Rafael Trevisan

Fabrício Flores-Nunes

Euler S Dolores

Jacó J Mattos

Clei E Piazza

Sílvio T Sasaki

Satie Taniguchi

Rosalinda C Montone

Márcia C Bícego

Afonso C D Bainy
email: afonso.bainy@ufsc.br

Isis M M Dos Reis

Flávia L Zacchi

Bárbara N M Othero

Camila L V Bastolla

Danielle F Mello

Ana Paula

M Fraga

Nestor Wendt

Guilherme Toledo-Silva

Guilherme Razzera

Alcir L Dafre

Cláudio M R De Melo

Adalto Bianchini ||

Maria R F Marques

Thiol oxidation of hemolymph proteins in oysters Crassostrea brasiliana as markers of oxidative damage induced by urban sewage exposure

Keywords: Sewage, Biomarkers, Protein oxidative damage, Oxidative stress, Bivalve

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

1.

INTRODUCTION

According to recent statistics, only 64% of the world population had access to improved sanitation (hygienically separation of human excreta from human contact) in 2012 [1].

Additionally, rapid urbanization, fast population growth, migration into urban centers, and insufficient urban coverage of sanitary sewage collection system, contribute to the sanitary issues [START_REF] Langergraber | Ecological Sanitation-a way to solve global sanitation problems?[END_REF]. Consequently, urban sewage contamination is an increasing concern not only due to its hazards to human health but also due its potential adverse effects on aquatic ecosystems. Raw or untreated urban sewage is a complex mixture, typically composed of pathogens, inorganic nitrogen and phosphorous, metals, chlorides, organic compounds (including proteins, carbohydrates, and urea), surfactants, phenols, polycyclic aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), pesticides, and emerging contaminants such as phthalates, pharmaceuticals, and personal care products [START_REF] Deblonde | Emerging pollutants in wastewater: A review of the literature[END_REF][START_REF] Sperling | Wastewater Characteristics, Treatment and Disposal[END_REF]. Moreover, as only 64% of the world population had access to improved sanitation in 2012, lower rates of access to sewage treatment (primary, secondary and tertiary) are expected. But even if sewage treatment options are available, none of the sewage treatment plants are 100% efficient [START_REF] Gardner | Performance of UK wastewater treatment works with respect to trace contaminants[END_REF]. Furthermore, sewage treatment process generates a sludge that contains toxic by-products, which can contaminate groundwater when applied as a fertilizer [START_REF] Deblonde | Emerging pollutants in wastewater: A review of the literature[END_REF]. Therefore, both raw and treated urban sewage may threaten aquatic ecosystems, thus raising concerns within the ecotoxicology and environmental health scientific community.

Sewage effluent contains various classes of contaminants, and many of these contaminants possess pro-oxidant properties [START_REF] Winston | Prooxidant and antioxidant mechanisms in aquatic organisms[END_REF], which may lead to oxidative damage and subsequent reversible and/or irreversible alterations in the structure and function of various cellular components, thereby negatively impacting cellular metabolism [START_REF] Go | The cysteine proteome[END_REF]. Cysteine (Cys) residues are among the main targets of reactive oxygen species (ROS), as their thiol groups are very sensitive to alterations in the cellular redox state. Reversible post-translational modifications of proteins include intra or intermolecular disulfide bridges (-SS-), glutathionylation (-SSG) or S-nitrosylation (-SNO), and oxidation to sulfenic acid [START_REF] Go | The cysteine proteome[END_REF].

Irreversible oxidation forms can also be produced, such as sulfinic (-SO2 -) and sulfonic acid (-SO3 -) [START_REF] Go | The cysteine proteome[END_REF]. Critical Cys residues on proteins are well evolutionary conserved, and due to this chemical flexibility of the thiol group and its oxidation states, Cys residues are frequently associated with important protein characteristics, such as enzyme catalysis, transcriptional regulation, protein folding, and metal coordination [START_REF] Go | The cysteine proteome[END_REF].

Given the sensitivity of thiol groups to ROS, assessment of protein oxidation in bivalves could be a useful biomarker for aquatic contamination, and several recent studies support this idea. For example, Cys oxidation after exposure to contaminants has been identified in proteins involved with cellular and metabolic functions, including glycolysis, citric acid cycle, stress response, lysosomal processes, and muscle contraction [START_REF] Hu | Toxicity of copper oxide nanoparticles in the blue mussel, Mytilus edulis: A redox proteomic investigation[END_REF][START_REF] Pedriali | A redox proteomic investigation of oxidative stress caused by benzoylecgonine in the freshwater bivalve Dreissena polymorpha[END_REF]. However, the direct link between thiol oxidation, loss of protein function/activity, and metabolic impairment in bivalves is yet to be fully understood. This is not the case for mammals, as Cys oxidation has been linked to conformational changes in proteins, leading to impaired function [e.g. microtubule elongation (tubulin) and DNA-binding (human estrogen receptor)] [START_REF] Riederer | Oxidation Proteomics: The Role of Thiol Modifications[END_REF]. Since oxidative stress is a common toxicity mechanism to several classes of contaminants, identifying proteins targets of oxidative damage in bivalves could help to identify cellular and metabolic functions that may be impaired due to contaminants (pro-oxidants) exposure.

As for detecting protein oxidation in various organs, studies in mussels suggest that hemolymph can be an important target of protein oxidation in bivalves [START_REF] Kaloyianni | Oxidative effects of inorganic and organic contaminants on haemolymph of mussels[END_REF]. This tissue also calls the attention to the presence of abundant thiol-containing proteins in different bivalve species.

For example, in oysters Crassostrea gigas and Crassostrea virginica, the major abundant hemolymph protein is the Extracellular Superoxide Dismutase or Cavortin (C. gigas) and Dominin (C. virginica) [START_REF] Gonzalez | Evidence in oyster of a plasma extracellular superoxide dismutase which binds LPS[END_REF][START_REF] Scotti | Characterisation of cavortin, the major haemolymph protein of the Pacific oyster (Crassostrea gigas)[END_REF][START_REF] Itoh | Characterization of the major plasma protein of the eastern oyster, Crassostrea virginica, and a proposed role in host defense[END_REF]. Both proteins have similar molecular weight (~20 kDa), contain 4 Cys residues, one lipopolysaccharide (LPS), and one integrin-binding domain, and are able to sequester iron. Interestingly, both Cavortin and Dominin have minimal (if at all) superoxide dismutase activity, despite having domains related to copper-zinc superoxide dismutase.

Although these proteins comprise ~50% of the plasma protein abundance, their functions remain unclear, but it is thought that they could be involved in bacterial recognition and phagocytosis events, antioxidant protection via superoxide dismutase activity, as well as metal transport. As abundant thiol-containing proteins, these and other hemolymph proteins may be susceptible to oxidation events due to contaminants and/or pathogens, leading to loss of protein function and potentially adverse outcomes.

Balneário Camboriú is an important tourist destination in southern Brazil, especially during summer. Although not a very populous city (~124,000 residents), Balneário Camboriú receives several millions of tourists over the course of a summer. Despite having urban sewage collection and treatment facilities that serve most of the regular population, this significant increase in population due to tourism may be a challenge to sewage treatment and to the water quality along the bay. In fact, microbiological seawater analyses by the local environmental agency indicate that Balneário Camboriú bay has poor water quality in several regions along the shoreline (available at http://www.fatma.sc.gov.br/). Notably, the water quality in these regions is persistently poor (i.e. not only during peak tourist season), suggesting that the sewage treatment facility is likely overwhelmed. Continuous worsening of water quality could pose a threat to many economic activities in the region.

Thus, taking into account that the urban sewage is a concerning issue and that Cys oxidative damage is a mechanism of toxicity shared by different class of contaminants, the present study investigated for the first time the effects of urban sewage on protein thiol oxidation in bivalves, and aimed to identify proteins sensitive to Cys oxidation in the hemolymph as potential biomarkers of oxidative stress. Consequently, we examined the extent of urban sewage contamination at Balneário Camboriú coast by assessing standard water quality parameters and organic contaminants. In addition, oysters Crassostrea brasiliana were exposed to seawater samples collected at Balneário Camboriú, followed by analysis of total protein thiol status in the gills, digestive gland, and hemolymph. The thiol oxidation profile of specific abundant hemolymph proteins was further explored as a simple and efficient method to assess pro-oxidant effects of environmental contaminants in bivalves. and stored in 100 L high-density polyethylene gallons, and an aliquot was collected for water quality analysis. In addition, approximately 250 g of sediment were collected at each site for chemical analysis using a Van Veen Grab Sampler.

MATERIAL AND METHODS

Study area and seawater sample collection

Animals and exposure conditions

Oysters C. brasiliana (males and females, 6 -8 cm length) were obtained from an aquaculture laboratory at Federal University of Santa Catarina (Marine Mollusks Laboratory, LMM). Animals were maintained at LMM in a flow through system for 11 d prior to the experiments, using filtered (0.45 μm) and UV treated seawater with constant temperature (25 °C) and salinity (33 ‰). During this period, animals were fed with a mixture of microalgae (50% Isochrysis galbana and 50% Chaetoceros muelleri, 20 x 10 4 cells/mL).

Following their transport to the laboratory, the animals were acclimated for 24 h in highdensity polyethylene tanks containing filtered seawater (0.45 μm, 25 °C and 33 ‰ salinity, 1 animal/L) with no further feeding. At the same time, seawater samples collected at Balneário Camboriú were maintained in the same high-density polyethylene plastic gallons used for water sampling and were allowed to stabilize to 25 °C for 24 h in the same laboratory.

