Rawad Assaf
email: rawad.assaf@isae.edu.lb

Walid Larbi
email: walid.larbi@cnam.fr

Finite Element Analyses of Double-wall Sandwich Structures with Viscoelastic Core

This paper presents a reduced order finite element model for sound transmission analysis through a double-wall sandwich structures with viscoelastic core inserted in an infinite baffle. The proposed model is derived from a multi-field variational principle involving structural displacement and acoustic pressure inside the fluid cavity. To solve the vibro-acoustic problem, the plate displacements are expanded as a modal summation of the plate's eigenfunctions in vacuo. Similarly, the cavity pressure is expanded as a summation over the modes of the cavity with rigid boundaries. Then, an appropriate reduced-order model is introduced. The structure is excited by a plane wave at the source side. An example of the normal sound transmission loss of a double glazed window with laminated glass is shown. This example illustrates the accuracy and the versatility of the proposed reduced order model, especially in terms of prediction of sound transmission.

INTRODUCTION

Double-wall panels are widely used in engineering applications in order to reduce structural vibrations and interior noise due to their superiority over single-leaf structures. Typical examples include double glazed windows, fuselage of airplanes, etc… By introducing a thin viscoelastic interlayer within the panels, a better acoustic insulation is obtained [START_REF] Basten | Noise reduction by viscothermal acousto-elastic interaction in double wall panels[END_REF]. In fact, sandwich structures with viscoelastic layer are commonly used in many systems for vibration damping and noise control especially at the medium and high frequency ranges. In such structures, the main energy loss mechanism is due to the transverse shear of the viscoelastic core. This paper describes a reduced order finite element models for the sound transmission analysis through a double sandwich panels with viscoelastic core inserted in an infinite baffle. The structure is excited by a plane wave at the source side and fluid loading is neglected. The proposed FE model is derived from a variational principle involving structural displacement and acoustic pressure in the fluid cavity. To solve the vibro-acoustic problem, the direct solution can be considered only for small model sizes. This has severe limitations in attaining adequate accuracy and wider frequency ranges of interest. Thus, a reduced order-model is then proposed to solve the problem at a lower cost. The presented methodology, based on a normal mode expansion, requires the computation of the uncoupled structural and acoustic modes. The uncoupled structural modes are the real and undamped modes of the sandwich panels without fluid pressure loading at fluid-structure interface, whereas the uncoupled acoustic modes are the cavity modes with rigid wall boundary conditions at the fluid-structure interface. Moreover, the effects of the higher modes of each subsystem can be taken into account through an appropriate so-called "static correction". A deep study of truncation effects, acceleration of convergence and error estimation, using for example various static corrections, is presently under investigation but outside the scope of this paper. Example of the normal sound transmission loss of a double glazed window with laminated glass is shown in order to illustrate the accuracy and the versatility of the proposed reduced order model.

FINITE ELEMENT FORMULATION OF THE COUPLED PROBLEM

Local equations

Consider a double-wall structure filled with an acoustic fluid shown in Figure 1. The harmonic local equations of this structural-acoustic coupled problem can be written in terms of structure displacement u and fluid pressure field p [START_REF] Morand | Fluid-structure interaction[END_REF][START_REF] Larbi | Vibration of axisymmetric composite piezoelectric shells coupled with internal fluid[END_REF])

Each wall occupies a domain

div σ(u)+ρ S ω 2 u = 0 in Ω S σ(u)n S = F d on Γ t σ(u)n S = pn on Γ u ∆p + ω 2 c F 2 p = 0 in Ω F ∇p⋅ n = ρ F ω 2 u⋅ n on Σ
where ω is the angular frequency, n S and n are the external unit normal to Ω S and Ω F ; ρ S and ρ F are the structure and fluid mass densities; c F is the speed of sound in the fluid; and σ is the structure stress tensor.

Constitutive relation for viscoelastic core. In order to provide better acoustic insulation and vibration attenuation, damped sandwich panels with a thin layer of viscoelastic core are used in this study (Figure 1). In fact, when subjected to mechanical vibrations, the viscoelastic layer absorbs part of the vibratory energy in the form of heat. Another part of this energy is dissipated in the constrained core due to the shear motion. The constitutive relation for a viscoelastic material subjected to a sinusoidal strain is written in the following form:

σ = C * (ω)ε
where ε denote the strain tensor and C * (ω) termed the complex moduli tensor, is generally complex and frequency dependent ( * denotes complex quantities). It can be written as:

C * (ω)= ′ C (ω )+i ′ ′ C (ω )
where i =-1.

Furthermore, for simplicity, a linear, homogeneous and viscoelastic core will be used in this work. In the isotropic case, the viscoelastic material is defined by a complex and frequency dependence shear modulus in the form:

G * (ω)= ′ G (ω )+i ′ ′ G (ω )
where ) (ω G′ is known as shear storage modulus, as it is related to storing energy in the volume and ) (ω G ′ ′ is the shear loss modulus, which represents the energy dissipation effects. The loss factor of the viscoelastic is defined as

η(ω ) = ′ G (ω ) ′ ′ G (ω )
and the Poisson's ratio ν is considered real and frequency independent. With these assumptions, the stress tensor of the sandwich structure is complex and frequency dependent.

Finite element system. After applying variational formulation to the harmonic local equations of this structural-acoustic coupled problem given in section 2.1, discretization by finite element method and using the constitutive relation for the viscoelastic core, we find the following matrix equation:

        =                         -         - * 0 F P U M C 0 M K 0 C K p T up u p up u 2 ) ( ω ω (1)
where U and P are the vectors of nodal values of u and p respectively, M p and K p are the mass and stiffness matrices of the fluid, M u is the mass matrix of the structure, K u * (ω) is the complex and also frequency dependent stiffness matrix of the structure, and F is the vector of nodal forces.

REDUCED ORDER MODEL

To solve the vibro-acoustic problem (Equation 1), the direct solution can be considered only for small model sizes. This has severe limitations in attaining adequate accuracy and wider frequency ranges of interest. A reduced order-model is proposed in this section to solve the problem at a lower cost. The proposed methodology, based on a normal mode expansion, requires the computation of the uncoupled structural and acoustic modes. The uncoupled structural modes are the real and undamped modes of the sandwich panels without fluid pressure loading at fluid-structure interface given by:

[K u 0 -ω si 2 M u ]Y si = 0
where K u 0 is the real and frequency-independent stiffness matrix calculated with a constant shear module's of the viscoelastic core such that K u * (ω) = K u 0 + δK u * (ω),

(ω si , Y si ) are the natural frequency and eigenvector for the i-th structural mode. The uncoupled acoustic modes are the cavity modes with rigid wall boundary conditions at the fluid-structure interface given by:

[K p -ω fi 2 M p ]Y fi = 0
where (ω fi , Y fi ) are the natural frequency and eigenvector for the i-th acoustic mode.

The vibro-acoustic coupled problem given by equation ( 1) can be reduced by projecting the mechanical displacement into the first N s structure eigenmodes Y si and the acoustic pressure into the first N f acoustic Eigenmodes Y fi , such as:

U = Y si q si (ω ) i=1 N s  and P = Y fi q fi (ω) i=1 N f  (2)
As a result, the reduced problem consists in solving the following system:

   = = = * = - + + - = - + + + - s f s N j sj ij fi fi fi fi fi fi N j i fj ij N k si ik si si si si si si q q q i q F q q q q i q 1 2 2 2 1 1 2 2 0 2 ) ( 2 β ω ω ξ ωω ω β ω γ ω ξ ωω ω (3)
where 3) is solved by updating γ ik * (ω ). After determining the complex amplitude vectors q si and q fi , the displacement and pressure fields are reconstructed using the modal expansion (Equation ( 2)).

F i = Y si T F is the mechanical excitation of the i-th mode; β ij = Y si T C up Y fj

NUMERICAL EXAMPLE

The proposed reduced order finite-element formulation is applied now to calculate the transmission loss factor of a double laminated glazing window. The system consists of two identical clamped laminated panels of glass separated by an air cavity of 12 mm thickness and inserted in an infinite baffle. Each laminated glass is composed of two glass plates (0.35 mm of length and 0.22 mm of width) bonded together by a Polyvinyl Butyral (PVB) interlayer. The thickness of outer and inner glass ply is 3 mm and that of the PVB interlayer is 1.14 mm. The glass ply is modeled as linear elastic material (density 2500 kg/m 3 , Young's modulus 72 GPa, and Poisson ratio 0.22). The material properties of the PVB are both thermal and frequency dependent. From dynamic and thermal tests, Havrillak and Negami have found an empirical law describing this dependence. The resulting complex frequency dependent shear modulus of the PVB is given at 20°C as [START_REF] Havriliak | A complex plane analysis of α-dispersions in some polymer systems[END_REF][START_REF] Koutsawa | Loss behavior of viscoelastic sandwich structures: A statistical-continuum multi-scale approach[END_REF]:

G * (ω ) = G ∞ + (G 0 -G ∞ )[1+ (iωτ 0 ) 1-α 0 ] -β 0
where G ∞ =0.235 GPa, G 0 =0.479 Mpa, α 0 =0.46, β 0 =0.1946, τ 0 =0.3979. The Poisson ratio of the PVB is 0.4 and density is 999 kg/m 3 .

