Radojka M Savic

Aurélie Barrail-Tran

Xavier Duval

George Nembot

Xavière Panhard

Diane Descamps

Céline Verstuyft

Bernard Vrijens

Anne-Marie Taburet

Cécile Goujard

Aur Lie Barrail-Tran

Xavi Re Panhard

Cile Goujard

R Ponses

Th Rapeutiques

Effect of adherence as measured

Keywords: Adenine, analogs & derivatives, therapeutic use, Adult, Aged, Alleles, Cytochrome P-450 CYP3A, genetics, Deoxycytidine, analogs & derivatives, therapeutic use, Drug Interactions, Drug Therapy, Combination, Female, Genotype, HIV Infections, drug therapy, HIV Protease Inhibitors, pharmacokinetics, pharmacology, therapeutic use, Humans, Male, Medication Adherence, Middle Aged, Models, Biological, Nonlinear Dynamics, Oligopeptides, pharmacokinetics, therapeutic use, Organophosphonates, therapeutic use, Pharmacogenetics, Pyridines, pharmacokinetics, therapeutic use, Ritonavir, pharmacology, therapeutic use, Young Atazanavir, Adherence, Pharmacogenetics, Population pharmacokinetics

INTRODUCTION

Atazanavir (ATV) is a potent HIV-1 protease inhibitor (PI) used as a principal component of combined antiretroviral therapy (cART) for first line HIV treatment since 2003 [START_REF] Piliero | Atazanavir: a novel HIV-1 protease inhibitor[END_REF][START_REF] Bms | Atazanavir Sulfate) Capsules . Summary Product Characteristics[END_REF]. Its pharmacologic characteristics allow for once daily dosing either as a 300 mg capsule boosted with ritonavir (100 mg) or 400 mg capsule administered with food. In addition to the convenience of once daily dosing, the advantage of atazanavir over other available PIs lies in its favorable safety profile with respect to the dyslipidemia risk [START_REF] Goldsmith | [END_REF].

Despite its favorable pharmacologic properties allowing for once daily dosing, atazanavir pharmacokinetics is associated with high variability between-and within-patients, posing a challenge for assessing and predicting not only individual exposures but also the target concentration time profile needed for optimal pharmacotherapeutic management (4 6). Potential sources of large between-and within--patient variability can be multiple: a) the food effects on oral bioavailability and absorption, b) drug-drug interactions, c) variability in ritonavir boosting, d) a large array of plausible pharmacogenetics interactions e) adherence variability. Additionally, high atazanavir concentrations have been associated with important toxicities, for example hyperbilirubinaemia. In patients with HIV virus sensitive to atazanavir, the current targets for the therapeutically optimal range of trough concentrations are at a lower boundary of 150 ng/mL, the minimum effective concentration (MEC) for successful viral suppression as reported in the US Department of Health and Human Services guidelines for antiretroviral therapy, and an upper boundary of 850 ng/mL, defined as a concentration threshold for bilirubinemia [START_REF] Colombo | Population pharmacokinetics of atazanavir in patients with human immunodeficiency virus infection[END_REF][START_REF] Cjll | Updated guideline to perform therapeutic drug monitoring for antiretroviral agents[END_REF].

The human cytochromes P450 3A4/3A5 (CYP3A5) are implicated in the hepatic metabolism of atazanavir [START_REF] Tiec | Clinical pharmacokinetics and summary of efficacy and tolerability of atazanavir[END_REF][START_REF] Anderson | Atazanavir pharmacokinetics in genetically determined CYP3A5 expressors versus non-expressors[END_REF]. CYP3A5 is mainly expressed in the liver and has a strong genetic basis [START_REF] Kuehl | Sequence diversity in CYP3A promoters and characterization of the genetic basis of polymorphic CYP3A5 expression[END_REF]. Low expression of CYP3A5 is found in homozygous carriers of the CYP3A5*3 allele, whereas homozygous and heterozygous carriers of the allele exhibit high expression of CYP3A5 [START_REF] Kuehl | Sequence diversity in CYP3A promoters and characterization of the genetic basis of polymorphic CYP3A5 expression[END_REF]. The decreased (26 CYP3A5*1

) atazanavir CL in CYP3A5 non-expressors has been recently reported in a study with healthy volunteers [START_REF] Kile | A Population Pharmacokinetic-Pharmacogenetic Analysis of Atazanavir[END_REF]. In addition, there are % known polymorphisms associated with UGT1A1, and functional deficiencies result in the accumulation of unconjugated bilirubin in the serum although there is variability in the phenotypic expression of patients carrying genetic polymorphism. Rotger , showed that et al individuals with the allele may develop jaundice when exposed to atazanavir or indinavir [START_REF] Rotger | Gilbert syndrome and the development of antiretroviral therapy-associated hyperbilirubinemia[END_REF]. UGT1A1 28 * Variable adherence to the prescribed therapy adds an additional general level of complexity in maintaining optimal ARV drug treatment. This topic has been in wide discussion in the last decade [START_REF] Blaschke | Variable adherence to prescribed dosing regimens for protease inhibitors: scope and outcomes[END_REF][START_REF] Osterberg | Understanding forgiveness: minding and mining the gaps between pharmacokinetics and therapeutics[END_REF]. Both, poor outcome of treatment and selection of resistant viral strains, have been linked to suboptimal adherence (15 20). Additionally, variable adherence is most likely one of the major contributors to the observed pharmacokinetic variability within and even between patients especially for long term treatments (21 24).

-Different methods have been proposed for measuring adherence. However in order to assess and quantify the impact of adherence on dynamic systems, such as time courses of the viral load, bilirubin concentrations or PI pharmacokinetics, the adherence pattern needs to be known as well. A precise assessment of adherence may be performed with Medication Event Monitoring System (MEMS) [START_REF] Vrijens | The impact of compliance in pharmacokinetic studies[END_REF][START_REF] Blaschke | Adherence to medications: insights arising from studies on the unreliable link between prescribed and actual drug dosing histories[END_REF][START_REF] Vrijens | Comparing compliance patterns between randomized treatments[END_REF], which records exact times of bottle opening for drug intake in combination with informative study design that allows for precise quantification of individual drug exposure and variability.

Undoubtedly, the interplay between individual pharmacokinetics, pharmacogenetics and adherence is complex and of critical importance to maintain atazanavir concentrations within the optimal therapeutic range, which would in turn minimize the incidence of therapeutic failure, development of drug-resistance and development of other toxicities Several previous studies developed population pharmacokinetic models for atazanavir (4 6). These studies reported high unexplained between subject variability in atazanavir PK parameters and suggested that adherence, pharmacogenetics and variability in ritonavir exposure are likely responsible for that but none of these studies had adherence measured via MEMS. Therefore, our study focused on elucidating these relationships in a data-driven quantitative manner. Our aims were: (i) to describe the population PK of atazanavir using accurate patient dosing-histories, (ii) to investigate how different assumptions involved in maximizing the accuracy of dosing-history data may impact the population PK analysis outcomes, (iii) to quantify pharmacogenetic effects of different relevant single nucleotide polymorphism (SNPs) on atazanavir pharmacokinetics, (iv) to establish a joint ritonavir atazanavir pharmacokinetic model to include the boosting mechanism and (v) to estimate realistically variables linked to effectiveness of cART [START_REF] Vrijens | Successful projection of the time course of drug concentration in plasma during a 1-year period from electronically compiled dosing-time data used as input to individually parameterized pharmacokinetic models[END_REF][START_REF] Vrijens | Modelling the association between adherence and viral load in HIV-infected patients[END_REF], using the established model, such as cumulative time and the number of trough samples below MEC during 24 weeks of trial.

RESULTS

Patients and data

The 35 patients included were 6 females and 29 males with a median age of 36 years (range 24 66).Median viral load (VL) and CD4 count at inclusion were 23,200 copies/mL (range, 100 457,000) and 436 cells/mm (range, 197 573) respectively. Clinical and safety -3 results of the trial were presented elsewhere [START_REF] Goujard | Virological Response to Atazanavir, Ritonavir and Tenofovir/Emtricitabine: Relation to Individual Pharmacokinetic Parameters and Adherence measured by Medication Events Monitoring System (MEMS) in Na ve HIV-Infected Patients (ANRS134 trial) ï[END_REF]. In brief, only 5 of the 35 patients did not achieve undetectable VL(<40 cp/mL) at W24, with a range of 47 to 152 cp/ml, one patient experienced a severe hyperbilirubinemia (grade 4) with a high atazanavir trough concentration and discontinued ritonavir and one patient experienced a transient cytolytic hepatitis (grade 4) of unknown origin.

In total, 272 atazanavir and 245 ritonavir concentrations from the 35 patients followed during a six-month period were available for the analysis. Raw atazanavir data are shown in Figure 1, where a full profile can be observed as well as trough values at different occasions. Inspection of the raw data indicated high variability in the absorption phase as well as substantial within-subject variability in the trough samples. Median observed maximal (C ) and trough concentrations (C

) of atazanavir at W4 were 4,021 ng/mL (range, max trough 1,903 2,907), and 304 ng/mL (range, 40 2,366), respectively.

--

Adherence data

Statistical analysis of raw adherence data indicated almost perfect adherence to medications in the studied population with a majority of the prescribed doses were taken as prescribed: median 100 (range 50 100) and median 99.7 (range 51 100)for atazanavir and twice. Similar adherence behavior was observed for tenofovir and emtricitabinepill. The dose-intensity heat maps showing adherence dynamics (incidence and amount of dose intake versus time for each patient) are shown in Figure 2.

