Amaury Bossion

Julien Nicolas
email: julien.nicolas@u-psud.fr

Synthesis of Poly(Asparagine-co-Phenylalanine) Copolymers, Analogy with Thermosensitive Poly(Acrylamide-co-Styrene) Copolymers and Formation of PEGylated Nanoparticles

Keywords: N-carboxyanhydride, Asparagine, Phenylalanine, Polypeptide, Nanoparticles, UCST

We presented optimized synthetic pathways to high purity L-phenylalanine (Phe) and Lasparagine (Asn) derived N-carboxyanhydrides (NCA) in one-pot processes and in a highly reproducible manner. Ring-opening homopolymerizations of Asn-NCA and Phe-NCA were successfully achieved together with their copolymerization in an attempt to mimic upper critical solution temperature (UCST) vinylic poly(acrylamide-co-styrene) (P(Aam-co-St)) copolymers. Poly(asparagine-co-phenylalanine) (P(Asn-co-Phe)) copolypeptides of different Asn-to-Phe ratio were prepared and their thermoresponsive behavior was investigated in aqueous solution. Unfortunately, polymer aggregation imparted by strong hydrophobic interactions favored due to presence of -sheet structures prevented achieving thermosensitive response in aqueous media in the 50-62°C range conversely to its vinylic counterpart. However, by taking advantage of those strong hydrophobic interactions, PEG-b-PAsn and PEG-b-PPhe diblock copolymers were prepared from amino-PEG initiators and PEG-b-PAsn was successfully formulated into PEGylated nanoparticles of ~270 nm.

Introduction

Synthetic poly(amino acid)s, commonly known as polypeptides constitute a well-established class of biodegradable and biocompatible polymers covering a wide range of applications, from drug delivery, tissue engineering to biosensors. [START_REF] Mazo | Ring opening polymerization of α-amino acids: advances in synthesis, architecture and applications of polypeptides and their hybrids[END_REF] Thanks to their unique amino-acid sequence and composition, these bio-inspired materials possess unique properties such as the possibility to self-assemble via non-covalent interactions or to endorse specific conformations such as -helices or -sheets. [START_REF] Bonduelle | Secondary structures of synthetic polypeptide polymers[END_REF] For years, solid phase peptide synthesis (SPPS) has been the technique of choice to prepare synthetic polypeptides. [START_REF] Merrifield | Solid Phase Peptide Synthesis. I. The Synthesis of a Tetrapeptide[END_REF] Although very attractive to obtain polypeptides with specific amino-acid sequences, this tedious method based on multiple coupling/deprotection steps usually prevents high molecular weight polypeptides to be obtained. [START_REF] Cavalli | Amphiphilic peptides and their cross-disciplinary role as building blocks for nanoscience[END_REF] Ring-opening polymerization (ROP) of -amino acid N-carboxyanhydrides (NCAs) initiated by nucleophiles is another widely known technique to synthesize polypeptides that, conversely to SPPS, enables achieving high molecular weights. [START_REF] Habraken | Block Copolypeptides Prepared by N-Carboxyanhydride Ring-Opening Polymerization[END_REF][START_REF] Siefker | Chapter 9:Ring-opening Polymerization of N-carboxyanhydrides Using Organic Initiators or Catalysts[END_REF] Controlled polymerization processes of NCA monomers enable to access a wide variety of novel and innovative polypeptidic biomaterials with unique properties for targeted applications. [START_REF] Deming | Living polymerization of α-amino acid-N-carboxyanhydrides[END_REF][START_REF] Kricheldorf | Polypeptides and 100 Years of Chemistry of α-Amino Acid N-Carboxyanhydrides[END_REF][START_REF] Deming | Polypeptide and Polypeptide Hybrid Copolymer Synthesis via NCA Polymerization[END_REF] As such, designing novel NCAs as building blocks to prepare polypeptidebased materials with new properties arouse considerable attention.

Polypeptides have indeed particularly gained an increase interest in the field of stimuli-responsive polymeric materials. [START_REF] Bordat | Thermoresponsive polymer nanocarriers for biomedical applications[END_REF][START_REF] Huang | Stimuli responsive synthetic polypeptides derived from Ncarboxyanhydride (NCA) polymerisation[END_REF][START_REF] Shen | Biodegradable stimuli-responsive polypeptide materials prepared by ring opening polymerization[END_REF][START_REF] Chécot | pH-responsive micelles and vesicles nanocapsules based on polypeptide diblock copolymers[END_REF][START_REF] Rodríguez-Hernández | Reversible Inside-Out Micellization of pHresponsive and Water-Soluble Vesicles Based on Polypeptide Diblock Copolymers[END_REF] Such materials, that are able to change their physico-chemical properties upon external stimulus, such as pH, light, electric/magnetic fields, mechanical force, and more particularly temperature, have been thoroughly studied over the past years. In the field of thermoresponsive polymers, researchers have aimed at designing polypeptidic analogues of well-known non-degradable thermoresponsive vinylic polymers. For example, polypeptide obtained by ROP of OEGylated L-glutamate NCAs analogous of oligo(ethylene glycol) (OEG) methacrylate (OEGMA) have been developed as alternative thermoresponsive materials with tunable lower critical solution temperature (LCST). [START_REF] Deng | Synthesis, Characterization, and thermoresponsive properties of Helical Polypeptides Derivatized from Poly(γ-4-(3chloropropoxycarbonyl)benzyl-L-glutamate)[END_REF][START_REF] Zhu | Synthesis and UCST-type phase behavior of OEGylated poly(γ-benzyl-l-glutamate) in organic media[END_REF] Inspired by poly(allylurea-co-allylamine) upper critical solution temperature (UCST) copolymers, Maruyama et al. prepared thermoresponsive poly(ornithine-cocitrulline) copolypeptides that mimic ureido groups of NCA derived from L-ornithine αamino-acids. [START_REF] Shimada | Ureido-Derivatized Polymers Based on Both Poly(allylurea) and Poly(l-citrulline) Exhibit UCST-Type Phase Transition Behavior under Physiologically Relevant Conditions[END_REF][START_REF] Kuroyanagi | Highly Ordered Polypeptide with UCST Phase Separation Behavior[END_REF] More recently, Argawal et al. reported poly(acrylamide-co-styrene) (P(AAm-co-St)) copolymers obtained by reversible addition fragmentation chain transfer polymerization (RAFT) exhibiting sharp UCST behavior in water in the range of 50-62°C. [START_REF] Pineda-Contreras | Importance of compositional homogeneity of macromolecular chains for UCST-type transitions in water: Controlled versus conventional radical polymerization[END_REF] The synthesis of structurally analogous polypeptides with pendant amide and phenyl functionalities of P(AAm-co-St) has, however, never been attempted. In the broad family of amino acids, L-asparagine and L-phenylalanine possess amide and phenyl groups that structurally resemble acrylamide and styrene repeating units, respectively. Despite this evidence, literature on the copolymerization of L-asparagine and L-phenylalanine derived NCAs (Asn-NCA and Phe-NCA, respectively) to prepare poly(asparagine-co-phenylalanine) (P(Asn-co-Phe)) copolypeptides is lacking. While polypeptides composed of Phe-NCA have been extensively studied in the literature, successful preparation of poly(asparagine) only relies on the aminolysis of poly(succinimide). [START_REF] Jeong | Polymer micelle-like aggregates of novel amphiphilic biodegradable poly(asparagine) grafted with poly(caprolactone)[END_REF][START_REF] Sun | Direct Formation of Giant Vesicles from Synthetic Polypeptides[END_REF][START_REF] Zhou | High Potency and Broad-Spectrum Antimicrobial Peptides Synthesized via Ring-Opening Polymerization of α-Aminoacid-N-carboxyanhydrides[END_REF][START_REF] Matsusaki | One-Step Advanced Preparation of Surface-Functional Peptide Nanospheres by the Polymerization of l-Phenylalanine N-Carboxyanhydride with Dual Initiators[END_REF][START_REF] Kim | pH-induced Micelle Formation of Poly(histidine-cophenylalanine)-block-Poly(ethylene glycol) in Aqueous Media[END_REF][START_REF] Dai | Surface modification of hydroxyapatite nanoparticles by poly(l-phenylalanine) via ROP of l-phenylalanine N-carboxyanhydride (Pha-NCA)[END_REF][START_REF] Kim | Synthesis and characterization of poly(l-glutamic acid)-block-poly(l-phenylalanine)[END_REF][START_REF] Kricheldorf | Primary Amine and Solvent-Induced Polymerizations of L-or D,L-Phenylalanine N-Carboxyanhydride[END_REF][START_REF] Kricheldorf | Cyclic Polypeptides by Solvent-Induced Polymerizations of α-Amino Acid N-Carboxyanhydrides[END_REF][START_REF] Ma | A process for production of polyasparagine and the high nitrogen content polymer formed thereby[END_REF] In the literature, two different carbonylation pathway prevailed for the preparation of NCA monomers. [START_REF] Kricheldorf | Synthesis and Characterization of NCAs[END_REF] The first one, called the Fuchs-Farthing method, involved the phosgenation under heating conditions of unprotected α-amino acids. [START_REF] Farthing | Synthetic polypeptides. Part I. Synthesis of oxazolid-2 : 5-diones and a new reaction of glycine[END_REF][START_REF] Fuchs | Über N-Carbonsäure-anhydride[END_REF] The second one, which derived from the Leuchs method, refers to the reaction of urethane-protected α-amino acids with halogenating agents including phosphorous halides, such as PBr 3 and PCl 5 . [START_REF] Leuchs | Ueber die Glycin-carbonsäure[END_REF][START_REF] Cheng | Synthesis of Optically Active β-Amino Acid N-Carboxyanhydrides[END_REF][START_REF] Hirschmann | Controlled synthesis of peptides in aqueous medium. VIII. Preparation and use of novel .alpha.-amino acid N-carboxyanhydrides[END_REF] In both cases, the intended NCAs are obtained with the generation of HCl or phosphoric acid respectively, as side products. These acids not only lower the reaction kinetic but can also cause the undesired ring opening reaction of the NCAs to generate acyl chloride or acyl phosphate which consequently yields lower purity monomer. [START_REF] Iwakura | The Synthesis and Reactions of 2-Isocyanatoacyl Chlorides[END_REF][START_REF] Daly | The preparation of N-carboxyanhydrides of α-amino acids using bis(trichloromethyl)carbonate[END_REF][START_REF] Smeets | A Scalable Synthesis of l-Leucine-N-carboxyanhydride[END_REF][START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF][START_REF] Kramer | General Method for Purification of α-Amino acid-Ncarboxyanhydrides Using Flash Chromatography[END_REF] Several approaches have already been described in the literature to overcome these drawbacks, such as the use of an acid scavenger including tertiary amines or alkenes, vacuum or inert gas flow conditions. [START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF][START_REF] Cornille | Process for the preparation of Ncarboxyanhydrides[END_REF][START_REF] Habraken | How controlled and versatile is N-carboxy anhydride (NCA) polymerization at 0 °C? Effect of temperature on homo-, block-and graft (co)polymerization[END_REF][START_REF] Gkikas | Well-Defined Homopolypeptides, Copolypeptides, and Hybrids of Poly(l-proline)[END_REF][START_REF] Kudo | Facile and Quantitative Synthesis of a Poly(ethylene glycol)-b-Poly(larginine) Block Copolymer and Its Use for the Preparation of Polyion Complex Micelles with Polyanions for Biomedical Applications[END_REF][START_REF] Cornille | Process for the preparation of N-carboxyanhydrides of amino acids[END_REF][START_REF] Carubia | Synthesis of amino acid, n-carboxyanhydrides[END_REF][START_REF] Wilder | The use of triphosgene in preparation of N-carboxy .alpha.-amino acid anhydrides[END_REF] The most popular route to date remains the use of an acid scavenger.

