Raphaela Araujo Mantovani

Pascaline Hamon

Florence Rousseau

Guilherme M Tavares
email: tavaresg@unicamp.br

Adriana Zerlotti Mercadante

Thomas Croguennec

Said Bouhallab
email: said.bouhallab@inrae.fr

Saïd Bouhallab

Unraveling the molecular mechanisms underlying interactions between caseins and lutein

Keywords:

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

Introduction

As the proportion of elderly people of the world's population increases, the incidence of chronic-degenerative diseases, the major cause of functional disability among this specific population, also increases. Thus, the development of bioactive-rich products arises as an alternative for maintaining health and life quality for as long as possible in this age group. Carotenoids are natural pigments found in fruits and vegetables. Such a class of bioactive compounds has been proposed to promote human health, mainly due to their antioxidant and anti-inflammatory activities. Lutein is a yellow-orange oxygenated carotenoid that positively modulates some risk diseases that predominate in the elderly, such as age-related macular degeneration [START_REF] Woodside | Carotenoids and health in older people[END_REF]. However, its addition to fat-free and low-fat products from food and pharmaceutical industries is challenging due to its hydrophobic character. Moreover, carotenoids are sensitive to heat, oxygen, and light [START_REF] Mercadante | Carotenoids in foods: Sources and stability during processing and storage[END_REF]. In this context, carotenoid binding to proteins has been studied aiming at improving its physicochemical stability [START_REF] Chen | Isorenieratene interaction with human serum albumin: Multispectroscopic analyses and docking simulation[END_REF][START_REF] Mora-Gutierrez | Complexes of lutein with bovine and caprine caseins and their impact on lutein chemical stability in emulsion systems: Effect of arabinogalactan[END_REF][START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF].

Caseins constitute up to about 80 percent of milk proteins and are found in milk as supramolecular aggregates, called casein micelles, in which the four casein fractions (αS1-, αS2-, β-, and κ-casein) are associated by mainly hydrophobic interactions and calcium phosphate nanocluster bridges [START_REF] Walstra | Dairy Science Technology[END_REF]. These casein micelles are considered natural vehicles of calcium, an important mineral in the human diet, especially for the elderly [START_REF] Tavares | Milk proteins as encapsulation devices and delivery vehicles: Applications and trends[END_REF]. To be used as ingredients, casein micelles are obtained from raw skim milk by microfiltration combined with diafiltration with water to remove whey proteins, peptides, lactose, among other components of the water-soluble phase of milk [START_REF] Broyard | Modifications of structures and functions of caseins: A scientific and technological challenge[END_REF]. Hence, casein micelles associated with their calcium phosphate are available and called phosphocaseinate (PPCN) [START_REF] Broyard | Modifications of structures and functions of caseins: A scientific and technological challenge[END_REF]. Conversely, sodium caseinate (NaCas) is obtained following the neutralization by sodium hydroxide of an acid-precipitate of casein [START_REF] Walstra | Dairy Science Technology[END_REF]. During this operation, the colloidal calcium phosphate is washed out of the casein micelles that lose its native structural organization. Thus, NaCas and PPCN are two caseinrich ingredients but with considerable structural differences. NaCas usually displays a hydrodynamic diameter between 10 and 100 nm, while PPCN has an average hydrodynamic diameter of around 150 nm and particle size distribution up to 600 nm [START_REF] Pan | Enhanced Dispersibility and Bioactivity of Curcumin by Encapsulation in Casein Nanocapsules[END_REF].

In general, investigations on the interactions between proteins and carotenoids have focused on protein conformational changes [START_REF] Li | β-Carotene and astaxanthin with human and bovine serum albumins[END_REF][START_REF] Mohan | Structural insights into the binding mode and conformational changes of BSA induced by bixin and crocin[END_REF][START_REF] Mora-Gutierrez | Complexes of lutein with bovine and caprine caseins and their impact on lutein chemical stability in emulsion systems: Effect of arabinogalactan[END_REF][START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. Some papers reported the potential of caseinate as carotenoid nanocarrier. [START_REF] Mora-Gutierrez | Complexes of lutein with bovine and caprine caseins and their impact on lutein chemical stability in emulsion systems: Effect of arabinogalactan[END_REF] assessed the interaction between caseinate from bovine and caprine milk and lutein at pH 7 and observed that the apparent solubility of lutein in the hydrophilic environment, as well as its chemical stability during storage after incorporation in emulsion-based system, improved due to the formation of casein/lutein complexes. Similar results were reported through the complex formation of lutein with whey protein isolate (WPI) or NaCas at 25 • C and pH 7.4 [START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. Results also showed that lutein stability was higher in NaCas/lutein complex than in the WPI/lutein one [START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. [START_REF] Paiva | Influence of protein conformation and selected Hofmeister salts on bovine serum albumin/lutein complex formation[END_REF] verified that the binding of lutein to bovine serum albumin (BSA) at pH 7.4 was independent of the protein conformation, folded or denatured. Moreover, [START_REF] Allahdad | Spectroscopic and docking studies on the interaction between caseins and β-carotene[END_REF] showed that β-carotene exhibited different interaction parameters with the individual casein molecules, i.e. β-, κ-and α s -casein.

Few studies concerning carotenoid-milk protein interactions took carotenoid solubility in the hydrophilic environment into consideration [START_REF] Chang | Binding to Bovine Serum Albumin Protects β-Carotene against Oxidative Degradation[END_REF][START_REF] Mora-Gutierrez | Complexes of lutein with bovine and caprine caseins and their impact on lutein chemical stability in emulsion systems: Effect of arabinogalactan[END_REF][START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. In a hydrophilic environment, carotenoids are expected to exist as self-aggregated forms. The carotenoid aggregation or self-assembly in the organic-water binary solvent is a process largely driven by hydrophobic effects, being influenced by two main factors: the steric properties of the molecule structure and the attractive forces such as H-bridges, dipole forces and van der Waals interactions between neighboring molecules [START_REF] Hempel | Structure related aggregation behavior of carotenoids and carotenoid esters[END_REF]. H-type and J-type carotenoid aggregates are characterized by strongly and weakly coupled aggregates, respectively [START_REF] Dong | Solvent tuning configurational conversion of lycopene aggregates in organic-aqueous mixing solvent[END_REF][START_REF] Hempel | Structure related aggregation behavior of carotenoids and carotenoid esters[END_REF]. A recent study observed that interactions between WPI and norbixin exhibited Stern-Volmer and quenching constants with a magnitude order of 10 4 M -1 and 10 13 M -1 s -1 , respectively, independent of the carotenoid form (soluble or Htype aggregate) [START_REF] Møller | Norbixin binding to whey protein isolate -alginate electrostatic complexes increases its solubility and stability[END_REF]. On the other hand, [START_REF] Zhu | Aggregation of Fucoxanthin and Its Effects on Binding and Delivery Properties of Whey Proteins[END_REF] reported that fucoxanthin aggregation affected fucoxanthin/whey protein binding. However, in general carotenoid aggregation before or after complexation with milk proteins has rarely received considerable attention.

Although some reports on the molecular interaction between caseinate or isolated casein fractions and carotenoids are available, to the best of our knowledge, the interaction between lutein and casein micelle (native phosphocaseinate) has not been investigated so far. In this context, this study aimed to assess the influence of the aggregation state of the caseins (sodium caseinate versus casein micelle) on their interaction with lutein by protein fluorescence quenching.