Population PK model for atazanavir

A one-compartment model described atazanavir disposition well. The transit compartment absorption model substantially improved the observed data fit compared to all investigated absorption models. When compared to the second best absorption model (first order with a lag time), the transit model decreased 2 log likelihood by 64 points (p<10 ), and also explained an additional 11 of residual

Impact of adherence assumptions on the outcome of the population PK analysis

With respect to population PK data analysis, the assumption that all patients are at SS gave rise to significant quantifiable inter-occasion variability in CL/F (26.5 CV). The second analysis (A ) in which patient actual MEMS dosing-history were used, led % MEMS to a negligible within-subject variability estimate indicating that MEMS data explained this variability term entirely. However, a biased estimate of the volume of distribution was observed, thereby potentially affecting the prediction of individual patient s drug exposures.

'

Numerical difficulties during the estimation procedure were also experienced. In the gold standard analysis, a small proportion of the records of time of dose intake (<5 ) were found to be discordant compared to the self-reported dose intake time, therefore excluded from % the analysis. That gold standard analysis (A ) based on adjusted dosing histories only, led to the negligible within-subject variability in GOLD CL; parameter estimates were reliable, and the estimation procedure was stable. The parameter estimates from the three different analyses are shown in the Table I.

Pharmacogenetics and covariates

Pharmacogenetic data analysis revealed a statistically significant (p<0.01) effect of the CYP3A5 polymorphism on the atazanavir CL.

Patients with at least one copy of the allele (n 12) exhibited 42 increased oral CL compared with patients with both CYP3A5 1

* = % CYP3A5*
allele. None of other demographic and genetic covariates deemed to be important. The visual predictive check for the final model 3 stratified for different CYP3A5 genotypes is shown in Figure 4.

Joint ritonavir-atazanavir model

Ritonavir concentration time profiles were best described with the one compartment model. Absorption was described well with the transit compartment absorption model. Parameter estimates of the final ritonavir PK model are given in the Table 2. Ritonavir exposure (AUC ) defined as dose divided by individual CL was a sufficient driver to explain the boosting mechanism of atazanavir CL. The 0-24 estimate of unboosted atazanavir CL, e.g. in the absence of ritonavir, was rather high (16 L/h). Ritonavir proved to be an efficient booster exhibiting maximal inhibitory effect of 98 with AUC of 6,230 ng.h/mL, which was on the lower end of the observed ritonavir exposure given in the Table II.

Model Predictions and Simulations

The number of trough samples and the cumulative time below MEC over 24 weeks were computed for each patient (180 trough values for each patient). If the adherence was perfect, none of the trough samples would be below MEC (150 ng/mL), except for one individual who had an extremely high CL and was a carrier, and whose trough values were all below the target level. And therefore CYP3A5 1 * similar result holds for the cumulative time below this threshold. However, when the true MEMS dosing histories were used, during the 24 weeks, 4patients [START_REF] Rotger | Gilbert syndrome and the development of antiretroviral therapy-associated hyperbilirubinemia[END_REF] had more than 10 trough samples below the MEC of 150 ng/mL and 8 patients [START_REF] Vrijens | Successful projection of the time course of drug concentration in plasma during a 1-year period from electronically compiled dosing-time data used as input to individually parameterized pharmacokinetic models[END_REF] spent more than 100 h % % below MEC.

DISCUSSION

Today, there are more HIV patients on the planet who do not have the access to powerful protease inhibitors than the ones who do have the access to PIs. For those HIV patients who do have the access to effective PI-based HIV treatment, successful management of the HIV therapy still presents a great challenge both for the physician and the patient. Complex interplay between highly variable drug specific pharmacokinetics, patient adherence, and genetic background of the patient poses difficulties in maintaining the optimal therapeutic levels of the PIs required in order on one hand, to minimize the risk of therapeutic failure associated with the risk of viral resistance, and on the other hand, to prevent drug-related toxicities. A fully integrated pharmacokinetic-pharmacogenetic model with an integrated ritonavir-related boosting mechanism and real time adherence data was developed for atazanavir pharmacokinetics.

In this study, atazanavir disposition was best described by a one compartment model, which is in line with previous modeling studies (4 6). Kile found that two compartment model was best fit for atazanavir pharmacokinetics, which was not the case for our data. This et al is likely due to the design: Kile collected very rich data in healthy volunteers (9 samples) while we collected6 samples in patients. It et al is common that with very rich design, more complex models can be applied. However, we do not anticipate that this would alter any of our major findings.

In the absence of ritonavir-related boosting and pharmacogenetic relationships, apparent atazanavir CL and V were 6.9 L/h and 81.1 L, respectively, resulting in an elimination half-life of 8.1 h, which is consistent with previously reported values (8.2 8.9 h) (4 6). Our work

- -
departs from previously published atazanavir models in reporting our evaluation of relevant absorption models. Our study implemented a semi-mechanistic transit compartment model in order to describe highly variable atazanavir absorption. The transit model assumes that the delay in the absorption process is a consequence of the drug passing through chain of linked compartments (steps), before reaching the absorption site [START_REF] Savic | Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies[END_REF]. Our analysis illustrates that the transit compartment model is an attractive alternative for the modeling of the variable absorption, especially for anti-infective agents [START_REF] Wilkins | Population pharmacokinetics of rifampin in pulmonary tuberculosis patients, including a semimechanistic model to describe variable absorption[END_REF][START_REF] Zvada | Effects of four different meal types on the population pharmacokinetics of single-dose rifapentine in healthy male volunteers[END_REF].

Ritonavir has been developed and used as a pharmacokinetic booster of protease inhibitors [START_REF] Hill | How much ritonavir is needed to boost protease inhibitors? Systematic review of 17 dose-ranging pharmacokinetic trials[END_REF]. Ritonavir is a potent inhibitor of CYP3A4, the primary enzyme responsible for the metabolism of PIs, therefore decreasing the clearance and increasing half life of PIs and providing a basis for increasing the dosing interval to once daily (QD). The most common dose used for boosting is a 100 mg capsule per PI dosing. In our integrated model, the ritonavir-related boosting mechanism of atazanavir CL/F has been introduced. It was best described by the inhibitory E model, where the baseline atazanavir CL value in the absence of ritonavir was estimated (16 L/h, which is similar to max previous reports [START_REF] Kile | A Population Pharmacokinetic-Pharmacogenetic Analysis of Atazanavir[END_REF]) as well as maximal extent of inhibition and ritonavir exposure needed for half maximal effect. Ritonavir is an established and proven potent booster with maximal (98 ) inhibition of atazanavir CL, suggesting that a majority of the patients have been % maximally boosted. Interestingly, a lower value of ritonavir exposure (6,230 ng.hr/mL) is estimated to be needed for half maximal ritonavir boosting effect. This estimated ritonavir exposure is at the lower end of the observed ritonavir exposures (7 percentile), which th suggest potential overdosing of ritonavir in most patients, whereby lower doses of ritonavir could produce the desired boosting effect in order to maintain once daily atazanavir dosing. This result may be of interest considering the fact that 100 mg qd ritonavir has been implicated in increased risk of lipid level increase [START_REF] Shafran | The effect of low-dose ritonavir monotherapy on fasting serum lipid concentrations[END_REF][START_REF] Collot-Teixeira | Impact of different low-dose ritonavir regimens on lipids, CD36, and adipophilin expression[END_REF]. Furthermore, ritonavir may also be responsible for gastrointestinal adverse events experienced during treatment with PIs, therefore potentially affecting the adherence to PIs and ultimately the success of HIV therapy [START_REF] Hill | Risk factors for gastrointestinal adverse events in HIV treated and untreated patients[END_REF].

Atazanavir is primarily metabolized by CYP3A4/A5 and pharmacogenetic differences are expected to be observed with respect to the bioavailability and clearance of the drug. Even though our study was rather small (35 patients), we have quantified a significant increase in atazanavir CL [START_REF] Goujard | Virological Response to Atazanavir, Ritonavir and Tenofovir/Emtricitabine: Relation to Individual Pharmacokinetic Parameters and Adherence measured by Medication Events Monitoring System (MEMS) in Na ve HIV-Infected Patients (ANRS134 trial) ï[END_REF] in the patients with at least one allele, which is similar to the previously reported values (9). Kile Adherence to the prescribed therapy has been repeatedly named as the key factor for successful treatment outcome. Importantly, adherence will contribute to the observed pharmacokinetic variability. This fact is critical when drug levels must be maintained within a desired therapeutic window, or specifically in the case of PIs, above minimal effective concentrations. Furthermore, the ultimate goal of all model-based analysis is not only to quantify random variability between subjects, but also to explain these differences by plausible covariates. Ultimately, if almost of the variability in drug response can be explained, it would provide a basis for personalized dosing regimens. However, even-though a large number of demographic and pharmacogenetic covariates are often available for the analysis, only a small portion of the observed variability is explained. We hypothesized that adherence fluctuations would explain the majority of the observed variability. Therefore, we performed a sub-analysis of our data focusing on assumptions surrounding dosing histories. Our first analysis, which is in line with an implicit assumption in most population PK analyses, assumed perfect adherence and that all patients were at steady state. Under the steady-state assumption, the random variability in CL/F was 74 , corresponding to 47 of between-subject % % variability and 27 within-subject (or between-occasion) variability. Once MEMS adherence data from only reliable-patients were

% " "
included, the between-subject variability in CL/F decreased to 40 , while the within-subject variability became negligible. This finding % suggests that almost half of the initially quantified variability was not true variability in clearance, but was attributable to the unwarranted assumption of perfect adherence by all patients. This finding also reminds one that important covariates (e.g., weight, age, pharmacogenetics, etc), do not explain such a large portion of variability. It is consistent however, with the conclusion of Harter and Peck that variability in adherence rivals pharmacokinetics as the leading source of variability in drug response [START_REF] Harter | Chronobiology. Suggestions for integrating it into drug development[END_REF].

