Amira Halabi

Amélie Deglaire

Pascaline Hamon

Said Bouhallab

Didier Dupont

Thomas Croguennec

Kinetics of heat-induced denaturation of proteins in model infant milk formulas as a function of whey protein composition

Keywords: Infant formula, whey proteins, heat denaturation Highlights

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

Introduction

Infant milk formulas (IMFs) constitute an adequate substitute of human milk when breastfeeding is not a possibility or a wish, although human milk is considered as the ideal infant food for the first five months of life (World Health Organization, 2001). The majority of standards IMFs is produced using defatted bovine milk and demineralized bovine whey proteins. However, human and bovine milks vary in terms of nutrient composition, particularly regarding the protein fraction. The protein content is approximatively 9-12 g.L -1 for mature human milk with an average caseins:whey proteins weight ratio of 40:60, versus about 34 g.L -1 for bovine milk with a caseins:whey proteins weight ratio of 80:20 [START_REF] Chatterton | Anti-inflammatory mechanisms of bioactive milk proteins in the intestine of newborns[END_REF]. In addition, the whey protein composition varies between human and bovine milks. In human milk, α-lactalbumin (α-LA) is the predominant whey protein (2.5 g.L -1 ) followed by lactoferrin (LF, 1.5 g.L -1 ), whereas β-lactoglobulin (β-LG) is absent. In contrast, β-LG is the predominant whey protein of bovine milk (3.5 g.L -1 ), followed by α-LA (1.3 g.L -1 ) while LF is at a lower content (5.0 x 10 -2 g.L -1 ) [START_REF] Chatterton | Anti-inflammatory mechanisms of bioactive milk proteins in the intestine of newborns[END_REF]. To mimic the human milk composition, the caseins:whey proteins ratio of bovine milk-based IMFs has to be equilibrated to match the human milk ratio, while the protein nature remains usually different. However, previous studies [START_REF] King | A double-blind, placebo-controlled, pilot study of bovine lactoferrin supplementation in bottle-fed infants[END_REF][START_REF] Sandström | Effects of α-lactalbumin-enriched formula containing different concentrations of glycomacropeptide on infant nutrition[END_REF] have demonstrated that infant feeding with IMFs supplemented with specific whey proteins (LF, α-LA) had the same physiological benefits (e.g. infection resistance, physical development, etc.) than breastfed infants, in contrary to infants fed IMFs without specific whey protein supplementation. Moreover, thanks to the high proportion of essential amino acids in α-LA and LF, the α-LA and LF supplemented IMFs allow reducing the IMF total protein content while respecting the regulatory amino acid profile. This may have some health benefits as lower protein content in 1 st age IMFs has been shown to be associated with a lower risk of obesity in 6-year-old children [START_REF] Totzauer | Effect of Lower Versus Higher Protein Content in Infant Formula Through the First Year on Body Composition from 1 to 6 Years: Follow-Up of a Randomized Clinical Trial: Protein in Infancy and Body Composition Until 6 Years[END_REF].

IMFs are submitted to several heat treatments during the manufacturing process to ensure the microbial safety and extend the shelf life. Depending on the heating conditions, changes of milk protein structure occur, varying potentially the properties and nutritional value of IMFs. It is established that heat treatments above 60°C have undesirable consequences on the structure of whey proteins, mainly α-LA and β-LG, leading to their polymerization and aggregation [START_REF] Nguyen | The effect of thiol reagents on the denaturation of the whey protein in milk and whey protein concentrate solutions[END_REF]. However, the behavior of whey proteins under heating is governed by medium conditions, like the content and composition of proteins [START_REF] Oldfield | Kinetics of heat-induced whey protein denaturation and aggregation in skim milks with adjusted whey protein concentration[END_REF], minerals [START_REF] Petit | Influence of calcium on β-lactoglobulin denaturation kinetics: Implications in unfolding and aggregation mechanisms[END_REF] and sugars [START_REF] Anema | Effect of protein, nonprotein-soluble components, and lactose concentrations on the irreversible thermal denaturation of β-lactoglobulin and αlactalbumin in skim milk[END_REF] of milk protein-based products. The heat denaturation of LF in bovine milk received very little attention compared to α-LA and β-LG, probably because of the very low LF quantity in bovine milk. Nevertheless, previous studies showed the heat-labile property of LF, depending on the presence of an iron ion in each of the two homologous globular N-and C-lobes of the protein. At low ionic strength and neutral pH, LF in the apo-form (iron free), native form (10-20% of iron saturation) and holo-form (iron saturated) began to aggregate at 60°C, 65°C and 70°C, respectively [START_REF] Brisson | Effect of Iron Saturation on the Recovery of Lactoferrin in Rennet Whey Coming from Heat-Treated Skim Milk[END_REF]. Overall, there is very limited information in the literature on the denaturation of whey proteins in IMFs, and even less in those that are mimicking the protein composition of human milk.

To fill the gap, the kinetics of heat-induced denaturation of individual whey proteins (α-LA, β-LG and LF) were investigated in IMFs at temperatures from 67.5°C to 80°C. Three model IMFs were produced at 1.3% total protein content (i.e. the protein content at which is applied the heat treatment during the manufacture of liquid IMFs) with a caseins:whey proteins ratio of 40:60. The IMFs differed by the whey protein composition: the "control IMF" had the same whey protein composition as bovine whey whereas the IMFs denoted "LF + IMF" and "LF + α-LA + IMF" respected the quantity of LF or of both LF and α-LA found in human milk, respectively. We assumed that the level of whey protein heat-denaturation was dependent on the whey protein composition of IMFs, since β-LG promotes whey protein denaturation [START_REF] Elfagm | Interaction of bovine α-lactalbumin and β-lactoglobulin during heating[END_REF] and LF is one of the most heat-sensitive protein in milk [START_REF] Law | A high-throughput method for the quantification of iron saturation in lactoferrin preparations[END_REF].

Material and methods

Chemicals

The low-heat skimmed milk powder (SMP) was obtained by drying raw milk supplied by Fromagerie Gillot (Saint-Hilaire-de-Briouze, France) at the semi-industrial drying unit Bionov (Rennes, France).

