Share, Act 2. What's Behind China's Anti-Corruption Campaign?

Keywords: China, anti-corruption, corruption, politics, economy, Xi Jinping

As we have seen in a previous working paper (« The lion's share: What's behind China's economic slowdown? »), China's elite have largely benefited from control of state assets and manipulation of the factors market (land, labor and capital) during the first decade of this century. Along with strong growth and social mobility, the accumulation of wealth has created some of the most flagrant social polarization worldwide, much higher than the official statistics. Instead of taking concrete measures to correct these inequalities, according to the new blueprint of reforms launched by the 3rd Plenum in November 2013, the new direction has focused on a gigantic campaign against corruption. The choice of the « tigers » targeted at the highest level reflect an aspect of political infighting. The top-down method as well as the creation of numerous « Central Leading Groups », allows the new secretary general and chairman Xi Jinping to concentrate power on a scale unprecedented since Deng Xiaoping. Behind these political stakes, the real goal of the campaign seems to destabilise vested interest groups in favor of the statuquo, but the social coalition supporting the power is still fragile, with the passive resistance of the local bureaucraties, the alienation of intellectuals and the uncertainties concerning the gains of the private sector.

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La part du lion, acte 2 : Les dessous de la campagne anticorruption en Chine

Résumé

Comme nous l'avons vu dans un précédent document de travail (« La part du lion : les dessous du ralentissement économique chinois »), l' élite chinoise a largement bénéficié du contrôle des actifs publics et de la manipulation du marché des facteurs (terrain, travail et capital), durant les années 2000. L'accumulation de richesses qui a suivi la forte croissance et la mobilité sociale, a créé l'une des plus fortes polarisation sociale au monde, bien supérieure aux chiffres officiels. Au lieu de prendre des mesures concrètes pour corriger ces inégalités, selon le plan de réformes lancé par le 3ème Plenum de novembre 2013, la nouvelle direction s' est concentrée sur une gigantesque campagne contre la corruption. Le choix des « tigres » visés au plus haut niveau n' est pas étranger à des règlements de compte politiques. La méthode très hiérarchique et la création de nombreux « Groupes de direction centraux », permettent au nouveau secrétaire général et président de concentrer le pouvoir sur une échelle sans précédent depuis Deng Xiaoping. Au delà des ces enjeux politiques, le vrai but de la campagne semble être de déstabiliser les groupes d'intérêts en faveur du statu quo, mais la coalition sociale soutenant le pouvoir reste encore fragile, avec la résistance passive des bureaucraties locales, l'aliénation des intellectuels et les incertitudes concernant les bénéfices des réformes pour le secteur privé.

Mots-clefs

Chine, anti-corruption, corruption, politique, économie, Xi Jinping Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92

Sommaire

The extent of social polarization : the anatomy of the lion's share 5

The campaign against corruption and the political power of Xi Jinping 6

The destabilisation of « stability » 11

The justification for « impartial justice » 13

The anti-corruption campaign and the rule by law 13

The top-down dynamic and the problematic social coalition

Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92

T he new cycle of reforms launched by the 3rd plenum of the 18th Central Committee of the Chinese Communist Party in November 2013 aims to implement a transition from an economic strategy financed by capital accumulation to one based on redistribution of the the state-party system revenues. As we have seeen in a previous study1, China's elite have largely benefited from control of state sector assets, and manipulation of the factors market (land, labor and capital). Along with strong growth which has allowed social mobility, the accumulation of wealth has benefited a minority of the population, creating some of the most flagrant social polarization, worldwide, a striking paradox for a regime led by a « communist » party. But instead of taking concrete economic measures to correct these inequalities, the new direction has focused on a gigantic campaign against corruption, which has changed the rules of the political game. This paper seeks to explain the reasons for this campaign, its possible outcome for the new round of economic reforms, and the legacy it will leave behind.

The extent of social polarization : the anatomy of the lion's share

In contrast to official statistics, a nationally representative survey, conducted in the summer of 2011 with a sample of 8,438 households and 29,450 individuals, indicates that China's Gini coefficient, a measure of inequality on a scale from complete equality (zero) to complete inequality (1), reaches 0,61, at the national level, with regional variations ranging from 0,60 in the east part, 0,56 in the centre and 0,54 in west. Income transfers such as pensions, social security and other social programs tend to reduce inequality on a much smaller scale than in other countries. Poor households in the countryside typically suffer from poor health, lack of medical insurance and low levels of education. Although the saving rate for Chinese households is around 30 percent of aggregate income, less than 55 percent of households saved money in 2010, and 45 percent did not save. According to income levels, the top 5 percent income households account for 50 percent of savings, the top 10 percent represent 66,2 percent, and the top 25 percent income households account for 83,5 percent of total savings. 2 The situation is even more inequitable with respect to wealth concentration. The Beijing University 2014 Report on the Development of the People's Livelihood in China, based on a nationally representative panel, covering 15,000 households and more than 50,000 individuals, indicates that the Gini coefficient for wealth inequality has grown from 0.45 in 1995, to 0.55 in 2002, and to 0.73 in 2012. The top 1 percent of households today concentrate more than a third of wealth, while the lowest 25 % of households account for 1 percent 3 . Although regional and town and country inequalities explain much of this gap, there are two other specific features of wealth inequalities : 1. Households « within the system » (体制内) have a much higher wealth level than those outside of it (体之外) ; 2. Middle income households' wealth has risen at a fast pace while the low income households and high income household wealth has risen more slowly than in the previous year.

The authors of this report underline the risk of a vicious circle where « the rich get richer and the poor get poorer ». As health expenditures and social insurance represent some 11 percent of household consumption, a larger share than in most developed countries, and as these expenditures influence the households' livelihood, particularly in the case of the poor and the vulnerable, who become marginalized in case of severe illness 4 , transfer payments and a real redistribution policy are seen by Li Gan as the most effective way to correct these inequalities. As shown in the following graph, after transfer payments the Gini coefficient declines from 0.50 to 0.30 in Germany, from 0.51 to 0.34 in the United Kingdom, from 0.46 to 0.33 in Japan, from 0.49 to 0.38 in the U.S, and from 0.5 to 0.3 in France 5 .

Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92

The campaign against corruption and the political power of Xi Jinping for this new reform cycle : « The most resistant (opposition) group is likely to be vested interests such as those enterprises that enjoy partial or full monopoly (or monopsony) in key markets, as well as firms, groups, institutions and individuals who obtain special privileges and benefits or enjoy special treatment from the current power structure and institutional setting. These groups gain from a special relationship with decision-makers or reap economic rents from distorsions implicit in the current price, institutionnal and administrative structure. They are likely to be influential, powerful, resourceful, and resolute in protecting their interests. Overcoming such opposition will require political courage, determination, clarity of purpose and skilled leadership qualities at the highest level of the government » 6 .

The political nature of this new set of reforms may explain a paradox in 2014. On the one hand, the promise of reforms has been more important The same logic applies to the actual fight against graft, although the unprecedented scale of the campaign deeply modifies the structure of power. Since the opportunities for corruption are dependent on the prerogatives of political decision-makers in the state-party system, they follow the hierarchical ladder. According to Ren Jianming, one of the leading corruption researchers in China « we say that about 30 percent of heads of prefectures are corrupt. name of « stability » go back to the noxious policies of the dignitaries (权贵). In these conditions, the potential for reform is quite narrow. It has to guard against the pitfalls of « leftist absolutism » and « rightist elitism ». It is easy to use « absolutism » to crush the power of the dignitaries, but if the dignitaries prevail, it seems possible that they would « launch a war to plunder the wealth of society and the masses ».

The issue is to make « an important leap at the beginning of the reform, to transform the fight against corruption into a systematic liquidation of the noxious policies of the dignitaries. » The fact that China has known land requisition, eviction and development on such a large scale, that it has failed repeatedly to pay migrants' salaries, « are for the most part directly linked to the process of plundering wealth by dignitaries». But on these grounds, where the masses' rights to defend their interests have been systematically crushed, without mercy, has emerged an ideological system of « stability », which is no more than a strategy to preserve vested interests.

This focus on « stability » to defend the interests of the elite works against majority rights and has exarcerbated the opposition between them and the government. At the same time, the preservation of stability at any cost has violated the law, to the point that one can no longer distinguish true from false, and that Chinese society becomes one without rule, where words count less than fits and shows of strength. Sun Liping's charge against « stability », which was the masterword of the post-Tian'anmen successive leaderships, is also founded on a critical analysis of the reform process, which has practically stopped, according to him, after the 1990s, despite official discourse to the contrary. On the surface, the power structure and the market seemed to combine, but in fact, the markets were instrumentalised by the power structure, which led to the formation of stable and powerful interest groups. These groups neither want to advance nor to go back ; their only goal is to maintain the status-quo. That is why their noxious policy was led in the name of « stability ». They are the forces behind four calamities, 1. the decline of economic vitality 2. social polarisation 3. social defeatism, and 4. environmental disaster. Moreover, they constitute a kind of « wall » blocking all roads to reform. Xi Jinping and Li Keqiang have underlined the importance of these interest groups after the third Plenum of November, 2013. « In this situation », writes Sun Liping, « the only possibility is to start with an anti-corruption campaign to lift up this wall 43 ». His attention is concentrated not on the efficiency of anti-corruption efforts, which takes the form of a campaign, but on the capacity of this movement to shake the power of vested interest groups.

