Asma Bahri

Corinne Henriquet

Martine Pugnière

Sylvie Marchesseau

Dominique Chevalier-Lucia
email: dominique.chevalier-lucia@umontpellier.fr

Binding analysis between monomeric β-casein and hydrophobic bioactive compounds investigated by surface plasmon resonance and fluorescence spectroscopy

Keywords: β-casein, curcumin, vitamin D3, surface plasmon resonance, fluorescence quenching, binding parameters. Chemical compounds studied

Curcumin (PubChem CID: 969516); Vitamin D3 (PubChem CID: 5280795)

Introduction

Over the past years, there has been a high demand for incorporation of biologically active natural ingredients into functional food to contribute to consumer's well-being (Vieira da Silva, [START_REF] Vieira Da Silva | Natural phytochemicals and probiotics as bioactive ingredients for functional foods: Extraction, biochemistry and protected-delivery technologies[END_REF]. However, most of these bioactives display low solubility, poor stability during processing, and low permeability in the gastrointestinal tract. Therefore, different encapsulation strategies have been developed in order to avoid these limitations and protect these molecules during processing and storage, maintaining their active molecular form until consumption and delivery to the physiological target within the organism [START_REF] Okuro | Structures design for protection and vehiculation of bioactives[END_REF]. Milk proteins, especially caseins, have unique and interesting functional properties making them effective nanocarriers for bioactives [START_REF] Ranadheera | Utilizing unique properties of caseins and the casein micelle for delivery of sensitive food ingredients and bioactives[END_REF]. As casein micelles is a natural self-assembly, some studies investigated the binding of hydrophobic compounds such as curcumin to native casein micelles [START_REF] Sahu | Fluorescence study of the curcumin-casein micelle complexation and its application as a drug nanocarrier to cancer cells[END_REF] or to modified casein micelles [START_REF] Benzaria | Interaction of curcumin with phosphocasein micelles processed or not by dynamic high pressure[END_REF]. Among the four different caseins, αs1-, αs2-, β-and κcaseins, a particular interest is paid to β-casein. This phosphoprotein, composed of 209 amino acids and with a molecular weight ~ 24 kDa, constitutes about 37% of the caseins in bovine milk and is the most hydrophobic casein thanks to its hydrophobic Cterminal tail rich in proline residues. Consequently, several studies have shown that βcasein can be used as a natural nanocarrier for hydrophobic bioactive molecules in order to increase their bioavailability [START_REF] Semo | Casein micelle as a natural nano-capsular vehicle for nutraceuticals[END_REF][START_REF] Shapira | β-Casein nanoparticle-based oral drug delivery system for potential treatment of gastric carcinoma: Stability, target-activated release and cytotoxicity[END_REF]. Particularly, the separation between its hydrophobic C-terminal domain and its hydrophilic highly charged N-terminal domain containing an anionic phosphoserine cluster makes it highly amphiphilic allowing the βcasein self-association in small oblate micelles [START_REF] Holt | Caseins as rheomorphic proteins: interpretation of primary and secondary structures of the αs1-, β-and κ-caseins[END_REF][START_REF] Swaisgood | Chemistry of the caseins[END_REF]. The intermolecular interactions to form β-casein micelles occur at concentrations above the critical micellization concentration (CMC) of ~ 0.5 -2 mg/mL at milk pH (6.8) and room temperature [START_REF] O'connell | Association behavior of βcasein[END_REF]. Several studies have investigated the encapsulation of hydrophobic molecules inside the hydrophobic core of β-casein micelles and have shown an improvement of the efficiency of poorly water-soluble compounds using this nanocarrier system [START_REF] Esmaili | β-casein-micelle as a nano vehicle for solubility enhancement of curcumin; food industry application[END_REF][START_REF] Mehranfar | Binding analysis for interaction of diacetylcurcumin with β-casein nanoparticles by using fluorescence spectroscopy and molecular docking calculations[END_REF]. At the same time, some studies have focused on the investigation of the binding between β-casein and hydrophobic bioactive molecules such as lipophilic vitamins [START_REF] Forrest | Interactions of vitamin D3 with bovine β-lactoglobulin A and β-casein[END_REF], flavan-3-ol derivatives [START_REF] Bohin | Efficacy of food proteins as carriers for flavonoids[END_REF] or naringenin [START_REF] Moeiniafshari | Exploring the interaction of naringenin with bovine β-casein nanoparticles using spectroscopy[END_REF]. The fluorescence spectroscopy is a commonly method used in these studies to evaluate the interaction between the hydrophobic bioactive compound and the protein. Indeed, fluorescence quenching analysis, recognized as a highly sensitive methodology with a fast and easy implementation, evaluates the changes in the local environment of the fluorophore and tryptophan residues, as a consequence of molecular interaction [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF].

Molecular interaction affinities can also be investigated using surface plasmon resonance (SPR). SPR is recognized as a technique giving the ability to detect highly dynamic complexes being difficult to investigate using other techniques [START_REF] Douzi | Protein-protein interactions: Surface Plasmon Resonance[END_REF]. This well-suited label-free optical technique for affinity characterization provides realtime monitoring of binding kinetics. The method is based on the immobilization of one of the binding partners on a functionalized sensor surface. The other partner, free in solution, is then injected over the surface containing the immobilized molecule. The binding is monitored by subsequent changes in the refractive index at the biosensor surface [START_REF] Homola | Surface plasmon resonance sensors: review[END_REF].

SPR has been used more and more in the last decade to characterize the interactions between proteins and low molecular weight molecules in biochemical, biophysical and biomedical fields [START_REF] Vachali | Surface plasmon resonance (SPR) studies on the interactions of carotenoids and their binding proteins[END_REF]Watrelot et al., 2016;[START_REF] Xiao | Interaction between a cationic porphyrin and bovine serum albumin studied by surface plasmon resonance, fluorescence spectroscopy and cyclic voltammetry[END_REF]. Some studies investigated SPR interactions between caseins [START_REF] Marchesseau | Casein interactions studied by the surface plasmon resonance technique[END_REF] or between caseins and polysaccharides [START_REF] Thompson | Use of surface plasmon resonance (SPR) to study the dissociation and polysaccharide binding of casein micelles and caseins[END_REF]. However, up to now, SPR has not been used to study and quantify the interaction between caseins and hydrophobic low molecular weight biomolecules.

Curcumin is a low-molecular weight, natural polyphenolic phytoconstituent isolated from the dried rhizome of the plant Curcuma Longa. It has been used for centuries as a naturally occurring medicine for disease treatment and displays potent antiinflammatory, antitumor and antioxidant activities [START_REF] Hewlings | Curcumin: a review of its' effects on human health[END_REF].

However, curcumin bioavailability is limited due to its low solubility in aqueous solution (2.99 x 10 -8 M) and it is characterized by a poor stability towards oxidation and light. Vitamin D3, one of the major forms of vitamin D, is hydrophobic in nature and highly susceptible to environmental conditions such as temperature and light. It is implicated in active intestinal calcium absorption but it was also shown recently that its role also includes immune function, cardiovascular health and cancer prevention (Gupta, Behera, Pawdal, Rawat, Baldi & Gupta, 2019). Nowadays, vitamin D 3 deficiency is a public health problem in many countries. Therefore, the supplementation of food products with curcumin or vitamin D3 could offer additional source of these essential hydrophobic bioactive compounds.

The objective of the present work was to study the interactions of β-casein with curcumin and vitamin D3 using surface plasmon resonance and fluorescence quenching spectroscopy. The binding kinetics were investigated using both methodologies by gradually adding higher concentrations of hydrophobic bioactives to β-casein. A comparison of binding affinities was then performed for the two different hydrophobic molecules.

