumeurs ont également été largement étudiés ; on peut citer let-7, miR-101 et miR-124. A l'inverse, des miARN oncogéniques ont également été décrits tels que miR-155, miR-21, miR-221/miR-222, miR-181, miR-224, et le cluster miR-17/92 (Figure 3). Tous ces miARN sont impliqués dans les processus de prolifération et d'apoptose (Tableau 4) ( [START_REF] Law | Emerging roles of microRNA in the intracellular signaling networks of hepatocellular carcinoma[END_REF] pour revue). L'un des miARN dont le rôle dans le développement et la progression des CHC est le mieux caractérisé est miR-221. Il est induit lors des atteintes chroniques et du processus de fibrogenèse (par activation des cellules étoilées [START_REF] Wang | MicroRNAs in liver disease[END_REF]). Un grand nombre de travaux a montré son induction dans les CHC [START_REF] Pineau | miR-221 overexpression contributes to liver tumorigenesis[END_REF], mais aussi dans les cholangiocarcinomes, tumeurs épithéliales développées à partir des cellules biliaires. Les cibles dérégulées en réponse à miR-221/222 dans les CHC sont les suppresseurs de tumeurs p27, p57, PTEN et la protéine TIMP-3 ([12] pour revue). Il fait l'objet de test d'invalidation in vivo que nous traiterons à la fin de cette revue. Enfin, en 2010, une étude de Cairo et coll. a mis en évidence les deux clusters de miARN, miR-100/let-7a-2/miR-125b-1 et le cluster miR-371-3, cibles de l'oncogène MYC, en tant que facteur de mauvais pronostic pour les tumeurs du foie [START_REF] Cairo | Stem cell-like micro-RNA signature driven by Myc in aggressive liver cancer[END_REF]. En mesurant l'expression des quatre miARN, miR-100, miR-371, miR-373 et let-7a, les auteurs discriminent sur une large cohorte de patients, les CHC présentant un phénotype proche des hépatoblastomes, tumeur maligne primitive du foie la plus courante chez l'enfant ; ce sous-groupe de CHC étant moins bien différencié et plus invasif. Cette étude met donc en relation une signature miARN commune entre hépatoblastome et CHC, et met en lumière l'intérêt de cette signature de quatre miARN pour le pronostic et le traitement de ces deux types de tumeurs.

Certains travaux ont, de plus, montré que cette signature miARN pouvait être un outil prédictif de la rechute après chirurgie, ou encore de la réponse aux traitements chimiothérapeutiques (miR-122 sensibilise à l'adryamycine et à la vincristine ; miR-199a-3p affecte la sensibilité à la doxorubicine et au 5-fluorouracil)( [START_REF] Giordano | MicroRNAs: New tools for diagnosis, prognosis, and therapy in hepatocellular carcinoma?[END_REF] pour revue). En outre, certains miARN sont caractéristiques d'un groupe ou sous-groupe de CHC. La perte de miR-375 est la marque des tumeurs mutées pour la β-caténine, miR-126* est quant à lui perdu lors d'une consommation abusive d'alcool, alors que miR-96 est associé à une infection au VHB [START_REF] Zucman-Rossi | Molecular classification of hepatocellular carcinoma. Digestive and liver disease : official journal of the Italian Society of Gastroenterology and the Italian Association for the Study of the[END_REF]. Le miARN miR-18a s'est avéré être un marqueur très intéressant pour le CHC. En effet, le CHC a une plus forte incidence chez les hommes (x2-6) et les femmes atteintes de CHC ont une espérance de vie plus longue. Ceci suggère l'importance de mécanismes moléculaires sexe-dépendant dans la progression des CHC, pouvant être liés aux oestrogènes, notamment. Or, miR-18a, qui cible la forme α du récepteur aus oestrogènes, est surexprimé dans les échantillons de CHC de patientes. Il semble donc que la réduction de l'expression de ce miARN soit associée à la perte de l'effet protecteur des oestrogènes chez ces femmes [START_REF] Liu | MicroRNA-18a prevents estrogen receptor-alpha expression, promoting proliferation of hepatocellular carcinoma cells[END_REF]. Récemment, il a été décrit comme un marqueur sérique des CHC liés aux infections chroniques par le VHB ( [START_REF] Ladeiro | miRNAs in cancer: the case of liver tumors[END_REF] pour revue).

