Andréa Kurtz-Chalot
email: kurtz-chalot@emse.fr

Jean-Philippe P Klein

Jérémie Pourchez

Delphine Boudard

Valérie Bin

G B Alcantara

Matteo Martini

Michèle Cottier

Valérie Forest

Adsorption at cell surface and cellular uptake of silica nanoparticles with different surface chemical functionalizations: impact on cytotoxicity

Keywords: Silica nanoparticles, macrophages, surface functionalization, uptake, proinflammatory effect, cytotoxicity

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

INTRODUCTION

Because amorphous silica is characterized by chemical stability and inertness independently of pH and temperature, it is used for biomedical applications like dental fillings, gel-catheters, biosensors and bioengineering of bone [START_REF] Auffinger | Drugloaded nanoparticle systems and adult stem cells: a potential marriage for the treatment of malignant glioma?[END_REF][START_REF] Colilla | Recent advances in ceramic implants as drug delivery systems for biomedical applications[END_REF][START_REF] Vallet-Regi | Silica Materials for Medical Applications[END_REF]. Recently amorphous silica has encompassed the emerging field of nanotechnology (as anti-caking agents in food, as nano-abrasive in cosmetics, as reinforcing fillers in rubber…) [START_REF] Napierska | The nanosilica hazard: another variable entity[END_REF]. It is also of particular interest for nanomedicine because of the advantages silane chemistry offers [START_REF] Slowing | Mesoporous silica nanoparticles as controlled release drug delivery and gene transfection carriers[END_REF][START_REF] Mignot | A top-down synthesis route to ultrasmall multifunctional Gd-based silica nanoparticles for theranostic applications[END_REF]. Indeed, the surface of silica nanoparticles can be modified with chemical functional groups like addition of specific antibodies or fluorescent labels for specific drug delivery (targeting of cancer cells) or specific diagnosis (tumor labeling) [START_REF] Chandolu | Treatment of lung cancer using nanoparticle drug delivery systems[END_REF]. As an example dye-doped fluorescent (Cyanine-5) silica nanoparticles (8 nm in diameter), known as "Cornell dots", have been approved in 2011 by the US Food and Drug Administration (FDA) for human stage I molecular imaging of cancer [START_REF] Benezra | Multimodal silica nanoparticles are effective cancertargeted probes in a model of human melanoma[END_REF]. Those confirm the importance of future clinical potentials of silica-based nanoparticles as effective and specific medical tools. However, those objects exhibiting novel and significantly improved physical and chemical properties due to the nanoscale, consequently exhibit a novel biological activity in human body [START_REF] Lidén | The European commission tries to define nanomaterials[END_REF][START_REF] Riehemann | Nanomedicine--challenge and perspectives[END_REF]. This is why current in vivo and in vitro researches are ongoing for a better knowledge of nanoparticles fate and to provide safer uses (Seaton and Donaldson 2012).

Nanoparticles whose size is close to that of cellular components, may interact specifically with cells [START_REF] Huang | Highly efficient cellular labeling of mesoporous nanoparticles in human mesenchymal stem cells: implication for stem cell tracking[END_REF]. They can adhere to the cell membrane or be entirely engulfed by different pathways, especially by macrophage cells due to their phagocytic capacity (Leclerc et al. 2012). In order to better understand these interactions, fluorescent labeled nanoparticles may be used and tracked through the cells. Literature highlights that the uptake of nanoparticles (pathway and rate) strongly depends on cell type [START_REF] Sohaebuddin | Nanomaterial cytotoxicity is composition, size, and cell type dependent[END_REF]) and on the nanoparticle physico-chemical features [START_REF] Musyanovych | Criteria impacting the cellular uptake of nanoparticles: A study emphasizing polymer type and surfactant effects[END_REF][START_REF] Chung | The effect of surface charge on the uptake and biological function of mesoporous silica nanoparticles in 3T3-L1 cells and human mesenchymal stem cells[END_REF][START_REF] Hu | Effect of PEG conformation and particle size on the cellular uptake efficiency of nanoparticles with the HepG2 cells[END_REF]. It is well admitted that these latter may play a role in nanoparticle cytotoxicity [START_REF] Greish | Effect of silica nanoparticles with variable size and surface functionalization on human endothelial cell viability and angiogenic activity[END_REF][START_REF] Yu | Impact of silica nanoparticle design on cellular toxicity and hemolytic activity[END_REF][START_REF] Chung | The effect of surface charge on the uptake and biological function of mesoporous silica nanoparticles in 3T3-L1 cells and human mesenchymal stem cells[END_REF], and several parameters to take into consideration to engineer safer nanoparticles were defined by ISO TS/13014 (2012a) ("safer by design" approach): size, shape, surface functionalization, state of agglomeration and agregation, composition, solubility, dispersibility, specific surface area, density of surface groups and surface chemistry [START_REF] Frohlich | The role of surface charge in cellular uptake and cytotoxicity of medical nanoparticles[END_REF][START_REF] Duffin | Nanoparticles-a thoracic toxicology perspective[END_REF][START_REF] Albanese | The effect of nanoparticle size, shape, and surface chemistry on biological systems[END_REF]. This study will focus on nanoparticle surface functionalization. Greish et al. already demonstrated that surface charge of silica nanoparticles (coated with amine or hydroxyl groups) significantly influenced their biodistribution in mice. But toxicity evaluated by animal weight loss did not seem to be influenced by the surface charge of the nanoparticles [START_REF] Greish | Effect of silica nanoparticles with variable size and surface functionalization on human endothelial cell viability and angiogenic activity[END_REF]. Landsiedel et al. showed that during short-term inhalation of silica particles (coated with amine or PEG) by rats, surface modifications changed the toxicity of the core material in terms of cytokine production in broncho-alveolar lavage fluid (BALF) [START_REF] Landsiedel | Application of short-term inhalation studies to assess the inhalation toxicity of nanomaterials[END_REF]. In a complementary way, in vitro assays are informative on the direct interactions between immune cells and nanoparticles. For example, Nabeshi et al., incubated unmodified or modified (with amine or hydroxyl groups) silica nanoparticles with murine macrophages and revealed that the cell proliferation decreased when cells were incubated with unmodified silica nanoparticles; they concluded that the surface functionalization by both amino and hydroxyl groups decreased their toxicity [START_REF] Nabeshi | Effect of surface properties of silica nanoparticles on their cytotoxicity and cellular distribution in murine macrophages[END_REF]). In the same way, Lankoff et al., showed that, in contrast to unmodified silica nanoparticle, positively charged nanoparticles with aminopropyl/vinyl coating expressed no cytotoxicity on lymphocytes (cell viability, apoptosis/necrosis…) [START_REF] Lankoff | Effect of surface modification of silica nanoparticles on toxicity and cellular uptake by human peripheral blood lymphocytes in vitro[END_REF]. Thus, nanoparticle coating may allow safer nanomedicine and number of studies point out the importance of surface functionalization of nanoparticles on their interaction with cells and biological responses [START_REF] Dausend | Uptake mechanism of oppositely charged fluorescent nanoparticles in HeLa cells[END_REF]El Badawy et al. 2011;[START_REF] Mura | Influence of surface charge on the potential toxicity of PLGA nanoparticles towards Calu-3 cells[END_REF]).

However, one of the particularities of nanoparticles to consider is that they are changing objects.

