Anaïs Marconnet

Baptiste Michon

Christel Le Bon

Fabrice Giusti

Christophe Tribet
email: christophe.tribet@ens.fr

Manuela Zoonens
email: manuela.zoonens@ibpc.fr

Solubilization and stabilization of membrane proteins by cycloalkane-modified amphiphilic polymers

Keywords: amphipols, extraction, membrane proteins, SMA co-polymers, stability, surfactants

published or not. The documents may come

Solubilization and stabilization of membrane proteins by

cycloalkane-modified amphiphilic polymers.

Introduction

As gatekeepers of all membrane compartments in cells, membrane proteins (MPs) fulfill essential biological functions and are key targets for drugs. [START_REF] Landry | Drugs and Their Molecular Targets: An Updated Overview[END_REF][START_REF] Rucevic | Mammalian Plasma Membrane Proteins as Potential Biomarkers and Drug Targets[END_REF] Their importance motivates structural and biophysical studies, which, however, critically depend on extraction/purification procedures that keep MPs in their native state. Detergents can disrupt biological membranes and keep MPs water-soluble, but they often entail MP inactivation, in part due to their propensity to detach from MPs endogenous lipids or cofactors needed for activity. This has prompted the development of macromolecular amphiphiles such as amphipols (APols), [START_REF] Tribet | Amphipols: Polymers That Keep Membrane Proteins Soluble in Aqueous Solutions[END_REF][START_REF] Zoonens | Amphipols for Each Season[END_REF][START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF] which were expected to be less aggressive dispersing agents and less prone to reach hidden hydrophobic regions in the protein. The prototypical APol, named A8-35, is a poly(acrylic acid) (PAA) polymer randomly modified with octylamine and isopropylamine side chains (Figure 1A). The mildness of APol association with MPs results in an increased life-time of the native state of APol-complexed MPs. [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF] Another advantage of APols is the improvement of images in the fast growing field of single-particle electron cryomicroscopy (cryo-EM) reconstitution. [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF][START_REF] Le Bon | Amphipathic Environments for Determining the Structure of Membrane Proteins by Single-Particle Electron Cryo-Microscopy[END_REF] Conventional APols are however poor solubilizing agents for biological membranes, by far less efficient than most detergents. [START_REF] Champeil | Interaction of Amphipols with Sarcoplasmic Reticulum Ca 2+ -ATPase[END_REF][START_REF] Picard | Stabilization of membranes upon interaction of amphipathic polymers with membrane proteins[END_REF] They can break liposomes (lacking MPs), [START_REF] Ladavière | Slow Reorganization of Small Phosphatidylcholine Vesicles upon Adsorption of Amphiphilic Polymers[END_REF][START_REF] Vial | Association of Octyl-Modified Poly(Acrylic Acid) onto Unilamellar Vesicles of Lipids and Kinetics of Vesicle Disruption[END_REF][START_REF] Tribet | Flexible Macromolecules Attached to Lipid Bilayers: Impact on Fluidity, Curvature, Permeability and Stability of the Membranes[END_REF] but in practice MP/APol complexes can rarely be directly obtained from biological membranes and must be prepared by transferring the protein from detergent-solubilized extracts. [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF][START_REF] Le Bon | Folding and Stabilizing Membrane Proteins in Amphipol A8-35[END_REF] Styrene maleic acid (SMA) co-polymers (Figure 1B) are APol variants with the distinctive property of enabling direct dispersion of proteolipidic membranes with no need for detergent. [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF][START_REF] Stroud | Purification of Membrane Proteins Free from Conventional Detergents: SMA, New Polymers, New Opportunities and New Insights[END_REF] They form lipid-protein-polymer mixed nanodiscs, called SMALPs. Spontaneous formation of lipid nanodiscs is not specific to SMAs as it has been observed with lipids and diisobutylene/maleic acid copolymers (DIBMA, Figure 1C) [START_REF] Oluwole | Formation of Lipid-Bilayer Nanodiscs by Diisobutylene/Maleic Acid (DIBMA) Copolymer[END_REF] and with copolymers similar to APols. [START_REF] Yasuhara | Spontaneous Lipid Nanodisc Fomation by Amphiphilic Polymethacrylate Copolymers[END_REF] Despite several limitations such as high UV absorbance, due to the presence of aromatic groups, and polydispersity of the discs, [START_REF] Jamshad | Structural Analysis of a Nanoparticle Containing a Lipid Bilayer Used for Detergent-Free Extraction of Membrane Proteins[END_REF] the use of SMAs has developed in the field of MPs thanks to their solubilizing property. However, in the field of structural biology, the frequent need to use harsh extraction conditions may explain the low number of high-resolution cryo-EM structures established using SMAs. [START_REF] Le Bon | Amphipathic Environments for Determining the Structure of Membrane Proteins by Single-Particle Electron Cryo-Microscopy[END_REF][START_REF] Autzen | Membrane Mimetic Systems in CryoEM: Keeping Membrane Proteins in Their Native Environment[END_REF] To date, only a small number of single-particle cryo-EM structures of SMALPs have been obtained. [START_REF] Le Bon | Amphipathic Environments for Determining the Structure of Membrane Proteins by Single-Particle Electron Cryo-Microscopy[END_REF] In comparison, despite the need for surfactant exchange, classical APols (mainly A8-35 and PMAL-C8) [START_REF] Tribet | Amphipols: Polymers That Keep Membrane Proteins Soluble in Aqueous Solutions[END_REF][START_REF] Nagy | Use of Amphipathic Polymers to Deliver a Membrane Protein to Lipid Bilayers[END_REF][START_REF] Gorzelle | Amphipols Can Support the Activity of a Membrane Enzyme[END_REF] represent the most frequently used polymers. [START_REF] Le Bon | Amphipathic Environments for Determining the Structure of Membrane Proteins by Single-Particle Electron Cryo-Microscopy[END_REF] To circumvent the need of surfactant exchange, improving the direct solubilization of membranes by APol-like polymers under mild experimental conditions would be highly desirable.

Figure 1. Chemical structures of amphipathic polymers used in this study. A) A8-35; molar percentages of each unit are from ref. [START_REF] Tribet | Amphipols: Polymers That Keep Membrane Proteins Soluble in Aqueous Solutions[END_REF] B) SMA co-polymers, with molar ratios of styrene to maleic acid units of 2:1 or 3:1 (n ≈ 9). [START_REF] Oluwole | Formation of Lipid-Bilayer Nanodiscs by Diisobutylene/Maleic Acid (DIBMA) Copolymer[END_REF] C) DIBMA co-polymer (n ≈ 37). [START_REF] Oluwole | Formation of Lipid-Bilayer Nanodiscs by Diisobutylene/Maleic Acid (DIBMA) Copolymer[END_REF] D) PAA modified with either linear or cyclic hydrocarbon groups (R) of 8 carbon atoms. The 𝑀 ! values for C 6 -C 2 -50, C 8 -C 0 -50 and A8-50 (sodium salt form) were calculated using 𝐷𝑃 ! ≈ 35 for the parent PAA [START_REF] Giusti | Characterization and Applications of a Perdeuterated Amphipol[END_REF] and the degree of grafting, y, determined by [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C, [START_REF] Landry | Drugs and Their Molecular Targets: An Updated Overview[END_REF] 1).

H NMR and potentiometric titration

We hypothesized that replacing the flexible n-alkyl side groups of classical APols by cyclic hydrophobic groups might possibly mimic the role of SMA's aromatic side groups. Of note, introducing cyclic groups in the aliphatic tail of dodecylmaltoside results in MP-stabilizing analogs. [START_REF] Hovers | A Class of Mild Surfactants That Keep Integral Membrane Proteins Water-Soluble for Functional Studies and Crystallization[END_REF] We therefore examined whether cyclic hydrocarbon groups grafted onto PAA might not i) improve the polymers' ability to break up MP-containing membranes while ii)

preserving the long-term stability of MPs. To this end, we prepared copolymers, named Cycl-APols, in which the linear octyl groups of A8-35-like APols were replaced by cyclic ones having the same number of carbon atoms (either cyclohexylethylamine or cyclooctylamine, yielding polymers C 6 -C 2 -50 and C 8 -C 0 -50, respectively, Figure 1D). Cycloalkanes were preferred over aromatic cycles in order to keep the CyclAPols UV-transparent. As references, we compared CyclAPols with SMA (2:1) and (3:1) of relatively short length, [START_REF] Stroud | Purification of Membrane Proteins Free from Conventional Detergents: SMA, New Polymers, New Opportunities and New Insights[END_REF][START_REF] Dörr | The Styrene-Maleic Acid Copolymer: A Versatile Tool in Membrane Research[END_REF][START_REF] Korotych | Evaluation of Commercially Available Styrene-Co-Maleic Acid Polymers for the Extraction of Membrane Proteins from Spinach Chloroplast Thylakoids[END_REF] We studied the membrane-solubilizing properties of CyclAPols using as a model the plasma membrane of Escherichia coli, a host cell widely used for producing recombinant MPs. [START_REF] Zoonens | Expression of Membrane Proteins at the Escherichia Coli Membrane for Structural Studies[END_REF][START_REF] Dilworth | Microbial Expression Systems for Membrane Proteins[END_REF] We expressed two different MPs, YidC of E. coli fused to a green fluorescent protein (GFP), and the bacteriorhodopsin of Haloquadratum walsbyi (HwBR). To further examine the solubilizing properties of CyclAPols, we used the native purple membrane from

Halobacterium salinarum, which is well known for its resistance to solubilization by polymers, be they SMA [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF][START_REF] Orwick-Rydmark | Detergent-Free Incorporation of a Seven-Transmembrane Receptor Protein into Nanosized Bilayer Lipodisq Particles for Functional and Biophysical Studies[END_REF] or classical APols. [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF] Finally, the thermal stability of BR from Hb. salinarum (HsBR) extracted with various APols was evaluated.