Material and methods

Sample preparation

Sodium caseinate (NaCas) (Eurial, France) and native phosphocaseinate (PPCN) (Promilk 852B, Ingredia, France) powders were used in the present study. These ingredients contained, respectively, 90.7 ± 0.2 and 83.1 ± 0.4% (w/w) protein (N × 6.38), based on the total nitrogen content determined by the Kjeldahl method. The stock solution of NaCas was prepared by dispersing NaCas powder at 7.81 g L -1 (corresponding to a protein concentration of 7.08 g L -1 or 300 µM, considering an average molecular weight of 23.6 kDa for individual molecules) in 10 mM of 4-(2-hydroxyethyl)-1-piperazine ethanesulfonic acid (Hepes) at pH 7. A homogeneous solution of NaCas was obtained by stirring the mixture at room temperature for 24 h. The protein concentration of the NaCas solution was determined by UV-absorbance at 280 nm (spectrophotometer SAFAS UV MC2, Safas, Monaco, France) using an extinction coefficient of 0.79 L g -1 cm -1 . This parameter was calculated considering that NaCas is composed of 40% α s1 , 40% β, 10% α s2 and 10% of κ-caseins, with the respective absorption coefficients of 1.01; 0.45; 1.04 and 1.05 L g -1 cm -1 [START_REF] Walstra | Dairy chemistry and physics[END_REF]. The stock solution of PPCN was prepared by dispersing PPCN powder at 8.52 g L -1 (corresponding to a protein concentration of 7.08 g L -1 ) in HEPES buffer at pH 7. Rehydration of PPCN powder was carried out by continuous stirring at room temperature during 10 h followed by heating at 40 • C for 12 h. Afterwards, PPCN solution was kept under slow stirring at room temperature during 12 h. Sodium azide at 0.5 g L -1 was added to both solutions to prevent microbial growth.

Lutein stock solution was prepared immediately before use by dispersing lutein powder (PHR1699, MW 568.87 g mol -1 , Sigma-Aldrich, St. Louis, MO, USA) at 1.8 mM in absolute ethanol or DMSO under slow stirring until complete dissolution. The absorption spectrum of lutein was obtained in a spectrophotometer (SAFAS UVmc2, Safas, Monaco, France), and the total lutein content was calculated by using the absorbance at 446 nm and the specific extinction coefficient of lutein in ethanol (E 1% 1cm = 2550, corresponding to a molar absorptivity of 145,100 L mol -1 cm -1 ). For DMSO solution, the total lutein content was calculated by using the absorbance at 461 nm and the specific extinction coefficient of lutein in DMSO (E 1% 1cm = 2369, corresponding to a molar absorptivity of 134,800 L mol -1 cm -1 ) (Davies, 1976).

Protein size distribution

Before analysis, NaCas and PPCN stock solutions were diluted 3 times (1:3) in 10 mM Hepes buffer at pH 7. The influence of the addition of 5% (v/v) ethanol or DMSO to NaCas and PPCN solutions on protein size distribution was assessed using a Zetasizer Nano Series (Malvern Instruments, Worcestershire, UK). The hydrodynamic diameter (Dh) of NaCas and PPCN at 25 • C was obtained by dynamic light scattering measurements using a backscattering angle of 173 • . The generalpurpose model was used for experimental data analysis. The Dh was calculated according to the Stokes-Einstein equation. The mean protein size was reported as average hydrodynamic diameter (D), calculated according to Eq. ( 1).

D = ∑ x i D i (1)
where x i is the fraction of a given particle i with a given scattering intensity and Di is the diameter of the particle i.

Intrinsic fluorescence

NaCas and PPCN solutions at 1 µM were obtained by diluting NaCas and PPCN stock solutions 300 times (1:300) in 10 mM Hepes buffer at pH 7. From both lutein stock solutions, another solution was prepared at 170 µM in absolute ethanol or DMSO. Protein intrinsic fluorescence was determined using a Safas FLX-Xenius fluorimeter (Monaco, France). The excitation wavelength was set at 280 nm and emission spectra were recorded between 300 and 400 nm, using excitation and emission slit widths of 5 nm. Diluted casein solution (2 mL) placed in quartz cuvette was titrated with 10 successive injections of 10 μL of lutein. The lutein/ casein molar ratios ranged from 0 to 8. The mixtures were aspired and expelled five times using a micropipette to guarantee a proper homogenization. Fluorescence measurements were taken after 15 min of equilibration. Ethanol and DMSO concentration in the final mixture was 5%. The effect of organic solvent on the carotenoid titration curves was corrected by subtracting the protein fluorescence in presence of organic solvent from that of proteins in presence of carotenoid/organic solvent at each point of the titration. Absorption spectrum (270-600 nm) of the lutein/casein mixture was measured in a spectrophotometer for the correction of the inner filter effect [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. Each titration was carried out in triplicate.

Isothermal titration calorimetry (ITC)

Immediately before analysis, ethanolic lutein solution at 400 µM was diluted 20 times in 10 mM Hepes buffer at pH 7, resulting in a lutein solution containing 5% (v/v) ethanol. The absorption spectrum of the diluted lutein solution was measured in a spectrophotometer. Before analysis, NaCas and PPCN stock solutions were diluted 3 times (1:3) in 10 mM Hepes buffer at pH 7. As a control, 5% (v/v) ethanol was added to diluted NaCas and PPCN solutions.

A VP-ITC microcalorimeter (Microcal, Northampton, MA, USA) was used to assess the binding energy of lutein to NaCas or PPCN at 25 • C. All the parameters for ITC analysis were based on those described by [START_REF] Velazquez-Campoy | Isothermal titration calorimetry to determine association constants for high-affinity ligands[END_REF]. Casein solutions (0.1 mM) and stock solutions of lutein (0.02 mM) were degassed under vacuum before titration experiments. The reference cell was filled with 10 mM HEPES buffer at pH 7 with 5% (v/v) ethanol and the sample cell (1.425 mL) was filled with lutein solution. Lutein solution was titrated with 29 successive injections of 10 μL of casein at 100 µM. Each injection lasted 20 s with an interval of 400 s between consecutive injections to reach thermodynamic equilibrium. During titration, the solution in the sample cell was stirred at 300 rpm to ensure complete homogeneity. For each ITC experiment, a reference titration was carried out by titrating casein solutions directly into 10 mM HEPES buffer with 5% (v/v) ethanol. The casein dilution data (reference experiment) were subtracted from casein/lutein binding experimental data using the Origin 7.0 software. The area under each injection peak was plotted as a function of the casein/lutein molar ratio.

Results

Lutein aggregates in organic-aqueous system

Most carotenoids are not water-soluble but may be dissolved by cosolvents [START_REF] Chang | Binding to Bovine Serum Albumin Protects β-Carotene against Oxidative Degradation[END_REF] such as ethanol and DMSO. Carotenoids form aggregates in a hydrophilic environment due to their highly hydrophobic character [START_REF] Dong | Solvent tuning configurational conversion of lycopene aggregates in organic-aqueous mixing solvent[END_REF][START_REF] Hempel | Structure related aggregation behavior of carotenoids and carotenoid esters[END_REF], as shown after comparing the lutein absorption spectra in a pure organic solvent and 10 mM Hepes buffer at pH 7 (Fig. 1A andB). The UV/vis spectrum of lutein in pure DMSO showed absorption maxima at 435, 461, and 491 nm, while the dissolved state of lutein in pure ethanol showed absorption maxima at 421, 446 and 474 nm, as expected. Upon aqueous dilution, loss of vibrational fine structure, large hypsochromic shift, and hypochromic effect were observed for both organic-aqueous systems. These solvent-induced changes in absorption characterize the formation of H-type aggregates [START_REF] Dong | Solvent tuning configurational conversion of lycopene aggregates in organic-aqueous mixing solvent[END_REF][START_REF] Hempel | Structure related aggregation behavior of carotenoids and carotenoid esters[END_REF]. Free hydroxyl groups at both ends of the lutein molecule promoted the formation of strongly coupled (H-type) aggregates due to the formation of intermolecular hydrogen bonds [START_REF] Hempel | Structure related aggregation behavior of carotenoids and carotenoid esters[END_REF]. Also, the almost complete disappearance of the initial monomer bands indicates that, after dilution in a buffer, lutein is mostly present in the aggregate form instead of dispersed molecules. Consequently, in aqueous solution, the interaction of lutein with macromolecules involves at least in part its aggregated forms, a fact that it is not always specified in the published studies.

Low volume of organic solvent does not affect the protein size distribution

The solutions of NaCas and PPCN in buffer presented bimodal and monomodal particle size distribution, respectively (Fig. 2). The average Dh of PPCN solution was about 200 nm. On the other hand, the major size peak of NaCas solution exhibited the average hydrodynamic diameter around 20 nm. As expected, the average hydrodynamic diameter of PPCN was 10-fold higher than that observed for NaCas in aqueous solution [START_REF] Casanova | pH-and ionic strength-dependent interaction between cyanidin-3-O-glucoside and sodium caseinate[END_REF][START_REF] Pan | Enhanced Dispersibility and Bioactivity of Curcumin by Encapsulation in Casein Nanocapsules[END_REF]. This result is directly related to the highest content of colloidal calcium-phosphate in PPCN which plays an important role in casein micelle stabilization. The addition of ethanol (5% v/v) did not significantly affect the observed protein size distribution. Similar results were also observed in the presence of 5% (v/v) DMSO (data not shown).