In our study, we have measured adherence using the MEMS caps, which record the exact time of the bottle opening. In most of the cases, the opening of the drug bottle corresponds to the drug intake; however some deviations to this assumption may occur. To obtain data closest to the truth, we asked subjects to keep a diary where these deviations were recorded. In addition, at each clinic visit, we asked them to report the time of drug intake from the previous day. This information was very helpful since we could compare the MEMS records with the individual s diary entry, and most of them agreed. A small proportion of the records (<5 ) were discordant, leading to ' % identifying these patient records as unreliable . Even though the proportion of unreliable data points was small, it was important to " "

exclude them from the analysis, in order to generate a gold standard cohort for comparison, increase model stability and guarantee analysis convergence.

In general, patient adherence in our study was very good. 98 of all atazanavir and ritonavir doses and 86 of the pills were taken by % % patients as prescribed. However, despite this high adherence rate, we showed that a few patients had atazanavir plasma levels below the target minimal effective concentration during the course of the treatment. Even though the median value of the time below MEC was low (<1 of the dosing interval), some of the patients spent up to 15 of the dosing interval below MEC. More precisely, there were five % % patients who were, over the treatment course, more than a cumulative 7days with unacceptably low levels of atazanavir. Two of these patients were non-responders at week 24 (out of the 5 non responders). The example of one of these patients is shown in Figure 6 where a full PK profile over 6 months is shown as well as the accumulated time below MEC. If the dosing regimen intake was perfect, none of the patients would be below MEC at any time during treatment. This suggests that even though overall adherence may be high, patients still fall below MEC, and are therefore at risk of treatment failure, if the drug intake is not-timely. This finding accentuates the importance of estimating adherence not only as an aggregate measure over a defined period of time, but also the precise time of each capsule intake. Only when we have this data in hand are we able to search and find plausible answers why treatment may have failed or resistance developed.

Two main limitations of the current study are small sample size (35 patients) and the protocol may have induced better adherence (Hawthorne effect).

In conclusion, a full, integrated pharmacokinetic-pharmacogenetic model for atazanavir with incorporated ritonavir-related boosting mechanism and real time adherence was developed for atazanavir pharmacokinetics. With the proposed model, we have delineated and quantified several important aspects of atazanavir-based HIV treatment. We have i) quantified a significant pharmacogenetic effect of CYP3A5 genotype on atazanavir CL, ii) characterized the pronounced ritonavir-related boosting mechanism of atazanavir CL at currently used ritonavir doses, and iii) assessed the large effect of adherence on atazanavir PK variability. The proposed model represents a useful basis for the individualized dosing of atazanavir and provides a precise tool for assessing the important PK-based variables (e.g. time below MEC) for successful HIV-treatment.

METHODS

Clinical trial

The ANRS 134 -COPHAR 3 trial was a multicenter prospective trial conducted in HIV-1-infected na ve patients starting a ï PI-containing cART treatment. The primary objective of the trial was to study pharmacokinetics/pharmacogenetics of atazanavir given with ritonavir using adherence measured by MEMS in PI treatment-na ve HIV-infected patient.

ï

The trial started and was completed in 2008. It included 35 na ve patients, who were started on treatment containing 300 mg of ï atazanavir boosted with 100 mg ritonavir and a fixed dose combination of two nucleoside analogs that are co-formulated: tenofovir (300 mg) and emtricitabine (200 mg) and were followed 24 weeks. Reyataz (atazanavir) and Truvada (tenofovir and emtricitabine) were

® ®
kindly provided by Bristol-Myers Squibb and Gilead, respectively. Viruses have to be sensitive to each component of therapy on a genotypic resistance assay performed before entry. No antacids or CYP inducing drugs were allowed during the trial. During the PK visit, drug intake was performed with food administration.

The study was performed according to the Declaration of Helsinki and its amendments. The protocol was approved by the Ethics Committee of Ile de France VII (Le Kremlin Bicetre, France) and all subjects provided written informed consent. The EUDRA CT number is 2007-003203-12.

Study design and Pharmacokinetic data

Patients were sampled during four visits at weeks (W) 4, 8, 16 and 24. During each visit, the patients were asked to report the exact time when the last dose was taken in the previous day. At W4, a trough blood sample was collected first, followed by the dose intake and collection of additional five samples at 1, 2, 3, 4, and 8 hours post-dose. At W8, W16 and W24, only the trough samples were collected.

Therefore, each individual had 9 PK samples available over a period of 6 months. Plasma concentrations were determined in the laboratories of the hospitals where the patients were followed by a specific high performance liquid chromatography (HPLC) protocol. The participant laboratories were cross-validated before starting the study. The lower limit of quantification was 50 ng/mL and 25 ng/mL for atazanavir and ritonavir, respectively.

Adherence data

Each patient was supplied with three MEMS capped bottles containing either atazanavir hard-capsules, ritonavir soft-capsules or tenofovir/emitricabine FDC tablets (Truvada ). The exact time of each opening of the cap was recorded. Therefore a full dosing history ® for the three capsules was available for all the patients. Patients were also requested to note any deviations from MEMS recorded drug intake, for example if a patient would leave for a short holiday and remove the requisite supply of pills in a single cap opening.

Additionally, at each clinic visit, patients were asked to report on a self administered questionnaire the time of the previous dose intake, which allowed for comparison with the MEMS recorded time.

Each patient whose MEMS record agreed with his or hers personal declared record within 3 hours was considered to have a reliable ± MEMS dosing history, indicating that the MEMS recorded time was similar to the time of actual drug intake. If a MEMS record did not agree with patient s personal record, this record was considered less reliable and the dosing history preceding the clinical visit was ' discarded from the analysis as well as collected sample at the clinical visit, when gold standard approach analysis was used (more details below).

Pharmacogenetic data

Six genetic polymorphisms were studied: MRP2 (rs717620), MRP4 (rs1751034), ORM1 (A721G), CYP3A5 (rs776746), MDR1

(rs1045642) and UGT1A1 28 (rs8175347).All of the genotyping analyses were performed in the same laboratory. The subjects were * genotyped by the TaqMan allelic discrimination assay or GeneScan analysis. For both methods, genomic DNA was extracted from peripheral blood mononuclaear cells using the Puregene Kit (Gentra systems, Minneapolis, USA) according to the manufacturer s protocol.

'

For each polymorphism, departure from Hardy-Weinberg proportions was tested using test with degrees of freedom equal to the number

χ 2
of observed genotypes minus 1.

Data analysis

Development of population model for atazanavir

All data were analyzed using the non-linear mixed effects approach available in NONMEM VI. The First Order Conditional Estimation with interaction (FOCEI) method was employed throughout the analysis. A basic model structure was established using the full PK profile data from W4 and assuming steady state conditions. As atazanavir exhibit highly variable absorption, special attention was paid to the modeling of this process. Several models were investigated, including the zero order absorption models, first order absorption model with lag time, sequential zero and first order model, transit absorption model. The individual parameters were assumed to be log-normally distributed and proportional error was employed for description of residual variability. The model building procedure was guided by the likelihood ratio test, diagnostic plots and internal model validation techniques, including visual and numerical predictive checks.

Adherence modeling

Adherence data were summarized in terms of following statistical quantities: percent ( ) of days with correct number of doses taken, % of total prescribed doses taken and of doses taken within 3 hours of the protocol specified dosing time. Adherence data were also % % ± explored using a graph where daily adherence behaviors, such as if dose was taken, taken twice or missed, were visualized for each patient and each drug. This plot is often referred to as a dose intensity gap map . In order to assess the impact of dosing history assumptions on " " the outcome of the population analysis, we performed three separate analyses from the entire atazanavir dataset (full PK profile from W4 and three additional trough samples at W8, W16 and W24). The first analysis, based on the assumption of full adherence to the protocol specified dosing history (A ), included the assumption that all patients were at steady state and that the time of last dose intake as reported ss by the patient before a PK visit was accurate. The second analysis, a MEMS recorded dosing history analysis (A ),assumed that each dosing-history data only, which consisted only in concentration data from which MEMS records of time of intake were concordant (within 3 hours) with patients last reported time of dose intake before a PK visit. When MEMS data were missing (no MEMS for some patients sometimes), the corresponding concentration data were not analyzed The previously established basic structural model was extended to include within-subject variability (WSW) in CL and was rerun using three different dosing history data as described above (A A and ss, MEMS A ). Parameter estimates were compared with particular attention to the magnitude of the variability parameters (between-subject, GOLD within-subject and residual variability).

Pharmacogenetic and demographic covariate analysis

Six genetic polymorphisms (MRP2, MRP4, MDR1, CYP3A5, UGT1A1,ORM1) were evaluated as possible genetic covariates influencing pharmacokinetic parameters of atazanavir. Potential impact of these genetic markers on atazanavir and ritonavir pharmacokinetics are described in Table 1 of supplementary material. Mutant and heterozygotic alleles were grouped together into one category in order to increase the power of the search. Categorizations in three classes were also tested: wild homozygotes versus heterozygotes versus mutant homozygotes.

Demographic covariates were also available: age, sex and body weight. The covariate search was performed using a stepwise covariate model building procedure described elsewhere [START_REF] Lindbom | Application and Evaluation of Statistical Tools in Pharmacometric Data Analysis[END_REF][START_REF] Lindbom | PsN-Toolkit--a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM[END_REF]. The procedure included a forward inclusion step, where parameter-covariate relationships are added to the model in a stepwise manner until no further relationship is statistically significant (p<0.05). Backwards elimination steps followed, where the identified relationships were excluded from the model if they failed to achieve stricter statistical significance (p<0.01), in order to account for the multiple testing.