Several methodologies have been presented for the synthesis of Phe-NCA. [START_REF] Sun | Direct Formation of Giant Vesicles from Synthetic Polypeptides[END_REF][START_REF] Zhou | High Potency and Broad-Spectrum Antimicrobial Peptides Synthesized via Ring-Opening Polymerization of α-Aminoacid-N-carboxyanhydrides[END_REF][START_REF] Matsusaki | One-Step Advanced Preparation of Surface-Functional Peptide Nanospheres by the Polymerization of l-Phenylalanine N-Carboxyanhydride with Dual Initiators[END_REF][START_REF] Kim | pH-induced Micelle Formation of Poly(histidine-cophenylalanine)-block-Poly(ethylene glycol) in Aqueous Media[END_REF][START_REF] Dai | Surface modification of hydroxyapatite nanoparticles by poly(l-phenylalanine) via ROP of l-phenylalanine N-carboxyanhydride (Pha-NCA)[END_REF][START_REF] Kim | Synthesis and characterization of poly(l-glutamic acid)-block-poly(l-phenylalanine)[END_REF][START_REF] Kricheldorf | Primary Amine and Solvent-Induced Polymerizations of L-or D,L-Phenylalanine N-Carboxyanhydride[END_REF][START_REF] Kricheldorf | Cyclic Polypeptides by Solvent-Induced Polymerizations of α-Amino Acid N-Carboxyanhydrides[END_REF][START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF][START_REF] Lee | Amphiphilic amino acid copolymers as stabilizers for the preparation of nanocrystal dispersion[END_REF][START_REF] Khuphe | The formation of biodegradable micelles from a therapeutic initiator for enzyme-mediated drug delivery[END_REF][START_REF] Khuphe | Glucose-bearing biodegradable poly(amino acid) and poly(amino acid)-poly(ester) conjugates for controlled payload release[END_REF][START_REF] Huang | Supramolecular Hydrogels with Reverse Thermal Gelation Properties from (Oligo)tyrosine Containing Block Copolymers[END_REF] Up to date, the reaction of L-phenylalanine with triphosgene in anhydrous THF under inert atmosphere at 50°C without any acid scavenger sometimes followed by tedious multiple recrystallization steps prevails. [START_REF] Sun | Direct Formation of Giant Vesicles from Synthetic Polypeptides[END_REF][START_REF] Zhou | High Potency and Broad-Spectrum Antimicrobial Peptides Synthesized via Ring-Opening Polymerization of α-Aminoacid-N-carboxyanhydrides[END_REF][START_REF] Matsusaki | One-Step Advanced Preparation of Surface-Functional Peptide Nanospheres by the Polymerization of l-Phenylalanine N-Carboxyanhydride with Dual Initiators[END_REF][START_REF] Kim | pH-induced Micelle Formation of Poly(histidine-cophenylalanine)-block-Poly(ethylene glycol) in Aqueous Media[END_REF][START_REF] Dai | Surface modification of hydroxyapatite nanoparticles by poly(l-phenylalanine) via ROP of l-phenylalanine N-carboxyanhydride (Pha-NCA)[END_REF][START_REF] Kim | Synthesis and characterization of poly(l-glutamic acid)-block-poly(l-phenylalanine)[END_REF][START_REF] Lee | Amphiphilic amino acid copolymers as stabilizers for the preparation of nanocrystal dispersion[END_REF] As for synthetic Asn-NCA, although commercially available, only one example can be found in the literature. In this early attempt, benzyloxycarbonyl-L-asparagine was treated with PBr 3 in dioxane at room temperature to afford Asn-NCA in 35 % yield upon purification by column chromatography. [START_REF] Hirschmann | Controlled synthesis of peptides in aqueous medium. VIII. Preparation and use of novel .alpha.-amino acid N-carboxyanhydrides[END_REF] The authors pointed out, however, the poor yields obtained upon using this anhydride in peptide synthesis.

Therefore, there is a need for an optimized synthetic pathway for this monomer.

Our motivation in this study was to: (i) develop reliable, sturdy and optimized synthetic pathways for the synthesis of both Phe-NCA and Asn-NCA; (ii) prepare for the first-time poly(asparagine-co-phenylalanine) (P(Asn-co-Phe)) copolypeptides; (iii) probe their potential thermoresponsivity in water in analogy with poly(acrylamide-co-styrene) copolymers and (iv) prepare amphiphilic PEG-b-PAsn and PEG-b-PPhe copolymer nanoparticles (Fig. 1).

Experimental part

2.1. Materials L-phenylalanine (>98.0 %), neopentylamine (>98.0 %), N-α-(tert-Butoxycarbonyl)-N-γ-trityl- L-asparagine (Boc-L-Asn(Trt)-OH, >98.0 %), N-α-(tert-Butoxycarbonyl)-L-asparagine (Boc-
L-Asn-OH, >98.0 %), N-methylmorpholine (NMM, >99.0 %), (1R)-(+)-α-pinene (>97.0 %), triisopropylsilane (>98.0 %) and triphosgene (>98.0 %) were purchased from TCI chemicals.

Triethylamine (TEA, 99 %), trifluoroacetic acid (TFA, 99 %), phosphorous tribromide (PBr 3 ) solution (1 M in DCM), anhydrous solvents THF (≥ 99.9%, inhibitor-free), DMF (99.8%), DCM (≥99.8 %, contains 40-150 ppm amylene as stabilizer), EtOAc (99.8 %) were purchased from Sigma Aldrich. Methoxypolyethylene glycol amine (PEG 5k -NH 2 , M n = 5,516 Da) was purchased from Iris Biotech. n-Hexane (technical grade) was purchased from VWR. Diethyl ether (99.8 %) was purchased from Carlo Erba. Deuterated solvents such as CDCl 3 , DMSO-d 6 was purchased from Eurisotop. All materials were used without further purification. All manipulations were performed under moisture and oxygen-free conditions using conventional Schlenk techniques.

Nuclear magnetic resonance (NMR) spectroscopy

NMR spectroscopy was performed in 5 mm diameter tubes in DMSO-d 6 at 25 °C. 1 H and 13 C NMR spectroscopy was performed on a Bruker Avance 300 spectrometer at 300 MHz ( 1 H) and 75 MHz ( 13 C), respectively. The chemical shift scale was calibrated based on the internal solvent signals (δ = 2.50 ppm for DMSO-d 6 and δ = 7.26 ppm for CDCl 3 ). Data were reported as: chemical shift, multiplicity (s = singlet, d = doublet, t = triplet, m = multiplet, br = broad), coupling constants (J) given in Hertz (Hz), and integration.

Fourier transform infrared (FTIR) spectroscopy

FT-IR spectra were obtained by FT-IR spectrophotometer (Spectrum One, PerkinElmer, USA) using attenuated total reflectance (ATR) technique. Spectra were recorded between 4000-525 cm -1 with a spectrum resolution of 4 cm -1 . All spectra were averaged over 10 scans.

Elemental analysis

The elemental analysis for carbon, hydrogen and nitrogen content determination was performed using a Perkin Elmer 2400 series elemental analyzer (PerkinElmer, USA).

Dynamic Light Scattering (DLS) and zeta potential

Nanoparticle diameters (Dz) and particle size distribution (PSD) were measured by dynamic light scattering (DLS) with a Nano ZS from Malvern equipped with a 4 mW He-Ne laser (633 nm wavelength) at a fixed scattering angle of 173° and temperature of 25°C. The surface charge of the NPs was investigated by ζ-potential (mV) measurement at 25 °C after dilution with 1 mM NaCl, using the Smoluchowski equation.

