Sandra Domenek

Marie-He Ä Le Å Ne Morel

Joe ¨lle Bonicel

Phane Guilbert

Polymerization Kinetics of Wheat Gluten upon Thermosetting. A Mechanistic Model

Keywords: Wheat gluten, polymerization, kinetic, mathematical model, heat treatment

Size exclusion high-performance liquid chromatography analysis was carried out on wheat glutenglycerol blends subjected to different heat treatments. The elution profiles were analyzed in order to follow the solubility loss of protein fractions with specific molecular size. Owing to the known biochemical changes involved during the heat denaturation of gluten, a mechanistic mathematical model was developed, which divided the protein denaturation into two distinct reaction steps: (i) reversible change in protein conformation and (ii) protein precipitation through disulfide bonding between initially SDS-soluble and SDS-insoluble reaction partners. Activation energies of gluten unfolding, refolding, and precipitation were calculated with the Arrhenius law to 53.9 kJ'mol -1 , 29.5 kJ'mol -1 , and 172 kJ'mol -1 , respectively. The rate of protein solubility loss decreased as the crosslinking reaction proceeded, which may be attributed to the formation of a three-dimensional network progressively hindering the reaction. The enhanced susceptibility to aggregation of large molecules was assigned to a risen reaction probability due to their higher number of cysteine residues and to the increased percentage of unfolded and thereby activated proteins as complete protein refolding seemed to be an anticooperative process.

INTRODUCTION

Temperature plays an important role in the processing of wheat gluten based products, as most texturization processes involve heat treatment of the material. On a molecular level, conformations of proteins, their polymeric state, and their interaction behavior are affected by temperature.

The application of texturization processes to wheat gluten, such as extrusion which is well studied in the field of food production (1-7), represents a real challenge to the production of biopolymers [START_REF] Cuq | Proteins as agricultural polymers for packaging production[END_REF]. To control the texturization processes and the properties of the final products, it is essential to get a better knowledge of the molecular changes in the proteins induced by shear on one hand and by temperature on the other. This work focuses on the effect of temperature on gluten protein studied at a molecular scale and attempts to model the kinetics of gluten protein aggregation.

Gluten comprises protein monomers (gliadin) and polymers (glutenin) in roughly equal weight fractions. The molecular size (M r ) of gliadin polypeptides ranges from approximately 20000 up to approximately 80000 (ω-gliadin). Gliadin, except ω-gliadin, carries cysteine residues which are involved in intrachain disulfide bonds. Glutenin consists of discrete polypeptides (subunits), which are linked together by interchain disulfide bonds to form a high-molecular-weight polymer. The M r of the subunits extends from about 36000 to 44000 for low M r and from 60000 to 90000 for high M r glutenin subunits. Glutenin polymers show a wide size distribution range, and their M r may exceed several million [START_REF] Wrigley | Giant proteins with flour power[END_REF][START_REF] Southan | Molecular weight distribution of wheat proteins[END_REF]. Flour glutenin is partly insoluble in most common solvents due to its huge size, even in the presence of denaturing agents such as sodium dodecyl sulfate (SDS). The wheat gluten solubility in SDS-phosphate buffer amounts to about 80-90% of the total protein mass. The wheat protein size distribution is usually studied by size exclusion highperformance liquid chromatography (SE-HPLC), which allows good resolution of gliadin monomers and glutenin polymers [START_REF] Redl | Extrusion of wheat gluten plasticized by glycerol: Influence of process conditions on flow behavior, rheological properties and molecular size distribution[END_REF][START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF][START_REF] Dachkevitch | Prediction of baking quality of bread wheats in breeding programs by size exclusion high performance liquid chromatography[END_REF][START_REF] Singh | Use of sonication and size-exclusion high-performance liquid chromatography in the study of wheat flour proteins. I. Dissolution of total proteins in the absence of reducing agents[END_REF][START_REF] Singh | Use of sonication and size-exclusion high-performance liquid chromatography in the study of wheat flour proteins. II. Relative quantity of glutenin as a measure of breadmaking quality[END_REF][START_REF] Gao | Polymeric glutenin of wheat lines with varying number of high molecular weight glutenin subunits[END_REF][START_REF] Gupta | Biochemical basis of flour properties in bread wheats. I. Effect of variation in quantity and size distribution of polymeric protein[END_REF][START_REF] Weegels | Effects on gluten of heating at different moisture contents. I. Changes in functional properties[END_REF][START_REF] Weegels | Effects on gluten of heating at different moisture contents. II. Changes in physico-chemical properties and secondary structure[END_REF][START_REF] Redl | Rheological properties of gluten plasticized with glycerol: dependence on temperature, glycerol content and mixing conditions[END_REF][START_REF] Morel | Effects of temperature, sonication time, and power settings on size distribution and extractability of total wheat flour proteins as determined by size-exclusion high-performance liquid chromatography[END_REF].

One of the most marked features of the heat-induced gluten denaturation is, e.g., the decrease of protein solubility in SDSphosphate buffer. It has been evidenced in the literature that a rise of temperature causes protein unfolding which results in the exposition of hydrophobic protein zones. Protein aggregation may occur, in consequence, primarily due to hydrophobic interactions. The unfolded state facilitates thiol/disulfide interchange between exposed groups, which locks the protein into the denatured state due to the disulfide bond rearrangement [START_REF] Li | Relationship of the extrusion temperature and the solubility and disulfide bond distribution of wheat proteins[END_REF][START_REF] Redl | Extrusion of wheat gluten plasticized by glycerol: Influence of process conditions on flow behavior, rheological properties and molecular size distribution[END_REF][START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF][START_REF] Weegels | Effects on gluten of heating at different moisture contents. II. Changes in physico-chemical properties and secondary structure[END_REF].

The temperature dependency of gluten protein denaturation upon heating has been investigated by several groups. Their results are summarized in Table 1. The activation energy of the denaturation reaction, which can be calculated from the Arrhenius law, is a valuable tool to predict the progress of a reaction in dependency of temperature and to compare different studies since it is independent from time and temperature. However, it does not provide much insight into the reaction kinetics and the underlying molecular mechanisms.

In this work we aim to investigate kinetically the influence of temperature on gluten plasticized with glycerol in order to provide a comprehensive model of the heat-induced changes in gluten protein. To achieve our purpose, we investigated the effects of three heating temperatures (70, 82, and 94 °C) on the gluten protein solubility in SDS-phosphate buffer. To analyze the heat-induced changes in gluten proteins of specific M r , we investigated the SDS-phosphate buffer extracts of the gluten samples with SE-HPLC. The continuous elution profiles were decomposed in individual protein peaks with the help of a Gaussian deconvolution fit. A mathematical model based on mechanistic reaction pathways was developed in order to calculate the solubility change of each protein species in SDSphosphate buffer. The model sums up the current knowledge on the molecular events occurring during the heat-induced gluten solubility loss and the present results.

MATERIALS AND METHODS

Vital wheat gluten was provided by Amylum (Aalst, Belgium). Protein, starch, lipid, and ash amounted to respectively 76.5%, 11.8%, 5.0%, and 0.8% of dry mass. Moisture content was 7.2% (dry mass basis). Anhydrous glycerol was purchased from Fluka Chemie (Buchs, Switzerland) in p.a. quality. Chemicals for biochemical analysis of the samples were obtained from Sigma in p.a. quality.

Preparation of Heat-Treated Gluten-Glycerol Samples. Gluten (32.68 g) and glycerol (17.32 g) were hand-mixed in a mortar and rested for 20 min. The blend (3 g) was subsequently hand-molded to give a disk of 2 mm thickness and 4 cm diameter. The gluten/glycerol disk was sealed in a plastic bag under vacuum and incubated for increasing times in a water bath (E110, Lauda) regulated in temperature at 70, 82, or 94 °C. The bag was cooled in ice-water to stop the reaction, and the sample was stored at -28 °C. The most severe heat treatment was performed under a heating press (Techmo, Nazelles-Negron, France) at 120 °C for 35 min. The control sample (untreated), the sample treated at 120 °C, and three randomly chosen samples of the series at 82 °C were fabricated in triplicate.

Protein Size Distribution: SE-HPLC. The samples were analyzed according to the protocol of Redl et al. [START_REF] Redl | Rheological properties of gluten plasticized with glycerol: dependence on temperature, glycerol content and mixing conditions[END_REF] with minor modifications. Ground samples (160 mg) were agitated for 80 min at 60 °C in 20 mL of 0.1 M sodium phosphate buffer (pH 6.9) containing 1% SDS (buffer A). The supernatant containing the SDS-soluble protein fraction (F s) was collected after centrifugation (37000g, 30 min). The residue consisting of the SDS-insoluble protein fraction (Fi) was extracted with 5 mL of buffer A containing 20 mM dithioerythriol (DTE). The samples were agitated for 60 min at 60 °C and tip sonicated to bring total gluten protein in solution. The supernatant (500 µL) recovered after centrifugation (37000g, 30 min) was mixed with 500 µL of buffer A containing 40 mM iodoacetamide (IAM). IAM alkylated the thiol groups and prevented their subsequent oxidation. Both extracts (20 µL), F s and Fi, were submitted to SE-HPLC fractionation.