Briefly, skimmed milk obtained by centrifugation of raw milk was microfiltered on 1.4 µm membrane at 50°C, concentrated by evaporation under vacuum at 64°C and spray dried. The characteristics of SMP are described in Table 1. The whey protein nitrogen index (WPNi) was 9 mg of nitrogen/g of SMP, which is a value for ultra-low heat SMP. Whey protein isolate (WPI; Prolacta®95), with a total protein content of 84% (w/w; N x 6.38) as determined by the Kjeldahl method, was purchased from Lactalis Ingredients (Bourgbarré, France). Bovine lactoferrin (LF, Prodiet Lactoferrin®) and αlactalbumin (α-LA) were kindly supplied by Ingredia Dairy Experts (Arras, France) and Agropur Inc (Appleton, USA), respectively. The protein content of the powder was 90% (w/w; N x 6.38) for LF and 84% (w/w; N x 6.38) for α-LA, as determined by the Kjeldahl method. The iron saturation level of LF, determined by absorbance at 465 nm using an UV-Visible spectrophotometry, was found to be of 16%. The purified proteins α-LA, β-LG and LF, used as chromatographic standards, were purchased from Davisco (MN, USA) for α-LA and β-LG, and from Ingredia Dairy Experts (Arras, France) for LF. All protein powders were stored at -20°C until use.

Lactose was supplied by Armor Proteines (Saint-Brice-en-Coglès, France). CaCl2•2H2O was from AnalaR (Leuven, Belgium), FeSO4•7H2O from Sigma-Aldrich (St-Louis, USA), KCl from Panreac (Barcelona, Spain), Na3PO4•12H2O from Merck (Darmstadt, Germany), and Na3C6H5O7•2H2O from Carlo Erba Reagents (Val-de-Reuil, France). Trifluoroacetic acid was from Fisher Scientific (Loughborough, UK) and acetonitrile (Chromasolv™ for HPLC) from Fisher Scientific (Muskegon, USA).

All other materials were standard analytical grade. Water was Milli-Q water.

Preparation of model IMFs

Three IMFs were formulated at 5.5% (w/w) total protein and then diluted at 1.3% (w/w) with Milli-Q water. A 40:60 caseins:whey proteins ratio was targeted for the formulation of IMFs, with either no modification of the bovine whey protein proportion ("Control IMF", mixture of SMP and WPI) or the replacement of a fraction of the whey proteins by LF ("LF + IMF", mixture of SMP, WPI and LF) or a mixture of LF and α-LA ("LF + α-LA + IMF", mixture of SMP, α-LA and LF) to reach the α-LA and LF concentrations similar to those found in human milk. Briefly, IMFs were prepared at room temperature by dispersing firstly the protein powders (WPI, LF, α-LA) and secondly the SMP, in a concentrated solution of lactose at 24%. Then, the protein solutions were supplemented by minerals CaCl2•2H2O, FeSO4•7H2O, KCl, Na3PO4•12H2O and Na3C6H5O7•2H2O to ensure a similar mineral composition for the three IMFs. The pH of the IMFs was adjusted at pH 6.8 with 1 M KOH, and then the IMFs were stored at 4°C for at least 18h. The IMFs were prepared in triplicate for biochemical characterizations and denaturation kinetic study at 75°C. The scheme of formulation is shown in Supplementary Figure 1. In parallel, a solution of α-LA and a solution of LF (proteins used to replace part of the WPI in IMFs) at identical α-LA and LF concentration as found in the LF + α-LA + IMF and respecting the mineral and lactose contents of IMFs were prepared and named "Pure protein solution".

Compositional analysis

Total nitrogen, non-protein nitrogen and non-casein nitrogen were determined by the Kjeldahl method, with a nitrogen-protein conversion factor of 6.38 (International Dairy Federation, 1993).

Lactose content was quantified by refractometry after separation by high-performance liquid chromatography (HPLC) using a Aminex A-6 ion exchange column (Bio-Rad, Hercules, CA, USA) as described by [START_REF] Aburjaile | Adaptation of Propionibacterium freudenreichii to long-term survival under gradual nutritional shortage[END_REF]. Calcium, iron, potassium and sodium contents were quantified by atomic absorption spectrometry as described by [START_REF] Brulé | Étude de la teneur en éléments minéraux des produits obtenus lors de l'ultrafiltration du lait sur membrane[END_REF]. Inorganic phosphorus content was quantified by using the molybdenum blue method according to [START_REF] Jean | Dosage du phosphore dans le lait[END_REF].

Chloride was quantified with the Sherwood Scientific chloride analyzer (Modele 926, Sherwood Scientific Ltd, Cambridge, UK) as described by [START_REF] Berdagué | Affinage et qualité du Gruyère de Comté. II. Influence de l'affinage sur l'évolution des caractéristiques physico-chimiques des fromages[END_REF]. Ash content was determined by weighing the dry mineral residue after water and volatile vaporization, and organic matter oxidative burning at 550°C for 5h in a muffle furnace.

Each of these compositional analysis was performed in triplicate on each of the three IMFs.

Heat treatments

Glass capillary tubes (8 mm inner diameter and 40 mm length, Waters, USA), containing 800 µL of IMFs pre-heated at 30°C during 1h, were placed in a thermally controlled water bath (Fisherbrand™ Isotemp™ water bath, Thermo Fisher Scientific, Newington, USA) set at different temperatures ranging from 67.5°C to 80°C (by step intervals of 2.5°C). For each condition, the heating ramp (i.e. the time to reach the target temperature) was controlled with a YC-747UD Data Logger Thermometer inserted in a reference tube. The heating ramp was converted into a heating time at target temperature (as explained in section 2.6.1).

At various time intervals, tubes were removed and instantaneously chilled on ice bath to stop whey protein denaturation/aggregation reactions. Unheated samples served as reference for determining the total amount of native proteins before heating. Holding times for each heating temperature were chosen to scan the denaturation/aggregation of whey proteins up to a yield of 80%. Three independent experiments were performed for the heat treatment at 75°C, considering the standard deviation equivalents at all heating temperatures investigated.