Following the acclimation period, a group of oyster (1 pool of LABs, steroids and organochloride pesticides were carried out according to the procedures detailed elsewhere [START_REF] Flores-Nunes | Changes in protein expression of pacific oyster Crassostrea gigas exposed in situ to urban sewage[END_REF][START_REF] Souza | Evaluation of tropical water sources and mollusks in southern Brazil using microbiological, biochemical, and chemical parameters[END_REF]. Briefly, samples (1 g for oysters and 20 g for sediments) were Soxhlet-extracted with a 50% mixture of residue grade n-hexane and dichloromethane. The organochlorine extract was purified in an alumina chromatographic column. The hydrocarbon extracts were fractionated into F1 (LABs), F2 (PAHs), and F3 (steroids, only for sediment) by silica gel-alumina column chromatography. F3 was evaporated to dryness, and steroids were derivatized to form trimethylsilyl ethers using bis(trimethylsilyl) trifluoroacetamide with 1 % trimethylchlorosilane. Organochlorine pesticides were analyzed in an Agilent Technologies gas chromatograph in splitless mode using an electron capture detector (GC-ECD). Steroids were determined on a gas chromatography with flame ionization detector (GC-FID). PAHs, PCBs, and LABs were analyzed by an Agilent 6890 gas chromatograph coupled to a 5973N mass spectrometer (GC/MS) in a selected ion mode (SIM). Certified standards at five different concentrations were used for calculations. PAH, PCB, and LAB identification were based on mass/charge ratio of the individual quantitation ion (m/z) and retention times of certified standards.

Sample preparation

Gills and digestive gland (approximately 100 mg wet weight each) were homogenized

(1:4 w:v) in 10 mM TRIS buffer pH 7.2, containing 1 mM EDTA, 0.5 M sucrose, 0.15 M KCl, and 1 mM PMSF, followed by centrifugation (12,000 g for 60 min at 4 °C). The supernatant was collected and used for further procedures. Hemolymph was used without any additional treatments. Total protein content was determined using Coomassie blue [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding[END_REF] and serum bovine albumin standards.

Reduced protein thiol groups (PSH) were assayed using the fluorophore 5iodoacetamide-fluorescein (5-IAF) based on a protocol with marine bivalves [START_REF] Tedesco | Gold Nanoparticles and Oxidative Stress in the Blue Mussel, Mytilus edulis[END_REF], with minor modifications. For this purpose, 100 µg protein for gills and digestive gland or 50 µg protein for hemolymph were incubated at room temperature for 30 min with 0.1 M TRIS pH 7.5 containing 0.2 mM 5-IAF. This fluorophore specifically recognizes reduced PSH. Excess 5-IAF was removed by acidification with 10% trichloroacetic acid (TCA) for 5 min at 4 °C, centrifuged (11,000 g for 3 min at 4 °C) and washed twice with cold acetone. Samples were further resuspended in SDS-PAGE sample buffer containing 5% β-mercaptethanol and stored at -20°C for further analyses.

Reversibly oxidized protein thiol groups (R-PSX) were also assayed using the fluorophore 5-IAF, but with the addition of steps for PSH alkylation and reduction of R-PSX [START_REF] Baty | Detection of oxidant sensitive thiol proteins by fluorescence labeling and two-dimensional electrophoresis[END_REF]. Briefly, 100 µg protein for gills and digestive gland or 50 µg protein for hemolymph were incubated with 100 mM N-ethylmaleimide (NEM) and 1 % sodium dodecyl sulfate (SDS) for 15 min at room temperature for PSH blocking, followed by NEM removal by protein precipitation with 10 % TCA and cold acetone washing. Proteins were resuspended in 6 M urea containing 1 % SDS and 10 mM dithiothreitol (DTT) for 30 min for the reduction of R-PSX. DTT was removed by 10 % TCA precipitation and the newly reduced thiols groups (originated from the reduction of R-PSX by DTT) were labeled by incubation for 30 min at room temperature in 6 M urea containing SDS 1 % and 0.2 mM IAF. Excess 5-IAF was removed by 10 % TCA precipitation and cold acetone washing. Samples were resuspended in SDS-PAGE sample buffer containing 5% β-mercaptethanol and stored at -20°C for further analyses.

In vitro exposure of hemolymph to oxidants

Hemolymph from reference animals (REF) was used for further exposure to hydrogen peroxide, cumene hydroperoxide (CHP) or hypochlorous acid (HOCl). A total of 4 samples (n = 4) were used for this experiment. Proteins extracts (60 µg) were incubated with 0.01, 0.1, 1, and 10 mM (in phosphate saline buffer pH 7.4 adjusted to 3 % NaCl) of each oxidant for 1.5 h in the dark and at room temperature. By the end of the incubation period, samples were immediately separated in two aliquots (30 µg each): the first was used for PSH determination, with the addition of 10 % TCA, while the second was used for R-PSX determination, with the addition of 100 mM NEM. Samples were further prepared and analyzed as stated in sections 2.4 and 2.5. An additional group was maintained in 3 % NaCl -phosphate saline buffer pH 7.4 under the same conditions described above for 1.5 h, and used as control (Ctl) for each sample.

Quantification of PSH and R-PSX

Protein digestion and MALDI-TOF and MALDI-TOF/TOF analyses of hemolymph

Computational analysis of C. brasiliana Dominin

After protein identification by mass spectrometry, the most abundant protein in the hemolymph of C. brasiliana (Dominin, see section 3.4) was investigated for amino acid sequence similarity with homologous extracellular superoxide dismutase in other oyster species by molecular phylogeny and multiple alignments analysis. The presence of reactive and surfaceexposed Cys residues was also investigated by 3D structural modeling. These analyses aimed to detect Cys residue prone to oxidation events in C. brasiliana Dominin, and based on the similarity of their amino acid sequences and domains, to predict such events in homologous oyster proteins.

The molecular phylogenetic analysis was carried out using the Maximum Likelihood Method [START_REF] Whelan | A General Empirical Model of Protein Evolution Derived from Multiple Protein Families Using a Maximum-Likelihood Approach[END_REF]. Protein sequences were initially analyzed by multiple alignments at MUSCLE 3.8 [START_REF] Edgar | MUSCLE: a multiple sequence alignment method with reduced time and space complexity[END_REF], and suitable alignment blocks were filtered on GBlocks Server [START_REF] Talavera | Improvement of Phylogenies after Removing Divergent and Ambiguously Aligned Blocks from Protein Sequence Alignments[END_REF] using default parameters. Resulting blocks were of filtered sequences were re-aligned at MUSCLE 3.8 and analyzed by MEGA6 [START_REF] Tamura | MEGA6: Molecular Evolutionary Genetics Analysis Version 6.0[END_REF], testing for the substitution model and using the lowest BIC scores (Bayesian Information Criterion) to define the best substitution pattern. Based on this model, a bootstrap consensus tree inferred from 1000 replicates was taken to represent the evolutionary history of the analyzed taxa.

Multiple alignments of C. brasiliana Dominin protein sequence against homologous proteins from Ostrea edulis (extracellular SOD, ADF80415.1), Saccostrea glomerata (extracellular SOD, ACQ73551.1), C. virginica (dominin, BAF30874.1), Crassostrea gigas (extracellular Cu-Zn SOD-like, 011414395.1; cavortin, AAT44352.1) were carried out using MUSCLE 3.8. The protein sequence was also analyzed for the presence of peptide signal [START_REF] Petersen | SignalP 4.0: discriminating signal peptides from transmembrane regions[END_REF] and putative conserved domains [START_REF] Punta | The Pfam protein families database[END_REF]. Motifs related to lipopolysaccharide (LPS) and integrin binding were identified based on C. gigas extracellular superoxide dismutase [START_REF] Gonzalez | Evidence in oyster of a plasma extracellular superoxide dismutase which binds LPS[END_REF], a homologous protein to C. brasiliana Dominin.

The protein 3D model was built using I-Tasser suite [START_REF] Yang | The I-TASSER Suite: protein structure and function prediction[END_REF][START_REF] Zhang | I-TASSER server for protein 3D structure prediction[END_REF][START_REF] Roy | I-TASSER: a unified platform for automated protein structure and function prediction[END_REF] for ab initio modeling following default parameters including multiple SOD sequence alignments. The quality of PDB structural model was checked by Procheck [START_REF] Laskowski | AQUA and PROCHECK-NMR: Programs for checking the quality of protein structures solved by NMR[END_REF] and LigPlot software was used to map copper and zinc coordinated amino acids [START_REF] Wallace | LIGPLOT: a program to generate schematic diagrams of protein-ligand interactions[END_REF].

Statistics

All data were checked for normality by Kolmogorov-Smirnov test prior to analyses. PSH and R-PSX levels from the in vivo exposure to water samples from Balneário Camboriú were analyzed by one-way ANOVA followed by Duncan post hoc or Kruskal-Wallis ANOVA & Median test when appropriated. Data from the in vitro exposure to oxidants were analyzed by repeated one-way ANOVA followed by Dunnet post hoc test. Differences were considered statistically significant at p < 0.05.

RESULTS

Water quality and chemical analysis

Analysis of seawater samples (Table 1) indicates an input of urban sewage at CAM1: higher coliforms levels (both TC and TtC), as well as higher organic nitrogen and total phosphorous. Suspended solids, detergents, and total phenol concentrations were similar among all groups while REF had the lowest BOD and highest COD.

