Pedro Salas-Ambrosio

Antoine Tronnet

Mostafa Badreldin

Sifan Ji

Sebastien Lecommandoux

Simon Harrisson

Pierre Verhaeghe

Colin Bonduelle

Effect of N-alkylation in N-carboxyanhydride (NCA) polymerization kinetics

Polypeptoids are an emerging class of biomimetic polymers prepared by ring-opening polymerization (ROP) of N-alkylated-N-carboxyanhydride (NNCA) monomers. The Nalkylation provides a unique structural isomerism with peptides but its influence on NNCA reactivity is not yet fully understood. In this report, we provide a comprehensive study using 12 monomers to better rationalize the contribution of the steric hindrance and electronic effects of the N-alkyl group toward the synthesis of NNCA and their reactivity in ring-opening polymerization (ROP) reactions. We found that varying the alkyl group does not significantly influence the formation of NNCAs prepared by the Leuchs' method. In marked contrast, depending on the alkyl group, the efficiency of the NNCA polymerization initiated by allylamine showed that electron-donating groups enhanced the ROP kinetic rates through significant inductive effect and could counterbalance the negative influence of bulky groups during the propagation steps.

slower than those of Sar-NCA for most NNCAs.19 Previous studies involved NNCAs with varying aliphatic chains 1,7,30-33 or with heteroatom-containing side chains N-(3-tertbutoxy-3-oxopropyl) NNCA,5 N-2-methoxyethyl-NCA (MeOEt NCA) and N-2-(2ʹmethoxyethoxy)ethylglycine derived NCA (Me(OEt)2 NCA).34 For most of these NCAs, the polymerization rate depended primarily on steric hindrance,35 but the electron-withdrawing effect of substituent could also inhibit the ROP.36 In this work, we present a study based on 12 NCA monomers for which synthesis and polymerization kinetics were evaluated by infrared spectroscopy and molecular modelling. The obtained polymers were also fully characterized by a combination of NMR, SEC and MALDI-TOF analyses. The objective of this study was to better understand the influence of N-alkylation on the efficiency of ring closure during the formation of NNCA and on ring opening, during their polymerization. While for the formation of NNCAs by the Leuchs method, N-alkylation did not strongly influence the cyclization kinetics, our study revealed that steric hindrance can be significantly counterbalanced by positive inductive electronic effects activating the propagation steps of the ROP.

The main text of the article should appear here with headings as appropriate. Experimental Materials and methods Materials. All chemicals and solvents were purchased from Sigma Aldrich, Fluorochem, Acros, TCI, Strem and, unless otherwise described, were used without further purification. Dimethylformamide (DMF) and tetrahydrofuran (THF) were obtained from a solvent system purifier (PureSolv, Innovative Technology), kept under argon atmosphere and freshly used. MilliQ water was obtained from a system purifier (Purelab Prima, ELGA). The monomers synthesized were stored at 4 °C under argon atmosphere and weighed in a glove box (Jacomex GP13 No. 2675) at the Laboratoire de Chimie des Polymères Organique (LCPO, Pessac, France). Methods. The IR spectra were recorded using an FTIR spectrometer (Vertex 70, Bruker), and the samples were measured with an ATR (GladiATR, Pike Technologies) from Fisher technologies performing 32 scans at the LCPO (Bordeaux, France). The raw data were obtained with Opus7.5 software and processed using Originlab 2016 software. The NMR spectra were recorded using a Bruker Avance III 400 spectrometer (LCPO, Bordeaux, France). The spectra were obtained at 295 K and data was analyzed using Mestrenova 14.1.2 software. The chemical shifts of the signals are given in ppm. The spectra obtained were calibrated using the residual solvent signals (CHCl3 7.26 ppm, H2O 4.79 ppm, DMSO-d6 2.50 ppm). The signals were categorized as follows: singlet (s), doublet (d), triplet (t), quartet (q), multiplet (m) and broad (br). Polymer molar masses were determined by Size Exclusion Chromatography (SEC) using: a) Dimethylformamide (DMF + lithium bromide LiBr 1g/L) as the eluent (LCPO, Bordeaux, France). Measurements in DMF were performed on an Ultimate 3000 system from Thermoscientific equipped with diode array detector DAD. The system also included a multi-angle light scattering detector MALS and differential refractive index detector dRI from Wyatt technology. Polymers were separated on two Shodex Asahipack gel columns GF310 and GF510 (300 x 7.5 mm) (exclusion limits from 500 Da to 300 000 Da) at a flow rate of 0.5 mL/min. Column temperature was held at 50°C. The chromatograms were recorded with Chromeleon 7.2 software and Astra 7.1.0 software and analyzed using Originlab 2016 software. The dn/dc were determined experimentally. b) Hexafluoro-2propanol (HFIP+ 0,05% KTFA) as the eluent (LCPO, Bordeaux, France). Measurements in HFIP were performed on an Ultimate 3000 system from Thermoscientific equipped with diode

Introduction

Peptoid polymers, also called poly(N-substituted-glycines) or polypeptoids are N-alkylated analogs of synthetic polypeptide polymers: they are polypeptides with an N-substituted amide bond.1,2 The physicochemical properties of polypeptoids can be tailored by the Nalkylation, enabling control over 1) the hydrophilic to lipophilic balance,3 2) the charge characteristics,4,5 3) the backbone conformation,6 4) the solubility,7 5) the thermal and crystallization properties.8,9 The most direct way to prepare polypeptoids is to polymerize N-alkylated-N-carboxyanhydride monomers (NNCA). Historically, the Leuchs method made use of thionyl chloride (SOCl2)10 or other halogenated electrophilic reagents such as PCl3 and PBr3.11,12 Adaptation of the Leuchs method later involved a mixture of acetyl chloride and acetic anhydride,13 or the use of alternative reagents.14 More recently, NNCAs production was also achieved using phosgene or its derivatives, a strategy called the Fuchs Farthing method. [START_REF] Fetsch | Polypeptoids from N-Substituted Glycine N-Carboxyanhydrides: Hydrophilic, Hydrophobic, and Amphiphilic Polymers with Poisson Distribution[END_REF] The advantage of this approach relative to the Leuchs method is that there are fewer chlorine acid traces in the reaction medium that can retard polymerization, even though recent improvements in purification processes tend to mitigate this advantage.15-17 NNCA polymerization is a controlled process when initiated with nucleophiles such as amines (primary or secondary),7 strong bases such as LiHMDS18 or N-heterocyclic carbenes.12 Recent developments includes the use of organocatalysis to speed up the ROP kinetics such as 1,3-bis [3,5-bis(trifluoromethyl)phenyl]urea,19 7-methyl-1,5,7triazabicyclo [4.4.0]dec-5-ene (MTBD),20 and 1,8-diazabicyclo [5.4.0]undec-7-ene (DBU). [START_REF] Dove | Controlled Ring-Opening Polymerisation of Cyclic Esters: Polymer Blocks in Self-Assembled Nanostructures[END_REF] These different methods all result in a living polymerization process: the addition of more NNCA monomers leads to a stoichiometric increase in the number average length of the polymer chains,22 and this enables the preparation of both random23-25 and block copolymers. [START_REF] Fetsch | Highly Defined Multiblock Copolypeptoids: Pushing the Limits of Living Nucleophilic Ring-Opening Polymerization[END_REF][START_REF] Secker | Thermo-Induced Aggregation and Crystallization of Block Copolypeptoids in Water[END_REF][START_REF] Xuan | Thermoreversible and Injectable ABC Polypeptoid Hydrogels: Controlling the Hydrogel Properties through Molecular Design[END_REF][START_REF] Gangloff | Linking Two Worlds in Polymer Chemistry: The Influence of Block Uniformity and Dispersity in Amphiphilic Block Copolypeptoids on Their Self-Assembly[END_REF] The most studied polypeptoid is obtained by polymerizing N-methylglycine-N-carboxyanhydride, also called sarcosine NCA, (Sar-NCA). Its polymerization proceeds in a controlled manner without chain transfer or termination events, producing polysarcosines with narrow molar mass distributions (ÐM = 1.1-1.3). [START_REF] Fetsch | Highly Defined Multiblock Copolypeptoids: Pushing the Limits of Living Nucleophilic Ring-Opening Polymerization[END_REF] The same behavior has been observed with other NNCAs bearing a range of N-alkyl side chains.7, [START_REF] Robinson | A Versatile Polypeptoid Platform Based on N-Allyl Glycine[END_REF] The chemical nature of the N-alkyl group strongly influences the ROP kinetics, which are much array detector DAD. The system also included a multi-angle light scattering detector MALS and differential refractive index detector dRI from Wyatt technology. Polymers were separated on PL HFIP gel column (300 x 7.5 mm) (exclusion limit from 100 Da to 150 000 Da) at a flow rate of 0.8 mL/min. Column temperature was held at 40°C. The chromatograms were recorded with Chromeleon 7.2 software and Astra 7.1.0 software and analyzed using Originlab 2016 software. The molar mass was calculated using either a calibration curve or the dn/dc value. The calibration curve was performed with polystyrene standards with molar masses in the range 0.9-364 kg/mol. The dn/dc were determined experimentally. MALDI-MS spectra were performed at CESAMO facility (Bordeaux, France) on an Autoflex maX TOF mass spectrometer equipped with a frequency tripled Nd:YAG laser emitting at 355 nm. Spectra were recorded in the positive-ion mode using the reflectron and with an accelerating voltage of 19 kV. For MALDI-MS analyses, polypeptoid deposits were prepared according to the two following recipes: 1) Polypeptoid and the cationic agent (NaI) were dissolved in methanol at 10 mg/mL. The α-CHCA matrix (α-cyano-4-hydroxycinnamic acid) solution was prepared by dissolving 10 mg in 1 mL of methanol and the solutions were combined in a 10:1:1 volume ratio (matrix:sample:salt). One microliter of this solution was deposited onto the grid and vacuum-dried before analysis. 2) the polymer and the cationic agent (NaI) were dissolved in methanol at 10 mg/mL. The dithranol matrix solution was prepared by dissolving 10 mg in 1 mL of dichloromethane and the solutions were combined in a 10:1:1 volume ratio (matrix:sample:salt). One microliter of this solution was deposited onto the grid and vacuum-dried before analysis. Kinetics study. The analyzed compounds were dissolved in anhydrous solvent in the Schlenk vessel under an argon atmosphere at 20 °C at 0.4 M. Samples (50 µL) were taken with an argon purged syringe at predetermined intervals. The samples were dropped onto the ATR unit of the IR spectrometer and measured in the range of 400-4000 cm-1. The monomer conversion was followed using the band height of the C=O stretching at about 1850 cm-1, whose increase is linear in the examined concentration range. The initial value for the band at 100% conversion was corrected using THF or DMF as blank. Samples were taken until no further change in band height was observed in order to determine the monomer conversion and corresponding reaction times (the point were no further change occurred was assumed to correspond to 100% conversion). Data analysis was carried out using Origin 2016 software (OriginLab). Molecular modelling. Calculation were performed usually on 4 cores on a "home-made" setup equipped with 4 Dual Intel Xeon Silver 4214 2.2GHz, 3.2GHz Turbo, 12C and 8x32GB DDR4 2933MHz RDIMM ECC Memory. Computations were performed on NNCA monomers, allylamine and methyl ester N-alkylated glycines structures. The structures were built and pre-optimized with the software Chemcraft. Geometry optimizations of the resulting structures were performed with the B3LYP density functional37 and the 6-311+G(d,p) basis set with the Orca program. [START_REF] Neese | The ORCA Quantum Chemistry Program Package[END_REF] The bulk solvent effects were described with the integral equation formalism polarizable continuum Model (IEFPCM) with DMF as solvent.39 Vibrational frequencies were computed to confirm the convergence to local minima and to calculate the unscaled zero-point-energy (ZPE), the Gibb's free energy at 298 K as well as the HOMO and the LUMO energies.