Experimental Section

1) Chemicals

DIBMA and n-Dodecyl β-D-maltoside (DDM) were supplied by Anatrace. As indicated by the supplier, DIBMA was a purified version of Sokalan CP9 from BASF. SMA (2:1) and SMA (3:1) were obtained from ProFoldin (SMA21S) and Polyscope (Xiran SL25010 P20), respectively. The number-average molecular masses (𝑀 ! ) of DIBMA and SMA (3:1) copolymers were ~8,400 g•mol -1 and ~4,000 g•mol -1 , respectively. [START_REF] Oluwole | Formation of Lipid-Bilayer Nanodiscs by Diisobutylene/Maleic Acid (DIBMA) Copolymer[END_REF] The lipid 1,2-dimyristoylsn-glycero-3-phosphocholine (DMPC) was purchased from Avanti Polar Lipids.

2) Synthesis of APols and composition determination

The synthesis of A8-35 was performed as previously reported. [START_REF] Tribet | Amphipols: Polymers That Keep Membrane Proteins Soluble in Aqueous Solutions[END_REF] APol derivatives carrying either octylamine, cyclohexylethylamine or cyclooctylamine were obtained after a single step of poly(acrylic acid) (PAA) modification. Briefly, the hydrophobic side chains were randomly grafted onto PAA of 𝑀 ! ~ 5.5 kDa in N-methylpyrrolidone (NMP) in the presence of dicyclohexylcarbodiimide (DCC). In each case, the resulting polymer obtained under the acidic form was purified by four cycles of precipitation/solubilization in water, performed at acidic and basic pH, respectively. The final polymer solution adjusted at pH 8-9 was dialyzed against MilliQ water and freeze-dried, yielding the expected APol. After synthesis, the final yields of APols were 98% and 96% for CyclAPols C 6 -C 2 -50 and C 8 -C 0 -50, respectively, and 86% and 52% for APols of reference A8-35 and A8-50, respectively.

The grafting ratio of hydrophobic side chains was determined by [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C and 1 H NMR spectroscopy (Figures S1 to S6) and potentiometric titration in a water/ethanol mixture (20:80, v/v) (Figure S7). The 13 C NMR spectra of polymers, at 100 g•L -1 in deuterated methanol, were obtained after a long acquisition time (48-60h) due to the long delay between each frequency pulse required for a complete relaxation of all carbon nuclei. The average degree of polymerization (𝐷𝑃 ! ) of the commercial PAA used in this study for synthesizing A8-35 and the APol derivatives was previously determined to be close to ~35 by size exclusion chromatography (SEC) analysis in organic solvent. [START_REF] Giusti | Characterization and Applications of a Perdeuterated Amphipol[END_REF] The number-average molar masses (𝑀 ! ) of sodium salts of APol derivatives were calculated with the 𝐷𝑃 ! value and the grafting ratio (y) averaged from [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C and 1 H NMR spectroscopy and pH-titration determination (Table 1 APols. The percentages of grafts and free carboxylates were deduced from an average of 1 H and [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C NMR analysis (yielding y 1 and x 1 ) and from acid-base titrations (yielding y 2 and x 2 ) for each APol. The values were averaged, giving the final x and y ratios. For the APol of reference A8-35, the averaged final ratios were x = 34%, y = 23% and z = 43%, and the 𝑀 ! value was 4276 g•mol -1 .

3) Expression of YidC-GFP of E. coli and BR of Hq. walsbyi in E. coli strain and quantification of protein extraction using polymers

The expression vectors encoding for YidC of E. coli fused at its C-terminus to GFP (YidC-GFP) and BR of Hq. walsbyi (HwBR) were kindly provided by the laboratories of Jan Whilem and Anant Menon, respectively. The strains E. coli C41 and C43 (DE3) were transformed with each vector, respectively, and growth at 37°C in LB in the presence of either ampicillin or kanamycin. When the optical density at 600 nm reached 0.6-0.8, the cultures were supplemented with IPTG. In the case of HwBR production, 5 μM all-trans retinal (Sigma) were also added. After induction, cells were harvested. The pellet of each culture was re-suspended with buffer containing 20 mM Tris-HCl, 150 mM NaCl, pH 8.0 and cell lysis was performed with a Cell Disruptor (Constant Systems). Unbroken cells and cellular debris were removed by centrifugation (20 min. at 10,000 × g). The membranes were harvested from supernatants by high-speed centrifugation (1h at 100,000 × g). The concentration of total MPs present in the membrane extracts was assessed with a calorimetric assay.

The solubilization of YidC-GFP from E. coli membranes was performed at a total MP concentration of 2 g•L -1 with either 1% w/v DDM, used as reference condition, or 2 g•L -1 polymers, corresponding to a total MP/polymer ratio of 1:1 (w/w). After 1 h incubation at 4°C, the samples were centrifuged 30 min. at 100,000 × g. The supernatants and the pellets, re-suspended in the initial volume of solubilization with buffer 20 mM Tris-HCl, 150 mM NaCl, pH 8.0 and 5% SDS, were loaded on 12-% acrylamide gels. After migration, the gels were washed with water and the fluorescence of GFP within the gel was detected with a Typhoon TLA 9500 (GE healthcare). The excitation and emission wavelengths were those of Alexa Fluor 488, i.e. 495 nm and 519 nm, respectively. The fluorescence of the band corresponding to YidC-GFP visible on the acrylamide gels was quantified using Image J software. The fluorescence of YidC-GFP measured for each supernatant was normalized with the fluorescence quantified for the 1%-DDM supernatant, which was defined as the maximum of solubilization. For the kinetic of YidC-GFP extraction, the solubilization was performed under the same experimental conditions except that aliquots taken off from samples were centrifuged 10 min. at 250,000 × g.

In the case of HwBR, the solubilization was carried out with both pure E. coli membranes and after the fusion of E. coli membranes with 100-nm extruded DMPC liposomes, prepared in 20 mM Tris-HCl, 150 mM NaCl, pH 8.0, by sonication in the dark for 30 min. using a bath sonicator (VWR). The total MP/DMPC ratio was 1:0.5 (w/w), as previously reported. [START_REF] Broecker | Crystallogenesis of Membrane Proteins Mediated by Polymer-Bounded Lipid Nanodiscs[END_REF] The membranes were then supplemented with either 0.2% w/v DDM or polymers at a final concentration of 2 g•L -1 , i.e. a total MP/polymer ratio of 1:1 (w/w). After incubation for 4 h at room temperature, the samples were centrifuged 30 min. at 100,000 × g and HwBR present in the supernatants was assessed with absorbance at 554 nm.

4) Quantification of native BR extracted from DMPC-fused purple membrane by polymers

The purple membrane was purified from Hb. salinarum as described. [START_REF] Oesterhelt | Rhodopsin-like Protein from the Purple Membrane of Halobacterium Halobium[END_REF] The concentration of native BR of Hb. salinarum (HsBR) was adjusted to 5 g•L -1 with buffer 20 mM sodium phosphate, 100 mM NaCl, pH 7.0 and the membrane preparation was stored at -80 °C until usage.

Fusion of the native purple membrane with DMPC liposomes was performed as reported. [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF][START_REF] Orwick-Rydmark | Detergent-Free Incorporation of a Seven-Transmembrane Receptor Protein into Nanosized Bilayer Lipodisq Particles for Functional and Biophysical Studies[END_REF] Briefly, an aliquot of purple membrane was mixed with 100-nm extruded DMPC liposomes to reach a final HsBR/DMPC ratio varying from 1:3 to 1:6 (w/w). The samples, at a HsBR concentration of 0.5 g•L -1 , were sonicated in the dark for 30 min. using a bath sonicator (VWR) and then stored at -80°C until usage.