After cooling, 20 or 10 µL of 1.4 M acetic acid/acetate buffer was added to 150 or 200 µL of heated and unheated IMFs or pure protein solutions, respectively, and the mixture was placed at 40°C for 2 min to precipitate the caseins and denatured/aggregated whey proteins. The proteins in the pH 4.6soluble fraction were separated from the precipitate by centrifugation at 14,000g for 20 min at 25°C, using an Eppendorf Microcentrifuge MicroStar 17R (VWR, Leuven, Belgium). The supernatant was diluted in Milli-Q water containing 0.106% (v/v) trifluoroacetic acid at 0.5 g.L -1 of proteins for analysis by reversed-phase high-performance liquid chromatography (RP-HPLC).

Quantification of native whey proteins

Native whey proteins were separated on a PLRP-S 300 Å, 8 µm, 150 x 3 mm separation column combined with a guard column (Agilent Technologies, UK) connected to a Dionex UltiMate 3000 HPLC System (Thermo Fisher, Dreieich, Germany), equipped with a detector VWD3400RS (Thermo Fisher, Dreieich, Germany) operating at 280 nm for the quantification of eluted proteins. Proteins were eluted at a flow rate of 0.2 mL.min -1 and at 40°C, using a gradient of acetonitrile obtained by mixing the mobile phase A (0.106% (v/v) of trifluoroacetic acid in Milli-Q water) and the mobile phase B (1% (v/v) of trifluoroacetic acid in acetonitrile). The acetonitrile gradient started with a plateau of 35.2% of mobile phase B during 14 min, and then continued with successive increases of mobile phase B to 38.4% in 6 min, 40% in 7 min, 42.4% in 14 min, 49.6% in 1 min, and finally 80% in 4 min.

Native whey proteins in unheated and heated samples were quantified using a calibration curve established by direct injection of α-LA, β-LG and LF at 0.5 g.L -1 of proteins. Chromatographs were analyzed by Chromeleon ® software (Version 7.2 SR4, Thermo Fisher, Waltham, USA). The term "native whey proteins" referred in this study to the proteins in the pH 4.6-soluble fraction that have the same retention time in RP-HPLC than the whey protein standards. Consequently, the whey proteins still soluble at pH 4.6 but that underwent structural modifications during heat treatment in such a way their RP-HPLC retention time is modified are not quantified as native proteins. versus holding time, as described by [START_REF] Dannenberg | Reaction kinetics of the denaturation of whey proteins in milk[END_REF].

Kinetic parameters of individual whey protein denaturation

Calculation of D-values, Z-values, and the equivalent heating time

The Arrhenius representation, corresponding to the relationship between the logarithm of the rate constant kn versus the inverse of heating temperature, was plotted according to the equation:

ln k " = ln,k ",* . - / 0 1.
(5)

The activation energy Ea (kJ.mol -1 ) was obtained from the slope of the linear regression of the Arrhenius plot and the denaturation/aggregation frequency factor logarithm, ln (kn,0), from the yintercept. R is the universal gas constant (8.314 J.mol -1 .K -1 and T the heating temperature (K).

Results

Composition of the three IMFs

IMFs were formulated at 1.3% of total proteins, with a caseins:whey proteins ratio of 40:60, and differing exclusively on the individual whey protein quantity, as shown in Table 2.

According to the RP-HPLC quantification of α-LA, β-LG and LF in unheated IMFs, the control IMF contained 0.14 g of α-LA and 0.51 g of β-LG/100 g of liquid IMF. Traces of LF were observed but the amount was too low to be quantified. In the LF + IMF, the quantities of α-LA, β-LG and LF were 0.10 g, 0.33 g and 0.17 g/100 g of liquid IMF, respectively. The LF + α-LA + IMF was constituted by 0.39 g of α-LA and 0.15 g of LF/100 g of liquid IMF. In the LF + α-LA + IMF, 0.06 g of β-LG/100 g of IMF came from the SMP. This amount was calculated from the amount of β-LG in the SMP and the proportion of SMP in the IMF. Thus, the whey protein composition differed among the three IMFs. The major whey proteins were α-LA and β-LG for the control IMF, α-LA and LF for the LF + α-LA + IMF, and the LF + IMF was a mixture of α-LA, β-LG and LF. Moreover, the LF contents of the LF + and LF + α-LA + IMFs were similar.

Kinetics of thermal denaturation of whey proteins

The denaturation kinetics of the individual whey proteins α-LA, β-LG and LF in the temperature range from 67.5 to 80°C were followed by RP-HPLC quantification of the soluble protein fraction at pH 4.6. This temperature range was selected from preliminary experiments. Heat treatments of the control IMF and LF + IMF at temperatures higher than 80°C induced a very fast denaturation of the whey proteins preventing the precise determination of the whey protein denaturation kinetic parameters.

In contrast, the very slow whey protein denaturation during the heating of LF + α-LA + IMF combined with the extensive lactosylation of the proteins for the longer holding times at temperatures lower than 67.5°C prevented the exact quantification of the proteins due to the elution of each protein as multi-peaks by RP-HPLC.

As expected, the increase of the heating temperature from 67.5 to 80°C or of the holding time at fixed temperature induced a higher decrease of the content of native whey proteins. To gain in clarity, only the whey protein denaturation kinetics at 70 and 75°C are presented on Figure 1 for the IMFs and on Supplementary Figure 2 for the pure protein solutions. Figure 1 compares the heatdenaturation of individual whey proteins among IMFs but similar trends were observed at other studied temperatures. The reaction orders n and the rate constant kn of the kinetics of denaturation of α-LA, β-LG and LF were calculated by the best fitting of the experimental data using the equation (4) (Table 3). The Arrhenius plot of α-LA, β-LG and LF (Fig 2 .1) was drawn using the values of rate constants of denaturation kn of each individual whey protein at different temperatures. Each Arrhenius plot was best described by a linear regression, the slope of which gave the activation energies of the denaturation of the whey proteins Ea and the y-intercept the frequency factor logarithms ln (kn,0) (Fig 2 .2).