Development of the population models for ritonavir and the joint ritonavir-atazanavir model

Full dosing history data were available for ritonavir and the gold standard approach was used. Ritonavir concentration time data were modeled using a similar methodology to the one described above for atazanavir.

Once separate ritonavir and atazanavir models were established, the next step involved development of the joint ritonavir-atazanavir model, where the boosting mechanism was introduced. A range of models was evaluated in which atazanavir CL/F was either: (i) a function of ritonavir concentrations, (ii) a delayed response to ritonavir concentrations, or (iii) a function of ritonavir steady state exposure.

For the models employing ritonavir concentrations as a driver of the boosting mechanism, both simultaneous and sequential approaches were tested. Steady state ritonavir exposure was computed as ritonavir dose divided by individual CL value. A model for the boosting mechanism utilized a nonlinear inhibitory E function, where the maximal boosting effect was estimated as well as AUC , which is the max 50 ritonavir exposure needed for half maximal effect (Equation 1). CL represents unboosted atazanavir CL.

0

Model simulations and predictions

The final PK-PG model for atazanavir using the dosing history data from the gold standard approach and the model-estimated

" "

individual parameters were used to predict different variables linked to effectiveness cART [START_REF] Vrijens | Successful projection of the time course of drug concentration in plasma during a 1-year period from electronically compiled dosing-time data used as input to individually parameterized pharmacokinetic models[END_REF][START_REF] Vrijens | Modelling the association between adherence and viral load in HIV-infected patients[END_REF]. For each patient we estimated, over the 24 weeks of the trial, (i) the number of trough samples below MEC (150 ng/mL) for wild-type viruses (4, 7), and (ii) the cumulative time with concentration below MEC. This information were estimated using first a hypothetical perfect dosing regimen, as if drug was taken every 24h and second using the actual dosing regimen as recorded by MEMS.

CPT Highlights

What is the current knowledge on the topic?

Population pharmacokinetics of CYP3A substrates ritonavir and atazanavir is well understood. Adherence to medication is a key factor in large concentration variability leading to poor treatment outcome.

What question this study addressed?

The study quantifies the relationship between adherence, CYP3A5 genotype, ritonavir and atazanavir pharmacokinetics in HIV-infected treatment-na ve patients.

ï

What this study adds to our knowledge?

Adherence is the major contributor to variability in atazanavir pharmacokinetics. Oral clearance is increased by 28 in patients with a % copy of in ritonavir presence. Optimal boosting effect is achievable by lower ritonavir exposures. CYP3A5 1,

*

How this might change clinical pharmacology and therapeutics?

The atazanavir therapeutic dose can be individualized based on CYP3A5 genotype. If good adherence is achieved, ritonavir dose can be lowered. Real time adherence allows calculation of cumulative drug exposure during a treatment period. TDM using a single plasma sample can be misleading.

= = = = = =

  cost of two additional parameters. The comparison of model fits with both the transit and the first order absorption model with a lag time are shown in Figure 3. The proposed transit compartment model was parameterized in terms of the following parameters: number of transit compartments (NN), mean transit time (MTT) which is the average time for a molecule to reach the absorption site, and absorption rate constant (ka).

  (7 percentile). The schematic view of the proposed model is shown in Figure5. The increase in atazanavir CL for the carriers th of the allele was 28 after inclusion of ritonavir-boosting mechanism. The parameter estimates for the final PKPG model are CYP3A5 1 * %

  in unboosted atazanavir CL/F in healthy volunteers with different CYP3A5 genotypes. Our study confirms their % findings in na ve HIV patients but also provides evidence that this effect is significant in presence of ritonavir and is of same magnitude at ï steady state.

MEMS dosing time recorded

  by MEMS was accurate. The third analysis, which we termed the gold standard analysis (A ),used reliable GOLD " "

Figure 1 Figure 2

 12 Figure 1Observed atazanavir concentration, full profile at week 4 (top) and troughs at various occasions (bottom)

Figure 3

 3 Figure 3Comparison of individual model fits with the transit compartment model and first order absorption model with a lag time for three patients.The best, average and worst fits were chosen based on the median value of absolute individual weighted residuals.

Figure 4

 4 Figure 4 Visual predictive check for the final atazanavir model stratified for different CYP3A5 genotypes: homozygote 3 3 shown in the left panel * * and heterozygote 1 3 and homozygote 1 1 shown in the right panel. Red solid line indicates observed data median, red dotted lines are 95 * * * * % observed percentiles, grey shaded area is the simulated median with uncertainty and dark grey shaded areas are simulated 95 percentiles %

Figure 5 Figure 6

 56 Figure 5 Schematic view of: left, effect of CYP3A5 genotype on ritonavir -atazanavir first pass effect; right, final linked ritonavir atazanavir model.-

  CL/F) atazanavir CL in absence of ritonavir, MTT mean transit time, NN number of transit compartments, ka absorption rate constant, AUC ritonavir exposure needed for half maximal Emax maximal effect of ritonavir boosting, factor of increase in atazanavir CL with at least one copy of CYP3A5 1 allele, RV residual variability

Table 1

 1 Comparison of atazanavir model parameters obtained with three different analyses with respect to dosing histories assumptions. Relative standard errors, expressed in percentages, are given in parenthesis (except for full MEMS where they were not obtained).

	PK Parameters	A : SS assumption ss	A	MEMS	: Full MEMS	A	GOLD	: Gold standard
	CL/F (L/h)	7.2 (4.4)			6.8			6.9 (8.1)
	V/F (L)	79.2 (8.9)			102			81.1 (6.8)
	ka (h ) 1 -	2.7 (26.8)			5.6			3.2 (42.1)
	MTT (h)	1.3 (11.2)			1.5			1.35 (11)
	NN	17.3 (46.7)			8		11.5 (26.4)
	BSV (CL/F) *	47.4 (28.7)			44.3		40.2 (32.7)
	WSV (CL/F) *	26.5 (16.9)			<1			<1
	BSV (V/F) *	30.0 (43.2)			61.4		30.1 (28.5)
	BSV (ka) *	73.5 (47.2)			120		78.4 (73.2)
	BSV (MTT) *	47.4 (28.7)			40.1		45.2 (31.8)
	RV (week 4) *	18.7 (16.9)			27.7		19.4 (15.5)
	RV (> week 4) *	38.0 (33.1)			47.4		43.4 (10.6)

* Note: All BSV, WSV and RV are expressed as CV ( ). % BSV Between-subject variability, WSV Within-subject variability, RV Residual variability, MTT mean transit time, NN number of transit compartments, ka absorption rate constant

Table 2

 2 Model parameter estimates for the final ritonavir (left column) and joint ritonavir-atazanavir (right column) PK-PG model using a gold standard analysis. Relative standard errors, obtained by nonparametric bootstrap (n 100) and expressed in percentages, are given in parenthesis.

	=
				Ritonavir	Atazanavir
	CL/F (L/h)			10.3 (9)	16.0 (64) **
	β CYP3A5 1 *			-	1.28 (59)
	AUC of RTV (ng.h/mL) 50	-	6,230 (91)
	E max			-	0.98 (3)
	V/F (L)			87.9 (11)	81.1 (6)
	ka (h ) 1 -			3.9 (58)	3.3 (146)
	MTT (h)			1.1 (16)	1.36 (14)
	NN			14.4 (95)	11.5 (29)
	BSV (CL/F) *			38.5 (33)	31 (28)
	BSV (V/F) *			37.3 (50)	31 (33)
	Correlation (CL/F-V/F)	0.74 (45)	-
	BSV (ka) *			248 (161)	81 (133)
	BSV (MTT) *			49.3 (77)	44 (39)
	RV week 4 ( ) %	*		40.8 (8)	19.4 (16)
	RV > week 4 ( ) %	*	40.8 (8)	42.3 (10)

* BSV Between-subject variability, RV Residual variability,

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

[START_REF] Bae | Medication persistence in the treatment of HIV infection: a review of the literature and implications for future clinical care and research[END_REF]

Acknowledgements:

We thank all the patients who participated in the ANRS 134 -COPHAR 3 trial. We thank Bristol-Myers Squibb and Abbott laboratories for providing atazanavir and ritonavir pure samples for drug assay, respectively. Radojka Savic was financially supported by a Postdoc grant from the Swedish Academy of Pharmaceutical Sciences (Apotekarsocieteten).

ANRS 134 -COPHAR 3 study group


W J Lafferty

J.-M Flaud

F Kwabia Tchana

The high resolution infrared spectrum of ethylene in the 1800 cm -1 to 2350 cm -1 spectral region

Keywords: Infrared, Ethylene, Rovibrational interactions, line positions and intensities

Fourier transform spectra of ethylene (C 2 H 4 ) have been recorded in the 1800 cm -1 to 2350 cm -1 (4.3 µm to 5.6 µm) spectral region using a Bruker IFS125HR spectrometer at a resolution of 0.004 cm -1 leading to the observation of six vibrational bands, ν 7 + ν 8 , ν 4 + ν 8 , ν 6 + ν 10 , ν 6 + ν 7 , ν 4 + ν 6 and ν 3 + ν 10 . The corresponding upper state ro-vibrational levels were fit using a Hamiltonian matrix accounting for numerous interactions. A satisfactory fit could be obtained using a polyad of nine interacting states {8 1 10 1 , 7 1 8 1 , 4 1 8 1 , 8 1 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 } among which three (8 1 10 1 , 8 1 12 1 and 3 1 7 1 ) are unobserved dark states. As a result a much more accurate and extended set of Hamiltonian constants were obtained than previously derived. The following band centers were determined: ν 0 (ν 7 + ν 8 ) = 1888.9783(20) cm -1 , ν 0 (ν 4 + ν 8 ) = 1958.2850(20) cm -1 , ν 0 (ν 6 + ν 10 ) = 2047.7589(20) cm -1 , ν 0 (ν 6 + ν 7 ) = 2178.011(60) cm -1 , ν 0 (ν 4 + ν 6 ) = 2252.8026(24) cm -1 and ν 0 (ν 3 + ν 10 ) = 2171.2397(20) cm -1 . Finally, a synthetic spectrum which could be useful for ethylene detection in planetary atmospheres was generated.