Synthetic Procedures.

The N-alkylated-N-Boc-glycine NNCA precursors were prepared according to the procedures presented in the ESI. In a second step, the synthesis of the different NCAs were operated using the Leuchs method, as previously reported18 and detailed below. Synthesis of sarcosine-NCA (N-Me-NCA 1): In a clean, dry Schlenk flask N-methyl-N-Bocglycine (2.27 g, 12 mmol, 1 equiv.) was dried for 10 min in vacuo, then 14 mL anhydrous THF was added, followed by thionyl chloride (0.88 mL, 12 mmol, 1 equiv.). The reaction was stirred for 2 h at RT. The solvent was evaporated in vacuo, and the residue was washed with 3×30 mL anhydrous hexane, filtered using a cannula, and the powder was dried. Then 7.5 mL of anhydrous DCM were added and the suspension was filtered over previously dried Celite.

The system was washed with 5×15 mL of anhydrous DCM and the solvent was evaporated in vacuo. The product was obtained as a white solid yielding 72% (0.99 g). Synthesis of N-cyclohexyl-NCA (N-ch-NCA 3): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a white power in 80% yield (0.57 g) starting from Ncyclohexyl-N-Boc-glycine (1 g, 3.9 mmol). C9H13NO3, MW = 183. Synthesis of N-benzyl-NCA (N-Bz-NCA 4): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a yellowish crystalline powder in 79% yield (0.57 g) starting from N-benzyl-N-Boc-glycine ( (COO). Both proton and carbon NMR were in agreement with a previously reported synthesis.40 Synthesis of N-gem-trifluoroethyl-NCA (N-gtfEt-NCA 5): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a white powder in 46% yield (0.32 g) starting from N-(trifluoroethyl)-N-Boc-glycine (1 g, 3.9 mmol). C5H4 F3NO3, MW = 183.01 g/mol, MS (CI+): m/z= 184.02 [M+H]+, 1H-NMR, CDCl3 400 MHz δ: 4.03 (q, 2H, J=8.5 Hz, CH2), 4.92 (s, 2H, CH2). 13C-NMR, CDCl3 100 MHz δ: 45.17 (q, J=35.9 Hz, CH2), 49.87 (CH2), 123.43 (q, J=279 Hz, CH2), 152. The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a colorless liquid in 60% yield (0.79 g). 1H NMR, CDCl3 400 MHz δ: 0.97 (t, 3H, CH3), 1.63 (m, 2H, CH2), 3.37 (t, 2H, CH2), 4.10 (s, 2H, CH2). Proton NMR were in agreement with a previously reported synthesis.7 Glycine and N-methylalanine NCA syntheses are developed in the ESI. Preparation of polymers. The polymers were prepared in DMF and at a monomer concentration of 0.4 M. To compare the kinetics, a degree of polymerization (M/I) of 20 was implemented using allylamine. The details specific to each polymerization are given below. Synthesis of poly(N-methyl)glycine (PSar 1'). Sarcosine-NCA monomer (0.2 g, 1.74x10-3 mol) was weighed in a glovebox under pure argon, introduced in a flame-dried Schlenk vessel, and dissolved in 4.3 mL of anhydrous DMF. A solution of allylamine (0.5 M in DMF) was prepared and 174 μL (8.69x10-5 mol) were added with an argon purged syringe. The solution was stirred at RT under argon until completion. The polymer was then recovered as a white solid by precipitation in diethyl ether and dried in vacuo. Yield: 60% (0.074 g). 1H-NMR DMSO-d6 400 MHz δ (ppm): 2.50-3.10 (m, 69H, CH3), 3.62-3.80 (m, 2H, CH2 allylamine), 3.80-4.42 (m, 42H, CH2), 5.0-5.20 (m, 2H, CH2 allylamine), 5.64-5.82 (m, 1H, CH allylamine). NH terminal missing in these experimental conditions. Synthesis of poly(N-isopropyl)glycine (PNiPr 2'). The synthesis was similar to the one described for 1'. The polymer was recovered as a white solid in 60% yield (72 mg) starting from N-iPr-NCA (174 mg, 1.22x10-3 mol). 1H-NMR TFA-d 400 MHz δ (ppm): 1.03-1.57 (m, 150H, CH3), 3.16-4.14 (m, 24H, CH), 4.52-4.15 (m, 55H, CH2), 4.78-4.91 (m, 2H, CH2 allylamine), 5.25 (m, 1H, CH allylamine). NH terminal missing in these experimental conditions. Synthesis of poly(N-cyclohexyl)glycine (PNch 3'). The synthesis was similar to the one described for 1'. The polymer was recovered as a white solid in 79% yield (0.12 g) starting from N-chG-NCA (0.2 g, 1.09x10-3 mol). 1H-NMR TFA-d 400 MHz δ (ppm): 1.08-2.32 (m, 275H, CH2), 3.27-3.69 (m, 26H, CH), 3.76-3.86 (m, 2H, CH2 allylamine), 4.08-4.59 (m, 57H, CH2), 5.14-5.40 (m, 2H, CH2 allylamine), 5.90-5.71 (m, 1H, CH allylamine). NH terminal missing in these experimental conditions. Synthesis of poly(N-benzyl)glycine (PNBz 4'). The synthesis was similar to the one described for 1'. The polymer was recovered as a yellowish solid in 68% yield (66 mg) starting from N-Bz-NCA (0.126 g, 6.59x10-4 mmol). 1H-NMR TFA-d 400 MHz δ (ppm): 3.71-3.91 (m, 2H, CH2 allylamine), 3.96-4.81 (m, 70H, CH2+CH2Ar), 5.00-5.20 (m, 2H, CH2 allylamine), 5.57-5.76 (m, 1H, CH allylamine), 6.73-7.51 (m, 85H, Ar). NH terminal missing in these experimental conditions. Synthesis of poly(N-(gem-trifluoroethyl))glycine (PNtfg 5'). We did not succeed in polymerizing this monomer (see discussion section). Synthesis of poly(N-(2-methylthioethyl))glycine (PNmt 6'). The synthesis was similar to the one described for 1'. The polymer was recovered as a white solid in 41% yield (0.12 g) starting from N-mtG-NCA (400 mg, 2.28x10-3 mol). 1H-NMR DMSO-d6 400 MHz δ (ppm): 1.98-2.23 (m, 86H, CH3), 2.53-2.72 (m, 47H, CH3), 3.67-3.79 (m, 2H, CH2 allylamine), 3.86-4.70 (m, 49H, CH2), 4.97-5.29 (m, 2H, CH2 allylamine), 5.66-5.93 (m, 1H, CH allylamine). NH terminal missing in these experimental conditions. Synthesis of poly(N-(p-nitrobenzyl))glycine (PNpBz 7'). The synthesis was similar to the one described for 1'. The polymer was recovered as a yellowish solid in 69% yield (88 mg) starting from N-pbz-NCA (157 mg, 6.62x10-4 mol). 1H-NMR DMSO-d6 400 MHz δ (ppm): 3.53-3.71 (m, 2H, CH2 allylamine), 3.78-4.84 (m, 72H, CH2+CH2Ar), 4.91-5.15 (m, 2H, CH2 allylamine), 5.56-5.78 (m, 1H, CH allylamine), 7.23-8.37 (m, 92H, Ar). NH terminal missing in these experimental conditions. Synthesis of poly(N-(Cbz-2-aminoethyl))glycine (PNzae 8'). The synthesis was similar to the one described for 1'. The polymer was recovered as a yellowish solid in 52% yield (81 mg) starting from N-Zae-NCA (185 mg, 6.65x10-4 mol). 1H-NMR DMSO-d6 400 MHz δ (ppm): 2.92-3.60 (m, 86H, 2CH2), 3.78-4.50 (m, 34H, CH2) 4.84-5.21 (m, 40, CH2), 5.59-5.90 (m, 1H, CH2 allylamine), 7.04-7.49 (m, 104H, Ar+NHCO). NH terminal missing in these experimental conditions. Synthesis of poly(N-(Cbz-2-aminobutyl))glycine (PNzab 9'). The synthesis was similar to the one described for 1'. The polymer was recovered as a yellowish solid in 64% yield (110 mg) starting from N-Zab-NCA (0.203 g, 6.63x10-4 mol). 1H-NMR DMSO-d6 400 MHz δ (ppm): 1.20-1.63 (m, 110H, 2CH2), 2.91-3.06 (m, 41H, CH2), 3.10-3.36 (m, 40H, CH2), 3.60-4.47 (m, 39H, CH2), 4.92-5.12 (m, 51H, CH2), 5.65-5.90 (m, 1H, CH allylamine), 7.05-7.46 (m, 156H, Ar+NHCO). NH terminal missing in these experimental conditions. Synthesis of poly(N-propyl)glycine (PNPr 10'). The synthesis was similar to the one described for 1'. The polymer was recovered as a white solid in 58% yield (0.08 g) starting from N-Pr-NCA (200 mg, 1.40x10-3 mol). 1H-NMR D2Oi 400MHz δ (ppm): 0.77-1.05 (m, 38H, CH2), 1.37-1.94 (m, 59H, CH3), 3.10-3.54 (m, 40H, CH2), 3.80-3.91 (m, 2H, CH2 allylamine), 3.97-4.62 (m, 39H, CH2), 5.16 (s, 2H, CH2 allylamine), 5.86 (s, 1H, CH allylamine), 7.49 (s, 1H, NH terminal). Synthesis of polyglycine, poly(L-alanine) and poly(N-methyl-L-alanine). The detailed procedures of these 3 syntheses are developed in the ESI.