Lutein binds to one binding site on NaCas and PPCN

Fig. 3 shows the UV-vis absorption spectra of the NaCas and PPCN solutions in HEPES buffer at pH 7 in the absence and presence of increasing concentrations of lutein (lutein/protein molar ratios from 0 to 8 µM). Casein/lutein mixture resulted in an absorption peak with an absorption maximum at 384 nm, typical of H-type aggregates of lutein. Thus, it is worth noting that although lutein was added to casein in a dispersed form (monomers), the absorption spectra show that lutein aggregates (H-type) are present after lutein addition to NaCas and PPCN buffer solutions. The casein/lutein absorption intensity increased linearly by increasing lutein concentration [START_REF] Chang | Binding to Bovine Serum Albumin Protects β-Carotene against Oxidative Degradation[END_REF][START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF], while the profile of the absorption spectra did not change after lutein additions. A linear concentration dependent absorbance in agreement with the Beer -Lambert law indicates that a homogeneous solution was formed for 0 -8 µM lutein in buffer solution of NaCas or PPCN with 5% (v/v) of ethanol or DMSO [START_REF] Chang | Binding to Bovine Serum Albumin Protects β-Carotene against Oxidative Degradation[END_REF]. Control experiments in the absence of casein (lutein in buffer) showed absorption intensities 25% lower than those values observed for casein/lutein (data not shown). Similar results were also observed in the presence of 5% (v/v) DMSO (data not shown).

The inner-filter effect distorts the fluorescence data since an absorbing compound added to a solution tends to reduce the number of excitation radiations that reach the fluorophore or absorb some of the radiations emitted by the fluorophore [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF][START_REF] Van De Weert | Fluorescence Quenching to Study Protein-ligand Binding: Common Errors[END_REF]. As the absorbance of the added ligand at the excitation (data not shown) and/or emission wavelength is above 0.1 at lutein concentration of 4-8 µM, the observed fluorescence intensities were corrected to avoid the inner-filter effect according to Eq. ( 2) [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF].

F corr = F obs × 10 Aexc+Aem 2 (2)
where F corr is the corrected fluorescence value, F obs the measured fluorescence value, A exc , and A em the absorption values at the excitation and emission wavelengths, respectively, determined in a 1 cm cuvette.

Protein fluorescence is mainly due to tryptophan residues (Trp) when excited at 280 nm. In bovine milk, both α s1 -casein and α s2 -casein have 2 Trp residues while β-casein and κ-casein have 1 Trp residue each [START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. Thus, casein fluorescence results from a combination of fluorophores located on different protein molecules. Ligand binding in regions near the fluorophores induces changes in the local environment and consequently in fluorescence intensity, proportionally to added ligand concentration. Fig. 4 presents the typical fluorescence emission spectra of NaCas and PPCN solutions at pH 7 in the absence and presence of increasing concentrations of lutein (lutein/protein molar ratios from 0 to 8 µM). After excitation at 280 nm, the maximum emission wavelength of NaCas and PPCN was recorded around 334 nm. Trp residues are likely placed in the supramolecular structure core when dispersed in a hydrophilic environment due to their hydrophobic character. The maximum emission wavelengths of NaCas and PPCN presented a blue shift of about 30 when compared to free Trp in water [START_REF] Teale | Ultraviolet fluorescence of the aromatic amino acids[END_REF], which corroborates the hypothesis that Trp residues were buried. Organic solvents can affect protein structure [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF], for instance, at high concentrations, ethanol may promote casein aggregation [START_REF] Celli | Solvent-mediated pressure-treated bixin-casein complexation for targeted color delivery[END_REF]. On the other hand, the presence of ethanol and DMSO at low concentration (5% v/v) practically did not affect the size of the different casein supramolecular structures (Fig. 2). Conversely, the fluorescence intensity of caseins decreased in ~ 20% even at low concentration of organic solvents (data not shown) suggesting changes in the microenvironment surrounding the Trp residues such as protein rearrangements [START_REF] Celli | Solvent-mediated pressure-treated bixin-casein complexation for targeted color delivery[END_REF].

The wavelength of maximum fluorescence intensity did not change after lutein addition in the presence of ethanol (Fig. 4), consistent with a previous study [START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF]. This fact shows that lutein-casein interaction did not affect the microenvironment of Trp residues in NaCas and PPCN. In the presence of DMSO, a slight blue shift of this maximum wavelength was observed with increasing lutein concentration. This hypsochromic shift in DMSO suggests the presence of two populations of fluorophores, indicating that the Trp residues emitting at larger wavelengths are quenched more readily than the Trp emitting at shorter wavelength [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. The fluorescence intensity of NaCas and PPCN gradually decreased (quenching mechanism) with increasing lutein concentration and a tendency to reach a plateau value was observed, regardless of the organic solvent used to prepare the lutein stock solution (DMSO or ethanol).

The fluorescence quenching data were analyzed according to Stern-Volmer (Eq. ( 3)).

F 0 F = 1 + k q τ 0 [Q] = 1 + K SV [Q] (3)
where F 0 and F are fluorescence intensities in the absence and presence of quencher, respectively, k q is the bimolecular quenching constant, τ 0 is the lifetime of the fluorophore in the absence of quencher (τ 0 value for Trp residue is 10 -8 s according to [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]), [Q] is the total concentration of quencher, and K SV is the Stern-Volmer quenching constant. Moreover, to confirm the number of sets of fluorophore populations of casein, as well as their accessibility to lutein, the fluorescence quenching data was also analyzed according to the modified Stern-Volmer equation (Eq. ( 4)).

F 0 F 0 -F = 1 f a K SV [Q] + 1 f a (4)
where f a is the fraction of the initial fluorescence that is accessible to quencher and K SV is the effective quenching constant for the accessible fluorophore. The modified form of the Stern-Volmer equation allows f a and K SV to be determined graphically from y-intercept, 1/f a (by extrapolation), and slope, 1/(f a K SV ). Fluorescence quenching data of ligand/protein binding are usually fitted according to Stern-Volmer equations. [START_REF] Gheonea | Binding mechanisms between lycopene extracted from tomato peels and bovine β-lactoglobulin[END_REF] reported a linear modified Stern-Volmer plot and f a < 1.0 for lycopene extract/β-lg binding, suggesting unequal accessibility of lycopene to two populations of Trp. Linear modified Stern-Volmer plots were also observed in previous studies of binding between bixin/whey proteins and norbixin/ whey proteins or norbixin/NaCas (Zhang & Zhong, 2012a, 2012b, 2013). Table 1. The fluorescence ratio F 0 /(F 0 -F) versus 1/[Q] for casein/lutein presented a linear evolution of both Stern-Volmer and modified Stern-Volmer plots and the fraction accessible to quencher (f a ) was lower than 1.0, which is typical of two populations of Trp on casein fractions composing both casein supramolecular structures at pH 7, one accessible to the quencher and the other inaccessible [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. This binding complexity is expected since NaCas and PPCN are composed of different fractions of casein molecules [START_REF] Casanova | pH-and ionic strength-dependent interaction between cyanidin-3-O-glucoside and sodium caseinate[END_REF], i.e., they are not isolated casein fractions. The f a values ranged from 0.57 to 0.69, meaning that 60 to 70% of the initial fluorophores in casein molecules are accessible for lutein binding. The values of K SV determined from the linear evolution of the Stern-Volmer plots presented a magnitude order of 10 5 M -1 .

