Domenik Schleier

Alexander Humeniuk

Prof. Dr Engelbert Reusch

Fabian Holzmeier

Dianailys Nunez-Reyes

Christian Alcaraz

Gustavo A Garcia

Jean-Christophe Loison

Prof. Dr Ingo Fischer
email: ingo.fischer@uni-wuerzburg.de

Roland Mitric
email: roland.mitric@uni-wuerzburg.de

Dr D N Reyes

J.-C Loison

Diborene: Generation and Photoelectron Spectroscopy of an Inorganic Biradical

Keywords: ionization energy, ab initio calculations, gas phase reaction, synchrotron radiation

Diborenes, R-BB-R' are of current interest in inorganic chemistry, because they offer the opportunity to tune the properties of a biradical by modifying the substituents of the diborene parent, HBBH. Here we synthesize the elusive diborene by H-atom abstraction from diborane, B 2 H 6 using fluorine atoms and report a vibrationally resolved photoelectron spectrum of the HBBH biradical. The spectrum is interpreted by comparison with high-level ab initio computations, taking into account the Renner-Teller splitting in the X + 2 Π ionic ground state, which show an excellent agreement with the experimental spectrum. An adiabatic ionization energy of 9.080±0.015 eV was determined and a vibrational progression in the boron-boron stretching vibration of 0.14 eV is visible. This is due to the reduction of bond order upon ionization, accompanied by an increase of the computed boron-boron bond length R BB from 1.514 Å to 1.606 Å.

3 Inorganic biradicals receive increasing attention due to their unusual binding properties that are still a challenge for theory, [START_REF] Miliordos | Unusual Inorganic Biradicals: A Theoretical Analysis[END_REF] but also due to the difficulties to prepare them. Diborenes R-BB-R` constitute particularly interesting candidates, because varying the ligands provides the opportunity to tune the properties of the biradicalic HBBH parent, which has the same number of electrons as C 2 . Only recently the synthesis and characterization of double-bond-containing species based on boron, as well as their fully twisted diradical congeners was reported. [START_REF] Böhnke | Isolation of Diborenes and their 90°-Twisted Diradical Congeners[END_REF] Such biradicals expand the wealth of binding motives [START_REF] Braunschweig | Double, Triple Bonds and Chains: The Formation of Electron-Precise BB Bonds[END_REF] in boron chemistry that range from stabilized diborenes with B=B double [START_REF] Auerhammer | Increasing the Reactivity of Diborenes: Derivatization of NHC-Supported Dithienyldiborenes with Electron-Donor Groups[END_REF][START_REF] Braunschweig | Highly Strained Heterocycles Constructed from Boron-Boron Multiple Bonds and Heavy Chalcogens[END_REF][START_REF] Wang | A Stable Neutral Diborene Containing a B = B Double Bond[END_REF] and diborynes with triple bonds [START_REF] Zhou | OCBBCO: A Neutral Molecule with Some Boron-Boron Triple Bond Character[END_REF][START_REF] Braunschweig | Ambient-Temperature Isolation of a Compound with a Boron-Boron Triple Bond[END_REF][START_REF] Frenking | A Boron-Boron Triple Bond[END_REF][START_REF] Bohnke | Experimental Assessment of the Strengths of B-B Triple Bonds[END_REF][START_REF] Li | B 2 (BO) 2 2--Diboronyl Diborene: A Linear Molecule with a Triple Boron-Boron Bond[END_REF] to singlet borylenes [START_REF] Bettinger | Direct Spectroscopic Characterization in Inert Gas Matrices[END_REF] and larger boron clusters including fullerene-type structures. [START_REF] Zhai | Observation of an All-Boron Fullerene[END_REF] However, in contrast to their organic counterparts, 14 accurate spectroscopic studies of inorganic reactive intermediates that yield structural and thermochemical information are scarce and in particular the diborene parent compound HBBH (1 in scheme 1) has remained almost elusive so far. The molecule has only been observed in rare gas matrices, where EPR (electron paramagnetic resonance) spectra indicated a triplet ground state [START_REF] Knight | ESR Investigation of the HBBH (X 3 Σ) Radical in Neon and Argon Matrices at 4 K. Comparison with ab Initio SCF and CI Calculations[END_REF] and an IR-spectrum revealed the ν 3 antisymmetric stretch at 2679.9 cm -1 . [START_REF] Tague | Reactions of Pulsed-Laser Evaporated Boron Atoms with Hydrogen. Infrared Spectra of Boron Hydride Intermediate Species in Solid Argon[END_REF] Previous photoion yield spectra gave approximate ionization and appearance energies for B 2 H 4 [START_REF] Ruscic | Molecular Structure and Thermal Stability of B 2 H 4 and B 2 H 4 + Species[END_REF] and B 2 H 5 , [START_REF] Ruscic | Structure and Bonding in the B 2 H 5 Radical and Cation[END_REF] but no data on smaller B x H y species were reported. Here we present a vibrationally resolved photoelectron spectrum of diborene 1, obtained by photoionization with synchrotron radiation (SR). The experiments are complemented by highlevel ab initio computations. A large number of theoretical studies are available for the neutral ground state of 1, [START_REF] Miliordos | Ab Initio Investigation of the Electronic Structure and Bonding of BH, BH-, and HBBH Molecules[END_REF][START_REF] Peric | Ab Initio Study of the Electronic Spectrum of B 2 H 2 .1. Vertical Spectrum and trans-and cis-Bending Potential Curves[END_REF][START_REF] Peric | Ab Initio Study of the Electronic Spectrum of B 2 H 2 .2. Potential Curves for Torsional Motion, Symmetric B-H Stretching, and B-B Separation[END_REF][START_REF] Brites | Rovibrational energies of B 2 H 2 (X 3 Σ -g ) from an explicitly correlated potential energy surface[END_REF] also focusing on the EPR properties [START_REF] Engels | Ab Initio Investigation of Vibrational Effects on Magnetic Hyperfine Coupling Constants in the X 3 Σ g -State of B 2 H 2[END_REF] and most recently on the competition between multicenter and classical bonding. [START_REF] Lundell | Tug-of-War Between Classical and Multicenter Bonds in H-(Be)n-H Species[END_REF] However, no computations of the Renner-Tellersplit cation have yet been reported. Scheme 1. Diborene 1 was produced from diborane 2 by the reaction with fluorine atoms.

Diborene 1 is a linear molecule of D ∞h symmetry with a 3 Σ g -ground state. [START_REF] Engels | Ab Initio Investigation of Vibrational Effects on Magnetic Hyperfine Coupling Constants in the X 3 Σ g -State of B 2 H 2[END_REF] The highest singly occupied molecular orbitals (SOMO) are the [1π u (p x )] 1 [1π u p y ] 1 binding orbitals, so the formal bond order is 2. However, since the unpaired electrons are situated in orthogonal MOs, the double bond used in a Lewis-description is questionable in MO theory and therefore omitted from Scheme 1.