Solubilization was initiated by mixing at a 1:1 volume ratio DMPC-fused purple membrane with polymer solutions to reach a final HsBR/polymer ratio varying from 1:3 to 1:9 (w/w). The samples were incubated overnight in the dark, at 25°C under shaking in a thermomixer. After an overnight incubation, all the samples were centrifuged at 4 °C for 20 min. at 200,000 × g. The UV-visible spectra of supernatants were recorded with a spectrophotometer (Hewlett Packard). The quantification of extracted HsBR was evaluated with the ratio of absorbance values at 554 nm measured before and after centrifugation.

Because APols and SMAs are polydisperse polymers, the representation of the molar ratios of HsBR/macromolecular chains depends on the weighted average of polymers mass.

Here, we used the number averaged experimental values of 𝑀 ! . For HsBR/polymer weight ratios of 1:3 and 1:9 (w/w), the corresponding molar ratios of HsBR/C 8 -C 0 -50 are then of ~1:16.7 and ~1:50.3, respectively. For SMA (3:1), the average molar ratios of HsBR/SMA correspond to ~1:20.3 and ~1:60.8, respectively. At (w/w) HsBR/DMPC ratio fixed to 1:5, the (w/w) HsBR/polymer ratios of 1:3 and 1:9 correspond in addition to molar ratios of DMPC/cycloalkane (from C 8 -C 0 -50) of ~1:1.6 and ~1:4.9, respectively. For SMA (3:1), the molar ratios of DMPC/phenyl rings was similarly of ~1:2.8 and ~1:8.3, respectively.

5) Dynamic light scattering (DLS)

The scattering intensity was measured at 25°C and an angle of 90° in a BI-200SM

Brookhaven Instrument system equipped with a 30 mW 637 nm laser and photomultiplier detection. Size distributions from all samples showed a monomodal distribution as analyzed by CONTIN. Hydrodynamic diameters (D H ) were calculated by fitting the correlation functions by the cumulant analysis method at quadratic order. For the kinetics of solubilization, a sample of DMPC-fused purple membrane (at 0.2 g•L -1 of HsBR) was mixed with a polymer solution (1:1 v/v) to reach a final HsBR/polymer ratio of 1:12.5 (w/w).

6) Size exclusion chromatography (SEC)

The solution dispersity of HsBR/DMPC/polymer complexes was characterized by SEC.

After HsBR extraction, the samples were injected onto a Superose 12 10/300 GL column connected to an Äkta purifier-10 system (GE Healthcare). The sample and elution buffer was 20 mM sodium phosphate, 100 mM NaCl, pH 7.0. Elution was carried out at room temperature and UV absorbance monitored at three wavelengths (220, 280 and 554 nm).

7) Stability assay

Samples of HsBR (extracted directly from DMPC-fused purple membrane with polymers)

were incubated at 50°C for 6h in the dark in a thermomixer. UV-visible spectra of samples were recorded each hour. The decrease of the absorbance value at 554 nm reflects the loss of retinal and a change in the native conformation of the protein. The absorbance values were normalized with the initial one, i.e. measured at 4°C.

Results

Synthesis of CyclAPols

The synthesis of the CyclAPol derivatives consists in the random grafting on a PAA backbone of cycloalkane moieties via the formation of amide bonds. The average degree of grafting was controlled quantitatively by introduction of ad hoc percentages of cycloalkylamine reactants to reach values similar to the hydrophobic moieties in SMA (2:1), i.e. 50 mol% (within experimental error). The average percentages of grafting of cyclohexylethylamine and cyclooctylamine, yielding C 6 -C 2 -50 and C 8 -C 0 -50, respectively, were then determined by both [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C and 1 H NMR spectroscopy and pH titration (Table 1). The resulting CyclAPols were highly soluble in aqueous solutions and UV-transparent (Figure S8).

The solubilizing properties of CyclAPols, assessed with biological membranes from two different origins, were compared with a set of five other polymers used as references: i) the commercially-available polymers SMA (2:1) and (3:1), which both carry cyclic aromatic rings as hydrophobic moieties with a density of 50 and 67 mol%, respectively, ii) the commercially-available polymer DIBMA, which carries short-length branched acyclic side groups present along the polymer at 33 mol%, and iii) the polyacrylate-based APols A8-35 and A8-50, which carry linear octyl chains grafted at 25 and 50 mol%, respectively. In contrast to A8-50, the archetypical APol A8-35 also comprises isopropyl moieties at 40 mol%, whose role is to reduce its charge density. The number-average molar masses (𝑀 ! ) of CyclAPol derivatives, A8-50, A8-35, and SMA (3:1) are comparable. In term of dispersity, CyclAPols, A8-50 and A8-35 were derived from the same PAA parent chain and, as a result, have the same polydispersity (Đ ≈ 2.0), whereas the polydispersity of SMAs is slightly broader (typically 2.0-2.5). [START_REF] Dörr | The Styrene-Maleic Acid Copolymer: A Versatile Tool in Membrane Research[END_REF] Regarding DIBMA, its 𝑀 ! value is larger and its polydispersity slightly narrower (Đ ≈ 1.8) [START_REF] Oluwole | Solubilization of Membrane Proteins into Functional Lipid-Bilayer Nanodiscs Using a Diisobutylene/Maleic Acid Copolymer[END_REF] than that of the other copolymers used in this study.

Solubilization by CyclAPols of E. coli plasma membrane fragments

The solubilizing properties of CyclAPols were tested with membrane fragments from E. Kinetics of YidC-GFP extraction from E. coli membranes after addition of polymers. Over 2 h of incubation, aliquots were taken off from each sample and centrifuged (10 min. at 250,000 × g). The fluorescence of the supernatants was quantified in gel (Figure S9).

The second MP expressed in E. coli and used as reporter was the archaebacterial bacteriorhodopsin of Hq. walsbyi (HwBR) produced under its native conformation as indicated by its spectroscopic signature. This protein is a light-driven proton pump, whose transmembrane domain folds in a bundle of 7 α-helices. [START_REF] Hsu | Structural and Functional Studies of a Newly Grouped Haloquadratum Walsbyi Bacteriorhodopsin Reveal the Acid-Resistant Light-Driven Proton Pumping Activity[END_REF] The amounts of HwBR extracted with A8-35 and SMA (2:1) were the lowest (Figure 3). In contrast to observations with YidC-GFP, the results obtained with HwBR revealed significant differences between A8-35 and the two SMAs. SMA (3:1) appeared to be more efficient at extracting HwBR from E. coli membranes than either SMA (2:1) or A8-35 (Figure 3). When solubilizing E. coli membranes with CyclAPols, the amounts of extracted HwBR were 2.5× higher than with SMA (3:1). As previously reported, the solubilization efficiency of SMA (3:1) can be improved by modulating the bilayer characteristics with the addition of synthetic phospholipids DMPC. [START_REF] Broecker | Crystallogenesis of Membrane Proteins Mediated by Polymer-Bounded Lipid Nanodiscs[END_REF] This treatment increased the amount of SMA (3:1)-solubilized HwBR (+50%), which remains nevertheless below the amount extracted by CyclAPols (Figure 3B). Intriguingly, no significant differences between CyclAPols and A8-50 were noted, in contrast to observations with YidC-GFP. Kinetics of solubilization over 4-h incubation of the E. coli membranes with polymers revealed that the maximal extraction of HwBR in CyclAPol-containing supernatants was reached in 1h, whereas extraction by SMA (3:1) progressed more slowly (Figure S10). (w/w) as described in ref. [START_REF] Broecker | Crystallogenesis of Membrane Proteins Mediated by Polymer-Bounded Lipid Nanodiscs[END_REF] In the case of A8-35 and SMA (2:1), the absorbance values at 554 nm measured for supernatants collected after solubilization of DMPC-fused E. coli membranes were equal to 0.

Solubilization by

A B

To further investigate the membrane-solubilizing capacities of CyclAPols, we tested them on the purple membrane from Hb. salinarum, which represents both a simpler model than E. coli membrane fragments, as it contains a single protein (HsBR), and a demanding one because of the high density and tight packing of proteins (HsBR is accounting for three quarters of the membrane mass). [START_REF] Oesterhelt | Rhodopsin-like Protein from the Purple Membrane of Halobacterium Halobium[END_REF] Indeed, purple membrane fragments proved resistant to solubilization by all of the polymers tested. Dilution of HsBR by fusion of the fragments with DMPC lipids was thus used to lower this resistance to solubilization. [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF][START_REF] Orwick-Rydmark | Detergent-Free Incorporation of a Seven-Transmembrane Receptor Protein into Nanosized Bilayer Lipodisq Particles for Functional and Biophysical Studies[END_REF] In order to be able to rank the polymers according to their solubilization efficiency, solubilization was assessed at various HsBR/DMPC ratios (Figure 4). A smaller pellet (Figure 4A) and higher recovery of native HsBR in supernatants (Figure 4B) indicated that SMA (3:1) was by far more efficient at extracting HsBR than SMA (2:1) and DIBMA (Figure S11). Under the same experimental conditions, A8-35 was unable to extract HsBR, confirming its poor detergency. Even the more hydrophobic A8-50, which differs from A8-35 by a two-fold higher density of n-octyl chains, did not perform better than SMA (2:1). In contrast, CyclAPols, with a similar degree of grafted side groups as A8-50, were efficient solubilizers. The amounts of native HsBR found in CyclAPol-and SMA (3:1)-containing supernatants were comparable (~80-85%). As expected, a decrease of extraction efficacy by SMAs was observed when lowering the DMPC content in proteoliposomes. In contrast, high percentages of solubilization were obtained with CyclAPols even at the lowest DMPC ratio, i.e. in the more demanding conditions (Figure 4B).

