Agnese Del Zozzo
email: adelzozzo@unibz.it

George Santi
email: gesanti@unibz.it

Physical and virtual classroom in the learning of mathematics: analysis of two episodes

Keywords: Virtual classrooms, didactical contract, Chevallard's triangle

Purpose of the study.

The aim of this study is to investigate how a virtual classroom can foster the physical classroom activities in order to create a new learning environment that enhances peer education. The introduction of a virtual space, in addition to the physical one, offers new forms of social interaction that could allow students to overcome their difficulties. This space is available beyond the school time shared in the physical classroom and gives students the opportunity to design it according to their needs, cognitive styles and social practices. Analyzing two episodes, we propose a tentative framework to design an effective implementation of a virtual classroom in the physical classroom.

Introduction.

In a secondary school of Bologna (Italy) where several teachers of different subjects used the G Suite for Education, some mathematics teachers started using Google Classroom (GC). The following two episodes involved two classes with different mathematics teachers. All the students were acquainted with the basic functions of GC. The first episode happened in a 10th grade class where the teacher proposed GC as a daily tool used by the students to share their questions and doubts with the teacher and the rest of the class. This episode regards the spontaneous behavior of a student who supports her classmates in the solution of an exercise. She shared on the GC Stream a photo of her notebook (with the solution in pen and some additional comments in pencil) supported by the comment "I was able to get the right answer. If you want, you can have a look. I added in pencil the passages that I skipped so that you can better understand them". This spontaneous behavior of the student inspired a further study for a deeper analysis of the potentiality of virtual classrooms in addition to the physical one.

The second episode regards an experiment carried out with a mathematics teacher available to introduce, for our research, GC in a 12th grade class for a limited period. The teacher proposed GC as a social environment where the students could share their ideas and support each other to overcome their difficulties. An item of a multiple-choice test carried out in the physical classroom highlighted students' difficulties in dealing with the domain of logarithmic functions. The teacher decided to trigger the students' social interaction in the GC to find the correct answer. Therefore, the teacher assigned the same multiple-choice exercise asking the students to answer and compare the results on the Stream. Students posted in the GC Stream only the letter (A, B, C or D) of their answer without discussing the inconsistencies of their results. The students, in the next lesson, admitted that they actually had a debate but on their WhatsApp group avoiding the use of the GC.

After this episode, the teacher decided to use GC only to assign homework and to communicate with the students.

Theoretical framework, research questions and methodology.

This study suggests that the introduction of a virtual classroom requires a didactical design that takes into account the relation between the vertices of Chevallard's Triangle [START_REF] Chevallard | Un exemple d'analyse de la transposition didactique: la notion de distance[END_REF]: teacher, pupil, and knowledge. From the two episodes, it emerges that the characteristics of the side pupil-teacher determines the students' interaction with the virtual classroom. In the first episode, the students did not perceive any imposition on the part of the teacher. They felt free to use the virtual space spontaneously. Instead, in the second episode the teacher explicitly invited the students to work on a specific task. We believe that an appropriate theoretical framework for an effective introduction of a virtual classroom is [START_REF] Brousseau | The theory of didactical situations in mathematics[END_REF] Theory of Didactical Situations. In fact, the first episode can be interpreted as a non-didactical situation where there is not a specific teaching design. Although the students used the GC as a peer education environment, there was no evolution after the episode we described. The second episode can be interpreted as a didactical situation that constrained the students in the clauses and effects of the didactical contract (D'Amore, Fandiño [START_REF] D'amore | El contracto didáctico en educatión matemática[END_REF]. The teacher had an explicit objective that she declared to her students and the potential of the virtual classroom seemed to be absorbed by the dynamics of Brousseau's Didactical Contract. The students, in the GC Stream, strictly attended the teacher's requests. The inconsistencies of the students' answers emerged on the GC Stream and triggered the expected social interaction but the discussion among students took place on the WhatsApp students' group. This kind of virtual group cannot be considered a true virtual classroom because it discards the teacher from Chevallard's triangle. The introduction of a virtual environment requires the presence of all the actors of Chevallard's triangle. The teaching design should realize an a-didactical situation that fosters personal implication on the part of the students and the breach of the didactical contract. Within this framework, the research questions that inform further studies are: how can we design an a-didactical situation in an enlarged learning environment that includes a virtual classroom entangled with the physical one? How do we manage this new variable, the virtual classroom, when designing an a-didactical situation? Within an effective interaction between the physical classroom and the virtual classroom, what artifacts and Semiotic Means of Objectification could emerge [START_REF] Radford | The ethics of being and knowing: Towards a cultural theory of learning[END_REF]?


Ana Donevska-Todorova

Katja Eilerts
email: eilertsk@hu-berlin.de

Design of a multi-dimensional instrument for reviewing the quality of apps for elementary geometry

Keywords: mathematics education, geometry, quality, technology, design

come

Design of a multi-dimensional instrument for reviewing the quality of apps for elementary geometry

Ana Donevska-Todorova, Katja Eilerts

Current state of research and theoretical framework

In contrary to the high speed of technological expansion, the research on didactical quality of technology-supported materials for school mathematics seems to have been less rapid in the last two decades. The current approaches for its evaluation are various but not extensive enough which grounds an intensive ongoing debate in the TWG 16 of the upcoming ERME congress. On the one hand, a conventional approach is the usage of criteria catalogues or checklist. On the other hand, researchers argue against their usage due to different reasons, e.g., their inconsideration of socioconstructivist view of learning [START_REF] Squires | Predicting quality in educational software[END_REF] or their tangible usage which is exposed to many factors that cannot be controlled [START_REF] Krawehl | Entwicklung eines Evaluationsinstruments zur fachdidaktischen Bewertung von Unterrichtssoftware für das Grundschulalter[END_REF], e.g., the dynamic feature of the online market changing on a daily basis. Moreover, the usefulness and effectiveness of technological tools may depend on the settings, context and instructional goals, what make it difficult to follow a straight-on checking list for their quality estimation. An undertaken analysis of geometry apps regarding pedagogical, mathematical and cognitive fidelity has shown that the majority of them had limited potential to support students in developing geometrical conceptual understanding [START_REF] Larkin | Geometry and iPads in Primary Schools: Does Their Usefulness Extend Beyond Tracing an Oblong?[END_REF]. It has emphasized the importance of further reviews and this is relevant not only in Australian context but in other contexts such as the German one. Another study has shown that the majority of existing apps are created for pre-and elementary schoolchildren but are not aligned to the content standards of the targeted audience [START_REF] Powell | Choosing iPad apps with a purpose: Aligning skills and standards[END_REF]. Therefore, this study focuses on a comprehensive approach for identifying essential potentials and limitations of apps along with analogue media that considers multimedia learning [START_REF] Mayer | Introduction[END_REF] in addition to educational standards and curricula for mathematics (e.g. in Berlin-Brandenburg schools) referring to content-related-and process-oriented competences as coherent, rather than distant proficiencies.

Research question and methodology

How can the quality of technology-enhanced resources for supporting the development of students' competences regarding "Space and shape" be analysed through a comprehensive approach, is the question to be tackled in the study.

The poster shows a multi-dimensional evaluation instrument (EI) that is a specific part of a comprehensive multidisciplinary and dynamic evaluation model, developed through a researchbased design involving qualitative approaches. The EI includes mathematics, didactics and media facets in an appropriate incorporation. A systematical peers-and experts review about its objectiveness, validation, and importance of its criteria items has taken place. Collected feedback was used for adaptation and re-design of the EI, and pilot trials as different phases of the design cycle.

Results and their implications in practice and research

The review criteria in the created EI are grounded on a national framework about excellence of learning environments. Hence, the development of the EI resulted with review criteria structured in six dimensions: (1) mathematical and didactical significance, (2) articulation, communication and social organization, (3) differentiation, (4) logistic and technical support, (5) assessment and ( 6) networking of resources similarly as the key characteristics of learning environments [START_REF] Wollring | Zur Kennzeichnung von Lernumgebungen für den Mathematikunterricht in der Grundschule[END_REF] and recommendations about implementation of digital media by [START_REF] Krauthausen | Digitale Medien im Mathematikunterricht der Grundschule[END_REF].