Their "biological identity" evolves in biological media over time [START_REF] Faunce | Integrated research into the nanoparticleprotein corona: a new focus for safe, sustainable and equitable development of nanomedicines[END_REF][START_REF] Dell'orco | Modeling the time evolution of the nanoparticle-protein corona in a body fluid[END_REF]. Proteins are adsorbed and desorbed from the nanoparticle surface. This so called "corona" becomes the first element of the nanomaterial in contact with the cells. It is difficult to determine precisely, therefore, it is important to characterize again nanoparticles in culture media in terms of surface charge and size (Walkey and Chan 2012).

The aim of the present study was to investigate the relationship between surface functionalization of silica nanoparticles and their cellular uptake and toxicity. For that purpose, three kinds of 50 nm fluorescent (fluorescein isothiocyanate -FITC) silica-based nanoparticles were synthetized at the laboratory scale: 1) sterically stabilized nanoparticles coated with neutral polyethylene glycol (PEG) molecules, 2) positively charged nanoparticles coated with amine groups and 3) negatively charged nanoparticles coated with carboxylic acid groups. Nanoparticles were incubated with murine macrophages as these cells represent the first line of defense against inhaled exogenous elements and are an in vitro reference model in nanotoxicology. Cellular uptake and adsorption at cell membrane was then assessed by fluorimetry and the cellular response was evaluated in terms of cytotoxicity: loss of cell membrane integrity (determined by the Lactate DeHydrogenase (LDH) assay), pro-inflammatory effect (TNF-α production) and oxidative stress (Reactive Oxygen Species (ROS) generation).

MATERIALS AND METHODS

Nanoparticles synthesis

Silica-based nanoparticles, called NP, were prepared according to a previous method developed by [START_REF] Martini | How Gold Particles Suppress Concentration Quenching of Fluorophores Encapsulated in Silica Beads[END_REF]). The fluorescence of FITC was increased by the gold core by Förster resonance energy homo-transfer (homo-FRET) non radiative.

Five kinds of nanoparticles were produced and referred according to charges profile of their surface chemical groups. Sterically stabilized were referred to as NP(0), positively charge stabilized nanoparticles were coated with a variable amount of amine groups: NP(++) and NP(+), negatively charge stabilized nanoparticles with a variable amount of carboxylic acid groups: NP(--) and NP(-).

The water/oil (W/O) microemulsion procedure was considered the best way to produce homogeneous and reproducible core-shell samples for systematic biological assays. Indeed, each reverse micelle (aqueous droplets sized ∼10 nm) acts as template for the controlled-growth of core-shell structures. Quaternary W/O microemulsions were prepared by mixing Triton X-100 (surfactant), n-hexanol (co-surfactant) and cyclohexane (oil), followed by sequential additions of specific polar-like precursors. An inclusion of gold clusters at the center of each particle was obtained by the reduction of gold salt in presence of ligands and NaBH 4 . The formation of polysiloxane matrix arised from the base-catalyzed hydrolysis and condensation of two silica precursors: 92 %w TEOS (tetraethoxysilane) and 8 %w dye conjugated-APTES ((3aminopropyl)triethoxysilane). APTES conjugates ensured a covalent bonding of dyes (Fluorescein molecules FITC) and their random distribution within nanoparticles. The colloidal stabilization was then achieved by the final addition of specific silane precursors that leads the specific surface charge for further biological assays (Table 1). In order to obtain an average number of negative charge per surface unit equal to 2/nm² (NP(--)), a controlled amount of 3-(Triethoxysilyl)propylsuccinic anhydride (Si-COOH) has been added, whereas for the positive charged nanoparticles (NP(++)), N-(2-Aminoethyl)-3-aminopropylmethyldimethoxysilane was chosen as precursor.

Neutral particles, NP(0), exhibit 1/nm² N-(3-Triethoxysilylpropyl)gluconamide molecules as well as 1/nm² mPEG-silane 2kDa at their surface, giving an additional steric contribution to the colloidal stability. Thereafter, all solvents were eliminated by the addition of acetone followed by several cycles of vortexing and centrifuging. Unreacted dyes and precursors were removed by ultrafiltration using 300 kDa PES membranes (with a purification rate higher than 108). Particles were dispersed in aqueous solution (2g/L) and stored at 4˚C.

Physico-chemical characterization of nanoparticles

The detailed structural and morphological characterization of the samples was carried out by Scanning Electron Microscopy (SEM) using an ESEM XL30-FEI microscope equipped with a thermal field emission gun (FEG) and Transmission Electron Microscopy (TEM) using a Philips

Cells/nanoparticles contacts

For cell morphology analysis, RAW 264.7 cells were seeded in a 12-well plate (1 million cells per well) and were allowed to attach for 4h. Cells were incubated with 50 or 300 µg/ml of nanoparticles suspension for 20h. Cells were harvested and 100µl of cell suspension were used to prepare cytospin after cytocentrifugation (cytospin IV Shandon, Thermo electric, France). Cells were stained by May-Grünwald Giemsa method and observed under camera microscope (NISelements, Nikon, France). A semi-quantitative analysis was conducted after the observation of 100 cells in order to determine the amount of activated macrophages.

Because in vitro experimental researches are not normalized in term of nanoparticles dose [START_REF] Bhattacharjee | Role of surface charge and oxidative stress in cytotoxicity of organic monolayer-coated silicon nanoparticles towards macrophage NR8383 cells[END_REF][START_REF] Yu | Impact of silica nanoparticle design on cellular toxicity and hemolytic activity[END_REF][START_REF] Deloid | Estimating the effective density of engineered nanomaterials for in vitro dosimetry[END_REF]) and a significant cell response is needed to compare the effects of the differently designed nanoparticles, the dose range was chosen after a preliminary study on a logarithmic scale as 5, 50 and 300 µg/ml.

For cellular uptake and cytotoxicity assays, macrophages were seeded in 96-well plates (100 000 cells in 200µl of medium per well) and were allowed to adhere for 4 h. Nanoparticles were diluted in cell culture medium to reach the following final concentrations: 5, 50, and 300 µg NP/ml. Nanoparticles were added to cells and incubation lasted 20h.

Cellular uptake assessment

Nanoparticle uptake was quantified using a fluorometer (Fluoroskan Ascent, Thermolabsystems, France). FITC labeled nanoparticles have an excitation peak at 485 nm and an emission peak at 538 nm (green fluorescence) with a large spectrum. Total nanoparticles fluorescence was measured at each dose in order to obtain a calibration curve. Then the fluorescence of nanoparticles in supernatant, adsorbed to cell membrane and internalized by cells were discriminated by a "trypan blue quenching" (TB) method previously developed by Leclerc et al.

from flow cytometry techniques [START_REF] Van Amersfoort | Evaluation of a flow cytometric fluorescence quenching assay of phagocytosis of sensitized sheep erythrocytes by polymorphonuclear leukocytes[END_REF][START_REF] Nuutila | Flow cytometric quantitative determination of ingestion by phagocytes needs the distinguishing of overlapping populations of binding and ingesting cells[END_REF][START_REF] Leclerc | Quantification of microsized fluorescent particles phagocytosis to a better knowledge of toxicity mechanisms[END_REF]). In addition to its principal function as an exclusion dye of dead cells, TB is known for its ability to "turn off" the green fluorescence emitted by FITC labeled particles outside the cells (Leclerc et al. 2012). This process allowed us to distinguish internalized nanoparticles from those just adhering to the plasma membrane [START_REF] Gratton | The effect of particle design on cellular internalization pathways[END_REF]. After 20 hours of contact between nanoparticles and macrophages, the fluorescence of nanoparticles remained in cell supernatant was measured as well as the fluorescence of nanoparticles adsorbed at the cell surface and the fluorescence of the nanoparticles uptaken by cells. For each condition, nanoparticles fluorescence was measured independently. Control wells without nanoparticles were used to assess the autofluorescence of cells in culture medium.