B

solubilized HsBR decreased sharply at low polymer concentration (Figure 5), indicating that a polymer/HsBR ratio of 3:1 (w/w) is not sufficient to fully disperse all of the HsBR. All three copolymers however enabled up to 90% solubilization at higher polymer/HsBR ratios. Surprisingly, the amount of SMA (3:1)-solubilized HsBR passed through a maximum, which is confirmed by the size of the purple pellets (Figure S12). The hydrodynamic diameter (D H ) of the complexes (at a HsBR/polymer ratio of 1:6. Next we assessed whether the copolymers solubilized the lipids along with HsBR. To this aim, kinetics were recorded by DLS at a HsBR/polymer ratio of 1:12.5 w/w (Figure 6).

The scattered intensity reflects mainly evolution of proteoliposome size and concentration, because the small particles (free polymer particles and MP/polymer complexes; D H < 40 nm) contribute less than 6% of the intensity. The scattered intensity typically decreased immediately after supplementation of the HsBR/DMPC proteoliposomes with a solution of polymer (1:1 v/v, see Experimental section), and gradually reached a plateau (in < 60 min. in the slowest case, that of A8-50). First, this kinetics validates that the 24-h incubation used to quantify the amount of solubilized HsBR was sufficient to reach maximal extraction. Second, the average D H as measured by DLS did not vary significantly with time and was about 130-200 nm (Table S1). This indicates that the proteoliposomes were the predominant scatterers during the whole solubilization. The absence of size variation, while the total intensity dropped down by up to 90%, rules out a gradual extraction of lipids or HsBR from all membranes, and is thus incompatible with the "cookie-cutter" model proposed for SMAs. [START_REF] Parmar | Artificial Membranes for Membrane Protein Purification, Functionality and Structure Studies[END_REF] In contrast, it is the number of proteoliposomes that decreases, without affecting the mean diameter of the residual ones. This probably indicates that once a liposome is destabilized (possibly due to the polymer gaining access to its internal surface), it rapidly disperses into small particles rather than undergoing a progressive size decrease. Interestingly, the plateau measured at long times correlates with the percentage of solubilized HsBR. Namely, the plateau reached with A8-35 was the highest, revealing that ~80% of the initial proteoliposomes were left intact. In the presence of efficient solubilizers, either SMA (3:1) or CyclAPols, the scattered intensity decreased by up to 90%, which can be compared with the 90% HsBR solubilization in Figures 4 and5.

Stability of CyclAPol-extracted HsBR

HsBR carries a retinal chromophore whose spectroscopic properties are extremely sensitive to the conformation of its binding pocket. [START_REF] Váró | Analogies between Halorhodopsin and Bacteriorhodopsin[END_REF] Accordingly, the stability of HsBR was assessed by measuring its absorbance at 554 nm. The kinetics of degradation were accelerated by incubating the complexes at 50°C. As shown in Figure 7, a rapid decrease of the fraction of native HsBR is observed for SMA (3:1), whereas the spectral properties of HsBR are stable for hours in CyclAPol-solubilized samples. were 1:5 and 1:6.25, respectively. The rate of inactivation in SMA (2:1) is similar to that in SMA (3:1) but, because they bear on very small amounts, the data have not been plotted here.

Discussion

Detergent-free extraction of MPs using amphipathic polymers presents two main interests for structural and functional investigations of MPs. First, it avoids exposing the protein to detergent, which is a frequent cause of inactivation. Second, it increases the probability that the protein will retain lipids that are important to its function and stability.

Among amphipathic polymers that can substitute for detergents, classical, polyacrylate-based APols (the prototype of which is A8-35) and SMA co-polymers are the most frequently used. [START_REF] Zoonens | Amphipols for Each Season[END_REF][START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF][START_REF] Stroud | Purification of Membrane Proteins Free from Conventional Detergents: SMA, New Polymers, New Opportunities and New Insights[END_REF] Classical APols like A8-35 are very mild surfactants, so that MPs must generally be first extracted with detergents before being transferred to the polymer. [START_REF] Le Bon | Folding and Stabilizing Membrane Proteins in Amphipol A8-35[END_REF] SMAs present the advantage of being more solubilizing, so that direct MP extraction is often possible. [START_REF] Stroud | Purification of Membrane Proteins Free from Conventional Detergents: SMA, New Polymers, New Opportunities and New Insights[END_REF] In the present study, improving the efficiency of polyacrylate-based APols at extracting MPs directly from membranes while preserving their stabilizing effect was attempted using newly designed APols carrying cycloalkane moieties (CyclAPols).

Although pure lipid liposomes can be dispersed with a comparable efficiency in the presence of many copolymers, such as A8-35, SMA (2:1) and CyclAPols (see Figure S14), this does not reflect their efficiency at extracting MPs. Biological membranes are indeed more complex systems than pure liposomes and the proteins to be extracted differ one from another.

In the present study, the archaebacterial BR from two different organisms, that of Hb. salinarum naturally present in the purple membrane and that of Hq. walsbyi produced as a recombinant protein in E. coli were used as target protein to assess the efficiency of polymers at solubilizing MPs. The two BRs share 56% sequence identity, their transmembrane domain adopts the same fold, i.e. a bundle of 7 α-helices, and they bind the same cofactor, retinal, which, when bound to the native protein, gives BR its spectroscopic signature. By looking at the conditions required to extract the highest amounts of the two BR versions from their respective membranes, i.e. the densely packed purple membrane and the more fluid E. coli membranes, the solubilizing properties of the polymers appear very similar. For instance, the efficiency of A8-35, SMA (2:1) and DIBMA at extracting BR is very limited regardless of the membrane used, whereas that of SMA (3:1) improves in the presence of exogenous lipids.

The predominant lipid components of the plasma membrane of E. coli are the zwitterionic lipid phosphatidylethanolamine (75%) and the anionic lipids phosphatidylglycerol (20%) and cardiolipin. [START_REF] Raetz | Biosynthesis and Function of Phospholipids in Escherichia Coli[END_REF] By fusing DMPC, a zwitterionic lipid, the overall charges of the membrane decreases and the fluidity of the membrane is modified. These parameters presumably affect the efficiency of SMA (3:1) at extracting HwBR. Under the same experimental conditions, i.e.

at low polymer concentrations, CyclAPols show better capacities to extract HwBR than either A8-35, SMA (2:1) or SMA (3:1). In addition, solubilization by CyclAPols is not as dependent on the addition of exogenous lipids as that by SMA (3:1) is. When the reporter protein is YidC-GFP, the protein-extraction efficiency of CyclAPols remains high, which suggests that the solubilizing properties of CyclAPols may be protein-independent. Recovering the highest amount of MPs i) at low polymer concentrations over a short period of incubation (typically 1 h) and ii) without the need to add exogenous lipids presents two advantages. First, it minimizes the risk of disruption of fragile interactions in MP complexes (amphipathic polymers, despite their lower dissociating character as compared to detergents, can also be disruptive when used at high concentrations). [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF][START_REF] Popot | Amphipols from A to Z[END_REF][START_REF] Sverzhinsky | Amphipol-Trapped ExbB-ExbD Membrane Protein Complex from Escherichia Coli: A Biochemical and Structural Case Study[END_REF] Second, the natural lipid composition in the vicinity of the MP to be extracted is not modified.

The comparison of CyclAPols with their counterpart A8-50 highlights the importance of the cyclic nature of the hydrophobic moieties. A8-50 and the two CyclAPols have the same density of hydrophilic and hydrophobic moieties, i.e. ~50 mol%. However, A8-50, which comprises linear aliphatic (octyl) tails, allows one to recover lower amounts of both HsBR from DMPC-fused purple membrane and YidC-GFP from E. coli membrane as compared to CyclAPols. The comparison of CyclAPols with DIBMA, which carries ~33 mol% of acyclic short-length branched (diisobutyl), also shows a more efficient extraction with CyclAPols.

