Ayman El Jundi

Matthias Mayor

Enrique Folgado

Chaimaa Gomri

Belkacem Tarek Benkhaled

Arnaud Chaix

Pascal Verdie

Benjamin Nottelet
email: benjamin.nottelet@umontpellier.fr

Mona Semsarilar
email: mona.semsarilar@umontpellier.fr

Ayman El Jundi

Pascal Verdié

Peptide-guided self-assembly of polyethylene glycol-b-poly(ϵ-caprolactone-g-peptide) block copolymers

Keywords: Solution self-assembly, ring opening polymerization, click reaction, thiol-yne, block copolymers, peptide, poly(caprolactone), poly(ethylene glycol), temperature induced crystallization induced self-assembly (TI-CDSA)

published or not. The documents may come

Introduction

The control of the structures of polymers in solution is of prime importance in biomedical applications as this structuring defines the activity of the resulting self-assemblies. This is in particular true when peptides are used to guide this structuring as they can confer biofunctionality (eg. collagen like peptides [START_REF] Luo | Collagen-Like Peptide Bioconjugates[END_REF]), or bioactivity (eg. IKVAV for fibroblasts and neurone proliferation [START_REF] Arsenie | Star-poly(lactide)-peptide hybrid networks as bioactive materials[END_REF]) to the self-assemblies. Not surprisingly, PEG has been largely used in peptide-polymer conjugates to evaluate the influence of the selected peptides on the peptideguided structures and formation of supramolecular self-assemblies ranging from micelles, to ribbons, membranes or even fibres. [START_REF] Borner | Strategies exploiting functions and self-assembly properties of bioconjugates for polymer and materials sciences[END_REF] On the other hand, PEG has also largely been used as hydrophilic block in amphiphilic block copolymers that are widely exploited for drug encapsulation and delivery. Among them, PEG-polyester block copolymers having a hydrophobic polylactide (PLA), polyglycolide (PGA, or poly(-caprolactone) (PCL) block are the most studied examples due to their long track record and regulatory acceptance. [START_REF] Lakkireddy | Building the design, translation and development principles of polymeric nanomedicines using the case of clinically advanced poly(lactide(glycolide))poly(ethylene glycol) nanotechnology as a model: An industrial viewpoint[END_REF] However, the combination of peptide-guided structuring and PEG-polyester block copolymers is rarely described and most examples relate to the copolymer chain-end functionalization with a targeting peptide moiety able to enhance the accumulation of the resulting self-assemblies into specific tissues. One of the best examples is the peptide Arg-Gly-Asp under its linear (RGD) or cyclic (cRGD) form that is able to target the integrins present at the surface of cells and overexpressed in most cancer cells and is therefore present in countless drug delivery systems. [START_REF] Alipour | Recent progress in biomedical applications of RGD-based ligand: From precise cancer theranostics to biomaterial engineering: A systematic review[END_REF][START_REF] Nieberler | Exploring the Role of RGD-Recognizing Integrins in Cancer[END_REF] The absence of PEG-polyester peptide guided self-assemblies is in particular true for PCL-based systems. PCL being less degradable and more hydrophobic than PLA and PGA, it is less used to develop novel self-assemblies for biomedical applications. However, these characteristics explain that PEG-PCL copolymers yield highly stable micelles and nanoaggregates, which make them particularly interesting to develop long lasting drug delivery systems. In this frame, PEG-b-PCL copolymers have been end-functionalized with various peptides including RGD for targeted bioimaging, [START_REF] Fang | Targeted glioma chemotherapy by cyclic RGD peptide-functionalized reversibly core-crosslinked multifunctional poly(ethylene glycol)-b-poly (epsilon-caprolactone) micelles[END_REF][START_REF] Wu | cRGD functionalized 2,1,3benzothiadiazole (BTD)-containing two-photon absorbing red-emitter-conjugated amphiphilic poly(ethylene glycol)-block-poly(epsilon-caprolactone) for targeted bioimaging[END_REF][START_REF] Zhou | c(RGDfK) decorated micellar drug delivery system for intravesical instilled chemotherapy of superficial bladder cancer[END_REF] cell penetrating peptide or gliomahoming peptides for enhanced gliomas treatment, [START_REF] Chi | Glioma homing peptide-modified PEG-PCL nanoparticles for enhanced anti-glioma therapy[END_REF][START_REF] Kanazawa | Nose-to-brain drug delivery system with ligand/cellpenetrating peptidemodified polymeric nano-micelles for intracerebral gliomas[END_REF] tumor metastasis targeting for delivery to metastatic cells. [START_REF] Mandaviani | Peptide functionalized poly ethylene glycol-poly caprolactone nanomicelles for specific cabazitaxel delivery to metastatic breast cancer cells[END_REF] Replacing peptides chain end by polypeptides was also recently illustrated with the design of PEG-b-PCL-b-polytyrosine triblock copolymers allowing enhanced drug/polymer interactions, higher drug loading and micelles stability. [START_REF] Guo | A novel polymer micelle as a targeted drug delivery system for 10-hydroxycamptothecin with high drug-loading properties and anti-tumor efficacy[END_REF] Alternatively to the modification at the PEG-b-PCL chain ends, central peptide block is also conveniently reported to yield enzyme-cleavable block copolymers with a sheddable PEG shell. [START_REF] Li | Smart Asymmetric Vesicles with Triggered Availability of Inner Cell-Penetrating Shells for Specific Intracellular Drug Delivery[END_REF] Multi-functionalization with targeting and/or enzyme-cleavable peptides has also been reported in more complex macromolecular topologies including comb and graft PCLbased copolymers to benefit from higher content of peptides and therefore obtain higher biological outputs. [START_REF] Pourcelle | Light-Induced Functionalization of Amphiphilic Block Copolymers: Application to Nanoparticles for Drug Targeting[END_REF][START_REF] Wang | Comb-shaped polymer grafted with REDV peptide, PEG and PEI as targeting gene carrier for selective transfection of human endothelial cells[END_REF][START_REF] Al Samad | Iterative Photoinduced Chain Functionalization as a Generic Platform for Advanced Polymeric Drug Delivery Systems[END_REF] In agreement with the final application as injectable drug delivery systems, all these copolymers were designed to self-assemble into spherical nano-micelles or nano-aggregates. More rarely, such amphiphilic PEG-PCL peptide conjugates have been directly used to generate bioactive materials, like for example RGD-functionalized nanofibers by electrospinning. [START_REF] Grafahrend | Biofunctionalized poly(ethylene glycol)-block-poly(epsilon-caprolactone) nanofibers for tissue engineering[END_REF] These examples clearly illustrate the interest in these PEG-PCL peptide conjugates to induce bioactivity. However, there are only few examples of studies dedicated to the impact of the peptides to physically control the association/dissociation and the morphology of the PEG-PCL self-assemblies. Katz et al. inserted a peptide between the PEG block and the PCL block using an approach inspired by solid-phase peptide synthesis. They prepared photolabile PEG-b-PCL copolymers containing a 2-nitrophenylalanine central unit to generate polymersomes that can undergo UV-induced cleavage. [START_REF] Katz | Modular Synthesis of Biodegradable Diblock Copolymers for Designing Functional Polymersomes[END_REF] In another example, Ding et al. prepared poly(ɛcaprolactone-co-lactide) (PCLA) triblock copolymers (PCLA-PEG-PCLA) able to form hydrogels via bridging of flower-micelles. This triblock was functionalized with cRGD moieties (ca. 10 mol% with respect to polymer chains) located either at both chain-ends via classical amidation, or randomly dispersed along the PEG block thanks to the photo-insertion of 4-(p-azidophenyl)-N-succinimidyl butanoate and subsequent addition of cRGD. Although the impact on self-assembly was not discussed, it was found that the chain conformations and therefore the spatial presentation of the cRGD had an impact on chondrocytes adhesion. [START_REF] Zhang | Effects of immobilizing sites of RGD peptides in amphiphilic block copolymers on efficacy of cell adhesion[END_REF] In this work, we prepared functional PEG-b-PCL copolymers with peptides grafted along the PCL block to investigate the impact of the selected peptides on the self-assembly behavior of the PEG-PCL peptide conjugates. The rational for selecting a functionalization along the PCL backbone and not on the PEG chain-end or between the blocks as reported in the literature is to take advantage of the multi-functionalization of the PCL backbone to enhance the potential impact of the peptides on the self-assembly. Three peptides containing the Phe-Phe motif for Pi-stacking interactions, Tyr-Tyr for Pi-stacking and H-bonding interactions, and Arg-Gly-Asp for H-bonding and electrostatic interactions, have been selected. These three peptides were selected based on their simple structure allowing comparison as a function of the interactions and an easier production, and for the last one its potential bioactivity.