Levels of organic contaminants were also measured in sediments collected at the two sites of Balneário Camboriú (CAM1 and CAM2), as well as in oysters prior to exposure (Preexposure) and after the laboratory exposure (REF, CAM1, and CAM2) (Table 2). Detailed tables presenting all analyzed organic compounds in sediments and in oysters are available as supplementary material (Supplementary Data, Tables S1-S5). Total PAHs concentrations were 4fold higher in the sediment sampled at CAM1 compared to CAM2. PCBs were detected in sediments from the CAM1 group, but not at other sites. Low concentrations of organochlorine pesticides were also detected, as traceable amounts of DTT in sediments from CAM2 (0.04 ng/g dry weight). LABs, an important group of markers of urban sewage, were also found in sediments from CAM 1 (52 ng/g), but not CAM2 (

Total PSH and R-PSX in tissues of oysters exposed to seawater samples from Balneário

Camboriú Levels of total protein thiol status in gills, digestive gland, and hemolymph (Figure 2 [START_REF] Baty | Detection of oxidant sensitive thiol proteins by fluorescence labeling and two-dimensional electrophoresis[END_REF]. Total PSH levels remained unaltered in gills and digestive gland after 24 h of exposure to Balneário Camboriú water samples (Figure 2A and C), while in hemolymph there was a 42 % decrease in CAM1 group in comparison to REF (Figure 2E). Total R-PSX levels did not change significantly in any analyzed tissues (Figure 2B, D and F).

PSH and R-PSX levels of hemolymph proteins after oyster exposure

As hemolymph contained proteins sensitive to PSH oxidation, the profile of protein thiol was assessed in the most abundant proteins detected in 1D SDS-PAGE gels (Figure 3).

Coomassie staining indicated 3 abundant proteins, namely P1 (~35 KDa), P2 (~55 KDa) and P3 (~71 KDa) (Figure 3A). While P1and P3 had significant and measurable 5-IAF signal for both PSH and R-PSX, P2 had detectable signal only for PSH (Figure 3A).

Quantification of PSH levels indicated a decrease in 5-IAF signal for P1 (25%, Figure 3B), P2 (50%, Figure 3D) and P3 (47%, Figure 3E) in the CAM1 group when compared to REF, similarly to total PSH levels in hemolymph (Figure 2E). R-PSX levels remained unaltered in P1 (Figure 3C) while it decreased in P3 at CAM1 group when compared to REF (Figure 3F).

The bands labeled as P1, P2, and P3 (Figure 3A) were excised, and in-gel trypsinized for later protein identification by MALDI-TOF and MALDI-TOF/TOF. Based on MASCOT analysis using a C. brasiliana protein database (see section 2.7), P1 was further identified as Dominin, P2 as Actin, and P3 as Segon (Table 3).

Sensitivity of Dominin thiols to oxidants

C. brasiliana Dominin accounted for approximately 60 % of total protein in coomassiestained SDS-PAGE gels, with an easily detectable 5-IAF signal for both PSH and R-PSX. Data showed decreased PSH levels for Dominin after exposure to CAM1 water samples. Therefore, it was considered a good candidate for protein thiol oxidation studies in oysters and the reactivity of its Cys residues was further assessed in vitro using H2O2, CHP, and HOCl.

Hemolymph sampled from REF organisms was further exposed in vitro for 90 min to oxidants, and Dominin PSH and R-PSX levels were analyzed by 5-IAF labeling, followed by 1D SDS-PAGE (Figure 4). Data indicate that free/reduced Cys at Dominin are promptly oxidized by all tested oxidants, as detected by the PSH levels (Figure 4A): 33 -40% decrease for H2O2, 40-56% for CHP and 70-72% for HOCl. On the other hand, no changes in R-PSX levels were observed for all oxidants and concentrations tested (Figure 4B). It was not possible to investigate the effects of 1 and 10 mM HOCl due to the high protein degradation rate at these concentrations (data not shown).

Computational analysis of Dominin

While reducing SDS-PAGE suggests a molecular weight of approximately 35 kDa for the Dominin, non-reducing electrophoresis revealed a 25 kDa band (Supplemental Data, Figure S1).

This shift in the apparent molecular weight indicates the presence of internal disulfide bridges, as already demonstrated for homologous proteins [START_REF] Gonzalez | Evidence in oyster of a plasma extracellular superoxide dismutase which binds LPS[END_REF][START_REF] Itoh | Characterization of the major plasma protein of the eastern oyster, Crassostrea virginica, and a proposed role in host defense[END_REF]. Intramolecular disulfide bridges can maintain a compact structure under non-reducing conditions, allowing for faster migration in the SDS-PAGE. Disulfide bridges can be readily disrupted by the addition of reducing agents, such as DTT and β-mercaptethanol.

The localization of the 4 Cys residues in the mature Dominin (without signal peptide) was investigated by 3D structural modeling through multiple alignment sequences (Figure 5). By assuming the presence of Cys residues as disulfide bridges, which are not further oxidized by ROS, it was expected the presence of free Cys residues close to the protein surface, which would be available and prone to oxidation events. The 3D structural model predicts a high conserved βsheet core with two pairs of cysteines (30-165 and 94-164) connecting a short helix, similar to the human extracellular Superoxide Dismutase (Hsapiens EcSOD, PDB ID: 2JLP) [START_REF] Antonyuk | The Structure of Human Extracellular Copper-Zinc Superoxide Dismutase at 1.7 Å Resolution: Insights into Heparin and Collagen Binding[END_REF]. Only 1 of these pairs was close enough to form a disulfide bridge (94-164), as the distance between the Cys 30-165 lateral chains is 2.4 Å and presents uncertainties about the feasibility of a disulfide bridge (Figure 5A; upper box). Assuming that the model was built using multiple alignments we are also considering the possibility of two disulfide bridges on C. brasiliana Dominin, but our in vivo and in vitro experimental data support the idea of the existence of at least 1 free and accessible cysteine residue. This hypothesis is based on our experimental data showing a direct 5-IAF labeling of Dominin, indicating the presence of reduced thiol groups.

Additionally, Dominin presents several loops, some of them involved in LPS and integrin binding sites (Figure 5A). The loop and short helix involved in Cu coordination are shorter, lacking the key residues Asn180, Asn182 and Arg 186 (Figure 5B; upper box). Other residues related to Cu bound are also substituted in C. brasiliana (His113 and His163 to Leu, His96 to Gln), as well as to Zn binding (His121 and His124 to Asp) (Figure 5; lower panel). Dominin also has a shorter C-terminus with no α-helix in the heparin binding site, as compared to Hsapiens EcSOD (Figure 5B). Dominin 3D.

Phylogenetic analysis of complete Dominin protein sequence (including peptide signal) revealed that it is homologous to extracellular SOD-like proteins from oysters, fishes, birds, amphibians and mammals (Supplemental Data, Figure S2). This same analysis grouped Dominin with extracellular SOD-like proteins from other oysters while sequences from vertebrates were grouped as another branch. Multiple alignments of Dominin against homologous proteins from other oyster species (Supplemental Data, Figure S3) indicate that the 4 Cys residues are conserved among the studied species, with O. edulis containing and additional Cys residue at the N-terminal end, and that both LPS and integrin-binding motifs are conserved among the genus Crassostrea while they are not shared with O. edulis and S. glomerata. In addition, while protein sequences related to the Cu/Zn SOD domain are similar among the oyster species, many amino acids are not conserved within the family domain (Figure 5).

DISCUSSION

Water analyses indicated that CAM1 is influenced by urban sewage more than CAM2.

CAM1 TC values were 15 and 175 times higher than those of REF and CAM2, respectively.

These data are in accordance with the higher concentrations of total phosphorous and nitrogen at CAM1, compounds commonly associated with urban sewage discharge [START_REF] Fuhrmeister | Estimates of Nitrogen, Phosphorus, Biochemical Oxygen Demand, and Fecal Coliforms Entering the Environment Due to Inadequate Sanitation Treatment Technologies in 108 Low and Middle Income Countries[END_REF]. CAM1 also presented the highest TtC levels, an indication of fecal contamination in this area. These levels were an order of magnitude lower than the TtC detected at the mouth of Bücheler river, an area heavily contaminated by urban sewage at Santa Catarina State [START_REF] Flores-Nunes | Changes in protein expression of pacific oyster Crassostrea gigas exposed in situ to urban sewage[END_REF][START_REF] Souza | Evaluation of tropical water sources and mollusks in southern Brazil using microbiological, biochemical, and chemical parameters[END_REF]. TtC levels detected in the present study in REF and CAM2 groups are in the same range as the ones found in aquaculture sites at Florianópolis (Santa Catarina State), the major oyster producer in Brazil [START_REF] Flores-Nunes | Changes in protein expression of pacific oyster Crassostrea gigas exposed in situ to urban sewage[END_REF].

Interestingly, data pertaining to BOD and COD were contrasting. According to BOD measurements CAM1 and CAM2 had higher concentrations of organic compounds relative to REF; however, according to COD measurements, REF had higher concentrations of organic compounds. It is noteworthy that although BOD and COD are similar in function, BOD is more specific as it measures the levels of only the biodegradable organic matter. Thus, in an effort to address the contrasting BOD and COD data, more specific chemical analyses were performed in sediments and oysters.

