Gérard Branlard
email: gerard.branlard@gmail.com

Angelina D'orlando
email: angelina.dorlando@inrae.fr

Ayesha Tahir
email: ayesha.tahir2007@gmail.com

Marc Schmutz
email: marc.schmutz@ics-cnrs.unistra.fr

Larbi Rhazi
email: larbi.rhazi@unilasalle.fr

Annie Faye
email: annie.faye@inrae.fr

Thierry Aussenac
email: thierry.aussenac@unilasalle.fr

Polymer conformation: genetic and environmental factors associated with this characteristic of glutenin in wheat grain

Keywords: Genetic and environmental factors, Glutenin alleles, Glutenin polymer characteristics, Gluten sensitivity, Higher temperature, NCGS, Polymer radius, Polymer counting simulation, Wheat

Original photos of the glutenin polymers (GPs) are shown.

Thousands of billions GPs are synthetized in each wheat grain.

GPs become bigger, more compact and less reticulated with higher temperature.

Introduction

Wheat dough has been used for more than two millenniums to make leavened bread. Due to the unique properties of the gluten network formed during dough mixing, it can retain gas. Grain storage proteins (GSPs), i.e., monomeric gliadins and polymeric glutenins, are well known to confer viscosity and elasticity, respectively, to wheat gluten [START_REF] Finney | Fractionating and reconstituting techniques as tools in wheat flour research[END_REF]; these properties are known to be largely influenced by wheat-growing conditions. The effect of nitrogen uptake and, more recently, the temperature occurring during GSP accumulation have been studied using both transcriptomics tools [START_REF] Perrotta | Analysis of mRNAs from ripening wheat seeds: the effect of high temperature[END_REF][START_REF] Hurkman | Effect of temperature on expression of genes encoding enzymes for starch biosynthesis in developing wheat endosperm[END_REF][START_REF] Altenbach | Genes encoding the PR-4 protein wheatwin are devel,opmentally regulated in wheat grains and respond to high temperature during grain fill[END_REF] and proteomics approaches [START_REF] Skylas | Heat shock of wheat during grain filling: proteins associated with heat-tolerance[END_REF][START_REF] Majoul | Proteomic analysis of the effect of heat stress on hexaploid wheat grain: characterization of heat-responsive proteins from total endosperm[END_REF][START_REF] Majoul | Characterization of heat-responsive proteins from nonprolamins fraction[END_REF][START_REF] Majoul-Haddad | Effect of short heat shocks applied during grain development on wheat (Triticum aestivum L.) grain proteome[END_REF][START_REF] Vensel | Developmental changes in the metabolic protein profiles of wheat endosperm[END_REF][START_REF] Hurkman | Effect of high temperature on albumin and Analysis of mRNAs from ripening wheat seeds: the effect of high temperature. globulin accumulation in the endosperm proteome of the developing wheat grain[END_REF][START_REF] Laino | Comparative proteome analysis of metabolic proteins from seeds of durum wheat (cv. Svevo) subjected to heat stress[END_REF]. High temperatures shorten the effective grain filling period and may significantly increase the protein concentration because of the more dramatic effect on starch than on protein accumulation (Blumenthal et al., 1991a(Blumenthal et al., , 1991b;;[START_REF] Corbellini | Effect of heat shock during grain filling on protein composition and technological quality of wheats[END_REF][START_REF] Altenbach | Temperature, water and fertilizer influence the timing of key events during grain development in a US spring wheat[END_REF][START_REF] Triboï | Environmentally-induced changes of protein composition for developing grains of wheat are related to changes in total protein content[END_REF]. For example, in response to heat shock (38°C for 4 h on for 4 consecutive days during grain filling), the volume occupied by the A starch granules compared to the normal control increased from 71 to 78.9%, whereas the B and C granules decreased from 27.8 to 20.1% and 1.2 to 1.0%, respectively, in mature grain [START_REF] Branlard | Coping with wheat quality in a changing environment -Proteomics evidence for stress caused by environmental changes[END_REF]. The synthesis of individual wheat GSPs, gliadins and glutenin, was not drastically affected by high temperature as opposed to glutenin polymers, analysed for the first time in only 6 of our 11 locations [START_REF] Branlard | Coping with wheat quality in a changing environment -Proteomics evidence for stress caused by environmental changes[END_REF].

Since the 1970s, numerous genetic and molecular GSP studies have been devoted to helping breeders better respond to the demand raised by technologists for flour use. Many advances in GSPs, which are the major gluten components and their influence on wheat quality, have recently been gathered in an international collaborative book (Igrejas et al., 2020). Moreover, a better understanding of the developing endosperm, particularly in stressed conditions resulting from its hypoxic status, came from studies carried out in maize [START_REF] Young | Programmed cell death during endosperm development[END_REF][START_REF] Rolletschek | Positional cues for the starch/lipid balance in maize kernels and resource partitioning to the embryo[END_REF][START_REF] Gayral | Responses to Hypoxia and Endoplasmic Reticulum Stress Discriminate the Development of Vitreous and Floury Endosperms of Conventional Maize (Zea mays) Inbred Lines[END_REF], rice [START_REF] Xu | Dynamic proteomic analysis reveals a switch between central carbon metabolism and alcoholic fermentation in rice filling grains[END_REF] and wheat [START_REF] Zhen | Dynamic metabolome profiling reveals significant metabolic changes during grain development of bread wheat (Triticum aestivum L.)[END_REF]. However, the technological abilities of wheat grain to make bread, biscuit or cookies for T. aestivum cultivars and pasta and semolina for T. durum cultivars are only a part of the final wheat quality, which must respond to consumer needs.

Numerous approaches have been carried out to improve the nutritional and health value of wheat.

These studies include the improvement of the lysine content, an essential amino acid [START_REF] Shewry | Do "ancient" wheat species differ from modern bread wheat in their contents of bioactive components[END_REF], mineral and vitamin content mostly in the aleurone layer [START_REF] Meziani | Wheat aleurone layer: A site enriched with nutrients and bioactive molecules with potential nutritional opportunities for breeding[END_REF], and healthy arabinoxylan and oligosaccharides content and the removal or reduction of numerous allergenic compounds, such as alpha amylase / trypsin inhibitors and the numerous epitopes in proteins involved in specific pathologies, including celiac disease (prevalence 1%) and baker asthma (first disease associated with a professional activity in Europe). These important requirements, which have received recent updates [START_REF] Brouns | Adverse reactions to wheat or wheat components[END_REF], will not be developed in the present study, focusing on gluten polymer conformation. Non-celiac gluten-related disorders, called non-celiac gluten sensitivity (NCGS), are a public concern [START_REF] Catissi | Non-celiac gluten sensitivity: The new frontier of gluten related disorders[END_REF]. Numerous NCGS symptoms are expressed by an increasing number of people, and their prevalence has increased, primarily attributable to gluten.

No specific sequences of GSP-i.e., either from gliadins or from glutenin subunits of high or low molecular weight (HMW-GS and LMW-GS, respectively), which could be characteristics of immune response-were significantly associated with NCGS [START_REF] Scherf | Gluten and wheat sensitivities -An overview[END_REF]. Consequently, several alternative hypotheses have been investigated to explain NCGSs [START_REF] Catissi | Non-celiac gluten sensitivity: The new frontier of gluten related disorders[END_REF][START_REF] Scherf | Gluten and wheat sensitivities -An overview[END_REF], such as the -amylase and trypsin inhibitors (ATIs), and fermentable oligo, di-, and monosaccharides and polyols (FODMAPS) [START_REF] Catassi | Gluten Sensitivity[END_REF] for review, see [START_REF] Brouns | Adverse reactions to wheat or wheat components[END_REF]. The reorientation of these hypotheses was probably due to the absence of dedicated tools used for glutenin polymer characterisation. When wheat varieties are studied for human health, the amount of insoluble polymers or unextractable polymeric protein (%UPP) is usually obtained after a two-step extraction using SDS, followed by sonication through SE-HPLC [START_REF] Gupta | Biochemical basis of flour properties in bread wheats. I-Effects of variation in the quantity and size distribution of polymeric proteins[END_REF][START_REF] Johansson | Wheat gluten polymer structures: The impact of genotype, environment and processing on their functionality in various applications[END_REF].