En sus des signatures tumorales, des travaux ont été menés visant à identifier une signature miARN pour les CHC métastatiques. Des résultats différents ont été obtenus, liés sans doute à des divergences dans les prélèvements et dans l'analyse des données. Bien qu'une étude récente de Wong et al. soit plutôt en faveur d'une perte plus marquée du même panel de miARN dans les métastases par rapport aux tumeurs [START_REF] Wong | Sequential alterations of microRNA expression in hepatocellular carcinoma development and venous metastasis[END_REF], le travail de Budhu et al. montre l'existence d'une signature de vingt miARN métastatiques [START_REF] Budhu | Identification of metastasis-related microRNAs in hepatocellular carcinoma[END_REF]. De nombreuses études portant sur un seul miARN ayant enrichi ces données hautdébit, il semblerait que les CHC métastatiques expriment à la fois certains miARN identifiés comme dérégulés dans les CHC tels que miR-122, miR-124, miR-17, let-7g, miR-21, miR-221 ou encore miR-96 mais qu'il y ait aussi une dérégulation d'autres miARN tels que miR-9-2, miR-148a, miR-125b , miR-30a ou miR-34a (Tableau 4) ( [START_REF] Law | Emerging roles of microRNA in the intracellular signaling networks of hepatocellular carcinoma[END_REF] pour revue).

Enfin, les patients atteints de CHC présentent également des modifications d'expression des miARN circulants. La quasi-totalité des études a été réalisée chez des patients atteints d'hépatite B. Bien qu'il y ait des discordances entre les panels de miARN discriminants, les quatre miARN miR-122, miR-221/222 et miR-21 sont surexprimés dans le sérum des patients [START_REF] Li | Serum microRNA profiles serve as novel biomarkers for HBV infection and diagnosis of HBV-positive hepatocarcinoma[END_REF][START_REF] Zhou | Plasma microRNA panel to diagnose hepatitis B virus-related hepatocellular carcinoma[END_REF]. Les causes de l'induction de miR-122 dans le sérum alors que ce miARN est perdu dans les tumeurs sont encore non élucidées (Tableau 4).

Au vu de toutes ces données, les miARN constituent donc de puissants marqueurs pouvant améliorer la classification des CHC, leur diagnostic et la prédiction de leurs réponses au traitement. Ils permettent également d'envisager un diagnostic non invasif par prélèvement sanguin ou même d'urine, sous réserve d'optimisation de leur détection dans les fluides biologiques. Enfin, les miARN tumoraux peuvent devenir de nouvelles cibles thérapeutiques comme nous allons le voir dans la suite de cette revue.

Les miARN : une nouvelle stratégie thérapeutique ? Bien que de nombreux efforts aient été menés pour améliorer le traitement du CHC, la chirurgie reste l'option thérapeutique la plus utilisée. Le Sorafenib, un inhibiteur des récepteurs tyrosine kinase, seule drogue acceptée pour le traitement du cancer du foie, n'a amélioré l'espérance de vie des patients que de trois mois. Les miARN apparaissent donc comme de nouvelles cibles prometteuses puisqu'ils pourraient permettre de cibler de nombreuses voies de signalisation par leur multiplicité d'action, mais surtout ils permettraient de cibler à la fois le contingent métabolique, inflammatoire et immunitaire à l'origine du développement du CHC. Suite à l'identification d'un panel de miARN dérégulés dans les CHC, un certain nombre d'études a été mené pour restaurer l'expression des ces miARN, dans un premier temps in vitro puis in vivo (Tableau 4). Les travaux menés in vitro sur des modèles de lignées cellulaires de CHC ont donné des résultats encourageants, et ont ainsi permis d'envisager l'administration de ces molécules à des modèles de rongeurs puis à l'homme. Comme nous l'avons précédemment évoqué, l'anti-miR-122 Miravirsen basé sur la technologie d'acide nucléique bloqué (LNA pour « locked nucleic acid »), a été la première thérapie basée sur les miARN à entrer en phase clinique en 2008. Le LNA est un acide nucléique chimiquement modifié par ajout d'un pont methylène dans le ribose de l'acide nucléique. Cette modification augmente son affinité pour sa cible et sa stabilité. Il est également résistant aux nucléases. Les premiers travaux menés chez les rongeurs et les primates infectés par le VHC ont montré une absence de toxicité de cette molécule et la diminution du taux d'ARN viraux plasmatiques en réponse au LNA [START_REF] Lanford | Therapeutic silencing of microRNA-122 in primates with chronic hepatitis C virus infection[END_REF]. En 2012, des résultats prometteurs ont été obtenus chez les patients atteints d'hépatite chronique C (diminution du taux plasmatique de cholestérol et des ARN viraux) [START_REF] Janssen | Treatment of HCV Infection by Targeting MicroRNA[END_REF]. Un autre type d'inhibiteur dirigé cette fois contre miR-221 a été testé chez la souris, et a montré son efficacité pour freiner le développement du CHC [START_REF] Park | miR-221 silencing blocks hepatocellular carcinoma and promotes survival[END_REF]. Cet inhibiteur est un antagomiR dont la séquence est complémentaire à la totalité du miARN, à la différence du LNA qui n'en cible qu'une partie. Il permet la séquestration ou la dégradation du miARN cible. Pour augmenter la stabilité des antagomiR in vivo, des modifications chimiques ont été apportées (ajout de groupement 2'-O-methyl ou 2'-O-methoxyethyl, squelette phosphorothioate). De même, une nouvelle classe d'inhibiteurs, les minuscules LNA (« tiny-LNA ») sont apparus; plus petits, ils présentent une meilleure distribution tissulaire et permettent d'inhiber une famille entière de miARN [START_REF] Obad | Silencing of microRNA families by seed-targeting tiny LNAs[END_REF].

