Chloé Marques

Pauline Frenoy

Thibault Fiolet

Amélie Crépet

Gianluca Severi

Francesca Romana Mancini
email: francesca.mancini@gustaveroussy.fr

Romana Mancini

Challenges of studying the dietary exposure to chemical mixtures: Example of the association with mortality risk in the E3N French prospective cohort

Keywords: chemical, mixture, diet, sparse non-negative matrix under-approximation, mortality, cohort

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Epidemiological studies frequently focus on studying the health effects of exposure to one chemical substance at a time. However, in real life, people are simultaneously exposed to hundreds of chemical substances. Exposure to these chemical mixtures may represent a greater risk for health than singlecontaminant exposure because chemical substances can cause additive toxicological effects on health, but also synergistic or antagonistic effects due to interactions between them [START_REF] Goodson | Assessing the carcinogenic potential of low-dose exposures to chemical mixtures in the environment: The challenge ahead[END_REF][START_REF] Hernández | Toxicological interactions of pesticide mixtures: An update[END_REF][START_REF] Kopp | Genotoxicity and mutagenicity assessment of food contaminant mixtures present in the French diet[END_REF][START_REF] Eskola | Towards a dietary-exposome assessment of chemicals in food: An update on the chronic health risks for the European consumer[END_REF]. The exposome approach with the study of chemical mixtures rather than single contaminants seems therefore more appropriate and may allow achieving different goals -i.e.: to identify the mixtures to which a population is exposed, to determine the most toxic agent of a mixture, to identify interactions between the components of a mixture, or to estimate the mixtures' health effects [START_REF] Gibson | Complex Mixtures, Complex Analyses: An Emphasis on Interpretable Results[END_REF]. However, the study of mixtures presents some inherent difficulties, in particular related to the high correlations between the substances of interest which may lead to multicollinearity if they are included in the same model. Indeed, multicollinearity may induce instability in the models and, in turn, to inconsistent results [START_REF] Henn | Chemical Mixtures and Children's Health[END_REF]. Moreover, the chemicals included in the study may individually have opposite effects (positive or negative association) on the studied outcome.

The diet represents the main source of exposure to several chemical contaminants, especially for the general population. Dietary exposure to contaminants is usually chronic, at low doses and can be associated with long-term health effects [START_REF] Goodson | Assessing the carcinogenic potential of low-dose exposures to chemical mixtures in the environment: The challenge ahead[END_REF][START_REF] Lee | A role of low dose chemical mixtures in adipose tissue in carcinogenesis[END_REF]. Studying dietary exposure to chemical mixtures is challenging as they are part of a complex food matrix which includes nutrients, additives, and contaminants whose health effects are difficult to separate, especially as they can interact with each other [START_REF] Cano-Sancho | Interactions between environmental pollutants and dietary nutrients: Current evidence and implications in epidemiological research[END_REF]. From a public health perspective, it would be relevant to advise on the optimal dietary balance to maximise the nutritional benefits and minimise the potential health risks of chemical mixtures when constructing nutritional recommendations.

Human studies on dietary exposure to chemical mixtures are mostly descriptive [START_REF] Béchaux | Identification of pesticide mixtures and connection between combined exposure and diet[END_REF][START_REF] Crépet | Identification of the main pesticide residue mixtures to which the French population is exposed[END_REF][START_REF] Traoré | To which chemical mixtures is the French population exposed? Mixture identification from the second French Total Diet Study[END_REF][START_REF] Lee | Identification of chemical mixtures to which Canadian pregnant women are exposed: The MIREC Study[END_REF][START_REF] Traoré | To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies[END_REF][START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF]Rebouillat, Vidal, Cravedi, Taupier-Letage, Debrauwer, Gamet-Payrastre, Touvier, Hercberg, et al., 2021). These studies aimed to identify the most relevant chemical mixtures to which the study population is exposed through the diet so to prioritise which mixtures should be further investigated through animal and analytical epidemiology studies, and addressed by public health policies. To date, only two epidemiological studies investigated the relationship between dietary exposure to mixtures of pesticides and health outcomes, respectively breast cancer and type 2 diabetes. Both studies were conducted in the NutriNet-Santé French cohort [START_REF] Rebouillat | Prospective association between dietary pesticide exposure profiles and postmenopausal breast-cancer risk in the NutriNet-Santé cohort[END_REF][START_REF] Rebouillat | Prospective association between dietary pesticide exposure profiles and type 2 diabetes risk in the NutriNet-Santé cohort[END_REF].

The main objective of the present study was to analyse the association between chemical mixtures to which women of the E3N cohort are most commonly exposed through the diet and the risk of mortality in the E3N (Etude Epidémiologique auprès de femmes de l'Education Nationale) French prospective cohort.

Material and methods

E3N cohort

The E3N cohort is an ongoing prospective cohort initiated in 1990 with the inclusion of 98 995 women.

All women were born between 1925 and 1950. They lived in France and were members of the MGEN (a French health insurance which covers workers of the national education system) at inclusion.

Women enrolled in the E3N cohort completed self-administered questionnaires sent every 2 or 3 years, including questions on their lifestyle (e.g., diet, alcohol consumption, smoking status, physical activity, etc.), socioeconomic status (e.g., education level, household income, etc.), reproductive history (e.g., number of pregnancies, breastfeeding, etc.) and health (e.g., anthropometric measures, family and personal medical history, incident health issues, drugs, etc.). All questionnaires are available on the E3N cohort website (http://www.e3n.fr/). Only 3% of the E3N women were lost to follow-up [START_REF] Clavel-Chapelon | E3N, a French cohort study on cancer risk factors. E3N Group. Etude Epidémiologique auprès de femmes de l'Education Nationale[END_REF][START_REF] Clavel-Chapelon | Cohort Profile: The French E3N Cohort Study[END_REF]. The CNIL (the French National Commission for Data Protection and Privacy) approved the study, and all participants signed informed consent.

Dietary questionnaire

In 1993, the participants received the third questionnaire (Q3), which included a semi-quantitative food frequency questionnaire with 208 food items. This questionnaire was made of two parts. The first one focused on the frequency and quantity of food groups and drinks consumed over the previous year. The portion sizes were estimated using an album including photos of 42 food groups; the other food groups were estimated in natural units (e.g. eggs). Questions were completed for 8 meal occasions, from breakfast to after-dinner snacks (including the aperitif before lunch and dinner) according to French meal patterns. The second part of the questionnaire included qualitative questions concerning food items within each food group listed in the first part. We estimated the daily food intakes (g/day or mL/day) by multiplying the frequency (eating occasions per week or month) by the amount consumed (g or mL) of each food item included in the questionnaire. The original questionnaire can be found on the E3N cohort website (http://www.e3n.fr/). The questionnaire's validity and reproducibility were previously reported [START_REF] Van Liere | Relative validity and reproducibility of a French dietary history questionnaire[END_REF].

Daily nutrient intakes were derived from the CIQUAL, the French food composition table of the French Information Center on Food Quality (ANSES, 2013). Adherence to a healthy dietary pattern was obtained by principal components analysis (PCA) [START_REF] Edefonti | Nutrient dietary patterns and the risk of breast and ovarian cancers[END_REF]. Furthermore, we estimated two nutritional scores depicting the antioxidant and inflammatory capacity of the diet. For each woman included in our study, the total antioxidant capacity of the diet was calculated by multiplying the consumption of each food item (excluding coffee) by its specific ferric ion-reducing antioxidant power (FRAP). The FRAP for each food item was obtained from the database developed by Pellegrini et al. [START_REF] Pellegrini | Total Antioxidant Capacity of Plant Foods, Beverages and Oils Consumed in Italy Assessed by Three Different In Vitro Assays[END_REF][START_REF] Pellegrini | Total antioxidant capacity of spices, dried fruits, nuts, pulses, cereals and sweets consumed in Italy assessed by three different in vitro assays[END_REF]. More details on this calculation in the E3N cohort can be found in [START_REF] Mancini | Dietary antioxidant capacity and risk of type 2 diabetes in the large prospective E3N-EPIC cohort[END_REF]. For the dietary inflammatory index, the adapted dietary inflammatory index (ADII) was estimated by the method developed by [START_REF] Van Woudenbergh | Adapted dietary inflammatory index and its association with a summary score for low-grade inflammation and markers of glucose metabolism: The Cohort study on Diabetes and Atherosclerosis Maastricht (CODAM) and the Hoorn study[END_REF], with the updated weights of Shivappa et al. [START_REF] Shivappa | Designing and developing a literature-derived, population-based dietary inflammatory index[END_REF]. The detailed methodology to adapt this score to the E3N cohort is presented elsewhere [START_REF] Laouali | Dietary inflammatory index and type 2 diabetes risk in a prospective cohort of 70,991 women followed for 20 years: The mediating role of BMI[END_REF].