Synthesis of L-phenylalanine N-carboxyanhydride (Phe-NCA)

Synthesis of Phe-NCA was carried out in an adapted version of Daly et al. [START_REF] Daly | The preparation of N-carboxyanhydrides of α-amino acids using bis(trichloromethyl)carbonate[END_REF] In a 250 mL round bottom flask equipped with a magnetic stirrer, L-phenylalanine (1 eq., 0.061 mol, 10 g) and α-pinene (2.1 eq., 0.12 mol, 19,2 mL) were added into 100 mL of anhydrous THF (0.6 M total). An additional funnel was affixed to the round bottom flask and charged with 6.65 g of triphosgene (0.37 eq., 0.02 mol, 6.65 g) and 30 mL of anhydrous THF. The setup was heated up to 50°C for 10 min. The triphosgene-THF mixture was dripped into the round bottom flask over a period of 15 min. After the addition of triphosgene, the reaction was stirred for an additional 2 h at 50°C at which time most of the L-phenylalanine had disappeared. The reaction mixture was filtered to remove the undissolved L-phenylalanine. The filtrate was then concentrated to 1/3 of its initial volume under vacuum and then added dropwise into excess cold n-hexane. The flask was placed at -20°C for 24 h to allow complete precipitation of the product. The white powder was then dried under vacuum at room temperature overnight (7.74 g, 67 % yield). 1 H NMR (300 MHz, CDCl 3 ): 7.38-7.29 (m, 3H); 7.20-7.17 (m, 2H); 6.14 (bs, 1H); 4.55-4.51 (dd, J = 8.7 Hz, 4.1 Hz, 1H); 3.25-3.31 (dd, J = 14.1 Hz, 3.9 Hz, 1H); 3.04-2.96 (dd, J = 14 Hz, 8.7 Hz, 1H). 13 [START_REF] Dai | Surface modification of hydroxyapatite nanoparticles by poly(l-phenylalanine) via ROP of l-phenylalanine N-carboxyanhydride (Pha-NCA)[END_REF][START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF][START_REF] Wilder | The use of triphosgene in preparation of N-carboxy .alpha.-amino acid anhydrides[END_REF][START_REF] Khuphe | The formation of biodegradable micelles from a therapeutic initiator for enzyme-mediated drug delivery[END_REF][START_REF] Khuphe | Glucose-bearing biodegradable poly(amino acid) and poly(amino acid)-poly(ester) conjugates for controlled payload release[END_REF][START_REF] Huang | Supramolecular Hydrogels with Reverse Thermal Gelation Properties from (Oligo)tyrosine Containing Block Copolymers[END_REF] 2.7. Synthesis of N-γ-trityl-L-asparagine N-carboxyanhydride (Asn(Trt)-NCA) Synthesis of Asn(Trt)-NCA was carried out in an adapted version of Rao et al. To a suspension of Boc-L-Asn(Trt)-OH (1 eq., 5 mmol, 2.4 g) in dichloromethane (50 mL, 0.1 M total) under N 2 was added PBr 3 (0.6 eq., 3 mmol, 3 mL) dropwise. α-pinene (3.5 eq., 18 mmol, 2.78 mL) was immediately added dropwise. The suspension turned to pale yellow and about 10 min later all the starting material had dissolved. The mixture was stirred at ambient temperature for 24 h. The solid was filtered, rinsed with dry DCM and dried under vacuum to give Asn(Trt)-NCA as a white powder (1.59 g, 80 % yield). 1 H NMR (300 MHz, DMSO-d 6 ):

8.97 (s, 1H); 8.86 (s, 1H); 7.14-7.30 (m, 15H); 4.53-4.56 (t, J = 3.7 Hz, 1H); 3.03-3.10 (dd, J = 16.4 Hz, 4.4 Hz, 1H); 2.72-2.79 (dd, J = 14.4 Hz, 3.5 Hz, 1H). 13

Deprotection of N-γ-trityl-L-asparagine N-carboxyanhydride (Asn-NCA, route A)

In a 25 mL round bottom flask equipped with a magnetic stirrer, Asn(Trt)-NCA (1 eq., 0.3 g, 0.75 mmol) was dissolved in neat anhydrous TFA (7.6 mL) under stirring. Triisopropylsilane (10 eq., 7.5 mmol, 1.5 mL) was then added and a white solid appeared (trityl). The whole mixture was allowed to stir at room temperature under N 2 atmosphere for 10 min. Then, the reaction mixture was filtered, concentrated under vacuum and then added dropwise to 10-fold cold THF (-20°C) where a white precipitate appeared. The whole was centrifuged at 10,000 rpm at 10 °C for 10 min. After discarding the liquid fraction, new THF was added, and the product was suspended in a sonic bath. The suspension was centrifuged again, and the procedure was repeated two times to give Asn-NCA as a white powder (0.39 g, 33 % yield).

Synthesis of L-asparagine N-carboxyanhydride (Asn-NCA, route B)

To a suspension of Boc-L-Asn-OH (1 eq., 10 mmol, 2.32 g) in THF (150 mL, 0.06 M total) under Ar was added PBr 3 (0.6 eq., 6 mmol, 6 mL) dropwise. α-Pinene (4 eq., 40 mmol, 6.35 mL) was immediately added dropwise. The suspension turned to pale white and about 10 min later all the starting material had dissolved. The mixture was stirred at ambient temperature for 24 h. The reaction mixture was then filtered, and the filtrate concentrated under vacuum.

THF was then added and a white precipitate appeared. The solid obtained was filtered, washed with THF and dried under vacuum to give Asn-NCA as a white powder (0.9 g, 57 % yield). 1 H NMR (300 MHz, DMSO-d 6 ): 8.79 (s, 1H); 7.51 (s, 1H); 7.05 (s, 1H); 4.50-4.53 (t, J = 4.1 Hz, 1H); 2.59-2.74 (ddd, J = 21.9 Hz, 16.9 Hz, 4.9 Hz, 2H). 13

General procedure for the ROP of Asn(Trt)-NCA and Phe-NCA ([M]/[I] = 25)

The P(Asn(Trt) 22.5 -co-Phe 2.5 ) polypeptide was prepared following conventional ROP procedure. Asn-Trt-NCA (90 mol.%, 22.5 eq., 0.63 mmol, 0.25 g) and Phe-NCA (2.5 eq., 0.07 mmol, 13.4 mg) (total mole = 0.7 mmol) were loaded into a flame-dry Schlenk tube equipped with a magnetic stirrer. The Schlenk tube was purged three times with argon/vacuum cycles. Then, 1.16 mL of dry DMF was added (0.6 M). For initiation, a total of 3.3 µL of neopentylamine (1 eq., 0.03 mmol) was directly added to the Schlenk tube via syringe. The reaction was let under stirring at 30°C for 4 days. Directly after completion of the reaction, the polymer was precipitated in cold diethyl ether and centrifuged at 10,000 rpm at 10 °C for 10 min. After discarding the liquid fraction, new ether was added, and the polymer was suspended in a sonic bath. The suspension was centrifuged again, and the procedure was repeated two times. The obtained protected copolymer was then dried under vacuum overnight.

Deprotection of P(Asn(Trt-co-Phe)

Deprotection of the protected copolymer was carried out similarly to the deprotection of Asn(Trt)-NCA (Asn-NCA, route A). Briefly, the copolymer was dissolved in neat TFA under stirring. Excess triisopropylsilane was then added and the mixture was allowed to stir for 10 min. The reaction mixture was then filtered, concentrated under vacuum and then added dropwise to 10-fold cold THF (-20°C) where a white precipitate appeared. After discarding the liquid fraction, new THF was added, and the product was suspended in a sonic bath. The suspension was centrifuged again, and the procedure was repeated two times.

General procedure for the ROP of Asn-NCA and Phe-NCA ([M]/[I] = 50)

The P(Asn 45 -co-Phe 5 ) polypeptides was prepared as follow. Asn-NCA (45 eq., 1.35 mmol, 0.21 g) and Phe-NCA (5 eq., 0.15 mmol, 0.03 g) (total mole = 1.5 mmol) were loaded into a flame-dry Schlenk tube equipped with a magnetic stirrer. The Schlenk tube was purged three times with argon/vacuum cycles. Then, 25 mL of dry DMSO (0.06 M) was added. For initiation, a total of 3.5 µL of neopentylamine was directly added to the Schlenk tube via syringe. The reaction was let under stirring at 30°C for 4 days. Directly after completion of the reaction, the polymer was precipitated to cold THF and centrifuged (10,000 rpm at 10 °C for 10 min). After discarding the liquid fraction, new THF was added, and the polymer was suspended in a sonic bath. The suspension was centrifuged again, and the procedure was repeated two times. The obtained copolymer was then dried at room temperature under vacuum overnight. Similar polymerization conditions were applied for the P(Asn 40 -co-Phe 10 ) and P(Asn 49 -co-Phe 1 ) polypeptides.

General procedure for the synthesis of PEG-b-PNCA diblock copolymer ([M]/[I] = 60)

Asn-NCA (60 eq., 2 mmol) was loaded into a flame-dry Schlenk tube equipped with a magnetic stirrer. The Schlenk tube was purged three times with argon/vacuum cycles. Then, 3 mL of anhydrous DMSO was added. For initiation, a total of 165 mg of PEG 5k -NH 2 (0.03 mmol) in 2 mL DMSO was directly added to the Schlenk tube via syringe (0.4 M total). The reaction was let under stirring at 30°C for 4 days. Directly after completion, the polymer was precipitated in cold THF and centrifugated at 10,000 rpm et 5°C for 10 min. After discarding the liquid fraction, new THF was added, and the polymer was suspended in a sonic bath. The suspension was centrifuged again, and the procedure was repeated two times. The obtained diblock polymer was then dried at room temperature under vacuum overnight. Similar polymerization conditions were applied for the PEG-b-PPhe polypeptide.

Nanoparticles preparation

Nanoparticles were prepared from the PEG-b-PAsnand PEG-b-PPhe diblock copolymers.

Nanoprecipitation was performed by the dropwise addition (1 mL.min -1 ) of the polymer solution (10 mg.mL -1 in TFA, 2 mL) into vigorously stirred (700 rpm) deionized water (20 mL). TFA was then gently removed under vacuum before DLS analysis.

