Marine Le Goas

Aurélie Paquirissamy

Dorra Gargouri

Giulia Fadda

Fabienne Testard

Caroline Aymes-Chodur

Emile Jubeli

Thierry Pourcher

Béatrice Cambien

Serge Palacin

Jean-Philippe Renault
email: jean-philippe.renault@cea.fr

Geraldine Carrot
email: geraldine.carrot@cea.fr

Irradiation Effects on Polymer-Grafted Gold Nanoparticles for Cancer Therapy

Keywords: Polymer-grafted AuNPs, irradiation, radiosensitization, SANS, SAXS, cytotoxicity, doxorubicin

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

INTRODUCTION

Nanotechnologies are being widely studied for medical applications, both diagnosis and treatment. They have already shown great promise, especially to treat cancer through various strategies such as chemotherapy, [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] photothermal therapy, 2 hyperthermia 3 or radiation therapies. [START_REF] Kuncic | Nanoparticle Radio-Enhancement: Principles, Progress and Application to Cancer Treatment[END_REF] High-Z elements nanoparticles are of particular interest for the latter, considering their ability to amplify damaging effects of both photon and ion radiations, and gold was among the most investigated elements.

First study on radiosensitization by gold nanoparticles (AuNPs) was done by Hainfield et al., [START_REF] Hainfeld | The Use of Gold Nanoparticles to Enhance Radiotherapy in Mice[END_REF] where they showed a significant increase in the one-year survival rate for carcinoma-bearing mice treated with gold nanoparticles prior to X-ray therapy. This in vivo study preceded several other in vitro ones to characterize the radiosensitizing effects of gold. [START_REF] Rosa | Biological Mechanisms of Gold Nanoparticle Radiosensitization[END_REF] A large variety of objects has been observed through these studies. For example, nanoparticles (NPs) size has ranged from 1.9 nm to 74 nm, [START_REF] Brun | Parameters Governing Gold Nanoparticle X-Ray Radiosensitization of DNA in Solution[END_REF][START_REF] Chithrani | Gold Nanoparticles as Radiation Sensitizers in Cancer Therapy[END_REF][START_REF] Zhang | Size-Dependent Radiosensitization of PEG-Coated Gold Nanoparticles for Cancer Radiation Therapy[END_REF] various NPs shapes have been designed [START_REF] Ma | Shape-Dependent Radiosensitization Effect of Gold Nanostructures in Cancer Radiotherapy: Comparison of Gold Nanoparticles, Nanospikes, and Nanorods[END_REF] and NPs surface coating could either be made of small molecules (citrate, [START_REF] Chithrani | Gold Nanoparticles as Radiation Sensitizers in Cancer Therapy[END_REF][START_REF] Mcmahon | Energy Dependence of Gold Nanoparticle Radiosensitization in Plasmid DNA[END_REF] thiol, [START_REF] Geng | Thio-Glucose Bound Gold Nanoparticles Enhance Radio-Cytotoxic Targeting of Ovarian Cancer[END_REF][START_REF] Butterworth | Preclinical Evaluation of Gold-DTDTPA Nanoparticles as Theranostic Agents in Prostate Cancer Radiotherapy[END_REF] glucose [START_REF] Kaur | In Vitro Studies on Radiosensitization Effect of Glucose Capped Gold Nanoparticles in Photon and Ion Irradiation of HeLa Cells[END_REF] ), polymers (mainly PEG) [START_REF] Zhang | Size-Dependent Radiosensitization of PEG-Coated Gold Nanoparticles for Cancer Radiation Therapy[END_REF][START_REF] Joh | Selective Targeting of Brain Tumors with Gold Nanoparticle-Induced Radiosensitization[END_REF][START_REF] Setua | Cisplatin-Tethered Gold Nanospheres for Multimodal Chemo-Radiotherapy of Glioblastoma[END_REF][START_REF] Zhang | Enhanced Radiation Therapy with Internalized Polyelectrolyte Modified Nanoparticles[END_REF] or biomolecules. [START_REF] Chattopadhyay | Molecularly Targeted Gold Nanoparticles Enhance the Radiation Response of Breast Cancer Cells and Tumor Xenografts to X-Radiation[END_REF] Used experimental conditions can also be very diverse, particularly the type and energy of the ionizing radiation source, the concentration of nanoparticles, the incubation time, the cell line, etc… A few studies have also focused on the radiosensitizing effects of NPs directly on DNA [START_REF] Brun | Parameters Governing Gold Nanoparticle X-Ray Radiosensitization of DNA in Solution[END_REF][START_REF] Butterworth | Variation of Strand Break Yield for Plasmid DNA Irradiated with High-Z Metal Nanoparticles[END_REF][START_REF] Xiao | On the Role of Low-Energy Electrons in the Radiosensitization of DNA by Gold Nanoparticles[END_REF] or proteins. [START_REF] Brun | Gold Nanoparticles Enhance the X-Ray-Induced Degradation of Human Centrin 2 Protein[END_REF] However, despite numerous studies in the literature, the mechanism behind this radiosensitizing effect remains difficult to study and is not fully understood yet. Many questions still arise: Where does the energy deposit take place? At which stage does this effect occur? Is it related to the radiolysis of water (indirect effect) or to the energy received by gold (direct effect)? Is the effect local or remote? A number of theoretical models have been developed, [START_REF] Rosa | Biological Mechanisms of Gold Nanoparticle Radiosensitization[END_REF][START_REF] Butterworth | Physical Basis and Biological Mechanisms of Gold Nanoparticle Radiosensitization[END_REF][START_REF] Her | Gold Nanoparticles for Applications in Cancer Radiotherapy: Mechanisms and Recent Advancements[END_REF] which envision either a proximity physical enhancement effect [START_REF] Lee | Geometry Enhancement of Nanoscale Energy Deposition by X-Rays[END_REF] due to low-energy secondary electrons, a remote physical enhancement effect [START_REF] Davidson | Average Physical Enhancement by Nanomaterials under X-Ray Irradiation[END_REF][START_REF] Chang | Electron Paramagnetic Resonance Spectroscopy Investigation of Radical Production by Gold Nanoparticles in Aqueous Solutions Under X-Ray Irradiation[END_REF] due to high-energy secondary electrons, a chemical enhancement effect [START_REF] Cheng | Chemical Enhancement by Nanomaterials under X-Ray Irradiation[END_REF][START_REF] Sicard-Roselli | A New Mechanism for Hydroxyl Radical Production in Irradiated Nanoparticle Solutions[END_REF] due to surface catalysis, or a biological enhancement effect. [START_REF] Taggart | The Role of Mitochondrial Function in Gold Nanoparticle Mediated Radiosensitisation[END_REF] For a better understanding of these effects, we tried to develop an integrated physical, chemical and biological method based on model objects.

To answer these questions, it is essential to have access to stable model nano-objects. In the present study, we chose to use polymer-grafted NPs to evaluate the impact of irradiation via the characterization of the polymer corona. To our knowledge, this is the first time that this type of nano-objects have been used for radiosensitization together with a detailed characterization to evaluate radiation effects. In a forthcoming paper, more detailed biological effects and particularly, in vitro and in vivo studies will be presented. [START_REF] Goas | Improving 131 I Radioiodine Therapy by Hybrid Polymer-Grafted Gold Nanoparticles[END_REF] A covalently grafted polymer corona does not only help to stabilize the nanoparticles (NPs) but it also improves the solubility, the diffusion inside cells, and permits additional effects via the grafting of a therapeutic agent. 31 Here, we synthesized AuNPs with different polymer corona via a "grafting through" or a "direct" process (polymer-AuNPs). [START_REF] Bach | Synthesis and Characterization of Chemically Anchored Adenosine with PHEMA Grafted Gold Nanoparticles[END_REF] Controlled radical polymerization (ATRP) was used to design polymer ligands of different nature with controlled molecular weights. Then, these polymer ligands were used directly for the synthesis of polymer-AuNPs. This strategy had several advantages compared to more conventional "grafting from" and "grafting to" methods. First, the prior preparation of polymer ligands allowed a good knowledge of molecular weights/polydispersity of the grafted chains, without the difficulties of a further degrafting reaction, as needed in the "grafting from" route. [START_REF] Carrot | Polymer-Grafted-Platinum Nanoparticles: From Three-Dimensional Small-Angle Neutron Scattering Study to Tunable Two-Dimensional Array Formation[END_REF][START_REF] Gal | Water-Soluble Polymer-Grafted Platinum Nanoparticles for the Subsequent Binding of Enzymes. Synthesis and SANS[END_REF][START_REF] Drockenmuller | Efficient Approaches for the Surface Modification of Platinum Nanoparticles via Click Chemistry[END_REF] Second, compared to "grafting to", we considered that the surface chemistry of finally afforded gold NPs was better controlled in the direct method. Indeed, in the case of gold nanoparticles, "grafting to" method usually involves reduction via citrate followed by ligand displacement, [START_REF] Zhao | State of the Art in Gold Nanoparticle Synthesis[END_REF][START_REF] Yilmaz | Methacrylic Acid)-Coated Gold Nanoparticles: Functional Platforms for Theranostic Applications[END_REF] thus leading to the presence of both charged molecules and polymer chains onto the surface. [START_REF] Park | Strong Resistance of Citrate Anions on Metal Nanoparticles to Desorption under Thiol Functionalization[END_REF][START_REF] Dinkel | Fast and Slow Ligand Exchange at the Surface of Colloidal Gold Nanoparticles[END_REF] In the present study, it was of particular importance to have good control and knowledge of the surface state of our nano-objects, as radiation effects were evaluated via polymer fragments analysis. The objective was to use the grafted polymer corona to map, on a nanometric scale, the production sites of reactive species in the vicinity of gold surface under irradiation. Note that these polymer-grafted NPs were particularly stable and solutions may be kept for several months without any formation of aggregates. For the irradiation study, a detailed characterization of the nano-objects was also performed via size exclusion chromatography (SEC), thermogravimetry (TGA), small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS). Polymer-grafted NPs were then studied regarding their biocompatibility (cytotoxicity measurements) before and after irradiation, prior to in vitro and in vivo radiosensitizing studies that will be fully described in a forthcoming paper. [START_REF] Goas | Improving 131 I Radioiodine Therapy by Hybrid Polymer-Grafted Gold Nanoparticles[END_REF] Two types of nano-objects were particularly studied: poly(methacrylic acid)-grafted gold nanoparticles (PMAA-AuNPs), and gold nanoparticles coated with poly(hydroxyethyl methacrylate-co-methacrylic acid) (P(HEMA-MAA)-AuNPs), that provided another corona structure, leading to different physico-chemical properties and potential for chemical modification. Indeed, nanoparticles can be inherently multifunctional and strategies combining radiotherapy and chemotherapy have already been proposed. [START_REF] Zhou | Enhanced Cancer Cell Killing by a Targeting Gold Nanoconstruct with Doxorubicin Payload under X-Ray Irradiation[END_REF][START_REF] Cui | Performance of Doxorubicin-Conjugated Gold Nanoparticles: Regulation of Drug Location[END_REF] To complete the radiation stability measurements on hybrid nanosystems, we performed the grafting of doxorubicin onto the polymer corona and analyzed the conservation of its biological effectiveness. Initiator preparation. Bis[2-(2′-bromoisobutyryloxy)ethyl]disulfide was obtained via an esterification between 2,2'-dithioethanol (≥ 85,0%) and α-bromoisobutyryl bromide (98%). This reaction has already been described in the literature. [START_REF] Bach | Synthesis and Characterization of Chemically Anchored Adenosine with PHEMA Grafted Gold Nanoparticles[END_REF] Briefly, 3.40 g of 2,2'dithioethanol and 4.2 g of pyridine were dissolved in 30 mL THF under an argon atmosphere at 0°C, before the addition of 12.2 g of α-bromoisobutyryl bromide. After 1 hour, the solution was left stirring at ambient temperature for 24 hours. After filtration, the resulting solution was dissolved in chloroform and washed twice with a 2M HCl solution. Solvent was then evaporated and a colorless oil was obtained (85% yield). [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] H NMR (CDCl3) δ (ppm): 4.44 (t, OCH2, 4H), 2.98 (t, SCH2, 4H), 1.94 (s, CH3, 12H).

