Dr Catherine Tamalet
email: ctamalet@ap-hm.fr

Hervé Richet

Xavier Carcopino

Mireille Henry

Laurence Leretraite

Patrice Heid

François-Xavier Leandri

Hélène Sancho-Garnier

Lucien Piana

Testing for human papillomavirus and measurement of viral load of HPV 16 and 18 in self-collected vaginal swabs of women who do not undergo cervical cytological screening in Southern France Running title: HPV testing of self-collected samples in France

Keywords: human papillomavirus, viral load, cervical cancer, self-obtained vaginal swabs, high-risk and low-risk HPV types

Testing for human papillomavirus and measurement of viral load of HPV 16 and 18 in self-collected vaginal swabs of women who do not undergo cervical cytological screening in Southern France

cervical cancer for women who do not attend regular cytological screening. The aim 5 of this study was to determine the prevalence of high and low-risk HPV types and of 6 HPV type 16 and 18 DNA load in self-collected vaginal swabs from 35-to 69-year-old 7

Southern French women of low socioeconomic level or migrant populations who do 8 not attend regular cervical screening. A good concordance (93.1%) was found 9 between cervical brush and vaginal swabs in 29 samples. Self-collected vaginal 10 swabs were examined from 120 women. HPV infection was found in 28 women 11 (23.3%; median age 48 years), 17 (14.1%) of whom harboured high-risk HPV types. 12 HPV type 16 was the high risk type found most frequently, followed by types 53, 31, 13 18, 58, and 66. The low-risk type detected most frequently was HPV type 6, followed 14 by types 61, 70, and 81. The mean HPV 16 and 18 load was 6.3 log 10 copies/10 6 15 cells and 2.4 log 10 copies/10 6 cells, respectively. These results suggest that vaginal 16 self-swabs can be a reliable tool for cervical cancer screening in non-attending and 17 inadequately screened elderly women. Cervical cancer is the second leading cause of cancer deaths among women 4 worldwide, with an estimated incidence of 500,000 cases each year and a quarter of 5 a million deaths [START_REF] Franco | The epidemiology of cervical cancer[END_REF]. In France, there are more than 3,600 new 6 cases of cervical cancer each year, resulting in more than 1000 deaths per year. 7

Human papillomavirus (HPV) is the major cause of cervical cancer in women. 8

Cytology-based screening ("pap-smear") is the major method of screening for 9 cervical cancer. However, the sensitivity of this method is limited, and the efficacy of 10 cytology-based screening programs largely depends on the coverage of the female 11 population. Thus, approximately 60% of cervical cancers are not adequately 12 screened [START_REF] Sawaya | Cervical cancer screening: which techniques 18 should be used and why?[END_REF]. In France, cervical cancer screening programs are 13 unorganized, and approximately 40% of women do not participate in such programs. 14

As such, French women are at a major risk of being diagnosed with cervical cancer 15 [START_REF] Schaffer | Cervical cancer screening in France[END_REF]. 16

Recent studies have demonstrated that performing HPV DNA testing, in addition to 17 cytology, is useful for primary cervical cancer screening [START_REF] Mayrand | Human papillomavirus DNA versus 11 Papanicolaou screening tests for cervical cancer[END_REF]18 Naucler et al., 2007;[START_REF] Bulkmans | Human papillomavirus DNA testing for 17 the detection of cervical intraepithelial neoplasia grade 3 and cancer: 5-year follow-18 up of a randomised controlled implementation trial[END_REF]. Detection of HPV type 16 or 18 in 19 cervicovaginal samples correlates with a higher risk for dysplasia or cervical cancer, 20 even if cervical cytology is normal [START_REF] Josefsson | Viral load of human 15 papillomavirus 16 as a determinant for development of cervical carcinoma in situ: A 16 nested case-control study[END_REF]Wright et al., 2000;Khan 21 et al., 2005;[START_REF] Brinck | High concordance of results 10 of testing for human papillomavirus in cervicovaginal samples collected by two 11 methods with comparison of novel self-sampling device to a conventional 12 endocervical brush[END_REF]. Moreover, the incidence of severe dysplasia and 22 cervical cancer within 10 years is elevated by HPV type 16/18 [START_REF] Khan | The elevated 10-year risk of cervical precancer and 24 cancer in women with human papillomavirus (HPV) type 16 or 18 and the possible 25 utility of type-specific HPV testing in clinical practice[END_REF], 23 and a relationship between HPV 16 viral load and the severity of cervical lesions has 24 been previously demonstrated [START_REF] Carcopino | Determination of HPV type 16 and 18 viral load in cervical smears of 22 women referred to colposcopy[END_REF][START_REF] Gravitt | High load for 17 most high risk human papillomavirus genotypes is associated with prevalent cervical 18 cancer precursors but only HPV16 load predicts the development of incident disease[END_REF]Saunier et 25 al., 2008]. 26

Cultural barriers, reluctance towards vaginal speculum examination, and refusal to 27 undergo routine pelvic examinations in the absence of symptoms are the most 28 common reasons for which women fail to undergo regular cervical screenings [Piana 29 et al., 2007]. Several studies have shown that detection of HPV by vaginal self-30 sampling can be a valuable alternative for women refusing cytological screening and 31 can also help to improve coverage [START_REF] Cuzick | Human Papillomavirus testing in primary cervical 26 screening[END_REF][START_REF] Holanda | Primary 9 screening for cervical cancer through self-sampling[END_REF]32 Karwalajtys et al., 2006;[START_REF] Brinck | High concordance of results 10 of testing for human papillomavirus in cervicovaginal samples collected by two 11 methods with comparison of novel self-sampling device to a conventional 12 endocervical brush[END_REF]Stenvall et al., 2007;[START_REF] Bais | Human 29 papillomavirus testing on self sampled cervicovaginal brushes: An effective 30 alternative to protect nonresponders in cervical screening programs[END_REF]. 33

Vaginal self-sampling is as sensitive as physician-collected endocervical cytobrush 34 sampling for detecting high-risk-HPV (HR-HPV) DNA [START_REF] Hillemanns | Screening 2 for cervical neoplasia by self-assessment for human papillomavirus DNA[END_REF] studies have demonstrated the reliability of self-sampling devices for the evaluation 4 of oncogenic HPV viral load [START_REF] Daponte | Use of real-time PCR to detect human papillomavirus-16 viral 31 loads in vaginal and urine self-sampled specimens[END_REF]. 5

The aim of this feasibility study was to assess the prevalence of HR-and low-risk 6 (LR)-HPV infection, as well as of HPV 16 and 18 DNA load, in women aged 35 years 7 and older, from low socioeconomic backgrounds and/or migrant populations in 8

Marseille, France who do not attend regular cytological screenings for cervical cancer 9 (referred to hereafter as "non-attending"). For this purpose, self-collected vaginal 10 swabs were evaluated as a valuable tool for virological investigation. Study population: a pilot sampling campaign was organized in 2 suburbs in the 29 northern part of Marseille, where the rate of low socioeconomic level is high (37,2 to 30 45,5%). The women of low socio-economic level and/or from migrant populations 31 selected for the study were aged 35 to 69years and without a pap smear indexed in 32 the National Insurance Register in the past 2 to 3 years. By individual mailing, the 33 women were randomly either re-invited for a pap smear or invited to perform a self-34 sampling of their vaginal fluid in a medical analysis laboratory close to their home.. After thawing, 250 µl of vaginal cell suspension was used for DNA purification using 11

F

QIAamp DNA Mini Kit (QIAGEN, Courtaboeuf, France) modified as follows: samples 12 were incubated at 56°C for 2 hours in lysis solution containing proteinase K. The 13 DNA was eluted in 100 µl of elution buffer and stored at -20°C until use. 14

HPV L1 gene amplification by single or nested PCR: 15

For primary PCR amplification, 5µl of vaginal cell DNA, 1µl of 10µmolar degenerate 16 MY09:5'GCMCAGGGWCATAATAATGG3'/MY11:5'CGTCCMARRGGAWACTGATC 17 3' primers, 0.2 µl of Hotstar polymerase (Qiagen), 5X ready to use polymerase buffer, 18

Dnase and Rnase free water were added in a final volume of 50µl. The PCR was 19 performed at 95°C 15 min followed by 40 cycles (95°C 30s, 52°C 45s, 72°C 1min). A 20 second amplification was performed using the same procedure, and 1µl of the first 21 amplification was used as sample. The primary and second amplification products 22 were analysed on BET agarose gel. 23 HPV type determination by sequencing, cloning, and phylogenetic analysis: 24 450bp PCR amplicons were purified and sequenced on ABI PRISM 3110 (Applied 25 Biosystems) using Big Dye terminator V1.1 Cycle sequencing Kit (Applied 26 Biosystems). The sequence obtained was introduced in a phylogenetic tree that 27 contained sequences of HPV L1 gene available in NCBI nucleotide database 28 http://www.ncbi.nlm.nih.gov/nucleotide/. Ambiguous determination was confirmed in 29 silico by NCBI Blast analysis http://blast.ncbi.nlm.nih.gov/Blast. 30

Cloning of PCR Product: when the sequence profile revealed a mixture, the PCR 31 product was cloned using pGEM-T easy System (Promega, Madison, WI); about 20 32 clones were sequenced and HPV types were determined by phylogenetic analysis. 33

HPV types considered as high-risk or probably high-risk included HPV To quantify the HPV 16 and 18 DNA, a quantitative, duplex real-time (RT)-PCR was 7 performed as previously described [START_REF] Carcopino | Determination of HPV type 16 and 18 viral load in cervical smears of 22 women referred to colposcopy[END_REF]. The quantitation plasmid 8 used contained the three target sequences of interest: HPV 16 (on E6 gene), HPV 18 9 (on E7 gene), and human albumin gene (on exon12). The plasmidic solution made it 10 possible to obtain a quantification scale from 10 7 to 1 copy for 5 µl of solution. 11

Positive, negative, and no template controls were introduced in each reaction plate. 12 In the experimental conditions used, the cycle threshold (CT) values for the standard 13 curve of the RT PCR varied from 17 CT (10 7 copies) to 39 CT (1 copy) and the slope 14 varied from -3.0 to -3.2. This allowed a lower detection limit of HPV16 or HPV 18 at 5 15 copies per 5 µl sample. It was established that the samples with a human albumin CT 16 value higher than or equal to 31 (10 2 copies of albumin gene, or 50 human nuclear 17 cells) were excluded from the analysis in order to avoid false negative results. 18

This method allowed HPV 16 and 18 and albumin gene copy number to be quantified 19 in the same assay. So, HPV viral load could be expressed as HPV copies per cell or 20 I. 11

Of the 29 participants tested, 12 (41.3%) had CIN1 or CIN2/3 lesions whereas HPV 12 infection was detected in 16 (55%) swab and 17 (58.6%) endocervical brush 13 samples, respectively, by either genotyping or RT-PCR. HPV 16 and 18 DNA loads 14 were comparable in both vaginal swabs and endocervical brush samples (mean HPV 15 16 viral load: 6.5 vs. 6.2 log, p = 0.17; Table I). For 27 women, HPV types were 16 concordant (12 were concordant positive and 15 negative) in both vaginal swabs and 17 endocervical brush samples (Table II). The overall concordance level between 18 vaginal swabs and endocervical brush samples was 93.1% (k= 0.86). There were 2 19 cases of discordance between vaginal swabs and endocervical brush samples: one 20 case of cervical brush sample harbouring multiple HPV types (6, 53, and 58) while 21 vaginal swabs harboured HPV type 6, and one case of vaginal swabs harbouring 22 HPV type 61 while the cervical brush sample was negative (Table I; Table III). 23

