Anne-Laure Chateigner-Boutin
email: anne-laure.chateigner-boutin@inrae.fr

Camille Alvarado

Marie-Françoise Devaux

Sylvie Durand

Loïc Foucat

Florent Gr élard, Fr éd éric Audrey Geairon

Florent Grélard

Frédéric Jamme

Hélène Rogniaux

Luc Saulnier

Marie-Franc ¸oise Devaux

Jamme

Élène Rogniaux

Fabienne Guillon

Marie-Françoise Devaux

The endosperm cavity of wheat grains contains a highly hydrated gel of arabinoxylan

Keywords: Cereal grain, arabinoxylan, hydroxycinnamic acids, endosperm cavity arabinoxylan, °DAF: Celsius degrees per day after flowering, FT-IR: Fourier Transform-InfraRed, µMRI: microscopic magnetic resonance imaging, HPLC-DAD: HPLC combined with UV diode array detection

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Introduction

Wheat is a major crop providing a substantial part of human and animal diet calories. The main biochemical components of wheat grains are starch, proteins, lipids and non-starch polysaccharides that all contribute to wheat nutritional properties and affect its processing quality [1].

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As other cereal grains, the wheat caryopsis contains several tissues: several layers of outer tissues (pericarp, seed coat, nucellar epidermis), an embryo and a storage tissue named endosperm (Fig. 1).

These tissues are the results of a precise programmed development, which takes place following fertilization [START_REF] Evers | Cereal grain structure and development: some implications for quality[END_REF]. Grain development is classically divided into the early (lag) phase, the filling phase and the maturation phase. After anthesis, the wheat grain mainly consists of the pericarp whose cells first divide and then extend. In the seed, the nucellus degenerates and the endosperm and embryo develop. The endosperm forms from free nuclei that divide and subsequently produce cell walls (cellularization). These endosperm cells then undergo cell division and cell differentiation into the aleurone layer, the modified aleurone (or aleurone transfer cells) and starchy endosperm cells which switch their metabolism to accumulate storage compounds. In parallel, the outer layers undergo drastic changes. The parenchyma cells of the pericarp are eliminated through a developmental programmed cell death. Other living outer tissues active in the early development phase collapse at the end of the development. This is the case for the photosynthetically active inner pericarp, the seed coat, and nucellar epidermis. At the end of the filling phase, the grain enters the maturation phase and desiccates [START_REF] Xiong | Structural and physiological characterization during wheat pericarp development[END_REF][START_REF] Sabelli | The Development of Endosperm in Grasses[END_REF].

During the stage of grain filling, precursors of storage compounds are transported from the wheat mother plant to the endosperm via the vascular tissues located in the pericarp in the grain ventral region [START_REF] Lingle | Development of the vascular tissue of the wheat and barley caryopsis as related to the rate and duration of grain filling[END_REF]. This region forms a crease, which is particularly deep in wheat (and in barley) when compared to other cereals [START_REF] Hands | Analysis of grain characters in temperate grasses reveals distinctive patterns of endosperm organization associated with grain shape[END_REF]. From the maternal vascular tissue, the route to the endosperm passes through the chalaza, the nucellar projection cells, towards the aleurone transfer cells and starchy endosperm cells [START_REF] Xurun | Structural development of wheat nutrient transfer tissues and their relationships with filial tissues development[END_REF] (Fig. 1). In wheat, as in barley, the nucellar projection cells and the endosperm transfer cells are separated by a cavity named endosperm cavity where nutrients and water are released [START_REF] Xurun | Structural development of wheat nutrient transfer tissues and their relationships with filial tissues development[END_REF][START_REF] Thiel | Development of endosperm transfer cells in barley[END_REF][START_REF] Zheng | Contrast observation and investigation of wheat endosperm transfer cells and nucellar projection transfer cells[END_REF]. Subsequently, the nutrients are captured by the aleurone transfer cells [START_REF] Ugalde | Route of substrate movement into wheat endosperm. II. Amino acids[END_REF], which exhibit specific features such as thickened cell walls and wall ingrowths facilitating nutrient uptake [START_REF] Xurun | Structural development of wheat nutrient transfer tissues and their relationships with filial tissues development[END_REF]. A recent study in barley revealed the importance of the integrity of the endosperm cavity and transfer cells for grain development and filling [START_REF] Lim | Overexpression of HvCslF6 in barley grain alters carbohydrate partitioning plus transfer tissue and endosperm development[END_REF].

The wheat endosperm cavity and its content named cavity "sap" were studied in the eighties/nineties [START_REF] Ugalde | Route of substrate movement into wheat endosperm. II. Amino acids[END_REF][START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VI. Gradients along the transport pathway from the peduncle to the endosperm cavity during grain filling[END_REF][START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF][START_REF] Wang | Sucrose Release into the Endosperm Cavity of Wheat Grains Apparently Occurs by Facilitated Diffusion across the Nucellar Cell Membranes[END_REF] and more recently in barley [START_REF] Peukert | Spatiotemporal dynamics of fructan metabolism in developing barley grains[END_REF][START_REF] Peukert | Spatiotemporal dynamics of oligofructan metabolism and suggested functions in developing cereal grains[END_REF]. It was described to contain sucrose, glucose, amino acids, potassium, and fructans (soluble fructose-based oligosaccharides) [START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VI. Gradients along the transport pathway from the peduncle to the endosperm cavity during grain filling[END_REF][START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF].

However, Fisher and Gifford [START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF] hypothesized that the cavity also contains high molecular weight compounds that cause the cavity content to appear viscous.

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While studying the histology and cell wall composition of developing wheat grains with respect to grain growth [START_REF] Robert | Change in wall composition of transfer and aleurone cells during wheat grain development[END_REF][START_REF] Chateigner-Boutin | Ferulate and lignin cross-links increase in cell walls of wheat grain outer layers during late development[END_REF][START_REF] Ghaffari | Multiexcitation hyperspectral autofluorescence imaging for the exploration of biological samples[END_REF][START_REF] Le | Use of X-ray micro computed tomography imaging to analyze the morphology of wheat grain through its development[END_REF], the crease region has captured our interest. Micro-computed X-Ray tomography revealed that the internal compartment comprising the endosperm, nucellar epidermis and seed coat is entirely filled from anthesis to the grain filling stage [START_REF] Le | Use of X-ray micro computed tomography imaging to analyze the morphology of wheat grain through its development[END_REF]. A gel-like structure was observed in the endosperm cavity of developing wheat grains, and this structure exhibited autofluorescence properties.

The objective of this work was to study the biochemical composition of the endosperm cavity content and its evolution during grain development, to identify the high molecular compound responsible for its gel-like appearance and to explore its biological function.

Material and methods

Plant material and growth conditions

Growth of the wheat (Triticum aestivum L. cv Recital) plants and grain harvesting was carried out as described in [START_REF] Verhertbruggen | The TaCslA12 gene expressed in the wheat grain endosperm synthesizes wheatlike mannan when expressed in yeast and Arabidopsis[END_REF]. Briefly, the plants were grown in a controlled glasshouse at INRAE Le Rheu (France), individual spikes were tagged at flowering and stages were assessed by the thermal time method (cumulated average temperature in Celsius degrees per day after flowering, °DAF). The two basal grains of the spike middle spikelets were harvested at different stages of development.

Sample preparation, sectioning and microscopy acquisitions

Wheat grain samples were prepared and imaged using different methods. The procedures of sample preparation, sectioning and acquisition settings are indicated in Table 1 with references.

For immunolabelings, the antibody used was anti-AX1 which targets cell wall arabinoxylans [START_REF] Guillon | Generation of polyclonal and monoclonal antibodies against arabinoxylans and their use for immunocytochemical location of arabinoxylans in cell walls of endosperm of wheat[END_REF].

The procedure was described in [START_REF] Chateigner-Boutin | The wheat grain contains pectic domains exhibiting specific spatial and development-associated distribution[END_REF]. Control experiments were performed without primary antibodies.

The grain samples used for staining and immunodetection were embedded, for all other image acquisitions, freshly harvested grain samples were directly frozen and cut immediately without further preparation.

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For confocal imaging and fluorescence profile analyses, sections were placed on a quartz slide and observed mounted in air using a confocal laser-scanning system (A1, Nikon). The microscope was equipped with a spectral detector unit. At the chosen magnification, the field of view was 312 × 312 µm and images were digitized as matrix of 512 × 512 pixels with a pixel size of 0.61 × 0.61 µm.

Hyperspectral images were recorded by collecting emitted light from 414 to 704 nm for UV excitation with a 10 nm step between spectral variables. A dichroic mirror was used to filter the excitation wavelengths. Three grains were imaged per development stage. Emission profiles of gels and nucellus epidermis cell walls were directly extracted from the images using the Nikon software. For the three grains per stage, on one image, several regions within the gel and within the nucellar epidermis cell walls were selected. Average emission spectra were calculated by integrating the results for the regions and the three grains.