Concerning the finite element discretization, we have used, for the structural part, 10 × 10 rectangular sandwich plate elements for each panel. The acoustic cavity is discretized using 10 × 10 × 5 hexahedric elements. The structural and acoustic meshes are compatible at the interface. For more details about these elements and the fluid-structure coupling element, we refer the reader to [START_REF] Larbi | Finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid[END_REF][START_REF] Larbi | Finite element modelling of double-wall sandwich panels coupled to an acoustic enclosure[END_REF] When the excitation (a normal incidence plane wave) is applied to the first plate, the second one vibrates and radiates sound caused by the coupling of air and plate 1. The normal incidence sound transmission loss is then computed using the Rayleigh's integral method [START_REF] Fahy | Sound and structural vibration[END_REF][START_REF] Larbi | Finite element modelling of double-wall sandwich panels coupled to an acoustic enclosure[END_REF]) which needs the finite element solution of surface velocities of plate 2. A comparison between a simple glass and a laminated glass with PVB interlayer with an equivalent surface mass is shown in Figure ( 2). Calculation was limited to 2000 Hz maximum. This comparison shows that laminated glass has a much lower acoustic radiation compared to conventional glass at resonance frequencies du to the effect of the viscoelastic layer. The reduction of sound radiation power is around 10 dB in lower frequencies and around 20 dB in higher frequencies. In fact, at low frequencies, the viscoelastic material is soft and the damping is small. At higher frequencies, the stiffness decreases rapidly and the damping is highest. Moreover, flexural vibrations causes shear strain in the viscoelastic core which dissipates energy and reduces vibration and noise radiation. Note that the thickness of the viscoelastic layer has a significant influence in terms of attenuation.

Figure. 3 nSTL through an air-filled double panel: comparison between the modal reduction approach and the direct nodal method.

Figure 3 shows a comparison between the normal incidence sound transmission (nSTL) of the coupled problem, obtained with the proposed modal reduction approach defined by Equations (3) with a truncation on the first twenty structural modes (Ns = 20) and first twenty acoustic modes (Nf = 20) and the direct nodal method (Equation ( 1)) where the displacement and pressure vectors are calculated for each frequency step. As can be seen, a very good agreement between the two methods is proved. In this respect, it should be noted that the resulting reduction of the model size and the computational effort using the reduced order method are very significant compared to those of the direct approach. For this example, the comparisons of computational times (using an implementation of the two methods in the Matlab software) showed that the reduced order model is much more faster than the direct technique (the CPU time ratio is about 10).

CONCLUSIONS

In this paper, a finite element formulation for sound transmission through double-wall sandwich structures with viscoelastic core is presented. A reduced-order model, based on a normal mode expansion, is then developed. The proposed methodology requires the computation of the eigenmodes of the structure in vacuo, and the rigid acoustic cavity. Despite its reduced size, this model is proved to be very efficient for simulations of steady-state analyses of structural-acoustic coupled systems. The Rayleigh integral method is used in order to estimate the sound transmission loss factor of the system. Examples are presented in order to validate and illustrate the efficiency of the proposed finite element formulation. Further investigations will concern introduction of (i) passive dissipation in the fluid and active one in the structure using piezoelectric materials and (ii) quasi-static corrections in the modal bases in order to accelerate the convergence.

Figure. 1

 1 Figure. 1 Double sandwich wall structure.

  is the fluid-structure modal coupling coefficient; ξ si and ξ fi are the introduced modal damping coefficients for structure and fluid respectively, γ ik * (ω )=Y si T δK u * (ω )Y sk the reduced residual stiffness complex coefficient. At each frequency step, the reduced system (

Figure. 2

 2 Figure. 2 Comparison of radiated sound power from a simple glass pane and a laminated glass with the same mass.A comparison between a simple glass and a laminated glass with PVB interlayer with an equivalent surface mass is shown in Figure(2). Calculation was limited to 2000 Hz maximum. This comparison shows that laminated glass has a much lower acoustic radiation compared to conventional glass at resonance frequencies du to the effect of the viscoelastic layer. The reduction of sound radiation power is around 10 dB in lower frequencies and around 20 dB in higher frequencies. In fact, at low frequencies, the viscoelastic material is soft and the damping is small. At higher frequencies, the stiffness decreases rapidly and the damping is highest. Moreover, flexural vibrations causes shear strain in the viscoelastic core which dissipates energy and reduces vibration and noise radiation. Note that the thickness of the viscoelastic layer has a significant influence in terms of attenuation.


Jeremy Lefort-Besnard

Camille Maumet

Boris Clenet

Elodie Germani

Crédit

Presentation of the project 'Narps Open Pipeline'

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

Crédit image: Elodie Germani

This project is supported by Région Bretagne (Boost MIND) and by Inria (Exploratory action GRASP) Camille Maumet Boris Clenet Elodie Germani Jeremy Lefort-Besnard Crédit image: Elodie Germani

This project is supported by Région Bretagne (Boost MIND) and by Inria (Exploratory action GRASP) This project receives contributions by Rémi Gau and during events such as OHBM Brainhack 2022 and 2023, e-ReproNim FENS NENS Cluster Brainhack 2023, ORIGAMI lab hackathon 2023 by : Arshitha Basavaraj, Trang Cao, Anna Menacher, Liz Bushby, Michael Dayan, Aimee Westbrook, Yaroslav Halchenko, Paul Taylor Camille Maumet Boris Clenet Elodie Germani Jeremy Lefort-Besnard Crédit image: Elodie Germani This project is supported by Région Bretagne (Boost MIND) and by Inria (Exploratory action GRASP) This project receives contributions by Rémi Gau and during events such as OHBM Brainhack 2022 and 2023, e-ReproNim FENS NENS Cluster Brainhack 2023, ORIGAMI lab hackathon 2023 by : Arshitha Basavaraj, Trang Cao, Anna Menacher, Liz Bushby, Michael Dayan, Aimee Westbrook, Yaroslav Halchenko, Paul Taylor

Come meet us and/or contribute during our next brainhack sessions:

-Monthly Narps Open hours -Marseille brainhack 2023 -OHBM brainhack 2024


Gwénola Simon

Laurie Casalot

Corinne Valette

Christopher Burot

Jean-François Rontani

Patricia Bonin
email: patricia.bonin@mio.osupytheas.fr

Jean- François Rontani

Singlet oxygen-induced alteration of bacteria associated with phytodetritus: effect of bacterial pigments

Keywords: Type II photosensitized oxidation, Singlet oxygen, Phytodetritus, Pigmented and unpigmented bacteria, Carotenoids, Vaccenic acid, DNA repair system Type II photosensitized oxidation, Singlet oxygen, Phytodetritus, Pigmented and unpigmented bacteria, Carotenoids, Vaccenic acid, DNA repair system

Introduction

Photosynthetic microorganisms (phytoplankton) such as diatoms, dinoflagellates and coccolithophores are the main primary producers in marine ecosystems, capable of producing organic matter using light energy and inorganic nutrients. This organic matter is heavily processed by bacteria, which mineralize approximately 50% of oceanic primary production (PP) [START_REF] Cole | Bacterial production in fresh and saltwater ecosystems: a cross-system overview[END_REF][START_REF] Ducklow | Stocks and dynamics of bacterioplankton carbon during the spring bloom in the eastern North Atlantic Ocean[END_REF] . The other 50% of PP either enters the marine food web or gets buried into seafloor sediments through a process called the 'biological pump' [START_REF] Eppley | Particulate organic matter flux and planktonic new production in the deep ocean[END_REF] . Bacterial activity in the oceans (secondary production) is therefore highly dependent on the abundance of primary producers [START_REF] Cole | Bacterial production in fresh and saltwater ecosystems: a cross-system overview[END_REF] , and varies with phytoplankton blooms at large or small scales [START_REF] Azam | Microbial structuring of marine ecosystems[END_REF] .

Phytoplankton-bacteria interactions are highly intertwined, and changes in composition of phytoplankton blooms (in terms of abundance and species assemblages) lead to changes in bacterial-community composition [START_REF] Riemann | Dynamics of Bacterial Community Composition and Activity during a Mesocosm Diatom Bloom[END_REF][START_REF] Pinhassi | Changes in Bacterioplankton Composition under Different Phytoplankton Regimens[END_REF][START_REF] Teeling | Substrate-Controlled Succession of Marine Bacterioplankton Populations Induced by a Phytoplankton Bloom[END_REF] . As this microbial secondary production is a key process to better understand the functioning of marine ecosystems, there has been intensive research into the phylogenetic composition of bacterioplankton communities (i.e. free-living planktonic bacteria in marine ecosystems).

Singlet oxygen ( 1 O2), which is produced by type II photosensitized oxidation processes in senescent phototrophic organisms [START_REF] Nelson | Rates and possible mechanism of light-dependent degradation of pigments in detritus derived from phytoplankton[END_REF] , is strongly electrophilic and lacks spin restriction [START_REF] Dmitrieva | Sustainable Development of Oil and Gas Potential of the Arctic and Its Shelf Zone: The Role of Innovations[END_REF] and therefore readily reacts with phytoplanktonic unsaturated lipids [START_REF] Rontani | Photo-and autoxidation of unsaturated algal lipids in the marine environment: An overview of processes, their potential tracers, and limitations[END_REF][START_REF] Rontani | Lipid Oxidation Products: Useful Tools for Monitoring Photo-and Autoxidation in Phototrophs[END_REF] , proteins [START_REF] Morgan | Protective mechanisms against peptide and protein peroxides generated by singlet oxygen[END_REF] , and nucleic acids [START_REF] Agnez-Lima | Mutation Spectrum Induced by Singlet Oxygen in Escherichia coli Deficient in Exonuclease III[END_REF][START_REF] Ravanat | Singlet Oxygen Induces Oxidation of Cellular DNA *[END_REF] . 1 O2 can also react with the octadec-11-enoic (vaccenic) acid of the bacteria attached to this algal material, affording isomeric trans allylic hydroperoxyacids [START_REF] Rontani | On the origin of cisvaccenic acid photodegradation products in the marine environment[END_REF][START_REF] Petit | Photochemical Production and Behavior of Hydroperoxyacids in Heterotrophic Bacteria Attached to Senescent Phytoplanktonic Cells[END_REF] . Recently, it was demonstrated that high solar irradiances strongly favor this transfer of 1 O2 to bacteria [START_REF] Burot | Singlet oxygen-induced alteration of bacteria associated to phytodetritus: effect of irradiance[END_REF] . The effect of exogenous pure 1 O2 on Gram-negative and Gram-positive bacteria has already been investigated [START_REF] Dahl | Pure Singlet Oxygen Cytotoxicity for Bacteria[END_REF][START_REF] Dahl | Pure exogenous singlet oxygen: Nonmutagenicity in bacteria[END_REF] , but the transfer of 1 O2 from senescent phytoplankton to their attached bacteria has been only demonstrated by Rontani et al. in 2003 [START_REF] Rontani | On the origin of cisvaccenic acid photodegradation products in the marine environment[END_REF] . Further studies demonstrated: (i) the good correlation between the photodegradation state of bacteria attached to phytodetritus and the photooxidation state of phytoplanktonic chlorophyll [START_REF] Petit | Photochemical Production and Behavior of Hydroperoxyacids in Heterotrophic Bacteria Attached to Senescent Phytoplanktonic Cells[END_REF] , and (ii) inhibition of 1 O2 transfer by the silica matrix of diatom frustules [START_REF] Petit | Transfer of singlet oxygen from senescent irradiated phytoplankton cells to attached heterotrophic bacteria: Effect of silica and carbonaceous matrices[END_REF] . This transfer of 1 O2 could strongly decrease the mineralization potential of bacteria attached and thus favor the preservation of phytoplanctonic material. The bacterial resistance to its deleterious effect could be a determining factor in the selection of microorganisms capable of interacting with senescent phytoplankton at the end of the bloom.