In contrast to 1980s, reforms, which benefitted from a large social coalition with the rehabilitation of « rightists » of the Hundred Flowers campaign (1957), intellectuals, officials and victims of the Cultural Revolution and the continuous rise in the economic conditions of the masses, linked with rural policies, the actual reforms, according to Sun Liping, do not benefit from such social consensus. The real danger does not happen during the launch of the reform process, as no group wants to appear as an opponent and face retaliation, but during the course of the reforms.

Vested interest groups and dignitaries may not oppose the reforms, but later distort the concrete measures by transforming them in a war of plundering wealth, exactly as in the 1990s, with the reform of the state sector.

Rapid economic growth over the past thirty years has accompanied slow income growth for most people. Sun Liping underlines the discrepancy between national and international statistics on poverty, which has fallen in China's official figures to 80 million inhabitants at the end of 2010 (living on less than 1500 RMB/year) 44 .

According to the international UN standard, 250 million Chinese were living at this time on less than 1,25 US$ per day, and 900 million were living on less than 2 US $ per day… The fruits of development have thus been won by dignitaries groups, who have privatized public assets, in the state sector, mines, land allocation, etc. Most of the social contradictions of China are directly linked to this plundering of public assets, which have been locked up in the name of « stability » at any cost.

Thus, behind the anti-corruption campaign, the real political objective is to destabilise the dignitaries, eradicate their noxious policies, and create a just society, based on impartial justice, the goal of the next 30 years of reform, after the last 30 years mainly devoted to the construction of a economic market system.

The justification for « impartial justice »

According to Sun Liping, the lack of impartial justice is at the root of the social problems and contradictions in Chinese society. From an economic point of view, the lack of economic vitality over the past years is mainly due to the lack of a competitive environment at the macro level, the concentration of ressources in the hands of governments, their intervention in markets, and the power of monopolies. The creation of a level playing field in terms of competition among enterprises and sectors is thus the key to economic revitalisation.

In terms of society, most of the actual contradictions in China are no longer the result of malnutrition, as was the case at the beginning of the 1980s, but the result of social injustice. Norms of justice have been set at the lowest level where there is hardly any room to settle conflicts, sometimes even for managers and local officials.

The crux of the issue here too, is political. Despite the fact that the masses call for justice, the fascination for « stability » has led not only to a lack of impartial justice in concrete situations, but also sometimes to its destruction. Many recent social surveys have shown that the destruction of impartial justice concerns not only disadvantaged groups, but also the groups most envied by the public, such as government officials, policemen, teachers, private entrepreneurs and even highlevel managers. All these groups feel vulnerable.

According to Sun Liping, reform towards impartial justice must be based on 1. Institutionnalized oversight and limits on the power of authorities so that the life of political society may be brought under the boundaries of law ; 2. Eradication of crony capitalism (权贵资本主义) and establishment of a representative mechanisms and pluralist pressure groups in society; 3. Promotion of a citizens' consciousness and development of social organisations to protect impartial rights and to advance the equality of civil rights. Funded on a legal basis, on the authority of the constitution, the rule of justice and the impartiality of government administration, such reform, in order to abolish the croony capitalism, implies that those in power must disassociate themselves from particular interests.

To those who find these objectives « idealistic », Sun Liping replies by citing Amartya Sen according to whom the consensus of people on what is unjust in reality goes far beyond the consensus on what is just philsophically. To get rid of what is felt as unjust is thus the most realistic way to progress towards a just society.

The anti-corruption campaign and the rule by law

It is striking to see the close fit between Sun Liping's arguments and the political agenda, not only with respect to the intensity of the anti-corruption campaign, but also with respect to the « rule by law » or « governance according to law » (依法治国), the main theme of the November 2014 Central Committee Plenum. His analysis seems more political and outspoken than many points of view developed about the links between corruption and state sector reform 45 .

That said, if rule by law is to protect the right of the people, the whole legal system has to be reformed in favor of judicial independence, the end of the supervision of the all powerful Party's Central Politics and Law Committee, which overseas « above the law » the nation's courts, prosecutors and police, as underlined by Jian Ping, former president of China's University of Political Science and Law 46 . This implies a reduction of the party's power and a kind of « westernization » which is not at all in the mind of Chairman Xi Jinping, who likes to portray his policies as rooted in national virtues and tradition, and has well shown to the party, after his access to power, in his 2012 southern tour, that he would not become a new Gorbatchev.

If we look at things from another angle, from the Chinese tradition of politics and power, The internet and the academy were identified as the main conduits of these « mistaken views and ideas », and then subject to further control, with the creation in 2014 of the Central Leading Group for Cyberspace Affairs, the strengthening of the Cyberspace Administration of China, and the strenghtening of the ideological leadership of the Party in higher education ( January 2015 Central Committee Document). Rogiers Creemers explains that the choice of academic institutions as a target is justified from the point of view of the actual leadership, by the fact that many well regarded Chinese professors may have views influenced by their education or long time stays abroad, they have considerable input into policymaking process and they shape the worldview of future generations in a country where political protest, from May Fourth 1919 to Tian'anmen in 1989, have The same logic applies to anti-corruption . In a context of a weak legal system, political supervision enforcing Party discipline appears to be a more efficient way to restrain bureaucratic corruption. The CCDI is a Party internal control structure that promotes internal supervision for its 87 millions members, and a mechanism of checks and balances within the system. It is clearly above the law in the sense that , once a case is approved, as underlined by Xuezhi Guo 55 charged officials are put under « double restraint » (双规)that is to say confined for questionning in off-site detention, accompanied by « protectors » 24 hours a day to prevent them from committing suicide….without judicial involvement or oversight. As officials are isolated, cut from from any contact in order to reduce the potential influence of networks, there is a complete assymetry of information between them and the CCDI investigators who generally gather evidence through cooperation of their friends and neighbors. Professor Zhang Qianfan, a leading member of the constitutionnalist movement, see this kind of pratice, applied for Bo Xilai, Zhou Yongkang and Ling Jihua, as a complete denial of any basic citizens' rights, which is praticed from the top of the profiteers to the bottom of Chinese society 56 .

The top-down dynamic and the problematic social coalition

The top down dynamic of Xi Jinping has allowed him, for the moment, to concentrate power and maintain the initiative. His anti corruption campaign and his vision of the « Chinese dream » as a rejuvenation of the nation and the enabling of a middle-class lifestyle, may be popular. 2015, one may expect further scandals in the pillar sectors of state power (banking, oil, infrastructure, transport, telecommunications) which are abusing of their market power, with oligopolistic practices.

At the same time, the cases of Zhou Yongkang, Ling Jihua and Xu Caihou have shown that political factions are linked with vested interest groups. The princelings for instance, have not only strategic positions in the army, but also in the SOE, especially in the banking and financial industry. Despite Sun Liping's wish that « those in power must dissociate from particular interests » one must not forget with Xue Zhiguo that « China's elite have pursued wealth and political influence through trading power for monetary and non monetary resources. The pattern of the corruption in China's new elite has now evolved into exchanging power for power, in which the vested interest groups cooperate with one another to secure or enhance their political influence or even aim at a monopoly of political power. This trade is also related to guanxi (relations) networking, in which some offer their absolute loyalty to others in exchange for protection and career growth. High ranking-leaders, especially top leaders such as Xi Jinping and Li Keqiang, were awarded their positions based on the compromise and bargaining of the political factions and interest groups ». 62 As politics appears completely mingled with economics, the anti corruption campaign has obvious repercussions on the economy. Economic slowdown has already accelerated, following the general climate of distrust among the most wealthy Chinese, who vote with their feet, of interference by the CCDI in the activities of business and finance, and of a wait and see attitude and foot-dragging among officials, who are delaying some investment decisions, out of the fear to be suspect in an eventual corruption probe, or due to the lack of incentive with the loss of their grey income 63 . The CCDI refutes the theory of any influence of its action on the economic climate, asserting that the economic slowdown is a part of the « new normal » (新常态) restructuring, that economic growth is still high in comparison to the rest of the world, and that its action is cleaning up the abuses of power and ostentatious consumption of some officials, while preparing the field for future reforms 64 .

Such a position is based on the assumption that the party-state is able to reform itself, and to go back, by the virtue of discipline to its ideal of representing the public good. This is a far cry from whas has prevailed over the last 23 years, where the the lion's share of wealth accumulation has been raised through the state-party system, the alliance of power and business. Wang Qishan adressed the view that corruption cannot be solved under a one party system, citing the words of Xi Jinping : « I don't believe that the members of our Communist Party are that evil » 65 . Behind this belief in the possibility of self-reform, it is puzzling to see the postponements until now or the mere refusal of implementing concrete measures applicable to everyone, such as the declaration of the assets of officials and their family, and the creation of a property tax, which would limit the capital gains and reallocate resources toward local governments, responsible for most public expenditures.