EXPERIMENTAL SECTION

Materials

Atom Transfer Radical Polymerization (ATRP).

All monomers, ligand (N,N,N′,N′′,N′′-Pentamethyldiethylenetriamine ; PMDETA), initiator and solvent were degassed prior to the reaction, whereas the whole setup was placed under argon atmosphere. The Cu I Br/PMDETA/initiator ratio was 2/2/1. After addition of Cu I Br (99,999%) and PMDETA (≥ 98,0%) in a very small amount of DMF, 20 mL of monomer (here tert-butyl methacrylate, tBuMA, 98%, or hydroxyethyl methacrylate, HEMA, 97% and/or polyethylene glycol methacrylate, PEGMA, average M n = 360 g.mol -1 ) was added to the solution. Finally, 0.26 mL of the initiator was inserted and the reaction started with the increase of temperature to 60°C. The resulting solution was left to react for 5 hours under inert atmosphere. The polymer was subsequently precipitated in a methanol (MeOH)/water mixture (90/10) and filtrated.

Samples were regularly collected during the reaction, in order to determine the conversion rate through gravimetric measurements (see supporting information, S. I.). The afforded polymer ligands were then denominated as poly(tert-butyl methacrylate)-disulfide: PtBuMA-DS; poly(hydroxyethyl methacrylate)-disulfide: PHEMA-DS; etc. Hydrolysis of polymer ligands. This procedure was used for all polymers and copolymers containing tert-butyl methacrylate units. [START_REF] Gal | Water-Soluble Polymer-Grafted Platinum Nanoparticles for the Subsequent Binding of Enzymes. Synthesis and SANS[END_REF] Briefly, 1g of PtBuMA-DS or P(HEMA-tBuMA)-DS were solubilized in 10 mL chloroform before the addition of 2.7 mL of trifluoroacetic acid (TFA). The reaction proceeded until the complete precipitation of poly(methacrylic acid) (PMAA) or P(HEMA-MAA). Efficiency of the hydrolysis reaction was evaluated from thermogravimetry (TGA) and 1 H NMR and was > 90% (see S.I.). Synthesis of polymer-grafted gold nanoparticles. 220 mg of HAuCl 4 (30 % wt in dilute HCl) were dissolved in 8 mL of methanol and mixed with 119 mg of polymer ligands in 8 mL of methanol. The solution was stirred during 30 minutes before the addition of 75.6 mg of NaBH 4 (75.6 mg in 4 mL of methanol). After 24 hours reaction, the resulting dark red solution was centrifuged to obtain a black precipitate which was subsequently washed in a MeOH/ether mixture and dried under nitrogen.

Characterization routine techniques. [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] H NMR spectra of disulphide initiator and polymer ligands were obtained from a Bruker AC-400 spectrometer. Organic content (% wt OC) was determined from Thermogravimetric Analysis (TGA) performed on a Mettler-Toledo TGA/DSC at a scan rate of 20 °C min -1 , up to 800 °C, under oxygen. The associated uncertainty was evaluated to 5%. Absorption spectra were recorded using a Shimadzu UV-2450 double-beam UV-Vis spectrophotometer.

Transmission electron microscopy (TEM).

Analyses were carried out on a JEOL-1400 instrument. Samples were prepared by placing 3 µL of the 0.33 mg/mL nanoparticles solution on a carbon-coated copper grid.

Size-exclusion chromatography (SEC). Number average molecular weights (M n ), weight

average molecular weights (M w ), and polydispersities (M w /M n ) were determined using a GPC 220 system from PolymerLabs (Agilent Technologies) in THF at 35°C, with a flow rate of 1 mL.min -1 . A series of two 7.5 mm diameter x 300 mm Polymer Labs, 5 µm particle diameter mixed-E PL gel columns were connected in line to the GPC system. Samples were detected using a refractive index detector. The system was calibrated using poly(ethylene glycol) or polystyrene standards (PolymerLabs) in the range of molecular weights 43580-106 g.mol -1 .

The calibration uncertainties were evaluated to be below 4%.

Small-angle neutron scattering (SANS).

Experiments were carried out on the PACE spectrometer (Laboratoire Léon Brillouin, Saclay). Three configurations (D = 1 m, λ = 4.6 Å; D = 3 m, λ = 4.6 Å and D = 4.7 m, λ = 13 Å) enabled to cover a q range of 5×10 -3 Å -1 -0.3 Å - 1 , which permitted to study objects with dimensions of R∼1/q, corresponding to sizes from 20 to 0.1 nm. Data treatment was done with a homemade program (PAsiNET, LLB), following standard procedures with H 2 O as the calibration standard. Incoherent background was determined with several H/D mixtures and interpolated for the desired concentrations.

Absolute values of the scattered intensity (in cm -1 ) were measured via a determination of the direct beam intensity. Samples were prepared and studied at different concentrations between 5 and 10 mg/mL in D 2 O. SANS also permitted to determine the molecular weight of the scattering object from a concentration study. [START_REF] Higgins | Polymers and Neutron Scattering[END_REF] Details of the calculation will be given in the results and discussion section.

Small-Angle X-ray Scattering (SAXS). Experiments were carried out on a home-made apparatus equipped with a source based on a Rigaku rotating molybdenum anode (λ Kα (Mo) = 0.711 Å) collimated by an Osmic mirror through two hybrid slits (1x1 mm 2 ). Scattering photons were collected on a MAR 345 image plate and a photodiode mounted on the beam stop could monitor the photon flux. Calibration of the sample to detector distance (72 cm) was obtained with tetradecanol while 3 mm Lupolen (I = 6 cm -1 ) and 3 mm water enabled to normalize detector counts into differential cross section per volume. [START_REF] Zemb | Improving Sensitivity of a Small Angle X-Ray Scattering Camera with Pinhole Collimation Using Separated Optical Elements[END_REF] Measurements were performed in the q range of 0.03-3.0 Å -1 . Samples were measured in 3 mm Kapton capillaries.

Data preanalysis was perfomed using PYSAXS program. [START_REF] Taché | A SAXS/WAXS Laboratory Instrument Dedicated to Nanomaterials[END_REF] Irradiation experiments. Nanoparticles solutions (at 10 and 2.6 mg/mL for physicochemical and cytotoxicity studies respectively) were irradiated with a GammaCell 3000 Elan irradiator equipped with a 137 Cs source emitting 660 keV gamma rays. Before performing analysis of the irradiated residues, dialysis against water (Spectra/Por, molecular weight cutoff of 50kDa) was conducted. The mean dose rate of the irradiator was determined to be of 5.5 Gy/min by a Fricke dosimetry (uncertainty 5%). To prepare the Fricke solution, 22 mL of 99% sulfuric acid were diluted in 250 mL deionized water and mixed with 0.06 g of NaCl and 0.392 g of iron (II) sulfate. Volume was then completed to 1L with deionized water and the resulting solution was left away from light for 24 hours prior to any use. After irradiation (doses ranging from 40 to 20000 Gy), the 303 nm absorbance was measured.

Degrafting of polymer chains. 10 mg of irradiated PMAA-AuNPs were precipitated and then solubilized in 100 µL of water. 2 mL of gold etchant (I 2 /KI) solution was then added and the mixture was stirred overnight. After being centrifuged to remove impurities, the dark solution was dialyzed (Spectra/Por, molecular weight cut-off of 3.5 kDa) against water. The resulting colorless solution was evaporated and then solubilized in THF to be analyzed by SEC. [START_REF] Ohno | Synthesis of Gold Nanoparticles Coated with Well-Defined, High-Density Polymer Brushes by Surface-Initiated Living Radical Polymerization[END_REF] Cell culture studies. Mouse fibroblasts (cell line L929), derived from subcutaneous and adipose tissues of a C3H/An male, were cultivated in DMEM supplemented with 10% fetal bovine serum at 37°C in a humidified incubator with 5% CO 2 . L929 cells were sub-cultured at 80-90% confluency. For MTT assays, cells were seeded in 96-well plates at a density of 2500 cells/well. After 24 hours, diluted suspensions (0.1-500 µg/mL) of polymer-AuNPs in DMEM supplemented with 10% fetal bovine serum, 0.25 µg/mL Amphotericin B and 10 µg/mL Gentamicin were added (only supplemented DMEM was used for controls). Both nonirradiated and irradiated solutions were tested. Incubation with NPs was performed during 48 hours in order to comply with the norm used to assess cytotoxicity for such nanomaterials (NF EN ISO 10993-5). After the 48-hour exposure, NPs suspensions were removed and 100 µL of clean DMEM were added in each well, followed by 25 µL of MTT solution (5 mg/mL in PBS) for a 2-hour incubation. Media was then eliminated and 200 µL of DMSO were finally added to dissolve the formazan crystals. Absorbance measurements were taken at 570 nm. To assess reproducibility, 6 wells were used for each condition. Cell viability was calculated as the absorbance ratio between cells exposed to our nano-objects and control (untreated) cells.

Grafting of Doxorubicin. 25 mg of PMAA-AuNPs were solubilized in 5 mL of phosphate buffer (PBS) at pH = 7.8. Then, 4.65 mg of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC) and 5 mg of N-hydroxysuccinimide (NHS) were added and the reaction proceeded under stirring for 2 h. Finally, 300 mg of doxorubicin (DOX) solution were added, and the mixture was allowed to react for 24h. Then, purification was performed via dialysis against water (Spectra/Por, molecular weight cut-off of 3.5 kDa).