It is still hard to generalize bacterioplankton-community structures, but some important bacterial groups, such as Bacteroidetes and Proteobacteria, are typically abundant during bloom events, regardless of phytoplankton species [START_REF] Pinhassi | Changes in Bacterioplankton Composition under Different Phytoplankton Regimens[END_REF][START_REF] Fandino | Variations in bacterial community structure during a dinoflagellate bloom analyzed by DGGE and 16S rDNA sequencing[END_REF][START_REF] Rink | Effects of phytoplankton bloom in a coastal ecosystem on the composition of bacterial communities[END_REF] . Amongst them, Roseobacter, a genus that falls within the Alphaproteobacteria class, are often dominant in marine phytoplanktonassociated bacterial communities [START_REF] Rüger | Marine star-shaped-aggregate-forming bacteria: Agrobacterium atlanticum sp. nov.; Agrobacterium meteori sp. nov.; Agrobacterium ferrugineum sp. nov., nom. rev.; Agrobacterium gelatinovorum sp. nov., nom. rev.; and Agrobacterium stellulatum sp. nov., nom. rev[END_REF][START_REF] González | Bacterial Community Structure Associated with a Dimethylsulfoniopropionate-Producing North Atlantic Algal Bloom[END_REF][START_REF] Alavi | Bacterial community associated with Pfiesteria-like dinoflagellate cultures[END_REF][START_REF] Buchan | Overview of the Marine Roseobacter Lineage[END_REF][START_REF] Jasti | Phylogenetic Diversity and Specificity of Bacteria Closely Associated with Alexandrium spp. and Other Phytoplankton[END_REF] . Many studies investigating this compositional balance have given explanations for why strains belonging to the Roseobacter genus are so efficient at colonizing phytoplankton, including their high colonization capabilities [START_REF] Dang | Bacterial Primary Colonization and Early Succession on Surfaces in Marine Waters as Determined by Amplified rRNA Gene Restriction Analysis and Sequence Analysis of 16S rRNA Genes[END_REF] , their production of quorum-sensing molecules [START_REF] Wagner-Döbler | Discovery of Complex Mixtures of Novel Long-Chain Quorum Sensing Signals in Free-Living and Host-Associated Marine Alphaproteobacteria[END_REF] , and their antimicrobial compounds [START_REF] Long | Antagonistic Interactions among Marine Pelagic Bacteria[END_REF] . Another physiological characteristic of the Roseobacter genus that could explain their high abundance in bacterioplankton assemblages is the particular aerobic anoxygenic phototrophic (AAP) metabolism that occurs among this taxon [START_REF] Allgaier | Aerobic Anoxygenic Photosynthesis in Roseobacter Clade Bacteria from Diverse Marine Habitats[END_REF] . AAP bacteria are capable of photoheterotrophy, a metabolic pathway that enables them to produce energy from light, using photosynthetic reaction centers composed of bacteriochlorophyll-a (BChl a; [START_REF] Yurkov | New Light on Aerobic Anoxygenic Phototrophs[END_REF] . AAP bacteria are also known to contain high amounts of pigments such as carotenoids [START_REF] Petit | Dynamic of bacterial communities attached to lightened phytodetritus[END_REF] , which may protect these organisms against oxidative damage such as type II photosensitized oxidation, a process that can happen during late bloom phases [START_REF] Rontani | Intense photooxidative degradation of planktonic and bacterial lipids in sinking particles collected with sediment traps across the Canadian Beaufort Shelf (Arctic Ocean)[END_REF] .

It has already been hypothesized that bacteria with high amounts of pigments such as carotenoids may be able to tolerate exposure to 1 O 2 [START_REF] Dahl | Pure exogenous singlet oxygen: Nonmutagenicity in bacteria[END_REF][START_REF] Glaeser | Singlet oxygen, a neglected but important environmental factor: short-term and long-term effects on bacterioplankton composition in a humic lake[END_REF] . This resistance to oxidative stress could explain why the Roseobacter genus is highly represented among bacterioplankton communities during late bloom phases when the phytoplankton cells are senescent.

Here, we compared the effect of 1 O2 produced during the senescence of a diatom (Thalassiosira sp.) on the lipids and DNA of two Gram-negative bacteria widely found in marine environments, one pelagic ubiquitous unpigmented bacterium, Pseudomonas stutzeri [START_REF] Lehmann | Atlas und Grundriss der Bakteriologie und Lehrbuch der speziellen bakteriologischen Diagnostik[END_REF] and one pigmented bacterium, Dinoroseobacter shibae [START_REF] Biebl | Dinoroseobacter shibae gen. nov., sp. nov., a new aerobic phototrophic bacterium isolated from dinoflagellates[END_REF] frequently associated with phytodetritus . For the first time, the impact of 1 O2 produced during algal senescence on the physiology of associated bacteria was studied at the membrane-lipid and DNA levels.

Material and methods

Phytodetritus production :

The non-axenic diatom Thalassiosira sp. RCC1714 was obtained from the Roscoff Marine station culture collection. Diatoms were grown in F/2 medium at 17°C in an environment-controlled cabinet under an irradiance of 83 µmol photon.m -2 .s -1 (Osram, Lumilux, 12 h:12 h light/dark cycles). After two months of growth, cell density was measured by counting under microscope. Thalassiosira sp. Cell death was induced by sonication on ice using a Branson Sonifier 450 ultrasound generator equipped with a Branson S450A cell disruptor probe at 240 W for 10 minutes (50% duty cycle). The sonicated cells were then aliquoted in 50-mL Falcon tubes and stored at -20 °C for later photooxidation experiments.

Bacterial cultures : P. stutzeri ATCC 14405 and D. shibae DSM 16493 were grown aerobically overnight on a rotary shaker in the dark at 17°C on marine broth medium (US Biological™) diluted 1:10 with sterilized artificial sea water [START_REF] Kester | Preparation of Artificial Seawater1[END_REF] . These pre-cultures were used to inoculate the same medium to obtain under the same conditions an initial OD620nm of about 0.020. In the middle of the exponential growth phase, the cultures were stopped and cell abundances were counted based on epifluorescence in the presence of fluorochrome (4P,6diamidine-2P-phenylindole dihydrochloride; DAPI) as previously described in Otto [START_REF] Otto | Chapter 11 DAPI Staining of Fixed Cells for High-Resolution Flow Cytometry of Nuclear DNA[END_REF] .

Photooxidation experiments: Based on the recent results of Burot et al. [START_REF] Burot | Singlet oxygen-induced alteration of bacteria associated to phytodetritus: effect of irradiance[END_REF] showing enhanced 1 O2 transfer to bacteria at high irradiances, experiments were carried out in 100-mL sterilized quartz tubes using an Altas Suntest CPS + solar simulator with a Xenon NXE 1500 lamp producing a solar irradiance (2285 µmol photon.m -2 .s -1 ) in the 300-800 nm range close to the levels generally observed at noon at the surface of Mediterranean Sea 40 . To limit irradiation to visible range, we also simultaneously carried out experiments in 100-mL glass (opaque to UV) tubes with irradiance reduced to 2038 µmol photon.m -2 . s -1 in this case.

Phytodetritus and bacteria were mixed (at a 1:5 algal:bacterial cells ratio) in K medium [START_REF] Keller | Media for the Culture of Oceanic Ultraphytoplankton1,2[END_REF] (K 25 × diluted with sterilized artificial sea water) at a final volume of 100 mL, and immediately exposed to light in the solar simulator. Tubes were held at 17°C by immersion in a water bath connected to a cryothermostat. Four sampling times were defined: 0.5, 2, 3.5 and 5 h. At each sampling time, 15 mL and 10 mL samples were collected in triplicate for q-RT PCR and lipids analysis, respectively. The 15-mL samples were filtered on 0.8-µm polycarbonate filters (to collect only attached bacteria on particles and not the free-living organisms) and stored at -80°C until further RNA extraction. The 10-mL samples were filtered on 0.8-µm glass fiber filters (GF/F) and stored at -20°C until further lipid extraction. Each experiment was conducted in four separate tubes prepared simultaneously in the same conditions. A single tube was sacrificed at each sampling timepoint.

Control experiments were conducted without phytodetritus. Bacteria were mixed with sterilized artificial sea water added with 0.1 g. L -1 of lactate/acetate (50:50) as carbon source, then placed in 100 mL sterilized quartz tubes and immediately exposed to light in the solar simulator. Three sampling times for the controls were defined: 0, 2 and 5 h. At each sampling time, a 15 mL sample was filtered on 0.2-µm polycarbonate filters (to recover bacteria that are all free-living in this case) and stored at -80°C until further RNA extraction. For the lipid analysis, the samples were centrifuged with a Beckman & Coulter Allegra X-22-series centrifuge at 20,000 g for 30 min, then pelleted and stored at -20°C. Here again, the three samplings were conducted in separate control tubes prepared in the same conditions.

