Tamiris Figueiredo

Jing Jing

Isabelle Jeacomine

Johan Olsson

Thibaud Gerfaud

Jean- Guy Boiteau

Claire Rome

Craig Harris

Rachel Auzély-Velty

Injectable self-healing hydrogels based on boronate ester formation between hyaluronic acid partners modified with benzoxaborin derivatives and saccharides

Keywords: Self-healing, injectable hydrogel, benzoxaborin-saccharide dynamic covalent cross-linking, cell delivery

We demonstrate here, for the first time, formation of injectable dynamic covalent hydrogels at physiological pH using benzoxaborin-saccharide complexation as a reversible crosslinking 2 method. The gels were prepared by simply mixing hyaluronic acid modified with an original boronic acid derivative, 3,4-dihydro-2H-benzo[e][1,2]oxaborinin-2-ol (1,2-ABORIN), and HA functionalized with 1-amino-1-deoxy-D-fructose. Dynamic rheological experiments confirmed the gel-like behavior (storage modulus (G') > loss modulus (G') in the frequency window explored) for the designed HA-1,2-ABORIN/HA-fructose network. Furthermore, this hydrogel exhibited excellent self-healing and injectability behaviors in aqueous conditions and was found to be responsive to pH. Additionally, fibroblast cells encapsulated in the HA network showed high viability (> 80 % after 7 days of cell culture), as monitored by Live/Dead staining. Taken together, this new class of boronate ester crosslinked hydrogel provides promising future for diverse biomedical applications.

Introduction

Recent advances in biomaterials research have encouraged the design of new injectable hydrogels with autonomous self-healing properties, i.e. having the ability to response to damage and regenerate function, without requiring the application of external physical or chemical stimuli. [START_REF] Brochu | Self-healing Biomaterials[END_REF][START_REF] Taylor | Self-healing Hydrogels[END_REF][START_REF] Zhang | Hydrogels with Self-Healing Attribute[END_REF] Such polymer networks can be pre-formed into syringes, extruded under application of shear (needle injection), and rapidly recover the gel state when the applied stress is removed. [START_REF] Loebel | Shear-Thinning and Self-Healing Hydrogels as Injectable Therapeutics and for 3D-Printing[END_REF] These materials have become particularly attractive for clinical uses as they can be surgically implanted in patients by minimally invasive methods. Such hydrogels can be crosslinked via non-covalent interactions (e.g. hydrophobic, hydrogen bonding, ionic, host-guest interactions) or dynamic covalent bonds. [START_REF] Wei | Self-Healing Gels Based on Constitutional Dynamic Chemistry and Their Potential Applications[END_REF] Among the latter, the boronic ester bond has presented great potential to prepare self-healing hydrogels as biomimetic scaffolds for cell encapsulation. [START_REF] Tang | Adaptable Fast Relaxing Boronate-Based Hydrogels for Probing Cell-Matrix Interactions[END_REF][START_REF] Wang | Self-Healing and Injectable Shear Thinning Hydrogels Based on Dynamic Oxaborole-Diol Covalent Cross-Linking[END_REF][START_REF] Wu | In Situ Forming, Dual-Crosslink Network, Self-Healing Hydrogel Enabled by a Bioorthogonal Nopoldiol-Benzoxaborolate Click Reaction with a Wide pH Range[END_REF][START_REF] Yesilyurt | Injectable Self-Healing Glucose-Responsive Hydrogels with PH-Regulated Mechanical Properties[END_REF] As the formation of crosslinks in these gels at physiological pH strongly depends on the affinity of the boronic acid towards the diol (K a ) and on their pK a , [START_REF] Yan | The Relationship among pKa, pH, and Binding Constants in the Interactions between Boronic Acids and Diols-It Is Not as Simple as It Appears[END_REF] their stiffness as well as their dynamics may be tuned by varying the nature of the boronic acid moiety [START_REF] Yesilyurt | Injectable Self-Healing Glucose-Responsive Hydrogels with PH-Regulated Mechanical Properties[END_REF] and/or the diol-containing molecule. [START_REF] Wu | In Situ Forming, Dual-Crosslink Network, Self-Healing Hydrogel Enabled by a Bioorthogonal Nopoldiol-Benzoxaborolate Click Reaction with a Wide pH Range[END_REF][START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF] Inspired by studies on the structure-property relationships of small arylboronic acid molecules, [START_REF] Mulla | A. 3-Methoxycarbonyl-5-Nitrophenyl Boronic Acid: High Affinity Diol Recognition at Neutral pH[END_REF][START_REF] Zhang | Hydrogel-Based Glucose Sensors: Effects of Phenylboronic Acid Chemical Structure on Response[END_REF][START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF][START_REF] Dowlut | An Improved Class of Sugar-Binding Boronic Acids, Soluble and Capable of Complexing Glycosides in Neutral Water[END_REF][START_REF] Adamczyk-Woźniak | Recent Developments in the Chemistry and Biological Applications of Benzoxaboroles[END_REF] several boronate-crosslinked hydrogels have been thus prepared at physiological pH using phenylboronic acid (PBA) [START_REF] Dong | Injectable and Glucose-Responsive Hydrogels Based on Boronic Acid-Glucose Complexation[END_REF][START_REF] Roberts | Dynamically Restructuring Hydrogel Networks Formed with Reversible Covalent Crosslinks[END_REF][START_REF] Tarus | Readily Prepared Dynamic Hydrogels by Combining Phenyl Boronic Acid-and Maltose-Modified Anionic Polysaccharides at Neutral PH[END_REF] and its derivatives, such as PBA substituted with fluorine as an electron-withdrawing group that can reduce pK a , [START_REF] Tang | Adaptable Fast Relaxing Boronate-Based Hydrogels for Probing Cell-Matrix Interactions[END_REF][START_REF] Yesilyurt | Injectable Self-Healing Glucose-Responsive Hydrogels with PH-Regulated Mechanical Properties[END_REF] and ortho-substituted PBA derivatives, [START_REF] Deng | Boronic Acid-Based Hydrogels Undergo Self-Healing at Neutral and Acidic pH[END_REF] in particular o-hydroxymethylphenylboronic acid (benzoboroxole, BOR, Figure 1). [START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF][START_REF] Chen | Injectable Self-Healing Zwitterionic Hydrogels Based on Dynamic Benzoxaborole-Sugar Interactions with Tunable Mechanical Properties[END_REF][START_REF] Chen | Bioinspired Self-Healing Hydrogel Based on Benzoxaborole-Catechol Dynamic Covalent Chemistry for 3D Cell Encapsulation[END_REF] Compared to PBA, BOR has a strained five-membered oxaborole ring, which is a contributing factor explaining its higher acidity (pK a of 7.3 [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF] ) than PBA (pK a of 8.8 [START_REF] Springsteen | A Detailed Examination of Boronic Acid-Diol Complexation[END_REF] ) and its exceptional carbohydrate-binding behavior at neutral pH. [START_REF] Adamczyk-Woźniak | Recent Developments in the Chemistry and Biological Applications of Benzoxaboroles[END_REF][START_REF] Liu | The Unique Chemistry of Benzoxaboroles: Current and Emerging Applications in Biotechnology and Therapeutic Treatments[END_REF] The capability of this class of arylboronic acid to bind non-reducing saccharides locked in their pyranose form (glycopyranosides) was first reported by the Hall group. [START_REF] Dowlut | An Improved Class of Sugar-Binding Boronic Acids, Soluble and Capable of Complexing Glycosides in Neutral Water[END_REF][START_REF] Bérubé | Benzoboroxoles as Efficient Glycopyranoside-Binding Agents in Physiological Conditions: Structure and Selectivity of Complex Formation[END_REF] This unique property was successfully used to produce highly elastic hydrogel networks, exhibiting slow dynamics, and crosslinked via complexation of BOR with mannopyranoside moieties covalently linked to synthetic polymers. [START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF] In addition to benzoboroxole, its six-membered ring homologue, ohydroxyethylphenylboronic acid (benzoxaborin, 2,1-BORIN, Figure 1), has recently been investigated as a synthetic building block for constructing bioactive molecules, [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF][START_REF] Sumida | Boron-Selective Biaryl Coupling Approach to Versatile Dibenzoxaborins and Application to Concise Synthesis of Defucogilvocarcin M[END_REF][START_REF] Saito | Nickel-Catalyzed Boron Insertion into the C2-O Bond of Benzofurans[END_REF] and as a recognition element for carbohydrate sensing. [START_REF] Bérubé | Benzoboroxoles as Efficient Glycopyranoside-Binding Agents in Physiological Conditions: Structure and Selectivity of Complex Formation[END_REF] However, in spite of the structural similarities between BOR and 2,1-BORIN, the latter is not able to complex saccharides in the pyranose form at neutral pH. [START_REF] Bérubé | Benzoboroxoles as Efficient Glycopyranoside-Binding Agents in Physiological Conditions: Structure and Selectivity of Complex Formation[END_REF] Indeed, studies published by Tomsho et al. explain the different binding capacities of these derivatives based on their geometrical structures. [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF] Regarding 2,1-BORIN, its less strained six-membered ring, compared to the strained five-membered ring of BOR, does not induce a distorted geometry around the boron atom, which results in a less reactive boronic center and a higher pK a (8.4). [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF] On the other hand, the slightly higher acidity of 2,1-BORIN in comparison with PBA appears to be related to a reduced flexibility of the intramolecular B-O bond of the former, which increases boron electronic deficiency. Nevertheless, despite increasing attention has been paid to assess the potential of benzoxaborin compounds as sugar-binding agents, no published studies have exploited benzoxaborin-saccharide complexation as a crosslinking strategy to form reversible boronate ester-crosslinked hydrogels.