Diborene 1 was produced from diborane 2 according to Scheme 1 by reaction with fluorine atoms, generated in a microwave discharge from F 2 . The driving force for this reaction is the large binding energy of HF (D e =592 kJ/mol). [START_REF] Peterson | Benchmark Calculations with Correlated Molecular Wave Functions. VII. Binding Energy and Structure of the HF Dimer[END_REF] H-abstraction by F-atoms has been utilized before to record photoelectron spectra of reactive intermediates, [START_REF] Baker | Photoelectron Spectroscopy of Unstable Molecules[END_REF][START_REF] West | Photoelectron Spectroscopy of Short-Lived Molecules Using Synchrotron Radiation[END_REF] but application has been limited by the unselectivity of the approach. In fact, the reaction with fluorine atoms produces a range of B x H y species, with the maximum of the distribution depending on the F-concentration, as demonstrated in Figure 1. We therefore applied photoelectron-photoion coincidence spectroscopy (PEPICO), [START_REF] Baer | Advances in Threshold Photoelectron Spectroscopy (TPEA) and Threshold Photoelectron Photoion Coincidence (TPEPICO)[END_REF] a method that permits to record mass-selected photoelectron spectra (ms-PES) for each composition by correlating ions and electrons. Several reactive molecules generated by fluorine discharges, 29,30 pyrolysis [START_REF] Holzmeier | H 2 CN + and H 2 CNH + : New Insight into the Structure and Dynamics from Mass-Selected Threshold Photoelectron Spectra[END_REF][START_REF] Holzmeier | Photoionization and Pyrolysis of a 1,4-Azaborinine: Retro-Hydroboration in the Cation and Identification of Novel Organoboron Ring Systems[END_REF][START_REF] Reusch | Isomer-Selective Generation and Spectroscopic Characterization of Picolyl Radicals[END_REF][START_REF] Steinbauer | Photoionization of C 7 H 6 and C 7 H 5 : Observation of the Fulvenallenyl Radical[END_REF][START_REF] Cunha De Miranda | Threshold Photoelectron Spectroscopy of the Methyl Radical Isotopomers, CH 3 , CH 2 D, CHD 2 and CD 3 : Synergy between VUV Synchrotron Radiation Experiments and Explicitly Correlated Coupled Cluster Calculations[END_REF] or photolysis [START_REF] Schleier | Kinetics of the a-C 3 H 5 +O 2 Reaction, Investigated by Photoionization Using Synchrotron Radiation[END_REF] have been studied using PEPICO, which is evolving into an analytical tool to probe elusive intermediates for example in model flames, [START_REF] Oßwald | In Situ Flame Chemistry Tracing by Imaging Photoelectron Photoion Coincidence Spectroscopy[END_REF][START_REF] Krüger | Photoelectron-photoion coincidence spectroscopy for multiplexed detection of intermediate species in a flame[END_REF] catalytic reactors [START_REF] Hemberger | Understanding the Mechanism of Catalytic Fast Pyrolysis by Unveiling Reactive Intermediates in Heterogeneous Catalysis[END_REF] and kinetics experiments. [START_REF] Schleier | Kinetics of the a-C 3 H 5 +O 2 Reaction, Investigated by Photoionization Using Synchrotron Radiation[END_REF][START_REF] Sztaray | Double Velocity Map Imaging Photoelectron Photoion Coincidence Spectroscopy for Reaction Kinetics Studies[END_REF] The molecule has been investigated by Dyke and coworkers, who reported an IE of 11.12 ± 0.01 eV for the transition into the X + 2 Σ + ground state of the cation. [START_REF] Dyke | Study of the Ionization Process BF'(X 2 X + ) + BF(X 1 X + ) by High-temperature Photoelectron Spectroscopy[END_REF] Beside BF a number of B 2 H y compounds are visible. The experimental conditions were chosen to maximize B 2 H 2 . As visible, BH 2 is present as well, but the intensity was not sufficient to record a photoelectron spectrum. In addition we observed peaks corresponding to B 4 H y , which originate from boron-clusters that have formed in the sample. previously. [START_REF] Garcia | Valence Shell Threshold Photoelectron Spectroscopy of C3Hx (x = 0-3)[END_REF][START_REF] Poully | Photoionization of 2-Pyridone and 2-Hydroxypyridine[END_REF] This yields the mass-selected slow photoelectron spectrum (ms-SPES), given as a white line in Figure 2, which is associated with a resolution comparable to the more common threshold PES, but with a higher signal-to-noise ratio.

The ms-SPES of 1 is shown in more detail in the upper trace of Figure 3. Note that contributions from 10 B 11 BH 3 will appear in the m/z=24 mass channel, but can be identified by comparison with the 11 B 2 H 3 spectrum recorded in the m/z=25 channel. In addition small contributions from The first band in Figure 3 The vibrational temperature might be slightly higher, but the small hot band intensity shows that the exothermicity of the H atom abstraction is mostly taken up by the HF vibration. At higher energies a vibrational progression with a spacing of 0.14 eV appears that can be qualitatively explained within molecular orbital theory: Upon photoionization an electron is removed from the 1π u binding orbital, the bond order is reduced from 2 to 1.5, and the boron-boron-bond length R BB will increase. Consequently, activity in the BB-stretching vibration is expected. However, analysis is impeded by the fact that the ionic ground state is a doubly degenerate 2 Π state, which exhibits Renner-Teller splitting. Complete active space multireference configuration interaction (CAS-MRCI) computations show that the two components (called D 0 and D 1 below for simplicity) are isoenergetic at the linear geometry. The degeneracy is lifted by excitation of a bending motion, but the minimum energy geometry remains linear. While for the totally symmetric vibrational mode ν 1 a wavenumber of 1108 cm -1 (0.137 eV) was computed for both D 0 and D 1 , the bending mode energies are slightly higher in D 1 . Therefore the latter state has a higher zero point energy (4801 cm -1 compared to 4518 cm -1 ), which should lead to the appearance of two progressions in the PES. This is evident from the Franck-Condon simulation based on the computations depicted in the lower trace of Figure 3. The two progressions cannot be fully resolved in the experimental spectrum, but the bands show a shoulder at the high-energy

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The Journal of Physical Chemistry Letters side, which is assigned to the T 0 → D 1 transition. Nevertheless, the agreement between experiment and simulation is excellent and both the ν 1 vibrational spacing and the intensities are well reproduced, indicating that the computations accurately reflect both the geometry change upon photoionization and the shape of the cationic potential energy surfaces. IE ad was computed to be 8.865 eV, i.e. roughly 0.2 eV lower than the experimental value. A bond length R BB of 1.514 Å was computed for the X 3 Σ g -state, comparable to B=B double bonds. [START_REF] Wang | A Stable Neutral Diborene Containing a B = B Double Bond[END_REF] For the X + 2 Π state R BB =1.606 Å was found, thus the bond length increases by almost 0.1 Å upon ionization.

Note that previous MRCI computations found slightly shorter R BB for the neutral ground state. 19- 21 The most important parameters are summarized in table 1.

Table 1. Important parameters for diborene 1. In conclusion we report the gas phase synthesis and the first photoelectron spectrum of diborene, a prototype inorganic biradical, yielding an IE ad =9.08 eV. Excellent agreement with high-level computations is observed. Despite the tendency of boron to form strong B-F bonds, HBBH was formed in sufficient concentration to record a vibrationally resolved photoelectron spectrum. The work represents a cornerstone for systematic studies of the effects that changes in the substitution pattern have on the electronic stability of diborenes.

X 3 Σ g -[a] X + 2 Π (D 0 ) [a] X + 2 Π (D 1 ) [a] Experiment R BB /Å 1.