The outcomes of the design-research process would be implemented in a teachers' professional development program about elementary geometry. The aim of the designed instrument is to offer teachers a possibility to systemize the overwhelming amount of apps and actively engage themselves in reviewing processes and sharing best-practice instances, which would enable them to think about the benefits and limitations of a meaningful usage of technology in their classrooms.

Other beneficiaries may also be designers who could consider potentials of technology in future redesigns and novel designs. Finally, the study may contribute in further research in mathematics-and media education towards development of a sustainable evaluation model that may have a potential for both national and international scaling up.

Formal presentation of the research work on the poster

Besides information about the theoretical framing, the poster (A0 size) illustrates the research design in a form of a diagram. Exemplary excerpts of the created on-line EI are presented as tables. Previews of selected apps for elementary geometry available in the German language also appear on the poster.


H Seigneuret

Jean-Francois Conjeaud
email: jean-francois.berret@univ-paris-diderot.fr

Berret

M Safi

J Courtois

M Seigneuret

H Conjeaud

J.-F Berret

The effects of aggregation and protein corona on the cellular internalization of iron oxide nanoparticles

Keywords: magnetic nanoparticles, polymer coating, protein corona, flow cytometry, living cells, internalization, endocytic compartment

The effects of aggregation and protein corona on the cellular internalization of iron oxide nanoparticles

I -Introduction

Nanotechnology´s ability to shape matter at the scale of the nanometer has opened the door to new generations of diagnostics, therapeutics, imaging agents and drugs for detecting and treating a number of physiological disorders [START_REF] Ferrari | Cancer nanotechnology: Opportunities and challenges[END_REF][START_REF] Kim | Multifunctional nanostructured materials for multimodal imaging, and simultaneous imaging and therapy[END_REF]. Engineered inorganic nanoparticles (NPs) are one of the key actors of this strategy. NPs are mostly made of metallic or rare-earth atoms with size-related optical or magnetic properties. These objects are promising agents since their sizes approach those of biological entities such as viruses, proteins or DNA [START_REF] Doak | Confounding experimental considerations in nanogenotoxicology[END_REF]. Several issues become however critical when the NPs are used in vivo, including colloidal stability, opsonization by the circulating immunoglobulins, clearance by the immune system and in some cases loss of physical properties. To circumvent these limitations, particles are usually coated with ligands or polymers, or functionalized with peptide sequences [START_REF] Kim | Multifunctional nanostructured materials for multimodal imaging, and simultaneous imaging and therapy[END_REF][START_REF] Gupta | Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications[END_REF]. These coating and functionalization strategies are a prerequisite for an accurate delivery to target cells and organs. Owing to the intrinsic complexity of biological fluids however, these efforts are not always sufficient. On the physico-chemical side, it has been realized recently that the interactions between living cells and NPs depend dramatically on the behavior of the NPs in biological fluids. Two main scenarios have been reported in the recent literature. When dispersed in biological fluids, the NPs can either i) become coated by a corona made of serum proteins and of other biomacromolecules, or ii) aggregate in a kinetically driven process and form clusters of various sizes. In i), with NPs surrounded by proteins, the corona will constitute the primary contact to the cells [START_REF] Mahmoudi | Irreversible changes in protein conformation due to interaction with superparamagnetic iron oxide nanoparticles[END_REF][START_REF] Rocker | A quantitative fluorescence study of protein monolayer formation on colloidal nanoparticles[END_REF][START_REF] Walczyk | What the Cell "Sees" in Bionanoscience[END_REF][START_REF] Casals | Time Evolution of the Nanoparticle Protein Corona[END_REF][START_REF] Jiang | Quantitative analysis of the protein corona on FePt nanoparticles formed by transferrin binding[END_REF][START_REF] Mu | Characterization of Protein Clusters of Diverse Magnetic Nanoparticles and Their Dynamic Interactions with Human Cells[END_REF][START_REF] Sund | Proteomic Characterization of Engineered Nanomaterial-Protein Interactions in Relation to Surface Reactivity[END_REF]. Recent reports described this phenomenon as ubiquitous and independent of the type of nanoparticles investigated [START_REF] Sund | Proteomic Characterization of Engineered Nanomaterial-Protein Interactions in Relation to Surface Reactivity[END_REF]. Organic particles such as carboxylated polystyrene, and inorganic NPs including nanometer-sized FePt, gold and quantum dots were shown to display the corona effect. The kinetics of adsorption and the resilience of the adsorbates on the inorganic cores were also investigated in details [START_REF] Jiang | Quantitative analysis of the protein corona on FePt nanoparticles formed by transferrin binding[END_REF] and revealed both equilibrium and non-equilibrium processes, yielding in some cases irreversible adsorption [START_REF] Rocker | A quantitative fluorescence study of protein monolayer formation on colloidal nanoparticles[END_REF][START_REF] Casals | Time Evolution of the Nanoparticle Protein Corona[END_REF]. In case ii), the NPs destabilize and aggregate into micron-size clusters. The destabilization and clustering of NPs in biological fluids have been reported repeatedly during the last decade and appear as a rather frequent phenomenon [START_REF] Auffan | In Vitro Interactions between DMSA-Coated Maghemite Nanoparticles and Human Fibroblasts: A Physicochemical and Cyto-Genotoxical Study[END_REF][START_REF] Boldt | Comparative Examination of the Stability of Semiconductor Quantum Dots in Various Biochemical Buffers[END_REF][START_REF] Williams | Evaluation of the microbial growth response to inorganic nanoparticles[END_REF][START_REF] Diaz | Assessing Methods for Blood Cell Cytotoxic Responses to Inorganic Nanoparticles and Nanoparticle Aggregates[END_REF][START_REF] Petri-Fink | Effect of cell media on polymer coated superparamagnetic iron oxide nanoparticles (SPIONs): Colloidal stability, cytotoxicity, and cellular uptake studies[END_REF][START_REF] Allouni | Agglomeration and sedimentation of TiO2 nanoparticles in cell culture medium[END_REF][START_REF] Villanueva | The influence of surface functionalization on the enhanced internalization of magnetic nanoparticles in cancer cells[END_REF]. In such conditions, "what the cell will see" is again not inorganic cores but rather large chunks of particles with eventually proteins and other biomacromolecules on the outer surface. The hydrodynamic properties of aggregated nanomaterials, including diffusion, sedimentation and coupling to a flow are also drastically changed with respect to single NPs, and so are the interactions with cells. A wellknown instance is that of sedimentation of micron-size clusters where, due to their own weight NP aggregates enter in contact with the cell membrane of adherent cells [START_REF] Teeguarden | Particokinetics in vitro: Dosimetry considerations for in vitro nanoparticle toxicology assessments (vol 95, pg 300[END_REF][START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF]. Although a general description is still missing, it is believed that the colloidal destabilization of NPs in biological fluids results from the adsorption of biological molecules (as in the protein corona adsorption), but also from the exchange and/or the removal of the protecting adlayer. As a result, the original coating is not sufficient to offset the van der Waals attraction, which leads to aggregation. Destabilization processes depend on many parameters, in particular on the nature and robustness of the coated adlayer [START_REF] Auffan | In Vitro Interactions between DMSA-Coated Maghemite Nanoparticles and Human Fibroblasts: A Physicochemical and Cyto-Genotoxical Study[END_REF][START_REF] Petri-Fink | Effect of cell media on polymer coated superparamagnetic iron oxide nanoparticles (SPIONs): Colloidal stability, cytotoxicity, and cellular uptake studies[END_REF][START_REF] Villanueva | The influence of surface functionalization on the enhanced internalization of magnetic nanoparticles in cancer cells[END_REF][START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF]. In the present paper, we investigate the interactions between anionically charged iron oxide (maghemite, γ-Fe 2 O 3 ) NPs and living mammellian cells. The coating of the magnetic 8.3 nm cores was ensured by low molecular weight ligands (citric acid) and by ion-containing polymers (poly(acrylic acid)), both being carboxylate terminated. In a recent report [START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF], interactions between these NPs and adherent murine fibroblasts were studied, and showed the dramatic effect of the coating on the internalization. From this survey, it was concluded that the strong uptake of the citrate-coated particles was related to the destabilization of the dispersion in the physiological conditions and their sedimentation down to the cell membranes. To avoid the sedimentation bias, we focus here on human lymphoblastoid cells growing in suspension. The particles were first investigated with respect to their stability in biological fluids. The mechanisms of precipitation of the citrate coated particles in the cell culture medium with and without serum were identified at both microscopic and thermodynamic levels. By contrast, the polymer coated NPs were stable in the same conditions and did not display the protein corona effect discussed previously. The interactions between NPs and the human lymphoblastoid cells were also studied by a combination of transmission electron microscopy (TEM) and flow cytometry [START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF][START_REF] Suzuki | Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis[END_REF]. We found that within the first minutes of contact, the citrate-coated NPs are massively adsorbed on the cell membranes and are still there after 24 h of incubation. Only a portion of the adsorbed NPs enter the cytoplasm via membrane-bound endosomal compartments, as revealed by TEM. A quantification of the partition between adsorbed and internalized iron was realized from the cytometry data, highlighting the importance of adsorption in NP/cell interactions. By contrast, the polymer coated NPs interacted only marginally with the cells [START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF][START_REF] Chanteau | Electrosteric Enhanced Stability of Functional Sub-10 nm Cerium and Iron Oxide Particles in Cell Culture Medium[END_REF].