The present study is a first demonstration of the applicability of dynamic benzoxaborinsaccharide complexation as a reversible crosslinking method to form hyaluronic acid networks at physiological pH. As illustrated in Figure 1, besides 2,1-BORIN, a new original derivative called 1,2-benzoxaborin (1,2-BORIN), containing a six-membered heterocycle like 2,1-BORIN but with the endocyclic oxygen linked to the phenyl ring, was also investigated as a binding site for D-fructose grafted on HA. Herein, D-fructose was selected to form reversible crosslinks with the benzoxaborin derivatives due to its higher affinity for arylboronic acids in comparison to other classical monosaccharides. [START_REF] Angyal | The Composition of Reducing Sugars in Solution[END_REF][START_REF] Wu | Selective Sensing of Saccharides Using Simple Boronic Acids and Their Aggregates[END_REF] Although the 1,2-BORIN molecule has never been tested and reported in the literature as a carbohydrate-binding agent, we hypothesized that its particular structure would provide a more acidic character to boronic acid (i.e. lower pK a ) compared to standard 2,1-BORIN, favoring its complexation with D-fructose at physiological pH.

In this work, the formation of HA hydrogel networks through reversible benzoxaborinfructose complexation was investigated and the dynamic rheological properties of the designed networks were compared to those obtained by mixing the HA-fructose conjugate with HA bearing BOR or PBA moieties. Their injectability and self-healing properties were further evaluated in detail by rheology and injection force measurements. Lastly, their suitability and biocompatibility for cell and tissue engineering was demonstrated by 3D encapsulation of fibroblast cells.

Experimental section

Materials. Sodium hyaluronate (HA) possessing a weight-average molar mass (M w ) of 360 kg/mol was donated by Galderma-Nestlé Skin Health. The molar mass distribution and the weight-average molar mass of these samples were determined by size exclusion chromatography using a Waters GPC Alliance chromatograph (USA) equipped with a differential refractometer and a light scattering detector (MALLS) from Wyatt (USA); the solution was injected at a concentration of 1 × 10 -3 g/mL in 0.1 M NaNO 3 , at a flow rate of 0.5 mL/min and at a column temperature of 30 °C. The dispersity (Đ) of the samples are M w /M n ≈ 1.5-2. The overlap concentration C* for the HA sample in buffer at 25 °C is around 1 g/L. This value was derived from the intrinsic viscosity assuming that C*[η] is about unity. [START_REF] Macosko | Rheology: Principles, Measurements, and Applications[END_REF] A HA sample with a lower M w (5 kg/mol), purchased from the same supplier, was used to synthesize HA derivatives for NMR studies (determination of binding constants). This low M w HA sample was used to circumvent limitations due to the high viscosity of concentrated solutions of high M w HA. 5-Amino-2hydroxymethylphenylboronic acid (6-aminobenzoboroxole, ABOR) was purchased from Combi-Blocks. 1-Amino-1-deoxy-D-fructose hydrochloride (fructosamine) was supplied by Carbosynth.

3-Aminophenylboronic acid hemisulfate salt (APBA), 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4methylmorpholinium chloride (DMTMM), picrylsulfonic acid solution (TNBS), 4-(2hydroxyethyl)piperazine-1-ethanesulfonic acid (HEPES), phosphate buffered saline (PBS) and other chemicals were purchased from Sigma-Aldrich-Fluka and were used without further purification.

Methods.