Ascertainment of chemical mixtures

Food contamination levels were obtained from the second French total diet study (TDS2) conducted by the French Agency for Food, Environmental and Occupational Health & Safety (Anses) (ANSES, 2011a(ANSES, , 2011b)). Briefly, from 2007 to 2009, 20 280 food items were purchased in 8 French regions in order to analyse the presence of more than 400 contaminants in 1 352 composite samples prepared as consumed (i.e. washing, pealing, etc.) according to the French dietary habits [START_REF] Sirot | Core food of the French food supply: Second Total Diet Study[END_REF].

The E3N food consumption database and the Anses food contamination database were then merged to obtain the individual daily dietary intake i to a chemical substance s (in g of substance/day), by summing over all food items, the quantity q of the food item f consumed (in g of food/day) multiplied by the contamination level c of the food item f by the substance s (in g of substance/g of food) [START_REF] Mancini | Estimation of the dietary exposure to chemical compounds in the French E3N prospective cohort: A study protocol[END_REF]:

𝑖 𝑠 = ∑ 𝑞 𝑓 × 𝑐 𝑠𝑓
We followed the lower bound scenario approach, meaning that we replaced by 0 the food contamination values below the limit of detection (LOD), and by the LOD the values below the limit of quantification (LOQ). When the LOD was not provided, values below the LOQ were replaced by 0.

In [START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF], the 8 main chemical mixtures to which the women of the cohort are exposed through the diet were identified using the sparse non-negative matrix under-approximation (SNMU), a method of dimension reduction of a non-negative matrix (which is adapted to exposure data) derived from the non-negative matrix factorisation (NMF) [START_REF] Gillis | Using underapproximations for sparse nonnegative matrix factorization[END_REF][START_REF] Gillis | Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis[END_REF][START_REF] Traoré | To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies[END_REF]. In that study, the dimension reduction method was applied to the matrix of dietary exposure to chemicals, which corresponds to the dietary intake divided by the body weight (bw).

Indeed, dietary exposure (g/kg bw/day) can be considered suitable when the objective is to identify and describe mixtures and for food risk assessment. However, when the aim is to model how mixtures affect health risks, dietary intake (g/day) is more appropriate as it allows explicit adjustment for body mass index (BMI), which plays an important role on health. Thus, in the present study, we applied the SNMU to the dietary intakes of 197 substances and we identified 6 main chemical mixtures. Briefly, using the same parameters as in the previous study [START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF], we obtained three matrices U, V and Ɛ (the matrix of residuals) such that the exposure matrix E=UxV+Ɛ. The matrix U contained the weights of the contribution of each substance to the mixtures. The matrix V comprised the individual weights of adherence to each mixture. The choice of the final number of mixtures to retain was based on a balance between statistical criteria such as the overall proportion of variance explained by the chosen number of mixtures, the residual sum of squares, the interpretability of the results and the toxicological and epidemiological relevance. More details about the approach used to identify the mixtures can be found elsewhere [START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF].

Assessment of mortality

We included all deaths that occurred during follow-up from the date of completion of Q3 until November 2014. Information concerning the vital status of the study population was obtained from the MGEN, postal service, municipal registries, physicians or next of kin. The Inserm-CépiDc, the French centre of epidemiology on medical causes of death, provided the causes of death coded according to the 9 th edition of the international classification of diseases (ICD9 for deaths before 2000) or the 10 th edition (ICD10 for deaths after 2000). Cause-specific analyses were conducted for cancer (ICD9 140-210 and ICD10 C00-C99) and cardiovascular diseases (CVD) (ICD9 390-459 and ICD10 I00-I99) mortality.

Study population

We included the 74 522 women who answered the dietary questionnaire sent in 1993. Women in the 1 st or 99 th percentile of the distribution of the ratio of energy intake on energy requirements were identified as outliers and therefore excluded from the analyses (N=1 491). Energy requirements are equal to the basal metabolic rate (derived from the Schofield equation based on sex, age and weight) multiplied by their physical activity level [START_REF] Schofield | Predicting basal metabolic rate, new standards and review of previous work[END_REF]. We also excluded 446 women lost to followup after the dietary questionnaire. Finally, the study population comprised 72 585 women, including 6 441 deaths and 66 144 non-deaths. For the cause-specific mortality analyses, we further excluded 169 participants with unknown causes of death, leading to a study population of 72 416 women. The flow chart is presented in Supplementary figure 1.

Statistical analyses

Descriptive analyses

We first conducted descriptive analyses of the study population. We identified the proportions of the causes of death and we described the baseline characteristics (mean and standard deviation (STD) for continuous variables, number and proportion for categorical variables) of the overall population, among cases and non-cases, and among each quartile group of the weights of adherence to each mixture.

We then performed descriptive analyses on the exposure, by calculating the proportion of each substance in each mixture and the Spearman rank correlation coefficients between the weights of adherence to the 6 mixtures. We also estimated partial Spearman rank correlation coefficients (i.e.

adjusted on the weights of adherence to the other mixtures) between the weights of adherence to the 6 mixtures and the consumption of 30 food groups and 2 nutritional scores.

Main analyses

Cox proportional hazard models with age as the time-scale were applied to estimate hazard ratios (HR)

and their 95% confidence intervals (CI) for the associations between the weights of adherence to each mixture and the risk of all-cause, cancer and CVD mortality. Age at the start of follow-up was the age when answering the dietary questionnaire, and age at the end was the age at death, at the last completed questionnaire or at the end of the follow-up period which corresponded to the last update of the mortality database (in November 2014), whichever occurred first.

The main exposure variables were the weights of adherence to each of the 6 chemical mixtures divided by their STD in order to estimate the HR for one STD increment. We excluded values below the 1 st (except if they were zero) or above the 99 th percentile of the main exposure variables from our models to reduce the potential impact of outliers.

Adjustment covariates were chosen from the known main factors associated with mortality and from the directed acyclic graph (DAG, http://www.dagitty.net) presented in Figure 1. Despite acknowledging the role of diet as a confounding factor, it was not possible to adjust on all items representing "diet" as these items entirely determined the exposure to the mixtures. We therefore tested different adjustment strategies including several dietary-related variables (e.g. specific food groups consumption, nutritional scores) to block the confounding paths between "diet" and "mortality". In order to respect temporality, we selected the other confounding covariates in the questionnaire sent in January 1992 (Q2), so before the dietary questionnaire (Q3) sent in 1993. If these variables were not available in Q2, we used variables from the first questionnaire (Q1) sent in 1990, or in Q3.

Five models were developed to study the risk of all-cause mortality. Model a was only adjusted on age (as the time scale, in years). Model b was further adjusted on BMI at Q2 (spline with 4 knots, kg/m 2 ), birth generation (<=1930, (1930 -1935], (1935 -1940], (1940 -1945], >1945), school education level (<12 years, 12 to 14 years, >14 years), smoking status at Q2 (never smoker, former smoker, current smoker), physical activity at Q3 (spline with 4 knots, MET-hours/week), and menopausal status and recent (i.e. in the last year) use of menopausal hormone therapy (MHT) at Q2 (premenopausal, menopausal and recent MHT use, menopausal and no recent MHT use, menopausal and no information on whether and when MHT was used). Model c was additionally adjusted on dietary variables, all measured at Q3: total energy intake excluding energy from alcohol and lipids (linear term, kcal/day), alcohol consumption (spline with 4 knots, g of ethanol/day), and lipids consumption (spline with 4 knots for mixture 1, linear term otherwise, g/day). Model d was equal to model c plus an adjustment on the weights of adherence to all other mixtures, and on the consumption of the food group which contributed the most (i.e. the most partially correlated) to the weight of adherence to the mixture of interest. In particular, we added "cheese, butter and cream" (linear term, g/day) for mixture 2, "bread and salty cereal products" (linear term, g/day) for mixture 3, "vegetables except roots"

(linear term, g/day) for mixture 4, "fruits" (linear term, g/day) for mixture 5, and "sea products"

(including fish and seafood, spline with 3 knots, g/day) for mixture 6. Since mixture 1 was equally correlated with many food groups, we decided to adjust model d on the adherence to a healthy dietary pattern (spline with 3 knots). Finally, we ran model e, equivalent to model c with further adjustments on the weights of adherence to all other mixtures, the dietary antioxidant capacity (linear term, mmol/day), and the adapted dietary inflammatory index (spline with 5 knots).