II -Materials and Methods

II.1 -Chemicals, synthesis and characterization

Nanoparticles synthesis : The iron oxide nanoparticles (bulk mass density ρ = 5100 kg m -3 ) were synthesized according to the Massart method [START_REF] Massart | Preparation and properties of monodisperse magnetic fluids[END_REF] by alkaline co-precipitation of iron(II) and iron(III) salts and oxidation of the magnetite (Fe 3 O 4 ) into maghemite (γ-Fe 2 O 3 ). The nanoparticles were then size-sorted by subsequent phase separations [START_REF] Massart | Preparation and properties of monodisperse magnetic fluids[END_REF][START_REF] Bee | Synthesis of very fine maghemite particles[END_REF]. At pH 1.8, the particles were positively charged, with nitrate counterions adsorbed on their surfaces. The resulting particle-particle electrostatic repulsion imparted an excellent colloidal stability of the dispersions, typically over several years. An image of transmission electron microscopy (TEM) obtained from a dilute aqueous dispersion exhibits compact and spherical particles (Fig. 1a). The size distribution of the particles was described by a log-normal function with a median diameter 8.3 nm and polydispersity 0.26 (Fig. 1b). The polydispersity was defined as the ratio between standard deviation and average diameter. The inset in Fig. 1a illustrates the electron microdiffraction scattering obtained for the γ-Fe 2 O 3 particles. The crystallinity of the nanoparticles was demonstrated by the appearance of five diffraction rings which wave vectors matched precisely those of the maghemite structure (Supporting Information SI-1). In contrast to recent investigations [START_REF] Soenen | Intracellular Nanoparticle Coating Stability Determines Nanoparticle Diagnostics Efficacy and Cell Functionality[END_REF], in the pH range 1.8-10 and for different coating and environments probed, the release rate of ferric ions was found to be extremely low (Supporting Information SI-2). In this work, the NP concentration are defined by the percentage by weight of γ-Fe 2 O 3 in the dispersion or by the iron molar concentration [Fe]. With these units, c = 8×10 -2 wt. % corresponds to [Fe] = 10 mM.

Coating : To improve their colloidal stability, different types of coating based on the electrostatic adsorption of an organic adlayer on the particles were developed. The complexation of the surface charges with ligands such as citrate ions was performed during the particle synthesis. It allowed to reverse the surface charge of the particles from cationic at low pH to anionic at high pH, through a ionization of the carboxyl groups. At pH 8, the particles were stabilized by electrostatic interactions mediated by the anionically charged ligands. As a ligand, citrate ions were characterized by adsorption isotherms, i.e. the adsorbed species were in equilibrium with free citrates molecules dispersed in the bulk. For the citrate coated particles (Cit-γ-Fe 2 O 3 ), the structural charge density was ascertained at -2e nm -2 by conductivity [START_REF] Dubois | Structural analogy between aqueous and oily magnetic fluids[END_REF][START_REF] Lucas | Surface Charge Density of Maghemite Nanoparticles:'Äâ Role of Electrostatics in the Proton Exchange[END_REF] and light scattering measurements [START_REF] Berret | Stoichiometry of electrostatic complexes determined by light scattering[END_REF], resulting in average structural charges of -430e. The affinity constant between the citrate ligands and the maghemite surface was derived from the adsorption isotherm and estimated at 1560 M -1 (Supporting Information SI-3). The cationic particles were also coated with M W = 2000 g mol -1 poly(acrylic acid) (PAA 2K ) using the precipitation-redispersion process [START_REF] Berret | Size distribution of superparamagnetic particles determined by magnetic sedimentation[END_REF]. The polymer of polydisperstiy 1.7 was purchased from Sigma Aldrich and used without further purification. To adsorb the PAA 2K chains onto the particle surface, the particles were first precipitated into a dilute solution containing a large excess of polymers (pH 1.8). The precipitate was separated by centrifugation and its pH was increased by addition of ammonium hydroxide. The precipitate redispersed spontaneously at pH 7 -8, yielding a clear solution that contained the individual polymer coated particles, dubbed PAA 2K -γ-Fe 2 O 3 in the following. This process resulted in the adsorption of a highly resilient 3 nm polymer adlayer surrounding the particles. The thickness layer was later determined by dynamical light scattering. The density of chargeable carboxylic groups was evaluated by acid titration at 25 ± 3 nm -2 . For the particles of diameter 8.3 nm, it corresponded to 5400 structural anionic charges in average. As a final step, the dispersions were all dialyzed against DI-water which pH was first adjusted to 8 (Spectra Por 2 dialysis membrane with MWCO 12 kD). At this pH, 90 % of the carboxylate groups of the citrate and PAA 2K coating were ionized.

II.2 -Experimental Methods

Transmission Electron Microscopy (TEM) : Electron microscopy on nanomaterials was carried out on a Jeol-100 CX microscope at the SIARE facility of Université Pierre et Marie Curie (Paris 6). It was utilized for the characterization of the uncoated γ-Fe 2 O 3 particles using magnifications ranging from 10000× to 160000×. An example of TEM image is illustrated in Fig. 1. For TEM experiments on cells, the 2139 lymphoblasts were first seeded onto a 6-well plate and incubated with the citrate and PAA 2K -coated particles during 10 min, 1 h and 24 h. Cells were then fixed with 2.5% glutaraldehyde in 0.1 M sodium cacodylate buffer, at pH 7.4 and room temperature for 2 hours. Fixed cells were washed in 0.2 M PBS. After washing, samples were post-fixed for 1 hour in a 1% osmium-phosphate buffer 0.1 M for 45 min at room temperature in dark conditions. The samples were then dehydrated in reagent-grade ethanol and embedded in an araldite CY212 epoxy resin. 90 nm ultra-thin sections were cut with an ultra-microtome (LEICA, EM UC6), stained with uranyl acetate and lead citrate, and then examined with a TECNAI-12 electron microscope (Philips).

