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Flow of gluten with tunable protein composition: from stress undershoot to stress overshoot and strain hardening

Understanding the origin of the unique rheological properties of wheat gluten, the protein fraction of wheat grain, is crucial in bread-making processes and questions scientists since polymeric glutenins. To better understand the respective role of the different classes of proteins in the supramolecular structure of gluten and its link to the material properties, we investigate here concentrated dispersions of gluten proteins in water with a fixed total protein concentration but variable composition in gliadin and glutenin. Linear viscoelasticity measurements show a gradual increase of the viscosity of the samples as the glutenin mass content increases from 7 to 66%. While the gliadin-rich samples are microphase-separated viscous fluids, homogeneous and transparent pre-gel and gels are obtained with the replacement of gliadin by glutenin. To unravel the flow properties of the gluten samples, we perform shear start-up experiments at different shear-rates. In accordance with the linear viscoelastic signature, three classes of behaviour are evidenced depending on the protein composition. As samples get depleted in gliadin and enriched in glutenin, distinctive features are measured: (i) viscosity undershoot suggesting droplet elongation for microphase-separated dispersions, (ii) stress overshoot and partial structural relaxation for near-critical pre-gels, and (iii) strain hardening and flow instabilities of gels. We discuss the experimental results by analogy with the behaviour of model systems, including viscoelastic emulsions, branched polymer melts and critical gels, and provide a consistent physical picture of the supramolecular features of the three classes of protein dispersions.

dispersions, (ii) stress overshoot and partial structural relaxation for near-critical pre-gels, and (iii) strain hardening and flow instabilities of gels. We discuss the experimental results by analogy with the behaviour of model systems, including viscoelastic emulsions, branched polymer melts and critical gels, and provide a consistent physical picture of the supramolecular features of the three classes of protein dispersions.

Introduction:
Gluten extracted from wheat flour is one of the most important commercial plant proteins isolate. It is used to improve the baking quality of cereal products consumed daily by many human beings through the consumption of bread, pasta, and biscuits among others 1, 2 . The exceptional mechanical properties of the gluten network, is essential for the growth of bubbles in bread dough and renders gluten very attractive as a food texture additive. Mechanical properties of gluten have been investigated for a long time, but gluten complexity in terms of composition and solubility makes studies difficult 3 . The gluten network comprises two main classes of proteins; the polymeric glutenins that have the ability to form inter-and intradisulfide bonds and the monomeric gliadins that participate in the network through hydrogen bonding exclusively 4,5 . Monomeric gliadins can be isolated from gluten extracted from wheat, whereas glutenin-rich extracts are never devoid of gliadins. Glutenin polymers display a very wide range of molecular weight M w (from 100 to 1000 kg/mol) 1 , and are considered as being soluble in acidic solutions. Gliadins on the other hand have M w comprised between 25 and 60 kg/mol and are soluble in aqueous ethanol (with an ethanol volume fraction between 50 and 70%). All gluten proteins are considered as being water-insoluble at neutral pH.
Nevertheless, protein mixtures comprising gliadins and glutenins dispersed in pure water at a protein concentration above 30% w/w form homogeneous viscoelastic networks. Unveiling the peculiar contribution of each of the main classes of gluten proteins to the mechanical properties of gluten network and wheat dough in relation to their structural features is of a great importance but scientifically challenging, especially because of gluten polymorphism and polydispersity, and solubility issues 6 .