The frequencies of HR-and LR-HPV types are presented in Table III were ≥60-years-old. Of the 120 women sampled, 28 (23.3%) were infected with HPV, 3 and 17 (14.1%) of them harboured HR-HPV types. HR-HPV types most frequently 4 found were HPV-16 (7), 53 (5), 31 (4), 18 (2), 58 (1), and 66 (1) (Table IV). 5 LR-HPV types most frequently found were HPV type 6 (6), 61 (5), 70 (2), and 81 (2). 6 Six (21.4%) women were infected with multiple HPV types (≥2) and two of them were 7 infected with HR-HPV types (≥1). HPV types 83 and 84 of undetermined risk were 8

found in 3 women. The median age of HR-and LR-HPV-infected women was 48-9 years-old (range: 37-61; IQR: 39-54 years) and 46-years-old (range: 37-59, IQR: 42-10 54 years), respectively. No differences related to age were found between HR-and 11 LR-HPV-infected women (p=0.6). Among the 17 HR-HPV-infected women, 7 (41.1%) 12 were ≥50-years-old, while 4 (36.3%) of the 11 LR-HPV-infected women were ≥50-13 years-old (p=1.0). As shown in Table V, no age-related differences were found 14 between groups of HPV-uninfected, HR-HPV infected, LR-HPV-infected, and multiple 15 HPV-infected women (p=0.6). The mean HPV 16 load, quantified from 5 women, was 16 6.3 log 10 copies/10 6 cells; the mean HPV 18 load, quantified from 2 women, was 2.4 17 log 10 copies/10 6 cells (Table IV). HPV 16 DNA loads did not differ significantly with 18 age (p=0.78). No correlation was found between the women's age and their 19 oncogenic viral load by linear regression (r 2 =0, p=0.70). 20

After discovery of the 28 positive DNA tests, 15 women among those harbouring HR-21 HPV types were referred to their physician. Eight women were referred for cytology 22 (4 HPV 16, 1 HPV 18, 3 other HPV types): 1 was abnormal, 5 normal, 2 without 23 information. Among the 17 women harbouring HR-HPV types, six were referred to 24 colposcopy (1 HPV type 18 and 5 other HR-HPV types): two women had high-grade 25 lesions and one had surgery. 26 women whose median age was 48.2 years. Moreover, 14.1% of the women were 3 infected with HR-HPV types and of them, 21.4% were infected with multiple HPV 4 types. These results contrast with data from previous studies conducted in Canada 5 and in the Netherlands, showing that 6% of women aged 30 to 69 years [Mayrand et 6 al., 2007] women will clear the infection within 7 to 10 months [START_REF] Ho | Natural history of 6 cervicovaginal papillomavirus infection in young women[END_REF]] and will not 12 develop lesions. In one recent Italian study, the prevalence of HR-HPV genotypes 13 was 13.1% in patients aged 25 to 34 years and 5.8% for women aged 35 to 60 years 14 [START_REF] Ronco | For the new technologies for cervical cancer working 8 group. Results as recruitment from a randomized controlled trial comparing human 9 papillomavirus testing alone with conventional cytology as the primary cervical 10 screening test[END_REF]. The present study shows a high prevalence rate of HPV 15 infection in women aged 35 to 69 years. These results agree with several studies that 16 have reported a second peak of HPV prevalence in women 50 years and older 17 [START_REF] Herrero | Design 29 and methods of a population-based natural history study of cervical neoplasia in a 30 rural province of Costa Rica: The Guanacaste project[END_REF][START_REF] Sellors | Prevalence of infection with carcinogenic human papillomavirus among older 33 women[END_REF][START_REF] Baay | Can cervical cancer screening be stopped at 50? The 3 prevalence of HPV in elderly women[END_REF]] and a particularly high 18 prevalence of HPV infection (15.5%) in women 60 years and older [Levert et al., 19 2000]. In addition, an Italian study has also reported an increased prevalence of HPV 20 in women aged 64 years and older (12.2%) [START_REF] Agarossi | Prevalence and type 19 distribution of high-risk human papillomavirus infection in women undergoing 20 voluntary cervical cancer screening in Italy[END_REF]. In the present 21 study, the reasons for the high prevalence of HPV infection in older women are 22 probably multifactorial and include the low socioeconomic level of women who are 23 reluctant to undergo gynecological examination, reactivation of latent infection in the 24 postmenopausal period due to decreasing specific immunity, and/or acquisition of 25 new infections in sexually active older women. 26

The HR-HPV type most frequently detected in this population was HPV 16, followed 27 by HPV, 53, 31, 18, 58, and 66. The observed frequencies of these HPV types are in 28 line with a recent Italian study of 9,947 women self-referred for cervical cancer 29 screening [START_REF] Agarossi | Prevalence and type 19 distribution of high-risk human papillomavirus infection in women undergoing 20 voluntary cervical cancer screening in Italy[END_REF]. In addition, a meta-analysis of HPV positive women 30 with normal cytology reported HPV 16, 18, 31, 58, and 52 as the most common types 31 worldwide [De San Jose et al., 2007]. A more recent study [START_REF] Lindau | Prevalence of high-6 risk human papillomavirus among older women[END_REF]] 32 analysing self-collected vaginal samples from 1,550 women in Chicago showed a 33 high prevalence of HPV types 61, 31, 52, 58, and 66 in women aged 57 to 85. One 34 could expect a potential protective effect of the vaccines Gardasil and Cervarix on 35 regularly survey the worldwide distribution of HPV in target populations in order to 5 adapt vaccines for protection against the prevailing HPV types. 6

The LR-type most frequently detected was HPV 6 followed by HPV 61, 70, and 81, 7 which is in line with a recent French epidemiological study [START_REF] Aubin | 24 Human papillomavirus genotype distribution in external acuminata condylomata: a 25 Large French National Study (EDiTH IV)[END_REF]. 8

In the present study, infection with multiple HPV types was found in 21.4% of HPV-9 infected women, a relatively low rate given that direct sequence analysis detects 10 fewer multiple HPV types than methods such as reverse hybridization methods, 11 Linear Array, or DNA chips. The prevalence rate of infection with multiple HPV types 12 reported in the literature ranges from 20% to 50% of infected subjects [Nielsen et al., 13 2008]. Although it is not definitively known whether co-infection with multiple HR-HPV 14 types increases a woman's risk for cervical neoplasia [START_REF] Bosch | The causal relation 6 between human papillomavirus and cervical cancer[END_REF]; Van der 15 Graaf et al., 2002], a study by Agarossi et al. [2007] showed that patients harbouring 16 multiple HR-HPV types had a 30% higher risk of presenting abnormal cytological 17

results. 18

One of the major observations of this study, with a potential impact in terms of public 19 health, was that an HPV 16 load >5.2 log/10 6 cells was found in 3 patients, which is 20 very close to the cut-off value of 5.3 log/10 6 cells predictive of the persistence of HPV 21 infection and its progression towards the appearance of precancerous lesions as 22 shown by Monnier-Benoit et al. [2006]. 23

This work provides important information on the unexpected high rate of HPV and 24 HR-HPV infection in 35 to 69-year-old migrant non-attending women of low socio-25 economic levels in France. The results suggest that this category of women is 26 probably at increasing risk for development of cervical cancer. Moreover, HPV type 27 16, which is associated with a high risk for the appearance of cervical lesions 28 [START_REF] Herrero | Design 29 and methods of a population-based natural history study of cervical neoplasia in a 30 rural province of Costa Rica: The Guanacaste project[END_REF][START_REF] Ho | Natural history of 6 cervicovaginal papillomavirus infection in young women[END_REF]Woodman et al., 2001], was detected in 2 29 women aged between 45 and 50 years and 2 women aged 50 years and older. 30

Altogether, these data have to be put back in their context; indeed, in France, 31 screening is organized in only 5 areas and stopped at the age of 65 years. Elsewhere 32 in France, screening generally decreases after menopause. Meanwhile, a tendency 33 towards increased cervical cancer incidence and mortality is observed from the age 34 of 65 (incidence of 17 cases p100.000 persons/year; rate of mortality between 5.3 One of the limitations of the present campaign was the low-response rate to self-4 sampling and follow-up cytology which was related mainly to low socio-economic 5 status and illiteracy; in the next screening campaign, it will be important to determine 6 the actual proportion of women with a persistent infection who have histological CIN-7 2-3 lesions. To this end, a heading requiring the women's telephone number and 8 physician's last name and address has been added to the record form accompanying 9 the self-sampling device. Thus, HR-HPV-infected women will be easily joined by 10 phone and strongly encouraged to follow-up cytology and colposcopy. Moreover, 11 after one year, HR-HPV-infected women will be re-invited to perform again a self-12 sampling. In case of persistent HR-HPV infection, they will receive an information 13 letter inviting them for a suitable follow-up and the non-responders will be joined by a 14 social worker. Another possible limitation of this study was the lack of individual data 15 regarding the socio-economic status of the women contacted, which makes it difficult 16 to determine if the prevalence estimates can be applied to the targeted population. 17 Overall, the results reported herein underline the importance of collecting follow-up 23 data that combine cytology/histology and HPV detection in elderly women, especially 24 since the clearance rate of HPV infection in these women is unknown. Self-sampling 25 could be used as a screening tool for elderly women who are not adequately 26 screened. Moreover, pap-smear is often uninterpretable in menopaused women. 27

Individual screening tests are performed less regularly after menopause and are 28 officially stopped after the age of 65. In this pilot feasibility study, it was demonstrated 29 that self-sampling provides only 2.4% (3 of 123) of uninterpretable samples related to 30 the paucicellularity of the samples. 31

In conclusion, this study, using self-collected vaginal samples for cervical cancer 32 screening in a target population of 35-to 69-year-old women, of low socio-economic 33 status who do not attend regular cytological screenings, demonstrates that there is a 34 high prevalence of HR-HPV infection, with an elevated HPV 16 viral load in some

20 21

 20 vaginal swabs 14Physician-collected vaginal swabs and auto-sampled cervical brushes were 15 compared for HPV diagnosis and HPV 16 and 18quantitation. A total of 29 paired 16 samples from 29 women referred to the gynecological outpatient department for 17 cytological screening or for colposcopy were obtained. The paired samples were 18 processed in the same assay. The median age of the women under study was 38 19 years (IQR: 30-48).Collection of cervical and vaginal swabs, HPV DNA quantification, and HPV 22 genotyping 23Flocked swabs (Copan Diagnostics) were used as self-sampling devices, and 24 cervical brushes were used by physicians. To compare self-collected vs. physician-25 collected samples, all vaginal samples were suspended in Universal Transport 26 Medium (UTM) tubes, sent to the Virology Laboratory of the Marseille University 27Hospital, and stored at -20°C until use. 28

8 9

 8 per million cells. All the specimens were tested by both MY09/MY11 nested PCR and 21 RT-PCR HPV16/18/human albumin. 22 23 Statistical analysis 24 Data were entered into an EXCEL spread sheet and analysed using EpiInfo software 25 version 3.4.1 (Centers for Disease Control and Prevention, Atlanta, GA). 26The Yates-corrected chi-square test or the Fisher exact test were used to compare 27 proportions. Continuous variables were compared by using either the ANOVA test or 28 the Mann-Whitney/Wilcoxon test according to the results of the Bartlett test for 29 inequality of population variances. For all analyses, a P-value of <0.05 was significant. For type-specific HPV prevalence, all genotypes 2 from single and multiple infections were computed individually. Agreement between 3 tests was measured by Cohen's kappa statistics.Preliminary assessment of vaginal swabs 10Results from vaginal swab versus endocervical brush samples are shown in Table