We used a reference model to determine how to model the quantitative variables (linear term vs restricted cubic splines). This model corresponded to model c described above, with an additional adjustment on the consumption of the food group which contributed the most to the weight of adherence to each mixture. The decision was based on the results of the non-linearity test [START_REF] Desquilbet | Dose-response analyses using restricted cubic spline functions in public health research[END_REF]: if the p-value was <0.1, the variable was considered non-linear and it was then modelled in splines. The number of knots (3 set at the 10 th , 50 th and 90 th percentiles, 4 set at the 5 th , 35 th , 65 th and 95 th percentiles or 5 set at the 5 th , 27.5 th , 50 th , 72.5 th and 95 th percentiles) was established according to the model with the smallest Akaike information criterion (AIC) for the main exposure variables, while we kept 4 knots by default for the other continuous covariates, as suggested by Harrell [START_REF] Harrell | Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis[END_REF]. For all-cause mortality analyses, weights of adherence to the mixtures 1, 3, 4 and 5

were included in the models with restricted cubic splines (with 4, 5, 3 and 3 knots, respectively). For these cubic spline regression models, the minimum value of the main exposure variable was taken as a reference to present the results. We also ran the models using the 6 main exposure variables as categorical variables divided into quartile groups (with the first quartile group as reference) to facilitate the comparison of the results between mixtures.

Following the same protocol, we also fitted models c, d and e separately for cancer mortality and for CVD mortality, by censoring all other causes of death at the age at death.

For covariates with less than 5% of missing values, we imputed them with the median for continuous variables and with the modal category for categorical variables. When missing values were more than 5% (i.e. menopausal status and recent MHT use), we created an "unknown value" category.

A p-value <0.05 was considered statistically significant. We employed R version 4.1.2 to perform statistical analyses and the Statistical Analysis Systems software package version 9.4 to build the database (SAS Institute, Cary, North California).

Sensitivity analyses

We performed three types of sensitivity analyses both on models d and e. First, we applied the energy adjustment residual method [START_REF] Willett | Adjustment for total energy intake in epidemiologic studies[END_REF]) by using as main exposure variables the residuals of the regression between total energy intake and weights of adherence to the mixtures. Second, we excluded cases that occurred during the first five years of follow-up to evaluate the potential influence of reverse causation bias, i.e. participants would have changed their diet due to the health condition that resulted in mortality. Finally, we performed multiple imputations to deal with missing data on menopausal status and recent MHT use (premenopausal, menopausal and recent MHT use, menopausal and no recent MHT use, menopausal and no information on whether and when MHT was used): women in the 4 th group were imputed in the 2 nd or 3 rd group. We generated 5 independent data sets and calculated pooled estimates. We imputed the variable with multinomial logistic regression models.

Results

Descriptive analyses

Around 81% of the variance was explained by the 6 mixtures described in Table 1, which lists the 25 substances contributing the most to each mixture. Mixture 1 was mainly composed of minerals, inorganic contaminants, and furans; mixture 2 of BFRs (brominated flame retardants), dioxins, PCBs (polychlorinated biphenyls), and furan; mixture 3 of mycotoxins, pesticide, and PAHs (polycyclic aromatic hydrocarbons); mixtures 4 and 5 of pesticides; mixture 6 of PFAS (per-and polyfluoroalkyl substances), BFRs, PCBs, Se (selenium), Hg (mercury), and furan.

Mixtures were not correlated or only moderately correlated except mixtures 1 and 2 (correlation=0.77), mixtures 2 and 6 (0.65) and mixtures 1 and 3 (0.53) (Supplementary table 1). Partial Spearman rank correlation coefficients between weights of adherence to the mixtures and dietary variables are listed in Supplementary table 2.

Among the 6 441 deaths reported during an average of 19 years of follow-up, a large number were due to cancer (N=3 473, 53.9%) and CVD (N=896, 13.9%). The detailed causes of death are listed in

Supplementary table 3.

We present the baseline characteristics of the study population among deaths and non-deaths in Table 2, and among quartile groups of the weights of adherence to each mixture in Supplementary tables 4 to 9. In short, compared to non-cases, cases are older (57.7 vs 52.5 years) and they have a higher average BMI (23.4 vs 22.7 kg/m 2 ). Cases were also more frequently menopausal (74.66 of menopausal women among cases vs 46.06% among non-cases) and had a lower school education level (14.42 vs 10.98% <12 years).

Weights of adherence to chemical mixtures and all-cause mortality

We observed a general tendency towards an inverse association between the weights of adherence to the mixtures and all-cause mortality although only some of these associations reached statistical significance. The results for linear terms (with HR (95% CI) and p-value), restricted cubic splines (pvalue of the overall association and of the non-linearity test), and quartile groups (HR (95% CI)) of the weights of adherence to the mixtures in relation to all-cause mortality in models c, d and e are shown in Table 3, and the related restricted cubic splines' graphs appear in Figure 2. The results of models a to e and of the reference model are presented by weight of adherence to each mixture in Supplementary tables 10 to 15, and the graphs of all the associated restricted cubic splines appear in Supplementary figure 2.

Mixture 1 (minerals, inorganic contaminants, and furans) was inversely associated with mortality in a non-monotonic manner (p-value of the overall association ≤ 0.003 for models c, d and e). From the analysis using quartile groups, we observed that relatively to the 1 st quartile group, mortality was lower for 3 rd and 4 th quartile groups but not for 2 nd in model c (HRQ2vsQ1 0.96, 95% CI 0.89-1.04; HRQ3vsQ1 0.83, 95% CI 0.75-0.91; HRQ4vsQ1 0.86, 95% CI 0.76-0.97). The general pattern of association between quartile groups of the mixture 1 distribution and mortality was consistent across the models but it appears weaker for models d and e than for model c, with statistical significance only for the 3 rd relative to the 1 st quartile group.

Mixture 2 (BFRs, dioxins, PCBs, and furan) was not associated with mortality in models c, d and e, both when considering it with a linear term or in quartile groups.

Mixture 3 (mycotoxins, pesticide, and PAHs) as a non-linear continuous variable was not associated with mortality in models c and d, while we observed a non-monotonic inverse and statistically significant association in model e (p-value of the overall association 0.017). In quartile groups, the association was not statistically significant in models c, d and e.

Mixture 4 (pesticides) was inversely associated with mortality in a non-monotonic manner in models c, d and e (p-values of the overall association <0.0001). We also observed a statistically significant inverse association when running models c, d and e using quartile groups. Indeed, we observed HRs Finally, mixture 6 (PFAS, BFRs, PCBs, Se, Hg, and furan) as a linear continuous variable was not associated with mortality in model c, while we observed a statistically significant inverse association in models d and e (HR 0.90, 95% CI 0.82-0.98 and HR 0.93, 95% CI 0.88-0.99, respectively). We did not observe a statistically significant association in quartile groups.

Weights of adherence to chemical mixtures and cause-specific mortality

For cancer and CVD mortality analyses, we present the results for models c, d and e.

When analysing the associations between the weights of adherence to the mixtures and cancer mortality risk, we observed similar results to those obtained for all-cause mortality (Supplementary table 16 and Supplementary figure 3).

We found differences between the associations with CVD mortality and those of all-cause mortality (Supplementary table 17 and Supplementary figure 4).

Indeed, for mixture 1 (minerals, inorganic contaminants, and furans), all the results (as a linear continuous variable or in quartile groups) were not statistically significant.