Different protocols have been used in previous studies to characterize the rheology of gluten gels [7][8][9][10][11][12][13] . Of particular interest, Ng et al. 12,13 investigated a native gluten dough containing 63% of water by weight through different protocols in the linear and nonlinear regime (including small and large amplitude oscillatory shear, step strain relaxation, creep, start-up of steady shear and uniaxial flow). The originality of this work consisted in the successful modification of the well-known power law relaxation model of critical gels 14 to describe the linear and nonlinear viscoelasticity responses of the gluten gel when investigated using several rheological protocols. Strain softening of gluten was measured by creep when the samples were submitted to sufficiently large stresses 10 , and by large amplitude oscillatory shear (LAOS) tests at moderate strains. Strain softening was modelled using a non-linear network destruction term that reflects the reduction in network connectivity as proteins are increasingly stretched. In addition, at larger strains (of the order of =6), strain hardening was evidenced before sample rupture due to the finite extensibility of the network 13 . Although evidencing some of the remarkable mechanical properties of gluten, previous studies fail to provide a complete mechanistic understanding of the rheology of gluten, in part because they remain limited in terms of samples and lack a proper control of the protein composition and biochemistry, and of the resultant microstructure. To overcome these limitations, we have developed protocols to produce model gluten extracts with a tunable proportion of gliadins and glutenins 15 . We first focused on the structure and the linear viscoelasticity response of model glutens comprising comparable amounts of gliadin and glutenin, as in native gluten, in a blend of water and ethanol [16][17][18][19] . In a 50/50 v/v water/ethanol mixture, homogenous transparent samples are obtained for a large range of protein composition and concentration 19,20 . The samples display a disordered polymeric structure and their linear viscoelasticity obeys the framework of the near critical gel theory 21 . For near critical gels, the self-similarity of the clusters that eventually percolate at a critical point results in criticality in the linear viscoelastic response 22,23 : the complex moduli and the relaxation times vary as a power law of the frequency, with a critical exponent related to the fractal dimension of the stress bearing network 24 . As consequence, following the near critical gel theory, we have demonstrated that the linear rheology of model gluten gels with comparable amounts of gliadin and glutenin but different protein concentrations and sample ages can be described by a unique master curve by applying a time-cure-concentration superposition principle 14,17,22,23,25,26 . The spontaneous gelation of samples was attributed to the rearrangement of both intermolecular hydrogen and disulphide bonds 17 . More recently, we have successfully extended the timecure-concentration principle to include solvent quality using water/ethanol mixtures with variable compositions from pure water to 60% v/v ethanol 27 . An important conclusion of this study is that the general framework to rationalize the structural and mechanical properties of model gluten protein extracts dispersed in a water/ethanol mixture, a good solvent for gluten proteins, also holds with pure water, which is usually considered as a bad solvent for gluten, thus extending our investigations towards food applications.
As for the impact of protein composition on rheology, it is generally accepted that gluten viscosity is related to gliadins, whereas elasticity and stiffness are associated to glutenins 3,28 .
Crude fractions of gliadin and glutenin were investigated in the linear regime but using a denaturing solvent (3M urea) that significantly modifies interactions, which are crucial for the gluten network 29 . Recently, Large amplitude oscillatory shear (LAOS) experiments performed on these fractions once dispersed in water showed that the nonlinear response of gliadin samples is essentially viscous and frequency-dependent, whereas the glutenin-rich fraction displays a stiffer response independent of frequency, thus confirming the overall physical understanding of the role of two main classes of proteins in gluten 30 . To better unveil the role of the two classes of proteins and their interplay in the rheology of gluten, we have studied the effect of gluten compositions on the structure and linear viscoelasticity of gluten gels using water/ethanol 50/50 %v/v as a solvent 20 . Thanks to an asymmetrical flow field flow fractionation technique, we have shown that dilute solutions are mainly composed of monomeric and polymeric species when the glutenin content is low, whereas additional supramolecular objects of hundred nanometers, namely assemblies, are identified in increasing proportion when the samples get enriched in glutenin (mass fraction of glutenin>25% ) 31 . Interestingly, these assemblies are composed of both high molecular weight glutenin polymers and gliadins 18,31 , demonstrating interactions between gliadins and glutenins. Moreover, the emergence of these assemblies in dilute regime coincides with the emergence of the viscoelasticity in semi-dilute samples of equivalent protein composition 20 .
Assemblies can thus be identified as playing a key role in the onset of gelation, and might be considered as precursors of the self-similar clusters in the framework of near critical gel model. Following these studies, this manuscript aims at exploring the nonlinear viscoelastic properties of model gluten samples with controlled composition, using the start-up shear protocol.