The improvement of solubilization achieved with CyclAPols is therefore due to the cyclic nature of the hydrophobic side-groups. In the case of detergents, the few available data suggest that cyclic hydrophobic groups markedly affect their solution behavior. [START_REF] Maiti | Comparison of the Aggregation Behavior of Di-and Triblock Nonionic Amphiphiles with Linear and Cyclic Hydrophobic Tails[END_REF][START_REF] Varadaraj | Influence of Hydrocarbon Chain Branching on Interfacial Properties of Sodium Dodecyl Sulfate[END_REF][START_REF] Sugiyama | Micellar Properties of Sodium Cyclododecyl Sulfate in Aqueous Solution[END_REF] In-tail cycles restrict packing possibilities, which is reflected in a lower propensity to self-assemble (up to 8 times higher critical micelle concentration compared to linear counterparts, lower aggregation number, more hydrated core). [START_REF] Maiti | Comparison of the Aggregation Behavior of Di-and Triblock Nonionic Amphiphiles with Linear and Cyclic Hydrophobic Tails[END_REF][START_REF] Varadaraj | Influence of Hydrocarbon Chain Branching on Interfacial Properties of Sodium Dodecyl Sulfate[END_REF][START_REF] Sugiyama | Micellar Properties of Sodium Cyclododecyl Sulfate in Aqueous Solution[END_REF] A lower stability of intra-polymer hydrophobic association in CyclAPols likely makes these groups more available to interact with lipid bilayers, and thus to extract MPs. But other molecular parameters may also play a role. Not surprisingly, a higher density of hydrophobic side-groups in amphiphilic copolymers enhance their interaction with liposomes, 9,10 which is in line with their relative efficiency at solubilizing BR (SMA (2:1) < SMA (3:1) and A8-35 < A8-50). Overall, however, the density of side groups does not suffice to account for solubilization efficiency. Thus, the density of hydrophobic moieties along C 8 -C 0 -50 (or C 6 -C 2 -50) is the same as in A8-50, whereas these polymers exhibit significant differences in extraction efficiency (C 8 -C 0 -50 >> A8-50).

Moreover, because cycloalkyl moieties expose less surface to water than linear chains, cyclic side groups are effectively less hydrophobic than linear ones, so that CyclAPols rank below A8-50 in term of effective hydrophobicity and could be expected to be less efficient solubilizers. A second possibly relevant parameter is the degree of ionization of the copolymer chains. [START_REF] Vial | Association of Octyl-Modified Poly(Acrylic Acid) onto Unilamellar Vesicles of Lipids and Kinetics of Vesicle Disruption[END_REF] As APols are weak acids, ionization of polymer chains is reported to lower the detergency by markedly increasing hydrophilicity. Potentiometric titrations of APols and CylAPols revealed a subtle shift in the degree of ionization, at fixed pH, of the various polymers (Figure S15). The degree of ionization at neutral pH, however, ranks the polymers as follows: A8-50 < C 8 -C 0 -50 < A8-35, which does not correlate with extraction efficiency. It seems reasonable to conclude that the cyclic nature of the side groups, rather than the hydrophilic/hydrophobic balance, plays the key role in improving MP extraction.

The relative efficiency of polymers with respect to MP extraction varies depending on the protein under consideration. For instance, the amounts of HwBR extracted from E. coli membranes with either A8-35 or SMA (2:1) were much lower than that obtained with SMA (3:1), whereas the amounts of YidC-GFP extracted with these three polymers were similar.

A8-50 showed also some variability depending on the protein and/or the membrane used.

Similarly, DIBMA showed a poor efficiency at extracting both YidC-GFP and BR, whereas it has been reported to be able to extract other MPs. [START_REF] Oluwole | Solubilization of Membrane Proteins into Functional Lipid-Bilayer Nanodiscs Using a Diisobutylene/Maleic Acid Copolymer[END_REF][START_REF] Barniol-Xicota | Stable and Functional Rhomboid Proteases in Lipid Nanodiscs by Using Diisobutylene/Maleic Acid Copolymers[END_REF] In the present series of experiments, the two CyclAPols showed little sensitivity to the nature of the proteins. In addition, an interesting observation is that HsBR is much more stable when extracted with CyclAPols than with SMAs: it retains 80-85% of its native conformation after 6 h at 50°C, vs. ~20% in SMAs.

How general this effect is and which mechanism underlies it will require further investigations.

Conclusions

In conclusion, we have shown that cyclic hydrophobic moieties improve the copolymer ability to solubilize membranes as compared to linear aliphatic chains. Detergentfree solubilization of HsBR by CyclAPols was as efficient as with SMA (3:1) and the CyclAPol-extracted HsBR was as stable as in A8-35 [START_REF] Popot | Membrane Proteins in Aqueous Solutions: From Detergents to Amphipols[END_REF] (a stability that SMAs failed to provide). The CyclAPols can also solubilize different MPs from E. coli membranes over a short period of incubation (typically 1h) and at low concentration. Recently, CyclAPols have been validated in structural studies of MPs using cryo-EM single particle analysis and electrospray ionization mass spectrometry. [START_REF] Higgins | Cycloalkane-Modified Amphiphilic Polymers for High Resolution Single Particle Cryo-EM and Mass Spectrometry[END_REF] Moreover, CyclAPols are compatible with UV-visible spectroscopic measurements (Figure S8). By ranking the various copolymers according to their detergent-like efficiency, it appears that differences between CyclAPols and classical APols correlate neither with their hydrophobicity nor with chain ionization, and thus likely reflect specific properties of cycloalkane side-chain self-assemblies and/or binding to membranes.

ASSOCIATED CONTENT Supporting Information. Polymer characterization by 1 H, [START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF]

UV-visible compatibility of CyclAPols

. UV-visible spectra of copolymers used in the study. Solutions of polymers were prepared at 1 mg/mL in deionized water. Spectra were recorded using a 10-mm path length cuvette. and elution buffers contained 20 mM sodium phosphate, 100 mM NaCl, pH 7.0. V 0 and V T stand for the void volume and total volume, respectively.

11. Evolution over time of the hydrodynamic diameters (D H ) of HsBR/DMPC proteoliposomes upon addition of polymer solutions Table S1. Average hydrodynamic diameters (D H ) as measured by DLS along the kinetics after supplementation of HsBR/DMPC proteoliposomes with a solution of polymer (1:1 v/v). The size measurements, performed at two incubation times, i.e. 2.7 h and 24 h (before and after centrifugation), are given with a standard error of +/-15 nm. The (w/w) ratios of HsBR/DMPC and HsBR/polymer were fixed to 1:5 and 1:12.5, respectively. liposomes in deionized water to reach a final polymer/DMPC ratio of 1:10 (w/w). This ratio ensures that neutralized polymer chains (prone to precipitate at low pH in water) can bind to liposomes, thus maintaining their solubility up to the end of titration. The polymers, at a final concentration of 0.25 mg/mL, were titrated with a 0.016-M HCl solution added dropwise in the sample while stirring. The pH values were measured with a nano-electrode (Inlab Nano, Mettler Toledo) at 25 °C after each addition of HCl.

Polymers

1 ,

 1 Figures S1 to S7 in SI and Table1).

  coli. Two different MPs were expressed and used as target MPs to estimate the extraction efficiency of each polymer. The first protein was YidC of E. coli, an insertase whose transmembrane domain comprises six α-helices.[START_REF] Kumazaki | Crystal Structure of Escherichia Coli YidC, a Membrane Protein Chaperone and Insertase[END_REF] A version of YidC fused at its C-terminus with GFP (YidC-GFP) was used as reporter to quantify the solubilization yields. In Figure2are reported the amounts of polymer-extracted YidC-GFP recovered in the supernatants after 1 hour of incubation at 4°C at a fixed total MP/polymer ratio of 1:1 (w/w). Under these experimental conditions, the yields of YidC-GFP extracted with CyclAPols were the highest as compared to the references, i.e. A8-35, A8-50, the two SMAs and DIBMA (Figure2A). The amounts of CyclAPol-extracted YidC-GFP were almost twice that obtained with A8-50 (~70-75% vs. ~40%). Monitoring the solubilization over 2-h incubation of the membranes with CyclAPols revealed a rapid increase of YidC-GFP fluorescence in supernatants before reaching a plateau after ~45 min. (Figure2B). A 1-h incubation suffices to reach the maximal extraction (Figure2A), whereas extraction by either one of the two SMAs or by A8-35 progresses more slowly (Figure2B).

Figure 2 .

 2 Figure 2. Fraction of YidC-GFP extracted from E. coli membranes upon addition of different

Figure 3 .

 3 Figure 3. Extraction of Hq. walsbyi BR (HwBR) from E. coli membranes using various

  CyclAPols of the purple membrane of Hb. salinarum

Figure 4 .

 4 Figure 4. Solubilization by copolymers of DMPC-fused purple membrane at HsBR/polymer

  25) were measured by DLS. Compared to SMA (3:1), the D H of complexes formed with CyclAPols were smaller. The population of solubilized objects was also analyzed by size exclusion chromatography (SEC), confirming that HsBR/DMPC/SMA (3:1) supernatants contained larger objects than those formed with CyclAPols (more material eluted in the void volume of the column; FigureS13). Therefore, whereas CyclAPols and SMA (3:1) can solubilize up to 90% HsBR, the complexes formed with CyclAPols appear smaller and more monodisperse.