La seconde approche basée sur les miARN consiste à ré-exprimer un miARN à l'aide d'une molécule d'ARN double brin mimant l'activité du miARN endogène, et donc appelé « mimic ». L'administration d'un mimic de miR-26 via un adénovirus dans un modèle de souris présentant des CHC mutés pour MYC a freiné avec succès le développement des tumeurs en corrélation avec une perte des cyclines E2 et D2 dans les tumeurs [START_REF] Kota | Therapeutic microRNA delivery suppresses tumorigenesis in a murine liver cancer model[END_REF]. De même, une étude de Hatziapostoulou a montré l'efficacité de l'administration d'un mimic de miR-124 encapsulé dans des liposomes dans des modèles murins de CHC induits par la diéthylnitrosamine [START_REF] Hatziapostolou | An HNF4alpha-miRNA inflammatory feedback circuit regulates hepatocellular oncogenesis[END_REF]. La société miRNAtherapeutics, spécialisée dans le développement de thérapies basées sur les mimic, a ainsi créé miRX34, un mimic de miR-34a encapsulé dans des liposomes, qui est actuellement en phase clinique pour les tumeurs solides notamment les tumeurs du foie. La survie de souris greffée avec des CHC humains est grandement améliorée avec miRX34, et ceci est corrélé à une absence de tumeurs détectables. Le test préclinique d'un mimic de let-7g est aussi en cours.

Bien que des résultats prometteurs aient été obtenus pour les thérapies basées sur les miARN, un certain nombre de challenges sont encore à relever pour améliorer l'efficacité de ces traitements. Leurs défauts sont les mêmes que ceux qui ont freiné le développement des thérapies basées sur les petits ARN interférants: augmentation de la stabilité, administration sous forme libre ou encapsulé dans des nanoparticules ou des exosomes, problème de spécificité, ciblage d'autres ARN ou d'ARN non identifiés, distribution aux différents tissus, persistance de la réponse, effets secondaires. Ce tableau compile les données concernant le rôle des miARN dans la prolifération, l'apoptose, la migration et l'invasion. Les miARN cités sont ceux au moins décrits dans deux papiers de différents groupes et dont les cibles sont clairement identifiées. Les miARN détectables dans le sérum sont référencés en dernière colonne. Les miARN en gras sont ceux pour lesquels une stratégie anti-miARN a été testée ; ceux en rouge sont ceux pour lesquels un miARN mimic a été administré aux modèles animaux.

Figures et légendes

  Conclusions L'essor de l'étude des miARN a permis d'identifier des signatures miARN pour une grande variété de tumeurs solides, et en particulier pour le foie. La mise en évidence d'un panel de miARN dérégulés dans les pathologies du foie, et notamment dans le CHC, permettent d'envisager l'apparition de nouveaux outils puissants pour le diagnostic, le pronostic et le traitement des patients. Bien que nombre d'études ait aidé au déchiffrage des différentes cibles d'un miARN d'intérêt, le défi majeur pour l'avenir est de comprendre comment les différentes cibles d'un miARN interagissent dans une pathologie donnée, mais également comment un même ARN, cible de plusieurs miARN, se comporte dans ce même contexte.

Figure

  Figure 1. Nombre de publications référencées dans PUBMED en février 2013 contenant les mots «miARN», «miARN cancer» et «miARN cancer foie»

1 .

 1 Figure 1. Nombre de publications référencées dans PUBMED en février 2013 contenant les mots «miARN», «miARN cancer» et «miARN cancer foie»

Figure 2 .