Results and Discussion

Synthesis and characterization of NCA monomers

Research for optimal acid scavenger which can be used in both carbonylation pathways describe in the introduction that allows easy recovery of high purity NCA with good yields and in a highly reproducible manner was initially carried out using L-phenylalanine as the model α-amino-acid (Scheme 1). Reaction of L-phenylalanine with triphosgene in anhydrous THF under inert atmosphere at 50°C was carried out using three different scavengers of acid byproducts that have proven effective for NCA synthesis in peculiar conditions: (i) the use of Ar flow in NaOH solution; (ii) the use of N-methylmorpholine as a weak base and (iii) the use of α-pinene. [START_REF] Smeets | A Scalable Synthesis of l-Leucine-N-carboxyanhydride[END_REF][START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF][START_REF] Cornille | Process for the preparation of Ncarboxyanhydrides[END_REF][START_REF] Carubia | Synthesis of amino acid, n-carboxyanhydrides[END_REF][START_REF] Khuphe | The formation of biodegradable micelles from a therapeutic initiator for enzyme-mediated drug delivery[END_REF][START_REF] Khuphe | Glucose-bearing biodegradable poly(amino acid) and poly(amino acid)-poly(ester) conjugates for controlled payload release[END_REF][START_REF] Huang | Supramolecular Hydrogels with Reverse Thermal Gelation Properties from (Oligo)tyrosine Containing Block Copolymers[END_REF] Using argon flow to trap HCl in a 0.1 M sodium hydroxide solution product lead to poor monomer recovery (24 % yield) whether the reaction was performed under concentrated (0.6 M) or diluted (0.06 M) conditions (Scheme 1.a). Similar behavior was obtained without any acid scavenger. In a recent study, Fuse and coworkers who prepared a library of NCAs in a micro flow reactor, using basic-to-acidic flash switching, have shown that N-methyl morpholine (NMM) was a suitable base to trap HCl without deprotonating NCA. [START_REF] Otake | Rapid and Mild Synthesis of Amino Acid N-Carboxy Anhydrides: Basic-to-Acidic Flash Switching in a Microflow Reactor[END_REF] When applied to our system, however, the use of NMM prevented to achieve controlled and efficient synthesis of Phe-NCA as polymerization occurred (Scheme 1.b). Consequently, we broadened our investigations with the use of terpenes as efficient scavengers of acid byproducts. In a patent from 2002, the use of alkenes for the chemical removal of HCl was reported. [START_REF] Cornille | Process for the preparation of Ncarboxyanhydrides[END_REF] A few years later, Hulshof et al. demonstrated a similar application of alkenes for the synthesis of L-leucine NCA, where, two different terpenes were selected, i.e. S-(-) αpinene and R-(+)-limonene. [START_REF] Smeets | A Scalable Synthesis of l-Leucine-N-carboxyanhydride[END_REF] α-pinene has already been successfully employed as acid scavenger for the synthesis of Phe-NCA, although the authors performed the reaction in harsh conditions (reflux) and multiple recrystallization steps were applied to achieve pure monomer. [START_REF] Khuphe | The formation of biodegradable micelles from a therapeutic initiator for enzyme-mediated drug delivery[END_REF][START_REF] Khuphe | Glucose-bearing biodegradable poly(amino acid) and poly(amino acid)-poly(ester) conjugates for controlled payload release[END_REF][START_REF] Huang | Supramolecular Hydrogels with Reverse Thermal Gelation Properties from (Oligo)tyrosine Containing Block Copolymers[END_REF] When implemented to our synthetic procedure, pure Phe-NCA monomer was similarly obtained in a good yield of 67 % but surprisingly without requiring multiple recrystallization procedures ( Because phosgene reacts with primary amide to yield nitrile, Asn-NCA cannot be prepared by the direct phosgenation of the corresponding L-asparagine amino acid. [START_REF] Speziale | The Reaction of Oxalyl Chloride with Amides. II. Oxazolidinediones and Acyl Isocyanates[END_REF][START_REF] Wilchek | Reaction of asparagine, glutamine, and derivatives with phosgene[END_REF] Moreover, asparagine-containing peptides suffer from low solubility in organic solvent as well as aggregation phenomenon due to numerous hydrogen bonds. Aiming to improve monomer synthesis as well as peptides formation, several substituents and notably trityl (Trt) group have been used as protecting carboxamide groups. [START_REF] Isidro-Llobet | Amino acid-protecting groups[END_REF] We envisioned two synthetic pathways to access Asn-NCA (Scheme 2). The first one involved the preparation of Asn(Trt)-NCA modelled on literature procedure (i.e. reaction of Boc-L-Asn(Trt)-OH with PBr 3 in DCM in the presence of triethylamine) followed by its deprotection under acidic condition (Scheme

2.a and b).[52]

Despite the reaction being described as quantitative, this synthetic route employing triethylamine as acid scavenger could not result in the isolation of pure monomer, as triethylamine acid salt precipitated out together with the product. In light of the encouraging results obtained with α-pinene as acid scavenger for the preparation of Phe-NCA, Boc-L-Asn(Trt)-OH was reacted with PBr 3 in the presence of 2.1 equiv. of the terpene. The purity of the monomer obtained was, however, altered by the formation of undesired byproduct as observed by NMR spectroscopy with signals at δ = 7.78 and 5.66 ppm. Anisole or organosilicon compounds, such as, triethylsilane are well known carbocation scavengers for the selective removal of protecting groups by acidolysis, such as Boc and related tert-butyl groups. [START_REF] Mehta | Improved efficiency and selectivity in peptide synthesis: Use of triethylsilane as a carbocation scavenger in deprotection of t-butyl esters and t-butoxycarbonyl-protected sites[END_REF][START_REF] Pearson | Trialkylsilanes as scavengers for the trifluoroacetic acid deblocking of protecting groups in peptide synthesis[END_REF][START_REF] Cavelier | Studies of selective Boc removal in the presence of silyl ethers[END_REF] While using a mixture of TFA/anisole (96/4 % v/v), only partial deprotection of the trityl group was observed, whilst employing 10 equiv. of triisopropylsilane led to quantitative yield. In addition, the work-up procedure was very straightforward as the protonated trityl group precipitated out in TFA, which after filtration allowed an easy recovery of Asn-NCA upon precipitation in diethyl ether (33 % yield). Clean and complete removal of the trityl protecting group was deduced from the disappearance of all the aromatic signals from the 1 H NMR at δ = 7.14-7.30 ppm. The appearance of two new signals associated to the deprotected amide was observed at δ = 7.50 and 7.05 ppm respectively (Fig. S5-S8 in ESI). Further confirmation was obtained from the change in solubility of the resulting monomer from Asn(Trt)-NCA, soluble in THF, to Asn-NCA, insoluble in THF.

The second synthetic pathway envisioned to achieve Asn-NCA was an improved methodology based on Denkewalter and coworkers' procedure, which notably increased the overall yield without requiring column chromatography purification (Scheme 2.c). [START_REF] Hirschmann | Controlled synthesis of peptides in aqueous medium. VIII. Preparation and use of novel .alpha.-amino acid N-carboxyanhydrides[END_REF] Applying our optimized Asn(Trt)-NCA synthetic procedure starting from N-α-Boc-L asparagine failed due to insolubility of both N-α-Boc-L asparagine and its corresponding NCA in DCM. As a consequence, the resulting Asn-NCA was formed in low yield, with approximately 30 % of unreacted N-α-Boc-L asparagine and a significant amount of hydrolysis product that could clearly be observed by 1 H NMR (Fig. S9 in ESI). Changing the solvation conditions by employing THF instead of DCM proved effective as reaction reached completion but again suffered from partial hydrolysis as traces of the analogous α-amino acid could be seen on 1 H NMR. Addition of a larger excess of α-pinene (4 equiv.) has proven to be beneficial as it prevented hydrolysis, but the reaction yield remained low (22 %) and thus, did not provide an improvement on the previously reported synthetic pathway. It has already been shown that introduction of alkenes into the reaction mixture lowers the overall polarity of the medium and consequently the reaction rate yielding to poor monomer recovery. Thus, in the pursuit of our effort to optimize our synthetic route, we then investigated the effect of concentration by performing the reaction under dilute conditions (0.06 M). This eventually provided considerable improvement, as crystalline Asn-NCA could be obtained in 57 % yield After developing enhanced synthetic procedures based on the utilization of α-pinene as effective acid scavenger to access acrylamide-like Asn-NCA and styrene-like Phe-NCA, assay to copolymerize these monomers to form potentially thermosensitive copolypeptides was then performed for the first time.

Ring-opening polymerization studies

As shown by Agarwal et al., vinylic copolymers obtained by copolymerization between St

and AAm possessed a rather narrow composition window, ranging from 14 to 16 mol.% of styrene, in which they exhibit a UCST. [START_REF] Pineda-Contreras | Importance of compositional homogeneity of macromolecular chains for UCST-type transitions in water: Controlled versus conventional radical polymerization[END_REF] Inspired by these results, we initially decided to introduce in the feed 90 mol. % of Asn(Trt)-NCA and 10 mol. % of Phe-NCA to yield P(Asn(Trt)-co-Phe) (Table 1, entry 1). However, attempts to prepare P(Asn(Trt)-co-Phe) at 30°C in anhydrous DMF using neopentylamine as initiator (([M]/[I] = 25) were partially successful. The copolymerization gave rather oligopeptides, most likely due to restricted chain extension during polymerization caused by: (i) the high steric hindrance induced by the bulky trityl protective group and (ii) the occurrence of -sheet secondary structures imparted by numerous intermolecular hydrogen bond interactions (see section 3.3 and Fig. 4 for details). [START_REF] Yamada | Phosgene-free synthesis of polypeptides using activated urethane derivatives of α-amino acids: an efficient synthetic approach to hydrophilic polypeptides[END_REF] As a result, the deprotected copolymer obtained after acidolysis in TFA, was of lower molecular weight than expected as characterized by 1 As such, our efforts then concentrated on performing the copolymerization between Phe-NCA and Asn-NCA instead of Asn(Trt)-NCA to directly yield P(Asn-co-Phe), as the less hindered non-protected monomer was postulated to lead to a more favorable polymerization. Adequate amide group protection is usually a requirement to prevent side reactions during peptide coupling synthesis from α-amino-acids such L-asparagine and L-glutamine. [START_REF] Isidro-Llobet | Amino acid-protecting groups[END_REF][START_REF] Gausepohl | Asparagine coupling in Fmoc solid phase peptide synthesis[END_REF][START_REF] Callahan | The Tertiary Butyl Group as a Blocking Agent for Hydroxyl, Sulfhydryl and Amido Functions in Peptide Synthesis[END_REF] Peptides obtained from these monomers often suffer from low solubility and aggregation caused by the numerous hydrogen bonds. However, by setting up proper polymerization conditions, we were able to minimize these inconveniences. We performed the ROP of Asn-NCA and Phe-NCA under identical experimental conditions as for entry 1 (Table 1, entry 2).