However, the maximum size sieving offered by chromatography columns is around 1 × 10 6 Da. The use of Asymmetric Flow Field Flow Fractionation Multi-Angular Laser Light Scattering (A4F-MALLS) allows for a deeper analysis of the polymer characteristics whose mass exceeds 10 7 Da [START_REF] Wahlund | Size characterization of wheat proteins, particularly glutenin, by asymmetrical flow field-flow fractionation[END_REF][START_REF] Lemelin | Impact of cultivar and environment on size characteristics of wheat proteins using asymmetrical flow field-flow fractionation and multiangle laser light scattering[END_REF]. A first attempt to measure the conformation of wheat polymers was performed using size exclusion chromatography (SEC-MALLS), revealing a conformation close to the theoretical compact sphere. Analytical difficulties (pH and SEC columns) have prevented the use of SEC-MALLS in routine analysis [START_REF] Mendichi | Molecular weight, size distribution and conformation of Glutenin from different wheat cultivars by SEC-MALL[END_REF]. A4F provides several characteristics of chemical macromolecules that can be very useful for understanding their technological properties, as well as their functional properties. Using A4F, the polymer mass (Mw), gyration radius (Rw), and polydispersity index (PI) of polymers were measured over a four-year, multi-location wheat trial in France, involving 11 locations and 192 cultivars, which revealed that Rw (MW and PI) increased linearly (exponentially) with the average mean temperature, registered hourly, of the last month of the wheat cycle [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. The highly significant increases of 189, 242 and 434% of the Mw, Rw and PI, respectively, were caused by a 3.5°C increase between trial locations. These findings attract more consideration on glutenin polymer characteristics. To this end, an update on the structure and assembly of glutenin polymers (GPs) has recently been proposed [START_REF] Shewry | Wheat glutenin polymers 1. structure, assembly and properties[END_REF]. Variations in GP characteristics, particularly regarding the response to global warming, require investigation. In addition to these 3 characteristics, little is known about the shape of glutenin polymers. What are the environmental and genetic influences on the conformation of the GPs; are they compact, partly reticulated or highly depolymerised with a fibrillar shape? Multi-angular laser light scattering computes the conformation (Conf) values of the polymers. Classic analyses of chemical polymers usually report the following classification of the polymer shape as a function of the Conf values, also called slope. For example, a coefficient < 0.30 indicates a compact spherical shape; a slope value between 0.5 and 0.6 corresponds to a polymer with random coils [START_REF] Wyatt | Light scattering and the absolute characterization of macromolecules[END_REF]. These characteristics corresponding to the physical A4F measures of the polymers were also compared to the visual observation using two specific techniques: atomic force microscopy (AFM) previously used in H20/D20 medium [START_REF] Haward | Force spectroscopy of an elastic peptide: Effect of D2O and temperature on persistence length[END_REF] and cryo-transmission electron microscopy (Cryo-TEM). These studies revealed, for the first time, glutenin polymers in lyophilised conditions and in solution, respectively. In addition, based on the masses of polymers measured by A4F and assuming their Gaussian distribution in wheat samples, the number of polymers was computed for wheat grains with different kernel weights and protein concentrations.

The polymer conformation (Conf) is the fourth parameter of the polymers, which was analysed using A4F on the same multi-location samples, allowing us to test factors associated with phenotypic variations of Conf. The influences of genetic factors (the 14 and 17 alleles encoding HMW-GS and LMW-GS, respectively) and environmental factors, such as rainfall and temperature, registered daily during the last three months of the wheat cycle were studied. The values of the Conf parameter may impact the degradation and hydrolysis of glutenin polymers. Consequently, the identification of glutenin alleles associated with the conformation of polymers is of prime importance and will be particularly discussed regarding possible further studies dealing with consumer health.

Materials and Methods

Multi-location trials

The material used in the present study was described in previous multi-location trials carried out for four years in France between 2004 and 2010 involving 11 locations and 192 hexaploid wheat cultivars originating from France, Germany, the Netherlands and the UK. [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. A total of 885 samples were analysed for several physical and technological characteristics [1000-kernel weight (TKW), test weight (TW), protein concentration (PC) and grain hardness (GH)]. A total of 14 alleles of HMW-GS encoded at the three Glu-1 loci and 17 alleles of LMW-GS encoded at the three Glu-3 loci were identified using SDS-Page. The 11 locations of the wheat trials and the frequencies of the 31 alleles are reported in Supplemental Tables S1 -S2, respectively [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. The cumulated daily temperature per month and daily water precipitation per month for May, June and July of the four experimental years are also given in Figures S1 -S2 of the previous publication.

Determination of the polymer's conformation

The glutenin polymers were extracted from whole meal flour and separated using the A4F-MALLS technique, as previously described for multi-location trials [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. The following three parameters of the glutenin polymers were determined: Mw = the average weight-average molar mass, expressed in g mol -1 or Da; Rw = the weight-average mean square radius or hydrodynamic radius, expressed in nm; PI = Mw/Mn the polydispersity index, where Mn is the average molar mass.

The Conformation characteristic (Conf) is computed by the A4F-MALLS software on the bases described by [START_REF] Wyatt | Light scattering and the absolute characterization of macromolecules[END_REF]. Each analysed sample may possess N polymers and the apparatus measures

Sequential protein extraction for AFM and Cryo-TEM

The procedure used here was performed according to [START_REF] Fu | Procedure for isolating monomeric proteins and polymeric glutenin of wheat flour[END_REF] and [START_REF] Rhazi | Changes in the glutathione thiol-disulfide status during wheat grain development[END_REF].

Flour samples (0.125 g) were stirred for 1 h at room temperature with 2.25 ml of 0.08 M Tris-HCl buffer (pH 7.5) containing 50% (v/v) 1-propanol. Samples were centrifuged at 15,900 × g for 30 min at 15°C.

Soluble polymeric proteins in 50% 1-propanol were precipitated by the addition of 1.5 ml of 1-propanol to bring the 1-propanol proportion of the supernatant to 70% (v/v). The dispersion was agitated and left to stand at room temperature for 1 h after centrifugation at 26,000 × g for 15 min at 15°C. The supernatant, mainly containing monomeric proteins, was removed. The pellet containing mainly aggregates of polymers was mixed with 1 ml of sodium phosphate buffer (0.1 M, pH 6.9) containing 1.5% (w/v) SDS, sonicated for 20 s at a power setting of 30% with a 3 mm microtip, and then allowed to stand at 60°C for 2 h. After centrifugation (12,500 × g for 30 min at 25°C), the supernatants were used for Cryo-TEM after dilution and freeze-dried for AFM observations.

Proteomics

Proteomics analyses carried out on 21 stages of wheat endosperm development of the cultivar 'Récital' grown in a greenhouse under controlled conditions were used to determine the expression of the major enzymes involved in the control of redox and reactive oxygen species (ROS) [START_REF] Tasleem-Tahir | Expression profiling of starchy endosperm metabolic proteins at 21 stages of wheat grain development[END_REF].

Atomic force microscopy (AFM) of the glutenin polymers

AFM images (height and error-signal phase images) of glutenin polymers were recorded in air, employing INNOVA AFM from Bruker (Berlin, Germany). The lyophilised polymers obtained from sequential protein extraction were deposited on new silicon substrates or piranha solution-cleaned silicon substrates, whose cleanliness was checked beforehand with optics and AFM. Images were registered with low scan rates (0.3 Hz) using nitride-coated silicon probes with spring constants of 2.8

N.m -1 (FESPA-V2, Bruker, Germany). The sizes of the images were all between 5 µm × 5 µm and 10 µm × 10 µm at a resolution of 512 × 512 pixels. Treatment to improve AFM images and height profiles was achieved using Gwyddion Software (Brno, Czech Republic).

Cryo-transmission electron microscopy (Cryo-TEM) of the glutenin polymers

The principle of Cryo-TEM of vitrified specimens was previously described [START_REF] Dubochet | Cryo-electron microscopy of vitrified specimens[END_REF]. The vitrification of the samples was carried out in a homemade vitrification system. The chamber was maintained at 22°C, and the relative humidity was 80%. A 5 µl drop of the sample was deposited onto a lacey carbon film covered with a 300 mesh Cu grid (Ted Pella-USA) rendered hydrophilic using an ELMO glow discharge unit (Cordouan Technologies, Pessac, France). The grid was automatically blotted to form a thin film and plunged in liquid ethane at -190°C, as maintained by liquid nitrogen. Thus, a vitrified film was obtained in which the native structure of the vesicles was preserved. The grid was mounted onto a cryo holder (Gatan 626-Pleasanton, CA, USA) and observed under low-dose conditions (10 e/A 2 ) in a Tecnai G2 microscope (FEI, Eindhoven, Netherlands) at 200 kV. Images were acquired using an Eagle slow scan CCD camera (FEI).

Estimation of the number of polymers in wheat grain

Preliminary considerations:

-The average polymer masses (Mw) measured in wheat samples using A4F were usually between 1 x 10 6 and 2 x 10 8 Da (or g mol -1 ).