For deep UV autofluorescence multispectral acquisitions, the full field so-called TELEMOS microscope of the DISCO beamline at the synchrotron SOLEIL was used [START_REF] Jamme | Synchrotron UV fluorescence microscopy uncovers new probes in cells and tissues[END_REF][START_REF] Jamme | Deep UV autofluorescence microscopy for cell biology and tissue histology[END_REF]. Deep UV excitation was set to 280 nm and fluorescence emission was recorded using 9 different band-pass filters with optimized acquisition time (Table 1). The samples were placed between quartz lamella (R52-5000, ESCO Optics). They included grain cryo-sections and reference samples (commercial ferulic and pcoumaric acid, purified ferulic acid ester-linked to arabinose, gluten, and lignin from maize stem). The field of view was 292 x 292 µm 2 and pixel size 0.2768 µm. Images were background subtracted and processed to compensate illumination inhomogeneity as in [START_REF] Vidot | Phenolic distribution in apple epidermal and outer cortex tissue by multispectral deep-UV autofluorescence cryo-imaging[END_REF]. Fluorescence emission was valued based on the grey scale intensity of pixels. Pseudospectra were obtained from the multispectral images: pixels were manually selected in targeted structures and their intensity profile was extracted using a home-made function in Matlab [START_REF] Corcel | Comparison of UV and visible autofluorescence of wheat grain tissues in macroscopic images of cross-sections and particles[END_REF].

Fourier Transform-InfraRed (FT-IR) spectroscopy

Cryo-sections (transverse, 30 µm thickness) of fresh grains were collected on ZnS windows. IR micro-spectroscopy was performed on a Tensor 27 (Bruker) spectrometer equipped with a Hyperion 2000 microscope (Bruker). The detector of the IR microscope was a liquid nitrogen cooled mercury cadmium telluride detector. Bright-field images were obtained using a Sony camera (Exwave HAD, SSC-DC80P). IR spectra were collected in transmission mode between 2000-700 cm -1 at a resolution of 8 cm -1 using a 15X objective (NA 0.4), using a double path single masking aperture size varying from 25x25 to 50x50 µm depending on the cavity shape. IR spectra resulted from the co-addition of J o u r n a l P r e -p r o o f unit vector normalized using Opus software 7.5. The second derivative data were obtained using Norris gap algorithm (Unscrambler software 10.1, Camo). Two series of analyses were conducted on grains harvested from wheat plants grown in two different years and for both years, 3 grains were analyzed per stage. The arabinoxylan fractions with different arabinose-to-xylose ratios (A/X, 0.41 and 0.67) used as reference were obtained as described in [START_REF] Dervilly | Isolation of homogeneous fractions from wheat water-soluble arabinoxylans. Influence of the structure on their macromolecular characteristics[END_REF].

Laser microdissection and biochemical analysis

Fourty grains coming from 10 spikes were cryo-sectioned for two stages (350°DAF and 650°DAF). Cryo-sections (100 µm thick) were placed on dissection slides (16x45 mm with 1.4 µm membrane in polyethylene terephthalate 11505151, LEICA). Laser assisted microdissection was carried out using a Laser assisted microdissecter LMD 7000 (LEICA). The sections were visualized in bright-field conditions. Parameters were: objective x10, power 43, opening 21, speed 37, point-topoint mode. The dissected regions were collected in PCR tubes in a drop of water and stored at -20°C.

Ester-linked phenolic compounds were analyzed after mild alkaline hydrolysis essentially as described in [START_REF] Ho-Yue-Kuang | Mutation in Brachypodium caffeic acid O-methyltransferase 6 alters stem and grain lignins and improves straw saccharification without deteriorating grain quality[END_REF]. 150 µL of 1 N NaOH were added to the sections and the reaction mixture was (pure aleurone layer, wheat and maize bran) and according to their UV absorption spectra [START_REF] Waldron | Cell wall esterified phenolic dimers: identification and quantification by reverse phase high performance liquid chromatography and diode array detection[END_REF].

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Microscopic Magnetic Resonance Imaging (MRI)

MRI experiments were carried out at room temperature on a Bruker AVANCE III 400 MHz NMR spectrometer equipped with a 9 Tesla/89 mm vertical-bore superconducting magnet and microimaging accessory. Individual grains were placed vertically in a homemade Teflon holder incorporating a capillary (inner diameter, 1 mm) filled with doped water for NMR signal amplitude normalization purpose. Proton density images were acquired using multi-slice gradient echo pulse sequence. A 30° excitation pulse (0.43 ms length; 3 kHz bandwidth) was used and the echo time was 1.2 ms. Repetition time of 1 s was sufficient for full relaxation of the magnetization. All transverse 2D

images had an acquisition matrix size of 100×100, with a slice thickness of 0.5 mm. Depending on grain dimensions, the field of view was 5×5 mm, 6×6 mm and 6.45×6.45 mm for 250, 850 and 650 °DAF, respectively, resulting in 2D in-plane pixel sizes of 50×50 µm, 60×60 µm and 64.5×64.5 µm.

Fourteen to sixteen contiguous slices were acquired to cover the whole grain. The number of averages was 72 for a total acquisition time of 2 h per grain. Three quantitative criteria were estimated from MRI images: (1) the water content of the grain,

(2) the water content of the cavity, and (3) the volume of the cavity. In order to obtain these measurements, each component was extracted by image segmentation. First, denoising was achieved by a non-local means method suited to MRI images [START_REF] Wiest-Daesslé | Rician noise removal by nonlocal means filtering for low signal-to-noise ratio MRI: applications to DT-MRI, in: medical image computing and computer-assisted intervention[END_REF]. The grain and the cavity were segmented by a region growing algorithm with a manually selected seed and threshold. The water content of a segmented component was determined by its average intensity relative to the average intensity of the water-filled capillary. The volume (in mm 3 ) was estimated by the total number of voxels in a segmented component multiplied by the voxel size.

Results and discussion

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3.1 The endosperm cavity of the wheat grain contains a "gel-like" structure that autofluoresces upon UV excitation.

In our studies of wheat grain development, we have imaged numerous sections of wheat grains at different stages [17-19, 23, 32, 33]. During the course of these studies, the endosperm cavity raised our attention. Indeed, the grain cavity content appears like a gel (Fig. 1). Upon grain sectioning, the contents of the cavity do not leak but remain in place. Microcapillar tubes and pipettes with small diameter tips (300 nm) were used to try and aspirate the cavity content for analysis, but these attempts failed. All these observations suggest that the content of the cavity is viscous as described by Fisher and Gifford [START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF].

The "gel" is visible on grain sections from the onset of grain filling (around 200°DAF for Recital; [START_REF] Chateigner-Boutin | Ferulate and lignin cross-links increase in cell walls of wheat grain outer layers during late development[END_REF]) to maturity, and in rehydrated mature grains (Fig. S1).

We conducted several studies on the fluorescence properties of wheat grain tissues [START_REF] Ghaffari | Multiexcitation hyperspectral autofluorescence imaging for the exploration of biological samples[END_REF][START_REF] Corcel | Comparison of UV and visible autofluorescence of wheat grain tissues in macroscopic images of cross-sections and particles[END_REF] in which we noticed another remarkable feature of the cavity content: it appeared to fluoresce under UV excitation. Examples of fluorescence imaging of wheat grain sections is given in Fig. S1. The cavity content fluoresces although less than other grain tissues. The fluorescence properties of the "gel"

were studied using multi/hyperspectral analysis and compared to that of other grain tissues. Analysis of the intensity profiles confirmed that upon excitation in UV the "gel" fluoresces with less intensity than its surrounding tissues (Fig. 2). The fluorescence intensity of "gels" from grains harvested at different stages of development increased from 250°DAF to 750°DAF (Fig. 2A).

Among the compounds known to autofluoresce in the wheat grain, there are hydroxycinnamic acids (ferulic and p-coumaric acids). Hydroxycinnamic acids have an absorption/excitability maximum below 350 nm [START_REF] Vidot | Phenolic distribution in apple epidermal and outer cortex tissue by multispectral deep-UV autofluorescence cryo-imaging[END_REF], but conventional microscopes are limited in this range with 350 nm cut-off. We decided to take advantage of the sensitivity of synchrotron deep UV microscopy to compare the fluorescence profile of the "gel" at one stage with that of autofluorescent compounds known to be present in the wheat grain. It exhibits two main emission peaks at 370-410 nm and 420-480 nm similar to that obtained for the walls of the nucellar epidermis and from ferulic acid ester-linked to arabinose (Fig. 2B). Ferulic acid is linked to several compounds including the arabinosyl residues of arabinoxylans (AX), a major class of polysaccharide present in cell walls of cereal grains [START_REF] Chateigner-Boutin | Ferulate and lignin cross-links increase in cell walls of wheat grain outer layers during late development[END_REF][START_REF] Barron | Relative amounts of tissues in mature wheat (Triticum aestivum L.) grain and their carbohydrate and phenolic acid composition[END_REF].