The choice of selective, top-down political action with anti-corruption measures, and the postponement of concrete measures to tax capital gains is indeed risky, as the multiplication of high-level corruption cases may have a negative impact on the reputation of the Party and aggravate internal divisions among vested interest groups. The fact that the two successive leaderships of the party since Tian'anmen are criticized in Sun Liping's text may suggest that there will be further settlings of scores… To prevent a house of cards scenario, where the Party's bad reputation would combine with further divisions to endanger its survival, the Party anti-corruption experts have called for a compromise with vested interest groups which would accept institutionnalized anti-corruption measures, as part of the « new normal » policy, against a conditional amnesty to offenders, as long as they return their illicit gains to the government 66 . But Xi Jinping seems resolute to sustain his intiative and to advance it according to his own agenda.

The social coalition sustained by the belief in the « Chinese dream », appears fragile. The alienation of intellectuals, and strengthening of cybercontrol, which may weaken R&D and innovation policy, the uncertainties of the private sector which is supposed to be the main beneficiary of opening up the state sector to competition, declining returns on investments and the economic slowdown which is far from assuring a « continuous rise in the economic conditions of the masses », such as the one observed at the beginning of Deng Xiaoping's reforms. Beyond the possible reaction of « vested interest groups », these uncertainties may be the true challenge of the Xi Jinping's reforms.

66. Xue zhi Guo, article cited, The China Quarterly, p.621.

  62. « ControlingCorruption in the Party », article cited, The China Quarterly , p.614-615. 63. http://www.dw.de/chinas-corruption-crackdown-is-The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign? Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92

almost half of China's most wealthy individuals, among the top one percent income households, are considering reloca- ting to a developed market within the next five years 32

  are much lower according to confidential documents, around 30 percent of decision makers, at this stage, it is practically impossible for the CDIC to tackle all these cases in a short time. At the highest level, the choice of targets depends largely on the capacity to forge a coalition among the 7 members Standing Committe of the Politburo, the Army and some of the retired leaders who keep networks in the Centre as well as in provinces. Thus the progress of the « tiger hunt » has been linked to political stakes since its beginning.After the arrest in early 2012 of former Poliburo member and Chongqing party boss Bo Xilai, a potential political rival of Xi Jinping, who was convicted of bribery, embezzlement and abuse of Liu Wei, who allegedley ran gambling rings, and executed in 2015 20 .At the end of July, 2013, the communist party officially announced an investigation into Zhou Yongkang. The downfall of the former Standing Committee Politburo member, and political ally of Bo Xilai, who used to oversee hundred of thousands of police and paramilitary forces with an annual budget of more than $ 100 billion, marks an extension of the anti-corruption campaign to more than 300 of his relatives, political allies and business associates, detained or questionned 21 .An investigation of the prosperous state-run oil industry, led to the fall of Jiang Jiemin in August 2013, the former CEO of China National Petroleum Corporation(CNPC), just four months after his appointment as the head of the powerful State-owned Assets Supervision and Administration Commission (SASAC). Jiang Jiemin was linked with his ex boss Zhou Yongkang at the CNPC, as well as with Bo Xilai, The investigation extended not only to high-level managers of CNPC, more than a dozen of whom were removed, but also to its international operations and investments, in Indonesia, Iran and Canada, where local representatives were fired 22 .

	The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign?	11/20
	In March 2014, the arrests of a political friend of Zhou Yongkang and Bo Xilai, general Xu Cai-hou, the ex vice-chairman of the Central Military Commission, and of general Gu Junshan, Deputy Director of the General Logistic Department of the People's Liberation Army, is the result of the anti-corruption investigations undertaken in 2012, by a long-time ally of President Xi Jinping, General Liu Yuan, the son of President Liu Shaoqi, political commissar of the PLA's Gene-ral Logistic Departement, in charge of contracts in land, housing, food, finance and services for China's 2.3 million-strong army 23 . This was fol-lowed in December, 2014, and in January, 2015, by a major reshuffle linked to the anti-graft push, 20. Financial Times, February 9, 2015 : http://www.ft.com/ intl/cms/s/0/9bba0d9e-b02b-11e4-a2cc-00144feab7de. html#axzz3SOTQsoD7 21. Reuter, 17/09/2014 ; Financial Times, March, 31, 2014 : http://www.ft.com/intl/cms/s/0/259ad956-a841-11e3-a946-00144feab7de.html#axzz3SOTQsoD7 22. friends-li Minsheng Bank, the nation's first privately owned lender, revealed a complex network of interests in relations to Ling Jihua 27 , Bo Xilai, Zhou Yongkang, Ling Jihua and Gene-ral Xu Caihou, who died of cancer in 2015, were rumoured to be the leaders of an « anti-Xi Jinping cabal » within the Party. Their fall for corruption is thus linked to political rivalry. 28 But far from being reduced to a power struggle, the anti-cor-ruption campaign by its scale and its intensity has already deeply modified the power structure. If one agrees with Akio Takahara, the University of Tokyo, that « political actors can contend for power through and around institutions, and ins-titutions can better carry out their mission if they increase their relative power » 29 , the anti-corrup-tion struggle has been used as a battle horse to strengthen the authority of the new Secretary General and President. The CCDI whose work was previously limited to clean governance, has extended its prerogatives to the whole adminis-tration, by stationing branch-offices in top Party and government units, such as the CCP Cen-tral Committee's General Office, the Organi-zation Department (in charge of personnel and promotions), the Propaganda Department, the General Office of the State Council, the Natio-nal People's Congress, and the Chinese People Political Consultative Conference (CPPCC). In 2015, it plans to station anti-corruption cells in all regional party and governement units as well as in important SOEs 30 . In addition, Xi Jinping has taken the initiative to preside over numerous Central Leading Groups, which cover not only foreign affairs, national security, military reform, cybersecurity and infor-mation technology, but also matters, that fall generally within the competence of the State Council, such as financial and economic affairs. The Central Leading Group on Comprehensi-vely Deepening Reforms, presided by Xi Jinping, includes five deputies CCDI Party Secretaries, among the 39 seniors cadres with the rank of 27. South China Morning Post, January, 11, 2015 ; The Natio-nal Interest, January, 20, 2015 ; English.caixin.com, Februray 2, 2015 ; Bloomberg, Februrary 1, 2015. 28. Willy LAM, article cited, http://www.jamestown.org/ chinabrief/ 29. Richard C. Bush III « American and Japanese Scholars View China's Economy and Politics », Brookings Research 30. Willy LAM, article cited, http://www.jamestown.org/ chinabrief/ lion) for the year 2014. CCDI has recovered more than 3 billion yuan ($ 483 mil-38. The Telegraph, 25/07/2014. Xinhua, January 7, 2015 : the Article, January 27, 2015. Chinese trying to gain residency or citizenship abroad 35 . This tendency already affects the external accounts. Illicit capital outflows, often via busi-nesses in Hongkong, have surged in the past few years, with a clear acceleration in 2014. Gold-man Sachs economists, MK Tang and Maggie Wei, note that the « errors and omissions » of the Chinese balance of payments, which reflect a mismatch between official records of cross-bor-der flows, were equivalent to net outflows of more than $ 300 billion since 2010, including a record $ 63 billion in the third quarter of 2014, as yuan sentiment soured and President Xi Jinping anti-corruption offensive strenghtened 36 . These illicit outflows combined in 2014, with a surge in Chinese out-going investment, whose rising rate has exceeded that of in-coming invest-ment flows. Slowing real estate activity, dimi-nishing return on investments and weakening economy have pushed Chinese companies to increase overseas business and diversify abroad. China's capital account posted its widest deficit since at least 1998 in the fourth quarter of 2014, with record outflows (including the net errors and omissions), of $ 91 billion. Even if the cen-tral bank has amassed the largest world reserves of foreign exchange in order to face any kind of speculative pressures and capital outflows 37 , illi-cit outflows linked to officials have become an important aspect of the anti-graft fight. The « Fox Hunt » project, launched in 2014, aims to return corrupt officials who have fled the country. Some 762 of them were returned to China in 2013, and 500 in 2014, on suspicion of « criminality in taking advantage of their posi-tions of power ». More than 10 billion yuan, (1,615 US $ billion) have been confiscated accor-ding to the Supreme Court 38 . The launch of the APEC anti-corruption network, in the summer of 2014, provides further evidence of the Chinese government's determination to institutionalize international cooperation in this field. Accor-35. Financial Times, January 13, 2015 : http://www.ft.com/ intl/cms/s/0/986bd08a-9b10-11e4-882d-00144feabdc0.ht ml?siteedition=intl#axzz3Shb3xUtz 36. Justina Lee, Bloomberg, January 13, 2015. http://ftalphaville.ft.com/ 37. David Keohane, Financial Times, February 4, 2015,	among the top military officers of the People's Liberation Army and the military regions. Six-teen generals were placed under investigation for graft, including the two successive deputy poli-tical commissars of nuclear forces (Yu Daqing and Zhang Dongshui, from the Second Artillery Corps), the deputy head of the PLA's logistic Department (Liu Zheng), and Guo Zhenggang, from Zhejiang military command, the son of Guo Boxiong, a former member of the Politburo 24 . The province of Sichuan is not the only example of the link between the CCDI inspections and a political purge at the central level. In Shanxi, as coal mine development, the main resource of the province, is decided by officials, it has favoured opportunities for collusion with entrepreneurs and corruption on a large scale. The campaign against graft has even become a governance issue. After the fall of the former vice-governor Du Shanxue and Chinese People Political Consul-tative Conference (CCPC) vice-chairman Ling Zhengce, five of 15 members of the provincial party standing committee were placed under investigation in 2014 25 . Ling Zhengce was the brother of Ling Jihua, the ex chief of staff of President Hu Jintao, as head of the General Office of the CCP Central Com-mittee, and one of the numerous vice chairmen of the Chinese Political Consultative Conference , an advisory body. The Shanxi born Ling Jihua, linked to Jiang Jiemin, has been under investiga-tion since December 2014, for having turned his native province into a kleptocratic bonanza, by forming the « Shanxi Gang », a corrupt network of officials and businessmen. In his report to the three day Plenum of the CCDI, presided by Xi Jinping in January 2015, Wang Qishan emphasized the links between corruption and key wrongdoings such as forming factions and cliques 26 . In the wake of Ling Jinghua's investi-gation, the successive arrests of Chinese spy Ma Jian, deputy Minister of the omnipotent security Ministry, and of executives of financial compa-nies such as the Founder Group, a Peking Uni-versity-owned technology conglomerate, and the 24. English.caixin.com, January 8, 2015 ; Kevin N. McCau-ministers or above, who seat on this body. These leading groups institutionalize the concentration of power in the hands of Xi Jinping. The division of labor and tendency of bargaining among inte-rest groups or regions which prevailed in the ex Politburo Standing Committee, under Hu Jintao and Wen Jiabao, has given way to a new concen-tration of political, economic and military power, where the new President is omnipresent on all fronts, With this new approach the whole political atmosphere has changed: the fight against dis-sidents is more resolute than ever, officials are worried about their work and careers, multina-tional corporations complain against accusations ding to Huang Shuxian, the vice-secretary of the CCDI in charge of these matters, « our campaign to seize fleeing officials and return what they have stolen will become an important aspect of our political and diplomatic ties with other nations… focused on persuading foreign governments not to harbour these criminals » 39 At this stage, with such a political and socio-eco-nomic impact, it seems reasonnable to ask what is the ultimate goal of the anti-corruption cam-paign, which has dominated the 2014 agenda and continues in 2015. The destabilisation of « stability » of tax-avoidance practices, or what they see as a onesided application of the anti-monopoly law 31 , and significantly, Their share of foreign purchases of real estate leaped to 16 percent in the year ending March 2014, from 5 percent in 2007. According to a recent journalistic investigation, Chinese natio-nals hold US $ 660 billion in personnal wealth offshore and they spent US $ 22 billion in U.S homes in 2013 33 . They paid a median price of $ 523,148 higher than any other nationality and more than double the $ 199,575 median price of all households sold 34 . Chinese applicants made up more than 85 percent of the nearly 11.000 people who received investors' visas in the US in the first eight months of 2014, and 43 percent of investors' visas in the UK. Statistics from the other prefe-red destinations such as Australia and Portugal, indicate an explosion of the number of wealthy 31. Li Jing, South China Morning Post, October 14 , 2014 ; Tao Jingzhou, Financial Times, August 8, 2014 : http:// www.ft.com/intl/cms/s/0/170f1536-2f9c-11e4-83e4-Wang Qishan, the head of the CDIC, suggests that the goal of the crackdown is to get rid of corruption and bad work styles in the party and the government, by focusing on treating symp-toms to buy time to solve the root cause of cor-ruption 40 . But behind this official position, there is a political strategy and vision which, without being explained at the highest level, has been discussed in intellectual circles close to the corri-dors of power. The arguments of Professor Sun Liping (Depart-ment of Sociology, Tsinghua University) may shed some light on this debate. For Sun Liping, who has the (false) reputation as having served as Xi Jinping's PhD advisor, the biggest threat to China is not social turmoil, but social decay. This diagnosis, developed in 2009, implies ano-ther vision of Chinese society and politics, in the sense that « the opposite of social turmoil is social stability and the opposite of social decay is social health » 41 . In his article, « The challenge to reform of vested interest groups has not yet really come 42 , » Sun Liping focuses on the centrality of vested inte-rest groups. These groups, he writes, can stop the reform process in mid-course and in the 00144feabdc0.html#axzz3G2E0UcYn; Tom Mitchell, Financial Times, October 7, 2014 : http://www.ft.com/intl/ cms/s/0/7082de52-4e3e-11e4-adfe-00144feab7de.html?sit eedition=intl#axzz3G2E0UcYn 32. According to Barclay's Wealth Insights, which surveyed more than 2000 individuals and investors : Bloomberg, Sept 14, 2014. 39. Xinhua, 10/10/2014. 40. Beijing's University Li Chenyan, interview by Zhou Dongxu, http://english.caixin.com 22/07/2014. 41. http://chinadigitaltimes.net/2009/03/sun-liping-%E5%AD%99%E7%AB%8B%E5%B9%B3-the-biggest-