Ethylene (C 2 H 4 ) is observed in the terrestrial atmosphere as a tropospheric pollutant produced by automobiles, forest fires and plant life [1]. In the atmosphere, photochemical reactions with molecular oxygen, the hydroxyl radical, and ozone produce formaldehyde, nitrous oxide, and formic acid [2]. C 2 H 4 is also detected in the atmospheres of the outer solar system bodies including Jupiter [3], Saturn [4], and Neptune and Titan [5][6][7]. In these atmospheres it is a by-product of methane photochemistry. Spectroscopically, ethylene is an asymmetric top molecule which has been the subject of a number of studies concerning either the normal isotopic species 12 C 2 H 4 or the 13 C 12 CH 4 istopomer. However these studies dealt mainly with the 10 µm region bands, where the strongest band is the C-type ν 7 band [8-10 and ref. therein, 11-12]. Nevertheless, prior to this work, only small portions of the 4.3 µm to 5.6 µm region, corresponding to the ν 7 + ν 8 and ν 4 + ν 8 bands have been analyzed [13][14][15]. More recently, three high-resolution infrared and Raman spectra of 12 C 2 H 4 were recorded and analyzed: the ν 12 band near 1450 cm -1 [16], the 2ν 10 overtone symmetric motion located around 1664 cm -1 [17] and the C-H stretching vibrations in the 3000 and 6000 cm -1 regions [18].

In this paper, we present an extensive analysis of the 4.3 µm to 5.6 µm region and have assigned six vibrational bands, ν 7 + ν 8 , ν 4 + ν 8 , ν 6 + ν 10 , ν 6 + ν 7 , ν 4 + ν 6 and ν 3 + ν 10 . This was carried out using two high-resolution Fourier transform spectra recorded at two different pressures in order to obtain precise line position for both the weak as well as the strong bands.

The upper state ro-vibrational levels were fit using a Hamiltonian (written in the I r (x = b, z = a, y = c) representation) model taking into account the numerous interactions affecting them. We note that it was necessary to consider interactions not only between levels of the observed states but also with levels of unobserved dark states. In this way a satisfactory fit was performed leading to Hamiltonian constants much more accurate than obtained in previous studies even though the accuracy of the fits was slightly worse than the experimental uncertainties. The ethylene (C 2 H 4 ) molecule possesses D 2h symmetry and its structure as well as its symmetry properties and nuclear spin statistical weights are illustrated in Figure 1. According to the Bruker definition (Resolution = 0.9/d MOPD ) this corresponds to a resolution of 0.004 cm -1 . This resolution is limited by the Doppler widths which is equal to 0.0042 cm -1 at 1800 cm -1 .

The White-type multipass absorption cell, made of pyrex glass and equipped with CsBr windows, was connected to the Fourier transform spectrometer with a dedicated optical interface (six mirrors) inside the back sample compartment of the Bruker spectrometer. Its base length is 0.80 m, and, for the experiment described here, an optical path of 19.2 m was used. The ethylene sample was purchased from Sigma Aldrich. The chemical purity of ethylene was specified to 99.99 % and was used without further purification. The following procedure was used for measurements: First a background spectrum was collected while the cell was being continuously evacuated. Next a calibration spectrum was recorded with carbonyl sulfide (high purity sample at low pressure). The absorption cell was then evacuated, and flushed several times with dry nitrogen until the base pressure of the cell 1.3 x 10 -3 Pa (10 -5 Torr) was achieved. Two ethylene 1 Certain commercial equipment instruments or materials are identified in this paper to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. Torr). Sample pressure in the cell was measured using a calibrated MKS Baratron capacitance manometer (266 Pa full scale) which has a stated uncertainty of 0.12 % of full scale, according to the manufacturer. The spectra were recorded at a stabilized room temperature of 22°C. Both spectra were ratioed against the empty cell, single-channel background spectrum which was taken at a resolution of 0.512 cm -1 , in order to ensure the best possible signal-to-noise in the ratioed spectra. The spectra were the result of the co-addition of 550 interferograms. For the Fourier transform a Mertz-phase correction, 0.5 cm -1 phase resolution and boxcar apodization function were applied to the averaged interferograms. The spectra were calibrated using OCS lines from HITRAN08 [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF] resulting in an accuracy of 0.00012 cm -1 (RMS) for well isolated lines. Fig. 2 gives an overview of the ethylene spectra showing the high signal-to-noise ratios which were obtained. The distinctive shape of the two A-type ν 7 + ν 8 (around 1889 cm -1 ) and ν 6 + ν 10 (around 2047 cm -1 ) bands with their narrow Q-branches are clearly visible.

Assignments and results.

The line assignment process proved to be very difficult since a number of bands fall in the 4.3 µm to 5.6 µm region and the number of ro-vibration interactions is high. This includes interactions not only between the levels of the observed states but also with dark state levels. We initially started the assignment process dealing with the strong ν 7 + ν 8 band, but, as pointed out in refs. [13][14][15], it soon became obvious that its transitions are strongly perturbed by ν 4 + ν 8 transitions through a C-type Coriolis interaction via the ξ a 7,10 and ξ b 4,10 Coriolis interaction terms [10]. In addition, we observed other interactions with the 8 1 10 1 and 8 1 12 1 energy levels which correspond with what has been observed at 10 µm where the polyad of interacting states {10 1 , 8 1 , 7 1 , 12 1 } was considered. Using a Hamiltonian matrix taking into account the necessary interaction terms, it was possible to assign many lines of ν 7 + ν 8 and ν 4 + ν 8 . During this process, it became very clear that the ro-vibrational levels of 4 1 8 1 and 7 1 8 1 are also perturbed by nearby rotational levels from bands belonging to other polyads [13]. We then started to assign transitions belonging to these other bands: ν 6 + ν 10 , ν 6 + ν 7 , ν 4 + ν 6 and ν 3 + ν 10 . This was done with the aid of a Hamiltonian matrix including the observed states as well as some resonating dark states (Fig. 3, Table 1). The assignment process was repeated until it was no longer possible to locate and assign new lines with confidence. The range of the assigned energy levels for each band is given in Table 2. Even if the experimental accuracy (ca. 0.0002 cm -1 for isolated lines) is not reached, given the fact that there are numerous resonances and that it was necessary to include dark states in the calculations, we feel that the fit is rather satisfactory, since the standard deviation is 0.002 cm -1 with a maximum difference of 0.016 cm -1 (see Table 2 for further details). The corresponding Hamiltonian constants can be found in Table 3.

Intensity measurements.

The intensity of a line is given in cm -1 /(molecule.cm -2 ) by [START_REF] Flaud | Water Vapour Line Parameters from Microwave to Medium Infrared[END_REF][START_REF] Camy-Peyret | Vibration-rotation dipole moment operator for asymmetric rotors[END_REF]:

( ) B A A n N R kT hcE kT hc g T hcZ k       -               - - = exp ẽxp 1 3 4 8 0 3 ~ν πε ν π ν (1)
where A and B are respectively the lower and upper levels of the transition, ν

~= (E B -E A )/hc is the wavenumber of the transition, Z(T) is the total partition function depending on the temperature (we used Z(296K) = 44165.84 [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF]) and g n is the nuclear spin statistical weight.

Finally, B

A R is the square of the matrix element of the transformed transition moment operator

' Z µ . ' Z µ is expanded as: ' v Z v ' B ' v 0 ' Z µ ∈ = µ ∑ (2)
where v' belongs to the upper B' polyad of interacting states.

Then depending on the band symmetry the transition moment operators can be written [START_REF] Flaud | Water Vapour Line Parameters from Microwave to Medium Infrared[END_REF]:

{ } 5 1 , x v y z x v x Z v iJ µ ϕ µ ϕ µ + = +.
..??????????? for a B-type band

.... 5 y v x J , z 1 y v y i Z v + µ       ϕ + µ ϕ = µ for a C-type band ??? (3) .... 4 z v x J , y i y iJ , x 2 1 1 z v z Z v + µ             ϕ -       ϕ + µ ϕ = µ
for an A-type band where φ x , φ y and φ z stand for the direction cosines Φ Zx , Φ Zy and Φ Zz respectively.

The transition moment constants (see Eqs.( 3)) are determined through a least squares fit of the experimental line intensities. Using the low pressure spectrum, 264 line intensities were measured (39, 94, 49, 11, 29 and 42 lines for ν 7 + ν 8 , ν 4 + ν 8 , ν 6 + ν 10 , ν 6 + ν 7 , ν 4 + ν 6 and ν 3 + ν 10 respectively.) and fit using Eq.(1-3). The fit is satisfactory since 71% of the experimental line intensities were calculated to within 7% with a maximum discrepancy of 28%. Finally the absolute intensities were calibrated using the PNL (Pacific Northwest Laboratory) measurements [START_REF] Sharpe | [END_REF]. In this way it was possible to determine the transition moment parameters gathered in Table 4. These parameters together with the wavefunctions derived from the diagonalization of the Hamiltonian matrix were used to generate a list of line positions and intensities (Cut off of 1.5 X 10 -24 cm -1 /(molecule.cm -2 ) at 296K) 2 . Fig. 2 presents a simulation of the whole spectral region performed using this line list: one notes the very good agreement between the observed and calculated spectra.