Sediments from CAM1 had the highest concentrations of total PAHs, PCBs, LABs, and steroids, while CAM2 had the highest concentrations of DDT. Notably, total PAHs were considerably lower (1 -3 orders of magnitude) when compared to contaminated areas with known petrogenic and pyrolytic inputs [START_REF] Rinawati | Distribution, source identification, and historical trends of organic micropollutants in coastal sediment in Jakarta Bay, Indonesia[END_REF][START_REF] Sinaei | Polycyclic aromatic hydrocarbons in the coastal sea water, the surface sediment and Mudskipper Boleophthalmus dussumieri from coastal areas of the Persian Gulf: source investigation, composition pattern and spatial distribution[END_REF], and similar to values found at major oyster farming areas in Brazil [START_REF] Flores-Nunes | Changes in protein expression of pacific oyster Crassostrea gigas exposed in situ to urban sewage[END_REF]. Total PCBs and DDTs were also detected at relatively low concentrations when compared to other contaminated areas [START_REF] Rinawati | Distribution, source identification, and historical trends of organic micropollutants in coastal sediment in Jakarta Bay, Indonesia[END_REF][START_REF] Janssen | PCB-induced changes of a benthic community and expected ecosystem recovery following in situ sorbent amendment[END_REF][START_REF] Veljanoska-Sarafiloska | Presence of DDT metabolites in water, sediment and fish muscle tissue from Lake Prespa, Republic of Macedonia[END_REF][START_REF] Wu | Significance of antifouling paint flakes to the distribution of dichlorodiphenyltrichloroethanes (DDTs) in estuarine sediment[END_REF]. Moreover, PAHs, PCBs and organochlorines pesticide concentrations in sediments at both sites were below the maximum concentration recommended by MMA, the Brazilian environmental agency (http://www.mma.gov.br/port/conama/legiabre.cfm?codlegi=693). LABs and steroid concentrations in sediments are not included in the Brazilian environmental agency regulations, but total LAB concentrations in the sediment of CAM1 were close to the values detected in industrialized areas of China [START_REF] Zhang | Assessment of aquatic wastewater pollution in a highly industrialized zone with sediment linear alkylbenzenes[END_REF] and areas with pronounced input of urban sewage in Brazil [START_REF] Flores-Nunes | Changes in protein expression of pacific oyster Crassostrea gigas exposed in situ to urban sewage[END_REF], suggesting a significant sewage input in the region. Total steroid concentrations in CAM1 were also high. In fact, it is possible to estimate the steroids specific to fecal contamination by applying the 5β/(5α+5β) stanol index and the coprostanol/epicoprostanol (c/e) ratio. The 5β/(5α+5β) index aids to discriminate between sewage and biogenic sources of steroids, where values greater than 0.7 indicate urban sewage pollution [START_REF] Reeves | Faecal sterols as indicators of sewage contamination in estuarine sediments of the Tay Estuary, Scotland: an extended baseline survey[END_REF]. For the c/e ratio, values above 1.55 indicate human waste as the fecal source of coprostanol [START_REF] Reeves | Faecal sterols as indicators of sewage contamination in estuarine sediments of the Tay Estuary, Scotland: an extended baseline survey[END_REF]. CAM1 presented values of 0.79 for the 5β/(5α+5β) and 10.4 for c/e ratio. It was not possible to calculate these ratios at CAM2 as epicoprostanol concentrations were below the limit of detection. Together, these data indicate a low input of effluents related to industry or agriculture at Balneário Camboriú, but the moderate contribution of urban sewage effluents as indicated by the concentrations of LAB and steroids (and the 5β/(5α+5β) and c/e ratios) at CAM1.

The presence of contaminants at CAM1 and CAM2 was also investigated in oysters exposed for 24 h under laboratory conditions to water samples collected at both sites. Oysters had relatively higher concentrations of total PAHs (mostly containing 2 or 3 rings) and PCBs before the exposure, which decreased in all groups after the 24 h exposure. It is not clear what would be the cause of such bioaccumulation in pre-exposure animals. Oysters were obtained from an aquaculture laboratory located in a bay with weaker circulation than Camboriú Bay, and motorized boats are used in the area for the aquaculture activities and by the local community.

This could be one of the causes of the higher PAHs and PCBs concentrations in pre-exposure oysters. In fact, di and trimethylated forms of naphthalene accounted for 67% of total PAHs in oysters prior to exposure, indicating a possible source of petrogenic activity (such as diesel fuel for boats), while other PAHs remained at considerably lower concentrations at pre-exposure organisms. Either way, according to the environmental assessment criteria used by the OSPAR Commission (http://www.ospar.org/documents?v=7167), PAHs and PCBs concentrations in pre-exposure animals can be considered low and acceptable, and suggests that they may not cause great effects on cellular function and animal physiology. Following exposure to REF, CAM1, and CAM2 water samples, oysters had a fast depuration of PAHs and PCBs, indicating that these classes of contaminants were not major components of the exposure protocol. It is not clear if the storage of water samples in high-density polyethylene plastic containers may have released chemicals to the water samples, what could contribute to the chemical bioaccumulation and toxicity observed in this study. On the other hand, the urban sewage input is clear at Balneário Camboriú bay, as the most significant bioaccumulation was related to total LABs concentrations at CAM1 (from <0.88 ng/g to 180 ng/g dry weight). Together with the higher LABs concentrations in the sediment from CAM1, these data reinforce the urban sewage input in the region. Even if pre-exposure animals were subjected to a pre-existent PAHs and PCBs contamination, the urban sewage-related exposure in animals from the CAM1 group was evident.

The potential toxicity of such effluents was further addressed by analyses of protein oxidative modifications in oysters C. brasiliana.

Considered as a complex mixture of chemicals and microorganisms, exposure of bivalves to urban sewage could result in adverse effects due to oxidative stress and damage as reported previously [START_REF] Souza | Evaluation of tropical water sources and mollusks in southern Brazil using microbiological, biochemical, and chemical parameters[END_REF][START_REF] Wan | Biochemical responses in the gills of Meretrix meretrix after exposure to treated municipal effluent[END_REF][START_REF] Bianchi | Biomarker responses to sewage pollution in freshwater mussels (Diplodon chilensis) transplanted to a Patagonian river[END_REF][START_REF] Flores-Nunes | Effect of linear alkylbenzene mixtures and sanitary sewage in biochemical and molecular responses in pacific oyster Crassostrea gigas[END_REF]. As such, protein thiol groups are likely the primary targets of chemicals present in the urban sewage; however, this has not been addressed extensively in aquatic species.

In the present study, PSH levels decreased in the hemolymph of oysters exposed for 24 h to seawater samples collected at CAM1. This decrease suggests the occurrence of thiol oxidation events in this tissue. Unchanged levels of R-PSX together with decreased PSH levels indicate that these oxidation events in hemolymph may lead to irreversible protein thiol modification. In fact, there are few studies regarding protein oxidative damage in hemolymph or hemocytes of invertebrates and most of them analyzed protein carbonylation. For example, increased protein carbonyl concentrations were reported in crabs and mussels in response to seasonal changes [START_REF] Schvezov | Baseline defense system of commercial male king crab Lithodes santolla from the Beagle Channel[END_REF] and exposure to organic contaminants, metals [START_REF] Kaloyianni | Oxidative effects of inorganic and organic contaminants on haemolymph of mussels[END_REF] and nanoparticles [START_REF] Taze | Toxicity assessment and comparison between two types of iron oxide nanoparticles in Mytilus galloprovincialis[END_REF]. Protein oxidation in other tissues, including gills and digestive gland, is also studied. In this context, it was suggested that thiol levels, such as PSH and glutathione (the major cellular non-protein thiol) in gills or digestive gland are important markers of toxicity in bivalves in oxidative stress scenarios [START_REF] Trevisan | Antioxidant deficit in gills of Pacific oyster (Crassostrea gigas) exposed to chlorodinitrobenzene increases menadione toxicity[END_REF][START_REF] Trevisan | Selenium in water enhances antioxidant defenses and protects against copper-induced DNA damage in the blue mussel Mytilus edulis[END_REF][START_REF] Trevisan | Zinc causes acute impairment of glutathione metabolism followed by coordinated antioxidant defenses amplification in gills of brown mussels Perna perna[END_REF][START_REF] Franco | Antioxidant status and stress proteins in the gills of the brown mussel Perna perna exposed to zinc[END_REF][START_REF] Grintzalis | Total thiol redox status as a potent biomarker of PAHmediated effects on mussels[END_REF][START_REF] Trevisan | Gills as a glutathione-dependent metabolic barrier in Pacific oysters Crassostrea gigas: Absorption, metabolism and excretion of a model electrophile[END_REF]. We did not find alterations in PSH or R-PSX levels in these tissues, but our data include hemolymph as another potential tissue for investigating the toxicity of environmental contaminants and protein thiol oxidation.