-Wheat storage protein analyses showed that, in general, for bread wheat cultivars, polymerised glutenin with a molecular weight greater that 10 6 g mol -1 , varied between 20 and 30% of total glutenins, as usually found in our analytical conditions using A4F [START_REF] Carceller | Size Characterization of Glutenin Polymers by HPSEC-MALLS[END_REF][START_REF] Aussenac | Molecular Weight Distribution of Polymeric Proteins in Wheat Grains: The Rheologically Active Polymers[END_REF]. To reduce the number of calculus, we chose the average of 25% of the total quantity of glutenins as part of the polymerised glutenins.

-If all glutenin polymers in the grain had the same identical mass (Mw; for example, 15 x 10 6 Da) then the number of glutenin polymers (NP) in a wheat grain (of 40 mg weight, having 12% protein concentration, including 80% of storage proteins (50% gliadins and 50% glutenins), of which 25% are polymerised) was obtained as follows:

The mass of glutenin polymers would be 40 × 0.12 × 0.80 × 0.5 × 0.25 = 4.8 × 10 -4 g Consequently, the number of glutenin polymers (NP) was: NP = 6.02 × 10 23 × 4.8 × 10 -4 /15 × 10 6 = 1927 x 10 9 polymers.

Instead of using a constant distribution of the masses (Mw) in wheat grain, the number of glutenin polymers was computed for Gaussian distribution around the following average polymer masses and limit values, often found on classic measures using A4F. For each of the average masses, the number of glutenin polymers was computed for grains having only the following kernel weights (30, 40, 50 and 60 mg) and the protein concentrations of 8.5, 10, 12, 14, 16 and 17%dw. The resulting 24 values of the total mass of glutenin polymers in wheat grain were used to compute the number of glutenin polymers based on a Gaussian distribution of the masses for each average polymer mass (Supplemental Figure S2 and Supplemental Table 2).

Statistics

As indicated in the first multi-location study, all statistical analyses, including Pearson correlations, analysis of variance (ANOVA) and partial least square regressions (PLS), were performed using Statgraphics® software. The broad-sense heritability, H 2 , of the Conf parameter was computed using the GLM procedure of variance analysis, as previously described [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF].

Results and discussion

Polymer conformation exhibits a large phenotypic variation

The conformation of the polymers had a global Gaussian distribution for the 885 samples analysed.

However, an asymmetric profile was reported, showing an excess of values lower than the mean 0.496.

The distribution evidenced a high range of phenotypic variations of the polymer conformation, from the lowest Conf value of 0.285, typical of a spherical polymer shape, to the highest value of 0.74, indicating a highly depolymerised macromolecule. These Conf values were significantly influenced by the 192 cultivars, as well as by the 11 locations in France and the 4 years of the wheat trials (2003-2004, 2004-2005, 2008-2009, and 2009-2010), as shown in Table 1. The percentages of the phenotypic variation explained by genotypes, locations and years were, however, lower for Conf compared to the percentages of its constitutive Mw and Rw parameters. The low broad-sense heritability coefficient (H² = 16.8) also confirmed the high influence of the environment (locations and years) on Conf values but may also have occurred because Conf is a computed ratio cumulating possible errors in measures on the two constitutive parameters. [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF].

Observation of the glutenin polymers using atomic force microscopy

The lyophilised polymers, first observed using an optical microscope, showed numerous aggregates of polymers whose sizes were several microns (not shown in Figure 1). However, using AFM, the isolated GPs directly spread on silicon substrate from lyophilised glutenins were revealed for the first time. The AFM perfectly confirmed the A4F data: the height of isolated polymers is of nanometric size and, for the sample shown in Figure 1, rather of spherical shape. The profiles in Figure 1B revealed that isolated spheric polymers in contact of substrate, then a little spread out, are of less than 100 nm diameter; height and diameter polymer sizes revealed by AFM are in full agreement with A4F measures.

Additional information on the GPs was shown by Cryo-TEM. The glutenin polymer presents a micellar structure using Cryo-TEM The use of Cryo-TEM revealed a micellar structure of the GPs issued from sequential glutenin extraction (Figure 2). The micelles were not homogenously distributed in the vitrous ice film but form larger assemblies, such as a grape of micelles indicating that glutenins were aggregated. Four of these larger structures, of about 100 nm diameter, were encircled. In the lower left corner, an enlargement of one grape is shown. The short white arrow points towards a micelle probably corresponding to a glutenin subunit of less than 10 nm diameter and the long arrow points towards a strain of the polymer linking two micelles. These observations revealed that GPs, as evidenced in Figure 1, were formed of individual polymers (or micelles) mainly associated with hydrogen bonds but with possible covalent bindings. These observations were in full agreement with previous findings revealing that during grain desiccation, (1) the mass of the polymers drastically increased [START_REF] Carceller | Accumulation and changes in molecular size distribution of polymeric proteins in developing grains of hexaploid wheat: Role of the desiccation phase[END_REF] and ( 2) the abundance of the protein disulphide isomerases (PDIs) was significantly decreased [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. They also confirmed the importance of hydrogen bonding in gluten properties, as revealed by [START_REF] Belton | Mini Review: On the Elasticity of Wheat Gluten[END_REF][START_REF] Belton | New approaches to study the molecular basis of the mechanical properties of gluten[END_REF].

The microscopy techniques that were used here may provide new insights on studies focusing on the structure of the polymers. The spherical and more or less reticulated glutenin structure of macropolymers in 1.5% SDS solution was previously shown using Confocal Scanning Laser Microscopy technique (CSLM) [START_REF] Don | Glutenin Macropolymer: A Gel Formed by Glutenin Particles[END_REF]. Using for example near isogenic wheat lines, the Cryo-TEM together with AFM and CSLM will be useful to further analyse the influence of glutenin alleles on the structure of the polymers that were revealed different in mass, radius or conformation. GSPs, particularly glutenin polymers, are synthesised during compound accumulation of wheat grains in protein bodies whose biogenesis received much attention in cereals (for review in cereals see [START_REF] Kumamaru | Protein body biogenesis in cereal endosperms[END_REF] and wheat [START_REF] Shewry | Wheat glutenin polymers 1. structure, assembly and properties[END_REF]. Protein bodies (PBs), which are derived from the endoplasmic reticulum (ER) inclusion membrane, were revealed to contain HMW-GS throughout grain development [START_REF] Tosi | Trafficking of storage proteins in developing grain of wheat[END_REF]. Once released into the cytoplasm, the PBs had diameters varying between 0.2 and 2 m. How many GPs can be stored in one PB? If we consider that all the polymers have a spherical shape and knowing their gyration radius (Rw), the hypothetical number of polymers stored in one PB can be estimated. If all GPs had an Rw of 5 nm (20 nm), their number would be as high as 10 6 (more than 15 thousand) into one PB of 1 m of diameter and 8x10 6 (125 thousand) into one PB of 2 m diameter (See Table S1).

Simulation of the number of glutenin polymers (GPs) in wheat grain and flour

Numerous factors are involved in the amount of polymerised glutenin in wheat grain. Together with the average mass of polymers (avMw), two major factors, kernel weight (KW) and grain protein concentration (PC), were used to compute the number of polymers in the wheat grain. One hundred and twenty combinations (4 KW, x 6 PC x 5 avMw) were used for an amount of polymerised glutenin per grain between 0.255 and 1.02 mg. Considering the different avMw, with individual masses following a Gaussian distribution, the number of GPs varied between 2.55 × 10 12 and 204.68 × 10 12 per grain (Table S2). The number of polymers per grain for a given protein concentration was the highest (lowest) when polymers were of low (high) average mass for bigger (smaller) grain weight (Figure 3A).

Similarly, the number of polymers per grain for a given grain weight was higher (lower) with high (low) PC values. Table S2 also shows the number of GPs for 100 gr of flour with 6 PCs. The amount of polymerised glutenin for PCs varying between 8.5 and 17%dw was between 0.85 and 1.7 g in these flours, giving a range of the expected number of polymers between 8.528 × 10 15 and 341.13 × 10 17 for 60 and 3 MDa of average polymer mass, respectively (Figure 3B). The calculated polymer numbers were obtained for an average percentage of 25% polymers in the glutenin fraction. Many genetic and environmental factors can influence the percentage of the polymerized fraction of glutenins and obviously may cause variation in the above calculated numbers as previously reported [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF], genetic and environmental factors are significantly associated with variations in polymer mass.

The following sections aim to test the possible factors influencing the polymer conformation.