Results and discussion

Even though they were first prepared over 100 years ago, the synthesis of NCAs from amino acids remains an important topic of research. [START_REF] Song | Recent Advances and Future Perspectives of Synthetic Polypeptides from N-Carboxyanhydrides[END_REF] The first examples of NCA synthesis were described with thionyl chloride (SOCl2)10 and various NCA compounds were successfully prepared from N-carboxybenzyl-or N-carboxyethyl-substituted amino acids including for instance glycine, L-phenylalanine and L-leucine.10,42,43 Reacting N-substituted amino acids with other chlorinated or brominated electrophilic reagents, such as PCl5 and PBr3 also afforded NCA including L-ornithine, L-phenylalanine, L-alanine, L-lysine and L-valine derivatives. 44,[START_REF] Ben-Ishai | Synthesis of N-Carboxy-α-Amino Acid Anhydrides from N-Carbalkoxy-α-Amino Acids by the Use of Phosphorus Tribromide[END_REF] This approach, called the Leuchs method, is an alternative to the Fuchs' and Farthing's method consisting in the reaction of unsubstituted amino acids with an excess of phosgene or its derivatives (diphosgene and triphosgene).46-48 The knowledge developed from the synthesis of N-carboxyanhydrides can be extended to the synthesis of N-alkylated-NCA. Several routes were investigated with NNCAs. For example, N-(benzyloxycarbonyl)glycine derivatives bearing various N-alkyl substituents were reacted with acetyl chloride and acetic anhydride.7,22,30 Other reagents such as PBr311,49 or PCl3 were used to prepared NNCAs from N-(tert-butoxycarbonyl)glycine derivatives bearing a wide range of alkyl and oligo(ethylene glycol) groups.6,9,12,13,29,34,50-52 Although both approaches can be considered to be variations of the Leuchs method, the original protocol using SOCl2 has scarcely been developed: early studies demonstrated the preparation of Nphenylglycine-NCA43 and more recent ones presented the preparation of lysine-, phenylalanine-like-and sarcosine-NCAs.18 Therefore, we decided in this work to focus on the use of the Leuchs method with SOCl2 (scheme 1). We first designed a method to prepare a library of N-alkylated-N-Boc-glycines, as NNCA precursors (scheme 1a).10 The N-alkyl-N-Boc intermediates are formed in a one-pot procedure consisting of i) the formation of N-alkyl-glycine (not isolated) from reductive amination of glyoxylic acid with various primary alkylamines and ii) Boc protection (using Boc2O) of the secondary amine without prior purification. We initially prepared five Nalkylated-N-Boc-glycine derivatives bearing alkyl side chains of increasing lipophilicity (methyl, propyl, isopropyl, cyclohexyl and benzyl groups). All compounds were isolated with good purity (60-77% yields) after liquid-liquid extractions, avoiding the use of chromatographic purification (see Supporting information). We then prepared five more Nalkyl-N-Boc-glycine derivatives bearing functionalized side chains (gem-trifluoroethyl, methylthioethyl and p-nitro-benzyl and two N-protected aminoalkyl groups). The last two intermediates were prepared from commercial 1,2-diaminoethyl-or 1,4-diaminobutylcontaining reagents on which one amine function was protected by a benzyloxycarbamate (Cbz or Z) group (see Supporting information). Finally, N-Boc derivatives of N-methyl-Lalanine and glycine were purchased or prepared according to a different method (see experimental part and esi). These synthetic efforts resulted in a library of 12 N-Bocaminoacid derivatives, enabling further study of i) the formation of each NNCA via the Leuchs reaction and ii) their ROP kinetics, initiated with allylamine (scheme 2). Scheme 2. The different NNCA monomers that were prepared and studied (polymerization kinetics) considering several key effects brought by the N-alkylation. Kinetics of NNCA formation via the Leuchs method.

Despite growing interest in the synthesis of NCA monomers, the effect of the N-alkyl side chains on the kinetics of the N-carboxyanhydride ring formation has not really been described. We addressed this question by i) conducting a kinetic study of the preparation of 10 N-alkylated NCA monomers bearing various alkyl side chains via the Leuchs method using SOCl2 and ii) achieving DFT calculation to optimize the geometry of the monomers and to determine the LUMO energy level of each different NNCA ring (see table 1 and exp. section). The rates of NNCA formation were measured by monitoring the IR absorbances corresponding to the C=O bond in NCO (1850 cm-1 stretching) (figure 1). Effects of steric hindrance (NNCAs 1-4), electron withdrawing or donating effects (NNCA 5-9) and carbon chain length (NNCA 8, 9) were therefore evaluated.