SDS-PAGE analysis indicated that the hemolymph of C. brasiliana contains 3 highly abundant proteins that are sensitive to thiol oxidation. They were identified by MALDI-TOF and MALDI-TOF/TOF as Dominin (ANB49597.1), Actin ( ANB49595.1) and Segon (ANB49596.1). Actin may be related to the presence of a cellular fraction (hemocytes, as total hemolymph was used for the present study), and it is also a protein known to be a target for thiol oxidation [START_REF] Hu | Toxicity of copper oxide nanoparticles in the blue mussel, Mytilus edulis: A redox proteomic investigation[END_REF]. Dominin and Segon (as well as homologous proteins) are the two most abundant plasma proteins that are presumably associated with the immune system, antioxidant defenses, wound repair, metal transport, and shell mineralization [START_REF] Gonzalez | Evidence in oyster of a plasma extracellular superoxide dismutase which binds LPS[END_REF][START_REF] Itoh | Characterization of the major plasma protein of the eastern oyster, Crassostrea virginica, and a proposed role in host defense[END_REF][START_REF] Xue | Identification of a novel metal binding protein, segon, in plasma of the eastern oyster, Crassostrea virginica[END_REF][START_REF] Duperthuy | Use of OmpU porins for attachment and invasion of Crassostrea gigas immune cells by the oyster pathogen Vibrio splendidus[END_REF]. PSH levels of these proteins decreased at CAM1 group while Dominin R-PSX levels remained unaltered. R-PSX levels of Segon also decreased at CAM1 group. These data also reinforce the existence of oxidation events in the hemolymph of animals exposed to CAM1 water samples, probably leading to irreversible modifications. As PAHs, PCBs and organochlorine pesticides levels at CAM1 appear to be low, it is possible that the oxidation could be associated with other compounds, such as LABs or bacterial pathogens (due to fecal contamination at this site), as well as metals, personal care products, pharmaceuticals, and nanomaterials (compounds not analyzed in the present study but commonly detected at urban sewage [START_REF] Sperling | Wastewater Characteristics, Treatment and Disposal[END_REF]). The toxic effects of LABs to aquatic species are still unknown, but it may cause upregulation of antioxidant defenses (e. g. glutathione reductase, glucose 6-phosphate dehydrogenase, superoxide dismutase) in oysters [START_REF] Flores-Nunes | Effect of linear alkylbenzene mixtures and sanitary sewage in biochemical and molecular responses in pacific oyster Crassostrea gigas[END_REF] as a possible response to a pro-oxidative scenario. Sewage-related bacterial pollution can cause accumulation of pathogens in bivalves [START_REF] Stabili | Sewage-exposed marine invertebrates: survival rates and microbiological accumulation[END_REF], causing an immune response to bacterial infection that may induce the production of reactive oxygen and nitrogen species by hemocytes [START_REF] Donaghy | The known and unknown sources of reactive oxygen and nitrogen species in haemocytes of marine bivalve molluscs[END_REF] with the potential to cause unspecific damage to plasma proteins [START_REF] Torreilles | In vitro production of peroxynitrite by haemocytes from marine bivalves: C-ELISA determination of 3-nitrotyrosine level in plasma proteins from Mytilus galloprovincialis and Crassostrea gigas[END_REF]. The other cited substances can have different mechanisms of toxicity, but commonly include induction of oxidative stress and cellular damage [START_REF] Kaloyianni | Oxidative effects of inorganic and organic contaminants on haemolymph of mussels[END_REF][START_REF] Martín-Díaz | The use of biochemical responses to assess ecotoxicological effects of Pharmaceutical and Personal Care Products (PPCPs) after injection in the mussel Elliptio complanata[END_REF][START_REF] Gagné | Occurrence of pharmaceutical products in a municipal effluent and toxicity to rainbow trout (Oncorhynchus mykiss) hepatocytes[END_REF][START_REF] Trevisan | Gills are an initial target of zinc oxide nanoparticles in oysters Crassostrea gigas, leading to mitochondrial disruption and oxidative stress[END_REF]. It is not clear which contaminants could be acting as pro-oxidants at CAM1 group, but our data point to hemolymph as a favorable tissue for the analysis of protein oxidative damage in bivalves exposed to urban sewage, and possibly to other contaminants. It is possible that higher PAHs and PCBs concentrations in pre-exposure oysters could have resulted in a pre-existing pro-oxidant scenario that decreased the sensitivity of thiol-containing proteins to further oxidative challenge. However, according to the OSPAR environmental assessment criteria, pre-existing concentrations of PAHs and PCBs would have minimal effects on basal protein oxidation levels. Even though, the susceptibility of Actin, Dominin, and Segon to Cys oxidation remains clear according to the current exposure protocol.

C. brasiliana Dominin was further studied in vitro to understand how the thiol groups might be oxidized by pro-oxidants, such as peroxides (H2O2 and CHP) and HOCl. The sensitivity to thiol oxidation was higher for HOCl and CHP, which are reported as potent thiol oxidants [START_REF] Pullar | Living with a Killer: The Effects of Hypochlorous Acid on Mammalian Cells[END_REF][START_REF] Chen | An oxidation-sensing mechanism is used by the global regulator MgrA in Staphylococcus aureus[END_REF]. The unchanged R-PSX levels indicate the possible irreversible thiol oxidation in Dominin after H2O2, CHP or HOCl. In both in vivo and in vitro experiments, this could be easier achieved in the plasma due to the absence/low abundance of thiol reducing systems such as the glutathione and thioredoxin systems [START_REF] Toledano | Functions and Cellular Compartmentation of the Thioredoxin and Glutathione Pathways in Yeast[END_REF]. Furthermore, the extracellular environment is typically oxidative, which would favor maintaining thiols in oxidized forms [START_REF] Jones | Redox analysis of human plasma allows separation of pro-oxidant events of aging from decline in antioxidant defenses[END_REF]. The presence of abundant proteins with thiols as sites of oxidation in hemolymph resembles the serum albumin, the most abundant plasma protein in mammals. It also has a partially accessible cysteine (Cys34) on the surface, whose oxidation state is associated with oxidative stress and commonly used as a biomarker of thiol oxidation in many pathological conditions [START_REF] Anraku | Redox properties of serum albumin[END_REF].

Detailed computational analysis of C. brasiliana Dominin suggest that 2 (Cys30 and Cys165) of the 4 available Cys residues would not be pairing as an intramolecular disulfide bridge, and the direct 5-IAF labeling points to the presence of reduced thiols in Dominin. It is possible that one or both Cys30 and Cys165 would be in the reduced state and could be the target of thiol oxidation detected at CAM1 group and by the in vitro experiments. As this protein appears to be a target of reactive oxygen and nitrogen species in the hemolymph, additional studies are necessary to identify which Cys residues are reactive to oxidants in Dominin.

Moreover, phylogenetic analysis indicates that these four Cys residues are also present in homologous proteins of O. edulis, S. glomerata, C. gigas and C. virginica. Therefore, it is possible that such events of protein thiol oxidation may also occur in other oyster species, not only after exposure to urban sewage but also to other environmental contaminants, biotic and abiotic stressors. Taking into account the suggested multiple functions of this protein in oysters, it could be a promising molecule for toxicity studies in marine bivalves.

CONCLUSIONS

The present study investigated the water quality of two sites at Balneário Camboriú, an important tourist destination at Santa Catarina State (southern Brazil) and an area with emerging

Figures subtitles

Figure 1: Area of study at Balneário Camboriú (Santa Catarina, southern Brazil). Two sites were analyzed: one close to the mouth of Camboriú River (CAM1), which contributes to the input of urban sewage to the bay, and another site approximately 1 kilometer away from the mouth of the river (CAM2) that could potentially be influenced by urban discharge. Table 1.

Table 2. Table 3.

  Two sites located at Balneário Camboriú, Santa Catarina State, southern Brazil (27° S and 48°38' W) were investigated (Fig1): (a) an area near the mouth of Camboriú River (CAM1), which receives urban effluents along its course and is a known source of pollutants to the Balneário Camboriú bay; and (b) an area approximately 1 kilometer away from the mouth of Camboriú River (CAM2). According to the local governmental environment agency (FATMA -SC), water quality at CAM1 or close regions was considered inadequate in approximately 20 -25% of the analyzed periods (available at http://www.fatma.sc.gov.br), demonstrating the negative impact of urban sewage in this region.On December (1 st ) 2014, seawater samples (70 L) were collected at CAM1 and CAM2

After 5 -

 5 IAF labeling, protein extracts (10 µg, except for the in vitro experiments with hemolymph which used 5 µg) were assayed by SDS-PAGE in 12 % polyacrylamide gels and immediately scanned for 5-IAF signal in a FUJIFILM FLA-9000 scanner (473/510 excitation/emission wavelengths). Gels were further stained with colloidal Coomassie and protein abundance was quantified in a Bio-Rad ChemiDoc MP. The 5-IAF signal was normalized to the Coomassie staining signal, and this ratio was used to quantify PSH and R-PSX levels. Total PSH and R-PSX were based on the signal intensity of the whole electrophoresis lane, while PSH and R-PSX of individual proteins were based on the signal intensity of the individual bands (n = 4 for in vitro experiments and n = 6 for in vivo experiments).

  ) of C. brasiliana exposed in the laboratory (24 h) to water samples collected at Balneário Camboriú (CAM1 and CAM2) or from a university aquaculture facility (REF) were investigated. After 24 h of exposure, tissues were collected and analyzed by fluorescent labeling and 1D SDS-PAGE. The fluorophore 5-IAF was used to label protein thiols by two different approaches: (i) direct labeling, where 5-IAF reacts specifically with reduced protein thiols (PSH) [19], and (II) indirect labeling, where PSH are first blocked by NEM, and reversibly oxidized protein thiols (R-PSX) are reduced by DTT and tagged by 5-IAF

  fishing and aquaculture activities. The investigation was based on standard water quality measurements, organic contaminants, and laboratory exposure of oysters to water samples collected in the area. Data suggest the influence of urban sewage, mostly near the mouth of Camboriú River (CAM1), which is probably related to an urban input. Such effluents were able to induce protein oxidation in oysters C. brasiliana. In fact, our data showed for the first time the use of 1DE SDS-PAGE to identify thiol oxidation in 3 hemolymph proteins. Additional studies with one of them (Dominin) indicated the presence of Cys residues (Cys30 and Cys165) as sites of thiol oxidation by classical pro-oxidant agents. These data were indicative of a potential toxicity of such urban sewage input to the local aquatic species and call for protective and preventive actions in the region. Moreover, Dominin computational analyses indicated that Cys oxidation events could also occur in homologous proteins of other oysters species, suggesting the use thiol oxidation of hemolymph proteins as a viable tool and a new biomarker of toxicity in bivalves exposed not exclusively to pro-oxidant contaminants or cellular stressors.

Figure 2 :

 2 Figure 2: Protein thiol status in tissues of oysters Crassostrea brasiliana exposed for 24 h in the laboratory to seawater collected at Balneário Camboriú (Santa Catarina, southern Brazil). Water sampling sites consisted of CAM1 and CAM2 (see legend to Figure 1 for details). The reference group (REF) consisted of water collected at the local university aquaculture laboratory from where the oysters were obtained. 1D SDS-PAGE analysis of reduced protein thiol (PSH, left) by direct 5-IAF labeling and reversibly oxidized protein thiol (R-PSX, right) by NEM/DTT incubation followed by 5-IAF labeling. PSH (left) and R-PSX (right) were assayed in gills (A

Figure 3 :

 3 Figure 3: Thiol status of abundant proteins in the hemolymph of oysters Crassostrea brasiliana exposed for 24 h in the laboratory to seawater collected at Balneário Camboriú (Santa Catarina, southern Brazil) at CAM1 and CAM2, as well as REF group (see legend to Figure 1 for details). (A) A representative SDS-PAGE of hemolymph from 3 C. brasiliana individuals (1 -3) after colloidal Coomassie staining, and visualization of reduced protein thiols (PSH) or reversibly oxidized protein thiols (R-PSX). The 3 most abundant proteins from hemolymph are shown as P1, P2, and P3 in the Coomassie-stained gel, with their respective signals for PSH and R-PSX, indicated by arrows. Molecular weight markers are shown as (M). Levels of PSH (left) and R-PSX (right) were assayed in P1 (B and C), P2 (D) and P3 (E and F) proteins. It was not possible to quantify R-PSX for P2 due to the faint fluorescent signal. Data were analyzed by one-way ANOVA followed by Duncan post hoc test. Groups not sharing letters are significantly different at p < 0.05 (n = 6).