NMR spectroscopy. [START_REF] Brochu | Self-healing Biomaterials[END_REF] H, [START_REF] Zhang | Hydrogel-Based Glucose Sensors: Effects of Phenylboronic Acid Chemical Structure on Response[END_REF] C and 11 B NMR spectra were recorded at 25 °C or 80 °C using a Bruker AVANCE III HD spectrometer operating at 400.13 MHz ( 1 H), 100.61 MHz ( 13 C) and 128.38 MHz ( 11 B). [START_REF] Brochu | Self-healing Biomaterials[END_REF] H NMR spectra were recorded by applying a 90° tip angle for the excitation pulse, and a 10 s recycle delay for accurate integration of the proton signals. [START_REF] Zhang | Hydrogel-Based Glucose Sensors: Effects of Phenylboronic Acid Chemical Structure on Response[END_REF] C NMR spectra were recorded by applying a 90° tip angle for the excitation pulse and a 2 s recycle delay.

Deuterium oxide (D 2 O) was obtained from Euriso-top (Saint-Aubin, France). Chemical shifts (δ in ppm) are given relative to external tetramethylsilane (TMS = 0 ppm) and calibration was performed using the signal of the residual protons of the solvent as a secondary reference. All NMR spectra were analyzed with Topspin 3.1 software from Bruker AXS.

Determination of the pK a of 1,2-ABORIN and 2,1-ABORIN by 11 B NMR spectroscopy. [START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF] B NMR chemical shifts of the aminobenzoxaborin compounds were determined with increasing pH (10 % D 2 O in H 2 O, 16 mM in 0.01 M phosphate buffer). Chemical shifts (δ in ppm) for each [START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF] B spectrum were given relative to external Et 2 O-BF 3 in deuterated chloroform as zero. The values of pK a were determined from the curve fitting of the variation of δ (in ppm) with the pH using the Boltzmann equation (Figures 4a and4b).

Synthesis of HA derivatives. HA-1,2-BORIN, HA-2,1-BORIN, HA-PBA, HA-BOR and HAfructose were synthesized by an amide coupling reaction from 1,2-ABORIN, 2,1-ABORIN, APBA, ABOR and fructosamine (containing free primary amine groups), respectively. To this end, 1,2-ABORIN (0.026 g, 0.12 mmol) or 2,1-ABORIN (0.0205 g, 0.12 mmol) or APBA (0.022 g, 0.12 mmol) or ABOR (0.025 g, 0.135 mmol) or fructosamine (0.024 g, 0.112 mmol) was added to a water/DMF (3/2, v/v) mixture containing DMTMM (0.207 g, 0.75 mmol) and HA (0.3 g, 0.75 mmol) and the pH was adjusted to 6.5 using 0.5 M aqueous NaOH. After stirring for 24 h at room temperature, the different HA derivatives were purified by ultrafiltration using deionized water and the products were recovered by freeze-drying (Table 1). The DS of the HA derivatives were found to be 0.1-0.15 from 1 H NMR analyses (Figure S1-S4) or from the reaction kinetics using the TNBS method (Figure S6). DS by [START_REF] Brochu | Self-healing Biomaterials[END_REF] H NMR (10 % of accuracy). Rheology. Oscillatory shear experiments were performed with a cone-plate rheometer (AR2000Ex from TA Instruments). The cone used for viscoelastic samples has a diameter of 2 cm and an angle of 4°, whereas viscous solutions were analyzed using a cone of 6 cm of diameter and an angle of 1°. To prevent water evaporation, the measuring system was surrounded with a low-viscosity silicon oil (50 mPa.s) carefully added to the edges of the cone.

Oscillatory frequency sweep (0.01-10 Hz) experiments were performed within the linear viscoelastic range (strain fixed at 5 %) to determine the frequency dependence of the storage (G') and loss (G") moduli. No frequency data beyond 10 Hz are presented because inertial artefacts (raw phase angle > 150°) were observed at frequencies higher than 10 Hz. [START_REF] Krieger | The Role of Instrument Inertia in Controlled-Stress rheometers[END_REF][START_REF] Hudson | An Enhanced Rheometer Inertia Correction Procedure (ERIC) for the Study of Gelling Systems Using Combined Motor-Transducer Rheometers[END_REF] Oscillatory amplitude sweep experiments at 1 Hz were used to determine the linear-viscoelastic range of the hydrogel networks and to derive the yield stress. They were immediately followed by time sweep experiments at 1 Hz and a strain of 5 % (linear viscoelastic region) to monitor the recovery of the rheological moduli. For the measurement of the self-recovery of the gels after four cycles of strain-induced breakdowns, four cycles of a time sweep experiment (strain of 350 % at 1 Hz) with a duration of 2 min followed by a time sweep experiment (strain of 5 % at 1 Hz) with a duration of 3 min were performed. The yield stress was determined by steady state stress sweep experiments, consisting in the variation of the viscosity as a function of the shear stress (0.1-1500 Pa) for 15 min.

Injection force measurements.

Hydrogel injection forces were measured using a mechanical testing machine (SHIMADZU EZ-SX). A "homemade" support was used to fix and stabilize the syringe during the test. The measurements were made using the tensile extension mode, at a flow rate of 1 mm/mL. Hydrogels were prepared as previously described and loaded into 1 mL syringes. The loaded syringes were kept at 4 °C overnight before analysis at room temperature.

Hydrogel injection forces were measured over time using a 27 G needle.

Determination of K a by ITC. Calorimetric titration experiments were carried out on a Microcal

VP-ITC titration microcalorimeter (Northampton, U.S.A.). All titrations were performed using solutions of 1,2-ABORIN (2,1-ABORIN or ABOR or APBA) and free D-fructose solubilized in 0.01 M PBS, with pH adjusted to 7.4 (± 0.1) using a pH-meter, by carefully adding 1 M NaOH when necessary. The reaction cell (V = 1.4478 mL) contained a solution of "molecule 2" (Table 2). A series of 28 injections of 5 or 10 µL of a solution of "molecule 1" was made from a computer-controlled 300 µL microsyringe at an interval of 400 s into the solution contained in the reaction cell, while stirring at 300 rpm at 25°C. The raw experimental data were reported as the amount of heat produced after each injection of boronic acid as a function of time. The amount of heat produced per injection was calculated by integration of the area under individual peaks by the instrument software, after taking into account heat of dilution. The data were analyzed using the one set of site fitting model (Origin 7.0 software package). Table 2 summarizes the experimental conditions used for the ITC measurements. 3D cell encapsulation and cell viability study. Mouse embryonic fibroblasts (MEFs) used in this study were isolated from mice from the age of embryonic day 12 to postnatal day 1. Culture of cells was performed as described in detail earlier. [START_REF] Petropoulos | Roles of paxillin family members in adhesion and ECM degradation coupling at invadosomes[END_REF] and red (dead cells) were counted using Image analysis software, ImageJ. Furthermore, 3D

images were taken using a laser scanning confocal microscope (Nikon, LSM710) equipped with a high-speed 97-actuator deformable mirror (DM) (AlpAO) for aberration correction. [START_REF] Leroux | Correction of cell induced optical aberrations in a fluorescence fluctuation microscope[END_REF] Images of cells encapsulated in 3D in the hydrogels (acquisition through encapsulated hydrogels in

Transwell ® cell culture inserts) were acquired using a Nikon 40× (NA = 1.15) water objective.