RESULTS AND DISCUSSION

Polymer-grafted gold nanoparticles. The synthetic strategy used here to prepare polymergrafted nanoparticles was the "grafting through" method, consisting in the preparation of polymer ligands, followed by the direct synthesis of gold nanoparticles (AuNPs) in the presence of these functional polymers. For the present study on radiation effects on nanoobjects, it was essential to have well-defined polymer chains to be able to evaluate this effect through the polymer corona characteristics (molecular weight and gyration radius). Therefore, this "direct" or "grafting through" method was much more adapted here rather than the usual "grafting from" technique that we usually used to form similar nano-objects. [START_REF] Carrot | Polymer-Grafted-Platinum Nanoparticles: From Three-Dimensional Small-Angle Neutron Scattering Study to Tunable Two-Dimensional Array Formation[END_REF][START_REF] Gal | Water-Soluble Polymer-Grafted Platinum Nanoparticles for the Subsequent Binding of Enzymes. Synthesis and SANS[END_REF] It was also much more appropriate than the conventional "grafting to" techniques which usually require AuNPs stabilized with anionic citrate, part of which may be left onto the surface, leading to uncontrolled surface chemistry. [START_REF] Park | Strong Resistance of Citrate Anions on Metal Nanoparticles to Desorption under Thiol Functionalization[END_REF][START_REF] Dinkel | Fast and Slow Ligand Exchange at the Surface of Colloidal Gold Nanoparticles[END_REF] and some toxicity. [START_REF] Uboldi | Gold Nanoparticles Induce Cytotoxicity in the Alveolar Type-II Cell Lines A549 and NCIH441[END_REF][START_REF] Freese | Uptake and Cytotoxicity of Citrate-Coated Gold Nanospheres: Comparative Studies on Human Endothelial and Epithelial Cells[END_REF] The "grafting through" process also permitted to reach critical small sizes [START_REF] Bach | Synthesis and Characterization of Chemically Anchored Adenosine with PHEMA Grafted Gold Nanoparticles[END_REF][START_REF] Wang | Design of Polymeric Stabilizers for Size-Controlled Synthesis of Monodisperse Gold Nanoparticles in Water[END_REF] required to enter the cell nucleus. [START_REF] Huo | Ultrasmall Gold Nanoparticles as Carriers for Nucleus-Based Gene Therapy Due to Size-Dependent Nuclear Entry[END_REF] Scheme 1. Synthesis of PMAA-grafted gold nanoparticles (PMAA-AuNPs).

Polymer ligands were prepared in two steps (see Scheme 1). First, methacrylate polymers were synthesized from a disulfide initiator using Atom Transfer Radical Polymerization (ATRP). Second, hydrolysis was performed to obtain water-soluble polymer chains. A library of different ligands (homopolymers and statistical copolymers) were obtained: PMAA-DS (polymethacrylic acid disulfide), PHEMA-DS (poly(hydroxyethyl methacrylate) disulfide)), P(HEMA-MAA)-DS (Poly(methacrylic acid-co-hydroxyethyl methacrylate disulfide)), This could be due to the use of a difunctional initiator, which might increase the probability of irreversible termination processes. This may also explain the slight divergence between theoretical and measured M n .

After hydrolysis to PMAA (hydrolysis rates were estimated through [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] H NMR measurements to be between 91 and 98%), molecular weights of polymer ligands were also evaluated.

Measured values were much lower than expected (regarding the difference of molar mass between tBuMA and MAA). Indeed, as values were almost half than expected, we concluded that chains had been cleaved via the disulfide bridge during the hydrolysis treatment.

Therefore, for the next step, i.e. the synthesis of nanogold, we were rather in the presence of thiol-functional polymers than disulfide ligands (in the case of PMAA-DS only). However, this was not really a problem as the final nano-object structure (gold core and corona) would remain the same. As said, the formation of AuNPs in the presence of disulfide (or thiolfunctional) polymers acting as ligands for the control of gold salt reduction corresponds to a "direct" or "grafting-through" method. Therefore, gold salt was reduced by sodium borohydride and nanoparticles' growth was controlled by the reaction of polymer ligands with gold (gold-sulfur bond), leading to a covalently-bonded corona.

After the synthesis of AuNPs, the presence of polymers was confirmed by [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] H NMR (see S.

I.

). The resulting nano-objects could easily be dispersed in water thanks to the presence of polymer corona. The afforded polymer-grafted AuNPs solutions were particularly stable in water and in all good solvents for polymers or copolymers forming the corona. Suspensions may be kept for months without any aggregation. As said, this was a particular advantage regarding the scope of our study (impact of irradiation onto polymer-grafted AuNPs) and the possible application in medicine (radiosensitizing nano-objects). However, the reverse drawback of this was the high difficulty to get completely rid of free polymers using usual techniques (precipitation/centrifugation). Indeed, several tests have been performed to selectively precipitate the grafted AuNPs using solvent mixtures (THF/Ethanol). At the ratio 60/40, it was possible to isolate partially free polymer chains. However, despite numerous efforts, we could not avoid the presence of remaining free polymers which was evidenced by TGA and SANS measurements. Nevertheless, we decided to turn this difficulty into an advantage by using these free polymers as an internal reference to measure impacts of irradiation.

B) A)

After the synthesis, a detailed characterization of the nano-objects was performed to get welldefined references prior to irradiation. As a first observation, samples were studied with TEM (Figure 1). With TEM, only the gold cores were visible and no aggregation was observed.

Both types of nanoparticles (with different polymer corona) were found to have rather monodispersed cores with a spherical morphology. Diameters could be estimated between 3 and 6 nm and between 4 and 6 nm, for PMAA-AuNPs and P(HEMA-MAA)-AuNPs, respectively (see size diagrams in S. I.). The spherical structure was also confirmed by UV-vis spectroscopy as only one plasmon band was measured: λ P(HEMA-MAA)-AuNPs = 515 nm, λ PMAA- AuNPs = 517 nm and λ P(PEGMA-MAA)-AuNPs = 510 nm (see S. I.). From UV-Vis spectroscopy, it was also possible to estimate NPs sizes which were in the range of values given by SAXS.

For the sake of clarity, the rest of the study was mainly focused onto PMAA-AuNPs and P(HEMA-MAA)-AuNPs. The size of metallic cores was further characterized by SAXS (Figure 2). Only the metallic part scatters X-rays, as the polymer corona does not scatter in water in this q range. [START_REF] Genix | Structure and Dynamics of Polymer Nanocomposites Studied by X-Ray and Neutron Scattering Techniques[END_REF] For both samples (PMAA-AuNPs and P(HEMA-MAA)-AuNPs), the Bragg peak of gold could be observed at 2.66 Å -1 (see S. I.). Based on TEM observations, a spherical model was used to fit experimental results, giving a radius of 15 Å for PMAA-AuNPs (Gaussian distribution, PDI = 0.5), and 21 Å for P(HEMA-MAA)-AuNPs (lognorm distribution, PDI = 0.3) (see S. I. and Figure 2). These results were quite consistent with the values obtained by TEM. Regarding the corona characterization, we first performed thermogravimetric analysis (TGA). Results are shown in S. I. For all samples, TGA curves could be divided in two parts: a slow decrease in % wt OC (% wt organic content) was observed, followed by a plateau and a final slope which was measured at T ≥ 500° C. The total % wt OC measured were 71 and 73% for PMAA-AuNPs and P(HEMA-MAA)-AuNPs, respectively.

However, we already suspected that this percentage was distorted by the presence of free chains. These results will further be completed by SANS. SANS analysis was performed to get a detailed characterization of the whole structure of nano-objects (Figure 3). Solutions of polymer-grafted AuNPs (PMAA-AuNPs and P(HEMA-MAA)-AuNPs) were prepared at 10 mg/mL in deuterated water. D 2 O was used to obtain a maximum contrast matching with the polymer corona regarding the corresponding neutron scattering length densities (ρ PMAA = 1.10 x 10 10 cm -2 ; ρ P(HEMA-PMAA) = 1.37 x 10 10 cm -2 ). In these conditions, and considering the small size of the gold core (ρ Au = 4.50.10 10 cm -2 ), the gold signal was found to be negligible, so that only the polymer corona contributed to the signal (Figure 3). In the low q domain, a plateau could be observed, which is typical of nonaggregated objects with finite size. For these q values, the radius of gyration R g could be estimated using Guinier approximation (qR g ≤ 1):

∝ exp - (1)
By plotting ln(I) versus q 2 we could determine R g for each type of ligand (see S. I.).

Calculated values were of 102 ± 2 Å for PMAA-AuNPs, and 84 ± 1 Å for P(HEMA-MAA)-AuNPs.

The decrease in q -2 in the intermediate domain indicated that the whole geometry was close to a Gaussian chain. Then, the total signal could be estimated from the Debye model with the following form factor:

P î , = ² !² "#$%²&'² % &' ² (2)
SANS plots were fitted using this model (Figure 3). Then, R g values calculated from these fits were found to be rather close to the Guinier values (120 ± 3 Å for PMAA-AuNPs and 90 ± 1 Å for P(HEMA-MAA)-AuNPs). Therefore, we decided to use this model and the corresponding R g values for the further study of irradiation effects onto the polymer corona (Table 2).

SANS also permitted to determine the molecular weight of the polymer corona. [START_REF] Higgins | Polymers and Neutron Scattering[END_REF] At a given concentration, the scattered intensity extrapolated at q = 0 was measured. From these values, it was possible to calculate the apparent molecular weight (M app ) of the object using the following equation:

lim +→- . / + = 0 1 1 -24 5 + ⋯ 89:ℎ 0 = < = > = / ? > ? / @ > A (3)
Where -corresponds to the scattered intensity at q = 0 of the polymer corona, B # and B -are respectively, the scattering length densities of the polymer and the solvent, C # and C -, their specific volumes, 4 , the second coefficient of the Viriel equation, and 1, the molecular weight of the polymer corona. atmosphere. As mentioned before, the major constraint in our system was the difficulty to separate free polymer chains from the polymer-grafted AuNPs. SANS characterization permitted to overcome this problem as only the polymer corona contributes to the scattering signal. Indeed, regarding the low molecular weight of the remaining free chains, they would not contribute to the scattering signal in this q range. Therefore, we could directly quantify the irradiation effect onto the corona (Table 2). Using the same model as described before and the molecular weight calculation, we could estimate R g and M app , which both showed a clear decrease with irradiation. R g was decreasing from 120 to 69 Å (20 kGy) and from 90 to 58 Å for PMAA-AuNPs and P(HEMA-MAA)-AuNPs, respectively. We also noticed a decrease in M app from 21000 to 7500 g.mol -1 for PMAA-AuNPs, and from 21850 to 9800 g.mol -1 for P(HEMA-MAA)-AuNPs.

At the same time, no change was observed in SAXS spectra which characterized the scattering of gold cores (Figure 2). This means that irradiation did not affect the nano-objects' core so that irradiation effects were only visible onto the polymer corona. 1 H NMR spectra also showed that there was no change in the chemical groups of the ligands (see S. I.).

To go further in the understanding of irradiation effects onto the polymer corona, we performed SEC analysis on both grafted and free polymer chains. In order to isolate grafted chains, dissolution of the gold core was done using iodine solution (see experimental section).

In this particular case, centrifugation and dialysis were used to isolate the grafted chains. As mentioned before, we did not succeed to completely wash our polymer-grafted AuNPs from the residual free polymers. However, after irradiation, several trials with centrifugation from THF permitted to isolate some free chains. Therefore, it was possible to measure both 'free chains' and 'grafted chains' molecular weights via SEC. Results are detailed in Table 3.