The endosperm cavity contains arabinoxylans and hydroxycinnamic acids which may form a gel

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In the literature, the endosperm cavity content of the wheat grain is reported to be composed of sucrose, glucose, amino acids, and fructans [START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VI. Gradients along the transport pathway from the peduncle to the endosperm cavity during grain filling[END_REF][START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF]. None of these compounds fluoresces under UV excitation. In order to identify the fluorescent compound in the cavity, the cavity content was laser-dissected without touching the surrounding tissues and analyzed. Fluorescence profiles suggested the presence of ester-linked hydroxycinnamic acids, therefore the dissected "gel" was submitted to alkaline hydrolysis to break ester-linkages and the released compounds were analyzed by HPLC with UV detection (Fig. 3). The chromatograms were compared with those obtained for wellcharacterized samples and a negative control without grain sections to discard contaminant peaks due to the membrane used in the laser dissection process. In the "gel" samples, peaks corresponding to ferulic, and p-coumaric acids were identified (Fig. 3). On investigated samples, the peak for ferulic acid has a more important area than the one corresponding to p-coumaric. Peaks corresponding to ferulic acid dimers were also observed. These structures cross-link AX chains in cereal grain cell walls [START_REF] Barron | Relative amounts of tissues in mature wheat (Triticum aestivum L.) grain and their carbohydrate and phenolic acid composition[END_REF].

Fisher and Gifford [START_REF] Fisher | Accumulation and conversion of sugars by developing wheat grains: VII. Effect of changes in sieve tube and endosperm cavity sap concentrations on the grain filling rate[END_REF] estimated that a yet-to be identified compound would be responsible to the cavity content viscous appearance. AX is known to have gelling properties [START_REF] Izydorczyk | Cereal arabinoxylans: Advances in structure and physicochemical properties[END_REF][START_REF] Saulnier | Plant Cell Wall Polysaccharides in Storage Organs: Xylans (Food Applications)[END_REF]. We therefore investigated the possibility that the cavity "gel" contains AX.

FT-IR is a method suitable to detect and identify polysaccharides in plant tissues and was already used to study AX in wheat grains [START_REF] Robert | Change in wall composition of transfer and aleurone cells during wheat grain development[END_REF][START_REF] Philippe | Deposition of cell wall polysaccharides in wheat endosperm during grain development: fourier transform-infrared microspectroscopy study[END_REF][START_REF] Jamme | Aleurone cell walls of wheat grain: high spatial resolution investigation using synchrotron infrared microspectroscopy[END_REF]. FT-IR analysis was conducted on cryo-sections of grains harvested at several development stages. The Bright-field camera coupled to the spectrometer allowed to target specifically the cavity content.

As for grain tissues, the cavity content comprises several compounds; therefore, the recorded spectra correspond to that of a mix of individual spectra. Different types of spectra were collected in the cavity "gel" and compared with reference spectra (Fig. 4A). On some spectra, a starch-specific peak (930 cm -1 ) and protein-specific signatures were recorded (amide I absorption bands around 1645 cm -1 (C=O and C-N) and amide II assignment at 1540 cm -1 (C-N, N-H)). On all samples, typical spectra of AX were detected (Fig. 4A,B). The band around 1041 cm -1 with a shoulder at 990 cm -1 assigned to C-C and C-O stretching modes of polysaccharides are typical bands of AX [START_REF] Jamme | Aleurone cell walls of wheat grain: high spatial resolution investigation using synchrotron infrared microspectroscopy[END_REF]. The 1160 cm -1 band is assigned to the C-O-C stretching mode of glycosidic linkages and the peak at about 898 cm -1 corresponds to the β(1-4) configuration of the xylan chain.

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The structure of AX varies according to the wheat grain tissue and the development stage.

This concerns the number of arabinosyl residues on the xylan backbone (degree of substitution with arabinose) and the number of hydroxycinnamic acids residues (ferulic and p-coumaric acid) esterlinked to the arabinose [START_REF] Chateigner-Boutin | Ferulate and lignin cross-links increase in cell walls of wheat grain outer layers during late development[END_REF][START_REF] Philippe | Deposition of cell wall polysaccharides in wheat endosperm during grain development: fourier transform-infrared microspectroscopy study[END_REF]. Relatively strong absorption bands at 1160 cm -1 and 990 cm -1 , and an absorption peak at 985 cm -1 , highlighted on the second derivative spectra (Fig. 4C), were previously described as marker of a relatively low degree of substitution with arabinose [START_REF] Robert | FT-IR investigation of cell wall polysaccharides from cereal grains. Arabinoxylan infrared assignment[END_REF]. The aromatic skeletal vibration at about 1590 and 1515 cm -1 associated with bands at about 810 and 850 cm -1 (out of plane C-H bending) was assigned to ferulic acid ester [START_REF] Sebastian | Molecular structure, spectroscopic studies and first-order molecular hyperpolarizabilities of ferulic acid by density functional study[END_REF][START_REF] Chazal | Investigating lignin key features in maize lignocelluloses using infrared spectroscopy[END_REF]. Thus, when comparing with reference spectra of AX, the AX FT-IR signal in the wheat cavity corresponded to AX with a relatively low level of substitution with arabinose and with ester-linked ferulic acid.

Only subtle variations were observed in the FT-IR AX spectra between development stages and mainly at late stages.

Among the reported favorable factors for the AX gelation, there are a high content of ferulic acid, a high molecular weight/hydrodynamic volume, and a low-substituted xylan backbone [START_REF] Izydorczyk | Cereal arabinoxylans: Advances in structure and physicochemical properties[END_REF][START_REF] Rattan | Structure and rheological behaviour of arabinoxylans from Canadian bread wheat flours[END_REF][START_REF] Dervilly-Pinel | Water-extractable arabinoxylan from pearled flours of wheat, barley, rye and triticale. Evidence for the presence of ferulic acid dimers and their involvement in gel formation[END_REF]. The gelation of feruloylated AXs occurs via covalent cross-links of AX chains due to oxidative coupling of ferulic acid residues [START_REF] Carvajal-Millan | Arabinoxylan gels: Impact of the feruloylation degree on their structure and properties[END_REF] resulting in the occurrence of ferulate dimers. The cavity AX has a low-substitution level with arabinose, it contains ferulic acid probably ester-linked to AX chains, and ferulate dimers. These results suggest that cavity AXs features are favorable for AX gelation.

Origins of the AX present in the gel

In order to identify the tissue origin of the cavity AX, immunolabeling experiments were carried out on sections of grains harvested at different stages of development from flowering (0°DAF)

to the onset of grain filling (200°DAF) with an antibody targeting AX. Anti-AX1 recognizes xylan and tolerates arabinose substitution [START_REF] Guillon | Generation of polyclonal and monoclonal antibodies against arabinoxylans and their use for immunocytochemical location of arabinoxylans in cell walls of endosperm of wheat[END_REF].

In wheat ovary at flowering and at 60°DAF, signals were observed in the cell walls of vascular cells and of some cells in the developing nucellar projection (Fig. 5). At 90°DAF the cell wall of the nucellar epidermis in contact with the endosperm appeared labeled. There is a clear polarity in the labeling since only one of the periclinal cell walls reacted with anti-AX1 at this stage (Fig. 5). From 110 °DAF, one cell layer of the nucellar projection is particularly labeled (Fig. 5). Cell walls of the endosperm transfer cells also reacted with anti-AX1 from this stage. At 200°DAF, the anti-AX1 labeling J o u r n a l P r e -p r o o f of the nucellar epidermis is detected in all cell walls of this cell layer. The anti-AX1 antibody positively labeled the "gel" present inside the cavity (Fig. 5 and Fig. 6). Positive labeling was also observed inside cells of the nucellar epidermis in Golgi apparatus and vesicles in the different regions of the grain, and in the apoplast between the nucellar epidermis and the endosperm (Fig. 6).

Considering the temporal coincidence between the labeling of the nucellar epidermis and that of the cavity content, considering the proximity of both structures, the intensity of the labeling of the nucellar epidermis and the high vesicular activity apparently associated, it is likely that the nucellar epidermis is the tissue that produces the AX of the cavity.

The cavity gel is highly hydrated even at late development stages

AX is a structural polysaccharide with major function in the cell wall architecture of cereal grains. In addition, this polysaccharide has gel-forming properties (as mentioned earlier in the text)

and high water-binding capacity [START_REF] Saulnier | Plant Cell Wall Polysaccharides in Storage Organs: Xylans (Food Applications)[END_REF][START_REF] Bonnand-Ducasse | Effect of wheat dietary fibres on bread dough development and rheological properties[END_REF]. The hydration properties of AX depend of the arabinose distribution on the xylan backbone. Films made with low substituted AXs absorb slightly more water than with highly substituted AXs [START_REF] Ying | Hydration and mechanical properties of arabinoxylans and β-D-glucans films[END_REF]. Cell wall AXs were also suggested to be involved in the modulation of water diffusion in the wheat grain [START_REF] Fanuel | Distribution of cell wall hemicelluloses in the wheat grain endosperm: a 3D perspective[END_REF][START_REF] Ying | Role of aleurone cell walls in water diffusion and distribution within cereal grains[END_REF][START_REF] Gao | Variation in cell wall structure and composition of wheat grain based on geography and regulatory effect of cell wall on water mobility[END_REF]. One of the hypothetical function of AX in the cavity might be to maintain hydration.