Three-dimensional views were first reconstructed from z-stack images (step size 1 μm) using NIS-Element AR software (Nikon). Living cells stained with calcein-AM (green) were determined from the FITC channel.

Results

To properly investigate the effect of the different small molecule crosslinkers on the rheological properties of the HA networks, all HA derivatives were synthesized from the same HA sample, possessing a weight-average molar mass (M w ) of 360 kg/mol (referred to as HA360), and with a similar degree of substitution (DS, average number of substituting group per repeating disaccharide unit). The synthesis of HA-benzoxaborin conjugates required first that of aminobenzoxaborin derivatives (1,2-ABORIN and 2,1-ABORIN, Figure 2). These custom-made products were synthesized in four-to seven-steps, as described in the Supporting Information, methylmorpholinium chloride (DMTMM) as a coupling agent (Figure 2). [START_REF] D'este | A Systematic Analysis of DMTMM vs EDC/NHS for Ligation of Amines to Hyaluronan in Water[END_REF] The DS of the HA conjugates was controlled by the amount of amine to carboxylic acid. Using DMTMM/HA and amine/HA molar ratios of 1 and 0.15, respectively, we obtained HA derivatives with a DS of 0.1-0.15 from 1 H NMR analysis (Figure S1-S4). In the case of HA-fructose, successful grafting was confirmed by 2D HSQC NMR analysis (Figure S5), and a DS of 0.15 was estimated from the reaction kinetics performed using 2,4,6-trinitrobenzene sulfonic acid (TNBS) to quantify the free primary amines in the reaction medium as a function of time (Figure S6). On the basis of these observations, we investigated the relationships between the macroscopic mechanical properties and the small molecule crosslinkers by analyzing the thermodynamics of boronic acid-fructose complexation. As the bound and unbound forms of these boronic acid derivatives in the presence of fructose are distinguishable by1 H NMR spectroscopy, [START_REF] Dowlut | An Improved Class of Sugar-Binding Boronic Acids, Soluble and Capable of Complexing Glycosides in Neutral Water[END_REF][START_REF] Ellis | Mediated Biologic Delivery[END_REF] we used this technique to measure their affinities for free/grafted fructose (Table 3, Figure S7-S14). The values of K a for free D-fructose were also examined by isothermal titration calorimetry (ITC) and were in the same order of magnitude as the values derived from From Table 3, we observe that relatively close values of K a (in the same order of magnitude) were determined for 1,2-ABORIN (ABOR) with free and grafted fructose as well as for APBA with grafted fructose (Table 3, entries 1, 3 and 4). These results are consistent with the gel-like behavior observed for the HA mixtures based on these derivatives (Figure 3). Regarding complexation with APBA, a 2-fold increase of K a was observed for HA-fructose compared to Dfructose (Table 3, entry 4). Moreover, despite the close values of K a found for the complexation of APBA (ABOR) with fructose grafted on HA, a lower elastic modulus was measured for the HA-BOR/HA-fructose mixture. This may be ascribed to competitive interactions between BOR and HA saccharides as demonstrated by steady shear flow and dynamic rheological experiments performed on HA-BOR alone and initial (native) HA360 at pH 7.4 (Figure S19). Indeed, these measurements showed that HA-BOR stands out among the other HA derivatives (HA-1,2-BORIN HA-2,1-BORIN and HA-PBA) by giving rise to solutions with higher dynamic moduli and viscosity compared to native HA360 (Figure S19). Moreover, 1 H NMR analysis of this derivative at neutral pH provided another evidence of the selective binding of benzoboroxole moieties to HA. This indeed showed additional 1 H signals in the aromatic region of grafted BOR moieties, suggesting the presence of free and complexed BOR species which are in slow exchange on the NMR timescale (Figure S3). Regarding the interaction of 2,1-ABORIN with free/grafted fructose, the low K a measured for these couples in comparison to the other pairs correlates with the low G' value at the plateau and faster dynamics of the HA-2,1-BORIN/HAfructose mixture (Table 3, entry 2).

K a b) ITC (M -1 ) n b) (n saccharide : 1 boronic acid) ∆H b) (kJ/mol) ∆S b) (J.mol/K)
Taken together, these results demonstrate that the macroscopic rheological behavior of the HA assemblies are closely related to the binding affinities of their small molecular crosslinkers.

Considering that all mixtures only differ in the nature of their boronic acid partner, the binding mechanism allowing boronate ester formation may strongly depend on the structure and physicochemical properties of each derivative used. In these systems, one determinant factor that may affect K a and boronate crosslinking formation is the pK a of the boronic acid group. Surprisingly, in the case of complexation between APBA (ABOR) and HA-fructose, boronate esters were formed with similar affinities in spite of their different structures and values of pK a (8.8 for PBA [START_REF] Springsteen | A Detailed Examination of Boronic Acid-Diol Complexation[END_REF] and 7.3 for BOR [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF] ). On the other hand, regarding the 2,1-ABORIN derivative, the weak interaction with fructose may be partially related to its relatively high pK a (8.59, Figure 4a), which is due to its structure containing a less strained six-membered heterocycle compared to benzoboroxole. [START_REF] Tomsho | Ring Structure and Aromatic Substituent Effects on the pKa of the Benzoxaborole Pharmacophore[END_REF] By contrast, the disposition of the endocyclic B-O bond in 1,2-ABORIN, with the oxygen atom between the phenyl ring and boron, suggests a more electron-deficient character of the boronic center and, therefore, a higher acidity. Indeed, a pK a value of 6.17 was determined for free 1,2-ABORIN by [START_REF] Lin | The Glyco-Stereoisomerism Effect on Hydrogelation of Polymers Interacting via Dynamic Covalent Bonds[END_REF] B NMR titration [START_REF] Dowlut | An Improved Class of Sugar-Binding Boronic Acids, Soluble and Capable of Complexing Glycosides in Neutral Water[END_REF][START_REF] Bérubé | Benzoboroxoles as Efficient Glycopyranoside-Binding Agents in Physiological Conditions: Structure and Selectivity of Complex Formation[END_REF] (Figure 4b). Interestingly, the dynamic rheological properties of the HA-1,2-BORIN (HA-2,1-BORIN)/HA-fructose networks at a pH range of 6-9 are consistent with the values of pK a measured for the free derivatives. As demonstrated in Figure 4c, formation of crosslinks in the HA-1,2-BORIN/HA-fructose system was observed in this pH range. This assembly showed a remarkable increase of the elastic modulus at pH 7 and a gel-like behavior from pH 7.4. By contrast, crosslinking in HA-2,1-BORIN/HA-fructose was effective only from pH 7.4, and a pH value around 9 is required to achieve a gel-like behavior (Figure 4d). The higher cross-linking efficiency of HA-1,2-BORIN/HA-fructose at physiological pH can be related to the lower pK a of 1,2-ABORIN, than that of 2,1-ABORIN (Figure 4e). Collectively, these results indicate that the contrasting acidities of these benzoxaborin compounds are a main factor determining the different rheological properties of the HA mixtures. On the basis of these results, the HA-1,2-BORIN/HA-fructose network, exhibiting slow relaxing properties at physiological pH, was considered more suitable as injectable cell carrier for regenerative medicine and tissue engineering applications. Therefore, in the next step, we investigated its self-healing and injectability properties in comparison to the HA-PBA/HAfructose hydrogel. The latter network was selected as a reference as some limitations were found when using the HA-BOR/HA-fructose assembly due to the increased rheological moduli and viscosity of the HA-BOR solution, as previously discussed, which caused difficulties to prepare the HA-BOR/HA-fructose gel homogeneously loaded with cells for 3D cell culture experiments.