The fractionation was performed on a TSK-G 4000 SW XL (TosoHaas) analytical size exclusion column (7.5 × 300 mm) with a TSK 3000-SW XL (TosoHaas) guard column (7.5 × 75 mm). Columns were eluted at room temperature with 0.1 M sodium phosphate buffer (pH 6.9) containing 0.1% SDS. The flow rate was 0.7 mL'min -1 ; proteins were detected at 214 nm. The apparent Mr of the proteins was estimated by calibrating the column with protein standards according to ref 12. The elution profile of the supernatant was divided into five fractions (Figure 1). The lowest points on the valleys were used as cutoff points between the fractions. The area of each fraction was expressed in percent of total proteins, estimated from the sum of the total areas of the first and second extract (F s and Fi) corrected for their different solid-to-solvent ratios. Fractions F1 and F2 include protein species having a M r ranging from 1.5 × 10 6 to 150 × 10 3 , which corresponds to the Mr of glutenin polymers [START_REF] Kasarda | Proteins and the amino acid composition of wheat fractions[END_REF]. Proteins eluted in fractions F3 and F4 have a Mr ranging from 1 × 10 4 to 15 × 10 3 and can be assigned as gliadin [START_REF] Singh | Use of sonication and size-exclusion high-performance liquid chromatography in the study of wheat flour proteins. I. Dissolution of total proteins in the absence of reducing agents[END_REF][START_REF] Kasarda | Proteins and the amino acid composition of wheat fractions[END_REF]. Fraction F5 consists mainly of metabolic proteins (albumins and globulins) and of R-gliadin. The coefficient of variation for the areas of the fractions, calculated from the triplicate experiments, did not exceed (5%.

Chromatogram Analysis. The SE-HPLC elution profiles were adjusted according to the protein content of the samples which was determined by the Dumas method (NA 2000, Fisons instruments). A Gaussian deconvolution of the elution profile was performed using PeakFit v4 software (Jandel Scientific Software). The AutoFit Peaks III option was employed, which is based on a Fourier domain procedure deconvolving a Gaussian instrument response function from the raw data. The Gaussian fitting of the elution profile of the untreated gluten sample, which resulted in the detection of 27 peaks, served as template. The setting parameters employed for the untreated gluten were applied during the deconvolution of the other profiles. The peak number and position were fixed and the peak width variation was limited to less than 5%, whereas the peak height was fully adjustable. Fitting was performed with a least-squares minimization method in order to achieve a correlation coefficient higher than 0.999.

Calculation of the Model. The numeric calculation of the kinetic model was performed with Matlab 5.3.0 software (Mathworks Inc.). The differential equation system was solved with a variable order Adams-Bashforth-Moulton PECE solver (Matlab function "ode113") suitable for solving nonstiff differential equation systems [START_REF] Shampine | Computer solution of ordinary differential equations: the initial Value problem[END_REF]. The reaction parameters were optimized by applying a least-squares minimization method (Matlab function "fmins") employing the Nelder-Mead simplex search algorithm [START_REF] Nelder | A simplex method for function minimization[END_REF][START_REF] Dennis | New computing enVironments: Microcomputers in large-scale computing[END_REF].

RESULTS AND DISCUSSION

Solubility Changes of Heat-Treated Gluten Protein: Fitting with a First-Order Rate Law. The soluble protein fraction of the heat-treated gluten/glycerol samples (at 70, 82, and 94 °C) was extracted using a sodium dodecyl sulfate (SDS)phosphate buffer, which dissolved about 85% of the total protein mass of a native gluten sample. Figure 1 shows the change in SE-HPLC profiles of the SDS-soluble gluten protein fraction (F s ) induced by a heat treatment at 82 °C. The elution profile is divided into five fractions. Fractions F1 and F2 correspond to glutenin polymers, fractions F3 and F4 can be assigned to gliadin proteins, and fraction F5 consists mainly of metabolic proteins (albumin and globulin) [START_REF] Singh | Use of sonication and size-exclusion high-performance liquid chromatography in the study of wheat flour proteins. I. Dissolution of total proteins in the absence of reducing agents[END_REF][START_REF] Kasarda | Proteins and the amino acid composition of wheat fractions[END_REF]. The well-defined resolution between gliadin and glutenin polymer is ensured thanks to the strong disruptive power of SDS that suppresses electrostatic and/ or hydrophobic interactions between the gluten proteins. An overall decrease in the total SE-HPLC area can be observed upon heating, indicating a progressive protein solubility loss. The elution profile with the largest area corresponds to the control sample, which was not heat-treated. The curve displaying the smallest area shows the SE-HPLC profile of the control sample treated at 120 °C for 35 min. Due to its severity, this treatment is likely to give the maximum solubility loss under the employed experimental conditions. F1 and F2 completely disappeared after this severe heat treatment, while fractions F3-F5 remained soluble in significant amounts (F3, 22%; F4, 23%; and F5, 48%). The total solubility loss added up to 83% of the SDS-soluble gluten protein fraction. The change of elution profiles of the sample series at 82 °C showed that fractions F1 and F2 were more susceptible to heat treatment than fractions F3-F5. The solubility of the different protein fractions, F1-F5, dropped after 420 min of heat treatment at 82 °C to 13%, 61%, 93%, and 92%, respectively.

Strecker and co-workers [START_REF] Strecker | Polymerization and mechanical degradation kinetics of gluten and glutenin at extruder melt-section temperatures and shear rates[END_REF] suggested that a step-grow polymerization mechanism accounted for the heat-induced aggregation of wheat gluten. The mechanism, which is appropriate for the radical-mediated synthesis of conventional polymers, describes the growth of polymer strands as a result of the sequential assembly of monomers. Step-growth polymerization typically results in a continuous shift of the size distribution profile toward larger species until their disappearance at the gel point [START_REF] Matyjaszewski | Preparation of hyperbranched polyacrylates by atom transfer radical polymerization. 2. Kinetics and mechanism of chain growth for the selfcondensing vinyl polymerization of 2-((2-bromopropionyl)oxy)ethyl acrylate[END_REF]. The change of the SE-HPLC profiles (Figure 1) did not support this hypothesis.

In contrast to the step-growth polymerization model, the solubility loss of glutenin polymers (fractions F1 and F2) seemed to proceed straightforward and all the more rapidly the larger the polymer size was (F1 before F2). We hypothesize that the direct conversion of soluble polymers to insoluble forms occurs through their covalent coupling with the already insoluble protein fraction. The cross-link is most likely a disulfide bond as the insoluble protein fraction was brought into solution after disulfide bond cleavage by DTE, as SDS buffer alone was not effective. Moreover, this is consistent with the well-known contribution of disulfide bonds to the heat-induced gluten polymerization [START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF].

In addition, we assume that the formation of a single disulfide bond between soluble and insoluble proteins is enough to ensure protein solubility loss. In consequence, the probability of coupling will rise with the polymer size because of the increasing number of cysteine residues per polymer chain.

To get further insight into the mechanism of gluten reactivity, we investigated the kinetics of the protein precipitation. Figure 2 shows the increase of the SDS-insoluble protein fraction with time at different temperatures (70, 82, and 94 °C). The experimental data (plain symbols, Figure 2) could be described with a first-order rate law (continuous line), which considered two protein classes of different reactivity, as gliadin is known to be more stable to heat treatment than glutenin [START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF][START_REF] Weegels | Temperature-induced changes of wheat products[END_REF]. Maximum protein solubility loss was set to 83.32% in accordance with the percentage of insoluble protein found in the heat-treated control sample (see above). A simple first-order rate law was already used by Pence et al. [START_REF] Pence | Heat denaturation of gluten[END_REF] and Becker and Sallans [START_REF] Becker | A study of the relation between time, temperature, moisture content, and loaf volume by the bromate formula in the heat treatment of wheat and flour[END_REF]. It is commonly applied to polymerization [START_REF] Litvinenko | General kinetic analysis and comparison of molecular weight distributions for various mechanisms of activity exchange in living polymerizations[END_REF][START_REF] Schmitt | Anionic polymerization of (meth)acrylates in the presence of tetraalkylammonium halide-trialkyl aluminum complexes in toluene. 3. Kinetic investigations on primary acrylates[END_REF] and to protein denaturation reactions [START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. I: First-order behavior[END_REF][START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. II: Biphasic and grace period behavior[END_REF].