EXPERIMENTAL SECTION

Materials

-methoxy,-hydroxyl poly(ethylene glycol) (PEG2k Mn=2000 g/mol), stannous octoate (Sn(Oct)2, 92.5-100%), ε-caprolactone (CL, 97%), 2.2-dimethoxy-2-phenyl-acetophenone (DMPA, 99%), propargyl bromide (PgBr, 80 wt% in toluene), lithium diisopropylamide (LDA, 2 M in THF/heptane/ethylbenzene) were purchased from Sigma-Aldrich (St-Quentin Fallavier, France). THF was dried using a Pure Solv Micro Single Unit (Inert®) system. Toluene was distilled over CaH2, and DMSO was dried over molecular sieves (4Å) prior to use. PEG was dried by an azeotropic distillation in dry toluene. ε-CL was dried over calcium hydride (CaH2)

for 48 h at room temperature and distilled under reduced pressure. Ac-Cys-Gly-Tyr-Tyr-CONH2 (peptide 1), Ac-Cys-Gly-Phe-Phe-CONH2 (peptide 2) and Ac-Cys-Gly-Arg-Gly-Asp-OH (peptide 3) were provided by the platform Synbio3 (https://ibmm.umontpellier.fr/synbio3/).

Characterizations and methods.

Nuclear magnetic resonance spectroscopy (NMR). 1 H NMR (300 MHz) spectra were recorded on a Bruker AMX300 spectrometer at 25 °C. Deuterated chloroform and deuterated dimethyl sulfoxide were used as solvent, chemical shifts were expressed in ppm with respect to tetramethylsilane (TMS).

Size exclusion chromatography (SEC).

The number-average and weight-average molar masses (Mn and Mw, respectively) and dispersity (Ð, Mw/Mn) of the polymers were determined by SEC using a Viscotek GPCmax VE2100 liquid chromatograph equipped with a Viscotek VE3580 refractive index detector operating at 35 °C. Tetrahydrofuran was used as the eluent and the flow rate was set up at 1.0 ml/min. Two LT5000L 300 x 7.8 mm columns operating at 29°C were used. Calibrations were performed with polystyrene standards. For analyses in DMF, a Waters Inc. equipment fitted with a 5 μm mixed C PLgel 5 μm MIXED-D (300×7.5 mm) operating at 60°C and SHODEX RI 101 refractometric detector was used. The mobile phase was DMF at 0.8 mL/min flow. Typically, the polymer (10 mg) was dissolved in DMF (2 mL) and the resulting solution was filtered through a 0.45 μm Millipore filter before injection of 20 μL of a filtered solution. Calibrations were performed with poly(methyl methacrylate) standards.

Differential scanning calorimetry (DSC).

The thermograms were obtained from a TA instrument Q20 DSC. The dry samples were placed in a sealed pan. The analyses were performed from -100°C to 150°C with a temperature gradient of 10°C/min. The results were analysed using TA Universal Analysis software.

Transmission electronic microscopy (TEM). TEM studies were conducted using a JEOL 1400+ instrument equipped with a numerical camera, operating with a 120 kV acceleration voltage at 25 °C. To prepare TEM samples, a drop (10.0 μL) of micellar solution was placed onto a Formvar/Carbon coated copper grid for 60 s, blotted with filter paper and dried under ambient conditions. All TEM grids were prepared from self-assembly experiment solutions without further dilution.

Dynamic light scattering (DLS). DLS measurements were conducted on an Anton-Paar

Litesizer 500 using a quartz cuvette without further dilution.

Synthesis and characterization of PEG-b-PCL-g-peptides

Synthesis of copolymer PEG-b-PCL (C1).

The amphiphilic PEG-b-PCL diblock copolymers were synthesized by ring opening polymerization (ROP) of ε-caprolactone in toluene at 100°C. -methoxy,-hydroxyl poly(ethylene glycol) and stannous octoate were used as initiator and catalyst, respectively. In a typical procedure, to a solution of PEG2K (3g; 1.5 mmol) in 25 mL of toluene in a Schlenk tube, CL (3g; 26 mmol) and Sn(Oct)2 (0.23 mL, 0.7 mmol) were added. Following freezepump-thaw cycles, the reaction was allowed to proceed for 24 h at 100 °C in a nitrogen atmosphere. The product was precipitated in a large excess of cold diethyl ether. PEG-b-PCL was obtained by filtration and dried 24 h in vacuo at room temperature (copolymer C1, Scheme 1). Yield 87% ). SEC (THF): Mn = 4500 g/mol, Ð = 1.1.

Propargylation of copolymer PEG-b-PCL (C2).

Propagylation of PEG-b-PCL was performed according to a procedure reported by our group. [START_REF] Jundi | Double-Hydrophilic Block Copolymers Based on Functional Poly(epsilon-caprolactone)s for pH-Dependent Controlled Drug Delivery[END_REF] Typically, PEG1900-b-PCL1700 (1g, 4.1 mmol of CL) was suspended in 25 ml of anhydrous toluene under inert gas in a 3-neck flask.

Grafting of peptides on PEG-b-PCL(YNE) (CP1-CP3)

Grafting of peptides on the multi-alkyne functional copolymer was achieved by adapting protocols of our group. [START_REF] Al Samad | Iterative Photoinduced Chain Functionalization as a Generic Platform for Advanced Polymeric Drug Delivery Systems[END_REF] Typically, PEG-b-PCL(YNE) (150 mg, 15% alkyne groups with respect to CL units) and peptide 1 (Ac-Cys-Gly-Tyr-Tyr-NH2 341 mg; 8 eq. with respect to initial alkyne group) were dissolved in 4 mL DMF in a Schlenk flask. In parallel, DMPA (81 mg; 4 eq. with respect to initial alkyne group) was dissolved in 0.5 mL DMF and the solution was protected from light using aluminium foil. The solution of the DMPA was then added to the polymer/peptide solution, the flask was closed by septum and purged with argon for 10 min under nitrogen in the dark. The reaction mixture was then irradiated with UV light. Reaction was carried out for 2 hours under constant stirring and constant UV light irradiation (Dymax Blue wave® 200, 100 mW/cm2). For purification, the reaction mixture was initially diluted with water to reach a 50:50 water/DMF ratio prior to dialysis against water using a centrifugal filter unit (MW cut-off 10 000 Da) (10 cycles of centrifugations). The copolymer was freezedried (copolymer CP1, Scheme 1). Yield 40%. For peptides 2 and 3, the conditions of reaction are listed in Table S2 (copolymer CP2 and CP3, Scheme 1).

Self-assembly of peptide-functionalized copolymers

Preparation of stock solutions

Stock solutions of 0.5 and 1 mg.mL -1 were prepared in DMF and DMSO, at room temperature.

To ensure full solubilization, solutions were left stirring for 3h.

Nanoprecipitation

Glass vials containing 1 mL of non-solvent or selective solvent for the PEG (i.e. water or ethanol) were placed on a stirring plate. To each vial, 0.1 mL of stock solution was added dropwise and left stirring for 1h. The solutions obtained were analysed by DLS and TEM.

Micellization

Vials containing 0.5 mL of stock solutions were placed in a shaker. Water was added slowly using a syringe pump at a fixed rate (0.04mL.min -1 or 2.4 mL.min -1 ). Samples were prepared at 1: 4; 1: 6 and 1: 8 solvent/ non-solvent ratios.

Scheme 1. Synthesis pathway for the preparation of peptide-functionalized copolymers CP1, CP2 and CP3.

RESULTS AND DISCUSSION

Synthesis of copolymers

The copolymers functionalized with peptides were prepared in three steps. First, an amphiphilic PEG2k-b-PCL2k block copolymer was prepared by ring opening polymerization of CL using PEG2k as a macroinitiator (C1, Scheme 1). A molecular weight of 2000 g/mol for the PCL block was targeted and confirmed both by 1 H NMR using the ratio between the integrals of peaks at 3.64 ppm and at 4.05 ppm corresponding to the methylene protons of EG and CL units, respectively (Figure S1). It was also confirmed by SEC with Mn = 4500 g/mol and a low dispersity of 1.1. In a second step, the PCL block was functionalized with alkyne groups by anionic modification of the CL units according to a well-established procedure (C2, Scheme 1). [START_REF] Jundi | Double-Hydrophilic Block Copolymers Based on Functional Poly(epsilon-caprolactone)s for pH-Dependent Controlled Drug Delivery[END_REF] Using LDA and PgBr, 15% of the CL units were functionalized with a pendant propargyl group. This substitution degree was calculated from the 1 H NMR spectra (Figure S2) by comparing the integral of the signal at 2.4-2.6 ppm with the integral of the PCL methylene signal at 4.1 ppm. The 1 H NMR spectrum also showed a limited molecular weight decrease of the PCL block from 2000 g/mol to 1600 g/mol (1% hydrolyzed ester bonds) that was also confirmed by SEC with Mn = 4200 g/mol and a dispersity of 1.3. The final step corresponded to the functionalization of the resulting PEG-b-PCL(YNE) with the selected peptides (Table S1). The grafting of peptides on the backbone of C2 was achieved by thiol-yne photoaddition between the thiol groups of the cysteine moieties present in the peptides and the alkyne groups of C2. Conditions were adapted from our previous work and are summarized in Table S2. [START_REF] Al Samad | Iterative Photoinduced Chain Functionalization as a Generic Platform for Advanced Polymeric Drug Delivery Systems[END_REF][START_REF] Jundi | Double-Hydrophilic Block Copolymers Based on Functional Poly(epsilon-caprolactone)s for pH-Dependent Controlled Drug Delivery[END_REF] The substitution degree was estimated using the 1 H NMR spectra by comparing the integrals of the methylene groups of PCL and the methyl group of the acetamide group at 1.85 ppm present on all peptides and results are listed in Table S2. The photoaddition efficiency was function of the nature of the peptide with 50% of peptide 1 photoaddition for CP1 (Cys-Gly-Tyr-Tyr-NH2 peptide) and 25% for CP3 (Cys-Gly-Arg-Gly-Asp-OH peptide). Grafting and purity were confirmed by DOSY-NMR and SEC as exemplified with CP1 (Figure S6 andS8).