Thermal denaturation of α-LA

The kinetics of α-LA heat-denaturation were in the same range in the control and LF + IMFs but they were systematically slower in the LF + α-LA + IMF (Fig 1 .A). The reaction orders of the kinetics of denaturation of α-LA in both control and LF + IMFs (n=1.2 ± 0.2) and in the LF + α-LA + IMF (1.5 ± 0.5) were higher than the one determined in the pure α-LA solution (n=0.5 ± 0.3). At all heating temperatures, the rate constants kn of α-LA were in the same range for the control and LF + IMFs in one hand and for the LF + α-LA + IMF and the pure α-LA solution in the other hand (Table 3). The kn values obtained for the LF + α-LA + IMF and the pure α-LA solution were between 3-fold and 10-fold lower than those determined for the control and LF + IMFs in the temperature range from 67.5°C to 80°C.

The thermodynamic parameters of the denaturation of α-LA (Ea and ln (kn,0)) were highly dependent on the amount of β-LG in the IMFs. Indeed, Ea and ln (kn,0) were similar between the control IMF (227 kJ.mol -1 and 75, respectively) and the LF + IMF (220 kJ.mol -1 and 73, respectively), which had higher content of β-LG (0.51% and 0.33% respectively). They were also similar between the LF + α-LA + IMF (110 kJ.mol -1 and 33 respectively) and the pure α-LA solution (100 kJ.mol -1 and 29) (Fig 2 .2), which contained traces or no β-LG.

Thermal denaturation of β-LG

The kinetics of denaturation of β-LG in the control and LF + IMFs at 70 and 75°C are presented in the At all heating temperatures, the heat-denaturation of β-LG was faster in the LF + IMF than in the control IMF. The reaction orders of the heat-denaturation of β-LG were similar for both IMFs (n=1.5 -1.6) (Table 3).

The rate constants of β-LG denaturation in the control and LF + IMFs are presented in the Table 3. The kn-values were between 2-fold and 7-fold lower for the control IMF than for the LF + IMF in the studied temperature range. The kn-values at 67.5°C were 0.3 x 10 -2 g -0.6 .L 0.6 .min -1 and 0.8 x 10 -2 g - 0.5 .L 0.5 .min -1 for the control and LF + IMFs respectively, whereas they were 10.8 x 10 -3 g -0.6 .L 0.6 .min -1 and 70.9 x 10 -2 g -0.5 .L 0.5 .min -1 at 80°C, respectively. The activation energy of β-LG heat-denaturation determined from the Arrhenius plot was slightly higher in the control IMF (305 kJ.mol -1 ) compared to the LF + IMF (273 kJ.mol -1 ) (Fig 2 .2). In contrast, the ln (kn,0) value was slightly lower for the control IMF (102) than for the LF + IMF (126).

Thermal denaturation of LF

The kinetics of LF heat-denaturation in the LF + and LF + α-LA + IMFs were compared (Fig 1 .C). In the control IMF, the amount of LF was too low to quantify the heat-induced denaturation. Interestingly, the kinetics of heat-denaturation of LF were similar between the two IMFs at all studied temperatures. The reaction orders of LF heat denaturation was 1.6 ± 0.2 and 1.8 ± 0.3 for the LF + and LF + α-LA + IMFs, respectively. A slightly lower reaction order (n=1.4 ± 0.4) was obtained for the heatdenaturation of LF in the pure protein solution. The rate constants of LF denaturation were in the same range between the LF + and LF + α-LA + IMFs (Table 3). In fact, in the temperature range between 67.5°C and 80°C, the rate constants of LF heat-denaturation varied between 3.6 x 10 -2 to 42.8 x 10 -2 g - 0.6 .L 0.6 .min -1 for the LF + IMF and between 2.6 x 10 -2 to 42.3 x 10 -2 g -0.8 .L 0.8 .min -1 for the LF + α-LA + IMF.

These values were higher than the rate constants determined for LF heat-denaturation in the pure LF solution at the same heating temperature (0.4 x 10 -2 to 17.6 x 10 -2 g -0.4 .L 0.4 .min -1 ). As expected, the activation energy of LF was similar in the LF + (202 kJ.mol -1 ) and LF + α-LA + (215 kJ.mol -1 ) IMFs. Likewise, the frequency factor logarithm of LF denaturation determined in the LF + IMF ( 68) is akin to the value determined for the LF + α-LA + IMF (73). Higher Ea and ln (kn,0) values were determined for the pure LF solution compared to the LF + and LF + α-LA + IMFs (286 versus 215 kJ.mol -1 and 96 versus 70 kJ.mol -1 , respectively) (Fig 2 .2).

Prediction of the amount of native whey proteins in IMFs after pasteurization treatments

Based on equation (4) and the thermodynamic parameters calculated in this study (Fig 2 .2), the proportion of native α-LA, β-LG and LF recovered in IMFs after the temperature/time conditions usually used to pasteurize milk can be predicted (Fig 3). A summary of the calculations is given in Supplementary Table 1. The whey protein denaturation yield simulated for the heat treatment 75°C/ 10 min was confirmed by RP-HPLC quantification.

The simulation of the holder pasteurization (i.e. 62.5°C during 30 min) induced the denaturation of 4% of native whey proteins in the control IMF and of 13% and 15% in the LF + and LF + α-LA + IMFs, respectively. denaturation yield (between 1% and 4% of denatured proteins) in the three IMFs. Rising up the temperature of the pasteurization treatment from 75°C to 90°C but keeping the holding time constant (15 s) resulted in a decrease of the fraction of native whey proteins in all IMFs, with 48%, 27% and 81% of residual native whey proteins in the control, LF + and LF + α-LA + IMFs, respectively. The native protein loss was mainly due to the heat-denaturation of β-LG and LF during the treatment at 90°C/15 s. A similar trend was observed when the holding time at 75°C was prolonged to 10 min but the proportion of the residual native proteins was slightly different: 61%, 32% and 71% of residual native whey proteins were calculated in the control, LF + and LF + α-LA + IMFs, respectively. The relative denaturation yield of α-LA and LF was higher after a heat treatment at 75°C/10 min compared to 90°C/15 s.