27 28 8 (

 278 . Infection with 24 multiple HPV types was detected in 3 of 16 HPV DNA positive vaginal swabs (HPV 25 6+16, HPV 16+31, HPV 16+58) and in 4 of 17 HPV DNA positive endocervical 26 samples (HPV 6+16,HPV 16+31, HPV 16+58, HPV 6+53+58).Assessment of the prevalence of HR-and LR-HPV infection and of HPV 16 and 2918 DNA load in self-collected vaginal swabs 30Data from 123 recruited women were recorded. To avoid false negative results, the 31 samples of 3 women (40-, 49-, and 50-years-old) were excluded from the study 32 because high CT values, that is, ≥31 (10 2 copies of the albumin gene in 50 human 33 nuclear cells), revealed a low cellular content of the sample. Samples from 120 34 (97.6%) women were further analysed (median age: 48.2±9 years; interquartile range 35 IQR): 42-54; range: 35-69). Forty-one (34.2%) women were ≥50-years-old and 18 2

  obtained from the comparison between vaginal swabs and 31 endocervical brush samples were highly concordant with respect to HPV type 32 diagnosis and HPV 16 and 18 load determination. These results validated the use of 33 vaginal swabs for virological investigation. Therefore, in the second part of the study 34 the prevalence of HPV infection was relatively elevated (23.3%) in 2

  HR-strains circulating in France since both vaccines confer a certain 2 degree of cross-protection against HPV 31, 33, 45, 52, and 58[START_REF] Harper | Sustained efficacy up 23 to 4.5 years of a bivalent L1 virus-like particle vaccine against human papillomavirus 24 types 16 and 18: follow-up from a randomised control trial[END_REF] 3 Paavonen et al., 2008]. Nevertheless, the present study underscores the need to 4

  persons/year in women aged 65 to 80 years [Remontet L et al., 2 2003]. 3

  Since collecting individual data is not allowed in France by the National Commission 18 for Information Technology and Civil Liberties, the targeted population was selected 19 in 2 districts of the city with a high deprivation index calculated from census data 20 recorded by the National Institute for Statistics and Economic Studies and from the 21 National Health Insurance. 22

  Gravitt et al., 2001; Nobbenhuis MA et al., 2002; Petignat et al., 2005; 2 Brinck et al., 2006; Karwalajtys et al., 2006; Petignat et al., 2007). To date, few 3

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  16,18, 26, 31, 34 33, 35, 39, 45, 51, 52, 53, 56, 58, 59, 66, 68, 73 and 82; while HPV types with low-35 risk or unknown oncogenic risk included HPV 6, 11, 34, 40, 42, 44, 54, 61, 62, 70, 2 71, 72, 81, 83, 84, and 89, based on the classification by Munoz et al [2006].

		6
	3
	4
	5	HPV 16 and 18 screening and viral load determination:
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  and 4.5% of women aged 29 to 56 (median age: 41.0 years) [Bulkmans et 7 al., 2007],respectively, exhibited HPV DNA positivity. Usually, the prevalence of HPV 8 infection decreases with age [Melkert et al., 1993; Munoz et al., 1996; Kitchener et 9 al., 2006] with the highest prevalence rate observed before the age of 30. Before the 10 age of 30, the HPV test has a poor positive predictive value since most HPV-infected 11

Table I . HPV test results for 29 paired vaginal samples and cervical brush samples

 I a broad diversity of HPV genotypes. A second broader screening study is 2 currently underway in the Marseille area. In addition, this work is relevant in view of 3 developing a safe and effective vaccine against the most frequent HR-and LR-HPV 4

				12 19
	2 3 4 5 5	Stenvall H, Wikstrom I, Backlund I, Wilander E. 2007. Accuracy of HPV testing of vaginal smear obtained with a novel self-sampling device. Acta Obstet Gynecol Scand 86:16-21. cases, and types.
	6 7 6 7	Vaginal sample results Van der Graaf Y, Molijn A, Doornewaard H, Quint W, Van Doorn LJ, Vanden Tweel J. Endocervical brush 2002. Human papillomavirus and the long-term risk of cervical neoplasia. Am J sampling method results
	8 8	Epidemiol 156: 158-164. HPV infection, n (%)	16 (55)	17 (58.6)
	9 9	Positive genotyping results*, n (%)	13** (81.3)	13*** (76.5)
	10 10	ACKNOWLEDGEMENTS Woodman CB, Collins S, Winter H, Bailey A, Ellis J, Prior P, Yates M, Rollason TP,
	11 12 13 14 11 12 13 14	F o r The authors thank Ms. Solange Riban for helping collect data and for her involvement in the study. F o r F o r F o r F o r F o r F o r F o r Positive Real-time PCR 6 6 Young LS. 2001. Natural history of cervical human papillomavirus infection in young women: A longitudinal cohort study. Lancet 357:1831-1836. Wright TC, Denny L, Kuhn L, Pollack A, Lorincz A. 2000. HPV DNA testing of self-F o r HPV 16 or 18 Mean HPV 16 load log 10 6.5 6.2 copies/10 6 cells (n =4) Mean HPV 18 load log 10 2.7 3.9 F o r
	15 16 15 16 17 18 19	P e e r P e e r P e e r P e e r P e e r P e e r P e e r P e e r collected vaginal samples compared with cytologic screening to detect cervical P copies/10 6 cells (n=2) P cancer. JAMA 283: 81-86. e e r e • *Including ≥1 HPV type • ** One vaginal sample harboured HPV type 6 only while endocervical sampling harboured HPV types 6+53+58 • *** One sample was PCR negative by endocervical brush and positive by vaginal e r
	20 21	sampling (HPV type 61)	R R R R R R R R R R
	22 23 24 25			e v i e e v i e e v i e e v i e e v i e e v i e e v i e e v i e e e v i e v i e
				w w w w w w w w w w

Table II . Concordance of genotyping results between vaginal swabs and endocervical brush samples Vaginal swabs Endocervical brush samples

 II

	Page 21 of 24	Journal of Medical Virology
			Positive Negative Total
		Positive Negative F o r	12 1	1 15	13 16
		Total Concordance rate: 93.10% (k = 0.86) (p<0.05) 13 16 P e	29
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Table III . Distribution of high-risk and low-risk HPV types from 29 paired vaginal swabs and endocervical brush samples by RT PCR and/or genotyping

 III • *Positive by Real-Time PCR and/or genotyping and including those detected in multiple HPV infection • ** Positive by Real-Time PCR only • *** Included in multiple HPV infection

				Vaginal	Endocervical
				Swabs	brush samples
		HPV type	N (%)	N (%)
	High-Risk F o 16* 18** 31 33 r		4 (25) 2 (12.5) 3 (18.7) 2 (12.5)	4 (23) 2 (11.8) 3 (17.6) 2 (11.8)
		52 53*** 58 P e	1 (6.2) 0 3 (18.7)	1 (5.8) 1 (5.8) 4 (23.5)
	Low-Risk	6 61	2 (12.5) 2 (12.2) e r	2 (11.8) 1 (5.8)
	Multiple HPV infection	81 6+16 16+31 16+58 6+53+58	1 (6.2) R 1 1 e 1 0 v i 1 (5.8) 1 1 1 1 e
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Table IV . Main virological characteristics of 28 HPV-infected females

 IV

	HPV infection, n (%)		28 (23.3%)
	Number of samples with high-risk HPV types	17(14.1%)
	Number of samples with ≥2 HPV types	6 (21.4%)
	Number of samples with ≥1 high-risk HPV type	2 (7.1%)
	High-risk HPV types	16	7 (25%)
		18	2 (7.1%)
		31	4 (14.3%)
		53	5 (17.8%)
	Low-risk HPV types F o r	58 66 6	1 (3.5%) 1 (3.5%) 6 (21.4%)
	61 70 81 Undetermined risk HPV types 83 P 84 e Mean HPV 16 load (n=5) HPV 18 load (n=2) e r	5 (17.8%) 2 (7.1%) 2 (7.1%) 2 (7.1%) 1 (3.5%) 6.3 2.4
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Table V . Age of the different groups of women according to the HPV status

 V

		Mean Age		Median Age
		±SD	Range	(IQR)
	HPV
	uninfected women	48.5 ± 9.1	35-69	46 (42-54)
	HR-HPV	46 ± 8.5	37-59	42 (39-59)
	infected women
	LR-HPV	48 ± 8.6	35-63	48 (39-63)
	infected women
	Multiple HPV	55 ± 8.4	49-61	55 (49-61)
	infected women
	No significant difference according to age between the different groups of
	women, p=0.6 (ANOVA test)

women were enrolled who performed vaginal self-sampling for HPV analysis. In


Andreas Johannes Schmidt

Jürgen-Christian Krieg

Ulrich Michael Hemmeter

Tilo Kircher

Eberhard Schulz

Hans-Willi Clement

Philip Heiser

Prof. Dr Med Philip Heiser

Impact of plant extracts tested in attention-deficit/hyperactivity disorder treatment on cell survival

Keywords: Pycnogenol, Enzogenol, Hypericum, cell survival, energy metabolism, neuroblastoma cells Pycnogenol ®, Enzogenol ®, Hypericum, cell survival, energy metabolism, neuroblastoma cells

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Over decades, the standard pharmacotherapy of attention-deficit/hyperactivity disorder (ADHD) had comprised psychostimulants like methylphenidate and amphetamine as well as the selective norepinephrine reuptake inhibitor atomoxetine later on. Since some patients do not respond to the classical ADHD drugs or show side effects, the use of herbal extracts like Hypericum perforatum or Pycnogenol ® (Pinus pinaster) as supplementation or as monotherapy has been discussed in the last few years. Concerning combinations of extracts, the results of a study by [START_REF] Lyon | Effect of the herbal extract combination Panax quinquefolium and Ginkgo biloba on attention-deficit hyperactivity disorder: a pilot study[END_REF] suggest a possible improvement of ADHD symptoms after a supplementation with an extract combination of Panax quinquefolium and Ginkgo biloba.

The extract of Hypericum perforatum is known to exert both antioxidative properties and protective effects (e.g. [START_REF] Benedi | Antioxidant properties and protective effects of a standardized extract of Hypericum perforatum on hydrogen peroxide-induced oxidative damage in PC112 cells[END_REF][START_REF] Breyer | Glutamate-induced cell death in neuronal HT22 cells is attenuated by extracts from St. John's wort (Hypericum perforatum L.)[END_REF][START_REF] El-Sherbiny | Hypericum perforatum extract demonstrates antioxidant properties against elevated rat brain oxidative status induced by amnestic dose of scopolamine[END_REF][START_REF] Sanchez-Reus | Standardized Hypericum perforatum reduces oxidative stress and increase gene expression of antioxidant enzymes on rotenone-exposed rats[END_REF]. However, no improvement of ADHD symptoms after a treatment of eight weeks has been found in a recently published randomised, double-blind, placebocontrolled study [START_REF] Weber | Hypericum perforatum (St John's wort) for attention-deficit/hyperactivity .disorder in children and adolescents[END_REF]. The patients had not received any other drugs during this study.