Fluorescence quenching can be a consequence of static and/or dynamic mechanisms. The dynamic quenching is caused by collisional encounters between the fluorophore and the quencher. Conversely, the formation of a ground-state complex between them is classified as static quenching [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. According to the correspondence K SV = k q τ 0 in Eq. ( 1), the values of k q for both caseins had a magnitude order of 10 13 M -1 s -1 , which is higher than the typical diffusion-controlled limit (~10 10 M -1 s -1 ). These values indicate that the quenching of NaCas and PPCN fluorescence by lutein followed a static mechanism [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. The static mechanism of fluorescence quenching seems to be quite widespread since it was also reported for the interactions between lutein and caseinate or whey proteins or bovine serum albumin [START_REF] Paiva | Influence of protein conformation and selected Hofmeister salts on bovine serum albumin/lutein complex formation[END_REF][START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF].

The quenching of casein fluorescence by lutein was analyzed according to the Scatchard representation (Eq. ( 5)) to better characterize the casein/lutein interaction [START_REF] Scatchard | The Attractions of Proteins for Small Molecules and Ions[END_REF]. The equilibrium binding constant, K b , was determined from the slope of the plot of (f i × P T )/ [Q] versus (f i × P T ). P T represents total protein concentration, and f i is the fraction of protein fluorescence that can be quenched by the ligand; it is directly proportional to the fraction of protein binding sites occupied by the ligand. The f i value was calculated according to the following equation (Eq. ( 6)).

f i [P t ] [Q] = nK b [P t ] -K b f i [P t ] (5)
f i = F -F 0 F ∞ -F 0 (6)
where F ∞ is fluorescence intensity value at saturation. Fig. 5E and 5F show the Scatchard plots of NaCas/lutein and PPCN/ lutein interactions in the presence of ethanol. A linear Scatchard plot typical of one class of binding sites was observed for lutein binding to both casein structures. The binding constant of casein/lutein complexation presented a magnitude order of 10 5 M -1 , whatever the casein supramolecular structure. This result reflects a moderate affinity between casein and lutein, similarly to that previously reported about the interaction between lutein and whey protein or sodium caseinate [START_REF] Yi | Characterization of milk proteins-lutein complexes and the impact on lutein chemical stability[END_REF] and lutein/human serum albumin [START_REF] Chen | Isorenieratene interaction with human serum albumin: Multispectroscopic analyses and docking simulation[END_REF]. The K b is also in the same magnitude order of that found for the interaction between casein micelles and hydrophobic compounds such as curcumin [START_REF] Khanji | Structure and gelation properties of casein micelles doped with curcumin under acidic conditions[END_REF][START_REF] Yazdi | Heating of milk alters the binding of curcumin to casein micelles. A fluorescence spectroscopy study[END_REF]. On the other hand, [START_REF] Paiva | Influence of protein conformation and selected Hofmeister salts on bovine serum albumin/lutein complex formation[END_REF] reported a magnitude order of binding constant 10fold lower for BSA/lutein complexation. Altogether, this information suggests that NaCas and PPCN have a higher affinity with lutein than BSA.

The data of fluorescence quenching for casein/lutein interaction in the presence of DMSO were also fitted according to Stern-Volmer, modified Stern-Volmer and Scatchard representation (see Fig. 1S, Supporting Information), as described above. The results observed for fluorescence quenching in the presence of DMSO were in the same order of magnitude for those observed in the presence of ethanol (Table 1). Thus, the magnitude order of the K b was not influenced by the supramolecular structure of casein or the organic solvent (ethanol or DMSO).

It means that both NaCas and PPCN presented similar affinity with lutein.

ITC enables the determination of the thermodynamic parameters of the interaction between protein and ligand. Preliminary assays were carried out by injecting lutein into casein solution, since most of the studies on ligand/protein binding usually place ligand and protein in the syringe and cell, respectively [START_REF] Casanova | pH-and ionic strength-dependent interaction between cyanidin-3-O-glucoside and sodium caseinate[END_REF][START_REF] Zhang | Effects of pH on the Molecular Binding between β-Lactoglobulin and Bixin[END_REF]Zhang & Zhong, 2012a). However, the high concentration of lutein in buffer with low content of organic solvent led to fast phase separation due to the formation of big aggregates of lutein. To avoid the destabilization of lutein solution during ITC analysis, a reverse titration was conducted as recommended by [START_REF] Velazquez-Campoy | Isothermal titration calorimetry to determine association constants for high-affinity ligands[END_REF]. It means that the less-soluble reactant (lutein) was placed in the sample cell. To the best of our knowledge, this is the first study conducting reverse ITC to investigate interactions between milk proteins and carotenoids despite the very low solubility of the latter in the presence of high content of water.

Fig. 6 shows the raw signal of isothermal calorimetric titration obtained from the injection of NaCas and PPCN into an aqueous dispersion of lutein (20 mM) containing 5% (v/v) of ethanol. Heat change associated with a single injection of NaCas and PPCN into lutein solution is represented by each peak. The injections of NaCas and PPCN into an aqueous dispersion of lutein resulted in exothermic peaks, consistent with bixin/whey protein binding (Zhang et al., 2013;Zhang & Zhong, 2012a). The energy contribution of casein dilution assessed by injection of the NaCas and PPCN solutions into the buffer containing 5% (v/v) of ethanol (see Fig. 2S, Supporting Information) practically did not differ when compared to the heat exchange associated with the lutein/casein binding. Similar results were also observed in the presence of DMSO (data not shown). It is worth emphasizing that the ITC profiles obtained from NaCas and PPCN dilution shown in Fig. 2S (Supporting Information) were very different. The heat effect associated with NaCas dilution was negligible (flat isotherm), whilst the PPCN dilution exhibited a profile similar to that classically obtained for ligand/protein binding that is characterized by a continuous decrease in heat released until a [START_REF] Lakowicz | Principles of fluorescence spectroscopy[END_REF]. c Parameter calculated by data fitting of casein/lutein fluorescence quenching according to Scatchard representation [START_REF] Scatchard | The Attractions of Proteins for Small Molecules and Ions[END_REF]. constant enthalpic value. It is known that PPCN has a much higher content of colloidal calcium-phosphate than NaCas. Then, a buffer saturated with calcium phosphate was used to evaluate the influence of this mineral on the isotherm of PPCN dilution. The injections of PPCN solution into the buffer, both saturated with calcium phosphate, resulted in much lower heat exchange (see Fig. 3S, Supporting Information) than that observed using a buffer without calcium phosphate (Fig. 2S-B, Supporting Information). This result confirmed that a large heat of PPCN dilution observed using a buffer without calcium phosphate was due to the release of calcium phosphate nano-clusters from casein micelle.

K SV b k q b K b c (-) (×10 5 M -1 ) (×10 13 M -1 s -1 ) (×10 5 M -
As the ITC profiles (Fig. 6) did not present a tendency of saturation of the binding sites, it was not possible to thermodynamically characterize lutein/casein interaction using such technique. Previous studies successfully confirmed by fluorescence quenching and ITC that the binding process of bixin and whey proteins was mainly driven by hydrophobic interactions (Zhang et al., 2013;Zhang & Zhong, 2012a). Bixin is a carotenoid with a free carboxyl end group and another esterified carboxyl end group [START_REF] Mercadante | Carotenoids in foods: Sources and stability during processing and storage[END_REF]. Despite being both xanthophylls, bixin differs significantly from lutein structure. It was likely the reason why a wide range of bixin/protein molar ratio could be studied, resulting in a tendency of saturation of protein binding sites. It is important to highlight that differently from the fluorescence quenching assays, a stock solution of lutein in a buffer (aggregated form) was used for ITC analysis instead of an ethanolic stock solution (dispersed form). [START_REF] Zhu | Aggregation of Fucoxanthin and Its Effects on Binding and Delivery Properties of Whey Proteins[END_REF] investigated the interaction between whey protein and fucoxanthin (FX) as monomers or aggregates by injecting FX dispersed in ethanol or 1:4 ethanol/water, respectively, into protein solution. Nevertheless, the absorption spectra of lutein/casein complexes in buffer showed the presence of lutein aggregates (H-type) even though lutein was directly added to casein solutions as monomers (Fig. 3). This suggests that under these conditions, casein particles interact with the aggregated forms of lutein, consistent with β-carotene/BSA binding [START_REF] Chang | Binding to Bovine Serum Albumin Protects β-Carotene against Oxidative Degradation[END_REF]. Consequently, we propose the following scheme (Fig. 7) to describe casein/lutein interaction in mixed water/solvent solution: aggregation of lutein molecules immediately occurs once injected into a buffer solution containing caseins, before their interaction with casein. Hence, as the aggregation constant (k1) is probably faster than the interaction constant (k2), the major part of the formed complexes involved casein-aggregated lutein. The presence of a small part of casein/lutein monomer complex is not excluded; its proportion depends on the solubility limit of lutein in the organic solvent/water mixture. This scheme allows us to suggest that particular attention should be paid to the interpretation of data on molecular interactions involving low-water-soluble hydrophobic ligands.