Discussion

The present paper evidences that the heat denaturation of whey proteins within IMFs depends on both the whey protein composition and the temperature/time combination treatment.

4.1. The heat-denaturation of LF is independent of the amount of α-LA and β-LG in the

IMFs

The reaction orders of LF determined for the LF + and LF + α-LA + IMFs and in the pure LF solution are in accordance with the one previously determined for the thermal denaturation of the recombinant human LF [START_REF] Castillo | Kinetic and thermodynamic parameters for heat denaturation of human recombinant lactoferrin from rice 1 This article is part of a Special Issue entitled Lactoferrin and has undergone the Journal's usual peer review process[END_REF]. These authors determined a reaction order of 1.5, independently of the iron saturation level of LF.

The present results show that LF heat-denaturation kinetics are independent of the change of α-LA and β-LG amounts in the IMFs in the whole range of the studied heating temperatures. Since LF is one of the most heat-sensitive protein in milk with a reported denaturation temperature around 60°C [START_REF] Bengoechea | Formation of protein nanoparticles by controlled heat treatment of lactoferrin: Factors affecting particle characteristics[END_REF], it is assumed that its denaturation occurs before the heat-denaturation of α-LA and β-LG with denaturation temperatures of about 68°C (Nielsen et al, 2018) and 78°C [START_REF] Brodkorb | Heat-Induced Denaturation, Aggregation and Gelation of Whey Proteins[END_REF], respectively. Consequently, these latter have no or very little influence on the heat-denaturation of LF explaining that the rate constants and the activation energy of the heat-denaturation of LF are similar in the LF + and LF + α-LA + IMFs, in spite of different contents in α-LA and β-LG.

Interestingly, the LF heat-denaturation rate constants were lower and the activation energy was higher in the pure LF solution compared to those obtained in the LF + and LF + α-LA + IMFs, indicating that the physicochemical environment in the IMFs favors the denaturation of LF during heating. LF is able to bind to casein micelles mainly by electrostatic interactions [START_REF] Anema | Lactoferrin binding to transglutaminase cross-linked casein micelles[END_REF] and this was confirm in this study since 43% of LF was recovered with the casein micelle fraction in the ultracentrifugation pellet (100,000g -1h -25°C) of the LF + and LF + α-LA + IMFs (data not shown). The binding of LF to caseins is facilitated by heating and results in the formation of LF-casein complexes (Li & Zhao, 2017). This binding is susceptible to modify the heat-stability of LF and can be an explanation for the faster heat-denaturation of LF in the IMFs compared to the pure protein solution.

Casein micelles also have the ability to bind various types of cations such as iron ions (Fe 2+ and Fe 3+ ). This binding was observed in a suspension of casein micelles [START_REF] Philippe | The effects of different cations on the physicochemical characteristics of casein micelles[END_REF] and in bovine milk [START_REF] Broyard | Modifications of structures and functions of caseins: a scientific and technological challenge[END_REF]. The binding of iron to casein micelles could reduce the amount of iron bound to LF, and therefore accelerate its heat-denaturation kinetics because LF heat-stability is dependent on the iron saturation level [START_REF] Brisson | Effect of Iron Saturation on the Recovery of Lactoferrin in Rennet Whey Coming from Heat-Treated Skim Milk[END_REF][START_REF] Sánchez | Kinetic Parameters for Denaturation of Bovine Milk Lactoferrin[END_REF][START_REF] Castillo | Kinetic and thermodynamic parameters for heat denaturation of human recombinant lactoferrin from rice 1 This article is part of a Special Issue entitled Lactoferrin and has undergone the Journal's usual peer review process[END_REF]. However, the quantification of LF and iron in the supernatant after ultracentrifugation of unheated LF + and LF + α-LA + IMFs indicated that LF was fully saturated with iron (iron/LF molar ratio of 3.7 ± 0.0, data not shown) considering a binding constant of about 10 22 -10 24 M -1 [START_REF] Law | A high-throughput method for the quantification of iron saturation in lactoferrin preparations[END_REF]. Therefore, the faster heat-denaturation of LF in IMFs compared to pure LF solution was rather a consequence of the binding of LF to casein micelles than a reduction of the iron saturation level of LF.

The heat-denaturation of α-LA is enhanced in the presence of β-LG

The reaction orders of α-LA determined for the three IMFs (between 1.2 and 1.5) were higher than the one reported in the literature for the heat-denaturation of α-LA in bovine milk (n=1.0, [START_REF] Anema | Effect of protein, nonprotein-soluble components, and lactose concentrations on the irreversible thermal denaturation of β-lactoglobulin and αlactalbumin in skim milk[END_REF][START_REF] Dannenberg | Reaction kinetics of the denaturation of whey proteins in milk[END_REF] and the value determined in the pure α-LA solution (n=0.5).

This could be a consequence of the different protein content [START_REF] Wehbi | Effect of Heat Treatment on Denaturation of Bovine α-Lactalbumin: Determination of Kinetic and Thermodynamic Parameters[END_REF] and/or distinct medium conditions between bovine milk, the pure α-LA solution and the IMFs.

The denaturation kinetics of α-LA in the different IMFs revealed that α-LA was more rapidly denatured in the control and LF + IMFs that contain 0.51 g and 0.33 g of β-LG/100 g of liquid IMF, respectively. When the β-LG content is as low as in the LF + α-LA + IMF, the denaturation rate constant of α-LA is comparable to that of α-LA in the pure solution. These results are in agreement with published data showing that the denaturation of α-LA is promoted by the presence of β-LG [START_REF] Wehbi | Effect of Heat Treatment on Denaturation of Bovine α-Lactalbumin: Determination of Kinetic and Thermodynamic Parameters[END_REF]. In the absence of β-LG, α-LA reversibly unfolds on heating but does not form irreversible aggregates (Nielsen et al, 2018). The aggregation of α-LA is enhanced in the presence of unfolded β-

LG molecule that exposes its free thiol group to the solvent, making it available to react with unfolded α-LA via thiol-disulfide interchanges (Dalgleish et al, 1997). This covalent cross-link between β-LG and α-LA traps α-LA in an irreversibly unfolded structure in the formed aggregates. The irreversible denaturation of α-LA induced by addition of thiol reagents [START_REF] Nguyen | The effect of thiol reagents on the denaturation of the whey protein in milk and whey protein concentrate solutions[END_REF] confirms that the presence of available thiol groups cleaving intramolecular α-LA disulfide bonds is necessary to promote α-LA denaturation/aggregation .