We therefore studied water level and water distribution in wheat grains at three stages of development. Global water content for the stages were 75 ± 1 % at 250°DAF (grain filling), 51 ± 2 % at 650°DAF (end of filling), 40 ± 1 % at 850°DAF (desiccation stage). Microscopic MRI experiments were conducted using multislice acquisitions along the grain longitudinal axis to cover the entire grain and allow the visualization of water distribution in the different tissues and regions. Variations were observed between the three stages (Fig. 7). A high NMR signal was obtained in the endosperm at 250°DAF and lower signal at 850°DAF. Local variations were highlighted. An intense NMR signal signifying high water content was obtained in the vascular bundle of the pericarp responsible for the grain water supply and in the endosperm cavity for the three stages (Fig. 7). By normalization to the water reference signal, the water content of the cavity was estimated to be 87 ± 3 %, whatever the stage and whatever the volume of the cavity (the cavity volume was estimated to be 0.57 ± 0.13 mm 3 , 2.34 ± 0.47 mm 3 and 0.62 ± 0.11 mm 3 at 250, 650 and 850°DAF, respectively).

J o u r n a l P r e -p r o o f from the filling stage to the desiccation stage although the grain water level drops at the desiccation stage [START_REF] Neghliz | Ear rachis xylem occlusion and associated loss in hydraulic conductance coincide with the end of grain filling for wheat[END_REF].

Conclusion:

Our study of the wheat endosperm cavity confirmed that it is filled with a gel-like structure.

In addition to the compounds already known to be present in the cavity, we showed the presence of AX and hydroxycinnamic acids, which are likely involved in the gel-like appearance of the cavity content. We also showed that the cavity content stays highly hydrated through the grain development and maturation. To address the biological significance of the cavity AX, mutants or variants altered in AX will be explored.

J o u r n a l P r e -p r o o f show the fluorescence of the grain tissues (left), the cavity gel (middle), and ferulic acid ester-linked to arabinose. Lines: pixels selected for the fluorescence intensity extraction. Pseudospectra averaged for all selected pixels of wheat grain tissues, cavity content and reference compounds. The gel pseudospectra is similar to that of nucellus epidermis and to that of FerAX, but different from that of ferulic acid especially in the spectral range 370-410 nm.

Se: starchy endosperm, al: aleurone layer, ne: nucellar epidermis, tc: transfer cells, p: pericarp. J o u r n a l P r e -p r o o f

  incubated overnight at room temperature. The tubes were centrifuged to discard the dissection membranes. The reaction mixture was then acidified with 35 µL of 6 M HCL. After centrifugation (1500 g, 10 min), the supernatant was deposited onto a solid-phase extraction cartridge (Waters Sep-Pak Plus Short tC18 cartridges) pre-conditioned before use. Washes and elution were conducted with 1 mL solutions. The samples were filtrated (0.45 μm) and concentrated three times using a concentrator SpeedVac Savant (Thermo Scientific) and then analyzed by HPLC combined with UV diode array detection (HPLC-DAD). The samples (2 µl) were injected onto a RP18 (Macherey Nagel 2x50 mm 2.7 μm particle size, Nucleoshell RP18plus) column with a flow rate of 0.3 ml.min -1 . The eluents were 0.1 % formic acid in water (A) and 0.1 % formic acid in acetonitrile (B), and the gradient was: 0-3 min, 8 % B; 3-20 min increase to 20 % B, 20-23 min 20 % B; 23-24 min increase to 60 % B; 24-26 min decrease to 8 % B; 26-28 min 8 % B. Peaks were assigned from the 320 nm DAD chromatograms according to their retention time by comparison with well-characterized samples

Four

  grains were analyzed by MRI per development stage. The global water content of grains harvested at the same time than those analyzed by MRI was determined on minimum 12 grains per stage. Grains were weighed immediately after harvesting, then oven-dried (60 °C for 48 h) and weighed afterwards to deduce the water content.

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. The cavity content autofluoresces upon UV-light excitation and its fluorescence intensity profile resembles that of the nucellar epidermis and aleurone cell walls and of ferulic acid esterlinked to arabinose (FerAX). Fluorescence studies of wheat grain sections and reference compounds: representative images and fluorescence profiles. Grains were harvested, immediately freezed and cryo-sectioned. The sections were placed on quartz slides.

Fig. 3 .

 3 Fig. 3. The endosperm cavity contains hydroxycinnamic acids. (A) Images of the wheat endosperm cavity before and after laser-dissection of the gel (stage 650°DAF). (B) Chromatogram showing compounds released from dissected cavity content upon mild alkaline hydrolysis and separation on a C18 HPLC column combined with diode array detection. p-coumaric acid (pCA), ferulic acid (FA), and dimers of FA (diFA) were identified according to their retention time and absorption spectra by comparison with commercial FA and pCA and well-characterized samples (wheat aleurone, and maize bran). Peaks annotated with a star were shown to correspond to contaminant compounds from the dissection membrane.

Fig. 4 .

 4 Fig. 4. Fourier Transform-InfraRed spectroscopy revealed the presence of arabinoxylans (AX), proteins and starch in the wheat grain endosperm cavity. (A) Different types of spectra recorded in the cavity of cryo-sectioned grains. (B) Average spectra with major AX signals obtained at different stages of development with B1 showing the second derivative of the signal to highlight the peak attributed to low substituted AX and B2 showing a zoom on the peaks attributed to ferulic acid. (C) Spectra of purified and characterized AX fractions with contrasted levels of substitution with arabinose (A/X ratio) and C1 Second-derivative of the spectra showing specific peaks for low and high substitution (Robert et al., 2005).

Fig. 5 .Fig. 6 .

 56 Fig. 5. Xylan deposition in the developing wheat grain. Fluorescence micrographs of representative samples of wheat grains at different stages of development from flowering (0°DAF) to the onset of grain filling (200°DAF). Immunolabeling experiments were carried out using the antibody anti-AX1,

Fig. 7 .

 7 Fig. 7. Microscopic Magnetic Resonance Imaging of the developing wheat grain. Transverse images obtained on representative grains at different stages: (A) 250°DAF, (B) 650°DAF and (C) 850°DAF. For each stage, eight contiguous slices are shown (numbered 1 to 8). For an example of complete wheat grain see figure S2. Images reveal the structure and water content of the grain. The color scale on the right indicates the normalized water content (in %).

Fig 1 J

 1 Fig 1

Fig 2 J

 2 Fig 2

Fig 4 J

 4 Fig 4

Fig 6 J

 6 Fig 6

Fig 7 J

 7 Fig 7

Table 1 Sample preparation, sectioning and acquisition settings for microscopy

 1

	Purpose	Sample	Sectioning		Section	Microscope		Acquisition settings
		preparation	(transverse in	treatments
			equatorial
			region if not
			mentioned
			otherwise)
	Macroscopic	None	Scalpel		None	Stereomicroscope	SMZ800	Bright-field
	observations		(transverse &		Nikon, objective x1 plan apo
	whole grain		longitudinal)		WD70; camera Digital Sight
	Fig. 1					DS-Fi2
	Tissue	Cryo-	Semi-thin		Toluidine	Multizoom	macroscope	Bright-field
	organization	substituted	sections	(1	blue	AZ100M Nikon, objective x5
	Fig. 1	(high pressure	µm, ultracut	staining	(zoom 8) AZ plan Fluor NA 0.5
	freezing and substitution with Lowicryl HM20) [33] None None None None Resin embedded LRWhite [23] Resin embedded J o u r n a l P r e -p r o o f UC7, Leica) WD 15; camera EXI Aqua QImaging 14 bits equipped with filter wheel RGB-HM-S-IR Tissue organization: gel Fig. 1 Cryo-sections (30 µm); cryotome (HM500 OM, Microm) None Confocal laser scanning system A1 Nikon, objective x20 (zoom 2); transmitted light detector Bright-field UV-vis autofluorescence spectral imaging Fig S1 Cryo-sections (30 µm); cryotome (HM500 OM, Microm) None Microscope DMRD Leica, objective x10 plan Fluotar NA 0.3; camera Nikon DS-1QM 12 bits Excitation (nm) band-pass 340-380 Emission (nm) > 425 Hyperspectral imaging Fig. 2A Cryo-sections (30 µm); cryotome (HM500 OM, Microm) None Confocal laser scanning system A1 Nikon, equipped with a 32 channel PMT spectral detector unit; objective x20 (zoom 2) Emitted light collected from 400 to 720 nm Excitation (nm) 375 Emission (nm) band-pass filter 425-475 414 to 704 (dichroic mirror) Deep UV autofluorescence spectral imaging Fig. 2B Cryo-sections (20 µm) cryotome (HM500 OM, Microm) None TELEMOS synchrotron SOLEIL Zeiss Axio Observer Z-1, objective x40; CCD camera Pixis BUV 16 bits Princeton instrument Excitation (nm) 280 Multispectral acquisitions Emission filters (nm) : 1:327-353 ; 2: 370-410; 3: 412-438; 4: 420-480; 5: 435-455; 6: 484-504; 7: 499-529; 8: 530-570, 9: 535-607 5 sec for all filters Cell wall polysaccharide immunodetection Fig. 5 and 6 Semi-thin sections (1 µm; ultracut UC7, Leica) Immuno-labelings Microscope DMRD Leica, objective x20 plan Apo NA 0.6 and x40 plan Apo NA 0.75; camera Nikon DS-1QM 12 bits Fluorescence [23] Excitation (nm) band-pass 515-560 Emission (nm) >590. For a given antibody, same time of exposure for all samples. Cell wall polysaccharide Ultra-thin sections (80 Immuno-labelings JEOL JEM 1230 transmission electron microscope; camera
	immunodetection	LRWhite and	nm, ultracut		GATAN ES500W Erlangshen
	Fig. 6	cryo-	UC7, Leica)			model 782
		substituted
		[23, 33]