By office (provincial level or central level), it is about 50 percent, ministers, about 80 percent. You can work out for yourself what it is on the Politburo »… 18 Even 15. According to Xinhua (22/01/2015), a survey published by China Youth Daily showed that 70 % of respondents were satisfied over the campaign. 16. Susan Shirk, The political logic of economic reform in China, Berkeley, University of California Press, 1993, p.87, cited in Xuezhi Guo, « Controlling corruption in the Party : China's Central Discipline Inspection Commission », The China

Quarterly, September 2014, n°219, p.617. 17. Xuezhi Guo, idem, p. 617. 18

. See note 9 : International New York Times, September 2, 2014. In his published studies, Ren Jianming cites different figures : up to one third of executives with the rank of ministers or above have accepted bribes and commissions or if the figures power, and is now serving a life sentence, Party inspectors looked closely at officials in Sichuan where they dismantled a network of collusion between politicians and business executives after the launch of the anti-corruption campaign, as early as December 2012. The focus of Sichuan is particularly interesting since one of the closest allies of Bo Xilai, Zhou Yongkang , was formerly a director of China's largest oil company, the China National Petroleum Corporation,

CNPC, (1988-1998)

and party secretary of Sichuan

Pro- vince (1999-2002)

before his rise to the Ministry of State Security (2002) and then to the permanent Politburo, the highest governing body, from 2007 to 2012. The arrest in March, 2013, of the mining tycoon Liu Han, 19 close to Zhou Yongkang, was followed by the resignation of numerous top-level officials and executives in the economic nomenklatura, industry, construction and financial sector. Liu Han was later accused of covering up murders committed by his brother helped their close relatives and cronies profit in commercial deals. This figure is similar to a 2014 internal report indicating that « more than 30 percent of party, government and military officials were found to be involved in some form of corruption » See. Willy LAM, « Growing CCDI Power Brings Questions of Politically-Motivated Purge », China Brief, The Jamestown Foundation, Vol. XV, Issue 3, February 5, 2015. http://www.jamestown.org/chinabrief/. On the difficulty of measuring corruption, by perception-based and non-perceptual approaches, see Paul M. Heywood and Jonathan Rose, « Close but no Cigar : the mesurement of corruption », Journal of Public Policy (2014), 34 :3, 507-529. 19. Wall Street Journal, 21/03/2013 : http://www. wsj.com/video/chinese-billionaires-whereaboutsunknown/004D5711-3214-49AF-B8FF-C835DA-2DA27B.html#!0 The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign? 9/20 Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92 http://english.caixin.com, 23, 24/07/2014. 23. John Garnaut, « Rotting from within », Foreign Policy, April 2012 ; Cheng Li, article cited : http://www.brookings. edu/research/articles/2014/07/18-xi-jinping-inner-circle-ley, China Brief, Vol. XV, Issue 3, February 5, 2015. ; Bloomberg, January 15, 2015 ; English .caixin.com March 3, 2015. 25. Ren Jianming, interview cited, note 9, Shanxi ribao, 23/07/2014. 26. South China Morning Post, January 12, 2015 ; Xinhua, January 29, 2015 The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign? 10/20 Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92 . The U.S is their favorite destination. 33. http://www.businessweek.com/articles/2014-10-15/ chinese-home-buying-binge-transforms-california-suburbarcadia 34. Gary Shilling, Bloomberg, View, January, 23, 2015. Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92 threat-to-china-is-not-social-turmoil-but-social-decay/ 42. 既得利益集团对改革的挑战还没有真正到来, 改 革内参 (Reforms' Internal References), 17/04/2014, published in Fenghuang Pinglun 凤凰评论,17/04/14:http://news. ifeng.com/a/20140417/40003398_4.shtml The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign? 12/20 Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92

  in these classics that Xi Jingping has cited on numerous occasions 47 , the rule by law is the basic principle of the « Legalist » (or absolutist) tradition in Chinese politics, illustrated by Shang Yang, the thinker and statesman (390-338 B.C) whose anti-elitist and egalitarian policy transformed the state of Qin into a powerful kingdom, able to unify China one century later, with the first emperor Qin Shihuangdi (260-210) . Xi Jinping cited Han Fei (280-233 B.C), the philosopher who synthetised the legalist and taoist school for the political use of the first emperor : « When those who uphold the law are strong, the state is strong. When they are weak, the state is weak » 48 . The reality seems to be more complex than this absolutist tradition.