Methods

Experiments were conducted at the DESIRS undulator beamline [START_REF] Nahon | A State-of-the-Art VUV Beamline Featuring High resolution and Variable Polarization for Spectroscopy and Dichroism at SOLEIL[END_REF] of the SOLEIL storage ring in St. Aubin/F, using the DELICIOUS 3 double imaging photoelectron/photoion coincidence (i2PEPICO) spectrometer. [START_REF] Garcia | DELICIOUS III: A Multipurpose Double Imaging Particle Coincidence Spectrometer for Gas Phase Vacuum Ultraviolet Photodynamics Studies[END_REF] HBBH was generated from B 2 H 6 (0.5% in Ar) via H-abstraction by fluorine according to Scheme 1 in a fast flow tube at low pressure that is described in detail elsewhere. [START_REF] Garcia | Synchrotron-Based Double Imaging Photoelectron/Photoion Coincidence Spectroscopy of Radicals Produced in a Flow Tube: OH and OD[END_REF] Fluorine atoms were produced in a microwave discharge of a mixture of around 5%

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The Journal of Physical Chemistry Letters F 2 diluted in He, introduced into the flow tube 50 cm before the reaction zone. The amount of F 2 was adjusted to maximize the signal of 1, the Fluorine atom density being typically around 10 13 atoms⋅cm -3 . After passage through the flow tube, the mixture is adiabatically expanded through a first skimmer into a differentially pumped chamber (few 10 -4 mbar), and through a second skimmer (f = 1 mm, Beam Dynamics Inc.) into the ionization chamber (few 10 -8 mbar). The VUV radiation was provided by a variable polarization undulator, which feeds the DESIRS beamline. Radiation with a narrow bandwidth was selected by a 6.65 m normal incidence monochromator with a 200 g/mm SiC grating and focused onto a 200/200 µm (H/V) spot at the ionization region. The entrance and exit slits were set to yield a resolution of around 5 meV at 9

eV for a flux of 2×10 12 photons/s. A gas filter filled with 0.25 mbar Ar cut off the higher order radiation from the undulator. [START_REF] Mercier | Experimental and Theoretical Study of a Differentially Pumped Absorption Gas Cell Used as a Low Energy-Pass Filter in the Vacuum Ultraviolet Photon Energy Range[END_REF] The photon energy was scanned in 5 meV steps and data were averaged for 300 s at each energy. Photoelectron spectra were obtained via the slow PES (SPES) technique described in Ref. [START_REF] Poully | Photoionization of 2-Pyridone and 2-Hydroxypyridine[END_REF] The spectral resolution is around 20 meV.

Electronic structure calculations were performed at the CAS-MRCI level with the ANO-RCC basis set using the software package MOLPRO. [START_REF] Werner | Version 2012.1, a Package of Ab Initio Programs[END_REF] The orbitals of an active space consisting of 10 electrons in 10 orbitals were optimized by minimizing the energy of one triplet and two ionic doublet states. This was followed by multireference CI calculations with the same active space to find the lowest triplet and the lowest two ionic doublet states. Geometry optimizations in the T 0 , D 0 and D 1 states at the same level of theory were followed by a frequency calculation. All 7 vibrational frequencies were positive and the remaining 5 frequencies were 0 within numerical precision. The Franck-Condon factors were computed using the pGopher program, [START_REF] Western | Automatic Assignment and Fitting of Spectra with PGOPHER[END_REF] including Duschinsky rotation.

Figure 1 .

 1 Figure 1. The mass spectrum of B 2 H 6 in a fluorine discharge.

Figure 1

 1 Figure 1 depicts a mass spectrum, integrated over all photon energies from 8.5 to 11.4 eV to

Figure 2 .

 2 Figure 2. Full photoelectron spectrum matrix of the m/z=24 mass channel. Note that around 9.65

  at 9.08±0.015 eV corresponds to the adiabatic ionization energy IE ad of HBBH. The error bars are taken from the full width at half maximum of the first band and reflect the underlying rotational distribution. No significant hot band activity is apparent, indicating that the molecules are approximately at room temperature. A rotational temperature of 200 K is deduced from the molecular beam velocity, which is extracted from the ion image.

Figure 3 .

 3 Figure 3. Experimental (upper trace) and computed photoelectron spectrum of HBBH. The

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 20 Scheme 1 71x13mm (300 x 300 DPI)

Figure_3

  Figure_3 272x208mm (300 x 300 DPI)

  [START_REF] Bohnke | Experimental Assessment of the Strengths of B-B Triple Bonds[END_REF] B 2 H 4 might appear. We computed the IE for three isomers of B 2 H 4 using the CBS-QB3 composite method and arrived at values of 10.38 eV (H 2 B-BH 2 ), 9.57 eV (bridged structure I, HB(H) 2 BH) and 8.43 eV (bridged structure II, B(H) 3 BH). The FC simulation of bridged structure 1 shows a long progression with a weak origin band, maximizing at the second overtone. Thus contributions from 10 B 2 H 4 to the spectrum can be excluded. A contribution of the higher energy isomer BBH 2 to m/z=24 has also to be considered. The IE was calculated to be 8.97 eV, but again a different vibrational progression is expected from a Franck-Condon simulation.

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ACKNOWLEDGMENTS: This work was performed on the DESIRS beamline under Proposal

No. 20170009. We acknowledge SOLEIL for provision of synchrotron radiation facilities and the DESIRS beamline team for their assistance. The work was financially supported by the Deutsche Forschungsgemeinschaft, research training school GRK 2112 (Molecular Biradicals) as well as Fi 575/13-1 and the Agence Nationale de la Recherche (ANR) under grant number ANR-12-BS08-0020-02 (project SYNCHROKIN). We would like to thank Maik Finze (University of Würzburg) for providing the B 2 H 6 sample.

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Sophie Laverroux
email: sophie.laverroux@inrae.fr

Fabienne Picard
email: fabienne.picard@inrae.fr

Donato Andueza
email: donato.andueza@inrae.fr

Benoît Graulet
email: benoit.graulet@inrae.fr

Vitamin B 2 concentration in cow milk: Quantification by a new UHPLC method and prediction by visible and near-infrared spectral analysis

Keywords:

Until now, there are few information on vitamin B 2 concentration variability in milk. In this study, a novel analytical method to quantify total vitamin B 2 in milk was developed and applied on 676 samples. In parallel, spectral analysis (colorimetry and near infrared spectroscopy) were performed to develop prediction models of vitamin B 2 concentration in milk. The analytical method includes an acid and enzymatic extraction followed by vitamin B 2 quantification by Ultra High Performance Liquid Chromatography coupled with fluorimetry. Samples analysis showed a wide range of concentration from 0.78 to 4.58 mg/L with a mean of 2.09 ± 0.48 mg/L. Two prediction models based on colorimetric analysis allow estimation of vitamin B 2 concentration in milk. Thus, this work shows an analytical method and, for the first time, a prediction method to enable enhancement of researches on vitamin B 2 content of milk and its variation factors.

Introduction

B-vitamins are essential micronutrients in human diet. Among them, vitamin B 2 and its principal component, riboflavin, play an important role in energy metabolism. Vitamin B 2 main food contributors in human nutrition are dairy products, offal and eggs and recommended nutrient intakes for riboflavin are 1.0-1.6 mg/day for adults and 0.4-1.4 mg/ day for children (depending to age and gender) (EFSA Panel on Dietetic Products, Nutrition and Allergies, 2017). However, an important proportion of the population of western countries suffer from insufficient vitamin B 2 consumption to cover the dietary recommendations. Riboflavin deficiency would affect 5 to 75% of the population in some European countries [START_REF] Kennedy | B vitamins and the brain: Mechanisms, dose and efficacy-A review[END_REF][START_REF] Troesch | Dietary surveys indicate vitamin intakes below recommendations are common in representative Western countries[END_REF].

Bovine milk and dairy products contribute significantly to the vitamin B 2 reference intakes in many countries, however very few research efforts have been directed on studying factors affecting its concentration in milk. Indeed, since 1950's, it was considered that Bvitamins provision to ruminants through diet and rumen bacterial synthesis was sufficient to cover animal requirements, and that concentration of these vitamins in cow milk was almost constant. However, during the last decade, a few studies showed variations of vitamin B 2 concentration in cow milk according to season and management practices [START_REF] Laverroux | Riboflavin secretion in cow's milk varies according to diet composition and season[END_REF][START_REF] Poulsen | Short communication: Genetic variation of riboflavin content in bovine milk[END_REF]Poulsen et al., 2015;[START_REF] Shingfield | Effect of forage conservation method, concentrate level and propylene glycol on the fatty acid composition and vitamin content of cows' milk[END_REF]. Considering the major role of dairy products in vitamin B 2 provision in human diet whereas a significant part of the population does not cover its dietary recommendations [START_REF] Troesch | Dietary surveys indicate vitamin intakes below recommendations are common in representative Western countries[END_REF], it led to a renewed interest in milk vitamin B 2 quantification and identification of main drivers of its concentration variations. Indeed, a greater characterization and comprehension of variation factors is necessary to have a better estimation of vitamin B 2 content in dairy products.