 2 Figure 2. Synthèse des microARN. Les miARN sont produits sous forme de précurseurs monocistroniques ou polycistroniques appelés pri-miARN. Après leur clivage par le complexe de protéines Pasha/Drosha, les pré-miARN résultants sont exportés du noyau via l'exportine-5. Dans le cytoplasme, la protéine Dicer permet la maturation des miARN sous forme d'un duplex de 22 nucléotides contenant le miARN et le miARN* complémentaire. Une fois sous forme simple, le miARN est pris en charge par le complexe RISC et notamment Ago2 pour permettre son association à la séquence complémentaire sur son ARNm cible. L'appariement miARN/ARNm conduit à la diminution du niveau d'expression de l'ARNm ciblé par inhibition de sa traduction ou par sa dégradation.

Figure 3 .Tableau 4 .

 34 Figure 3. Expression des miARN dans le foie normal et pathologique. La figure montre les miARN impliqués dans les différents stades des maladies du foie. La modification de l'expression des miARN dans toute cellule du foie (hépatocyte, cellule étoilée, cellule endothéliale et cellule immunitaire telle que la cellules de Kupffer) participe à la progression des maladies chroniques du foie et à l'apparition de cancer.


Luis H Gallardo -

Olivier Rahavandrainy

Luis H Gallardo
email: luis.gallardo@univ-brest.fr-olivier.rahavandrainy@univ-brest.fr

Keywords: Bi-unitary divisors, Mersenne primes, finite fields b) Mathematics Subject Classification (2010): 11T55, 11T06

We give all non splitting bi-unitary perfect polynomials over the prime field of two elements, which have only Mersenne polynomials as odd irreducible divisors.

Introduction

Let S ∈ F 2 [x] be a nonzero polynomial. We say that S is odd if gcd(S, x(x + 1)) = 1, S is even if it is not odd. A Mersenne (prime) is a polynomial (irreducible) of the form 1 + x a (x + 1) b , with gcd(a, b) = 1. A divisor D of S is called unitary if gcd(D, S/D) = 1. We denote by gcd u (S, T ) the greatest common unitary divisor of S and T . A divisor D of S is called bi-unitary if gcd u (D, S/D) = 1. We denote by σ(S) (resp. σ * (S), σ * * (S)) the sum of all divisors (resp. unitary divisors, bi-unitary divisors) of S. The functions σ, σ * and σ * * are all multiplicative. We say that a polynomial S is perfect (resp. unitary perfect, bi-unitary perfect) if σ(S) = S (resp. σ * (S) = S, σ * * (S) = S). Finally, we say that a bi-unitary perfect polynomial is indecomposable if it is not a product of two coprime nonconstant bi-unitary perfect polynomials. As usual, ω(S) designates the number of distinct irreducible factors of S. Several studies are done about (unitary) perfect polynomials over F 2 . In particular, we gave ( [START_REF] Gallardo | There is no odd perfect polynomial over F 2 with four prime factors[END_REF], [START_REF] Gallardo | Even perfect polynomials over F 2 with four prime factors[END_REF], [START_REF] Gallardo | All unitary perfect polynomials over F 2 with at most four distinct irreducible factors[END_REF]) the list of them with ω(A) ≤ 4 and that of all which are divisible only by x, x + 1 and by Mersenne primes ( [START_REF] Gallardo | On even (unitary) perfect polynomials over F 2[END_REF] and [START_REF] Gallardo | All even (unitary) perfect polynomials over F 2 with only Mersenne primes as odd divisors[END_REF]).

We are interested in indecomposable bi-unitary perfect (i.b.u.p) polynomials (over F 2 ) with only Mersenne primes as odd divisors and we get Theorem 1.1.

If A is a nonconstant b.u.p polynomial, then x(x + 1) divides A so that ω(A) ≥ 2 (see Lemma 2.1). Moreover, the only b.u.p polynomials over F 2 with exactly two prime divisors are x 2 (x + 1) 2 and x 2 n -1 (x + 1) 2 n -1 , for any nonnegative integer n (Lemma 2.1 and [1] Theorem 5).

Note that in the integer case, 6, 60 and 90 are the only b.u.p numbers ( [START_REF] Wall | Bi-Unitary Perfect numbers[END_REF]).

In the rest of the paper, for S ∈ F 2 [x], we denote by S (resp. S * ) the polynomial obtained from S with x replaced by x + 1 (resp. the reciprocal of S): S(x) = S(x + 1), S * (x) = x deg(S) • S(x -1 ). As usual, N (resp. N * ) denotes the set of nonnegative integers (resp. of positive integers).