	The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign?	14/20
		up and the socialist nature of socialism with Chinese characteristics, by calling it « capitalist socialism », « state capitalism » or « new bureau-cratic capitalism » 50 .
	On the one hand, Xi has progressively neutralised the liberal reformers' collective call for « consti-tutionnal governance » (宪政) after he came to power at the end of 2012 49 . Document n°9, of April 2013, a secret circular of the CCP Cen-tral Committee General Office, identified seven noteworhty problems in the ideological sphere : promoting western constitutionnal democracy, promoting universal values such as western human rights, promoting civil society through « citizens movements » attempting to dismantle the ruling party's social foundation, promo-ting neo-liberalism by arguing that state owned enterprises (SOE) are national monopolies, and trying to weaken the governement's control on the economy, promoting the « freedom of press » and challenging China's principle that the media and publishing sectors should be subject to Par-ty's discipline, promoting historical nihilism by « reassessing history » of new China and rejecting the accepted conclusions on historical events and figures, and finally questionning reform, opening
	47. The CCP has published online (in Chinese) a collection of the chairman's citations of numerous classics in many different speeches : http://cpc.people.com.cn/n/2014/0529/ c164113-25080175.html
	48. taps-into-chinese-classics-in-seeking-to-cement-power. http://www.nytimes.com/2014/10/12/world/leader-html? ; http://sinosphere.blogs.nytimes.com/2014/10/14/ xi-jinping-on-exceptionalism-with-chinese-characteris-tics/?_php=true&_type=blogs&_r=0; For a debate on « Rule of Law » see China File : « Rule of Law, Why Now ? »: http://www.chinafile.com/conversation/rule-law-why-now	45. China News Analysis, Les nouvelles de Chine, Aout 2014 p.7-20 : http://www.centreasia.eu/publications/china-ana-lysis
	49. See the fascinating account of the debate around constitutionalism , by Rogier Creemers, « China's constitutionalism debate, content, context and implications », Working Paper, published in a revised version in The China Journal, n ° 74, July 2015 : https://chinacopyrightandmedia. wordpress.com/publications/	com/2014-09-16/100729435.html?mc_cid=6a4d78fe62&mc_ eid=c480cfc6eb

46. For a discussion of « The long journey to the rule of law », see Jiang Ping, former president and tenured professor at China's University of Political Science and Law, in Caixin, 16/09/2014: http://english.caixin.Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92 transmitted

  tended to originate from universities. According to the new Central Committee instructions, research should now focus on material issues, not on philosophical or ideological debate 51 . Fondation Maison des sciences de l'homme -190 avenue de France -75013 Paris -France http://www.fmsh.fr -FMSH-WP-2015-92 organization or individual may enjoy the privilege of being above the Constitution and the law » 53 . That may explain the virulence of the 2013 debate against constitutionnalists who pleaded for the strict implementation of the 1982 Constitution.

	The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign?	15/20
	In Xi's rhethoric, the Party and the people are the same. At the central conference on political and legal work in January, 2015, he recommanded that « Party committees at all levels should set an example of abiding by the law, they should enable law enforcement agencies and judidicial departements to work independantly »…. while « law enforcement agencies and judicial departments should be loyal to the Party ». This apparent contradiction between independance and loyalty hides a recentralisation of the legal apparatus, in order to tackle the corruption and inefficiency of the legal process as well as the local protectionism and the usual interventions of local officials in the roughly 3,000 local courts, which are unable to enforce citizens' constitutionnal rights against corrupt public servants. Thus, as Jerome Doyon and Hugo Winckler underline, « independance from local governments comes at the price of recentralization and therefore an increased dependance on higher levels of the Chinese government » 54 . If « the power is in the cage of law », its key remains in the hands of the Standing Committee of the Politburo...	On the other hand, for the first time in CCP history, Article 5 of the Constitution specifies that « no constitutionnalist movement, according to whom of Beijing University Law School, a leader of the view than the one defended by Zhang Qianfan, choice of the people » 52 . This is a totally different Communist Party emerging from history and the established the leadership position of the Chinese out revolution, contruction and reform, and it of the Party's leadership of the people in carrying expression of our basic law, is a reflection of fruits journal (2014, n°21) : « Our constitution, as an 是), the CCP Central Committee theoretical power in the cage of law » in Seeking Truth (求 has clearly explained what he meant by « placing to the country's legal development. Xi Jinping a Central Committee Plenum has been devoted
		50. For a complete English translation, see China File, August 11, 2013: http://www.chinafile.com/document-9-chinafile-translation
		51. Robert Creemers, « Ideology Matters: Parsing Recent Changes in China's Intellectual Landscape, Sinocism China Newsletter, February 2015: https://sinocism.com/?p=11410 and Roger Creemers, China Copyright and Media Blog : https://chinacopyrightandmedia.wordpress.com/
		52. David Bandurski, China Media Project, January 6, 2015.

The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign?

« The Lion's Share : What's Behind China's Economic Slowdown ? » October 2013 , FMSH Working Paper : http://www.fmsh.fr/fr/c/4005

The Lions's


Didier Devaurs

Kevin Molloy

Marc Vaisset

Amarda Shehu

Thierry Siméon

Juan Cortés

Characterizing Energy Landscapes of Peptides using a Combination of Stochastic Algorithms

Keywords: energy landscape, peptides, stochastic algorithms

Obtaining accurate representations of energy landscapes of biomolecules such as proteins and peptides is central to the study of their physicochemical properties and biological functions. Peptides are particularly interesting, as they exploit structural flexibility to modulate their biological function. Despite their small size, peptide modeling remains challenging due to the complexity of the energy landscape of such highlyflexible dynamic systems. Currently, only stochastic samplingbased methods can efficiently explore the conformational space of a peptide. In this paper, we suggest to combine two such methods to obtain a full characterization of energy landscapes of small yet flexible peptides. First, we propose a simplified version of the classical Basin Hopping algorithm to reveal low-energy regions in the landscape, and thus to identify the corresponding metastable structural states of a peptide. Then, we present several variants of a robotics-inspired algorithm, the Transition-based Rapidly-exploring Random Tree, to quickly determine transition path ensembles, as well as transition probabilities between metastable states. We demonstrate this combined approach on metenkephalin.

I. INTRODUCTION

Global thermodynamic and kinetic properties of molecules can be extracted from an analysis of their conformational energy landscapes [START_REF] Wales | Energy Landscapes: Applications to Clusters, Biomolecules and Glasses[END_REF]. In particular, obtaining an accurate representation of a molecule's energy landscape is a significant first step to conducting detailed structure-function studies for bio-molecules of central importance in the cell, such as proteins and peptides [START_REF] Shehu | Probabilistic search and optimization for protein energy landscapes[END_REF].

In this work, we focus on small peptides. Despite their modest size, they represent in many ways a more challenging setting than larger proteins. Peptides exhibit high structural flexibility, which enables them to recognize different molecular partners in the cell, and thus to modulate their biological function [START_REF] Paine | Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. III. Probable and average conformations of enkephalin[END_REF]. Contrary to proteins, that are often characterized by a unique native state and a funnel-shaped energy landscape, peptides are characterized by several meta-stable structural states; their energy landscape may contain a multitude of competitive low-energy basins.

The existence of multiple local minima in a molecule's energy landscape makes it particularly challenging to map this landscape and reconstruct all the functionally-important regions in it. Experimental methods, such as X-ray crystallography or nuclear magnetic resonance (NMR), cannot reveal such maps, as they can uncover only few structures at best [START_REF] Amodeo | Conformational sampling of bioactive conformers: A low-temperature NMR study of 15 N-Leu-Enkephalin[END_REF]. It is therefore the task of computational techniques to obtain detailed representations of energy landscapes.

Currently, only sample-based representations of the energy landscape can be afforded. Even for small peptides, the space of possible conformations is vast, and the effective degrees of freedom needed to represent a conformation are numerous. The high dimensionality of the space is accompanied by a complex (non-linear, non-convex) expression for the conformational energy, which is the result of competing local and non-local inter-atomic interactions. Probing this landscape is therefore very computationally-costly. Currently, only stochastic optimization techniques provide the right balance between accuracy and computational efficiency [START_REF] Wales | Energy Landscapes: Applications to Clusters, Biomolecules and Glasses[END_REF], [START_REF] Shehu | Probabilistic search and optimization for protein energy landscapes[END_REF].