Figure 4 shows the chromatograms obtained from isolated grafted chains, before and after irradiation, for both PMAA-AuNPs and P(HEMA-MAA)-AuNPs. It is clear from these that in both cases, SEC peaks were shifted to higher retention times with irradiation. Quantitative results from these measurements have been summarized in Table 3. Note that in the case of P(HEMA-MAA)-AuNPs, only the isolation of grafted chains from NPs was performed successfully (isolation of free chains was more difficult). From these values and knowing the molecular weight of total polymer corona, it was then possible to estimate a grafting density of polymer chains of 4.6 ± 0.2 to 4.4 ± 0.1 chains/ AuNP for PMAA-AuNPs and P(HEMA-MAA)-AuNPs, respectively (corresponding to 0.15 ± 0.006 and 0.07 ± 0.003 chains/nm 2 , Table 3). These values were in the range of what was

B)

0 Gy expected regarding the very small size of the gold core (R g = 1.5 to 2 nm) and slightly lower than what was obtained from "grafting from" routes, [START_REF] Carrot | Polymer-Grafted-Platinum Nanoparticles: From Three-Dimensional Small-Angle Neutron Scattering Study to Tunable Two-Dimensional Array Formation[END_REF][START_REF] Gal | Water-Soluble Polymer-Grafted Platinum Nanoparticles for the Subsequent Binding of Enzymes. Synthesis and SANS[END_REF] probably due to a more important steric hindrance effect.

Table 3. SEC characteristic values of free and grafted chains before and after irradiation. Quantification and localization of the cuts. From results given by SEC and SANS, it was possible to propose a model to explain the degradation of the polymer corona. After being degrafted from AuNPs, polymer chains showed a decrease in molecular weight. A number of scission events (r) could then be obtained using the following equation: 51

Nanoobjects

Dose

1 E 9FF = G E H - #$I (4)
In order to be exhaustive, we also chose to measure the scission yield for the initial polymer ligand (PMAA-DS, see Scheme 1). The corresponding scission yield (calculated with respect to the dose received by the solution) could be evaluated at 2 x 10 -7 mol.J -1 . Comparatively, the one obtained for PMAA-AuNPs is 1.6 x 10 -7 mol.J -1 (see all yield values in S. I.). Analysis of free polymer in solution in the presence of AuNPs could be more complex as its contribution may be masked by the polymer corona fragments' one. However, it was showed that this latter contribution was minimal at 4000 Gy. Thus, this allowed us to consider the scission yield calculated at this dose. The resulting value of 1.6 x 10 -7 mol.J -1 for free polymer in the presence of AuNPs was comparable to the two others given above. The scission yield obtained for degrafted P(HEMA-MAA) was much lower: 2.7 x 10 -8 mol.J -1 . This is probably due to its longer side chain which could scavenge radicals without leading to scissions.

An original feature for both grafted P(HEMA-MAA) and PMAA was that polydispersity values (M w /M n ) did not increase with the radiation dose, as expected for random scissions (Table 3). Results obtained for the grafted polymers could be explained by scissions occurring towards chain ends (the so-called percent cuts). [START_REF] Bose | Mathematical Modelling and Computer Simulation of Linear Polymer Degradation: Simple Scissions[END_REF] Indeed, the shape of SEC curves was very similar to the one presented in Bose et al. for this type of mechanism. Since the probability of scission is higher for long polymers, they are preferentially attacked compared to smaller ones, thus reducing their size and leading to a decrease of the polydispersity. This therefore suggested an external shaving of the polymer corona (Scheme 2).

In complement to previous measurements (SEC, TGA…), SANS (small angle neutron scattering) was used to quantify the amount of grafted polymers. Indeed, as surface events may lead to some polymer degrafting, we evaluated the total number of chains grafted onto one nanoparticle, using the Debye analysis of SANS data at different doses (Table 3). We could first notice that the decrease in R g was in agreement with the molecular weight evolution measured by SEC. This tends to confirm the external shaving process of the corona described previously. We also observed that the total molecular weight (M app ) of the polymer corona decreased when the irradiation dose increased (Table 2). Therefore, grafting densities (Table 3) could be calculated from SANS and SEC, and were also found to decrease when the dose increased, confirming that there were scission events occurring near the surface. The Au-S bond was the most probable site but scissions may also occur onto monomer units located in the immediate vicinity of the Au surface. Degrafting yields could also be calculated from these data. For PMAA-AuNPs, a 1.1 x 10 -8 mol.J -1 yield was calculated with respect to the dose received by water. For P(HEMA-MAA)-AuNPs, the value was 4.8 x 10 -8 mol.J -1 . Yields of polymer scissions occurring onto the external corona (Scheme 2) were completely compatible with an effect of radicals produced in solution. Indeed, scissions in PMAA are triggered by hydrogen abstraction radicals (OH• and H•) with a total yield of 3.2 x 10 -7 mol.J - 1 . [START_REF] Tabata | Handbook Radiation Chemistry[END_REF] Apart from their regioselectivity, these external radical effects were not very different in yield compared to the ones occurring in solution. Therefore, we cannot identify long distance (µm) and/or medium range (5-10 nm) dose enhancements in our system. This absence of dose enhancement was not really surprising since the stopping power of AuNPs regarding both gamma rays and Compton electrons is close to the one of water, in the considered energy range. [START_REF]Estar -Stopping power and range tables for electrons[END_REF] Scheme 2. Impact of external and near-surface scissions on polymer-grafted AuNPs.

Analysis of the origin of near-surface scissions was obviously more complex. A direct effect of irradiation onto AuNPs cannot be ruled out. The effective scission yield calculated with respect to the amount of energy directly received by nano-objects, would be 10 per 100 eV for PMAA-AuNPs and 50 for P(HEMA-MAA)-AuNPs (see S. I.). This yield is far too high for a classical radical production through water ionization (the total yield in radicals is roughly 6/100 eV, [START_REF] Tabata | Handbook Radiation Chemistry[END_REF] even with a two times dose enhancement through Auger electrons). [START_REF] Wälzlein | Simulations of Dose Enhancement for Heavy Atom Nanoparticles Irradiated by Protons[END_REF] Therefore this may be compatible with the low-energy electron production through plasmon excitation mechanism invoked on the gold surface, which produces 10 times more reactive species per unit volume. [START_REF] Verkhovtsev | Electron Production by Sensitizing Gold Nanoparticles Irradiated by Fast Ions[END_REF][START_REF] Verkhovtsev | Revealing the Mechanism of the Low-Energy Electron Yield Enhancement from Sensitizing Nanoparticles[END_REF] Indeed, mild reductive processes could lead to thiol desorption by Au-S bond disruption (-1 eV required), [START_REF] Azzaroni | Electrodesorption Potentials of Self-Assembled Alkanethiolate Monolayers on Ag(111) and Au(111). An Electrochemical, Scanning Tunneling Microscopy and Density Functional Theory Study[END_REF] and hot electrons near gold surface were proved to be efficient enough for such reduction processes. [START_REF] Cortés | Plasmonic Hot Electron Transport Drives Nano-Localized Chemistry[END_REF] Hot electrons in the eV range have also been shown to be able to fragment polymethacrylate type of backbone. [START_REF] Hobbs | Mapping Photoemission and Hot-Electron Emission from Plasmonic Nanoantennas[END_REF] However, polymer desorption from gold surface could also occur by oxidation in stringent conditions. [START_REF] Wong | Oxidative Desorption of Thiols as a Route to Controlled Formation of Binary Self Assembled Monolayer Surfaces[END_REF] Therefore, we cannot completely exclude a surface catalytic effect, similar to the one leading to oxidation of coumarin derivatives. [START_REF] Cheng | Chemical Enhancement by Nanomaterials under X-Ray Irradiation[END_REF][START_REF] Sicard-Roselli | A New Mechanism for Hydroxyl Radical Production in Irradiated Nanoparticle Solutions[END_REF] This surface catalysis is an indirect effect, not completely elucidated, where radiolytic species (H 2 O 2 or superoxide) produced in water are activated on gold surface. However, this hypothesis is limited by the fact that polymer degrafting was not observed in our system using H 2 O 2 alone, and required prior dissolution of the gold core. Either triggered by hot electron or surface catalysis, an interesting point in the degrafting process was its higher efficiency for P(HEMA-MAA) compared to PMAA (whereas external scissions, mainly triggered by HO radicals, were less efficient in P(HEMA-MAA)). Therefore, degrafting is probably not mediated by a hydrogen abstraction mechanism, due for example to HO/H surface production, but by a more exotic reactive species. It can also imply that the copolymer structure is more favorable for the action of this species, and probably to the radiosensitizing action of AuNPs.

Cytotoxicity.

In order to complete this physical and chemical description by a first biological insight, we ensured that neither the initial objects nor the polymer fragments released under irradiation would induce toxicity. To evaluate cell viability, MTT assay was performed on murine fibroblasts with both non-irradiated and 400 Gy-irradiated PMAA-AuNPs and P(HEMA-MAA)-AuNPs solutions for a large range of concentrations (Figure 5). Compared to the previous physico-chemical study, we shifted from high doses (4000 Gy) to an intermediate one (400 Gy) which covers all therapeutic ranges.

Non-irradiated PMAA-AuNPs showed some toxicity for NPs concentrations higher than 100 µg/mL, whereas for P(HEMA-MAA)-AuNPs, the toxicity threshold was found to be 500 µg/mL. The difference of toxicity between the two nano-objects shows the impact of surface properties on NP-cell interactions. This feature is the object of the in vitro and in vivo studies that will be showed in a forthcoming paper. [START_REF] Goas | Improving 131 I Radioiodine Therapy by Hybrid Polymer-Grafted Gold Nanoparticles[END_REF] Overall, the assessed toxicity should be tempered by the conditions used here. Indeed, the incubation time (48 hours) was longer than the average time used elsewhere (see experimental section). [START_REF] Khlebtsov | Biodistribution and Toxicity of Engineered Gold Nanoparticles : A Review of in Vitro and in Vivo Studies[END_REF] Solutions irradiated at 400 Gy showed no additional toxicity for both types of nano-objects.

These results demonstrated that irradiated samples were not harmful, and that no other longlived toxic species were created under irradiation. In the context of medical use, this property would be highly beneficial as it implies that our nano-objects can be used for their radiosensitizing properties without any risk of inherent toxicity. To complete this study, we also showed via SANS that our nano-objects remained stable in solution (meaning that no size decrease of the polymer corona has been observed) for irradiation below 400 Gy (see SANS spectra in S. I.), i.e. in the range of doses used classically in radiotherapy. We could therefore consider the possibility of incorporating drug molecules onto the polymer corona. Grafting of a chemotherapy drug. One interesting improvement of those systems relied on the possibility to graft biologically active molecules such as anticancer drugs. [START_REF] Zhou | Enhanced Cancer Cell Killing by a Targeting Gold Nanoconstruct with Doxorubicin Payload under X-Ray Irradiation[END_REF][START_REF] Cui | Performance of Doxorubicin-Conjugated Gold Nanoparticles: Regulation of Drug Location[END_REF] The most To verify that the grafted DOX was still active, we conducted again MTT assays onto these new functional nano-objects (Figure 6). They were compared to free DOX mixed with PMAA-AuNPs. Grafted DOX was found to be toxic for NPs concentrations higher than 5 µg/mL, i.e. equivalent DOX concentrations higher than 0.5 µg/mL (0.17 µM). Compared to free DOX, no significant difference in toxicity was found, showing that the grafting procedure kept the drug active. 400 Gy-irradiated solutions of DOX-PMAA-AuNPs and free DOX combined with PMAA-AuNPs were also tested regarding cytotoxicity (Figure 6). For both samples, irradiated NPs showed very small additional toxicity at intermediate concentrations.