Figure 1. Monitoring of the NNCA formation. A) Synthesis scheme and B) evolution of the C=O (NCO) stretching signal during the NNCA formation monitored by FITR at 1850 cm-1. NNCA formation were carried out at RT (20 °C) in THF solution (0.4 M). We first studied the effect of the different aliphatic side chains with increasing steric hindrance by following the preparation of N-methyl-glycine-NCA (Sar-NCA 1), N-isopropyl-glycine-NCA (N-iPr-NCA 2), Ncyclohexyl-glycine-NCA (N-ch-NCA 3) and N-benzyl-glycine NCA (N-Bz-NCA 4, figure S1) from the corresponding N-Boc glycine derivatives. We used the conversion at 50-60 min to determine the speed of the NNCA formation. We observed a decrease in NNCA conversion when a bulkier alkyl substituent was introduced. First, Sar-NCA showed the highest conversion of 99.4% at 58 min, while N-ch-NCA presented a lower conversion of 73.2% at 50 min, followed by N-Bz-NCA (82.6% conversion at 60 min, table 1). The slight difference observed between N-cyclohexyl and Sar-NCA was attributed to a conformational effect of the cyclohexyl inducing a higher steric hindrance while the higher conversion rate of Nbenzyl could be explained by an inductive effect. Second, formation of N-iPr-NCA was associated with the lowest conversion rate of 56.7% at 60 min, a behavior that was attributed to stronger steric hindrance in the vicinity of the amine function that ring-closed, as confirmed by the calculated value of the LUMO energy (-0.93 eV) found in the same range as the LUMO energy values found for 1, 3 and 4.35 We then studied the effect of different heteroatom-containing side chains by following the preparation of N-gem-trifluoroethyl-glycine NCA (N-gtfEt-NCA 5), N-methylthioethyl-glycine NCA (N-MeSEt-NCA 6), N-para-nitrobenzyl-glycine NCA (N-pnBz-NCA 7), N-Z-aminoethylglycine NCA (N-ZNEt-NCA 8) and N-Z-aminobutyl-glycine NCA (N-ZNBu-NCA 9). The N-Bocglycine intermediates when they were mixed with SOCl2 were all fully converted to their corresponding NNCAs (see figure S1). The conversion rates of the cyclization reaction were not significantly influenced by the presence of the heteroatoms, as evidenced first by the N-pnBz-NCA formation (98.5% conversion at 60 min, table 1) that was found in the same range as the one found for N-Bz-NCA formation (82.6% conversion at 60 min). As an exception to this observation, the N-trifluoroethyl derivative showed that the formation of the corresponding NNCA monomer was significantly slowed down (46.6% conversion at 60 min), an effect that we attributed to the very strong attractive effect of the fluorine atoms toward the electron density on the nitrogen atom during ring-closing. This electronic effect was further confirmed by the calculated LUMO energy value that was found at -1.14 eV, the lowest value calculated for any of the NNCA monomers (see table 1). In summary, we prepared a small library of NNCAs using an optimized protocol involving a 2step synthesis: 1) reductive amination between primary amines and glyoxylic acid followed by the N-Boc protection in a "one-pot" procedure (yields 60-77%)) without any chromatography purification; 2) cyclization using the Leuchs method with SOCl2 (yields 44-89%). A kinetic study of the cyclization step established that bulkier alkyl groups slowed down the NNCA formation (time range: 1 to 7 h to complete conversion), while electronic effects were negligible. Kinetics of the ring opening polymerization: During the NCA synthesis, the Leuchs method releases HCl and chlorinated byproducts that may persist even after recrystallization.53-56 Acidic contaminants retard the ROP process,7 and their elimination is therefore important to obtain an efficient and reproducible polymerization. [START_REF] Semple | Large-Scale Synthesis of α-Amino Acid-N-Carboxyanhydrides[END_REF] We found that filtration over celite could successfully remove chlorides reflected in 0.6-3.8 fold increase in the first-order rate coefficients and afforded the fastest polymerization of Sar-NCA (k = 0.53 h-1, see figure S2) in comparison to the non-purified and crystallized monomers at DP = 100. Therefore, we employed this method to purify all our NNCA monomers in the different ROP kinetic studies. N-alkylation versus C-alkylation. The N-alkylation of NNCAs or the C-alkylation of NCAs strongly influences the polymerization kinetics.57,58 In this work, we investigated the ROP kinetics of glycine NCA, Sar-NCA and N-methyl-alanine-NNCAs in DMF at 0.4 M under argon and at a targeted ratio of Monomer/Initiator (M/I) = 20, using allylamine as initiator. The kinetics were determined by FTIR monitoring : decrease of the signal of the carbonyl stretching band (C=O) at 1850 cm-1. After almost 2 days, all polymerization reactions had reached complete conversion and the polymers were characterized by 1H-NMR and MALDI-TOF (see ESI figures S3-5, S15-17 ). To determine the first-order rate coefficients, the data were fitted by NNLS using an exponential decay (Mt = 1 -exp(-k.(t-t0)), where the Mt is the intensity at t time. The resulting plots were consistent with first order kinetics for all 3 ROP reactions (figure 2 and table 2). a] The polymer was not soluble even in HFIP. [b] The Mn was determined by SEC in DMF.

[c] The Mn was determined by SEC in HFIP.

Steric versus electronic effect of the N-alkylation. The methylation data showed that the effect of N-alkylation was more complex than just steric hindrance. Previous works have suggested that the electronic effect could be as strong as the steric hindrance in some cases. For instance, the recent ROP of N-(3-tert-butoxy-3-oxopropyl)-NCA demonstrated the relatively fast preparation of polypeptoid analogues of polyglutamic acid with a propagation rate constant, kp, of 181 M-1•h-1.5 This work provided a unique opportunity to rationalize the influence of different N-substitutions on the ROP kinetics of NNCAs. We set up the polymerization of NNCA using allylamine as initiator (targeting a M/I = 20) in anhydrous DMF under argon. The reaction mixtures were monitored by FTIR: the direct observation of the disappearance of the NNCA stretching band indicated that the reaction time to reach full conversion varied significantly, ranging from 3 h for PSar (1') to more than 12 days for PNch (3'). Upon ROP, all the homopolymers were purified by precipitation using diethyl ether. The yields were good for almost all polypeptoids (60 to 80% of the mass was recovered) except for PNmt (6') that afforded a low yield of 41%. This low yield was attributed to several precipitation steps performed on an oily product for which a high affinity to DMF was observed. All the polymers were fully characterized by 1H-NMR analyses, size exclusion chromatography (SEC), MALDI TOF and FTIR analyses (see figures S4-25, except MALDI TOF for PNiPr (2') because we could not determine it using either dithranol or α-CHCA). Solubility was a very important parameter for the characterization and most of the copolymers were soluble in polar solvents or in water (table S1). Molar masses determined by SEC showed a lower value than the theoretical one in most cases which was also found in previous works. [START_REF] Fetsch | Polypeptoids from N-Substituted Glycine N-Carboxyanhydrides: Hydrophilic, Hydrophobic, and Amphiphilic Polymers with Poisson Distribution[END_REF][START_REF] Robinson | A Versatile Polypeptoid Platform Based on N-Allyl Glycine[END_REF][START_REF] Xing | Charge-Determined LCST/UCST Behavior in Ionic Polypeptoids[END_REF] Despite this deviation, the polypeptoids synthesized presented low dispersities in the range ÐM = 1.08-1.30, except for PNpBz (7') (ÐM=1.91). MALDI TOF analysis confirmed that allylamine efficiently initiated the ROP and FTIR analyses revealed the expected amide I stretching band at ~1650 cm-1 (figure S25).7 With aliphatic groups, the experimental kinetics of NNCA monitored by FTIR were highly influenced by steric hindrance. For instance, PNPr (10') reached full conversion after 48 h with a kinetic constant of k = 6.3 ± 0.4 x10-2 h-1 (table 3) that was 64 times lower than the kinetic constant of the ROP forming PSar (1', k = 4.0 ± 0.4 h-1). This influence was even more pronounced when we performed the ROP of more sterically hindered monomers such as N-iPr-NCA and N-ch-NCA. The full conversion into PNiPr (2') was reached after 15 days and into PNch (3') after 20 days respectively (figure 3). Comparatively, the steric effect was reduced during the synthesis of PNPr (10'). The effect of such steric hindrance was surprising when we monitored the polymerization of N-benzyl-NCA towards PNBz (4', k = 1.5 ± 0.08 x 10-2 h-1). These results showed that the steric hindrance was significantly counterbalanced by another effect attributable to the benzyl group. We also followed the ROP of several NNCAs with heteroatoms on their side chains (figure 3). First, we studied the ROP kinetics of N-pnBz-NCA that possesses a nitro electronwithdrawing group, to compare it with the N-benzyl side chain (N-Bz-NCA, figure 3). Inttersestingly, after about 15 days of reaction, we reached a full conversion and monitored a zero-order kinetic rate of k = 26 ± 1.0 x10-2 mol•L-1•h-1 (table 3). We thus noticed that PNpBz (7') was slower (25.7% conversion at 50 h) as compared with PNBz (4', 54% conversion at 48 h), confirming that the electron withdrawing effect can strongly influence the ROP reactivity. This effect increased the electron density on the nitrogen atom and thus its nucleophilicity: it is this same effect that is at the origin of a higher pKa for secondary amines compared to primary amines.60