For S, T ∈ F 2 [x] and n ∈ N * , we write:

S n ∥T if S n |T but S n+1 T .
We consider the following polynomials:

M 1 = 1 + x + x 2 = σ(x 2 ), M 2 = 1 + x + x 3 , M 3 = M 2 = 1 + x 2 + x 3 , M 4 = 1 + x + x 2 + x 3 + x 4 = σ(x 4 ), M 5 = M 4 = 1 + x 3 + x 4 , C 1 = x 3 (x + 1) 4 M 1 , C 2 = x 3 (x + 1) 5 M 1 2 , C 3 = x 4 (x + 1) 4 M 1 2 , C 4 = x 6 (x + 1) 6 M 1 2 , C 5 = x 4 (x + 1) 5 M 1 3 , C 6 = x 7 (x + 1) 8 M 5 , C 7 = x 7 (x + 1) 9 M 5 2 , C 8 = x 8 (x + 1) 8 M 4 M 5 , C 9 = x 8 (x + 1) 9 M 4 M 5 2 , C 10 = x 7 (x + 1) 10 M 1 2 M 5 , C 11 = x 7 (x + 1) 13 M 2 2 M 3 2 , C 12 = x 9 (x + 1) 9 M 4 2 M 5 2 , C 13 = x 14 (x + 1) 14 M 2 2 M 3 2 , C 14 = x 8 (x + 1) 10 M 1 2 M 4 M 5 , C 15 = x 8 (x + 1) 12 M 1 2 M 2 M 3 M 5 , C 16 = x 10 (x + 1) 13 M 1 2 M 2 2 M 3 2 M 4 , C 17 = x 13 (x + 1) 13 M 1 2 M 2 4 M 3 4 M 4 M 5 , C 18 = x 12 (x + 1) 13 M 1 2 M 2 3 M 3 3 , C 19 = x 9 (x + 1) 13 M 2 2 M 3 2 M 4 2 , C 20 = x 8 (x + 1) 13 M 2 2 M 3 2 M 4 , C 21 = x 9 (x + 1) 10 M 1 2 M 4 2 M 5 , C 22 = x 7 (x + 1) 12 M 1 2 M 2 M 3 , C 23 = x 9 (x + 1) 12 M 1 2 M 2 M 3 M 4 2 . The polynomials M 1 , . . . , M 5 are all Mersenne primes. Theorem 1.1. Let A = x a (x + 1) b P 1 h 1 • • • P r hr ∈ F 2 [x] be such that the P j 's are Mersenne primes, a, b, h j ∈ N and ω(A) ≥ 3. Then A is i.b.u.p if and only if A, A ∈ {C j : 1 ≤ j ≤ 23}.
The polynomials C 1 , . . . , C 13 in Theorem 1.1 are already given in [START_REF] Beard | Bi-Unitary Perfect polynomials over GF (q), Annali di Mat[END_REF]. Our method consists in determining the possible irreducible divisors of such b.u.p polynomials and the upper bound of their exponents, without considering several distinct cases. We then use Maple computations to obtain our list.

Preliminaries

We need the following results. Some of them are obvious or (well) known, so we omit their proofs. We put

M := {M 1 , M 2 , M 3 , M 4 , M 5 }. Lemma 2.1. If A is a nonconstant b.u.p polynomial over F 2 , then x(x + 1) divides A, so that A is even and ω(A) ≥ 2.

Lemma 2.2. If

A = A 1 A 2 is b.u.p over F 2 and if gcd(A 1 , A 2 ) = 1, then A 1 is b.u.p if and only if A 2 is b.u.p. Lemma 2.3. If A is b.u.p over F 2 , then A is also b.u.p over F 2 .
Lemma 2.4 is obtained from [START_REF] Gallardo | Characterization of Sporadic perfect polynomials over F 2[END_REF] (Lemma 2.6) and from Canaday's paper [START_REF] Canaday | The sum of the divisors of a polynomial[END_REF] (Lemmas 4, 5, 6, Theorem 8 and Corollary on page 728).