This could be explained by a toxicity of the degradation species produced when DOX is irradiated [START_REF] Varshney | Radiation Effect Studies on Anticancer Drugs, Cyclophosphamide and Doxorubicin for Radiation Sterilization[END_REF] higher than the one of DOX itself. However, considering the very low concentrations of these degradation species [START_REF] Varshney | Radiation Effect Studies on Anticancer Drugs, Cyclophosphamide and Doxorubicin for Radiation Sterilization[END_REF] and the minor additional toxic effect observed at 400 Gy, no significant impact should be observed for smaller therapeutic doses. Also, no protection or amplification of irradiation onto the drug was observed for grafted DOX compared to free DOX. Overall, these results showed that toxicity of grafted DOX was maintained even after irradiation.

B) A)

CONCLUSION A detailed study has been presented here on irradiation effects onto polymer-grafted nanoparticles. Such a study has never been performed before, even though metal NPs are widely investigated for radiotherapy applications. Well-defined polymer-grafted AuNPs were particularly interesting as they led to very stable nano-objects in solution. Also, direct characterization of surface effects induced by irradiation could be performed via the polymer corona. Particularly, scattering techniques (SAXS and SANS), together with SEC measurements and scission yield calculations, showed how nano-objects had been impacted by irradiation. Polymer corona analysis permitted to localize the active sites and the comparison with free polymers showed that no long-range effects were involved. Also, variation of the polymer nature highlighted the presence of short-range effects, either caused by the production of hot electrons or by surface catalysis. The methodology developed here could be applied to other types of hybrid nano-objects. Indeed, it is of particular importance to verify the stability of nano-objects under irradiation in the scope of bio-application. Regarding our objective of designing nano-objects for radiosensitization, we confirmed that they were stable under low dose and that they remained nontoxic after irradiation. As mentioned before, a detailed study of the radiosensitizing properties of these nano-objects will be described in a forthcoming paper. [START_REF] Goas | Improving 131 I Radioiodine Therapy by Hybrid Polymer-Grafted Gold Nanoparticles[END_REF] Finally, we also performed the grafting of a model chemotherapy drug onto the polymer corona, thus showing the possibility to combine chemotherapy and radiotherapy.

Table of Content/Abstract Graphic (TOC).

.

  Monomers were all distilled prior to use. All other reactants were mainly purchased from Sigma-Aldrich (France) and used as received. L929 mouse fibroblast cell line was purchased from the American Type Culture Collection (ATCC, USA). Dulbecco's Modified Eagle Medium (DMEM), Dulbecco's Phosphate Buffer Saline (DPBS), Trypsin and Gentamicin/Amphotericin B were obtained from Fisher Scientific (France). Fetal Bovine Serum and MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-di-phenyl tetrazolium bromide) were bought from Sigma-Aldrich (France).

1 H

 1 NMR (CDCl 3 ) δ (ppm): PtBuMA-DS. 1.81-2.06 (m, CCH 2 , 2H), 1.41 (s, CH 3 , 9H), 1.11-1.02 (m, CCH 3 , 3H); P(HEMA-tBuMA)-DS. 4.10-4.25 (m, CH 2 -OH, 2H), 3.75-3.90 (m, CH 2 -O, 2H), 1.70-2.10 (m, CCH 2 , 3H), 1.30-1.50 (m, CH 3 , 8H), 0.75-1.25 (m, CCH 3 , 6H). PHEMA-DS. 4.00-4.20 (m, CH 2 -OH, 2H), 3.70-3.90 (m, CH 2 -O, 2H), 1.80-2.20 (m, CH 2 , 2H), 0.80-1.20 (m, CCH 3 , 3H); P(PEGMA-tBuMA)-DS. 3.60-3.75 (m, CH 2 -CH 2 -O, 15H), 3.30-3.40 (m, CH 3 -O, 3H), 1.75-2.00 (m, CCH 2 , 3H), 1.40-1.50 (m, CH 3 , 8H), 0.75-1.25 (m, CCH 3 , 7H); P(PEGMA-HEMA)-DS. 4.00-4.20 (m, CH 2 -OH, 2H), 3.75-3.90 (m, CH 2 -O, 2H), 3.50-3.75 (m, CH 2 -CH 2 -O, 15H), 1.60-2.20 (m, CH 2 , 5H), 0.70-1.20 (m, CCH 3 , 6H).

1 H

 1 NMR (CDCl3) δ (ppm): PMAA-DS. 1.80-2.20 (m, CCH2, 2H), 1.00-1.20 (m, CCH3, 3H); P(HEMA-MAA)-DS. 4.00-4.10 (m, CH2-OH, 2H), 3.70-3.80 (m, CH2-O, 2H), 1.80-2.20 (m, CCH2, 3H), 0.80-1.25 (m, CCH3, 6H); P(PEGMA-MAA)-DS. 3.60-3.75 (m, CH 2 -CH 2 -O, 14H), 3.30-3.40 (m, CH 3 -O, 3H), 1.75-2.00 (m, CCH 2 , 3H), 0.75-1.25 (m, CCH 3 , 6H).

Figure 1 .

 1 Figure 1. TEM micrograph of (A) PMAA-AuNPs and (B) P(HEMA-MAA)-AuNPs.

Figure 2 .

 2 Figure 2. SAXS spectra of polymer-grafted AuNPs (10 mg/mL solutions in water) before and

Figure 3 .

 3 Figure 3. SANS spectra of (A) PMAA-AuNPs and (B) P(HEMA-MAA)-AuNPs, before and

Figure 4 .

 4 Figure 4. Irradiation effects on PMAA-AuNPs: SEC measurements after irradiation of

Figure 5 .

 5 Figure 5. Cytotoxicity of non-irradiated and irradiated (A) PMAA-AuNPs and (B) P(HEMA-

  doxorubicin (DOX). To perform grafting onto grafted polymer chains, we took advantage of amine groups and used the standard technique based on intermediate activated esters. We created succinimide groups along the chain from the reaction of PMAA's carboxylic acid groups with EDC and NHS (see experimental section for details). The resulting intermediate activated ester groups then reacted efficiently with the amino groups of DOX. To estimate the amount of grafted DOX, we performed UV spectroscopy (see S. I.) using the absorption peak of doxorubicin at 234 nm. A calibration curve was established for a fixed concentration of PMAA-AuNPs. It was therefore possible to calculate the quantity of grafted DOX, giving a result of one DOX molecule per polymer chain.

Figure 6 .

 6 Figure 6. Cytotoxicity of non-irradiated and irradiated (A) DOX-PMAA-AuNPs and (B)

  µg/mL) Non-irradiated PMAA-AuNPs + free DOX 400 Gy-irradiated PMAA-AuNPs + free DOX

Table 1 .

 1 Molecular weight (M n ) and polydispersities (M w /M Molecular weights (M n ) obtained from SEC measurements have been reported in Table1.Polydispersity values were slightly higher than what we expected from ATRP process (≥ 1.3).

	P(PEGMA-MAA)-DS	(Poly(polyethyleneglycol	methacrylate-co-methacrylic	acid)),
	P(PEGMA-HEMA)-DS	(Poly(polyethyleneglycol	methacrylate-co-hydroxyethyl

methacrylate))

. All functionalized polymers were characterized through gravimetric measurements (kinetics study),

[START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF]

H NMR and SEC (size exclusion chromatography).

Polymerization kinetics studies (see supporting information, S. I.) gave final polymer conversions between 45 and 70 % after 2 hours reaction, depending on the initial monomer(s). Also, a good control of the polymerization was stated by the linear variation of ln([M 0 ]/[M]) as a function of t 2/3 (see S. I.). n ) of polymers disulfide obtained from ATRP, determined from size-exclusion chromatography (SEC); before and after hydrolysis.

Table 2 .

 2 SANS characteristic values of PMAA-AuNPs and P(HEMA-MAA)-AuNPs before and after irradiation.

	Nano-objects	Dose (Gy)	I 0 (cm -1 )	R g of nano-objects (Å)	M app of the corona (g/mol)
	PMAA-AuNPs	0 4000 20000	0.53 ± 0.02 0.35 ± 0.01 0.19 ± 0.01	120 ± 3 98 ± 3 69 ± 2	21000 ± 800 14200 ± 350 7500 ± 400
	P(HEMA-	0	0.49 ± 0.01	90 ± 1	21900 ± 450
	MAA)-	4000	0.37 ± 0.01	74 ± 1	16500 ± 450
	AuNPs	20000	0.22 ± 0.01	58 ± 1	9800 ± 450
	Impact of irradiation. Using both SAXS, SANS and SEC, it was possible to evaluate
	quantitatively the effects of irradiation onto the polymer corona. Polymer-grafted AuNPs
	solutions were irradiated using gamma rays (at 4000 and 20000 Gy), under O 2 (air)

ASSOCIATED CONTENT

Supporting Information. Polymerization kinetics, [START_REF] Parhi | Nanotechnology-Based Combinational Drug Delivery: An Emerging Approach for Cancer Therapy[END_REF] H NMR spectroscopy and TEM of polymer-grafted PtNPs, UV-Vis spectroscopy of the aqueous solutions, complementary SAXS, SANS and SEC data, TGA, as well as calibration curves for the evaluation of the DOX content, are all described in the supporting information.

AUTHOR INFORMATION

Corresponding Author.

*E-mail: geraldine.carrot@cea.fr; jean-philippe.renault@cea.fr. Tel: +33 ( 0


Mélanie Emile
email: melanie.emile@unice.fr

Arripe-Longueville Fabienne D'

Nice

Massimiliano Amato

An ego depletion account of aging stereotypes' effects on health-related variables

Keywords: Age stereotypes, subjective vitality, ego depletion, physical activity, multilevel growth modeling

Objectives. This study examined whether stereotypes may predict health outcomes independently from their internalization into the self. Specifically, we tested whether endorsement of negative age stereotypes in the physical activity (PA) domain is related to decreased subjective vitality among active older adults, illustrating ego depletion.

Method. This longitudinal study included 192 retired individuals aged 60 to 92 years who regularly participated in organized PA, and who completed the measures on three occasions (9-month period).

Results. Multilevel growth models tested whether within-person variation in age stereotypes endorsement across waves predicted subjective vitality, after controlling for self-perceptions of aging and relevant covariates. Results showed that (a) within-person increases in endorsement of age stereotypes of self-efficacy (b = 0.17, p < .01) were associated with increases in subjective vitality, (b) between-person mean difference in endorsement of age stereotypes of PA benefits (b = 0.21, p < .05) positively predicted subjective vitality, and (c) subjective vitality mediated the relationship between endorsement of self-efficacy stereotype and self-rated health.

Discussion. This study confirmed that endorsement of age stereotypes of PA predicted subjective vitality among active older adults. These results suggest that stereotypes may be related to health-related outcomes notably through ego depletion effects.