Lipid analyses

Lipid extraction: Samples (GF/F filters) were reduced with excess NaBH4 after adding MeOH (25 mL, 30 min) to reduce labile hydroperoxides (resulting from photo-or autoxidation) to alcohols, which are more amenable to analysis using gas chromatography-mass spectrometry (GC-MS) as described elsewhere [START_REF] Rontani | Control of the preservation of sympagic algal material in surficial sediments of central and eastern Baffin Bay by bactericidal hydroperoxides and free fatty acids[END_REF] . Briefly, Water (25 mL) and KOH (2.8 g) were then added, and the resulting mixture was saponified by refluxing (2 h), then cooled, acidified with HCl (2 N) to pH 1, and extracted with dichloromethane (DCM; 3 × 20 mL).

Derivatization: Dry TLEs were silylated in a mixture of pyridine/bis-(trimethylsilyl) trifluoroacetamide (BSTFA; Supelco; 2:1, v/v) as previously described [START_REF] Rontani | Control of the preservation of sympagic algal material in surficial sediments of central and eastern Baffin Bay by bactericidal hydroperoxides and free fatty acids[END_REF] and analyzed by gas chromatography-tandem mass spectrometry (GC-MS/MS).

Gas chromatography-tandem mass spectrometry (GC-MS/MS): GC-MS and GC-MS/MS

analyses were performed on an Agilent 7890A/7010A tandem-quadrupole gas chromatograph system (Agilent Technologies, Les Ulis, France) using a cross-linked 5% phenylmethylpolysiloxane (Agilent; HP-5MS ultra inert, 30 m × 0.25 mm, 0.25-µm film thickness) capillary column. The operating conditions used have been described previously by Rontani et al. [START_REF] Rontani | Control of the preservation of sympagic algal material in surficial sediments of central and eastern Baffin Bay by bactericidal hydroperoxides and free fatty acids[END_REF] . Vaccenic acid photooxidation products were quantified in multiple-reaction-monitoring (MRM) mode using the transitions m/z 339 → 131 for the parent vaccenic acid and m/z 199 → 129, m/z 213 → 129, m/z 357 → 129 and m/z 371 → 129 for its oxidation products [START_REF] Rontani | Lipid Oxidation Products: Useful Tools for Monitoring Photo-and Autoxidation in Phototrophs[END_REF] . Precursor ions were selected from the most intense ions (and specific fragmentations) observed in electron ionization (EI) mass spectra. Collision-induced dissociation (CID) was optimized by using collision energies at 5, 10, 15 and 20 eV. Quantification involved peak integration and determination of individual response factors using standards and Mass Hunter software (Agilent Technologies, Les Ulis, France).

Standard compounds: Vaccenic acid was obtained from Sigma-Aldrich and oxidized using Fe 2 +/ascorbate [START_REF] Loidl-Stahlhofen | Generation of α-hydroxyaldehydic compounds in the course of lipid peroxidation[END_REF] . Subsequent reduction of the resulting hydroperoxides in methanol with excess NaBH4 afforded the corresponding hydroxyacids.

Quantitative RT-PCR : RNA extractions were performed with the High Pure RNA Isolation Kit (Roche Applied Science, United States) as per the supplier's instructions. After extraction, any potential DNA contaminations were removed using the TURBO DNA-free™ kit (Ambion® by Life Technologies™) as per the manufacturer's instructions. RNA quantification and 260/230 and 260/280 ratio measurement were performed by spectrophotometry (NanoDrop 2000c, Thermo Scientific). Absence of DNA contamination was verified on RNA samples for each targeted gene (as described below) by PCR without the reverse transcription step. Reverse transcription (RT) reactions were carried out using random primers with the PrimeScript™ RT reagent Kit (TaKaRa) as per the supplier's instructions.

To plot the standard curves, fragments of the targeted genes were amplified and cloned into pGEMT-easy vectors (Promega) following the supplier's instructions. The primers used to amplify and clone the targeted genes for P. stutzeri and D. shibae are reported in Table S1. The PCR reactions (20 µL) contained 50 ng of genomic DNA from P. stutzeri or D. shibae, 0.5 µM of each primer, and 10 µL of GoTaq® G2 Hot Start Master Mix (Promega). The PCR program consisted in an initial denaturation step of 5 min at 98°C to activate the polymerase, then cycling (30 repetitions) with a 30 s denaturation step at 98°C, a 30 s hybridization step at the appropriate temperature for the selected primer pair, and an elongation phase of 20 s at 72°C. A final elongation phase at 72°C for 2 min was added for easy cloning in a T vector. The cloned DNA fragments were checked by sequencing. After purification, the plasmid concentrations were

Results and discussion

The aim of this work was to determine whether bacterial pigmentation plays a protective role against the 1 O2 damage when the bacteria are attached to lightened phytodetritus. To do so, we irradiated senescent cells of the diatom Thalassiosira sp. associated with the bacterial strains P. stutzeri (a ubiquitous heterotrophic bacterium without carotenoids) and D. shibae (an AAP containing a high proportion of the carotenoid spheroidenone). Experiments were carried out under two radiative fluxes (1) at high solar irradiance (PAR, Photosynthetically active radiation,+ UV) close to that generally observed at noon at the surface of the Mediterranean Sea 40 and (2) after limiting irradiation to visible range (PAR only) to determine the effect of 1 O2 only. Analysis focused on the effects of 1 O2 on photooxidation of the major MUFA of these bacteria (vaccenic acid) and on activation of their DNA repair systems.

Type II photosensitized oxidation of bacterial vaccenic acid : Oxidative damage in attached cells of P. stutzeri and D. shibae was monitored using the concentration of photooxidation products of vaccenic acid (pmol.L -1 ). Indeed, vaccenic acid is found in high proportions in P. stutzeri and D. shibae [START_REF] Biebl | Dinoroseobacter shibae gen. nov., sp. nov., a new aerobic phototrophic bacterium isolated from dinoflagellates[END_REF][START_REF] Rainey | Genome and Fatty Acid Analysis of Pseudomonas stutzeri[END_REF] but is only present in trace amounts in the bacterial community associated with the non-axenic strain of Thalassiosira sp. Employed 17 . Type-II photosensitized oxidation of vaccenic acid involves the addition of 1 O2 to the two carbon atoms of its  11 double bond to afford 11-hydroperoxyoctadec-12(trans)-enoic and 12-hydroperoxyoctadec-10(trans)enoic acids [START_REF] Rontani | Lipid Oxidation Products: Useful Tools for Monitoring Photo-and Autoxidation in Phototrophs[END_REF] . These hydroperoxides can be easily converted to 13-hydroperoxyoctadec-11(trans)-enoic and 10-hydroperoxyoctadec-11(trans)-enoic acids, respectively, via stereoselective radical allylic rearrangement [START_REF] Porter | Mechanisms of free radical oxidation of unsaturated lipids[END_REF] . We used stable allylic hydroxyacids arising from NaBH 4 reduction of these hydroperoxyacids as tracers of photooxidation of bacterial membranes.

For both bacterial strains, only trace amounts of vaccenic acid photooxidation products were detected before irradiation and in the different algae-free controls (Fig. 1). As previously observed [START_REF] Rontani | On the origin of cisvaccenic acid photodegradation products in the marine environment[END_REF][START_REF] Petit | Photochemical Production and Behavior of Hydroperoxyacids in Heterotrophic Bacteria Attached to Senescent Phytoplanktonic Cells[END_REF][START_REF] Burot | Singlet oxygen-induced alteration of bacteria associated to phytodetritus: effect of irradiance[END_REF] , oxidation of vaccenic acid strongly increased when irradiation was carried out in the presence of senescent phytoplankton cells (Fig. 1). The production of vaccenic acid oxidation products appeared to be maximal at 803 KJ.m -2 , which corresponds to 30 min of exposure only.

In the case of P. stutzeri, the concentration of vaccenic acid oxidation products was significantly higher in the presence of solar light (PAR+UV) radiation compared with non-UV levels (Figs. 1A and1B, t-test, n=18, p=0.0005< 0.05). The sensitizer (chlorophyll of senescent Thalassiosira sp. cells), which catalyzes type-II photosensitized oxidation of bacterial vaccenic acid, absorbs in both the PAR [START_REF] Nelson | Rates and possible mechanism of light-dependent degradation of pigments in detritus derived from phytoplankton[END_REF] and UV [START_REF] Quesada | Strategies of adaptation by Antarctic cyanobacteria to ultraviolet radiation[END_REF] ranges. Consequently, an additional amount of 1 O2 is produced during PAR+UV irradiation, thus inducing higher oxidation of vaccenic acid in membranes of P. stutzeri. In contrast, there was no significant difference in concentrations of vaccenic acid photooxidation products in D. shibae cells after irradiation by solar (PAR+UV) or PAR-only irradiance (Figs. 1C and 1D, t-test, n=18, p=0.203>0.05). This observation clearly shows that the additional amount of 1 O2 produced by UV radiations is quenched by the carotenoid spheroidenone in the membranes of D. shibae. Although this carotenoid cannot totally prevent type-II photosensitized oxidation of MUFAs in D. shibae membranes (Fig. 1C and 1D), it seems to limit the damage caused by overproduction of 1 O2 in the presence of UV.

Carotenoids containing two polar hydroxy groups (e.g. zeaxanthin), which lie across the monolayer membrane [START_REF] Ourisson | Bacterial Carotenoids as Membrane Reinforcers: A General Role for Polyterpenoids: Membrane Stabilization[END_REF] , can efficiently protect against 1 O2-mediated bacterial killing [START_REF] Tatsuzawa | Quenching of singlet oxygen by carotenoids produced in Escherichia coliattenuation of singlet oxygen-mediated bacterial killing by carotenoids[END_REF] . In contrast, carotenoids such as spheroidenone that lack hydroxy groups can become completely embedded in the lipid layer of the membrane [START_REF] Strzałka | Effect of β-carotene on structural and dynamic properties of model phosphatidylcholine membranes. I. An EPR spin label study[END_REF] . This embedment makes them less likely to react with 1 O 2 , which can therefore go on to rapidly damage unsaturated molecules in its vicinity. This can explain why spheroidenone cannot totally prevent vaccenic acid oxidation in membranes of D. shibae. Note that spheroidenone may play a key role in photoprotection of D. shibae against UV radiation-induced damage: as spheroidenone absorbs strongly between 300 and 400 nm [START_REF] Niedzwiedzki | Carotenoid-induced non-photochemical quenching in the cyanobacterial chlorophyll synthase-HliC/D complex[END_REF] , it can absorb harmful UV radiation.