Allelic variants of glutenin have a limited influence on polymer conformation

The protein concentration and grain hardness have very low but significant influences on the phenotypic variations of Conf. These two variations in grain quality characteristics were reported as significantly decreasing the polymer mass (Mw), whereas the gyration radius (Rw) was positively increased by PC and decreased by GH (Figure S3; [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. The hard type of wheat kernel has been shown to be associated with the unfolded protein response (UPR), inducing earlier endosperm cell death [START_REF] Lesage | Proteomes of hard and soft near-isogenic wheat lines reveal that kernel hardness is related to the amplification of a stress response during endosperm development[END_REF]. This UPR probably resulting from oxidative stress caused earlier shutdown of polymer accumulation and lower values for polymer mass and gyration radius. The Conf was the coefficient obtained from the slope (1/a) of the linear relationship of Log (Rw) = f [Log (Mw)]. Conf variations were then logically associated with Rw, decreasing with PC and increasing with GH (Figure 4). As reported in Table 2, PC and GH together explained only 1.1% of the phenotypic variations in the Conf values, as revealed by the PLS regression involving the 885 samples analysed from 11 locations. When the 14 HMW-GS alleles were introduced in the PLS regression, in addition to PC and GH, explanations of the Conf variations were also rather low (4.66%). When the 17 LMW-GS alleles were introduced instead of the HMW-GS alleles, the percentage explained of phenotypic Conf variations increased to 10.75%. A previous study reported that LMW-GS diversity contributed two times more than HMW-GS for Mw and Rw variations; here, LMW-GS explained more than two times the variation explained by HMW-GS in Conf variations. The total contribution of the glutenin alleles (together with PC and GH) was 14.21% (Table 2) lower than the percentage reported [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF] for its components, Mw and Rw (20.78% and 25.49%, respectively). The specific contributions of the alleles encoding HMW-GS and LMW-GS in the Conf values resulting from the PLS regressions using the 885 wheat samples are shown in Figure 4.

Table 2. Contribution (%) of the total phenotypic variance of the polymer conformation (Conf)

explained by the following variables using partial least square regression (PLS): grain protein concentration (PC), grain hardness (GH), high molecular weight glutenin subunits (HMW-GS) alleles, low molecular weight glutenin subunits (LMW-GS) alleles, cumulative mean temperature (Tmean) and cumulative water precipitation (WatSum) in the three final months in the 11 experimental fields of wheat crops involving 192 cultivars and previously detailed data [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF] S3). These results clearly confirm the hypothesis that was proposed, using a proteomic approach, about the involvement of asparaginyl endopeptidases in the post-translational processing of the By-type subunits [START_REF] Nunes-Miranda | Wheat glutenin: the "tail" of the 1By protein subunits[END_REF]; these asparaginyl endopeptidases are cysteine endopeptidases also described to mediate the maturation process of other storage proteins, such as 2S albumins and 11S globulins [START_REF] Hara-Nishimura | Vacuolar processing enzyme responsible for maturation of seed proteins[END_REF][START_REF] Tan-Wilson | Mobilization of seed protein reserves[END_REF]. The proteolytic cleavage observed for the By-type glutenin subunits leads to the loss of the unique conserved cysteine residue in the C-terminal domain. The resulting reduced polymerisation was more pronounced on the gyration radius Rw than on the polymer mass (Mw); consequently, the Conf parameter increased (Figure 4). In addition to the seven Gli-B1 alleles (namely 6-8, 7, 7-8, 7-9, 13-16, 14-15, 17-18) the following five LMW-GS alleles had a greater positive contribution, increasing the Conf value: Glu-A3a and b, Glu-B3a and b, and Glu-D3a. Moreover, the well-known Glu-D1d allele, subunits 5-10, slightly increased the conformation of the polymers, whereas null alleles, such as Glu-A1c, Glu-A3e (here noted Glu-A3ef) and Glu-B3j (translocation 1BL-1Rs), decreased the Conf value. Interestingly, strongly decreased Conf values were found for alleles that were previously ranked between medium to a rather good effect on rheological properties [START_REF] Branlard | Genetic diversity of wheat storage proteins and bread wheat quality[END_REF], such as Glu-D1b 3-12, Glu-B3g

and Glu-D3b. Their subunits increased Mw and Rw (Figure S3; [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF], but the polymerisation process had a greater impact on the gyration radius (Rw) than on Mw. Although the glutenin alleles had limited influence on the Conf values, they may be considered for genetic breeding aimed at improving the degradability of glutenin polymers, which is obviously expected for a Conf higher than 0.5 (corresponding to depolymerised polymers). values of the glutenin polymers measured using A4F-MALLS over the 885 wheat samples. The protein concentration of the grain (PC; noted protein) and grain hardness (GH; noted hardness) were explanatory variables first introduced in the regression, followed by alleles of HMW-GS and LMW-GS.

High temperatures during grain maturation increase the compactness of glutenin polymers

Considering the variables PC, GH and 31 alleles encoding the glutenin subunits, the cumulative daily average temperature of the last three months (TmeanMay, TmeanJune and TmeanJuly) of the wheat crop were introduced as three additional explanatory variables in the PLS regression. As was the case for the previous variables (Mw, Rw and PI), the explanation of the phenotypic Conf values was greatly increased (from 14.21 to 42.37%, Table 2) by the cumulative daily average temperature occurring in these three months in the 11 experimental locations. The standardised coefficients attributed to all variables clearly showed the greater influence of the temperature of the last month, July, which corresponds to grain maturation (Figure S3a, S3b and S3c). The atmospheric temperature during June increased the Conf value in allowing normal storage protein accumulation, increasing Mw and Rw without any physiological perturbations. In June, the photosynthetic carbohydrates and nitrogen remobilisation were actively engaged in grain filling, generally without severe heat and drought, compared to less favourable conditions that occurred during July in France. Considering June, the average daily temperatures (day + night) were, from location to location, between 15.7 and 18.7°C for the mean temperature and between 21.3 and 24.6°C for the maximum registered temperature, whereas for July, these values were 17.2-21.8°C and 23.7-27.9°C, respectively. The simple regression of the Conf values on the cumulative daily mean temperature measured in 11 locations during July clearly revealed that lower Conf values were caused by higher temperatures (Figure 5). The Conf values of the glutenin polymers were greatly reduced by the high temperatures occurring in the last month of the wheat cycle. The partially depolymerised and reticular polymers usually observed for a Conf value around 0.5 acquired a compact and spherical shape (Conf around 0.35) under the effect of higher temperatures during grain maturation. By analysing the glutenin polymer variations using A4F-MALLS, we revealed that the daily average temperature (i.e., 3.5°C of difference per day between the two extreme thermal locations during the last month of grain development, caused an increase of more than 189% and 242% in Rw and Mw, respectively [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. As opposed to the two above polymer parameters the Conf parameter was instead decreased when the daily average temperature increased. According to the regression equation (Figure 5), the mean Conf values decreased by 20.79% between the two extreme thermal locations. This revealed a major influence of the daily average temperature on the gyration radius of the polymers (Rw) compared to the mass of the polymers (Mw). In addition, the simple Pearson correlation of phenotypic values between Conf and Mw or Rw, computed in each of the 11 locations, revealed no consistent correlations (see Table S3). These results indicate that polymerisation involves a more complex process than the simple addition of glutenin subunits, increasing both Mw and Rw.

Limits of the redox system in hypoxic environments

The phenotypic Conf values revealed noticeable variations within locations, particularly due to genotypic differences, maturity earliness and resistance to water stress. Rainfall was also registered over the last three months in each trial location. The average rainfall in May, June and July significantly influenced Mw and Rw [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF]. The percentage of explained phenotypic Conf values over the 11 locations, including the 885 wheat samples, increased from 42.34 to 58.67% (Table 2). In particular, July rainfall contributed to an increase in Rw, which, together with the cumulative daily average temperature of that month, decreased the Conf values (Figure S3c). PC was the grain characteristic with the highest significant influence on reducing the Conf value of the glutenin polymers (Figure S3c). The PLS regression clearly showed that the coefficient attributed to PC was more important than any other coefficient attributed to glutenin alleles or to July rainfall in reducing the polymer Conf value. This association of PC in the explanation of the reduction of the Conf value can be seen as a "marker" of environmental factors occurring during polymerisation. Higher temperatures and heat stress reduce photosynthesis, photo-assimilates and starch synthesis in grain, thereby increasing the PC.