The fitted rate constants showed that the temperature dependency of the reaction rate constants could be described with the Arrhenius law. The preliminary activation energy was calculated to 168 kJ'mol -1 .

Lencki et al. [START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. I: First-order behavior[END_REF][START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. II: Biphasic and grace period behavior[END_REF] showed that, with appropriate assumptions with regard to the relative magnitudes of various reaction rates, many complex denaturation pathways can display apparent first-order behavior. The use of a first-order rate law, even if considering two protein classes, was still an oversimplified view of the gluten protein polymerization. The results presented in Figure 1 showed evidence that glutenin (fractions F1 and F2) and gliadin (fractions F3 and F4) differed widely in their reactivity but also indicated that among glutenin polymers the larger proteins were more reactive.

Solubility Changes of Heat-Treated Gluten Protein: Fitting with a Mechanistic Model. To provide a more accurate interpretation of the observed rate constants, we separated the gluten denaturation in two different reaction steps: (i) reversible change in protein conformation and (ii) irreversible protein precipitation reaction through disulfide bonding.

The assumptions were coherent with the known biochemical changes during heat denaturation of gluten. Circular dichroism measurements on gliadin and low M r glutenin subunits heated to 80 °C revealed that changes in the secondary protein structure were reversible, when proteins were cooled back to room temperature [START_REF] Tatham | The conformation of wheat gluten proteins. The secondary structures and thermal stabilities of alpha-, beta-, gamma-, and omega-Gliadins[END_REF][START_REF] Tatham | The conformations of wheat gluten proteins, II, aggregated gliadins and low molecular weight subunits of glutenin[END_REF].

We describe the change in the protein conformation by where P s and P s * represent a SDS-soluble protein before and after this transformation, respectively, and k 1,d and k -1,d are the corresponding rate constants. As a first approximation, we neglect their possible dependence on the molecular weight of the protein. In particular, this should be applicable to very large proteins, such as the SDS-insoluble macropolymer P i : P s y \ z

k 1,d k -1,d P s * (1a)
Unfolding of gluten protein resulted in the exposition of hydrophobic groups and cysteine residues, usually buried in the core of the molecule [START_REF] Li | Effect of extrusion temperature on solubility and molecular weight distribution of wheat flour proteins[END_REF][START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF][START_REF] Weegels | Effects on gluten of heating at different moisture contents. II. Changes in physico-chemical properties and secondary structure[END_REF]. We suppose the cross-linking reaction between SDS buffer soluble protein and the SDSinsoluble macropolymer is responsible for the protein precipitation. We write this irreversible process as where p i * (in contrast to P i *) denotes merely a section (of yet unknown size) of the protein P i *. For the following we quantify its mass m pi* with the help of the relation m Ps* ) Rm pi* , where R is a freely adjustable parameter. In the same way p a * stands for a section of the aggregated protein and k 2,p is the corresponding rate constant. The protein precipitation may progress additionally through a P s *, becoming part of P a *, when reacting with it, i.e.

P a * will finally contain all of the insoluble protein mass. The reaction is driven by the rate constant k 3,p . The formation of covalent bonds between precipitated proteins may lock them into the denaturated state and thereby render complete refolding impossible. This hypothesis is supported by the observations of Schofield et al. [START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF]. In summary, the polymerization process of wheat gluten can be described by eqs 4-8, where the operator [ ] yields the actual mass of the given protein species (normalized with the total mass in the system). Equations 4-8 are in accordance with the mass balance given in eq 9:

where P t denotes the total amount of proteins in the system and P nr the percentage of nonreactive proteins. This percentage corresponds to the 16.68% of total gluten protein that remained soluble even after the severe heat treatment (120 °C for 35 min). Preliminary calculations showed that the temperature dependency of the reaction rate constants of protein denaturation (k 1,d , k -1,d ) and precipitation (k 2,p ,k 3,p ) followed the Arrhenius law:

A is the Arrhenius frequency factor, E a the activation energy, R the gas constant, and T the absolute reaction temperature.

Computing the rate constants directly with the Arrhenius law offers the advantage that the model constants can be optimized on the whole data set. Figure 3a shows that experimental and fitted data for F s changes at different experimental temperatures (70, 82,, and 94 °C). The corresponding fitted parameters are given in Table 2. Figure 3b shows a zoom on the time curves of the different reactive species at 94 °C. We observe that the amount of unfolded SDS-soluble protein P s * reached its maximum after 20 min. The maximum coincided with the almost total disappearance of P i and P i * and the slowing down of F s disappearance. The first reaction phase seemed to be governed by k 2,p (P i * reaction) and the second slower phase by k 3,p (P a * reaction). The large difference between rate constants k 2,p and k 3,p (frequency factors differing by 100; see Table 2) may be caused by two different effects. On one hand, gliadin is known to react more slowly than glutenin. The proportion between the two fractions would therefore shift with time toward an accumulation of gliadin in the soluble fraction. Consequently, rate constant k 2,p would express the precipitation rate of glutenin and k 3,p the precipitation rate of gliadin. This equals essentially the simplistic view adopted for our preliminary calculations and described in Figure 2. On the other hand, glutenin polymers (F1 and F2) summed up to about 29% of the total SDS buffer soluble protein mass, but F s loss during the first reaction phase accounted only for 14% of the total soluble protein and coincided with the disappearance of P i and P i * (ca. 16% of the total protein mass). This finding led us to the hypothesis that the reaction slowdown came from the depletion of P i *, which was more reactive than P a *. The reactivity differences may be explained by the following considerations. The natively linear SDS-soluble polymers may be progressively incorporated into a three-dimensional insoluble network, which is building up. The protein network formation upon heating was indicated by rheological investigations on extruded and mixed glutenglycerol samples [START_REF] Redl | Rheological and biochemical approaches describing changes in molecular structure of gluten proteins during extrusion[END_REF][START_REF] Redl | Rheological properties of gluten plasticized with glycerol: dependence on temperature, glycerol content and mixing conditions[END_REF]. The increasing cross-link density within the network might decrease the reaction rate by hindering the molecular mobility. From this point of view, the use of two precipitation rate constants (k 2,p and k 3,p ) offered a simplified description of a continuous development.

P i y \ z k 1,d k -1,d P i * (1b)
The computed activation energy for the precipitation reactions 2 and 3 was 172 kJ'mol -1 . The value agreed well with previous studies, which are summarized in Table 1. The activation energies shown in Table 1 were calculated with the help of simple first-order rate laws. Pence et al. [START_REF] Pence | Heat denaturation of gluten[END_REF] determined the activation energy directly from solubility loss experiments; the other teams measured the decrease in loaf volume of bread made from flour supplemented with heat-treated gluten. The different studies indicated that the reactivity of gluten was dependent on the water content of the sample [START_REF] Weegels | Effects on gluten of heating at different moisture contents. II. Changes in physico-chemical properties and secondary structure[END_REF][START_REF] Becker | A study of the relation between time, temperature, moisture content, and loaf volume by the bromate formula in the heat treatment of wheat and flour[END_REF][START_REF] Schreiber | Reaktionskinetische Untersuchungen u ¨ber den Einfluss der Trocknung auf die Qualita ¨t von Weizen[END_REF][START_REF] Kasarda | Proteins and the amino acid composition of wheat fractions[END_REF][START_REF] Shampine | Computer solution of ordinary differential equations: the initial Value problem[END_REF][START_REF] Nelder | A simplex method for function minimization[END_REF][START_REF] Dennis | New computing enVironments: Microcomputers in large-scale computing[END_REF][START_REF] Strecker | Polymerization and mechanical degradation kinetics of gluten and glutenin at extruder melt-section temperatures and shear rates[END_REF][START_REF] Matyjaszewski | Preparation of hyperbranched polyacrylates by atom transfer radical polymerization. 2. Kinetics and mechanism of chain growth for the selfcondensing vinyl polymerization of 2-((2-bromopropionyl)oxy)ethyl acrylate[END_REF][START_REF] Litvinenko | General kinetic analysis and comparison of molecular weight distributions for various mechanisms of activity exchange in living polymerizations[END_REF][START_REF] Schmitt | Anionic polymerization of (meth)acrylates in the presence of tetraalkylammonium halide-trialkyl aluminum complexes in toluene. 3. Kinetic investigations on primary acrylates[END_REF][START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. I: First-order behavior[END_REF][START_REF] Lencki | Effect of subunit dissociation, denaturation, aggregation, coagulation, and decomposition on enzyme inactivation kinetics. II: Biphasic and grace period behavior[END_REF][START_REF] Weegels | Temperature-induced changes of wheat products[END_REF]. The good concordance found here with the values of other groups despite the use of glycerol as an alternative to water might indicate that glycerol did not to affect the energy of activation of the gluten polymerization upon heating.