Light scattering : Static and dynamic light scattering were performed on a Brookhaven spectrometer (BI-9000AT autocorrelator, λ = 632.8 nm) for measurements of the scattered intensity I S and of the diffusion constant D dif . In this study, the suspending solvents were 18.2 MΩ de-ionized water, phosphate buffer (PBS) or RPMI cell culture medium with or without fetal calf serum (FCS). The concentrations targeted in the present work were in the dilute regime, and comprised between [Fe] = 0.01 mM and 10 mM, corresponding to 8×10 -5 -8×10 -2 wt. %. Using dynamical light scattering, the collective diffusion coefficient D Diff was determined from the second-order autocorrelation function of the scattered light. From the value of the coefficient, the hydrodynamic diameter of the colloids was calculated according to the Stokes-Einstein relation, D H = k B T/3πη S D Diff , where k B is the Boltzmann constant, T the temperature (T = 298 K) and η 0 the solvent viscosity. The viscosity of the various solvents used in this work were measured as a function of the temperature between 15 and 40 °C (Supporting Information SI-4). The autocorrelation functions were interpreted using the cumulant and the CONTIN fitting procedure provided by the instrument software. In the dilute regime of concentration, the scattering intensity varies as I S scales with the product KM W c, where K is the scattering contrast, M W and c the molecular weight and weight concentration of the scatterers. To evaluate the NP stability in the solvents mentioned previously, the scattering intensity and hydrodynamic diameter were monitored as a function of the time. If the dispersion destabilizes, the particles aggregate and both I S and D H increase due to the augmentation of the size and molecular weight of the elementary scatterers. If the dispersion remains stable, I S and D H are flat and equal their initial values. In some flow cytometry experiments, the suspending medium turned out to be turbid immediately upon addition of iron oxide. The turbidity was interpreted as a destabilization and an aggregation of the NPs. To study the kinetics of aggregation, light scattering experiment was performed using the same protocol as for incubation. A test tube containing 1 ml of the cellular medium (without cells) was placed on the spectrometer and a small volume (~ 10 µL) of a concentrated iron oxide dispersion was poured rapidly in the tube and the sample was homogenized with a pipette. The final NP concentration was [Fe] = 1 mM, corresponding to c = 8×10 -3 wt. %. The scattering intensity I S and the hydrodynamic diameter D H were then monitored as a function of the time for 2 hours after the NP fast injection, a time that was considered to be sufficient to conclude about the NP behavior in the solvent [START_REF] Chanteau | Electrosteric Enhanced Stability of Functional Sub-10 nm Cerium and Iron Oxide Particles in Cell Culture Medium[END_REF].

Human lymphoblastoid cells and culture

Lymphoblast are one of the different stages of physiological differentiation inside the lymphoïd line leading to the lymphocytes. This differentiation stage appears after the activation of the small lymphocytes, inside the lymph nodes by an antigen in the organism. The lymphoblastoid cell line 2139 used in this study is a normal line provided to us by Dr Janet Hall from the Institut Curie (Orsay, France). This cell line was immortalized by the virus Epstein-Barr (EBV) which was obtained by Dr Gilbert Lenoir from the Institut Gustave Roussy (Villejuif, France). These immortalized cells were mostly used as a model or control for different studies in ataxia-telangiectasia-mutated dependent functions like the kinase activity, cell cycle progression and viability [START_REF] Angele | ATM haplotypes and cellular response to DNA damage: Association with breast cancer risk and clinical radiosensitivity[END_REF][START_REF] Gutierrez-Enriquez | Use of the cytokinesis-block micronucleus assay to measure radiation-induced chromosome damage in lymphoblastoid cell lines[END_REF][START_REF] Gutierrez-Enriquez | Functional consequences of ATM sequence variants for chromosomal radiosensitivity[END_REF]. 2139 human lymphoblastoid cells were grown in T25-flasks in RPMI with high glucose (2.0 g L -1 ) and stable glutamine (PAA Laboratories GmbH, Austria). This medium was supplemented with 10% fetal bovine serum (FBS) and 1% penicillin/streptomycin (PAA Laboratories GmbH, Austria), referred to as cell culture medium. Exponentially growing cultures were maintained in a humidified atmosphere of 5% CO 2 and 95% air at 37°C and passaged twice weekly. The cells were pelleted by centrifugation at 1200 rpm for 5 min. Supernatants were removed and cell pellets were resuspended in assay medium and counted using a Malassez counting chamber.

(SS) intensities versus forward scatter (FS) intensities in double logarithmic and in linear scale, respectively. In a), Gate A includes the dead and the living cells. In b), Gate B excludes part of the dead cells. c) Histogram of the red fluorescence intensities of events in gate A (double logarithmic scale). d) Histogram of the side scatter intensities of events in gates A and B and N corresponding to living cells. e) Same as in d) but for the forward scatter intensities. f) Histogram of the side scatter intensities of events in gates A and P for the dead cells.

Flow Cytometry : Forward scatter (FS), side scatters (SS) and propidium iodide (PI) fluorescence of individual cells incubated for various times with nanoparticles were measured on an EPICS 4C flow cytometer (Beckman Coulter). Forward scatter FS and SS intensities (measured at 488 nm) were digitalized on both linear and logarithmic scale (4 decades). Red fluorescence intensities emitted by dead cells (measured at 610 nm) was digitalized on a logarithmic scale. Cellular debris and most of the NP aggregates were eliminated by using a large gate in a FS versus SS cytogram (Figs. 2a and2b, gate A). Dead cells and living cells were identified by their forward scatter and red fluorescence intensities (gates N and P in Fig. 2c). FS and SS histograms (logarithmic scale) of living cells (A and B and N, Figs. 2d and2e) and dead cells (gate A and P, Fig. 2f) were visualized and median values calculated in each experimental condition. Nanoparticles at concentrations ranging from 0.3 to 10 mM of iron were mixed with exponentially growing 2139 cells (10 6 ml -1 ) in complete medium supplemented with 1% HEPES and incubated for various times (indicated in the legends), at 4°C or 37°C, under constant agitation to prevent sedimentation of cells and particle aggregates. Two minutes before cytometric analysis, propidium iodide (10 µM final concentration) was added to the cell suspension.

III -Results and discussion

III.1 -Colloidal stability in physiological media III. 1.1. -Stability of the citrate coated nanoparticles in RPMI Figs. 3a and 3b display the scattering intensity (I S ) and hydrodynamic diameter (D H ) versus time for 5 different solvents, which were PBS1x, RPMI, RPMI containing citrate ions at concentration 1 mM and 10 mM, and DI-water containing calcium nitrate (Ca(NO 3 ) 2 ) and magnesium chloride (MgCl 2 ). The molar concentrations of Ca 2+ and Mg 2+ were identical to those present in the RPMI formulation (Supporting Information SI-5). In PBS1x, the Cit-γ-Fe 2 O 3 NPs are found to be stable, as both the intensity and the diameter remain unchanged. In RPMI by contrast, both I S and D H increase drastically and display characteristic S-shaped curves as a function of the time. Starting at 19 nm, D H reaches rapidly 300 nm after 2 min, and build up to values of about 3 µm. With a progressive addition of citrate ions in RPMI, from 0.1 mM to 10 mM, the initial increase is delayed and it eventually ceases for citrate concentration above 5 mM. The data obtained in the presence of 10 mM of citrates demonstrate that the Cit-γ-Fe 2 O 3 dispersion with an excess of ligands is again stable for more than two hours, a result in good agreement with the literature [START_REF] Wilhelm | Deformation of intracellular endosomes under a magnetic field[END_REF][START_REF] Luciani | Reactivity of the monocyte/macrophage system to superparamagnetic anionic nanoparticles[END_REF]. The rapid aggregation kinetics observed with RPMI, as well as the stabilizing effect of the citrate ligands above 5 mM suggest that in RPMI the ligands desorb from the NP surfaces because they are preferentially complexed by chemical species present in the RPMI formulation. To get a better insight into this mechanism, all compounds present in RPMI at concentrations larger than 50 mg L -1 were tested against the citrate-coated particles. These chemicals are inorganic salts, such as calcium nitrate, magnesium sulfate, sodium chloride etc…, amino acids such as L-alanyl-L-glutamine, L-glutamine, or other components such as D-glucose. The list of these compounds is provided in Supporting Information, Section SI-5. Among this list, only calcium and magnesium ions at concentrations equal or above those of the RPMI formulation gave positive results. Upon addition of Ca 2+ and Mg 2+ ions, the destabilization kinetics exhibits the same S-shaped curve as that of pure RPMI (Fig. 3a). Isothermal titration calorimetry experiments (data not shown) performed by titrating calcium chloride with trisodium citrate ions yielded an affinity constant of 1.5×10 4 M -1 , i.e. 10 times larger than that of citrate for the maghemite surface (Supporting Information SI-3). These findings indicate that the divalent calcium and magnesium cations present in the cell medium are causing the precipitation of Cit-γ-Fe 2 O 3 NPs through a preferential complexation with the ligands.