Acknowledgements

The authors acknowledge particularly J.-C. Helleisen and B. Rolland (INRAE Le Rheu) for growing and labeling the wheat plants. We are indebted to C. Lapierre for sharing protocols and expertise. µMRI experiments were performed at the BIBS facility (UR1268 BIA, IBiSA, Phenome-Emphasis-FR (grant number ANR-11-INBS-0012)). Laser microdissection was performed at the APEX platform in Nantes, we acknowledge C. Babarit for training on laser microdissecter. J o u r n a l P r e -p r o o f

Fig 5 J o u r n a l P r e -p r o o f

Fundings BIBS facility (UR1268 BIA, IBiSA, Phenome-Emphasis-FR (grant number ANR-11-INBS-0012)) Part of this work was funded by the synchrotron SOLEIL under the proposal number 20190336.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Damien Bigourd
email: damien.bigourd@femto-st.fr

Coralie Fourcade Dutin

Olivier Vanvincq

Emmanuel Hugonnot

Numerical analysis of broad band fiber optical parametric amplifiers pumped by two chirped pulses

Optical parametric amplifier pumped by two chirped pump pulses has been analytically and numerically investigated to predict the spectral gain bandwidth and its temporal distribution. We highlight that the properties of the amplifier depend strongly on the relative chirp values and a uniform spectro-temporal gain can be obtained when the two chirps have opposite signs. A chirped signal pulse owing a very broad bandwidth has also been injected and we demonstrate the amplification of ultra-short pulse with this type of amplifiers.

Introduction

Ultra-fast four wave mixing parametric process in guided systems has been investigated in various configurations since it can exhibit a very large gain-bandwidth suitable for wide tunability and for the amplification of ultrashort pulses [START_REF] Faccio | Optical amplification in the near-infrared in gas-filled hollow-core fibers[END_REF][START_REF] Flory | Kerr-gated generation of fewcycle mid-IR pulses in a four-wave mixing parametric amplifier[END_REF][START_REF] Nodop | Efficient high-power generation of visible and mid-infrared light by degenerate four-wave-mixing in a large-mode-area photonic-crystal fiber[END_REF][START_REF] Hanna | Fiber optical parametric chirped pulse amplification in the femtosecond regime[END_REF][START_REF] Bigourd | High-gain fiber, optical parametric chirped pulse amplification of femtosecond pulses at 1 µm[END_REF]. Ultra-short pulses with high peak power can be directly injected in hollow core fibers or capillaries that have high optical damage threshold [START_REF] Ouzounov | Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers[END_REF]. When solid core fibers are the amplification medium, the ultra-short pulse is firstly chirped to decrease the peak power before amplification. In this case, the amplifier is often pumped by a strong quasi-continuous wave (CW) with long (few ps or ns) pulse duration to temporally overlap with the stretched signal [START_REF] Bigourd | High-gain fiber, optical parametric chirped pulse amplification of femtosecond pulses at 1 µm[END_REF][START_REF] Caucheteur | Experimental demonstration of optical parametric chirped pulse amplification in optical fiber[END_REF][START_REF] Zhou | All-fiber based ultrashort pulse generation and chirped pulse amplification through parametric processes[END_REF][START_REF] Cristofori | Dynamic characterization and amplification of sub-picosecond pulses in fiber optical parametric chirped pulse amplifiers[END_REF]. The parametric gain bandwidth defines the spectrum that can be amplified and thus the minimum pulse duration delivered by the amplifier. Some efforts have already been done to enhance the parametric bandwidth with different configurations, for instance, by employing an idlerband distributed fiber loss [START_REF] Xu | Synthesis of broad band and Flat parametric gain by idler loss in optical fiber[END_REF], a specific fiber with tailored properties [START_REF] Marhic | High nonlinearity fiber optical parametric amplifier with periodic dispersion compensation[END_REF][START_REF] Fourcade-Dutin | 12 THz flat gain fiber optical parametric amplifiers with dispersion varying fibers[END_REF] or a single stretched short pulse which pumps a standard fiber [START_REF] Bigourd | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses[END_REF]. Another possibility is to pump the fiber by two quasi-CW pulses [START_REF] Marhic | Broad band fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra[END_REF][START_REF] Vedadi | Investigation of gain ripple in two-pump fiber optical parametric amplifiers[END_REF]. This configuration exhibits very large spectral gain up to 300 nm between the two pump waves [START_REF] Gao | Two-pump fiber optical parametric amplifiers with three-section fibers allocation[END_REF] which is a key feature for an ultra-fast amplifier [START_REF] Mussot | Amplification of ultra-short optical pulses in a two pump fiber optical parametric chirped pulse amplifier[END_REF]. However, this system requires several pump lasers emitting spectrally shifted CWs that are synchronized with the stretched signal. In this manuscript, we are investigated the parametric process with two pump pulses with large bandwidth. There are several advantages to use chirped pulses instead of quasi-CWs. Firstly, the peak power can be much higher leading to a stronger gain. Secondly, the experimental set-up is easier to implement since the signal and pumps are in pulse mode as it is the case in most laser architectures delivering ultra-short pulses. Self-synchronized pump and signal pulses can be derived from an unique laser system by generating non linearity in fibers [START_REF] Ishii | Widely tunable soliton frequency shifting of few-cycle laser pulses[END_REF][START_REF] Heidt | Pulse preserving flat-top supercontinuum generation in all-normal dispersion photonic crystal fibers[END_REF], by selecting parts of the ultra-wide bandwidth of the signal [START_REF] Schultze | Few-cycle OPCPA system at 143 kHz with more than 1 µJ of pulse energy[END_REF] or by using a two color amplifier seeded by a continuum [START_REF] Al-Kadry | Generation of 400 µW at 17,5 µm using a two-color Yb fiber chirped pulse amplifier[END_REF]. Each pulses are chirped with a standard grating based stretcher or compressor to pump the fiber. A chirped fiber Bragg grating can also be employed to realize a monolithic all fiber system. All the timing between the pulses can be adjusted only by delay stages without complex electronic devices. For example, in parametric amplifiers with nonlinear crystals, it is common to derive the pump and signal from one source [START_REF] Schultze | Few-cycle OPCPA system at 143 kHz with more than 1 µJ of pulse energy[END_REF]. Similar experimental setup can be implemented with our configuration and incorporated in a high power laser chain [START_REF] Morin | µJ range optical parametric chirped pulse amplification of short pulses at 1 µm[END_REF] or in a laser-matter experiment [START_REF] Krebs | Towards isolated attosecond pulses at megahertz repetition rates[END_REF]. However, when pump chirped pulses are used, instantaneous frequencies are temporally separated and thus, a temporal distribution of the spectral gain is expected. In a previous work investigating parametric amplifier pumped by a single chirped pulse, we have observed and predicted the temporal distribution of the gain [START_REF] Bigourd | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses[END_REF][START_REF] Vanvincq | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses Part I : Analytical model[END_REF]. Although the amplifier exhibits very large gain bandwidth, up to 36 THz, capable of amplifying sub-30 fs pulses [START_REF] Fourcade-Dutin | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses Part II : Sub-30 fs pulse amplification at high gain[END_REF], the amplified pulse needs to be firstly tailored such as the signal chirp matches the properties of the amplifier. In the case of the parametric amplifier pumped by two chirped pulses, this temporal distribution can be uniform, provided the chirps have opposite signs. The amplifier exhibits similar performances as the one pumped by two CWs. For other chirp relative signs, the amplifier properties become completely different and are not relevant for ultra-fast pulses. In the next section, an analytical model is presented to predict the behavior of the amplifier and several cases are discussed to highlight the role of the pump chirps and the group delay mismatch between all the pulses. In the third section, a chirped signal pulse with a very broad bandwidth is combined to demonstrate the amplification of ultra-short pulse with this amplifier.