•L-1•h-1
It was also interesting to compare the ROP kinetics of N-benzylated-NCAs with NNCA monomers bearing ethyl substituents with a N-methylthioether (N-MeSEt-NCA) or a N-gemtrifluoroethyl functional group (N-gtfEt-NCA). The formation of PNmt 6' (k = 2.4 ± 0.2 x10-2 h-1) was 1.5 times faster than PNBz 4' (figure 3), an effect we attributed to enhanced nucleophilicity of the secondary amine during the propagation. In marked contrast, the PNgtfEt (5') took more than two weeks to achieve less than 5% of conversion (data not shown). This result indicated that electron-withdrawing groups (negative inductive effect) could strongly decrease the nucleophilicity during the propagation and consequently the ROP kinetics. Finally, we also compared the ROP kinetics of N-ZNEt-and N-ZNBu-NCAs. Interestingly, PNZae (8') presented a zero-order kinetics profile (figure 3) whereas PNzab (9') showed the characteristic of a first-order kinetics profile reaching full conversion in both cases at 135 h. NNCA was consumed at the same speed as the CO2 was released, presenting an apparent zero-order for PNzae 8' (k = 0.94 ± 0.04 mol•L-1•h-1) while in the case of PNzab 9', the longer alkyl chain enhanced the constant rate (k = 3.3 ± 0.1 x10-2 h-1) when we compared with PNBz 4' (improvement of 2.1 fold). Notably, the kinetics were not fitted with the first-order model for 7' and 8', similarly to the kinetics from 2' (k = 0.33 ± 0.02• mol•L-1•h-1) and 3' (k = 0.27 ± 0.02 mol•L-1•h-1 figure 3B). Indeed we observed an induction period within the first hours of polymerization where the kinetics seemed to present a slower kinetics rate. We attributed this to two possible effects: 1) in the case of polymers 2' and 3' could be explained due to solubility effect because they become turbid during the course of the polymerization; 2) in the case of polymer 8' and 7' the effect could be due to the stabilization of the carbamate formed during the ROP (scheme S1), with the decarboxylation step the rate determining step. To better estimate the influence of the electronic effect of the N-alkylation over the ROP of the proposed NNCA, DFT calculations of the HOMO energy levels of allylamine and of the propagating end extremities have also been performed using the B3LYP level of theory with the 6-311+G** basis set in DMF (CPCM, see experimental section). Based on the energy differences between these HOMO energy values and the LUMO of the different NNCA monomers, a higher reactivity is expected if the energy difference is smaller between these energy values (see figures 4 and S26). The difference observed with the experimental kinetics could then be attributed to another effect such as the steric hindrance. These DFT calculations showed for instance that the electronic effect had a significant influence for the propagation steps (figure 4) but not for the initiation steps (figure S26). First, theoretical calculations indicated that for the propagation steps, N-alkylation activated the reactivity significantly (5.98 eV for glycine as compared to 5.48 eV for sarcosine). As this electronic effect was not increased with C-methylation, the DFT calculation confirmed that the slower kinetics during PNMeAla formation were attributable to the steric hindrance. Then, with aliphatic groups (propyl, isopropyl, cyclohexyl and benzyl), LUMO-HOMO energy difference values were all in the same range (5.32 to 5.47 eV), and even indicative of a less reactive system with N-benzylation (5.47 eV). This was in marked contrast to ROP kinetics of 4 suggesting an enhanced propagation rate attributable to Pi-Pi stacking. Finally, positive and negative electronic effect were confirmed by molecular modelling for the other NNCAs bearing heteroatoms on their side chains notably, i) a strong inductive acceptor effect for the ROP of 5 (5.76 eV) and ii) significantly stronger inductive donor effects for 8 and 9 (5.26 and 5.32 eV respectively) as compared to N-methylation (5.48 eV).

Conclusions

The nature of the N-alkyl group on polypeptoids is an effective chemical lever to tune physico-chemical properties such as solubility, amphiphilicity, conformation and even crystallization behavior.1 This structural feature also influences the kinetics of NNCA monomer formation and further polymerization which are still poorly understood. In this work, we successfully prepared a library of 12 NCAs (including 5 original ones) using a methodology based on the Leuchs method. Kinetics of NNCA formation showed that the nature of the alkyl group, considering both steric and electronic effects, had a modest influence on the cyclization reaction (time to complete conversion ranging from 1 to 7 h). In contrast to NNCA formation, steric and electronic effects were important features in the ROP reaction, with bulky groups slowing down the kinetics of ROP while electron-donating groups accelerated it. In some cases, surprisingly, N-alkylation was also found to retard the CO2 release, leading to deviation from first-order order kinetic profiles. This study opens interesting perspectives to develop new catalytic systems based on our findings to further improve the preparation of polypeptoid polymers. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Conflicts of interest There are no conflicts to declare.

  21 g/mol, MS (CI+): m/z= 184.09 [M+H]+¬, 1H-NMR, CDCl3 400 MHz δ: 1.02-1.19 (m, 1H, CH), 1.25-1.49 (m, 4H, 2CH2), 1.65-1.76 (m, 1H, CH), 1.98-1.77 (m, 4H, 2CH2), 3.72-3.97 (m,1H, NCH), 4.04 (s, 2H, CH2). 13C-NMR, CDCl3 100 MHz δ: 25.09 (CH2), 25.18 (2CH2), 30.47 (2CH2), 45.63 (CH), 52.71 (CH2), 151.44 (NCOO), 166.13 (COO).

  16 (NCOO), 163.74 (COO). Synthesis of N-(2-methylthio)ethyl-NCA (N-MeSEt-NCA 6): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a yellow viscous oil in 71% yield (0.49 g) starting from N-[2-(methylthio)ethyl]-N-Boc-glycine (1 g, 4.0 mmol). C6H9NO3S, MW = 175.20 g/mol, MS (CI+): m/z= 176.03 [M+H]+¬¬, 1H-NMR, CDCl3 400 MHz δ: 2.16 (s, 3H, CH3), 2.76 (t, 2H, J=6.4 Hz, CH2), 3.63 (t, 2H, J=6.4 Hz, CH2), 4.24 (s, 2H, CH2). 13C-NMR, CDCl3 100 MHz δ: 15.29 (CH3), 32.00 (CH2), 41.99 (CH2), 49.70 (CH2), 152.36 (NCOO), 165.34 (COO). Synthesis of N-p-nitrobenzyl-NCA (N-pnBz-NCA 7): The product was prepared according to the synthesis of N-Me-NCA 1 and was isolated as a yellowish powder in 65% yield (0.49 g) starting from N-(p-nitrobenzyl)-N-Boc-glycine (1 g, 3.2 mmol). C10H8N2O5, MW = 236.18 g/mol, MS (CI+): m/z= 237.05 [M+H]+, 1H-NMR, CDCl3 400 MHz δ: 4.03 (s, 2H, CH2), 4.68 (s, 2H, CH2), 7.43-7.55 (m, 2H, CH Ar), 8.20-8.37 (m, 2H, CH Ar). 13C-NMR, CDCl3 100 MHz δ: 47.71 (CH2), 48.43 (CH2), 128.42 (2CH), 128.89 (C), 129.36 (2CH), 133.85 (C), 152.29 (NCOO), 165.37 (COO). Synthesis of N-benzyloxycarbonyl-aminoethyl-NCA (N-ZNEt-NCA 8): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a white powder in 47% yield (0.63 g) starting from N-(Cbz-aminoethyl)-N-Boc-glycine (1.7 g, 4.8 mmol). C13H14N2O5, MW = 278.26 g/mol, MS (CI+): m/z= 279.09 [M+H]+, 1H-NMR, CDCl3 400 MHz δ: 3.36-3.48 (m, 4H, 2CH2), 4.16 (s, 2H, CH2), 5.07 (s, 2H, CH2), 5.29 (s, 1H, NH), 7.31-7.37 (m, 5H, Ar). 13C-NMR, CDCl3 100 MHz δ: 38.41 (CH2), 43.90 (CH2), 49.39 (CH2), 67.30 (CH2), 128.21 (2CH), 128.46 (CH), 128.75 (2CH), 136.24 (C), 153.00 (NCOO), 157.09 (NCOO), 165.42 (COO). Synthesis of N-benzyloxycarbonyl-aminobutyl-NCA (N-ZNBu-NCA 9): The product was prepared according to the synthesis of N-Me-NCA 1 and isolated as a white powder in 44% yield (0.6 g) starting from N-(Cbz-aminobutyl)-N-Boc-glycine (1.7 g, 4.5 mmol). C15H18N2O5, MW = 306.32 g/mol, MS (CI+): m/z= 307.12 [M+H]+, 1H-NMR, CDCl3 400 MHz δ: 1.38-1.75 (br, 4H, 2CH2), 3.25 (q, 2H, J=6.4 Hz, CH2), 3.42 (t, 2H, J=7.1 Hz, CH2), 4.04 (s, 2H, CH2), 4.84 (s, 1H, NH), 5.09 (s, 2H, CH2), 7.31-7.39 (m, 5H, Ar). 13C-NMR, CDCl3 100 MHz δ: 24.39 (CH2), 27.16 (CH2), 40.24 (CH2), 43.31 (CH2), 49.05 (CH2), 66.76 (CH2), 128.11 (2CH), 128.25 (CH), 128.62 (2CH), 136.63 (C), 152.28 (NCOO), 156.69 (NCOO), 165.68 (s, COO). Synthesis of N-propyl-NCA (N-Pr-NCA 10):

Figure 2 .