III.1.2. -Stability of the citrate coated nanoparticles in complete cell culture medium

In a second set of experiments, the role of the serum on the stability of Cit-γ-Fe 2 O 3 NPs in RPMI was outlined. Figs. 3c and3d show the intensities and diameters for three media : RPMI containing 10 vol. % of fetal bovine serum, RPMI with FBS and 10 mM of citrate ions and a cellular medium composed of RPMI and 10 mM citrate that was incubated with lymphoblasts during 24 h. This later medium was considered because we anticipated that the cell released species might be active towards the NP surfaces. In the three cases, a similar behavior is observed : both I S and D H exhibit an initial and rapid increase. D H for instance jumps abruptly from 20 to 40 -50 nm within the first seconds, after which it grows slowly up to 100 nm. After a few hours, the particles sedimented at the bottom of the test tube. Interestingly, this initial jump of 20 -30 nm corresponds to twice the size of the proteins/biological molecules present in the complete culture medium (Supporting Information SI-6). These findings are interpreted as the formation of a protein corona around the particles at short times, and as a destabilization of the dispersion at long times. Here the kinetics is slower than that of Figs. 3a and3b, and does not impart a S-shape profile. From the above results, it can be concluded that in the conditions of the cell cultures with 10 vol.% FBS and at iron concentrations relevant for in vitro [START_REF] Mahmoudi | Irreversible changes in protein conformation due to interaction with superparamagnetic iron oxide nanoparticles[END_REF][START_REF] Auffan | In Vitro Interactions between DMSA-Coated Maghemite Nanoparticles and Human Fibroblasts: A Physicochemical and Cyto-Genotoxical Study[END_REF][START_REF] Petri-Fink | Effect of cell media on polymer coated superparamagnetic iron oxide nanoparticles (SPIONs): Colloidal stability, cytotoxicity, and cellular uptake studies[END_REF][START_REF] Villanueva | The influence of surface functionalization on the enhanced internalization of magnetic nanoparticles in cancer cells[END_REF][START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF][START_REF] Brunner | In vitro cytotoxicity of oxide nanoparticles: Comparison to asbestos, silica, and the effect of particle solubility[END_REF][START_REF] Rad | Quantification of Superparamagenetic Iron Oxide (SPIO)-Labeled Cells Using MRI[END_REF][START_REF] Shaw | Perturbational profiling of nanomaterial biologic activity[END_REF] and in vivo [START_REF] Shaw | Perturbational profiling of nanomaterial biologic activity[END_REF][START_REF] Lutz | One-Pot Synthesis of PEGylated Ultrasmall Iron-Oxide Nanoparticles and Their in Vivo Evaluation as Magnetic Resonance Imaging Contrast Agents[END_REF] assays, Cit-γ-Fe 2 O 3 NPs are colloidally unstable, and precipitate.

III.1.3. -Stability of the PAA 2K coated nanoparticles in complete cell culture medium

In a third experiment, the same iron oxide cores, coated this time with PAA 2K were investigated by light scattering in various conditions. As for the Cit-γ-Fe 2 O 3 , the media were RPMI, RPMI containing 10 vol. % FBS, and a cellular medium composed of RPMI (with or without FBS) that was incubated with the lymphoblasts for 24 h. Fig. 3e displays the intensities versus time after the fast injection of the PAA 2K -γ-Fe 2 O 3 NPs in the media. There, I S and D H (data not shown) remain flat for two hours, indicating that the dispersions are indeed stable. These results confirm those obtained with the same particles and coating using Dulbecco's Modified Eagle's Medium (DMEM) as culture medium [START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF][START_REF] Chanteau | Electrosteric Enhanced Stability of Functional Sub-10 nm Cerium and Iron Oxide Particles in Cell Culture Medium[END_REF]. Light scattering is a very accurate technique which can detect an increase in diameter of a few nanometers [START_REF] Qi | Redispersible hybrid nanopowders: Cerium oxide nanoparticle complexes with phosphonated-PEG oligomers[END_REF]. Fig. 3f shows the first order autocorrelation function g (1) (t) for particles at [Fe] = 25 mM (c γ-Fe2O3 = 2×10 -2 wt. %) in 4 media : PBS1x, RPMI, RPMI with serum and RPMI with serum incubated with the lymphoblasts during 24 h. In the four assays, the autocorrelation functions are found to superimpose, indicating an identical distribution of the NPs sizes. Derived from the second coefficient of the cumulant analysis, these diameters are respectively D H (± 1 nm) = 28.4, 28.6, 27.8 and 28.8 nm with a polydispersity of 0.2. From these data, it can be concluded that PAA 2K coated particles are colloidally stable in RPMI-based culture media on a broad range of concentrations, and are devoid of a protein corona. Because the binding affinity of PAA 2K towards the NP surfaces is high, the polymeric segments are not removed by the modifications of the physico-chemical conditions. As such, the PAA 2K -γ-Fe 2 O 3 should be regarded as a kinetically frozen organic/inorganic hybrid rather than a NP characterized by dynamical and reversible exchanges of its surface ligands. As shown below, the propensity of the particles to remain disperse or to aggregate play a noticeable role on the interactions with living cells.

III.2 -Transmission Electron Microscopy

The lymphoblasts seeded with iron oxide NPs were further investigated by TEM. Figs. 4 and 5 provide representative images from lymphoblastoid cells incubated with Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 , respectively. The experimental conditions were an incubation time of 10 min (Fig. 4c and Fig. 5a) and 24 h (in Fig. 4b, 4d and Fig. 5b) and a NP concentration of 0 mM (control, Fig. 4a), 1 mM (Fig. 4b) and 10 mM (Fig. 4c,4d, 5a and 5b). A careful analysis of the TEM images allows us to identify two distinctive locations for the NPs, either adsorbed at the surface of the cells, or in the cytoplasm in membrane-bound compartments. Among the 100 images of cells collected for this study, NPs were never found in the cytosol nor in the nucleus. Figs. 4c and 4d compare the impact of the incubation time on the uptake of Cit-γ-Fe 2 O 3 at [Fe] = 10 mM. In both images, the adsorbed NPs form an heterogeneous 200 -500 nm thick layer. In the field of view of Fig. 4, the layer surrounds almost entirely the cell. Close-up views of the delimited areas (c1) and (d2) indicate that the NPs are actually aggregated into polydisperse clusters, either directly deposited on the plasma membrane or linked to it through other clusters. At 10 min, the topology of the coated membrane is rough and irregular, whereas it is much smoother at 24 h. The close-view (c1) in Fig. 4 highlights an invagination where the NP-coated membrane has the morphology of a nascent endosome. In the cytoplasm, membrane-bound compartments are also visible and have an average diameter of 500 nm, such as in the close-up views (c1) and (d1). Figs. 4b and4d illustrate the dose effect on the NP/cell interactions and provide a comparison of the data obtained at [Fe] = 1 mM and [Fe] = 10 mM. The same patterns as those discussed previously are observed. NP clusters are adsorbed onto the membrane (b1) or enclosed into endosomal compartments (b2). At 1 mM however, both adsorbed and internalized clusters are less and also smaller than those found at 10 mM, an observation that was later confirmed by light scattering and by flow cytometry. The close-up views (b1) and (b2) reveal an average size in the 100 nm range.

b) Cells incubated for 24 h at [Fe] = 1 mM; b1) and b2) are close views of the delimited areas in b). c) Cells incubated for 10 min at [Fe] = 10 mM; c1) displays a close-up view of the cell surface. d) cells incubated for 24 h at [Fe] = 10 mM; d1) and d2) show NPs enclosed in an endosome and NP clusters adsorbed on the cell membrane, respectively. Bars in a-d) are 2 µm, 200 nm in b2

) and c1), 300 nm in d1) and d2) and 500 nm in b1). Figs. 5a and 5b depict the representative behavior of PAA 2K -γ-Fe 2 O 3 NPs after incubation times of 10 min and 24 h, respectively ([Fe] = 10 mM). In marked contrast with the citrate coated NPs, very few particles can be visualized on these images. The NPs are again located either at the surface (a1) or in endosomes (b1). At the surface, the particles are single or clustered into aggregates of a few units. These clusters have an average size of 50 nm or less. After 24 h of incubation, the NPs are removed from the cell surface and localized in membrane-bound compartments of average size of 250 nm. Within these compartments (b1) the particles are randomly spread and not aggregated, again a noticeable difference with Citγ-Fe 2 O 3 . Put together, these findings lead to the conclusions that although the particles have the same magnetic core and are carrying the same carboxylate groups at their surfaces, the internalization rates and amounts of Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 NPs are very different. Similar results were reported for the NIH/3T3 adherent fibroblasts [START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF].