As the neopentylamine initiator was added in one shot in the medium ( and the appearance of a polypeptide C=O stretching band (amide I) at 1654 cm -1 (Fig. S15 in ESI). Unfortunately, because the polymer obtained was insoluble in common SEC solvents such as DMF, THF, DMSO and CHCl 3 , it was impossible to measure neither number-average molecular weight (M n,SEC ) nor dispersity Đ, that could be broad. Different solutions have been studied to weaken hydrogen bonds and favor solubilization, such as, the use of heat or the addition of concentrated salts such as NaCl and KCl. [START_REF] Wang | Peptide self-assembly: thermodynamics and kinetics[END_REF][START_REF] Pattanayak | Effects of concentrated NaCl and KCl solutions on the behaviour of aqueous peptide bond environment: single-particle dynamics and H-bond structural relaxation[END_REF] To avoid precipitation and achieve higher conversions, we investigated the effect of the polymerization temperature.

Raising the temperature to 60°C still resulted in early precipitation and a polymer exhibiting a chain length of ≈ 17 was obtained (Table 1, Entry 3 and Fig. S16 in ESI). Recent studies have already reported that an increase in temperature generally inhibited polymerization due to the formation of N-formyl group at the polymer chain end resulting from the reaction between the propagating species and DMF. [START_REF] Kricheldorf | Primary Amine and Solvent-Induced Polymerizations of L-or D,L-Phenylalanine N-Carboxyanhydride[END_REF][START_REF] Kricheldorf | Cyclic Polypeptides by Solvent-Induced Polymerizations of α-Amino Acid N-Carboxyanhydrides[END_REF] Thus, we maintained the polymerization temperature to 30°C and switched solvent to DMSO, which is more polar than DMF. We believed that polymer-solvent interactions would be stronger than polymer-polymer intermolecular interactions, resulting in better solvation conditions while avoiding potential termination reactions. Again, we noted that DP n,NMR remained largely invariant of the conditions (≈ 17) (Table 1, Entry 4 and Fig. S17 in ESI). However, the polymer behavior in solution drastically changed as no aggregation was observed during the first 72 h. Small aggregates could however be observed only at the end of polymerization. Despite being at the cost of reduced polymerization rate due to a decrease concentration of the propagating chains, the copolymerization between Asn-NCA and Phe-NCA initiated by neopentylamine was investigated by reducing the concentration by a factor of 10 (0.06 M) (Table 1, Entry 5). In doing so, not only we were able to fully suppress aggregation phenomenon but we also attained the targeted DP n (M n = 3 kg.mol -1 , DP n = 25), with 90.2 % and 9.2 % of Asn and Phe units, respectively, as determined by 1 H NMR (Fig. S18 in ESI).

Thermosensitivity assays

After optimizing the polymerization conditions, we tested potential UCST behavior of P(Asnco-Phe). We synthesized three different copolymers using a range of Asn-NCA-to-Phe-NCA initial molar ratios (98:2; 90:10 and 80:20) initiated with neopentylamine at a monomer-toinitiator ratio of 50 ([M]/[I] = 50) (Table 2). End group analysis by 1 The solubility in water of the copolymers obtained (1 wt.%) was then tested at different temperatures. As can be seen on the pictures (Fig. S19 in ESI), none of the copolymers yielded a thermosensitive response in aqueous media (neither in deionized water nor PBS solution), independently of their composition or the temperature. Polymer suspensions obtained in both deionized water and PBS solution tended to precipitate after a few hours. In fact, the three copolymers were insoluble in most organic solvents, such as THF, DMSO, DMSO with 10 mM LiCl, DMAc, DMF, CHCl 3 and DCM. Only an aqueous solution of 75 % v/v TFA in water was able to solubilize the copolypeptides. The tendency of the copolymers to phase out in solution was probably due to the occurrence of strong β-sheet structures enhanced by the numerous intermolecular hydrogen bond interactions between amide NH proton donors and amide C=O and phenyl ring proton acceptors which was evidenced by FTIR spectroscopy. [START_REF] Fändrich | The behaviour of polyamino acids reveals an inverse side chain effect in amyloid structure formation[END_REF] The C=O stretching vibration (amide I) band with a maximum at 1654-1640 cm -1 and a shoulder at 1717 cm -1 , and the N-H bending vibration (amide II) band at 1544 cm -1 characterized -helical secondary conformation of polypeptide chain (Fig.

4).[66]

The presence of -sheet structures is illustrated here by the existence of a notable shoulder of amide I at 1620 cm -1 . [START_REF] Chirgadze | Infrared spectra and resonance interaction of amide-I vibration of the antiparallel-chain pleated sheet[END_REF][START_REF] Chirgadze | Infrared spectra and resonance interaction of amide-I vibration of the parallel-chain pleated sheet[END_REF][START_REF] Palanisamy | Upper Critical Solution Temperature Layer-by-Layer Films of Polyamino acid-Based Micelles with Rapid, On-Demand Release Capability[END_REF][START_REF] Caillol | Synthesis and Self-Assembly Properties of Peptide-Polylactide Block Copolymers[END_REF] Alteration of the β-sheet structures by strong acids such as TFA, acting as proton donor, weaken the interchain peptidic hydrogen bonds, favoring solubilization. Although, the copolymers present structural similarity with UCST P(AAm-co-St) polymers, the prevalence of strong intermolecular hydrogen bonds and βsheets supramolecular association prevents from obtaining a thermoresponsive behavior.

Nonetheless, we were able to produce for the first-time copolypeptides of Asn-NCA and Phe-NCA by optimizing the polymerization conditions. Taking advantage of this naturally occurring peptide self-assembly, researchers have aimed at associating polypeptides to other biocompatible polymers, such as polyesters or polyethers to prepare well-defined nanoparticles for use in drug delivery applications. [START_REF] Suk | PEGylation as a strategy for improving nanoparticle-based drug and gene delivery[END_REF][START_REF] Osada | Drug and Gene Delivery Based on Supramolecular Assembly of PEG-PolypeptideHybrid Block Copolymers[END_REF] In the light of our solubility assay, we aimed at accessing amphiphilic polypeptide-based nanoparticles via nanoprecipitation of designed PEGylated PAsn et PPhe polymers.

Preparation of PEG-b-PNCA diblock copolymers and nanoparticles

It has already been shown that hydrophobic interaction coupled with inter and intramolecular hydrogen bonding in polypeptides are driving forces for spontaneous self-assembly into micelles or vesicles regardless of the polymer molar masses.

Conclusion

The aim on this study was plural. First, a new optimized synthetic approach to pure L-

Fig 1 .

 1 Fig 1. Preparation of poly(asparagine-co-phenylalanine) (P(Asn-co-Phe)) copolypeptides by ROP of L-asparagine and L-phenylalanine-derived N-carboxyanhydrides obtained from optimized synthetic pathways and potential applications envisioned.

Scheme 1 .

 1 Scheme 1. Synthetic pathways to (S)-4-benzyloxazolidine-2,5-dione (Phe-NCA). Reagents: (a) Ar flow in NaOH solution (10 mM); (b) N-methylmorpholine (4.5 equiv.); (c) α-pinene (2.1 equiv.).

Fig 2 .

 2 a and Fig.S1-S2 in ESI). It is worth pointing out that the introduction of an alkene as HCl scavenger into the reaction mixture resulted in the formation of pinene hydrochloride byproducts, also named bornyl chloride. Nevertheless, this component was easily washed away during precipitation in n-hexane. While the yield obtained was in the same range as those described in the literature, this procedurewhich does not require purification stepsoffered better reliability as yield achieved without acid scavengers often depends on the multiple recrystallization efficiency.[START_REF] Sun | Direct Formation of Giant Vesicles from Synthetic Polypeptides[END_REF][START_REF] Daly | The preparation of N-carboxyanhydrides of α-amino acids using bis(trichloromethyl)carbonate[END_REF]

Fig 2 .

 2 Fig 2. 1 H NMR spectra of (a) Phe-NCA (CDCl 3 ), (b) Asn(Trt)-NCA (DMSO-d 6 ) and (c) Asn-NCA (DMSO-d 6 ). Residual solvent traces have been noted by *.

Employing 3 .Scheme 2 .

 32 Scheme 2. Synthetic pathways to (S)-2-(2,5-dioxooxazolidin-4-yl)acetamide (Asn-NCA). Reagents/Methods: (a) α-pinene (3.5 equiv.); (b) triisopropylsilane (10 equiv.); (c) α-pinene (4 equiv.).

  after precipitation in THF, which is almost three times the one obtained in concentrated medium (Fig 2.c and Fig. S10-S11 in ESI). Overall, this optimized synthetic pathway gives several key improvements over the other reported methods: (i) the use of low-cost and potent acid scavenger; (ii) work-up procedure have been greatly reduced as no recrystallization or column chromatography are needed and (iii) Asn-NCA is obtained in high yield.

  H NMR spectroscopy (M n = 2 kg.mol -1 , DP n = 10) (Fig. S12-S13 in ESI).