Cellular uptake of nanoparticles was also observed using transmission electron microscopy (TEM). TEM images were obtained using a JEOL 2010F FEG microscope at a 200 kV accelerating voltage. Samples were prepared by dropping sample suspension on a carbon-coated holey film supported on a 3 mm mesh copper grid.

Cytotoxicity assays

Membrane integrity

The release in the cell culture supernatant of the cytoplasmic lactate dehydrogenase (LDH) from cells with damaged membranes was assessed using the CytoTox-96™ Homogeneous Membrane Integrity Assay (Promega, Charbonnières les bains, France) according to the manufacturer's instructions. The optical density of the samples was determined using a microplate reader (Multiskan RC; Thermolabsystems, Helsinki, Finland) set to 450 nm. The activity of the released LDH was reported to that of total cellular LDH (measured after control cells lysis) and was expressed as a percent of the control lysed cells. Each experiment was repeated independently three times for each sample.

As nanoparticles could potentially interfere with the different kit reagents, it was verified that there was no artifact in the measure. To that purpose, nanoparticles were incubated with cells for 20h and the LDH assay was performed. Then the samples were lyzed and the LDH assay was carried out again. No significant difference was detected between lysed cells incubated with or without nanoparticles, showing the reliability of the assay.

Pro-inflammatory effect

After incubation with nanoparticles, the production of TNF-α was assessed in the supernatant using a commercial ELISA Kit (Quantikine® Mouse TNF-α Immunoassay; R&D Systems, Lille, France) according to the manufacturer's instructions. The optical density of each sample was determined using a microplate reader (Multiskan RC; Thermolabsystems, Helsinki, Finland) set to 450 nm. A standard curve was established, and results were expressed in picograms per milliliter of TNF-α. Each experiment was repeated independently three times for each sample and included controls: cells alone (negative control) and DQ12 quartz (toxicological positive control) [START_REF] Bruch | Variation of biological responses to different respirable quartz flours determined by a vector model[END_REF][START_REF] Fubini | Relationship between the state of the surface of four commercial quartz flours and their biological activity in vitro and in vivo[END_REF].

In order to verify the absence of any artifact caused by the presence of the nanoparticles, the concentration of a standard solution of TNF-α was assessed with the ELISA test (in cell free conditions). Particles were then added to this solution and the TNF- concentration was assessed again. No significant difference in TNF- concentration was observed between the sample with and the sample without nanoparticles indicating that no artifacts occurred in the assessment due to the nanoparticles.

Oxidative stress

A large array of reactive oxygen species (ROS) activity can be assessed with the OxiSelect™ ROS Assay Kit (Euromedex, Mundolsheim, France). The assay uses the conversion of a nonfluorescent substrate, 2.7′-dichlorodihydrofluorescein diacetate that can easily diffuse through cell membranes and be converted into a fluorogenic molecule 2′.7′-dichlorodihydrofluorescein (DCF) in presence of ROS and which fluorescence is proportional to total ROS level. DCF production was detected using a Fluoroskan Ascent fluorometer (Thermolabsystems) using excitation and emission wavelengths of 480 and 530 nm respectively, and the generation of ROS was expressed as nanomolar. Each experiment was repeated independently three times for each sample.

In order to verify that no artifact was induced by the nanoparticles, a standard solution of DCFHDA was assessed either in presence or in absence of nanoparticles. No significant difference was detected between the samples indicating that no artifacts were involved.

Statistical analysis

Analysis and graphics were performed on Prism 5.0 software (GraphPad, San Diego, CA).

Significance was established with two-way-ANOVA test (compared to negative control: cells alone) or one-way-ANOVA (compared to each other) and data considered significant with p < 0.05 are marked with an asterisk (*) sign. Each data point represents the mean of three independent experiments (n = 3) and is presented with the arithmetic standard error means (± SEM).

RESULTS

Nanoparticles characterization

In Fig. 1, the spherical shape was clearly observed by SEM. The dark gold core and the grey silica shell can easily be observed using TEM. Geometric diameters were measured from electron microscopy. Hydrodynamic diameters and zeta potential were measured using DLS. These data are reported in Table 1.

In water and for each type of nanoparticles, the hydrodynamic diameter was correlated with the geometric diameter, whereas in DMEMc it was significantly increased. Similarly, zeta-potentials of the five kinds of nanoparticles were distinct in water but in DMEMc all zeta-potentials became negative, with the most important decrease of surface charges observed for the nanoparticles exhibiting the highest initial charges: NP(--) and NP(++).

Cellular uptake

Cellular uptake was then quantified using a quantitative assessment by fluorimetry as reported in Fig. 2. The amounts of nanoparticles in supernatant, adsorbed at cell membrane or uptaken were determined. It clearly appeared that nanoparticles mainly remained in the supernatant whatever the surface functionalization. Moreover uptake and adsorption were found to be dose-dependent irrespective of the nanoparticle type.

Therefore, at the same dose, the amount of nanoparticles uptaken and adsorbed at the cell surface was surface charge-dependent: the uptake was more important for the nanoparticles exhibiting negative charges: NP(--),NP(-) or neutral charges NP(0). Almost no uptake was detected for positively charged NP(+) and NP(++). In contrast, a higher adsorption at cell membrane was observed for the positively charged nanoparticles NP(++) and then NP(+).

Cellular uptake was also investigated by TEM. Similar patterns of cellular uptake were observed for the different types of nanoparticles. An illustration is given in Fig. 3 for control cells and cells incubated with 300 µg/ml of NP(0) or NP(++). The observations were in good accordance with the quantitative uptake presented in Fig. 2 except for NP(++). Indeed, no uptake of NP(++) was detected by fluorescence even at the high dose of 300µg/ml while uptake of NP(++) by microscopy was actually observed.

Cytotoxicity

Cell morphology

Fig. 4 shows the global morphology of cells after a 20h contact with NP(0) and the nanoparticles exhibiting the highest charges: NP(--) and NP(++). Two concentrations of nanoparticles were tested: 50 and 300 µg/ml. At low dose, large vacuoles clearly appeared in cytoplasm of cells in contact with NP(++) suggesting the macrophages activation [START_REF] Luzio | Membrane dynamics and the biogenesis of lysosomes[END_REF]. At high dose, the amount of vacuoles was increased in cells incubated with each type of nanoparticles. Similarly, cells with a lysed membrane and condensed nucleus, called "ghost" cells, were clearly identified demonstrating advanced cytotoxicity, especially with NP(++).

Table 2 is a semi-quantification of the cell morphology evolution. It took a high dose of NP(--)

and NP(0) to activate macrophages without inducing a significant mortality (5 and 16% of ghost cells respectively). On the contrary, at low dose NP(++) activated much more macrophages (79%) and provided a high level of mortality at high dose (77% of ghost cells) suggesting that NP(++) were the most cytotoxic nanoparticles.

