Claudio Palazzo

Gilles Ponchel

Jean Jacques Vachon

Sarah Villebrun

Florence Agnely

Christine Vauthier
email: christine.vauthier@u-psud.fr

Obtaining non-spherical poly(alkylcyanoacrylate) nanoparticles by the stretching method applied with a marketed water-soluble film

Keywords: stretching, nanoparticles, shape factor, polymer film, poly(isobutylcyanoacrylate)

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Obtaining nonspherical poly(alkylcyanoacrylate) nanoparticles by the stretching method applied with a marketed water-soluble film

Introduction

Encapsulation of drugs in polymeric carriers is a widely investigated strategy aiming to manage stability concerns and/or inadequate biodistribution of unprotected drugs in the body [1]. In the last decades, a step by step accumulation of knowledge have shown that modulation of their physicochemical characteristics, including size and chemical surface composition, could strongly impact the in vivo fate of nanoparticles in the body [2][START_REF] Clogston | Frontiers in nanobiomaterial research Vol 1: Handbook of immunological properties of engineered nanomaterials[END_REF][START_REF] Wang | [END_REF][5]. Conversely, only very few experimental reports have investigated so far the influence of the shape of nanoparticles on their biodistribution [START_REF] Cauchois | Conception, Preparation & Characterization of nanoparticles of complex shapes: Study of their in vivo fate[END_REF] and phagocytosis by cells [START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Barua | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Mathaes | [END_REF][11]. Commonly used nanoparticle preparation methods could only generate sphere-shaped nanoparticles [12-14] while the obtaining of non-spherical shapes polymeric nanoparticles was described more recently [START_REF] Wang | [END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][15][16][17]. First investigations of their in vivo fate have revealed that elongated nanoparticles behaved markedly differently from their corresponding spherical counterparts [6-8,10,18-23]. Thus shape has become a new parameter to consider while designing nanoparticles for drug delivery. However, only few methods of fabrication of nanoparticles with shapes that differ significantly from a sphere have been proposed so far, each with pros and cons. The PRINT method is one of them, which has been initially proposed for the preparation of non-spherical microspheres. Basically, it consists in molding a polymer in a hard material template, followed by a recovery process. In theory, it allows the generation of particles with many different shapes that are defined by the shape of the template [16]. Because of the process it-self, the shape and size characteristics of the population of particle produced are expected to be highly homogeneous. This method was used to produce nanocubes and nanorods. Alternatively, nanoparticles with an elongated shape could be generated by the method of nanoprecipitation which is widely used to produce spherical nanoparticles from polymers [START_REF] Cauchois | Conception, Preparation & Characterization of nanoparticles of complex shapes: Study of their in vivo fate[END_REF]24]. However, it requires the use of specifically conformed polymers, including a few polypeptides, able to self-associate together to form crystalline domains that are believed to give an elongated shape to nanoparticles [24]. Alternatively, elongated nanoparticles were also produced by stretching spherical nanoparticles, which can be previously prepared by a suitable method [START_REF] Wang | [END_REF][START_REF] Cauchois | Conception, Preparation & Characterization of nanoparticles of complex shapes: Study of their in vivo fate[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF]. Although obtaining non spherical nanoparticles by the nanoprecipitation method is reserved to a few types of polymers having the right characteristics as explained above, the application of the stretching method may be suitable to obtain non-spherical nanoparticles made of wide range of polymers. It can be assumed that this method could be used to produce homogeneous series of elongated nanoparticles differing only from their shape as produced from the same parent spherical nanoparticles. The obtaining of consistent series of nanoparticles with different shapes are required to evaluate the influence of the shape factor of the nanoparticles on their in vivo fate to help in the understanding of the effect of the shape of nanoparticles on their interactions with cells and their capacity to go across different biological barriers.

The aim of the present work was to set up experimental conditions to prepare elongated nanoparticles of poly(alkylcyanoacrylate) nanoparticles from parent spherical nanoparticles applying the stretching method. The parent nanoparticles used in the present study were selected for several reasons. They can be prepared with different characteristics in a well-controlled manner by highly reproducible methods of emulsion polymerization [25][26][27][28][29][30]. Their interest to improve in vivo delivery of drug is well documented considering a wide range of drug and therapeutic applications [31][32][33][START_REF] Soma | RSC Drug Discovery Series No. 22: Nanostructured Biomaterials for Overcoming Biological Barriers[END_REF][35][START_REF] Zhou | [END_REF][37][38].

They are one of the very few nanomedicines made of polymer nanoparticles that are considered in an ongoing clinical trial phase II/III [START_REF] Soma | RSC Drug Discovery Series No. 22: Nanostructured Biomaterials for Overcoming Biological Barriers[END_REF][35][START_REF] Zhou | [END_REF]. Additionally, poly(alkylcyanoacrylate) nanoparticles were developed as model nanoparticles to investigate the influence of the size and surface properties on interactions with biological systems and in turn on their in vivo fate [27,[39][40][41][42]. Having the corresponding elongated species of this series would provide with the required model nanoparticles to also investigate the influence of the nanoparticle shape. The chitosan-coated poly(isobutylcyanoacrylate) (PIBCA) nanoparticles were selected to carry on the present work. These nanoparticles were designed as mucoadhesive drug delivery systems to promote oral administration of drugs [28]. They were also tested as an antitumor treatment based on the delivery of siRNA by intravenous injection [37,38,43].

The stretching method was applied to produce elongated micro-and nanoparticles from their spherical parent particles [START_REF] Cauchois | Conception, Preparation & Characterization of nanoparticles of complex shapes: Study of their in vivo fate[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF]11,44]. It can be applied to any type of particles that are made of a material that can be soften at the operating temperature of the stretching machine. Elongated microparticles made of both non-biodegradable and biodegradable polymers have been produced.

In contrast, to the best of our knowledge, the method was only applied with nanoparticles made of non-biodegradable polymers (i.e. polystyrene) [11]. The method was not applied yet to the production of elongated biodegradable particles in the nano-size range. Interestingly, the stretching method can be scaled up to produce large amount of elongated particles thanks to a possible automatization [44]. As described above, the method implies basically: (i) the dispersion of preformed spherical nanoparticles (supposed to eventually contain a drug if any pharmaceutical application are foreseen) into a polymeric material film, followed by the stretching of the nanoparticles containing material at a high temperature (generally above 120°C). At the end of the stretching process, the stretched particles need to be extracted from the polymeric material film [6,7,11]. In the present work, our aim was to set conditions for the application of the method to the elaboration of elongated nanoparticles made of biodegradable polymer. It was also aimed to apply the method at a much lower temperature (50°C) as those used in previous work (>120°C) [START_REF] Cauchois | Conception, Preparation & Characterization of nanoparticles of complex shapes: Study of their in vivo fate[END_REF][START_REF] Champion | Proc. Natl. Acad. Sci. USA[END_REF]11].

Although in previous work, the polymer films in which the nanoparticles were incorporated to be stretched were formulated in home from solution of poly(vinyl alcohol), for this work, we have selected a water soluble and stretchable film available on the market as the material to prepare the film incorporating the spherical nanoparticles to be stretched. The paper reports the different steps of the preparation of the film loaded with nanoparticles from the material of the marketed film and results on the application of the stretching method to prepare elongated nanoparticles of chitosan coated poly(isobutylcyanoacrylate) nanoparticles.

2 Materials and methods

Materials

Chitosan (CS, MW 20 kDa, deacetylation degree 92% was purchased from Amicogen.Inc. (Jinju, South Korea), isobutylcyanoacrylate (IBCA) was gift from Henkel Biomedical (Loctite, Dublin, Ireland); a poly(vinylalcohol) (PVA) based water soluble polymer film (STBT ® 30µm) (STBT ® ) was purchased from Soluble Technology Ltd. (Chechire, United Kingdom) for the elongation experiments. Milli-Q ® water was produced using the Milli-Q ® direct 8 water purification system from Merck Millipore (Millipore SAS, Guyancourt, France).

Methods

Preparation of the parent spherical nanoparticles.

Poly(isobutylcyanoacrylate) nanoparticles coated with chitosan (CSPIBCA) were prepared by redox radical polymerization according to a previously described protocol [26,30,43]. Briefly, chitosan (130 mg) was dissolved in HNO 3 0.2 M (8 mL) at 42°C under vigorous stirring and argon atmosphere. Once the dissolution was completed, a solution of ammonium cerium (IV) nitrate (8x10 -2 M) in HNO 3 0.2 M (2 mL) and IBCA (0.5 mL) were added successively, the argon flux was stopped and the reaction was allowed to continue at 42°C for 50 min. Then, the nanoparticles were purified by dialysis (cut-off 100,000 g/mol, Spectra/Por membranes) three times against Milli-Q ® water for 1 h and once overnight. The obtained CSPIBCA nanoparticle dispersion was stored at 4°C until use.

The concentration in nanoparticles of the dispersion was evaluated by gravimetry performed by measuring the mass of the dried residue obtained after lyophilisation of 0.5 mL of sample. The experiment was done in triplicate.

The mean hydrodynamic diameter of the nanoparticles was determined by dynamic light scattering using a Zetasizer ® ZS90 (Malvern Instrument, Orsay, France). Measurements were performed at 25°C at a scattered angle of 90°. Samples were diluted in Milli-Q ® water to a concentration of 0.35 mg/mL. Results were expressed as the mean hydrodynamic diameter deduced from size measurements performed on 3 different preparations of nanoparticles.

The ζ potential was deduced from the electrophoretic mobility of the particles measured by Laser Doppler Electrophoresis after dilution of CSPIBCA suspension in NaCl solution (1 mM, 1/100 (v/v)).

Determination was achieved using a Zetasizer ® ZS90 (Malvern Instrument, Orsay, France).