A plant extract which has been discussed extensively in terms of ADHD treatment over the last few years is Pycnogenol ® . Pycnogenol ® stands for a bark extract of the French maritime pine (Pinus pinaster) and mainly consists of procyanidines as well as catechins and phenolic acids [START_REF] Packer | Antioxidant activity and biologic properties of a procyanidin-rich extract from pine (Pinus maritima) bark, Pycnogenol ® . Free Rad[END_REF]. The antioxidant activities of this extract have been described. It could be been shown in vitro that Pycnogenol® is a free radical scavenger [START_REF] Packer | Antioxidant activity and biologic properties of a procyanidin-rich extract from pine (Pinus maritima) bark, Pycnogenol ® . Free Rad[END_REF], that it stimulates activities of antioxidant enzymes like Cu, Zn superoxide dismutase [START_REF] Fitzpatrick | Endothelium-dependent vascular effects of Pycnogenol ®[END_REF] and that it influences the glutathione metabolism [START_REF] Berryman | Influence of treatment of diabetic rats with combinations Pycnogenol, beta-carotene and alpha-lipoic acid on parameters of oxidative stress[END_REF]. Furthermore, protective effects of Pycnogenol ® on neuronal cells in context with toxic insults like acrolein [START_REF] Ansari | Protective effect of Pycnogenol in human neuroblastoma SH-SY5Y cells following acrolein-induced cytotoxicity[END_REF] et al., 2002), ethanol (Siler-Marisiglio et al., 2004) or glutamate [START_REF] Kobayashi | Antioxidants and herbal extracts protects HT-4 neuronal cells against glutamate-induced cytotoxicity[END_REF] have been shown. These characteristics of Pycnogenol ® may be important factors for the treatment of ADHD, because indices for reactive oxygen species induced oxidative stress have been discussed in children and young adults, in part controversially [START_REF] Antalis | Omega-3 fatty acid status in attention-deficit/hyperactivity disorder[END_REF][START_REF] Chovanova | Effect of polyphenolic extract, Pycnogenol ® , on the level 8-oxoguanine in children suffering from attention deficit/hyperactivity disorder[END_REF][START_REF] Joshi | Supplementation with flax oil and vitamin C improves the outcome of Attention Deficit Hyperactivity Disorder (ADHD)[END_REF][START_REF] Ross | Increased levels of ethane, a noninvasive marker of n-3 fatty acid oxidation, in breath of children with attention deficit hyperactivity disorder[END_REF][START_REF] Spahis | Lipid profile, fatty acid composition and pro-and anti-oxidant status in pediatric patients with attention-deficit/hyperactivity disorder[END_REF] as well as in adults suffering from ADHD [START_REF] Bulut | Malondialdhyde levels in adult attention-deficit hyperactivity[END_REF][START_REF] Selek | Oxidative imbalance in adult attention deficit/hyperactivity disorder[END_REF]. [START_REF] Chovanova | Effect of polyphenolic extract, Pycnogenol ® , on the level 8-oxoguanine in children suffering from attention deficit/hyperactivity disorder[END_REF], measuring with comet essay, have found a significantly increased level of oxidative DNA damage in children with ADHD in comparison to healthy controls. [START_REF] Spahis | Lipid profile, fatty acid composition and pro-and anti-oxidant status in pediatric patients with attention-deficit/hyperactivity disorder[END_REF] have described significantly reduced plasma malone dialdehyde levels in ADHD children, whereas [START_REF] Ross | Increased levels of ethane, a noninvasive marker of n-3 fatty acid oxidation, in breath of children with attention deficit hyperactivity disorder[END_REF] have found significantly increased ethane levels in the alveolar breath of children with ADHD. Ethane is a non-invasive marker of oxidative damage to n-3 fatty acids. On the other hand, [START_REF] Joshi | Supplementation with flax oil and vitamin C improves the outcome of Attention Deficit Hyperactivity Disorder (ADHD)[END_REF] have found no significant alterations of lipid peroxidation products in the plasma of children with ADHD compared to controls, while [START_REF] Antalis | Omega-3 fatty acid status in attention-deficit/hyperactivity disorder[END_REF] have detected no significant differences of urinary isoprostanes comparing a young adult ADHD population with controls.

In order to investigate alterations of the antioxidant vitamin status in ADHD, [START_REF] Spahis | Lipid profile, fatty acid composition and pro-and anti-oxidant status in pediatric patients with attention-deficit/hyperactivity disorder[END_REF] have measured the plasma levels of retinal, β-carotene and vitamin E in children with ADHD. The two vitamin E forms, αand γ-tocopherol, have been found to be significantly higher in ADHD children compared with control subjects, whereas retionol and β-carotene contents showed no modifications.

Regarding adult patients, [START_REF] Bulut | Malondialdhyde levels in adult attention-deficit hyperactivity[END_REF] have described significantly elevated malondialdehyde plasma levels, as a product of lipidperoxidation, which is induced by reactive oxygen species. In a recently published study, [START_REF] Selek | Oxidative imbalance in adult attention deficit/hyperactivity disorder[END_REF] could show a significantly reduced activity of total Cu, Zn superoxide dismutase as well as significantly enhanced levels of oxidant nitric oxide in the serum of adult patients with ADHD. Aiming at evaluating the effects of Pycnogenol ® on ADHD symptoms, Trebaticka et al. (2006) could demonstrate in a randomised, placebo-controlled, double blind study, that a supplementation with Pycnogenol ® for one month had caused a significant reduction of hyperactivity in children with ADHD, had improved attention and visual-motoric coordination and their ability to concentrate. One month after the treatment had finished, a relapse of symptoms had been observed. On the other hand, a study with adult patients had shown no reduction of ADHD symptoms after treatment with Pycnogenol ® [START_REF] Tenenbaum | An experimental comparison of Pycnogenol ® and methylphenidate in adults with attention-deficit/hyperactivity disorder (ADHD)[END_REF].

An extract similar to Pycnogenol ® is Enzogenol ® , which is a bark extract of the New Zealand pine Pinus radiata containing flavonoids. In combination with vitamin C, Enzogenol ® has improved the cognitive performance in older individuals [START_REF] Pipingas | Improved cognitive performance after dietary supplementation with a Pinus radiata bark extract formulation[END_REF]. Vitamin C alone has failed to reach this effect. Previous studies (e. g. [START_REF] Young | Comparative effects of enzogenol and vitamin C supplementation versus vitamin C alone or endothelial function and biochemical markers of oxidative stress and inflammation in chronic smokers[END_REF] which have been using this combination have indicated improvements of oxidative stress parameters. Also Ginko biloba has been shown to be effective for treating ADHD however being less effective than methylphenidate [START_REF] Niederhofer | Ginkgo biloba treating patients with attention-deficit disorder[END_REF][START_REF] Salehi | Ginkgo biloba for attention-deficit/hyperactivity disorder in children and adolescents: a double blind, randomized controlled trial[END_REF].

Summarizing the studies cited above, only little is known about the effects of plant extracts on cell metabolism. Therefore, the aim of the present study was the examination of effects of both pine bark extracts and Hypericum perforatum on cell survival of human neuronal (SH-SY5Y) and on energy metabolism.

Materials and Methods

Preparation and incubation of cells

Human SH-SY5Y neuroblastoma cells were cultured in a 5% CO 2 atmosphere in heatinactivated Roswell Park Memorial Institute medium (RPMI) (Gibco/BRL, Eggenstein, Germany), supplemented with 15% fetal calf serum (FCS) (Biochrom, Berlin, Germany), 1% penicillin-streptomycin and 1% glutamine. The Hypericum perforatum extract was a kind gift

Measurement of metabolic activity and survival

Cells were exposed to drugs in the above-mentioned concentrations for 24 h at a temperature of 37° C, using 96-well dishes with 36,000 per well. The survival of cells was determined by a biochemical assay using a modified tetrazolium method (EZ4U, Biozol, Eching, Germany). This test is based on the ability of living cells to transform colourless tetrazolium salts into deeply coloured formazans by mitochondrial dehydrogenases. Cell viability was quantified by photometric determination of formazan-like products with an ELISA-reader (Dynex, Stuttgart, Germany).

Measurement of ATP content

36,000 cells per well were plated into 96-well dishes and exposed to the tested drugs in concentrations of 500 and 5000 ng/ml for 24 h at a temperature of 37°C. The ATP content of cells was determined by using an ATP Bioluminescence Assay (Boehringer, Ingelheim, Germany).

The amount of ATP was measured by using a microplate scintillation counter "TopCount" (Perkin Elmer, Ueberlingen, Germany), which allows for quantitative measurement via luminescence which is detected by single photon counting. In order to evaluate the effects of treatment, Kruskal Wallis tests were used to determine differences among the treatment groups. In case of significance, Dunn's method was performed. The level of significance was set to P<0.05. Statistical evaluation was carried out using SigmaStat software (Jandel Scientific, Erkrath, Germany).

Results

Effects of plant extracts on survival of SH-SY5Y cells

The impact of the plant extracts Hypericum perforatum, Pycnogenol ® and Enzogenol ® on cell survival was tested in human neuroblastoma SH-SY5Y cells in concentrations ranging from 31.25 to 5000 ng/ml. The treatment of cells with Hypericum perforatum in concentrations of 5000 ng/ml (90 ± 2 %, p < 0.05) has significantly decreased the survival of cells (Fig. : 1). The treatment of cells with lower concentrations of Hypericum perforatum has exerted no significant effects (Fig. : 1). Pycnogenol ® has induced a significant increase of cell survival after its incubation in concentrations of 32.25 ng/ml (112 ± 2 %, p < 0.05), 125 ng/ml (113 ± 3 %, p < 0.05) and 250 ng/ml (113 ± 2 %, p < 0.05), while concentrations of 62.5 ng/ml, 625 ng/ml (102 ± 2 %), 1250 ng/ml (104 ± 2 %), 2500 ng/ml (101 ± 2 %) and 5000 ng/ml (96 ± 2 %) have failed to exert significant effects (Fig. : 2). Treatment of SH-SY5Y cells with Enzogenol ® has not led to significant changes in cell survival (Fig. : 3).

Effects of plant extracts on energy metabolism of SH-SY5Y cells

The impact of plant extracts on the ATP content of human neuroblastoma cells was measured by using concentrations of 500 and 5000 ng/ml. The incubation of cells with Pycnogenol ® (500 ng/ml: 98 ± 6 %, 5000 ng/ml: 90 ± 7 %) and with Enzogenol ® (500 ng/ml: 86 ± 4 %, 5000 ng/ml: 98 ± 7 %) has exerted no significant effects (Fig. : 4 and 5), while the incubation with Hypericum perforatum in a concentration of 5000 ng/ml (135 ± 9, p < 0.05) has resulted in a significant increase of ATP levels, whereas using a concentration of 500 ng/ml (106 ± 5 %) had no significant impact (Fig. : 4 and5).

Discussion

A group of substances for the treatment of ADHD which have been tested intensively over the last few years, are plant extracts with antioxidative or neuroprotective capacities like Pycnogenol ® , Hypericum perforatum or Panax quinquefolium and Ginkgo biloba. Regarding these extracts, the focus of interest has been on Pycnogenol ® in the last years. A chemically similar extract has been Enzogenol ® . The aim of the present study has laid on evaluating the effects of these plant extracts on both cell survival and energy metabolism of human neuroblastoma SH-SY5Y cells.

The neuroprotective impact of Hypericum perforatum (e.g. [START_REF] Breyer | Glutamate-induced cell death in neuronal HT22 cells is attenuated by extracts from St. John's wort (Hypericum perforatum L.)[END_REF] and

Pycnogenol ® (e. g. [START_REF] Peng | Pycnogenol ® protects neurons from amyloid β peptide-induced apoptosis[END_REF] has been described in the literature. It has to be mentioned that in the course of our study, none of the tested substances have exerted any intense cytotoxic effect. In our study, treatment with Hypericum perforatum in a concentration of 5000 ng/ml has significantly decreased survival of cells, whereas using lower concentrations of Hypericum perforatum has exerted no significant effects. The incubation with Pycnogenol ® , using concentrations of 32.25 ng/ml and 250 ng/ml has induced a significant increase of cell survival, whereas the incubation with Enzogenol ® has not led to any significant reactions at all. Both [START_REF] Benedi | Antioxidant properties and protective effects of a standardized extract of Hypericum perforatum on hydrogen peroxide-induced oxidative damage in PC112 cells[END_REF] and [START_REF] Breyer | Glutamate-induced cell death in neuronal HT22 cells is attenuated by extracts from St. John's wort (Hypericum perforatum L.)[END_REF] have not found any significant effects of Hypericum perforatum on neuronal cell survival in comparable studies, whereas it has been shown that Pycnogenol ® exerted protective effects against various neuronal cell insults. [START_REF] Ansari | Protective effect of Pycnogenol in human neuroblastoma SH-SY5Y cells following acrolein-induced cytotoxicity[END_REF] have detected protective effects of Pycnogenol ® following acrolein-induced cytotoxicity in SH-SY5Y cells. It could be shown that pre-treatment with Pycnogenol ® in concentrations of 50 and 100 µg/ml) has significantly reduced the amount of acrolein-induced reactive oxygen species, has reduced superoxide levels and reduced cell death. Furthermore, an attenuation of the decline of reduced glutathione has followed the preincubation of cells with Pycnogenol in concentrations of ( 50and 100 µg/ml), while a decrease of oxidized glutathione has followed the preincubation of cells with Pycnogenol ® in a concentration of 50 µg/ml. Pre-treatment with Pycnogenol ® in concentrations of 50 and 100 µg/ml has also reduced the products of oxidative protein and membranlipid damage induced by acrolein significantly. The exclusive use of Pycnogenol ® in concentrations of up to 200 µg/ml has had no effects on cells. Used in concentrations ranging from 20 to 100 µg/ml, neuroprotective effects of Pycnogenol ® could be observed, whereas no impacts on cell survival could be observed in this concentration range. On the other hand, our study has demonstrated that Pycnogenol ® led to a significant enhancement of cell survival at lower concentrations (31.25, 125 and 250 ng/ml).