Figure 4 :

 4 Figure 4: Thiol status of Dominin from the hemolymph of oysters Crassostrea brasiliana exposed in vitro to oxidants. Hemolymph from reference animals was incubated with hydrogen peroxide, cumene hydroperoxide (CHP) or hypochlorous acid (HOCl) at the indicated concentrations for 1.5 h. Samples were further assayed for reduced protein thiols (PSH) and reversibly oxidized protein thiols (R-PSX) by 1D SDS-PAGE. Data (n = 4) were analyzed by paired one-way ANOVA followed by Dunnet posthoc. * (p < 0.05), ** (p < 0.01) and *** (p < 0.001) indicate significantly differences to the respective control group (n = 4).

Figure 5 :

 5 Figure 5: Crassostrea brasiliana Dominin 3D model. (A) Dominin overall folding showing the β-sheet core in green and α-helices in red. The LPS binding site (DDED) and the integrin binding site (RGB) motifs are represented by sticks. The upper box shows the Cys pairs between positions 30-165 and 94-164. Only Cys 94-164 pair forms a disulfide bridge. (B) Overlay of Dominin and human Extracellular Superoxide Dismutase 3 (Hsapiens EcSOD, PDB ID:2JLP, in

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2.

Figure 3 .

 3 Figure 3.

Figure 4 .

 4 Figure 4.

Figure 5 .

 5 Figure 5.

  and 50 % acetonitrile) was used for MALDI-TOF and MALDI-TOF/TOF analyses, with an internal peptide calibration standard for MS (Bruker Daltonics 206195). Mass spectra of peptides were collected with positive reflectron MS and MS/MS on a MALDI auto flex III smart beam (Bruker Daltonics). The resulting mass spectra were searched by MASCOT v2.3 software installed on a local server. A C. brasiliana protein database was constructed based on an in-house de novo assembled transcriptome (gills and digestive gland) of C. Brasiliana (kindly provided by Dr. Karim H. Lüchmann, Santa Catarina State University, Brazil). The

	55 mM iodoacetamide in 100 mM ammonium bicarbonate pH 8.5 for 20 min at room
	temperature. Samples were further distained with 50 % acetonitrile and 45 mM ammonium
	bicarbonate pH 8.5 at 37 °C, dehydrated with 100 % acetonitrile and air dried. Gel pieces were
	saturated with trypsin (20 µg/mL in 40 mM ammonium bicarbonate pH 8.5 and 9 % acetonitrile)
	and digested overnight at 37 °C. Remaining peptides were extracted from the gel with 0.1 %

proteins

After SDS-PAGE, proteins of interest from hemolymph samples were excised and digested in-gel with trypsin

[START_REF] Shevchenko | In-gel digestion for mass spectrometric characterization of proteins and proteomes[END_REF]

. Briefly, samples were reduced with 10 mM DTT in 100 mM ammonium bicarbonate pH 8.5 for 30 min at 56 °C, washed with acetonitrile, and alkylated with trifluoroacetic acid and 50 % acetonitrile at 37 °C for 30 min and samples were dried out in a vacuum centrifuge. The α-cyano-4-hydroxy-cinnamic acid matrix (5 mg/mL in 0.1 % trifluoroacetic acid following parameters were adopted: tryptic peptides with ≤ 1 missed cleavage site, complete carbamidomethylation of cysteines and partial oxidation of methionines, peptide mass tolerance ranging from ± 75 to 250 ppm (MS) or ± 1 Da (MS/MS).

Table 2

 2 to CAM2 (1.45 µg/g dry weight). Steroids related to animal feces (cholesterol, coprostanol, epicoprostanol, and cholestenol) were detected at higher concentrations in sediment from CAM1 (3.39 µg/g) compared to CAM2 (0.08 μg/g).Pre-exposure organisms had the highest total PAHs concentrations (540 ng/g dry weight). This value decreased 67% at REF and was almost completely eliminated (>95% decrease) after 24 h of exposure to water sampled at both CAM1 and CAM2 sites. Pre-exposure organisms presented the highest concentrations (35 ng/g dry weight) of total PCBs, which decreased to 60 % at REF and to 22 -25 % at CAM1 and CAM2, respectively. Organochloride pesticides were relatively stable in oysters of all exposed groups (0.99 -1.85 ng/g dry weight), except at CAM2,

). Steroids concentrations were also detected in the sediments, presenting higher concentrations at CAM1 (4.92 µg/g dry weight), compared where they were not detected. LABs were not detectable in pre-exposure oysters, or in the CAM2 group, but reached 180 ng/g dry weight in CAM1 group. Steroids were not analyzed in oysters.

Acknowledgment

This work was supported by INCT-Toxicologia Aquática, CNPq grant #573949/2008-5. R. Trevisan, G. Toledo-Silva, and F. Flores-Nunes are postdoc fellows of CNPq, CAPES, and Petrobras, respectively. E.S. Dolores, C.E. Piazza, I.M.M. Reis, F.L. Zacchi, B.N.M. Othero, D.F. Mello and A.P.M. Fraga are recipients of scholarships awarded by CAPES. A.L. Dafre, M.R.F. Marques, R.C. Montone, M.C. Bícego, and A.C.D. Bainy are research fellows of CNPq.

We are thankful to CEBIME -UFSC for the technical assistance. We are grateful to Dr. A. Massarsky (Duke University) for kindly revising the manuscript.

DISCLOSURE

All authors declare to have no actual or potential conflict of interest including financial, personal or other relationships with other people or organizations. The work described has not been published previously (except in the form of an abstract); it is not under consideration for publication elsewhere, and its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and if accepted, it will not be published elsewhere in the same form, in English or any other language, without the consent of the copyright holder. The authors also declare that all experiments were carried out according to the local Research Ethics Committee at the Federal University of Santa Catarina.

All authors declare to have participated in this study, as following: project coordinators AB, MRFM and ACDB; experimental design, field work and sampling FFN, ESD, JJM, CEP and CMRM; chemical analyses STS, ST, RCM and MCB; animal exposure and tissue sampling FFN, ESD, JJM, CEP, IMMR, FLZ, BNMO and CLVB; sample processing, protein electrophoresis and in vitro studies RT, DFM and ALD; protein identification by mass spectrometry RT, APMF and GTS; bioinformatics and computational analyses RT, NW, GTS and GR; manuscript preparation all authors.


Laetitia Andrieu
email: laetitia.andrieu@edf.fr

Michel De Lara
email: delara@cermics.enpc.fr

Babacar Seck
email: seck@cermics.enpc.fr

Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions

Keywords: Risk measures, Utility functions, Nonexpected utility theory, Maxmin, Conditional Value-at-Risk, Loss aversion

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a "generalized expected utility maximizer" in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and

Motivation

Taking risk into account in decision problems in a mathematical formal way is more and more widespread. For instance, liberalization of energy markets displays new issues for electrical companies which now have to master both traditional problems (such as optimization of electrical generation) and emerging problems (such as integration of spot markets and risk management, see e.g. [START_REF] Eichhorn | Mean-risk optimization models for electricity portfolio management[END_REF]). The historical issue which consisted in managing the electrical generation at lowest cost evolved: liberalization of energy markets and introduction of spot markets lead to consider a problem of revenue maximization under Earning-at-Risk constraint, because financial risks are now added to the traditional risks.

Let us now be slightly more formal. Consider a decision maker (DM) whose return J(a, ξ) depends on a decision variable a (for instance, proportions of assets) and a random variable ξ (random return of assets, for example). The question of how to take risk into account in addition has been studied since long. Let us briefly describe two classical approaches to deal with risk in a decision problem. On the one hand, the DM may maximize the expectation of J(a, ξ) under explicit risk constraints, such as variance (as in [START_REF] Markowitz | Portfolio selection[END_REF]) or Conditional Value-at-Risk; we shall coin this practice as belonging to the engineers or practitioners world. On the other hand, the DM may maximize the expectation of U J(a, ξ) where U is a utility function wich captures more or less risk aversion (in the so called expected utility theory, or more general functionals else); this is the world of economists. In this paper, we shall focus on the links between these two approaches.

The paper is organized as follows. In Section 2, we specify a wide class of risk measures which will prove useful to provide an economic interpretation of profit maximization under risk constraint. Section 3 gives our main result and points out a specific nonexpected utility theory which is compatible with the original problem. Our approach uses duality theory and Lagrange multipliers. However it does not focus on the optimal multiplier, and this is how we obtain a family of utility functions and an economic interpretation (though belonging to nonexpected utility theories), and not a single utility function. This differs from the result in [START_REF] Dentcheva | Portfolio optimization with stochastic dominance constraints[END_REF] where the authors prove, in a way, that utility functions play the role of Lagrange multipliers for second order stochastic dominance constraints. With this, [START_REF] Dentcheva | Portfolio optimization with stochastic dominance constraints[END_REF] prove the equivalence between portfolio maximization under second order stochastic dominance constraints and expected utility maximization, for one single utility function. However, such utility function is not given a priori and may not be interpreted economically before the decision problem. A concluding economic discussion is given in Section 4. Proofs are gathered in Appendix A.

The infimum of expectations class of risk measures

Let be given a probability space (Ω, F , P) with P a probability measure on a σ-field F of events on Ω. We are thus in a risk decision context. The expectation of a random variable on (Ω, F , P) will be denoted by E. We introduce a class of risk measures which covers many of the usual risk measures and which will be prove adequate for optimization problems. We will also briefly examine the connections with coherent risk measures.