The optimization of the model constants resulted in two different activation energies of protein unfolding and refolding (Table 2), which were roughly five to ten times lower than the E a of precipitation. The energy barrier for unfolding was higher than the energy barrier for refolding, which reflects the fact that the native conformation of a protein corresponds to the conformation with the lowest energetic level. The equilibrium constant K 1,d of reactions 1a and 1b can be calculated with the help of the relation:

Using the van't Hoff equation we obtain the standard reaction enthalpy ∆ r H θ , which equals to 24.4 kJ'mol -1 . Lullien-Pellerin et al. [START_REF] Lullien-Pellerin | Reversible changes of the wheat γ46 gliadin conformation submitted to high pressure and temperatures[END_REF] investigated the conformational changes of γ46-gliadin under pressure. They calculated the free energy change of the conformational change of gliadin to be 38.4 kJ'mol -1 .

The standard reaction enthalpy calculated with the present model has thus the same order of magnitude as the experimentally determined Gibbs energy.

Sensitivity of Gluten Protein Species to Heat Treatment: Effect of Molecular Size (M r ). The use of two rate constants (k 2,p k 3,p ) resulted in a simplified but accurate description of the presumed effect of the setup of an insoluble protein network. However, the changes in the SE-HPLC elution profiles (Figure 1) indicated that the precipitation rates varied even within fractions F1 and F2. To investigate the effect of the protein size on the reaction kinetics, a Gaussian deconvolution of the SE-HPLC profiles was performed. Figure 4 shows the decomposition of the gluten control sample SE-HPLC elution profile into 27 individual protein species having molecular weights ranging from 1150000 to 3000. The protein solubility loss of each single peak was subsequently analyzed.

The solubility loss of gliadin monomers (F3 and F4; M r 50000-38000-19000) can be fitted successfully with a firstorder rate law. A striking exception was the gliadin monomer of M r 74000, which showed no significant solubility loss even after 5 h at 94 °C. However, this finding was consistent with the known behavior of ω-gliadin (M r 72000), which is claimed to be the only gluten protein that remains soluble even after severe heat treatments [START_REF] Schofield | The effect of heat on wheat gluten and the involvement of sulphydryldisulphide interchange reactions[END_REF]. Its heat stability is commonly attributed to its cysteine deficiency.

Protein peaks deconvolved in fraction F5 (M r e16000) showed steady solubility drop as well as transient increases. However, change of the total area of F5 could be modeled with a first-order rate law.

The protein species belonging to fractions F1 (M r 1150000-843000) and F2 (M r 676000-92000) displayed complex solubility drops, which could not be fitted without considering two levels of reactivity in each individual protein peak. The behavior is consistent with the main feature of the mechanistic model, which says that the deceleration of the precipitation rate due to steric hindrance caused by the concomitant network formation results in two apparent rate constants. The different rate constants may be attributed to the reactivity difference of P i * and P a *. The precipitation of gliadin monomers, which appears to be slower than the glutenin reaction, may essentially proceed through the reaction with P a * in the later phase, as P i * is already depleted. This may explain why first-order rate laws successfully model the solubility drops of gliadin. The mechanistic model was solved for each individual peak within fractions F1 and F2. The following suppositions were made. The precipitation activation energy of 172 kJ'mol -1 applies to all gluten proteins, which means that the rate of the disulfide-bonding reaction was independent for M r . The rate constants of the protein unfolding (k 1,d and k -1,d , reaction 1b) represent an average value over all M r , which can be applied to the unfolding reaction of the macropolymer. For the following, constants k 1,di and k -1,di denote the unfolding and refolding rate constants of an individual soluble protein. The start ratio between F s and F i was set to 29/16, which equals the ratio between the SDS-soluble protein belonging to fractions F1 and F2 (28.82%) and F i (15.64%). The assumption implies that (i) P i * consumption results only from the reaction with glutenin polymers (fractions F1 and F2) and (ii) P i * reacts randomly with glutenin polymers.

K 1,d ) k 1,d k -1,d (11)
d ln(K 1,d ) d(1/T) ) - ∆ r H θ R ( 12
)
Figure 5 shows typical fitted time curves obtained for the different reacting species. The protein solubility loss (plain symbol) is described accurately for both protein peaks respectively from F1 and F2 (Figure 5). We observe an initial P s * burst due to protein unfolding, so that the model curve corresponding to P s * overlaps with the curve corresponding to F s (Figure 5a). Then, P s * reacted essentially with P i * according to eq 2 until the P a * concentration approximated that of P i *. Subsequently, after the near depletion of P i *, protein solubility loss slowed, being now governed by eq 3.

The model constants fitted for all of the peaks obtained from fractions F1 and F2 are given in Table 3. The percent of the denatured and thereby activated protein fraction F * can be calculated according to where K 1,di is the unfolding equilibrium constant of an individual protein. Figure 6 shows the percentage of activated protein and the refolding rate constant versus their molecular weight. The percent of activated species increased gradually with protein size to 100% (calculated at 82 °C) above M r 373000. This behavior was mainly caused by the drop of the refolding rate constant. The renaturation of large polymer seems to be an anticooperative process. The increased proportion of the activated forms of large polymers may thus contribute to their higher precipitation rates compared to smaller molecules.

The Arrhenius frequency factor A 2,p appears to be exponentially related to the molecular weight of the polymeric chains.

Figure 7 shows the dependency of the precipitation Arrhenius factor on the molecular size of the proteins. The rise of the frequency factor expresses the enhanced probability of large molecules to react with insoluble partners (P i * and P a *). The hypothesis, assuming that the protein precipitation results from a See text for details. b Ea,D,i and A1,di: activation energy and frequency factor of the unfolding reaction. c Ea,R,i and A-1,di: activation energy and frequency factor of the refolding reaction. d A2,p and A3,p: frequency factors for the two precipitation reactions (Ea,D, see Table 2). e R 2 : correlation coefficient between the experimental data and the model calculation (n ) 30).

F* ) 100 - the formation of a single disulfide bond between soluble and insoluble protein species, would thus be indirectly confirmed. Large polymers including more cysteine residues would present higher probability to cross-link with an insoluble partner. Both effects, higher percentage of activated species and higher reaction probability for the largest molecules, might provide a valuable explication for the reactivity differences within the glutenin fractions observed in Figure 1.

100 1 + K 1,di (13)

CONCLUSION

A mechanistic model that fits the precipitation of wheat gluten protein was established and proved valid for the temperature range investigated. Due to the known biochemical changes involved during heat denaturation of gluten, we proposed that protein aggregation would involve two steps: first, a reversible change in protein conformation and, second, a precipitation reaction through disulfide bonding. The slowdown of the precipitation rate with the progress of the reaction was assigned to steric hindrance resulting from the formation of a threedimensional protein network in place of the linear native glutenin polymers.

The rise of the precipitation rates of SDS-soluble proteins with the increase of their molecular size supports the hypothesis that the protein solubility proceeds through a direct disulfide bonding between soluble and insoluble protein. The analysis of the reaction mechanism and its mathematical description may provide further insight in the formation of the gluten protein network upon thermosetting. Thereby, it could help to under-stand, at a molecular scale, the effects of temperature during gluten mixing and extrusion.

Figure 1 .

 1 Figure 1. Changes of SE-HPLC profiles of the SDS-soluble protein fraction during heat treatment at 82 °C. Sample heat treatment (top to bottom): 0 (control sample, highest F1), 25, 120, 300, 420, 1140, and 1440 min at 82 °C. The lowest curve (no F1 or F2) corresponds to a sample treated for 35 min at 120 °C.

Figure 2 .

 2 Figure 2. Increase of the percentage of the SDS-insoluble protein fraction due to heat treatment at different temperatures: 70 °C (9), 82 °C (b), and 94 °C (2). Lines were calculated with a first-order exponential rate law considering two reaction constants.

Figure 3 .

 3 Figure 3. Fit of the mechanistic model (continuous line) to the experimental data of the gluten protein solubility loss in SDS buffer. Panel a shows the experimental data at different temperatures: 70 °C (0), 82 °C (O), and 94 °C (4). Panel b shows the zoom on the model calculation of the intermediates at 94 °C: native soluble protein P s (-'-), native insoluble protein P i (-'-), unfolded soluble protein P s * (--), unfolded insoluble protein P i * (s), and aggregated protein P a * (--).