Preparation of the polymer film incorporating the nanoparticles

At first, STBT ® film (100 mg) was dissolved in 1.5 mL of Milli-Q ® water, under magnetic stirring for 4 hours at room temperature. The concentration of the solutions was 67 mg.mL -1 . Then, a dispersion of CSPIBCA nanoparticles at the concentration in nanoparticles of 31 mg.mL -1 was added to this solution to a weight percentage of nanoparticles and STBT ® of 10 % (323 μL), 13% (419 μL) and 15% (484 μL). The resulting mixture was gently stirred for 30 min. The mixture STBT ® -CSPIBCA was spread on a glass slide (25x75 mm²) and dried in an incubator (Memmert, Grosseron, France) at different temperatures, 25, 37 and 50 °C for 24 h, to allow the evaporation of the water and the formation of a new film of STBT ® incorporating the CSPIBCA nanoparticles. For control experiments films were prepared by the same procedure but without nanoparticles. The films were used immediately after preparation

Characterization of film properties

Films containing various amounts of nanoparticles (0, 10, 13, 17, 20 % w/w) and prepared at different temperatures (25°C, 37°C, 50°C,) were obtained according to the procedure described in 2.2.2. At first, the homogeneity of the dispersion of nanoparticles in the polymer solution was appreciated by visual inspection and under light microscopy using the contrast phase mode (Olympus BH2). Pictures were recorded using a Mightex USB2.0 color camera. After the film was formed, the homogeneity of the films was also appreciated by the same method. The purpose of these observations was to check for the occurrence of phase separation. All systems that appeared heterogenous were discarded.

Only homogenous films were selected to determine the percent elongation at break using a TA.XT2 texture analyser (Stable Micro Systems, London, United Kingdom). Films with same dimensions as the ones used to prepare elongated nanoparticles (25 x 75 mm, 30 µm thick) were tightly attached to grips on the TA.XT2 machine. The initial grip separation was checked prior to the start of each experiment. It corresponded to the initial length of the sample (L 0 ). The cross head was moving at a rate of 0.1 mm.s -1 while the stretching experiment was performed at room temperature (20°C) until breakage of the film. The curves gave the tensile strength (TS) as the function of the strain. The TS was calculated dividing the measured force, F (in newton), by the section of the film, s (in m²) (Equation 1).

𝑇𝑆 Equation 1

The strain was deduced from the ration between the extension length, ΔL, and the initial length (L 0 ) (Equation 2).

𝑆𝑡𝑟𝑎𝑖𝑛 ∆ Equation 2
The elongation at breakage (EAB) was calculated following equation [START_REF] Clogston | Frontiers in nanobiomaterial research Vol 1: Handbook of immunological properties of engineered nanomaterials[END_REF].

𝐸𝐴𝐵 % ∆ 100 Equation 3
Where ΔL AB was the extension length at breakage. Measurements were performed at least 3 times on each film.

The maximal elongation (𝐸 capacity of the film could be calculated from the equation ( 4).

𝐸 Equation 4

Elongation of the film producing elongated nanoparticles

To achieve preparation of elongated nanoparticles (E(CDPIBCA) nanoparticles), films were prepared with a concentration of 13% nanoparticles as explained in section 2.2.3. Second generation films recovered from the glass slide were placed in a home-made stretching machine as described in Figure 1. The initial grip separation length (𝐿 ) was 65 mm. The stretching machine was placed in an incubator (Memmert, Grosseron France) at 50°C and let to equilibrate for 30 min. The film was stretched at a temperature of 50°C and at a speed of 0.5 mm.min -1 to a final length, L, of 150 mm giving an elongation capacity, E c , of 231% as calculated from equation 5.

𝐸 Equation 5

Immediately after the stop of the stretching, the film was rapidly cooled down to 20 °C using a flux of cold air (temperature -16.5 °C) while it was maintained on the maximum stretched position. Then, the parts of films used to secure the film in the elongation machine were discarded (Figure 1).

Effectively elongated parts were kept to recover nanoparticles embedded in the stretch film.

Recovery of E(CSPIBCA) nanoparticles from the films after stretching

The stretch part of the film was dissolved in 500 μL of water or nitric acid 0.2 M (pH 1) for 30 minutes at room temperature under gentle stirring. After complete dissolution of the film, E(CSPIBA) nanoparticles were purified by Size Exclusion Chromatography (SEC) using a column of Sephacryl ® S-1000 gel (5 cm x 1.4 cm). The column was equilibrated in acetate buffer at pH 3.2. Elution was performed using the same acetate buffer. The presence of nanoparticles in the eluate was detected from the turbidity and the reactivity with ninhidrin that was used to reveal the presence of amino groups of chitosan in fractions containing nanoparticles. The dispersions of purified E(CSPIBCA)

nanoparticles were stored at +4°C.

Characterization of the elongated nanoparticles by Transmission Electron Microscopy.

The morphology of the nanoparticles was investigated by transmission electron microscopy (TEM).

The nanoparticle dispersion (50 µL) was dropped on the grid, let to dry and the nanoparticles were stained with a solution of phosphotungstic acid at 1% (pH 7.3) for 5 minutes. Electron micrographs were acquired using an electron microscope JEOL 1400 MET operating at 80 kV (Electron Microscopy Facility of I2BC, CNRS, Gif sur Yvette, France) equipped with a high-resolution digital CCD Gatan digital camera (11 megapixels). The nanoparticles were characterized by measuring their long and short axis. Measurements were performed on 300 nanoparticles to determine the shape factor (SF) defined as the ratio between the length of the long and short axis (Figure 2).

Statistical analysis

Statistical comparisons were performed utilizing analysis of variance (ANOVA) followed by the Tukey post hoc tests (GraphPad Prism v. 4 forWindows, Graph-Pad Software, San Diego, CS). Differences were considered statistically significant at p < 0.05. 3

Results and discussions

Successful production of elongated nanoparticles from parent spherical nanoparticles by the stretching method depends on the achievement of several experimental steps. At first, the parent nanoparticles need to be dispersed in a solution of polymer that will then be used to produce a stretchable film. During this step neither flocculation nor coagulation phenomena should occur.

Second, colloidal stability of the nanoparticles is needed during film formation. The film should show a homogenous dispersion of the nanoparticles in the volume of the polymer film. Then, the film should be stretchable in reasonable conditions of temperature so that they will be suitable to further apply the method to particles loaded with a wide range of drugs including fragile molecules.

After stretching, the stretched nanoparticles should be recovered after the dissolution of the film in water. The E(CSPIBCA) nanoparticles were prepared from parent CSPIBCA nanoparticles that occur as spherical nanoparticles and are obtained by emulsion polymerization of isobutylcyanoacrylate.

Several reasons were behind the choice of the nanoparticles used in this study. At first, they are part of a large family of drug carriers that have shown interests for a broad range of therapeutic applications and considering many types of drugs [31][32][33][START_REF] Soma | RSC Drug Discovery Series No. 22: Nanostructured Biomaterials for Overcoming Biological Barriers[END_REF][35][START_REF] Zhou | [END_REF]. More specifically, the CSPIBCA nanoparticles efficiently delivered anti-tumoral siRNA to tumor after intravenous administration at a distant place from the implanted tumor [37,38]. In this case, the siRNA was associated with the nanoparticles after preparation of the carrier. So the preparation of non-loaded nanoparticles with an elongated shape could be of interest for future studies aiming to achieve in vivo delivery of siRNA. Secondly, the parent nanoparticles have already been extensively characterized. Importantly, they are composed of a PIBCA-chitosan copolymer in which the PIBCA moiety composed the core of the nanoparticles and serve as anchor for the chitosan chains that arranged on the core surface to form a corona [30]. In that way, chitosan is covalently anchored on the surface of the nanoparticles.

All soluble components that eventually remained after the synthesis of the particles were removed during the purification step. The marketed polymer film STBT ® was selected because it was claimed to dissolve rapidly in cold water and to be stretchable. Its composition based on PVA would be of good compatibility for a use in a pharmaceutical process. Water solubility and fast dissolution were mandatory characteristics. It was intended to incorporate nanoparticles within a film of polymer prepared from the material recovered from the dissolution of the marketed STBT ® film to which the nanoparticles were added. So, these characteristics were needed to incorporate the nanoparticles in the film and also to be able to recover the nanoparticles embedded in the film after stretching.

Viscoelastic properties of the marketed film were requested to have a suitable matrix to stretch the embedded nanoparticles. According to the supplier, the STBT ® film has elongation capacities of 185% at room temperature and 250% at 50°C. Besides, the marketed film showed another interesting property for the intended application. Its transparency was found useful to observe eventual occurrence of aggregation of nanoparticles introduced in the film made from the marketed film material.

The work included the following 3 steps:

-Determination of the maximal load in nanoparticles that can be incorporated in the film.

-Production of elongated nanoparticles -Determination of the shape factor of the nanoparticles recovered from the film after elongation.

Characteristics of the parent nanoparticles

The parent CSPIBCA nanoparticles used in the present study consisted of core-corona type nanoparticles. The core was composed of PIBCA that was coated by a layer of chitosan covalently anchored to the nanoparticle core by PIBCA chains [30,38]. Characteristics of the nanoparticles synthesized for this work were consistent with those of our previous works [28,30,38] with a mean hydrodynamic dynamic diameter of 394 ± 1 nm and a zeta potential of + 22.7 ± 0.6 mV evaluated at neutral pH. The concentration of the parent dispersion was 31 mg.mL -1 . The number of nanoparticles, N p , found in 1 mg can be calculated from the hydrodynamic diameter of the nanoparticles converted in cm, d H , and the volumetric mass, ρ that is 1140 mg.mL -1 for poly(isobutylcyanoacrylate) nanoparticles [45] (Equation 6).

𝑁 Equation 6

By applying equation 1, it could be determined that one mg of nanoparticles contained 27.4 10 9 nanoparticles.

Determination of the maximal concentration in nanoparticles that can be incorporated in the film.

It is known that colloids can flocculate or coagulate in the presence of polymers [46]. Thus, the first step of the work was dedicated to the preparation of films incorporating nanoparticles in which the nanoparticles would be homogenously dispersed while the new film would show interesting stretching properties for the intended application. As indicated by the supplier, the STBT ® film dissolved easily in water. A solution of the polymer obtained from the dissolution of the film could be prepared at a concentration of 67 mg.mL -1 . Addition of nanoparticles to the polymer solution led to homogenous dispersions from both visual and microscopic observations up to a load in nanoparticles of 15% expressed as the percentage of nanoparticles in weight added from the weight of polymer dissolved. Above this load, a phase separation was observed. Films were prepared only with nanoparticle containing dispersions that appeared homogenous. Films prepared at room temperature and at 50°C showed the occurrence of a phase separation (Figure 3). Conversely, films obtained from a working procedure carried out at 37°C were homogenous at both macroscopic and microscopic scales up to a load in nanoparticles of 13% (Figure 3). For a film obtained from a solution composed of STBT ® at a concentration of 67 mg.mL -1 and nanoparticles at a concentration of 6.8 mg.mL -1 (10% load), the calculated number of nanoparticles per unit surface area dispersed in the film, n, was 14.5 x 10 9 nanoparticles.cm -². This number could be calculated from equation 7 with N p , the number of nanoparticles in 1 mg deduced from equation 6, v, the volume of dispersion of nanoparticles added during the preparation of the film (0.323 mL), C the concentration in nanoparticle of the dispersion (31 mg.mL -1 ) and the area of the film, A (2.5 x 7.5 cm²).