Conclusion

Fluorescence quenching results suggest that lutein binds to one set of binding sites on NaCas and PPCN in ethanol-aqueous or DMSO-aqueous solutions. Lutein/casein complexation is mainly driven by hydrophobic interactions with binding constant of a magnitude order of 10 5 M -1 , independently of the supramolecular casein structure. Considering that casein-lutein interaction is not affected by casein supramolecular structure, PPCN arises as a potential nanocarrier for new lutein-rich functional foods, mainly for the elderly since PPCN is also a natural delivery system of calcium. The understanding of the mechanism of interaction between food proteins and carotenoids constitutes the preliminary step in designing efficient protein-based and functional systems for carotenoid delivery. However, further studies on the effect of the supramolecular structure of casein on chemical stability and bioaccessibility of lutein in complex systems are needed to confirm such potential application.

Fig. 1 .

 1 Fig. 1. Absorption spectra of 3.6 µM lutein in DMSO (A) and ethanol (B). Full lines correspond to the absorption spectrum of lutein in a pure organic solvent. Dashed lines correspond to the absorption spectrum of lutein in 10 mM Hepes buffer at pH 7 containing 5% (v/v) of organic solvent.

Fig. 2 .

 2 Fig. 2. Particle size distribution (PSD) of NaCas (A) and PPCN (B) at a concentration of 100 µM. Full lines correspond to the PSD of caseins in 10 mM Hepes buffer at pH 7. Dashed lines correspond to the PSD of caseins in 10 mM Hepes buffer at pH 7 containing 5% (v/v) ethanol.

Fig. 3 .

 3 Fig. 3. Interaction between caseins (1 µM) and lutein in the presence of ethanol. Absorption spectra of 1 µM NaCas (A) and PPCN (B) at pH 7 in the absence and presence of an increasing concentration of lutein in ethanol (from 0 to 8 µM).

  Fig. 5A-D show the Stern-Volmer plots of the fluorescence quenching of NaCas and PPCN in the presence of ethanol. The binding parameters are given in

Fig. 4 .

 4 Fig. 4. Interaction between caseins (1 µM) and lutein in the presence of ethanol (A and B) and DMSO (C and D). Fluorescence emission spectra of NaCas (A and C) and PPCN (B and D) at pH 7 in the absence and presence of an increasing concentration of lutein (from 0 to 8 µM). Black lines correspond to the fluorescence spectrum of lutein 8 µM in Hepes buffer containing 5% (v/v) ethanol or DMSO.

Fig. 5 .

 5 Fig. 5. Interaction between caseins (1 µM) and lutein (from 0 to 8 µM) in the presence of ethanol. Stern-Volmer plots of the quenching of NaCas (A) and PPCN (B) by lutein at pH 7. Modified Stern-Volmer plots of the quenching of NaCas (C) and PPCN (D) by lutein at pH 7. Derived Scatchard plots of NaCas (E) and PPCN (F) quenching by lutein at pH 7.

Fig. 6 .

 6 Fig. 6. Raw data (top panel) and binding isotherm (bottom panel) of the titration of 0.02 mM lutein with successive injections of casein (concentration) as NaCas (A) or PPCN (B). The experiments were carried out at 25 • C in 10 mM Hepes buffer, pH 7.0, with 5% (v/v) ethanol.

Fig. 7 .

 7 Fig. 7. Scheme of lutein aggregation versus lutein/casein binding.

Table 1

 1 Binding parameters of casein/lutein in the presence of ethanol and DMSO. a, *

	Solvent	Casein	f a	b

Acknowledgments

We are grateful for the financial support from the São Paulo Research Foundation (FAPESP) (grants 2013/07914-8, 2017/09214-4, 2017/ 26237-8, 2018/18374-8) and INRAE France. AZM also thanks CNPq (grant 309182/2018-2).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.foodres.2020.109781.


Seeun Jung

Radu Vranceanu
email: vranceanu@essec.edu

Juyoung Cheong

Dong Ook Choi

Delphine Dubart

Kwangki Kim

Marie- Noelle Koebel

Sophie Magnanou

Emmanuelle Le Nagard

Ilsoon Shin

Student satisfaction with distance education during the COVID-19 first-wave: A cross-cultural perspective

Keywords: JEL Classification: I23, I28, I19 Distance education, Student satisfaction, Synchronous teaching, COVID-19 stress

This research note reports results of a survey on student satisfaction with distance education in Korea and France as implemented in May 2020 on 510 respondents. At that time, both countries closed the facilities of higher education institutions and imposed the extensive use of on-line education. A majority of French students express a preference for in-class teaching compared with on-line teaching, while preferences of the Korean students are more balanced. On average, Korean students express higher satisfaction with online teaching compared to French students. Women students also report higher satisfaction scores. The COVID-19 stress is negatively related to satisfaction with online teaching in Korea, but not in France.

Introduction

Distance education (DE), defined as an educational experience where instructors and learners are separated in time and space [START_REF] Keegan | The future of learning: From elearning to mlearning[END_REF]), has been present in the higher education landscape for decades. While in its early years DE comprised essentially correspondence courses, in the last thirty years the Internet revolution pushed this service toward the production of online content and learning interaction.

One can distinguish between asynchronous learning, through which students have access to online resources such as short videos, MOOCs, etc. in an autonomous way, and synchronous instruction through which teachers and learners meet online for a session at a predetermined time [START_REF] Fidalgo | Students' perceptions on distance education: A multinational study[END_REF].

Synchronous instruction has developed along the lines of existing video-conference systems. The most valuable feature of the new systems was the dialogue or interaction between the teacher and the students, or among the students, referred to as synchronous and interactive online education (SIOE). With the progress of Internet bandwidth and data compression technology, the quality of synchronous and interactive instruction greatly improved, by allowing simultaneous contacts for larger groups, and for a more fluid transfers of sound and video images between the participants. For sure, there is substantial room for further improvements: today "Zoom fatigue" due to communication micro-lags, and the "life behind the screen" has been criticized as a major flaw of this approach [START_REF] Fosslien | How to combat zoom fatigue[END_REF]). Synchronous teaching can be recorded in a cloud, which provides for an interesting asynchronous complement. Software initially developed for the purpose of video conferences become an important vector of SIDE development, to mention only Microsoft Team, Professional Skype, Google Meet, and Zoom.

Not a long time ago many observers were betting on the asynchronous DE as the future of higher education.1 SIOE was seen as for sure a fancy device, but not yet mature for mass applications. In "normal times", SIOE would have followed the standard technology adoption path, with some shy, then accelerating dynamic, and probably deemed to disappear when a more efficient system would become available. The major catastrophe of the COVID-19 pandemic turned down all these predictions. The first wave of the COVID-19 pandemic started in the late 2019 in Wuhan, China and then spread globally, with a devastating impact on the planet.

To slow down the unexpected and rapid propagation of the virus, in early 2020 many governments imposed stringent social and physical distancing measures. Korea provided a leading example of good management of the crisis, with self-imposed measure of social distancing, the widespread use of masks and generalized testing. However, many countries were unprepared to fight such a powerful epidemic and had no choice but to resort to lockdowns that limited people mobility to the bare economic necessity.

Governments in a large majority of countries, including Korea and France, decided to close the brick and mortar facilities of the schools. On short notice, teachers were asked to switch from a traditional teaching way, as performed for at least two centuries, to an untested online teaching mode. In France the change was largely unprepared, many professors having to rely on their own material resources and preexisting computer skills to manage this transition. Students and pupils in schools meet the same difficulties. In less than three days, parents had to become education coaches, with significant variation in the ability to adapt to this unexpected mission, depending on their educational background, number of children and spare time.