Mixture 2 (BFRs, dioxins, PCBs, and furan) was not associated with CVD mortality when considering it with a linear term for all models. In quartile groups, the associations were not statistically significant in model c, while we observed an inverse association for the 4 th quartile group relative to the 1 st 16 quartile group in model d (HRQ4vsQ1 0.63, 95% CI 0.43-0.94) and in model e (HRQ4vsQ1 0.58, 95% CI 0.39-0.87).

The results were not statistically significant in all models for mixture 3 (mycotoxins, pesticide, and PAHs), in spline and in quartile groups.

Mixture 4 (pesticides) was inversely associated with CVD mortality in a non-monotonic manner in models c, d and e (p-values of the overall association of 0.032, 0.025 and 0.044, respectively). In quartile groups, mixture 4 was also inversely associated with CVD mortality, with a statistically significant association only for the 3 rd quartile group in relation to the 1 st quartile group in model c (HRQ3vsQ1 0.82, 95% CI 0.68-0.98) and in model d (HRQ3vsQ1 0.81, 95% CI 0.67-0.98).

Mixture 5 (pesticides) was not associated with CVD mortality in all models, in quartile groups and as a linear continuous variable.

Finally, when considering mixture 6 (PFAS, BFRs, PCBs, Se, Hg, and furan) as a linear continuous variable or in quartile groups, all the results were not statistically significant.

Sensitivity analyses

Generally, in sensitivity analyses, the results remained unchanged regarding HR values, statistical significance, and curves' shapes compared to the results of the main analyses.

In the analyses based on the energy adjustment residual method, the results didn't change, except for the weight of adherence to mixture 3 for which the association became not statistically significant (Supplementary table 18 and Supplementary figure 5). When running the sensitivity analyses based on the exclusion of the cases that occurred during the first five years of follow-up or on the multiple imputations, the results remained unchanged (results not shown).

Discussion

In this study, we observed either no association or an inverse association between the weights of adherence to the mixtures and all-cause or cause-specific mortality risk. These results may not be surprising for certain mixtures such as mixture 1 which is inversely associated with mortality risk.

Indeed, mixture 1 is composed of many substances (n=28) including several minerals which are beneficial for health, as shown in a previous scoping review [START_REF] Thomsen | Human health risk-benefit assessment of fish and other seafood: A scoping review[END_REF]: chromium (Cr), potassium (K), iron (Fe) and zinc (Zn) (Table 1). On the other hand, we also found some unexpected results, such as the non-linear inverse associations between mixtures 4 or 5 and the risk of mortality.

As mixtures 4 and 5 are composed of pesticides and for which the main contributing food groups are "vegetables except roots" and "fruits", respectively, the known beneficial effects of consuming such foods may have overtaken the potentially detrimental effect of dietary exposure to the pesticide mixtures. A recent study investigating the health effects related to the consumption of fruits and vegetables containing pesticide residues concluded that the benefits of fruits and vegetables consumption outweigh the long-term health effects linked to exposure to pesticides [START_REF] Valcke | Human health risk assessment on the consumption of fruits and vegetables containing residual pesticides: A cancer and non-cancer risk/benefit perspective[END_REF]. In addition, a prospective cohort study found that the association between fruits and vegetables intake and lower mortality risk was limited to the consumption of fruits and vegetables with a low level of contamination with pesticides while no association with mortality was observed for the consumption of fruits and vegetables highly contaminated with pesticides [START_REF] Sandoval-Insausti | Intake of fruits and vegetables according to pesticide residue status in relation to all-cause and disease-specific mortality: Results from three prospective cohort studies[END_REF]. It is thus likely that, despite our adjustment strategies, we did not succeed in separating the beneficial effect of certain foods and nutrients from the potentially detrimental effect of exposure to chemical mixtures. On the basis of the causal model represented in Figure 1, we attempted to account for the nutritional contribution of diet by using two adjustment strategies. In the first strategy (corresponding to model d), we chose to adjust on the consumption of the food group which was most strongly correlated with the weight of adherence to each mixture, and that we interpreted as the food group which contributed the most to the exposure to the mixture. Such an adjustment should remove the confounding coming from the total quantity consumed of a given food group potentially linked to both the exposure and the outcome. In the second strategy, we attempted to consider diet at a more global scale, using indexes based on nutrient intakes (corresponding to model e). Since it was not feasible to choose specific nutrients to include in the model for each specific mixture, we adjusted the model on two nutritional scores reflecting the antioxidant or inflammatory capacity of the diet (FRAP and ADII, respectively) as oxidative stress and chronic systemic inflammation are often linked to noncommunicable diseases (such as cancer or CVD). Nevertheless, despite the different adjustment strategies tested, it seems that we did not succeed in fully separating the effect of the exposure to chemical mixtures from the overall effect of the diet in relation to mortality risk, especially for mixtures 4 and 5, but probably also for other mixtures. This can be partly explained by the fact that the intake of contaminants is directly estimated from dietary consumption, which makes it particularly difficult to control for dietary confounding in our study. Moreover, despite the adjustment on lifestyle variables in the models, confounding may derive also from unmeasured lifestyle factors associated with both diet and mortality.

The notion of the number of substances considered in our analyses also raises questions. Firstly, although in the present study we derived the mixtures from the estimated dietary exposure to almost 200 different chemical substances, leading to mixtures including between 21 and 52 contaminants (the rationale is explained elsewhere [START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF])), we are aware that in real life many more food contaminants exist that may contribute differently to the mixtures and thus to the association with mortality. However, while, from an exposome perspective, it could be interesting to identify chemical mixtures from the intake of more substances, a higher number of substances is likely to lead to greater difficulties with the interpretation of the mixtures and their associations with health outcomes. Thus it may also be advisable to reduce the number of studied substances by a priori grouping substances, according to their structures, modes or mechanisms of action, toxicological effects associated with the outcome of interest, and/or common target organ/system [START_REF] De Jong | Roadmap for action on Risk Assessment of Combined Exposure to Multiple Chemicals (RACEMiC)[END_REF]. For example, starting from more than 400 pesticides, Crépet et al. included only those related to steatosis in the SNMU and thus fell to 144 pesticides [START_REF] Crépet | Selecting mixtures on the basis of dietary exposure and hazard data: Application to pesticide exposure in the European population in relation to steatosis[END_REF]. The approach just described may be effective for outcomes related to well-defined pathogenic processes while it is likely to be more difficult to apply it for outcomes such as mortality.

To the best of our knowledge, the SNMU (used in [START_REF] Traoré | To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies[END_REF][START_REF] Mancini | Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort[END_REF] and other statistical methods of reduction of dimension like NMF or PCA were previously applied mainly to identify chemical mixtures [START_REF] Béchaux | Identification of pesticide mixtures and connection between combined exposure and diet[END_REF][START_REF] Traoré | To which chemical mixtures is the French population exposed? Mixture identification from the second French Total Diet Study[END_REF][START_REF] Lee | Identification of chemical mixtures to which Canadian pregnant women are exposed: The MIREC Study[END_REF]Rebouillat, Vidal, Cravedi, Taupier-Letage, Debrauwer, Gamet-Payrastre, Touvier, Hercberg, et al., 2021), and generally not to test the association between the identified mixtures and a health outcome. Only two studies applying NMF have investigated the associations between dietary exposure to pesticide mixtures and the risk of breast cancer and type 2 diabetes. They found positive associations between a component of the NMF (correlated with dietary exposure to synthetic pesticides) and the risk of developing breast cancer and type-2 diabetes [START_REF] Rebouillat | Prospective association between dietary pesticide exposure profiles and postmenopausal breast-cancer risk in the NutriNet-Santé cohort[END_REF][START_REF] Rebouillat | Prospective association between dietary pesticide exposure profiles and type 2 diabetes risk in the NutriNet-Santé cohort[END_REF]. However, it must be noted that in these studies the authors included only 25 substances which are all classified as pesticides, while in the present study we included 197 chemical substances among which 58 were pesticides. This main methodological difference could explain the better interpretability of the results obtained by Rebouillat et al. To summarise, as suggested previously by others [START_REF] Gibson | Complex Mixtures, Complex Analyses: An Emphasis on Interpretable Results[END_REF], the SNMU is a method adapted to identify mixtures of correlated substances, so with a descriptive purpose, while it may have some limitations when used in analytical epidemiology. Indeed, the SNMU, being a non-supervised method, identifies the mixtures exclusively on the basis of the correlations between the exposure variables, not directly taking into account the links between the exposure variables and the outcome of interest. As a result, substances are not necessarily grouped according to the direction of their associations with the outcome, which means that a given mixture may include substances that have opposite effects on the studied outcome. It is thus possible to observe a null association between a mixture and the outcome which is in reality the result of a combination of opposite effects of the individual substances on this outcome. Supervised methods could therefore be particularly suitable in this context of analytical epidemiology, by selecting and grouping substances taking into account their relation with the outcome. Nevertheless, these approaches would answer to a different research question than ours: "Which are the chemical mixtures mostly associated with mortality risk?". While this research question is very interesting per se, it cannot be excluded that the identified mixtures could correspond to mixtures to which women are more rarely exposed to in real life.