= P (x 3 ). iv) If σ(x 2n ) is only divisible by Mersenne primes, then 2n ∈ {2, 4, 6}. v) If σ(x 2r ) is a Mersenne prime, then 2r ∈ {2, 4}. vi) If σ(x h ) = σ((x + 1) h ), then h = 2 n -2, for some n ∈ N * . vii) If σ(P 2n ) = Q m , then m ∈ {0, 1}. Lemma 2.5 ([8], Theorem 1.2). Let M ∈ M be such that σ(M 2m ) (resp. σ(M 2m+1 )) has only Mersenne primes as odd divisors, then 2m = 2 (resp. 2m + 1 = 3 • 2 α -1 for some α ∈ N * ) and M ∈ {M 2 , M 3 }. All odd divisors of σ(M 2m ) (resp. of σ(M 2m+1 )) lie in {M 1 , M 4 , M 5 }.
Lemma 2.6. Let T be an irreducible polynomial over F 2 and k, l

∈ N * . Then, gcd u (T k , T l ) = 1 (resp. T k ) if k ̸ = l (resp. k = l). In particular, gcd u (T k , T 2n-k ) = 1 for k ̸ = n, gcd u (T k , T 2n+1-k ) = 1 for any 0 ≤ k ≤ 2n + 1. Corollary 2.7. Let T ∈ F 2 [x] be irreducible. Then i) σ * * (T 2n ) = (1 + T )σ(T n )σ(T n-1 ), σ * * (T 2n+1 ) = σ(T 2n+1 ). ii) For any c ∈ N, T does not divide σ * * (T c ). Proof. i): σ * * (T 2n ) = 1 + T + • • • + T n-1 + T n+1 + • • • + T 2n = (1 + T n+1 )σ(P n-1 ) = (1 + T )σ(T n )σ(T n-1 ). σ * * (T 2n+1 ) = 1 + T + • • • + T 2n+1 = σ(T 2n+1 ). ii) follows from i). Corollary 2.8. Let T ∈ F 2 [x] be irreducible. i) If a = 4r, where 2r -1 is of the form 2 α u -1, u odd, then σ * * (T a ) = (1 + T ) 2 α • σ(T 2r ) • (σ(T u-1 )) 2 α and gcd(σ(T 2r ), σ(T u-1 )) = 1. ii) If a = 4r + 2, where 2r + 1 is of the form 2 α u -1, u odd, then σ * * (T a ) = (1 + T ) 2 α • σ(T 2r ) • (σ(T u-1 )) 2 α and gcd(σ(T 2r ), σ(T u-1 )) = 1. iii) If a = 2 α u -1 is odd (with u odd), then σ * * (T a ) = (1 + T ) 2 α -1 • (σ(T u-1 )) 2 α .
We explicit the following formulas (useful for

T ∈ {x, x + 1} ∪ M).    σ * * (T 2 ) = (1 + T ) 2 , σ * * (T 4 ) = (1 + T ) 2 σ(T 2 ), σ * * (T 6 ) = (1 + T ) 4 σ(T 2 ), σ * * (T 8 ) = (1 + T ) 4 σ(T 4 ), σ * * (T 10 ) = (1 + T ) 2 (σ(T 2 )) 2 σ(T 4 ), σ * * (T 12 ) = (1 + T ) 2 (σ(T 2 )) 2 σ(T 6 ), σ * * (T 14 ) = (1 + T ) 8 σ(T 6 ). ( 1
)
3 The proof of Theorem 1.1

Sufficiencies are obtained by direct computations. For the necessities, we shall apply Lemmas 2.11, 2.12, 2.13 and 2.14. We fix:

A = x a (x + 1) b ∏ i∈I P h i i = A 1 A 2 ,
where a, b, h i ∈ N, P i is a Mersenne prime,

A 1 = x a (x + 1) b 5 ∏ i=1 M h i i and A 2 = ∏ P i ̸ ∈M P i h i .
We suppose that A is i.b.u.p:

A 1 A 2 = A = σ * * (A) = σ * * (A 1 )σ * * (A 2 ).

First reduction

Lemma 3.1. For any P j ̸ ∈ M, one has: gcd(P

h j j , σ * * (A 1 )) = 1 and h j = 0, so that A = A 1 . Proof. Any odd irreducible divisor of σ * * (x a ) (resp. of σ * * ((x + 1) b ), of σ * * (M h i i ), with M i ∈ M) must belong to M. Thus, for all P j ̸ ∈ M and M i ∈ M, P j divides neither σ * * (x a ), σ * * ((x + 1) b ) nor σ * * (M h i i ). Hence, gcd(P h j j , σ * * (A 1 )) = 1. Moreover, P h j j divides σ * * (A 2 ) because it divides A = σ * * (A) = σ * * (A 1 )σ * * (A 2 )
and gcd(P h j j , σ * * (A 1 )) = 1. Hence, A 2 divides σ * * (A 2 ). So, A 2 is b.u.p and it is equal to 1, A being indecomposable.

Corollary 3.2.