Effect of 1 O2 on the DNA repair system genes : The other aim of this work was to monitor the response to 1 O2 of the DNA repair system in pigmented and non-pigmented bacteria. [START_REF] Cole | Bacterial production in fresh and saltwater ecosystems: a cross-system overview[END_REF] O2 is known to react with a wide range of cellular compounds, such as lipids, proteins, and DNA [START_REF] Morgan | Protective mechanisms against peptide and protein peroxides generated by singlet oxygen[END_REF][START_REF] Agnez-Lima | Mutation Spectrum Induced by Singlet Oxygen in Escherichia coli Deficient in Exonuclease III[END_REF][START_REF] Ravanat | Singlet Oxygen Induces Oxidation of Cellular DNA *[END_REF] .

Bacteria respond to adverse conditions by activating regulation pathways that increase their chances of survival. One such pathway-the aptly named SOS response-is induced by genome damage or disruption of DNA replication, and results in the synthesis of DNA repair enzymes and the inhibition of bacterial cell division. Bacterial cells use different strategies to protect themselves against the toxicity of 1 O2. These strategies usually involve 'preventive' detoxification enzymes, such as superoxide dismutase (SOD) or catalase (CAT) [START_REF] Kim | Control of Singlet Oxygen-induced Oxidative Damage in Escherichia coli[END_REF][START_REF] Glaeser | Chapter 4 -Singlet Oxygen Stress in Microorganisms[END_REF] , an efficient "Go system" with three detoxification proteins, i.e. MutM, MutT and MutY 53 assigned to DNA repair, or the quenching of 1 O2 with antioxidant compounds such as carotenoid pigments [START_REF] Conn | The singlet oxygen and carotenoid interaction[END_REF] .

Amongst the nucleotides, 1 O2 preferentially reacts with guanine (Fig. 2) as it has the lowest oxidation potential [START_REF] Cadet | Comparative Study of Oxidation of Nucleic Acid Components by Hydroxyl Radicals, Singlet Oxygen and Superoxide Anion Radicals[END_REF][START_REF] Steenken | How Easily Oxidizable Is DNA? One-Electron Reduction Potentials of Adenosine and Guanosine Radicals in Aqueous Solution[END_REF] . This leads to the formation of d-8-oxoGTP [START_REF] Ravanat | Mechanistic aspects of the oxidation of DNA constituents mediated by singlet molecular oxygen[END_REF] . This modified nucleotide has high mutagenic potential, as it can mispair with adenine, leading to G → T transversion [START_REF] Shibutani | Insertion of specific bases during DNA synthesis past the oxidation-damaged base 8-oxodG[END_REF] , which is the main mutation observed. To monitor activation of the DNA repair system in response to 1 O2 exposure, we measured the relative expression of several genes related to DNA repair after 1 O2-related damage as well as several stress-response transcription factors. In the genomes of both strains, three genes code for the detoxifying proteins of the "Go system": mutM (or fpG), mutY and mutT. As shown in Fig. 2, MutM and MutY proteins are glycosylases. MutM removes cytosine-paired d-8-oxoG while MutY removes adenine mispaired with d-8-oxoG [START_REF] Tchou | 8-oxoguanine (8-hydroxyguanine) DNA glycosylase and its substrate specificity[END_REF][START_REF] Boiteux | Substrate specificity of the Escherichia coli Fpg protein formamidopyrimidine-DNA glycosylase: excision of purine lesions in DNA produced by ionizing radiation or photosensitization[END_REF][START_REF] Agnez-Lima | DNA damage by singlet oxygen and cellular protective mechanisms[END_REF] . MutT is a nucleotide triphosphatase that detoxifies the nucleotide pool, hydrolyzing d-8-oxoGTP into d-8-oxoGMP [START_REF] Costa | The eukaryotic nucleotide excision repair pathway[END_REF] .

1 O2 is also involved in regulation of the expression of genes associated with the bacterial SOS response to oxidative stress. Knowledge of the 1 O2-specific regulatory mechanisms in microorganisms is based on only a few model systems, including the anoxygenic bacterium Rhodobacter sphaeroides and several heterotrophic species such as Escherichia coli. In R.

sphaeroides, stress response involves gene regulation by various alternative sigma factors RpoE and RpoH [START_REF] Glaeser | Chapter 4 -Singlet Oxygen Stress in Microorganisms[END_REF][START_REF] Anthony | Interactions Between the Rhodobacter sphaeroides ECF Sigma Factor, σE, and its Anti-sigma Factor, ChrR[END_REF][START_REF] Anthony | A transcriptional response to singlet oxygen, a toxic byproduct of photosynthesis[END_REF] . The sigma factor RpoE is maintained in an inactive state by forming a complex with its cognate anti-sigma factor ChrR [START_REF] Glaeser | Chapter 4 -Singlet Oxygen Stress in Microorganisms[END_REF] . Recent studies have shown that under exposure to 1 O2, RpoH becomes activated due to the rapid proteolysis of the RpoE:ChrR complex. RpoH (σ32) is the primary sigma factor controlling the heat shock response, but it is also known to be induced by other conditions (for a review, see [START_REF] Yura | Regulation of the heat shock response in Escherichia coli: history and perspectives[END_REF] ). Amongst all the genes involved in the potential response to 1 O 2 exposure, we chose to focus on one representative of each type of response: mutY, rpoH (involved in stress response), and chrR (involved in 1 O2-induced response and rpoH regulation). Fig. 3 shows the relative expression of these genes in P. stutzeri and D. shibae after exposure to artificial (PAR) and solar (PAR + UV) light in the presence of senescent Thalassiosira cells. Note, however, that 8-oxoDG is not specific to 1O2-induced alteration of DNA, but is also produced during the oxidation of DNA by other reactive oxygen species (ROS) (e.g., peroxyl or hydroxyl radicals arising from hydroperoxide homolysis or H2O2). Consequently, the alteration of DNA observed in bacterial cytoplasm may also result from the action of these ROS (notably by H2O2, which is known to readily cross cell membranes [START_REF] Omar | Diffusional Interactions among Marine Phytoplankton and Bacterioplankton: Modelling H2O2 as a Case Study[END_REF][START_REF] Omar | Genomic capacities for Reactive Oxygen Species metabolism across marine phytoplankton[END_REF] In P. stutzeri, mutY and rpoH were expressed from the beginning of exposure and reached peak expression (803 KJ.m -2 ) from 30 minutes (the experimental conditions did not allow samples to be taken earlier) (Fig. 3A). In addition to being very fast, the response did not seem to be influenced by algae nor by UV light (Table S2), and so the slightest trace of singlet oxygen in an unpigmented organism leads to the expression of mutY and rpoH. The lower expression at 5 h under PAR + UV exposure (8028 kJ.m -2 ) could be explained by cells entering the stationary phase of growth, which arrives earlier than during exposure to PAR. chrR showed no difference in expression level under UV exposure but showed a very strong decrease in expression under PAR conditions.

In D. shibae, the presence of UV induced a significant increase of mutY and chrR expressions which is only observed in the presence of senescent Thalassiosira cells (Fig. 3B, Table S2). In the same way, rpoH expression showed completely different patterns between solar and PAR conditions but was not influenced by the presence of the algae.

These observations suggest that 1 O2 arising from the algae has more difficulty penetrating the pigmented cells (comparison between pigmented and unpigmented cells in response to PAR exposure; Fig. 3, dotted bars). When UV is absent, only 1 O 2 -related oxidation remains. In this case, carotenoids are efficient enough to fight against this oxidant, therefore not allowing the 1 O2 to enter the cell, and all three genes are expressed at a lower level. When algae and UV are present, leading to the production of more 1 O2, there is not enough carotenoid in the pigmented cell to fight against the increased oxidative stress, and so mutY and chrR show higher expression. However, relative expression levels increased more with the unpigmented than the pigmented bacteria, showing some kind of protection due to the presence of spheroidenone. This protection is evidenced by a lower expression of rpoH observed in D. shibae (Fig. 3B) indicative of the lack of oxidative stress in this pigmented attached bacterium.

Conclusion

In this work, we studied the impact of type II photooxidation processes on different bacteria attached to senescent phytoplanktonic cells, with analysis focused on the photooxidation of bacterial membrane lipids (vaccenic acid) and the expression of genes involved in DNA repair systems. The aim was to determine whether the presence of carotenoids can actively protect bacteria against the damaging effects of 1 O2 under PAR and PAR+UV irradiations. Comparison of the results obtained with the bacteria D. shibae (pigmented) and P. stutzeri (not pigmented) showed that under high irradiance conditions (that strongly favor the transfer of 1 O2 from senescent algae to bacterial cells; [START_REF] Burot | Singlet oxygen-induced alteration of bacteria associated to phytodetritus: effect of irradiance[END_REF] ), the presence of spheroidenone in D. shibae cannot totally prevent 1 O2-induced oxidative alterations of unsaturated membrane lipids.

However, the carotenoid spheroidenone appears to limit 1 O2 damage, and it can absorb damaging UV radiation.

We also investigated the activation and regulation of the DNA repair system in response to exposure to 1 O2 and UV radiation. In P. stutzeri cells, the 1 O2 produced in senescent algae is not entirely scavenged by bacterial membrane MUFAs and so some 1 O 2 is able to reach the cytoplasm (Fig. 4A). Due to the lack of photoprotection across the membranes, DNA is thus damaged by both 1 O2 and UV radiations. (Fig. 4A). However, in D. shibae, scavenging by bacterial membrane MUFAs quenching by spheroidenone limit the effects of 1 O2 on bacterial membranes. Only a small fraction of UV radiation reaches the cytoplasm, where the efficient detoxifying activity of mutY limits its impact on the DNA of this strain, thus preventing oxidative stress (Fig. 4B). This limited impact is supported by the apparent inactivity of the rpoH gene responsible for oxidative stress response in photoheterotrophic bacteria.