It also has to be considered that exposure to chemical contaminants could be associated with an increased incidence of certain non-communicable diseases without being necessarily associated with an increased risk of mortality. Further studies investigating the relationship between dietary exposure to chemical mixtures and the incidence of specific outcomes are warranted.

When interpreting our results, some limitations linked to the E3N cohort study should also be considered. The E3N cohort is composed of middle-aged French women. Indeed, as population groups can have different susceptibilities towards the adverse health effects related to the presence of contaminants in the diet, we can't exclude the possibility of finding different results in another population. Moreover, the participants of the E3N cohort are not representative of middle-aged

French women as they are on average leaner and have a higher education level, so the generalizability of our results should be done with caution [START_REF] Clavel-Chapelon | Cohort Profile: The French E3N Cohort Study[END_REF]. Nevertheless, comparisons between high and low levels of adherence to the mixtures remain possible. The lack of associations observed in the present study could be due to the reduced variability in the exposure within the E3N cohort compared to the variability expected in the French general population.

Moreover, we cannot exclude that women in our study are not sufficiently exposed to chemical mixtures to see an association with mortality which could appear at higher levels of exposure.

Furthermore, the period elapsed between the estimation of dietary consumption in 1993 and the estimation of food contamination levels in 2007-2009 has to be acknowledged. Indeed, the dietary consumption and contamination levels could have varied over time. However, concerning dietary consumption, a study highlighted the stability of the dietary pattern among middle-aged women [START_REF] Thorpe | Education and lifestyle predict change in dietary patterns and diet quality of adults 55 years and over[END_REF]. Furthermore, food contamination levels may have changed overtime, leading to an imperfect estimation of the dietary intakes. However, except for pesticides that suffer more from spatial and temporal variations, many of the contaminants considered in this study are persistent and ubiquitous in the environment. Thus we can assume that their presence in the environment does not change rapidly and that these changes are similar in all food groups, resulting in a correct ranking of the participants according to their exposure. Moreover, the potential measurement error in the estimation of the substances' intake can have induced a classification error that is non-differential with respect to the outcome, leading to an attenuation of the estimated associations [START_REF] Kipnis | Structure of Dietary Measurement Error: Results of the OPEN Biomarker Study[END_REF][START_REF] Thiébaut | Is it necessary to correct for measurement error in nutritional epidemiology[END_REF][START_REF] Freedman | Dealing with dietary measurement error in nutritional cohort studies[END_REF]. Finally, in this study, no specific information concerning organic and not organic food is available, nor for food consumption data, nor for food contamination data. This limitation can lead to a potential misclassification of the exposure, especially for pesticide intake.

This study also benefits from several strengths. The analyses on more than 70 000 women followed for an average of 19 years allow the study of possible long-term health effects based on a sufficient number of cases to achieve adequate statistical power. The numerous sensitivity analyses ensure the robustness of the results. Furthermore, mortality cases were obtained from the mortality database with causes of death validated by the Inserm-CépiDc, which permits to accurately classify the participants in relation to the outcome. In addition, the measurement error of the exposure is reduced because the dietary questionnaire was previously validated [START_REF] Van Liere | Relative validity and reproducibility of a French dietary history questionnaire[END_REF], and because the food samples were prepared "as consumed" in order to take into account potential changes in contamination levels due to the preparation method, such as pealing or washing [START_REF] Sirot | Core food of the French food supply: Second Total Diet Study[END_REF].

Finally, extensive information about the participants' individual characteristics and lifestyle was available and allowed to take into account several potential confounders through adjustments in the models.

Conclusion

To conclude, we observed either no association or an inverse association between dietary exposure to chemical mixtures and mortality risk. Despite the different adjustment strategies, it seems that we did not fully succeed in excluding the residual confounding from the overall effect of the diet, especially for mixtures composed of pesticides, which appear to be inversely associated with mortality risk.

The present study also raises the question of how to strike a balance between a higher number of contaminants and the interpretability of the identified mixtures and their association with the outcome. An approach to this problem is to integrate a priori knowledge (e.g. toxicological data) to group substances and obtain more parsimonious and interpretable mixtures.

Finally, supervised statistical methods should be tested in future studies to identify the chemical mixtures to which people are exposed through the diet directly in relation to the health outcome of interest.

  , 3 rd , and 4 th quartile groups to the 1 st quartile group in model c. These results were very similar in models d and e.

	We reported a statistically significant and non-monotonic inverse association between mixture 5
	(pesticides) and mortality in models c, d and e (p-value of the overall association <0.0001 for models c
	and d, and of 0.023 for model e), as well as in model c (HRQ2vsQ1 0.91, 95% CI 0.85-0.98; HRQ3vsQ1 0.89,
	95% CI 0.83-0.95; HRQ4vsQ1 0.89, 95% CI 0.83-0.95) and in model d (HRQ2vsQ1 0.90, 95% CI 0.84-0.97;
	HRQ3vsQ1 0.86, 95% CI 0.80-0.93; HRQ4vsQ1 0.81, 95% CI 0.74-0.90) in quartile groups. The association was
	no longer statistically significant for model e in quartile groups.

[95% CI] of 0.84 [0.79; 0.90], 0.80 [0.75; 0.86], and 0.80 [0.75; 0.86] when respectively comparing the 2 nd

Acknowledgements

The authors want to thank all the women participating in the E3N cohort. They also acknowledge all the members of the "Exposome and Heredity" team.

Funding This work was realized with the data of the E3N cohort of the Inserm and supported by the Mutuelle Générale de l'Education Nationale (MGEN), the Gustave Roussy Institute, and the French League against Cancer for the constitution and maintenance of the cohort. This work has benefited from State aid managed by the National Research Agency under the program "Investment in the future" bearing the reference ANR-10-COHO-0006 as well as subsidy from the Ministry of Higher Education, Research and Innovation for public service charges bearing the reference n°2103586016. This work was also supported by a doctoral funding from the University Paris-Saclay Doctoral School of Public Health EDSP.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author Contributions Statement

All authors contributed to the study conceptualization and methodology. CM performed statistical analyses. CM wrote the first draft of the manuscript and all authors reviewed and edited the manuscript. All authors read and approved the final manuscript.


Olivier Guézou

Maître De Conférences

Hdr Uvsq

PUBLIC ET NUCLEAIRE, ENTRE FUSION ET FISSION »

teaching and research institutions in France or abroad, or from public or private research centers.

1. « Comme il est profond, ce mystère de l'Invisible ! »1 . Et ce qui est mal connu inquiète, menace, fait imaginer les pires catastrophes, les pires dissimulations.

Il faut dire que, s'agissant de la structure atomique des choses, de cet « Invisible » composant la matière, Hiroshima et Nagasaki sont une marque indélébile dans la mémoire de l'Humanité.