Figure 5 .

 5 Figure 5. Fraction of native HsBR extracted as a function of polymer concentration. The

Figure 4 .

 4 Figure 4. Asterisks point to samples used for D H measurement in supernatants by DLS at

Figure 6 .

 6 Figure 6. Kinetics of disruption of DMPC/purple membrane proteoliposomes upon addition of

Figure 7 .

 7 Figure 7. Kinetics of inactivation of HsBR incubated at 50°C after extraction from DMPC-

4 .

 4 Figure S7. Acid-base titrations of polymers. The titrations of free carboxylate groups of C 6 -C 2 -50 (A), C 8 -C 0 -50 (B), and A8-50 (C) were performed at 20 °C in a mixture of water/ethanol (80:20, v/v).

7 .

 7 Figure S9. SDS-PAGE analysis of YidC-GFP extracted from E. coli membranes using polymers. Over 2-h incubation, aliquots were taken off from samples and centrifuged (10 min. at 250,000 ×g). Supernatants (S) and pellets (P) were loaded on 12-% acrylamide gels. After migration, the band of YidC-GFP was visualized on the gels upon exposition to excitation and emission wavelengths (495 and 519 nm, respectively) revealing the GFP fluorescence at the expected position of YidC-GFP.

Figure S13 .

 S13 Figure S13. SEC profiles of HsBR/lipid/polymer particles. The DMPC-fused purple membrane was solubilized overnight, in the dark at room temperature with either SMA (3:1), C 6 -C 2 -50, or C 8 -C 0 -50. After centrifugation (20 min at 200,000 ×g), each sample was injected onto a Superose 12 10/300 GL column connected to an Äkta purifier-10 system. The sample

Figure S14 . 13 .

 S1413 Figure S14. Kinetics of disruption of pure DMPC liposomes upon addition of polymers. Extruded DMPC liposomes with a diameter of 100 nm were prepared in buffer 20 mM sodium phosphate, 100 mM NaCl, pH 7.0. Solubilization was initiated by mixing one volume of liposomes to one volume of polymer solutions to reach a final lipid/polymer (w/w) ratio of 1:1.25. Kinetics were monitored by measuring light scattering intensity, I, at 90° angle and 25°C.

- (x 1 /x 2 , %) Hydrophobic groups (y 1 /y 2 , %) x (%) y (%) 𝑴 𝐧 (g•mol -1 )

  ).

	APol	CO 2
	C 6 -C 2 -50	47/46	53/54	46.5 ± 0.5	53.5 ± 0.5	4919
	C 8 -C 0 -50	52/46	48/54	49 ± 3	51 ± 3	4843
	A8-50	47/40	53/60	43.5 ± 3.5	56.5 ± 3.5	5050

Table 1 .

 1 Chemical compositions and number-average molecular masses of polyacrylate-based

Proton Number of proton per monomer δ (ppm) Theoretical value

  C NMR spectroscopy and potentiometric titrations, UV-visible spectra of polymers, SDS-PAGE analysis of YidC-GFP, kinetics of HwBR extraction, photographs of tubes containing polymer-extracted HsBR after ultracentrifugation, size exclusion chromatography profiles, hydrodynamic diameters of Chemical composition of C 6 -C 2 -50 analyzed by 1 H and 13 C NMR spectroscopy Chemical composition of C 8 -C 0 -50 analyzed by 1 H and 13 C NMR spectroscopy

	Supplementary Figures: 2.
	HsBR/DMPC proteoliposomes upon addition of polymer solutions, solubilization of pure liposomes by polymers, potentiometric titrations of polymers in the presence of DMPC liposomes. 2 3.16 2y ! ! a + c b + d f + g + h + i e j Carbon Number of carbon per monomer δ (ppm) Theoretical value Free carboxylate 1 183.78 x Carboxamide 1 177.46 y e + f 2 36.17-41.52 2y g + h 3 33.47-35.52 3y i + j 3 26.63-28.38 3y ! ! -CO 2 -Na + -CONH-e + f g + h 1. e i + j
	a + c	1 + 1	1.97-2.51	x + y
	b + d Figure S2. 13 C NMR analysis of C 6 -C 2 -50 and signal assignments. 2 + 2 1.56-1.91	2(x + y)
	f + g + h + i	11	0.70-1.55	11y
	j	2	0.96	2y
	Figure S1. 1 H NMR analysis of C 6 -C 2 -50 and signal assignments.

Proton Number of proton per monomer δ (ppm) Theoretical value

  Chemical composition of A8-50 analyzed by 1 H and[START_REF] Knowles | Membrane Proteins Solubilized Intact in Lipid Containing Nanoparticles Bounded by Styrene Maleic Acid Copolymer[END_REF] C NMR spectroscopy

	3.
					g + h + i
					f
			!		f + g + h + i
		-CONH-			e
	-CO 2	-Na +		!
					!
				b + d
		e		a + c
	!
	!	Carbon	Number of carbon per monomer	δ (ppm)	Theoretical value
		Free carboxylate	1	183.62	x
		Carboxamide	1	176.22	y
		e e	1 1	3.86 50.57	y y
		a + c f	1 + 1 2	2.00-2.60 33.13	x + y 2y
		b + d g + h + i	2 + 2 5	1.70-2.0 24.94-29.70	2(x + y) 5y
		f + g + h + i	14	1.05-1.70	14y
	Figure S4. 13 C NMR analysis of C 8 -C 0 -50 and signal assignments.
	Figure S3. 1 H NMR analysis of C 8 -C 0 -50 and signal assignments.

Proton Number of proton per monomer δ (ppm) Theoretical value

								g + h + i + j
							b + d + f
						!		l
						a + c
					e
	!	Carbon	Number of carbon per monomer	δ (ppm)	Theoretical value
		Free carboxylate	1		184.31		x
		Carboxamide	1		177.70		y
		e		1		40.66		y
		e f + g + h + i + j	5	2	2.86-3.30 28.38 -33.07	2y	5y
		k	a + c	1	1 + 1	2.00-2.55 23.73	x + y	y
		l	b + d + f	1	2 + 4	1.43-1.98 14.50	2(x + 2y)	y
		g + h + i + j + k	10	1.07-1.41	10y
	l Figure S6. 13 C NMR analysis of A8-50 and signal assignments. 3 0.80-0.98	3y
	Figure S5. 1 H NMR analysis of A8-50 and signal assignments.

  12. Solubilization of pure DMPC liposomes in the presence of polymers

			D H (nm)
	) a+er)2.7)h)		after 24 h
			0	+	centrifugation
	A8035	210	202	110
	A8050	153	120	51
	SMA)(2:1)	170	180	32
	SMA)(3:1)	220	214	nd
	C 6 0C 2 050 C 8 0C 0 050)	127 206,	75 nd,	30 nd,

AUTHOR INFORMATION

Corresponding Author

* Correspondence should be addressed to Christophe Tribet (christophe.tribet@ens.fr) and Manuela Zoonens (manuela.zoonens@ibpc.fr).

Present Addresses †ICSM, Univ Montpellier, CEA, CNRS, ENSCM, Marcoule, France.

Author Contributions


Simon Gabay

Thibault Clérice

Jean-Baptiste Camps

Jean-Baptiste Tanguy

Matthias Gille-Levenson

Standardizing linguistic data: method and tools for annotating (pre-orthographic) French

Keywords: Applied computing → Arts and humanities;, Computing methodologies → Natural language processing linguistic annotation, pre-orthographic language, lemmatisation, POStagging

With the development of big corpora of various periods, it becomes crucial to standardise linguistic annotation (e.g. lemmas, POS tags, morphological annotation) to increase the interoperability of the data produced, despite diachronic variations. In the present paper, we describe both methodologically (by proposing annotation principles) and technically (by creating the required training data and the relevant models) the production of a linguistic tagger for (early) modern French (16-18th c.), taking as much as possible into account already existing standards for contemporary and, especially, medieval French.

INTRODUCTION

If medievalists have been working for years on the creation of high quality corpora as well as the tools to build and analyse them (e.g. the Base de français médiéval (BFM) [START_REF] Guillot | Base de français médiéval : une base de référence de sources médiévales ouverte et libre au service de la communauté scientifique[END_REF] and TXM [START_REF] Heiden | TXM : Une plateforme logicielle open-source pour la textométrie -conception et développement[END_REF]), the situation is different for more recent periods of French literature. As far as we know, for texts written between the 16th and the 18th c., Presto is the only project that has developed a corpus [START_REF] Blumenthal | Presto, un corpus diachronique pour le français des XVIe-XXe siècles[END_REF] with some computational resources [START_REF] Diwersy | Ressources et méthodes pour l'analyse diachronique[END_REF]]. However, both are not maintained anymore, which leaves more than three centuries of French literature computationally understudied. It becomes therefore important DTUC '20, October 15-17, 2020, Online, Tunisia 2020. https://doi.org/10.1145/3423603.3423996 to overcome this difficulty, and to create the tools that we desperately need for (early) modern French (henceforth EMF).