Membrane integrity

Quantitative results for membrane integrity assay are shown in Fig. 5. The LDH release triggered by NP(-), NP(0) and NP(+) was not significantly different from that of control cells (incubated without nanoparticles). On the opposite, NP(++) were found to be cytotoxic at doses as low as 5 µg/ml and NP(--) became significantly cytotoxic at the highest concentration (300 µg/ml). A dose-dependent effect appeared for those two types of nanoparticles.

TNF-α pro-inflammatory production

Pro-inflammatory effects of the nanoparticles were determined by the TNF-α assay. Results are shown in Fig. 6. Basal level of TNF-α production was increased by the presence of nanoparticles for the five types of nanoparticles only at high doses. The inflammatory effect was dosedependent and nanoparticles biological effect exceeded the positive control DQ12 signal at high doses of 300 µg/ml. NP(++) induced the highest pro-inflammatory signal from doses of 50 µg/ml.

Oxidative stress

No significant oxidative stress was detected when cells were incubated with the different types of nanoparticles. Relative quantification of ROS probe DCF in cells in contact with each kind of nanoparticles was around 45 nM (data not shown) and was not statistically different from 48 nM detected for control cells.

DISCUSSION

This study aimed at understanding the relationship between the surface chemical functionalization of 50 nm silica-based nanoparticles, their toxicity and ability to be uptaken by cells. A series of fluorescent nanoparticles constituted by a polysiloxane-coated gold cluster that encapsulates FITC were prepared by a microemulsion method. SEM analysis confirmed the presence of well-organized film of nanoparticles with spherical shape (Fig. 1(A)). TEM images revealed gold/polysiloxane nanoparticles with an average size of 54 nm and a standard deviation value less than 2 nm (Fig. 1(B)). A thorough physico-chemical characterization of the nanoparticles was carried out in water and in cell culture medium DMEMc by dynamic light scattering instrument. It was observed that the hydrodynamic diameter and the zeta potential of the nanoparticles exhibiting the highest charges (i.e. NP(--) and NP(++)) were the most evolving in DMEMc. Both diameters became superior to 100 nm and zeta potentials decreased to about -95mV due to the buffered culture medium. Those changes between water and culture medium are very likely due to the adsorption of proteins from the culture medium at the nanoparticles surface forming the so-called "corona" [START_REF] Cedervall | Understanding the nanoparticle-protein corona using methods to quantify exchange rates and affinities of proteins for nanoparticles[END_REF]. Therefore, chemical groups initially grafted onto the nanoparticle surface are hidden by proteins and nanoparticle surface charge is rather related to the nature of the adsorbed proteins. Thus, initially positively charged and initially negatively charged nanoparticles may exhibit a similar global negative zeta potential in cell culture medium. Moreover it does not imply an equivalent protein corona [START_REF] Lundqvist | Nanoparticle size and surface properties determine the protein corona with possible implications for biological impacts[END_REF][START_REF] Tenzer | Rapid formation of plasma protein corona critically affects nanoparticle pathophysiology[END_REF]. This difference in protein corona composition may consequently mediate different interactions with cells. And indeed, we observed that initially positively charged nanoparticle were less uptaken than initially negatively charged nanoparticles (Fig. 2).

The initial nanoparticle charge can thus indirectly influence the interactions with cells through the chemical nature of the corona. Qiu et al. showed as well that proteins quickly adsorbed onto gold nanorods of different surfaces and turned the nanoparticles surface charges negatively. When incubated with a human breast adenocarcinoma cell line (MCF-7) it resulted that surface charge of nanoparticles may not directly affect the cellular uptake, but the amount of serum proteins adsorbed on the nanoparticles was positively correlated with the capacity of nanoparticles to enter into cells [START_REF] Qiu | Surface chemistry and aspect ratio mediated cellular uptake of Au nanorods[END_REF].

Hydrodynamic diameter and zeta potential of NP(-) and NP(+) did not evolve much certainly due to a poor density of charged surface groups. Similarly, NP(0) coated with PEG did not significantly vary in the transition from water to DMEMc. This was consistent with literature data as it is admitted that « PEGylation », i.e. the grafting of linear chains of PEG at nanomaterial surface, allows reducing protein adsorption by blocking protein-binding sites and creating a steric hindrance (Walkey et al. 2012).

Nanoparticles were incubated with macrophages and their uptake was assessed before the evaluation of their in vitro toxicity. Concerning the uptake of NP(++), results from TEM and fluorimetry analyses seemed contradictory at first sight. However it should be kept in mind that these two techniques were performed with a different aim and can hardly be directly compared.

Indeed, TEM images were used to verify the presence (or not) of nanoparticles in cells [START_REF] Gratton | The effect of particle design on cellular internalization pathways[END_REF]. They also allowed obtaining information on the subcellular localization of nanoparticles within cells. Indeed, TEM visualization confirmed the cellular uptake of the five kinds of studied nanoparticles with an accurate localization in vacuoles (Fig. 3). However, this method, takes into account only survival cells and was not representative to all cells initially in contact with nanoparticles. Besides, this technique is essentially qualitative and does not permit to rigorously quantify the number of nanoparticles uptaken. Moreover, the preparation of the samples and the technique itself are too heavy to perform enough analyses to get statistically relevant results. On the opposite, fluorimetry was used to obtain quantitative data and to compare the capacity of different types of nanoparticles to be uptaken by cells. Furthermore, this method, combined with the use of the Trypan Blue dye, allows to distinguish FITC fluorescent nanoparticles uptaken from nanoparticles adsorbed [START_REF] Nuutila | Flow cytometric quantitative determination of ingestion by phagocytes needs the distinguishing of overlapping populations of binding and ingesting cells[END_REF] at the cell membrane by quenching the fluorescence of nanoparticles outside cells. Those data were expressed as means of detected fluorescence per cell related to the total amount of previously seeded cells in each well. It should be noted that FITC fluorescence might be altered in endocytosis vesicles because of their high acidity [START_REF] Munkholm | Intramolecular fluorescence selfquenching of fluoresceinamine[END_REF][START_REF] Ohkuma | Fluorescence probe measurement of the intralysosomal pH in living cells and the perturbation of pH by various agents[END_REF]. Thus, the number of nanoparticles per cell could be slightly underestimated but it allowed to compare the ability of each type of nanoparticles to be uptaken by cells.

Interestingly, NP(++) was the kind of nanoparticles the most adsorbed at the cell surface,. Many authors already reported that high adsorption of positive nanoparticles may be related to electrostatic interactions with the negatively charged cell surface [START_REF] Ge | Effect of surface charge and agglomerate degree of magnetic iron oxide nanoparticles on KB cellular uptake in vitro[END_REF]El Badawy et al. 2011). But, as previously mentioned, initially positively charged nanoparticles exhibited a negative zeta potential in cell culture medium due to the formation of a protein corona. This suggests that the assumption of a high adhesion of positive nanoparticles to cell membrane through electrostatic interactions should be revisited in favor of an indirect effect due to the protein corona. These interactions need further investigations to be better understood.