𝑛 Equation 7

Only films that appeared homogeneous under the microscope were further used. Obviously, embedding nanoparticles into the films could considerably influence their mechanical and viscoelastic characteristics, compared to a nanoparticle-empty STBT ® films. The stretching characteristics of the films, both unloaded and embedding nanoparticles, could be a critical determinant of the elongation efficacy. Therefore, the maximal elongation at breakage, EAB, of the films prepared with various loads of nanoparticles was determined using a universal mechanical testing machine (Texture analyser). The figure 4a presents tensile stress of the films monitored during the elongation process. Consistently to what was expected, the tensile stress increased up to a maximum where the curves showed a sudden break that corresponded to the breakage of the film. The general shape of the curves suggested that the films behaved like a ductile material. The breakage occurred in the plastic domain of the film. The maximum elongation determined at breakage, ΔL AB was used to calculate the EAB assessing the stretchable characteristics of the films loaded with different percentage of nanoparticles.

Incorporation of nanoparticles in the films reduced the EAB in comparison with measurements performed on a film prepared without nanoparticles. The decrease was moderate with films loaded with 10 and 13% of nanoparticles and was not significantly different between the two-film load. The decrease was more important for the film loaded with 15% of nanoparticles and significantly different from the films loaded with 10 and 13% nanoparticles (figure 4b). This result was not so surprising as the addition of particles in films of polymer can create defaults that may induce the breakage at lower extension length compared with a film produced in the same conditions without a load of particles. A compromise between the maximal concentration in nanoparticles in the film and the elongation property was adopted to produce elongated nanoparticles. The choice was guided giving the priority to keep at a maximum the elongation property of the film. Thus, the film loaded with 13% (w/w) of nanoparticles was chosen as its EAB was evaluated at 136 ± 5% (n = 3). It can be calculated from equation 4 that the theoretical maximal elongation capacity of this film was 2.36 ± 0.05 (n = 3). Thus, it could be assumed that nanoparticles embedded and stretched in this film at its maximal elongation capacity could reach a maximal theoretical value of their shape factor of 2.36.

3.2. Production of elongated nanoparticles.

The selected film loaded with 13% nanoparticles was placed in the stretching machine to be stretched at 50°C. The machine was set to perform an elongation of the film giving more than twice its original length (230%) but remaining slighly below the EAB predetermined for this film to avoid film breakage. At the end of the experiment, it was assumed that a tempering of the film would be necessary to preserve the new shape acquired by the nanoparticles that were submitted to the elongation stress. Thus, films were cooled down immediately after the elongation was stopped by blowing cold air (-16°C) and allowing the temperature of the film to drop down to the ambient temperature in less than 30 sec. The effective experimental elongation that was calculated from the measurement of the length of the film before and after recovery from the elongating machine was 2.3 consistently with the applied operating conditions.

Nanoparticles embedded in the film were then recovered by dissolution of the film in water and observed by TEM to evaluate the efficacy of the stretching procedure (Figure 5). Nanoparticles recovered from stretched films after dissolution in pure water showed an elongated shape (Figure 5b). Parent nanoparticles recovered from non-stretched films appeared spherical (Figure 5a). In both cases, particles recovered from the dissolution of films were embedded in a foreign material and the background of the preparation observed in microscopy appeared very dusty that was unusual for these nanoparticles. Observations of a solution obtained from the dissolution of a piece of film that was prepared without nanoparticles revealed the presence of insoluble material occurring as more or less aggregated particles suggesting that the film did not dissolve totally in the experimental condition used for this study (Figure 6). The material of the dusty background that remained on the nanoparticle surface after extraction from the film was attributed to this insoluble material. A purification step was needed to clean nanoparticles from contaminant material left by incomplete dissolution of the film. On the TEM image, the size of the insoluble material appeared much smaller than that of the parent CSPIBCA nanoparticles (D H = 394 ± 1 nm as evaluated by dynamic light scattering) suggesting that it could be separated by size exclusion chromatography provided that it was removed from the nanoparticle surface. Evaluation of the zeta potential of CSPIBCA nanoparticles as obtained after synthesis and of the particles formed of the insoluble material obtained after dissolution of the film revealed that the two types of particles had an opposite value of zeta potential at neutral pH. While the CSPIBCA nanoparticles showed a positive zeta potential of +22.7 ± 0.6 mV, that of the insoluble particles of the STBT ® film was negative at -1.0 ± 0.1 mV (Figure 7a). Opposite values of zeta potential could explained the observed accumulation of contaminant material on the surface of CSPIBCA nanoparticles recovered from the dissolution of the film on the TEM images (Figure 5a,b). Consistently, zeta potential evaluated on particles recovered after dissolution of the film showed a single peak with an almost neutral value of zeta potential (Zeta potential = +2.9 ± 0.2 mV) that was close to the one of the insoluble particles of the STBT ® film. By decreasing the pH down to a value of 3.2, particles from the insoluble part of the film became neutral (Zeta potential = +0.3 ± 0.4 mV). At this pH, the zeta potential of the CSPIBCA based nanoparticles was still frankly positive (Zeta potential = +50.5 ± 2.9 mV). Evaluation of the zeta potential of a dispersion obtained from the dissolution of a film loaded with CSPIBCA nanoparticles at this pH revealed two peaks which values corresponded to the insoluble particles of the STBT film (Zeta potential = +7.1 ± 5.6 mV) and to the CSPIBCA nanoparticles (Zeta potential = +26.4 ± 5.3 mV) respectively (Figure 7b). It is noteworthy that the zeta potential of the CSPIBCA nanoparticles recovered after dissolution of the film (Zeta potential = +26.4 ± 5.3 mV) was very closed to that of the CSPIBCA nanoparticles before their incorporation into the film (+22.7 ± 0.6 mV). This indicated that the surface of the nanoparticles recovered from the film was not chemically modified by the incorporation in the film and the recovery method. This was consistent with the fact that chitosan was stably bound on the nanoparticle surface thanks to a covalent anchor of PIBCA that composed the core of the nanoparticles [30,38]. The nanoparticles could be purified by SEC after dissolution at acidic pH and performing the separation at pH 3. The nanoparticles were eluted at first as revealed by the purple colour developed in the presence of ninhidrine acknowledging the presence of the CSPIBCA nanoparticles. The contaminant particles produced during the process of dissolution of the film were eluted later (Figure 8). The purification was efficient to purify the nanoparticles as suggested by the TEM images that showed perfectly isolated and clean nanoparticles (Figure 5c). TEM images also provided evidence of the presence of chitosan on the surface of the E(CSPIBCA) nanoparticles. It is shown as a less dense to electrons layer on the surface of the core of the nanoparticles that appears denser to electrons on the TEM images (Figure 2, Figure 5c). 3.4 Determination of the shape factor of the nanoparticles recovered from the film after elongation.

The elongated nanoparticles exhibited an oblate shape, some having a "lemon" like figure. The determination of the shape factor of the stretched nanoparticles was achieved on the samples using the maximum elongation allowed for the film before breakage. It was assumed that these conditions would provide the maximum elongation we could expect for the CSPIBCA nanoparticles in the experimental conditions used based on the nature of the film and the operating temperature.

Characterizations were performed within a period of 2 weeks from the production of the elongated nanoparticles.

The figure 9 shows the distribution of the shape factor calculated from measurements performed on TEM pictures obtained from 300 individual nanoparticles. It is noteworthy that only very few methods are suitable to evaluate morphological characteristics of elongated nanoparticles [47]. Here TEM was selected as it is one of the microscopic techniques that give direct evidence of the morphology of particles at this scale of size. The mean shape factor of the recovered elongated nanoparticles was of 1.76 ± 0.29. All nanoparticles recovered from a stretched film were elongated since none of them showed an elongation factor of 1 corresponded to spherical particles. Up to 80% of the E(CSPIBCA) nanoparticles displayed a shape factor above 1.5 and 10% of the particles were having a shape factor that corresponded to the maximal value expected (i.e., 2.3) that could be calculated from the elongation capacity of the film. The nanoparticles embedded in the film were significantly distorted during the stretching procedure. However, the discrepancy between the film elongation and the one of the particles suggest that micro-rheological behaviour of the CSPIBCA nanoparticles dispersed in the PVA matrix of the film, as well as the temperature and the imposed macroscopic rate of deformation could be important determinants of the attainable deformation, which would deserve further investigations.

Conclusion

The procedure proposed in the present work was suitable to prepare E(CSPIBCA) nanoparticles with a shape factor up to 2.3 working at a reasonable temperature at 50°C with marketed water-soluble film forming materials. Many drugs are stable at this temperature that makes this procedure suitable to be applied to produce elongated nanoparticles being loaded with a wide range of drugs. Further, film loads in nanoparticles was high (up to 13% expressed in dry weight) and the method allows the recovery of an aqueous suspension of elongated nanoparticles simply by dissolution of the watersoluble PVA film. Besides, the method was applied to prepare elongated species of poly(alkylcyanoacrylate) nanoparticles from their spherical counterparts. The elongated species will constitute a new model of nanoparticles complemental to the already available series of spherical species. They will be used in studies considering the influence of the shape of nanoparticles on their in vivo fate under various situations for their application as drug delivery systems. They will also be used to investigate the influence of the nanoparticle shape with biological systems by in vitro methods. For instance, they are of interest to investigate the influence of the nanoparticle shape on (i) nanoparticle interactions with biomacromolecules, particularly with proteins present in biological fluids, (ii) the capacity of the nanoparticles to go through biological barriers, including epithelia and endothelia as well as (iii) their propensity to be endocytosed by cells. This new model of nanoparticles will also be interested to investigate the influence of the shape of the nanoparticles in drug delivery methods that consider a mucosal route of administration.

Figure 1 .

 1 Figure 1. Scheme of the film before (a) and after (b) stretching and placed in the elongation machine (c).

Figure 2 .

 2 Figure 2. Calculation of the shape factor from TEM images of the E(CSPIBCA) nanoparticles.

Figure 3 .

 3 Figure 3. Optic micrographs of the films obtained with 13% nanoparticles after drying at room temperature (a), 37°C (b) and 50°C (c). The films dried at room temperature and 50°C showed clear phase separation while the film dried at 37°C appeared homogenous. Scale bar: 100 µm.