Obtaining a representation of an energy landscape can be divided into two sub-problems: (1) determining meta-stable structural states (i.e. local energy minima); [START_REF] Shehu | Probabilistic search and optimization for protein energy landscapes[END_REF] computing transition paths between the identified states. Both can be addressed by achieving an effective sampling of the conformational space. In this paper, we propose to combine two sampling-based techniques to obtain a full characterization of energy landscapes of small yet highly-flexible peptides. First, we present a simple variant of the Basin Hopping algorithm [START_REF] Wales | Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms[END_REF] to sample local minima in a peptide's energy landscape. Local minima are then organized via density-based clustering to reveal meta-stable structural states. Second, we present several variants of a robotics-inspired algorithm, the Transition-based Rapidly-exploring Random Tree (T-RRT) [START_REF] Jaillet | Randomized tree construction algorithm to explore energy landscapes[END_REF], to map out the connectivity between these states, thus completing the reconstruction of the peptide's energy landscape. In particular, we propose a new variant of T-RRT allowing the computation of transition path ensembles and transition probabilities between meta-stable structural states. In a preliminary version of this paper [START_REF] Devaurs | Sampling-based methods for a full characterization of energy landscapes of small peptides[END_REF], we presented proof-of-concept results on a minimalist peptide: the terminally-blocked alanine. Here we present results on a larger and much more challenging system: met-enkephalin.

II. METHODS

The work presented in this paper is motivated by recent studies showing that robotics-inspired sampling-based algorithms provide a good basis for efficient conformational exploration in computational structural biology [START_REF] Gipson | Computational models of protein kinematics and dynamics: Beyond simulation[END_REF], [START_REF] Al-Bluwi | Motion planning algorithms for molecular simulations: A survey[END_REF]. The Transition-based RRT (T-RRT) algorithm is an example of such algorithms [START_REF] Jaillet | Randomized tree construction algorithm to explore energy landscapes[END_REF], [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]. It is based on the Rapidly-exploring Random Tree (RRT) [START_REF] Lavalle | Rapidly-exploring random trees: progress and prospects[END_REF], a popular path planning algorithm that can tackle complex problems in high-dimensional spaces. RRT has been successfully used in various disciplines, such as robotics, aerospace, computer animation, and computational structural biology. T-RRT is an extension of RRT involving a probabilistic transition test based on the Metropolis criterion. Like Metropolis Monte Carlo (MC) methods [START_REF] Frenkel | Understanding Molecular Simulations: From Algorithms to Applications[END_REF], it applies small moves to the molecular system; but, instead of generating a single path over the search space, it constructs a tree, providing a more efficient exploration. Moreover, the tree construction is intrinsically biased toward unexplored regions of the space, and favors expansions in low-energy areas.

This work is partly based on an existing variant of T-RRT, called Multi-T-RRT [START_REF] Devaurs | A multi-tree approach to compute transition paths on energy landscapes[END_REF], and on a new extension to it, called Multi-T-RRT with Cycles. These algorithms are combined with an in-house variant of the Basin Hopping algorithm involving a simplified minimization process. Together they are used to obtain a complete representation of the energy landscape of highly-flexible peptides. Details of these methods are presented in the next sections.

A. Basin Hopping

The Basin Hopping (BH) algorithm is a popular method for sampling local minima of an energy landscape. It was originally introduced to obtain the Lennard-Jones minima of small atom clusters [START_REF] Wales | Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms[END_REF]. Recently, BH has gained new attention to predict protein structure [START_REF] Olson | Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface[END_REF], and to find intermediate structures of chemical reactions [START_REF] Kim | Efficient basin-hopping sampling of reaction intermediates through molecular fragmentation and graph theory[END_REF]. The method consists of repeatedly applying a structural perturbation followed by an energy minimization, which yields a trajectory of minima. The result is a (discrete) coarse-grained representation of the energy landscape that can be seen as a collection of interpenetrating staircases.

Our implementation of BH (presented in Algorithm 1) differs from the classical one in that it does not involve local, gradient-based minimizations, but relies on simple Monte-Carlo-based (MC-based) minimizations. The algorithm follows a random restart procedure performing several rounds, each one starting from a conformation randomly sampled in the search space. Every round builds a trajectory of minima by performing a succession of structural perturbations followed by MC-based minimizations. Every MC-based minimization starts from a conformation obtained by performing a largeamplitude perturbation of the minimum reached at the previous step, or from the random sample, in the first step. An MC-based minimization is an iterative succession of smallamplitude perturbations. At each iteration, the perturbed conformation replaces the previous one if the Metropolis criterion is satisfied. More precisely, a downhill move in the energy landscape is always accepted. An uphill move is accepted or rejected based on the probability e -(Ej -Ei) / (K•T ) (where K is the Boltzmann constant), which decreases exponentially with the energy variation E j -E i for a given temperature T , where E i and E j are the energies of the old and the perturbed state, respectively. Every MC-based minimization produces a q ← doLargeAmplitudePerturbation(qp) 9 q ← doMonteCarloBasedMinimization(q) 10 if MetropolisTest(q,qp) then 11 addMinimum(T , q) 12 qp ← q 13 addTrajectory(L, T ) 14 return L low-energy conformation that we call a minimum in a minor abuse of language. It is compared to the minimum obtained in the previous iteration, and accepted or rejected also based on the result of a Metropolis-like transition test. Different temperatures can be used for the transition test inside the local energy minimization procedure and for the one at each iteration of BH (usually, the former being much lower than the latter). Every round produces what we call a milestone: the minimum (along the trajectory) having the lowest energy. Note that, in order to speedup computation, a round can be stopped based on a consecutive number of rejections, similarly to the MC-based minimization procedure.

All the milestones (or the minima) produced by BH have to be grouped to provide a comprehensible list of metastable structural states. This clustering can be done in several ways. In this work, we have applied a density-based clustering technique that has been shown to provide good results for small peptides [START_REF] Kim | Density-based clustering of small peptide conformations sampled from a molecular dynamics simulation[END_REF].

B. Multi-T-RRT with Cycle-Addition

The Rapidly-exploring Random Tree (RRT) algorithm [START_REF] Lavalle | Rapidly-exploring random trees: progress and prospects[END_REF] is a well-known path planning method in robotics. It can deal with complex problems by performing an efficient exploration, even in high-dimensional search spaces. Starting from an initial conformation q init , RRT iteratively constructs a tree T that tends to rapidly expand over the conformational space C. The nodes and edges of T correspond to states (i.e. molecular conformations) and small-amplitude moves between states, respectively. At each iteration of the tree construction, a conformation q rand is randomly sampled in C. Then, an extension toward q rand is attempted, starting from its nearest neighbor q near , in T . This means performing a linear interpolation between q near and q rand , at a distance equal to the extension step-size δ, from q near . If the extension succeeds, a new conformation q new is added to T and an edge is built between q near and q new . The criteria on when to stop the exploration can be reaching a given target conformation q goal , a given Algorithm 2: transitionTest (G, E i , E j ) input : the current temperature T ; the temperature increase rate Trate; the Boltzmann constant K output: true if the transition is accepted, false otherwise

1 if Ej ≤ Ei then return True 2 if e -(E j -E i ) / (K•T ) > 0.5 then 3 T ← T / 2 (E j -E i ) / energyRange(G) ; return True 4 else 5 T ← T • 2 T rate ;
return False number of nodes in the tree, a given number of iterations, or a given running time.

The Transition-based RRT (T-RRT) algorithm is a variant of RRT developed to explore a conformational space while taking the conformational energy into account [START_REF] Jaillet | Randomized tree construction algorithm to explore energy landscapes[END_REF], [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]. T-RRT extends RRT by integrating a stochastic transition test used to evaluate the local move from q near to q new based on their respective energies E i and E j , aiming to favor the exploration of low-energy regions of the space. This transition test is based on the Metropolis criterion, as explained for BH in the previous subsection.

The level of selectivity of this transition test is controlled by the temperature T : low temperatures limit the expansion to gentle slopes of the energy landscape, and high temperatures enable it to climb steep slopes. The basic MC method, as well as BH, consider constant temperature. In contrast, T is a self-adaptive parameter of the T-RRT algorithm. After each accepted uphill move, T is decreased to avoid over-exploring high-energy regions: it is divided by 2 (Ej -Ei) / energyRange(G) , where energyRange(G) is the energy difference between the highest-energy and the lowest-energy conformations in the graph G built so far. After each rejected uphill move, T is increased to facilitate the exploration and avoid being trapped in a local energy minimum: it is multiplied by 2 Trate , where T rate ∈ (0, 1] is the temperature increase rate. The pseudo-code of the T-RRT transitionTest is presented in Algorithm 2.

The Multi-T-RRT algorithm is a multiple-tree variant of T-RRT [START_REF] Devaurs | A multi-tree approach to compute transition paths on energy landscapes[END_REF]. Instead of building a single tree rooted at some initial conformation, the idea is to build n trees rooted at n given conformations q k init , k = 1..n. The pseudo-code of the Multi-T-RRT is presented in Algorithm 3. At each iteration, a tree T is chosen for expansion in a round-robin fashion. Then, an extension is attempted toward a randomly sampled conformation q rand , starting from its nearest neighbor q near , in T . If the extension succeeds, the new conformation q new is added to T , and connected to q near . Then, we search for the conformation q near , which is the closest to q new within all trees other than T . If the distance between q new and q near is less than or equal to the extension step-size δ, T is linked to and merged with T , the tree to which q near belongs. In that case, the number of trees is decreased by 1. The space exploration continues until all trees are merged into a single one or another stopping criterion (number of nodes, number of expansions, running time) is met.