If A 1 is b.u.p, then h 3 = h 2 , h 2 ∈ {0, 2, 4, 6, 2 n -1, 3 • 2 n -1 : n ∈ N * } and h i ∈ {0, 2, 2 n -1 : n ∈ N * }, for i ∈ {1, 4, 5}.
Proof. If M 2 (resp. M 3 ) divides σ * * (A 1 ), then it divides V = σ * * (x a )σ * * ((x+ 1) b ). Therefore, M 3 (resp. M 2 ) also divides V and σ * * (A 1 ). Hence, h 2 = h 3 . Suppose that h j ≥ 1. The polynomial σ * * (M

h j j ) must factor in {x, x + 1} ∪ M. Thus, if j ̸ ∈ {2, 3}, then h j ∈ {2, 2 n -1 : n ∈ N * }. If j ∈ {2, 3}, then h j ∈ {2, 4, 6}
or it is of the form 2 n u -1, where n ≥ 1 and u ∈ {1, 3}.

In the rest of the paper, we prove the following

Proposition 3.3. If A 1 is b.u.p, then A 1 , A 1 ∈ {C 1 , . . . , C 23 }.
Now, for i ∈ {1, 4, 5} with h i odd, one has: h i = 2 n -1 ≤ a ≤ 27, so that n ≤ 4 and h i ∈ {1, 3, 7, 15}.

• If u, v ≤ 5, then h 3 = h 2 = 0. For j ∈ {1, 4, 5}, M j divides σ * * (A 1 ) if and only if it divides σ * * (x a )σ * * ((1 + x) b ).

-The case u = v = 1 does not happen because A 1 does not split.

-If u = 1 and v = 3, then

h 1 = 2 β ≤ 2, 2 α -1 ≤ b = 3 • 2 β -1, β = 1, α ≤ 2. -If u = 1 and v = 5, then h 5 = 2 β ≤ 2, 2 α -1 ≤ b = 5 • 2 β -1, β = 1, α ≤ 3. -If u = v = 3, then h 1 is even and h 1 = 2 α + 2 β ≥ 4, which is impossible. -If u = 3 and v = 5, then h 1 = 2 α ≤ 2, h 5 = 2 β ≤ 2, α = β = 1. -If u = v = 5, then h 4 = 2 α ≤ 2, h 5 = 2 β ≤ 2 and α = β = 1.

Maple Computations

According to Lemmas 3.5 and 3.6, we determine, in 4 parts, the set L of all 7-uples [a, b, h 1 , h 2 , h 3 , h 4 , h 5 ] such that a ≤ b. Then, we search

S = x a (x + 1) b M 1 h 1 M 2 h 2 M 3 h 3 M 4 h 4 M 5 h

Lemma 2 . 4 .

 24 Let P, Q ∈ F 2 [x] be odd and irreducible and let n, m ∈ N. i) If P is a Mersenne prime, then σ(P 2n ) is odd and square-free. ii) If P is a Mersenne prime and if P = P * , then P = M 1 or P = M 4 . iii) If σ(x 2n ) = P Q and P = σ(x 2m ), then n = 4, m = 1 and Q

  5 satisfying: σ * * (S) = S. The case where a ≥ b is obtained from the substitution: x ←→ x + 1. 1) If a and b are even, then b ∈ {0, 2, 4, 6, 8, 10, 12, 14} and h i ∈ K 1 . We get (after 6 mn) #L = 35000 and C 3 , C 4 , C 8 , C 13 , C 14 , C 15 as b.u.p polynomials. 2) If a is even and b odd, then b ∈ {0, 1, 3, 5, 7, 9, 11, 13, 19, 23, 27, 39, 55}, a ∈ {0, 2, 4, 6, 8, 10, 12, 14} and h i ∈ K 1 . We get (15 mn): #L = 70000 and as b.u.p polynomials: C 5 , C 9 , C 16 , C 18 , C 20 . 3) If a is odd and b even, then a ∈ {0, 1, 3, 5, 7, 9, 11, 13, 19, 23, 27, 39, 55}, b ∈ {0, 2, 4, 6, 8, 10, 12, 14} and h i ∈ K 1 . We get (5 mn): #L = 35000 and C 1 , C 6 , C 10 , C 21 , C 22 , C 23 . 4) If a and b are both odd, then a, b ≤ 27 and h i ∈ K 2 . Moreover, h 2 = h 3 = 0 if u, v ≤ 5. We get (30 mn): #L = 97500 and C 2 , C 7 , C 11 , C 12 , C 17 , C 19 . The function σ * * is defined as Sigm2star > Sigm2star1:=proc(S,a) if a=0 then 1;else if a mod 2 = 0 then n:=a/2:sig1:=sum(S^l,l=0..n):sig2:=sum(S^l,l=0..n-1): Factor((1+S)*sig1*sig2) mod 2: else Factor(sum(S^l,l=0..a)) mod 2:fi:fi:end: > Sigm2star:=proc(S) P:=1:L:=Factors(S) mod 2:k:=nops(L[2]): for j to k do S1:=L[2][j][1]:h1:=L[2][j][2]: P:=P*Sigm2star1(S1,h1):od:P:end:

Corollary 2.9. i) For any j ≤ 5, neither M 2 nor M 3 divides σ * * (M h j j ). ii) σ * * (M 2 4 ) = x 2 (x + 1) 4 M 1 M 5 and σ * * (M 3 4 ) = x 4 (x + 1) 2 M 1 M 4 . iii) If j ̸ ∈ {2, 3} and r ≥ 2, then σ * * (M j 2r ) has a non Mersenne prime divisor. iv) If M 2 divides σ * * (x a ), then a ∈ {12, 14, 7 • 2 n -1 : n ∈ N * }. In this case, M 3 also divides σ * * (x a ). Corollary 2.10. i) The polynomial σ * * (x a ) splits over F 2 if and only if a = 2 or a = 2 α -1, for some α ∈ N * . ii) Let T ∈ F 2 [x] be odd and irreducible. Then σ * * (T c ) splits over F 2 if and only if T is a Mersenne prime and (c = 2 or c = 2 γ -1 for some γ ∈ N * ). Lemma 2.11. If σ * * (x 2m ) has only Mersenne primes as odd divisors, then 2m ∈ {4, 6, 8, 10, 12, 14}. In this case, all its divisors lie in M.

Proof. -Case 1: 2m = 4r, with r ≥ 1 and 2r -1 = 2 α u -1, u odd. We obtain:

Therefore, 2r ∈ {2, 4, 6} and u ∈ {1, 3, 5, 7}, 2r = 2 α u. So, 2m ∈ {4, 8, 12}.

-Case 2: 2m = 4r + 2, with r ≥ 0 and 2r + 1 = 2 α u -1, u odd. One has:

We get from Lemma 2.5 (with similar proofs): Lemma 2.12. If σ * * (x 2m+1 ) has only Mersenne primes as odd divisors, then 2m + 1 = 2 α u -1 for some α ∈ N * and u ∈ {3, 5, 7}. In this case, all its odd divisors lie in M.

Proof. We apply Lemmas 2.11 and 2.13.

Proof of Proposition 3.3

We write:

Proof. If a = 2 n -1 and b = 2 m -1 for some n, m ≥ 1, then

Thus, a = b and

By direct computations (sketched in Section 3.3), we get Proposition 3.3 from Lemmas 3.5 and 3.6. Set K 1 = {0, 1, 2, 3, 4, 5, 6, 7, 11, 23} and K 2 = {0, 1, 2, 3, 4, 6, 7, 15}.

Lemma 3.5. i) If a and b are both even, then a, b ≤ 14 and h

Proof. According to Corollary 3.2, it remains to give upper bounds for a, b and for h i , if h i is odd. i): If a and b are both even, then a (resp. b) is of the form 4r or 4r + 2, (resp. 4s or 4s + 2). Thus, σ(x 2r ) and σ((x + 1) 2s ) are both odd divisors of σ * * (A 1 ) = A 1 . Hence, 2r, 2s ≤ 6 and a, b ≤ 14. If h i is odd, then it is of the form 2 n u -1, with u ∈ {1, 3}. So,

)) 2 n . Thus, 2 n -1 ≤ a ≤ 14, by considering the exponents of x in A 1 and in σ * * (A 1 ). We get n ≤ 3 and h i ∈ K 1 . ii): In this case, 2 β ≤ a ≤ 14 so that β ≤ 3. Moreover, σ((x + 1) v-1 ) lies in {1, M 1 , M 2 M 3 , M 5 }. We deduce that v ≤ 7. As above, h i ∈ K 1 . Lemma 3.6. If a and b are both odd, then a

Proof. We give upper bounds for a, b and for h i , if h i is odd. One has: σ * * (x a ) = (x + 1) 2 α -1 (σ(x u-1 )) 2 α , σ * * ((x + 1) b ) = x 2 β -1 (σ((x + 1) v-1 )) 2 β . Without loss of generality, we may suppose that u ≤ v.

• If u = 7 or v = 7, then h 2 ̸ = 0 and h 2 ∈ {2 α , 2 β , 2 α + 2 β } (compare h 2 with all possible exponents of M 2 in σ * * (A 1 )). So, h 2 is even and thus h 3 = h 2 ≤ 6, α, β ≤ 2 and a, b ≤ 27.