R 2 f 0. 9910 a

 9910 A1,d b (min -1 ) 71.3 × 10 5 A3,p e (min -1 ) 0.0985 × 10 22 A-1,d c (min -1 ) 0.00998 × 10 5 See text for details. b Ea,D and A1,d: activation energy and frequency factor of the unfolding reaction. c Ea,R and A-1,d: activation energy and frequency factor of the refolding reaction. d Ea,P: activation energy of both protein precipitation reactions. e A2,p and A3,p: frequency factors of the precipitation reactions. f R 2 : correlation coefficient between the experimental data and the model calculation (n ) 30).

Figure 4 .

 4 Figure 4. Gaussian deconvolution of the SE-HPLC profile of the SDS buffer soluble wheat gluten protein fraction of the control sample (no heat treatment).

Figure 5 .

 5 Figure 5. Fit of the mechanistic model (continuous line) to the solubility loss of the deconvolved protein species (O) at 94 °C. Panel a shows the solubility loss of the protein species M r 842800 and panel b the solubility loss of the protein species M r 250500. Lines correspond to the calculated intermediates: native soluble protein P s (-'-), native insoluble protein P i (-'-), unfolded soluble protein P s * (--), unfolded insoluble protein P i * (s), and aggregated protein P a * (--).

Figure 6 .

 6 Figure 6. Dependency of the percentage of activated protein (3, left scale) and the refolding constant k -1 (+, right scale) on the molecular weight of individual peaks at 82 °C.

Figure 7 .

 7 Figure 7. Dependency of the precipitation Arrhenius frequency factor A 2,p (1) on the molecular size.

Table 1 .

 1 Activation Energy (E a ) of the Heat-Induced Denaturation of Wheat Gluten Protein Determined with Several Indicators

			water	Ea
	indicator	sample	content (%)	(kJ'mol -1 )	ref
	protein solubility	gluten	64.0-67.0	183	21
	loaf volume	flour	8.0-19.9	270	22
		wheat	10.0	173	23
		wheat	20.0	164	23
		flour	21.6	137	38
		gluten	64.0-67.0	145	21

Table 2 .

 2 Fitted Model Parameters of the Heat-Induced Gluten Protein Precipitation a

	constant	value	constant	value
	Ea,D b (kJ'mol -1 ) Ea,R c (kJ'mol -1 )	53.9 29.5	Ea,P d (kJ'mol -1 ) A2,p e (min -1 )	172 11.7 × 10 22

Table 3 .

 3 Fitted Model Parameters of the Heat-Induced Precipitation of Wheat Gluten Proteins of Specific M r a

		A1,di (min -1 )	A-1,di (min -1 )	A2,p (min -1 )	A3,p (min -1 )	Ea,D,i	Ea,R,i
	Mr	(×10 -5 )	(×10 -5 )	(×10 -22 )	(×10 -22 )	(kJ'mol -1 )	(kJ'mol -1 )	R 2
	1151069	80.5	0.0100	177	3.84	46.3	34.3	0.9906
	1015636	55.1	0.00462	108	1.64	43.2	54.4	0.9669
	842773	55.5	0.00727	70.3	2.92	46.9	37.0	0.9923
	676309	59.8	0.00822	52.7	2.94	45.8	38.0	0.9948
	553093	61.5	0.00748	35.0	2.67	45.2	32.9	0.9954
	454051	75.6	0.0103	26.2	2.27	44.4	36.2	0.9955
	372757	84.5	0.00988	18.7	1.85	46.8	34.6	0.9955
	305808	82.4	0.0100	15.1	1.85	46.8	34.6	0.9955
	250482	58.5	0.0145	14.7	1.62	48.6	28.6	0.9954
	205109	59.2	0.0154	12.5	2.09	49.8	28.3	0.9952
	168262	62.9	0.0165	13.7	1.74	51.0	27.6	0.9944
	137719	58.2	0.159	12.4	2.33	52.2	27.6	0.9906
	112994	57.5	0.0162	12.2	2.21	52.7	26.8	0.9792

J. Agric. Food Chem., Vol. 50, No. 21, 2002 Domenek et al.

J. Agric. Food Chem., Vol. 50, No. 21, 2002 Domenek et al.

J. Agric. Food Chem., Vol. 50, No. 21, 2002 Domenek et al.

J. Agric. Food Chem., Vol. 50, No. 21, 2002 Domenek et al.


Sandra Domenek

Lothar Brendel

Marie-He ´le `ne Morel

Ste ´phane Guilbert

Swelling Behavior and Structural Characteristics of Wheat Gluten Polypeptide Films

Wheat gluten films were subjected to controlled thermomechanical treatments to increase the percentage of aggregated sodium dodecyl sulfate (SDS)-insoluble gluten protein, the aggregation reaction being disulfide bonding. The rheological properties of the films were measured under immersion in water, where wheat gluten films are stable and show only slight swelling. The equilibrium swelling of the gluten films in water decreased with the increase of the percentage of SDS-insoluble protein aggregates, and the frequency the independent shear modulus increased sharply with increasing percentage of SDS-insoluble aggregates. Both findings confirm that disulfide bonding between gluten proteins is the predominant cross-linking reaction in the system. A relationship between shear modulus and aggregated protein compatible with a power law (of exponent 3) suggests the existence of a protein network at a molecular scale. However, the classical Flory-Rehner model failed to describe the relationship between the plateau modulus and the gluten volume fraction (a very drastic increase, compatible with a power law of an exponent of about 14). This result shows that gluten cannot be described as an entangled polymer network. The interpretation of both relationships is a network of mesoscale particles which in turn have a fractal inner structure (with a fractal dimension close to 3).

Introduction

Wheat gluten is particularly interesting as a raw material for the development of new biomaterials based on renewable resources, because it is annually renewable and available in large quantities at competitive prices. Additionally, wheat gluten has interesting technological features among which are insolubility in water and viscoelasticity. The unique viscoelastic properties of wheat gluten are the subject of a great research effort. Most studies relate to the field of food chemistry, because gluten plays a key role in the breadmaking properties of wheat flour dough. Despite all these efforts, the structure of the gluten polymer system and the mechanisms of its viscoelasticity are still debated.

From a biochemical point of view, gluten is a protein mixture, containing a polymeric protein fraction (glutenin) and a monomeric one (gliadin). The polymeric protein fraction consists of polypeptides linked together with disulfide bonds, forming the so-called glutenin macropolymer with M r ranging from 150 000 to more than 2 000 000. The monomeric protein fraction is formed by single polypeptide chains (M r ranging from 15 000 to 150 000), which interact with the glutenin macropolymer "backbone" through secondary bonds. 1,2 The rheological investigation of plasticized gluten showed that it behaved like a transient network. [3][4][5] Furthermore, the rheological investigation of wheat flour dough showed that only the glutenin macropolymer contributes to the elastic properties at large deformation, while gliadin contributes to the viscous behavior. [6][7][8] Several models of the structural basis of this rheological behavior have been proposed. A widely used approach is to consider the gluten system as a polymer network that is stabilized by various interactions, such as covalent bonds, noncovalent interactions (hydrogen bonds, hydrophobic interactions), and entanglements (to list all of them). According to the "loop and train" model, 9 the gluten system is mainly stabilized by hydrogen bonds. In the dry state, those bonds are predominately formed between different protein chains. Upon hydratation, the protein-protein interactions (trains) become little by little replaced with protein-water interactions, which cause local disaggregating of the chains termed "loops". When the system is stretched, first the loops are deformed and then the trains are pulled apart. 9 Another model consists of describing the gluten system as an entangled polymer network. 8,10,11 In such a network, physical entanglements exist that add resistance to flow. For a long polymer chain, there may be many of such points acting thus as transient cross-links. The extensional properties of gluten would be in consequence determined by two processes; first, the breaking of secondary bonds and, second, slippage of chains through entanglements. 11 A quite different structure of the gluten system was suggested very recently. It was proposed that gluten is organized as a transient particle network. [START_REF] Hamer | Wheat Gluten -Proceedings of the 7th International Workshop Gluten[END_REF]13 With the help of confocal laser scanning microscopy, a particle structure was revealed in wheat gluten gels in 1.5% sodium dodecyl sulfate (SDS). This structural organization may reflect the structure as it was originally formed in the wheat endosperm. 14,15 Technological modifications, such as dough mixing, cooking, or extrusion, imply temperature treatment of the material. It is known that temperature treatments cause gluten proteins to aggregate as a result of disulfide bond interchange reactions. [16][17][18][19][20] A sound parameter to measure the aggregation reaction is the extractability of wheat gluten in SDS. 4,19,20 Above a temperature of ∼40 °C, an increase of the shear modulus of the gluten network can be observed, 3,5 which is related to the formation of interchain disulfide bonds. 5 The aim of this study is to examine the quantitative relationship between gluten aggregation, shear modulus, and equilibrium swelling in the light of the two structural models just described (molecular network vs particle network).