Based on these results, the dominance of the Roseobacter genus in bacterioplankton communities associated to algal blooms could be attributed in part to the protective action of their carotenoids against 1 O 2 and UV-driven damage.

  determined by spectrophotometry and used to produce the standard curves for qPCR allowing quantification of the synthetized cDNAs.The various target cDNAs were quantified by qPCR (qPCR Master Mix, Promega) as per the supplier's instructions. Each qPCR run performed used 1 µL of the obtained cDNA and 0.5 µM of each primer in a final 20 µL reaction volume. The qPCR program consisted in an initial denaturation step of 2 min at 98°C, then cycling (40 repetitions) with a 20 s denaturation step at 98°C, a 20 s hybridization step at the appropriate temperature for the selected primer pair, and an elongation phase of 20 s at 72°C. Experiments were done using the CFX Opus Real-Time PCR system (Bio-Rad) and the associated software. The starting quantity was determined using Bio-Rad CFX manager 2.1 software and transformed into copies per µL of cDNA. The quantified expression level of the housekeeping gene (rpoD) encoding for a σ 70 subunit of the RNA polymerase was used to normalize gene expression. Each extracted RNA was analyzed in 6 technical replicates (two independent reverse transcriptions and three qPCR analyses per cDNA). Data Availability : The sequences generated during the current study are available in the Genbank repository, the accession numbers are : #2741504, #2741532, #2741540, #2741543, #2741547, #2741570, #2741574, #2741584 Ethical approval. Tis article does not contain any studies with human participants performed by any of the authors.

Fig. 1 :

 1 Fig. 1: Production of vaccenic acid oxidation products (pmol. L-1) during irradiation of Thalassiosira sp. cells associated with bacterial strains Pseudomonas stutzeri (A & B) orDinoroseobacter shibae (C & D) with PAR and PAR + UV radiation, respectively.

Fig. 2 :

 2 Fig. 2: The different scenarios related to 1O2 DNA damage and the role of the "Go system" proteins in repair. (°G = 8-oxo-7,8-dihydro-2'-deoxyguanosine = d-8-oxoG).

BFig. 3 :

 3 Fig. 3: Log2 of the relative expression of the targeted genes in Pseudomonas stutzeri (A) or Dinoroseobacter shibae (B) with PAR (plain bars) and PAR + UV (dotted bars) radiation. The hatched bars represent the controls, conducted without Thalassiosira cells. The results are relative to the expression of the rpoD gene and relative to that of the controls (0). Means ± SD (n=3).

Fig. 4 :

 4 Fig. 4: Conceptual scheme showing the effect of singlet oxygen photochemically-producted in phytodetrituson membrane components and DNA of unpigmented (A) and pigmented (B) associated bacteria.

Table S2 :

 S2 ANOVA analyses of data comparing the effects of Thalassiosira sp. input with solar irradiance, UV, solar light and PAR light on the vaccenic-acid oxidation product and the level of expression of mutY, chrR and rpoH (threshold, p< 0.005).

		Source	DDL	Somme des carrés	Moyenne des carrés	F	Pr > F
		Thalassiosira sp. effect with solar Irradiance	1	9615978,78	9615978,78	82,91	0,00000
	Vaccenique Ac	specific effect of UV	1	19299253,72 19299253,72	23,47	0,00008
	oxidation product	solar Light dose	1	5143869,38	5143869,38	9,13	0,01287
		PAR Light dose	1	2366453,91	2366453,91	4,78	0,05358
		Thalassiosira sp. effect with solar Irradiance	2	12,30	6,15	2,81	0,08675
	mutY	specific effect of UV solar Light dose	3 1	0,76 14,41	0,25 14,41	0,17 12,99	0,91785 0,00482
	P Stutzeri	PAR Light dose Thalassiosira sp. effect with solar Irradiance	1 2	0,94 1,30	0,94 0,65	1,99 0,33	0,18852 0,72188
	chrR	specific effect of UV solar Light dose	3 1	34,81 4,46	11,60 4,46	6,37 1,27	0,00331 0,28665
		PAR Light dose	1	0,94	0,94	1,99	0,18852
		Thalassiosira sp. effect with solar Irradiance	2	23,80	11,90	4,46	0,02664
	rpoH	specific effect of UV solar Light dose	3 1	0,99 10,79	0,33 10,79	0,19 5,39	0,90177 0,04269
		PAR Light dose	1	0,78	0,78	1,96	0,19213
		Thalassiosira sp. effect with solar Irradiance	1	1142347,63	1142347,63	16,31	0,00237
	Vaccenique Ac	specific effect of UV	1	833878,21	833878,21	0,73	0,40090
	oxidation product	solar Light dose	1	1557444,57	1557444,57	2,00	0,18718
		PAR Light dose	1	5287382,51	5287382,51	5,09	0,04769
		Thalassiosira sp. effect with solar Irradiance	2	16,22	8,11	24,56	0,00001
	mutY	specific effect of UV solar Light dose	3 1	129,74 2,99	43,25 2,99	151,30 12,68	0,00000 0,00517
	D. Shibae	PAR Light dose Thalassiosira sp. effect with solar Irradiance	1 2	0,00 9,61	0,00 4,81	0,00 23,14	0,98159 0,00001
	chrR	specific effect of UV solar Light dose	3 1	828,10 0,60	276,03 0,60	4090,43 6,99	0,00000 0,02458
		PAR Light dose	1	0,01	0,01	0,22	0,65006
		Thalassiosira sp. effect with solar Irradiance	2	1,10	0,55	1,96	0,17018
	rpoH	specific effect of UV solar Light dose	3 1	117,53 0,06	39,18 0,06	236,09 0,24	0,00000 0,63195
		PAR Light dose	1	0,35	0,35	4,73	0,05478

Acknowledgements. The project leading to this publication has received funding from

European FEDER Fund under project 1166-39417. The laboratories, where all the experiments were performed, are in compliance with ISO9001-2015. The authors wish to thank the OMICS platform of MIO for providing the technical means and skills of its personnel and making available equipment and protocols.

Originality-Significance Statement. For the first time, the impact of 1 O2 produced during algal senescence on the physiology of associated bacteria was studied at the membranelipid and DNA levels which places this current work in the top 10% of current research in environmental microbiology.

Table S1. Sequences and hybridization temperatures (°C) of primers used for the cloning and amplification of targeted genes in P. stutzeri (Ps) and D. shibae (Ds).

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Franck Delpal
email: fdelpal@ifm-paris.com

The worldwide expansion of luxury firms: forms, objectives and effects

Keywords: Luxury, France, Italy, Internationalization, Retail networks, Corporate strategy, Entry barriers

The globalization of the luxury market is not a recent phenomenon. However, the forms of this global presence have undergone significant changes during the last decades. While new markets have emerged, luxury companies have switched to a more integrated model of distribution developed their global presence and clearly become retailers.

First, we examine the various forms of distribution used by the companies to reach the foreign markets over time. We then show that if some external factors (conditions to establish subsidiaries, evolutions in the local distribution networks) influenced the modes of entry of luxury firms, strategic and economic reasons also explain this movement of integration and the increasing share of retailing in the companies' activity. We underpin these theoretical approaches by a series of French and Italian case studies to show the reasons provided by the companies themselves to justify this strategic evolution.

2 Eventually, we analyze the consequences of this general movement of downstream integration. This strategy has led to the setting of strong entry barriers at a sector level. In addition to their brand identity and in certain cases their specific know-how and assets, the "insiders" now have a bigger market power on their environment. Moreover, this strategy can partly explain the structure of the luxury industry for many consumer goods: a few big companies whose supremacy can with great difficulty be challenged by their smaller scale competitors.

b)

European luxury on global markets Whether for haute couture or high end craftsmanship, the US market has been the main destination for the French luxury companies. Central at the beginning of the 20th century, this market has suffered during the crisis of the 1930's, but has ensured the French couturiers a consequent development of their activity after the Second World War [START_REF] Verley | Marchés des produits de luxe et division international du travail (XIXè-XXè siècle)[END_REF].

Luxury and internationalization go hand in hand systematically. Indeed, it is starting from the exchanges of luxury goods that the international trade was structured; in addition, the luxury companies are systematically strong exporters. These characteristics can be explained by the basic conditions of the luxury market:

• In a context where transportation costs are substantial, only products enjoying an positive or constant price elasticity of their demand can be exported, which is the case for luxury items. Indeed, the cost overrun related to transport, included in the retail price, will not have a negative effect on the level of consumption. Traditional products, whose consumption decrease as the price increases, are on the contrary penalized and can't be exported when the transportation costs are significant.

•

In addition, since luxury products are addressed to a negligible fraction of the population, the narrowness of the interior market can represent a handicap for the development of luxury companies, which are naturally export-oriented in order to find a wider clientele.

• Lastly, luxury items are carrying an identity linked to their manufacturers and their country of origin, and are strongly embedded in its culture. They have thus the ability to be exchanged because they do not have equivalents on the worldwide markets.

The exportations of luxury products were, until in the 1970's, primarily directed the United States and Europe. Soavi (1999) shows thus that in 1921, the European markets weigh for 45% in French exports of luxury items, the United States for 27%. From the 1970's, the strong economic development operated by Japan is at the origin of a new phase of growth for the French luxury companies, in particular for fashion and leather goods. [START_REF] Jacomet | Le luxe: une industrie entre héritage et modernité[END_REF] Since the middle of the 2000's, the Asia-Pacific zone, consisting in China, India and many other countries experiencing strong economic growth (Singapore, Taiwan…), clearly took over and represents the principal pool of growth for the years to come. By way of an example, the following graph shows the evolution of the respective weight of the different areas in Hermès' turnover. Dynamism of the Asian markets (except Japan) unrelentingly made decrease the share of the markets known as mature (United States, Japan, Europe), although the sales in those always post a solid growth.