A drawback of the Multi-T-RRT is that it returns a single

: C → R; the initial conformations q k init , k = 1..n output: the tree T 1 for k = 1..n do 2 T k ← initTree(q k init ) 3 while not stoppingCriteria({T k | k = 1..n}) do 4 T ← chooseNextTreeToExpand() 5 q rand ← sampleRandomConformation(C) 6
q near ← findNearestNeighbor(T , q rand ) 7 qnew ← extend(q near , q rand , δ) Starting from the tree produced by the Multi-T-RRT, the idea is to allow the space exploration to continue, and to add edges leading to the creation of cycles. This enables us to construct a graph from which several paths can be extracted between two given conformations. The pseudo-code of this T-RRT with Cycles is shown in Algorithm 4. It differs from T-RRT only in that, after every successful extension, an edge is added between q new and each conformation in the graph G that is not already connected to q new , and whose distance to q new is less than or equal to the extension step-size δ. The stopping criteria can involve the number of iterations or the running time, as well as a convergence test.

As several paths may exist in the graph G between two given conformations, a quality criterion is required to compare paths. This is achieved by associating weights with the edges of G, based on the notion of mechanical work [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]. More precisely, the weight of the directed edge connecting q i and q j is equal to max{ 0 , E(q j ) -E(q i ) } , i.e. to the positive energy variation between q i and q j . This constitutes the amount of energy that has to be added to the molecule for the transition from q i to q j to happen. Note that using the mechanical work as a quality criterion requires to create two directed edges between q i and q j , instead of creating a single undirected edge. Finally, given two conformations in G, the best (directed) path linking them is defined as the one minimizing the mechanical work, and is obtained using Dijkstra's algorithm.

In this work, we use the mechanical work as a path-quality criterion because it has been shown that T-RRT tends to generate paths having a low mechanical work [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]. Furthermore, in many situations, the mechanical work can assess the quality of a path better than a simple criterion such as the integral of the cost along the path [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]. Other criteria could be considered, such as the minimum resistance (linked to the MaxFlux algorithm [START_REF] Huo | The MaxFlux algorithm for calculating variationally optimized reaction paths for conformational transitions in many body systems at finite temperature[END_REF], [START_REF]Direct computation of long time processes in peptides and proteins: reaction path study of the coil-to-helix transition in polyalanine[END_REF]) or the maximum flux [START_REF] Zhao | Maximum flux transition paths of conformational change[END_REF]. However, finding which criterion is the most relevant is out of the scope of this paper.

III. RESULTS AND DISCUSSION

In a preliminary version of this paper [START_REF] Devaurs | Sampling-based methods for a full characterization of energy landscapes of small peptides[END_REF], we presented results provided by the combination of BH and Multi-T-RRT to characterize the conformational energy landscape of the terminally-blocked alanine. The energy landscape of this minimalist peptide, which involves several local minima connected by multiple pathways, can be projected on a single and meaningful 2-dimensional map. Thus, it is a very good benchmark system to illustrate the performance of computational methods in physical chemistry. Results on the terminally-blocked alanine are not presented again here because of space limitations. For details on this illustrative test system, the interested reader is referred to [START_REF] Devaurs | Sampling-based methods for a full characterization of energy landscapes of small peptides[END_REF].

Here, we present results on met-enkephalin, a pentapeptide with sequence: Tyr-Gly-Gly-Phe-Met. Despite its relatively small size, studying met-enkephalin is challenging from a structural point-of-view because of its great conformational variability. Met-enkephalin is still the focus of a large amount of work (e.g. [START_REF] Sicard | Reconstructing the free-energy landscape of met-enkephalin using dihedral principal component analysis and welltempered metadynamics[END_REF], [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF]). This endogenous opioid peptide is of significant interest due to its important roles in physiological processes, mostly related to pain and depression [START_REF] Sauriyal | Extending pharmacological spectrum of opioids beyond analgesia: Multifunctional aspects in different pathophysiological states[END_REF].

A. Met-Enkephalin Model and Settings

In this work, we consider an internal-coordinate representation of the molecule, assuming constant bond lengths and bond angles. Therefore, the conformational parameters are the {ω, φ, ψ} dihedral angles of the backbone of each amino-acid residue plus the χ i dihedral angles of the side-chains, which adds up to 23 degrees of freedom. We assume that all the angles but the ω angles can take values in the full angular range [-180 • , 180 • ). As the peptide bond torsions are known to undergo only small variations, the ω angles are allowed to vary only up to 10 • from the planar trans conformation.

Measuring the distance between two conformations is required to select neighbor nodes in RRT-based algorithms and for clustering. Here we use a weighted l 2 -norm in the space of the φ and ψ backbone dihedral angles (excluding the first and the last angle of the molecular chain), because they are the most relevant variables describing conformations of peptides. The weight of each dihedral angle within the norm is chosen as the Euclidian distance between its rotation axis and the farthest atom to it. In other words, greater weights are assigned to angles whose rotation results in larger conformational variation.

To illustrate the performance of the algorithms, we project their output on Ramachandran maps (i.e. φ-ψ maps) of the three middle residues (Gly2, Gly3, Phe4). Other representations are possible, such as projections on the first components provided by dimensionality reduction techniques (e.g. PCA, Isomap), or on pairs of structural descriptors (e.g. RMSD to a reference structure vs. end-to-end distance). However, we believe that a small set of φ-ψ maps is a clearer representation to identify conformational regions of a small peptide. Each 2-D map was generated using an exhaustive search procedure, by varying both dihedral angles with a 10 • step-size and finding the lowest-energy conformation corresponding to each (φ, ψ) pair using an MC-based minimization procedure, such as the one involved in the BH algorithm. Note that such a computationally expensive procedure is only used here to visualize and validate our results.

To compute conformational energy values, we use an inhouse implementation of the AMBER parm96 force-field [START_REF] Kollman | The development/application of a "minimalist" organic/biochemical molecular mechanic force field using a combination of ab initio calculations and experimental data[END_REF] with an implicit representation of the solvent using the Generalized Born approximation. All programs have been run on a singe core of an Intel c Xeon c CPU E5-2650 at 2.00GHz.

B. Local Energy Minima of Met-Enkephalin

We have used the Basing Hopping (BH) algorithm, as described in Section II-A, to sample low-energy conformations of met-enkephalin. The parameters of BH were set as follows: 500 rounds were performed, with each round executing a maximum of 1000 MC-based minimizations. The number of consecutive rejections to estimate the convergence of each local minimization and of each BH round was set to 100. The large-amplitude perturbations in the inner loop of the BH algorithm affected only the φ and ψ dihedral angles, with a maximum step-size of 2 radians. The small-amplitude perturbations performed during an MC-based minimization affected all variables, with a maximum step-size of 0.2 radians. Only one angle was perturbed at each iteration. The temperatures T for the Metropolis-like transition tests at each iteration of BH and in the MC-based minimization method were set to 1000 K and 0.01 K, respectively.

The 232,440 minima and 500 milestones produced by the BH algorithm are projected in the three Ramachandran maps shown in Figure 1. 1 The algorithm required about 24 CPU hours. Note however that this computing time can be significantly reduced by using a more efficient implementation of the energy function, and by means of parallel computation (parallelization of the main loop in Algorithm 1 is straightforward). Computational efficiency issues are further discussed in Section IV. Note also that the use of a more sophisticated, gradient-based local minimization method would help speeding up the performance of BH.

The plots in Figure 1 show that the minima provide a good coverage of all the low-energy regions, the milestones being more concentrated in a few areas. The density-based clustering algorithm identified 8 clusters, some of which are not clearly separated. The clusters containing the lowest-energy minima correspond to folded conformations of met-enkephalin, whereas clusters of higher-energy minima contain stretched conformations of the peptide. Intermediate conformations are grouped into several medium-energy clusters. These results are consistent with those presented in other related work on met-enkephalin.

Here we take a closer look at results presented in some recent work providing a meaningful representation of the energy landscape of met-enkephalin through a Markov State Model (MSM) built from Molecular Dynamics simulations (MD) [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF]. Even though this other approach applies a different energy model (GROMOS96 force field), a different conformational sampling method (MD) and a different clustering algorithm (hybrid kcenter-kmedoid), results show striking similarities to ours. Results in [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF] suggest that four out of the eight backbone dihedral angles involved in our metric are sufficient to characterize the conformational space of metenkephalin. These four angles are the ψ angles of Gly2, Gly3 and Phe4, and the φ angle of Gly3: {ψ 2 , ψ 3 , ψ 4 , φ 3 }. The authors define a 4-sign code to characterize conformations with respect to the values (positive or negative) of these four angles. The two regions most frequently sampled by MD correspond to conformations of type (----) and (+--+). As can be seen in Figure 1, a large number of the BH milestones are found in these two regions. Interestingly, these two classes are correctly identified among the clusters of BH milestones, and they contain the lowest-energy conformations. The class (+ -+ +), which is also significantly sampled by MD, is well represented in our results. Only a few milestones appear in the region (-+ + -), although results in [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF] suggest a relatively more important population of this type of conformation. This is probably due to differences in the forcefields. The highest-energy cluster of BH milestones contains stretched conformations of both types (+++ +) and (-++ -) merged together. We refer to this cluster as ( + + ).