Our investigation of the plant extracts Pycnogenol ® and Enzogenol ® has shown no significant effects on energy metabolism when used in concentrations of 500 and 5000 ng/ml. However, treatment with Hypericum perforatum extract in a concentration of 5000 ng/ml has induced a significant increase of ATP content in SH-SY5Y cells. This result has been in line with some other examinations (e. g. [START_REF] Breyer | Glutamate-induced cell death in neuronal HT22 cells is attenuated by extracts from St. John's wort (Hypericum perforatum L.)[END_REF], describing that the extract has been able to counteract the glutamate induced energy loss, suggesting that Hypericum perforatum has antioxidative and neuroprotective properties. The concentrations of the drugs which we applied here ranging from 31.25 to 5000 ng/ml were derived from clinical studies. In clinical studies the concentrations of the drugs ranged from 1mg/kg/day to 1g/kg/day.

In summary, the efficiency of plant extracts has been shown in clinical studies of patients with ADHD. Hence, plant extracts seem to be alternatives for patients who do not respond to the classical ADHD treatment with psychostimulants or atomoxetin. In order to identify the plant extracts' exact mechanism of action, further investigations on the components of oxidative stress and apototic parameters will be mandatory. There exists a theory on the mechanism of action of psychostimulants, stating that reduced dopamine contents in cells lead to decreased contents of both hydrogen peroxide and other products of oxidative stress, as a lowered number of dopamine is deaminated by monoaminooxidase.

These parameters would be of particular interest in terms of possible relations to psychostimulants.

F

  medGmbH & Co. KG (Köln, Germany). The pine bark extracts were obtained from the Department of Child and Adolescent Psychiatry at the Albert-Ludwigs-University of Freiburg. All drugs were dissolved in dimethylsulfoxide and concentrations of31.25, 62.5, 125, 250, 625, 1250, 2500 and 5000 ng/ml were applicated. A respective dissolvent was applied for controls. Each concentration was tested by a minimum of three single experiments.

  Data are expressed in a percentage of respective controls and are displayed as mean values ± standard error of the mean (S.E.M.).

  [START_REF] Peng | Pycnogenol ® protects neurons from amyloid β peptide-induced apoptosis[END_REF] have examined the neuroprotective effects of Pycnogenol ® on PC12 cells, describing the prevention of Aβ 25-35 -induced losses of cell viability after pre-treatment with Pycnogenol ® in concentrations of 20-60 µg/ml. Furthermore, they have described a significantly decreased number of apoptotic cells after pre-treatment with Pycnogenol ® in concentrations of 10-60 µg/ml Pycnogenol ® as well as a dose-dependent reduction of caspase-3 activity. The neuroprotective effects of Pycnogenol ® against the cytotoxicity of ethanol in cerebral granule cells, including the reduction of reactive oxygen species' products and the effects on antioxidative enzyme activities, has been shown bySilar-Marsiglio et al. (2004) by using Pycnogenol ® in a concentration of 50 µg/ml.

Figure1:Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure1: Effects of Hypericum perforatum extract on cell survival of SH-SY5Y cells

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http://mc.manuscriptcentral.com/ptr Phytotherapy Research

Philip Heiser received compensation for professional services from Janssen-Cilag, Shire and Novartis.

Acknowledgement

We thank Mrs. Sabine Fischer for the technical composition and realization as well as Mrs. Sibylle Tomakidi for the linguistic revision and refinement.

Conflict of Interest

Ulrich M. Hemmeter received grants from Böhringer and Lilly Schweiz.

Eberhard Schulz received grants from Janssen-Cilag, Eli Lilly, Novartis, Shire and Pfizer.


B Sicardy

Stability of the triangular Lagrange points beyond Gascheau's value

Keywords: Three-body problem, Lagrange points, Global stability, Routh's critical mass ratio, Feigenbaum cascade

We examine the stability of the triangular Lagrange points L 4 and L 5 for secondary masses larger than the Gascheau's value μ G = (1 -√ 23/27/2) = 0.0385208 . . . (also known as the Routh value) in the restricted, planar circular three-body problem. Above that limit the triangular Lagrange points are linearly unstable. Here we show that between μ G and μ ≈ 0.039, the L 4 and L 5 points are globally stable in the sense that a particle released at those points at zero velocity (in the corotating frame) remains in the vicinity of those points for an indefinite time. We also show that there exists a family of stable periodic orbits surrounding L 4 or L 5 for μ ≥ μ G . We show that μ G is actually the first value of a series μ 0 (= μ G ), μ 1 , . . . , μ i , . . . corresponding to successive period doublings of the orbits, which exhibit 1, 2, . . . , 2 i , . . . cycles around L 4 or L 5 . Those orbits follow a Feigenbaum cascade leading to disappearance into chaos at a value μ ∞ = 0.0463004 . . . which generalizes Gascheau's work.

Introduction

Euler and Lagrange were both awarded the Prix de l'Académie Royale des Sciences de Paris in 1772 for their work on the three-body problem. Euler was the discoverer of the collinear equilibrium points, now known as L 1 , L 2 and L 3 [START_REF] Euler | Considérations sur le problème des trois corps[END_REF][START_REF] Euler | Considerationes de motu corporum coelestium[END_REF][START_REF] Euler | De motu rectilineo trium corporum se mutuo attrahentium[END_REF], while Lagrange had a more general approach, revealing also the triangular (equilateral) equilibrium points L 4 and L 5 [START_REF] Lagrange | Essai sur le problème des trois corps[END_REF].

B. Sicardy (B) Observatoire de Paris and Institut Universitaire de France, LESIA -5, Place Jules Janssen, 92195 Meudon Cédex, France e-mail: bruno.sicardy@obspm.fr Gascheau1 was the first to study the stability of the L 4 and L 5 points [START_REF] Gascheau | Examen d'une classe d'équations différentielles et applications à un cas particulier du problème des trois corps[END_REF], showing that the motion of three non-zero masses m 1 , m 2 and m 3 in a rotating equilateral configuration becomes linearly unstable if

(m 1 + m 2 + m 3 ) 2 m 1 • m 2 + m 1 • m 3 + m 2 • m 3 ≤ 27.
(1)

This result was published more than thirty years earlier than [START_REF] Routh | On Laplace's three particles, with a supplement on the stability of steady motion[END_REF], see also [START_REF] Routh | Dynamics of a System of Rigid Bodies, part. II[END_REF]. Routh actually extended the result to a general attraction law ∝ 1/r κ . He showed that the triangular points are linearly unstable for all masses if κ is larger than 3, and linearly stable for all masses if κ is smaller than -1. For κ between -1 and 3, the triangular points are linearly unstable for:

(m 1 + m 2 + m 3 ) 2 m 1 • m 2 + m 1 • m 3 + m 2 • m 3 ≤ 3 1 + κ 3 -κ 2 ,
which is identical to Gascheau's expression for the gravitational case, κ = 2. Note that further studies on the stabiltiy of the equilateral configuration as a function of κ can be found in [START_REF] Santoprete | Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials[END_REF].

The value of μ G = m 2 /(m 1 + m 2 ) = (1 -√ 23/27)/2 = 0.03852 . . . at which linear unstability is reached in the restricted case (m 3 = 0, see see Eq. 4) is often referred to as the Routh value, but should actually be called Gascheau's value in view of the precedence of his result.

The linear stability of the triangular Lagrange points was subsequently studied by [START_REF] Danby | Stability of the triangular points in the elliptic restricted problem of three bodies[END_REF] and [START_REF] Bennett | Characteristic exponents of the five equilibrium solutions in the elliptical restricted problem[END_REF] in the elliptic restricted case. These authors show, among others, that the maximum possible value of μ allowing a linearly stable motion near L 4 or L 5 is μ = 0.04698 . . ., reached for an orbital eccentricity of e = 0.3143 . . . of the primary and secondary. Above μ = 0.04643 . . . the triangular points are always linearly unstable, whatever the orbital eccentricities may be.

Further studies have gone beyond the first order analysis to investigate whether all values of μ between 0 and μ G = 0.03852 . . . provide linear stability for L 4 or L 5 . It was shown in [START_REF] Deprit | Stability of the triangular Lagrangian points[END_REF] that for μ 3:1 = (15 -√ 233)/90 = 0.01352 . . . and μ 2:1 = (45 -√ 1833)/90 = 0.02429 . . ., the triangular points are linearly unstable. These values actually correspond to the 3:1 and 2:1 resonances between the two eigenfrequencies of motion near L 4 or L 5 , see the review by [START_REF] Marchal | The three-body problem[END_REF]. In the same review, it is also mentioned that μ 3:1 and μ 2:1 are actually the only values between 0 and μ G yielding linearly unstable motion around the triangular points.

Note that the stability of motions around L 4 has been extensively considered for the special case of the Trojan asteroids, for which Jupiter's mass is fixed at about 0.001 of the solar mass.

In that case, one may for instance want to estimate the stability of Trojans asteroids initially placed farther and farther away from the L 4 , see e.g. [START_REF] Sándor | The phase space structure around L4 in the restricted three-body problem[END_REF] and [START_REF] Efthymiopoulos | Formal integrals and Nekhoroshev stability in a mapping model for the Trojan asteroids[END_REF]. This problem will not be tackled here.

Rather, we study here the behavior of a massless particle near the triangular equilibrium points L 4 and L 5 for a secondary masse just above Gascheau's value in the simplest possible case, namely the restricted, circular and planar problem.

Notations are standard, 1 -μ being the mass of the more massive body (the primary), μ being the mass of the less massive body (the secondary), with μ ≤ 0.5. The case 0.5 ≤ μ ≤ 1 can be studied by a trivial exchange of the primary and secondary. The secondary moves on a circular orbit of radius r s = 1 and position vector r s relative to the primary, with mean motion n s = 1 and period T s = 2π. Finally, a test particle moves with position vector and distance r and r , respectively, relative to the primary. Here we call "corotating frame" the frame centered at the primary and rotating at the secondary mean motion n s = 1. The particle motion will be studied in this frame, so that "motionless" will mean that the particle has zero velocity in the corotating frame.

The linear stability of points L 4 and L 5 is treated in many textbooks, see e.g. [START_REF] Murray | Solar System Dynamics[END_REF]. The proper frequencies λ in the vicinity of the triangular points are solutions of:

λ 4 + λ 2 + 27 4 μ • (1 -μ) = 0. ( 2
)
For μ → 0, solutions are purely imaginary, λ 1 ≈ √ 27/4μ • j and λ 2 ≈ j, and their opposite values, with j = √ -1. The frequency λ 1 correspond to stable slow oscillations of the particle around L 4 or L 5 , along the so called "tadpole" orbits, while λ 2 correspond to the fast stable epicyclic motion with period 2π. As μ increases, |λ 1 | increases and |λ 2 | decreases, until 27μ • (1 -μ) = 1, at which point the two frequencies merge together at

|λ 1 | = |λ 2 | = 1/ √ 2. When 1 ≤ 27μ • (1 -μ), (3)
the solutions of Eq. 2 have non-zero real parts, so that the triangular points become linearly unstable. Note that Eq. 3 is identical to Eq. 1 once we take

m 3 = 0, μ = m 2 /(m 1 + m 2 ) and m 1 + m 2 = 1.
Gascheau's value is the smaller solution of 27μ • (1 -μ) = 1:

μ G = 1 - √ 23/27 2 = 0.0385208965 . . . ( 4
)
The other solution, 1 -μ G , is obtained by permutating the primary and the secondary.