Historically, vitamin B 2 was quantified with microbiologic or global fluorometric methods [START_REF] Hampel | Micronutrients in human milk: Analytical methods[END_REF]. In 90's, novel methods using High Performance Liquid Chromatography (HPLC) with spectrophotometric or fluorometric detection were developed and showed more reproducibility and less dependency on matrix content [START_REF] Kanno | Simple method for separate determination of 3 flavins in bovine-milk by high-performance liquid-chromatography[END_REF][START_REF] Russell | Non-degradative extraction and simultaneous quantitation of riboflavin, flavin mononucleotide, and flavin adenine-dinucleotide in foods by HPLC[END_REF]. They also conduced to highlight the vitamin B 2 composition in milk. Vitamin B 2 in bovine milk includes riboflavin as the prevalent form but also a non-negligible proportion (5-25%) of some other flavins as 5′-phosphate-riboflavin (FMN) and flavin-adenine-dinucleotide (FAD) [START_REF] Kanno | Simple method for separate determination of 3 flavins in bovine-milk by high-performance liquid-chromatography[END_REF]. In the last few years, HPLC methods with mass spectrometric detection have emerged and permitted greater sensitivity [START_REF] Hampel | Ultra-performance liquid chromatography tandem mass-spectrometry (UPLC-MS/MS) for the rapid, simultaneous analysis of thiamin, riboflavin, flavin adenine dinucleotide, nicotinamide and pyridoxal in human milk[END_REF][START_REF] Schmidt | Rapid determination of the various native forms of vitamin B-6 and B-2 in cow's milk using ultra-high performance liquid chromatography[END_REF]. Currently, the common technique for vitamin B 2 analysis is HPLC separation followed by fluorescence detection. However this technique is skewed for flavins other than riboflavin [START_REF] Hampel | Micronutrients in human milk: Analytical methods[END_REF]. In order to increase the intensity of research on vitamin B 2 content of milk, our laboratory chose to develop a method of quantification for the sum of all forms of vitamin B 2 by flavins conversion into riboflavin.

However, since the knowledge level is poor, an additional rapid method useful for research purposes as well as for in-farm or in dairy plant determination, could allow increase data acquisition in less time and for a lower price. As vitamin B 2 is a pigment that affects the yellow color of milk [START_REF] Noziere | Carotenoids for ruminants: From forages to dairy products[END_REF], a spectrophotometric method could be an interesting approach for a quick estimation of its concentration. However, β-carotene also impacts the milk yellowness [START_REF] Calderon | Variations in carotenoids, vitamins A and E, and color in cow's plasma and milk during late pregnancy and the first three months of lactation[END_REF], so it could interfere in the vitamin B 2 estimation by spectrophotometry. A more complete spectral analysis (including the infrared segment) could also be proposed to take account not only the pigment property of vitamin B 2 but rather its complete spectral signature, both in the visible and the near-infrared ranges.

The aim of this work was in a first step to set the quantitative method developed in our laboratory for vitamin B 2 analysis in milk by fluorometry after Ultra-High Performance Liquid Chromatography (UHPLC) and to validate its use to study variation factors of vitamin B 2 concentration in milk, and in a second step to evaluate spectral analysis as spectrophotometry (color) and near-infrared spectroscopy (NIRS) in their abilities to estimate vitamin B 2 content of milk. For this, raw cow milks were analyzed for vitamin B 2 concentration, color and NIRS. Additionally, some raw cow milk samples were also analyzed for βcarotene concentration to estimate influence of this component on vitamin B 2 prediction by spectral analysis.

Material and methods

Sample collection

A total of 676 cow raw milk samples were collected. They were obtained from single cows (356 samples from 67 cows, INRA Experimental Unit Herbipole, UE1414, Saint-Genès-Champanelle, France) or farm tanks (320 samples from 68 commercial farms). Samplings were conducted on milk from one milking (morning or evening, 31%), milk corresponding to day milk (morning plus evening, 22%) and milk from tanks which had grouped 2 days of milkings (47%). All seasons were represented with 59%, 16%, 15% and 10% of samplings in winter, spring, summer and autumn, respectively. Samples came from several geographical origins (all single samples from Auvergne region of France; 36% from Bretagne lowland region of France, 42% from Auvergne-Rhône-Alpes mid-mountain region of France and 22% from Po valley of Italy for tank samples). Samples also differed gradually by the breeding and feeding system, from highly intensive systems rich in concentrate diets (n = 72) to highly extensive systems exclusively based on grazing (n = 133). All these differences were supposed to let get a wide range of milk composition. All milk samples were kept at 4 °C until the evening then frozen and brought to the laboratory for storage at -20 °C until analysis.

Analytical method

Standards and reagents

Riboflavin standard was purchased from Sigma-Aldrich (St Louis, USA, purity = 98%). Solvents were of "gradient grade for HPLC" and other chemical products were of "analytical grade" and all were purchased from Sigma-Aldrich (St Louis, USA) or VWR (Radnor, USA). For enzymatic hydrolysis, papain from Papaya latex and acid phosphatase from potato were purchased from Sigma-Aldrich. Ultrapure water from Simplicity® system (Merck Millipore, Darmstadt, Germany) was used for sample preparation and chromatographic analysis. Certified reference material (milk-based infant/adult nutritional formula powder, SRM 1849a, NIST®) was purchased from LGC Standards (Molsheim, France).

Vitamin B 2 analysis

As vitamin B 2 is sensitive to natural light, especially ultraviolet radiations, all preparation steps were performed in a dark room with a yellow light. Milk samples were unfrozen at room temperature during 30 min on a balancer. For each analytical series, a control cow milk was analyzed in triplicate either with or without a known added quantity of riboflavin to calculate a mean recovery for the series. A blank (where water replaced milk sample) was also analyzed to quantify vitamin B 2 potentially present in enzymes preparation. Experimental samples were analyzed in duplicate.

The first step of extraction consisted to an acid hydrolysis for milk protein breakdown and most of vitamin B 2 release [START_REF] Jakobsen | Optimisation of the determination of thiamin, 2-(1-hydroxyethyl) thiamin, and riboflavin in food samples by use of HPLC[END_REF]. In a glass tube with screw cap, 2 mL of milk were mixed with 2 mL of 0.1 M HCl. Tubes were incubated for 30 min at 100 °C in a dry block heater. After cooling at room temperature, pH was adjusted to 4.5 with 120 µL of 2 M sodium acetate. The second step of extraction was an enzymatic hydrolysis for complete release of vitamin B 2 bound to proteins and conversion of phosphorylated forms to riboflavin simplest form [START_REF] Jakobsen | Optimisation of the determination of thiamin, 2-(1-hydroxyethyl) thiamin, and riboflavin in food samples by use of HPLC[END_REF][START_REF] Santschi | Fate of supplementary B-vitamins in the gastrointestinal tract of dairy cows[END_REF]. For this, 200 µL of 1% reduced glutathione and 400 µL of a mixture of papain (60 U) / acid phosphatase (14 U) were added to tubes. Then, they were vortexed and incubated under constant agitation 85 min at 45 °C in a water bath. The activity of enzymes was stopped by 10 min incubation in an ice water bath, and enzymes were inactivated by 10 min incubation at 100 °C in a dry block heater. After cooling at room temperature, tubes were centrifuged at 2000 g for 10 min at room temperature. Supernatants were filtered through a 0.2 µm GHP filter (Pall, Port Washington, USA) before UHPLC analysis.