Definition and examples

Let a function ρ : R × R → R be given. Let L ρ (Ω, F , P) be a set of random variables X defined on (Ω, F , P) such that ρ X, η is integrable for all η and such that the following risk measure

R ρ (X) := inf η∈R E ρ X, η , (1)
is finite (R ρ (X) > -∞).

In the sequel, we shall require the following properties for the function ρ : R × R → R and for L ρ (Ω, F , P).

H1. η → ρ(x, η) is a convex function,
H2. for all X ∈ L ρ (Ω, F , P) , η → E ρ X, η is continuous1 and has limit +∞ when η → +∞.

The random variable X represents a loss. Hence, risk constraints will be of the form R ρ (X) ≤ γ. For the so called safety measures, the safety constraint is rather S ρ (X) ≥ γ. We pass from one to the other by

S ρ (X) = -R ρ (-X) = sup η∈R E -ρ -X, η .
Several well-known risk measures belong to the infimum of expectations class of risk measures.

Variance

In [START_REF] Markowitz | Portfolio selection[END_REF], Markowitz uses variance as a risk measure. A well known formula for the variance is

var X = inf η∈R E X -η 2 .
The function

ρ var (x, η) := (x -η) 2
is convex with respect to η (H1.). Taking L ρ (Ω, F , P) = L 2 (Ω, F , P), assumption H2. is satisfied.

Conditional Value-at-Risk [START_REF] Rockafellar | Optimization of Conditional Value-at-Risk[END_REF] give the following formula for the Conditional Value-at-Risk risk measure CVaR at confidence level2 0 < p < 1:

CVaR p (X) = inf η∈R η + 1 1 -p E max{0, X -η} .
The function

ρ CVaR (x, η) := η + 1 1 -p max{0, x -η} is convex with respect to η. Taking L ρ (Ω, F , P) = L 1 (Ω, F , P), assumption
H2. is satisfied.

Weighted mean deviation from a quantile

Let us introduce ψ -1 X the left-continuous inverse of the cumulative distribution function ψ X of the random variable X and ψ -2

X (p) = p 0 ψ -1 X (α)dα. The weighted mean deviation from a quantile WMd is WMd p (X) = E[X] p -ψ -2 X (p) .
In [START_REF] Ogryczak | From stochastic dominance to mean-risk model: semideviations as risk measures[END_REF], one finds the expression

WMd p (X) = inf η∈R E max p(X -η), (1 -p)(η -X) .
The function

ρ WMd (x, η) := max p(x -η), (1 -p)(η -x) ,
is continuous, convex with respect to η.

Optimized Certainty Equivalent

The Optimized Certainty Equivalent was introduced in Ben-Tal and Teboulle (1986) (see also [START_REF] Ben-Tal | An old-new concept of convex risk measures: the optimized certainty equivalent[END_REF]). This concept is based on the economic notion of certainty equivalent. Let U : R → [-∞, +∞[ be a proper closed concave and nondecreasing utility function 3 . The Optimized Certainty

Equivalent S U of the random return X defined on (Ω, F , P) is

S U (X) = sup ν∈R ν + E U(X -ν) .
The associated risk measure is

R ρ (X) := -S U (-X) = inf η∈R η -E U(η -X)
where

ρ U (x, η) := η -U(η -x)
satisfies assumptions H1. and H2. whenever U satisfies appropriate continuity and growth assumptions.

A Summary Table

We sum up the above cases. We denote a + := max{a, 0}. Notice that all the functions x → ρ(x, η) in Table 1 are convex.

3 With additional assumptions:

U has effective domain domU = {x ∈ R | U (x) >
-∞} = ∅, supposed to satisfy U (0) = 0 and 1 ∈ ∂U (0), where ∂U denotes the subdifferential map of U .

Risk measure R ρ ρ(x, η) (1999). When the risk measure R ρ is given by (1), we shall provide sufficient conditions on ρ ensuring monotonicity, translation invariance, positive homogeneity, convexity, subadditivity.

Variance (x -η) 2 Conditional Value-at-Risk η + 1 1-p (x -η) + Weighted Mean Deviation max p(x -η), (1 -p)(η -x) Optimized Certainty Equivalent η -U(η -x)
Proposition 1 Under the assumption that the set L ρ (Ω, F , P) in §2.1 is a vector space containing the constant random variables, we have the following properties.

1. If x → ρ(x, η) is increasing, then R ρ is monotonous. 2. If ρ(x + m, η) = ρ(x, η ′ m ) -m where η → η ′ m is one-to-one, then R ρ satisfies translation invariance. 3. If ρ(θx, η) = θρ(x, η ′ θ ) where η → η ′ θ is one-to-one for θ > 0, then R ρ satisfies positive homogeneity. 4. If (x, η) → ρ(x, η) is jointly convex then R ρ is convex. 5. If (x, η) → ρ(x, η) is jointly subadditive, then R ρ is subadditive.
Proof: We shall only prove item 4 since item 5 is proved in the same way, and that all other assertions are straightforward.

Assume that (x, η) → ρ(x, η) is jointly convex. Let X 1 and X 2 be two random variables, (η 1 , η 2 ) ∈ R 2 and θ ∈ [0, 1]. We have

ρ(θX 1 + (1 -θ)X 2 , θη 1 + (1 -θ)η 2 ) ≤ θρ(X 1 , η 1 ) + (1 -θ)ρ(X 2 , η 2 ).
By using expectation operator and positivity of θ, one obtains

inf η E ρ(θX 1 + (1 -θ)X 2 , η) ≤ inf (η 1 ,η 2 )∈R×R θE ρ(X 1 , η 1 ) + (1 -θ)E ρ(X 2 , η 2 ) .
It yields

R ρ (θX 1 + (1 -θ)X 2 ) ≤ θR ρ (X 1 ) + (1 -θ)R ρ (X 2 ) .
For the Conditional Value-at-Risk,

ρ CVaR (x + m, η) = ρ CVaR (x, η ′ m ) -m where η ′ m = η+m. For the Weighted Mean Deviation, ρ WMd (θx, η) = θρ(x, η ′ ) where η ′ θ = η/θ.
3 Profit maximization under risk constraints:

a reformulation with utility functions

We now state our main result, which is an equivalence between a profit maximization under risk constraints problem and a maxmin problem involving an infinite number of utility functions. We relate this (non) expected utility economic interpretation to the "maxmin" representation proposed in [START_REF] Maccheroni | Maxmin under risk[END_REF]. For the specific case of CVaR risk constraint, we exhibit a link with "loss aversion utility functions" à la Kahneman and Tversky (see [START_REF] Kahneman | Advances in prospect theory: cumulative representation of uncertainty[END_REF]).

A maxmin reformulation

To formulate a maximization problem under risk constraint, let us introduce

• a set A ⊂ R n of actions or decisions,

• a random variable ξ defined on a probability space (Ω, F , P), with values in R p ,

• a mapping J : R n × R p → R, such that for any action a ∈ A, the random variable J(a, ξ) represents the prospect (profit, benefit, etc.) of the decision maker,

• a risk measure R ρ defined in (1), together with the level constraint

γ ∈ R.
Our main result is the following (the proof is given in Appendix A).

Theorem 2 Assume that ρ and L ρ (Ω, F , P) satisfy assumptions H1. and H2. in §2.1, that J(a, ξ) ∈ L ρ (Ω, F , P) for all a ∈ A, and that the infimum in (1) is achieved for any loss X = -J(a, ξ) when a varies in A.

The maximization under risk constraint4 problem

       sup a∈A E J(a, ξ) R ρ -J(a, ξ) = inf η∈R E ρ -J(a, ξ), η ≤ γ, (2)
is equivalent to the following maxmin problem

sup (a,η)∈A×R inf U ∈U E U J(a, ξ), η . (3)
The set U of functions R 2 → R over which the infimum is taken is

U := U (λ) : R 2 → R , λ ≥ 0 | U (λ) (x, η) = x + λ -ρ(-x, η) + γ .
Table 2 sums up parameterized functions corresponding to usual risk measures.

Notice that the formulation (3) of Problem (2) leads us to introduce a new decision variable η ∈ R. This decision variable comes from our choice of risk measure given by (1).

We shall now see that the formulation (3) has connections with the so called "maxmin" representation of [START_REF] Maccheroni | Maxmin under risk[END_REF], that we briefly sketch.

Let us consider a continuous and convex weak order over the set ∆Z of all lotteries (simple probability distributions) defined on an outcome space

Risk measure R ρ U (λ) (x, η), λ ≥ 0 ρ(-x, η) x -λρ(-x, η) + λγ Variance x -λ(x + η) 2 + λγ Conditional Value-at-Risk x -λ 1-p (x + η) --λη + λγ Weighted Mean Deviation x -λ max -p(x + η), (1 -p)(x + η) + λγ Optimized Certainty Equivalent x + λU(x + η) + λη + λγ
Table 2: Usual risk measures and their corresponding family functions Z. The main result of [START_REF] Maccheroni | Maxmin under risk[END_REF] is the following: if there exists a best outcome5 and if decisions are made independently of it, then there exists a closed and convex set U of utility functions defined on Z such that, for any lotteries r and q, we have

r q ⇔ min U ∈U U(z)dr(z) ≥ min U ∈U U(z)dq(z) .
The interpretation given by Maccheroni for this decision rule is the following one: a conservative investor has an unclear evaluation of the different outcomes when facing lotteries. He then acts as if he were considering many expected utility evaluations and taking the worst one6 .