Such a task cannot be done without taking into account longstanding annotation practices, in order to allow (minimal) interoperability with already existing datasets. uch a statement is sadly easier said than done, because EMF is an intermediary stage between medieval (12th-15th c.) and late modern and contemporary (from c. 1750) French, two states of language that tend to have different needs regarding annotation: EMF is then caught in between two (potentially incompatible) practices, one for each extreme of the continuum. Facing such a dilemma, we have decided first to look up, in diachrony, and align (when possible) our choices with those of medievalists, rather than to look immediately down at what synchronists dowhich tends to be the norm. Our project is indeed to create a tagger for EMF producing data as much as possible compatible with existing medieval corpora, and therefore build the technical frame for the computational study of pre-orthographic French, understood as the forms of this tongue prior to their standardisation based on the recommendations of the Académie française.

Textual production before the implementation of this "academic" French (c. mid-18th c., rather than the publication of its Dictionnaire in 1694) share common features [START_REF] Catach | Histoire de l'orthographe française[END_REF]]. Among many others, the most important one is to undergo a significant graphematic variation, i.e. a relative instability regarding the spelling (estoit vs étoit) and the segmentation (à fin que vs afin que). Thus, to bypass this problem, the linguistic annotation has to be thought as a pivot format [Auroux 2000, p. 393] that allows users to navigate across heterogeneous data.

Several options are available, such as the conflation by phonetic identity or by lemma [START_REF] Jurish | Finite-state canonicalization techniques for historical German[END_REF]] -proto-forms being currently investigated as a potential solution, without being yet fully operational [START_REF] Fourrier | Comparing Statistical and Neural Models for Learning Sound Correspondences[END_REF]]. Among all possibilities, we have decided to opt for lemmatisation+POS tagging as a joint solution for two main reasons: on the one hand many resources are already available (cf. infra), and on the other hand it is already used for other tasks such as collation [Camps et al. 2019b] or stylometric analysis [START_REF] Camps | Why Molière most likely did write his plays[END_REF].

ANNOTATION PRINCIPLES

Since all choices have been carefully discussed in our annotation manual [START_REF] Gabay | vue de la création de modèle de lemmatisation et d'annotation morpho-sytaxique et morphologique du français des XVI-XVIIIème s[END_REF] we will here present the main problems raised by annotating EMF: tokenisation, lemmatisation, POS and morphological tagging.

Tokenisation

As any language, French has undergone phenomena of agglutination at the graphematic (ce pendant → cependant) and at the lexical (e.g. bien que) level. Such a process is not easily datable, because it varies from one region or one phenomenon to the other: in long diachrony, it is therefore impossible to decide precisely when such occurrences have to be tagged as two, or one token. For this reason, we have decided to use the blank space as the main separator for the tokenisation, with hardly any exception to this rule: all locutions, may they be conjunctive (tandis que), adverbial (à demi) or prepositional (quant à), are segmented in two parts rather than one (tandis and que, à and demi, quant and à).

Following this maximalist approach, none of the compounds are analysed as one token: peut être, long temps,. . . are all considered as multiple tokens (peut + être, long + temps) -and this despite the presence of the hyphen, which is considered as a token itself (peutêtre → peut + -+ être, long-temps → long + -+ temps. . . ). For the same reason (absence of blank space), words that are already welded (monsieur < mon sieur) are treated as one token.

Such a choice to respect the actual segmentation of original witnesses introduces a bias, because it follows the scripta (i.e. the writing practice) of printers in (early) modern France [START_REF] Pellat | L'évolution de l'orthographe des imprimés au XVIIe s. (libraires français et hollandais)[END_REF] and not necessarily the preference of authors. This decision is however more in line with our philological approach, because it relies less on today's linguistic understanding of EMF and outsources complex decisions to historical speakers.

Lemmatisation

This tokenising strategy creates some lemmatisation problems. The most important one is the absence of coherent lemmas for agglutinated forms that have no autonomy outside a locution such as parce (in parce que, < par ce) or afin (in afin que, < à fin), but also with portmanteau words (tresobeissant < tres+obeissant). A simple solution is the creation of compounded lemmas, with an underscore separating the original lemmas (tres_obeissant), but such a method cannot be generalised: on the one hand, in diachrony, (too) many tokens could need one (mon_sieur? autre_fois?), and on the other hand we take the risk to end up with (too) many compounded lemmas for a single token (audit→à_le_dit). In order to limit our logic, tokens that have subsisted into contemporary French are therefore analysed as a simple lemma (parce, afin), but those that have not subsisted are analysed as a compounded lemma (tres_obeissant): this limits the creation of lemma, and maintains interoperability with other language states.

For other words, we have decided to use, when possible, the contemporary form of each token as a canonical form. It usually is the infinitive form (for verbs: mangeons → manger) or the masculine singular (for nouns or adjectives: comtesses → comte). Such a process is diachronically problematic, since some words have lost (dominus/domina > dame but also old fr. dom), or almost lost (damoiseau vs demoiselle), their masculine counterpart over time: in such cases, we only choose the feminine version if the masculine one is not attested anymore at the end of the 18th c.

In order to control the consistency of the annotation, several authority lists have been created. The main one derives from the lexicon of medieval French inflected forms LGeRM [START_REF] Souvay | LGeRM Lemmatisation des mots en Moyen Français[END_REF] in its mode version (i.e. moderne étendu) produced for the Presto project [START_REF] Diwersy | Ressources et méthodes pour l'analyse diachronique[END_REF]. The LGeRM lexicon is based on the Freeling version of the Lefff [START_REF] Sagot | The Lefff, a freely available and large-coverage morphological and syntactic lexicon for French[END_REF]], augmented with Morphalou [START_REF] Romary | Standards going concrete: from LMF to Morphalou[END_REF] for contemporary lemmas, and the Dictionnaire du Moyen Français (DMF) [ATILF-CNRS and Université de Lorraine 2015] for (early) modern ones. Such an approach should help us maintain minimal interoperability with the medieval version of

LGeRM, but also the Trésor de la Langue Française informatisé (TLF ) [START_REF] Pierrel | Le TLFi ou Trésor de la Langue Française informatisé[END_REF]. Two other authority lists have been created: one for named entities (people, places. . . ) and an other one with foreign words.

POS-tagging

Regarding POS-tagging, we have decided to use CATTEX [START_REF] Prévost | Jeu d'étiquettes morphosyntaxiques CATTEX[END_REF] for three reasons: first it is already used for the BFM and by several other corpora [Camps et al. 2019a], second it already benefits from a detailed annotation manual [Guillot et al. 2013a], third, it has been designed to cope with the complexity of old states of the French language.

Between the options exposed by Guillot et al. [2013b], we have opted for morpho-syntactical annotation: we take into account the context when categorising tokens and adjectives can be tagged as adverbs (il parle fort) or adverbs as substantives (il fait le bien). It allows us to follow the evolution of uses over time for a single word. However, following CATTEX as well as Presto recommendations, we never categorise present and past participles as adjectives, because if such distinctions are already difficult in synchrony, they are even harder to identify in diachrony. It would be too complicated to precisely differentiate the past participle of perdre (perdu) from the adjective perdu over the very centuries during which the verb has undergone a slow process of adjectivisation, especially without clear markers such as the determiner for the substantivization (il fait bien vs il fait le bien).

Our (maximalist) tokenisation principles incitate (but do not force) us to tag words with their original part of speech: bien in bien que is an ADVgen and not a member of a potential LOCconj (that does not exist within CATTEX). This choice considerably simplifies the interoperability with Old and Middle French. It does create some problems though, and we are forced to use analogies to tag certain tokens: pource in pource que is therefore ADVgen, such as bien in bien que.

Morphology

We have decided to implement CATTEX-max [START_REF] Prévost | Jeu d'étiquettes morphosyntaxiques CATTEX[END_REF], that is to say to annotate each token with morphological information (gender, mood, tense. . . ). Contrary to lemmas and POS, this linguistic information has been added for technical purposes (it has helped maximise the efficiency of the final model): if it has been proofread to avoid major mistakes, its perfection is not guaranteed.

TRAINING A MODEL

Based on the previously introduced annotation choices, we have decided to train a lemmatiser and a POS-tagger.

Data recycling

A substantial amount of heterogeneous data is already available (cf. tab. 1). Considering the cost of creating a gold corpus, we have decided that it would be more efficient to re-process existing data rather than create new ones from scratch. Two corpora come from a previous study [START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]] and are almost ready to use:

• The CornMol corpus has been created to carry stylometric studies [START_REF] Camps | Why Molière most likely did write his plays[END_REF]. It is based on 41 comedies written in the 17th c., carefully sampled and proofread, which have been thoroughly described [START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]].