The experimental approach consists of the fabrication of gluten film samples with different technological processes resulting in a wide range of protein extractabilities. The samples are subsequently characterized by the measurement of the frequency-independent shear modulus and of the equilibrium swelling.

The analysis of the experimental data in light of the structural model considering gluten to be a cross-linked polymer network will be done with the help of the Flory-Rehner theory. [START_REF] Flory | Principles of polymer chemistry[END_REF] In this treatment, the swollen polymer is considered an elastic solution. The extent of swelling represents a competition between two forces. The free energy of mixing will cause the solvent to penetrate and try to dilute the polymer phase. As the polymer chains in the cross-linked polymer network begin to elongate under the swelling action of the solvent, they generate an elastic retracting force in opposition to this deformation. The volumetric swelling reaches steady state (equilibrium swelling) when both forces balance each other. To account for the change of the chemical potential of the solvent accompanying the formation of the real solution, the interaction parameter χ has to be introduced, which in turn depends on the temperature and composition of the system. Following these assumptions, the equilibrium swelling of a cross-linked polymer network is a direct function of the cross-linking density in the network, which is linearly related to the frequency-independent shear modulus. [START_REF] Ferry | Viscoelastic properties of polymers[END_REF] In consequence, swelling measurements are a simple, low-cost method for the determination of the network crosslinking degree.

The analysis of the experimental data in light of the structural model considering the presence of a particle network will be done with the help of a weak-link fractal scaling theory. [START_REF] Marangoni | [END_REF] According to the theory, the elastic modulus of a colloidal aggregate network is influenced by the amount and spatial distribution of network mass and by particle properties, including size, shape, rigidity, and particleparticle interactions. In the weak-link rheological regime, flocs are mechanically stronger than the links between them. The Young modulus scales with the change of internal energy per floc-floc bond as a result of deformation multiplied by the volume fraction of the polymer in the fractal aggregate network. The scaling relation allows, thus, conclusions to be drawn on the spatial distribution of the aggregates within the network.

Materials and Methods

Vital wheat gluten was provided by Amylum (Aalst, Belgium). Protein, starch, lipid, and ash contents were 76.5, 11.8, 5.0, and 0.8% of dry mass, respectively. The moisture content was 7.2% (wet mass basis). Chemicals were obtained from Sigma in p.a. quality unless stated differently.

Gluten Film Preparation. To produce pressed glutenwater films, vital wheat gluten was equilibrated for 4 days at 100% relative humidity. Thereafter, the average water content, which was determined by drying the samples overnight at 105 °C, was found to be 19.40 ( 0.11% (wet mass basis). The wet gluten powder (3 g) was hot-molded under a heating press (Techmo, Nazelles-Negron, France) between two Teflon sheets for 10 min at 150 bar and different press temperatures (70, 80, 100, 120, and 150 °C). The resulting films were immediately cooled to 0 °C and stored at -28 °C in a commercial freezer. Samples fabricated by this process are labeled with "eq" (equilibrated) and the corresponding press temperature.

For the fabrication of mixed and pressed gluten-water films, vital wheat gluten (39.89 g) was mixed with water (10.11 g) in a two-blade counter-rotating batch mixer, type Plasticorder 50 W (Brabender, Duisburg, Germany) turning at 3:2 differential speed. The mixing chamber (50 cm 3 ) was thermoregulated at 20 °C with a cryostat. Samples (50 g) were mixed for 5 min at 30 rpm. The water content of the resulting blend was 22.49 ( 2.20%. The blend was subsequently pressed for 10 min at different temperatures (70, 80, 100, 120, and 150 °C, respectively). The film samples were cooled and stored as described previously. Samples fabricated by this process are labeled with "mi" (mixed) and the corresponding press temperature.

To produce pressed gluten-glycerol blends, vital wheat gluten was hand-mixed with glycerol (35% glycerol, Fluka Chemie, Buchs, Switzerland) in a mortar for 3 min and subsequently rested for 30 min. The blend (3 g) was pressed under the heating press at 150 bar for various times at different press temperatures (70, 80, 100, and 120 °C). The resulting films were immediately cooled and stored as described previously. The film samples' labels contain the plasticizer name, the fabrication temperature, and the press time. Therefore, the label "gly70-120" stands for at glutenglycerol film pressed at 70 °C for 120 min.

Gluten Protein Solubility. The gluten samples were analyzed according to Domenek et al.. 20 The ground glutenstarch blend (160 mg) was agitated for 80 min at 60 °C in 20 mL of 0.1 mol/L sodium phosphate buffer (pH 6.9) containing 1% SDS and subsequently centrifuged (Beckmann Avanti J30-I, 37 000 g, 30 min). The supernatant contained the SDS-soluble protein fraction (F s ). The SDS-insoluble protein fraction (F i ) was extracted with 5 mL of SDSphosphate buffer containing 20 mmol/L dithioerythriol (DTE) for 60 min at 60 °C, and the tip was sonicated for 3 min to bring the gluten proteins into solution. The supernatant (centrifugation 37 000 g, 30 min) was mixed 1:1 with SDSphosphate buffer containing 40 mmol/L iodoacetamide (IAM). IAM alkylated the thiol groups, which prevented their subsequent oxidation. Both extracts (20 µL), F s and F i , were submitted to size-exlusion HPLC (SE-HPLC) fractionation. SE-HPLC analysis was carried out on a TSK-G 4000 SWXL (TosoHaas) size exclusion analytical column (7.5 × 300 mm) preceded by a TSK 3000-SW XL (TosoHaas) guard column (7.5 × 75 mm). The columns were eluted at room temperature with a 0.1 mol/L sodium phosphate buffer (pH 6.9) containing 0.1% SDS. The flow rate was 0.7 mL/min, and proteins were detected at 214 nm. The column was calibrated with protein standards according to Dachkevitch and Autran. 24 In the following, F i , is expressed in percent of the total protein quantity, which was estimated from the sum of the F s and F i areas (once corrected for their different solid-to-solvent ratios).

Swelling Measurement. For the determination of the swelling of the gluten films, dry samples were immersed in deionized water (containing 0.1% NaN 3 to avoid microbial growth) at a constant temperature (25 °C) for 24 h (according to standard method ASTMD2765-95, method C). To weight the swollen samples, excess water was carefully removed with a paper towel. The samples were subsequently dried over P 2 O 5 at room temperature until constant weight. For the calculation of the sample swelling, the dry weight measured after swelling and drying was used to take into account the sample weight loss due to the solubility of glycerol in water. The swell ratio q is defined as where V 2 denotes the polymer volume fraction, W d is the sample dry weight (g) after swelling, W s denotes the swollen sample weight (g), and K is the ratio of the densities (g/mL) of the polymer to the solvent ) 1.2/0.997; density values from Redl et al.). 10 Each determination was repeated at least four times.

Rheological Investigation of the Cross-Link Density. Tensile experiments on gluten films were conducted with a Dynamic Mechanical Thermal Analyzer MK III (DMTA, Rheometric Scientific, Piscataway, NJ). To standardize the plasticizer content, measurements were performed on samples immersed in deionized water, whereby the plateau modulus can be obtained at ambient temperature using a medium frequency range. The maximum deformation applied was 0.05% (within the domain of a linear elastic response) under a constant static force of 2 g, and the frequency ranged from 1.59 to 0.0159 Hz. Samples were pre-equilibrated in water prior to measurement. The pre-equilibration times had no significant influence on the measured moduli for all the types of films, a behavior which is most likely due to the film geometry (thickness between 150 and 300 µm, length 20 mm, width 5 mm). Therefore, the pre-equilibration of gluten-water films was shortened from 24 h (equals swelling time) to 2 h. The pre-equilibration time of gluten-glycerol films was between 10 min and 2 h. The investigation of the glycerol loss during the pre-equilibration phase revealed that glycerol was completely dissolved after 15 min. Each experiment (irrespective of the equilibration time) was repeated at least four times. In Figure 1 are shown typical results for the average storage modulus of the three types of film samples (eq80, mi70, and gly120-35). The storage and loss moduli were independent of the frequency at 22.5 °C