As shown in Figure 5a, strain-dependent oscillatory measurements displayed a broad linear viscoelastic region with network failure at high strain (700 %). The network was then found to immediately recover its rheological properties when the strain was reduced to 5 %. Then, the gel was exposed to a series of four cycles of breaking and reforming, which consisted in applying high strains (350 %) for 3 min, intercalated with low strains (5 %) for 2 min (Figure 5b). After this series of four cycles, the hydrogel was able to recover its initial rheological moduli, demonstrating its self-healing property. Although dynamic rheological moduli and self-healing capacity are important parameters for determining injectability, quantification of the viscosity and yield stress, [START_REF] Mouser | Yield Stress Determines Bioprintability of Hydrogels Based on Gelatin-Methacryloyl and Gellan Gum for Cartilage Bioprinting[END_REF] as well as the injection force required to extrude a gel through a needle, are also important to determine whether or not it is relevant for injection uses. [START_REF] Chen | Methods To Assess Shear-Thinning Hydrogels for Application As Injectable Biomaterials[END_REF] Next, we examined the potential of these hydrogels for cell encapsulation by simply mixing solutions of HA-1,2-BORIN (PBA) and HA-fructose loaded with mouse embryonic fibroblasts (MEFs). In these experiments, cells were encapsulated in the HA-1,2-BORIN (PBA)/HA-fructose hydrogels at a density of 5×10 5 cells/mL and cultured in growth media for 7 days (37 °C, 5 % CO 2 ). For a control, MEFs were incubated only in growth media at a density of 2x10 4 cells/mL. Thanks to the quasi-instantaneous gelation of the HA-1,2-BORIN (PBA)/HAfructose mixtures, the cells could be homogeneously distributed in 3D in the two hydrogels. A live/dead assay was used to quantify the live (green) and dead (red) cells by fluorescence and laser scanning confocal microscopy imaging of three-dimensionally encapsulated MEFs in the gel structure (Figure 6a and6b). The two HA assemblies showed high cytocompatibility over the course of 7 days of cell culture (> 80 % of cell viability, Figure 6c). These data correlate with the low cytotoxicity of individual solutions of HA derivatives, as assessed by a MTT assay including incubation of HA-BORIN, HA-PBA and HA-fructose (solutions at 7.5 g/L) with MEFs for 72 h at 37 °C. This revealed a cell viability > 80 % for the HA-PBA and HA-fructose conjugates, whereas 75 % of viable cells were observed after incubation with HA-1,2-BORIN (Figure S20).

Together, these results reveal not only the ability of our HA hydrogels to encapsulate cells in 3D, but also to provide a microenvironment conducive to maintaining cellular function over one week.

Conclusion

In this work, we demonstrated the feasibility of HA hydrogel formation at physiological pH through complexation of an original benzoxaborin derivative (1,2-BORIN) grafted on HA with a second HA conjugate modified by fructose moieties. This new hydrogel exhibited rheological properties similar to the HA networks obtained by combining classical PBA-or BOR-modified HA and HA-fructose. By contrast, the use of HA functionalized with conventional benzoxaborin (2,1-BORIN) as a boronic acid partner of HA-fructose only allowed formation of a viscoelastic solution with a low elastic modulus. The different macroscopic rheological properties observed for the mixtures based on HA-1,2-BORIN (2,1-BORIN) and HA-fructose were found to be closely linked to the different structures and pK a values of these boronic acid derivatives. Indeed, the former showed polymer association at lower pH correlating with the low pK a of free 1,2-ABORIN, whereas the latter exhibited viscoelastic properties only at basic pH due to its higher pK a . Besides, these original materials showed injectable and selfhealing properties together with a high cell viability as demonstrated by 3D cell encapsulation for several days. Continued investigation of the applicability of these HA hydrogels as promising injectable scaffolds for encapsulation of cells or bioactive molecules will expand their application in many innovative biomedical fields.

ASSOCIATED CONTENT

Supporting Information.

The Supporting Information is available free of charge on the ACS Publications website.

Synthesis of aminobenzoxaborin (ABORIN) compounds

Figure 1 .

 1 Figure 1. HA hydrogels crosslinked by boronic acid-fructose complexation at physiological pH.

  b) DS estimated from the reaction kinetics using TNBS. Preparation of HA-1,2-BORIN (HA-2,1-BORIN or HA-BOR or HA-PBA) and HA-fructose mixtures. The different HA derivatives were solubilized in 0.01 M HEPES buffer containing 0.15 M NaCl pH 7.4. The dissolution time was at least 12 h at 4 °C. The solutions of HA-1,2-BORIN or HA-2,1-BORIN or HA-BOR or HA-PBA and of HA-fructose were mixed undervigorous stirring at room temperature, at a total polymer concentration of 15 g/L and with boronic acid/sugar molar ratio of 1. The mixtures were then allowed to rest at 4 °C overnight before rheological analysis. To study the rheological properties of HA hydrogels as a function of pH, the same buffer was prepared at pH values adjusted to 6, 6.5, 7, 8 and 9.