So distance education appeared as a "miracle" efficient solution to continue education during the lockdowns and under strict physical distancing, with thousands of teachers and maybe millions of students throughout the world being obliged to switch, at short notice, to distance education. The most appealing, and dominant system was SIOE. This research note presents the results from a survey on student satisfaction with SIOE, carried out during the strict lockdown period of France, in Mai 2020, with undergraduate students in France and Korea. 2 The analysis aims to provide a comparison of learning effectiveness and satisfaction levels with online education between the two countries, and study factors that might contribute to the satisfaction level and the stated preference for distance education relative to in-classroom teaching.

The two countries are a meaningful basis for cross-cultural studies: their level of economic development is relatively similar and their population sizes are close; at the same time, they are representative of the Western and Asian cultures along Hoofstede multi-dimensional approach [START_REF] Hofstede | Culture's Consequences: Comparing Values, Behaviors, Institutions, and Organizations Across Nations[END_REF]). 3 Data downloaded on October 13, 2020 from Hofstede Insights show an individualism index of 71 for France, and 18 for Korea. 4 . Long-term orientation is also higher in Korea compared to France, while the differences are much smaller on all the other dimensions of the cultural orientation.

Other studies have investigated satisfaction with online teaching. 5 A survey and metaanalysis of 24 studies by [START_REF] Allen | Comparing student satisfaction with distance education to traditional classrooms in higher education: A meta-analysis[END_REF] reveal that, at that period, students slightly prefer in-class courses to distance education; furthermore, they do not attach positive value to classroom interactions. [START_REF] Summers | A comparison of student achievement and satisfaction in an online versus a traditional face-to-face statistics class[END_REF] show that, controlling for the experience of the professor and evaluation method, students exposed to online courses were less satisfied than their campus-based peers. [START_REF] Wei | Online learning performance and satisfaction: do perceptions and readiness matter?[END_REF] use survey data to estimate a structural equation model to analyze factors that explain satisfaction with online classes. They find that students' computer/Internet self-efficacy and motivation for learning exerted a direct, positive effect on their online discussion score and course satisfaction.

However, there is a major difference between these studies and ours. In the past, schools (and maybe students too) had the choice between on-campus and on-line instruction and use to test freely various DE methods. In the COVID-19 period, neither teachers nor students had other choice but to adopt the online technology. A majority of schools chose spontaneously the SIOE model, although they were experimenting for many years with asynchronous DE. This choice reveals that the value proposition of synchronous interactive online instruction was better fitted to the need of massive online education than the asynchronous format. This "external justification" or "scapegoat role" of the epidemic to adopt SIOE might have had a positive impact on student satisfaction.

Data collection

The data was collected by means of an online survey, administered in early May 2020, on undergraduate students in two business schools in France (one in the Ile-de-France region, the other in Burgundy regions)6 and one University in Incheon, South Korea.

A majority of students (98%, 235 students out of 239) were following more than 4 classes online at the time the survey was implemented. Most of the classes were delivered through Zoom and Google Meeting in France (with the possibility of recording the course), Zoom and recorded video via Youtube or LMS (Learning Management System) in Korea.

Korean students were two year older on average; in France, 59 per cent of the respondents were women, and 44 per cent of the respondents were women in Korea.

We also rely on survey questions to determine the degree of overconfidence and tolerance to risk, using for the latter the self-reported measure of the eagerness to accept risks as introduced by [START_REF] Dohmen | Individual risk attitudes: Measurement, determinants, and behavioral consequences[END_REF]. A higher level indicates a higher degree of overconfidence, and a better tolerance to risk.

Also, the survey elicits their "cultural orientation" using individualistic and collectivist scores. For so doing, we use four "horizontal" items from the individualism/collectivism scale as developed by [START_REF] Triandis | Individualism and collectivism scale (also known as the culture orientation scale)[END_REF]. The two individualism items are "I rely on myself most of the time; I rarely rely on others" and "I often do "my own thing". The two collectivism items are "The well-being of my coworkers is important to me" and "To me, pleasure is spending time with others". Our narrow scale sums the scores with the reverse sign for the individualism score. The maximum score of one indicates an extremely collectivist stance, the lowest (zero) score, an extremely individualist stance.

An important question elicited their ability to fix simple technical problems (computer selffix), which is probably related to a student's broader interest in computer based technology. Other measures were the time they spent -before the pandemic -on computer games (time-use game) and also on cellular phones (time-use online), as proxies for online habits and resilience.

The self-reported time used per week for sport activity (sport practice) can be seen as a proxy for the preference for mobility, and also may be an indication of their health status.

Finally, we asked them the level of stress with respect to the COVID-19 risk at the time when the survey was implemented.

As the data shows in Table 1, 63 percent of the Korean students had a previous experience with online teaching, while French students did not. The fact that Korean student have a previous exposure to DE is not innocuous. Also, while French students followed only synchronous DE, Korean student were exposed to a mix of synchronous and asynchronous teaching. Therefore, any comparisons between the two samples should be performed with extreme caution.

The descriptive statistics by country are presented in Table 1.

French students are significantly more tolerant to risk. French students also report a higher collectivist attitude compared to Korean students, with an index of 0.56 for France, and 0.48 for Korea. In France B-Schools have a tradition of teaching and encouraging social values that might justify these figures. It turns out that for these categories, cultural differences might be much smaller than initially expected.

Korean students appear be have a higher score in the ability to fix computer problems and seem to spent more leisure time online prior to the burst of the epidemic.

The self-reported COVID-19 stress is much larger in Korea. In Appendix Tables 1 and2 we provide these statistics by country and by gender of the respondent. In both countries male subjects report better computer-fix skills and do more sports. The other gender differences are statistically weak: female students report a higher COVID-19 stress, are less risk tolerant, less overconfident and are less interested in gaming than male students in France; these gender differences are not statistically significant in Korea.

Descriptive statistics

Table 2 presents the key variables of our analysis.

1. "Satisfaction" is the index of self-reported global satisfaction with on-line teaching, normalized to one.

2. "Preference for online teaching" is an expression of revealed preference for online teaching, as the answer to the question "If you can choose between an online class an a similar in-class course available without any constraint, please state your preference for the in-class teaching". Answers from 0 (strong preference for in-class) to 5 (strong preference for on-line) were normalized to [0, 0.2, 0.4, 0.6, 0.8, 1].

3. "Effective time" is the self-reported proportion of time they effectively stay focused, in percent of total teaching time.

The overall satisfaction with online teaching turns out to be significantly higher in Korea compared to France. In both countries, a majority of students prefer in-class to on-line teaching; the balance against on-line teaching is extremely strong in France.

The proportion of effective time is much lower in France (51 per cent) compared to Korea (81 per cent). The French average score hides some variation in satisfaction scores between the two institutions where data were collected. No difference is observed with respect to the stated preference for online teaching (see Appendix Table A5). The other variables in Table 2 are components of total satisfaction, which are answers to these items:

Q1. Compared to a face-to-face course, online courses brings you more/less satisfaction with respect to the learning process Q2. Compared to a face-to-face course, the online course allows for the transmission of a smaller/larger volume of knowledge Q3. Compared to a face-to-face course, the online course allows you to worse/better assimilate the concepts Q4. Compared to a face-to-face course, the online course allows for poorer/richer courserelated interactions between students Q5. Compared to a face-to-face course, the online course allows for poorer/richer courserelated interactions between a student and the professor Q6. Compared to a face-to-face course, the online course makes it possible to socialize, or to create interactions between participants independent of the content of the course, more important Q7. Compared to a face-to-face course, attention during a session decreases more/less quickly Q8. Compared to the face-to-face course, the interactive online course requires less/more preparation on your part.

Items from 1 to 7 are positively and significantly correlated to the global satisfaction score. Q8 (preparation for the class) is not correlated, thus cannot be seen as a dimension of quality. The pairwise correlation matrix is presented in the Appendix Table A3. We also use Principal Component Analysis (PCA) to build an index of satisfaction using information contained in the Figure 1 represents the size of the various dimensions of satisfaction (items 1 to 7 as defined before). French students are extremely negative with respect to Q3 (content assimilation) and Q7 (declining attention).