Analytical model of a parametric amplifier pumped by two chirped pulses 2.A. General principle and notations

The general principle is based on a non-degenerate parametric process generally used with two continuous pump waves that provides very large gain bandwidth [START_REF] Marhic | Broad band fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra[END_REF][START_REF] Vedadi | Investigation of gain ripple in two-pump fiber optical parametric amplifiers[END_REF]. In the following, the pumps are in pulse mode and have relatively large bandwidth to allow high peak power and an experimental implementation from an unique laser source. The parametric amplifier pumped by two chirped pulses is described as a wave mixing of four pulses injected in a nonlinear fiber, including two pumps (P 1 , P 2 ) with the large bandwidth, a signal S and a generated idler I with a center angular frequencies ω p10 , ω p20 , ω s0 and ω i0 , respectively (Fig. 1). In order to amplify an ultra-short pulse with very large bandwidth, the signal is a stretched pulse and after amplification the chirp is compensated leading to an amplified and compressed ultra-short pulse (Fig. 1). Fig. 2 displays schematic spectrograms of the injected chirped pulses and introduces the notation required for the model. The temporal phase applied to each pump pulse Φ p10 (τ ), Φ p20 (τ ) induces a delay τ on each spectral component. The instantaneous angular frequencies are given by the time derivative of the phase. In the case of linear chirped pump pulses, the angular frequency shifts (Fig. 2) can be written as

ω p1 (τ ) -ω p10 = α p1 • τ (1)
ω p2 (τ ) -ω p20 = α p2 • τ (2)
with α p1,p2 =-∂Φ p1,p2 (τ )/∂τ . When pumping the amplifier with the two pulses owing relatively broad bands, two instantaneous pump frequencies generate an instantaneous parametric gain at the time τ with specific features. Since FOPA is well described analytically with CWs [START_REF] Marhic | Fiber Optical Parametric Amplifiers, Oscillators and Related Devices[END_REF], we consider the chirped pump pulses as the sum of independent monochromatic waves temporally separated by delays defined by their chirps. Accordingly, all the frequencies are derived from the central frequency

ω c0 = ωp20+ωp10 2
at τ = 0. We defined the central frequency ω c (τ ), half of the pump spectral spacing W p (τ ) and the angular frequency detuning between the signal and the central frequency Ω as (Fig. 2) :

ω c (τ ) = ω p2 (τ ) + ω p1 (τ ) 2 = ω c0 + α p2 + α p1 2 τ (3) W p (τ ) = ω p2 (τ ) -ω p1 (τ ) 2 = W p0 + α p2 -α p1 2 τ (4) Ω(τ ) = 2π × f (τ ) = ω s (τ ) -ω c (τ ) = Ω 0 - α p2 + α p1 2 τ (5)
with W p0 = W p (τ = 0) and Ω 0 = Ω(τ = 0). The dispersion coefficients involved in the derivation are evaluated at the central frequency ω c (β 2c , β 3c , β 4c0 ) and therefore evolved with time from those at τ = 0, (β 2c0 , β 3c0 , β 4c0 ) :

β 2c (τ ) = β 2c0 +β 3c α p2 + α p1 2 τ + β 4c0 2 ( α p2 + α p1 2 τ ) 2 (6) β 3c (τ ) = β 3c0 + β 4c0 α p2 + α p1 2 τ (7)

2.B. Description of the model

A previous analytical model has been developed to describe the parametric amplification when a fiber is pumped by a single chirped pulse [START_REF] Vanvincq | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses Part I : Analytical model[END_REF]. In the following, we present the modification of the model to predict the behavior of parametric amplifier pumped by two chirped pump pulses with the relevant parameters (Eq. 3-7) in the appropriate frame. In order to calculate the amplifier properties, a CW signal is preferentially injected and tuned over the full gain bandwidth; i.e ω s (τ ) = ω s0 . All the waves have the same polarization states. No Raman scattering contribution is considered and the pumps are not depleted; i.e the pump powers are much stronger than all the other waves. From Eq. 3-7, the appropriate angular frequencies and the dispersion parameters evolve with time and this variation can impact directly the temporal distribution of the spectral gain. When the two pump pulses are injected into a loss-less fiber with a nonlinear coefficient γ along the z propagation direction, the signal and idler electric field can be calculated from the equations obtained with two CW pump waves [START_REF] Marhic | Fiber Optical Parametric Amplifiers, Oscillators and Related Devices[END_REF]. P p1 and P p2 are the instantaneous power of the two pumps. For sake of clarity, the time dependency of all parameters is not written in the following equations. By including the previous variables (Eq. 3-7), we obtained :

S(z, Ω 0 , τ ) = e j( 3 2 γPpt+ 1 2 β2cω 2 p + 1 6 β3cΩ 3 + 1 24 β4cω 4 p )z S 0 (Ω 0 ) cosh(gz) + j κ 2g sinh(gz) + jI * 0 (-Ω 0 ) 2γ P p1 P p2 g sinh(gz) (8)
I * (z, -Ω 0 , τ ) = e -j( 3 2 γPpt+ 1 2 β2cω 2 p -1 6 β3cΩ 3 + 1 24 β4cω 4 p )z I * 0 (-Ω 0 ) cosh(gz) -j κ 2g sinh(gz) -jS 0 (Ω 0 ) 2γ P p1 P p2 g sinh(gz) (9)
with S 0 and I 0 the input signal and idler electric field, P pt = P p1 + P p2 the total pump power, and g the parametric gain coefficient given by

g = g(Ω 0 , τ ) = 4γ 2 P p1 P p2 - κ(Ω 0 , τ ) 2 4 ( 10
)
The total phase matching parameter is κ(Ω 0 , τ ) = ∆β(Ω 0 , τ ) + γP pt where ∆β is the linear phase matching parameter given by

∆β(Ω 0 , τ ) = β 2c Ω 2 -W 2 p + β 4c0 12 Ω 4 -W 4 p (11)
From Eq. 11, we deduce that the linear phase matching parameters depends strongly on the two chirp values and their signs leading to a direct impact on the spectrotemporal distribution of the gain. Two cases are detailed in the following where the two chirps have identical or opposite signs. For sake of simplicity, we do not take into account β 4c0 in the following derivation. We also assume the pump bandwidths are much smaller than the spectral spacing between the two pumps and the signal angular frequency detuning (α p1,p2 • τ << W p0 , Ω 0 ) and Ω 0 is away from W p0 . The relative variation of the phase matching from the value at τ =0 is calculated as δ = ∆β(Ω0,τ )-∆β(Ω0τ =0) ∆β(Ω0,τ =0)

. We can show that δ can be written for α p1 = α p2 = α (case δ 1 ) and α p1 = α p2 = -α (case δ 2 ) as :

δ 1 (α p1 = α p2 = α p ) ≈ β 3c0 β 2c0 α p τ (12)
δ 2 (α p1 = -α p2 = -α p ) ≈ 0 ( 13
)
When the two chirps have opposite values, the linear phase matching is uniform for a wide range of signal angular frequency (Ω 0 ) provided the bandwidth is relatively small compared to the pump frequency spacing (Eq. 13). Therefore, we can expect a flat spectrotemporal distribution of the gain during the pump pulse durations while the spectral gain will change over the time for identical chirp values (Eq. 12).

∂ 2 ψ ∂t 2 -i β 3 6
∂ 3 ψ ∂t 3 + β 4 24
∂ 4 ψ ∂t 4 +γ |ψ| 2 ψ = 0 (14)
describing the evolution of the slowly varying total electric field ψ in an optical fiber. Eq. 14 has been solved with the standard split-step Fourier. The temporal resolution is 8 fs and the number of points is 2 18 . The input electric field includes a weak random initial condition that mimics quantum fluctuations, the two chirped pump pulses and a weak CW signal whose frequency is tuned over the full gain bandwidth. After propagation, the signal is selected by a spectral filter and the gain is calculated in the temporal domain for each frequency to map its distribution.

2.D. Discussion of selected cases

To illustrate the discussion, we consider several cases with parameters close to those used in previous experiments [START_REF] Bigourd | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses[END_REF] and numerical analysis [START_REF] Vanvincq | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses Part I : Analytical model[END_REF]. The two pump pulses have a duration of 900 ps full width at half maximum (FWHM) with a super-Gaussian temporal profile. The central angular frequencies are ± (2π)×15 THz (ω c0 = 0). The peak powers are P p1 = P p2 = 10 W and the temporal chirp of pulse 1 is α p1 = -(2π) × 2.25 THz/ns while α p2 varies. Therefore, the spectral bandwidth of pulse 1 is (2π) × 2.02 THz (FWHM) while it changes for the second pulse. For example, when α p2 =0, the wave is quasi-monochromatic. The pumps are injected in a fiber owing a nonlinear coefficient γ = 35 W -1 km -1 and β 20 , β 30 , β 40 equal to 1 × 10 -28 s 2 /m, 1×10 -40 s 3 /m, -1×10 -55 s 4 /m, respectively. The propagation distance is L=10 m.