 2 Figure 2. Kinetics of the ROP process for NNCA in DMF 0.4 M having an M/I = 20 varying the methylated position on different peptidomimetic polymers. *PNMeAla is depicted in hours.

Table 1 .

 1 Summary of the kinetics obtained for the synthesis of NNCA using the Leuchs method.

	NNCA Yield
	(%)	Conversion
	(%)
	at 60 min	LUMO
	(eV) NNCA Yield
	(%)	Conversion
	(%)
	at 60 min	LUMO
	(eV)
	Sarcosine-NCA (1)	72	99.4a -0.99
	N-MeSEt-NCA (6)	71	74.5 -1.00

Table 2 .

 2 Kinetic rates of the ROP of NNCA with different methylations

	Polymer	kobs
	(h-1) t0 (h) Mn (kg/mol) Ð
	PGly 9.54 ± 0.42 -0.058 ±0.003 n.aa -
	PSar 4.02 ± 0.36 -0.008 ± 0.013	1.0 b 1.03
	PNMeAla	0.084 ± 0.006 1.2±0.2	2.7c 1.18
	[

Table 3 .

 3 Characterization of the polypeptides and polypeptoids bearing different N-alkyl groups.

	Polymer	Reaction order	kobs (x10-2 h-1)	t0 (h) Mn (kg/mol) ÐM
	PSar (1')	First 402 ± 36	-0.008 ± 0.01 1.0	1.03
	PNiPr (2')	Zero-likea	0.33 ± 0.02 -10 ± 2 1.5	1.16
	PNch (3')	Zero-likea	0.27 ± 0.02 -12 ± 3 0.8	1.29
	PNBz (4')	First 1.55 ± 0.03 -0.4 ± 0.3	1.6	1.19
	PNmt (6')	First 2.4 ± 0.2	-0.9 ± 0.7	5.4	1.22
	PNpBz (7')	Zero-likea	0.26 ± 0.01 10 ± 1 4.0	1.91
	PNzae (8')	Zero-likea	0.94 ± 0.04 -9 ± 3 1.0 ± 0.3	1.29
	PNzab (9')	First 3.3 ± 0.1	-3.0 ± 0.3	5.6	1.08
	PNPr (10')	First 6.3 ± 0.4	0.4 ± 0.4	2.0	1.09
	[a] units of mol

Acknowledgements

The authors acknowledge Amelie Vax and Sylvain Bourasseau for assistance with sizeexclusion chromatography. Christelle Absalon is acknowledged for MALDI TOF analysis. This work has benefited from the facilities and expertise of the CESAMO platform (Bordeaux University). PSA received support from CONACYT (scholarship holder No. 548662). This work was supported by the French national agency for research (ANR): grant N° ANR-17-CE07-0039-01. ORCID Pedro Salas-Ambrosio: 0000-0002-0922-4620 Antoine Tronnet: 0000-0002-7158-9305 Mostafa: 0000-0001-6701-5280 Sifan Ji: 0000-0002-4466-5907 Sebastien Lecommandoux: 0000-0003-0465-8603 Simon Harrisson: 0000-0001-6267-2599 Pierre Verhaeghe: 0000-0003-0238-2447 Colin Bonduelle: 0000-0002-7213-7861 ABBREVIATIONS NCA (N-carboxyanhydrides), NNCA (N-alkylated carboxyanhydride), ROP (ring-opening polymerization), Me (methyl), Et (ethyl), Pr (propyl), iPr (isopropyl), Bz (benzyl), pnBz (paranitrobenzyl), MeSEt or Nmt (2-methylthioethyl), gtfEt or Ntfg (gem-trifluoroethyl), ZNEt or Nzae (Cbz-aminoethyl), ZNBu or Nzab (Cbz-aminobutyl).


Guillaume Rémy
email: guillaume1.remy@orange-ftgroup.com

Sidi-Mohammed Mohammed Senouci
email: mohammed.senouci@u-bourgogne.fr

François Jan
email: francois2.jan@orange-ftgroup.com

Yvon Gourhant
email: yvon.gourhant@orange-ftgroup.com

LTE4V2X: LTE for a Centralized VANET Organization

Keywords: Vehicular networks, organization, selforganization, clustering, LTE, WAVE, 802.11p, centralization, Floating Car Data

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

I. INTRODUCTION

Considering our increased mobile society, we have witnessed in the recent years novel Information and Communication Technologies (ICT) solutions providing Internet connectivity on the move, notably in vehicles in which we spend an increasing daily time. This development has emerged new paradigm known as Vehicular ad hoc networks (VANETs). VANETs are attracting an extensive attention from both academia and industry. The most important feature of these networks is their ability to extend the horizon of drivers and on-board devices and, thus, to make the time spent in vehicle more enjoyable to both driver and passengers and improve road traffic safety and efficiency. However, vehicular networks have to deal with many constraints, like the high mobility of nodes and the natural fragmentation of the network (vehicles are often grouped as isolated clusters). Then, offering sufficient quality of service and limiting overhead in vehicular networks are major issues that are still an opened topic. A lot of works propose solutions to some of these issues [START_REF] Cherif | Vehicular network self-organizing architectures[END_REF] [2] [START_REF] Cherif | A new framework of self-organization of vehicular networks[END_REF]. Most of them are based on the creation, in a decentralized way, of dynamic clusters to self-organize a non-heterogenous 802.11p vehicular network. With a highly dynamic environment such as vehicular networks, a decentralized clustering is not appropriate since it creates a large ammount of overhead within the network.

In this paper, we propose a novel framework for the organization of vehicular networks. This framework is centralized and uses the existing LTE network. We chose LTE for different reasons: (i) it is well suited to support the traffic induced by our protocol (a total of 20 kBps for 400 vehicles); (ii) LTE coverage is about 1 km 2 and is hence adapted to the vehicular network organization/management: about 400 vehicles to manage for a single eNodeB in an urban area; (iii) The usage of a centralized mechanism is intuitively better than the usage of decentralized mechanism, since the eNodeB has a global view of its coverage area which can improve the clusters' management; (iv) Most of the proposed VANET architectures (like CALM) proposes multiple interfaces in the vehicle, including 802.11p and LTE. This framework can have a lot of applications. Indeed, vehicles have become more sophisticated and are aware of not only their operational state but also of their surroundings, through sensors, radars or GPS receivers. Different kind of sensing devices are available on-board and also off-board to gather information about the driver's environment (speed, acceleration, temperature, road condition, electrical car battery level, tire swelling, etc.). Such collected information present an opportunity to service providers/municipalities in order to offer a set of new vehicle urban sensing applications that could be proposed to the drivers/passengers. Gathering such huge information is a challenging aspect that our centralized clustering protocol is able to solve efficiently.

Our framework, named LTE4V2X, uses both 802.11p and LTE to provide an efficient way to collect data periodically from vehicles and send them to a central server. We studied its performances against a decentralized clustering protocol for a well known urban sensing application, FCD application. Floating Car Data (FCD) are based on the collection of localization data, speed, direction of travel and time information from vehicles in order to feed a traffic management server. Based on these data, traffic congestion can be identified, travel times can be calculated, and traffic reports can be rapidly generated. In contrast to traffic cameras, number plate recognition systems, and sensor loops embedded in the roadway, no additional hardware on the road network is necessary. The FCD version used in this architecture is Decentralized Floating Car Data (DFCD), which means that each vehicle generates its own data (it retrieves its position, velocity and heading) before transmitting it through the network.

LTE4V2X: LTE for a Centralized VANET Organization

LTE4V2X is inspired by CDC (Centralized Dynamic Clustering protocol) [START_REF] Bajaber | Centralized dynamic clustering for wireless sensor network[END_REF], a wireless sensor adaptive clustering protocol, which organizes the network into clusters. This protocol dynamically creates clusters, but it changes the cluster head each round in order to avoid premature energy outage of the cluster head. As our architecture uses vehicles instead of wireless sensors, the energy consumption aspects are not so restrictive. Then, this protocol was reinvented with the constraints related to vehicular networks (high mobility speed, unlimited electrical energy,...).

This document is structured in four parts. In section 2, a summary of background knowledge and related work are presented. After a presentation of the proposed architecture in Section 3, LTE4V2X protocol is detailed in Section 4. Section 5 presents and discusses the simulation results of our protocol for FCD case study. Section 6 concludes the paper and discusses some directions of future research.