Ces noms sonnent comme les symboles toujours présents d'un nucléaire dépassant en puissance et en horreur une imagination humaine pourtant sans borne. L'image du nucléaire, même si selon certains les Bombes auraient permis une fin plus rapide de la guerre, souffre ainsi d'un mal originel incontestable. Et puis, cette idée, si chère à la « guerre froide » que l'Humanité peut détruire plusieurs fois la planète qui l'accueille, a marquépresque traumatisé -, des générations. La peur du nucléaire se confond alors obscurément avec l'inquiétude face à la guerre. Le nucléaire est avant tout chose militaire. Son image, en devenant civile, aurait pu s'améliorer. Mais une peur chasse l'autre. Et la crainte est alors celle de l'accident, de la catastrophe industrielle. La peur du feu, de l'incendie qui touche un quartier entier et que l'on connaît, que l'on sent, que l'on voit, est remplacée par celle de la radioactivité, mal invisible et déloyal, quasi-magique qui vient comme un courant d'air anéantir toute vie dans une ville, une région, un continent… Pour ne citer que les cas les plus emblématiques, quelques cruelles piqûres de rappel sont venues remettre le nucléaire sur le terrain d'un péril qui, s'il est civil cette fois, conserve son aura d'absolu. Three Mile Island (28 mars 1979) et Tchernobyl (26 avril 1986) sont des noms qui ont particulièrement marqué des opinions publiques américaine et européenne, pourtant parfois assez mal informées2 .

Les peurs, ensuite, n'ont cessé d'évoluer. La peur du réchauffement climatique et de ses conséquences planétaires à tous les niveaux ne cesse de croître tout en étant doublée, désormais, de craintes liées aux pandémies, aux catastrophes naturelles ou encore aux risques d'actions terroristes de grande ampleur. La diversification de ces peurs, si elle rend la situation pour le moins anxiogène, a semble-t-il banalisé pendant un temps le risque nucléaire, le ravalant au rang de dangerpresquecomme les autres. C'est alors que les événements et Mais lorsque la vision d'ensemble de la matière est délaissée pour ses composantes, son contenu, lorsque l'oeil se rapproche, lorsqu'à l'unité du droit public succède la diversité des matières qui le nourrissent, la relation entre nucléaire et droits publicsau pluriel cette foisquitte alors le domaine de la nature pour celui de l'artifice, du fabriqué. L'étude, de statique, devient dynamique, révélant des réactions en chaîne. La rencontre conduit alors à la séparation en des éléments différents, des éléments qui se télescopent, s'opposent. C'est de fission dont il est question, ce phénomène qui n'existe pas naturellement, mais que l'homme sait provoquer (Partie II).

Dans la présente contribution introductive, le choix a été fait de ne pas donner de références bibliographiques, celles-ci apparaissant dans les contributions du présent ouvrage. Seules ces dernières sont mentionnées ici.

PREMIERE PARTIE DROIT PUBLIC ET NUCLEAIRE : LA FUSION

3. Lors de la rencontre, de la percussion entre nucléaire et droit public, l'explosion n'a pas lieu. Ces deux éléments entrent en résonance l'un avec l'autre. Les moyens mis en oeuvre, les finalités poursuivies, voire la nature même du nucléaire et du droit public se répondent assez bien. Pour eux, l'extraordinaire est habituel et l'exorbitance la norme commune (A). Cette communauté entre droit public et nucléaire rend le premier naturellement adapté au second et contribue à renforcer la teinte publique du droit applicable. Le curseur des qualifications juridiques est comme décalé vers toujours davantage de singularité : les décideurs concernés sont les plus hautes autorités politiques de l'Etat ; les logiques sont celles de la police, de l'autorisation préalable, de l'encadrement, de la contrainte, de la surveillance, du contrôle ; l'acte de droit privé ou le contrat est généralement délaissé au profit d'un acte administratif unilatéral qui évolue parfois en acte de gouvernement. Même la relation entre droit international et nucléaire conduit à constater un renforcement réciproque. Qu'il suffise de dire que l'Agence internationale de l'énergie atomique, cette organisation internationale fondée en 1957 sous l'égide de l'ONU, a pour première attribution « d'encourager et de faciliter, dans le monde entier, le développement et l'utilisation pratique de l'énergie atomique à des fins pacifiques et la recherche dans ce domaine ». Le ton est clairement donné en faveur du soutien au développement du nucléaire civil. Et réciproquement, le droit international est renforcé par les caractéristiques du nucléaire. Le risque nucléaire par nature transfrontalier ne peut être saisi globalement que par le droit international. Dès lors, celui-ci a-t-il un rôle fondamental à jouer en matière de sureté nucléaire des centrales, de gestion des déchets, de responsabilité en matière de dommage nucléaire 14 , etc. S'agissant du nucléaire militaire, certains actes de droit international, notamment en matière de coopération industrielle ou stratégique, ont favorisé, par leur existence même, le développement du nucléaire. Toutefois, force est de constater que c'est principalement de la limitation ou de la non-prolifération des armes nucléaires dont il est L'importance planétaire de ces questions et les conséquences d'un conflit nucléaire seraient tellement dramatiques que le droit international revêt en la matière une importance considérable, soulignée par les crises récentes notamment avec l'Iran. Adaptant certains de ses principes les plus fondamentaux, et notamment celui tenant à la protection de la souveraineté étatique, le droit international organise des mécanismes de vérification et de surveillance des Etats dont l'efficacité méritera d'être vérifiée 15 . 11. Droit public et nucléaire forment donc un couple terrible où la puissance accompagne l'exorbitance, mais aussi un couple uni dont les éléments s'enrichissent et se renforcent mutuellement par un mécanisme de fusion naturelle permise par leurs points communs. Il convient maintenant de vérifier si droit public nucléaire ne conservent pas tout de même des caractéristiques propres, conduisant entre eux à une véritable lutte d'influence, la fission s'installant dans le couple. 14 L. Grammatico-Vidal, « Quand la science se heurte au droit : responsabilité civile nucléaire et installations de fusion », § 207. 15 T. Fleury, « La modulation des principes du droit international face à la menace nucléaire », § 119.

2°) LA S UP ER I O R I T E D ES I N T ER

SECONDE PARTIE DROITS PUBLICS ET

A ACTION : UNE REGULATION SUR-MESURE

13. Les activités nucléaires ne peuvent être laissées à elles-mêmes et les risques, réels ou supposés, cristallisent autour de l'Etat des craintes et des attentes qui ne peuvent être ignorées 16 . La prévention de ces risques suppose une régulation publique spécialisée (1°) prenant en compte les impératifs de transparence et de démocratie (2°).

B REACTIONS : LES REGLEMENTATIONS GENERALES FACE AU NUCLEAIRE

16. La régulation ne suffit pas. Le nucléaire a besoin aussi d'un encadrement réglementaire propre à assurer la sécurité. Le droit public doit alors se décliner dans la diversité de ses composantes : de nombreuses matières de droit public rencontrent, dans leur domaine respectif, la chose nucléaire et contribuent ainsi à son encadrement.

1°) DIVERSITE D E S D R O I T S P UB LI C S SO L LI CI T ES

17. Le droit de l'environnement, ce droit touche-à-tout, véritable coucou qui faitpour le bien communsa place dans le nid des autres est évidemment au premier rang des droits susceptibles d'encadrer les activités nucléaires. Il s'impose notamment par le biais du droit des installations classées pour la protection de l'environnement (ICPE). Le nucléaire est un sujet important d'un droit de l'environnement qui semble peiner parfois à l'encadrer [START_REF]S'il faut conclure une contribution introductive, qu'il soit permis de dire simplement qu'entre « droit public et nucléaire[END_REF] . La notion de risque est alors tout à fait cardinale, qu'il s'agisse de risques catastrophiques ou plus quotidiens comme en matière de rejet d'effluents radioactifs 20 ou s'agissant des utilisations médicales du nucléaire 21 . Mais le droit de l'environnement ne peut suffire. D'autres disciplines juridiques sont sollicitées, permettant de saisir toutes les dimensions et conséquences des activités nucléaires.

Le droit de l'urbanisme a, en la matière, un rôle pratique fondamental conduisant à l'intervention de nombreux acteurs, notamment à l'échelon local 22 . Les installations nucléaires sont de grande dimension, présentent un impact important en termes d'occupation des sols, de nuisances sonores, visuelles et sanitaires, tout en constituant souvent une manne importante pour les territoires concernés. Leur implantation locale pose évidemment la question de l'acceptation de ce voisin parfois encombrant.