Discussion

As found previously [13] as well as observed in this work, a large number of resonances perturb the ro-vibrational levels of the polyad of interacting states {8 1 10 1 , 7 1 8 1 , 4 1 8 1 , 8 1 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 }. We describe them here in some detail in order to demonstrate the resonance scheme used to build the Hamiltonian matrix. 2 The list of line positions and intensities is available upon request to J.-M. Flaud or W. J.

Lafferty.

γ γ γ ′ ′ ′ ′ = ′ ′ ′ ∑ ∑ ′ ∈ ′ ′ ′ ′ ′ ′ K J v C K K J v P v K v K c a i , ' , (2)
where the are the classical Wang-type functions:

( )

K J JK JK - + = γ γ 2 1 (for 1 , 0 ± = ≠ γ K ) (3) 0 1 0 J JK = + = = γ
and where P' is the polyad of interacting upper states {8 1 10 1 , 7 1 8 1 , 4 1 8 1 , 8 1 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 }. Then the mixing coefficients of the ro-vibrational level I J' onto the state can be defined as 100

2 ' × ∑ ′ ′ ′ K v K C
where the are the coefficients appearing in Eq.( 2). Fig. 4 presents the mixing coefficients of the µm between the levels of 7 1 and 4 1 . On the other hand, we have also observed very localized resonances linking ro-vibrational levels belonging to different polyads of interacting states. For example, the 8 0 8 level of the 6 1 7 1 state which gives rise to the forbidden band ν 6 + ν 7 (A u symmetry species, Fig. 1) is observed only because it resonates (mixing coefficient of 18%) with the 8 1 7 level of 3 1 10 1 . In fact, all the transitions involving 8 0 8 borrow their intensities from those involving 8 1 7 . Fig. 5 presents a portion of the spectrum where the forbidden transition 8 0 8 -9 2 8 of ν 6 + ν 7 is clearly observable together with the allowed transition 8 17 -9 2 8 of ν 3 + ν 10 .

As far as the intensities are concerned we estimated an accuracy of about 5%. Figures 5, 6 behavior is due to the interactions between the corresponding upper levels (see the mixing coefficients in Fig. 4). Finally Fig. 8 presents the band intensities derived from the calculations.

One can see that the ν 3 + ν 7 and ν 8 + ν 12 bands are, as discussed previously, very weak.

Summary.

Using high-resolution Fourier transform spectra an extensive analysis of the 1800 cm -1 to 2350 cm -1 spectrum of ethylene ( 12 C 2 H 4 ) has been performed. The upper state energy levels have been fit to within 2 x 10 -3 cm -1 using a Hamiltonian matrix which takes into account the numerous interaction terms coupling the interacting states {8 1 10 1 , 7

A g 1 1 1 1 1 1 1 1 ν 1 ,ν 2 ,ν 3 A u 1 1 1 1 -1 -1 -1 -1 ν 4 B 1g 1 -1 1 -1 1 1 -1 -1 R y ν 5 ,ν 6 B 1u 1 -1 1 -1 -1 -1 1 1 T y ν 7 B 2g 1 1 -1 -1 1 -1 1 -1 R x ν 8 B 2u 1 1 -1 -1 -1 1 -1 1 T x ν 9 ,ν 10 B 3g 1 -1 -1 1 1 -1 -1 1 R z B 3u 1 -1 -1 1 -1 1 1 -1 T z ν 11 ,ν 12
Nuclear spin statistical weights for the ground state rotational levels

3 1 1 0 1 B 2 u 4 1 8 1 B 2 u 6 1 1 0 1 B 3 u 6 1 7 1 A u 4 1 6 1 B 1 u 8 1 1 2 1 B 1 u 7 1 8 1 B 3 u
E n e r g y ( c m M i x i n g C o e f f i c i e n t ( % ) Obs. C a l c . Table 2. Range of quantum numbers observed for experimental energy levels of the vibrational states {7 1 8 1 , 4 1 8 1 , 6 1 10 1 , 3 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 } of ethylene and statistical analysis of the results.

Calc. Absorbance

Table 3. Vibrational band centers, rotational and anharmonic and Coriolis interaction constants (in cm -1 ) for the ground state and the {8 1 10 1 , 7 1 8 1 , 4 1 8 1 , 8 1 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 } interacting states of ethylene.

Footnotes:

a Ground state values from ref. [1].

b Uncertainties are given in parentheses in units of the last significant digits as stated, in terms of one standard deviation σ in the least squares adjustment. c Fixed at ground state values. d For the sake of clarity, we give here the operator rather than the corresponding constant.

Footnote:

a Uncertainties are given in parentheses in units of the last significant digits as stated, in terms of one standard deviation σ in the least squares adjustment.

F C B C C H W 3 1 10 1 C C C B H W Herm conj 3 1 7 1 C A H W v-diagonal operators: ( ) [ ] ( ) ( ) 2 xy v v 2 1 2 v v 2 1 2 z v v 2 1 v v W J C B J C B J C B A E H - + + + + - + = ( ) { } 2 2 xy v J 2 xy 2 z v K 2 2 v J 2 2 z v JK 4 z v K J 2δ J , J δ ∆ J ∆ J ∆ J J J - - - - - ( ) ( ) 3 2 v J 2 2 2 z v JK 2 4 z v KJ 6 z v K H J H J H J H J J J + + + + { } { } ( ) 2 2 2 y x v J 2 2 xy 2 z v KJ 2 xy 4 z v K J 2h J , J h J , J h J J + + + ( ) ( ) ( ) 4 2 v J 3 2 2 z v JJK 2 2 4 z v KJ 2 6 z v KKJ 8 z v K L J L J L J L J L J J J J + + + + + { } { } { }( ) ( ) 3 2 2 y x v J 2 2 2 xy 2 z v JK 2 2 xy 4 z v KJ 2 xy 6 z v K J 2l J , J l J , J l J , J l J J J + + + + ... J P J P J P 4 6 z v KKJ 2 8 z v KKKJ 10 z v K + + + + J J v-off-diagonal operators: F = F 1 h + F 2 h J 2 + F 3 h J z 2 + F 4 h J xy 2 +… C A = A 1 h J z + A 2 h {i J y , J x }+… C B = B 1 h J x + B 2 h {i J y , J z }+ … C C = C 1 h i*J y + C 2 h {J x , J z }+… with { } BA AB B A + = , , y

  The high-resolution absorption spectra of ethylene were recorded with the Bruker IFS125HR Fourier transform spectrometer1 (an upgraded version of the IFS120HR) located at the LISA facility, in Créteil. A KBr beamsplitter, Globar source (Silicon Carbide, SiC) and a liquid nitrogen-cooled Indium Antimonide (InSb) detector were employed for these experiments. The optical path of the spectrometer was continuously evacuated to below 6.7 Pa (0.05 Torr) for the duration of all spectral measurements. Spectra were recorded with an aperture diameter of 1.3 mm, 40 kHz scanner frequency, and a maximum optical path difference (d MOPD ) of 225 cm.

  recorded with 16.41 (1) Pa (0.1231 (1) Torr) and 65.97 (8) Pa (0.4948(6)

8

 8 Field Code Changed Formatted: Indent: First line: 0 pt Formatted: Font: 12 pt, Not Superscript/ Subscript Formatted: Font: Times New Roman, 12 pt, Not Superscript/ Subscript Formatted: English (U.S.), Not Superscript/ Subscript Deleted: ¶ Page 7 of 27 URL: http://mc.manuscriptcentral.com/tandf/Once the Hamiltonian matrix has been diagonalized, the wave function of a ro-vibrational level can been determined as:

=

  levels onto the 41 81 and the 4 1 6 1 states. While the mixing coefficients of both level series vary smoothly, differences are observed even if the mechanism is identical, i.e. a C-type Coriolis interaction. In particular the crossing of levels happens at different values: J = 9 and J = 12 for 7 1 8 1 and 6 1 7 1 respectively. Such resonances are analogous to those observed at 10

and 7 9 ν 7 +

 797 show comparisons of the observed and calculated spectra. The good agreement between observation and simulation demonstrates the quality of the analysis and the fitting. Of particular interest is Fig.6where one can see on both sides of the central part of the Q-branch region of ν 8 series of lines concerning the Ka = 8 (Ka = 7) transitions of ν 7 + ν 8 (ν 4 + ν 8 ). Such a

Fig. 1 .Fig . 2 .Fig. 3 Fig. 4 .

 1234 Fig. 1. Structure and symmetry properties of the ethylene molecule.Fig . 2. Overview of the ethylene spectrum studied in this work. The distinctive shape of the two A-type bands ν 7 + ν 8 and ν 6 + ν 10 with their narrow Q-branches are clearly recognizable. Upper trace: observed spectrum recorded with a resolution of 0.004 cm -1 and an optical path length of 19.2 m, at a C 2 H 4 pressure of 16.41 (1) Pa (0.1231 (1) Torr) and a stabilized room temperature of 22 °C. Lower trace: synthetic spectrum, calculated at the same experimental conditions using the line list generated in this work. The observed and synthetic spectra are in absorbance (-ln(I/I 0 )) and shifted vertically for clarity.Fig. 3 Resonating scheme of the ro-vibrational levels of ethylene in the 1700 cm -1 to 2400 cm -1 region. Fig. 4. Mixing coefficients of the K a = 8 rotational levels of the 7 1 8 1 , 6 1 7 1 states onto the 4 1 8 1 , 4 1 6 1 states respectively.