The water uptake in July may have partially alleviated the oxidative stress occurring in wheat endosperm during that month, since the majority of nitrogen translocation in the spike and protein accumulation in grain is usually achieved at the beginning of July in France. The polymerisation peak was shown to occur at the end of the water plateau, that is, the initiation of dehydration and grain maturation [START_REF] Carceller | Accumulation and changes in molecular size distribution of polymeric proteins in developing grains of hexaploid wheat: Role of the desiccation phase[END_REF][START_REF] Koga | Polymerization of gluten proteins in developing wheat grain as affected by desiccations[END_REF]. The process of storage protein accumulation and polymerisation in ER involves a tremendous number of SS links catalysed by oxidative molecules, such as protein disulphide isomerases (PDI), sulfhydryl oxidases and reactive oxygen species (ROS), such as hydrogen peroxide (H2O2), hydroxyl radical (OH -) and super oxide (O2 .-; [START_REF] Sevier | Ero1 and redox homeostasis in the endoplasmic reticulum: redox regulation of protein folding[END_REF]Kaiser 2008, Lal et al., 2021). Plants may reduce the excess and detrimental effects of ROS with several antioxidant molecules, such as ascorbic acid (ASC) and glutathione (GSH), and scavenging enzymes, such as ascorbate peroxidases (APX), glutathione reductases (GR), superoxide dismutases (SOD) and catalases (CAT). Proteomic analysis of the developing endosperm of wheat grown in normal controlled conditions offered the opportunity to identify the expression of the 19 following enzymes involved in ROS scavenging: 7 APX, 3 Dihydro-ascorbate reductases (DHAR), 5 SOD, 1 Glutathione Stransferase (GST), 1 Thioredoxin reductase and 1 1-Cys-peroxyredoxin. The evolution of these ROS scavenging enzymes (Figure 6), expressed in the cytosol of the endosperm, during the 21 sampling stages [START_REF] Tasleem-Tahir | Expression profiling of starchy endosperm metabolic proteins at 21 stages of wheat grain development[END_REF], clearly showed the decreasing abundance for APX, CAT and DHAR and increasing abundance for GST, NADPH thioredoxin reductase and SOD of wheat grain after 500°CDay and maturation. The controlled conditions for the wheat growing environment were chosen as normal conditions with a full nutritional and water supply without any stress. These enzymes were reported to be overexpressed in response to heat stress during grain compound accumulation [START_REF] Skylas | Heat shock of wheat during grain filling: proteins associated with heat-tolerance[END_REF][START_REF] Majoul | Proteomic analysis of the effect of heat stress on hexaploid wheat grain: characterization of heat-responsive proteins from total endosperm[END_REF][START_REF] Majoul | Characterization of heat-responsive proteins from nonprolamins fraction[END_REF][START_REF] Majoul-Haddad | Effect of short heat shocks applied during grain development on wheat (Triticum aestivum L.) grain proteome[END_REF][START_REF] Vensel | Developmental changes in the metabolic protein profiles of wheat endosperm[END_REF][START_REF] Hurkman | Effect of high temperature on albumin and Analysis of mRNAs from ripening wheat seeds: the effect of high temperature. globulin accumulation in the endosperm proteome of the developing wheat grain[END_REF][START_REF] Laino | Comparative proteome analysis of metabolic proteins from seeds of durum wheat (cv. Svevo) subjected to heat stress[END_REF]. This overexpression may be insufficient to properly oxidise the free thiols potentially engaged in the polymerisation process in the small protein bodies (PBs) sequestered in the ER [START_REF] Galili | Wheat storage proteins: Assembly, transport and deposition in protein bodies[END_REF]. The post-translational processing of the Glu-B1y subunits, as evidenced in the 192 wheat varieties, removed their cysteine residue in the C terminal domain and consequently had limited branching in subunits. The excess ROS causes the unfolded protein response (UPR) initially described in yeast and mammals cells and has been shown to induce numerous signal transduction pathways involving many genes, impacting various processes, such as lipid biosynthesis, N-linked glycosylation, ER-associated degradation (ERAD), vacuolar function and chaperones [START_REF] Jonikas | Comprehensive characterization of genes required for protein folding in the endoplasmic reticulum[END_REF]. The UPR was revealed in different plant tissues, including the wheat endosperm, in relation to grain hardness [START_REF] Lesage | Proteomes of hard and soft near-isogenic wheat lines reveal that kernel hardness is related to the amplification of a stress response during endosperm development[END_REF] and can be elicited during plant development in regulating basal immunity responses [START_REF] Bao | The Unfolded Protein Response Supports Plant Development and Defence as well as Responses to Abiotic Stress[END_REF]. Because of excess ROS, the phospholipids forming the lipidic bilayer polar membrane of ER are degraded. It can be hypothesised that this degradation of membrane lipids by hydroperoxide prevents the ER from performing additional membrane inclusions to surround more protein bodies. The accumulation of polymers thus continues in the PBs already present in the ER. The polymers are then packed in fewer PBs, as they should be, and reach higher mass, becoming less reticulated for less volume hindrance and obtaining a global spheric shape. The insufficient amount of phospholipids forming the cytoplasm membranes, such as for ER and PBs, is strongly emphasised in wheat under heat stress. A survey of 539 wheat accessions, cultivated in France during the two last centuries, revealed a significant opposition between the oldest and modern cultivars; the former being richer in poly-unsaturated fatty acids and the latter with more saturated fatty acid (stearic, palmitic) and monounsaturated oleic acid [START_REF] Roussel | NIRS analysis reveals temporal trends in the chemical composition of French bread wheat accessions cultivated between 1800 and 2000[END_REF]. Modern cultivars had more phospholipids, but this seemed insufficient to allow them to respond to the current heat stress. The use of marker-assisted selection in breeding wheat with higher polymer conformation, together with agronomic practices aimed at improving soil water retention, should help to reduce the consequences of high temperatures [START_REF] Chaudhary | Identification and Characterization of Contrasting Genotypes/Cultivars for Developing Heat Tolerance in Agricultural Crops: Current Status and Prospects[END_REF][START_REF] Lal | Physiological and molecular insights on wheat responses to heat stress[END_REF], particularly for wheat glutenin polymers.

Conclusions

As noted in a previous companion publication [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF], the high temperatures registered in France during our four experimental years can also be encountered in many other countries. The influence of high temperatures is the cause of higher masses and a higher gyration radius of polymers. Importantly, we revealed here that the polymer becomes less reticulated, more spherical, and more compact when the average temperature of the last month of the wheat cycle is increased. These observations make the very numerous glutenin polymers the most reliable hypothesis to explain non-celiac gluten sensitivity (NCGS) that many people suffer from in countries subjected to global warming. The polymers of glutenin have to be seized by wheat geneticists, technologists, food manufacturers and nutritionists for developing healthier foods for consumers.

There are numerous fields to investigate. Basic research on molecular mechanisms occurring in endoplasmic reticulum involved in the polymerisation process and in redox system or oxidative stress has to be investigated specifically with wheat grown in controlled environments. To face the global warming consequences, geneticists can use glutenin alleles, increasing the polymer conformation and reticulation. Numerous allelic effects remain to be tested from world wheat collections and several genetic approaches are available today for breeding future wheat possessing better control of the characteristics of glutenin polymers accumulated in high temperature environments. These investigations will take years and we fear that environmental factors may lead to variations in polymer characteristics in the years to come. The technologists, more rapidly, may develop adapted processes with the aim of manufacturing healthy, baked products for consumers. During bread baking, the amylose released from the starch granules can surround the gluten films, yielding gelatinised amylose;

this resistant starch prevents the rapid hydrolysis of these glutenin polymers, which are more compact and less reticulated today. The new processes should obviously include longer fermentation times compared to those routinely practiced today and a controlled hydrolysis of glutenin polymers.

Nutritionists are also encouraged to measure polymer characteristics that could be digestible without any trouble in the intestines of sensitive people. The above genetic and environmental information on the polymer characteristics of wheat should help the scientific community to propose an efficient answer for people suffering from NCGS. Moreover, considering that Alpha-, Beta-, and Gamma-gliadin bound by an additional odd SH to glutenins can be sequestered in these polymers, the present findings could be of some help to alleviate other pathologies linked to gluten consumption.

Tables legends

Table 1. Values of statistical distribution (Mean, SD and Min-Max) of the 192 cultivars experimented in 11 locations for the Conformation of glutenin polymers (Conf). The percentage (R 2 %) of phenotypic variance was obtained using one factor ANOVA, and the heritability H 2 coefficient was averaged over the H 2 computed per experimental year.