  Briefly, cells were plated onto TCPS in standard growth media based on low-glucose Dulbecco's modified Eagle's medium (DMEM) supplemented with 5% FBS, 1% GlutaMAX (Gibco) and 1% penicillin-streptomycin. Cells were expanded when they reached 70-80 confluency. All experiments were performed using cells at passage 13-16. MEFs were then trypsinized, pelleted and resuspended into growth media for cell counting. An aliquot of growth media containing MEFs were then taken to obtain a final density of encapsulated cells in the hydrogels of 5x10 5 cells/mL. Cells were pelleted and resuspended with a solution of the HA-fructose derivative in PBS. The cell-laden solution of HA-fructose and the HA-1,2-BORIN (PBA) solution were pipetted several times and quickly transferred individually to a syringe barrel. 200 μL of cell-encapsulated hydrogels were prepared by mixing the two HA components using a double-barrel syringe equipped with an extruder (MEDMIX, Switzerland) and transferred to Transwell ® cell culture inserts (0.4 µm porous membrane;Corning ® ) contained in 24-well plates. Cell-laden gels were supplemented with standard growth media and incubated for evaluating cell viability over 7 days (37°C and 5% CO 2 ). For a control, MEFs were incubated only in growth media at a density of 2x10 4 cells/mL. Further studies of cytotoxicity by a MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide) assay of modified polymers was performed as previously described.[START_REF] Mosmann | Rapid Colorimetric Assay for Cellular Growth and Survival: Application to Proliferation and Cytotoxicity Assays[END_REF] Mouse embryonic fibroblasts (MEFs) were cultured in 96-well plates containing 5000 cells incubated with individual solutions of HA derivatives (HA-1,2-BORIN, HA-PBA, HA-fructose) or native HA at 7.5 g/L in standard growth media. After incubation at 37 °C for 72 h, a MTT solution was added in each well at a final concentration of 0.5 g/L. After 2 h, the incubation media was removed and the blue MTTformazan product was extracted with DMSO. After 15 min extraction at room temperature, the absorbance of the formazan solution was measured spectrophotometrically at 570 nm. The percentage of living cells was calculated based on values of absorbance measured for cells cultured only in growth media. The experiment was repeated 2 times independently.Live/Dead assay and image acquisition. The live/dead assay was performed to determine cell viability using a staining kit (calcein-AM/propidium iodide) purchased from Sigma-Aldrich. The staining solution was made according to supplier information, by adding 10 μL of the calcein-AM solution (green, excitation/emission 490/515 nm) and 5 μL of the propidium iodide solution (red, excitation/emission 535/617 nm) in 5 mL PBS. After 7 days of cells incubation in the hydrogels, the cell media was removed and the staining solution was then added to the gels with incubation for 15 minutes at 37 °C. Hydrogels containing labeled MEFs were then analyzed under fluorescence microscope (ZEISS Axio Observer 7 ApoTome.2). 2D images were captured from 4 random fields of view for each sample. Fluorescently labeled cells in green (live cells)

  and were isolated with yields comprised between 81 and 82 %. The HA-1,2-BORIN, HA-2,1-BORIN, HA-BOR, HA-PBA and HA-fructose conjugates were prepared by an amide coupling reaction carried out in aqueous solution between 3,4-dihydro-2H-benzo[e][1,2]oxaborinin-), 3-aminophenylboronic acid (APBA) and 1-amino-1-deoxy-Dfructose (fructosamine), respectively, and HA, using 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-

37

 37

Figure 2 .

 2 Figure 2. Synthetic scheme for the preparation of HA derivatives via amide coupling reaction.

Figure 3 .

 3 Figure 3. Dynamic rheological behavior of HA networks (M w HA = 360 kg/mol) based on

  least two 1 H NMR experiments; b) measured from at least two ITC experiments; c) not determined because the bound and unbound forms of 1,2-ABORIN are not sufficiently separated to be properly integrated; d) calorimetric curve fitting by applying a fixed value of n = 1.

Figure 4 .

 4 Figure 4. Values of pK a determined for (a) free 2,1-ABORIN and (b) free 1,2-ABORIN by 11 B

  Therefore, we evaluated the yield stress and viscosity of the new HA-1,2-BORIN/HA-fructose hydrogel in comparison to the HA assembly based on HA-PBA/HA-fructose. The yield stress is defined as the stress at which the network starts to flow, indicated as the first read-out of viscosity on the rheometer. As illustrated in Figure5c, the viscosity of both HA assemblies increased with increasing shear stress. As expected, a higher viscosity was observed for the HA-PBA/HAfructose hydrogel (η max of approximately 30000 Pa.s) compared to the HA-1,2-BORIN/HAfructose networks (η max of 8000 Pa.s). The yield stress for these formulations were found to be 940 and 1650 Pa, respectively. Moreover, values of injection force close to 10 N were required to extrude HA-1,2-BORIN (PBA)/HA-fructose from a 1 mL plastic syringe with a 27 G needle at a flow rate of 1 mm/min (Figure5d). Despite the fact that the injection force of a gel depends on several factors such as flow rate, needle gauge and needle length, clinically relevant values are 21 often below 20 N.[START_REF] Chen | Methods To Assess Shear-Thinning Hydrogels for Application As Injectable Biomaterials[END_REF] These experiments thus indicate that both networks are promising candidates as injectable scaffolds for regenerative medicine and tissue engineering.

Figure 5 .

 5 Figure 5. Self-healing ability of the new HA-1,2-BORIN/HA-fructose gel: (a) dynamic

Figure 6 .

 6 Figure 6. Cytocompatibility of boronate-ester crosslinked HA hydrogels after 7 days of 3D cell

; 1 H

 1 NMR spectra of HA-1,2-BORIN, HA-2,1-BORIN, HA-BOR and HA-PBA derivatives synthesized by amide coupling reaction (M w HA = 360 kg/mol); 2D HSQC NMR characterization of HA-fructose conjugate synthesized by amide coupling reaction (M w HA = 360 kg/mol); determination of the degree of substitution (DS) of HA-fructose from the kinetics of the amide coupling reaction (M w HA = 360 kg/mol); methodology for K a measurements by 1 H NMR spectroscopy; determination of K a by 1 H NMR for 1,2-ABORIN (2,1-ABORIN) and fructose (free fructose and HA-fructose); determination of K a by 1 H NMR for APBA (ABOR) and fructose (free fructose and HA-fructose); calorimetric titration of 1,2-ABORIN (2,1-ABORIN) with free D-fructose; calorimetric titration of APBA

Table 1 .

 1 Reaction conditions for the synthesis of HA360 conjugates.

	HA derivative	R-NH 2 /HA molar ratio	DS	Coupling (%)	Yield (%)
	HA-1,2-BORIN	0.16	0.15 a)	94	81
	HA-2,1-BORIN	0.16	0.15 a)	94	90
	HA-BOR	0.16	0.1 a)	75	91
	HA-PBA	0.16	0.15 a)	94	98
	HA-fructose	0.15	0.15 b)	100	96
	a)

Table 2 .