Similarly, it is commonly accepted in the literature that positively charged nanoparticles are more uptaken than other kinds of nanoparticles [START_REF] Chung | The effect of surface charge on the uptake and biological function of mesoporous silica nanoparticles in 3T3-L1 cells and human mesenchymal stem cells[END_REF][START_REF] Yue | Surface charge affects cellular uptake and intracellular trafficking of chitosan-based nanoparticles[END_REF]. For instance Guarnieri et al. reported that (25 to 115 nm) particles surface functionalized with positively charged groups were more uptaken than those functionalized with negatively charged groups [START_REF] Greish | Effect of silica nanoparticles with variable size and surface functionalization on human endothelial cell viability and angiogenic activity[END_REF]. Likewise, Rancan et al. reported that the functionalization of the particle surface with positively charged groups enhanced the in vitro cellular uptake [START_REF] Rancan | Skin Penetration and Cellular Uptake of Amorphous Silica Nanoparticles with Variable Size, Surface Functionalization, and Colloidal Stability[END_REF].

These data appear in contradiction with our results, showing that NP(++) and NP(+) were less uptaken than NP(0) or NP(--) and NP(-). This could be due to a difference of functionalization in group types and density as suggested by Graf et al. Indeed, they discussed that one type of (55 nm) positively charged particle (AHAPS) was easily internalized by macrophages, while another type of positively charged particle (short alkyl chain aminosilanes) was uptaken by cells in a lower amount [START_REF] Graf | Surface functionalization of silica nanoparticles supports colloidal stability in physiological media and facilitates internalization in cells[END_REF].

These studies also established a link between a low uptake and particles aggregation. In particular, Guarnieri et al. demonstrated that the fact that positive nanoparticles were more internalized than negative nanoparticles was contrasted by the tendency of particles to form agglomerates leading to lower internalization efficiency. This could explain our observations. In fact, among the DLS data, size measurements showed several peaks corresponding to different hydrodynamic diameters were represented, which is a characteristic of a polydisperse suspension.

For example, for the sample of NP(0) in DMEMc, peaks of 10 nm, 88 nm and 450 nm in diameter were observed. For each sample, the assumption was made that the peak with the closest value to the nanoparticle geometric diameter (measured on TEM images) corresponded to the nanoparticle population and indicated its hydrodynamic diameter. For example, NP(0) hydrodynamic diameter was determined as being 88 nm (the 10 nm population was certainly debris and the 450 nm population was certainly aggregates of proteins and nanoparticles).

Moreover, the DLS data indicated for each peak a distribution rate, which was assumed to be equivalent to the percentage of monodispersed nanoparticles. This leaded to estimate that 5% of NP(++) were monodispersed against 40 and 30 % for NP(0) and NP(--) respectively. Therefore, NP(++) were less internalized than NP(0) and NP(--) possibly in relation to their agglomeration state.

Discrepancies between our results and that of Guanieri et al. can also be explained by the fact that experiments were carried out using different cell models. This hypothesis is supported by Chung et al. study (Chung et al. 2007) where the surface charge of mesoporous silica nanoparticles varied by the degree of surface modification with N-trimethoxysilylpropyl-N,N,Ntrimethylammonium chloride and their uptake was detected by flow cytometry in different cell lines (3T3-L1 and human mesenchymal stem cells). Results showed that particle uptake by human mesenchymal stem cells can be regulated by a threshold of positive surface charge but also implied that the modulation of surface charge on nanoparticles uptake was specific to cell type.

Nevertheless, those quantitative results may be differently interpreted considering morphological May-Grünwald Giemsa microscopic images (Fig. 4). Taken together, fluorescent uptake quantification and morphology images of cells in contact with NP(++) showed that NP(++) exhibited the lowest uptake and the highest cytotoxicity. Considering those results, two assumptions could be made: (1) A simple contact between nanoparticles and the cell membrane is sufficient to induce the cytotoxicity. In other words, NP(++) do not need to be uptaken to be cytotoxic.

(2) The low amount of internalized NP(++) might not necessarily be related to a lower uptake but could be due to an important release of the nanoparticles outside of the cell in relation to their high cytotoxicity, precluding the detection of previously engulfed nanoparticles and a very important ghost morphology. Consistent with this hypothesis is the fact that NP(++) induced a significant loss of membrane integrity (LDH release) from the lowest doses (5 and 50 µg/ml) and a significant pro-inflammatory effect from low dose (50 µg/ml) while no cytotoxicity is detected for other nanoparticles types. Moreover, this second assumption could explain contradictory results obtained from TEM and fluorimetry analyses for NP(++). As a mater of fact, TEM images mainly showed intracellular nanoparticles in observed cells while fluorimetry quantification method showed very low content of internalized NP(++). If we consider that NP(++) induce a high level of loss of membrane integrity that lead to a high release of NP(++), we deduced that only the few surviving cells and cells containing NP(++) were not representative of the high amount of cells put in contact with nanoparticles. Besides, the relative lower detection limit of the fluorimetry method does not allowed to detect this very low uptake.

20

Results from cytotoxicity assessments also showed that nanoparticles exhibiting a poorly negative or a poorly positive surface charge may exhibit the same cytotoxic profile than neutral nanoparticles. Indeed, NP(0), NP(-) and NP(+) did not show a significant loss of membrane integrity but provided pro-inflammatory effect at high dose (300 µg/ml). No significant oxidative stress was detected which is consistent with a similar study carried out by Panas et al. where the same RAW264.7 macrophages were incubated with engineered silica nanoparticles of 25 nm diameter [START_REF] Panas | Screening of different metal oxide nanoparticles reveals selective toxicity and inflammatory potential of silica nanoparticles in lung epithelial cells and macrophages[END_REF].

Conclusion

The present study clearly demonstrated that surface chemical functionalization plays a key role in the interactions between silica-based nanoparticles and cells with a significant impact on their uptake and biological in vitro toxicity. The highly positively charged nanoparticles were the most adsorbed at cell surface but were negligibly uptaken and triggered more cytotoxicity than other nanoparticles types. The highly negatively charged nanoparticle, were the most uptaken by cells and triggered cytotoxicity only at high dose. Neutrally charged nanoparticles and poorly, positively or negatively, charged nanoparticles expressed the same cytotoxic profile with a proinflammatory effect at high dose. Importantly, our findings suggest that nanoparticles adsorption at the cell membrane seems to play a more important role in cytotoxicity than nanoparticles uptake. Further investigations are needed to better understand how nanoparticle surface charge may impact biological responses in order to provide a "safer by design" approach for the engineering of new nano-objects.

21

  CM200 microscope. The samples were prepared by depositing a drop of diluted colloidal solution onto a carbon grid (200 meshes) and allowing the solvent to evaporate at room temperature. The direct measurement of hydrodynamic size as well as zeta potential was performed by Dynamic Light Scattering (Zetasizer NanoZS, Malvern). The monoexponential correlation function obtained allowed determining the hydrodynamic size, and zeta potential values for nanoparticles dispersed at dose of 100µg/ml in MilliQ water or cell culture medium Dulbecco's modified Eagle's medium (DMEM, Invitrogen, Cergy Pontoise, France) supplemented with 10% of fetal calf serum (Invitrogen) and 1% penicillin-streptomycin (penicillin 10,000 units/ml, streptomycin 10 mg/ml; Sigma-Aldrich, Saint-Quentin Fallavier, France) (DMEMc). Measurements were performed in triplicate at room temperature of 25°C. Refractive index (RI) and viscosity values were applied for water and cell culture medium (1.3 mPa•s viscosity for culture medium and 0.8 mPa•s viscosity for water).Cell cultureRAW 264.7 cell line derived from mice peritoneal macrophages transformed by the Abelson murine leukemia virus and was provided by ATCC Cell Biology Collection (Promochem, LGC, Molsheim, France). Cells were cultured in DMEMc at 37°C and under a 5% carbon dioxide humidified atmosphere.