Our main scope in this paper is to present an as simple as possible account of a particle's behavior near L 4 and L 5 for values of μ just above μ G . We actually want to answer the two following questions:

-Let us consider a particle initially motionless at L 4 or L 5 . What is the global stability of the particle near those points for μ ≥ μ G ? Namely, can the particle remain in a bounded region encircling L 4 or L 5 for some values of μ ≥ μ G , even if L 4 and L 5 are linearly unstable? -Are there stable periodic orbits encircling the triangular points for μ ≥ μ G ? These questions may have some pertinence when studying the stability of a spacecraft motion near one of the triangular Lagrange points of a binary system with μ ≥ μ G . It may also be relevant to systems where particles are trapped near the L 4 or L 5 points of a system where the secondary undergoes a progressive mass increase, which eventually leads to μ ≥ μ G .

To tackle those problems, we perform numerical simulations using Poincaré surfaces of section, which help clarifying the structure of the web of orbits in the vicinity of L 4 or L 5 , as μ goes beyond Gascheau's value. From the symmetry of the L 4 and L 5 points, we will only consider motions near L 4 , unless otherwise stated. All our conclusions will however be applicable to the L 5 point, even if only L 4 is quoted in the text for sake of brevity.

123

Numerical integrations

The restricted circular three-body problem has an energy-like integral of motion, the Jacobi constant:

C J = r 2 + 2 (1 -μ) r -2μ r • r s - 1 |r -r s | -v 2
where v is the particle velocity measured in a frame fixed at the primary center and corotating with the secondary. Here, we will first restrict ourselves to the case where the particle is initially motionless at L 4 (v = 0). Those orbits are thus uniquely parametrized by the Jacobi constant, C J = 3 -μ.

Since the particle planar motion has two degrees of freedom and one integral of motion, we can readily construct Poincaré surfaces of section of its motion. As we study orbits encircling the triangular Lagrange points, we will plot the two conjugate quantities r and ṙ = dr/dt everytime the particle crosses the line joining the primary and the L 4 point. Note that if = L -L s denotes the difference between the true longitudes of the particle and the secondary, then the surface of section corresponds to = π/3. A given orbit will in general intersect the surface = π/3 twice, once with ˙ ≥ 0, and once with ˙ ≤ 0. We will not restrict the plotting of (r, ṙ ) to one of those two cases, so that the surfaces of section will have a roughly symmetrical aspect (see e.g. Fig. 1), with both sides of the diagram containing the same information.

Orbits are calculated using a 4th order Runge-Kutta integrator with time step h = 0.01. Intersections with the surface of section are calculated through a classical Newton's method. Conservation of energy is ensured at typical levels of | C J /C J | ≈ 2 × 10 -7 over typical times of t ≈ 10 5 , at which stage ≈ 10 4 intersections with the surface of section are calculated. A particle resting at L 4 will have r = 1 and ṙ = 0, so that this particular solution will be represented by a fixed point at the intersection of the vertical r = 1 and horizontal ṙ = 0 lines, as shown in Figs. 1, 2 and 3.

3 Global stability of orbits emanating from L 4 or L 5

Figure 1 shows a surface of section obtained slightly above Gascheau's value, namely with μ = 0.039, with a close up view of L 4 vicinity shown in Fig. 2, left panel. The value of the Jacobi constant, C J = 3 -μ = 2.961, ensures that a particle passing at L 4 is motionless at that point, as explained before. The orbit followed by such a particle is shown in red in the surfaces of section of Figs. 1 and2. The corresponding orbit in the corotating frame is shown in Fig. 5 [orbit (a)], where it appears to densely fill a limited region around L 4 in physical space.

The surface of section for μ = 0.039 actually indicates that all the orbits surrounding the red one (including the latter) are regular. Thus, globally stable orbits exist around L 4 for μ ≥ μ G , even if L 4 is linearly unstable.

One may wonder whether this situation perdures as μ increases. For μ = 0.0394, one can see that the orbit emanating from L 4 becomes chaotic (Fig. 2, right panel) and can diffuse in phase space. However, because it is surrounded by regular orbits, it cannot escape from L 4 vicinity. For μ = 0.0395 (Fig. 3, left panel), we can observe that the chaotic zone near 123 Fig. 4 Escape time of a particle starting motionless at L 4 (or L 5 ), as a function of the secondary mass μ, illustrating the global stability of the triangular Lagrangian points. Below μ = 0.0397, the particle remains in the L 4 vicinity over the whole integration time, i.e. until t = 10 8 (i.e. 10 8 /2π = 1.6 × 10 7 orbital periods of the secondary). Above μ = 0.04, the particle escapes the L 4 or L 5 vicinity in less than t ≈ 1000. Gascheau's value μ G is shown as the vertical dot-dashed line L 4 (r = 1, ṙ = 0) is more and more prevalent, even though regular orbits still prevent escape from L 4 vicinity.

An abrupt transition occurs just below μ = 0.04: chaos now prevails, the regular orbits fade away (Fig. 3, right panel), and chaotic diffusion allows the particle to escape L 4 vicinity. Figure 4 shows the survival time t escape of a particle initially launched motionless at L 4 , i.e. the time after which the particle escapes from the L 4 vicinity. In all the cases we have examined, this ends up by a close encounter with the secondary, and an escape on a hyperbolic orbit, see an example in the lower part of Fig. 5, with μ = 0.0405.

Because the particle has to chaotically diffuse away from L 4 before escaping, this time of escape is exponentially sensitive to round-off errors and errors associated with the finite order of our integrator, so that it can only be evaluated in a statistical way. Figure 4 actually shows fluctuations of t escape as μ increases, as expected in a chaos-dominated process.

The interesting point is that for μ ≤ 0.0397, the particle remains in L 4 vicinity for times larger than the duration of our integration, t = 10 8 , while this time drastically drops to less than 10 3 (corresponding to 10 3 /2π ∼ a few hundreds of orbital periods of the primaries) between μ = 0.0397 and μ ≈ 0.04.

In that sense, the value μ ≈ 0.04 may be viewed as a more meaningful stability threshold than μ G , from a physical standpoint. For instance, a spacecraft initially posted still at one of the triangular Lagrange points of a system where μ G ≤ μ ≤≈ 0.0397 will remain around the vicinity of the corresponding triangular point for an infinite, or very long, time, even though the triangular point is linearly unstable.

Previous works actually focussed on the global stability of a particle in the neighborhood of L 4 , for μ just above μ G . For instance [START_REF] Bardin | On motions near the Lagrange equilibrium point L 4 in the case of Routh's critical mass ratio[END_REF] shows that a particle sufficienlty close to L 4 can stay forever in a finite domain around the triangular point for values of μ larger but sufficienlty close to μ G . Other works investigated the global stability of L 4 in the frame of the elliptic restricted three-body problem, see [START_REF] Nauenberg | Stability and eccentricity for two planets in a 1:1 resonance, and their possible occurrence in extrasolar planetary systems[END_REF] or Érdi et al. (2009). The latter authors have calculated the escape time of a test particle initially motionless at L 4 , in the μe plane, where e is the orbital eccentricity of the primary and secondary. By examining Fig. 5 Two examples of a a globally stable orbit of a particle starting motionless at L 4 for μ = 0.039 (corresponding to the orbit plotted in red in Fig. 1), and b an unstable orbit starting at L 5 for μ = 0.0405. After a chaotic diffusion inside a region surrounding L 5 , the particle escapes that region at t ≈ 5960, has a close approach with the secondary, and acquires a hyperbolic orbit. The particle motion is plotted in a frame centered on the primary [larger dot at (x rot , y rot ) = (0, 0)] and corotating with the secondary [smaller dot at (x rot , y rot ) = (1, 0)]. The dotted circle centered on the primary has a radius equal to unity the Fig. 2 of Érdi et al. (2009), one can see that the global stability of L 4 is actually ensured beyond μ = 0.03852 . . . when e = 0. A sharp transition actually occurs around μ ≈ 0.040, in agreement with our Fig. 4.

We note finally that particular stable orbits may exist around L 4 or L 5 for μ ≥ 0.04 (see e.g. [START_REF] Henrard | The web of periodic orbits at L 4[END_REF], or even that orbits may connect the two triangular points for values of μ as large as 0.5 [START_REF] Henrard | Families of periodic orbits emanating from homoclinic in the restricted problem of three bodies[END_REF]. So, our present result deals with the global stability of orbits starting at L 4 or L 5 for values of μ just above μ G , and has a statistical meaning only. In particular, it does not exclude the existence of stable orbits for large values of μ.

Periodic orbits around L or L 5

The story of the Lagrange triangular points does not end at μ ≈ 0.04, however. Figure 1 shows the presence of two fixed points, labelled "PO", which actually correspond to a unique stable periodic orbit encircling L 4 . This orbit is shown in the upper left corner of Fig. 6. It intersects the surface of section twice, once for ˙ ≥ 0 (left dot in Fig. 1), and once with ˙ ≤ 0 (right dot in Fig. 1), as explained earlier.

Let us consider a situation where μ is a parameter slowly varying with time t. Then the particle orbit will remain arbitrarily close to a periodic orbit by virtue of the adiabatic invariance of action. This allows us to determine the locus of the fixed points in the (r, ṙ ) phase space, corresponding to various μ's. This locus is shown as the dotted curves in Figs. 1, 2 and 3, and as the solid curves in Fig. 7.

123 Care must be taken to have a sufficiently slow variation of μ, by choosing a small enough parameter = μ (t)/μ(t). This ensures that the instantaneous orbit for a given μ(t) stays close enough to the periodic orbit that would be obtained for that particular value of μ. Typical values of are 10 -6 near Gascheau's value, and 2 × 10 -10 near the limiting value μ = 0.0463004 . . . that will be discussed later.

Figure 6 shows sample examples of periodic orbits obtained as μ increases. Just above Gascheau's value, the size of the periodic orbit encircling L 4 rapidly increases while keeping one "braid" (i.e. consisting in a 1-cycle periodic orbit around L 4 ), then it suffers a period doubling at μ = 0.045452 . . . and exhibits two braids (i.e. a 2-cycle periodic orbit). A series of period doubling occurs subsequently, with the number of cycles also doubling at each etap, while the size of the orbit keeps on increasing.

Those bifurcations are better seen in the (r, ṙ ) phase space (Fig. 7). One can note the two branches originating from the L 4 point, and corresponding to 1-cycle periodic orbits. Several ramifications can be observed as μ increases. An exploration of the phase space around those

= μ G = (1 -23/27)/2),
and that the Feigenbaum constant for area-preserving 2-D maps is δ = 8.7210978 . . . [START_REF] Tabor | Chaos and Integrability in Nonlinear Dynamics: An Introduction[END_REF] fixed points shows that the latters are imprisoned in smaller and smaller regular islands, and surrounded by a more and more prevalent chaotic "sea". This is the classical behavior of a periodic dynamical system en route to a chaotic behavior, as can be seen in Fig. 8. In that diagram, the values of r obtained in Fig. 7 is now plotted against μ. One recognizes a Feigenbaum cascade, first observed in one-dimensional iterative maps [START_REF] Feigenbaum | The universal metric properties of nonlinear transformations[END_REF]. During this cascade, the fixed points of the map suffer period doublings at particular values μ 0 , μ 1 , . . . , μ i , . . . of μ, each value corresponding to the appearance of a new 2 i -cycle orbit.

i μ i δ i = μ i -μ i-1 μ i+1 -μ i 0 0.038520… - 1 0.045452… 9.24… 2
It has been shown that the μ i 's approach geometrically a limiting value μ ∞ as i → ∞. Actually, there exists a constant δ = lim i→∞ (μ i -μ i-1 )/(μ i+1 -μ i ), called the Feigenbaum constant, which is common to a wide class of one-dimensional maps [START_REF] Tabor | Chaos and Integrability in Nonlinear Dynamics: An Introduction[END_REF], with a value of δ = 4.66920160 . . . For area-preserving two-dimensional maps, as it is the case for the Poincaré surface of section examined here, it has been shown that δ = 8.7210978 . . . [START_REF] Tabor | Chaos and Integrability in Nonlinear Dynamics: An Introduction[END_REF]. Table 1 shows that the ratio (μ i -μ i-1 )/(μ i+1 -μ i ) does get close to that constant as n increases.