 2 Experimental conditions of the calorimetric titrations.

	Entry	Molecule 1 in syringe	[Molecule 1] (mM)	Molecule 2 in cell	[Molecule 2] (mM)
	1	D-fructose	75	1,2-ABORIN	2
	2	D-fructose	125	2,1-ABORIN	3.5
	3	D-fructose	175	APBA	5
	4	D-fructose	75	ABOR	2

Table 3 .

 3 Binding constants of complexes based on 1,2-ABORIN (2,1-ABORIN or ABOR or APBA) with free D-fructose or grafted fructose (HA-fructose).

	Entry Derivative	Saccharide	a) NMR K a (M -1 )

Table of Contents graphic

 of

H NMR (Table3, FigureS15-S18).

(ABOR) with free D-fructose; rheological analysis of the HA-1,2-BORIN (2,1-BORIN, BOR or PBA) alone at pH 7.4 (M w HA = 360 g/mol); cytotoxicity (MTT) assay of individual solutions of HA derivatives incubated with mouse embryonic fibroblasts (MEFs).

AUTHOR INFORMATION

Corresponding Author

* E-mail: rachel.auzely@cermav.cnrs.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT

This work was supported by Galderma-Nestlé Skin Health. The authors thank Dr. C. Bouix-Peter at Galderma R&D for valuable discussions; Bellen Chemistry and GVK Biosciences for the custom synthesis of aminobenzoxaborin derivatives; the NMR platform of ICMG (FR2607) for its support; and Dr. Alexei Grichine, Dr. Antoine Delon and Tom Delaire from the IAB microscopy platform (Grenoble) for the confocal imaging of fibroblasts cells cultured in our hydrogels.


𝑎 Lorenzo Périssé
email: lorenzo.perisse@cea.fr

Xavier Mougeot

Anthony Onillon

Matthieu Vivier

𝑏 Anthony

𝑐, 𝑛𝑜𝑤 𝑎𝑡 𝑑 Onillon 𝑎

Improved modeling of reactor antineutrino spectra

Over the last decades, Inverse Beta Decay antineutrino experiments conducted at short and long baselines from nuclear reactors have revealed significant discrepancies on both the rate and shape of the measured spectra compared to state-of-the-art predictions. No evidence for an experimental bias has been demonstrated, and the sterile neutrino interpretation of the reactor antineutrino anomaly is currently disfavored by recent very short baseline reactor experiments. The validity of the predictions is then questioned as the source of the observed discrepancies. This motivates a revision of the reactor antineutrino spectrum modeling, which will also be useful for a new generation of reactor experiments investigating Coherent Elastic Neutrino-Nucleus Scattering. In this context, a revisited prediction of reactor antineutrino spectra using the summation method is currently underway, including the construction of a comprehensive uncertainty budget associated to both modeling and nuclear data. The ingredients of this new prediction along with preliminary results are presented in this proceeding.

Introduction

Nuclear reactors emit a huge number of electronic antineutrinos (𝜈 𝑒 ) originating from the fission of uranium and plutonium contained in the nuclear fuel, as well as from neutron activation of structural and fuel elements. Each fission produces two unstable fission products (FP) that undergo successive 𝛽-decays before reaching stability. About six 𝜈 𝑒 are emitted per fission and a reactor emits 2 × 10 20 𝜈 e • s -1 • GW th . Below 10 MeV, the Inverse Beta Decay (IBD) cross-section is about 𝜎 𝐼 𝐵𝐷 ∼10 -42 cm 2 and the Coherent Elastic Neutrino-Nucleus Scattering (CE𝜈NS) cross-section is about 𝜎 𝐶 𝐸𝜈 𝑁 𝑆 ∼10 -40 cm 2 . Nonetheless, the gigantic number of 𝜈 𝑒 produced, associated to large long baseline or smaller short baseline detectors, balance their very low interaction cross-section. Reactor 𝜈 𝑒 spectra can be predicted using two methods. The summation model (SM) uses available nuclear and fission data to build a reactor spectrum based on the 𝑉 -𝐴 theory of weak interaction, but faces the incompleteness of databases. The second method is the conversion method. It consists in fitting a measured electron spectrum using virtual 𝛽 branches that are converted to 𝜈 𝑒 spectra in order to obtain the total 𝜈 𝑒 spectrum. The conversion method is used in state-of-the-art predictions, but several discrepancies have been observed between such predictions and experimental data. In 2011, a new evaluation of reactor 𝜈 𝑒 spectra was performed independently by the Saclay group [START_REF] Mueller | Improved predictions of reactor antineutrino spectra[END_REF] and P. Huber [START_REF] Huber | Determination of antineutrino spectra from nuclear reactors[END_REF]. These two new predictions led to consistent deficits of about 6% statistically significant at more than 2𝜎 when compared to measured IBD rates of short baseline experiments, called the reactor antineutrino anomaly [START_REF] Mention | Reactor antineutrino anomaly[END_REF]. Furthermore, a shape difference manifesting mostly in the 4-6 MeV range between the measured IBD spectra and the predictions has been observed in several experiments, including recent ones at very short baselines. Several scenarios have been proposed to explain these anomalies. The sterile neutrino hypothesis is disfavored and detector effects are unlikely, but a misprediction with an underestimated uncertainty budget could explain them. In order to investigate the origin of these anomalies, the modeling of reactor spectra and their uncertainty budget must be revisited.

Revised summation calculations

In the SM, 𝛽 (𝜈 𝑒 ) fission spectra are calculated as the sum of 𝛽 (𝜈 𝑒 ) spectra of every FP 𝛽 - transition. At the level of a single 𝛽-branch 𝑏 of a FP 𝑓 , the associated 𝛽 spectrum 𝑆 𝑏 𝑓 is described by the 𝑉 -𝐴 theory of weak interaction as

𝑆 𝑏 𝑓 (𝑍 𝑓 , 𝐴 𝑓 , 𝐸 𝑏 0, 𝑓 , 𝐸) = 𝐾 𝑏 𝑓 Normalization 𝑝𝐸 (𝐸 𝑏 0, 𝑓 -𝐸) 2
Phase space

F (𝑍 𝑓 , 𝐴 𝑓 , 𝐸) Fermi function 𝐶 𝑏 𝑓 (𝐸) Shape factor × Corrections, (1)
where 𝑍 𝑓 and 𝐴 𝑓 are the daughter nucleus charge and mass numbers, 𝐸 𝑏 0, 𝑓 is the endpoint energy of the considered transition, 𝑝 and 𝐸 are the 𝛽 particle momentum and total energy. 𝐾 𝑏 𝑓 is a normalization factor such that