Fig1Fig3Fig5

  Fig1Images of sterically stabilized silica nanoparticles NP(0) by (A) Scanning electron microscopy and (B) Transmission electron microscopy.

Table 1 -

 1 Characteristics of the nanoparticles used in the present study.

Table 2 -

 2 Evolution of cell morphology after incubation with NP(--), NP(0) and NP(++) at 50 or 300µg/ml: macrophages initially have a normal morphology with homogeneous cytoplasm. Activated macrophages cytoplasm contains vacuoles, and then close to death, cell without defined cytoplasm but a condensed nucleus and a lysed membrane are called "ghost". 100% of control cells exhibit a normal morphology.

	Cell morphology
	evolution depending
		NP(--)	NP(0)	NP(++)
	on type and dose of
	nanoparticles
		86% normal	96% normal	17% normal
	50 µg/ml	9% activated	1% activated	79% activated
		5% ghost	3% ghost	4% ghost
		63% normal	12% normal	4% normal
	300 µg/ml	32% activated	58% activated	19% activated
		5% ghost	16% ghost

ACKNOWLEDGEMENT

The authors would like to acknowledge the financial support of the Région Rhône-Alpes and the Conseil Général de la Loire.


Keywords: Localisation, positionnement, réseau mesh, méthode de sélection, Optimized Link State Routing protocol (OLSR), relais multipoint, enveloppe convexe

Utilisation des relais multipoint pour estimer la position des noeuds dans un réseau sans fil maillé Résumé : Dans ce papier, nous traitons du problème de la localisation dans un réseaux sans fils hétérogène et plus particulièrement de la sélection de noeuds ancre à partir desquels on estime la position. Le protocole de routage OLSR (Optimized Link State Routing protocol) [1] utilise des noeuds spéciaux appelés relais multipoint (MPR Multipoint Relay ) pour diffuser les messages de controle dans le réseau. Nous proposons une approche nouvelle basée sur ces relais multipoint comme noeuds ancre pour estimer la position des noeuds. Nous évaluons sa performance par simulation et comparons celle-ci à d'autres techniques de sélection telles que la sélection de l'enveloppe convexe ou encore l'approche gloutonne.

Introduction

With the tremendous growth in the number of wireless devices over the last decade, many new fields of research have opened up. In such conditions and in such wireless networks, the position of network nodes now represents valuable information. At the same time, being able to maintain network connectivity using network nodes as relays can be very useful to develop new applications.

A node can estimate its position by using a GNSS (Global Navigation Satellite System) like GPS [START_REF] Hofmann-Wellenhof | Global Positioning System : Theory and Practice[END_REF] or Galileo. It gives good position precision but GNSS chips are still costly for low cost wireless devices, and this position estimation method does not work in an indoor environment. A node with no self-location capabilities can estimate its position by several means. Neighbor nodes can be used as "anchors" to estimate its position. To estimate its position, a node can evaluate its distance to the anchors with several methods like the RSSI (Received Signal Strength Indicator) [START_REF] Savarese | Localization in distributed ad-hoc wireless sensor networks[END_REF][START_REF] Beutel | Geolocalisation in a picoradio environment[END_REF], Time of Arrival (TOA) [START_REF] Capkun | Gps-free positioning in mobile ad-hoc networks[END_REF] or by a connectivity approach [START_REF] Doherty | Convex optimization methods for sensor node position estimation[END_REF][START_REF] Guha | Sextant: A unified node and event localization framework using non-convex constraints[END_REF]. But estimating a position in a greedy way (all anchor nodes are used in the position estimation method) is not a good solution. Ermel et al [START_REF] Ermel | Improved position estimation in wireless heterogeneous networks[END_REF] show that with a simple convex hull selection among the anchors, the precision of the estimated position is enhanced by up to 20% for configurations with the same number of anchors.

In addition to node localization, a crucial task in wireless network is to maintain its connectivity. To do so the ad hoc network has to use a routing protocol. Many studies have been carried out on routing protocols for Mobile Ad Hoc Networks (MANETs) especially at the IETF in the working group MANET. Two kinds of routing protocols have been proposed: reactive protocols and proactive protocols. In reactive protocols, the routes are built only upon demand. The source node wishing to obtain a route to a destination floods the network with a request packet. When the destination node receives the request packet it responds to the source node and the path used by the request packet will be the route from the source to the destination node. AODV [START_REF] Perkins | Ad hoc On-demand Distance Vector (AODV) routing[END_REF] and DSR [START_REF] Johnson | The Dynamic Source Routing protocol for mobile ad hoc networks (DSR)[END_REF] are examples of such protocols. On the other hand, proactive protocols maintain the knowledge of the network topology through the exchange of periodic packets. In such protocols the main issue is to reduce the control overhead. When a link state protocol is used, it is important to optimize the broadcast in the network. OLSR and TBRPF [START_REF] Adjih | Optimized link-state routing protocol[END_REF][START_REF] Ogier | Topology dissemination Based on Reverse-Path Forwarding (TBRPF)[END_REF] are examples of such protocols. In this article we intend to show that the genuine optimization of OLSR can be used to estimate a node's position. We present a novel anchor selection method to estimate a position based on OLSR Multipoint Relay (MPR) nodes. This method is based on node connectivity. Details on MPR nodes will be given in Section 3.

The paper is structured as follows. Section 2 presents the assumptions and definitions used in this paper. Section 3 details the MPR nodes selection method. Section 4 presents our simulation results. Section 5 concludes the paper.

Definitions and assumptions

In this paper, we will not use distance measurements as they can be derived, for instance, from signal strength measurements to compute a node's position. A node only exploits its neighboring nodes connectivity to estimate its position; additionally it can know the position of its neighbor nodes. A node will generally use special neighbor nodes called anchors to estimate its position. In this paper we limit our approach to selecting only 1-hop anchors i.e. anchors who are neighboring nodes.

Two types of nodes are considered in a heterogeneous wireless network: Self-Locating Nodes (SLN) which are nodes with self-locating capabilities e.g. nodes with a GPS, and Simple Nodes (SN) which have to estimate their position by other means. SN (simple nodes) estimate their position by a simple centroid formula [START_REF] Adjih | Optimized link-state routing protocol[END_REF], in which all the nodes are given the same weight.

(X est , Y est ) = n i=1 X i n , n i=1 Y i n . (2.1)
When a node selects anchors to compute its position formula (1) computes the centroid only of these anchors.

Let S be a simple node. Let S est be the estimated position of the node S, and S real be the coordinates of its real location. Note that S real information is only used by simulations to evaluate the precision of our algorithm. We can not possess such information in a real world as it represents what we are looking for. Let R max be the maximum theoretical transmission range of S. We define the accuracy of the node position C acc , as a function of the localization error represented by the distance between S real and S est :

C acc = 1 - (S real , S est ) 2 R max (2.2)
By definition, 0 ≤ C acc ≤ 1. Self-locating nodes (SLN) with accurate coordinates have a position accuracy of 1. Conversely, simple nodes (SN), which have to estimate their own position, have a position accuracy of C acc /in[0, 1[.

We also define the theoretical mean number of neighbor nodes N th as:

N th = N A A coverage (2.3) INRIA
where N is the total number of nodes, A is the simulation area and A coverage is the radio coverage area.