Table 2. Part (%) of the total phenotypic variance of the polymers conformation (Conf) explained by the following variates using partial least square regression (PLS): grain Protein Concentration (PC),

Grain Hardness (GH), High Molecular Weight Glutenin Subunits (HMW-GS) alleles, Low Molecular

Weight Glutenin Subunits (LMW-GS) alleles, cumulative mean temperatures (Tmean) and cumulative water precipitations (WatSum) for the three final months in the 11 experimental fields of crop involving 192 cultivars and previously detailed [START_REF] Branlard | Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat[END_REF].

Figures legends

Fig. values of the glutenin polymers measured using A4F-MALLS over the 885 wheat samples. The protein concentration of the grain (PC; noted protein) and grain hardness (GH; noted hardness) were explanatory variables first introduced in the regression, followed by alleles of HMW-GS and LMW-GS.

n

  times the characteristics (mass Mw, radius Rw, etc…) of each polymer. The software compute several additional characteristics including the conformation of the polymer. Then having analysed the N polymers present in a given sample, the Conf value of the polymers in the sample is determined from the slope (1/a) of the following Log-Log plot: abscissa Log (Mw) and in ordinate Log of root-mean square (RMS) of Rw, ie : (∑ (Rw𝑖)² 𝑛 𝑛 𝑖=1 ) 0.5 . An example of that Log-Log plot for a glutenin sample is shown in Supplemental Figure S1. The characteristics of the chemical polymers according to the Conf values were classically described as follows (Wyatt, 1993): Conf < 0.33: Compact and spherical; Conf 0.33-0.50: Partly depolymerised and reticulated; Conf > 0.50: Depolymerised and fibrillar; Conf = 1: Polymer shape of a rigid rod.

Fig. 1 .

 1 Fig. 1. Photos of the glutenin polymers issued from sequential glutenin extraction, as revealed using Cryo-Transmission Electron Microscopy. The black arrow points to a micelle (less than 10 nm in diameter). Short and long white arrows are explained in text.

Fig. 2 .

 2 Fig. 2. Photos of the glutenin polymers issued from sequential glutenin extraction, as revealed using Cryo-Transmission Electron Microscopy. The black arrow points to a micelle (less than 10 nm in diameter). Short and long white arrows are explained in text.

Fig. 3A .

 3A Fig. 3A. Glutenin polymer number (×10 12 ) per grain as a function of average polymer mass and kernel weight for grain having a protein concentration of 12% dw.

Fig. 3B .

 3B Fig. 3B. Glutenin polymers number (×10 15 ) in 100 g of flour as a function of average polymer mass and grain protein concentration.

Fig. 4 .

 4 Fig. 4. Standardised coefficients of the PLS regressions aimed at explaining the conformation (Conf)

Fig. 5 .

 5 Fig. 5. Regression between the conformation of the glutenin polymers, measured using asymmetric flow field-flow fractionation multi-angle laser light scattering (A4F-MALLS), and the cumulative daily mean temperatures (°C) in July (noted TmeanJly) in the 11 wheat trial locations in France between 2004 and 2010, involving 192 hexaploid cultivars.

Fig. 6 .

 6 Fig. 6. Evolution of the major enzymes involved in the Redox function, revealed using proteomics analysis over 21 stages of grain formation and maturation (Tasleem-Tahir et al., 2012). Evolution of the average of normalised spot volumes for 7 APX, 3 DHAR, 5 SOD, 1 Catalase, 1 GST, 1 NADPH Thioredoxin reductase and 1 1-Cys Peroxiredoxin reductase during grain formation, in cumulative thermal time (°Cd). Red continuous and blue dotted lines indicate increased and decreased abundance, respectively, for enzymes during polymer formation and grain desiccation; for each individual enzyme, the confidence interval (not shown for clarity of the figure) of each data point was between 5 and 12% of the data mean value computed on 6 replicates of 2DE.

  Fig. 1. A) AFM error image of lyophilised glutenin polymers on a silicon substrate; B) the topographic image corresponding to the error image in A) and; C) polymer profiles. The areas where the height profiles were measured are indicated with green lines on image B).

Fig. 2 .

 2 Fig. 2. Photos of the glutenin polymers issued from sequential glutenin extraction, as revealed using Cryo-Transmission Electron Microscopy. The black arrow points to a micelle (less than 10 nm in diameter). Short and long white arrows are explained in text.

Fig. 3A .

 3A Fig. 3A. Glutenin polymer number (×10 12 ) per grain as a function of average polymer mass and kernel weight for grain having a protein concentration of 12% dw.

Fig. 3B .

 3B Fig. 3B. Glutenin polymers number (×10 15 ) in 100 g of flour as a function of average polymer mass and grain protein concentration.

Fig. 4 .

 4 Fig. 4. Standardised coefficients of the PLS regressions aimed at explaining the conformation (Conf)

Fig. 5 .Fig. 6 .

 56 Fig. 5. Regression between the conformation of the glutenin polymers, measured using asymmetric flow field-flow fractionation multi-angle laser light scattering (A4F-MALLS), and the cumulative daily

Fig. 1

 1 Fig. 1

Fig. 2

 2 Fig. 2

  Fig. 3A

  Fig. 3B

Table 1 .

 1 Values of statistical distribution (Mean, SD and Min-Max) of the 192 cultivars in 11 locations for the conformation of glutenin polymers (Conf). The percentage (R 2 %) of phenotypic variance was obtained using one-factor ANOVA, and the heritability (H 2 ) coefficient was averaged over H 2 computed

	per experimental year.
	Parameters (unit)	Total samples	Mean	SD	Min	Max	R 2 % Genotype (192)	R 2 % Location (11)	R 2 % Year (4)	H 2 (4)
	Mw (KDa)*	885	9554.4 5485.6 1142.0	48777.5	55.00	70.10	59.10 11.80
	Rw (nm)*	885	42.40	20.94	6.70	116.20	79.6	85.20	82.60 25.00
	Mw/Mn (--)*	885	12.58	11.81	1.04	82.94	61.50	85.60	74.10 21.20
	Conf (--)	885	0.496	0.064	0.285	0.740	46.60	54.60	48.20 16.80
	(*) Data from the multi-local trials previously reported by

  The figure clearly shows the high positive coefficients of all Glu-B1 alleles contributing to an increase in the Conf values. All alleles encoded at Glu-B1 decreased both parameters, Mw and Rw(Branlard et al., 2020; Figure

	PC + GH	PC + GH	PC + GH	PC + GH	PC + GH	PC + GH	PC + GH
		+ HMW-GS	+ LMW-GS	+ HMW-GS	+ Tmean May	+ Tmean May	+ WatSum May
				+ LMW-GS	+ Tmean Jun	+ Tmean Jun	+ WatSum Jun
					+ Tmean Jly	+ Tmean Jly	+ WatSum Jly
						+ HMW-GS	+ Tmean May
						+ LMW-GS	+ Tmean Jun
							+ Tmean Jly
							+ HMW-GS
							+ LMW-GS
	1.11**	4.66***	10.75***	14.21***	41.34***	42.37***	58.64***
							. With: n= 885;
	(**) p<10 -2 ; (***) p<10 -4 .

Acknowledgements

The authors thank the FSOV (Fond de Soutien à l'Obtention Végétale) for its financial support (programme "Indice of Quality" and programme "Tenacity-Extensibility Bread Loaf Volume"-Leader G. Branlard, INRAE, UCA UMR1095 GDEC) and the majority of European private breeding companies operating in France (Caussades semences, Desprez, Momont-Hennette, Saaten Union, Serasem, Syngenta Seeds, and Verneuil LVH) for the provision of their wheat cultivars and their logistical support. The authors also thank all engineers and technicians of the private breeding companies and public institutes who participated in the FSOV-particularly, Sylvie Dutriez (Caussades semences), Jane Stragliati (Verneuil LVH), Volker Lein (Saaten Union), Philippe Lonnet et Thierry Demarquet (F Desprez), Eric Margale (Serasem), Benoit Méléard (ARVALIS), Fabrice Lagoutte and François Xavier Oury (INRAE), Patrice Senellart (Syngenta Seeds), and Stephen Sunderwirth (Momont-Hennette). Catherine Ravel (INRAE Clermont Ferrand) and Didier Marion (INRAE Nantes) are greatly acknowledged for their useful discussions. Julien Branlard is also greatly thanked for his help with Gaussian simulation.

Funding

This research was partly funded by FSOV (Fond de Soutien à l'Obtention Végétale) and FSOV breeding members, programme "Indice of Quality" and programme "Tenacity-Extensibility Bread Loaf Volume."

Data availability

The data supporting the findings of this study are available from the corresponding authors, (Gérard Branlard and Thierry Aussenac), upon request.

Supplementary data

The following supplementary data are available at JXB online.