Figure 6 : a) Side Scatter (SS) intensity of living cells incubated for 4 hours with, or without, Cit-γ-Fe 2 O 3 coated NPs at [Fe] = 10 mM. b) Same as in a) but for the Forward Scatter (FS) intensity. The intensity distributions were fitted by a log-normal distribution function shown in Eq. 1. For the SS distributions, the median values (shown by dotted lines) increased with [Fe] but the polydispersity remained constant. The SS intensity changes due to the adsorption/internalization of NPs by cells were expressed as ratio R SS of the median intensities of cells incubated with NPs over the mean values of control cells. The FS distributions were mostly unchanged upon NPs addition.

III.3 -Flow cytometry

III.3.1 -Comparison between citrate and PAA2K coated particles

In flow cytometry experiments, the forward (FS) and side (SS) scatter intensities generated by the cell illumination are probing the cellular size and refractive index respectively. Figs. 6a and6b show respectively the FS and SS intensities of the 2139 lymphoblastoid cells that were incubated with Cit-γ-Fe 2 O 3 NPs. The experimental conditions were an incubation time of 4 h at 37 °C and a concentration [Fe] = 10 mM. Under these conditions, the SS intensity exhibits a shift from 142 ± 7 in arbitrary units for the control to 806 ± 40 for the incubated cells, whereas the FS signal remains unchanged at 821 ± 41 and 858 ± 43 respectively. This result indicates that the refractive index of the lymphoblastoid cells was enhanced because of their interactions with the NPs, but that their average sizes did not vary noticeably. Similar results were reported on Chinese hamster ovary cells [START_REF] Suzuki | Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis[END_REF] and on human hepatoma cells treated with titanium dioxide and with starch-coated magnetic NPs [START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF]. A quantitative analysis of the cytometry spectra revealed that both SS and FS intensities could be well accounted for by a log-normal distribution :

p(I, I 0 ,s) = 1 2!"(s)I exp # ln 2 (I / I 0 ) 2"(s) 2 $ % & ' ( ) (1)
where I denotes the FS or SS intensities, I 0 their median values and β(s) is related to the polydispersity s via the relationship !(s) = ln(1+ s 2 ) . The polydispersity is defined as the ratio between the standard deviation and the average intensity. For the data collected in this study, the polydispersity s is found to be 0.50 ± 0.05 whatever the incubation time and concentration. As a result, the cytometry data were characterized by a unique parameter, noted R SS . R SS is defined as the median side scatter intensity obtained from the seeded cells, divided by the same quantity obtained from the control cells : As noted in earlier reports [START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF][START_REF] Suzuki | Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis[END_REF][START_REF] Soenen | Intracellular Nanoparticle Coating Stability Determines Nanoparticle Diagnostics Efficacy and Cell Functionality[END_REF], the evolution of the side scatter intensities recorded at 37 °C imparts two interaction mechanisms of the NPs : their adsorption on the plasma membrane and their internalization into endocytic vesicles. The later mechanism is blocked at 4 °C and so the R SS -ratios observed at this temperature reflect only the adsorption of the NPs at the cell surface.

R
Upon addition of NPs at 0.3 mM and 1 mM, the R SS -ratios do not increase significantly. For PAA 2K -γ-Fe 2 O 3 , weak increases are also observed at 3 and 10 mM at the two temperatures (R SS = 1.4 at 10 mM, see Fig. 7d). In contrast, the addition of Cit-γ-Fe 2 O 3 NPs at 3 mM and 10 mM induces strong R SS increases : within the first minutes of contact with NPs (first data point in Fig. 7a and7b), the R SS -ratio jumps to an initial value noted R SS (t Inc ! ") which depends on both concentration and temperature. The initial jump is followed by a saturation (noted R SS (t Inc ! ") ) after 2 hours for all concentrations tested. This initial rise corresponds to about 2/3 and 1/2 of the stationary 4°C and 37°C values. The continuous lines between the data points are exponential growth functions of the form :

R SS (t Inc ) = R SS (t Inc ! 0) + "R SS 1# exp(# t Inc $ ) % & ' ( ) * (2)
where !R SS = R SS (t Inc " #) $ R SS (t Inc " 0) denotes the shift between the initial and stationary states and τ the characteristic time of the kinetics. Note that the ΔR SS 's at 4 °C are weaker than at 37 °C, indicating that during the transient phase the NPs were indeed internalized. For the four profiles, one finds τ = 60 ± 10 min. Note also that for PAA 2K -coated NPs there is no initial jump of the side scatter ratio, i.e. R SS (t Inc ! 0) = 1.

III.3.2 -Effect of dilution

To ensure that SS intensities were not contaminated by particles passing trough the laser beam at the same time as the cells, we compared the intensity distributions obtained from two samples, one for which the cells were incubated with Cit-γ-Fe 2 O 3 (t Inc = 1 h, [Fe] = 10 mM and T = 4 °C) and a second that was diluted five times with RPMI. Working here at 4 °C guarantees that the NPs were not internalized. As shown in Fig. 8, the SS intensities are peaked at 399 ± 20 and 360 ± 18, and have similar R SS (3.27 and 2.95 respectively). This assay demonstrates that the side scatter increases resulted only from interactions of NPs with lymphoblastoid cells, and not from NP aggregates of comparable sizes. Furthermore, the analysis of the same sample at different times after the dilution (30 min, 1 and 2 h, data not shown) reveals no significant change in the intensity distributions, with R SS -values similar to those of the undiluted sample. These findings underline the remarkable stability of the NP/cell interactions. The previous tests were repeated under different t Inc and [Fe] conditions and the results were similar. In conclusion of this part, we infer that Cit-γ-Fe 2 O 3 aggregates heavily adsorb onto the cell surfaces, forming in some cases layers up to 500 nm. The adsorbed are not prone to desorb after 4 h.

III.3.3 -Concentration dependence of the side scatter intensity

As seen in Figs. [START_REF] Walczyk | What the Cell "Sees" in Bionanoscience[END_REF], the stationary values of the side scatter R SS (t Inc ! ") depend on iron oxide dose in a nonlinear manner. For citrate coated particles at 4 °C, i.e. in absence of active internalization processes, it is around 1 at 1 mM and reaches a value of 4 at 10 mM (t Inc = 240 min). A possibility to account for the concentration dependence of the R SS -ratios is to assume that cells interact mostly with aggregates of particles, and that the sizes of these aggregates depend on the concentration. To support this assumption, light scattering was performed on Cit-γ-Fe 2 O 3 NPs dispersed in RPMI at different concentrations between 0.01 and 10 mM. After 4 hours, the hydrodynamic diameters were measured and found to grow from 70 nm at [Fe] = 0.01 mM to 700 nm at [Fe] = 10 mM (Fig. 9). Studied by electrophoresis using Zetasizer Nano ZS Malvern Instrument, the clusters were found to be electrostatically neutral, with a ζ-potential round 0 ± 5 mV. Under physiological conditions, citrate coated particles precipitate and form neutral clusters, which spontaneously adsorb on the cellular membranes when incubated with cells. Fig. 10a shows the quantity R SS -1 as a function of [Fe] for Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 NPs for the dead 2139 lymphoblasts (t Inc = 5 min; T = 4°C). The data points were found to be well fitted by a power law with exponent 0.6 (straight line in Fig. 10a). The figure evidences that the presence of citrate or PAA 2K -coated particles inside permeant cells induces similar increases of their SS intensities, regardless of their state of aggregation. It also indicates that the cellular refractive index is correlated to the total amount of iron present inside the cells, and not to its spatial distribution. Complementary studies discussed in Supporting Information (SI-7) describe a method to measure the amount of internalized and/or adsorbed iron oxide. This protocol was applied to lymphoblastoid cells seeded with PAA 2K -γ-Fe 2 O 3 but not with Cit-γ-Fe 2 O 3 NPs because of the presence in this later sample of large aggregates that could not be separated from the cells (e.g. by magnetophoresis). Here the PAA 2K -γ-Fe 2 O 3 particles serve as a calibration of the mass of internalized iron per cell, M Fe . The inset in Fig. 10b displays the relationship between the internalized mass of iron and the quantity R SS ! 1 for this compound. Using this calibration curve, the R SS (t Inc )-evolutions in Fig. 7 were translated into M Fe (t Inc ). The masses of iron per cell incubated with 10 mM of Cit-γ-Fe 2 O 3 particles at 4 °C and 37 °C are shown in Fig. 11. After 2 min of incubation, M Fe -data exhibit a jump from 0 to 2.8 pg/cell at 4 °C and from 0 to 7.4 pg/cell at 37 °C, showing that adsorption at 37 °C is twice that observed at 4 °C. At both temperatures, the initial jump is followed by a levelling-off and a saturation of the masses after two hours at levels reaching 7.0 pg/cell at 4°C and 21.6 pg/cell at 37°C. All together, these results suggest that at 37 °C, two thirds of the particle interacting with cells (~15 pg/cell at 10 mM Fe) are on the cell surfaces, while one third is internalized (7 pg/cell). These values are in good agreement with those of the literature on similar compounds [START_REF] Luciani | Reactivity of the monocyte/macrophage system to superparamagnetic anionic nanoparticles[END_REF][START_REF] Rad | Measurement of quantity of iron in magnetically labeled cells: comparison among different UV/VIS spectrometric methods[END_REF][START_REF] Zhang | Surface Modiffication of Superparamagnetic Magnetite Nanoparticles and their Intracellular Uptake[END_REF].