Fig. 5 .( 1 )Fig. 6 . 13 Fig. 7 .( 1 )

 5161371 Fig. 5. A transition of the forbidden ν 6 + ν 7 band. This transition appears only because of borrowed intensity from the permitted ν 3 + ν 10 line. Upper trace: observed spectrum recorded with a resolution of 0.004 cm -1 and an optical path length of 19.2 m, at a C 2 H 4 pressure of 16.41 (1) Pa (0.1231 (1) Torr) and a stabilized room temperature of 22 °C. Lower trace: synthetic spectrum, calculated at the same experimental conditions using the line list generated in this work. The observed and synthetic spectra are in absorbance (-ln(I/I 0 )) and shifted vertically for clarity. Fig. 6. Q-branch area of the ν 7 + ν 8 band. Because of the strong resonance (Fig. 4) the K = 8 line of ν 7 + ν 8 and the K = 7 perturbation induced transitions of ν 4 + ν 8 are degraded in opposite directions. Upper trace: observed spectrum recorded with a resolution of 0.004 cm -1 and an optical path length of 19.2 m, at a C 2 H 4 pressure of 16.41 (1) Pa (0.1231 (1) Torr) and a stabilized room temperature of 22 °C. Lower trace: synthetic spectrum, calculated at the same experimental conditions using the line list generated in this work. The observed and synthetic spectra are in absorbance (-ln(I/I 0 )) and shifted vertically for clarity.

  Fig.1

2 K a = 8 t r a n s i t i o n s o f ν 7 + ν 8 1

 28 Fig.5

8 Q -b r a n c h r e g i o n o f ν 7 + ν 8 K a = 7 p e r t u r b a t i o n i n d u c e d t r a n s i t i o n s o f ν 4 + ν 8 O 6 Fig. 7 Page

 88867 Fig.7

φ z x 10

 10 φ x ,iJ y }-{i φ y ,J x }

  1 8 1 , 4 1 8 1 , 81 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 }. In this way, accurate band centers, rotational, centrifugal distortion and coupling constants have been determined. Also individual line intensities as well as total band intensities have been measured and fit satisfactorily, and an accurate list of line positions and intensities has been generated.

	F o F o F o
	r r r
	P P P
	e e r e e r e e r
	R e v i e w R e v i e w R e v i e w
	O n O n O n
	l y l y l y

12

Captions to figures:

Table 1 .

 1 Hamiltonian matrix used to calculate the {8 1 10 1 , 7 1 8 1 , 4 1 8 1 , 8 1 12 1 , 6 1 10 1 , 6 1 7 1 , 4 1 6 1 , 3 1 10 1 , 3 1 7 1 } interacting states of ethylene.

	8 1 1 0 1
	F i g . 8

URL: http://mc.manuscriptcentral.com/tandf/tmph

Table 4 .

 4 Transition moment constants (in Debye) for the ν 7 + ν 8 , ν 4 + ν 8 , ν 6 + ν 10 , ν 4 + ν 6 and ν 8 + ν 10 bands of ethylene.

Table 1 .

 1

	Page 22 of 27

Table 2 .

 2

	Page 23 of 27										Molecular Physics
	J	±	=	J	x	m	iJ	and	J	2 xy	=	J	2 x	-	J	2 y	.

URL: http://mc.manuscriptcentral.com/tandf/tmph URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics F o r P e e r R e v i e w O n l y

Table 3 .

 3

		0 0	8 1 10 1	7 1 8 1	4 1 8 1	8 1 12 1
	E v /hc		1765.603 (31) b	1888.9783 (20) b	1958.2850 (20) b	2369.72 (130) b
	A	4.86462016 a	4.789826 (440)	4.70879 (130)	4.68617 (300)	4.875 (140)
	B	1.00105650	1.003269 (230)	0.9952615 (460)	0.992108 (120)	1.04244 (820)
	C	0.82804599	0.821647 (220)	0.830599661 (860)	0.8302158 (110)	c
	∆ K x 10 4	0.864798	0.69506 (9900)	0.57329 (3700)	0.23714 (1700)	c
	∆ JK x 10 4	0.1023214	c	c	c	c
	∆ J x 10 5	0.1470224	c	0.1405264 (1400)	0.233635 (3600)	c
	δ K x 10 4	0.101590	c	0.23497 (2400)	0.68669 (3600)	c
	δ J x 10 6	0.281684	c	0.283051 (8900)	0.61546 (4200)	c
	H K x 10 8	0.6196	c	c	c	c
	H KJ x 10 9	-0.424	c	c	c	c
	H JK x 10 9	0.1845	c	c	c	c
	H J x 10 11	0.2501	c	c	c	c
	h K x 10 8	0.346	c	c	c	c
	h KJ x 10 9	0.1138	c	c	c	c
	h J x 10 11	0.1098	c	c	c	c
		6

1 10 1 6 1 7 1 4 1 6 1 3 1 10 1 3 1 7 1

	Page 25 of 27
	E v /hc	2047.7589 (20) b	2178.011 (60) b	2252.8026 (24) b	2171.2397 (20) b	2285.048 (50) b
	A	4.94859 (210)	5.0754 (250)	4.902101 (240)	4.89652 (320)	4.93033 (300)
	B	1.00580 (220)	0.99400 (170)	0.99557 (220)	0.9844828 (710)	0.99517 (450)
	C	0.8232976 (140)	0.82334 (200)	0.8244953 (270)	0.8274741 (180)	c
	∆ K x 10 4	1.3271 (2100)	2.799 (1000)	0.62587 (9500)	0.3000 (1200)	c
	∆ JK x 10 4	-0.27411 (6800)	c	0.78471 (9300)	c	c
	∆ J x 10 5	0.153455 (8300)	c	0.15844 (1500)	0.07439 (3100)	c
	δ K x 10 4	c	c	0.22507 (6900)	0.19622 (9400)	c
	δ J x 10 6	0.33335 (4700)	c	0.33426 (8900)	-0.1496 (1000)	c

URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics F o r P e e r R e v i e w O

n l y Coupling constants d Operator <7 1 8 1 |8 1 10 1 > <8 1 12 1 |4 1 8 1 > <6 1 7 1 |6 1 10 1 > <3 1 7 1 |3 1 10 1 >

								J z					-4.47108 (4300) -3.825 (1600)	-3.6308 (3800)	-4.59692 (3900)
			{	i	J	y	,		J	x	}	×	10	3	-7.2682(1900)	-12.2157 (7000)
				J	z	J	2	×	10	4	-2.7184 (1300)
			{	J	z	,	J	xy 2	}	×	10	4	-4.1497 (8000)
	{	{	i	J	y	,	J	x	} ,	J	z 2	} 10 ×	6	6.647 (2500)	46.02 (1200)
						J	3 10 × z	3	-1.91320 (7200)
					Operator	<4 1 8

1 |8 1 10 1 > <8 1 12 1 |7 1 8 1 > <4 1 6 1 |6 1 10 1 > <3 1 10 1 |6 1 7 1 >

							J x			1.789851(7200) 1.705810(7700)	2.0381(1100)	-0.0012311(4000)
	{	i	J	y	,	J		z		} 10 ×	2	-4.3918 (1800)	-9.4562(3400)	-3.5923(2300)
			J	x	J	2	×	10	5	-6.536(2900)
	{	J	x	,	J		} 2 × z	10	3	-1.1786(2300)
	(	J	3 -	+	J	3 +	)	×	10 5	2.2733 (4000)
			Operator	<4 1 8

1 |7 1 8 1 > <4 1 6 1 |6 1 7 1 > <3 1 10 1 |6 1 10 1 > <6 1 10 1 |4 1 8 1 >

															Molecular Physics	Page 26 of 27
			(	J	3 -	-		J	3 +	)	×	10	5	-1.6251(1500)	-4.5424(9700)	2.9109(5200)	-2.1243(5300)
		J	2	(		J	3 -	-	J	3 +	)	×	10	9	2.477(1400)
						Operator	<6 1 10 1 |7 1 8 1 >	<4 1 6 1 |8 1 12 1 >
				J 2 x 10 3 3 2 10 × J xy F o r P e e r R e v i e w O n l y -6.0037(4700) -2.0718(3100) { } 10 J J xy z 5 2 2 , × 9.743(1900)
										J i y	-0.247161(8600)
			{	J	x	,	J	z		} 10 ×	2	-1.3048(2600)	-1.7127(1800)	4.7478(2600)
	{	{	J	x	,	J	z	} ,	J	z 2	} 10 ×	6	9.938(1900)
		{	J	x	,	J	z	} J × 2	10 6	-4.5131(8300)

URL: http://mc.manuscriptcentral.com/tandf/tmph

Table 4 .

 4 Operator ν 7 + ν 8 ν 4 + ν 8 ν 6 + ν 10 ν 4 + ν 6 ν 6 + ν 10

URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics

Acknowledgements

The portion of this work which was carried out at the Optical Technology of NIST was supported by the Upper Atmospheric Research Program of NASA. One of authors (JMF) thanks the Optical Technology Division for support during a stay at NIST.