Conclusions

We have examined the dynamics of a particle near the triangular Lagrange's points L 4 and L 5 , in the frame of the restricted planar and circular three-body problem, and for values of the secondary mass μ just beyond Gascheau's value μ G = (1-√ 23/27)/2) = 0.0385208965 . . ., for which L 4 and L 5 are linearly unstable.

123

We have specifically examined two aspects of the problem. One aspect concerns the global stability of the triangular points, namely the fate of a particle initially placed motionless (in the corotating frame) at L 4 or L 5 for μ ≥ μ G . The other aspect concerns the existence of periodic stable orbits encircling L 4 or L 5 , parametrized by μ, and emanating from the point-like solution at the triangular points for μ = μ G .

Global stability of the triangular Lagrange points. Figures 2 and3 indicate that for μ ≥ μ G , the orbit starting at L 4 or L 5 first remains regular in a finite interval beyond μ G , e.g. for μ = 0.039. In that case, the particle follows a regular orbit that densely fills a finite region near L 4 or L 5 [orbit (a) in Fig. 5], although those points are linearly unstable. For larger values of μ (e.g. 0.0394), an orbit starting at the triangular points is chaotic, but remains nevertheless trapped inside regular orbits in phase space. This ensures that L 4 and L 5 are effectively globally stable in the sense that a particle released motionless at L 4 or L 5 will remain indefinitely trapped around those points.

Between μ = 0.0397 and μ = 0.04, the regular "imprisoning orbits" disappear, and chaotic diffusion allows the particle to escape from L 4 or L 5 vicinity [orbit (b) in Fig. 5]. Thus, the value μ ≈ 0.04 should be regarded as the threshold beyond which the triangular Lagrange points L 4 and L 5 are no longer globally stable.

Stable periodic orbits around the triangular Lagrange points. There exists a family of stable periodic orbits encircling L 4 or L 5 , parametrized by μ beyond Gascheau's value. Those orbits start as a point at L 4 or L 5 for μ = μ G , and then increase in size as μ increases (see upper left panel of Fig. 6).

This family undergoes a bifurcation at μ 1 = 0.045452 . . . with the appearance of two cycles in the orbit, yielding a period doubling (upper right panel of Fig. 6). A series of bifurcations is subsequently observed at values μ i , each yielding new 2 i -cycle orbits (Table 1).

Those bifurcations are readily observed in the phase space (r, ṙ ), see Fig. 7, and in a plot of r versus μ (Fig. 8). We recognize a classical Feigenbaum cascade, with a series of period doublings, eventually yielding to chaos. The series μ i closely follows a geometrical progression, with an associated Feigenbaum constant δ = lim n→∞ (μ i -μ i-1 )/(μ i+1μ i ) consistent with the value expected from area-preserving two-dimensional maps, δ = 8.7210978 . . ..

A closer examination of the branchings in Fig. 8, and an extrapolation of the series using the Feigenbaum constant both provide a limiting value of μ ∞ = 0.0463004 . . . for the mass ratio at which the periodic orbits surrounding L 4 or L 5 dissolve themselves into a chaotic region of the phase space. So, it appears that Gascheau's value μ G is the first of a series μ 0 (= μ G ), μ 1 , . . . , μ i , . . . corresponding to successive period doublings, and leading to the disappearance of this family of periodic orbits for μ ∞ = 0.0463004 . . .. The latter quantity may be thus considered as a limiting value which generalizes the finding of Gascheau.

As a final remark, we note that in Feigenbaum's diagrams, there may exist small intervals of μ beyond μ ∞ where regular behavior shortly appears, although chaos prevails in those regions. So, we do not exclude the existence of stable periodic orbits around L 4 and L 5 beyond μ ∞ = 0.0463004 . . .. Exploring this possibility remains, however, out of the scope of this paper.

Fig. 1

 1 Fig.1Poincaré surface of section for orbits with μ = 0.039 and C J = 2.961, see text for details. The two thin lines labelled "ZVC" are the zero-velocity curves, between which no motion is possible. The thick red curve is the orbit going through L 4 , at (r, ṙ ) = (1, 0), with zero velocity. It corresponds to the orbit labelled (a) in Fig.5. The two points labelled "PO" are the fixed points corresponding to the periodic orbit encircling L 4 for μ = 0.039, and shown in Fig.6(upper left orbit). The dotted curves are the locus of the fixed points when μ is increased slowly beyond Gascheau's value, see also Fig.7(colour version is available in the online version)

Fig. 2

 2 Fig. 2 Left panel An enlargement of the central region of Fig. 1 (μ = 0.039). Right panel Same as left panel, but with μ = 0.0394 (colour version is available in the online version)

Fig. 6 Fig. 7

 67 Fig. 6 Examples of four stable periodic orbits beyond Gascheau's value. The crosses indicate the location of the L 4 point. Each orbit has been displaced with respect to each other for better viewing. The horizontal bar provides the scale. Upper left the periodic orbit corresponding to the fixed points "PO" of Fig. 1, with μ = 0.039. Upper right periodic orbit with μ = 0.0461953059. This orbit has undergone a period doubling and has now two cycles before completing a period. Lower left periodic orbit corresponding to μ = 0.0462600179, with four cycles. Lower right periodic orbit corresponding to μ = 0.0462979898, with eight cycles (not all visible at that scale)

Fig. 8

 8 Fig. 8 Left panel Values of r obtained in Fig. 7 as a function of μ. The vertical lines mark the values of μ i where successive bifurcations occur (see alsoTable 1). Right panel Enlargement of the box drawn in the left panel

Table 1 )

 1 . Right panel Enlargement of the box drawn in the left panel

Table 1

 1 Values of the mass ratio μ at bifurcations

	Note that
	μ 0

Gabriel Gascheau was born in 1798, he was a professor at Toulouse University, France. His thesis on "Mouvements relatifs d'un système de corps. Sur deux cas particuliers d'un problème des trois corps" was published in Paris in 1843.

Acknowledgments I would like to thank Jacques Henrard, who substantially contributed to this paper with detailed discussions and by sending me several reprints on the dynamics of the Lagrange points. I also thank Michel Hénon for providing reprints on that topic. I furthermore benefited from discussions and insights from Alain Albouy and Giancarlo Benettin. We acknowledge the reviewers for constructive comments.


Sandrine D'hoedt
email: sandrine.dhoedt@fundp.ac.be

Benoît Noyelles

Julien Dufey

Anne Lemaître

A secondary resonance in Mercury's rotation

Keywords: Mercury, Planetary rotation, Hamiltonian formalism, Resonance, Great Inequality, Kernel models

The resonant rotation of Mercury can be modelised by a kernel model on which we can add perturbations. Our kernel model is a two-degree of freedom one written in Hamiltonian formalism. For this kernel, we consider that Mercury is solid and rotates on a Keplerian orbit. By introducing the perturbations due to the other planets of the Solar System, it appears that, in a particular case, our slow degree of freedom may enter into a 1:1 resonance with the Great Inequality of Jupiter and Saturn. Actually, as the moments of inertia of Mercury are still poorly known, this phenomenon cannot be excluded.

Introduction

The missions MESSENGER and BepiColombo being real catalysers for the research on Mercury, more and more precise studies and theories emerge until a few years. Let us cite a few of the most recent ones: [START_REF] Margot | A Mercury orientation model including non-zero obliquity and librations[END_REF], who presents revised values of the north pole orientation, [START_REF] Dufey | Planetary perturbations on Mercury's libration in longitude[END_REF], who model the planetary perturbations on Mercurys libration in longitude and D 'Hoedt and Lemaître (2008), who show that Mercury stays in the Cassini forced state in an adiabatic way under the action of planetary long periodic terms.

However, shorter planetary periodic terms can, in some cases, induce a secondary resonance, it is for instance the case of Titan [START_REF] Noyelles | Titan's rotational state: the effects of a forced "free" resonant wobble[END_REF]. To model this secondary resonance due to the influence of other planets of the Solar System in Mercury's rotation, we have to add the planetary perturbations to our kernel model. Our kernel model (D'Hoedt and Lemaître 2004) is a two-degree of freedom one written in Hamiltonian formalism. Moreover we make the following hypothesis: Mercury is a solid body, its orbit is Keplerian orbit, it rotates around its axis of greatest inertia and no dissipative forces acts on its movement. If we compare the free precession period of our model with the one of the Great Inequality of Jupiter and Saturn, they are clearly of the same order of magnitude (respectively 1,065.08 and 883.28 years). However, the 1,065.08 period computed from our model was based on the hypotheses that Mercury is a rigid body and if we introduce a liquid core as, e.g., [START_REF] Dufey | Latitudinal librations of Mercury with a fluid core[END_REF]; [START_REF] Peale | Does Mercury have a molten core?[END_REF]; [START_REF] Peale | Interpretation of Mercury's rotation state[END_REF][START_REF] Peale | Resonant forcing of Mercury's libration in longitude[END_REF], we may obtain the exact equality between the two periods for a peculiar value of C m /C where C is the polar moment of inertia of Mercury and C m the one of its mantle. This assumption, even though theoretical, must not be excluded because this latest ratio is still poorly known. The missions Messenger and BepiColombo should give us a better knowledge of it [START_REF] Milani | Gravity field and rotation state of Mercury from the BepiColombo radio science experiments[END_REF].

In Sect. 2, we give a summary of our kernel rigid model and of the main results (equilibrium values, proper periods) obtained from it.

In Sect. 3, we consider that Mercury has a liquid core with the value of C m /C needed to have a 1:1 resonance with the Great Inequality of Jupiter and Saturn that we introduce in the orbital elements thanks to Simon's series at first order.

In Sect. 4, we define the secondary resonant angle from the action-angle coordinates and we compute its proper period.

In Sect. 5, we analyse the influence of the secondary resonance on the main degrees of freedom.

Summary of the kernel model

In this model, we consider Mercury as a rigid body, we do not take into account the planetary perturbations and we assume that the Spin axis and the axis of greatest inertia are aligned. In this way, our two-degree of freedom Hamiltonian averaged on the mean anomaly can be written as follows (see D'Hoedt and Lemaître (2004) for details): In this Hamiltonian, the first term comes from the two-body problem, the second one is the kinetic energy of rotation and the third big one is the potential of the gravity field. The variables and their conjugated momenta are

H = - m 3 μ 2 2 o - 3 1 2 2 + 2 1 2C - G Mm 7 μ 3 R 2 e ( 0 -3 2 1 ) 6 × 1 2 C 0 2 1 + 3 e 2 2 - 1 4 -1 + 3 cos i 2 o -1 + 3 cos 2 K -3 cos i o cos K cos(σ 3 ) sin i o sin K - 3 4 1 -cos 2 i o 1 -cos 2 K cos(2 σ 3 ) + 3 C 2 2 7 e 2 - 123 e 3 16 1 16 (1 -cos i o ) 2 (1 -cos K ) 2 cos(2 σ 1 + 4 σ 3 ) + 1 4 (1 -cos i o ) (1 -cos K ) sin i o sin K cos(2 σ 1 + 3 σ 3 ) + 3 8 sin 2 i o sin 2 K cos(2 σ 1 + 2 σ 3 ) + 1 4 (1 + cos i o ) (1 + cos K ) sin i o sin K cos(2 σ 1 + σ 3 ) + 1 16 (1 + cos i o ) 2 (1 + cos K ) 2 cos(2 σ 1 ) (1)
σ 1 = 2(g+h)-3l o 2 -h o -go 1 σ 3 = -h + h o 3 = 1 (1 -cos K )
where g, h and K are Euler's angles linking the body frame to the ecliptic frame (see Fig. 1), h o is the longitude of the ascending node, g o is the pericenter argument and 1 is the angular momentum norm. σ 1 is thus the 3:2 spin-orbit resonant angle and K is called the ecliptic obliquity. The equilibrium values of this model found for the present state of Mercury were the following:

σ 1 = 0, σ 3 = 0,
(2)

1 = 13.303 m R 2 e year , K = 7 o ,
and the proper periods of angles were:

T 1 = 15.8573 years, (3) T 3 = 1,065.08 years.