V -Conclusion

In the present paper we have established a relationship between the phase behavior of anionically coated iron oxide NPs in biological fluids and their interactions with mammalian cells growing in suspension. Iron oxide NPs coated with negatively charged citrate ligands are found to destabilize in cell culture media and to interact strongly with human lymphoblastoid cells. Particles made from the same magnetic core, but coated with a 3 nm anionic polymer adlayer exhibit much weaker interactions with cells. These findings confirm those obtained with adherent murine fibroblasts and treated with the same particles [START_REF] Safi | Interactions between sub-10-nm iron and cerium oxide nanoparticles and 3T3 fibroblasts: the role of the coating and aggregation state[END_REF]. The destabilization kinetics of Cit-γ-Fe 2 O 3 NPs in biological fluids was monitored by static and dynamic light scattering. The precipitation of the Cit-γ-Fe 2 O 3 NPs in biological fluids without serum is attributed to the displacement of the citrates from the particle surfaces towards the bulk, as they are preferentially complexed by calcium and magnesium counterions of the culture medium. In the presence of 10 vol. % serum, the aggregation is slowed down due to the presence of a protein corona surrounding the particles. Given the rather wide use of citrates for coating engineered NPs (as in the cases of gold [START_REF] Casals | Time Evolution of the Nanoparticle Protein Corona[END_REF][START_REF] Kim | Antibiofouling polymer-coated gold nanoparticles as a contrast agent for in vivo x-ray computed tomography imaging[END_REF] and rare-earth oxide [START_REF] Berret | Stoichiometry of electrostatic complexes determined by light scattering[END_REF][START_REF] Biggs | Effects of Citrate Adsorption on the Interactions between Zirconia Surfaces[END_REF][START_REF] Munnier | Novel method of doxorubicin-SPION reversible association for magnetic drug targeting[END_REF][START_REF] Peyre | Compression and Reswelling of nanometric Zirconia Dispersions : Effect of Surface Complexants[END_REF]), the present results, together with those of the recent literature [START_REF] Kuckelhaus | Biological investigation of a citrate-coated cobalt-ferrite-based magnetic fluid[END_REF][START_REF] Ojea-Jimenez | Instability of Cationic Gold Nanoparticle Bioconjugates: The Role of Citrate Ions[END_REF][START_REF] Maiorano | Effects of Cell Culture Media on the Dynamic Formation of Protein-Nanoparticle Complexes and Influence on the Cellular Response[END_REF] confirm the rather poor coating performances of such low-molecular weight ligands. By contrast, in all biological fluids tested, the polymer coated NPs exhibited a remarkable colloidal stability and an absence of protein corona. The reasons for the outstanding stabilization behavior of polymercoated particles were reviewed recently [START_REF] Ballauff | Polyelectrolyte brushes[END_REF]. Polymers at interfaces form a dense brush which acts as a physical barrier against aggregation, even in complex media. In addition, when the polymers are bearing anionic charges as in the present specimen, the organic layer imparts an additional electrostatic repulsion between the tethered surfaces, resulting in an electrosteric interaction [START_REF] Chanteau | Electrosteric Enhanced Stability of Functional Sub-10 nm Cerium and Iron Oxide Particles in Cell Culture Medium[END_REF].

In this study, we ascertain two types of NP-cell behaviors : NPs are either adsorbed on the cellular membranes, or internalized into membrane-bound endocytic compartments. The visualization of these cytoplasmic compartments was made possible thanks to transmission electron microscopy. In the case of adsorption, the layer of materials deposited on the membranes can grow up to 500 nm and remains unperturbed after 24 h of incubation, pointing out the remarkable stability of the NP/cell interactions. Flow cytometry on treated lymphoblastoid cells displays important shifts of the intensity distribution as compared to control cells. We demonstrate here that this effect was due to an increase in the scattering contrast (and not in the size) of the seeded cells passing through the laser beam. The exploitation of flow cytometry data to evaluate the uptake of NPs in mammalian cells was alluded to by Suzuki et al. [START_REF] Suzuki | Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis[END_REF], and later on confirmed by Xia et al. [START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF]. Our results support this earlier work. Here, the displacements of the intensity distribution are analyzed as a function of the coating, incubation time, dose and temperature. Working both at 4 °C and at 37 °C allowed us to discriminate between the adsorbed and internalized NPs. The kinetics of NP/cell interactions reveal two main features : for the precipitating citrate coated particles, the cytometry signal at 4 °C exhibit a massive and rapid adsorption of iron oxide on the cell surfaces. At this point, it is unclear whether the NPs precipitated directly on the cellular membranes, or if there was first the formation of aggregates and then a deposition of the cells. As anticipated, the polymer coated NPs exhibit a reduced adsorption and/or uptake towards the cells. Extended analysis of the cytometry data emphasizes the possibility to quantify the intensity shifts in terms of internalized and adsorbed amounts, a technique that could find relevant applications in in vitro experimentation.

analyzed using the Langmuir formulation in SI-3. Static viscosity of the all RPMI biological fluids used in this work are provided in SI-4. The composition of cellular medium RPMI 1640 is recalled in SI-5 whereas light scattering properties of cell culture medium yield the size of the biological molecules and proteins present in the medium (SI-6). Details of the protocol for measuring the mass of metal internalized/adsorbed by living cells (MILC) are provided in SI-7. This information is available free of charge via the Internet at http://pubs.acs.org/.

Figure 1

 1 Figure 1 : a) Transmission electron microscopy of iron oxide γ-Fe 2 O 3 at the magnification of ×120000. The bar is 40 nm. Inset : Bragg scattering rings obtained by electron beam microdiffraction and identifying the structure of maghemite (Supporting Information SI-1). b) Size distribution of the γ-Fe 2 O 3 nanoparticles adjusted by a lognormal distribution function (continuous line) with median diameter 8.3 nm and polydispersity 0.26.

Figure 2 :

 2 Figure 2 : Cytometric analysis: a) and b) Dot plots of the side scatter (SS) intensities versus forward scatter (FS) intensities in double logarithmic and in linear scale, respectively. In a), Gate A includes the dead and the living cells. In b), Gate B excludes part of the dead cells. c) Histogram of the red fluorescence intensities of events in gate A (double logarithmic scale). d) Histogram of the side scatter intensities of events in gates A and B and N corresponding to living cells. e) Same as in d) but for the forward scatter intensities. f) Histogram of the side scatter intensities of events in gates A and P for the dead cells.

Figure 3 :

 3 Figure 3 : a) and b) Scattering intensity (I S ) and hydrodynamic diameter (D H ) as a function of the time for Cit-γ-Fe 2 O 3 NPs dispersed in PBS1x, RPMI, RPMI containing citrate ions at concentration 1 mM and 10 mM, and DIwater containing calcium nitrate and magnesium chloride. The S-shaped curves found for I S and D H are the signatures of a rapid destabilization of the dispersion. c) and d) I S and D H versus time for Cit-γ-Fe 2 O 3 NPs dispersed in RPMI containing 10 vol. % of fetal bovine serum, RPMI with FBS and 10 mM of citrate ions and a cellular medium composed of RPMI and 10 mM citrate that was incubated with lymphoblasts during 24 h. The data are interpreted at short times as the formation of a protein corona and at long times later as a destabilization of the dispersion. e) Scattering intensity versus time for the same solvent as in a)for PAA 2K -γ-Fe 2 O 3 NPs. f) First order autocorrelation function g(1) (t) for PAA 2K -γ-Fe 2 O 3 particles at [Fe] = 25 mM in PBS1x, RPMI, RPMI with serum and RPMI with serum incubated with the lymphoblasts during 24 h.