To the best of our knowledge, the effect of LF on the heat-denaturation of α-LA was less studied than that of β-LG. The similarities of the activation energies of α-LA in the LF + α-LA + IMF and in the pure α-LA solution, both containing the same quantities of α-LA and the same lactose and mineral contents, demonstrate that LF does not interfere with the mechanism of heat-denaturation of α-LA. LF has 34 cysteine residues in its structure, all involved in intramolecular disulfide bonds, but no free thiol group [START_REF] Pierce | Molecular cloning and sequence analysis of bovine lactotransferrin[END_REF]. The absence of a free thiol group in the structure of LF is a plausible explanation for the absence of LF effect on α-LA heat-denaturation that is promoted by thiol containing molecules. However, the profile of the α-LA denaturation kinetics in the LF + α-LA + IMF and the pure α-LA solution differs due to the variation of the reaction order (1.5 ± 0.5 and 0.5 ± 0.3, respectively). The higher reaction order in the LF + α-LA + IMF could be a consequence of the presence of other proteins (LF, caseins, β-LG traces) facilitating the aggregation of denatured α-LA.

The heat-denaturation of β-LG is enhanced in the presence of LF

The reaction orders of the heat-denaturation of β-LG determined for the control and LF + IMFs (n=1.5-1.6) are in adequacy with the reaction order widely reported in the literature for the heatdenaturation of the protein in bovine milk [START_REF] Anema | Reaction kinetics of thermal denaturation of whey proteins in heated reconstituted whole milk[END_REF].

The heat-denaturation of β-LG was faster in the LF + IMF (containing LF protein) than in the control IMF (lacking of LF protein), with the rate constants of denaturation of β-LG being 2 to 6-times higher in the LF + IMF than in the control IMF, and the denaturation activation energy being higher in the control IMF than in the LF + IMF (305 versus 273 kJ.mol -1 , respectively).

The mechanism of heat-denaturation of β-LG has been well-described [START_REF] De Wit | Thermal behaviour of bovine β-lactoglobulin at temperatures up to 150°C. a review[END_REF]. Upon heating, the dimer/monomer equilibrium of native β-LG is shifted to the monomeric form that unfolds and exposes its free thiol group and hydrophobic patches to the solvent. This reactive entity aggregates with proteins in its close surrounding mainly via disulfide interchange reactions, but also by hydrophobic driven association reactions. β-LG reacts rapidly with proteins having exposed disulfide bonds such as α-LA (Dalgleish et al, 1997) or LF [START_REF] Brisson | Effect of Iron Saturation on the Recovery of Lactoferrin in Rennet Whey Coming from Heat-Treated Skim Milk[END_REF]. Among these proteins, LF is particularly rich in disulfide bonds (17 disulfide bonds) and is already unfolded when β-LG starts to denature. This could facilitate the formation of intermolecular disulfide bonds between LF and β-LG supporting the hypothesis of [START_REF] Brisson | Effect of Iron Saturation on the Recovery of Lactoferrin in Rennet Whey Coming from Heat-Treated Skim Milk[END_REF], who showed that upon heating, LF aggregates with proteins containing cysteine residues such as β-LG to form disulfide bound aggregates.

The impact of the pasteurization treatments is dependent on the whey protein composition of IMFs

The simulation of the heat treatments at 90°C/15 s and 75°C/10 min revealed a lower content of native whey proteins in the pasteurized LF + IMF than in the control and LF + α-LA + IMFs, explained by the simultaneous presence of LF that rapidly denatures on heating and β-LG that initiates covalent cross-links between unfolded whey proteins. Surprisingly, the decrease of the native whey protein fraction in the control and LF + IMFs heat-treated at 90°C/15 s is mainly explained by the heatdenaturation of β-LG, and to a lesser extent by the heat-denaturation of LF. However, it is probable that the fraction of native β-LG in these heated IMFs is underestimated because the Arrhenius plot of β-LG exhibits a specific profile with a change of the denaturation activation energy around 80°C. In the aggregation-limited domain (temperatures above 80°C), the denaturation activation energy is between 2 and 3-times lower than in the unfolding-limited domain (temperatures below 80°C) [START_REF] Petit | Influence of calcium on β-lactoglobulin denaturation kinetics: Implications in unfolding and aggregation mechanisms[END_REF]. As the denaturation of the whey proteins in IMFs was not studied above 80°C for the reasons presented above (section 3.2), the change of the denaturation activation energy at temperature higher than 80°C cannot be taken into account for the estimation of the residual native β-LG after heating the IMFs at 90°C. Consequently, the rate constant used to calculate the fraction of residual native β-LG is likely overestimated, thus potentially explaining the lower amount of native whey protein fractions in the control and LF + IMFs heat-treated at 90°C/15 s than at 75°C/10 min. Almost all whey proteins remained native after simulation of HTST treatment (75°C/15 s) for the three IMFs. This is consistent with previous work that showed that HTST treatment of human [START_REF] Cavallarin | Effect of two pasteurization methods on the protein content of human milk[END_REF] and bovine [START_REF] Douglas | Effects of ultra-hightemperature pasteurization on milk proteins[END_REF] milks did not significantly denature whey proteins.