Shear start-up protocol is classically used to monitor the transient response of different model systems, such as polymer melts and solutions 32 , colloidal gels and glasses 33 , worm-like micelles solutions 34 and emulsions 35 . A common phenomenology emerges from these studies. At low shear rates, a monotonic increase of the stress with time goes towards a plateau value, corresponding to a steady state. At higher shear rates or by varying the molecular characteristics of the system (concentration, volume fraction, molecular weight, particle size, etc ...), the stress passes through an overshoot, before reaching its steady state.
The general physics behind the transient behaviour consists in a competition between the shear rate and the relevant relaxation rate in the system. When the shear rate is slower compared to the sample characteristic relaxation rate, no overshoot is observed because the structure has time to relax the stress within the shear time. However, in the regime where the shear rate is higher than the sample relaxation rate, a stress overshoot is measured. The position and the amplitude of the overshoot depends on the maximum deformation allowed by the structure and its relaxation at a given shear rate. The steady state regime on the other hand reflects the competition between the stress induced by the flow and the stress relaxed by the sample through structural changes. Despite the fact that the general physics that drives the overshoot is the same, the structural origin differs from a system to another, and questioning the physical origin of stress overshoots is still gathering a lot of attention 36 . In addition, for some systems and in specific conditions (such as high shear rate, confinement…), a stress undershoot was observed; however its origin remain not totally understood so far 35, 37-40 . In the present paper, we provide a systematic investigation of model gluten samples prepared in water at a fixed protein concentration but with different compositions in terms of glutenin content. We use the shear start-up protocol that allows one to study the samples with different shear rates and, in the same time, reach a high cumulative deformation up to 2000. The manuscript is organised as follows. We first describe the materials and the techniques. We then present the experimental data in the linear and in the non-linear regimes that evidence three classes of rheological behaviours depending on the protein composition. We finally discuss results in comparison with different model systems to propose a structural view of samples.

Materials:
We investigate gluten samples with a fixed total protein concentration but different proportions of monomeric gliadin and polymeric glutenin. Six samples with mass fraction of glutenin (GLU) ranging from 7 to 66% are investigated. The extraction of the gluten powder with controlled and tuneable compositions is detailed elsewhere 15  Samples are prepared by dispersing the required mass of gluten extract in the appropriate volume of deionized pure water to obtain a fixed concentration of 500 g/L for all samples using a specific volume value of gluten proteins,  = 0.76 mL/g. The deionized water contains 0.1% g/g of sodium azide (NaN 3 ) to prevent microbial growth. Dispersion of the protein extracts in the solvent is achieved through hand-mixing using a stainless-steel spatula for 3 min. The dispersions are then kept to rest for 5 days at room temperature, prior to measurements, in order to obtain homogenous samples. The relatively long rest period allows an efficient hydration of the proteins and a complete relaxation of the stresses induced by the mixing step. Transparent samples are obtained for GLU≥50%, while turbid samples, macroscopically stable over several weeks, are obtained for GLU=7% and 23% (Fig. 1). Light microscopy imaging of the turbid samples reveals the presence of micrometric spherical objects, suggesting a liquid-liquid phase separation between a phase enriched in protein and one depleted in proteins. This observation is consistent with a previous study which indicate that gliadins become insoluble in distilled water for concentration higher than 15% wt 41 .      Figure 2a and tan=G"/G' is plotted in Figure 2b. The error bars on the data for the sample with GLU=52% represent the standard deviation as computed based on a dozen of measurements performed on independent samples prepared and measured in the same conditions. The relative error on G' and G" ranges between 30 % and 40 % and the relative error on tan  is lower (8 to 20%).