To illustrate the application of the Multi-T-RRT, presented in the next subsection, we have selected the lowest energy conformation of each class (+ --+), (----), (+ -+ +) and ( + + ). The first two correspond to folded conformations, the last one is a stretched/unfolded conformation and the third one is an intermediate conformation. Other intermediate states identified by clustering are not considered in the following analysis. Table I shows a structural representation of these four conformations (only the backbone is represented for clarity), together with the corresponding 4-sign code and the potential energy. A geometric symbol is associated to each conformation and used in the tables and Ramachandran maps to identify these conformations.

C. Transition Paths of Met-Enkephalin

We have applied the Multi-T-RRT algorithm to quickly discover many transition paths between the aforementioned meta-stable states of met-enkephalin, presented in Table I. We have used the following parameter settings: The extension step-size δ is set to 2.0, which means that, in the worst case, the maximum displacement of an atom between two conformations connected by an edge is of 2 Å. Note however that this distance is usually significantly smaller. At the beginning of the exploration, we impose the probability of accepting an energy increment of 0.1 kcal/mol to be approximately 50% by using the Boltzmann constant (1.987 • 10 -3 kcal/mol/K) together with an initial temperature to 70 K. The temperature increase rate T rate is set to 0.1.

Starting from four roots at the given states, Multi-T-RRT returns a single tree in approximately 2 minutes. Paths connecting the minima are extracted for analysis. To study the diversity of the transition paths of met-enkephalin, we run Multi-T-RRT 100 times. As an illustrative example, paths between the folded (+ --+) and unfolded ( + + ) states are visualized on the same Ramachandran maps in Figure 2. The average cost for the transition from (+--+) to ( ++ ) is 49.8 (MW) and in the reverse direction is 44.6 (MW), with a standard deviation across all the runs of 14.5. We observe that all of these paths avoid the high-energy regions in all projections. The paths are extremely diverse, although the standard deviation of their cost is not very high. This indicates that the energy landscape between these minima is relatively flat. One can see in the figure that a few paths go across saddle regions corresponding to values of φ 2,3,4 close to zero. This shows that Multi-T-RRT is able to effectively explore vast portions of the conformational space.

D. Capturing Distinct Transitions of Met-Enkephalin

We have employed Multi-T-RRT with Cycles to compute transition probabilities between all pairs of energy minima for met-enkephalin. We have executed the method 100 times with a maximal running time of 10 minutes as stopping condition. Figure 3 shows the projection of one of the resulting graphs, which covers all the low-energy regions on the Ramachandran maps and constructs connections through transition regions. To estimate transition probabilities amongst the 100 executions, we count how many runs yield a graph from which a direct transition path can be extracted between a given pair of minima. More precisely, we consider that a run produces a direct transition path between two minima if the best path (with respect to the cost in terms of mechanical work) in the graph between them does not go through another minimum. Table I shows the probabilities of direct transitions between minima and the costs (average and standard deviation) associated to them. We can observe that direct transitions between all pairs of states are highly probable in most cases. Since the mechanical work is an additive function, we can also compute the cost of indirect paths going through a sequence of minima from the values in Table I. Table II presents the costs of different pathways from one of the two folded states (+--+) and (----) to the unfolded state ( ++ ). In the aforementioned related work on met-enkephalin [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF], different costs are also associated to alternative transition pathways from folded to unfolded states based on the Markov state model generated form MD. Although our cost rankings do not match perfectly to those in [START_REF] Banerjee | Transition paths of met-enkephalin from markov state modeling of a molecular dynamics trajectory[END_REF], most likely because of differences in the landscapes inferred by the different force-fields, the overall conclusion is the same: direct transitions from folded states to unfolded states are more probable than transitions going through intermediate states. IV. CONCLUSION

In this paper, we have presented a methodology to explore and characterize the energy landscape of flexible peptides. This methodology combines variants of two stochastic, samplingbased algorithms: Basin Hopping (BH) and Transition-based Rapidly-exploring Random Tree (T-RRT). A simplified version of the BH algorithm, where local, gradient-based energy minimization steps are replaced by simple Monte-Carlo-based minimization steps, achieves a relevant exploration of the energy landscape yielding numerous samples around energy minima. This leads to a quick determination of meta-stable structural states, which can be used as a starting point for the analysis of conformational transitions. The multiple-tree version of T-RRT is very fast at generating transition paths between a set of states. Running this algorithm several times produces a good description of the transition path ensembles. Finally, Multi-T-RRT with Cycles yields diverse transition paths in a single run of the algorithm.

Results on met-enkephalin presented in this paper, and results on the terminally-blocked alanine described in a preliminary version [START_REF] Devaurs | Sampling-based methods for a full characterization of energy landscapes of small peptides[END_REF], show that the combination of BH and T-RRT quickly produces a meaningful representation of the energy landscape of small yet highly-flexible peptides. The identified meta-stable states and the transition pathways between them are comparable to those obtained with other, more expensive computational methods. Our results also illustrate the fact that stochastic algorithms can compete with MD-based approaches in providing accurate and insightful findings about flexible biomolecules. Nevertheless, this is an early work, and many aspects still have to be improved and further investigated in terms of theory and implementation. Directions of future work include exploiting the graph produced by a single run of the Multi-T-RRT with Cycles to describe transition path and transition state ensembles. This will allow us to make better use of computational resources, as opposed to aggregating paths extracted from several runs of the Multi-T-RRT. In addition, Markov-based transition-step analysis can be conducted on the graph produced by one or more runs of T-RRT. This analysis allows one to estimate the stability of each computed state, and provides a rigorous basis for the designation of a state as stable or semi-stable.

We also aim to improve the implementation in order to efficiently deal with larger peptides and proteins. We have initiated some experiments with larger systems to identify the efficiency of our algorithms. One of our current test systems is chignolin, an artificial "mini-protein" composed of 10 residues. Chignolin presents an interesting energy landscape that has been investigated with other methods [START_REF] Satoh | Folding free-energy landscape of a 10-residue mini-protein, chignolin[END_REF]. Our first tests with chignolin show that our methods are still applicable in practice to larger systems, although computing time increases significantly. When running the Multi-T-RRT using four conformations as input (one folded, one unfolded and two intermediate states identified by BH), computing a graph connecting them takes about 100 minutes on average. To reduce the computation time, it will be necessary to carefully implement the underlying methods in the algorithms, in particular the nearest neighbor search and energy computation. We are also working on the parallelization of Multi-T-RRT, building on our previous experience with the basic RRT algorithm [START_REF] Devaurs | Parallelizing RRT on largescale distributed-memory architectures[END_REF].

Algorithm 1 :

 1 Basin Hopping input : the conformational space C the number of rounds nbRounds the number of Monte Carlo minimizations nbM C output: the list of trajectories of minima L 1 L ← φ 2 for r = 1..nbRounds do 3

8

 8

Algorithm 3 :

 3 Multi-T-RRTinput : the conformational space C; the extension step-size δ;the energy function E

8 if

 8 qnew = null and 9 transitionTest(T , E(q near ), E(qnew)) then 10 addNewNode(T , qnew) 11 addNewEdge(T , q near , qnew) 12 (T , q near ) ← findNearestTree(qnew) 13 if distance(qnew, q near ) ≤ δ then 14 T ← merge(T , qnew, T , q near ) ; n ← n -1 15 return T Algorithm 4: T-RRT with Cycles input : the conformational space C; the extension step-size δ; the energy function E : C → R; the tree built by the Multi-T-RRT T output: the graph G 1 G ← initGraph(T ) 2 while not stoppingCriteria(G) do 3 q rand ← sampleRandomConformation(C) 4 qnear ← findNearestNeighbor(G, q rand ) 5 qnew ← extend(qnear, q rand , δ) 6 if qnew = null and 7 transitionTest(G, E(qnear), E(qnew)) then 8 addNewNode(G, qnew) 9 addNewEdge(G, qnear, qnew) 10 for qcan ∈ G \ {qnew} do 11 if distance(qnew, qcan) ≤ δ and 12 noEdgeBetween(qnew, qcan) then 13 addNewEdge(G, qnew, qcan) 14 return G path connecting each pair of initial conformations, possibly not being the most likely transition path. To address this issue, we propose a new extension to T-RRT, based on a cycle-addition procedure.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Sampling the energy landscape of met-enkephalin using the Basin Hopping algorithm. The black markers represent the sampled minima and the white markers represent the milestones. The four large violet symbols indicate representative states identified by clustering (see TableI).

Fig. 3 .

 3 Fig. 3. Projection of a graph obtained by a single run of Multi-T-RRT with Cycles starting from four meta-stable states of met-enkephalin.

TABLE II COSTS

 II OF TRANSITION PATHWAYS FROM FOLDED TO UNFOLDED STATES

	Pathway	Cost
	→	48.2
	→ →	178.1
	→ →	219.2
	→ → →	253.4
	→	93.7
	→ →	127.9
	→ →	172.0
	→ → →	301.9

Color figures are available in the online version of this manuscript.

ACKNOWLEDGMENT

This work has been partially supported by the French National Research Agency (ANR) under project ProtiCAD (project number ANR-12-MONU-0015).