Chromatographic analysis was performed on a Waters Acquity UPLC® system (Milford, USA) equipped with a fluorescence detector. Injection volume was set at 15 µL. Separation of riboflavin was performed using an Acquity UPLC® HSS T3 column (150 × 2.1 mm, 1.8 µm particle size, Waters) following a Waters application note [START_REF] Doneanu | Application note: UPLC/MS monitoring of water-soluble vitamin Bs in cell culture media in minutes[END_REF] with some modifications to improve the separation of interfering compounds of the biological matrix. Column temperature was set at 30 °C and gradient elution was operated at a flow rate of 0.3 mL/min with two mobile phases. Mobile phase A was 10 mM ammonium formate, 0.1% formic acid in ultrapure water, and mobile phase B was 10 mM ammonium formate, 0.1% formic acid in methanol. The gradient of mobile phase B was as follows: 0% for 2 min, exponential increase to 20% until 8 min, linear increase to 35% until 12 min, linear increase to 90% until 18 min, stay at 90% for 1 min, decrease to 0% until 20 min and stand-by for 2 min. In these conditions, riboflavin was eluted after 14.3 min and was quantified fluorometrically with 450/520 nm as excitation and emission wavelengths, respectively. Calibration curves corresponded to peak areas of standard solutions injected at five different concentrations. Vitamin B 2 concentration in a sample milk resulted from the analytical concentration corrected for extraction dilution (calculated with final extract weight and initial milk weight), blank concentration and series recovery.

Method validation

The analytical method was validated for linearity, limit of detection (LOD), limit of quantification (LOQ), recovery, precision and accuracy in accordance with ICH guidelines and Eurachem guide (Harmonised Tripartite Guideline, 2005;[START_REF] Magnusson | Eurachem Guide: The Fitness for Purpose of Analytical Methods -A Laboratory Guide to Method Validation and Related orimetry to estimate the carotenoids content in ultrafrozen orange juices[END_REF].

Range chosen to study performances of the analytical method was from 0.6 to 3.5 mg/L in milk that corresponded respectively to half and twice concentrations traced in food composition databases.

Linearity, LOD and LOQ were evaluated on calibration curves. Standards solutions with five different concentrations of riboflavin (0.3, 0.6, 0.9, 1.2 and 1.5 mg/L) were injected at 16 different days. These concentrations corresponded to milk extract concentration (due to extraction dilution). Calibration curves were obtained by plotting peak areas against concentration, and linear regression model was performed on these. Linearity was evaluated by p-value and correlation coefficient.

LOD and LOQ were determined as 3σ/S and 10σ/S, respectively, where σ was standard error of intercept and S was slope of linear regression.

Recovery was calculated by spiking a control cow milk with a known amount of riboflavin (in triplicate at 16 different days, known amount = 1.7 mg/L of sample). Recovery was also studied on the five levels of standard solutions to compare to milk samples and evaluate matrix effect.

Repeatability and reproducibility were estimated by triplicate extraction / injection of a control cow milk sample, at 16 different days.

Accuracy was validated by 23 extractions / injections of a certified milk powder NIST® 1849a dispatched on 10 days. This certified reference material (CRM) was dissolved in ultra-pure water prior to injection (approximately exactly 0.2 g in 2 mL) to reflect vitamin B 2 concentration of test samples.

Spectral analysis

Before scanning, milk samples were unfrozen at laboratory temperature for 30 min on a balancer.

Color analysis was performed with a spectrophotometer (CM-2600d, Minolta, Tokyo, Japan). 20 mL of milk sample were placed in a glass cell (CR A502, Minolta) and analyzed thrice for percentage of light reflectance (10 nm step between 400 and 700 nm). Due to the large volume used, only 352 milk samples were analyzed for color. Color data were used as follows: 1) data were expressed using the CIELAB color space: L* as lightness (from 0 for black to 100 for white), a* as color under green-red axis and b* as color under blue-yellow axis (both from -120 to + 120), C* as chromaticity and h* as hue (both calculated from a* and b* to have another visualization of color); 2) reflectance (R) values were converted into absorbance (A) using the formula A = log (1/R) and color spectrum was built for each milk sample.

A Foss NIRSystems model 6500 scanning visible-near-infrared spectrometer equipped with an auto cup module (Foss NIRSystems, Silver Spring, MD, USA) produced the near-infrared spectra. 500 µL of milk were placed on a GF/A glass microfibre filter (Whatman, Maidstone, UK), oven-dried at 30 °C during 24 h and placed in a 50 mm diameter ring cup according to the methodology proposed by [START_REF] Thyholt | Near infrared spectroscopy of dry extracts from high moisture food products on solid support-A review[END_REF]. Then they were scanned in reflectance mode at 2 nm intervals from 400 to 2498 nm. Spectra were recorded using ISIscan (version 2.21 Infrasoft International, South Atherton St. State College, PA, USA). Each spectrum was time averaged from 32 scans. Reflectance values were converted into A using the formula A = log (1/ R) to obtain NIRS absorbance spectra.

Development of predictive models of vitamin B 2 concentration using spectral data

A total of 88 milk samples analyzed for vitamin B 2 concentration, color and NIRS spectra together, were randomly chosen from the initial population samples. These samples were used for comparison purposes. This number of samples corresponded to 30% of samples containing these three determinations. Predictive models were developed using all other data. They were validated using the cross-validation method (4fold).

Models from CIELAB parameters were developed using multiple linear regression models of R software (version 3.5.1 assisted by RStudio 1.1.463, "lm" function). Samples with vitamin B 2 concentration not included in ± 2 standard error area were considered as outliers and were not used for models development. Cross-validation of these models was performed with "train" function of "caret" package.

Models from color or NIRS spectra were developed using the modified partial least squares regression (MPLS) of WinISI 4 (version 4.12.0.15440, Foss Analytical A/S, Hilleroed, Denmark). Spectral similarity was assessed with the standardized Mahalanobis distance (H). Predicted samples showing an H-distance to the center of model population higher than 3 were considered as outliers and were removed for model development [START_REF] Shenk | The application of near-infrared reflectance spectroscopy (NIRS) to forage analysis[END_REF]. NIRS data were subjected to standard normal variate and detrending [START_REF] Barnes | Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra[END_REF]) and first-derivative treatments (1,4,4), where the first digit is the number of the derivative, the second is the gap over which the derivative is calculated, and the third is the number of data points in the first smoothing. As Foss NIRSystems spectrometer allowed analyzing spectrum from visible to near-infrared area (400-2498 nm each 2 nm), three models were performed: using data of the visible part of spectrum (400-1098 nm), the near-infrared part of spectrum (1100-2498 nm) and the whole spectrum (400-2498 nm). Models were validated by cross-validation using WinISI4 program (version 4.12.0.15440).

All calibration models were evaluated by the coefficient of determination of calibration (R 2 C) and of cross-validation (R 2 CV) and by the standard error of calibration (SEC) and of cross-validation (SECV).

Obtained models were then applied to the external dataset. Prediction results were evaluated by the coefficient of determination of prediction (R 2 P), standard error of prediction (SEP), bias and SEP corrected by the bias (SEPc).

Influence of β-carotene on vitamin B 2 prediction

A total of 115 samples of the population analyzed for vitamin B 2 were also quantified for β-carotene concentration as described by Chauveau-Duriot, Doreau, [START_REF] Chauveau-Duriot | Simultaneous quantification of carotenoids, retinol, and tocopherols in forages, bovine plasma, and milk: Validation of a novel UPLC method[END_REF]. Extraction consisted to an alcoholic deproteinization followed by a purification using organic solvents (ethanol, diethyl ether and ethyl acetate) and then a potassium hydroxide saponification. Chromatographic analysis was performed on a Waters Acquity UPLC® System (Milford, USA) equipped with a PhotoDiodeArray detector and β-carotenes were quantified at 450 nm by comparison to peak areas of standard solution. The total concentration of β-carotene was the sum of the concentrations of all-trans-β-carotene, 9-cis-β-carotene and 13-cis-β-carotene isoforms.