Results:
In addition, note here that the data of G' for the two samples depleted in glutenin (GLU=7 and 23%) are not plotted at low frequencies because measurements are not reliable (weak signal due to the rheometer torque limits). We observe that the samples present qualitative and quantitative different features as their protein composition varies. First, the higher the content in glutenin the stronger the viscoelasticity of the gluten sample is. The strengthening of the viscoelasticity is evidenced by the fact that the shear viscoelastic moduli, G' and G'', systematically increase when GLU increases (Fig. 2a). The frequency dependence of the LVE spectra also changes significantly with the protein composition. On the one hand, for the two samples with the lowest amounts of glutenin (GLU=7% and GLU=23%), the loss modulus, G'', is significantly higher than the storage modulus, G'. The loss modulus exhibits a power law dependence with the frequency with an exponent close to 1 (G''~ ω) at low frequency, which is the signature of a completely flowing fluid. The evolution of the elastic modulus, G', is more complex with a faster increase with frequency at high frequency and a lower one at low frequency, with a cross-over between the two regimes around 10 rad/s, and 2 rad/s, for the sample with GLU=7%, and GLU=23%, respectively. The viscoelastic spectra of the two  We compute the transient viscosity, η + = + , where ̇ is the imposed shear rate, and + is the measured stress, as a function of time, t, where the origin of time is the time at which the shear rate is applied. Figure 3 shows the time evolution of η + at different shear rates, in the The error bars represent the standard deviation. The relative error ( ~ 40%) iscomparable to the relative error computed from the repetition of the LVE measurements (as described above, see Fig. 2a) and is presumably due to a slight sample ageing. For samples with GLU=57 and 66%, the linear envelope is obtained from LVE data measured before the NLVE protocol, because the NLVE protocol significantly modifies the LVE signature of these samples.
Interestingly, for all samples, we find consistency between the complex viscosity and the transient viscosity at short times.  At long time, a steady viscosity, η steady , is reached for samples with GLU=7, 23, 50 and 52%, although some irregularities (slight decrease at high shear rate or some erratic oscillations) are measured. In that case the steady viscosity value reported in figure 4 is averaged over the most stable range. Figure 4 shows the steady viscosity η steady , as a function of the shear rate, γ̇, together with the complex viscosity η* as a function of the frequency, ω. Both   The two samples with the lowest amounts of glutenin (GLU=7% and 23%) show a stress undershoot before reaching a steady state (Fig. 3a,b). We define the amplitude of the stress undershoot as d U = steady state at long time, respectively. We find that the data sets for the two samples superimpose nicely and that decreases continuously as the shear rate increases, from 1 down to 0.8 (Fig. 6a). The time of occurrence of the undershoot, , defined as the time corresponding to the minimum stress σ Min , is plotted in Figure 6b as a function of the shear rate γ̇. For both samples, t U is measured to be inversely proportional to the shear rate, indicating an occurrence of the undershoot at a constant strain of γ U = 15 ± 3 for GLU=7% and γ U = 9.3 ± 1.6 for GLU=23%. The two samples comprising intermediate amounts of glutenin show a stress overshoot (Fig.   3c,d). The amplitude of the overshoot, σ Max /σ Steady , with σ Steady the stress in the steady state, is plotted as a function of the shear rate in Figure 7 for the two samples with GLU=50 and 52%. In the two cases, we find a weak increase of σ Max /σ Steady with the shear rate (at most by a factor of 2 when the shear rate varies by two orders of magnitude). Nevertheless, significantly different results are obtained for the two samples, with a stress overshoot systematically higher for the sample with the largest amount of glutenin and a stronger dependence with the shear rate.

Discussion:
We have identified three families of samples based on their distinctive linear and non-linear viscoelasticity features. Below we discuss sequentially the three families, whose structures are schematically sketched in Figure 7:  44 . The lower moduli measured at high frequency for the sample with GLU=7% suggests that the terminal relaxation of the continuous phase is shorter than that for the sample with GLU=23%.
However, a deeper and more quantitative analysis would require a detailed knowledge of several parameters (including e.g. the surface tension between the two phases, the size distribution of the droplets of dispersed phases, the composition and rheological properties of the continuous and dispersed phases) that are still unknown for the gluten samples.