Anchor selection methods

The goal of this paper is to enhance the accuracy of an estimated position by selecting anchors that are likely to improve the position estimation process. In this section we detail our MPR node selection method and two other approaches: the greedy and the convex hull methods.

MPR Selection

In Wireless Mesh Networks (WMN), the medium is usually shared thus: when a packet is flooded, the same packet is sent many times to the same receiver. Not only is this a waste of bandwidth but also, since the load of broadcast packets is increased in the network, it may increase the collision rate and the actual packet delivery may then be decreased. The multipoint relay technique is used to reduce the overhead induced by transmitting of broadcast packets. The concept of multipoint relay was first introduced in [START_REF]Broadband Radio Access Networks (BRAN); HIgh PErformance Radio Local Area Network (HIPERLAN) type 1; functional specification[END_REF] for HiPERLAN type 1 and the multipoint relay optimization is the core optimization of OLSR [START_REF] Adjih | Optimized link-state routing protocol[END_REF]. The main idea of the multipoint relay optimization is that only a subset of neighbors has to relay a flooded packet that has been flooded. It can be easily understood that if a conveniently chosen subset of one's neighbor nodes can relay a flooded packet to all one's 2-hop neighbors; then the relay of these nodes will be sufficient to ensure the proper delivery of the packet to the node m's 2-hop neighbors, see Figure 1. This subset of nodes is called the multipoint relay set of node m; of course the smaller the number of nodes in the multipoint relay set, the greater the optimization.

Multipoint relay optimization must be repeated recursively when the packet is flooded. At each hop a flooded packet is relayed by the next hop multipoint relay set. Of course an already transmitted packet is not retransmitted twice; this is controlled by a duplicate table.

The interesting point is that the notion of multipoint relay is deeply embedded in the OLSR protocol. To maintain the knowledge of the network topology OLSR uses two kinds of control. The first kind of packet called "hello" is used to build the neighborhood. The second kind of packet called "TC" is used by each node to disseminate the neighborhood within the network. The two main OLSR functionalities, Neighbor Discovery and Topology Dissemination, are now detailed.

Neighbor Discovery

Each node must detect the neighbor nodes with which it has a direct link. For this, each node periodically broadcasts Hello messages, containing the list of neighbors known to the node and their link status. The link status can be either symmetric (if communication is possible in both directions), asymmetric (if communication is only possible in one direction), multipoint relay (if the link is symmetric and the sender of the Hello message has selected this node as a multipoint relay), or lost (if the link has been lost). The Hello messages are received by all 1-hop neighbors, but are not forwarded. They are broadcasted once per refreshing period called the "HELLO_INTERVAL". Thus, Hello messages enable each node to discover its 1-hop neighbors, as well as its 2-hop neighbors. This neighborhood and 2-hop neighborhood information has an associated holding time, the "NEIGH-BOR_HOLD_TIME", after which it is no longer valid.

On the basis of this information, each node independently selects its own set of multipoint relays among its 1-hop neighbors in such a way that all 2-hop neighbors of m have symmetric links with M P R(m). This means that the multipoint relays cover (in terms of radio range) all 2-hop neighbors (Figure 1). The multipoint relay set is computed whenever a change in the 1-hop or 2-hop neighborhood is detected. In addition, each node m maintains its "MPR selector set". This set contains the nodes which have selected m as a multipoint relay. Node m only forwards broadcast messages received from one of its MPR selectors.

INRIA

It can be noticed that "Hello" messages are ideal to carry a node's position. This information can simply be added at the end of the messages.

Topology Dissemination

Each node of the network maintains topological information about the network obtained by means of TC (Topology control) messages. Each node m selected as a multipoint relay, broadcasts a TC message at least every "TC_INTERVAL". The TC message originated from node m declares the MPR selectors of m. If a change occurs in the MPR selector set, the next TC can be sent earlier. The TC messages are flooded to all nodes in the network and take advantage of MPRs to reduce the number of retransmissions. Thus, a node is reachable either directly or via its MPRs. This topological information collected in each node has an associated holding time "TOP_HOLD_TIME", after which it is no longer valid.

The neighbor information and the topology information are refreshed periodically, and they enable each node to compute the routes to all known destinations. These routes are computed with Dijkstra's shortest path algorithm [START_REF] Bertsekas | Data Networks[END_REF]. Hence, they are optimal as concerns the number of hops. The routing table is computed whenever there is a change in neighborhood or topology information.

OLSR's routes which are optimal in terms of the number of hops are constructed with MPR nodes. Thus, we can intuitively understand that the MPR nodes of a node A will optimally "surround" A and that they are good candidates for being anchors to estimate a position.

The proposed heuristic for MPR selection

Finding the smallest (in term of number of nodes) multipoint relay set has been shown to be NP hard [START_REF] Viennot | Complexity results on election of multipoint relays in wireless networks[END_REF] however efficient heuristics exist. The first proposed heuristic is described in [START_REF] Qayyum | Multipoint relaying technique for flooding broadcast messages in mobile wireless networks[END_REF] and uses a greedy approach. This algorithm can be simply described as follows. Let us consider a given node A and its 2-hop neighbors N 2h ; the 2-hop neighbors of A are the neighbors of A s neighbors who are not already A s neighbors. The algorithm first selects as multipoint relays the neighbors who are the only path to a given 2-hop neighbor. When these nodes are selected the 2-hop neighbors that are reachable through these nodes are removed from the 2-hop neighbors set N 2h . The algorithm then select the neighbor which covers the highest number of 2-hop neighbors in N 2h . In the case of equality between two nodes a simple tie is used. When a node is selected, the 2-hop neighbors of N 2h that are reachable through these nodes are removed from N 2h . The process is carried on until there is no node left within N 2h .

An example of such a selection is presented in Figure 2. Node B is first selected because it is the only path to a 2-hop neighbor. Then nodes D and C which cover four nodes in the two neighborhood are selected. Then node E which covers three nodes in the 2hop neighborhood of A is selected. Node F allows the two remaining nodes in the hops neighborhood of A to be covered.

Greedy and Convex Hull anchor selection methods

To evaluate the performance of our MPR selection method, we will compare its performances to two other approaches: the greedy and the convex hull selection methods.

Greedy approach

No selection is made among the nodes, all neighbor nodes are used in the position estimation process. This approach is called the greedy approach.

INRIA

Convex Hull

The main idea of using a convex hull as a selection method among nodes is to choose only nodes which are at the greatest distance from anchors. In the plane, the convex hull can be visualized as the shape assumed by a rubber band that has been stretched around a set of points and released to conform as closely as possible all neighbor nodes. As the position estimation process is based on trilateration, the further apart the anchors are, the better the accuracy of the estimated position will be, see Figure 3). To solve this geometrical problem, computational geometry algorithms have to be used e.g. Gift Wrapping (Jarvis's March) [START_REF] Chand | An algorithm for convex polytopes[END_REF], [START_REF] Preparata | Convex hulls of finite sets of points in two and three dimensions[END_REF][START_REF] Shamos | Computational geometry[END_REF][START_REF] Preparata | Computational Geometry: An Introduction[END_REF][START_REF] Graham | An efficient algorithm for determining the convex hull of a planar set[END_REF][START_REF] Barber | The quickhull algorithm for convex hulls[END_REF][START_REF] Aurenhammer | Voronoi diagrams -a survey of a fundamental geometric data structure[END_REF]. All these approaches are well detailed in [START_REF] Berg | Computational Geometry, Algoritms and Application[END_REF][START_REF] O'rourke | Computational Geometry in C[END_REF][START_REF] Lemaire | Triangulatation de delaunay et arbres multidimensionnels[END_REF]. We choose the Quick Hull algorithm [START_REF] O'rourke | Computational Geometry in C[END_REF] as our convex hull selection method. In our convex hull selection we de not take into account the position accuracy of the neighbor nodes.