  [M]/[I] = 25), the reaction became translucent and finally turned a milky-white color within minutes. After 1 h, the reaction turned completely opaque. After precipitation of the polymer in cold THF, formation of the polypeptide was first assessed by 1 H NMR. It displayed the shifts of characteristic NCAs methylene protons (-CH 2 -) adjacent to the α-methylene proton (-CH-) resonances at δ = 2.59-2.74 ppm and δ = 2.96-3.31 ppm downfield towards new broader signal at δ = 3.37 ppm. Meanwhile, the signals centered at δ = 4.51 and 4.53 ppm (-CH-in monomers) disappeared as the reaction progressed, and a new broader triplet centered at δ = 4.49 ppm (-CH-in polymer) appeared (Fig. S14 in ESI). Neopentylamine end group analysis revealed that the targeted DP n was nearly achieved (≈ 21). As a result of early precipitation during polymerization, the reactive polymer chain end was indeed not any longer accessible for further propagation, resulting in a slightly lower molecular weight polypeptide. Further characterization by FTIR-ATR provided additional evidence of the formation of polypeptide by the disappearance of the monomers C=O stretching vibration bands at 1850 and 1843 cm -1

  H NMR revealed polymer DP n s ≈ 38 (98:2); 42 (90:10) and 45 (80:20) and molar masses M n ranging from 4.2 to 5.4 kg.mol -1 , based on the integration of the tert-butyl neopentylamine resonances at δ = 0.81 ppm against those of the methylene -CH-protons from the main polymer chain at δ = 4.49 ppm (Fig. 3). For %.Asn and %.Phe determination, we resulted again in the signals of the amide NH resonances at δ = 7.31-7.53 ppm and the signal of the Phe phenyl ring at δ = 7.14-7.31 ppm. The data obtained were in good correlation with the theoretical values for Asn-to-Phe ratios of 95:5 (98:2 in the feed), 90.5:9.5 (90:10 in the feed) and 85:15 (80:20 in the feed). Yet the technique was not completely accurate as signals from Asn amide NH and Phe penyl ring tends to slightly overlap.

Fig 3 . 1 H

 31 Fig 3. 1 H NMR in DMSO-d 6 of the P(Asn-co-Phe) copolymers with Asn-to-Phe molar ratio of: (a) 98:2; (b) 90:10 and (c) 80:20. Residual solvent traces have been noted by *.

Fig. 4 .

 4 Fig. 4. FTIR of P(Asn-co-Phe) (ratio 90:10) obtained from the ROP of Asn-NCA and Phe-NCA in DMSO ([M]/[I] = 50) at 30°C (0.06M) in the 1800-1450 cm -1 region. The amide bands indicative for -helical conformation of the peptide chain are assigned in green, the one indicative for -sheet structures is marked in red.

[ 63 ]Fig. 5 and

 635 Fig. 5 and Fig. S22 in ESI).

Table 3 .a

 3 Macromolecular and colloidal characteristics of NPs prepared by nanoprecipitation of PEG-b-PNCA diblock copolymers. Determined by 1 H NMR. b Intensity-average diameter measured by dynamic light scattering (DLS) as an average of three different measurements before TFA removal. c Measured by dynamic light scattering (DLS) as an average of three different measurements after TFA removal. d Precipitation occurred.

Fig. 5 .

 5 Fig. 5. Colloidal characteristics of NPs prepared by nanoprecipitation of PEG-b-PAsn diblock copolymers before TFA removal (top) and after TFA removal (bottom) as measured by DLS.

  phenylalanine and L-asparagine N-carboxyanhydrides (Phe-NCA and Asn-NCA, respectively) in one-pot process has been developed based on two different carbonylation pathways. Low solubility and aggregation phenomena caused by the numerous inter-and intramolecular hydrogen bonding interactions were minimized by setting proper polymerization conditions and as analogy with well-known poly(acrylamide-co-styrene) (P(Aam-co-St)) UCST copolymers, poly(asparagine-co-phenylalanine) (P(Asn-co-Phe)) copolypeptides of different Asn to Phe ratio were obtained. Thermoresponsivity of our P(Aam-co-St)-inspired polypeptides were assessed but polymer association via strong hydrophobic interactions favored by the presence of -sheet structures that not only prevented the occurrence of a thermosensitive response in aqueous media but also precluded their solubilization in most organic solvents. Taking advantage of this naturally occurring selfassembly, PEGylated PAsn and PPhe polymers were prepared and nanoparticles formulation showed that PEG-b-PAsn could form NPs with relatively low particle size and narrow particle size distribution for potential application in drug delivery.

  C NMR (75 MHz, DMSOd 6 ): 171.4, 167.7, 152.2, 144.4, 128.5, 127.5, 126.4, 69.6, 53.9, 36.7. IR (ATR, cm -1 ): 3414, 3357, 1858, 1787, 1665, 1508, 1495, 1447, 1401, 1366, 1332, 1284, 1267, 908, 901.

Characterization data are consistent with previous report.

[START_REF] Pirrung | Total synthesis of fellutamides, lipopeptide proteasome inhibitors. More sustainable peptide bond formation[END_REF]

  H NMR (DMSO-d 6 ): 8.78 (s, 1H); 7.50 (s, 1H); 7.05 (s, 1H); 4.50-4.53 (t, J = 4.1 Hz, 1H); 2.59-2.73 (ddd, J = 21.5 Hz, 16.9 Hz, 4.5 Hz, 2H). 13 C NMR (75 MHz, DMSO-d 6 ): 171.7, 169.8, 152.5, 53.7, 35.5. IR (ATR, cm -1 ): 3417, 3187, 1835, 1791, 1778, 1674, 1659, 1435, 1425, 1389, 1366, 1297, 1270, 940, 912.

1

  C NMR (75 MHz, DMSO-d 6 ): 171.7, 169.9, 152.5, 53.7, 35.5. IR (ATR, cm -1 ): 3417, 3186, 1843, 1780, 1766, 1683, 1670, 1434, 1401, 1353, 1295, 1270, 941, 908. Anal. Calcd for C 5 H 6 N 2 O 4 : C, 37.98; H, 3.82; N, 17.72; O, 40.48. Found: C, 38.2; H, 3.93; N, 16.75.

Table 1 . Experimental conditions and macromolecular characteristic of the copolymers prepared in this study.

 1

		Monomer
	Entry	(90 mol.	Comonomer (10 mol. %)	Solvent	M 0 (M)	Temperature (°C)	Reaction time (h)	DP n,th DP n,NMR.	a	a (kg.mol -1 ) M n,NMR.
		%)
		Asn(Trt)-
	1		Phe-NCA	DMF	0.6	30	96	25	10		2
		NCA
	2	Asn-NCA	Phe-NCA	DMF	0.6	30	96	25	21		2.9
	3	Asn-NCA	Phe-NCA	DMF	0.6	60	96	25	17		2
	4	Asn-NCA	Phe-NCA	DMSO 0.6	30	96	25	17		2
	5	Asn-NCA	Phe-NCA	DMSO 0.06	30	96	25	25		3

a . Determined by 1 H NMR.

Table 2 . Macromolecular characteristics of P(Asn-co-Phe) copolymers prepared by ROP of Asn-NCA and Phe-NCA.

 2

		Feed		Polymer
	Entry	(mol. %)	(%) a		Reaction time (h)	DP n,th	DP n,NMR.	a	a (kg.mol -1 ) M n, NMR.
		Asn-NCA Phe-NCA Asn	Phe
	1	98	2	95	5	96	50	38		4.2
	2	90	10	90.5	9.5	96	50	42		5.2
	3	80	20	85	15	96	50	45		5.4
	a . Determined by 1 H NMR.

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 771829). The CNRS is also acknowledged for financial support.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.


Liwen Zhang
email: liwen.zhang@berger-levrault.com

Christophe Bortolaso

Marianne Sargent

Elyes Lamine
email: elyes.lamine@univ-jfc.fr

Mustapha Derras
email: mustapha.derras@berger-levrault.com

Franck Fontanili
email: franck.fontanili@mines-albi.fr

Hervé Pingaud
email: herve.pingaud@univ-jfc.fr

BLPAD.Core: a Multi-functions Optimizer towards Daily Planning Generation in Home Health Care

Keywords: BLPAD, Home Health Care, Use case generation, Benchmark, Optimization, Planning Visualization

Today, a majority of the elderly want to live longer in autonomy and comfort. Since there is not enough space available in specialized institutions, Home Health Care Services (HHCS) constitute an important addition that reinforces the traditional system. With the increase in HHCS demands, the main challenge in this distributed system is the organization of care services in an HHC institution. This organizational problem is widely studied as a Home Health Care Scheduling and Routing Problem (HHCSRP) in the Operations Research (OR) community. Facing the diversity and complexity of demands, as done in OR, the formulated solution-oriented model aims at providing decision making support for the decision maker in HHC systems. This leads obstacles in the dataset / benchmark based experimental environment and critical analysis such as the degree of the optimality regarding generated solutions and the comprehensive visualization of solutions. In this paper, based on a systemic analysis of the existing benchmark and the solution approach for HHCSRP, a prototype named BLPAD.Core is introduced. It provides a full decision support system to the decision-maker in the HHC system. The functionality consists of an instance generation based on the real dataset, operational planning generation and solution visualization. This research highlights the scientific challenges and attempts to respond to the complicated expectations of HHC systems in a comprehensive manner.

I. INTRODUCTION

Due to the rapid development of public health and medical science and technology, various acute infectious diseases have been controlled, the average life expectancy has been greatly extended, the population is rapidly aging. Also, chronic infectious diseases have become the main factor endangering people's health. These diseases have multiple etiologies and complex pathogenesis and are often accompanied by many psychosocial problems. There is no specific radical cure. Once an individual is sick, he will need continuous medical services for life. For these diseases, preventive health care and treatment such as medicine, psychological and social services are indispensable. This has caused significant changes in the quality and quantity of society's demand for medical and health services. On the other hand, the highly specialized medical service system has been difficult to adapt to the needs of social health care services. Its main disadvantage is that it focusses on physiological and biological causes and ignores the impact of psychosocial factors on health and disease. Emphasis on the diagnosis and treatment of diseases, neglecting the prevention and health care is limited to hospital services, unable to meet the rapidly growing social needs.