∫ 𝐸 𝑏 0, 𝑓 0 d𝐸 𝑆 𝑏 𝑓 (𝐸) = 1.
The phase space factor comes from the density of states accessible to the emitted particles. The Fermi function specifically accounts for the deceleration of the electron in the Coulomb field created by the 𝑍 𝑓 positive charges, and is the leading order QED correction [START_REF] Huber | Determination of antineutrino spectra from nuclear reactors[END_REF]. The shape factor 𝐶 𝑏 𝑓 (𝐸) is a modification to the Fermi function depending on the forbiddenness degree (FD) of the transition. The FD of a 𝛽 transition

PoS(PANIC2021)296

Improved modeling of reactor antineutrino spectra Lorenzo Périssé is a classification based on spin and parity changes between the parent and daughter nuclei. Shape factors are constant for transitions of the lowest FD (called allowed transitions), and are expressed as polynomials in the electron and neutrino momenta for transitions of higher FD (called forbidden transitions). Previous summation calculations used analytical Fermi functions derived for point-like daughter nuclei and constant coefficients for the shape factor polynomials. In this work, a code was developped to compute exact corrections to the Fermi functions and energy dependent shape factor coefficients for every nucleus, including the so-called nucleus finite-size and atomic screening effects. Finally, radiative corrections from QED [START_REF] Sirlin | Radiative correction to the 𝜈 𝑒 (𝜈 𝑒 ) spectrum in 𝛽 decay[END_REF] and weak current corrections (commonly referred to as weak magnetism) due to the nucleon finite size [START_REF] Hayes | Systematic uncertainties in the analysis of the reactor neutrino anomaly[END_REF] are considered in Eq. 1. The 𝜈 𝑒 spectrum of a transition is then given by energy conservation, if recoil effects are neglected [START_REF] Huber | Determination of antineutrino spectra from nuclear reactors[END_REF]. It consists in replacing the 𝛽 energy by the 𝜈 𝑒 energy in Eq. 1, 𝐸 → 𝐸 𝜈 𝑒 = 𝐸 𝑏 0, 𝑓 -𝐸. The spectrum 𝑆 𝑓 of a FP is obtained as the sum of the 𝑛 𝑓 𝛽-branch spectra weighted by their corresponding branching ratio 𝐵 𝑏 𝑓 . The actinide fission spectra 𝑆 𝑘 (𝑘 = 235 U, 238 U, 239 Pu, 241 Pu) are then obtained by summing the respective FP spectra weighted by their corresponding 𝛽 decay activity A 𝑓 . Activities can be replaced by cumulative fission yields if the reactor is assumed to be at equilibirum. Fission yields from the JEFF3.3 database [START_REF] Plompen | The joint evaluated fission and fusion nuclear data library[END_REF] are used in this work. Branching ratios, 𝛽 intensities, endpoint energies and spin-parity information are retrieved from the ENSDF database [START_REF]From ENSDF database as of[END_REF]. ENSDF data of high Q-value FP are subject to the Pandemonium effect, which is due to the partial blindness of HPGe detectors to high-energy or weak emission 𝛾-rays, resulting in an overestimation of the 𝛽-feedings of low energy levels. Identified Pandemonium-impacted FP contribute at least to ∼45% of a reactor IBD yield. Their data are corrected based on data from total absorption 𝛾-spectroscopy and from direct 𝛽 spectrum measurements. Finally, contributions of FP with no available data are estimated using an effective modeling assuming three allowed transitions with evenly distributed endpoint energies up to the maximum decay energy of the FP. Fission yield uncertainties are analytically propagated and induce a ∼1.1% uncertainty on a reactor IBD yield. Uncertainties of branching ratios, 𝛽 intensities, endpoint energies and spin-parity information are propagated using a Monte-Carlo simulation. The former two sources induce a ∼0.6% IBD yield uncertainty, while the other two induce a ∼0.2% IBD yield uncertainty. Beside nuclear data uncertainties, spectrum mismodelings are also treated as uncertainty sources. Non-unique forbidden transitions are especially very complicated to compute, and contribute to ∼35% of a reactor IBD yield. Nonunique transitions of degree 𝑁 are approximated as unique transitions of degree 𝑁 -1, i.e. transitions of same spin change but different parity change, which introduces modeling errors. This is called the 𝜉-

Uncertainty treatment

PoS(PANIC2021)296

Improved modeling of reactor antineutrino spectra Lorenzo Périssé approximation, and it has been shown to be abusively applied to all non-unique transitions wihtout any theoretical argument [START_REF] Mougeot | Reliability of usual assumptions in the calculation of beta and nu spectra[END_REF]. In this work, three of the most important non-unique transitions from 92 Rb, 96 Y and 144 Pr, contributing to ∼10% of a reactor IBD yield, are estimated with nuclear structure calculations using the NuShellX program. The uncertainty associated to the modeling of these three branches is based on a comparison between the nuclear structure calculations and their 𝜉-approximated versions. Estimating the uncertainty associated to all other 𝜉-approximated transitions is on-going. Modeling uncertainties are derived for the radiative correction and the weak magnetism for each transition by comparing their spectra with and without the corrections. Some FP may still be uncorrected from the Pandemonium effect. An uncertainty must be derived for those FP, which is an on-going work. Lastly, an uncertainty must be associated to the contribution of FP with no decay data. This work is also in progress. The preliminary 235 U spectrum obtained with this new SM is shown in Fig. 1. The impact of modeling three of the main non-unique transitions with nuclear structure calculations is shown in the bottom plot, with an important effect above 6 MeV.

Conclusion

A new reactor 𝜈 𝑒 spectrum has been modeled with a revised SM using up-to-date nuclear data. Several corrections have been refined and an advanced calculation has been employed for three important non-unique transitions. This is a first step to bypass the 𝜉-approximation commonly used in other summation calculations. More non-unique transitions will be computed in the near future. The derivation of an uncertainty budget is also on-going. Uncertainties associated to possible Pandemonium-impacted FP, to non-unique transitions and to FP with no data treated with the effective modeling are still under investigation. Once done, a comprehensive uncertainty budget will be established, which to our knowledge has never been done in any summation calculations.

*

  ** Particles and Nuclei International Conference -PANIC2021 *** *** 5 -10 September, 2021 *** *** Online ***

Figure 1 :

 1 Figure 1: Top: 235 U 𝜈 𝑒 fission spectrum (in blue) and FP spectra (in grey) composing it, obtained with the revised SM. Bottom: ratio of 235 U fission spectra using nuclear structure calculations (𝑆 adv ) or the 𝜉-approximation (𝑆 𝜉 ) for the three nonunique transitions of 92 Rb, 96 Y and 144 Pr.