In previous work [START_REF] Ermel | Improved position estimation in wireless heterogeneous networks[END_REF], we introduced the convex hull as a selection method in wireless networks. The resulting position accuracy using a convex hull node selection method is greater than a greedy scheme by up to 20%.

Complexity of the selection methods

Let us denote by n the number of a node's neighbors. To select MPR nodes the main cost consists in finding for each neighbor node the number of 2-hop neighbors for this node. This does not depend only on the number of neighbor nodes n but also on the two hop neighborhood. To get an evaluation only depending on n we will assume that the graph has a degree bounded by n. In such a case it is easy to show that this task can be done in less than n 2 steps. This evaluation corresponds to a worst case. Thus MPR selection is actually upper-bounded by 0(n 2 ). The complexity of the convex hull algorithm is in mean O(nln(n)). Thus from the complexity point of view, the convex hull approach seems better than the MPR method. However the given complexity of the convex hull is given for the mean case while the MPR selection complexity is for the worst case. It can be thought that that the complexity of the two algorithms is actually similar. Moreover in a MANET (Mobile Ad Hoc NETwork) using OLSR as routing protocol, the MPR selection is already made by the routing protocol.

Simulation Results

The Wireless Mesh Network (WMN) comprises 100 nodes randomly located in a square of 1000 m × 1000 m. Self-locating nodes and simple nodes are also randomly elected. The maximum theoretical transmission range R max was set to 170 m. The estimated position is obtained by a simple centroid formula. The simulations were performed under Java.

Position accuracy for a given number of anchors

We compare the accuracy of the three different described selection methods : MPR, convex hull and greedy. The simulation provides the average accuracy of the estimated position for each selection method : MPR, hull and greedy. During the simulation and for a given node we keep track of the number of neighbors with their type: #SLN denotes the number of its self-locating neighbor nodes and #SN denotes the number of its simple neighbor nodes 1 .

By running a large number of simulations, we obtain the average accuracy of the estimated position of this given node for each combination of number of self-locating neighbor nodes and of simple neighbor nodes (#SLN,#SN) for the three selection algorithms. The results of these extensive simulations are given in Figure 5. The relative confidence intervall of average position accuracy is 0.1% with a confidence of 95%. Thus the results shown in Figure 5 are meaningfull and error bars can not be seen.

In Figure 5 the graphs plot in (a),(c),(e) (respectively (b),(d),(f)) the average accuracy of the estimated position as a function of the number of simple nodes (resp. self-locating nodes) in the neighborhood. The number of self-locating nodes (resp. simple nodes) used by the position estimation process is set to 0 for figures (a) and (b). The number of selflocating nodes (resp. simple nodes) used by the position estimation process is set to 2 for figures (c) and (d) and the number of self-locating nodes (resp. simple nodes) used by the position estimation process is set to 4 for figures (e) and (d). As could be expected, we observe that the average position accuracy increases with the number of anchors. We also observe that the average position accuracy is better for a given number of self-locating nodes than for the same given number of simple nodes. The simulation confirms that the more precise the position information retrieved from the neighborhood is, the greater the accuracy of the estimated position.

Figure 5 shows that the selection algorithms significantly increases the position accuracy compared to the greedy approach. The convex hull selection increases the position accuracy by up to 20%, compared to the greedy approach. Figure 5 also shows that in every case, the MPR selection gives a better position accuracy than the convex hull approach, up to 15%. Thus the MPR selection can increase the position accuracy of a node by up to 45% compared to the greedy algorithm.

It can also be noticed in Figure 5 that MPR plots are only provided up to a given number of anchors. This is due to the fact that, in our simulations, a node has got a mean number of N th = 10 neighbors. With such a node density the MPR set generally contains seven or less nodes.

Position accuracy without considering the number of anchors

In Figure 6 we compare the greedy, the hull and the MPR algorithm for a given node in the network, we no longer consider the number of anchors as the parameter to compare the algorithms. We see that except for a very small density the three algorithms offer similar performances. We can even see that when the network nodes have more than 10 neighbors the MPR algorithm offers slightly better performances. This is interesting since this number of neighbors has been shown to be the lower limit above which a Wireless Mesh Network (WMN) is connected, see [START_REF] Blough | The lit k-neigh protocol for symmetric topology control in ad hoc networks[END_REF].

[a] Of course the number of selected anchors in each algorithm is quite different. Figure 7 compares the number of selected nodes for the MPR selection, the convex hull and the greedy algorithm as a function of the mean number of neighbor node N th . For N th = 10 the greedy algorithm selects 1.5 more anchors than the hull algorithm and 4 more anchors than the MPR algorithm. It can be seen from the simulation that most of the MPR set form a subset of the Hull nodes, see Figure 8 for an example given by the simulation. In Figure 9 we show the percentage of inclusion of MPR nodes in the Hull nodes as a function of the node density. For a node density leading to a maximum of 30 neighbors, the percentage of inclusion is above 90%. This result is somewhat surprising since MPR selection considers the connec-tivity metric to elect nodes whereas the convex hull selection only considers the distance. Note however that it is easy to construct examples for which {M P R} ⊂ {Hull} but the probability of such a node configuration is small in a random network.

Conclusion

In this paper, we have presented the use of MPR nodes to estimate the position of nodes in a wireless (mesh) network. Using such a technique the position accuracy, for a given number of anchors, is increased by up to 45% compared to the case where no selection is made (greedy algorithm).

When we compare the greedy, the hull and the MPR algorithms without constraining the number of anchors, we find similar position accuracy while the number of selected anchors is 4 times greater for the greedy algorithm than for the the MPR algorithm and 1.5 times greater than for the hull algorithm. We also show that the MPR nodes set is very often a subset of the convex hull nodes set. If geographical information is needed in an OLSR wireless mesh networks, the genuine OLSR MPR optimization is particularly useful to select anchors to estimate node position while the control OLSR message can be easily used to exchange information on the nodes' positions in the network.

We will focus our future work on determining the interesting uses of geographical information for OLSR networks.

Figure 1 :

 1 Figure 1: Multipoint relays of node m

Figure 2 :

 2 Figure 2: Greedy algorithm for the MPR selection.

Figure 3 :

 3 Figure 3: Convex hull: simple convex hull considers the distance metric to elect hull nodes.

Figure 4 :

 4 Figure 4: Different selections.

Figure 5 :

 5 Figure 5: Impact of the anchor selection method on the average accuracy of the estimated position.

Figure 6 :

 6 Figure 6: Comparison of the algotithm without constraint on the number of anchors.

Figure 7 :

 7 Figure 7: Number of selected nodes versus node density.

Figure 8 :

 8 Figure 8: Random simulation topology case example.

INRIA

  Theoritical number of neighbors nodesPercentage of inclusion of MPR c Hull

Figure 9 :

 9 Figure 9: Percentage of inclusion MPR nodes into Hull nodes.

RR n˚6072

We assume that that these simple neighbor nodes have already an inferred position.INRIA