Conditional Value-at-Risk and loss aversion

Suppose that the risk constraint R ρ is the Conditional Value-at-Risk. The utility functions associated to this risk measure are

U (λ) (x, η) = x - λ 1 -p (-x -η) + -λη + λγ .
We consider only the x argument (profit, benefit, etc.). We interpret the -η argument as an anchorage parameter: for x ≥ -η, x → U (λ) (x, η) =

xλη + λγ has slope 1, while it has slope θ := 1 + λ 1p for x lower than -η, as in Figure 1. We interpret the parameter θ as a loss aversion parameter introduced by Kahneman and Tversky (see [START_REF] Kahneman | Advances in prospect theory: cumulative representation of uncertainty[END_REF]). Indeed, this utility function x → U (λ) (x, η) expresses the property that one monetary unit than the anchorage -η gives one unit of utility, while one unit less gives -θ.

An illustration

Suppose that a DM splits its investment between a risk free asset ξ 0 (deterministic 7 and a risky asset ξ 1 (random following a Normal law N (M, Σ) 8 , in proportion 1a ∈ [0, 1]), giving the value of the portfolio The portfolio maximization problem subject to Conditional Value-at-Risk risk constraint is:

J a, ξ = aξ 0 + (1 -a)ξ 1 = µ(a) + σ(a)N, N ∼ N (0, 1) with µ(a) = aξ 0 + (1 -a)M and σ(a) = (1 -a)Σ .
sup a∈[0,1] µ(a) (4a) σ(a)CVaR p -N -µ(a) ≤ γ . (4b)
By duality we find solutions of problem (4): Table 3: Loss aversion parameter with confidence levels p=0.95 and p=0.99

a ♯ = M + ΣCVaR p (-N) -γ M -ξ 0 + ΣCVaR p (-N) and λ ♯ = 1 1 + ΣCVaRp(-N ) M -ξ 0 . p=0.95 p=0.99 γ a ♯ η ♯ θ γ a ♯ η ♯ θ -630 = C 0 - 735
Hence the optimal value of η is

η ♯ = σ(a ♯ )VaR 1-p (N) -µ(a ♯ ).
For two confidence levels p = 0.95 and p = 0.99, we exhibit the loss aversion parameter in Table 3. This latter takes high values, well above the empirical findings (median value of 2.25 in [START_REF] Kahneman | Advances in prospect theory: cumulative representation of uncertainty[END_REF]).

Economic discussion

Our main result establishes a connection between some risk measures and parameterized families of multi-attribute "utility functions". We hope to be able to "read" some properties of the risk measure from these latter. For instance, focusing only on the x argument in utility functions of Table 2, we notice that the variance risk measure is associated to quadratic utility functions. Now, the latter are well known for their poor economic qualities (see [START_REF] Gollier | The economics of risk and time[END_REF]), such as exhibiting risk aversion increasing with wealth, for instance. In the CVaR risk constraint case, the corresponding utility function is interpreted as loss aversion utility function à la Kahneman and Tversky (see [START_REF] Kahneman | Advances in prospect theory: cumulative representation of uncertainty[END_REF]).

The role of the variable η can also be discussed. It is known that the optimal η is the expectation of the optimal profit in the variance case, and

the Value-at-Risk in the Conditional Value-at-Risk. Our formalism amounts to attributing a cost (disutility) to such a variable η when it is let loose, not necessarily fixed at its optimal value. In the Optimized Certainty Equivalent case the optimal η gives the optimal allocation between η consumption and (Jη) investment.

Acknowledgments. We thank Alain Chateauneuf (Université Paris 1 Panthéon-Sorbonne) and Fabio Maccheroni (Università Bocconi, Milano) for fruitful discussions. We acknowledge Électricité de France for their funding.

A Appendix: proof of the main result

We shall show that (2) is equivalent to

sup a∈A sup η∈R inf λ∈R + E J(a, ξ) -λ ρ -J(a, ξ), η -γ .
We suppose that all assumptions of Theorem 2 are satisfied.

Equivalent Lagrangian formulation

As is well known, the Lagrangian associated to maximization problem (2) is

L(a, λ) := E J(a, ξ) -λ R ρ -J(a, ξ) -γ ,
where λ ∈ R + is a Lagrange multiplier, and we have (2) ⇐⇒ sup a∈A inf λ≥0 L(a, λ).

We have:

L(a, λ) = E J(a, ξ) -λ inf η∈R E ρ -J(a, ξ), η -γ by (1) = E J(a, ξ) -λ -sup η∈R E -ρ -J(a, ξ), η -γ = E J(a, ξ) + λ sup η∈R E -ρ -J(a, ξ), η + λγ = sup η∈R E J(a, ξ) + λE -ρ -J(a, ξ), η + λγ , because λ ≥ 0 and E J(a, ξ) does not depend upon λ = sup η∈R E J(a, ξ) -λρ -J(a, ξ), η + λγ . Since (2) ⇐⇒ sup a∈A inf λ≥0 L(a, λ), it follows that (2) ⇔ sup a∈A inf λ∈R + sup η∈R E J(a, ξ) -λρ -J(a, ξ), η + λγ . (5)
We now show that we can exchange inf λ∈R + and sup η∈R .

Exchanging inf λ∈R + and sup η∈R Let a ∈ A be fixed. Define Ψ a : R 2 → R by Ψ a (λ, η) := E J(a, ξ)λρ -J(a, ξ), η + λγ .

We can exchange inf λ∈R + and sup η∈R in (5) by the two following Lemmas.

Lemma 3 Let a ∈ A be fixed. If γ < R ρ -J(a, ξ) , then inf λ∈R + sup η∈R Ψ a (λ, η) = sup η∈R inf λ∈R + Ψ a (λ, η) = -∞.
Proof.

By (1) and λ ≥ 0, we have sup

η∈R Ψ a (λ, η) = E J(a, ξ) -λ R ρ -J(a, ξ) -γ . Thus inf λ∈R + sup η∈R Ψ a (λ, η) = -∞, since γ < R ρ -J(a, ξ) .
We always have sup

η∈R inf λ∈R + Ψ a (λ, η) ≤ inf λ∈R + sup η∈R Ψ a (λ, η).
It holds that sup

η∈R inf λ∈R + Ψ a (λ, η) = -∞.
The proof of the following Lemma is based on the Theorem hereafter (see (Barbu and Precupanu, 1986, Chap. 2. Corollary 3.8)).

Theorem 4 Assume that Φ : R p × R q → R ∪ {-∞} ∪ {+∞} is a convexconcave 9 and l.s.c.-u.s.c. 10 mapping. Assume that Y and Z are two closed convex subsets of R p and R q respectively, and that there exists Proof.

(y * , z * ) ∈ Y × Z such that    Φ(y * , z) → -∞,
Let η ⋆ be such that R ρ -J(a, ξ) = E ρ -J(a, ξ), η ⋆ . We have indeed supposed that the infimum in (1) is achieved for any X = -J(a, ξ) when a varies in A. We distinguish two cases.

9 convex with respect to its first argument, and concave with respect to its second argument.

10 lower semicontinuous with respect to its first argument and upper semicontinuous with respect to its second argument.

a. If γ = R ρ -J(a, ξ) , any (λ, η ⋆ ) is a saddle point because (6) gives Ψ a (λ, η ⋆ ) = E J(a, ξ) .

b. Assume now that γ > R ρ -J(a, ξ) , and let us check the conditions of existence of a saddle point in Theorem 4.

The function Ψ a (λ, η) = E J(a, ξ) -λE ρ -J(a, ξ), ηγ is

• linear with respect to λ and thus convex in λ;

• concave with respect to η (the function : η → -ρ -J(a, ξ), η is concave, λ ≥ 0 and the expectation operator preserves concavity). Now, by assumption ρ and L ρ (Ω, F, P) satisfy assumption H2 with J(a, ξ) ∈ L ρ (Ω, F, P), we have

• η → E ρ -J(a, ξ), ηγ is continuous;

• lim η→+∞ E ρ -J(a, ξ), ηγ = +∞.

Thus, the function Ψ a is convex-concave, l.s.c.-u.s.c. and satisfies Ψ a (λ, η) → -∞, when η → +∞ for any λ > 0 .

Since γ > R ρ -J(a, ξ) = E ρ -J(a, ξ), η ⋆ , we have Ψ a (λ, η ⋆ ) = E J(a, ξ) + λ γ -R ρ -J(a, ξ) → +∞, when λ → +∞ .

Hence, the function Ψ a admits a saddle point in R + × R.

7Figure 1 :

 1 Figure 1: Utility function attached to CVaR

  when z → +∞ and z ∈ Z Φ(y, z * ) → +∞, when y → +∞ and y ∈ Y .Then Φ admits a saddle point (ȳ, z) ∈ Y × Z:Φ(ȳ, z) ≤ Φ(ȳ, z) ≤ Φ(y, z) ∀(y, z) ∈ Y × Z .Lemma 5 If γ ≥ R ρ -J(a, ξ) then Ψ a defined by (6) admits a saddle point in R + × R and thus supη∈R inf λ∈R + Ψ a (λ, η) = inf λ∈R + sup η∈R Ψ a (λ, η).

Table 1 :

 1 Risk measures given by an infimum of expectations

2.2 Infimum of expectations and coherent risk measures

Coherent risk measures were introduced in Artzner et al.

We could also formulate assumptions directly on the function ρ, ensuring Lebesgue dominated convergence validity, but this is not our main concern here.

In practice, p is rather close to 1 (p = 0.95, p = 0.99). The Value-at-Risk VaR p (X) is such that P(X ≤ VaR p (X)) = p. Then CVaR p (X) is interpreted as the expected value of X knowing that X exceeds VaR p (X).

The risk constraint is not on the prospect J(a, ξ), but on the loss -J(a, ξ).

A best outcome for a preference relation is an element z * ∈ Z such that z * r for all r ∈ ∆Z.

This reformulation is, in a sense, dual to the well known form inf P∈P U (w) dP(w), where P is a convex set of probability measures[START_REF] Gilboa | Maxmin expected utility with a nonunique prior[END_REF]).