Table S1. The simulated number of glutenin polymers accumulated in protein body having either 1-or 2-micron diameter is given.

Table S2. The glutenin polymer number in wheat grain and flour is simulated assuming gaussian distribution of the polymer masses.

Table S3. Pearson correlation between Phenotypic values of glutenin polymers characteristics (Conf-Mass Mw) and (Conf-Radius Rw) of the polymers as measured using A4F-MALLS.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.


Louis Noizet

Alan Schmitt

Necro ML: Kit de Nécromancie (Démonstration)

On présente Necro ML, un outil pour générer des interpréteurs OCaml à partir de sémantiques en Skel, un langage minimaliste de description de sémantiques. Ces interpréteurs sont modulaires, en exploitant des monades pour interpréter les calculs.

Introduction

Ce travail est initialement basé sur les travaux de Courant et al. [START_REF] Courant | Necro: Animating Skeletons[END_REF]. En particulier, le langage Skel a été largement amélioré, avec du polymorphisme, des fonctions de première classe, et du filtrage. L'interpréteur OCaml généré est maintenant modulaire pour l'interprétation des branches, ce qui permet d'en changer aisément. La section 1 présente le langage Skel. La section 2 décrit comment un interpréteur est généré. Enfin, la section 3 montre comment les monades d'interprétations peuvent être utilisées pour représenter différents comportements de l'interpréteur. Lors de la démonstration, nous présenterons le fonctionnement de Necro ML et l'usage de différentes monades d'interprétations pour traiter le non-déterminisme.

Skel

Skel [START_REF] Bodin | Skeletal Semantics and their Interpretations[END_REF] est un langage statiquement typé pour décrire des sémantiques opérationnelles de langages. Il est à la fois léger et puissant, et une sémantique squelettique peut notamment être extraite vers un générateur OCaml, une formalisation Coq, et un débogueur. Le langage Skel est basé sur ML avec une construction supplémentaire appelée le branchement pour traiter les calculs non-déterministes, et la possibilité de sous-spécifier.

Une des fonctionnalités principales de Skel est la séparation entre squelettes et termes. Les premiers représentent des calculs, et les seconds des valeurs. Cela est inspiré du λ-calcul computationnel de Moggi [START_REF] Moggi | Computational lambda-calculus and monads[END_REF].

Skel est proche de langages ML comme OCaml ou SML, mais son AST est léger, de manière à pouvoir être manipulé plus simplement. Il est défini dans [START_REF] Noizet | Necro Library[END_REF], et contient uniquement 126 lignes de spécification, ce qui permet de gérer et extraire facilement des sémantiques.

Necro ML

Necro est un écosystème pour manipuler les sémantiques squelettiques. Il repose sur Necro Lib [START_REF] Noizet | Necro Library[END_REF], une bibliothèque OCaml qui définit la syntaxe de Skel, et un ensemble de fonctions pour manipuler les sémantiques squelettiques, y compris la fonction parse_and_type, qui lit un fichier et renvoie une sémantique squelettique typée.

Ainsi, n'importe qui a accès à la syntaxe et à des fonctions de base, pour pouvoir créer des outils qui exploitent les sémantiques squelettiques et étendent l'écosystème Necro. En plus de Necro Lib, nous fournissons plusieurs outils. L'un d'eux, celui que nous présentons ici, est Necro ML [START_REF] Crance | Necro Ocaml Generator[END_REF], qui génère des interpréteurs OCaml depuis des sémantiques squelettiques. Comme nous l'avons précisé dans la section 1, il y a dans les sémantiques squelettiques des données non-spécifiées. Cela est traité par Necro ML de manière modulaire. On génère un foncteur MakeInterpreter, qui produit un interpréteur quand on lui fournit une implémentation des termes et types non-spécifiés.

Le plongement est principalement superficiel, mais on doit gérer les branches avec prudence, puisque OCaml n'a pas de construction native équivalente. Nous allons donc montrer comment cela est traité dans la section 3.

Monade d'interprétation

Comme expliqué plus haut, on ne peut pas utiliser un simple plongement profond, en raison des constructions non-déterministes. À cette fin, on utilise une monade de plongement, ou monade d'interprétation, pour décrire les calculs. Ainsi, les termes de type 'a sont plongés superficiellement dans des expressions OCaml de type 'a, tandis que les squelettes de type 'a sont plongés profondément dans des expressions OCaml de type 'a M.t. Necro ML propose plusieurs monades d'interprétations, et d'autres peuvent être définies par l'utilisateurice. L'aspect principal est qu'il est très simple de changer la monade d'interprétation sans avoir à réécrire aucun code.

Conclusion

Necro ML est un outil flexible pour générer des interpréteurs. Il effectue un plongement superficiel des types, et semi-profond des expressions pour gérer le non-déterminisme. Il a été testé sur des fichiers de taille significative, notamment dans le travail en cours de formalisation de JavaScript [START_REF] Khayam | JSkel: Towards a Formalization of JavaScript's Semantics[END_REF]. D'autre projets sont intimement liés. D'abord, Necro Debug est une exécution pas-à-pas d'une sémantique squelettique. 1 Il utilise la même approche et les même signatures de modules que Necro ML, ce qui permet de réutiliser l'instanciation des termes non-spécifiés. Ensuite, Ambal et al. ont présenté un générateur d'interpréteurs certifiés à l'aide de Necro Coq et du mécanisme d'extraction [START_REF] Ambal | Certified Abstract Machines for Skeletal Semantics[END_REF].

Figure 1 :

 1 Figure 1: The Necro ecosystem

https://skeletons.inria.fr/debugger/index_while.html


Chiheb Sakka

Amina Guermouche

Olivier Aumage

Emmanuelle Saillard

Mark Potse

Yves Coudière

Denis Barthou

A comparison of multithreading, vectorization, and GPU computing for the acceleration of cardiac electrophysiology models

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

Introduction

In a monodomain reaction-diffusion model of cardiac electrophysiology the integration of the membrane state and the computation of transmembrane ionic currents at each model node is the most expensive part of the simulation. Acceleration of these tasks is interesting especially for large models with millions of nodes or elements on which membrane models must be integrated. Even though this task is embarrassingly parallel (it requires no communication between model nodes) a straightforward parallelization using OpenMP, MPI, CUDA, or OpenCL usually performs far below the expected performance of the CPU or GPU. In this study we tested a variety of acceleration techniques, ranging from compiler options to code transformations, using the Ten Tusscher-Panfilov model [START_REF] Tusscher | Alternans and spiral breakup in a human ventricular tissue model[END_REF], a commonly used and moderately complex model for the human ventricular myocyte, and identified data bandwidth as the main bottleneck both on CPU and on GPU.

Methods

The baseline code for this work was a simplified version of Propag-5 [START_REF] Krause | Hybrid parallelization of a large-scale heart model[END_REF], able to run large monodomain reactiondiffusion simulations with hybrid MPI-OpenMP parallelism. To determine the impact of optimizing the shared memory parts, in particular the membrane model, on this code, we tested, with different approaches, the performance of a model of the whole human ventricles with model sizes of 10 7 and 8 • 10 7 nodes (table 1), using either 1) up to 64 compute cores on two compute nodes each equipped with two 16-core Intel Xeon E5-2683 v4 "Broadwell" CPUs with a clock frequency of 2.1 GHz, an NVIDIA Tesla P100 GPU, and 256 GB memory and equipped with AVX2 extensions, or 2) up to 72 compute cores on two compute nodes each equipped with two 18core Intel Xeon Gold 6240 "Cascade Lake" CPUs with a clock frequency of 2.6 GHz and 192 GB memory and equipped with AVX512 extensions. In each test we integrated a monodomain reaction-diffusion equation with an explicit Euler method for 50 ms simulated time.

Tests with model S were run on one or two machine nodes. Tests with model M required two nodes.

x 3 y 3 z 3 x 4 y 4 z 4 x 5 y 5 z 5

x n y n z n ...

Array-of-Structs

x 3 x 4 x 5

x n y 1 y 2 ... Figure 1. Different data layout representation, in Arrayof-Structs-of-Arrays (AoSoA), each component is stored in smaller contiguous chunks corresponding to the size of the vector extension. In SoA, the large contiguous chunks of memory for each variable have benefit in terms of contiguous memory accesses for CUDA kernels 2.1.