In particular, DOSY-NMR analysis of CP1 showed peaks characteristics of peptide 1 and of C2 at the same coefficient of diffusion (Figure S8). It should be noted that it was not possible to calculate the extent of functionalization for CP2 due to the presence of free residual peptide 2 that was detected as a second peak on the SEC chromatogram despite the purification steps (Figure S6). For CP3 the SEC chromatograms showed three populations with a first low intensity peak corresponding to low amounts of residual free peptide 3, a peak of highest intensity corresponding to the copolymer CP3 and a last peak towards higher molecular weights that was attributed to CP3 aggregates (Figure S6). The grafting of peptide 3 was further confirmed by DOSY-NMR with signals characteristic of peptide 3 and of C2 at the same coefficient of diffusion ((Figure S9). Of notice, free Peptide 3 was not visible on this analysis confirming the low content of non-grafted peptide in CP3. "It should be noted that, the broadening of the distribution and apparent decrease of the molecular weight after peptidefunctionalization was noticed. For example, for CP1 Mn of 2800 g/mol and a dispersity of 2.4

were measured. However, this result should be considered with care as the hydrodynamic behavior of the copolymers is known to be strongly affected by their amphiphilicity and architecture. This is why the presented copolymers with changes of chain conformations due to both a shift from a linear PEG-b-PCL(YNE) to a polymer with bulky grafted peptides and a change of amphiphilicity that depends on the peptides nature."

Self-assembly

The synthesized peptide functionalized copolymers were self-assembled via two pathways: micellization (gradual addition of non-solvent to the polymer solution) or nanoprecipitation (addition of polymer solution to non-solvent). Due to the difficulties encountered to purify CP2 that contained high amount of free peptide 2 despite purification steps, this copolymer was not further investigated in this part. Both CP1 and CP3 were soluble in DMF and DMSO. CP1 and CP3 were designed to be amphiphilic thanks to the PCL hydrophobic block and the PEG hydrophilic block. The difference resides in the nature of the pending peptides on the PCL segment. Having two tyrosine per substituent, CP1 is expected to present Pi-stacking and Hbonding interactions. [START_REF] Neffe | Knowledge-Based Tailoring of Gelatin-Based Materials by Functionalization with Tyrosine-Derived Groups[END_REF] In contrast, the CP3 with arginine and aspartic acid amino acids is expected to exhibit only H-bonds.

CP1 Micellization

DMF was used as the common solvent for the blocks and water as a non-solvent (selective solvent for PEG). Different ratios of solvent/ non-solvent were used. A mother solution with concentration of 1 mg / mL in DMF was used and 1: 4; 1: 6 and 1: 8 ratios of solvent/ nonsolvent were prepared. For the ratio 1: 4, particles of 20 nm and 1µm were detected by DLS.

For the other two ratios, particles of 30 nm and 1.5µm were measured. TEM images of these samples showed mainly aggregates (Figure 1). Spherical particles and nanoaggregates of different size were detected for the three ratios tested. Some flat structures were also observed for 1: 6 and 1: 8 ratios (Figure 1D-E). One reason for the ill-defined structures observed could be the poor solubility of the PCL block in DMF. [START_REF] Bordes | Determination of poly(epsilon-caprolactone) solubility parameters: Application to solvent substitution in a microencapsulation process[END_REF] The same behaviours was observed for the PEG-b-PCL (C2) with no grafted peptide used as the control reference (Figure S10). 1:8 ratio. The scintillating dots (Figure 2A) suggests certain degree of crystallinity. This is certainly due to the crystalline PCL (Figure S13). It was observed that the structure became amorphous after being exposed to the electron beam. This is due to the thin self-assembled structure.

In order to increase the solubility of the PCL block, instead of DMF, DMSO was used. [START_REF] Bordes | Determination of poly(epsilon-caprolactone) solubility parameters: Application to solvent substitution in a microencapsulation process[END_REF] The self-assembly in 1:4 ratio of DMSO/ H2O resulted in the formation of two populations; nanoobjects around 30 nm along with larger objects with average size of 2µm as measured by DLS.

These size where in agreement with the size observed in TEM images. As shown in Figure 3, well defined large lamellar micelles along with small spheres could be seen. Increasing the water content did not change the morphology. This is most probably due to the combination of the crystallinity of the PCL at room temperature and of the potential strong interactions between the tyrosine groups (Pi-stacking and H-bonding) that both could inhibit the evolution of the morphology. In addition, the high substitution degree of substitution of CP1 the tyrosinefunctionalized PCL block could lead to behaviors close to the ones of PEG-b-Poly(tyrosine) recently reported that lead to supramolecular assemblies such as micelles, fibrils or even βamyloid structures as a function of the hydrophilic/hydrophobic balance. [START_REF] Iakimov | Evaluation of critical packing parameter in the series of polytyrosine-PEG amphiphilic copolymers[END_REF] It should be noted that using the same conditions with C2 did not result in formation of such lamellar micelles, confirming the role of the Tyr-Tyr moieties in driving the self-assembly of CP1 (Figure S11). Next, micellization of PC1 in DMF/ H2O was carried out in a sonication bath at 60 °C, under temperature-induced crystallization-driven self-assembly (TI-CDSA). [START_REF] Li | Temperature-induced and crystallization-driven self-assembly of polyethylene-b-poly(ethylene oxide) in solution[END_REF] Performing the selfassembly at 60 °C mean that the PCL block would be at molten state. As observed under TEM, this time crystalline individual needles of 250 nm along with bundles of them resembling sea urchins were formed (Figure 4). These needles are definitely the result of self-assembling chains while PCL was at molten state and the gradual cooling and crystallization.

CP1 Nanoprecipitation

Nanoprecipitation was performed first with DMF/ H2O. As shown in Figure 5, similar flat lamella objects were formed as in the case of micellization (Figure 1 and3). The DLS results

were very different from the results observed in TEM. This difference is mainly due to the shape of the nano-objects that are far from the spherical morphology model inbuilt in the DLS software. Repeating this self-assembly path using a sonication bath at 60°C, well-defined multilamellar micelles of different size (2-3µm) were formed. The dark centres and lighter edges suggest that several different layers of different size, flat lamellar micelles have over lapped upon drying (Figure 6). As in the case of micellization, such structures were not observed for C2 (Figure S12). Changing the non-solvent (selective solvent for PEG) to ethanol did not result in formation of well-defined objects either as mainly aggregates were observed (Figure 7). Changing the solvent mixture to DMSO/ water or ethanol, only resulted in the formation of not very defined aggregates (Figure 8). As presented above CP1 mainly formed lamellar structures in the solvent/ non-solvent pairs tested. Although, using the TI-CDSA at 60 °C resulted in formation of more defined lamellar structures. DMSO/ethanol at ratio of 1:4.

CP3 Micellization

As in the case of CP1 same solvent/ non-solvent system along with self-assembly pathways were used. The self-assembly using DMF/ H2O at different ratios of 1: 4; 1: 6 and 1: 8 from a 1 mg/mL polymer solution resulted in formation of aggregates of 2 µm no matter which solvent/ non-solvent ratio was used as judged by DLS. Even lowering the concentration of the polymer solution to 0.5 mg/mL did not change the size of the aggregates. TEM images (Figure 9) also confirmed the formation of large flat aggregates. Keeping the CP3 stock solution concentration constant while changing the solvent/ non-solvent ratio (Figure 9 A, C, D) as well as changing the polymer concentration while keeping the same solvent/ non-solvent ratio (Figure 9 A-B)

did not change the size or the morphology of the structures. Electron diffraction on micelles presented in Figure 9A, showed scintillating dots (Figure 10) suggesting some degree of crystallinity.