Figure 4 .

 4 Figure 4. Elongating properties of the STBT ® film loaded with different weight percentages of CSPIBCA nanoparticles. (a) Exemple of tensile strength (TS) of films monitored during stretching and recorded with a texture analyser (load in nanoparticles expressed in weight percentage of STBT ® : 0% (bleu diamonds), 10% (red squares), 13% (green triangles), 15% (orange circles), (b) Maximal elongation at breakage (EAB) expressed as a percentage from the initial length (L 0 ) of the film, (c) Maximal elongation capacity (Ec max ) of the film as determined from the total length of the film at breakage divided by the initial length (L 0 ). Statistics: No significant difference was found comparing STBT ® films loaded with 10 and 13% nanoparticles.

Figure 5 .

 5 Figure 5. Transmission Electron Microscographs (TEM) of the parent CSPIBCA nanoparticles (a) and of the E(CSPIBCA) nanoparticles recovered after dissolution of the film in pure water (b). E(CSPIBCA) nanoparticles recovered from the film after dissolution at pH 1 and purification by SEC performed at pH 3.5 (c).

Figure 6 .

 6 Figure 6. Transmission electron micrographs of STBT ® film after dissolution in water.

Figure 7 .

 7 Figure 7. Zeta potential of the insoluble material remaining after dissolution of the STBT ® film (solid line), of the CSPIBCA parent nanoparticles (dotted line) and the dispersion recovered from the dissolution of a STBT ® film loaded with CSPIBCA nanoparticles (semi solid line). (a) Dispersions were prepared at pH 7, (b) dispersions were prepared at pH 1.

Figure 8 .

 8 Figure 8. Purification of the E(CSPIBCA) nanoparticles by size exclusion chromatography on Sephacryl S-1000 gel. Elution of the material contained in the dispersion obtained after dissolution of an elongated film loaded with nanoparticles (a), Elution of purified E(CSPIBCA) nanoparticles (b) and of the insoluble material recovered after dissolution of the STBT ® film (c).

Figure 9 .

 9 Figure 9. Distribution of the shape factor of the E(CSPIBCA) nanoparticles recovered from a films of STBT ® of 2 nd generation loaded with 13% nanoparticles (wt/wt) and stretch to an elongation of 230% at 50°C with the stretching machine. The nanoparticles were recovered after dissolution of the film at pH 1 and purification by size exclusion chromatography. Measures were performed from TEM images as illustrated in figure 2.

Acknowledgments

C. Palazzo received a fellowship from "Ministero dell'Istruzione dell'Università e della Ricerca", MIUR, Italy. The present work has benefited from the facilities and expertise of the Electron Microscopy facilities of I2BC, CNRS, Gif sur Yvette, France (http://www.cgm.cnrsgif.fr/spip.php?article282&lang=fr).


N Razaaly

G Gori

O Le Maître

G Iaccarino A N

D P M Congedo

Robust optimization of ORC turbine cascades operating with siloxane MDM

This work presents the application of a robust optimization approach to improve the efficiency of an Organic Rankine Cycle (ORC) cascade subject to uncertain operating conditions. The optimization algorithm is based on the minimization of a high quantile of a random cost function. The system under consideration employs siloxane MDM (Octamethyltrisiloxane) as a working fluid. The thermodynamic behavior of MDM requires the utilization of complex Equations-of-State (EoS) that rely on material-dependent parameters. Discussed here are the aleatory uncertainties affecting both the cascade operating conditions and the fluid model parameters. An uncertainty quantification framework is used to forward propagate the considered uncertainties to some performance estimators. The performances of the robust blade design are compared against performances characterizing the optimal design obtained using a deterministic optimization approach. Results show that the quantile-based approach yields to a significant improvement in cascade performance in variable operating conditions.

Introduction

Organic Rankine Cycle (ORC) applications take advantage of low-quality heat sources such as solar energy ponds, waste heat recovery, biomass combustion, etc, to convert the recovered heat into useful work. ORCs operate at high-pressure conditions, in the order of the critical point, and close to the liquid-vapor equilibrium curve. Under such conditions, organic compounds do not abide by the well-known Ideal Gas law. Namely, the thermodynamics admits different complex phenomena that are of the utmost relevance for industrial applications. For instance, the non-ideal decrease of the flow Mach number in supersonic expansions [START_REF] Cramer | Steady, isentropic flows of dense gases[END_REF], the non-ideal evolution of the Mach number in diabatic supersonic nozzle flows [START_REF] Schnerr | Diabatic supersonic flows of dense gases[END_REF] and the Mach number increase across non-ideal oblique shock waves (Gori et al. 2017a;[START_REF] Vimercati | Non-ideal oblique shock waves[END_REF]. Besides ORCs, non-ideal effects are also relevant to supercritical CO 2 power systems, refrigerating systems, chemical or pharmaceutical industry and to many other applications (Colonna et al. 2008b;Congedo et al. 2011a;[START_REF] Wheeler | The role of dense gas dynamics on organic Rankine cycle turbine performance[END_REF][START_REF] Vitale | Extension of the SU2 open source CFD code to the simulation of turbulent flows of fluids modelled with complex thermophysical laws[END_REF].

Non-ideal flows are a novel research topic and may questions still remain to be addressed. For instance, the design of ORC devices relies largely on numerical tools and techniques developed for ideal fluids only. Moreover, the few available experimental data are affected by large uncertainties [START_REF] Cinnella | Quantification of thermodynamic uncertainties in real gas flows[END_REF][START_REF] Cinnella | Sensitivity analysis of dense gas flow simulations to thermodynamic uncertainties[END_REF][START_REF] Merle | Bayesian quantification of thermodynamic uncertainties in dense gas flows[END_REF], making the development of high-fidelity EoS highly questionable (see Congedo et al. (2011a)).

Fluid-dynamic Shape Optimization (FSO) approaches offer the possibility of dealing with complex optimization problems at a reduced computational cost [START_REF] Pironneau | On optimum design in fluid mechanics[END_REF]. Those methodologies are perfectly suited to ORC applications, for which there is little design experience and limited experimental information [START_REF] Harinck | Performance improvement of a radial organic rankine cycle turbine by means of automated computational fluid dynamic design[END_REF]. Gradientbased and gradient-free algorithms were successfully applied to carry out the deterministic optimization of ORC nozzles and turbine blades (see [START_REF] Pini | Adjoint method for shape optimization in real-gas flow applications[END_REF][START_REF] Pini | Robust adjoint-based shape optimization of supersonic turbomachinery cascades[END_REF]; [START_REF] Vitale | Fully turbulent discrete adjoint solver for non-ideal compressible flow applications[END_REF]; [START_REF] Rubino | Adjoint-based fluid dynamic design optimization in quasiperiodic unsteady flow problems using a harmonic balance method[END_REF]).

Nevertheless, in ORC applications, the low quality of the heat and cold sources often result in significant variations of the fluid conditions at the turbine inflow and outflow. Clearly, the robustness to operating conditions variability must be taken into account at an early stage in the development process. In this context, [START_REF] Lee | A global robust optimization using kriging based approximation model[END_REF] propose a Robust Optimization (RO) formulation based on the minimization of a target performance variance. In [START_REF] Janusevskis | Simultaneous kriging-based estimation and optimization of mean response[END_REF], the mean performance optimization is achieved through a Bayesian Optimization (BO) framework exploiting a Gaussian-Process (GP) -based model. Moreover, multi-objective optimization [START_REF] Colonna | TSI metamodels-based multi-objective robust optimization[END_REF]Bufi et al. 2017;Bufi & Cinnella 2017) and a multi-point approach [START_REF] Pini | Turbomachinery design optimization using adjoint method and accurate equations of state[END_REF] have been proposed for ORC optimization problems.

In this work, we present the application of a quantile-based Bayesian optimization framework in the context of ORC turbine blade optimization. This robust shape optimization approach is applied to a typical 2D ORC turbine cascade (Colonna et al. 2008a). Section 2 describes the turbine cascade and the parametrization adopted to control the geometry of the blade in the optimization process. In Section 3, we summarize and discuss the aleatory uncertainties affecting our model. Section 4 briefly presents the deterministic and the quantile-based formulations for the optimization problem. Finally, Section 5 reports and compares performances of blade designs obtained using the two different formulations.

Turbine blade model

The Biere is a famous ORC blade geometry which is typically employed in supersonic axial turbine stators. The Biere represents a reference two-dimensional benchmark case to test the design of devices operating with siloxane fluid MDM (Octamethyltrisiloxane, C 8 H 24 O 2 Si 3 ). The blade profile is meant to obtain a convergent-divergent cascade passage which serves to accelerate the fluid up to a supersonic speed. Across the cascade, the fluid is expanded from superheated conditions close to the saturation line (P T in = 8 bar, T T in = 545.15 K) to a static pressure in the order of P ≈ 1 bar. As the flow past the cascade is supersonic (M ≈ 2 at the blade trailing edge), compressibility effects play a key role. Indeed, because of the high Mach number achieved at the nozzle exit, a typical fish-tail shock pattern is generated downstream the trailing edge (see [START_REF] Saracoglu | Effects of blunt trailing edge flow discharge in supersonic regime[END_REF]). The presence of strong shocks past stator vanes may result in large losses and thus the design of the trailing edge region is critical to turbine efficiency [START_REF] Denton | The trailing edge loss of transonic turbine blades[END_REF][START_REF] Mee | An examination of the contributions to loss on a transonic turbine blade in cascade[END_REF]). Moreover, shock-waves propagate through the vane and usually interact with the boundary layer developing over the suction side of the neighboring blade, thus further compromising the efficiency of the cascade.

The numerical domain is periodic over the vertical axis (y) with a stagger spacing of 45 mm. The flow is simulated up to a distance of 0.5 -0.6 and 2 chord-lengths ahead and past the blade, respectively. The Biere pressure and suction sides are parametrized using a unique B-spline curve of degree 3 (see [START_REF] Hoschek | Fundamentals of computer aided geometric design[END_REF][START_REF] Farin | Curves and Surfaces for CAGD: A Practical Guide[END_REF]). In this work, the B-splines were defined over a total number of 30 Control Points (CP). Only a subset of 11 CPs, mostly located on the suction side and trailing edge, is moved to seek for the optimal blade shape. The motion of the selected CPs is allowed in the direction normal to the baseline geometry. The maximum displacement of each CP was limited to a predefined range of values. In the following, x ∈ IR 11 will denote the vector collecting the displacement of each CP i.e., the design control variables.