The aging population and a medical system which focuses on treatment rather than prevention contributes in a rapid growth of medical expenses. This leads to the unreasonable distribution and great waste of medical resources. The sharp increase of medical expenses has brought an increasingly heavy burden to the country and its enterprises and has affected the development of our society and economy. How to use the limited health resources to control the growth of medical expenses and improve the health level of the whole population has become a worldwide research question. Home Health Care Services (HHCS) in this respect is an important reason for its rapid development. The main challenge in this distributed system is the organization of the care services in an HHC structure. Guaranteeing the good coordination between the caregivers and the care beneficiaries will facilitate the planning of the care services to achieve business objectives while respecting the constraints inherent in an operational field. This issue is often addressed as a problem in optimizing practitioners' schedules, a subject that is widely studied by the Operations Research (OR) community. It is described in the literature under the heading Home Health Care Scheduling and Routing Problem (HHCSRP) [START_REF] Fikar | Home health care routing and scheduling: A review[END_REF] [START_REF] Cissé | OR problems related to Home Health Care: A review of relevant routing and scheduling problems[END_REF]. Without going into a detailed analysis of these studies, we were able to identify sources of diversity in this available research. In addition, the HHCSRP model can also be declined in a large number of variants depending on the HHC business constraints that need to be satisfied, and it would be inappropriate to assume that it is a static list. The rise of activity in the operational field will inevitably reveal new characteristics. Facing this diversity, the solution-oriented mathematical models that are trying to find the best operational coordination solution by using the OR approach are various as well. When the mathematical model is well built in conformity to the requirements specified by an HHC structure, it is difficult to find a real dataset that with 100% confirmation to the assumptions, the objectives function and the constraints modelled in our mathematical formulation. Consequently, this will lead to another obstacle regarding the solution evaluation and the determination of the optimality of the generated solutions, as well as the solution visualization for providing a systemic decision-making support to the deciders in the HHC structure.

In this respect, there are three primary aims of this research work: 1) To investigate the existing benchmark among the literature, then establish a standard in conjunction with the special parameters regarding our formulated mathematical model. 2) To ascertain the most adapted algorithms in the HHCSRP, for the purpose of solving our formulation by the different algorithms through a comparative evaluation platform and 3) to provide a decision-making visualizer to visualize the solution in a comprehensive manner in order to help the decision-maker doing the critical analysis regarding the generated solution.

The content of the remaining sections is structured as follows. Firstly, we will review the previous research works about the existing benchmark and the solution approach for the HHCSRP. Next, the 3 modules of BLPAD.Core are introduced to respond to the formulated HHC operational coordination requirement. The detail software structure and the data structure with respect to input/output of each module, will be presented, respectively. Finally, we conclude this work and address the outlook.

II. STATE OF THE ART

A. Solution approch of HHCSRP

Studies over the past two decades have many approaches to solve the HHCSRP addressed previously. Normally the approach is categorized into two groups : 1) the exact method which is trying to find the optimum solution concerning the formulated mathematical model based on Integer Linear Programming (ILP) or Mixed Integer Linear Programming (MILP), in spite of the computing time. For example, a human resource's synchronization problem [START_REF] Di Mascolo | Synchronization between human resources in Home Health Care context[END_REF] a lunch break requirement [START_REF] Xiao | Mathematical model for the home health care scheduling and routing problem with flexible lunch break requirements[END_REF], a care plans satisfaction problem [START_REF] Bachouch | A decision-making tool for home health care nurses' planning[END_REF] and a multiples treatments problem [START_REF] Torres-Ramos | Mathematical Model for the Home Health Care Routing and Scheduling Problem with Multiple Treatments and Time Windows[END_REF] are formulate under MILP. This approach is frequently solved by the commercial mathematic such as CPLEX, Gurobi, LocalSolver. 2) the approximate method is used to find an approximate solution to solve optimization problems. Based on the metaheuristic or algorithm, this approach can usually derive a solution with quality assurance in a reasonable computing time. In light of the efficiency of the algorithm in order to evaluate the solution generated under the different approaches, we opt for the approximate method as our solution approach developed in BLPAD.Core. Among the recent research works, Decerle et al. [START_REF] Decerle | A memetic algorithm for a home health care routing and scheduling problem[END_REF] introduced a memetic algorithm involving two original crossing operators to address HHCSRP with time windows and synchronization constraints at the care services level. A harmony search algorithm is presented by Lin et al. [START_REF] Lin | Jointly rostering, routing, and rerostering for home health care services: A harmony search approach with genetic, saturation, inheritance, and immigrant schemes[END_REF]. to handle jointly the rostering, routing and re-rostering for HHC services. The algorithm Tabu Search (TS) is largely used for solving the HHCSRP, Hertz and Lahrichi [START_REF] Hertz | A patient assignment algorithm for home care services[END_REF] consider the deterministic patients to caregivers assignment for HHC service by using TS. A daily planning generation using public transport [START_REF] Rest | Daily scheduling of home health care services using time-dependent public transport[END_REF], a periodic home health care logistics [START_REF] Liu | Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics[END_REF] [13], a sustainable delivery scheduling [START_REF] Szander | Algorithm for Efficient and Sustainable Home Health Care Delivery Scheduling[END_REF], a robust planning model considering the temporal uncertainty [START_REF] Shi | A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times[END_REF], a real-time scheduling problem with the disruption management [START_REF] Yuan | Disruption Management for the Real-Time Home Caregiver Scheduling and Routing Problem[END_REF] are solved by TS with the good performance. Moreover, Simulated Annealing (SA) is widely used for approximate solution generation in HHCSRP, such as an interdependent services based scheduling problem [START_REF] Manavizadeh | Using a metaheuristic algorithm for solving a home health care routing and scheduling problem[END_REF], a bi-objective green routing problem [START_REF] Braekers | A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience[END_REF], a simultaneous delivery and pick-up problem [START_REF] Shi | Modeling and Solving Simultaneous Delivery and Pick-up problem with Stochastic Travel and Service Times in Home Health Care[END_REF], a workforce scheduling problem [START_REF] He | Workforce Scheduling and Routing for Home Health Care Services[END_REF], a multimodal scheduling problem [START_REF] Hiermann | Metaheuristics for solving a multimodal home-healthcare scheduling problem[END_REF]. This is performed very well by SA in terms of computing time and gap study in comparison with the optimum objective function value. This literature review set out to investigate the usefulness and the efficiency of SA and TS as our target metaheuristic solutions approaches embedded in our optimizer of BLPAD.Core. The choice of algorithmic parameters of TS and SA is studied by [START_REF] Sarmady | An Investigation on Tabu Search Parameters[END_REF] and [START_REF] Ben-Ameur | Computing the Initial Temperature of Simulated Annealing[END_REF].

B. Benchmark study

According to our review, there are 5 accessible benchmarks among the literature addressing the HHCSRP recently. They all aim to solve the HHCSRP with time windows but taking into consideration the different business constraints. The benchmark proposed by Decerle et al. [START_REF] Bredström | Combined vehicle routing and scheduling with temporal precedence and synchronization constraints[END_REF] consists of 10 instances, the instance characterized by the number of visits, the number of care staff members, the number of synchronized visits, the average distance between the visits and the average time window size for each category. The second is introduced by Decerle et al. [START_REF] Decerle | A memetic algorithm for a home health care routing and scheduling problem[END_REF], including 7 instances of which the last 3 are the combinations of the 4 previous instances. The instance is characterized by the number of care services to be performed by a nurse or by an auxiliary nurse, the number of available nurses and auxiliary nurses, the number of home health care offices, the number of synchronized visits and the average distance between the visits. The third is published by Mankowska et al. [START_REF] Mankowska | The home health care routing and scheduling problem with interdependent services[END_REF], including 7 groups with 70 instances total (each group has 10 instances, randomly generated), characterized by number of patients, number of patients who request single service, number of patients who request double service and number of caregivers. The fourth is presented by Braekers et al. [START_REF] Braekers | A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience[END_REF] including 90 instances : 30 small ones (10-25 services) and 60 realistic size ones (50-300 services). They are characterized by number of full-time nurses (8-10 hours/day), number of part-time nurses (4-6 hours/day), number of care services, number of patients and the transportation mode (car, public or mixed). At last, Hiermann et al. [START_REF] Hiermann | Metaheuristics for solving a multimodal home-healthcare scheduling problem[END_REF] presents a benchmark with 4 large size instances. They are characterized by number of caregivers, number of services, number of patients and the detail characteristics for each element such as qualification of caregivers, qualifications required for services.

Our contribution in this paper is resumed in 3 essential points. 1) Based on the benchmark [START_REF] Hiermann | Metaheuristics for solving a multimodal home-healthcare scheduling problem[END_REF] which is similar to our problem, we can define the standard format of our use case for feeding our optimizer in BLPAD.Core, combined with the special parameters required regarding our mathematical formulation presented in our recent research work [START_REF] Zhang | Home Health Care Daily Planning Considering the Satisfaction of all the Stakeholders[END_REF]. 2) Two powerful metaheuristics (TS and SA) are ready to find a daily HHCSRP solution. 3) A comprehensive visualizer aims at providing the decision-making supports for the decision maker.

III. BLPAD.CORE: HHCRSP CASES GENERATOR, SOLUTIONS

OPTIMIZER AND VISUALIZER BLPAD [START_REF] Zhang | A Decision-Making Support System for Operational Coordination of Home Health Care Services[END_REF], the previous version of BLPAD.Core, included Simulated Annealing (SA) algorithm to generate an optimized solution. However, we lacked a reference to evaluate the quality of the solutions obtained at the end of BLPAD. Moreover, BLPAD is not capable performing a complete experiment based on the real dataset. We have therefore launched an extensive study on this particularly important point relating to the proposal of a set of decisions that would make the operational coordination of the HHC visible. Fig. 1 schematizes the 3 modules of BLPAD.Core, as well as the information flow between these modules.

The interest of the BLPAD.Core is to create a software environment suitable to addressee the real cases in HHCSRP. The prototype of BLPAD.Core is composed of 3 modules (case generator, optimizer, visualizer) with the successive objectives of :

• Generating instances adapted to the metaheuristic-oriented mathematical model presented in [START_REF] Zhang | Home Health Care Daily Planning Considering the Satisfaction of all the Stakeholders[END_REF]. The data structure is inspired by the similar benchmark in the literature, based on real dataset in operational field.