Materials and methods

Materials and chemicals

β-casein from bovine milk (> 98%), curcumin (PubChem CID: 969516, ≥ 65%), chloramphenicol (PubChem CID: 5959), absolute ethanol (PubChem CID: 702), dimethyl sulfoxide (DMSO, PubChem CID: 679) and 4-(2-hydroxyethyl)-1piperazineethanesulfonic acid (HEPES, PubChem CID: 23831) were purchased from Sigma-Aldrich (Saint-Quentin Fallavier, France). Vitamin D3 (PubChem CID: 5280795, 99%) was obtained from Thermofisher Acros Organics (Geel, Belgium).

Sodium acetate was purchased from Merck (Darmstadt, Germany). CM5 sensor chips, HBS-EP buffer (0.01 M HEPES pH 7.4, 0.15 M NaCl, 3 mM EDTA and 0.005% v/v surfactant P20), HBS-EP+ buffer (0.01 M HEPES pH 7.4, 0.15 M NaCl, 3 mM EDTA and 0.5% v/v surfactant P20), HBS-N buffer (0.01 M HEPES pH 7.4, 0.15 M NaCl), Nethyl-N'-(dimethylaminopropyl)carbodiimide hydrochloride (PubChem CID: 2723939, EDC), N-hydroxysuccinimide (PubChem CID: 80170, NHS) and 1M ethanolamine-HCl pH 8.5 were all sourced from GE Healthcare Life Sciences (Velizy-Villacoublay, France). All solutions were prepared using Milli-Q water (Millipore®).

Surface plasmon resonance (SPR) studies

SPR analyses to evaluate the interaction of curcumin or vitamin D3 (analyte) with βcasein (ligand) immobilized onto a carboxymethylated dextran sensor surface (CM5 sensor chip) were performed using a Biacore T200 apparatus at 25°C (GE Healthcare Life Sciences, Uppsala, Sweden). During the analyte-ligand interaction, the change of the refractive index was measured in real time that allowed to plot the results of interaction as response units (RU) versus time (one RU represents the binding of 1 pg of protein per square mm).

Covalent immobilization of β-casein on CM5 sensor chip

β-casein was covalently immobilized on the CM5 sensor chip by a standard aminecoupling chemistry according to the manufacturer's protocol (GE Healthcare). Briefly, the surface was functionalized with 0.4 M EDC and 0.1 M NHS mixture. 40 µM βcasein stock solution was prepared in HBS-EP buffer (pH 7.4). The ß-casein monomeric state in the experimental conditions was checked by dynamic light scattering analysis (data not shown). The solution was vortexed and placed in an ultrasonic bath for 10 min. Prior to covalent immobilization, a preconcentration test at different pH values was performed to obtain the optimum pH for the immobilization procedure. Thus, β-casein stock solution was diluted at 20-30 µg/mL in 10 mM acetate buffer at pH 3.6 and was injected at 10 µl/min on two flow cells to reach two different immobilization levels of 2700 RU and 6900 RU, respectively. These two different β-casein immobilization levels were explored in order to monitor the effect of mass transport hindrance caused by the surface binding sites located at different points [START_REF] Schuck | The role of mass transport limitation and surface heterogeneity in the biophysical characterization of macromolecular binding processes by SPR biosensing[END_REF]. The unreacted carboxyl groups of the dextran were blocked with 1 M ethanolamine-HCl, pH 8.5 and the surface was washed with HBS-N buffer. One other flow cell, treated with the same procedure but without protein was used as a control surface. Coated surfaces were stable for at least 2 days.

Kinetic analysis of β-casein-hydrophobic bioactive compound interaction

Bioactive compound stock solutions were prepared by dissolving curcumin (34 mM) in DMSO and vitamin D3 (53 mM) in ethanol. For each bioactive compound, a specific solvent was selected to ensure a high solubility of the bioactive compound; curcumin solubility in DMSO is 68 mM and vitamin D3 solubility in ethanol is 78 mM. Stock solutions were filtered through a 0.2 µm cellulose-acetate membrane (Sartorius, Goettingen, Germany) and protected from light during experiments. The bioactive compound stock solution concentrations were spectrophotometrically determined at 420 nm for curcumin using a molar absorption coefficient (ε) of 49,000 AU/mol/cm in DMSO [START_REF] Khumsupan | Apolipoprotein E LDL receptor-binding domain-containing high-density lipoprotein: a nanovehicle to transport curcumin, an antioxidant and anti-amyloid bioflavonoid[END_REF] and at 265 nm for vitamin D3 using a molar absorption coefficient (ε) of 18,300 AU/mol/L in ethanol [START_REF] Vieth | Randomized comparison of the effects of the vitamin D3 adequate intake versus 100 mcg (4000 IU) per day on biochemical responses and the wellbeing of patients[END_REF]. Prior to SPR analysis, bioactive compound stock solutions were diluted using HBS-EP+ buffer to obtain bioactive compound concentrations between 3 and 1000 µM. The final concentration of DMSO and ethanol did not exceed 3% (v/v) in diluted bioactive compound solutions injected in flow cells.

HBS-EP+ containing 3% (v/v) DMSO or 3% ethanol was used as running buffer. The diluted bioactive compound solutions at various increasing concentrations were successively injected. The analysis cycle for each bioactive compound concentration consisted, for the control cell and both β-casein coated flow cells, in the injection of the running buffer at a flow rate of 30 µL/min, then the diluted bioactive compound solution for 60 s (association phase) and finally the running buffer for 100 s (dissociation phase). The signal of the control surface flow cell was subtracted from the signal of the ß-casein flow cells. Chloramphenicol, a negative control, was also injected at 500 and 1000 µM in HBS-EP+ containing 3% (v/v) DMSO. Each experiment series included blanks (running buffer), injection of bioactive compound, negative control, and solvent corrections. Experiments were repeated three times. Sensorgrams were analyzed using BIA evaluation 3.0 software by steady-state fitting with the one-to-one Langmuir binding model to obtain KD value. When a bioactive compound, injected in the flow system as the analyte, reacts with ß-casein, immobilized as the ligand, to form a complex, the rate of the complex formation depends on the free concentrations of the bioactive compound ([Bioactive]) and ß-casein ([ß-casein]) as well as the stability of the formed complex ([Bioactive-ß-casein]) and can be described by the Langmuir binding model equation (Eq. 1) [START_REF] Myszka | Equilibrium analysis of high affinity interactions using Biacore[END_REF]:

d[Bioactive-ß-casein]/dt = Ka [Bioactive] [ß-casein] -Kd [Bioactive-ß-casein] (1)
where Ka is the association rate constant and Kd is the dissociation rate constant.

In SPR experiment, the Langmuir binding model equation (Eq. 1) can be written as Eq. 2:

dR/dt = Ka C (Rmax-R) -Kd R (2)
where the bound bioactive concentration ([Bioactive-ß-casein]) is directly proportional to the SPR response (R), the concentration of the analyte ([Bioactive]) is the injected concentration (C) and the free ß-casein concentration ([ß-casein]) is obtained as the difference between Rmax, maximum response due to analyte binding directly proportional to the total ß-casein concentration, and R.

At steady state, dR/dt = 0 and Eq. 2 can be written as Eq. 3:

C (Rmax-R) = KD R (3)
where KD= kd/ka. The effectiveness of the fitting is evaluated by the χ 2 value.