In a first step, the "cor.test" function of R software calculated the correlation between β-carotene and vitamin B 2 concentrations in milk. In a second step, models developed for predicting vitamin B 2 in section 2.4 and showing better performances were applied to the dataset composed by the 115 samples analyzed for vitamin B 2 and β-carotene contents. Then, residuals (difference between predicted and observed values) were calculated for each individual sample. Finally the "lm" function of R software (version 3.5.1 assisted by RStudio 1.1.463) permitted to evaluate effect of β-carotene concentration on residuals obtained for each method.

Results

Vitamin B 2 concentration in cow milk

Vitamin B 2 analytical method performances

Chromatograms (Fig. 1) obtained for milk extracts showed a single peak with a retention time and a UV-visible spectrum corresponding to riboflavin. Table 1 shows performances of the method developed for vitamin B 2 quantification as chromatographic analysis or complete procedure (extraction and chromatographic analysis). Calibration curves were performed with standard solutions and showed a linearity range between 0.304 and 1.520 mg/L (p < 0.001, r 2 = 0.98), a LOD of 0.049 mg/L and a LOQ of 0.167 mg/L.

The mean recovery was 96% with variations between 87 and 107%. Variations were both intra-assay and inter-assays. Recoveries of standard solutions and milk samples were similar within a same assay. Therefore, we decided to include a recovery rate on a control cow milk in triplicate in all extraction series.

To validate analytical method on milk samples, it was necessary to calculate linearity range, LOD and LOQ in samples. The extraction procedure lead to a sample dilution (about 2.3). It also bring a small amount of riboflavin (concentrations in blank samples, with enzymes but without milk sample substituted by water, ranged from 0.012 to 0.133 mg/L). Thus, values obtained with standard solutions analysis were corrected for dilution, blank result and recovery rate. Therefore, analytical method allow quantification of vitamin B 2 in milk from 0.656 to 3.548 mg/L with LOD of 0.048 mg/L and LOQ of 0.330 mg/L.

Repeatability and reproducibility, calculated on a control cow milk are 2.07% (0.053 mg/L) and 5.90% (0.152 mg/L) respectively for an average concentration of 2.581 mg/L.

Analysis of the CRM milk powder NIST® 1849a allowed evaluating the accuracy of the method at 99.2%. Indeed, the mean vitamin B 2 concentration obtained was 20.20 mg/kg ( ± 1.20 mg/kg, n = 23 determinations) for a certified concentration of 20.37 ± 0.52 mg/kg.

Vitamin B 2 concentration in cow milk

This new method was used to quantify vitamin B 2 in 676 milk samples. According to the method, mean vitamin B 2 concentration in raw cow milk was 2.09 ± 0.47 mg/L with a range from 0.78 to 4.58 mg/L. Five samples had a concentration greater than the application area of the method. According to sample type, average vitamin B 2 concentration was 1.98 ± 0.35 mg/L [from 1.33 to 3.07, n = 320] in tank milk, and 2.20 ± 0.54 mg/L [from 0.78 to 4.58, n = 356] in individual milk. According to season, mean vitamin B 2 concentration was 2.06 mg/L in autumn and winter, 2.13 mg/L in spring and 2.18 mg/L in summer, with equivalent variations inside seasons. According to geographical origin of tank milk, samples from French lowland region contained 2.05 ± 0.33 mg/L, samples from French mid-mountain region contained 2.06 ± 0.38 mg/L and samples from Italian lowland region contained 1.70 ± 0.14 mg/L of vitamin B 2 . Milk samples from highly intensive systems rich in concentrate diets contained 1.70 ± 0.14 mg/L and samples from highly extensive systems based on grazing contained 2.51 ± 0.59 mg/L of vitamin B 2 .

Predictive models of vitamin B 2 content

Means, standard deviations and minimal and maximal values of calibration and external datasets are presented in Table 2. Calibration and external datasets had equivalent mean and standard deviation values as the whole database. Calibration and validation statistics of prediction models for vitamin B 2 content in milk are given in Table 3. On the basis of the CIELAB parameters, multiple linear regression model using all the three L*, a* and b* indexes (called Lab* thereafter) provided the best prediction potency (per comparison to models using one or two of these indexes only, data not shown) and was characterized by R 2 CV of 0.73 and SECV of 0.23 mg/L (10.4% of the mean). MPLS model developed with color spectral data was characterized by R 2 CV of 0.88 and SECV of 0.16 mg/L (7.3% of the mean). MPLS models developed with NIRS spectral data were characterized by R 2 CV of 0.51 and SECV of 0.29 mg/L (14.3% of the mean) for the visible segment, 0.23 and 0.34 mg/L (17.0% of the mean) for the near-infrared segment, and 0.52 and 0.29 mg/L (14.3% of the mean) for the whole spectrum.

Application of these models on an external dataset showed R 2 P of 0.82 for Lab* model, 0.87 for model with Minolta visible spectrum, 0.59 for model with Foss visible spectrum, 0.44 for model with Foss near-infrared spectrum and 0.51 for model with Foss total spectrum. SEP were 0.17 (8.0% of the mean) for Lab* model, 0.16 (7.2% of the mean) for model with Minolta visible spectrum, 0.26 (12.7% of the mean) for model with Foss visible spectrum, 0.31 (15.4% of the mean) for model with Foss near-infrared spectrum and 0.29 mg/L (14.0% of the mean) for model with Foss total spectrum. Fig. 2 illustrates predicted vs. observed values of external dataset for the best models. Model developed with Minolta visible spectrum shows the best adequacy on the largest range of concentrations. LOD: limit of detection. LOQ: limit of quantification.

Influence of β-carotene on prediction of vitamin B 2 concentration in milk

One hundred and fifteen milks were analyzed both for vitamin B 2 and β-carotene concentrations. In this sub-population, vitamin B 2 average concentration was 1.99 ± 0.35 mg/L [from 1.33 to 2.88 mg/ L] and β-carotene average concentration was 0.092 ± 0.050 mg/L [from 0.024 to 0.294 mg/L]. Fig. 3a illustrates relationships between vitamin B 2 and β-carotene concentrations. Correlation coefficient between observed vitamin B 2 and β-carotene concentrations is 0.327. Fig. 3b andc show that β-carotene concentration have no significant effect on residues of predicted vitamin B 2 concentration (p = 0.78 for Lab* model, and p = 0.64 for model based on Minolta visible spectrum).

Discussion

Reliability of the analytical method for milk vitamin B 2 analysis

The analytical method developed for vitamin B 2 quantification in milk shows an analytical range from 0.65 to 3.55 mg/L that includes mean riboflavin concentration in whole cow milk traced in food composition databases (1.70 mg/L for Ciqual-Anses (France) in pasteurized whole cow milk, 1.80 mg/L for EFSA (Europe), 1.69 mg/L for USDA (USA) and 1.88 mg/L for Health Canada in whole cow milk). LOQ of 0.167 mg/L as a standard and of 0.321 mg/L as a milk sample are similar to previous chromatographic methods proposed in the literature and allow analysis of samples with low vitamin B 2 content [START_REF] Guneser | Effect of ultraviolet light on water-and fat-soluble vitamins in cow and goat milk[END_REF][START_REF] Sunaric | Evaluation of riboflavin content in dairy products and non-dairy substitutes[END_REF]. A more recent analytical method achieved to a lower limit of quantification (0.019 mg/L; [START_REF] Schmidt | Rapid determination of the various native forms of vitamin B-6 and B-2 in cow's milk using ultra-high performance liquid chromatography[END_REF], however we didn't try to improve this parameter to evaluate lower concentration than 0.3 mg/L as no publication showed it in milk. Instead, we prefer to focus on the accuracy of the method. This objective was reached since the mean accuracy value obtained is 99.2% of a CRM (NIST® 1849a) certified value. Reproducibility for extraction and chromatographic analysis is 5.90% and is in accordance with method of [START_REF] Schmidt | Rapid determination of the various native forms of vitamin B-6 and B-2 in cow's milk using ultra-high performance liquid chromatography[END_REF]. The method developed in our laboratory to quantify vitamin B 2 in milk also allows quantification of the three vitamin B 6 forms (pyridoxamine, pyridoxal and pyridoxine) with good performances (data not shown).