Chart 1 -Hermès sales breakdown by area (1993-2010)

Source: Annual reports

The swing of the European companies towards the Asian markets constitutes over the long period a new upheaval of the luxury market. This change was in addition accompanied by a radical modification in the forms of presence of the companies on these markets.

/ Internationalization and Retail

For about twenty years, an abundant literature has been devoted to the relationship between internationalization and distribution on the one hand, and to the choice of entry mode by the firms on the international markets.

1) Theoretical approaches

The theoretical works exploring the process of internationalization of firms are organized around three main themes [START_REF] Melin | Internationalization as a strategy process[END_REF]):

•

The way in which the companies penetrate the worldwide markets. These approaches analyze the choice between integration and outsourcing for the management of a foreign branch.

•

The nature of the international exchanges within the organizations (transfer pricing, transaction costs…) or between institutions.

• Coordination processes (monitoring systems, relations with the local government…).

Concerning the first topic, which interests us particularly, various models describing the stages of internationalization exist. A first approach was to decline Vernon's model of the product lifecycle, but this one applies better to a macroeconomic level that on the level of a company in particular. In addition, it is more relevant for products with long life cycles than for those whose obsolescence is fast. One of the most recognized models was developed by [START_REF] Johansson | The internationalization process of the firm: a model of knowledge development and increasing foreign market[END_REF] and is called Internationalization Process Model or Uppsala model. These authors explain the worldwide development of firms by their need to limit the psychic distance with their markets of establishment. They will enter in priority on the markets which they understand best, in general the countries bordering, before penetrating the more distant markets once the psychic distance with those will have decreased thanks to the better knowledge and improved competences of the company on international presence. This model has been criticized because of its deterministic conclusions. Moreover, it is more adapted to explain the first phases of internationalization than for already well-established firms with a global presence. Lastly, a third kind of models, gathered under the name of "eclectic paradigm" [START_REF] Dunning | The Eclectic Paradigm of International Production: a restatement and some possible extensions[END_REF], explains the nature of the internationalization of the firms by three types of variables: ownership-specific advantages, internalization advantages and location advantages. The ownership-specific advantages relate to the assets a company has generated from its possession of certain specific features (international experience, marketing skills, trademarks, unique know-how…) ; the internalization advantages are related to the theory of transaction costs and explain the global presence of companies by the existence of market imperfections which makes the hierarchy more efficient than the use of the market; finally, the location advantages are related on the potential of the host market and the reduction of risks inherent in a direct presence of the company. This model was based on an analysis of manufacturers and was later adapted to the retail sector [START_REF] Park | The global retailer's strategic proposition and choice of entry mode[END_REF]. The main critics that it faced were its static character: this model is adapted for a descriptive approach but doesn't explain the way in which the companies generate little by little these advantages by themselves.

Chan [START_REF] Kim | Global strategy and multinationals' entry mode choice[END_REF] for their part proposed an eclectic model based on three types of variables: strategic variables of the industry (global concentration, strategic synergies and motivations), variables linked with the environment of the companies (country risk, uncertainty of demand, intensity of competition…) and transaction-specific variables (level of firm-specific know-how, tacit nature of know-how). This approach shows that companies tend to proceed to integration of their subsidiaries when 1/ the country risk is weak, 2/ they have experiment in the country, 3/ global synergies and concentration are strong and finally 4/ when its know-how is of tacit nature, i.e. inarticulable and not transmissible. They add that integration has as a virtue to reduce the transaction costs which can arise from an opportunist behavior on behalf of the partner of the company, which can use the assets of this one (knowhow, brand…) in an inappropriate way. The principal limit of this approach is that it explains internationalization on a global level but doesn't really explain the development process of companies on worldwide markets.

This economic approach was also developed by [START_REF] Horstmann | Licensing versus direct investment: a model of internalization of the multinational enterprise[END_REF], which propose a model offering the choice to a company between giving a license for its products to a foreign partner and investing itself on this market, in a context of imperfect information of the consumer on quality. The authors show that to guarantee its reputation, the company will be encouraged to ensure itself its activity abroad, more especially if its products are high quality products. This result is completely relevant to understand the strategy of fashion and luxury companies, such as Gucci, Christian Dior or Yves Saint Laurent which have given up in the 1990's the massive use of the licenses which they made hitherto.

More specifically, a whole side of the theoretical literature relates to the activities of retail (for a survey over the last twenty years, see Alexander and [START_REF] Doherty | International retail research: focus, methodology and conceptual development[END_REF]. The explored sets of themes are more or less the same ones as in the generic models of internationalization.

Subjects such as the motives for internationalization, the selection of the target markets, the choice of entry mode or the strategies of setting in market (standardization vs. adaptation) are thus listed [START_REF] Swoboda | Internationalisation of retail firms: state of the arts after 20 years of research[END_REF].

Lu, Karpova and Fiore (2011) have analyzed the factors influencing the entry mode chosen by fashion retailers. After having defined the four degrees of presence on an exterior market (export, franchise, joint venture and wholly owned subsidiary), they list the conditions under which must be exerted a precise control on its distribution by a company. Some concern the company itself (existence of specific assets, significant brand equity, required financial capacities, strong international experience), other its environment (weak country risk, cultural proximity, weak governmental restrictions), others finally its market (strong potential of market, small degree of competition). [START_REF] Wigley | The operationalisation of international fashion retailer success[END_REF] match these explanatory factors of three critical success factors: complete consistence between the brand management at a global scale, the distribution channel choice and between the imagery of the brand and its incarnations (shops, staff…).

Doherty, Moore and Doyle (2010) were specifically interested in the strategy of luxury companies to use their flagship stores as modes of entry on new markets. This new kind of entry mode has to be added to the five types already defined by [START_REF] Dawson | The internationalization of retailing[END_REF]: internal expansion (the company opens individual shops using in-company resources), merger or takeover, standard franchise agreements, joint ventures (in-stores concessions), exchange without controlling interest. Flagship stores must be distinguished from the traditional boutiques both by their physical or tangible features (their size, their installation, their localization and their cost) and the functions which are assigned to them. Beyond the basic commercial role, the authors show that flagship stores are also used to establish the reputation of the company and its brand on the market, as supports of communication and reception for the press and the business partners (franchisee, external distributers), to accommodate consumers in search for a greater exclusiveness in products and services. This kind of shops is logically systematically managed directly by luxury companies, because of their cost and of the control required on all the plans.

2) Cases of luxury companies

Our approach consists in confronting the approaches we have just presented to the evolution of the practices of a selection of luxury companies. Due to their seniority and available testimonials over long period, we will particularly focus on the companies Louis Vuitton, Hermès and Gucci. Source: Annual reports Nowadays, the necessity to tightly control their distribution makes consensus among all the researchers (see Moore et al., 2005[START_REF] Wigley | The operationalisation of international fashion retailer success[END_REF]Moore et al., , 2010) ) and managers of luxury companies. It is however advisable to remind that only a few decades ago, in the 1980's, these companies did not at all have such an international visibility nor exclusive control of their distribution.

Louis Vuitton

The case of Louis Vuitton is emblematic with many regards. Kyojiro Hata, former president of the Japanese subsidiary of Louis Vuitton, described in detail the situation at the time (Hata, 2004). In 1977, the company had only two fully owned shops in France (in Paris and Nice)

and secured a presence on the US and Japanese markets through trade agreements. In the United States, the company had a license with Saks Fifth Avenue. And for Japan, Louis

Vuitton treated with the importer Mitsui & Co and the wholesaler Sann Frères. In spite of that, many Japanese customers went to the Parisian shop and bought products in great quantity. The company thus ordered a study which highlighted the presence of its products in many Japanese shops that it had not selected, which clarified the existence of reseller networks based in Paris and selling their goods in Japan with profit (the price change was then substantial between the French and Japanese shops). This led the company to limit the sales to the Japanese customers. The study carried out by Mr. Hata also explored the methods of establishment used by luxury companies in Japan, highlighting the need for inventing a new and original model. This one took the shape of a double contract between on the one hand Louis Vuitton France and the Japanese department stores (distribution contract) on the one hand, and between Louis Vuitton France and Louis Vuitton Japan on the other hand (management contract). Indeed, recent changes in the legislation authorized the foreign companies to establish themselves in Japan without any local partner, which was little known by many Western businessmen at that time. Moreover, Louis Vuitton and its future representative in Japan had a critical point of view on joint ventures, which were seen as sources of conflicts and consequently of bad management.

Initially, the Japanese subsidiary had essential mission of ensuring a policy of distribution and communication in conformity with the requirements of the House. Even though the shops and the salespersons belonged to the department stores, the company wanted to behave as a retailer and soon became one. Starting from 1981, the subsidiary was turned into in private company having for additional missions the importation of products and the distribution through wholesale. In parallel, the company organized the multiplication of the retail stores directly controlled by Louis Vuitton. From the middle of the 1990's, the company reinforced its implication on this market by replacing the department stores salespersons by its own employees. Since, the will of Louis Vuitton is to have a direct presence on every market, except those presenting legal constraints to foreign installation or very strong specificities.

The motivations to internationalization are in this case at the same time offensive and defensive. Offensive because the surge of Japanese customers in France testified of their noteworthy appetite for Vuitton products and thus the strong potential this market represented.

Defensive because retail stores opening in Japan also aimed to counter the presence of resellers (in particular through the reduction of price differences between France and Japan)

and to preserve the company image.