Evaluation of β-casein-hydrophobic bioactive compound interaction by fluorescence spectroscopy

Fluorescence measurements were performed on a Cary Eclipse spectrofluorimeter at 25°C using a 1 cm quartz cuvette (101-QS, Hellma Analytics). A 20 µM β-casein stock solution was freshly prepared in a 10 mM HEPES buffer (pH 7.1). The solution was then vortexed and placed in an ultrasonic bath for 1 h before being filtered through a 0.2 µm cellulose-acetate membrane (Sartorius, Goettingen, Germany). The β-casein concentration was checked by absorbance measurement at 280 nm using an extinction coefficient E (1%/1 cm) of 4.65 [START_REF] De Kruif | Micellisation of β-casein[END_REF]. Concurrently, curcumin and vitamin D3 stock solutions (3 mM) were prepared in absolute ethanol then filtered through a 0.2 µm cellulose-acetate membrane (Sartorius, Goettingen, Germany). The bioactive compound concentrations in ethanol were evaluated by measuring the absorbance at 427 nm for curcumin solution and at 265 nm for vitamin D3 solution with a molar extinction coefficient of 61,864 AU/mol/L/cm [START_REF] Majhi | Binding of curcumin and its long chain derivatives to the activator binding domain of novel protein kinase C[END_REF] and 18,300 AU/mol/L/cm [START_REF] Vieth | Randomized comparison of the effects of the vitamin D3 adequate intake versus 100 mcg (4000 IU) per day on biochemical responses and the wellbeing of patients[END_REF] for curcumin and vitamin D3, respectively. For both bioactive compounds, β-casein intrinsic fluorescence was measured at a concentration of 8 µM in the presence of increasing concentrations of curcumin and vitamin D3by adding 1 to 100 µL of bioactive compound solution to βcasein dispersion. The mixture was immediately vortexed for 15 s and allowed to equilibrate for 5 min before fluorescence measurements. The emission spectra were recorded from 290 to 500 nm with an excitation wavelength of 280 nm. Both the excitation and emission slit widths were set at 5 nm. A control experiment was performed on β-casein without an addition of bioactive compound and treated exactly as the sample containing bioactive compound. The measurements have been repeated three times and the mean values were reported.

Statistical analysis

All measurements were made in triplicates at least. The differences were considered significant at p < 0.05 level.

Results and discussion

Surface plasmon binding experiments

β-Casein immobilization on CM5 sensor chip

To minimize the effects of mass transport, steric hindrance, crowding and aggregation of high capacity surface, it is recommendable to have low protein density surface and high running flow rate for kinetics evaluation by SPR [START_REF] Xiao | Interaction between a cationic porphyrin and bovine serum albumin studied by surface plasmon resonance, fluorescence spectroscopy and cyclic voltammetry[END_REF]. Nevertheless, for the binding analysis with low molecular weight molecules, such as curcumin and vitamin D3, the mass transport effect is minimized and a high density of protein immobilization is necessary to enhance the binding between β-casein and hydrophobic compounds in order to obtain a maximum of response in RU.

Two experimental conditions require special attention to optimize the immobilization of β-caseins on CM5 sensor chip. Firstly, the β-casein dispersion has to be prepared at a low concentration (20-30 µg/mL) in order to prevent its self-association occurring at concentrations above 0.5 to 2 mg/mL at milk pH (6.8) and 25°C prior to immobilization [START_REF] O'connell | Association behavior of βcasein[END_REF]. Besides, the highest level of immobilization of a protein on a carboxymethyl dextran chip (CM5) is obtained when the running buffer has a pH approximately one unit below the protein isoelectric point (pI). At this pH, the protein has a net positive charge and, consequently, electrostatic interactions between the positively charged protein and the negatively charged carboxymethyl dextran matrix increase the pre-concentration of the protein at the chip surface for the amine coupling establishment [START_REF] Johnsson | Immobilization of proteins to a carboxymethyldextran-modified gold surface for biospecific interaction analysis in surface plasmon resonance sensors[END_REF]. Consequently, it is impossible to immobilize β-casein at milk pH (∼6.8). Thus, the pH was lowered to 3.6 since the β casein pI is 4.8 [START_REF] Walstra | Dairy Science and Technology[END_REF]. These optimized conditions have enabled high β-casein immobilization densities (i.e.6900 RU and 2700 RU, the two different levels tested) on CM5 sensor chip. The N-hydroxy succinimide esters activated by the functionalization of the CM5 carboxyl groups by EDC/NHS have enabled protein binding to the surface by amine coupling. As primary amines are highly reactive, there is a strong probability that β casein was covalently linked to the CM5 chip thanks to the N terminus hydrophilic region. Besides, according to the amino acid sequence of β-casein, the other primary amines from lysine are mostly located on the hydrophilic region close to the N-terminus region [START_REF] Fischer | Amine Coupling Through EDC/NHS: A Practical Approach[END_REF][START_REF] Holt | Caseins as rheomorphic proteins: interpretation of primary and secondary structures of the αs1-, β-and κ-caseins[END_REF]. Consequently, the hydrophobic fragment of β casein should be more available for hydrophobic interactions with hydrophobic molecules.

Surface plasmon resonance kinetic analysis

The sensorgrams and the concentration-dependence of the specific binding of curcumin to immobilized β-casein after DMSO and double blank correction are presented in Fig. 1A-B and Fig. 1C-D, respectively. These results are shown for two β-casein immobilization levels, 6900 RU for Fig. 1A and C and 2700 RU for Fig. 1B andD. No association was observed for either the control flowcell or the negative control. As expected for small molecular weight molecules, the box-shape of the sensorgram revealed fast association and dissociation rates, which makes difficult to quantify them.

As curcumin is poorly soluble in aqueous solutions (2.99 × 10 -8 M) [START_REF] Letchford | Solubilization of hydrophobic drugs by methoxy poly(ethylene glycol)-block-polycaprolactone diblock copolymer micelles: theoretical and experimental data and correlations[END_REF], different organic solvents like dimethyl sulfoxide (DMSO) and ethanol were considered. As the solubility information for curcumin according to the supplier was of 10 mg/mL and 25 mg/mL in ethanol and DMSO, respectively, DMSO was chosen as solvent in order to reach higher concentrations of curcumin in the diluted solution injected during the association phase. Unlike curcumin, vitamin D3 shows higher solubility in ethanol (30 mg/mL) than in DMSO. Therefore, ethanol was used as a solvent for vitamin D3 prior to SPR study. However, vitamin D3 was unsuccessfully analyzed using the same procedure as for curcumin tested in HBS EP+ containing 3% ethanol (Fig. 2) and in 3% DMSO (v/v) (data not shown). The responses of vitamin D3 under these both conditions were under the limit of T200 Biacore apparatus sensitivity.

It clearly means that no interaction was observed between β-casein immobilized on CM5 chip and vitamin D3 under these SPR conditions. According to the manufacturer (GeHealthcare), the sensitivity of Biacore T200 apparatus enables precise affinity analysis of low molecular weight molecules with a maximal dissociation constant (KD) value in the millimolar range.

Concerning curcumin binding to β-casein and in order to obtain accurate estimations of the binding constants, SPR data have been analyzed by fitting the SPR sensorgrams using non-linear fitting of the SPR signal at the steady state with a Langmuir binding isotherm model [START_REF] De Mol | Kinetic and thermodynamic analysis of ligandreceptor interactions: SPR applications in drug development[END_REF]. The response in RU is then considered as directly proportional to the injected analyte concentration (C) (Fig. 1 A-B). The curves shown in Fig. 1 C-D represent steady-state affinity analysis of curcumin binding to βcasein fitted to 1:1 Langmuir interaction model. The KD value obtained from the SPR analyses is 4.1 ± 0.7 × 10 -4 M for curcumin in DMSO. The calculated χ 2 value (χ 2 = 4.54) indicates a good accuracy of the fitting. Figure 2 shows a comparison of doseeffect of curcumin and vitamin D3 in different solvents. The kinetic study obtained for curcumin dissolved in ethanol reveals similar kD value 6.9 ± 0.9 × 10 -4 M as that obtained in DMSO. However, vitamin D3 gave too low responses to be analyzed in 3% ethanol. Although the study of interactions between low molecular weight molecules and bovine proteins starts to be carried out by SPR technique [START_REF] Park | Effects of pH and protein conformation on in-solution complexation between bovine α-lactalbumin and oleic acid : Binding trend analysis by using SPR and ITC[END_REF]Watrelot et al., 2016), this analytical technique has not been used previously to study interactions between β-casein and hydrophobic low molecular weight molecules such as curcumin. To further explore the binding of β-casein to curcumin and vitamin D3, fluorescence spectroscopy was also performed to complement the SPR analyses.