CP3 Nanoprecipitation

Nanoprecipitation was performed in water or ethanol from a solution of CP3 dissolved in DMF

(1 mg/mL). When nanoprecipitation was carried out using magnetic stirring, flat ribbons were formed. They looked disconnected, as if flat narrow layers of self-assembled micelles were overlapping to form long fibres (Figure 12 A-B). Next, the self-assembly was carried out in an ultra-sonication bath at 60 °C. As shown in Figure 12 C-D, large flat structures with dark centres were observed. Formation of such structures are more likely due to the fact that the selfassembly took place above the melting point of the crystalline PCL. Being at molten state, along with gradual cooling allows the slow re-crystallization of the PCL chains, giving time to the entire system to self-assemble into a more defined morphology. Changing the non-solvent to ethanol (with magnetic stirring) did not allow formation of well-defined structures as many aggregates could be seen on the TEM grid (Figure 12 E-F). The DLS analysis of these samples were not conclusive as the structures are very irregular.

Finally, the self-assembly via nanoprecipitation was repeated using DMSO as the good solvent.

When both water and ethanol were used as the non-solvent, instead of fibrous structures (as in the case of DMF/ water) only ill-defined spheres and some bilayers were formed (Figure 13).

These results suggest that DMSO is not as good solvent for CP3 as compared to CP1, since well-defined objects were formed with CP1 using DMSO as the solvent. Comparing these results we could say that as in the case of CP1 a more efficient stirring method (sonication) and performing the self-assembly above the melting point of the PCL results in formation of better defined and more stable structures. This is explained by the higher substitution degree of CP1 compared to CP3, and the nature of the peptides. For CP1 the Tyr-Tyr peptide allows Pi-Pi stacking and H-bonding and a more hydrophobic character of the functional PCL block, leading to more defined structures. In contrast, with the hydrophilic RGD only H-bonding is expected in the considered conditions, with a lower hydrophobic character of the functional PCL block, leading to less defined structures. Table 1. Summary of optimised morphologies and self-assembly conditions for the three copolymers studied.

Conclusions

The self-assembly of two amphiphilic PEG-b-PCL copolymers functionalized along the PCL block by peptides pending groups (with Tyr-Tyr or RGD units) was studied. Self-assembly was performed using two pathways; micellization and nanoprecipitation. Factors such as solvent / non-solvent system and ratio, concentration, temperature and stirring during self-assembly were studied and optimized. It was observed that using the ultrasonic bath at 60 °C, close to the melting temperature of the PCL block (60-65 °C), induced the formation of well-defined flat micelles and needles upon cooling. Such self-assembly is induced by the crystallization of the crystalline PCL blocks forming the core of the objects. Concentration does not play a very important role and the effect of working with more dilute stock solutions did not improve results. On the other hand, the solvent used to solubilize the copolymer is important. DMSO seems to be a better solvent for the micellization of the two systems studied (better solvent for the PCL block) unlike the results of the nanoprecipitation where DMF results in better-defined structures. However, the impact of the non-solvent was important since with water defined micelles were formed as opposed to ethanol (at room temperature ethanol is a bad solvent for the PEG block and not a good solvent for the peptide). Based on the comparison with the PEGb-PCL control, it could be stated that the presence of the peptide sequence is having a major effect on the self-assembly, since no defined structures were observed with PEG-b-PCL in opposition to the peptide-functional copolymers. The influence of the nature of the peptide was also very important for the self-assembly since among the 2 different peptide sequences tried the Tyr-Tyr directed the self-assembly toward the formation of more defined and stable structures due to its higher hydrophobicity and combination of Pi-Pi stacking and H-bonding.

1 H

 1 NMR CP1 (300 MHz, DMSO-d6): δ =8.5-7.5 (m, NHCO), 7.5-7.0 (m, CH ar and NH2), 4.50-4.25 (m, NHCHCO and -OH), 4.05 (t, CH2CH2OCO), 3.75 (m, NHCH2CO), 3.64 (m, OCH2CH2O), 3.20-2.60 (m, CHCH2), 2.30 (t, COCH2CH2), 1.85 ppm (s, CH3CO) 1.65 (m, COCH2CH2CH2CH2CH2O), 1.39 (m, COCH2CH2CH2CH2CH2O). SEC (DMF): Mn = 2800 g/mol, Ð = 2.4.

Figure 1 :

 1 Figure 1: TEM images of self-assembled CP1 via micellization in DMF/H2O at ratios of (A-B) 1:4 (C-D) 1:6 (E-F) 1:8.

Figure 2 .

 2 Figure 2. Diffraction pattern and TEM image of CP 1 with lamella flat structure.

Figure 2 ,

 2 Figure 2, shows the diffraction pattern of the flat lamella structure observed for the DMF/H2O

Figure 3 .

 3 Figure 3. TEM images of self-assembled CP1 via micellization in DMSO/H2O at ratio of 1:4.

Figure 4 .

 4 Figure 4. TEM images of self-assembled CP1 via TI-CDSA in DMF/H2O at ratio of 1:4.

Figure 5 .

 5 Figure 5. TEM images of self-assembled CP1 via nanoprecipitation in DMF/H2O at ratio of 1:4.

Figure 6 .

 6 Figure 6. TEM images of self-assembled CP1 via TI-CDSA in DMF/H2O at ratio of 1:4.

Figure 7 .

 7 Figure 7. TEM images of self-assembled CP1 via nanoprecipitation in DMF/ethanol at ratio of 1:4.

Figure 8 .

 8 Figure 8. TEM images of self-assembled CP1 via nanoprecipitation in (A) DMSO/H2O, (B)

Figure 9 .

 9 Figure 9. TEM images of self-assembled CP3 via micellization in DMF/H2O from (A) 1mg/mL in 1:4 (B) 0.5 mg/mL in 1:4 (C) 1mg/mL in 1:6 (D) 1mg/mL in 1:8.

Figure 10 .

 10 Figure 10. Diffraction pattern and TEM image of CP3 with lamella structure.

Figure 11 .

 11 Figure 11. TEM images of self-assembled CP3 via micellization in DMSO/H2O at 1:4.

Figure 12 .

 12 Figure 12. TEM images of self-assembled CP3 via nanoprecipitation in (A-B) DMF/H2O at 1:4 using magnetic stirring, (C-D) DMF/H2O at 1:4 using sonication bath (60 °C), (E-F) DMF/ethanol at 1:4 using magnetic stirring.

Figure 13 .

 13 Figure 13. TEM images of self-assembled CP3 via nanoprecipitation in (A) DMSO/H2O at 1:4 (B) DMSO/ethanol at 1:4 using magnetic stirring.

  After cooling to -50°C, a solution of LDA (2.1 mmol, 0.5 eq. per CL unit) in a mixture of THF/heptane/ethylbenzene was added under agitation via injection through a septum. After stirring for 15 min at -50 °C, a solution of PgBr (8.2 mmol, 2 eq. per CL unit) in toluene was added. The reaction was quenched after 15 min by addition of 1 M HCl solution until neutral pH. The crude reaction mixture was transferred

	to a dialysis bag (MWCO 3500 g/mol, Spectra-Por) and dialyzed against a mixture of water and
	acetone (1/1, v/v) for 1 d. After evaporation of acetone under reduced pressure, PEG-b-
	PCL(YNE) was obtained by lyophilization (copolymer C2, Scheme 1). Yield 85%.
	1 H NMR (300 MHz, CDCl3): δ = 4.1 (t, CH2CH2OCO), 3.65 (m, OCH2CH2O), 3.33 (s, CH3O),
	2.6-2.4 (m, COCHCH2CCH and CH2CCH), 2.30 (t, COCH2CH2), 2.0 (s, CH2CCH), 1.85 (m,
	COCHCH2CH2CH2CH2O),	1.65	(m,	COCH2CH2CH2CH2CH2O),	1.38	(m,
	COCH2CH2CH2CH2CH2O). SEC (THF): Mn = 4200 g/mol, Ð = 1.3. Substitution degree with
	respect to CL units 15% (from NMR analysis).

Acknowledgements

The authors also thank CNRS for funding this work via the "Osez l'interdisciplinarité-2017" programme awarded to MS.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

TOC

Peptide-guided self-assembly of polyethylene glycol-b-poly(-caprolactone-gpeptide) block copolymers


L Bodizs

M Titica

N Faria

B Srinivasan

D Dochain

D Bonvin

Oxygen Control for an Industrial Pilot-scale Fed-batch Filamentous Fungal Fermentation

Keywords: Bioprocesses, Filamentous fungal fermentation, Rheological properties, Oxygen control, Dissolved oxygen setpoint, Cascade control

Industrial filamentous fungal fermentations are typically operated in fed-batch mode. Oxygen control represents an important operational challenge due to the varying biomass concentration. In this study, oxygen control is implemented by manipulating the substrate feed rate, i.e. the rate of oxygen consumption. It turns out that the setpoint for dissolved oxygen represents a trade-off since a low dissolved oxygen value favors productivity but can also induce oxygen limitation. This paper addresses the regulation of dissolved oxygen using a cascade control scheme that incorporates auxiliary measurements to improve the control performance. The computation of an appropriate setpoint profile for dissolved oxygen is solved via process optimization. For that purpose, an existing morphologically structured model is extended to include the effects of both low levels of oxygen on growth and medium rheological properties on oxygen transfer. Experimental results obtained at the industrial pilot-scale level confirm the efficiency of the proposed control strategy but also illustrate the shortcomings of the process model at hand for optimizing the dissolved oxygen setpoints.