(Figure 1), demonstrating the occurrence of the rubbery plateau. [START_REF] Ferry | Viscoelastic properties of polymers[END_REF] As a result of the profound weight loss (35%), the gluten-glycerol films were extremely fragile, a problem that was amplified for lightly cross-linked gluten-glycerol films. As a consequence, either such samples were torn apart during the frequency sweep experiment or the force, which is measured in response to the deformation, was close to the detector limit, which caused nonreproducible and scattered data. Because all the samples that allowed the frequency sweep experiment to be carried out showed the plateau zone in the same frequency range (Figure 1), the value of the modulus was approximated by the Young modulus (E) measured at a given frequency within the plateau zone. E was determined with the DMTA (Rheometric Scientific, Piscataway, NJ) by unidirectional elongation experiments (strain rate 0.001 s -1 ) on immersed samples at room temperature (22.5 °C). Experiments were repeated at least five times. The Young modulus was computed from the slope of the initial linear increase in engineering stress caused by the strain increase. The points at 0.001 Hz shown in Figure 1 correspond to the so-measured Young modulus. In the following, we will only use the shear modulus (G) of the film samples, which was computed from the modulus measured in tensile experiments (E) by virtue of the relation which applies to isotropic incompressible solids. [START_REF] Ferry | Viscoelastic properties of polymers[END_REF]

Results and Discussion

Relationship between Gluten Solubility, Shear Modulus, and Film Swelling. Wheat gluten films show a good stability under immersion in water. The experimental results of the sample series, prepared according to three different protocols, are given in Table 1. The percentage of SDSinsoluble protein (F i ) rises with the severity of the heat

E ) 3G

(2)

q ) 1 V 2 ) W d + |W s -W d |K W d (1)
treatment from 13.63 to 87.22%. We observe that the value for the native gluten is quite high, which is explained by the industrial provenance of the gluten. Interestingly, the highest F i value is obtained for the sample treated at 120 °C (eq120, 87.22%) and not for the sample treated at 150 °C (eq150, 75.58%). Obviously, above a certain severity degree of heat treatment the material begins to degrade. The hypothesis is supported by the observation of an important browning reaction. It had already been shown with kinetic studies that the maximum F i , attainable with the present experimental setup, is about 90%. 20 The Young moduli are similar to the moduli measured on hydrated elastin (at 28-45% H 2 O), a well-studied elastomeric protein, 25 and at low F i (<35%), similar to the Young modulus reported for chemically crosslinked glutenin subunits measured in water (∼1.1 × 10 2 kPa; strain rate not given). 26 The range of the swelling values is quite restricted. The maximum swelling of vital gluten (polymer volume fraction V 2 ) 0.315) corresponds to the water holding capacity of native gluten (ca. 2.8 g of water for 1 g of gluten). The minimum swelling value obtained was observed for sample eq120 (V 2 ) 0.612) and corresponded to a water uptake of 0.83 g/g gluten. Gluten materials show, thus, a quite satisfying form stability when brought into contact with water. Let's first investigate the relationship between the biochemical parameter F i and the structural parameters equilibrium modulus (G) and polymer volume fraction (V 2 ). Figure 2 shows V 2 as a function of F i , where we observe the previously described large change of F i and the restricted range of V 2 . Furthermore, we see that the film swelling decreases significantly with more severe heat-treatments and that there is a unique and quite satisfying correlation between both parameters irrespective of the film preparation procedure. Figure 3 shows the relationship between the Young modulus E (and thus G) and F i , where we observe that G rises over 3 orders of magnitude with increasing F i . This proves increasing network connectivity within the film samples. In our case, the cross-links may correspond to different types of interactions, because the gluten protein network is supposed to be stabilized by covalent (disulfide) bonds as well as by noncovalent interactions; the latter being hydrogen bonds and hydrophobic interactions. It is known that the F i rise is caused by the formation of disulfide bonds between different gluten polypeptides, 2,6,7,16,[START_REF] Weegels | In Interactions: The keys to cereal quality[END_REF][START_REF] Kasarda | [END_REF][29] which is indirectly proven by the analytical method used. Actually, a reducing agent of disulfide bonds (DTE) is required to bring the SDS-insoluble proteins (F i ) into solution. SDS alone is insufficient because it has a strong disrupting effect only on noncovalent interactions. A single continuous relationship was found, between the parameters F i and G, indicating the predominant influence of covalent bonds on the rheological a Preparation conditions: pressed gluten-water films "eq", mixed and pressed gluten-water films "mi", and pressed gluten-glycerol films "gly". b Fi: biochemically determined content in aggregated protein. c E: equilibrium Young modulus at 0.001 Hz. d v2: gluten volume fraction; the values inside the parenthesis denote the standard deviation of the measurement. behavior. The single relationship notwithstanding, the film fabrication method shows furthermore that differences in the physical treatment or in the type of the plasticizer do apparently not change the structure of the protein system. Furthermore, the strong variation of G when changing F i shows that either the contribution of the noncovalent bonds is negligible or increases in parallel with the covalent crosslinks. The power law relationship between F i and G was found to result in Such behavior is known from the field of gelation, which in turn is a percolation problem. Above a certain critical concentration of activated cross-links (N c ), a macroscopic cluster appears. Its mass fraction, which is essentially our quantity F i , is found to vary linearly with the distance from N c , which is the normalized cross-links number above the critical value (N -N c )/N c . 30 The system's shear modulus G, on the other hand, varies like the cube of this distance. 30 Taken together, this predicts G to vary as F i 3 , which is in good agreement with eq 3. Note that the critical cross-link number will be reached at F i ) 0.

Gluten Network Structure. Both structural parameters, G and V 2 , were well-correlated to F i , which raises the question of the theoretical basis of the relationship between G and V 2 . The relationship in the case of our data is given in Figure 4, which shows a steep increase of the modulus with increasing polymer volume fraction. In the field of rubber elasticity, widely accepted and commonly used for entangled (and cross-linked) polymers, a classical model exists to formalize this relationship, the Flory-Rehner theory of rubber elasticity. [START_REF] Flory | Principles of polymer chemistry[END_REF] According to this theory, the density of cross-links (G/RT) and, thus, the equilibrium shear modulus G, [START_REF] Flory | Principles of polymer chemistry[END_REF]31 is related to the polymer volume fraction V 2 by where φ 1 is the solvent's molar volume (here water with φ 1 ) 18.0182 mL/mol) and the interaction parameter χ describes the energy gain (χ < 0) or penalty (χ > 0) of a monomer surrounded by the solvent. However, as shown in Figure 4, no correspondence is achieved by implementing eq 5 with a constant χ.

The possibility of a nonconstant χ has already been considered in the original work, [START_REF] Flory | Principles of polymer chemistry[END_REF] and it is not uncommon to fit the function χ(V 2 ) (obtained by solving eq 4 for χ) by a polynomial (typically of degree 2). [31][32][33] The corresponding fit to our data yields with an, at first sight stunningly, excellent correlation coefficient of 0.9992. However, as already indicated by Figure 4, we deal with a discrepancy of a shear modulus G that is several orders of magnitude lower (for a given value of φ 1 and range for V 2 ) than typical values given by the Flory-Rehner theory, and a comparison with Figure 5 shows that the latter permits these very low values only in a very narrow region in the vicinity of the line G ) 0, beyond which the system becomes thermodynamically unstable. As shown in Figure 5, our data practically coincide with this line; that is, the obtained result χ(V 2 ) bears little physical meaning.

An alternative approach would be the introduction of an effective molar volume φ j 1 and an effective relative solvent volume V j 2 , which corresponds to rescaling the axes in the plot G versus V 2 . Figure 6 shows this approach in a double logarithmic plot, where rescaling reduces to shifting the curve. Obviously, no agreement between data and modeled curves can be obtained, whatever the rescaling of the axes. Irrespective of the actual V 2 dependence of G, it can be clearly seen from Figure 6 that the variation of G over 3 orders of magnitude cannot be a generic result of the Flory-Rehner theory [which is able to produce such variations only at its very limits, and for that it needs an extremely well-tuned interaction "parameter-function" χ(V 2 )]. Therefore, something other than a gradual change of rubber elasticity must be going on. Actually, the data are fitted rather well by a power law, albeit with an unusually large exponent of about 14, that is, Another answer is that of a particle network. Marangoni [START_REF] Marangoni | [END_REF] derived a relationship between the shear modulus and the volume fraction in a particle network where the mesoscopic particles are formed by microscopic entities (i.e., proteins in our case) in a fractal manner:

G ∝ F i 3 (3) G RT ) 1 φ 1 ln(1 -V 2 ) + V 2 + χV 2 2 V 2 /2 -V 2 1/3 (4)
where D is the fractal dimension of the packing within the particles and 3 is the Euclidian dimension in which the particles themselves pack. Accordingly, an exponent of about 14 would correspond to a fractal dimension of the gluten particles of D ≈ 2.93, which is close to the range of dimensions observed for fractal flocs in different types of foodstuff (2.37-2.88). [START_REF] Marangoni | [END_REF] There are other hints that support this interpretation: Hamer and van Vliet [START_REF] Hamer | Wheat Gluten -Proceedings of the 7th International Workshop Gluten[END_REF] proposed that the gluten network is organized as a particle network, and recently their research team showed such a structure for the gluten macropolymer in solution in SDS 14 using confocal scanning laser microscopy. The authors supposed this structure to reflect the initial structure of gluten particles deposed in the wheat endosperm. Although Don et al. 15 showed that the particle structure was quite stable even during the mixing process, the observation of an artifact due to the use of SDS cannot be ruled out completely. On the other hand, a hint for a fractal inner structure of particles was found by means of small angle neutron scattering and light scattering by Popineau (Yves Popineau, personal communication) and at least the existence of a particle network is discussed by Lefebvre et al.. 13 The rather high value of the fractal dimension might indicate a quite "dense packing" inside the particles, but we have also to keep in mind that the cause of the higher volume fraction (i.e., the greater number of cross-links) can have a simultaneous effect on the structures inside the particles, something that is not contained in the theory. [START_REF] Marangoni | [END_REF] A quantitative hint to this complicated interdependence is given by the relationship between F i and V 2 (Figure 2), obtained from combining eqs 3 and 6 as On the other hand, it should be admitted that the quality and the span of the data is not sufficient to actually proVe a power law exponent of 14 for the algebraic dependence of G on V 2 (already due to their scattering, a lower exponent of about 11 cannot be ruled out), but it indicates the possibility of the suggested scenario, resulting in such a strong variation of G.