Fluorescence spectroscopy analysis of β-casein interactions with curcumin and vitamin D3

Fluorescence spectroscopy dealing with transitions from the excited state to the ground state has a widespread application in the field of biophysics, pharmaceuticals but also food science [START_REF] Williams | Protein-Ligand Interactions: Methods and Applications[END_REF]. In order to get an additional insight on the interaction between small hydrophobic molecules and β-casein, the intrinsic fluorescence emission of β-casein solution excited at 280 nm wavelength was investigated after a progressive addition of each bioactive compound (vitamin D3 and curcumin). As for SPR study, the β-casein concentration is below its CMC in order to prevent its self-association. Fluorescence emission spectra of β-casein display a peak at 345 nm as shown in Fig. 3. The protein excitation at 280 nm caused the emission of mainly tryptophan residues and, in aqueous solution, the emission maximum wavelength of free tryptophan is close to 352 nm. A lower λmax of 345 nm was observed for the single tryptophan of individual β-casein located in its hydrophobic fragment. This blue shift could be attributed to the apolar environment location of this residue [START_REF] Benzaria | Interaction of curcumin with phosphocasein micelles processed or not by dynamic high pressure[END_REF]. The emission spectra of the β casein solution containing increasing content of curcumin (Fig. 3A) or vitamin D3 (Fig. 3B) show that the increase of bioactive compound concentration induced a gradual decrease of β-casein fluorescence intensity. This fluorescence quenching is attributed to curcumin-β-casein or vitamin D3-β-casein complex formation reducing the fluorescence intensity of the tryptophan residues residue. The maximum of the fluorescence emission spectra (λmax) was plotted against curcumin and vitamin D3 concentration in Fig 3C and3D, respectively. Curcumin-β-casein binding generates a blue shift of fluorescence emission maximum wavelength by ~12 nm in the presence of curcumin (Fig. 3C). This λmax shift points out the change in the polarity of the β-casein tryptophan residue microenvironment, as consequence of curcumin binding which strongly suggests the hydrophobic character of curcumin and β-casein interactions. This hydrophobic contact of curcumin with hydrophobic domain of β-casein was also reported by [START_REF] Bourassa | Binding sites of resveratrol, genistein, and curcumin with milk α-and β-caseins[END_REF]. Conversely, no shift was observed for vitamin D3-βcasein complexation (Fig. 3B) suggesting that the transfer of vitamin D3 from the polar aqueous environment to the apolar hydrophobic region of β-casein does not modify the hydrophobicity region close to the tryptophan residue as concluded for curcumin. This was in accordance with a previous study showing that the interactions of β-casein with vitamin D3 are mainly hydrophobic inducing a disturbance in the phenylalanine residues located in the hydrophobic domain of β-casein [START_REF] Forrest | Interactions of vitamin D3 with bovine β-lactoglobulin A and β-casein[END_REF]. Besides, as the phenolic hydrogens of curcumin have pKa values of 8.38, 9.88, and 10.51 in aqueous solutions, at experimental pH (~7.1), curcumin is in a neutral form and its binding due to charge interactions can be neglected [START_REF] Sahu | Fluorescence study of the curcumin-casein micelle complexation and its application as a drug nanocarrier to cancer cells[END_REF].

The binding constants were evaluated from the fluorescence quenching of β-casein in presence of bioactive compound. In order to check the presence of static or dynamic quenching in bioactive compound-β-casein complexes, Eq. 4 was used to evaluate the Stern-Volmer constant [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]:

S0/S =1+Ksv[Q] (4)
where S0 and S are the fluorescence areas in the absence and presence of bioactive compound, respectively, [Q] is the bioactive compound concentration and Ksv is the Stern-Volmer quenching constant. The Stern-Volmer plots for β-casein quenching by curcumin and vitamin D3 are presented in Fig. 4A and 4B, respectively. A linear dependence at bioactive compound concentrations lower than 10 µM clearly appeared for the two hydrophobic bioactive compounds indicating that the quenching is mainly static in nature with some degree of dynamic quenching at high bioactive compound concentrations. The Stern-Volmer quenching constants (KSV) for curcumin and vitamin D3 were evaluated to 13.5 ± 2.0 × 10 4 M -1 and 3.4 ± 0.3 × 10 4 M -1 , respectively.

When small molecules are bound independently to a set of equivalent sites on a macromolecule, the binding constant and the number of binding sites can be comparatively calculated assuming the static quenching by Eq. 5:

Ln[(S0-S)/S]= lnKA + n ln[Q] (5)
Here, S, S0, and [Q] are the same as the parameters in the Stern-Volmer equation (Eq. 4), KA is the association constant and n is the number of binding sites. The plots of ln[(S0-S)/S] versus ln[curcumin] and ln[vitamin D3] are shown in Fig. 4C and Fig. 4D, respectively. The n, KA, and KD estimated values for the β-casein-bioactive compound complexes are summarized in Table 1. The obtained KA and the number of binding sites value (n) for curcumin were 23.5 ± 1.9 × 10 4 M -1 and 0.74 ± 0.05, respectively. This association constant is in good agreement with that reported for bisdemethoxycurcumin of about 2.01 ± 0.03 × 10 5 M -1 [START_REF] Mehranfar | Spectrofluoremetric and molecular docking study on the interaction of bisdemethoxycurcumin with bovine β-casein nanoparticles[END_REF].

However, a four times lower KA value of 4.4 ± 0.03 × 10 4 M -1 was obtained for diacetylcurcumin-ß-casein interactions evaluated by fluorescence quenching in another previous study [START_REF] Mehranfar | Binding analysis for interaction of diacetylcurcumin with β-casein nanoparticles by using fluorescence spectroscopy and molecular docking calculations[END_REF]. These results suggest that the phenolic OH groups of curcumin and bisdemethoxycurcumin play an important role in the interaction with ß-casein [START_REF] Mohammadi | Analysis of binding interaction of curcumin and diacetylcurcumin with human and bovine serum albumin using fluorescence and circular dichroism spectroscopy[END_REF]. Lower KA values in the order of 1.10 3 M -1 were obtained for other polyphenols [START_REF] Hasni | Interaction of milk α-and β-caseins with tea polyphenols[END_REF].

The fluorescence quenching results obtained in a previous study investigating the interaction between curcumin and whole casein showed a higher binding constant (13.43 × 10 5 M -1 ) than that obtained in the present study (Nadi et al., 2014). This difference could be attributed to the presence of α and κ-caseins in the whole casein dispersion tested. The thermodynamic parameters evaluated in this study confirmed the hydrophobic nature of casein-curcumin interactions. Besides, the fluorescence results suggested that curcumin was located at the vicinity of the caseins tryptophanyl side chains due to a fluorescence energy transfer from the fluorophores (tryptophans) to the quencher (curcumin).

Concerning vitamin D3, a previous study on vitamin D3 and bovine β-casein interactions [START_REF] Forrest | Interactions of vitamin D3 with bovine β-lactoglobulin A and β-casein[END_REF] reported significantly higher KA values (3.8-7.7 × 10 6 M -1 ) compared to the KA presented in Table 1 (5.8 ± 1.1 × 10 4 M -1 ). This difference could be attributed to the ionic strength effect on the protein charges by the ions enhancing hydrophobic interactions due the decrease of the protein solubility.