As already mentioned, overall Korean students report a higher satisfaction compared to French students (Figure 2).

In both countries the satisfaction level presents single-peak distributions, representative of significant variation among the respondents (Figure 3). This variation requires to develop a more precise analysis.

In both countries women express higher satisfaction with online teaching, and so do people with a high computer self-fix ability (knowing that male declare better ease with computers).

Figure 7 indicates the distribution the the answers to the "if you can choose between in class and online, what do you prefer" question (0 is strong preference for in-class teaching, 1 is strong preference for online teaching).

The graph reveals a very high density of the strong preference for in-class teaching in France, and a more homogeneous distribution in Korea.

Finally, Figure 8 indicates the distribution of the effective time. Many Korean students report full intensity. This can possibly be explained by the fact that a substantial part of the DE is based

Regression analysis

Regression analysis allows us to move beyond these descriptive statistics. Tables 3 and4 present results from OLS regression models, separately for France and Korea, and for the full sample, using as dependent variables "Satisfaction with online" , and the "Preference for online (against in-class) teaching" as previously defined. Because data for France come from two different institutions, errors are clustered by institutions.

As we can see, in both countries women express a higher satisfaction with online teaching. The relationship between COVID-19 stress and satisfaction with online teaching can go either ways. On the one hand, online teaching is increasing physical distance, and reduces the risk of contamination. On the other hand, a higher COVID-19 stress can have a negative effect on satisfaction with education in general, because of the negative emotions it can generate. In Korea the correlation is negative -the latter effect is stronger, but not in France, where the positive (social distance) effects seems to take over the former. A similar result is obtained in Table 4 (in France the two effect just cancel each other).

An important factor of satisfaction for the Korean sample is the ability to fix simple computer breakdowns, which depends on their experience, previous training and IT talent. In the all-data It is difficult to interpret the coefficient of the cultural orientation. In the preference for online teaching, the sign is negative. This is aligned with intuitive reasoning, with less individualistic subjects being more averse to online teaching. However, the sign is positive in the all-sample satisfaction model, which is somehow puzzling.

Gamers who use to spent time before the computer screens, express higher satisfaction with online teaching (in the overall sample).

The practice of sport is positively related to satisfaction in the overall sample. Table A4 in the Appendix presents similar regression models, using as a dependent variable the effective time spend on line, and reveal, mostly similar results.

These results suggest that satisfaction with online teaching is to some extent difficult to explain by elementary traits of personality, and furthermore, can significantly differ from one country to another.

Concluding Remarks

The outbreak of the COVID-19 pandemic imposed on many governments the hard choice of closing schools and higher education institutions. Synchronous and Interactive Online Education (SIOE) became, at short notice, the main solution for maintaining the continuity of the education process, seconded by asynchronous DE methods (MOOCs, recorded videos).

This paper reports the results from a survey on student satisfaction with on-line teaching as implemented in France and Korea in May 2020. At that time France was imposing a ban on all non-essential activities and restricted the mobility of persons by administrative authorizations. In Korea the sanitary situation was under control with a reduced number of case fatalities; however, in Korea too higher education institutions were using only distance education.

The results show that while DE is seen by respondents as a workable solution in an emergency situation, for many students it is not the preferred solution compared to traditional, in-class teaching. In particular, students exposed to SIOE are critical with respect to the limited social interactions, and the difficulty in maintaining attention focused.

French students are more critical than Korean students with respect to all dimensions of satisfaction. In both countries women appear to have a more favourable appreciation toward online teaching, compared to men.

The COVID-19 stress has two opposite effects on satisfaction. In general, it will generate negative emotions (anxiety, sadness, etc.) that bring about a negative effect on satisfaction in general. On the other hand, DE is limiting the risk of contagion, which should have a positive effect on satisfaction. In Korea the COVID-19 related stress is negatively associated to satisfaction with online classes, representative of a stronger first effect. In France, the association between the COVID-19 stress and satisfaction is positive, indicative of a stronger second effect.

For sure, results from such a small sample survey, on a non-representative sample of students, should be interpreted with extreme caution. Despite these important limitations, these answers reveal that the satisfaction with education depends on many subtle and sometimes hidden factors, going well beyond the plain transmission of knowledge. Students exposed to DE miss the group interaction and the specific emotions generated by a in-the-classroom education experience. The quality of computer communication is often harmed by the speed of Internet which adds small transmission lags and entails a poor quality of sound and image. In turn, these psychological and technical limitations adversely affect student capacity to stay focused, to assimilate concepts, and ultimately harm their satisfaction with the education process.

Figure 1 :

 1 Figure 1: Components of Satisfaction with Online Teaching

Figure 7 :

 7 Figure 7: Distribution of Effective Online Time

Figure A1 :

 A1 Figure A1: Components of Satisfaction with Online Teaching: French Institutions

Table 1

 1

		: Summary Statistics
		(1)		(2)		(3)
		France	Korea		ttest
		mean	sd	mean	sd	b	se
	Age	20.83 1.25 22.76 1.92 1.93 * * * (0.14)
	Female	0.59 0.49 0.44 0.50 -0.15 * * * (0.04)
	Covid19 Stress	0.48 0.29 0.63 0.25 0.15 * * * (0.02)
	Online Before	0.06 0.24 0.63 0.48 0.57 * * * (0.03)
	Risk Tolerence	0.68 0.19 0.42 0.23 -0.26 * * * (0.02)
	Overconfidence	0.32 0.34 0.35 0.42	0.03	(0.03)
	Culture Orientation 0.56 0.15 0.48 0.13 -0.08 * * * (0.01)
	Computer Self-fix	0.60 0.28 0.82 0.20 0.22 * * * (0.02)
	Sport Practice	0.60 0.28 0.64 0.27	0.03	(0.02)
	Time-use Online	0.75 0.18 0.82 0.17 0.07 * * * (0.02)
	Time-use Game	0.31 0.21 0.60 0.28 0.29 * * * (0.02)
	Observations	271		239		510

Table 2 :

 2 Summary Statistics

		(1)		(2)			(3)
		France	Korea	ttest
		mean	sd	mean	sd	b	se
	Satisfaction	0.55 0.24 0.64 0.22 0.10 * * * (0.02)
	Preference Online	0.15 0.24 0.40 0.29 0.25 * * * (0.02)
	Effective Time Spent	0.51 0.25 0.81 0.21 0.30 * * * (0.02)
	Q1. Learning Process	0.44 0.22 0.53 0.21 0.09 * * * (0.02)
	Q2. Volume	0.48 0.23 0.58 0.20 0.10 * * * (0.02)
	Q3. Concept Transmission 0.39 0.20 0.61 0.25 0.22 * * * (0.02)
	Q4. Interaction Students	0.36 0.23 0.39 0.20	0.03	(0.02)
	Q5. Interaction Professor	0.38 0.22 0.42 0.19 0.04 * (0.02)
	Q6. Social Interaction	0.31 0.17 0.40 0.19 0.10 * * * (0.02)
	Q7. Losing Attention	0.18 0.24 0.40 0.28 0.22 * * * (0.02)
	Observations	271		239		510

Table 3 :

 3 Satisfaction

		(1)	(2)	(3)
		France	Korea	All
	Covid19 Stress	0.0973**	-0.174*** -0.173***
		(0.00234)	(0.0575) (0.00276)
	Female	0.0792**	0.0782** 0.0791**
		(0.00128)	(0.0334) (0.00801)
	Online Before	0.0675	-0.0722**	-0.0431
		(0.0862)	(0.0298)	(0.0395)
	Age	0.00698	0.00271	0.00483
		(0.0177)	(0.00827) (0.00423)
	Overconfidence	0.118***	0.0486	0.0428**
		(0.000157) (0.0356) (0.00716)
	Culture Orientation	-0.0672	0.201*	0.192***
		(0.160)	(0.113)	(0.0167)
	Risk Tolerence	-0.0548	-0.0119	-0.0116**
		(0.133)	(0.0645) (0.00199)
	Time-use Online	0.212	-0.0429	-0.0487**
		(0.229)	(0.0894) (0.00838)
	Time-use Game	0.111	0.0696	0.0720***
		(0.0460)	(0.0539) (0.00267)
	Computer Self-fix	0.165	0.171**	0.175***
		(0.0926)	(0.0741) (0.00601)
	Sport Practice	0.0840**	0.0761	0.0722***
		(0.00560)	(0.0534) (0.00447)
	France			-0.295
				(0.209)
	France × Covid19 Stress			0.0270***
				(0.00157)
	France × Female			-0.00164
				(0.00997)
	France × Overconfidence			0.0878**
				(0.0104)
	France × Culture Orientation			-0.264
				(0.161)
	France × Risk Tolerence			-0.0224
				(0.123)
	France × Time-use Online			0.0431
				(0.0320)
	France × Time-use Game			0.00824
				(0.00395)
	France × Compueter Self-fix			-0.0194
				(0.0892)
	France × Sport Practice			0.000200
				(0.00124)
	Constant	-0.00212	0.399*	0.339*
		(0.122)	(0.228)	(0.102)
	Observations	271	239	510
	Adjusted R 2	0.092	0.065	0.111
	Significant level: * 0.1 ** 0.05 *** 0.01
	Standard Errors are clustered by institutions