An ego depletion account of aging stereotypes' effects on health-related variables

A growing body of research has started to question the assumption that the aging process can be explained exclusively as a physiological process of inevitable decline [START_REF] Levy | Stereotype embodiment a psychosocial approach to aging[END_REF][START_REF] Rothermund | Effects of age stereotypes on self-views and adaptation[END_REF]. This psychosocial approach to aging considers that age stereotypes (i.e., beliefs about older people in general) may also substantially affect health. For example, there is evidence that older individuals who hold positive age stereotypes recover more rapidly from a disability [START_REF] Levy | Association between positive age stereotypes and recovery from disability in older persons[END_REF], and have better memory [START_REF] Levy | Memory shaped by age stereotypes over time[END_REF] abilities than those who hold negative age stereotypes [START_REF] Levy | Stereotype embodiment a psychosocial approach to aging[END_REF].

Aging Stereotypes and Health Outcomes: The Stereotype Internalization Approach

To explain these relationships, the stereotype internalization hypothesis proposes that age stereotypes are internalized into self-perceptions of aging (SPA) (older adults' beliefs about their own aging), which act as a lens through which aging experiences are interpreted [START_REF] Levy | Stereotype embodiment a psychosocial approach to aging[END_REF]. In line with this idea, SPA have been shown to predict health outcomes, with positive SPA being related to better physical functioning (balance and gait speed) [START_REF] Sargent-Cox | The relationship between change in self-perceptions of aging and physical functioning in older adults[END_REF], and increased survival [START_REF] Sargent-Cox | Longitudinal change of self-perceptions of aging and mortality[END_REF]. According to the internalization hypothesis, SPA predict health outcomes through their influence on adoption of health behaviors [START_REF] Levy | Preventive health behaviors influenced by selfperceptions of aging[END_REF]): because people with negative SPA consider their functional decline as an inevitable part of the aging process, they are more likely to consider health-related behaviors as useless than people with positive SPA.

Therefore, the latter engage in healthy behaviors (e.g., being physically active) more than the former. In line with this hypothesis, there is evidence that positive SPA are associated with healthy behaviors such as regular engagement in PA (Emile, Chalabaev, Stephan, Corrion, & d'Arripe-Longueville, 2013;[START_REF] Wurm | On the importance of a positive view on ageing for physical exercise among middle-aged and older adults: Cross-sectional and longitudinal findings[END_REF]. Moreover, SPA have been shown to mediate the relationship between stereotype endorsement and adoption of an active lifestyle [START_REF] Chalabaev | Development and validation of the Aging Stereotypes and Exercise Scale[END_REF], providing further support to the stereotype internalization hypothesis.

Interestingly, the study of [START_REF] Chalabaev | Development and validation of the Aging Stereotypes and Exercise Scale[END_REF] also revealed a direct relationship between stereotype endorsement and adoption of an active lifestyle, even after controlling for SPA. This study focused on stereotypes in the domain of PA, which is usually associated with beliefs that older adults are too weak to be physically active [START_REF] Roters | A preliminary study of perceptions of aging in athletes and non-athletes[END_REF]. Results indicated that the more older adults endorsed positive age stereotypes in the domain of PA, the more they adopted an active lifestyle, independently of how they perceived their own aging. This suggests that SPA are not the only pathway through which stereotype endorsement may affect older adults' health. The present study explored a complementary pathway, by testing the novel hypothesis that endorsement of age stereotypes may be related to ego depletion, a concept issued from the strength model of self-control [START_REF] Muraven | Self-regulation and depletion of limited resources: Does self-control resemble a muscle[END_REF]. The theoretical rationale underlying this hypothesis is described below.

Aging Stereotypes and Health Outcomes: An Ego Depletion Approach

The strength model defines self-control as the mental energy individuals use to effortfully regulate their emotions, thoughts, impulses, or other automatic behavioral responses that interfere with goal-directed behaviors. A major tenet of the model is that engaging in acts of self-control draws from a limited 'reservoir', which, when depleted, results in reduced capacity for further self-regulation, a phenomenon known as ego depletion [START_REF] Muraven | Self-regulation and depletion of limited resources: Does self-control resemble a muscle[END_REF]. In other words, ego depletion refers to the depletion of energy necessary to regulate one's behaviors. For example, depleted individuals have been found to regulate physical demands more poorly, and to exercise less regularly (Hagger, Wood, Stiff, & Chatzisarantis, 2010). Relevant here, a few studies suggest that endorsement of stereotypes may affect ego depletion. Drawing on stereotype threat hypothesis that negative self-stereotypes may be stressful, [START_REF] Inzlicht | Stereotype threat spillover: How coping with threats to social identity affects aggression, eating, decision making, and attention[END_REF] showed that females who faced negative gender stereotypes during a math task had difficulties to exert self-control afterwards: they responded more aggressively, ate more unhealthy food, and made more risky decisions. To explain these results, the authors proposed that coping with stereotype threat when performing a math task consumed the mental energy necessary for self-regulation, leaving females with fewer resources to overcome environmental temptations and override impulses. In the same vein, Levy, Hausdorff, Hencke, and Wei (2000) observed that older adults who were exposed to negative age stereotypes demonstrated a heightened cardiovascular response to stress compared with those exposed to positive age stereotypes, suggesting that stereotypes may act as direct stressors. Given that people who endorse negative self-stereotypes are more susceptible to experience stereotype threat than people who do not [START_REF] Schmader | The costs of accepting gender differences: The role of stereotype endorsement in women's experience in the math domain[END_REF], these results suggest that stereotype endorsement may affect ego depletion.

The Present Research

Based on these results, we examined whether endorsement of age stereotypes in the domain of PA may be related to ego depletion among older adults who are physically active.

It was hypothesized that the more individuals would endorse negative age stereotypes, the lower their energy for self-regulation. More particularly, we reasoned that if individuals believe that older adults in general are too old to exercise, this belief would be in conflict with their goal to stay physically active. In this case, engaging in regular PA would need selfcontrol resources to override their negative stereotype-based beliefs, leading to increased ego depletion. We examined age stereotypes in the PA domain, because stereotypes that are specific to a life domain may affect individuals' functioning in this domain [START_REF] Kornadt | Contexts of aging: Assessing evaluative age stereotypes in different life domains[END_REF] more than other-domain stereotypes. Therefore, we reasoned that negative age stereotypes of PA would likely affect the self-control resources used to participate in PA on a regular basis.

Ego depletion was indexed by subjective vitality, defined as the energy that one can harness or regulate for purposive actions [START_REF] Ryan | A self-determination theory approach to psychotherapy: The motivational basis for effective change[END_REF]. In line with theoretical assumptions, the meta-analysis of Hagger et al. (2010) showed that subjective fatigue (i.e., fatigue that is consciously felt) may be one explanation for the self-control deficits observed in ego depletion experiments, reflecting the effortful nature of self-control tasks. Past research indicates that subjective vitality, which may be situation-specific, is a valid marker of ego depletion [START_REF] Muraven | Helpful self-control: Autonomy support, vitality, and depletion[END_REF][START_REF] Rouse | Effects of motivation and depletion on the ability to resist the temptation to avoid physical activity[END_REF]. For example, [START_REF] Muraven | Helpful self-control: Autonomy support, vitality, and depletion[END_REF] showed that declines in self-control performance after a depleting task were mediated by decreased subjective vitality. These findings suggest that subjective vitality and behavioral assessments of ego depletion tap into the same phenomenon, with subjective vitality having the advantage of being a highly accessible, phenomenologically-based variable [START_REF] Ryan | A self-determination theory approach to psychotherapy: The motivational basis for effective change[END_REF].

In addition, subjective vitality is an important predictor of health outcomes. It has notably been associated with more resilience to stressors and less susceptibility to illness [START_REF] Benyamini | Positive affect and function as influences on self-assessments of health expanding our view beyond illness and disability[END_REF], better regulation of negative emotions [START_REF] Rozanski | The epidemiology, pathophysiology, and management of psychosocial risk factors in cardiac practice The emerging field of behavioral cardiology[END_REF], and higher mental health [START_REF] Ryan | On energy, personality, and health: Subjective vitality as a dynamic reflection of well--being[END_REF]. Therefore, if endorsement of negative age stereotypes predicts subjective vitality, this would suggest that ego depletion is a pathway through which age stereotypes may affect older adults' health that complements the internalization pathway.

To provide further support to this hypothesis, an additional objective was to examine whether age stereotypes in the PA domain were related to self-rated health, through the mediating role of subjective vitality. We hypothesized that the more individuals would endorse negative age stereotypes, the lower their subjective vitality, which would in turn result in lower perceived health.

Overview of the study

Multilevel models

The hypothesis that endorsement of age stereotypes predicts lower subjective vitality was examined in a longitudinal design. Measures were assessed on three occasions over a 9month period, among older adults who participated in PA in leisure clubs on a regular basis. This allowed us to examine whether within-person variability in stereotype endorsement across waves predicted subjective vitality. This hypothesis was tested using multilevel models [START_REF] Raudenbush | Hierarchical linear models: Applications and data analysis methods[END_REF].

Covariates

Several covariates were included in this study. First, SPA were taken into account, as the study aimed at examining a pathway of stereotype influence that complements the stereotype internalization approach. As such, we investigated whether stereotype endorsement may be ego depleting independently of how older adults have internalized stereotypes into perceptions of their own aging. SPA were indexed by participants' attitude toward their own aging (e.g., "Things keep getting worse as I get older"). Self-perceptions related to the physical domain were also measured, in order to rule out the possibility that the stereotype measure would not tap into a domain not being assessed by the SPA measure. These selfperceptions were assessed by physical self-worth (i.e., general feelings of happiness, satisfaction, pride, respect, and confidence in the physical self).

In addition, we controlled for individual differences in motivation for PA. We reasoned that although engaging in health-related behaviors on a regular basis may require self-control resources, this is not systematically the case. Based on self-determination theory (Deci & Ryan, 2000), past research indicates that engaging in self-control behaviors for autonomous reasons (free choice) is less depleting than exerting self-control for controlled reasons (external or internal pressure) [START_REF] Muraven | Helpful self-control: Autonomy support, vitality, and depletion[END_REF]. Therefore, we measured older adults' motivations for PA (autonomous vs. controlled motivations) and examined whether stereotype endorsement affects subjective vitality independently of these motivations.

Other covariates included self-reported level of PA (leisure and daily activities), selfrated health, and perceived loneliness. These variables were chosen because past research has shown that they are related to PA stereotype endorsement (Chalabaev et al., 2013), and health-related variables [START_REF] Levy | Stereotype embodiment a psychosocial approach to aging[END_REF] in older adults.

Method

Participants 192 retired individuals (24 men and 168 women) aged from 60 to 92 years (M years = 73.22; SD = 7.53), and residing in the south of France, participated in this study on a voluntary basis. Participants met the following criteria: (a) participating in at least one session of organized PA per week (based on the timesheets completed by PA instructors at each session), and (b) living independently in the community. Among the initial 362 contacted participants, 72 were not included because they did not meet these criteria. Moreover, we excluded from the analyses 98 participants who participated in the study on one occasion only. Indeed, as our main goal was to examine the relationship between stereotype endorsement and ego depletion among active older adults, we wanted to ascertain that participants were regular PA participants. Concerning education level, 71.1% of participants had completed high school. The study complied with APA ethical standards.