Curcumin has clearly a significantly higher affinity to β-casein than vitamin D3. Firstly, the hydrophobicity of vitamin D3 (logP = 7.9) is significantly higher than that observed for curcumin (logP = 3.6), as evaluated by [START_REF] Costache | Polymer-drug interactions in tyrosine-derived triblock copolymer nanospheres: a computational modeling approach[END_REF], potentially limiting its flexibility in the aqueous medium during fluorescence measurements. Besides, the higher interaction obtained for curcumin could be attributed to its phenolic hydroxyl groups playing an important role in bioactive compoundprotein interactions. In fact, the two phenyl rings of curcumin are involved most likely in π-π stacking interaction with the aromatic side chains of β-casein [START_REF] Hobani | A comparative molecular docking study of curcumin and methotrexate to dihydrofolate reductase[END_REF][START_REF] Mcgaughey | π-stacking interactions alive and well in proteins[END_REF].

Comparing the binding kinetic results obtained using SPR and fluorescence quenching, it clearly appears that the equilibrium association constant (KA) obtained from fluorescence quenching is significantly higher than that evaluated by SPR (Table 1).

Same observations were previously reported by studies comparing SPR and fluorescence quenching for bimolecular interaction determination highlighting also lower association constants for SPR [START_REF] Plesa | Interaction between MMACHC and MMADHC, two human proteins participating in intracellular vitamin B12 metabolism[END_REF][START_REF] Xiao | Interaction between a cationic porphyrin and bovine serum albumin studied by surface plasmon resonance, fluorescence spectroscopy and cyclic voltammetry[END_REF]. This difference may be attributed to the different experimental conditions of these two techniques. The fluorescence quenching method is based on quenching of tryptophan residues when the excitation wavelength is set at 280 nm. That is to say, this method focuses on the interaction between tryptophan and hydrophobic molecules. When the fluorescence intensity decreases with the bioactive molecule addition, it means that the microenvironment of the tryptophan changed and the binding occurred between βcasein and the hydrophobic bioactive. Thus, the fluorescence quenching method does not consider the interaction between bioactive compounds and other sites on β-casein.

Concerning SPR method, it is based on refractive index change on the sensor chip surface. The entire signal is caused by any interaction recorded without consideration of the binding sites. However, in the case of our experiments, the β-casein monomers were immobilized on the sensor chip surface by amine coupling involving the binding of free amine groups mainly present on its hydrophilic tale which could favor the hydrophobic fragment available to interact with other molecules. The SPR allows the description of binding events of a number of different molecules to the immobilized ß-casein, which can be monitored in real-time without labeling requirements. The major advantage of SPR is the evaluation of specific interactions since the unspecific binding is evaluated on a control channel and thus removed from the measured signal. Therefore, both methods can be used to evaluate the interactions between hydrophobic bioactive compounds and β-casein while bearing in mind that the fluorescence method is focused on binding sites around the fluorophore residues while SPR is more accurate for all kinds of binding sites investigation.

Conclusion

ß-casein, the most hydrophobic casein in bovine milk, displays an open conformation which is easily accessible to gastric proteases. Hence, it may be used as an oral delivery vehicle to release hydrophobic bioactive molecules such as curcumin and vitamin D3.

The investigation of the affinities and kinetics of the interaction between ß-casein and two hydrophobic compounds was performed to understand how these bioactive compounds could be associated to ß-casein prior to their delivery in the organism. We have evaluated the interactions between curcumin and vitamin D3, as model hydrophobic nutraceutical compounds, and ß-casein by a multimethodological approach using surface plasmon resonance (SPR) biosensor in comparison with fluorescence spectroscopy as a traditional and classical method to evaluate the association constants.

The fluorescence quenching data show that curcumin has higher affinity to β-casein (KA = 23.5 ± 1.9 × 10 4 M -1 ) than vitamin D3 (KA = 5.8 ± 1.1 × 10 4 M -1 ). The KA value for curcumin-β-casein interaction has been successfully evaluated (2.45 ± 1.4 × 10 3 M -1 ) using SPR by fitting data to a 1:1 Langmuir interaction model. Conversely, the SPR responses obtained for vitamin D3 show that the interactions between this hydrophobic compound and the β-casein immobilized on the sensor chip were below the sensitivity of the SPR apparatus. It clearly appears that the equilibrium association constant (KA) obtained from fluorescence quenching is significantly higher than that evaluated by SPR. This difference may be attributed to the different principles of these two techniques. The fluorescence quenching method is based on quenching of tryptophan residues when they interact with hydrophobic molecules without consideration of the interactions with other sites on β-casein. Unlike fluorescence quenching, SPR, a powerful non-destructive and label-free technique, offers a direct and real-time monitoring of the interaction kinetics regardless of the binding sites. The fluorescence quenching is more accurate to study the binding sites around the tryptophan residues while the SPR technique offers the opportunity to study all kinds of binding sites. In summary, both SPR and fluorescence results provided evidence about the higher affinity of curcumin with β-casein compared to vitamin D3. The SPR developed method is versatile for measuring the binding of β-casein to other bioactive molecules, promising applications in many other protein-small molecules interactions. β-casein immobilization level was 2 700 RU.

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2: Steady-state affinity analysis of β-casein binding to curcumin and vitamin D3

Figure 3 :

 3 Figure 3: β-casein intrinsic fluorescence emission spectra (T=25°C, λex=280 nm) and

Figure 4 :

 4 Figure 4: Sterne-Volmer plots of the fluorescence quenching of the β-casein by

Figure 1 Figure 2 Figure 3 Figure 4 Table 1 :

 12341 Figure 1

Acknowledgements

The authors would like to acknowledge the French Ministry of Higher Education and Research for financial support.


A Thiam

C Martinez-Cisneros

Y Molmeret

Cristina Iojoiu

Jean-Yves Sanchez

Y Molméret

J-Y Sanchez

PEO: an Immobile Solvent?

Keywords: immobile solvent? PEO, POE, immobile solvent, ionic transport, polymer electrolyte, purification 1. Introduction

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

(Li/VOx). Based on solvent-free polyether electrolytes, LPB are currently revisited, owing to their safety asset (very high Flash Point, Fp) and their ability to absorb the volume changes of electrodes. As thick binder-free ceramic electrodes can be reversibly cycled [START_REF] Sanchez | Thick LTO ceramic electrodes: processing and performances[END_REF], ASSB based on solvent-free polymer electrolyte [START_REF] Gauthier | Large Lithium Polymer Battery Development: the Immobile Solvent concept[END_REF] can be considered, meeting both safety (Fp) and cost-cutting (high areal capacity) requirements. Among the poly(oxyalkylene)-based electrolytes, the host polymer, poly(oxypropylene) POP (or PPO) undergoes microphase separation [START_REF] Vachon | Microphase separation and conductivity behavior in poly(propylene oxide)-Lithium salt electrolytes[END_REF], while poly(oxytetramethylene) (or PTHF) exhibits conductivities significantly lower than POP and poly(oxyethylene) POE (or PEO) [START_REF] Alloin | Electrochemical comparison of several polyethers[END_REF]. The main limitations of high molecular weight POE homopolymers are wellidentified: (i) high crystallinity ratio, leading to poor conductivities at r.t, (ii) poor mechanical strength above the melting point of POE electrolytes and (iii) an anodic stability limited to about 3.9 V vs Li/Li + . Salts based on bulky anions as LiTFSI [7[8] and Li methide were found to decrease crystallinity and melting temperature of POEelectrolytes [START_REF] Benrabah | Comparative study of new poly(oxyethylene)-Li salts complexes[END_REF], without producing any improvement regarding the mechanical strength issue. As polymer electrolytes don't include any macroporous separator, they must sustain, without creeping, 90°C (operating temperature range of LPB: 60 to 90°C) and even retain their mechanical integrity up to at least 160°C. POE networks based electrolytes made of copolymers [10[13] and polycondensates [14- [START_REF] Alloin | Electrochemical behavior of lithium electrolytes based on new polyether networks[END_REF] allow both, suppressing crystallinity and avoiding creeping at high temperature. Nonetheless, these promising materials are not commercially available. Due to its availability in a wide range of molecular weights, POE is therefore extensively used in the polymer electrolytes literature, being considered as the reference host polymer for solvent-free polymer electrolytes. At salt concentrations compatible with LPB, i.e. 20 ≤ O/Li ≤ 30, the amorphous networked electrolytes exhibit much higher conductivities than the POE ones up to their melting. On the other hand, the latter lead generally to conductivity maxima higher than that of cross-linked electrolytes. This gap whether originates from defectsfree linear POE leading to a perfect macromolecular solvent, from the stiffening induced by the cross-linking of polyether chains or, possibly, from low molecular weight unentangled chains (molecular weight below the entanglement threshold, i.e. 3,200 g/mole) present in the commercial POE grades. Indeed, Vincent et al. [START_REF] Vincent | Ion transport in Polymer Electrolytes[END_REF], through electrochemical impedance spectroscopy and PFGNMR performed on POE electrolytes, in a wide range of POE molecular weights, demonstrated that below this threshold, Mg 2+ moves together with the oligoether chains and, beyond, becomes immobile. Suspecting the gap in conductivity maxima might result from the presence, in commercial POE, of unentangled oligomers, we performed ultrafiltration of POE aqueous solutions using a membrane cut-off at 3,000 g/mole. A POE grade of 300,000 g/mole was selected as we previously proved that POE solutions of higher molecular weights undergo dramatic chain breakings, even when a mild stirring as magnetic stirring was applied [START_REF] Bossard | Influence of dispersion procedures on rheological properties of aqueous solutions of high molecular weight PEO[END_REF]. This contribution reports on the electrochemical (conductivities and cationic transference numbers) and thermomechanical discrepancies between, on the one hand POE electrolytes consisting on unpurified commercial POE (raw-POE) and, on the other hand, those consisting on the oligomers-free one (UF-POE).