Uncertainty treatment

Generally, ORC cascades are subject to a wide variability of the operating conditions. According to [START_REF] Pini | Turbomachinery design optimization using adjoint method and accurate equations of state[END_REF], the operating conditions, namely the total pressure (P t in ) and total temperature (T t in ) at the turbine inflow and the static pressure past the cascade (P s out ), can be modeled as uniformly distributed variables. The random vector ξ is defined as ξ = [P t in , T As mentioned, ORC systems take advantage of complex compounds that do not generally abide by the ideal gas law and thus more complex EoS are needed. Among others, hereinafter we will consider the Peng-Robinson (PR) thermodynamic model [START_REF] Peng | A new two-constant equation of state[END_REF]), which includes a set of material-dependent parameters: the fluid pressure and the temperature at the critical point (P cr and T cr , respectively) and the acentric factor ω. Several authors have provided discrepant reference values for the materialdependent parameters, and these translate into aleatory uncertainties on the PR fluid model. Moreover, under the polytropic gas assumption (i.e., the heat capacity is assumed to be constant with temperature), the PR EoS ultimately depends also on a fourth parameter, the specific heat ratio γ.

In this work, a first attempt to infer the true value of the PR fluid model parameters for MDM was carried out based on experimental data. However, the available measurements are still not sufficient (both in terms of quantity and quality) and little, if nothing, can be learned from them. Nevertheless, the performances of the Biere blade, at the conditions of interest here, are almost insensitive to the variability of the fluid parameters. Indeed, a thorough investigation carried out using the Reynolds-Averaged Navier-Stoke (RANS) model pointed out that the quantities of interest do not change significantly, even if the PR parameters are allowed to vary considerably (even pushing the limit of physical admissibility). This result has also been confirmed in the past (see Congedo et al. (2011b[START_REF] Colonna | TSI metamodels-based multi-objective robust optimization[END_REF]; [START_REF] Geraci | High-order statistics in global sensitivity analysis: Decomposition and model reduction[END_REF]). Therefore, any uncertainty underlying the PR fluid model in not considered and the nominal parameters values, according to [START_REF] Thol | Speed of sound measurements and fundamental equations of state for octamethyltrisiloxane and decamethyltetrasiloxane[END_REF], are used throughout the rest of this work.

Optimization framework

In this section we describe the optimization framework. First, we recall the standard formulation for deterministic and unconstrained design problems. We then introduce the quantile-based formulation used to design the optimal and robust Biere blade. Finally, we present the Uncertainty Quantification (UQ) framework needed to propagate the uncertainties on the operating conditions to the performance parameters, to assess the characteristics of the final blade design.

Deterministic optimization

The classical formulation for constrained optimization problems in a deterministic framework reads min x∈Ω f (x) s.t. g(x) ≤ 0.

(4.1)

The cost function f depends on the design vector x ∈ Ω ⊂ IR 11 , corresponding to the vector of variables in the B-spline parametrization of the blade profile (see Section 2).

The optimum must satisfy a set of n c constraints g ∈ IR nc . In this work, we consider only the unconstrained optimization problem, that is n c = 0.

To solve the optimization problem, we rely on a classical Bayesian framework for Surrogate-Based Optimization (SBO), the popular Efficient Global Optimization (EGO) [START_REF] Brochu | A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning[END_REF]. Specifically, we consider a sequential approach where GP-based surrogate models are built to approximate the objective function f . At each step of the sequence, a new design x is obtained maximizing the so-called Expected Improvement (EI), which expression analytically depends on the current GP surrogate. This approach permits both to identify promising regions of Ω (exploitation) and to explore portions of the design space characterized by high uncertainty on the GP surrogate. The Improvement is defined as

I(x) = max(0, f min -f (x)), (4.2)
where f min is the current optimum of the objective function obtained while exploring the design space Ω and f (x) denotes the current Gaussian predictor of f (x). Note that I(x) ∈ IR + is random, since f (x) is an univariate Gaussian variable. Therefore, the new design point x is found solving

x = arg max x∈Ω EI(x), (4.3)
where EI(x) = IE f (x) [I(x)] is the so-called Expected Improvement and IE f (x) the expectation operator related to the randomness of the gaussian predictor f (x). The analytical expression of the expected improvement in the case of Gaussian surrogates is given in [START_REF] Brochu | A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning[END_REF].

Since the optimization problem in Eq. ( 4.3) involves the surrogate model f only, it can be solved by means of any advanced optimization procedure, e.g. using Covariance Matrix Adaptation (CMA) (Nikolaus Hansen 2018). A full CFD simulation is then performed at the new design point x * , providing the objective function value f (x ), and the surrogate model is subsequently updated. This procedure is repeated until either a stopping criterion on the optimum is met or the budget of CFD simulations is exhausted.

Robust optimization: quantile minimization

When we are dealing with a system affected by uncertainties, the objective function h also depends on random quantities, modeled as the random vector ξ. A mono-objective formulation of the minimization under uncertainties would consist in replacing the random objective function by a statistics of h(x, ξ). One natural choice is to minimize the mean of the random function. The sole minimization of an expected cost function usually results in a non-robust optimum as it does not incorporate any variability in the cost due to the uncertain parameters. This observation suggests consideration of the minimization of composite objective functions combining the first two (or more) statistical moments of h. For instance, a robust optimization approach could aim at minimizing the mean of h while penalizing its variance with some weight. Finding appropriate weights is, however, difficult and somewhat arbitrary and the performance and robustness of the resulting optimal design can be highly sensitive to the penalization selected, as pointed out in [START_REF] Cook | Horsetail matching: a flexible approach to optimization under uncertainty[END_REF]. In addition, the accurate estimation of high-order statistical moments often incurs high computational costs.

Therefore, here we follow a quantile-based robust optimization, which aims at minimizing a usually high quantile of h(•, ξ). The problem is formulated as follows

min x∈Ω q α [h(x, ξ)],
(4.4)

where, for α ∈ (0, 1), we have denoted q α [h(•, ξ)] the α-quantile of h(•, ξ) defined as

IP ξ (h(•, ξ) < q α [h(•, ξ)]) = α. (4.5)
This quantile-based minimization problem is solved using a nested approach, where for each proposed design point x, the α-quantile is estimated using an adaptive sampling method. Briefly, for a fixed x, we start building a GP surrogate in the stochastic space of h(x, ξ), based on an initial Latin Hypercube Sampling (LHS) sample set of N LHS points. This sample set is then adaptively enriched with new points selected using a criterion designed to improve the surrogate accuracy for the evaluation of the targeted quantile value (see [START_REF] Schöbi | Rare event estimation using polynomialchaos kriging[END_REF]). Denoting h α (x) the surrogate-based estimate of the α-quantile of h(x, ξ), the SBO method described above is used to solve Eq. ( 4.4), substituting the objective function f by h α .

Results

In this section we present results for the optimization problem for the trailing edge shock reduction in a turbine stator cascade. The optimization is carried out considering an inviscid and adiabatic flow model governed by Euler's equations. The SU2 open-source suite [START_REF] Economon | Performance optimizations for scalable implicit RANS calculations with SU2[END_REF] was used for the CFD simulations. We used a generalized Approximate Riemann solver (ARS), of Roe type, with the SU2's library of thermodynamic models for complex fluid flows in the non-ideal regime [START_REF] Vitale | Extension of the SU2 open source CFD code to the simulation of turbulent flows of fluids modelled with complex thermophysical laws[END_REF]Gori et al. 2017b). An implicit Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) scheme, with van Albada slope limiter, is used to ensure second-order accuracy and prevent spurious oscillations in the steady-state solution. Non-Reflecting Boundary Conditions (NRBC) [START_REF] Giles | Nonreflecting boundary conditions for Euler equation calculations[END_REF]) are also implemented to suppress the non-physical reflection of acoustic pressure perturbations at inflow and outflow boundaries. Detailed convergence analyses (not shown) have been performed, leading to computational mesh of the flow domain with 36, 000 triangular elements, which represents a trade-off between accuracy and computational cost.

Following [START_REF] Rodriguez-Fernandez | Automatic of ORC turbine profiles using evolutionary algorithms[END_REF], the optimization aims at minimizing the pressure deviations in an azimuthal section located at half an axial chord downstream the trailing edge. The pressure deviations are measured by ∆P , the spatial Root Mean Square (RMS) of the pressure within the considered section. We contrast two optimal designs: the deterministic design corresponding to the minimization of ∆P for the deterministic conditions, that is considering the objective function f (x) = ∆P (x, ξ 0 ), and the 95% quantile-based robust optimization using f (x) = q 0.95 [∆P (x, ξ)].

In order to assess the validity of the study, an Uncertainty Quantification (UQ) is performed considering a LHS set of 100 samples in the stochastic space for the two optimized profiles, based on Euler and RANS simulations, the latters using the Menter's Shear Stress Transport (SST) model (see Menter, F.R. (1993)). For these viscous sim- 1. The interest of the robust optimization is evidenced by confronting the statistics of ∆P for the deterministic and robust designs. Note that the robust design not only exhibits a lower quantile (12.6 against 29.9), as expected, but also a lower variance and mean value of the pressure RMS ∆P than for the optimal design for the nominal conditions, denoting the lack of robustness of the latter. As reported in the right part of Table 1, although optimized on the non-viscous flow model, the quantile-based design significantly improves the statistics of both ∆P and Y when evaluated using the physically more complex model.

To gain further understanding of the impact of the robust optimization, we present in Figure 1(a,b) the Probability Density Functions (PDF) of ∆P for the baseline geometry (prior to any optimization), the deterministic optimal design, the q 95 robust design and for both the inviscid (a) Euler and viscous (b) RANS simulations. The deterministic and the quantile-based optimal designs have distributions of ∆P that are significantly displaced toward the lowest values (to the left), with lower mean values, compared to the nonoptimized baseline design. Comparing the distributions of the deterministic and quantile-based optima, the effect of the robustness is obvious: whereas the deterministic design has a rather flat distribution, the robust design not only has a lower mean and variance (as shown in Table 1) but also its support is much tighter.

Finally, Figure 2(a) reports the baseline (black curve), deterministic (red) and quantilebased (green) optimal blade profiles. We also report the corresponding local coefficients of variation (ratio of standard deviation to the mean value) of the Mach number M in the flow domain in Figure 2(b,c,d). Again, the reduction of the Mach number CoV for the robust design is significant compared to other designs, in particular in the wake of the blades past the cascade.