The gain profile in the anti-Stokes side is calculated at each time from Eq. 8 and Eq. 9. Gain maps representing the spectral gains as a function of time τ are displayed in Fig. 3 for three cases in which α p2 = -α p1 (Fig. 3.a), α p2 = +α p1 (Fig. 3.b) and α p2 = 0 (Fig. 3.c). Fig. 3.gh-i (solid lines) represent the instantaneous gain profiles at τ = 0 (white dashed lines in the maps). Fig. 3.j shows the temporal distribution of the gain at the central frequency (f =0 T Hz) for the three cases : α p2 = -α p1 (blue line), α p2 = +α p1 (red line) and α p2 = 0 (green line). The temporal distributions of the gain change considerably for the three cases. For α p2 = -α p1 , the spectral gain is uniform at each τ since the variation of the phase matching is weak during the pump pulse duration as expected from δ 2 (Eq. 13). The maximum gain is ∼55 dB and varies by less than 8 dB from 0 to 22 THz (Fig. 3.g). The ripples and the number of extrema depend on the amplifier properties as in the case of an amplifier pumped by two CWs. The flatness is improved for reduced β 40 value and higher γP pt [START_REF] Chavez Boggio | Spectrally flat and broad band doublepumped fiber optical parametric amplifiers[END_REF]. The extrema between the two pumps are located at 0 THz (maximum) and ± 12.3 THz (minimum) in good agreement with the expected location, ± 1 2π -6β2c0 β4c0 derived from the case with two CW pumps [START_REF] Chavez Boggio | Spectrally flat and broad band doublepumped fiber optical parametric amplifiers[END_REF]. We checked that the spectral distribution of the gain is nearly the same as the one calculated for two continuous pump waves. The corresponding curve displaying the gain evolutions as respect to the time at f =0 THz (Fig. 3.j) and to the frequency at τ = 0 (Fig. 3.g) are similar to the one ob-tained with the chirped pulses. The variations are not observed on these scales : the gain is unchanged over the full temporal profile for the CW while it changes by 1 dB in the case of the chirped pulses. For the case where α p2 = +α p1 , the spectral gain changes strongly with time (Fig. 3.b) as expected from Eq. 12. Similarly, for α p2 =0, the map is not uniform (Fig. 3.c) mainly due to the variation of the dispersion over the pump bandwidth. For α p2 = +α p1 , β 2c changes from -6x10 -28 to +8x10 -28 s 2 /m when the pump frequency is swept during the pulse duration leading to a significant change of the gain profile. The maximum gain is similar to the previous case but it extends to higher frequency up to ∼40 THz at τ ∼-300 ps (for α p2 = +α p1 ) and ∼32 THz at τ ∼-350 ps (for α p2 = 0). However, each frequency is amplified at a given time making the amplifier less convenient than the previous case (α p2 = -α p1 ). For example, the maximum gain at f =0 THz only occurs at ∼-30 ps and -70 ps for α p2 = +α p1 (Fig. 3.a-red line) and α p2 = 0 (Fig. 3.a-green line), respectively. In addition, the temporal width of the gain depends on τ . Consequently, the efficient amplification of a chirped signal pulse with large bandwidth will require to match the signal chirp with the temporal distribution of the gain. Numerical simulations have been performed with the same parameters as those used in the analytical model. The temporal distributions of the spectral gain are displayed in Fig. 3.d-e-f next to the maps obtained with the analytical model together with the gains at τ = 0 (g-cyan dashed line, h-magenta dashed line,i-light green dashed line). Excellent agreements are obtained for the three discussed cases confirming the correct behavior of the analytical model. Weak additional informations are provided by the numerical simulations. Beyond ∼40 THz, weak degenerated four wave mixings between the pumps appear. In addition, the contribution of the idler can be observed with the simulation. For example, the gain at f =0 THz as respect to the time is displayed in Fig. 3.k for α p2 =-α p1 (cyan dashed line) and α p2 = +α p1 (magenta line) together with the corresponding curves obtained from the analytical model (blue and red solid lines). In fact, the idler generated and filtered at f =0 THz interferes with the signal wave at the same frequency. However, the frequency of the generated idler changes with time during the interaction with the other pulses. From the photon energy conservation, the frequency is given by

f i = (α p1 + α p2 )τ /(2π) -f =(α p1 + α p2 )τ /(2π) . When α p2 = -α p1
, the idler at 0 THz is generated for each τ value simultaneously with the signal at f =0 THz. Therefore, no spectral modulation from interferences is observed in the time domain. The gain is 3 dB higher (Fig. 3.k-cyan dashed line) than the one obtained with the analytical model since both signal and idler contribute to the output at f =0 THz. For α p2 = α p1 , the idler at f =0 THz is generated only around τ = 0 and interferes with the signal leading to temporal modulation (Fig. 3.k-magenta line).

2.E. Influence of the group delay mismatch

During the propagation, each pulses propagate with different group velocity and the monochromatic signal experiences a range of pump frequencies from the two pulses along the propagation. The group delay (GD) is given by the frequency derivative of the phase. During propagation, the two pumps have been delayed by :

τ 1,2 = ∓β 2c W p + β 3c 2 W 2 p ∓ β 4c0 12 W 3 p z ( 15
)
The GD of the signal is calculated by assuming that the amplifier is phase matched and we only use the exponential term in Eq. 8. The group delay of the signal is

τ s = β 3c 2 Ω 0 - α p1 + α p2 2 τ 2 z ( 16
)
The GD effect has been included in the model by calculating step by step the Stokes and anti-Stokes amplitudes (Eq. 8 and Eq. 9) along the fiber. Delays T 1,2 =τ s -τ 1,2 have been added at each step shifting the parameters ω c , W p (Eq. 3 and Eq. 4) by ∆ω c = αp2T2+αp1T1 2

and ∆W p = αp2T2-αp1T1 2

, respectively. These equations clearly show that the effect of the GD will depend on the value of both chirps. Gain maps are displayed in Fig. 4.a-b. for an amplifier pumped by two chirped pulses but with P p1 = P p2 =1 W with L=100 m for α p2 = ∓α p1 .

The spectral gain has ripples with much higher modulation depth than in the previous case since they increase with lower pump power, as observed in a two CW pump amplifier [START_REF] Chavez Boggio | Spectrally flat and broad band doublepumped fiber optical parametric amplifiers[END_REF]. For comparison, the same map has been analytically calculated with no GD mismatch between the pulses (Fig. 4.c-d). We can notice that the effect of the GD is negligible when α p2 =-α p1 while the gain decreases for frequency away from the pump when α p2 =+α p1 . For example, for Ω 0 =0 THz and τ =0 ps, τ 1,2 ∼44 ps and τ s =0 in both cases. However, ∆ω c and ∆W p are equals to 0 and ∼-0.7 THz (α p2 =-α p1 ) while they are equal to ∼-0.7 THz and 0 THz (α p2 =+α p1 ). In the latter case, the important variation of ω c in comparison to the central frequency at L=0 m (ω c =0) leads to a drop of the gain. The fiber length should be short to limit the GD effect. For example, the GD does not impact the gain shape when the fiber length is decreased to L=10 m. Fig. 4.e-f are the corresponding maps obtained from the NLSE simulation and excellent agreements are obtained with the analytical model when the GD effect is included.

2.F. Impact of the pump chirps on a chirped signal pulse

A chirped signal has a quasi-linear temporal distribution of the spectrum. Each frequency needs to be amplified at the appropriate time. However, the spectral gain of the amplifier varies strongly with time in several cases making the parametric amplifier not convenient for the amplification of this stretched signal pulse; i.e the properties of the amplifier need to be engineered. For efficient amplification of a large bandwidth, the spectrotemporal distribution of the signal needs to match the gain map. This optimization is similar to the case of a single chirped pump [START_REF] Fourcade-Dutin | Ultra-broad band fiber optical parametric amplifier pumped by chirped pulses Part II : Sub-30 fs pulse amplification at high gain[END_REF] and some suitable configurations can be found if the signal chirp is preliminary adjusted. However, when the two pump chirps have opposite values, the gain profile does not change with time. This means that any chirped signal with the correct spectral bandwidth are expected to be amplified. Firstly, we consider a signal with a linear chirp α s = 2π×50 THz/ns corresponding to a frequency sweep from -20 THz to +20 THz when τ changes from -400 ps to +400 ps. Fig. 5 displays the instantaneous gain for selected signal frequencies when α p1 is fixed and α p2 is varied. The gain changes significantly excepted for f =0 THz (τ = 0) where the gain is constant since the dispersion does not vary with the chirp at this time.