The Great Inequality of Jupiter and Saturn

By introducing the perturbations due to the other planets of the Solar System on our kernel model, it appears that, in a particular case, our slow degree of freedom may enter in a 1:1 resonance with the Great Inequality of Jupiter and Saturn. This was already underlined by [START_REF] Dufey | Latitudinal librations of Mercury with a fluid core[END_REF] who apply a perturbation theory based on the Lie triangle to re-introduce short periodic terms due to planetary perturbations into our averaged kernel Hamiltonian and so compute the evolution of the rotational variables [START_REF] Dufey | Planetary perturbations on Mercury's libration in longitude[END_REF].

So, the period T J S of the Great Inequality of Jupiter and Saturn, obtained thanks to Simon's series,1 is T JS = 883.28 years.

(4)

The proximity of the two periods T 3 and T J S led us to look for a perfect equality for a more realistic model of Mercury with a liquid core. Effectively, if we take a value of C m /C = 0.82931, this phenomenon may occur. However, according to [START_REF] Margot | Large longitude libration of Mercury reveals a molten core[END_REF]), this value is not very probable but the parameters of Mercury are so poorly known that we must not exclude it (Figs. 5 and 6 in [START_REF] Dufey | Latitudinal librations of Mercury with a fluid core[END_REF].

So, in this particular case, there is a 1:1 resonance between σ 3 and σ 25 = 2l J -5l S where l J is the mean anomaly of Jupiter and l S the one of Saturn.

Let us thus introduce this angle σ 25 in the orbital elements thanks to Simon's series at first order: where l o 0 the mean anomaly without perturbations.

Our Hamiltonian can now be written:

H 25 = - m 3 μ 2 2 o - 3 1 2 2 + 2 1 2C m + V G (σ 1 , σ 3 , σ 25 , 1 , 3 ) + ν 25 (11)
with ν the frequency and 25 the conjugated momentum of σ 25 . Let us note that the last term has to be added in order to keep an autonomous Hamiltonian. The complete expression of G is given in the Appendix.

Secondary resonant angle

In order to define our secondary resonant angle, we have to express our Hamiltonian in action-angle coordinates.

To do this, we have to perform a succession of transformations (D'Hoedt and Lemaître 2006):

-a canonical transformation into cartesian coordinates, -a translation to the equilibrium, -a Mac Laurin's expansion up to the order 2 for our first degree of freedom and up to the fourth order for our third degree of freedom, -an untangling transformation [START_REF] Henrard | Untangling transformation[END_REF] to eliminate the mixed terms, -a scale transformation to associate to each variable and its conjugate momentum the same coefficient, -a transformation into action-angle coordinates (J 1 , J 3 , ψ 1 , ψ 3 ) where ψ 1 and ψ 3 are the angles of free libration around the equilibrium.

Let us note that we had to develop up to the fourth order to have terms in J 2 3 . We can now define our 1:1 secondary resonant angle

α = ψ 3 -σ 25 . ( 12
)
Our canonical set of action-angle variables is thus now

ψ 1 J 1 α J 3 σ 25 25 = J 3 + 25 .
The first degree of freedom (J 1 , ψ 1 ) being of no interest for the calculation of the period of our secondary resonant angle, we consider it as constant and drop it.

After that simplification, we average our Hamiltonian about σ 25 ( 25 becomes thus a constant) and obtain this expression:

H 25 = -0.000184 J 2 3 + 5.50471 10 -10 J 3 cos α -2.97662 10 -10 J 3 sin α.

(13)

We again compute the equilibria of this Hamiltonian, perform a variables change to centre the Hamiltonian at the equilibrium and expand it in Mac Laurin's series up to the second order.

After a scaling transformation and an action-angle transformation, the final form of the Hamiltonian is H 25 = -5.727 10 -8 Z + 2.307 10 -5 Z 2 -1.15 10 -6 Z 3/2 cos ζ +1.15 10 -6 Z 3/2 cos 3ζ -2.307 10 -5 Z 2 cos 4ζ .

(

) 14
The frequency of ζ being the coefficient of Z in ( 14), we can deduce the period of ζ and thus the proper period of the free librations of α:

T α = 1.0972 10 8 years.

(15)

Actually, the period of ζ is also the one of the movement of α because during a complete run of ζ around its equilibrium, α performs one going and coming between its minimum and maximum values of libration (see Fig. 2).

Influence of the secondary resonance on the other degrees of freedom

If we compute and numerically integrate the equations of motion obtained from (11), we can see the influence of the secondary resonance on our principal degrees of freedom. As expected, since the resonance is between σ 3 and the Great Inequality, its influence on σ 3 and K is much bigger than on σ 1 : on σ 1 , the amplitude is of 1.64 arc sec (to be compared with a maximum amplitude of libration of 40 arc sec [START_REF] Dufey | Latitudinal librations of Mercury with a fluid core[END_REF]), while it is of 161.49 arc sec on σ 3 (Fig. 3) and of 0.3132 • = 18.79 arc min on the ecliptic obliquity K (Fig. 4). This amplitude is especially large because if we examine the others effects that can introduce a forced libration on the ecliptic obliquity, we can see the most important of them is due to the precession of the ascending node of Mercury for which the amplitude of the variations are only of 0.414 arsec on a period of 63,315 years [START_REF] Dufey | Latitudinal librations of Mercury with a fluid core[END_REF]). However, in both cases, the periods being very long, all what could be observed is constant offsets.

Conclusion

Due to the proximity of the period of one of our degree of freedom and of the Great Inequality of Jupiter and Saturn, we built a theoretical but nevertheless possible (with a weak probability) model taking into account this 1:1 secondary resonance. Even if the influence of this resonance on our main degrees of freedom is non negligible concerning the amplitudes, the proper period is so long that it could only be observed as a constant offset.

Fig. 1

 1 Fig.1The ecliptic frame (X 0 , Y 0 , Z 0 ) with X 0 and Y 0 fixed in the ecliptic plane at a determined epoch and Z 0 normal to the ecliptic plane and the body frame (X 3 ,Y 3 ,Z 3 ) with X 3 in the direction of the axis of biggest inertia and Z 3 in the direction of the axis of smallest inertia of Mercury. h, g and K are the Euler's angles linking both frames

e

  = 0.206 + 3.03045 10 -8 cos σ 25 + 2.05414 10 -8 sin σ 25 (5) cos i o = cos 7 o + 9.37904 10 -10 cos σ 25 + 1.33666 10 -9 sin σ 25 (6) sin i o = sin 7 o -7.63861 10 -9 cos σ 25 -1.08862 10 -8 sin σ 25 (7) g o = 29.12478 o + 8.74537 10 -8 cos σ 25 -4.94628 10 -7 sin σ 25 (8) l o = l o 0 + 5.71111 10 -8 cos σ 25 + 5.16281 10 -7 sin σ 25 (9) h o = 48.33 o + 5.62001 10 -8 cos σ 25 + 2.07223 10 -7 sin σ 25 (10)

Fig. 2

 2 Fig. 2 During ζ performs a complete run, α oscillates between its minimum and maximum values

Fig. 3 Fig. 4

 34 Fig. 3 Influence of the Great Inequality on σ 1 and σ 3

These series were given by J.-L. Simon in a private communication and are obtained from the VSOP theory(Fienga and Simon

2005).

Acknowledgments

The authors were supported by the contract Prodex C90253 ROMEO from BELSPO. The authors also would like to thank Jean-Louis Simon for kindly providing the planetary series.

Appendix: Complete expression of V

-3 2 C 0 2 (0.536 + 0.52 cos 2 K + 8.939 10 -9 cos σ 25 + 1.064 10 -8 cos 2 K cos σ 25 + 0.004 cos 2σ 3 -0.004 cos 2 K cos σ 3 -4.256 10 -10 cos σ 25 cos 2σ 3 + 4.256 10 -10 cos 2 K cos σ 25 cos 2σ 3 + 0.129 cos K cos σ 3 sin K -5.677 10 -9 cos K cos σ 25 cos σ 3 sin K + 5.689 10 -9 sin σ 25 + 8.323 10 -9 cos 2 K sin σ 25 -6.584 10 -10 cos 2σ 3 sin σ 25 + 6.584 10 -10 cos 2 K cos 2σ 3 sin σ 25 -9.784 10 -9 cos K cos σ 3 sin K sin σ 25 + 7.231 10 -9 cos K cos σ 25 sin K sin σ 3 -2.666 10 -8 cos K sin K sin σ 25 sin σ 3 + 4.439 10 -10 cos σ 25 sin 2σ 3 -4.439 10 -10 cos 2 K cos σ 25 sin 2σ 3 -1.637 10 -9 sin σ 25 sin 2σ 3 + 1.637 10 -9 cos 2 K sin σ 25 sin 2σ 3 )

+ 2.27 10 -6 cos (2σ 1 + 4σ 3 ) -4.541 10 -6 cos K cos (2σ 1 + 4σ 3 ) + 2.27 10 -6 cos 2 K cos (2σ 1 + 4σ 3 ) + 0.04 cos (2σ 1 + σ 3 ) sin K + 0.04 cos K cos (2σ 1 + σ 3 ) sin K + 2.169 10 -9 cos σ 25 cos (2σ 1 + σ 3 ) sin K + 2.169 10 -9 cos K cos σ 25 cos (2σ 1 + σ 3 ) sin K + 0.0002 cos (2σ 1 + 3σ 3 ) sin K -0.0002 cos K cos (2σ 1 + 3σ 3 ) sin K + 3.794 10 -8 cos σ 25 sin 2σ 1 + 7.587 10 -8 cos K cos σ 25 sin 2σ 1 + 3.794 10 -8 cos 2 K cos σ 25 sin 2σ 1 + 1.307 10 -8 cos 2σ 1 sin σ 25 + 2.614 10 -8 cos K cos [2σ 1 sin σ 25 + 1.307 10 -8 cos 2 K cos 2σ 1 sin σ 25 -3.621 10 -10 cos (2σ 1 + 2σ 3 ) sin σ 25 + 3.621 10 -10 cos 2 K cos (2σ 1 + 2σ 3 ) sin σ 25 -3.747 10 -10 cos (2σ 1 + σ 3 ) sin K sin σ 25 -3.747 10 -10 cos K cos (2σ 1 + σ 3 ) sin K sin σ 25 +1.58 10 -7 sin 2σ 1 sin σ 25 + 3.16 10 -7 cos K sin 2σ 1 sin σ 25 + 1.58 10 -7 cos 2 K sin 2σ 1 sin σ 25 + 1.151 10 -8 cos σ 25 sin K sin (2σ 1 + σ 3 ) + 1.151 10 -8 cos K cos σ 25 sin K sin (2σ 1 + σ 3 ) + 3.044 10 -8 sin K sin σ 25 sin (2σ 1 + σ 3 ) + 3.044 10 -8 cos K sin K sin σ 25 sin (2σ 1 + σ 3 ) + 1.261 10 -9 cos σ 25 sin (2σ 1 + 2σ 3 ) -1.261 10 -9 cos 2 K cos σ 25 sin (2σ 1 + 2σ 3 ) + 2.0377 10 -9 sin σ 25 sin (2σ 1 + 2σ 3 ) -2.038 10 -9 cos 2 K sin σ 25 sin (2σ 1 + 2σ 3 ))

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