Figure 4 :

 4 Figure 4 : Transmission electron microscopy (TEM) images of lymphoblastoid cells incubated with Cit-γ-Fe 2 O 3 NPs. a) Control. b) Cells incubated for 24 h at [Fe] = 1 mM; b1) and b2) are close views of the delimited areas in b). c) Cells incubated for 10 min at [Fe] = 10 mM; c1) displays a close-up view of the cell surface. d) cells incubated for 24 h at [Fe] = 10 mM; d1) and d2) show NPs enclosed in an endosome and NP clusters adsorbed on the cell membrane, respectively. Bars in a-d) are 2 µm, 200 nm in b2) and c1), 300 nm in d1) and d2) and 500 nm in b1).

Figure 5 :

 5 Figure 5: Transmission electron microscopy (TEM) images of lymphoblastoid cells incubated with PAA 2K -γ-Fe 2 O 3 NPs. a) Cells incubated for 10 min at [Fe] = 10 mM; a1) is a close view of the cell membrane delimited in a). b) Cells incubated for 24 h at [Fe] = 10 mM; b1) displays NPs enclosed in 200 nm endosomes. Bars in a-b) are 2 µm, 400 nm in a1) and 300 nm in b1).

FS= 1 ,

 1 as shown in Fig. 6b. In the sequel of the paper, the R SS - ratios are investigated as a function of the incubation time t Inc and of the iron concentration [Fe].

Figure 7 :

 7 Figure 7 : Transient behaviors of the cellular side scatter intensity (SS) induced upon incubation of human lymphoblastoid cells with Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 NPs. The investigated concentrations are [Fe] = 0 (control), 0.3, 1, 3 and 10 mM at temperatures T = 4° C (a,c) and T = 37° C (b,d). The results are expressed as the ratios R SS between the median SS intensity obtained from seeded cells, divided by the same quantity obtained from the control (Eq. 1).

Fig. 7

 7 Fig. 7 displays the variations of the R SS -ratios with the incubation time at 4 °C (a,c) and 37 °C (b,d) upon addition of citrate (a,b) and of PAA 2K (c,d) coated particles. The data are compared to those of untreated cells. The investigated concentrations were [Fe] = 0.3, 1, 3 and 10 mM.As noted in earlier reports[START_REF] Xia | The Relationship Between Internalization of Magnetic Nanoparticles and Changes of Cellular Optical Scatter Signal[END_REF][START_REF] Suzuki | Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis[END_REF][START_REF] Soenen | Intracellular Nanoparticle Coating Stability Determines Nanoparticle Diagnostics Efficacy and Cell Functionality[END_REF], the evolution of the side scatter intensities recorded at 37 °C imparts two interaction mechanisms of the NPs : their adsorption on the plasma membrane and their internalization into endocytic vesicles. The later mechanism is blocked at 4 °C and so the R SS -ratios observed at this temperature reflect only the adsorption of the NPs at the cell surface.

Figure 8 :

 8 Figure 8 : Side scatter intensity histograms of IP negative cells incubated at 4 °C for 60 minutes with 10 mM Cit-γ-Fe 2 O 3 NPs (full grey), of the same suspension diluted 5 times and incubated 10 min more at 4 °C (red line), and of control cells (grey line). Numbers over the histograms indicated median values of the distributions.

Figure 9 :

 9 Figure 9 : Hydrodynamic diameter (D H ) of Cit-γ-Fe 2 O 3 NPs dispersed in a complete cell culture medium (RPMI + 10 vol. % serum) as a function of the iron concentration [Fe]. The incubation was set to 4 h. The diameters were found to be larger than to that of particles dispersed in PBS1x and to increase with time and concentration

Figure 10 :

 10 Figure 10 : a) Concentration dependence of the quantity R SS -1 measured for dead lymphoblasts incubated with Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 during 5 min at T = 4°C. Dead cells were identified by their red fluorescence linked to the nuclear incorporation of propidium iodide. The straight line shows a power law variation with an exponent of 0.6. b) Same as in Fig. 10a, but for living cells incubated with Cit-γ-Fe 2 O 3 for t Inc = 4 h at T = 37 °C. Together with the scaling proposed in the inset, the straight line of equation R SS ! 1 = 0.2[Fe] 1.2 was later used to translate the side scatter intensities into mass of iron interacting with the cells. Inset : Experimental relationship between the mass of iron internalized and the quantity R SS -1, as obtained from cells seeded with PAA 2K -γ-Fe 2 O 3 .

Fig. 10b illustrates

  Fig.10ashows the quantity R SS -1 as a function of[Fe] for Cit-γ-Fe 2 O 3 and PAA 2K -γ-Fe 2 O 3 NPs for the dead 2139 lymphoblasts (t Inc = 5 min; T = 4°C). The data points were found to be well fitted by a power law with exponent 0.6 (straight line in Fig.10a). The figure evidences that the presence of citrate or PAA 2K -coated particles inside permeant cells induces similar increases of their SS intensities, regardless of their state of aggregation. It also indicates that the cellular refractive index is correlated to the total amount of iron present inside the cells, and not to its spatial distribution. Fig.10billustrates the concentration dependence of the quantity R SS -1 measured for living cells incubated with Cit-γ-Fe 2 O 3 (t Inc = 4 h and T = 37 °C). The figure discloses again a power behavior of the form R SS ! 1 = 0.2[Fe] 1.2 observed over two decades in concentration. Complementary studies discussed in Supporting Information (SI-7) describe a method to measure the amount of internalized and/or adsorbed iron oxide. This protocol was applied to lymphoblastoid cells seeded with PAA 2K -γ-Fe 2 O 3 but not with Cit-γ-Fe 2 O 3 NPs because of the presence in this later sample of large aggregates that could not be separated from the cells (e.g. by magnetophoresis). Here the PAA 2K -γ-Fe 2 O 3 particles serve as a calibration of the mass of internalized iron per cell, M Fe . The inset in Fig.10bdisplays the relationship between the internalized mass of iron and the quantity R SS ! 1 for this compound. Using this

Figure 11 :

 11 Figure 11 : Mass of iron M Fe interacting with the human lymphoblastoid cells as a function of the incubation time. The data are for Cit-γ-Fe 2 O 3 at [Fe] = 10 mM and the continuous lines are from best fits exponential growth laws similar to Eq. 2.

Acknowledgments

We thank Loudjy Chevry, Jérôme Fresnais, Jean-Pierre Henry, Olivier Sandre, Minhao Yan for fruitful discussions. The Laboratoire Physico-chimie des Electrolytes, Colloïdes et Sciences Analytiques (UMR Université Pierre et Marie Curie-CNRS n° 7612) is acknowledged for providing us with the magnetic nanoparticles and with their characteristics. Berengère Abou and Rémy Colin are acknowledged for their support in the light scattering experiments. We thank Mabel San Roman and Alexis Canette from the imaging facility (ImagoSeine) at the Jacques Monod Institute (Paris, France) for their precious help in the transmission electron microscopy studies. This research was supported in part by the Agence Nationale de la Recherche under the contracts BLAN07-3_206866 and ANR-09-NANO-P200-36, by the European Community through the project : "NANO3T-Biofunctionalized Metal and Magnetic Nanoparticles for Targeted Tumor Therapy", project number 214137 (FP7-NMP-2007-SMALL-1) and by the Région Ile-de-France in the DIM framework related to Health, Environnement and Toxicology (SEnT).

Supporting Information

The Supporting Information section shows the full characterization of the iron oxide nanoparticle in terms of size and crystallinity (SI-1). The release amounts and release rates of ferric ion Fe 3+ at neutral and acidic pH for the Massart dispersions used in this work are estimated in SI-2. The adsorption isotherm of citrate ions on γ-Fe 2 O 3 nanoparticles is