• Solution optimization by using 2 metaheuristic algorithms based on our metaheuristic-oriented mathematical model, taking the instance generated by the generator. Thus, we are able to perform the comparative study and critical analysis with regard to the solutions generated by the different algorithms but under the same formulation.

• Visualization of these solutions in a comprehensible form to enable the quality assessment and the drawing of conclusions on the comparison exercise.

A. Case generator

This generator makes it possible to transform data provided by the real dataset into structured data in a .txt format, respecting the format provided by an HHCSRP benchmark published quite recently [START_REF] Hiermann | Metaheuristics for solving a multimodal home-healthcare scheduling problem[END_REF]. The output file of this generator can then feed our optimizer in order to find an optimum operational planning solution.

Fig. 2 Graphical interface of BLPAD.Core -Case generator Fig. 3 is a metamodel of the input and output knowledge of case generator. The data is first grouped according to the geographic areas of each care service. Then, users can choose in which geographic area(s) they want to carry out the planning. According to this study configuration, the interface (Fig. 2) will display the key information from the real dataset that characterizes the use case. The general information, such as the total number of active caregivers, the total number of care services to be performed, the total number of patients, is displayed in "general informational parameter" section. The displayed care services are also grouped by the period of day in order to observe their temporal distribution and then facilitate the definition of indicators to identify the difficulty of each instance. Some explanations shown in red for giving some detail information, for example the request in the morning (a.m.) is from 7:00am to 1:00pm. As the real dataset is not sufficient by itself to feed the optimizer (e.g. lack of the distance matrix or time windows for each care service), the interface provides options for users to complete them in order to meet the requirements of our formulation developed in optimizer. In the "Special parameters for our formulation" section, the given option is to complete our instance to fit our own formulation for characterizing caregivers' and patients' satisfaction. These special parameters are customizable by users, some of these fields are restricted, which is indicated below the corresponding field, written in red. The result is finally generated pseudo-randomly between this given maximum and minimum value. Having completed all of these intelligence operations, the case generator finally delivers a particular instance of a scheduling problem, partly based on the real dataset from the operational field.

B. Optimizer

This optimizer embeds a metaheuristic-oriented mathematical model and a solver with the two selected metaheuristics (Simulated Annealing (SA), Tabu Search (TS)), developed in Java. The solver aims at generating an optimum HHCSRP daily solution that formulated by the mathematical model. The description of the mathematical model such as data declaration, retained assumptions, considered constraints and optimization criteria were presented in our research work [START_REF] Zhang | Home Health Care Daily Planning Considering the Satisfaction of all the Stakeholders[END_REF]. Fig. 3 presents a metamodel of the input and output knowledge of Optimizer.

The interface of the optimizer enables the choice of a metaheuristic among the 2 available options, with the input of the corresponding algorithmic parameters (Fig. 4). As for the parameters for each metaheuristic embedded in the optimizer, we present them based on the study by [START_REF] Silberholz | Comparison of Metaheuristics[END_REF] , which has drawn I).

The optimizer starts its operations by reading an instance generated by the case generator and then needs an initial point in the decision variable's space. This will be the starting point for searching a solution. The rule for this initialization is very simple: all the care services to be executed are assigned to all the caregivers according to a distribution called the randomly average distribution. For example, for a use case including 100 care services and 10 caregivers, the initial solution leads to 10 care services picked randomly in 100 care service per caregiver. The interface also allows to enter the number of neighborhood solutions to be created during an optimization cycle (one iteration). The different possible "exchanges" to compose a new order of care services in the current neighborhood. These are operations to be performed on an ordered list of care services, for example changing the scheduling of care services in a round, or even changing the round to which a care service is assigned. The stop criteria of the algorithms is controlled by a maximum number of iterations set by the user, with the exception of SA, which will be stopped when a minimum required temperature is reached. When the optimization is finished, the optimizer generates 2 output files in .csv format:

• The first output contains the planning solution with each line the performed care services in theirs daily round, characterized by the performed caregiver id. One caregiver performs only one round in their working day, each round consists of several steps. Each step represents one care service operated by this caregiver, with the characteristics such as care service's start time, end time, duration, and the travel time to next location. The round of a caregiver denotes the caregiver start his working day from the HHC structure and finish her/his assigned care service at the HHC structure.

• The second output contains the performance about an optimal solution, whose objective function is maximum over several iterations . The information including the objective function value, computing time and the value of its 5 components: 1) feasibility: presenting if all the care services are assigned correctly, the value is equal to the total number of the care services in a use case. 2) patients' waiting time satisfaction: checking if the scheduled time for each care service is correctly included in the time window requested by the patients, the maximum value of this part equal to the number of all patients. 3) patients' interoperation satisfaction: similar to 2), it aims at checking the patient's satisfaction in terms of interoperation between the successive requested care services, the maximum value is the same as 2). 4) caregivers' overtime satisfaction: the caregivers' total satisfaction about over working time regarding their legal workload (10h max/day in our case), the maximum value equals the number of all caregivers. 5) caregiver's difficulty balance: the difficulty balancing indicator with respect to the rounds performed by all caregivers. The difficulty of each round is the sum of the care services' weight indicator that performed by a caregiver. The maximum value is approximated to the number of all caregivers.

C. Visualiser

This generator transforms a daily planning result in .csv format into a .json format adapted to AmCharts, a JavaScript library. This library was chosen mainly for its visual aesthetics and implementation flexibility. Different types of charts and axes can easily be manipulated. For example, Bar Charts (Column Series) can be used with nontraditional axes such as Date Axes to create a unique visualization that answers specific needs. Being able to combine axes and chart types as needed is powerful because unique visualizations can be achieved. One way of visualizing a caregiver's round is through a Gantt Chart. Traditionally, these charts are task oriented: each line represents a specific task. In our case, it is more interesting to create a caregiver-oriented chart. This gives an effortless visualization of one's round for a workday. The library's flexibility allows the use of four main elements to answer our needs straightforwardly: Chart Data (.json), a Date Axis (timeline), a Category Axis (caregivers) and a Column Data Series (care services). Once the .csv data is converted to an appropriate .json format through a JavaScript parsing program, and the data is bound to the series correctly, a Gantt Chart is generated.

The JSON data is composed of two types of objects: care service objects, Itinerary Time objects. A JSON object represents a task that will be placed in the Gantt Chart. Task information such as the name of the caregiver, the starting time, the ending time, the duration, the complete title, the difficulty of a care service, the patient concerned by a care service and a color associated to the task. From this formatted data, multiple views of the Gantt Chart have been developed.

The basic view is a simple color code: different colors with the legend for a care service requested by a patient, orange for an itinerary. The care service id is written on its associated task so that the care service is rapidly identified. When the user hovers over a task, a pop up appears. Inside this popup are the following elements:

• The complete title of the task, for clarity.

• The starting time and ending time. This way, the user can get a precise time rapidly without needing an overcrowded Date Axis.

• The duration of the task, so the user does not have to calculate the duration.

In the case of a care service task, there is also:

• The difficulty of the care service, so the user can estimate what effort needs to be put into a care service.

• The patient concerned by the care service.

The Gantt Chart visualization is shown in Fig. 5. The objective is to visualize the result of rounds through a graphic and then, in a second step, to fix the useful indicators to identify the quality of a solution thus presented. To clarify the example shown in Fig. 5, the result show the Gantt chart visualization regarding the solution generated by TS for a use case with 13 care service requested by 6 patients and 3 available caregivers. The daily working round for each caregiver is therefore:

• caregiver 11: 143►61►89►85

• caregiver 41: 20►54►21►50

• caregiver 50 :16►17►23►144►94

The light orange zone shows the itinerary time between the living place of the patients. The color of the care services represents their requestors. For example, there is no travel time between the service 16 and 17 as these 2 services are requested by the same patient ( patient 11). The pop-up shows the complete information for the assigned care service such as

IV. CONCLUSION AND RESEARCH PERSPECTIVES

This research work proposes a decision-making support platform named BLPAD.Core to solve the HHCSRP systematically based on the solution approach and benchmark studies. 3 modules included in BLPAD.Core : 1) Based on the real dataset, case generator is to create a standard structure for feeding our own metaheuristic oriented mathematical formulation, by inspiring the similar open access benchmark among the literature. 2) An optimizer embedding two popular metaheuristics for generating the optimum solutions, which will also allow us to assess comparatively the quality of the solutions generated by these two algorithms in a next step. 3) a visualizer which provides a comprehensive view regarding the solution to the decision maker.

In the future, by using BLPAD.Core, this environment will enable us to draw conclusions on the comparison of the 2 metaheuristics from experimental studies. Then, an indicatorsoriented dashboard will be developed to provide the decision maker an evaluation platform regarding the different optimal solutions. In addition, we wish to enrich our platform by developing an exact method or another approach such as multi-agent systems, to invest the comparisons field between the different resolution approaches in a near-real simulated environment or even a real-environment.

Fig. 1

 1 Fig. 1 Architecture of the research prototype BLPAD.Core

Fig. 4

 4 Fig. 4 Graphical interface of BLPAD.Core -Optimizer

Fig. 3

 3 Fig. 3 BLPAD.Core input and output knowledge metamodel -Case generator and Optimizer

Fig. 5

 5 Fig. 5 Graphical representation under Gantt chart for the solution of a use case: 13 care services performed by 3 caregivers

TABLE I STANDARD

 I PARAMETERS OF THE METAHEURISTICS DEVELOPED IN THE BLPAD.CORE -OPTIMIZER

	Metaheuristic	Algorithmic parameter	BLPAD.Core -Optimizer
		Pheromone evaporation
	Ant Colony
		Pheromone weighting
		Crossover Probability
	Genetic Algorithm	Mutation Probability
		Population size
		Distance Bandwidth
		Memory Size
	Harmony Search	Pitch Adjustment Rate
		Rate of Choosing from
		Memory
	Simulated Annealing	Annealing rate Initial temperature	X
	Tabu Search	Tabu list length	X
	Variable
	Neighborhood	N/A
	Search