Interestingly, the complex viscosity of these samples is nearly constant in the range of frequencies investigated, with a value η * ~10 Pa s. This numerical value is of the order of a pure gliadin sample at the same concentration prepared in an ethanol/water mixture which is a good solvent of these proteins 48 . However, our results are significantly different from those obtained by Kokini et al. 30 , who measured aqueous gliadin-rich samples with no mention of phase separation and found essentially elastic samples (G'>G'') over a wide range of frequencies. The discrepancy could be due to the presence of large molecular weight glutenin polymers in their crude fraction. On the other hand, during a shear start-up experiment, we measure that the stress increases with time up to a maximum value, , which grows with the applied shear rate, while the strain at the maximum stress, , is constant. We find ≅ 1 (Fig. 5b), which may suggest that the stress transiently relaxes when the flow is strong enough to deform droplets by a distance equivalent to their size (100%). Interestingly, and uniquely for this first family of samples, the stress is relaxed through a pronounced undershoot before it reaches a steady state (Fig. 3a,b). The amplitude of the undershoot is larger and the time of its occurrence is faster as the shear rate increases (Fig. 6). Viscosity undershoots have been previously observed experimentally and numerically for a few polymeric systems 38,[49][50][51][52][53] and anisotropic colloid dispersions due to tumbling relaxation of anisotropic objects 40 . Interestingly, similar stress undershoots, in terms of amplitude and strain of occurrence, were also measured 39 and predicted in immiscible polymer melts 54 .
These systems were treated as mixtures of two immiscible viscoelastic liquids whose interfacial area evolves under flow. The maximum stress was related to a slight deformation and orientation of the dispersed phase in the direction of the flow, while the stress undershoot was associated to an increase of the interfacial area due to the stretching of the dispersed phase 54 . In view of the biphasic nature of gliadin rich samples, their nonlinear behaviour could be rationalized considering a similar mechanism. Note that the increase of the amount of glutenin in the samples, from 7% to 23%, weakly affects the linear viscoelasticity but does not significantly impact the characteristics of the undershoot.
The second family corresponds to pre-gel samples, which are characterized by a balanced proportion of gliadin and glutenin (GLU=50 and 52%). Linear viscoelasticity measurements show G''>G' in the whole accessible frequency window, and tan = G"/G'>1 decreases with frequency. However, a terminal regime, which would be characterized by G'~ 2 and G"~ at low frequency is not reached, testifying for a non-fully relaxed state in the time scale probed experimentally. Accordingly, a shear-thinning behaviour is observed (Fig. 4), with a zeroshear viscosity not reached in the range of frequencies probed, giving evidence for their complex non-Newtonian behaviour. In addition, tan tends to reach a frequency-independent value at high frequency, as expected for a near-critical pre-gel state. Indeed, the critical state of a gel is reached when G'~ G''~   , and consequently tan  is frequency-independent 21, 23 .
The sample with GLU=52% is closer to its gel point than the sample with GLU=50%, as supported by higher shear moduli and a weaker evolution of tan  with frequency.
Microscopically, near critical pre-gel samples are characterized by power law distributions of cluster size (and hence of associated relaxation times) (Fig. 8), which shift towards higher values approaching the critical gel at percolation. Interestingly, in our experiments, very weak differences in terms of composition (GLU=50 and 52%) lead to a significant evolution of the viscoelastic properties of the two samples (Figs. 2, 4). This finding can be associated to a state very close to the critical gel for these two samples, where a divergence of viscosity is expected. On the other hand, shear start-up experiments reveal an overshoot of the transient viscosity + with a clear softening (+ remaining below the linear envelope) before reaching a steady state (Fig. 3c,d). In polymeric systems, the occurrence of an overshoot is observed only when the applied shear rate is faster than the inverse of the terminal relaxation time. Our findings suggest that the terminal relaxation time is longer than 10s for the samples with GLU=50 and 52%. Furthermore, we find that the stress overshoot, Max , is significantly higher for the sample closer to the critical gel point (GLU=52%) (Fig. 5a), whereas the maximum strain, , is independent of the shear rate and the GLU content. Note though that is significantly higher for this second family ( ≈ 10) as compared to the flowing samples of the first family ( ≈ 1) (Fig. 5b). It indicates that the energy stored by the samples before their partial relaxation during shear increases with the GLU content due to the sample slower dynamics. It also corroborates with the ratio Max σ Steady significantly higher for the sample with GLU=52% than for the one with GLU=50% (Fig. 7), which indicates that, as the amount of GLU increases, clusters relax partially less stress, while being still deformed by the flow. Interestingly, high maximum strain values, such as those measured here for pre-gel samples ( ≅ 10), are usually observed in branched polymeric systems 32,[55][56][57] . This is consistent with the structural view of near-critical pre gels 22 and percolation 58 on the one hand, and with recent experimental evidences for the branched structure of gluten pre-gels and gels with GLU=45% in water/ethanol solvent on the other hand 16 . This structural view of the pre-gel gluten samples is also consistent with the large size distribution of objects measured in the dilute regime using a fractionation technique that evidenced the joint presence of monomeric proteins, polymeric proteins and supramolecular assemblies with a branched structure when GLU ≥ 30% 31 . Finally, the good overlap of steady and complex viscosities within the experimental error (Fig. 3) validates the Cox-Merz rule 47 , which discriminates any relevant irreversible change of samples due to the solicitation in the nonlinear regime.