A côté des droits de l'environnement et de l'urbanisme, qui sont en première ligne, de nombreuses autres matières de droit public sont sollicitées pour encadrer les activités nucléaires de manière peut-être plus diffuse, moins directe, mais également importante : le droit administratif généralresponsabilité, police administrative, droit des actes et contrats [START_REF]S'il faut conclure une contribution introductive, qu'il soit permis de dire simplement qu'entre « droit public et nucléaire[END_REF]

  les peurs se sont télescopés dans une tragique collision : le séisme, le tsunami et l'accident nucléaire se sont ainsi rencontrés le 11 mars 2011 à Fukushima, pour écrire une fable macabre dont les leçons ou la morale restent encore à tirer. C'est de cet événement que l'idée de cet ouvrage est venue. Très modestement bien sûr, car il ne s'agit de voir ni la technique, ni la science, ni la morale, ni la psychologie, ni la sociologie ni même d'avoir une approche citoyenne ou politique des choix nucléaires. L'objectif est de contribuer dans notre spécialitéle droit publicà mieux cerner les problématiques juridiques du nucléaire, à les présenter de manière aussi équilibrée que possible en ne versant ni dans le plaidoyer ni dans la diatribe. 2. « Droit public et nucléaire » : le rapprochement n'est pas si curieux. L'un et l'autre relèvent de l'exceptionnel, du hors du commun, de l'exorbitance… Telle est leur nature, leur matière fondamentale qui transparaît lors d'une étude statique de deux éléments qui, comparés l'un à l'autre, révèlent qu'ils se ressemblent. Entre nucléaire et droit public au singulier, la rencontre conduit à l'enrichissement et au renforcement mutuels, comme si deux devenait un. Apparaît ainsi un phénomène naturel qui existe, nous dit-on, au coeur des étoiles : la fusion (Partie I).

  Dès lors, droit public et nucléaire peuvent s'allier dans une union raisonnée, volontaire et profitable aux deux protagonistes : le droit public en sort renforcé dans sa dimension exorbitante du droit commun, tout en ayant contribué au développement du nucléaire en France (B). A -PERCUSSION : L 'EXORBITANCE COMMUNE 4. Dans leur contexture, dans chacune de leurs fibres, presque génétiquement, nucléaire et droit public sont extraordinaires : les moyens mis en oeuvre sont exorbitants (1°) et les fins poursuivies hors du commun (2°). 1°) LA P UI SS AN C E DE S MO Y E N S 5. Classiquement, la doctrine de la Puissance publique chère à Hauriou révèle la spécificité du droit public par les moyens particuliers qui sont mis en oeuvre. Le parallèle avec le nucléaire est assez aisé puisque ce voyage au centre des atomes implique des connaissances, des techniques, des compétences et des outils littéralement extraordinaires. Mais la singularité des moyens du droit public ne suppose pas seulement leur différence. Elle traduit également une stature hors du commun, une véritable Puissance dont les prérogatives de puissance publique ne sont que le révélateur. La détention du pouvoir de déclencher le feu nucléaire est probablement le symbole ultime et archétypal du Pouvoir 3 . Mais la main mise sur l'énergie -d'une énergie présentée comme accessible, bon marché et dé-carbonée -, confère également la puissance. La complexité et la dangerosité des moyens utilisés ainsi que la dépendance à l'énergie de nos sociétés modernes confèrent à ceux qui les maîtrisent un pouvoir qui rend les acteurs du secteur incontournables. L'importance des enjeux politiques, économiques et sociaux en cause renforcent encore les différents acteurs de la « filière nucléaire » 4 .

7 . 9 .

 79 ET S 6. L'exorbitance du droit public ne se traduit pas seulement par les moyens employés, mais aussi par les objectifs poursuivis : l'intérêt général et son accomplissement dans la notion de service public constituent le fondement, la raison d'être mais également le révélateur du droit public.Là encore, de tels objectifs sont indissociables du nucléaire et de son développement en France. La politique nucléaire française a pour objectif de protéger l'intérêt général qui se confond alors en pratique avec l'intérêt national. Il faut donner à la France une place de choix sur le plan diplomatique, politique et militaire (dissuasion nucléaire) mais également économique (indépendance énergétique). Concrètement le droit, et particulièrement le droit public, n'est pas alors le carcan parfois imaginé. Au contraire, il vient soutenir, accompagner et renforcer les activités nucléaires françaises selon une approche très patriotique.Les notions clés du droit public qui reposent sur les finalités de l'action sont, au même titre que celles centrées sur les moyens mis en oeuvre, incontournables s'agissant du nucléaire.Ainsi, les contraintes et qualifications d'intérêt général, de service public, d'utilité publique, qui forgent et justifient l'autonomie du droit public vis-à-vis du droit privé, occupent une place clé en matière nucléaire. La protection de l'ordre public dans toutes ses dimensions et notamment s'agissant de la sécurité et de la salubrité publiques, ainsi que la logique de prévention qui irrigue les activités de police administrative, sont même alors d'une importance vitale. Lorsque la collision a eu lieu, que les logiques se sont télescopées, démontrant que droit public et nucléaire se rejoignent largement, une seconde phase peut commencer, présentant les répercussions de cette rencontre. Un phénomène de convergence apparaît alors dans lequel droit public et nucléaire se renforcent mutuellement.B REPERCUSSION : L'UNION PROFITABLE8. La communauté de logiques et de natures fondamentales entre droit public et nucléaire permet la convergence de deux Puissances qui vont se renforcer mutuellement, le nucléaire devenant possible grâce au soutien du droit public, qui en tire un approfondissement de son exorbitance. Ce mouvement apparaît d'abord sur le plan organique où les acteurs sont particulièrement puissants et revêtent une dimension publique marquée (1°). Mais il existe également, quoique de manière plus ambivalente, sur le plan matériel des sources juridiques puisque ces dernières contribuent ou ont contribué au développement du nucléaire tout en étant elles-mêmes renforcées par lui (2°).1°) LA « P UI S S AN C E P U B LI Q U E » D E SA CT E UR S La complexité, le coût, les enjeux des programmes nucléaires, qu'ils soient civils ou militaires, les font relever de la quintessence de la puissance publique. Dans la pyramide des pouvoirs, l'extrémité de la plus haute pointe est en cause. Au sein de la sphère publique, le nucléaire est chose de l'Etat et au sein de l'Etat, les autorités politiques les plus élevées vont intervenir, et dans leur fonction les plus emblématiques, celles qui relèvent des stratégies nationales qu'elles soient diplomatiques, militaires 5 , politiques, scientifiques, économiques, etc. La puissance nucléaire est celle du Président de la République dont l'aura est magnifiée par la maîtrise du feu nucléaire, instrument d'une approche régalienne d'une fonction présidentielle centrée sur le destin d'un homme, véritable incarnation de l'Etat 6 .Mais la puissance du nucléaire repose aussi sur la création et le développement d'une filière nucléaire nationale7 . En France, les entreprises du nucléaire sont de très grande dimension en termes de chiffres d'affaires, de nombre d'employés, de puissance économique, de capacité de recherche, etc. Elles font partie des entreprises les plus importantes et les plus puissantes sur les marchés mondiaux concernés.Par ailleurs, si la recherche, l'industrie et la dissuasion nucléaire s'entrecroisent, et utilisent la voie de l'entreprise, voire du marché, c'est toujours en conservant des particularités publiques importantes. Le triomphe d'un mode de fonctionnement économique fondé sur le libre échange et les relations de marché a nécessairement un impact tant sur le droit public que sur le nucléaire. Pourtant, dans ces domaines, plus qu'ailleurs, un noyau dur hors du commun semble demeurer fermement. En matière nucléaire, les entreprises publiques sont, peut-être moins encore qu'ailleurs, des entreprises tout à fait comme les autres. L'encadrement très strict du droit de grève au profit du principe public de continuité des services publics est un bon exemple d'une sorte de publicisation du droit applicable aux entreprises du nucléaire[START_REF] Einaudi | Continuité du service, sûreté nucléaire et droit de grève des salariés[END_REF] .2°) SOURCES D E DR O I T P UB LI C ET N U CL E AI R E : UN RE N FO R C E M EN T A M BIV A L EN T 10. Historiquement, le droit public français a permis de favoriser l'émergence du nucléaire militaire comme du nucléaire civil. La Constitution de la V ème République fait la part belle à la rencontre entre un homme et un peuple et donne au Président de la République une place prééminente qui n'est peut-être pas sans lien avec la détention du feu nucléaire 9 . Le droit financier et le droit administratif retiennent également des postures, au moins en pratique, plutôt favorables au nucléaire 10 . La période d'apparition du nucléairela seconde guerre mondiale et la reconstruction qui a suiviexplique dans une large mesure qu'il ait été élevé au rang de grande cause nationale. L'intérêt général est alors principalement pronucléaire et commande de doter la France d'une force de dissuasion et d'une industrie nucléaire compétitive. Le droit public se présente comme un droit adapté pour permettre ce développement. Dans la relation entre droit public et nucléaire, l'Histoire du pays est l'une des raisons du soutien important apporté par le droit public au nucléaire. Mais le temps ne s'arrête pas et le contenu de l'intérêt général dépend des événements et des évolutions de l'opinion publique. Une mise en perspective chronologique fait apparaître que la relation entre intérêt général/droit public et nucléaire a évolué progressivement, avec un basculement qui peut être symboliquement datémême si le phénomène est plus diffus et plus continude la catastrophe de Tchernobyl. L'intérêt général intègre alors davantage la nécessité d'organiser une protection contre le ou les risques nucléaires 11 . Le droit public peut s'adapter à cette évolution ou plutôt à cette ambivalence de l'intérêt généralqui est invoqué par les pro comme par les anti-nucléairescar il possède lui-même ce double visage d'un droit dont l'adaptation aux actions publiques permet leur développement optimal mais également leur encadrement de manière efficace (voir la seconde partie). En droit communautaire, un mouvement de même nature apparaît 12 . Ainsi, entre l'Europe et le nucléaire, le renforcement est, comme pour le droit interne, réciproque. D'abord, la puissance de l'Europe et sa place sur la scène internationale viennent en partie de la maîtrise par certains de ses Etats de l'arme nucléaire. Ensuite, et peut-être surtout, la construction européenne est aussi celle d'une Europe de l'atome. L'objectif est de favoriser la création dans les Etats membres d'une industrie nucléaire solide. Cette construction communautaire est spécifique, d'un genre nouveau. Elle repose sur des mécanismes particulièrement interventionnistes, sur des ressorts aux teintes publiques marquées. Le libre jeu des mécanismes du marché, qui est généralement l'alpha et l'oméga des politiques européennes, est, s'agissant du nucléaire, appréhendé de manière singulière, et ici, le marché commun ne l'est pas tant que cela. Lorsque la question nucléaire est portée devant les juges de l'Union européenne, le mouvement se confirme 13 .