Experimental

Materials and films processing

POE 300,000 g/mole was dissolved in distillated water (8 wt.%) and ultrafiltrated under pressure through a membrane (cut-off: 3,000 g/mole) using a Millipore 8200. The ultrafiltration cell is equipped with a magnetic stirrer in order to avoid aggregate formation and subsequent pore clogging. Ultrafiltration must be carried out on diluted solution. Typically, purification of a POE sample requires three days of ultrafiltration.

After lyophilization, the obtained powder and LiTFSI were dissolved in acetonitrile and cast in a glove-box under argon atmosphere. After a slow removal of acetonitrile, the films were heated under vacuum.

Dynamic mechanical analysis (DMA)

Dynamic mechanical analysis (DMA) measurements were carried out with a TA instruments DMA Q800 analyzer working in tensile mode. A strain magnitude fixed at 0.05% guarantees that tests were made in the linear viscoelastic domain. Measurements on the thin samples were performed in isochronal condition (1 Hz) in the temperature range from -100 to +100°C at 3°C/min.

Differential scanning calorimetry (DSC)

Glass transition temperatures, Tg, melting temperatures, Tm, and the enthalpy of fusion, ∆Hm, were measured by DSC (Differential Scanning Calorimetry) using a GC20 from Mettler Toledo. Samples of approximatively 5 µg were introduced in aluminum pans in a glove box, under argon. In a typical procedure, samples were submitted to two heating cycles from -100 to 100°C with a heating ramp of 10°C/min. During the cooling step (from room temperature to -100°C and from 100 to -100°C), the cooling rate was set at 20°C/min. Before the heating or cooling steps, samples were submitted to an isotherm of 3 minutes in order to stabilize the temperature.

Conductivity measurements

Conductivity measurements were carried out by electrochemical impedance spectroscopy using a HP4192A impedance analyzer, over the frequency range 5 Hz-13 MHz. The samples were sandwiched, under argon, between two stainless steel electrodes in a Swagelok cell with Teflon o-rings. Measurements were performed in the temperature range from 20°C to 80°C; values were taken in both, heating (from 20 to 80°C, up) and cooling (from 80 to 20°C, down) steps. A dwell time of one hour was set between measurements.

Results and discussion

Differential scanning calorimetry (DSC)

To investigate the impact of ultrafiltration on the characteristic temperatures, as well as the crystallinity content, we performed DSC and TGA characterizations. However, since no significant differences on behavior were noticed regarding thermogravimetric analyses, TGA measurements were discarded from this contribution. Table 1 gathers the thermal characteristics, obtained during the second heating cycle, of raw and ultrafiltrated samples at two O/Li compositions. At high LiTFSI concentration, i.e. around O/Li = 8, the crystallinity seems to vanish but it is not suppressed in high molecular weight POE electrolytes, where it slowly reappears.

The delay in crystallization is however sufficient to allow the conductivities, in an evenly amorphous POE electrolyte, to be significant from ambient temperature on. Furthermore, by quenching melted samples, it is possible to determine the Tg of an amorphous phase unconstrained by the crystalline one. Using lower salt concentrations, i.e. 20 and 30, leads to polymer electrolytes that we could not quench efficiently into their amorphous state. Thus, as usual, the measured Tg of such semi-crystalline electrolytes are not representative of the segmental mobility [START_REF] Martinez-Cisneros | Development of sodium-conducting polymer electrolytes: comparison between film casting and films obtained via green processes[END_REF]. Due to both Li + interchain solvation, i.e. transient cross-linking, and the non-specific interaction occurring in any mixture, as described by the Flory-Fox semi-empirical relationship [START_REF] Paillard | Electrochemical investigation of polymer electrolytes based on lithium 2-(phenylsulfanyl)-1,1-2,2 tetrafluoroethanesulfonate[END_REF], a Tg increase with the salt concentration would be expected. On the contrary, it was found that Tg is unmodified or is even slightly increased. Indeed, increasing LiTFSI concentration decreases crystallinity and melting temperature, Tm. Due to the crystallinity decrease, so to the decrease in the constraining of amorphous phase, the Tg measured is artificially lower for O/Li=20 compared to O/Li=30. Nevertheless, the gaps found in crystallinity and Tm for raw and UF-POE based electrolytes are not significant for both salt concentrations.

Thermomechanical characterization

The thermomechanical behavior of the raw and ultrafiltrated POE host polymers was found to be similar. Therefore, as shown in figure 1, DMA measurements were afterwards extended to their LiTFSI-based polymer electrolytes, prepared with a salt concentration O/Li=30. At low temperatures, between -100 and -40°C, the storage modulus, E', remains constant and close to approximately 4 GPa. Afterwards, E' declines sharply, down to 500 MPa at -20°C. The relaxation α, Tα, measured at the maximum of tan δ, is associated to the molecular motions of the amorphous phase segments and characterizes the drop in storage modulus associated to the glass transition of the polymer electrolyte.

Although very close, the tan δ maxima for electrolytes based on raw and ultrafiltrated POE were found to be -28.9º C and -24.6ºC, respectively. We ascribe this small gap to the plasticizing effect of the unentangled oligomers contained in the raw POE. Both Tα values exceed by 6 to 9ºC the Tg measured by DSC. The Tα-Tg gap is related to the thermal treatment applied to the samples during DSC measurements, which involves heating followed by cooling, while samples do not undergo any thermal treatment before DMA measurements. Such heating-cooling cycle performed during DSC decreases the crystallinity and, consequently, the constraining of the amorphous phase that slows down the chain mobility, vide supra. Regarding the electrolyte behavior around Tm and beyond, the electrolyte based on the raw POE exhibits a classical behavior, experiencing creeping above Tm. A distinct and interesting behavior of the ultrafiltrated POE-based electrolyte, which exhibits a plateau around 0.5 MPa after Tm and up to at least 100°C, must be highlighted. This unexpected reinforcement is ascribable to interchain Li + solvation (transient cross-links) that, in the case of the ultrafiltrated material, occurs between entangled chains while it probably involves unentangled chains, i.e. oligomer oligomer and oligomer long POE chain in the case of the raw POE.