Hermès

Created in 1837, Hermès faced major evolutions carried by each successive generation which directed the company [START_REF] Guerrand | Souvenirs cousus sellier[END_REF]. Thierry Hermès, the founder, sold through wholesale harnesses and saddles. His son Charles opened the first shop and started retailing. The third generation, incarnated by Emile Hermès, understood the nearest end of horse transport and diversified the company towards leather goods, fashion, silk… He also started to lead the company on the worldwide markets. In the first times, the company did not open shops but employed "travelers" who where selling saddles, harness, covers for horses all around the world. The first subsidiaries were created in France in first half of the 20th century in order to follow the high net worth customers in her vacation resorts (Vittel, Deauville, Le Touquet, Biarritz, Cannes). As for the European distribution, the company first privileged representatives for the main French cities (franchisees are named "concessionnaires" by Hermès) whom were chosen on strict criteria: to conduct an extremely detailed market study on the potential of the cities and sites, to have a lease in a promising city, three years of rent and two years of business expenses in bank. This distribution through "concessionaires" was primarily structured after the Second World War, with the increasing complexity of the international trade. This system showed some limits, in particular the matter of the price change between France and the other countries: "So that our representatives can make some benefit without practicing excessive prices, we were obliged to increase our retail prices to be able to make them a rebate. Obviously, if people had to spend 50 to 80% more abroad than in Paris, they would have taken a plane and our agents would not have had a raison d'être" [START_REF] Guerrand | Souvenirs cousus sellier[END_REF]. Then, the passage of a system of representatives to sales in directly operated stores is relatively recent, since it dates from the 1990's. Ever since, the share of directly operated stores clearly surged, even if the number of franchisees also progressed.

It is also interesting to state that the share of franchisees in the network is greater in the nearest markets than in the far ones. In Europe, only 56% of the stores are directly operated by Hermès. This share is of 69% in the Americas, 64% in Asia and 78% in Oceania. In the Middle East, the company only relies on local partners. These figures show that the way Hermès enters foreign markets is more linked with the period it enters than the location of the country. According to the Uppsala model, the company should have a greater control on its European stores network than in Asia, for instance, which is not the case.

The mode of entry seems more linked with the period Hermès entered the market than their cultural or geographical proximity with the company. When Hermès started to expand in the mature markets (Europe, USA, Japon), it used both subsidiaries and franchises; that's why the distribution networks in those countries are still mixed. Nowadays, for new locations such as China, it mostly uses subsidiaries. Another interesting phenomenon described by J.R. Guerrand is that the opening of a shop abroad does not generate a decrease in the number of customers of this nationality in the French shops. On the contrary, the increase in the reputation of the brand thanks to its settlement in new countries tends to increase the frequentation of the other shops of the company by the tourists of those countries.

Gucci

Created in 1921, Gucci is from the start directed towards retailing. In 1951, it has three shops in Italy; the first boutique abroad is established in 1953 in New York. Until in the 1990's, the international distribution network increases, primarily through the use of franchise agreements. Thus, in the 1970's, Gucci signs a contract of agency with a specialized retailer to ensure its representation on the Japanese market. The arrival of a new team of leaders in 1995 (Domenico de Sole is named CEO this year) marked a turning in the distribution strategy of the company. This one, largely involved in debt, needed to increase its performances and to clarify its strategy. That passed in particular by the buying-back of licenses and the drastic reduction amongst franchises which were replaced by directly owned stores, as testifies the figures below. Source : Mark [START_REF] Lee | Celebrating 85 years, Gucci stronger than ever[END_REF] How to justify this choice? Cristina Ventura, head of retail operations for Europe, quoted by Martinez Jerez, Corsi and Dessain (2010) explains: "When a franchise becomes DOS, sales increase by 30%. This is due to a range of factors: DOS are more systematic in calling for the in-store events, the sales force is more service-oriented, and the stores carry more merchandise, as they put more weight on having the right handbag or the right jacket for their customers and less on the financial cost of the stock".

The only remaining franchises concern countries where the company believes not to have sufficient knowledge of the market or those whose legal framework does not allow the establishment of fully controlled shops.

These three cases show very well that the switch to a directly controlled internationalization is relatively recent for luxury companies. They also validate most of the previously detailed theoretical approaches.

In terms of ownership-specific and internalization advantages, this strong control was indeed supported by the existence of specific assets (high brand value, know-how, control of the productive process, exclusiveness…), as well as their will to ensure a deep internal control on the whole dimensions of product development, from creation to distribution. Moreover, concerning location advantages, the existence of strong potential markets and easier installation requirements created favorable conditions for this new strategy.

The increasing deregulation of the international trade and the global integration of economies facilitated a direct approach of the markets by the companies. Another significant element is the change in the distribution structures in the host countries. A Goldman Sachs study (2010) highlights a close link between the level of development of a country and its distribution structure. If the department stores had a central role in Japan in the 1970's and 1980's, it is not any more the case today. Same manner, in South Korea, after a domination of the market by the department stores, the specialized circuits emerged thereafter. Little by little, the foreign companies can enter these countries with their own shops.

Today, this development scheme is the dominant strategy of luxury brands, the only preserved territories being those where the foreign establishment is not fully authorized, where market conditions are not optimal or those where the companies did not wish to turn their network in Directly Operated Stores because of long relationships with a local partner.

/ Retail and luxury

The evolution of most of the distribution networks under the mode of direct control constitutes a major strategic axis for luxury companies. This form of downstream integration finds its justifications in business strategy. We also will show starting from tools for industrial economy that these changes had consequences on the degree of competition within the luxury industry and constitutes one of the means used by the companies to organize a market foreclosure. [START_REF] Porter | Choix stratégiques et concurrence[END_REF] enumerates four advantages suitable for integration towards distribution:

1) A better capacity to differentiate the product. The creation of an favorable environment for the products of the company, the presence of a trained staff, knowing the product perfectly, are significant ways to create value and to distinguish a company from its competitors.

2) Suppression of bargaining power of the purchaser. Facing customers, the company is in a better position to propose its offer than with a department store or a chain with higher market power.

3)

The access to information concerning the market. The manufacturer can thus follow in real time the nature and the evolution of the tastes of the customers and answer them quickly.

4)

The fixing of higher prices. The company cumulates the margins of wholesaler and retailer (who are added in certain cases to those of manufacturer and importer) which can reinforce its economic model. Free to fix its own prices, the company is not forced by a partner to practice sales or promotions. In addition, in the case of international distributers, the possibility of having a price policy on a worldwide scale also constitutes an advantage.

The justifications of vertical integration by the economic theory corroborate those proposed by the literature of management and strategy. [START_REF] Mahoney | The choice of organizational Form: vertical financial ownership versus other methods of vertical integration[END_REF] explains for instance the recourse to vertical integration by the existence of agency or transaction costs, which make the internalization of functions preferable. Other authors, such as [START_REF] Richardson | Vertical integration and rapid response in fashion apparel[END_REF], also justify vertical integration by the need for giving a prompt response to the market, starting from the case of the fashion sector. [START_REF] Mcguire | An Industry Equilibrium Analysis of Downstream Vertical Integration[END_REF] for their part studied the choices of distribution of two companies according to the degree of substitutability of their products. A small degree of substitutability is accompanied by a direct control of the distribution. The luxury companies, whose major strategic axis is to differentiate themselves from their competitors, chose their distribution mode suitably. [START_REF] Lafontaine | Retail contracting: theory and practice[END_REF] analyzed the issue of retail contracting and conclude that a firm will be likely to be downstream integrated if:

• The risk of market is weak,

• The retail formats are substantial,

• The cost of control of the agent by the principal is noteworthy.

In addition to its advantages in terms of efficiency for the company, it seems necessary to us to highlight that this increasing downstream integration by the companies also plays a part in their competing context. Indeed, the cost required by the existence of a distribution network and consequently the visibility of a luxury company at an international scale became prohibitory. As we showed, the direct presence of luxury companies in the various worldwide markets constitutes a pledge of credibility and acts positively on their reputation.

In addition to their strong brand identity and in certain cases their specific know-how and assets, the "insiders" now have a bigger market power on their environment. This will to be directly present on the markets can be seen as what [START_REF] Dixit | Recent developments in oligopoly theory[END_REF] named a strategic precommitment. He describes a market where are present an installed company and a potentially entering company. By a series of expenditure showing that it is strongly engaged and in an irreversible way, the installed firm will notify the potential entrant that its entry will cause a reaction and that it would be preferable that the entrant does not penetrate on its market. The rise in the cost of the entry generated by the firm installed thus constitutes a threat which, it is credible, will prevent all new entry on the market.

It results from this race to downstream integration that the cost of entry on the luxury market became extremely heavy. It is partly what explains the relative fixity of the structures of this sector. The concentration of the turnover between a few big companies is very strong and there is a growing difference in terms of size and performances between the leaders of the luxury sector and their challengers. The main luxury firms profit indeed from the best exposure in terms of brand and product portfolio, of distribution networks (mainly through retail), and of markets (strong presence on the emerging markets with strong potential). They thus still will accentuate their advance on their competitors and will continue to affirm their domination on the market.

Table 1 -Sales breakdown by area (2010)

 1

		Europe	Americas	Japan Asia-Pacific RoW	Total
	LVMH Fashion & Leather goods	29%	18%	16%	30%	7%	100%
	Gucci	30%	18%	12%	36%	4%	100%
	Hermès	38%	16%	19%	26%	1%	100%

Table 2 -Hermès -Evolution of the distribution network

 2

		1995 1996	1999	2001	2004	2006	2008	2010
	Nb of Directly operated stores	67	77	98	109	133	145	166	193
	Nb of Franchisees ("Concessionnaires")	78	77	97	97	104	107	121	124
	Source: Hermès Annual reports

The company first chose the closest markets to France (Swiss, Germany, Italy), in terms of culture and legal framework, before settling in the United States and Japan. Afterwards many problems and a long period of presence in department stores, a Hermès subsidiary was established in New York in 1983. Concerning the entry of the company on the Japanese market, it was first done through a representation contract with a chain of department stores.

Table 3 -Hermès -Directly Operated Stores and "Concessionnaires" by Area Nb of Directly Operated Stores Nb of "Concessionnaires"

 3

	Europe	71	56
	Of which France	15	20
	Italy	11	11
	Germany	10	8
	Americas	34	15
	Of which USA	25	9
	Asia	81	45
	Of which Japan	28	22
	China	17	4
	Middle East	0	6
	Oceania	7	2
	Total	193	124

Table 4 -Gucci -Evolution of the distribution network

 4

		1996	1999	2002	2003	2004	2005
	Nb of Directly operated stores	69	130	173	187	198	207
	Nb of Franchisees	111	51	32	31	32	33