Moreover, the lower native whey protein quantity for the LF + and LF + α-LA + IMFs after the holder pasteurization simulation, a classical heat treatment used in human milk bank to ensure the sanitary quality before feeding newborn, is due to the denaturation of LF, which is more heat-sensitive at low temperature than other whey proteins [START_REF] Law | A high-throughput method for the quantification of iron saturation in lactoferrin preparations[END_REF]. This confirms previous experiments showing that the holder pasteurization of human milk mainly lead to the LF denaturation, whereas α-LA was not affected [START_REF] Deglaire | Impact of human milk pasteurization on the kinetics of peptide release during in vitro dynamic digestion at the preterm newborn stage[END_REF].

Conclusion

This study demonstrates that the kinetics of heat-denaturation of α-LA, β-LG and LF were influenced by the whey protein composition of the IMFs. The heat-denaturation of LF was not modified by the presence of α-LA or β-LG in the IMFs. As expected, the heat-denaturation of α-LA was enhanced in the presence of β-LG, but LF did not modify it. The presence of LF in the IMFs boosted the heatdenaturation kinetics of β-LG, probably by exposing numerous disulfide bonds that are accessible to the free thiol group of β-LG. The simulations of pasteurization treatments revealed that the yield of total whey protein denaturation is function of both the whey protein composition of the IMFs and the heat-treatment intensity. Standard IMF, formulated with WPI and SMP as protein sources, preserved a higher amount of native whey proteins after heat treatment at 62.5°C/30 min or at 75°C/15 s than IMF mimicking human milk protein content (enriched in α-LA and LF), whereas a reverse trend was observed for heat treatments at higher temperature (90°C/15 s) or longer holding time (75°C/10 min). Finally, the formulation of IMFs containing both α-LA and LF, and so mimicking the protein profile of human milk, is a way to preserve a higher proportion of native whey proteins after heating, as long as the heat intensity applied is in the upper range of the intensity tested in the present study, conditions usually encountered at industrial scale to ensure microbial safety and to extend IMF shelf-life.

Figure legends

Figure 1. Kinetics of thermal denaturation of α-LA (A), β-LG (B) and LF (C) in the control (green), LF + (orange), LF + α-LA + (blue) IMFs and the pure protein solutions (grey) at 70°C (square) and 75°C (circle). Residual native fractions were calculated as a Ct/C0 ratio. Ct (g.L -1 ) is the native protein concentration at t holding time (min) and C0 is the native protein concentration of unheated IMFs or protein solutions (g.L -1 ). The results at 75°C represent means ± error deviations from three independent experiments. Kn is the unfolding reaction rate constant (g 1-n .L n-1 .min -1 ) and 1/T the inverse of the heating temperature (K -1 ). The point at 75°C represents an average ± error deviation of three independent experiments. 2. ln (kn,0) represents the frequency factor logarithm and Ea the activation energy (kJ.mol -1 ), determined by Arrhenius plots shown in the The reaction orders n and the reaction rate constants kn were determined by the linear regression slope of the equation ( 4). The n-values are the means ± error deviation of reaction order values at each temperature. The Z-values correspond to means ± error deviations from data calculated at each temperature. The kn-values and D-values at 75°C represent an average ± error deviation of three independent experiments. The unit of kn is g 1-n .L n-1 .min -1 . The "Pure protein solutions" correspond to the solutions of pure α-LA or LF with the identical quantity within the LF + α-LA + IMF and respecting the mineral and lactose contents of IMFs.

  considering different values of n. The rate constants kn were determined from the linear

Figure 1 .

 1 Figure 1.B. No data was recorded for the LF + α-LA + IMF because of the low amount of β-LG (0.06 %).

Figure 1 1 .

 1 Figure 1 1. Arrhenius plots for the thermal denaturation of α-LA (A), β-LG (B) and LF (C) for the control (green), LF + (orange), LF + α-LA + (blue) IMFs, the pure protein solutions (grey) and 2. Kinetic parameters associated. 1.

Figure

  Figure 2.1.

Figure 2 .

 2 Figure 2. Whey protein contents and fractions of total native whey proteins for pasteurization treatments of the control (green), LF+ (orange) and LF+ α-LA+ (blue) IMFs. The patterns represent the amount of native α-LA (hatched bars), β-LG (spots) or LF (without pattern). The data are estimations from the equation = 1 + n -1 × e

  Figure 1

Table 1

 1 Biochemical characteristics of the skim milk powder (SMP).

	Figure 3

4 TN, NCN, NPN determined by the Kjeldahl method

Table 2

 2 Composition of the model IMFs -Comparison with the commercial IMFs and human term milk.

	Elements			Model IMFs		Commercial IMF 5	Human term milk 6
			Control	LF +	LF + α-LA +
	Total proteins		1.33 ± 0.01	1.35 ± 0.01	1.31 ± 0.01	1.20 ± 0.07	0.90
	Whey proteins		0.83 ± 0.04	0.82 ± 0.00	0.75 ± 0.00	0.72 ± 0.05	0.60
	α-LA β-LG LF Caseins	g / 100 g liquid, w/w	0.14 ± 0.00 0.51 ± 0.01 n.d. 0.50 ± 0.03	0.10 ± 0.00 0.33 ± 0.00 0.17 ± 0.00 0.53 ± 0.01	0.39 ± 0.02 0.06 7 0.15 ± 0.01 0.56 ± 0.01	0.19 0.35 0.48.10 -3 0.48 ± 0.05	0.25 Trace 0.15 0.40
	Lactose		5.6 ± 0.4	5.8 ± 0.4	5.6 ± 0.2	6.7 ± 0.9	7.6
	Calcium		41.4 ± 0.7	41.1 ± 1.4	42.2 ± 0.7	52 ± 6	27
	Chloride Iron Inorganic phosphorus Potassium	mg / 100 g liquid, w/w	65.8 ± 1.7 0.42 ± 0.02 21.1 ± 0.6 60.2 ± 6.3	69.6 ± 0.9 0.41 ± 0.02 20.6 ± 0.6 63.4 ± 1.3	68.5 ± 0.4 0.43 ± 0.01 20.8 ± 0.3 62.4 ± 0.4	44 ± 5 0.70 ± 0.11 30 ± 3 67 ± 4	40 0.50 15 54
	Sodium		21.5 ± 1.5	20.9 ± 1.2	25.0 ± 0.7	20 ± 2	18
	Ash	%, w/w	0.18 ± 0.04	0.17 ± 0.04	0.16 ± 0.03	n.d.	n.d.
	pH		6.82 ± 0.03	6.80 ± 0.02	6.81 ± 0.04	n.d.	n.d.