The third family encompasses the two samples with the largest amounts of glutenin (GLU = 57% and GLU = 66%). These samples are in a gel state. Their linear viscoelasticity is characterized by G'>G'' (tan  <1) with tan  that increases with the frequency and moves toward a constant value at high frequency as expected for a near-critical post-gel state 21,22 .
Clearly, for these samples, the gel point is exceeded and a stress bearing network is formed, through the percolation of the clusters (Fig. 8). The structure is thought to form a permanent gel that does not relax at rest, as suggested by the fact that the elastic modulus tends to reach a plateau at low frequency. According to rubber elasticity theory, '~− 3 , where is the network mesh size 59 . Assuming a same pre-factor for the two samples, we expect the mesh size to decrease by 20%, when GLU increases from 57 to 66% showing a clear impact of glutenin in building the elastic network. During shear start up tests, these samples strongly resist flow because of their solid-like viscoelasticity. Measurement issues are observed, such as gap opening and sample expulsion, as one forces the gels to flow. In future work, smaller geometries combined with cone and partitioned plate technology should be used for these samples to delay such instabilities, and more reliably characterize the strain hardening evidenced for the sample GLU = 57% at 0.1 s -1 (Fig. 3e). The hardening is understood as the ability of the flow to induce a nonlinear stretching of the stress bearing chains due to the finite extensibility of the network strand [60][61][62] . The large value of the deformation at which strainhardening is measured (around 10) is consistent with a loosely connected polymer-like gel sample.
Overall, the evolution of the gluten response to shear start-up, from pre-gel samples to postgel samples is qualitatively similar to the response described for ionomers with different degrees of sulfonation: pre-gel samples show strain softening whereas strain hardening is measured for samples close to the gel point, and above the gel point samples fracture 63 . Shear start-up experiments on native gluten are scarce. Noticeable studies include the works described in references 11,13 but which are limited to one shear rate and one sample composition. Interestingly these previous results are consistent with those obtained for the post-gel samples of the present study, in terms of strain hardening, maximum stress and maximum strain values. In addition, the authors also mentioned problems related to sample ejection from the rheometer. In native gluten the glutenin content (around 50%) is lower than in the present post-gel samples (GLU≥57%), and the fact that native gluten behaves as gel is presumably related to the presence of very high molecular weight glutenin polymers, which are insoluble in aqueous ethanol, and thus are absent in the model gluten extracts investigated in this work. Indeed, the extraction procedure used to extract model gluten with tunable composition discards these ethanol-water insoluble proteins 15 . Our unique protocol allows the formulation of well-controlled glutenin-rich samples and the detailed investigation of the role of glutenin in the mechanical and flow properties of gluten.

Conclusion:
We have investigated the linear and nonlinear viscoelasticity of model gluten samples with a wide range of protein composition but a fixed total protein concentration (500g/L). Gliadinrich samples form micro-phase separated dispersions in water whose rheological response is