Introduction

Filamentous fungi are among the most frequently used cell factories in the fermentation industry. Their success is due to the relatively well-established fermentation technology and the versatility of strains available, thus allowing the production of a wide variety of products: primary metabolites, antibiotics, enzymes, and proteins [START_REF] Mcintyre | Metabolic engineering of the morphology of Aspergillus[END_REF].

Traditionally, filamentous fungal fermentations are operated in fed-batch mode, with the feed rates being manipulated manually. As a result of the filamentous structure of the biomass, its concentration is considerably higher than in other biological processes. High biomass concentration induces high viscosity, which makes oxygen transfer difficult [START_REF] Li | Fungal morphology and fragmentation behavior in fed-batch Aspergillus oryzae fermentation at the production scale[END_REF]. In addition, other factors such as the initial properties of the biomass (inoculum) can lead to situations with insufficient oxygen and lower performance of the microorganisms. The goal of this work is to propose an oxygen control strategy that ensures high productivity and limits the risk of running into oxygen limitation.

Usually, the level of dissolved oxygen (DO) is controlled by manipulating the airflow or the stirrer speed. However, when applied to large-scale industrial reactors, which is the ultimate goal of this work, this strategy often leads to unacceptable power consumption. Additionally, this culture is rather shear sensitive because of the filamentous structure of the microorganisms. Hence, in these cases, the dissolved oxygen concentration can be controlled by limiting its consumption [START_REF] Oliveira | Design of a stable adaptive controller for driving aerobic fermentation processes near maximum oxygen transfer capacity[END_REF], [START_REF] Simon | Identification and control of dissolved oxygen in hybridoma cell culture in a shear sensitive environment[END_REF], [START_REF] Chung | Design of metabolic feed controllers: Application to high-density fermentations of Pichia pastoris[END_REF]. This is achieved by manipulating the substrate feed rate, i.e. the feed of the substance being oxidized. Both manual and PID control have been used for regulating the dissolved oxygen concentration, but the range in which this concentration could be confined is fairly wide. One way to cope with this difficulty is to operate with a sufficiently high setpoint for oxygen concentration so that, despite these large variations, oxygen limitation does not occur. However, this policy corresponds to feeding less substrate, which reduces production and is economically unacceptable. Hence, the objective is to control oxygen concentration tightly at a reasonably low setpoint so that oxygen limitation can be avoided without sacrificing production. Consequently, the objective of this project is twofold: i) optimization to determine a setpoint profile that maximizes production, and ii) control to follow this setpoint while avoiding oxygen limitation.

The first objective is addressed by solving a model-based optimization problem. A first-principles model of the filamentous fungal (α-amylase producing strain of Aspergillus oryzae) fermentation process is proposed in [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF], while a data-driven model is described in [START_REF] Rasmussen | Experimental investigation of data-driven modelling for control of fed-batch cultivation[END_REF]. Here, the former is utilized. This first-principles model is morphologically structured and provides a description of biomass, glucose and enzyme concentrations of submerged cultures of fil-amentous fungi without oxygen limitation. However, since oxygen dynamics are crucial in the operation of fed-batch cultivations, the influence of dissolved oxygen limitation on the biomass and enzyme production needs to be incorporated. These effects are included in the model, which is fitted and validated on experimental data from fed-batch fermentations provided by Novozymes, Denmark.

The control objective is met by a cascade-type controller. The poor performance of standard PID control can be attributed to the fact that it only uses information on the controlled variable, though much more information is available via auxiliary measurements such as the oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER). Hence, the idea to incorporate some of these measurements in the control algorithm. By analyzing the structure of the process model, a simple cascade control scheme is proposed, whereby the outer-loop oxygen controller provides the setpoint for the OUR/CER signal that is controlled in the inner loop.

Experimental results show that the setpoint chosen by model-based optimization is not appropriate for the real process. Though the model was fitted and validated on experimental data, its extrapolative power remains poor due to plant-model mismatch. However, the cascade controller is quite effective in keeping the dissolved oxygen in a tight range.

The paper is organized as follows. Section 2 describes the process under consideration and its operation in industry. Section 3 details a first-principles model of filamentous fungal fermentation and develops oxygen transfer relationships. Oxygen control is considered in Section 4, with optimization to determine the DO setpoint and cascade control for its regulatation. Section 5 presents experimental results carried out in a pilot plant at Novozymes. Finally, conclusions are provided in Section 6.

Process Description and Industrial Practice

Fungal Fermentation

The process studied in this paper is the α-amylase production by Aspergillus oryzae. The same substrate is consumed for both biomass growth and enzyme production. The main difficulty with this process is oxygen limitation in the liquid phase. This depletion is usually caused by high biomass concentration, which, due to its filamentous structure, increases the viscosity and makes oxygen transfer difficult.

Current Operation

The fermentation at Novozymes Pilot Plant, (Bagsvaerd, Denmark) is carried out in a 2500 L stirred vessel. pH is controlled through dosing ammonia (g) and phosphoric acid. The fermenter is aerated at the constant rate of 1 vvm and agitation speed of 275 rpm. Temperature and pressure are kept at a constant level by the process control system DeltaV, from Fisher Rosemount.

The typical way of operating the fermentation process is presented in Figure 1. For the sake of confidentiality, the experimental results have been normalized and thus no measurement units are presented. The substrate feeding policy takes into account the problem of oxygen limitation and consists of:

(1) a batch or growth phase, during which the substrate concentration is reduced from a high initial value to its operational range, (2) a linearly-increasing feed rate whose role is to avoid oxygen limitation in the early phase of the fed-batch, and (3) a 'constant' feed rate that is chosen in order to exactly fill the reactor in the remaining operation time and keep the dissolved oxygen around the desired value DO desired = 25.

As can be seen in Figure 1, the range of dissolved oxygen is fairly wide (20-40%). Also, towards the end of the batch, increasing the feed rate causes oxygen limitation. A larger feed rate means more biomass, higher viscosity and thus reduced oxygen transfer. This phenomenon has been encountered and analyzed by the biologists in Novozymes. It can be explained as follows.

Once under oxygen limitation, the biomass changes morphology, whereby the viscosity of the medium increases significantly. However, this increase in viscosity reduces oxygen transfer even more. This positive feedback effect leads to lower and lower oxygen levels and eventually to the death of the microorganisms. Hence, if tight oxygen control is not ensured, the risk of running into oxygen limitation is very high.

Measurements

The measurements available are the volume V , the viscosity η, the dissolved oxygen pressure DO, the aeration rate Q g , the amount of oxygen consumed ∆[O 2 ], and the amount of carbon dioxide produced ∆[CO 2 ].

The volume is calculated from weight measurements, assuming constant density throughout the fermentation. The viscosity is determined by a viscosimeter Hydramotion, York England. DO is determined by an electrode Ingold, from Mettler Toledo. The oxygen and carbon dioxide concentrations in the exhaust gases are determined by a mass spectrometer VG Prima dB, from Thermo.

The oxygen uptake rate OUR and the carbon dioxide evolution rate CER are determined from gas analysis. The inlet flow rate is measured, as are the mass fractions of oxygen and carbon dioxide in the inlet and the outlet flows. By using these quantities and a nitrogen (inert) balance, the volumetric output gas flow rate G out can be determined as follows:

G out y N 2 ,out = G in y N 2 ,in (1)
G out = G in 1 -y O 2 ,in -y CO 2 ,in 1 -y O 2 ,out -y CO 2 ,out -y W,out (2)
where The output water mass fraction can be be calculated from the dilution of oxygen measurement, by purging the reactor without reaction [START_REF] Herwig | On-line exploitation tools for the quantitative analysis of metabolic regulations in microbial cultures[END_REF]:

G
y W,out = y O 2 ,in -y O 2 ,out (3)
Once the output gas flow rate has been computed, OUR and CER can be determined from balance equations without accumulation terms:

OUR = G in y O 2 ,in -G out y O 2 ,out V ρ M O 2 (4) CER = G out y CO 2 ,out -G in y CO 2 ,in V ρ M CO 2 ( 5
)
where ρ is the average density of the gas flow, while M O 2 and M CO 2 are the molecular weights for oxygen and carbon dioxide, respectively.