Procedure

Participants were contacted through a leisure club for older adults, comprising roughly 1400 members. The membership fee costs ten euros per year, making this club accessible to individuals with various income levels. Eligibility requirements include: (a) living in the southeast region of France, (b) being retired, (c) being aged 49 years and older, and (d) presenting a medical certificate attesting that the individual was free from severe functional, mental or cognitive impairment. They were informed about the study on site, during their PA lessons. Written informed consent was obtained from all participants. After their PA lesson at the leisure club, participants were asked to fill out individually a questionnaire that included the variables of interest. The average time of completion was 15 minutes. Measures were assessed on three occasions over a 9-month period, with an interval of 4 to 5 months between each occasion.

Measures

Subjective vitality. Subjective vitality was measured by the Subjective Vitality Scale [START_REF] Ryan | On energy, personality, and health: Subjective vitality as a dynamic reflection of well--being[END_REF], which includes five items (e.g., "I feel alive and vital").

Participants responded on a 7-item Likert scale ranging from 1 (completely disagree) to 7 (completely agree). The scale presented good reliability (α = .90).

Age stereotypes in the PA domain. Endorsement of age stereotypes was assessed using the Aging Stereotypes and Exercise Scale (Chalabaev et al., 2013). This questionnaire consists of 12 items divided into three subscales: (a) four items measure stereotypes about older adults' self-efficacy to participate in PA on a regular basis (e.g., "older adults are convinced that they are capable of being physically active"), (b) four items measure stereotypes about positive outcomes (i.e., benefits) of PA for older adults (e.g., "PA raises older adults' spirits"), and (c) four items measure stereotypes about negative outcomes (i.e., risks) of PA for older adults (e.g., "the physical capacities of older adults are too diminished for being physically active"). Participants responded on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree), such that lower scores indicate lower beliefs in older adults' self-efficacy, positive outcomes of PA, and negative outcomes of PA. Each subscale presented good reliability (α self-efficacy = .78, α benefits = .80, α risks = .83).

Covariates.

Self-perceptions of aging. SPA were measured by a French version [START_REF] Allard | L'influence des relations familiales et sociales sur la consommation de médicaments psychotropes chez les personnes âgées [The influence of family and social relationships on psychoactive drugs among older adults[END_REF] of the Attitude Toward Own Aging scale [START_REF] Liang | The structure of the Philadelphia geriatric center morale scale: A reinterpretation[END_REF], which consists of five items (e.g., " Things keep getting worse as I get older "). Participants responded on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree). This scale has been used to assess self-perceptions of aging (Levy et al., 2002;[START_REF] Sargent-Cox | The relationship between change in self-perceptions of aging and physical functioning in older adults[END_REF]. This scale presented good reliability (α = .78).

Self-determined motivation. Motivation for PA was measured with the French version (Gourlan, Sarrazin, & Trouilloud, 2013) of the Behavioural Regulation in Exercise Questionnaire (BREQ-2) of [START_REF] Markland | A modification to the behavioural regulation in exercise questionnaire to include an assessment of amotivation[END_REF]. This questionnaire consists of 15 items assessing four types of regulations: (a) external (4 items, e.g., "I exercise because other people say I should"), (b) introjected (3 items, e.g., "I feel guilty when I don't exercise"), (c) identified (3 items, e.g., "I value the benefits of exercise"), and (d) intrinsic (4 items, e.g., "I exercise because it's fun"). Participants responded on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree). Finally, in agreement with previous studies on self-determination (e.g., [START_REF] Silva | Exercise autonomous motivation predicts 3-yr weight loss in women[END_REF], the intrinsic motivation and identified regulation subscales were averaged to form a score of autonomous motivation, whereas a score of controlled motivation was created by averaging the responses provided to the introjected regulation and external regulation subscales. Each subscale presented good reliability (α autonomous = .82, α controlled = .79).

Physical self-worth. Physical self-worth was measured using the corresponding subscale of the Physical Self Inventory (PSI-25), the French version of the Physical Self-Perception Profile (PSPP) of Fox and Corbin (1989) [START_REF] Ninot | L'évaluation de l'estime de soi dans le domaine corporel. [The assessment of self-esteem in the physical domain[END_REF]. It consists of five items (e.g., "Overall, I am satisfied with my physical capacities"). Participants answered on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree). This subscale presented good reliability (α = .87).

Level of general PA. Level of PA was measured with the Dijon Physical Activity

Score of [START_REF] Robert | Le Score d'activité physique de Dijon : Reproductibilité et corrélations avec l'aptitude physique de sujets sains âges. [The Dijon Physical Activity Score: Reproducibility and correlation with exercise testing in healthy elderly subjects[END_REF]. This 9-item questionnaire was specifically developed to assess PA in a population of healthy, elderly subjects. The scale includes: (a) an overall appraisal of one's PA ("Do you consider yourself to be physically: from (1) very active and athletic, to (4) completely sedentary?"); (b) two items on everyday activities (e.g., "On a weekly basis, your everyday activities take you: from (1) more than 10 hours, to (5) no time spent"); (c) five items on sport and leisure activities (e.g., "For how many months of the year do you engage in these activities (sport or leisure)?"); and (d) one item on rest (e.g., "On a daily basis, you rest (sleep, nap or wakeful rest): from (1) less than 12 hours, to (4) more than 20 hours"). Then the scores on each item are summed up, and this total score indicates participant's level of physical activity (individuals who score below 18 (out of 30 points) being considered as sedentary). This measure has been shown to be reproducible and to be a valid measure of PA.

The score notably correlates with maximal oxygen consumption and maximal power attained during a stress test in older adults [START_REF] Robert | Le Score d'activité physique de Dijon : Reproductibilité et corrélations avec l'aptitude physique de sujets sains âges. [The Dijon Physical Activity Score: Reproducibility and correlation with exercise testing in healthy elderly subjects[END_REF], and with energy expenditure measured using an accelerometer in coronary artery disease patients (Guiraud, Granger, Bousquet, & Gremeaux, 2012).

Perceived loneliness. Perceived loneliness was measured by the following item "I feel lonely" (Philadelphia Geriatric Center Morale Scale; [START_REF] Lawton | The Philadelphia geriatric center morale scale: A revision[END_REF]. Participants answered on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree).

Self-rated health. Self-rated health was measured by the following item "In general, how would you rate your current health status". Participants answered on a 6-point Likert scale ranging from 1 (very bad) to 6 (very good) [START_REF] Benyamini | Elderly people's ratings of the importance of health-related factors to their self-assessments of health[END_REF].

Data Analysis

Multilevel models tested whether within-person variation in age stereotypes endorsement across waves predicted subjective vitality, after controlling for relevant covariates. Multilevel models extend multiple regressions to data that are hierarchically structured [START_REF] Singer | Applied longitudinal data analysis: Modeling change and event occurrence[END_REF]. Given that we had several observations for each individual, repeated measurements (level 1 units of analysis) were nested within individuals (level 2 units of analysis). This method has several advantages over ordinary least squares regression. Multilevel models are a flexible approach that can be applied to evaluate interindividual differences in intra-individual changes over time. That is, these models separate inter-individual variance from intra-individual variance, so that each participant has his or her own curve [START_REF] Raudenbush | Hierarchical linear models: Applications and data analysis methods[END_REF]. Indeed, traditional regression models are based on the assumption that all observations are independent, which may not be the case with nested data. In addition, multilevel models do not require equal numbers of responses from each participant, which is usually the case in longitudinal designs (for use in aging research, see [START_REF] Birditt | Enacted support during stressful life events in middle and older adulthood: an examination of the interpersonal context[END_REF]. By taking into account the hierarchical structure of the data, multilevel models provide unbiased estimates of the parameters [START_REF] Singer | Applied longitudinal data analysis: Modeling change and event occurrence[END_REF].

The hypothesis that endorsement of age stereotypes predicts subjective vitality was thus tested in several steps. First, unconditional models (i.e., with no predictor) were estimated for each variable. Intraclass correlations were calculated from these models to estimate the amount of variance at the between and within-individual levels, which allowed us to determine whether conducting multilevel models was relevant or not. Next, all explanatory variables were added in the conditional growth model, along with time (the baseline time point, wave 1, was given a value of 0 on the timescale). This model explored whether withinperson variation in age stereotypes endorsement predicted subjective vitality, after controlling for covariates (i.e., SPA, self-determined motivation for PA, physical self-worth, perceived loneliness, self-rated health, level of general PA).

Preliminary models included time × predictor interaction terms to test whether the relationships changed significantly over the course of the study. However, as these interactions were not significant, they were not included in the final model. Similarly, inclusion of the random effects of the linear slope and of the covariance slope-intercept did not improve fit of the model, and were therefore not included in the final model.

We therefore tested a two-level random intercept model that led to the following Level 1 model: In this equation, person i's score of vitality at time t is a sum of his/her rating intercept (β 0i ), linear change over time (β 1 ), the regression coefficients associated with explanatory variables and covariates (β 2 to β 11 ), and a residual term e it .

Vitality it = β 0i + β 1 time it + β 2 self-
The present study included time-varying (Level 1) and time-invariant (Level 2) predictors. Time-varying predictors were centered on each individual's unique mean over time (i.e., group mean centering), which enabled for a pure estimation of the intra-individual effects (Enders & Tofighi, 2007). Time-invariant predictors were centered on the sample mean (i.e., grand mean centering). We added these mean scores to ensure that our estimates of within-person change at level 1 were not confounded with between-person differences [START_REF] Raudenbush | Hierarchical linear models: Applications and data analysis methods[END_REF]. This led to the following Level 2 model: β 0i = γ 0 + γ 1 mean self-efficacy stereotype i + γ 2 mean PA benefits stereotype i + γ 3 mean PA risks stereotype i + γ 4 mean SPA i + γ 5 mean autonomous motivation i + γ 6 mean controlled motivation i + γ 7 mean physical self-worth i + γ 8 mean perceived loneliness i + γ 9 mean self-rated health i + γ 10 mean level of general PA i + u 0i . This equation indicates that β 0i is equal to a constant (γ 0 ), the regression coefficients associated with time-invariant explanatory variables and covariates (γ 1 to γ 10 ), and a residual term u 0i . We did not include predictors of the slopes because the time x predictor interaction was not significant.

The fit of the model was tested using a chi-square test of the differences in -2 log likelihood values (LLV) between this model and the unconditional growth model (with time as the only predictor), with degrees of freedom equal to the difference between each model's total number of estimated parameters. The difference in -2 LLV may be useful to assess whether adding fixed effects to a model increases its overall fit to the data [START_REF] Singer | Applied longitudinal data analysis: Modeling change and event occurrence[END_REF]; see for example [START_REF] Trouilloud | Relation between teachers' early expectations and students' later perceived competence in physical education classes: Autonomy-supportive climate as a moderator[END_REF]. Finally, we calculated pseudo R1 2 (within-person level) and R2² (between-person level) values to estimate the proportion of variance accounted for by the predictors from the unconditional growth model to the conditional model [START_REF] Singer | Applied longitudinal data analysis: Modeling change and event occurrence[END_REF]. These values are an estimate of effect size, similar to the R 2 value in traditional ordinary least squares regression analyses [START_REF] Hox | Multilevel analysis: Techniques and applications[END_REF].