  NUCLEAIRE : LA FISSION 12. Le droit public, qui s'adapte aux spécificités de l'action publique, la permet et la renforce mais il pose également le cadre et les limites qu'elle doit respecter. Face au nucléaire, il intervient d'une double manière. D'abord, il prend l'initiative et s'adapte à ses spécificités, dont les dimensions scientifique et technique, mais également politique et économique rendent une simple réglementation insuffisante. C'est le temps de l'action, par un cadrage sur-mesure qui doit prendre la forme d'une régulation particulière (A). Ensuite, les matières qui composent le droit public et constituent autant d'ensembles juridiques contraignants pour la Puissance publique, sont sollicitées. C'est le temps de la réaction des réglementations générales confrontées aux questions nucléaires (B).

  1°) UNE R E G UL AT I O N P U BLI Q U E S P ECI A LI SE E14. En France, la régulation des activités nucléaires est au premier chef confiée à l'Autorité de sureté nucléaire17 , une autorité administrative indépendante, qui préside à la création des normes de prévention du risque nucléaire, assure une partie de leur contrôle et contribue à la production d'une information aussi fiable que possible en la matière. Le recours à une telle autorité, selon une approche en termes de régulation, est de nature à permettre, davantage qu'une simple réglementation, la prise en compte d'enjeux complexes aux dimensions multiples (économiques, de santé, technologiques, etc.). Si le recours à une administration de mission, resserrée, empreinte d'autorité, avec des pouvoirs assez complets, semble bien adapté au domaine du nucléaire, le fait qu'elle soit en dehors de la pyramide administrativo-politique des pouvoirs est plus étonnant. En effet, cela revient à confier à une administration théoriquement déconnectée de l'Etat et échappant à la subordination administrative au gouvernement, le pouvoir de réguler une matière régalienne par nature et marquée du sceau de la souveraineté nationale. Pour être efficace et légitime, le régulateur doit détenir suffisamment de pouvoirs et d'autorité, mais il doit surtout être impartial et indépendant. Reste à savoir de qui, et il est probable que, plus encore que par rapport à l'Etat, c'est vis-à-vis des entreprises de la filière nucléairedes opérateurs -qu'il est impératif que l'autorité régulatrice soit indépendante.2°) LES EN J EU X D E L A T R A N S PA R EN C E 15. La loi qui organise le cadre général du nucléaire en France est « relative à la transparence et à la sécurité en matière nucléaire » (loi n° 2006-686 du 13 juin 2006, préc.). La transparence présente en matière nucléaire deux vertus cardinales qui la rendent indispensable. Elle permet d'abord de rompre avec le déficit démocratique souvent dénoncé dans le domaine des activités nucléaires et qui semble n'être pas totalement résorbé. Elle permet également d'améliorer la sécurité nucléaire en renforçant son contrôle et en incitant les responsables à davantage de rigueur et de responsabilité.Mais la transparence -ou l'image de la transparencea également un autre effet induit. Elle permet, potentiellement du moins, de renforcer le nucléaire lui-même en légitimant les décisions prises en la matière, en lui donnant l'apparence rassurante d'une activité maîtrisée, assumée, qui n'a ou n'aurait rien à cacher.Démocratie, sécurité voire développement du nucléaire, tout concorde pour rendre indispensable l'existence d'une transparence qui a besoin de supports concrets pour la rendre effective. Ainsi, la transparence se matérialise par des notions juridiquement plus faciles à saisir comme celles de « droits subjectifs d'accès à l'information », de « documents communicables » ou encore de « devoir d'information » pesant sur les personnes et autorités concernées. La transparence repose également sur l'institution d'organes, d'instances ou d'organismes dont les missions sont de contribuer à l'information en matière nucléaire 18 .

  C. Cans, « Droit nucléaire et droit de l'environnement : mariage de raison, mariage sans raison », § 186. 20 M. Moliner-Dubost, « L'évolution de la réglementation des rejets d'effluents radioactifs », § 199 ; L. Grammatico-Vidal, préc. § 207. 21 J.-P. Markus, « La médecine nucléaire, entre droit nucléaire et droit de la santé », § 215. 22 M. Yazi-roman, préc. § 173. évolutive et ambivalente, à la fois de fusion et de fission. Le droit public aide, s'occupe, favorise le nucléaire, il contribue à son développement et le protège. Mais il a également vocationrôle ô combien importantà le diriger, le cadrer, le contraindre et offrir, cette fois contre lui, une protection. Dans le terrible opéra du nucléaire, la règle de droit public doit, comme l'héroïne chère à Pergolèse, tenir fièrement son rang de « servante maîtresse ». Paris, janvier 2013.

Guy de Maupassant, « Le Horla ».

A propos du « mensonge d'Etat » relatif à ce nuage, voir S. Manson « « L'Autorité de sûreté nucléaire au confluent des risques », spéc. § 145 ; Y. Poirmeur, « Du spectre de l'État sécuritaire à la dénonciation de l'État in-sécuritaire », spéc. § 139.

J. Massot, « Le président nucléaire », § 23 ; J.-C. Videlin, « Droit public et activités nucléaires militaires », § 36.

S. Grandvuillemin, « Les entreprises publiques de la filière nucléaire », §

J.-C. Videlin, préc., § 36.

J. Massot, préc., § 23.

Y. Poirmeur, préc., spéc. § 136.

D. Blanc, « L'Euratom et la constitution d'une Europe de l'énergie nucléaire : une politique publique à la vitalité paradoxale », § 94.

E. Saulnier-Cassia, « La question nucléaire devant les juges de l'Union européenne » , § 107.

Y. Poirmeur, préc., spéc. § 189.

S. Manson, préc. § 143.

P. M. Cloix, « Documents administratifs, données sensibles et nucléaire », § 161 ; K. Lucas, « Démocratie participative et nucléaire civil », § 154 ; M. Yazi-Roman, § 173.