Conclusions

This work presents the application of a robust optimization procedure to the design of a typical ORC turbine cascade operating under uncertain conditions. The optimization method minimizes a high quantile of the random cost function. The quantile-based optimal design is compared to the design obtained from a deterministic optimization 5 1 0 1 5 2 0 2 5 3 0 3 5 ΔPΔ[kPa] Baseline Optim q 95 -Optim for the nominal conditions. Results indicate that significant improvements are obtained using the quantile-based framework, with an optimal performance distribution having much lower mean and much compact support. Other quantities of interest, such as the Mach number and total pressure drop, benefit of the robustness although they were not directly optimized.

Figure 1 :

 1 Figure 1: PDFs of ∆P for the baseline (dashed curve), deterministic (red curve) and to the robust (green curve) designs. Diamonds mark the mean values µ, cross symbols indicate the µ ± σ points, and stars mark the 5% and the 95% quantiles. The optimal designs are computed with Euler model, whereas the PDFs are estimated from (a) Euler and (b) RANS simulations.

Figure 2 :

 2 Figure 2: (a) Comparison of the baseline (black), deterministic (red) and robust (green) blade designs. Coefficients of Variations of the Mach number for the baseline (b), deterministic (c), and robust (d) designs. CoVs are computed with the RANS Model.

Table 1 :

 1 Blade designs assessment. The table reports the averages, standard deviations and 95% quantiles of the pressure deviation (∆P ) and total pressure loss (Y ) in uncertain conditions for the optimal designs obtained with the deterministic and robust optimization. Also shown are the results for the viscous flow model (RANS). ulations, a refined hybrid mesh with approximately 180, 000 elements was employed to ensure sufficient resolution of the boundary layers. A Monte-Carlo Sampling (MCS) combined to a GP-surrogate permits to evaluate meaningful statistics of the Quantities of Interest (QoI) ∆P and the total pressure loss Y = (P t in -P t out )/(P t in -P s out ), reported in Table

	Design		Euler			RANS
		∆P [kPa]		Y [%]	∆P [kPa]		Y [%]
	µ	σ	q95	µ	σ q95	µ	σ q95	µ	σ q95
	Deterministic 16.2 10.1 29.9 13.8 7.2 26.5 16.0 9.7 28.6 17.8 6.8 29.7
	Quantile-based 8.9 2.4 12.7 11.3 2.4 16.2	8.8 2.4 12.5 15.2 2.3 19.8

Acknowledgments

The authors acknowledge use of computational resources from the Certainty cluster awarded by the National Science Fundation to CTR. G. Gori and P.M. Congedo would like to thank the European Commission's H2020 programme, through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant Agreement number 722734.


Jean-Baptiste Coty

Fanny Varenne

Jean-Jacques Vachon

Dr Christine Vauthier
email: christine.vauthier@u-psud.fr

Serial multiple crossed immunoelectrophoresis at a micro scale: A stamp-sized 2D immunoanalysis of protein C3 activation caused by nanoparticles

Keywords: 2D-IE: Two-dimensional immunoelectrophoresis, ANOVA: Analysis of Variance, C 3 A 50 : Protein C3 activation at 50%, CARPA: Complement Activation Related PseudoAllergy, C-IE: Crossed immunoelectrophoresis, D H : Hydrodynamic diameter, DLS: Dynamic light scattering, ELS: Electrophoresis light scattering, EP: Emulsion polymerization, GUM Surface concentration, VBS: Veronal Buffer Saline, MultiCrossed-IE: Serial multiple crossed immunoelectrophoresis Complement system, crossed immunoelectrophoresis, protein C3, robustness

Serial multiple crossed immunoelectrophoresis at a micro scale: a stamp-size 2D immunoanalysis of protein C3 activation caused by nanoparticles

Jean-Baptiste Coty, Fanny Varenne, Jean-Jacques Vachon, Christine Vauthier*

Introduction

It is now quite well established that nanomaterials circulating in the blood, either intentionally when used as nanomedicines, or accidentally after exposition to pollutants, are subjected to recognition by the immune system [1][START_REF] Boraschi | Nanoparticles and the immune system: safety and effects[END_REF][START_REF] Dobrovolskaia | [END_REF]. Although still not fully established, it seems that the activation of the complement system may be one of the first event responsible for the clearance of nanomaterials from the blood, associated with uptake by macrophages of the immune system [4]. The complement system is also at the root of hypersensitivity and allergic reactions. Among them, the development of Complement Activation Related PseudoAllergy (CARPA) that is still not entirely understood, and can have a dramatic issue for patients [5,6]. Thus, there is an interest to evaluate the propensity of a nanomaterial to activate the complement system, as it is one of the possible ways to assess its nanotoxicity.

In vitro tests on this purpose are well established including western blot, CH50 assay (Total Hemolytic Complement assay), ELISA, C-IE or immunoprecipitation tests [7][START_REF] Salvador-Morales | Handbook of immunological properties of engineered nanomaterials[END_REF][START_REF] Mollnes | [END_REF][START_REF] Neun | Analysis of Complement Activation by EIA[END_REF][11]. Among them, the C-IE (or 2D-IE) of the complement C3 protein was not so much applied due to the tedious operating conditions, although it allows to reveal the cleavage of the protein C3 of the cascade in a non-debated manner [12][13][14]. Complement protein C3 is a protein that intervenes in the final pathway of the complement cascade, being common to all known pathways that trigger activation of the cascade [15,16]. Measurement of protein C3 cleavage allows the assessment of complement activation, independently of the pathway triggering the activation. In the obtained electrophoregram, a first peak corresponds to native C3, which may partially or totally disappear after activation, to be replaced by a second and sometimes a third peak, corresponding to cleaved components of C3 [17]. The method can be applied on samples directly obtained from the incubation with the serum without the need to remove the tested nanomaterial, as it is the case with other methods such as CH50 assay [START_REF] Salvador-Morales | Handbook of immunological properties of engineered nanomaterials[END_REF] and Western Blot.

Today, there is a need for methods to the study of complement activation by a large number of nanomaterials. The demanding protocol of the C-IE hampers its development at the expense of the direct information provided from the reading and analysis of gels.

The purpose of the present work was to develop a high throughput analytical method based on C-IE, by achieving serial multiple crossed immunoelectrophoresis at a micro scale (MultiCrossed-IE) on a single agarose gel plate. Although several migrations of samples can be achieved in parallel on a gel plate, the novelty of the work was to incorporate samples to be analyzed on the same line of migration. The new approach was applied to the investigation of the activation of component C3 of the complement system triggered by three types of known nanoparticles, tested at different levels of activation. The robustness of the method was assessed by testing the influence of sample's position on the gel plate, the electrophoresis apparatus, the analyst and the sample preparation. The precision of the method was evaluated via the intra-and inter-day variation.

The method was then applied to the evaluation of the amount of NP's surface that induces a cleavage of 50% of the native C3 into fragments (C 3 A 50 ). This value could be proposed as a new parameter characterizing nanomaterials in terms of their capacity to trigger activation of the complement system, thus breaking the limit of previous methods that only allowed comparison of few nanomaterials tested for a same concentration expressed as the exposed surface.

Materials and Methods

Materials

Isobutylcyanoacrylate (IBCA) was purchased from Orapi (Saint-Vulbas, France). Dextran 17.7 kDa and cerium (IV) ammonium nitrate were provided by Fluka (Saint-Quentin-Fallavier, France). Dextran 66.7 kDa, Tricine, Tris base (Sigma 7-9 ® ), Sodium chloride, EDTA sodium salt and Bromophenol blue were purchased from Sigma (Saint-Quentin-Fallavier, France). Nitric acid was supplied by Prolabo (Paris, France). Human serum was prepared from plasma provided by Etablissement Français du Sang (EFS) (Rungis, France). Polyclonal anti-human C3 antibody raised in goat was purchased from Fitzgerald antibodies (Acton, USA). Coomassie brilliant blue R-250, calcium lactate and glacial acetic acid were supplied by Thermo Fisher Scientific (Villebon-sur-Yvette, France). Gel-Fix™ for agarose (265x150 mm) was purchased from Serva Electrophoresis (Heidelberg, Germany). Nafamostat mesylate (NM) was obtained from Abcam (Cambridge, UK).

Nanoparticle preparation and characterization

Preparation of the NPs

NPs were prepared by emulsion polymerization (EP) adapting protocols proposed by Chauvierre et al. [18], according to Bertholon et al. [14]. The NPs R17 and R66 were obtained by redox radical EP using dextran 17.7 kDa and 66.7 kDa respectively. Cerium IV ammonium nitrate (2 mL, 8.10 -2 M in HNO 3 0.2 N) and IBCA (0.5 mL) were successively added in a solution of dextran (0.136 g in 8 mL HNO 3 0.2 N, 40°C), purged with argon. The polymerization was pursued for 1h at 40°C. NP A66 was prepared by anionic EP with dextran 66.7 kDa. IBCA (0.5 mL) was added to a solution of dextran (0.136 g in 10 mL HNO 3 0.2 N, 40°C). The polymerization was pursued for 24h at 40°C. At the end the polymerization, dispersions were cooled in an ice bath and purified by dialysis against Milli-Q ® water using Spectra/Por membrane (MWCO 100,000 Da, Spectrum Laboratories, Irving, USA). Purified NP dispersions were stored at 4°C until use.

Nanoparticle characterization

Evaluation of the size and surface charge: Hydrodynamic diameter (D H ) of nanoparticles was measured at 20°C by dynamic light scattering (DLS). Surface charge was assessed evaluating the zeta potential from measurements of the electrophoretic mobility by electrophoresis light scattering (ELS), using Smoluchowski's model. Measurements were carried out using a ZetaSizer Nano ZS90 (Malvern Instruments, Orsay, France). Determination of the mass concentration: Mass concentration of NP in dispersions (M C in mg.mL -1 ) was determined by a gravimetric method. Known volume of the dispersion (300 µL) was freeze-dried with a Christ Alpha 1-2 LDplus (Bioblock Scientific, Illkirch, France) for 24h. The dried weight was used to determine the M C .

Calculation of the NP surface area concentration: The surface concentration (S C in cm 2 .mL -1 ) developed by the NP per mL of dispersion was calculated from Eq. 1 [19], using the mass concentration (M C in mg.mL -1 ), the D H (in cm), and the density of tested nanoparticles (d in mg.cm -3 ), which was previously reported by Vauthier et al. [20].