Transport properties

Conductivity comparison

The Arrhenius plots of POE-electrolytes are gathered in Figure 2. Impedance measurements were performed either by heating from 20º C to 80ºC (up) and by cooling from 80º C (down) to 21ºC. The former reveals the material performances in its equilibrated state while the latter, due to crystallization delay (supercooling), artificially increases the conductivities below Tm. For convenience, the Arrhenius plots were divided into "down" and "up" for cooling and heating, respectively, the data 'up' appearing as insets. Hosting LiTFSI in UF-POE results in a conductivity decrease for the whole temperature range, when compared to LiTFSI hosted by the raw POE. For instance, the conductivity gap at the salt concentration O/Li=20 reaches, at 70°C, 37%. As expected for both electrolytes, based on raw POE and UF-POE, the conductivity was significantly lower for both salt concentrations at temperatures below Tm in the "up" Arrhenius plots.

At room temperature, the conductivity gap between UF and raw POE electrolytes exceeds 500% for both salt concentrations and is roughly the same in "up" and "down" impedance measurements. This neat conductivity decrease could be ascribed to the removal of unentangled oligomers, which behave as non-volatile plasticizers. These results are supported by LiTFSI conductivity data collected by Balsara et al. [START_REF] Teran | Effect of molecular weight on conductivity of polymer electrolytes[END_REF] on a wide range of quasi-monodisperse POE solvents.

In figure 3 we compare the conductivity behavior of UF-POE electrolytes with those of optimized POE network ones, moderately cross-linked and amorphous from roughly 25ºC [START_REF] Thiam | Lithium salts based on a series of new anilinyl-perfluorosulfonamide salts and their polymer electrolytes[END_REF]. The latter, which do not creep, are obtained from the cross-linking of a pre-polymer that underwent ultrafiltration (cut-off: 3,000 g/mole) and partial hydrogenation (75%).

This comparison unambiguously demonstrates that optimized polymer electrolytes can lead, in a wide temperature range, to significantly improved performances with regard to electrolytes based on UF-POE.

Transference numbers

Beyond ionic conductivity measurements, the cationic transference number is a key parameter, since it highly influences cationic conductivity and conductance. The cationic transference numbers, T + , were determined by both electrochemical impedance spectroscopy and Pulse Field Gradient NMR (PFGNMR). Even though several T + have been previously reported on POE/LiTFSI electrolytes based on raw POE, we opted for its characterization, as (i) the POE applied usually has very high molecular weight, undergoing chain scissions during sample preparation, and (ii) a thorough comparison requires using the same material and protocols. T + determinations were performed at 70ºC in order to discard any doubt about a possible creping of POE electrolytes during the EIS experiments.

T + from PFGNMR experiments

Table 2 collects the data obtained for the concentration O/Li=30. From the obtained data, it can be seen that the Li + diffusion coefficient is only slightly increased (~ 4.5%), while the anion diffusion coefficient remains almost unchanged. Indeed, the gap in Li + mobility remains in the margin of error. As removed materials (i) are mainly unentangled oligomers and not volatile molecules and (ii) are embedded in the POE long chains, the results are not surprising as, especially, the samples do not undergo electrical polarization.

T + from EIS experiments

Cationic transference numbers were determined using the Sorensen method [START_REF] Sorensen | Conductivity, charge transfer and transport number-An AC investigation of the polymer electrolyte LiSCN-poly(ethylenexide)[END_REF]. From EIS, it was observed that T + increases by ~ 30% when comparing LiTFSI hosted in UF-POE (0.13) and in raw-POE (0.17). From these data, we can infer that unentangled oligomers, which should have the same solvating ability versus Li + than the POE long chains, move together with the anion and cation. These results are in line with Shi results [START_REF] Shi | The effect of molecular weight on cation mobility in polymer electrolytes[END_REF]. The dual decrease in ionic conductivity and T + in UF-POE electrolytes, leads to a substantial decrease in cationic conductivity (σ + = σ.T + ), which drops by more than 100% as compared to the unpurified electrolyte (Table 3).

Conclusions

Both electrochemical impedance spectroscopy, i.e. ionic conductivities and cationic transference numbers data, as well as Dynamic Mechanical Analyses are in perfect agreement and highlight the significant influence of unentangled oligomers on the ionic transport in LiTFSI/raw POE polymer electrolytes. Polyether networks alternatives to POE undergoing generally, a purification step, e.g. by precipitation, lead to the partial or total removal of unentangled oligoether chains. Hence, their electrolytes should be compared not to raw POE electrolytes but to ultrafiltered ones. In that sense, some of them should exhibit higher conductivities and cationic conductivities, in the whole range of LPB operating temperatures (25 to 90ºC). Pending industrial development of POE alternatives, POE electrolytes remain attractive even though it would be difficult to cut the crystallinity and lower significantly their Tm, at the moderate salt concentrations required in LPB. From a practical point of view, why removing by ultrafiltration unentangled oligomers that increase both conductivity and cationic transference numbers? Indeed ultrafiltration (i) allows both removing oligomers but also impurities and (ii) leads to aqueous POE solutions that can be cast into polymer electrolyte films and can be used to formulate the positive electrode without using organic solvents. Even though polymer electrolytes based on ultrafiltered POE have slightly higher mechanical strength than those based on raw POE, this gain nevertheless remains insufficient both to thinner the electrolyte film, in order to optimize the ionic conductance, and to protect the battery from a thermal runaway. Fortunately, this poor thermomechanical stability it can be remedied by a nanocomposite approach. Thanks to the formation of a network by hydrogen bonding and to the tremendous E' of the highly crystalline nanofibers, crystalline nanocellulose, NCC, hugely increases the storage modulus of POE electrolytes [START_REF] Masa | Cellulose Nanocrystals reinforced poly(oxyethylene)[END_REF] without compromising the ionic conductivity and allows a sharp thickness of the electrolyte film to be considered. Regarding a possible thermal runaway, as the NCC network starts decomposing from roughly 250ºC, it provides an indisputable safety asset to LPB. It can be pointed out that the ultrafiltered solutions of POE, free of oligomers and impurities, can be blended to the NCC aqueous dispersions to prepare the nanocomposite polymer electrolytes by an overall green approach.

  Figure 1. Storage modulus E' (A) and Tan δ (B) vs temperature at 1Hz for raw and

Figure 2 .

 2 Figure 2. Conductivity measurements at different O/Li ratios: 20 (A) and 30 (B) while cooling and heating (insets) for samples based on raw and ultrafiltrated POE.

Figure 3 .

 3 Figure 3. Comparison of conductivity performance of ultrafiltrated and partial

Table 2 .

 2 Diffusion coefficients obtained for O/Li=20 usingPFGNMR

	Tables

Table 3 .

 3 Diffusion coefficients obtained from EIS experiments

	O/Li = 30	σ (70°C) mS.cm -1	T +	σ.T +
	Raw-POE/LiTFSI	0.634	0.17	0.108
	UF-POE/LiTFSI	0.366	0.13	0.048

Acknowledgments

Jean-Yves Sanchez acknowledges the CONEX Programme, funding received from Universidad Carlos III de Madrid, the European Union's Seventh Framework Programme for research, technological development and demonstration (Grant agreement nº 600371), Spanish Ministry of Economy and Competitiveness (COFUND2013-40258) and Banco Santander. Amadou Thiam acknowledges ANR for his fellowship. Yannick Molméret acknowledges KICINNO Energy for the granting of his post-doc fellowship, in the frame of the project PENLiB coordinated by Prof. Jean-Yves Sanchez.