5

The data of commercial IMF are obtained from

[START_REF] Chatterton | Anti-inflammatory mechanisms of bioactive milk proteins in the intestine of newborns[END_REF]

for the α-LA, β-LG and LF contents and mean of the five 1 st age commercial IMFs for the rest of elements: Guigoz, Gallia, Milumel 1 Lactel, Novalac and Bledilait Bledina.

6

The data of human term milk are obtained from

Lönnerdal, Forsum, & Hambraeus, 1976, Altomonte, Salari, Licitra, & Martini, 2019, Wack, Lien, Taft, & Roscelli, 1997. 7

Value of β-LG content in the LF + α-LA + IMF is determined by calculation from the amount of β-LG in SMP and the proportion of SMP in the IMF.

Table 3

 3 Reaction orders n, Z-values, reaction rate constants kn and D-values for the thermal denaturation of α-LA, β-LG and LF for the control, LF + , LF + α-LA + IMFs and pure protein solutions, at temperature range 67.5-80°C.

	IMFs	Whey proteins	Temperatures	kn	R²	D-value
			(°C)	(10 -2 g 1-n .L n-1 .min -1 )		(min)
	Control	α-LA	67.5	0.5	0.994
			70	1.3	0.968
		n = 1.2 ± 0.2	72.5	1.9	0.953
		Z-value = (8.0 ± 1.6)°C	75	6.0 ± 1.0	0.994	36 ±
			77.5	6.7	0.988	32
			80	7.9	0.997	27
		β-LG	67.5	0.3	0.999
			70	0.4	0.995
		n = 1.6 ± 0.1	72.5	0.9	0.997
		Z-value = (9.8 ± 2.7)°C	75	2.2 ± 0.1	0.999	42 ±
			77.5	5.5	0.998	17
			80	10.8	0.988	9
	LF +	α-LA	67.5	0.7	0.980
			70	2.4	0.993	96
		n = 1.2 ± 0.2	72.5	3.3	0.972	70
		Z-value = (7.8 ± 1.7)°C	75	6.6 ± 0.4	0.996	35 ±
			77.5	8.8	0.999	26
			80	12.5	0.965	19
		β-LG	67.5	0.8	0.997
			70	1.3	0.994	99
		n = 1.5 ± 0.2	72.5	3.0	0.994	42
		Z-value = (7.9 ± 1.7)°C	75	8.1 ± 0.8	0.997	16 ±
			77.5	26.2	0.996	5
			80	70.9	0.986	2
		LF	67.5	3.6	0.990	46
			70	5.0	0.980	34
		n = 1.6 ± 0.2	72.5	6.9	0.989	24
		Z-value = (15.1 ± 3.0)°C	75	12.2 ± 1.8	0.998	14 ±
			77.5	25.3	0.995	7
			80	42.8	0.973	4
	LF + α-LA +	α-LA	67.5	0.2	0.971
			70	0.3	0.977
		n = 1.5 ± 0.5	72.5	0.4	0.983
		Z-value = (18.5 ± 2.7)°C	75	0.6 ± 0.1	0.993	204 ±
			77.5	0.7	0.995
			80	0.9	0.990
		LF	67.5	2.6	0.969	63
			70	8.1	0.988	20
		n = 1.8 ± 0.3	72.5	16.9	0.972	10
		Z-value = (8.2 ± 2.0)°C	75	21.3 ± 7.4	0.993	8 ± 3
			77.5	36.7	0.982	5
			80	42.3	0.993	4
	Pure protein solutions	α-LA n = 0.5 ± 0.3	67.5 70 72.5	0.3 0.3 0.5	0.975 0.994 0.997	1230 1019
		Z-value = (23.4 ± 4.4)°C	75	0.6	0.960
			77.5	0.9	0.990
			80	0.9	0.978
		LF	67.5	0.4	0.980
			70	1.3	0.994
		n = 1.4 ± 0.4	72.5	2.8	0.984	71
		Z-value = (6.4 ± 1.4)°C	75	5.1	0.985	39
			77.5	6.6	0.990	30
			80	17.6	0.936	11

Acknowledgments

The authors thank Ingredia Dairy Experts and Agropur Inc for providing LF and α-LA powders. The authors also thank Leduc, A. for the mineral analysis of IMFs and Maillard, M.B. for the lactose analysis of IMFs. The authors have declared no conflict of interest.

For each IMF and heating treatment, the equivalent time tθ (min) was calculated, corresponding to the time required at the temperature θ (°C) to obtain the same rate of protein denaturation than the reference treatment (θref (°C) at tθref (min)). tθ was determined using the following equation:

with z (°C) corresponding to the mean of Z-values (i.e. temperature increase required to obtain a tenfold reduction of the whey protein denaturation time) estimated for each protein [START_REF] Jeantet | Handbook of Food Science and Technology 2: Food Process Engineering and Packaging[END_REF]. Z-values were calculated from the equation:

with D1 and D2 (min) the whey protein denaturation times for having 90% whey protein denaturation at heating temperature T1 (°C) and T2 (°C), respectively. The D-values were determined as the inverse of the slope of the linear regression of the logarithm of individual whey protein concentrations versus heating time. The D-and Z-values are presented in the Table 3.

Determination of the kinetic parameters for the heat denaturation/aggregation of whey proteins

The reaction orders n and the rate constants kn were determined by the integration of the general rate equation, according to [START_REF] Croguennec | Caseinomacropeptide modifies the heat-induced denaturation-aggregation process of βlactoglobulin[END_REF]:

which gives, for n ≠ 1:

Ct (g.L -1 ) is the native whey protein concentration at holding time t (min), C * (g.L -1 ) the native whey protein concentration of the unheated sample and kn (g 1-n .L n-1 .min -1 ) the rate constant.