Conclusion

We have investigated the wheat gluten network structure upon immersion in water. Both the equilibrium shear modulus and the equilibrium swelling were well-correlated to the biochemically determined percentage of aggregated proteins in gluten, showing the high importance of disulfide bonds for the gluten protein network structure. The single relationship between aggregated proteins and the modulus or swelling notwithstanding the sample fabrication conditions shows that the network formed is independent from the thermomechanical treatment of gluten. The failure of the Flory-Rehner model to describe the swelling properties of gluten shows clearly that the protein network, although elastic, cannot be modeled with the classical theories of rubber elasticity. Entropy as the primary driving force for the elasticity of gluten is, therefore, quite questionable. In terms of the Flory-Rehner model, the network strands are not completely floppy (i.e., free from free energy contributions) as assumed by this meanfield model, but rather rigid, not being able to give rise to a significant swelling, despite their comparatively low moduli. This implies further that wheat gluten cannot be considered as an entangled network. Instead, the very strong rise of the modulus with increasing polymer volume fraction indicates a structure being organized as a dense network of mesoscale particles with an inner irregular, fractal structure. This mesoscale image strengthens the suggestion that the network organization reflects the gluten structure as deposited during the growth of the wheat endosperm. 14 How the cross-link structure acts in detail as confining "laces" to yield the gluten's high volume fraction and in how far it influences the particles' inner structure directly, giving rise to the observed scaling exponents, remain to be investigated. V 2 ∝ F i 3/14 (8)

Figure 1 .

 1 Figure 1. Mechanical spectrum of the storage modulus E′ for gluten film samples prepared with varying methods. The value at 0.001 Hz corresponds to the measure of the Young modulus in simple extension. The measurement was conducted on water-immersed samples. Preparation conditions: Gluten-glycerol film pressed at 120 °C for 35 min ([), gluten-water film mixed for 5 min and subsequently pressed at 70 °C for 10 min (9), and gluten-water film pressed from wet gluten powder at 80 °C for 10 min (2).

Figure 2 .

 2 Figure 2. Polymer volume fraction (v2) as a function of the percentage of aggregated proteins (Fi). Data show a good agreement with a power law of exponent 0.23 (solid line). Symbols signify the different sample preparation methods: eq (b), mi (9), and gly ([).

Figure 3 .

 3 Figure 3. Shear modulus (G) as a function of the percentage of aggregated proteins (Fi). Data are aligned on a power law of exponent 3 (solid line). Sample preparation methods: eq (b), mi (9), and gly ([).

Figure 4 .

 4 Figure 4. Comparison between the Flory-Rehner theory for two constant interaction parameters (using the water's φ1 ) 18.0182 mL/ mol) and the experimental data.

Figure 5 .

 5 Figure5. Logarithmic contour plot of g ≡ φ1G/(RT) for 10 different values: log(g) ) -∞, -3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, and 1 (from left to right). The region above g ) 0, marking a thermodynamically unstable system, defines a border of the theory's applicability. Our data (eq 4 solved for χ, open circles) are found in the immediate vicinity of the limiting curve G ) 0, because of the small shear modulus, that is, G/(RT) , 1/φ1.

Figure 6 .

 6 Figure 6. System's shear modulus in a double logarithmic plot compared to (rescaled by an unphysical factor of 1800 with respect to the molar volume of water) results of the Flory-Rehner theory for χ ) 0.5 and χ ) 0.7. The exponent of the indicated power law amounts to 14.

Table 1 .

 1 Biochemical and Rheological Properties of Gluten Films Fabricated under Different Conditions

	sample a	Fi b (%)	E c (kPa)	v2 d
	vital	13.63 (0.52)	n.d.	0.315
	eq70	27.48 (0.41)	2.60 (0.10) × 10 1	0.436 (0.012)
	eq80	38.94 (0.58)	1.81 (0.16) × 10 2	0.485 (0.008)
	eq90	46.79 (0.70)	4.30 (0.74) × 10 2	0.521 (0.009)
	eq100	68.32 (1.02)	1.90 (0.21) × 10 3	0.572 (0.004)
	eq120	87.22 (1.31)	2.99 (0.23) × 10 3	0.612 (0.002)
	eq150	75.58 (1.13)	3.69 (0.24) × 10 3	0.589 (0.004)
	mi70	37.29 (0.56)	4.53 (0.42) × 10 2	0.520 (0.003)
	mi80	53.53 (0.80)	1.02 (0.26) × 10 3	0.546 (0.004)
	mi90	61.72 (0.93)	1.15 (0.011) × 10 3	0.564 (0.002)
	mi100	80.89 (1.21)	2.83 (0.46) × 10 3	0.579 (0.004)
	mi120	86.97 (1.30)	2.55 (0.22) × 10 3	0.582 (0.027)
	mi150	69.66 (1.04)	1.72 (0.24) × 10 3	0.532 (0.029)
	gly100-2	21.52 (0.33)	7.56 (2.09) × 10 1	0.454 (0.004)
	gly70-300	27.94 (0.07)	8.69 (0.61) × 10 1	0.389 (0.010)
	gly80-80	29.66 (0.33)	9.67 (0.54) × 10 1	0.465 (0.010)
	gly80-240	32.50 (1.00)	1.51 (0.19) × 10 2	0.468 (0.015)
	gly80-140.	33.22 (0.51)	1.35 (0.32) × 10 2	0.461 (0.010)
	gly100-10	34.86 (1.61)	9.95 (2.23) × 10 1	0.481 (0.010)
	gly100-25	42.75 (0.06)	1.64 (0.30) × 10 2	0.484 (0.021)
	gly120-2	45.75 (0.34)	2.74 (0.38) × 10 2	0.485 (0.022)
	gly100-60	53.91 (0.69)	2.39 (0.32) × 10 2	0.499 (0.020)
	gly120-20	78.61 (2.60)	7.53 (0.063) × 10 2	0.544 (0.20)
	gly120-35	83.31 (2.40)	9.91 (0.50) × 10 2	0.553 (0.005)

10.1021/bm034499b CCC: $27.50 © 2004 American Chemical Society Published on Web 03/10/2004 Downloaded via INRAE on December 21, 2022 at 15:10:39 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Biomacromolecules, Vol. 5, No. 3, 2004 Domenek et al.

(solid line). Sample preparation methods: eq (b), mi(9), and gly ([).

Biomacromolecules, Vol. 5, No. 3, 2004 Domenek et al.

Biomacromolecules, Vol. 5, No. 3, 2004 Domenek et al.

Acknowledgment. The authors would like to thank J. Lefebvre for providing useful comments on the subject and valuable suggestions on the manuscript


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  Thermosetting of wheat protein based bioplastics : modeling of mechanism and material properties Sandra Domenek, Marie Helene M. H. Morel, Andreas Redl, Stephane Guilbert To cite this version: Sandra Domenek, Marie Helene M. H. Morel, Andreas Redl, Stephane Guilbert. Thermosetting of wheat protein based bioplastics : modeling of mechanism and material properties. 7. World Conference on Biodegradable Polymer and Plastics, Jun 2002, Pisa, Italy. Verlag Wiley-Blackwell, Macromolecular Symposia, 197, 2003, 10.1002/masy.200350717. hal-02763439

© 2003 WILEY-VCH Verlag GmbH & KGaA, Weinheim DOI: 10.1002/masy.200350717 182 © 2003 WILEY-VCH Verlag GmbH & KGaA, Weinheim

© 2003 WILEY-VCH Verlag GmbH & KGaA, Weinheim