Note that, in general, an acceptable approximation is to simply consider OUR ≈ OT R, since the solubility of oxygen is very low [START_REF] Pedersen | k L a characterization of industrial fermentors[END_REF]. Typically, the same does not hold for CER and CT R since the solubility of carbon dioxide depends on the physical and chemical properties of the medium, such as temperature and pH. However, since here the fermentor is operated at constant temperature, pressure and pH in the fed-batch phase (Figure 1), it can be assumed that the rate at which CO 2 is formed by microbial metabolism corresponds to the carbon dioxide transfer rate and thus CER ≈ CT R.

Filamentous Fungal Fermentation Model

In this section, the influence of dissolved oxygen is incorporated within the kinetic equations using Monod expressions, and an additional state -for dissolved oxygen -is introduced in the model.

Morphology and Rate Expressions

Growth kinetics. The morphologically structured model proposed by [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF] is based on the division of the biomass into three different compartments:

• Active region (X a ) -responsible for the uptake of substrate and growth of the hyphal elements. It is assumed that only the active region is responsible for enzyme production. • Extension region (X e ) -responsible for new cell wall generation and extension. • Hyphal region (X h ) -the degenerated part of the hyphal elements that is inactive.

The macroscopic reactions for growth and production can be expressed as:

S + O 2 Xa → X e (6) S + O 2 Xe → X a (7) X a → X h (8) S + O 2 Xa → P (9)
where S stands for the substrate (glucose), O 2 for the dissolved oxygen and P for the product (α-amylase).

The corresponding kinetic expressions read:

Branching (Equation ( 6)):

q 1 = x a DO DO + K DO k 1 s a t (s + K s1 ) (10)
Growth of the active region (Equation ( 7)):

q 2 = a t x e DO DO + K DO k 2 s s + K s2 (11)
Differentiation (Equation ( 8)):

q 3 = k 3 x a ( 12
)
The specific growth rate of total biomass is:

µ = q 2 x t ( 13
)
where x t = x e + x a + x h represents the total biomass concentration, x e , x a and x h are the concentrations of the extension, active and hyphal zones, respectively, s and DO are the substrate and dissolved oxygen concentrations, a t represents the number of tips per unit mass of the extension zones. The parameter a t is described as a function of µ (see [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF][START_REF] Bodizs | Optimal feeding strategy for bioreactors with biomass death[END_REF] for details concerning the morphological model). The kinetic expressions and the model parameters are presented in Appendix A.

Specific rate of enzyme production. Enzyme production in filamentous fungi is a classical example of growth-associated product formation. The enzyme production is subject to glucose (substrate) inhibition and oxygen limitation:

r ps =   µ 0 s K s + s + s 2 K I + k c s s + K cor   DO DO + K DO ( 14
)
The expression used in [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF] describes the substrate inhibition by an exponential decrease in the specific production rate of the enzyme when the substrate concentration exceeds a certain threshold value. In this study, the expression of the specific rate of enzyme production is modified by using a Haldane expression to describe the substrate inhibition. This modification has been motivated by the application of an extremum-seeking controller to this process [START_REF] Titica | Adaptive extremum-seeking control of enzyme production in filamentous fungal fermentation[END_REF]. The parameter k c quantifies the constitutive level of enzyme production at high glucose concentrations (during the batch phase).

The specific rate of dissolved oxygen consumption is expressed as:

r DO = Y XO q 2 x t + Y P O r ps x a x t + m o DO DO + K DO ( 15
)
where Y XO and Y P O are the yields of dissolved oxygen consumption for growth and enzyme production, respectively, and m o is the maintenance coefficient that represents the oxygen consumption of biomass.

The specific rate of substrate consumption is expressed as:

r s = Y XS q 2 x t + Y P S r ps x a x t + m s DO DO + K DO ( 16
)
where Y XS and Y P S are the yields of substrate consumption for growth and enzyme production, respectively, and m s is the maintenance coefficient (based on the total amount of biomass).

Mass Balance Equations

The model proposed in [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF] consists of a set of five balance equations for the three regions of biomass, the substrate and the product concentrations, as given in equations ( 17) -( 19). An additional mass balance is included here to describe the dissolved oxygen concentration in the bioreactor (20). Furthermore, eq. ( 21) describes the bioreactor volume that varies with time and determines the end of the fermentation process.

Morphological states x e , x a and

x h ẋe = q 1 -F V x e , x e (0) = x e0 ẋa = q 2 -q 1 -q 3 -F V x a , x a (0) = x a0 ẋh = q 3 -F V x h , x h (0) = x h0 (17) Glucose s ṡ = -r s x t + F V (s f -s), s(0) = s 0 (18) Enzyme p ṗ = r ps x a -F V p, p(0) = p 0 (19) Dissolved oxygen DO ḊO = -r DO x t + k L a(DO * -DO) - F V DO, DO(0) = DO 0 (20) Volume V V = F -F evap , V (0) = V 0 (21)
In these equations, F represents the substrate feeding rate, s f is the substrate concentration in the feed, F evap is the evaporation rate, k L a the specific gasliquid mass transfer coefficient for oxygen, and DO * the oxygen saturation concentration.

The model parameters and their numerical values are given in Appendix A.

The parameters related to the microscopic morphology ( 10)-( 11) are taken from [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF]. The kinetic parameters for the Haldane expression [START_REF] Dochain | State and parameter estimation in chemical and biochemical processes : A tutorial[END_REF] are identified by fitting the model to simulated data generated by the model in [START_REF] Agger | Growth and product formation of aspergillus oryzae during submerged cultivations: Verification of a morphologically structured model using fluorescent probes[END_REF]. The yield coefficients Y XS , Y P S , Y XO , Y P O are identified from experimental data provided by Novozymes. The data used for model fitting include both on-line measurements (DO, viscosity, OUR, CER, and V ) and off-line measurements (p and x t ).

Modeling Oxygen Transfer

The effect of oxygen on growth and production is crucial due to the positive feedback effect mentioned in Section 2.2. Hence, it is necessary to understand and model the factors that affect oxygen transfer. This will be done via an empirical model that relates k L a to the state variables x t and DO. This link will be established through the viscosity and consists of various steps:

(1) Estimation of k L a. In stirred bioreactors, the oxygen transfer coefficient, k L a, depends on the impeller characteristics and the rheological properties of the fermentation medium. The value of k L a can be determined experimentally by the dynamic OTR method (oxygen transfer rate measurement) that gives an average k L a value for the bioreactor [START_REF] Moser | Bioprocess Technology. Kinetics and Reactors[END_REF]. Online measurements of oxygen transfer rate (OTR), viscosity, and DO are available, as well as off-line measurement of the total biomass x t . The k L a-value is calculated as:

k L a = γ OT R (DO * -DO) ( 22
)
where γ is a proportionality factor. (2) Calibration of k L a as a function of viscosity. An empirical relationship between k L a and viscosity is determined experimentally. Under maximum air flow rate and constant agitation speed, the substrate feed rate is varied in such a way that oxygen limitation occurs. k L a is estimated as mentioned above and viscosity is measured. The relationship can be approximated by the linear equation (Figure 2):

k L a = c 0 -c 1 η ( 23
)
where η represents the on-line measurement of viscosity, and c 0 and c 1 are linear regression coefficients (R 2 = 0.94).

(3) Calibration of viscosity as a function of x t and DO. The use of eq. ( 23) in the dynamic model ( 17) -(21) requires knowledge of viscosity. For a given stirrer speed, the viscosity of the filamentous suspension is influenced by two main factors: the biomass concentration and the fibrous structure of the biomass. Due to the lack of quantification of the fibrous structure, the viscosity is simply regressed with available experimental data.

A linear relationship between viscosity and biomass concentration is adequate to represent experimental observations (data not shown). This is also in agreement with literature data for fermentations of Penicillium chrysogenum and Aspergillus niger [START_REF] Moser | Bioprocess Technology. Kinetics and Reactors[END_REF]. Nevertheless, this relation can be improved by introducing the effect of dissolved oxygen to give:

η = η 0 + a X x t -a DO DO ( 24
)
where η 0 , a X , and a DO are linear regression coefficients (R 2 = 0.84). A negative effect of DO on the viscosity is found. This effect can be explained intuitively by the behavior of the filamentous organisms considered in this paper. Following a decrease in the DO level, the microorganisms react by 'reaching out for air', that is changing their fibrous structure so as to increase the zone of the reaction mass from where they can absorb oxygen. As a consequence, viscosity increases (see Section 2.2). Also, when the level of DO is high, there is enough 'air to breathe' within the immediate neighborhood, so there is no need to stretch any further, thereby keeping viscosity low. The performance of the viscosity model is shown in Figure 3.