The mean vitamin B 2 concentration of the 676 analyzed samples is 2.09 mg/L with a wide range from 0.78 to 4.58 mg/L. To compare these results with food composition databases and literature, it's important to separate samples of tank milk to individual milk. Actually, tank milk, and even more milk from dairy industry, were averaged. Concentrations of constituents should be thus less variable in tank milk samples than in individual milk samples. Range of vitamin B 2 concentration in analyzed tank milk samples was from 1.33 to 3.07 mg/L. Food composition databases concentrations (1.69-1.88 mg/L) are in this range, but in the lower moiety. Literature studying tank milk reported mean concentration close to 1.65 mg/L with a range from 1.30 to 2.12 mg/L (Amador-Espejo, Gallardo-Chacon, Nykanen, [START_REF] Amador-Espejo | Effect of ultra high-pressure homogenization on hydro-and liposoluble milk vitamins[END_REF][START_REF] Kim | The effect of high pressure-low temperature treatment on physicochemical properties in milk[END_REF]Poulsen et al., 2015b;[START_REF] Sunaric | Evaluation of riboflavin content in dairy products and non-dairy substitutes[END_REF], that corresponds to our observations. Range of vitamin B 2 concentration in individual milk samples of our study was from 0.78 to 4.58 mg/L. Poulsen et al. (2015a) have studied individual variations in riboflavin content and found concentrations from 0.73 to 2.84 mg/L. Therefore, range of vitamin B 2 concentrations analyzed with our method is in accordance with variability known for dairy milk as well as individual milk. The whole database, calibration datasets and the external dataset are characterized by number of samples (n), mean, standard deviation (Sd), minimal (Min) and maximal (Max) values. SEC: standard error of calibration, mg/L (percent of the mean). R 2 C: coefficient of determination of calibration. SECV: standard error of cross-validation, mg/L (percent of the mean). R 2 CV: coefficient of determination of cross-validation. SEP: standard error of prediction, mg/L (percent of the mean). SEPc: standard error of prediction corrected for the bias, mg/L. R 2 P: coefficient of determination of prediction.

Five prediction models were developed and cross-validated. There performances were compared by application of these models to an external dataset.

On average, food composition databases and literature include slightly lesser concentrations (1.77 and 1.65 mg/L, respectively) than our analyzed samples (2.09 mg/L). However, it should be highlighted that vitamin B 2 in milk includes several forms, free or bound to proteins, phosphorylated or not [START_REF] Kanno | Simple method for separate determination of 3 flavins in bovine-milk by high-performance liquid-chromatography[END_REF][START_REF] Koop | Determination of free and bound riboflavin in cow's milk using a novel flavin-binding protein[END_REF]. Nevertheless, food composition databases and much of the literature only analyzed riboflavin and not others flavins such as FMN and FAD. However, proportions of FMN and FAD were estimated to 5-25% of total flavins in milk [START_REF] Kanno | Simple method for separate determination of 3 flavins in bovine-milk by high-performance liquid-chromatography[END_REF][START_REF] Russell | Non-degradative extraction and simultaneous quantitation of riboflavin, flavin mononucleotide, and flavin adenine-dinucleotide in foods by HPLC[END_REF]. Therefore we developed an extraction method based on an acid hydrolysis followed by a protease / phosphatase hydrolysis, first to improve the release of vitamin B 2 linked to milk proteins and second to convert phosphorylated forms into riboflavin. Consequently, this method allowed to analyze the sum of all vitamin B 2 forms. This point was confirmed by chromatograms of milk extracts that showed only one peak corresponding to riboflavin. Thus, mean riboflavin concentration of 1.70 mg/L reported by databases and literature and mean vitamin B 2 concentration of 2.09 mg/L obtained with our analytical method were in accordance, as our method allowed to include the 20% of complex flavins forms not analyzed with previous methods. So our method permits to study the sum of vitamin B 2 forms present in milk.

Vitamin B 2 concentration in cow milk

We observe that vitamin B 2 concentration is lower and less variable in tank milks than in individual milks (1.98 ± 0.35 vs. 2.20 ± 0.54 mg/L, respectively, p < 0.001). No articles in the literature compared these two types of milk samples. However, Poulsen et al. (2015a) analyzed 892 individual milk samples grouped in 42 milk samples of herds and found riboflavin concentration ranging from 1.20 to 2.20 mg/L in herd milks while it varied from 0.73 to 2.84 mg/L in individual milk samples. Therefore, variability of vitamin B 2 concentration is more important in individual milk samples and analysis of this type of milks should allow advances in studies of variation factors.

The database of analyzed milk samples used for the present work was not built to compare vitamin B 2 concentrations between milk samples but rather to reach a large variability in milk production conditions. However, observation of the whole results would suggest that vitamin B 2 concentration varies according to season, geographical origin, breeding and feeding system. It would tend to increase during spring and summer and with more extensive systems. These observations consolidate first studies on variations of vitamin B 2 content in milk that mentioned a seasonal variation with some management practices and some variations with breed and lactation stage (Poulsen et al., 2015a(Poulsen et al., , 2015b)).

Therefore, the level of variability in our sample population is highly interesting to evaluate the application field of the method as well as to develop a prediction method based on spectral analysis of milk samples.

Prediction of vitamin B 2 concentration in cow milk

Color data allow to develop models for prediction of vitamin B 2 content in milk (R 2 CV = 0.73 and 0.88, Table 3). However the MPLS model based on spectral data is a bit more adjusted than the multiple regression Lab* model. Actually, SEP obtained on an external dataset is lower for spectral model than for Lab* model (0.16 vs. 0.17 mg/L, respectively) and R 2 P is higher (0.87 vs. 082, respectively) (Table 3). success in the ability to get predicting models of milk vitamin B 2 concentration is not really a surprise considering both its concentration level as well as the spectral activity of its molecule (orange-yellow pigment).

Models developed with spectra obtained with NIRS are not enough accurate, either with visible part and/or near-infrared part of spectra (R 2 CV < 0.55, Table 3). Difference of results between Minolta visible spectrum and Foss visible spectrum raises questioning. The analysis with the Minolta spectrophotometer was performed using 20 mL of milk corresponding to around 40 µg of vitamin B 2 (considering a mean concentration of 2.0 mg/L) whereas only 500 µL of milk were used for analysis with the Foss spectrometer, corresponding to 1 µg of vitamin B 2 spotted on to the filter (40-fold less). Moreover, it should be noticed that milk preparation is different before the acquisition of spectra by both instruments. To interfering noise signal due to milk water, milk samples were heat dried prior analyzing with Foss spectrometer, which was not the case with Minolta spectrophotometer. Some tests in our laboratory, with vitamin B 2 additions in milk (data not shown), showed differences between milk Foss spectra obtained with liquid sample or with warm dried sample. But it remains to be explored in the specific case of vitamin B 2 quantification. To date, estimation of vitamin B 2 content with NIRS analysis cannot be discarded but remains to be performed with another type of preparation.