𝑆𝐶 * 𝐶 * 𝐻 (1)

Preparation of samples to be analyzed by C-IE and MultiCrossed-IE

Human serum (25 µL) was incubated with a given surface of nanoparticles (50 µL) dispersed in Veronal Buffer Saline (VBS) (25 µL). The VBS contained 0.15 mM Ca 2+ and 0.5 mM Mg 2+ ions and was prepared as described by Kazatchkine et al. [START_REF] Kazatchkine | Techniques du complément[END_REF]. Samples were incubated for 1h at 37°C. Then, they were immediately cooled to 4°C in an ice bath. For the robustness and precision study, EDTA and NM were added in order to stop proteolytic reactions occurring in the process of complement system activation [START_REF] Bergseth | [END_REF] (4.13 µL of EDTA disodium salt 0.5 M and 2.16 µL of NM at 10 mg.mL -1 ). Samples were then either immediately analyzed by C-IE or stored at -20°C until use within the few next days. The surface of NP exposed in the sample (s sample in cm 2 .mL -1 ), can be calculated using Equation 2, with the volume of NP dispersion (v in mL) in the total volume of incubation (Vtot in mL).

𝑠𝑠𝑎𝑚𝑝𝑙𝑒 𝐶 *

(2)

Crossed Immunoelectrophoresis

C-IE classical method

The C-IE method was detailed by Walker [START_REF] Walker | The Protein Protocols Handbook[END_REF], then applied to C3 protein by Passirani et al. [11]. Samples were prepared as described in 2.3. Then, 5µL of each sample were filled into wells formed on a 1% agarose gel plate (13x10 cm) for the first dimension of electrophoresis. After 1h15min of separation, bands corresponding to each sample were cut and disposed on Gel-Fix™ films (5x7 cm each). Agarose gel 1% containing the antibody was then casted on the remaining free area of the film for the second dimension electrophoresis that lasted for 18h using a Multiphor II electrophoresis system (GE Healthcare, Velizy-Villacoublay, France). Five samples were run at the same time on five different gel slabs (5x7cm).

New serial multiple crossed IE at a micro scale (MultiCrossed-IE)

Evaluation of the heat resistance of the antibody

The heat resistance of the antibody was assessed by radial immunodiffusion [START_REF] Mancini | [END_REF]. A gel plate was prepared on a Gel-Fix™ film with a solution of agarose 0.7% containing human serum (0.17 µL/cm 2 of gel), in Tricine buffer (Calcium Lactate 1 mM, TRIS 63 mM, Tricine 27 mM, in MilliQ ® water, pH 8.6). Wells were formed in the agarose gel to receive 4 µL of pre-heated (20, 50, 55, 60, 65, 70, 75, 80 and 90°C) antibody solutions (1.4 mg.mL -1 in PBS) for 4 minutes. The gels were placed in a humid chamber for 24h prior drying and staining with Coomassie blue [START_REF] Walker | The Protein Protocols Handbook[END_REF]. The diameter of the precipitated rings was measured to calculate the areas of circles. The latter were plotted against the corresponding temperature at which the antibody was heated.

Preparation of the gel for MultiCrossed-IE

Agarose gel 1% (40 mL) was prepared in Tricine buffer. When the temperature of the gel reached 60°C, 1.17 mL of anti-C3 antibody at 1 mg.mL -1 in PBS was added. After rapid homogenization, the solution was spread on a 15x20 cm Gel-Fix™ film (Fig. 1A).

Figure 1: Preparation of the gel plates for MultiCrossed-IE. A) Agarose gel slab containing anti-C3 antibody. B) Cutting of gel bands following a template. C) Removing pre-cut bands with a spatula. D) Gel with cut bands. E) Agarose gel filling of the bands. F) Application of the comb for wells formation. G) Final gel ready for sample loading. H) Gel loaded with samples and indicator for first dimension migration. I) Numerized gel after 2D migration, staining and drying. J) Example of integration of electrophoregram peaks. K) Comparison with a stamp at the same size scale (La Poste, 2001, Eve Luquet).

After solidification, five 8 mm bands were removed as illustrated in Figure 1B, C,D. Each gap was then filled with 1.8 mL of a 1% agarose gel prepared in Tricine buffer (Fig. 1E). Wells were formed at the same time using a homemade comb (Fig. 1F). A distance of 2.5 cm was left between wells, allowing seven samples to be run in series in a band of 20 cm long (i.e. 35 samples to be run in a 15x20 cm gel, Fig. 1G). A second well on the left side of each band was made under the sample well, in order to run Bromophenol blue as an indicator of migration for the first dimension of the electrophoresis.

Electrophoresis runs

The tricine buffer was used as electrophoresis buffer. The gel was placed in Multiphor II electrophoresis system (GE Healthcare, Velizy-Villacoublay, France) and wells were filled with 2.5 µL of samples for the serial migration. Bromophenol blue (1.3 mg.mL -1 , 2.5 µL) was placed in the secondary wells on the left (Fig. 1H). Samples were then subjected to the first dimension electrophoresis (600 V, 16 mA, 100 W), freely migrating in the agarose gel band according to their molecular weight and charge. Electrophoresis was stopped when the blue indicators have crossed 6 cm. Then, the gel was turned by 90° to achieve the second dimension corresponding to the rocket immunoelectrophoresis (500 V, 12 mA, 100 W), that lasted for 3h30min. Gels were dried and stained as described previously [START_REF] Walker | The Protein Protocols Handbook[END_REF].

Scanning and quantification

The gels were scanned at a resolution of 800 dpi (Scanner Epson Perfection V100 Photo) (Fig. 1I). Area under peaks was integrated using ImageJ software (Fig. 1J). The first peak on the left side was recognized as native C3, whereas the second peak from the left was attributed to protein fragments derived from C3 cleavage. The % of activation was expressed as the ratio of peak area of cleaved protein regarding the total peak area of C3 native and fragments.

Robustness and precision of the method 2.5.1. Sample preparation

Three samples with different degrees of activation of the C3 protein were prepared from dispersions R66, R17 and A66 used at a surface concentration of 1934, 1874 and 3934 cm 2 .mL -1 respectively. These samples appropriately corresponded to low (A0), partial (A50) and full activation (A100) of the protein C3 and were prepared as mentioned in section 2.3.

Exploration of robustness and precision of the method

Several factors were tested in order to investigate the robustness and precision of the method, as described by ICH [START_REF] Walker | Validation of analytical procedures: Text and Methodology Q2(R1), Current Step 4 version[END_REF] and ISO standard [START_REF]Accuracy (trueness and precision) of measurement methods and results -Part 1: General principles and definitions[END_REF]. The robustness of a method reflects its capacity to give unaffected results under small variation of the measurement conditions and thus give indications about its reliability for a normal usage [START_REF] Walker | Validation of analytical procedures: Text and Methodology Q2(R1), Current Step 4 version[END_REF][START_REF]Accuracy (trueness and precision) of measurement methods and results -Part 1: General principles and definitions[END_REF].

Factors considered in the robustness study were:

-The position of the sample on the slab gel. Two different gels containing the same samples disposed at different positions were run on the same day on the same electrophoresis tank. -The electrophoresis system. Two different gels with samples at the same position in both gels were simultaneously run on two distinct electrophoresis systems. -The influence of the analyst. Two different experimenters did the same experiment, using the same samples on the same system. Each experimenter prepared its own gel, ran the electrophoresis independently and analyzed the obtained gel after coloration. -The sample preparation. A total of five preparations of each sample (A0, A50 or A100) were realized the same day. Each sample was analyzed on one gel slab.

The precision of a method expresses the closeness between a series of measurements under defined conditions [START_REF] Walker | Validation of analytical procedures: Text and Methodology Q2(R1), Current Step 4 version[END_REF][START_REF]Accuracy (trueness and precision) of measurement methods and results -Part 1: General principles and definitions[END_REF]. The precision was investigated through intra-day variation (repeatability) and inter-day variation (intermediate precision).

Three models of NP samples [14,[START_REF] Labarre | [END_REF] were repeated and analyzed for their ability to give the same activation under variations of the above mentioned experimental factors as summarized in Table 1. It is noteworthy that the gel preparation was independent for each experiment.

Statistical analysis of the MultiCrossed-IE

The investigation of the robustness and precision of the method was performed by means of ANOVA tests, as described in the GUM [START_REF]Guide to the expression of uncertainty in measurement[END_REF] and the standard ISO [START_REF]Accuracy (trueness and precision) of measurements methods and results -Part 3: Intermediate measures of the precision of a standard measurement method[END_REF]. The General Linear Model of ANOVA test in Minitab 16.0 was used on this purpose. Briefly, ANOVA test allows determining whether one or several factors have a significant influence on the response of the measured variable, here the % activation of the protein C3. ANOVA was applied after verification of the hypotheses allowing its applicability, namely the normal distribution of residuals (Ryan-Joiner's test) and variances homoscedasticity (Levene's model).

The robustness was assessed through the factors position, system, analyst and sample preparation by means of the p-value. The p-value corresponds to the probability to find the observed, or more extreme, results when the null hypothesis is true i.e. the studied factor has no significant effect on the variable response. If the p-value is higher than the significance level fixed at 0.05 in this work, it suggests that the data are consistent with the assumption that the null hypothesis is true and the null hypothesis has to be accepted. So, the tested factor did not introduce significant difference on the response variable when p-value resulting from its associated ANOVA was higher than 0.05. The threshold for the p-value was chosen consistently with those generally found in the literature. To study the precision of the method, we assessed the intermediate precision and the repeatability via the calculation of the RSD of % C3 activation values determined for A0, A50 and A100.

Characterization of C3 activation induced by nanoparticles

Samples of the three types of NP were prepared with different amounts of surface area (ranging from 500 to 4950 cm 2 .mL -1 ) and analyzed by MultiCrossed-IE. The % of activation of protein C3 was determined and plotted against the concentration of NPs expressed in surface area (cm 2 .mL -1 ). The concentration in NPs producing 50% of the cleavage of the protein C3 was defined as the C 3 A 50 .

Results

Nanoparticle characterization

Hydrodynamic diameter, Polydispersity index (PDI), zeta potential, mass and surface concentration of NP in dispersions are summarized in Table 2 and were consistent with those found in previous works [14,[START_REF] Labarre | [END_REF][START_REF] Bertholon | [END_REF].