Keywords: fistuleuse, forage, Monaco, paléosismicité, spéléothème borehole, Monaco, paleoseismicity, sodastraw, speleothem

Monaco is a medium seismicity zone. The Cave of Observatoire, a well decorated show cave, is a good place for paleoseismicity studies. On the floor of the cave it is possible to observe a great number of collapsed sodastraws. The breakages are attributed to the 1887 ligurian earthquake. A bore hole in a flowstone shows several levels of collapses that may indicate ancient earthquakes.

to cite this paper : GILLI E., 1999 -Evidence of paleoseismicity in a flowstone of the Observatoire cave (Monaco). Geodinamica Acta,vol 12,[3][4] contact : e.gilli@wanadoo.fr 8, place Garibaldi 06300 Nice FRANCE ------------------------------------------------------------------------------------------------------------------------Han 98 -Tectonics, karst and seisms Evidence of paleoseismicity in a flowstone of the cave of the Observatoire (Monaco). Indices de paléosismicité dans un plancher stalagmitique de la grotte de l'Observatoire (Monaco) Eric GILLI

RESUME:

La grotte de l'Observatoire, située au coeur de la Principauté de Monaco, est une cavité d'origine tectonique très concrétionnée. Elle est placée dans un environnement favorable aux recherches de paléosismicité. Les séismes de magnitude inférieure à 3 sont fréquents dans ce secteur mais des épisodes plus importants sont connus. Dans la grotte, de nombreuses chutes de fistuleuses sont attribuables au séisme ligure de 1887 durant lequel des dégâts d'intensité VII ont été signalées à Monaco. Un forage carotté a été réalisé dans un plancher stalagmitique pour y rechercher des traces de séismes anciens. L'examen d'une coupe révèle plusieurs niveaux de chutes, probablement témoins de séismes inconnus. Une datation du niveau de chute au 14 C donne un âge supérieur à la limite de la méthode.

-PRESENTATION

-Description and history

The Cave of the Observatoire (fig. 1) is located in the Rock of the Exotic Garden in Monaco. The entrance was closed but it was excavated for archeological purpose and new parts were then discovered. In 1948, the cave was adapted for tourism. The entrance of the cave is a narrow descending gallery that is partially artificial. It goes to a depth of 50 m to a group of very well decorated large rooms. Before the rooms, a lateral gallery goes to a deeper zone, where, after a series of narrow passages, it is possible to reach the water table at a depth of 80 m (Gilli and Mangan, 1989). 1.2. -Regional structural context. Monaco unit, where the cave is located, belongs to the south-western front of the "Arc de Nice" subalpine chains, whose settlement results from the rising up of Argentera-Mercantour (Alps) and the detachment of its sedimentary belt over Triassic clays during alpine orogenesis. This flexible architecture with parallel overthrusting units is complicated by a plio-quaternary shortening that caused extrusion of the Jurassic blocks inside the cretaceous masses; this increased the tectonic cut of sedimentary series by renewed moving of the different fault families.

The structural features of Monaco area were influenced by large sinistral strike-slip faults that formed lateral pitches during the arriving of alpin overlaps and by the presence of front-country shallows that formed front buffers [START_REF] Mangan Ch | Etude hydrogéologique de la Principauté de Monaco[END_REF].

-Geological description of the cave:

The cave is in a narrow limestone block which is limited by a thrust fault, at the southern part and by a vertical fault at the northern part. This tiny block that has moved several times during its geological history is now intensely fractured. The different parts of the cave are aligned on a tectonic canvas ( fig. 2) A more precise study should be done but it is probable that this cave is of tectonic origin. The voids are individualized between two faulted planes that surround a crushed zone (fig. 3). The rocks of the crushed zone migrate toward the bottom of the cave. This may be caused by dissolution in the karstic water table. Renewed movement of the faults may also explain the rocks migration.

-SEISMOTECTONIC ANALYSIS

-Historical seismicity

Like the whole of the Côte d'Azur area, the Principalty of Monaco is considered a medium seismicity area that is periodically shaked by small earthquakes. The last destructive one was the Ligurian earthquake in 1887 (fig. 4). The estimated magnitude was 6 -6.5 . It caused damage in Monaco with an intensity greater than VII [START_REF] Lambert | Les tremblements de terre en France[END_REF]. The last important earthquake was a Ms 4.7 one in February 1995. The epicenter was in the sea, south to Monaco.

Monaco was probably affected by the most important Provence earthquakes in 1494, 1564, 1618, 1644, [START_REF] Levret-Albaret | Mille ans de séismes en France[END_REF], but it is difficult to evaluate the damages and the local intensity as the population was not important at this time.

Study of underground damages.

In the cave there is evidence of damage to stalagmites and calcite pillars. These had first been attributed to subsidence as the cave is filled with crumbled-down rocks. A more precise inspection revealed a great number of collapsed sodastraws and small stalactites in places where subsidence is not possible. Sodastraws are fixed on the flowstone and sometimes inside a calcite coating (phot. 1). The thickness of the coating and the location of some sodastraws prove that these damages were not caused by human presence. The cave was virgin until the beginning of the works in 1946 and the damages caused by the works are not yet covered with new calcite.

Phot. 1: Fragments of collapsed sodastraws on a flowstone in the cave of the Observatoire (Monaco). Fragments de fistuleuses sur un plancher stalagmitique de la grotte de l'Observatoire (Monaco).

The collpases of sodastraws may be caused by a seismic shake. This was described in Turkey (Gilli, 1995) and in St Paul-de-Fenouillet (France) [START_REF] Delange | Recherche des effets du séisme du 18 février 1996 sur les cavités karstiques de la région de St Paul de Fenouillet[END_REF]. Other causes of breakage are however possible:

-action of cave bears, but no signs of these animals were found in the cave, -action of men, but the cave was closed before the fitting works and most of the places are difficult to reach, -subsidence when clay is washed out below stalagmites, but here, the formations are not founded on clay, -waterflows in phreatic active caves, but there is no water flow in the cave -movements of cave filling-in, but there is no sign of important filling-in. As these different points are eliminated, it is possible that the damages observed in Monaco cave were caused by the ligurian earthquake in 1887. This hypothetical age is only based on the light calcite coating that could indicate a recent age. A more precise dating has to be done (uranium series and 14 C).

-Research of ancient damage.

Since this cave has a tectonic origin and is located on a limestone crest, it is a good place to look for ancient signs that are fossilised in flowstones (fig. 5). Furthermore, the cave was virgin and the speleothems were already damaged when the cavers arrived in the rooms. We have done several bore holes below well decorated ceilings. We have looked for basin-shaped places that could have collected collapsed sodastraws. The difficulty was to estimate the underground shape of the basins. For instance, if the substructure of a present basin was a declivous flowstone, the collapsed sodastraws have rolled out of the bore hole place.

Phot. 2:

The drilling machine used for the bore hole in the flowstone in the cave of the Observatoire (Monaco) La machine de forage utilisée pour le sondage dans le plancher stalagmitique de la grotte de l'Observatoire (Monaco) Phot. 3: Flowstone sample collected in the cave of the Observatoire (Monaco). Echantillon prélevé dans le plancher de la grotte de l'Observatoire (Monaco);

A drilling machine was loaned by oceanographic Museum of Monaco (phot. 2). The equipment was able to collect samples 15 cm large and 50 cm long. Three drills were realised but only one was totally successful (phot. 3). The sample was cut and polished.

On the section, several levels of collpased sodastraws are visible (fig. 6, phot. 4). At the top, a sodastraw, that was visible on the flowstone, is partially covered with a 6 mm thick calcite coating. If the cause of the breakage is the 1887 earthquake this amount was produced in 100 years. 3 cm below the top, a second level shows only one soda straw. At 9 cm, there is the top of a cave formation which is probably a small stalagmite as there is no central pipe but a little stone heart. At 17 cm, 3 objects could be pisolites (cavern pearls) At 18 cm, a stalactite is visible and an object that could be a simple stone, is visible on the side of the sample. We observe then several sodastraws from 18.5 cm to 21 cm. They appear to be organised in three levels, but it is possible that there is only one level. A 1 to 3 cm thick beige calcite bed separates this zone from the substratum (black limestone).

Phot. 4: Polished section of the sample where different collapse levels are visible (cave of the Observatoire, Monaco).

Coupe polie de la carotte montrant différents niveaux de chutes dans la grotte de l'Observatoire (Monaco). Coupe schématique de la carotte de la grotte de l'Observatoire (Monaco).

-Interpretation:

The polished cross section shows 3 or 5 levels of collapses : -a first level, at the top of the sample, is attributed to the 1887 earthquake.

-a second level with only one collapse could be the 1564 earthquake.

-a third level with important collapses of sodastraws, stalagmites and stalactites is an older and probably more destructive shake. The substratum of the last level has been dated with radiocarbon method, but the age is out of the method limit (higher than 35 000 yrs).

-CONCLUSION:

On the flowstone of the Observatoire Cave recent collapses are visible that are attributed to 1887 earthquake. The bore hole indicates that similar collapses occurred 2 or 4 times in the past.

The regularity in the calcite deposit and the absence of hiatus, eliminate a cause inside the cave. So we suppose that the breakages were caused by ancient earthquakes. We have to remain prudent and to complete these investigations with dating on the different levels where collapses are observed.

The same operations must be done in different parts of the same cave but also in different caves in Ligurian area. Similar observations have already been done in two caves near Finale Ligure (Italy). New research will be done on the fragments' orientation to see if a preferential direction is observable, this could give information on the shake direction if the seismic cause for the damage is accepted (Gilli and [START_REF] Delange | Recherche des effets du séisme du 18 février 1996 sur les cavités karstiques de la région de St Paul de Fenouillet[END_REF].

Fig. 1 :

 1 Fig. 1: Map and cross section of the cave of the Observatoire (Monaco).Plan et coupe de la grotte de l'Observatoire (Monaco).

Fig. 2 :

 2 Fig. 2: Structural context of the cave of the Observatoire (Monaco).Contexte structural de la grotte de l'Observatoire (Monaco).

Fig. 3 :Fig. 4 :

 34 Fig. 3: Schematic cross section of the cave of the Observatoire (Monaco).Coupe schématique de la grotte de l'Observatoire (Monaco).

Fig. 5 :

 5 Fig. 5: Principle of ancient seisms recording in a cave flowstone. Principe de l'enregistrement des séismes anciens dans un plancher stalagmitique.

Fig. 6 :

 6 Fig. 6: Schematic section of the sample in the cave of the Observatoire (Monaco).Coupe schématique de la carotte de la grotte de l'Observatoire (Monaco).