OpenMP and Vectorization and memory access optimization

Modern processors can execute single-instruction multiple-data (SIMD) instructions, also called vector instructions, allowing to perform up to 8 floating-point operations at once. However, compilers have difficulty recognizing opportunities for vectorization and may be unable to perform the data reorderings that are necessary to use them efficiently. Therefore we enforced vectorization using a portable high-performance C++ SIMD library called MIPP [START_REF] Cassagne | MIPP: A portable C++ SIMD wrapper and its use for error correction coding in 5G standard[END_REF], for SSE, AVX and AVX-512 instructions.

Data layout is particularly important for the status variables of the membrane model. In the baseline code these were organized as an array with all variables of a single node stored contiguously. To take advantage of SIMD we used an AoSoA (Array of Structures of Arrays) order, in which a single variable is contiguous for a small group of model nodes, such as to constitute a "data vector."

GPU CUDA

Graphics processing units (GPUs) have developed into mainstream accelerators for computing. They have parallelization levels that range into the thousands, but their computing capabilities are limited and automated compilation for GPUs often leads to speedups that are orders of magnitude smaller than the number of compute cores in the GPU. Several cardiac simulation codes have already been adapted for use with GPUs [START_REF] Sato | Acceleration of cardiac tissue simulation with graphic processing units[END_REF][START_REF] Shen | Parallelized computation for computer simulation of electrocardiograms based on whole-heart models using personal computers with multi-core CPU and GPGPU[END_REF][START_REF] Neic | Accelerating cardiac bidomain simulations using graphics processing units[END_REF][START_REF] Mena | GPU accelerated solver for nonlinear reaction-diffusion systems. Application to the electrophysiology problem[END_REF][START_REF] Kudryashova | Virtual cardiac monolayers for electrical wave propagation[END_REF][START_REF] Vandersickel | Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry?[END_REF][START_REF] Hustad | Solving the monodomain model efficiently on GPUs[END_REF].

A preliminary analysis showed that compute time in our code was small compared to the time needed to transfer data between the CPU and GPU. This pertains to the transmembrane potential, the ionic current, stimulation and diffusion current, and depolarization time of cells. The membrane status variables, a much larger amount of data, stayed on the GPU during the entire simulation. We used CUDA streams to overlap computations with transfers.

Results

Figure 2 shows the speedup obtained by different parallel algorithms for model S on the Broadwell architecture: cumulated time for membrane model computation and total program execution. The speedup is measured with respect to the execution time of the multithreaded original code compiled with gcc. It shows the relative increase of the vectorised version's performance using the MIPP wrapper, compiled with icpc version 19.0.4.243 with options -O3 -inline-forceinline. The vectorized version used AVX2 extensions, the most advanced available on the machine. The CUDA version shows that concurrently executing copies and kernels using up to 4 streams improves the performance.

Figure 3 shows the speedup obtained by different parallel algorithms for model M on the Broadwell architecture. CUDA-enabled versions use concurrency up to 64 streams due to the size of this model. Using the same compilation options, it shows approximately the same relative performance increase for the vectorised version as for the CUDA version. On the Cascade Lake platform, we could test different SIMD instruction sets (SSE, AVX2 and AVX-512). Figure 4 shows that an optimised data layout increases the performance of the vectorised version: SSE extensions allow to use vectors of 2 double elements (theoretical speedup can reach at maximum 2), but allowed a three-fold performance increase. The AVX2 instructions further increased performance, but AVX512 had no further impact.

In order to understand this behavior, we studied the effect of cache and memory bandwidth on the performance of tp06 using a roofline model [START_REF] Williams | Roofline: An insightful visual performance model for multicore architectures[END_REF]. A roofline model visualizes how kernel performance is affected by the memory bandwidth of a specific architecture. When the performance is close to the peak performance of the architecture, then the kernel is compute-bound and is not affected by the memory bandwidth. In contrast, when the kernel performance is far from the peak performance, then it most likely limited by some cache level bandwidth or by the memory bandwidth. Figure 6 shows the behavior of tp06 on the Cascade Lake architecture. The figure shows that the vectorization improves the performance compared to the baseline implementation. Moreover, it shows that there is no performance difference between AVX2 and AVX512. This shows that the performance is limited by the level-3 cache and the memory bandwidth, which explains the results of Figure 4.

Discussion

On our test platforms, both vectorization and the use of GPUs allowed for a roughly three-fold acceleration of the membrane model compared to multithreaded execution on the CPUs alone with no special care to leverage the SIMD capabilities of the compute cores. Since this probably constitutes the current state of many cardiac simulation codes, this is a useful investigation into two very different avenues for acceleration.

The outcome of our study indicates that vectorization and GPU coding allow for significant acceleration, and that the optimal solution would be to perform both and divide the computations between the CPU and the GPU.

A second important outcome is that memory transfers are the bottleneck for GPU performance on our tested systems. A practical consequence is that investing in more CUDA cores is useless if it is not combined with a higher data transfer rate between the GPU and the main memory.

The outcome of a comparison such as ours obviously depends on the capabilities of the CPUs and GPUs involved. We used CPU types that are currently mainstream in powerful workstations. With cheaper CPUs or more powerful GPUs the outcome would likely have been different. Speedups reported in the literature indeed vary widely. For example, Sato et al. [START_REF] Sato | Acceleration of cardiac tissue simulation with graphic processing units[END_REF] reported a factor 30 speedup with an NVIDIA Geforce 9800 GX2 GPU, but this was in comparison to a two-core CPU. Given that we used 32 times as many cores for our baseline code, our speedup was actually 3 times better than theirs, if we assume that both CPUs and GPUs improved by the same amount in the 13 years that passed since their study was published. In other words: in the study by Sato et al. a GPU appeared to be worth 60 CPU cores, and in ours 192 CPU cores.

In a more recent study by Neic et al. [START_REF] Neic | Accelerating cardiac bidomain simulations using graphics processing units[END_REF], a single GPU appeared to be worth about 15 CPU cores. This implementation was quite different from ours, because also the partial differential equations were solved on the GPUs.

Although the cited codes and hardware are very different from each other, it is clear that the performance of a GPU core is, in practice, for large-scale cardiac electrophysiological models, one or two orders of magnitude lower than that of a CPU core.

We tested either vectorization or GPU optimization. Optimization of code with such fixed choices requires man- ual adaptation to each specific platform and depends on the performance of its CPUs, GPUs, the data transfer rates between them, and on the balance between computational load and memory requirements of the simulation. An alternative for such manual tuning would be to use a runtime scheduler [START_REF] Augonnet | StarPU: A Unified Platform for Task Scheduling on Heterogeneous Multicore Architectures[END_REF], which can find the optimal partitioning of the workload at runtime.

Figure 2 .Figure 3 .

 23 Figure 2. Speedup for model S on 1 node (32 threads) on Broadwell architecture. The graph shows the impact of improving membrane model performance on the membrane model alone ("TP06") and on the whole program ("total"). Str2. . . Str8 stands for 2 to 8 CUDA streams.

Figure 4 .Figure 5 .

 45 Figure 4. Comparison of the speedup of vectorization according to Vector Extensions for model S on 1 node (36 threads) on Cascade Lake architecture.

L 1 B 6 .

 16 a n d w id th : 1 .2 6 e + 4 G B /s e c L 2 B a n d w id th : 5 9 4 1 .4 2 G B /s e c L 3 B a n d w id th : 8 8 0 .2 8 G B /s e c DP Vector FMA Peak: 2851.61 GFLOPS SP Vector Add Peak: 2851.61 GFLOPS Scalar Add Peak: 185.34 GFLOPS DP Vector Add Peak: 1425.67 GFLOPS SP Vector FMA Peak: 5703.48 GFLOPS D R A M B a n d w id th : 2 3 6 .0 3 G B /s e Roofline model comparison for the baseline tp06 loop (represented as circle) and vectorised algorithms (represented by a square (SSE), triangle (AVX2) and diamond (AVX512)) using Intel Advisor for model S on 1 node (36 threads) on Cascade Lake architecture.

Table 1 .

 1 Models used for the tests.

	Model ∆x (µm) ∆t depolarization nr. of nodes
	S	200	0.0500	10,040,000
	M	100	0.0125	80,160,000

Struct-of-Arrays: CUDA

	...	z 1 z 2 z 3	...	z n

Array-of-Structs-of-Arrays: SIMD

	x 1 y 1 z 1	x 2 y 2 z 2
	x 1	x 2						y 3	y 4		y n		z 4
	x 1	x 2	y 1 y 2	z 1	z 2	x 3 x 4	y 3 y 4	z 3	z 4	...	x n-1 x n	y n-1 y n	z n-1	z n
	SIMD Width

Acknowledgments

This work was supported by the French National Research Agency, grant references ANR-18-CE46-0010 (EXACARD) and ANR-10-IAHU04-LIRYC.