Eric Le Bourg
email: eric.le-bourg@univ-tlse3.fr

New life expectancy forecasts are too optimistic

Keywords:

Life expectancy at birth (e0) forecasts are used to estimate future pension costs. Previous French official forecasts have often overestimated e0. Recent forecasts published by demographers provide higher e0 estimates than official forecasts for France, Sweden, Japan and the USA, and do not consider that e0 could decrease, as in previous years because of flus, heatwaves, or other outbreaks. Too optimistic forecasts make that governments may overestimate future pension needs.

Forecasting life expectancy at birth (e0) is of importance, particularly because "forecasts are used to estimate future needs and assess policies, e.g., estimate future pension costs" [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF]. It is thus of the highest importance to rely on realistic forecasts, in order for policy makers to reach appropriate decisions. These forecasts can be too pessimistic, as it was often the case in past decades [START_REF] Oeppen | Broken limits to life expectancy[END_REF], or too optimistic, which implies that future pension needs can be estimated in excess. (COR 2021, page 23). Figure 1 shows the three scenarios for each of the INSEE forecasts. Figure 2 shows that privileging the central scenario has often been an error, by illustrating the gap in 2019 between e0 and the three scenarios (the data for 2020 are still provisional and this year is strongly affected by Covid-19). For men, the 2005-2050 high scenario is more appropriate than the central and low ones, the 2007-2060 central scenario is better than the other ones, and for the 2013-2070 forecast the low scenario is the most appropriate: the central scenario used by the COR first underestimates and then overestimates e0 in men. For women, the central scenario is appropriate for 2005-2050, but the low scenario is better for the 2007-2060 and 2013-2070 forecasts, and the COR has thus overestimated e0 of women during many years. In summary, the COR has for a long time relied on the central scenario overestimating e0 and therefore pension needs. Because these central scenarios have been used by French policy makers to decide, for instance, delaying retirement age in next years and decades, relying on realistic forecasts in the future is crucial. However, too optimistic forecasts are not only the case for France. 2021) have published various scenarios for women's e0 in France, Japan, Sweden, and USA, for the period up to 2050 and 2070. In addition, the authors relied on the updated best-practice estimate previously used by [START_REF] Oeppen | Broken limits to life expectancy[END_REF], which adjusts a linear regression to e0 of the record-holding country from 1840 (Norway) to the current years (Japan). This scenario was also updated by removing "problematic country-years" brought to the fore by [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF]. However, as indicated below, one may argue that most of these forecasts have a poor chance to provide an appropriate estimate of e0 in the coming decades. [START_REF] Oeppen | Broken limits to life expectancy[END_REF] shows this estimate for 1840-2000. The main contrast between the two figures is that the current record-holding country, Japan, was very close to the regression line in [START_REF] Oeppen | Broken limits to life expectancy[END_REF] up to 2000 but, after 2000, it is below the line in [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF]. In other words, the best-practice regression line now fails to estimate e0 of the record-country, because record-e0 increases at a lower speed than previously observed. There is thus no longer a linear rise of record-e0, which casts some doubt that a linear best-practice e0 rise "close to 100 by 2070" could be observed, as stated by [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF]. This is in accordance with the conclusion of [START_REF] Marck | Are we reaching the limits of Homo sapiens ? Front[END_REF] that "predicting a continuous linear growth of lifeexpectancy in the long term may probably not be relevant if the major progresses have already been accomplished."

Vaupel et al. (

Secondly, Figure 5 in [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF] shows the results for France, Japan, Sweden, and USA, of six methods extrapolating e0 up to 2070, in addition to the official forecast of these countries: Figure 3 reports USA results. As emphasised by the authors, there can be a huge variation between these methods (e.g. 8.4 years in USA, from 85.7 to 94.1 years in 2070), which is not an issue if forecasts are biologically plausible. However, forecasting that e0 could reach 102.8 years in Japan means that most of Japanese women would die in a very few years, as maximal lifespan is close to 115 years. This seems hardly possible "because the variability of lifespan would be very low, 50% of the cohort dying in a very few years, while it is known that there is a high variability of lifespans even in inbred strains and in monozygotic human twins [START_REF] Finch | relatif au systeme universel de retraite[END_REF][START_REF] Kirkwood | What accounts for the wide variation in lifespan of genetically identical organisms reared in a constant environment?[END_REF])" (Le Bourg 2012). One could obviously hypothesise that variability could remain the same because maximal lifespan would increase: [START_REF] Vallin | Towards a new horizon in demographic trends: the combined effects of 150 years life expectancy and new fertility models[END_REF] showed that if e0 would be 105 years maximal lifespan would be around 140 years. Such a maximal lifespan is a very strong hypothesis and thus a nearly 105 years e0 is not very probable, no matter maximal lifespan increases or not. In addition, the stability of US centenarians' death rates since the 1940s, in contrast with the decreasing rates of younger people [START_REF] Gavrilov | The future of human longevity[END_REF], seems to indicate that increasing the lifespan of the last survivors is a challenge. Therefore, it seems that at least some of the forecasts in Vaupel et al. ( 2021) provide results without any biological ground.

However, another issue with the six 2018-2070 forecasts in Figure 5 of [START_REF] Vallin | The segmented trend line of highest life expectancies[END_REF] is that most of them show e0 increasing suddenly at a higher pace than before 2018. In contrast, the official forecasts keep on the same trend as before 2018. In addition, except for France, all forecasts provide estimates higher than the official forecasts (see the USA results in Figure 3). To sum up, sudden changes are observed in 2018 simply because forecasts begin in 2018, and not because of any biological or medical breakthrough, and the six forecasts overestimate official ones. These forecasts most probably exaggerate future e0 and thus could be of no help to estimate future pension -4costs. In addition, at a time when e0 is stalling or decreasing from time to time in some countries, because of flu or heatwave in France (Le Bourg 2019), or deaths of despair in the USA (e.g., Case and Deaton 2015), and obviously of the Covid-19 outbreak, taking into account the hypothesis that e0 could stall or decrease from time to time in coming decades could also be useful [START_REF] Bourg | Epidemics and forecasts of life expectancy[END_REF]. Forecasting only monotonous e0 increases is outdated in an epoch that is clearly highly different from the last decades of the last century. Elaborating e0 forecasts is not an easy challenge and it seems that, while old forecasts underestimated e0 increases, as discussed by [START_REF] Oeppen | Broken limits to life expectancy[END_REF], new forecasts overestimate them. These new forecasts can lead policy makers to erroneous decisions, particularly regarding pension needs, as they can conclude that e0 will strongly increase in coming decades.

Following this conclusion, policy makers could decide, for instance, to delay the retirement age to lower the increasing cost of future pensions, while this cost is overestimated because of these wrong forecasts. It is thus necessary to avoid both traps of e0 under and over-estimations and also to take into account the hypothesis that e0 could also stall or even decrease in coming years and decades.

The

  French National Institute of Statistics and Economic Studies (Institut national de la statistique et des études économiques, INSEE) has published forecasts for 2005-2050, 2007-2060, 2013-2070 with different e0 scenarios (high, central or low), which are used by the French Pensions Advisory Council (Conseil d'orientation des retraites, COR) to estimate pension funding needs. The "central scenario" was the one put forward by the government in its 2020 bill (Article 56, French Government 2020) in a failed attempt to introduce a new pension funding system and was until 2020 the one preferred by the COR (COR 2020, page 23), its 2021 report being now based on the low scenario

  Figure1in[START_REF] Oeppen | Broken limits to life expectancy[END_REF] shows this estimate for 1840-2000. The main contrast

Figure 1 :Figure 2 :

 12 Figure 1: INSEE forecasts for 2005-2050, 2007-2060, 2013-2070, and observed life expectancy at birth from 1994 to 2020 (provisional for 2020). For each forecast, the low, central and high scenarios show life expectancy at birth.