Heat resistance of the antibody

To prepare agarose gel plates for the MultiCrossed-IE, the agarose gel must be spread on a 15x20 cm Gel-Fix™ film. During this operation, the antibody is added to a hot agarose solution and must resist to the high temperature required to cast a homogeneous gel plate. A preliminary experiment aimed to determine the maximum temperature at which full activity of the antibody was preserved. This was assessed by a radial immunodiffusion method designed on this purpose. As shown in Figure S1, decrease of the immunodiffusion circle areas was clearly observed for anti-C3 antibody samples heated above 60°C that can be explained by the denaturation of the antibody. The full activity of the antibody was preserved after heating at 60°C which was the maximum temperature that can be used to prepare gel plates. Gels for the MultiCrossed-IE were then casted at 60°C.

MultiCrossed-IE (versus orginal method)

The gel plate was conceived to achieve the migration of 7 samples on the same horizontal line. 5 bands were built in the gel for a parallel migration of samples. Compared with the original method [11] allowing 5 samples to be analyzed at once on individual 5x7 cm gel plates, the designed serial electrophoresis provided 35 stamp-sized electrophoregrams (2.8x3 cm). It was checked that performances of the original method were preserved in the stamp-size electrophoregrams obtained from the MultiCrossed-IE (Table 3 and Fig. S2).

Study of the robustness and precision of the method

For the evaluation of robustness and precision, samples A0, A50 and A100 were prepared with inhibitors of complement cascade added at the end of the incubation. Same samples could be analyzed several times to investigate the robustness and precision of the MultiCrossed-IE using statistical analysis by ANOVA. Different factors were independently assessed. Hypotheses verifications for the ANOVA analysis are shown in S3. The obtained p-values and RSDs for the different tested factors are depicted in Table 1. Results showed that there was no significant bias introduced by the position of a sample on the gel plate, the electrophoresis system, the analyst doing the experiment and the preparation of the sample. It is noteworthy that no significant difference was found even when two different analysts applied the experiment. This means that the results were not significantly different analyzing the 3 different samples (A0, A50 and A100) while the method was performed on gels made by the two independent analysts and the analyses of the electrophoregrams were carried out independently by the two analysts. Robustness was verified for a confidence level of 95% performing MultiCrossed-IE on identical samples. For the precision, RSDs of intra-day variation reflecting the repeatability and RSDs of inter-day variation corresponding to intermediate precision were summarized in the lower part of Table 1B. The RSD values found for the inter-day were below 4% for all samples (A0, A50 and A100). This indicated that there was no variation added by the day of the experiment. The repeatability remains constant from one day to another. The p-value associated to inter-day variation was also determined giving p-values of 0.814, 0.169 and 0.300 for A0, A50 and A100 respectively. As all these values were superior to 0.05 showing that no significant variation was introduced by the factor day (see paragraph 2.5.3).

Table 3: Comparison of the main features between the original method and MultiCrossed-IE.

*See more in Fig. S2 3.

Complement C3 activation triggered by nanoparticles

The interaction of nanomaterials with blood proteins is a matter of contact between these two entities and is thus driven by the amount of surface engaged in this process. Hence, the surface of NP exposed to serum proteins impacts on the strength of interaction triggered and this phenomenon can be exploited to define a characteristic of a given nanomaterial toward its ability to activate the complement cascade. Protein C3 activation patterns were studied for the three nanoparticles used as reference samples providing with different levels of activation. Investigating the % of cleaved C3 fragments produced by different amounts of NP's incubated in serum, the surface of NP that activates 50% of protein C3 present in the sample was determined (C 3 A 50 ). NPs R17 and A66 have reached full activation with the highest tested concentrations. The curve giving the % activation as a function of the concentration showed a sigmoidal shape (Fig. 2).

Figure 2: Determination of C 3 A 50 for the three model NPs R17 (A), A66 (B) and R66 (C). Top -Graph representing the values of C3 % activation obtained in function of NP concentration for R17, A66 and R66 respectively. Bottom -Electrophoregrams obtained by MultiCrossed-IE with increasing concentration in NP added in the sample test.

Values correspond to tested surface of NP in cm 2 .mL -1 .

The C 3 A 50 that could be determined were 1625 cm 2 .mL -1 (6.0 mg.mL -1 ) for R17 and 1500 cm 2 .mL -1 (2.5 mg.mL -1 ) for A66 (Table 2). The results were consistent with data of the literature reporting a high % of activation of these two types of NP at a tested surface of 2000 cm 2 .mL -1 [14,[START_REF] Labarre | [END_REF]. Nanoparticle R66 does not activate the complement above 20% up to a surface concentration of 4950 cm 2 .mL -1 (26.4 mg.mL -1 ) (Fig. 4C). The activation observed was just above the level of the spontaneous activation of C3 observed in the experimental conditions used in this study (9% of activation). These results were also consistent with previous data provided at a surface of 2000 cm 2 .mL -1 [START_REF] Labarre | [END_REF]. The very low capacity of these NP to activate the complement system revealed here is consistent with their stealth properties reported in vivo [32] and the property of their dextran corona to hamper interactions of the NP core with protein C3 [33].

Discussion

C-IE is a quite old method [34], which was used in several immunological applications [35]. The originality of the proposed method includes the possibility to migrate samples in series during the first and second dimensions. Traditional methods used to make several migrations in parallel during the first dimension, before cutting bands of the 1 st dimension gel to transpose on the second dimension gel containing the antibody for the IE [11,35]. The method proposed in this work greatly simplifies the complex handling found in previous methods while it did not affect the performance. With the new method, one single gel is prepared and the only manipulation between the first and the second electrophoresis is to turn the gel by 90°. The overall time required to perform the 2D electrophoresis runs was also considerably reduced (4h45min against 19h15min with the previous method). Simultaneously, the number of analysis performed in one run was multiplied by 7. Because the size of gel for one sample was reduced to the size of a stamp (from 5x7 cm to 2.8x3 cm), a significant reduction of the amount of reagents was also achieved (Gel-Fix™, gel, antibody, sample), hence reducing the cost for one analysis. The different improvements are summarized in Table 3.

ANOVA is commonly used in validation of chromatographic methods [36,37]. In the present study, it was applied to validate an electrophoretic method. To carry on this validation, we have performed experiments with a large number of gels. The results have demonstrated that the method is remarkably robust varying different factors. Indeed, the robustness study of the developed MultiCrossed-IE showed that position, electrophoresis system, analyst and preparation of the sample did not have a significant influence on the results of C3 activation. RSDs for intra and inter-day variations conformed with values found in the literature. Level of complement C3 activation is a complex process that is not fixed and evolves with time. For this study, standards did not exist, it was thus necessary to halt the evolution of C3 activation after the time of incubation, in order to use a sample several times for the validation purpose. Further activation was blocked by addition of EDTA and NM. We could then store and re-use the same sample for validation of the tested factor.

The proposed method of the MultiCrossed-IE was applied to determine the pattern of activation of C3 triggered by the three model NPs used in the present work. NP concentration was expressed by means of the exposed surface. Indeed, NPs have different size while protein adsorption depends on the available area on nanoparticle surface. Contact of proteins with NP surface are responsible for the activation of the complement cascade and it appeared logical to express the quantity of nanoparticles by the surface exposed reported to the volume of sample.

Thanks to the high throughput capacity given by the new MultiCrossed-IE method, it was applied to screen the influence of the amount of surface of NP tested on the level of complement C3 activation. A new parameter was defined as the surface concentration that induces 50% of protein C3 cleavage after 1h of incubation with serum at 37°C (C 3 A 50 ). The values determined for the three types of NP may be of interest to class them and could eventually help to anticipate their accumulation in the immune system after intravenous administration or their capacity to induce a CARPA reaction. The new MultiCrossed-IE now provides with the opportunity to determine this characteristic from a validated method of evaluation of complement C3 protein activation. This is in contrast with many other methods that only allow comparisons at a single tested concentration and are eventually based on an indirect evaluation of C3 activation such as the CH50.

New modalities of the application of C-IE were established allowing high throughput and making easier the handling by performing MultiCrossed-IE on a single gel plate. Demonstration of the robustness of the proposed protocol towards different factors and improvements of the method should renew the interest of C-IE methods for the analysis of specific proteins. A straightforward application is the evaluation of the activation of protein C3 of the complement system triggered by nanomaterials. It allows the evaluation of nanomaterial interactions with the immune system, which are important to anticipate their safety and biodistribution. This work was financially supported by BPI France -Project NICE.

S1: Heat resistance of the antibody

S2: Comparison between classical IE and MuliCrossed-IE

Table 1 :

 1 Evaluation of robustness and precision of the MultiCrossed-IE monitoring the activation of the protein C3 by three samples of nanoparticles showing low activation (A0), medium activation (A50) and high activation (A100) of the protein C3. A: General design of ANOVA tests used for factors influence of the position of the sample (Position), electrophoresis system (System), analyst (Analyst), sample preparation (Sample prep) and day (Intra-day and Inter-day). i and ii represent the number of levels of the tested factor and the number of replicates made for a given sample in each gel respectively. B: Results of the statistical analysis by ANOVA tests. Robustness was evaluated by pvalues (The factor did not introduce a significant difference for a p-value > 0.05, see paragraph 2.5.3.). Precision was assessed by RSD values.

Figure S1 :

 S1 Figure S1: (A) Immunoprecipitated rings obtained after 24h of radial immunodiffusion for indicated heating of antibodies. (B) Plot of immunoprecipitated circles areas against temperature of antibody heating.

Figure S2 :

 S2 Figure S2: Comparison of the original size immunoelectrophoregrams (raw on the top) with the stamp-size obtained from the MultiCrossed-IE (raw on the bottom). A stamp (La Poste, 2001, Eve Luquet) is shown for size comparison with stamp-size electrophoregram. -A, B and C correspond to A0, A50 and A100 respectively. Percentages correspond to the % of C3 activation.

  : Distribution of residues and Ryan-Joiner's Test results for robustness study of tested factors: Position (a), System (b), Analyst (c), Sample preparation (d) and Day (e).

  Robustness study -

Table 2 :

 2 Characteristics of the three dispersions of model NPs used in the study and values of C 3 A 50 determined by MultiCrossed-IE.

  Results for Levene's test

	Factor	Levene's test p-value
		A0	A50	A100
	Position	0.461	0.772	0.926
	System	0.296	0.461	0.711
	Analyst	0.135	0.312	0.146
	Sample preparation	0.156	0.449	0.384
	Day	0.814	0.169	0.300

The authors declare no conflict of interest.

Supporting information