In summary, by combining equations ( 23) and ( 24), it is possible to model the oxygen transfer coefficient k L a in terms of total biomass and dissolved oxygen. The accuracy of the DO prediction using equation (20) to model the dynamics of DO and equations ( 23) and (24) to express k L a in terms of x t and DO is presented in Figures 4 and5 for two different data sets. It is seen that the oxygen model performs satisfactorily.

The simulated behavior of the reactor is presented in Figure 6. It can be observed that the substrate concentration is much higher at the beginning, in the batch phase, than later on, in the fed-batch phase. This strategy favors biomass growth in the batch phase and production in the fed-batch phase. It is also observed that, in the fed-batch phase, the amount of inactive biomass X h increases. As a consequence, the viscosity of the medium increases, leading to a decrease of the oxygen transfer rate (k L a decreases). This decrease, in turn, reduces the dissolved oxygen concentration, which might lead to oxygen limitation.

Oxygen Control

Setpoint Computation for Dissolved Oxygen

The model given in the previous section can be used to determine the dissolved oxygen profile that would maximize the bioreactor performance while avoiding oxygen limitation. This optimization problem can be formulated mathematically as follows [START_REF] Titica | Modeling and optimization of fed-batch filamentous fungal fermentation[END_REF]: min 23), ( 24)

F (t),t f t f (25) s.t. (10) -(21), (
p(t f )V (t f ) ≥ [p(t f )V (t f )] min V (t f ) ≤ V max F min ≤ F (t) ≤ F max
where t f is the final time, [p(t f )V (t f )] min is the minimum amount of enzyme to be produced, V max is the maximum volume, F min and F max are the minimum and maximum feed rates, respectively.

Note that this optimization can be performed once before the beginning of the batch or repeated several times during the batch. If the optimization is repeated, the available measurements can be used in the optimization via a software sensor that estimates the current states (Figure 7). In this study, a software sensor based on open-loop model prediction is used [START_REF] Dochain | State and parameter estimation in chemical and biochemical processes : A tutorial[END_REF]. This software sensor is based on the model used for optimization, except that the equations corresponding to the measured states DO and V are discarded since the state values are known from measurements. Furthermore, k L a is computed as in equation ( 22).

Usually, the goal of such an optimization is to compute the control inputs directly [START_REF] Srinivasan | Dynamic optimization of batch processes: I. Characterization of the nominal solution[END_REF]. In this study, however, not the feed rate profile F (t) but the dissolved oxygen profile DO(t) is sought. This profile is used as reference profile for the cascade controller to be discussed in the next subsection. The strategy is illustrated in Figure 7.

Cascade Control

A cascade control structure is chosen since it has been observed experimentally at Novozymes that simple output controllers for DO control do not perform well. Hence, additional measurements are sought to improve the control performance. The auxiliary measurements that are available for this process are pH, pressure, viscosity, V , OUR and CER. Since pH and pressure have not been incorporated in the model and the viscosity sensor is not always reliable, the idea is to develop a control strategy that uses the OUR, CER and V measurements.

An interesting feature can be taken from the oxygen dynamics. The feed rate has two main effects on the dissolved oxygen concentration: (i) an immediate effect through dilution (the last term on the right-hand side of eq. ( 20)) since increasing F decreases DO, and (ii) integral effect through oxygen consumption (first term) since increasing F increases the amount of substrate in the reactor and thus also its consumption, which in turn decreases DO. Furthermore, the influence of F on the oxygen transfer between the gaseous and the liquid phases (second term) is quite negligible compared to the other two terms.

If the DO level is controlled through dilution only (the last term on the righthand side of eq. ( 20)), the resulting change in the amount of substrate may itself induce a change in DO, which gives rise to oscillations and poor performance. This is typical of systems where the zero dynamics play an important role in process performance [START_REF] Mullhaupt | Cascade control of the toycopter[END_REF].

This problem can be better understood by considering a simplified linearized version of Problem ( 17)-( 21) with both a direct and an integral effect of u: ẋ1 = a x 2 + u and ẋ2 = u, where a 0 is a coefficient that represents the relative importance of the integral effect (Figure 8). With the input u and the controlled output x 1 the transfer function reads X 1 (s) U (s) = s+a s 2 . Using the proportional controller k shown in Figure 9 , the closed-loop characteristic polynomial becomes s 2 + ks + ak, which will have real roots for k 4a.

Hence, in the presence of a fast zero (a large), one needs to use a very large controller gain to ensure non-oscillatory behavior. Such a large gain may not be admissible in practice due to model mismatch and measurement errors.

An efficient way of controlling this second-order system is to use the cascade scheme given in Figure 10,i

.e. u = k i [k o (x 1,sp -x 1 ) -x 2 ]
. Note that this cascade scheme corresponds to full-state feedback for this second-order system. The characteristic polynomial is s 2 + k i (k o + 1)s + ak i k o , the poles of which can be placed anywhere independently of the value of a.

Hence, the proposed cascade scheme is one way of implementing state feedback for the part of the dynamics that concerns dissolved oxygen.

The term r DO x t can be evaluated via OUR and CER measurements. This can be understood from eq. ( 15) that shows that r DO is the total oxygen consumptions for growth, production and maintenance. This oxygen consumption is approximately reflected by the OUR measurement. Furthermore, the CER measurement is an indication of biomass activity and its concentration in the medium. For the operating conditions used in this experiment (constant CO 2solubility), OUR and CER are both directly related to r DO x t . Hence, r DO x t can be approximated as β OU R+CER V , where β is a proportionality factor. Note that a controller using only OUR measurements would probably work as well. Unfortunately, such a controller was not tested as part of this work.

The idea of the cascade control is to use (r DO x t ) sp as the manipulated variable to control DO, while F is used to control r DO x t , x t being a function of F as shown by eq. ( 17). This leads to the cascade structure of Figure 11, in which the role of the inner loop is to regulate the substrate consumption based on OUR and CER measurements, while the outer loop gives the setpoint for this consumption.

Controller Tuning

Since, for the system at hand, cascade control corresponds to state feedback, there are sufficient degrees of freedom to place the poles of the closed-loop system arbitrarily in the complex plane. Hence, the performance of the closed-loop system (including its stability) is determined by placing the poles appropriately in the complex plane. Ideally, the desired poles are determined from some theoretical considerations, as explained in standard textbooks [START_REF] Seborg | Process Dynamics and Control[END_REF]. For this, however, the nonlinear process model has to be linearized and the controller gains determined on the basis of the linear approximation.

In this study, controller tuning was carried out directly on the nonlinear process model by trial and error. The advantage of this approach is that it avoids the errors induced by linearization, while having the disadvantage of being empirical. Nevertheless, the controller tuning was successful, as shown in the next section. Furthermore, a PID controller was also tuned empirically. However, due to the presence of a zero in the oxygen dynamics, as pointed out in the previous section, a PID controller does not have sufficient degrees of freedom for arbitrary pole placement, thereby resulting in less satisfactory results. Note, however, that PID control may, in some cases, provide good regulatory performance; for example, a system without zero is handled successfully by PI control in [START_REF] Chung | Design of metabolic feed controllers: Application to high-density fermentations of Pichia pastoris[END_REF].

Experimental Results

The performance of PID control to regulate the process around a constant setpoint (DO sp = 25) is illustrated in the second phase of Experiment II (Figure 12). The performance is rather poor, with a large DO variability (25 ± 10). In contrast, the cascade controller used in the third phase of the experiment is able to keep the DO concentration within the interval 25 ± 2, which is a major improvement to both manual operation and standard PID control.

The cascade controller is further tested in Experiment III (Figure 13). The setpoint for this experiment has been obtained by solving the optimization problem (25) off-line before the beginning of the batch, i.e. without the soft-ware sensor given in Figure 7. Since the resulting DO-profile is nearly constant, it is approximated by a constant value for ease of implementation [START_REF] Titica | Modeling and optimization of fed-batch filamentous fungal fermentation[END_REF]. The controller works satisfactorily for most of the time. However, the oscillatory behavior typical of oxygen limitation starts after 0.75 time units. Since this phenomenon of oxygen limitation is highly nonlinear, the linear cascade controller is unable to bring the fermentation back to normal operation. The on-line reoptimized DO setpoint given in Figure 7 is used in the second phase of Experiment IV (Figure 14). Unfortunately, the optimization provides setpoints that are well below DO sp = 20%, already known from Experiment III to lead to oxygen limitation. Since this is considered unacceptable, a safe and constant setpoint is used in the third phase of this experiment. In this third phase, several external perturbations act on the system, ranging from sensor failure at time 0.55 to manual setpoint changes at time 0.7.

These experiments have demonstrated that, even though the model has been fitted to give good one-step ahead prediction and fairly reasonable multi-step simulations, the setpoints provided by solving optimization problem (25) offline (Experiment III) or on-line (Experiment IV) are in the region of oxygen limitation. This observation can be explained by the plant-model mismatch present in the oxygen dynamics. However, these experiments have shown that the cascade controller is able to follow the desired DO setpoint more accurately than traditional PID control.