Influence of β-carotene concentration on vitamin B 2 content prediction

CIELAB parameters, especially b* index, are known to predict concentrations of yellow pigments, like carotenoids, in different feed [START_REF] Kljak | Reflectance colorimetry as a simple method for estimating carotenoid content in maize grain[END_REF]Melendez-Martinez, Vicario, & Heredia, 2003). In milk, 75-85% of carotenoids are β-carotene [START_REF] Graulet | Contrasted effects of dietary extruded linseed supplementation on carotenoid and liposoluble vitamin status in lactating Holstein or Montbeliarde cows fed hay or corn silage[END_REF] and some authors showed correlation between b* index and β-carotene in milk [START_REF] Agabriel | Tanker milk variability according to farm feeding practices: Vitamins A and E, carotenoids, color, and terpenoids[END_REF][START_REF] Calderon | Variations in carotenoids, vitamins A and E, and color in cow's plasma and milk during late pregnancy and the first three months of lactation[END_REF][START_REF] Noziere | Carotenoids for ruminants: From forages to dairy products[END_REF]. Therefore, it is important to ensure that no interaction and/or interference due to variation of βcarotene content occurs on milk vitamin B 2 prediction by color/spectral analysis.

For this, 115 samples among our milk total population were analyzed both for vitamin B 2 and β-carotene content. Vitamin B 2 concentrations were in agreement with the total population concentration, and β-carotene concentrations were in the variation range of the literature, still in the lowest part [START_REF] Agabriel | Tanker milk variability according to farm feeding practices: Vitamins A and E, carotenoids, color, and terpenoids[END_REF][START_REF] Noziere | Carotenoids for ruminants: From forages to dairy products[END_REF]. First, evolution of both components contents was studied with a correlation test. Coefficient of correlation between the two components was 0.327 (p < 0.001; Fig. 3a). The significance indicated that the two parameters generally evolved in the same way. Data distribution illustrates a large variability, but generally, a milk rich in vitamin B 2 is also rich in β-carotene. In a second step, we studied if prediction errors of vitamin B 2 content were explained by β-carotene concentration. Thus, we observed that β-carotene concentration has no link with residuals of models (Fig. 3b andc). These two results showed that there seems to be no influence of β-carotene concentration on vitamin B 2 prediction models. However, these tests must be made on milk samples containing more β-carotene to validate these results on the complete variation range of β-carotene concentration.

Several points could explain these results. In milk, mean concentrations are 10-fold higher for vitamin B 2 than for β-carotene (2.0 mg/L i.e. 5 µM and 0.2 mg/L i.e. 0.4 µM, respectively). On the other hand, their molecular extinction coefficients are 13 cm -1 .mM -1 and 140 cm -1 .mM -1 at 450 nm, respectively. So milk contains 10 more times of vitamin B 2 than β-carotene, but coloring strength is 10 times more important for β-carotene than for vitamin B 2 (at least for the maximal absorption at 450 nm). Therefore, the two components could perform simultaneously on intrinsic spectral parameters. However, environmental elements could interfere in their respective spectral response since vitamin B 2 is mainly present as free form or non-covalently bound [START_REF] Kanno | Simple method for separate determination of 3 flavins in bovine-milk by high-performance liquid-chromatography[END_REF][START_REF] Ndaw | Extraction procedures for the liquid chromatographic determination of thiamin, riboflavin and vitamin B-6 in foodstuffs[END_REF] in the aqueous part of milk, while β-carotene is mainly retained in the core of fat globules because of its strong hydrophobicity [START_REF] Bernard | Milk fat globule in ruminant: Major and minor compounds, nutritional regulation and differences among species[END_REF]. So impact on color could not be the same for these two components.

Conclusion

The analytical method developed for quantification of vitamin B 2 in milk was evaluated and its accuracy was validated according to reference procedure. Analysis of 676 milks allowed to validate that range, limit of quantification and reproducibility of this method are consistent with variations potentially obtained with milk from various origins (breed, diet, season, geographical area). Spectrophotometer analysis allowed to estimate vitamin B 2 concentration in milk with models based on CIELAB parameters or spectral data. Using our dataset, we observed that there is no interaction of β-carotene on prediction.

These results are promising to study the effects of husbandry practices (like ruminant diet), characteristics of animals (species, breeds, physiological stages) as well as technological treatments on milk vitamin B 2 concentration. Moreover, the spectral approach provides a quick-and-easy solution to predict the vitamin B 2 concentration (especially as an indicator of the nutritional quality of milk) in very large experimental designs, in commercial farms or dairy plants.

Fig. 1 .

 1 Fig. 1. Chromatograms of a standard solution (a) and a control cow milk extract (b).

Fig. 2 Fig. 2 .

 22 Fig. 2. Performances of prediction models of vitamin B 2 concentration in milk evaluated using an external dataset. Predicted vs. observed values of vitamin B 2 concentration when Lab* linear regression model (a), MPLS model with Minolta visible spectra (b), and MPLS model with Foss total spectra (c) were applied on an external dataset.

Fig. 3 .

 3 Fig. 3. β-carotene concentration vs. vitamin B 2 concentration (a), and β-carotene concentration vs. vitamin B 2 residues (predicted -observed values) from Lab* model (b) and MPLS model based on Minolta visible spectra (c).

Table 1

 1 Performances of the analytical method of vitamin B 2 quantification in milk developed in our laboratory.

		Vitamin B 2 as standard = chromatographic analysis	Vitamin B 2 in milk = complete procedure
	Application area (mg/L)	0.304 -1.520	0.656 -3.548
	LOD (mg/L)	0.049	0.048
	LOQ (mg/L)	0.167	0.330
	Repeatability		2.07% (i.e. 0.053 mg/L)
	Reproducibility		5.90% (i.e. 0.152 mg/L)

Table 2

 2 Characteristics of vitamin B 2 concentrations in milk sample datasets used for prediction models.

	Dataset	Analysis	Parameter used for prediction model	n	Mean	Sd	Min	Max
					mg/L
	Whole database	Vitamin B 2 content		676	2.09	0.47	0.78	4.58
	Calibration datasets	Vitamin B 2 content and color	CIELAB parameters	241	2.19	0.43	1.33	3.24
			Visible spectrum: 400-700 nm (10 nm)	208	2.24	0.47	1.33	3.59
		Vitamin B 2 content and NIRS	Visible spectrum: 400-1098 nm (2 nm)	504	2.06	0.42	1.22	3.49
			Near-infrared spectrum: 1100-2498 nm (2 nm)	510	2.02	0.39	1.22	3.17
			Total spectrum: 400-2498 nm (2 nm)	519	2.05	0.42	1.17	3.49
	External dataset			88	2.12	0.41	1.44	3.16

Table 3

 3 Calibration and validation statistics and comparison of prediction models of vitamin B 2 content of milk.

	Analysis / Material	Data used for models	Calibration		Cross-validation		Comparison with external dataset
			SEC	R 2 C	SECV	R 2 CV	SEP	SEPc	R 2 P	Bias
			mg/L(%)		mg/L(%)		mg/L(%)	mg/L		mg/L
	Color / Minolta spectrophotometer	Lab* parameters	0.22 (10.2%)	0.74	0.23 (10.4%)	0.73	0.17 (8.0%)	0.17	0.82	-0.04
		Visible spectrum	0.15 (6.7%)	0.90	0.16 (7.3%)	0.88	0.16 (7.2%)	0.16	0.87	-0.03
	NIRS / Foss NIRSystems spectrometer	Visible spectrum	0.28 (13.4%)	0.57	0.29 (14.3%)	0.51	0.26 (12.7%)	0.26	0.59	0.00
		Near-infrared spectrum	0.32 (15.7%)	0.33	0.34 (17.0%)	0.23	0.31 (15.4%)	0.31	0.44	0.00
		Total spectrum	0.26 (12.9%)	0.60	0.29 (14.3%)	0.52	0.29 (14.0%)	0.29	0.51	-0.03

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.foodchem.2020.128310.

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