II. RELATED WORK

Many works related to vehicular networks organization [START_REF] Chao | Network connectivity of layered self-organizing wireless networks[END_REF] [6] [3] [START_REF] Wang | A self-organizing backbone construction scheme for efficient inter-vehicle communications[END_REF] proposes self-organized architectures. Such architecture takes advantage of node properties to issue a global virtual structure enabling the network self-organization. In general, the architecture is sufficiently autonomous and dynamic to deal with any local change. Typically, in the case of vehicular networks, it often leads to a decentralized organization using clustering and virtual backbone. The idea of defining a virtual backbone structure is brought from the wired networks. The principle of this solution is to constitute a dorsal of best interconnected nodes. The only constraint is the judicious choice of backbone members (BM) to avoid the rapid loss of interconnection between BMs. The second self-organizing structure is clustering. It is the partition of the network in homogeneous zones named clusters. Each cluster has at least one cluster head and a set of members. Generally, the members of one cluster have some common characteristics as contiguous velocities or coordinates, etc. Cluster-based solutions represent a viable approach for vehicular sensing applications. The clustering structure is usually used as a support of backbone structure.

In [START_REF] Chao | Network connectivity of layered self-organizing wireless networks[END_REF], the authors take inspiration from the organization of the cellular network in adjacent cells to propose the division of the service area into a number of sub service areas (SSA). One base station (BS) is settled in each SSA. The SSA area is set larger than a service coverage area of one BS. Then, a self-organizing process is executed in each SSA to ensure the communication between the BS and Mobile Stations (MS) that are outside its coverage area. In this method, some MSs may be selected as relaying MS, so they support two radio communication channels, one for link establishment control and one for data transmission. In [START_REF] Bononi | A cross layered mac and clustering scheme for efficient broadcast in vanets[END_REF] the authors propose, within the context of VANET, DBA-MAC (Dynamic Backbone Assisted MAC), a proactive distributed scheme to form a virtual backbone in a dynamic way in order to send a broadcast alert message to a group of potential receivers in a risk zone. To create the backbone, a node elects itself as a backbone member (BM) then it broadcasts a beacon message to spread the backbone creation process impulsion. After that, all the receivers enter in a distributed MAC access phase based on contention mechanism to elect the next backbone member. Since a reactive scheme for repairing the backbone would need break-detection capability and overhead, DBA-MAC proactively refreshes the backbone. In [START_REF] Taleb | Design guidelines for a network architecture integrating vanet with 3g & beyond networks[END_REF], the authors propose CSP (Cluster-based Self-organizing Protocol), a vehicular network proactive self-organizing architecture that is based on geographical clustering to ensure a permanent self-organization of the whole network. CSP adapts itself to vehicular network characteristics and permits to improve intervehicles or vehicle-to-infrastructure connectivity.

Using a decentralized organization is totally justified in these works since the authors assume that vehicles have a single 802.11p interface, and no cellular network interface. The vehicles organize themselves into clusters in order to provide a better connectivity with other nodes and infrastructures in an non-heterogeneous network.

However, nowadays we can easily assume that vehicles have multiple interfaces, which give 802.11p and cellular network (UMTS/LTE) connectivity. In a recent work [8] [9], the authors propose a clustering algorithm for an heterogenous network composed of a vehicular network and a cellular network. In their proposed architecture, cellular network is used to download data from vehicles, but also has indirect effect on cluster formation: the headings of the vehicles in relation to the eNodeB is taken in consideration in their cluster formation algorithm. As the previous works, the clustering process is decentralized: the vehicles manage the clusters around them autonomously. But it would be interesting to take advantage of the cellular network to help cluster formation. Indeed, it could have an overview of the VANET and could be used to organize it, in a centralized manner. The centralized approach allows the clusters manager (e.g. NodeB, eNodeB) to have a global view of the road traffic, and then create better clusters than a decentralized approach could do. Moreover, this global view also allows to easily see topology changes, like nodes arrivals in the network or departures from the network. Then, our proposed protocol uses this approach to create clusters, each of them containing a CH which will act as a gateway between the VANET and the LTE network.

III. LTE4V2X ARCHITECTURE

In this work, we consider that all vehicles have both LTE and 802.11p interfaces. The organization of the vehicular network is constituted of clusters that are managed by the eNodeBs (clusters can also be managed by a remote server, if it is not possible to implement that directly in the eNodeB). As indicated before, we will demonstrate our framework for a well known urban sensing application, FCD application. However, LTE4V2X is used to organize the network and permits to deploy a wide panoply of other applications.

The size of a cluster is at most the range of 802.11p, so that each node can reach the other nodes of the cluster (the CH more particularly). Each vehicle sends FCD periodically and each eNodeB manages the vehicles that are under its coverage area. In each cluster, a cluster head (CH) is elected (see Figure 1). The CH has the responsibility to send application data of itself and its cluster members to the eNodeB via LTE. Cluster members only send their application data via 802.11p to their CH.

All nodes (i.e. vehicles) can be elected as CH. CHs aggregate data of cluster members before sending it to the eNodeB. This will lower LTE goodput by avoiding to send useless data (e.g. when the heading and velocity of a vehicle is unchanged, CH can avoid to send data of this node to the eNodeB). The CH can also use a compression algorithm on the aggregated data to save more bandwidth. After the initialization phase (see next Section), the system runs in a cyclic manner (see Figure 2): each round contains three phases and is repeated indefinitely. The three round phases are: (i) Setup phase, in which the eNodeB creates and updates clusters (ii) ADV (Advertisement) phase, in which CHs send a notification frame in the VANET, and (iii) Collection and aggregation phase, in which cluster members send their FCD to CHs, and CHs send aggregated FCD to the eNodeB. Note that nodes use TDMA in each cluster to send their FCD (position, velocity and heading) to the CH.

First, the initialization phase, which is run only at the start of the system, is detailed. After that, we describe how the organization in clusters is maintained by the eNodeB, and hence how the eNodeB manages the arrival and departure of the nodes (vehicles) within the clusters. Finally, we explain the data collection and aggregation phase where eNodeB collects FCD from the vehicular network.

A. Initialization Phase

During the initialization phase, the eNodeB receives FCD directly from all vehicles. This phase is executed only one time, when the network starts, and allows the eNodeB to know vehicles positions and then to create coherent clusters. At the beginning, the vehicular network is not organized and there is no clusters created. All the vehicles send an ID request using the frame shown in figure 3, until they receive an ID from the eNodeB. After that, the nodes send their FCD (position, speed and heading) to the eNodeB (see Figure 7), using the same mechanism as if they were entering the network (see section IV-B1). At the end of this phase, the eNodeB runs an algorithm to organize the vehicular network and form the clusters (see section IV-B3). After that, the eNodeB broadcasts this organization using a frame that defines the cluster heads and their associated cluster members. The payload of this frame is described in figure 4.

The ID request frame is used to add a new IPv6/ID association, to delete an existing association or to ask for the IPv6 address corresponding to a given ID.

B. Maintenance

In this Section, we detail how LTE4V2X maintains the clusters using the eNodeB: how the eNodeB manages the

1) Arrival of New Nodes:

The arrival of a new node in a cluster is quite simple: First, the new node waits for the reception of an ADV frame in the VANET, a "Cluster update" frame from the eNodeB, or when a timeout counter expires. The reception of this frame allows the new node to know when the Collection and Aggregation phase will be initiated. During the next Collection and Aggregation phase, the new node sends an FCD frame directly to the eNodeB, like in the Initialization phase (with 0x0000 as Cluster ID). After that, the eNodeB will integrate the new node in the next "Cluster Update" frame.

2) Leaving Nodes: The behavior will obviously be different if the leaving node is a CH or if it is a simple member node.

When the leaving node is a member node, it is detected at most a round duration after its disconnection, because the eNodeB can easily notice when it did not received FCD from it. The leaving node will be removed from the clusters when the eNodeB does not receive FCD for a given number of consecutive seconds.

When the leaving node is a cluster head, the process is different. If the leaving CH node leaves before sending the aggregated FCD, all the cluster FCD will be lost for this round. The eNodeB will also notice this loss and fix the cluster for next round. 3) Periodic Operations: A periodic check is executed by the eNodeB each round in the Setup phase.

The eNodeB tries to create clusters which have a lifetime as long as possible. The size of a cluster is at most the range of 802.11p, so that each node can reach the other nodes of the cluster (the CH more particularly). eNodeB creates clusters which contains the largest number of nodes circulating in the same direction (see Figure 1). This algorithm is executed periodically by the eNodeB during the Setup phase.

If the calculated clusters are different from the current ones, the eNodeB broadcasts a "Cluster Update" frame (see Figure 5). The "Cluster Update" frame contains commands for each cluster that needs an update. The commands can notify the addition of a node, the removal of a node, the ID a the new CH of a cluster, or the new ID of a cluster.

In the ADV phase, the clusters configuration is spread in the VANET: each CH broadcasts a short frame which contains the next CH ID of its cluster (see Figure 6) and the number of cluster members. Indeed, the CH can take the initiative of choosing an other node as CH. This frame also allows the cluster members to know that their CH is still alive.