Unfortunately, though the regulatory performance of the controller is excellent, the transients exhibit some overshoot. This is mainly due to input saturation not being accounted for in the control design. Other strategies, such as controlling OUR, could be applied since they give a more reliable indication of biomass activity than DO early in the batch.

Conclusions

The main outcome of this study is the cascade controller for dissolved oxygen. The proposed scheme efficiently regulates the DO level, but a proper setpoint needs to be chosen to keep the process away from oxygen limitation. The advantage of the proposed control strategy is that it is simple to apply and not specific to the strain of microorganism studied in this paper. Thus, it is applicable to a wide variety of fungal fermentations.

A mechanistic model of enzyme production by filamentous fungal fermentation has been extended to include rheological considerations. The effect of medium viscosity on the oxygen dynamics is described by empirically modeling the dependence of the mass transfer coefficient k L a on viscosity and that of vis-cosity on biomass and dissolved oxygen concentration. The resulting model is used to determine the optimal DO setpoint, while the insight gained from the model is also used to design a cascade controller. This study has also indicated several model shortcomings. The most important one is that the effect of pH is completely discarded. As a consequence, the model predicts feasible operation at low dissolved oxygen values that could not be verified experimentally. Also, the model-based optimization is not capable of computing reliable DO setpoints.

In future experiments, one could focus on determining experimentally the best setpoint for dissolved oxygen, e.g. using extremum-seeking techniques [START_REF] Titica | Adaptive extremum-seeking control of enzyme production in filamentous fungal fermentation[END_REF]. Fig. 14. Experiment IV -Batch phase followed by cascade control using first a reoptimized and then a constant DO setpoint. Note that the curve corresponding to the setpoint is hidden behind the measurement curve. The perturbations in the third phase are due to sensor failure and attempted manual setpoint changes.

Fig. 3 .

 3 Fig. 3. Evolution of viscosity during fed-batch operation. Measured value (--) and calculated value using eq. (24 (-)).

Fig. 4 .

 4 Fig. 4. Dissolved oxygen evolution during fed-batch operation -Data Set 1. Measured (--) and predicted (-) values as a function of time.

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Dissolved oxygen evolution during fed-batch operation -Data Set 2. Measured (--) and predicted (-) values as a function of time.

Fig. 8 .

 8 Fig.8. Illustration of direct (1) and integral (2) effects using a second-order numerical example.

Fig. 9 .

 9 Fig.9. Output control for the second-order numerical example.

Fig. 10 .

 10 Fig.10. Cascade control for the second-order numerical example.

Fig. 11 .

 11 Fig. 11. Cascade control of dissolved oxygen. The oxygen consumption r DO x t is approximated as β OU R+CER V

Fig. 12 .

 12 Fig. 12. Experiment II -Batch phase followed by PID control and cascade control.

Fig. 13 .

 13 Fig.[START_REF] Titica | Modeling and optimization of fed-batch filamentous fungal fermentation[END_REF]. Experiment III -Batch phase followed by cascade control. The DO setpoint, which has been obtained to optimize the bioreactor performance, is lower than in Experiment II.

  Fig.2. Relationship between k L a and during a fed-batch fermentation process. As expected, k L a decreases with increasing viscosity.

	Table A.1 B Variables used in the Fed-batch Filamentous Fermentation Model q 1 -rate of branching (g/(kg DW h)) Model parameter values q 2 -growth rate of the active region (g/(kg DW h)) Batch Constant Linear
	Parameter q 3 -rate of hyphal cell formation (g/(kg DW h)) Value Measurement unit phase feed feed
	a DO a t -number of tips per unit mass (tips/(kg DW)) 0.04 R -universal gas constant (L atm/(mmol K)) 1 1 kg/(m s %) a x 0.094 kg DW kg/(g m s) β 1 L / mmol a DO -regression coefficient (kg/(m s %)) a x -regression coefficient (kg DW kg/(g m s)) β -proportionality coefficient (L/mmol) γ -proportionality coefficient (1/mmol) r DO -oxygen consumption rate (kg DW/(g h)) 0.9 0.8 r ps -specific α-amylase formation rate (FAU kg DW/(L g h)) r s -substrate consumption rate (kg DW g glucose /(g L h)) 0.4 0.6 0.8 OUR ρ -hyphal density (g/cm 3 ) γ 1 1 / mmol c 0 67.2 h -1 c 1 4.3816 m s/(kg h) 100 % η 0 4.185 DO -dissolved oxygen concentration (%) x e -concentration of extension zone (g/kg DW) 80 kg/(m s) ∆[CO 2 ] -change in carbon dioxide concentration over the reactor (%) ∆[O 2 ] -change in oxygen concentration over the reactor (%) w -hyphal water content (g/kg DW) 0.4 x a -concentration of active region (g/kg DW) 100 DO * CER -Carbon Evolution Rate (mmol/(L h)) c 0 -regression coefficient (h -1 ) c 1 -regression coefficient (m s/ (kg h) ) d -hyphal diameter (µ m) s -substrate concentration (g glucose / L) 0.5 V -volume (L) time T ref -reference temeprature (K) 0 0.2 0.4 0.6 0.8 1 0.6 0 k s f -feed substrate concentration (g glucose / L) 0.7 0.2 L A
	f F evap k 3 f -fraction of the active region (%) 80 % 1.25 0.08 Y XO -stoichiometric coefficient for oxygen consumption for growth (% kg 0 h -1 η 0 -regression coefficient (kg/(m s)) 20 tion (% L / FAU) L/h DO * -equilibrium dissolved oxygen concentration (%) η -viscosity (kg/(m s)) x h -concentration of hyphal region (g/kg DW) Y P O -stoichiometric coefficient for oxygen consumption for product forma-40 60 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.3 DO DO desired = 25 Viscosity
	k bran F -feed flow rate (L/h) 0.0017 DW / g) 0 k c 8 F AU -1 FAU is the amount of enzyme that hydrolyzes 5.26 g starch/h at 0.2 0.4 0.6 0.8 1 tip / (µm h) time FAU kg DW/(L g h) 30 • C 1
	K cor K I K DO K S m h)) F evap -evaporation rate (L/h) 10 -6 1.5 • 10 -3 g glucose/L g/L 2.5 % 0.0211 0 g glucose /L k 1 -specific branching frequency (tips/(kg DW h)) k 2 -maximal tip extension rate (kg DW/(tips h)) k 3 -rate constant (h -1 ) k bran -specific branching frequency determined by image analysis (tip/(µ 0.2 0.4 0.6 0.8 Feed flow rate
	K s1 k c -constitutive α-amylase production rate (FAU kg DW/(L g h)) 0.003 g glucose /L 0 0.2 0.4 0.6 0.8 1
	0.006 K cor -correction constant for the product formation (g glucose/L) g glucose /L time K s2 k tip,max 49 limitation occurs (%) µm / (tip h) K DO -limit value of dissolved oxygen concentration, below which oxygen 8
	m o K I -Haldane parameter (g glucose/L) 0.01 % kg DW/(g h) 7
	m s µ 0 k L a -specific gas-liquid mass transfer coefficient (1/(L h)) 0.01 kg DW g glucose /(g L h) 227 FAU kg DW/(L g h) K s1 -saturation constant for branching (g glucose /L) 6 K S -Haldane parameter (g glucose/L) pH
	ρ K s2 -saturation constant for tip extension (g glucose /L) 1 g/cm 3 k tip,max -maximal tip extension rate determined by image analysis (µm / 0 0.2 0.4 0.6 0.8 1 5
	s f (tip h))	430	g glucose / L time
	w m o -maintenance coefficient (% kg DW/(g h)) 0.67 g/kg DW Y XS 1.75 m s -maintenance coefficient (kg DW g glucose /(g L h)) g glucose kg DW / L g µ 0 -Haldane parameter (FAU kg DW/(L g h))
	Y P S Y XO OUR -Oxygen Uptake Rate (mmol/(L h)) 1.88 • 10 -4 g glucose / FAU 57 % kg DW / g Fig. 1. Experiment I -Current operation in manual mode with three phases (batch p -α-amylase concentration (FAU / L) p ref -reference pressure (atm) operation, linearly-increasing feed, constant feed).
	Y P O	35	% L / FAU

Y P S -yield coefficient for α-amylase on substrate (g glucose / FAU) Y XS -stoichiometric coefficient for the uptake of substrate (g glucose kg DW / L g)

Acknowledgements: This paper presents the results of the Knowledge-driven Batch Production (BatchPro) European Project HPRN-CT-2000-00039. The authors would like to thank F. Lei and H. Jorgensen from Novozymes, Bagsvaerd, Denmark, for their suggestions and for making possible to carry out the experimental work.

A Kinetic Expressions and Model Parameters for the Fed-batch

Filamentous Fermentation Model