For α p2 =-α p1 , all the selected frequencies have similar gain (∼49 dB±3 dB) making this configuration suitable for the amplification of large bandwidth. For f =± 20 THz, the corresponding time is ± 400 ps where the pump power decreases by ∼20 % leading to a gain drop. The gain of a chirped signal pulse is displayed in Fig. 6 for α s =2π×50 THz/ns, α s =2π×100 THz/ns, α s =2π×200 THz/ns, in the frequency (Fig. 6.a-c) and temporal (Fig. 6.b-d) domains.

For α p2 =+α p1 (Fig. 6.c-d), the gain changes considerably and is structured when the signal chirp varies. However, the amplification can occur at higher frequency for selected chirp in which the spectro-temporal distribution matches the gain map at high frequencies (Fig. 3.b). For example, for α s =2π×200 THz/ns (green curves), -30 THz occurs at τ =-150 ps and therefore can be amplified (Fig. 6.d). For α p1 =-α p2 (Fig. 6.a,b), the spectral gain does not change for any signal chirp value. For α s =2π×50 THz/ns, the frequencies beyond ∼20 THz are amplified by the edge of the pump leading to a decrease of the gain, as already observed in Fig. 5. By adjusting the signal chirp, the signal pulse duration increases and the instantaneous spectral gain occurs at other times (Fig. 6.b). Accordingly, the amplification of a chirped signal pulse with large bandwidth is very flexible when the pump chirps have opposite signs. The choice of the signal chirp is not defined by the properties of the amplifier and therefore this configuration is very promising for the design of a laser architecture.

Ultra-short pulse amplification with two chirped pump pulses

To confirm the possibility to amplify ultra-short pulses with an amplifier pumped by two chirped pulses, numerical simulations have been performed as in Section 2.B. The signal has a Fourier transform limited pulse duration equals to 50 fs with a Gaussian profile corresponding to a spectral bandwidth of ∼8.76 THz (FWHM). The pulse duration is increased to 300 ps with a standard stretcher to match the pulse duration of both pumps and to decrease the peak power. The signal spectrum is centered between the two pumps (Ω 0 = 0 THz) to take benefit from the full gain bandwidth. The spectrogram of the input pulse together with the temporal and spectral shapes are shown in Fig. 7. The black lines display the central frequencies of the two pumps. The fiber length L=6.5 m has been chosen to amplify the signal in an unsaturated regime. A spectrogram of the total electric field is calculated at the output of the fiber. The two configurations of the pumps are considered; i.e α p1 =α p2 (Fig. 8.a) and α p1 =α p2 (Fig. 8.b). They are compared to the case where two quasi-CW pumps are used for the amplification (Fig. 8.c). In the three cases, the spectrograms show a "X" shape as observed in [START_REF] Mussot | Amplification of ultra-short optical pulses in a two pump fiber optical parametric chirped pulse amplifier[END_REF] in the case of two CW pumps. At each time, the signal is amplified at its instantaneous frequency while the idler is generated at ω i = ω p1 + ω p2 -ω s . The contribution of both pump chirps and bandwidths are actually weak and impact marginally the idler. Thus, the idler frequencies are generated with an opposite temporal distribution as respect to the signal. The combined contribution of the signal and idler leads to the shape observed on the spectrogram. The spectrum contains the same components generated at different time leading to interferences of the total electric field in the spectral and temporal domain. The results obtained with the opposite pump chirps (Fig. 8.b) are the same as the ones obtained with two CW pump waves (Fig. 8.c) confirming the suitable behavior of the dual chirped pump pulse amplifiers. The peak gain is ∼35 dB and the amplified bandwidth has not been significantly narrowed during the amplification. On the contrary, the signal amplified by two pumps with the same chirp values exhibits a narrowed spectrum with a shift toward lower frequencies (Fig. 8.a).

At the output of the fiber, the two pumps have been filtered out to keep only the signal and idler pulses. Then, a standard compressor has been optimized to reduce the pulse duration of the signal near the Fourier transform limit (Fig. 9). The compressor has two gratings owing 1200 grooves/mm. The angle and the grating separation have been adjusted to best compress the signal pulse in each case. They are ∼81 • and 0.9 m, respectively. For opposite value of the pump chirps, the compressed pulse is ∼60 fs (Fig. 9, blue line) near the input pulse duration (Fig. 9, black line). The compressed pulse amplified by the two CW pumps has the same pulse duration (Fig. 9, red line). We also checked that shorter pulse duration can be reached in the saturation regime as in [START_REF] Mussot | Amplification of ultra-short optical pulses in a two pump fiber optical parametric chirped pulse amplifier[END_REF]. For example, the compressed pulse duration is 50 fs when the signal is amplified in a L =7 m long fiber. When the two pumps have the same chirp value, the pulse duration is increased to ∼200 fs (Fig. 9, magenta line) as expected from its gain narrowed spectrum (Fig. 8.a). Fig. 9.b shows an enlargement of the compressed pulses in the few hundred ps window. The long pulses correspond to the generated idler. As it has the same spectrum, it cannot be filtered and also experiences the phase from the compressor device. Therefore, as the idler has an opposite chirp from the signal, it is stretched further by the compressor to twice the input pulse duration of the signal; i.e 600 ps. In this case, the temporal contrast is ∼38 dB. For α p1 =+α p2 , the idler pulse duration is shorter than the one in the other cases because of the gain narrowed spectrum and the contrast is ∼30 dB.

We have also calculated the optical to optical conversion efficiency defined as the energies of the signal and idler divided by the input energy of both pumps. We found that the efficiency reaches 60 % at saturation (for L=15 m) when two CWs or two pulses with opposite chirps pump the fiber while it is only 15 % when the pulses have the same chirps.

Conclusion

We have analytically and numerically investigated optical parametric amplifier pumped by two chirped pump pulses with relatively large bandwidth. In particular, we highlighted that the properties of the amplifier depends strongly on the relative chirp values and a uniform spectro-temporal gain can be obtained when the two chirps have opposite values. We also demonstrate the possibility to amplify ultra-short pulses with this scheme particularly suitable for laser architectures that deliver several ultra-short pulses.

Acknowledgments Computations have been per-

Fig. 1 .

 1 Fig. 1. Generic scheme of the parametric amplifier pumped by two chirped pulses. In this example, the pumps and signal are stretched by chirped fiber Bragg gratings (CFBG).

Fig. 2 .

 2 Fig. 2. Schematic spectrograms of the injected chirped pulses.

  2.C. Numerical simulations performed for the validation of the model In order to validate the analytical model, realistic numerical simulations have been conducted by integrating the nonlinear Schrödinger equation (NLSE) along the propagation z i ∂ψ ∂z -β 2 (z) 2

Fig. 3 .

 3 Fig. 3. Gain maps calculated in the Anti-Stokes side from the analytical model and the NLSE simulation for αp2 = -αp1 (a-d), αp2 = +αp1 (b-e) and αp2 = 0 (c-f). The spectral gain at τ =0 ps for αp2 = -αp1, αp2 = +αp1 and αp2 = 0 are shown in (g), (h) and (i). The dashed and solid lines correspond to the results obtained with the simulation and the model, respectively. The gain as a function of τ at f=0 THz are displayed in (j) for αp2 = -αp1 (blue line), αp2 = +αp1 (red line) and αp2 = 0 (green line). The dashed brown line is calculated for two CW pumps. The blue and red lines are reproduced in (k). The corresponding curves obtained with the NLSE simulation are also shown in (k) (αp2 = -αp1 (cyan line), αp2 = +αp1 (magenta line))

Fig. 4 .

 4 Fig. 4. Gain maps calculated in the Anti-Stokes side from the analytical model αp2 = -αp1 (a) and αp2 = +αp1 (b) including the GD effect. (c,d) are the maps when the GD is neglected and (e,f) are the corresponding gain obtained with the NLSE simulation. The colorbar is the same as in Fig.3.

Fig. 5 .

 5 Fig. 5. Gain as a function of αp2 for f =-20 THz (blue line),-10 THz (red line), -7 THz (light green line), 0 THz (cyan line), +7 THz (magenta line), +10 THz (black line), +20 THz (dark green) when a signal is injected with a chirp αs=2π×50 THz/ns. αp1 = -(2π) × 2.25 T Hz/ns.

Fig. 6 .

 6 Fig.6. Gain as a function of the signal frequency (left column) and the time (right column) for αp2=-αp1 (top line) and αp2=+αp1 (bottom line) for αs=2π×50 THz/ns(red lines), αs=2π×100 THz/ns (blue lines), αs=2π×200 THz/ns (green curves).

Fig. 7 .

 7 Fig. 7. Spectrogram, temporal and spectral profiles of the input signal.

Fig. 8 .

 8 Fig. 8. Spectrogram, temporal and spectral profiles of the output electric field for two pumps with the same (a) and opposite chirps (b) and with two quasi-CW pumps (c).

Fig. 9 .

 9 Fig. 9. (a)Temporal profile of the input pulse (black line) and the compressed pulse for two CW pumps (red line), two pumps with the opposite (blue line) and the same chirps (magenta line). (b) Observation of the pedestals in the larger time window.The dashed square corresponds to the zone of enlargement