Results

Means, standard deviations, Cronbach's alpha coefficients for all variables at each wave are presented in Table 1 along with their intraclass correlation (ICC). Correlations are reported in Table 2.

On average, at time 1, participants reported high endorsement of self-efficacy stereotype (M = 5.66), benefits of PA stereotype (M = 6.31), and low endorsement of risks of PA stereotype (M = 2.49). Moreover, they reported high autonomous motivation (M = 6.48) and low controlled motivation (M = 2.74). Finally, they presented high SPA (M = 5.03), physical self-worth (M = 4.85), self-rated health (M = 4.65), subjective vitality (M = 4.96), and perceived loneliness (M = 5.32).

Intraclass correlations showed that a significant amount of variance was located at the between-individual level for all variables, including subjective vitality (57%), stereotype endorsement (57% to 65%), SPA (61%), motivations for physical activity (59% to 69%), physical self-worth (75%), perceived loneliness (80%), self-rated health (68%), and level of general PA (57%). This indicates several sources of variation (between and withinindividuals) in our variables, justifying our rationale for using multilevel modeling [START_REF] Hox | Multilevel analysis: Techniques and applications[END_REF].

We next tested whether stereotype endorsement predicted subjective vitality, after controlling for covariates. First, this model provided a better fit to the data, the reduction of the deviance of this model, compared with the unconditional growth model, being significant (Δ = 161.1; df = 20; p < .001). At level 1, increases in endorsement of age stereotypes of selfefficacy (b = 0.17, p < .01) were associated with increases in subjective vitality (ß 2 ). Some covariates were also significant predictors of subjective vitality, and notably SPA (b = 0.17, p < .01) (ß 5 ), autonomous motivation (b = 0.17, p < .05) (ß 6 ), physical self-worth (b = 0.44, p < .001) (ß 8 ), perceived loneliness (b = -0.08, p < .05) (ß 9 ), and self-rated health (b = 0.22, p < .01) (ß 10 ). All of these predictors accounted for 38.2% of the within-person variance in subjective vitality. At level 2, results revealed that between-person mean differences in endorsement of age stereotypes of PA benefits (b = 0.21, p < .05) positively predicted subjective vitality (γ 2 ), along with SPA (b = 0.39, p < .001) (γ 4 ), physical self-worth (b = 0.45, p < .001) (γ 7 ), perceived loneliness (b = -0.07, p < .05) (γ 8 ), and self-rated health (b = 0.44, p < .001) (γ 9 ). This model accounted for 38.2% of the within-person and 37.5% of the betweenperson variance in subjective vitality.

In order to examine whether stereotypes predicted health beyond subjective vitality, we tested whether age stereotypes affected self-rated health through the mediating role of subjective vitality. To do so, we added subjective vitality to the multilevel model (at both Level 1 and Level 2), with self-rated health as the outcome. This allowed testing whether the mediator (vitality) predicted self-rated health, after controlling for the predictor (stereotypes) and relevant covariates. Results showed that subjective vitality positively predicted self-rated health at the within-individual level (b = .21, p < .001), along with stereotypes of self-efficacy (b = .10, p < .05). We then tested the significance of the indirect effect of age stereotypes on self-rated health using the distribution of products test [START_REF] Mackinnon | A comparison of methods to test mediation and other intervening variable effects[END_REF]. Results showed that the indirect effect was significant (P = 11.22, p < .001). In other words, within-individual endorsement of self-efficacy stereotypes predicted self-rated health through its indirect effect on vitality.

Discussion

In line with a psychosocial approach to aging, the study examined whether stereotypes may predict health outcomes independently from their internalization into the self [START_REF] Levy | Stereotype embodiment a psychosocial approach to aging[END_REF]. Based on the strength model of self-control [START_REF] Muraven | Self-regulation and depletion of limited resources: Does self-control resemble a muscle[END_REF], we hypothesized that endorsement of negative age stereotypes may be related to depletion of resources for self-regulation as indexed by subjective vitality. Results corroborated this hypothesis, showing that the less participants believed in the benefits of PA and in older adults' self-efficacy to stay physically active, the less they experienced vitality, over a 9month period. Importantly, these results were observed after controlling for SPA and a number of potential correlates of subjective vitality (i.e., self-rated health, level of PA, selfdetermined motivation for PA, physical self-worth, and perceived loneliness). Results also revealed that subjective vitality acted as a mediating variable between endorsement of selfefficacy stereotype and self-rated health.

These findings open new avenues of research by suggesting that age stereotypes may affect health through multiple pathways, and not only through their internalization into the self. Although the internalization hypothesis is important in predicting the aging process, our results suggest that other mechanisms may be involved. This idea is reinforced by the fact that the findings were observed among active older adults, in other words, among individuals who are the least likely to have internalized negative aging stereotypes in the PA domain.

If age stereotypes may affect subjective vitality and health independently from their internalization into SPA, what are the mechanisms involved? Stereotype threat research could help explain the results. There is indeed evidence that coping with threatening negative stereotypes may consume the mental energy necessary for self-regulation [START_REF] Inzlicht | Stereotype threat spillover: How coping with threats to social identity affects aggression, eating, decision making, and attention[END_REF]. Moreover, people who endorse stereotypes may be more susceptible to experience stereotype threat [START_REF] Schmader | The costs of accepting gender differences: The role of stereotype endorsement in women's experience in the math domain[END_REF]. Based on these results, it is possible that endorsement of negative age stereotypes conflicted with older adults' goal to stay physically active, which required self-control resources to override stereotype-based beliefs, leading in turn to decreased subjective vitality. As we used a correlational design, it is difficult to establish causality links from the observed relationships: stereotype endorsement may have impacted vitality, but vitality may have also affected stereotype endorsement by generating a general "optimistic outlook". A recent study tested the direction of the SPA-functional health relationship over a 16-year period, and found that the best fitting model was that which allowed SPA to predict change in functional health [START_REF] Sargent-Cox | The relationship between change in self-perceptions of aging and physical functioning in older adults[END_REF]. Given that SPA index stereotype internalization, one may wonder whether the same results could be observed with regard to the stereotype endorsement-vitality relationship. However, given that we did not measure the same constructs as in Sargent-Cox et al.'s (2012) study, it is not possible to draw conclusions. The next step consists in conducting experiments to better ascertain the direction of this relationship, as well as the mechanisms underlying it, and we hope that other researchers will join us to start investigating this stereotype-related ego depletion hypothesis. Although we cannot infer causality relationships, one strength of this correlational study was to use a rigorous methodology for validity purposes, by using a longitudinal design including relevant covariates, and multilevel modeling.

In addition, the predominance of women is specific to our sample. Given that women may have to face negative sex stereotypes (e.g., women have lower physical and motor abilities than men) in the domain of PA [START_REF] Chalabaev | The strength model of self-control: A meta-analysis[END_REF], it would be interesting to examine whether stereotype endorsement affects subjective vitality similarly among men. Another potential moderator refers to older adults' goal to stay physically active. Although fulfilling such goal may require self-control resources, this may depend on the reasons of engagement. Engaging in self-control behaviors for autonomous reasons may be less depleting than engaging for controlled reasons [START_REF] Muraven | Helpful self-control: Autonomy support, vitality, and depletion[END_REF]. As our sample was characterized by a high degree of autonomous reasons to engage in PA, it would be interesting to compare it with a sample of older adults who engage in PA for controlled reasons. We may expect the latter to exhibit higher levels of ego depletion.

Beyond the question of the mechanisms that underlie stereotype effects, the present study has implications with regard to health more generally. Indeed, subjective vitality is an important predictor of health outcomes, as it is associated with more resilience, less susceptibility to illness [START_REF] Benyamini | Positive affect and function as influences on self-assessments of health expanding our view beyond illness and disability[END_REF], and higher mental health [START_REF] Ryan | On energy, personality, and health: Subjective vitality as a dynamic reflection of well--being[END_REF]. Our results were in line with this literature, as they showed significant correlations between vitality and self-rated health. It is therefore crucial to better understand the health consequences of aging stereotypes endorsement through subjective vitality on the long term.

Moreover, future research should examine whether decreased vitality is associated with selfcontrol failures, which may be reflected in decreased adherence to an exercise program.

Finally, results indicated that aging stereotypes differentially affected subjective vitality depending on their specific content. For example, time-varying endorsement of selfefficacy stereotypes positively predicted subjective vitality, but not time-varying endorsement of outcomes stereotypes. These results may be due to different relations between these stereotypes and intention to be physically active. Indeed, it seems that self-efficacy is a better correlate of older adults' PA intention than outcomes expectancies [START_REF] Caudroit | Social cognitive determinants of physical activity among retired older individuals: An application of the health action process approach[END_REF]. It is therefore possible that the less participants believed in older adults' selfefficacy to be physically active, the less they intended to continue being physically active, increasing in turn ego depletion. Future research should be conducted to better understand the different implications of specific stereotypes. influence of sex stereotypes and gender roles on participation and performance in sport and exercise: Review and future directions. Psychology of Sport andExercise, 14, 136-144. doi: 10.106/j.psychsport.2012.10.005. Deci, E. L., &Ryan, R. M. (2000). The" what" and" why" of goal pursuits: Human needs and the self-determination of behavior. Psychological Inquiry,11,.1207/S15327965PLI1104_01. Emile, M., Chalabaev, A., Stephan, Y., Corrion, K., & d'Arripe-Longueville, F. (2013). Aging stereotypes and active lifestyle: Personal correlates of stereotype internalization and relationships with level of physical activity among older adults. Psychology of Sport and Exercise, 15, 198-204. doi: 10.1016/j.psychsport.2013.11.002. Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121-138. doi: 10.1037/1082-989X.12.2.121. Fox, K. H., & Corbin, C. B. (1989). The physical self-perception profile: Development and preliminary validation. Journal of Sport & Exercise Psychology, 11, 408-430. Gourlan, M., Sarrazin, P., & Trouilloud, D. (2013). Motivational interviewing as a way to promote physical activity in obese adolescents: A randomised-controlled trial using self-determination theory as an explanatory framework. Psychology & Health, 28, 1265-1286. doi: 10.1080/08870446.2013.800518 Guiraud, T., Granger, R., Bousquet, M., & Gremeaux, V. (2012). Validity of a questionnaire to assess the physical activity level in coronary artery disease patients. International Journal of Rehabilitation Research, 35, 270-274. doi: 10.1097/MRR.0b013e3283531023. Hagger, M. S., Wood, C., Stiff, C., & Chatzisarantis, N. L. (2010). Ego depletion and the

  efficacy stereotype it + β 3 PA benefits stereotype it + β 4 PA risks stereotype it + β 5 SPA it + β 6 autonomous motivation it + β 7 controlled motivation it + β 8 physical self-worth it + β 9 perceived loneliness it + β 10 self-rated health it + β 11 level of general PA it + e it.

Acknowledgments

This study was supported by a PhD grant from the Provence-Alpes Cote d'Azur Regional Council. We are grateful to people who have contributed to this research, and notably to the executive staff and employees of the older adults' Cannes Bel Age club.

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