4) Collection and Aggregation Phase: During this phase, each node sends its FCD (position, speed and heading) to its CH, in the attributed time slot (see Figure 7). The time slots correspond to the order used by eNodeB in the last update frame. If the node does not know the IPv6 address associated with its CH ID, it sends an ID request frame (see section IV-A))

Just before the end of this phase, each CH sends the aggregated data (which may be compressed) to the eNodeB (see Figure 8). The size of this frame depends on the compression algorithm, the aggregation process, and obviously the number of nodes in the cluster. For example, with 30 nodes in the cluster and the compression algorithm used in tar-gzip format, the frame size reaches about 128 bytes.

V. S IMULATIONS

A. Simulation Assumptions

The simulations were made with network simulator NS-3.10 [10]. LTE4V2X was implemented upon the IP layer with FCD as an application.

We simulated an area of 1x1 km 2 , which matches the coverage area of an eNodeB. We chose a urban topology, generated with VanetMobiSim [11]. The eNodeB is placed in the middle of the area. Vehicles are circulating with a mean speed if 20 km/h in residential areas, 30 km/h in downtown areas and 50 km/h in suburban areas. The choice of an urban topology was motivated by the fact that we first want to analyze the limits of our protocol in front of a high density of vehicles. We plan to simulate, in a future work, an inter-urban topology (i.e. highways) in order to analyze the impact of high velocity in our ptotocol. We compared our protocol against a decentralized clustering protocol (DCP). In DCP, the VANET is self-organized in a decentralized manner. Indeed, the vehicles compute the clusters each seconds, and send an ADV frame if they are cluster head. Then, all non-CH nodes send their FCD to their CH. The CH sends, after that, the aggregated data to the eNodeB. Simulations were run 10 times for each use case (i.e. vehicles number).

The performance metrics used to evaluate the simulation results are:

• Goodput: This application level metric reflects the useful bytes of information that transits on the network (for our application it reflects FCD bytes that are transmitted)

• Overhead: This reflects all non-useful bytes exchanged in the network, i.e. control messages (ID, ADV, "Cluster update" and "Cluster topology" frames)

• Packet loss: This is the percentage of packets that are sent by a given network interface but never received by the destination interface

• Cluster lifetime (or cluster stability): We evaluate cluster lifetime in measuring the average consecutive time a CH remains CH

B. Simulation Results and Analysis

Figure 9 presents the obtained packet losses for the two protocols. This Figure enlightens a huge packet loss for DCP. The decentralized approach creates less optimized clusters and vehicles are not aware of topology changes, and they can send packets to non-existent nodes or the cluster heads can miss the inclusion of a member in its cluster and then not send all the FCD it should send. Moreover, in LTE4V2X, all nodes are synchronized by the "Cluster update" frames that LTE4V2X creates a larger overhead at the eNodeB, but it can easily be handled by LTE. This overhead is induced by the fact that we have a low packet loss. Indeed, this implies that more vehicles are maintained correctly in the clustering process, and then more control messages have to be exchanged to maintain all those received FCD up-to-date.

Figure 11 presents the obtained goodput for the two protocols, on the LTE link and inside the VANET. The Figure shows clearly that LTE4V2X generates a very low 802.11p goodput, and a high LTE goodput. To understand this behavior, we have first to come back to Figure 9: DCP has a high packet loss, and this induce a lower LTE goodput (few FCD arrive to the eNodeB). Second, the low VANET goodput of LTE4V2X comes from the fact that LTE4V2X creates smaller clusters than DCP, and then less FCD are exchanged inside the VANET. LTE4V2X creates smaller clusters because its global overview allows it to see that those big clusters are not optimized (e.g. it knows that some nodes are unreliable). Finally, we can observe in Figure 12 that LTE4V2X has a lower average cluster lifetime than DCP (i.e. less clusters stability). In LTE4V2X, clusters are optimized whenever it is possible, and the eNodeB sees more potential optimizations because it has a global view of the network. This explains a shorter lifetime of the clusters. To conclude, our protocol benefits of a very low packet loss, while DCP looses half of its FCD sent to the eNodeB. The overhead generated by the eNodeB is not so large (7.1 kBps for 400 vehicles), and allows a better cluster management, while keeping the VANET bandwidth free for other applications, like online video streaming or other non-critical applications.

VI. CONCLUSION

This paper presented LTE4V2X, a novel framework which uses the eNodeBs of the LTE network as a cluster management infrastructure for the VANET. This new approach has been compared to a decentralized approach, and the results show that our protocol is better than DCP (even if clusters are less stable): it creates less overhead in the VANET, and looses only 2% of FCD. We are currently extending this work into the following directions. First, we want to perform other extensive simulation study to check teh behavior of LTEV2X in an interurban topology(highways) with very high speeds. Second, we want to simulate other decentralized clustering protocols or even decentralized approaches without clustering mechanisms, in order to have a wider comparison basis with LTE4V2X. Finally, we will work on extending our centralized approach to VANET applications other than data collection.

Figure 1 .

 1 Figure 1. LTE4V2X architecture

Figure 4 .

 4 Figure 2. Round phases

  Figure 5. "Cluster update" frame

Figure 8 .

 8 Figure 8. Aggregated FCD frame

Figure 9 .Figure 10 .

 910 Figure 9. Packet loss vs vehicles number

Figure 12 .

 12 Figure 11. Goodputs vs vehicles number


L Gaume

H Chabrolles

I Simon

L Dehouck

F Gosselet

C J Archimbaud

J L Bailly

In vitro BBB models

Luminal

INTRODUCTION MATERIAL & METHODS

CD34+-derived endothelial cells Bovine pericyte

Cultivated on the apical side of Transwell TM and coating with Matrigel TM Cultivated on the basal side of Transwell TM and coating with type I-rat collagen

Evaluation of the BBB integrity after free viral infection

Immunofluorescence (IF)

Detection of tight junction protein zonula-occludens 1 (ZO-1).

Paracellular Permeability

Basal fluorescence was measured after incubation (1h) with a hydrophilic compound : Lucifer Yellow (LY).

Trans-Endothelial Electrical Resistance (TEER)

The higher the measured resistance, the stronger the tight junction.

Enterovirus A71 (EV-A71) is an RNA non-polio enterovirus that belongs to the Picornaviridae family. This virus is implicated in epidemic disease of hand-foot-mouth disease (HFMD) mostly in infants and children, especially in Asian countries. In Europe since 2015, the emergence of a multirecombinant C1-like EV-A71 (C1v2015) induced outbreak of meningitis and brainstem encephalitis in Spain (2016) and

France (2016,2018). Damage to the blood-brain barrier (BBB) could explain such increase in the severity of symptoms.

The BBB is the larger interface between blood and brain, very selective, with a microvasculature of 600 km. Endothelial cells (ECs) constitute the wall of brain capillaries and confer to the barrier its function by expression of many adherent and tight junction proteins (ZO-1, claudin-5), specific transporters (Glut-1) and efflux pumps (P-gp, BCRP). Pericytes, astrocytes end feet and neurons, which compose the neurovascular unit, surrounds ECs and influences them.

This work aimed to investigate the passage of free EV-A71 strain through a multi-cellular in vitro model of BBB.

Inflammatory environment (TNF-α)

BBB was exposed to TNF-α (10 ng/ml)

Detection of viral RNA replication (green). Infection efficiency was evaluated by IF.

Functional test : presence of efflux pump P-gp

Comparison of intracellular fluorescence of Rhodamine 123 which naturally enter into EC, release by the efflux pumps P-gp, in the presence or not of a pump inhibitor (Elacridar).

RESULTS

CONCLUSION

Luminal

A.

An increase of permeability is observed 24h pi between the positive control and negative control. No difference is observed between the negative control and EV-A71 infections.

Luminal

  and basal supernatant were analysed at different time post-infection (pi) → Presence of infectious virus : Titration → Presence of viral RNA : • RT-PCR • Immunofluorescence Two EV-A71 strain were tested : C1/16 and C4/04 (MOI =1), and echovirus 6 (E6) was used as a positive control.

Fig. 3 Fig. 4

 34 Fig. 1 Percentage of infected cells at 24h pi

  Endothelial cell-CD34+ are weakly sensitive to EV-A71: at 24h pi, less than 5% of cells are infected; in contrast, 13% of cells are infected with the E6 positive control. viral RNA is detected in the luminal side than in the basal side (Fig 3.A). The yield of infectious virus was quantifiable only in the luminal side (Fig 3.B). A moderate amount was produced : less than 10,000 infectious particles at 48h pi. Of note, infectious virus is detected in small amount in the basal side. Basal The TNF-a treatment increases the permeability at 24h with or without infection (Fig 4.A). The infectious virus is quantifiable only in the luminal side (below 40,000 infectious particles) (Fig 4.B). Contact : lea.gaume@uca.fr The integrity of the BBB-like model generated in vitro by a co-culture of CD34+-derived ECs and pericytes displayed limited alteration after EV-A71 infection. Results provide evidence of a low viral replication in ECs and limited crossing through the in vitro BBB model even in an inflammatory environment. Future investigations will focus on the transmigration of EV-A71 through infected leukocytes.