Table 4 :

 4 Online Preference

		(1)	(2)	(3)
		France	Korea	All
	Covid19 Stress	0.000254	-0.286*** -0.287***
		(0.000795)	(0.0759)	(0.00135)
	Female	-0.0183	0.0754*	0.0835***
		(0.0630)	(0.0441)	(0.00782)
	Online Before	-0.0439	-0.0281	-0.0319
		(0.0677)	(0.0393)	(0.0140)
	Age	0.0180***	0.00562	0.0102
		(0.0000708) (0.0109)	(0.00450)
	Overconfidence	0.0358	-0.00518	-0.00582
		(0.0540)	(0.0471)	(0.00269)
	Culture Orientation	-0.337	-0.192	-0.184***
		(0.124)	(0.149)	(0.00880)
	Risk Tolerence	0.0217	-0.0452	-0.0431***
		(0.141)	(0.0852)	(0.00199)
	Time-use Online	-0.000470	-0.227*	-0.226***
		(0.0862)	(0.118)	(0.00317)
	Time-use Game	0.175	0.0428	0.0440***
		(0.0987)	(0.0713)	(0.00150)
	Computer Self-fix	-0.0377	0.0856	0.0851***
		(0.0741)	(0.0979)	(0.00212)
	Sport Practice	0.0657	0.0518	0.0490***
		(0.0741)	(0.0705)	(0.00320)
	France			-0.461**
				(0.0943)
	France × Covid19 Stress			0.0292***
				(0.000278)
	France × Female			-0.101
				(0.0531)
	France × Overconfidence			0.0429
				(0.0556)
	France × Culture Orientation			-0.158
				(0.108)
	France × Risk Tolerence			0.0662
				(0.128)
	France × Time-use Online			0.0385*
				(0.0132)
	France × Time-use Game			0.0213
				(0.0146)
	France × Compueter Self-fix			-0.119
				(0.0691)
	France × Sport Practice			0.00164
				(0.00661)
	Constant	-0.117	0.609**	0.501**
		(0.126)	(0.301)	(0.108)
	Observations	271	239	510
	Adjusted R 2	0.047	0.049	0.222
	Significant level: * 0.1 ** 0.05 *** 0.01
	Standard Errors are clustered by institutions

Table A2 :

 A2 Summary Statistics: Korea

		Table A4: Effective Time spent
					(1)	(2)	(3)
					France	Korea	All
		Covid19 Stress Female	(1) Female	0.195* (0.0221) 0.0369*	(2) 0.00682 Male (0.0549) 0.00487	0.00801* (3) (0.00250) ttest -0.00464
			mean	sd (0.00298) (0.0319) mean sd	b (0.0170)	se
	Age	Online Before	21.80 1.33 23.51 1.98 1.71 * * * (0.22) -0.0457 -0.0506* -0.0491**
	Covid19 Stress Online Before Age	(0.0592) 0.66 0.23 0.61 0.26 -0.05 (0.03) (0.0284) (0.0102) -0.0149 0.0000338 -0.00554 0.69 0.47 0.59 0.49 -0.10 (0.06) (0.0222) (0.00789) (0.00960)
	Risk Tolerence Overconfidence	0.38 0.22 0.44 0.24 0.0714 0.0400	0.06 0.0413*** (0.03)
	Overconfidence	0.32 0.41 0.38 0.44 (0.0367) (0.0340)	0.06 (0.00135) (0.06)
	Culture Orientation 0.48 0.13 0.48 0.13 Culture Orientation -0.193 -0.0670	0.00 -0.0753** (0.02)
	Computer Self-fix Sport Practice Risk Tolerence Time-use Online Time-use Online	(0.187) 0.79 0.21 0.85 0.18 0.06 * (0.03) (0.107) (0.0170) -0.0740 -0.0498 -0.0523*** 0.58 0.28 0.68 0.26 0.09 * * (0.04) (0.0641) (0.0615) (0.00431) 0.86 0.13 0.79 0.19 -0.07 * * (0.02) 0.0817 0.0517 0.0503***
	Time-use Game	0.57 0.30 0.62 0.26 (0.382) (0.0854)	0.05 (0.00384) (0.04)
	Observations Time-use Game	105	134 0.00287 (0.00443) (0.0515) -0.0659	-0.0674*** 239 (0.00231)
		Computer Self-fix			0.230*	-0.103*	-0.103***
					(0.0218)	(0.0708)	(0.00128)
		Sport Practice			0.0120	0.119**	0.123***
				(0.00462) (0.0510)	(0.00582)
		France				-0.567
						(0.371)
		France × Covid19 Stress Table A3: Pairwise Correlation	0.0181** (0.00286)
		France × Female				0.0412* (1) (0.0149)
		France × Overconfidence			sat 0.0274
		Satisfaction PCA			0.602 * * * (0.0297)
		France × Culture Orientation Satisfaction compared to Initial Expectation 0.740 * * * -0.111 Preference Online (0.186) 0.481 * * * Q1. Learning Process France × Risk Tolerence -0.0254 0.531 * * * Q2. Volume (0.0634) 0.476 * * * France × Time-use Online 0.00412
		Q3. Concept Transmission	0.559 * * * (0.0552)
		Q4. Interaction Students France × Time-use Game Q5. Interaction Professor Q6. Social Interaction France × Compueter Self-fix Q7. Losing Attention France × Sport Practice		0.0121*** 0.258 * * * (0.000920) 0.350 * * * 0.329*** 0.319 * * * (0.00774) 0.438 * * * -0.0110***
		Observations				510 (0.00103)
		Constant			0.631*	0.877***	1.010**
					(0.0586)	(0.218)	(0.228)
		Observations			271	239	510
		Adjusted R 2			0.082	0.013	0.340

Significant level: * 0.1 ** 0.05 *** 0.01 Standard Errors are clustered by institutions

Table A5 :

 A5 Satisfaction French Institutions .23 0.63 0.23 0.13 * * * (0.03) Preference Online 0.17 0.24 0.14 0.22 -0.03 (0.03) Effective Time 0.46 0.21 0.58 0.29 0.12 * * * (0.03)

	(1)		(2)		(3)
	IDF		Burgundy	ttest
	mean	sd	mean	sd	b	se
	Satisfaction 0.49 0Observations 162		109		271

An an example of such optimistic beliefs,[START_REF] Garrison | Theoretical challenges for distance education in the 21st century: A shift from structural to transactional issues[END_REF] once stated: "Asynchronous collaborative learning may well be the defining technology of the postindustrial era of distance education." (p.12).

On May

31st 2020, the Johns Hopkins Coronavirus Research Center reported a cumulative 28800 case fatalities in France.3[START_REF] Jung | Competitive compensation and subjective well-being: The effect of culture and gender[END_REF] provide an analysis of cross-cultural differences in the attitude toward competing and further discuss the cultural differences of Korean and French students 4 See www.hofstede-insights.com/product/compare-countries/ 5 See[START_REF] Weerasinghe | Students' satisfaction in higher education literature review[END_REF] for a survey on the literature on student satisfaction in general.

A total of 162 students in Ile-de-France and 109 students in the Burgundy region participated in this survey.

A Appendix Tables