• The Frantext open access data [ATILF-CNRS and Université de Lorraine

2018] is composed of 32 texts, mainly written in the 18th (7 texts), 19th (24 texts) and 20th c. (4 texts). Because the corpus is already tagged and lemmatised (but not fully corrected) following other guidelines than ours, the lemmas have been aligned according to our standards, as much as we could. Regarding Presto, because it is composed of four different subcorpora (for a detailed description of the different levels and variations, cf Vigier [2018]), it requires some selection, processing and correction:

• A gold corpus is made of 60 000 tokens, taken from 5 texts written in the 16th (1 text), 17th (2 texts) and 18th c. (2 texts). These texts have all been sampled, tokenised, tagged, lemmatised and proofread to create training data for a TreeTagger model. • The final Presto corpus is a three-fold one: noyau ("core"), contrôlé ("controlled") and étendu ("extended"). We have limited ourselves to a selection of its core version (cf. Appendix).

Preparation

Because the CornMol and Frantext Open Access corpora have already been prepared for our previous experiment on normalisedspelling French, it already follows closely our choices regarding tokenisation and POS-tagging (minor changes have been made in between), and the shift of authority list from Morphalou to LGeRM is of almost no impact since the latter derives from the former. All the effort have therefore been put on the correction and the alignment on our standards of the two Presto sub-corpora, which was problematic for three reasons. First, our choices differ strongly from Presto's regarding tokenisation and POS-tagging -but not lemmatisation, since they also use LGeRM. Second, because their training data has been mainly prepared for POS-tagging and not lemmatisation, and also because the annotation has been done with an older and less precise tool (TreeTagger), the result is far from being perfect. Third, it is impossible to recycle some texts of their final corpus into training data, because we need (fairly) clean texts -Jean de Léry's Voyage en terre du Brésil had therefore to be withdrawn because of the noise produced by hyphenation. Most of the correction work has been done with Pyrrha [Clérice et al. 2019].

In order to deal with more complex data than the one we use for training, we have artificially added a very limited number of glyphs typical of (early-)modern prints such as the long s (ſ ), the eszett (ß) or tilded letters traditionally used as abbreviations (õ, ã, ũ, ĩ).

Out of all these data, two different corpora have been produced:

• A primary corpus, fully annotated with lemma, POS and morphology, based on tokens with normalised and non-normalised spelling, has been created out of the two gold corpora (Corn-Mol and the revised version of Presto gold). • A secondary corpus, with lemmas only, has been produced

out of Frantext open access data, the corrected versions of Presto gold and Presto core, and CornMol.

These two corpora are used to train two separate models: one for the POS and the morphology, and another for lemmatisation only. Therefore, two training datasets have been created using Protogénie [Clérice 2020b] (cf. tab. 2): they contain a train set, a development set (for evaluation during training) and a test set (for in-domain testing). The breakdown of tokens between the train, dev and test set is dependent on the the total amount of data and has been done on an empirical basis, in order to keep as much tokens for training as possible, while still keeping a reliable test set. As such, it is dependent on the total size of the corpus (the bigger the corpus, the smaller the fraction of it which is necessary for reliable training).

Corpus

Train Because of the size of the corpus, it is impossible to control each token. The general quality is therefore guaranteed by the use of already existing corpora, which have already been carefully prepared for previous tasks. The consistency of the annotation is controlled with authority lists, but also with intermediary models, which help inspect the consistency of the data sets. After each training, the creation of a confusion matrix allows to identify frequent confusions between predictions and ground truth data, that could be due to inconsistencies in the human annotation.

Set up

We use Pie [START_REF] Manjavacas | Improving Lemmatization of Non-Standard Languages with Joint Learning[END_REF] as our main training and tagging software . For training, Pie is used for lemma-and POS-tagging. At inference time, we use Pie-extended [Clérice 2020a] which wraps the former with more user-friendly functionalities (model sharing, advanced post-and preprocessing options. . . ). Several architectures have been tested for our previous study on normalised texts (for more detailed scores, cf. [START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]) , the best one being:

• RNN with 300 dimensions for characters • Sentence and word embeddings (150 dimensions) using 343 drama texts from [START_REF] Fièvre | Théâtre classique[END_REF]] and those of the FranText Open Access that we presented supra, for a total of c. 7M tokens.

• Hidden size of 150 • Forward and backward language models However, additional tests have proven since the possibility of increasing even more the accuracy with a bigger number of dimensions for the RNN (300→400) and the hidden size (150→256), and NFKD unicode normalisation of the data, without word embeddings. Based on these new results, we have decided to test this new successful M3 configuration rather than the M1 and M2 previously presented as the most efficient. Two versions have been tested: the first with one linear layer, the second with two linear layers. For each configuration, due to the stochastic nature of the process, three models were trained, using early stopping with threshold 0.001 and patience 7. The best one was retained. For time and ecological purposes, NFKD normalisation has been tested on the most relevant architecture only.

Previous tests included a comparison with Marmot for POS-tagging, and results were equivalent to those obtained with Pie [START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]] "Unknown tokens" are tokens never seen during training, while "ambiguous tokens" are forms that can correspond to different lemmas. "Unknown targets" are lemmas never seen in training, but that the neural network can still sometimes accurately predict, thanks to its character level modelling.

Results

First, the existence of spelling variation seems to have a limited impact, or to be efficiently counter-balanced by our data augmentation: the accuracy remains similar to the one of models trained exclusively on normalised spelling data for lemmatisation (98.62% vs 99.28%) and even higher for POS-tagging (97.18% vs 97.01%). Such results are very promising. When looking into the details, we observe that two linear layers have an almost null (+0.001 pt of % for POS) or slightly negative impact (-0.0002 pt of % for lemmas). Considering the (much) larger training time and energy use, it does not seem to be a satisfactory solution. Because NFKD lowers the amount of characters (235 → 164) we have decided to lower the amount of dimensions for the RNN character embeddings (400 → 300). The final results show a slightly negative impact on the accuracy, which proves that the efficiency of NFKD on the CornMol corpus is linked to the smaller size of the corpus and that unicode decomposition and normalisation is probably less relevant on big corpora -similar scores could be achieved with fine tuning, especially by lowering the number of dimensions. The significant increase of training data (90,000 to 150,000 tokens) have a significant effect on the efficiency of the POS-tagging model, and we improve the results of the previous model based on normalised-spelling data only.

Impact of spelling variation

The score for "ambiguous tokens" given by Pie evaluates its efficiency regarding homographs, i.e. its capacity to disentangle tokens like entre which can be both a form of the verb entrer (il entre dans la pièce) or the preposition (entre les murs). However, lemmatising historical variation-rich languages is also about handling polymorphism, because a same word can frequently have different graphematic realisations (e.g. besoin vs besoing). We have therefore decided to evaluate the robustness of our best model regarding the graphematic volatility of (early-modern) texts, as [START_REF] Millour | Unsupervised Data Augmentation for Less-Resourced Languages with no Standardized Spelling[END_REF] did for their study on dialectal variation.

214 pairs of two different tokens sharing the same lemma, POStag and morphology have been extracted from the whole presto gold corpus, so that we have a Form A and a Form B in each pair: afin vs affin, changements vs changemens. . . . It is to be noted that, by including only pairs that are actually present in the final training data, we have limited the significance of our results for out-of-domain and/or rare graphematic realisations.

In order to evaluate the effect of spelling variation, we designed a simple algorithm: in the test set, for each pair, all sentences containing a token matching the lemma and one of the variant of the pairs are extracted. This group of sentences is then duplicated: the first set is left untouched, while, in the second set, all occurrences of variant are replaced by the alternative variant . Both groups are then lemmatised and the accuracy is compared to evaluate the robustness of the model despite spelling variation in strictly equivalent contexts.

By doing so, we are able to evaluate the recognition of the spelling variants while neutralising variations due to the left and right contexts (each form is artificially given the same number of occurrences and the same contexts). We then test our model on both set, and compare accuracy for (

) and for ( ), with a simple difference:

Δ = | - |
For all these pairs, the median Δ , the geometric mean Δ , and the weighted geometric mean, using the frequency of variant in the training data as weight, are all equal to 0 (arithm. mean is 0.025; weight. arithm. mean is 0.011). We can therefore conclude that spelling variation has a very limited impact on the accuracy, as long as both forms are present in the training data. In the future, it would be necessary to extend this kind of analysis to pairs for which one variant is unseen by the model .

Out-of-domain tests

We have tested our best lemma and our best POS models on the same out-of-domain testing data than the one used for our previous study. There are two test sets for each century: one made only of theatre, the other one of everything but theatre. Each test set is composed of 10 short samples (c. 100 tokens), as representative as possible of the linguistic production of the century (female and male authors, decade of publication, genre. . . ).

Because the model built for the previous study was trained on normalised-spelling data, out-of-domain data had been normalised too. For this new study, the out-of-domain test set has been duplicated and now exists in both original and normalised transcriptions for the 16th, 17th and 18th c. texts only, and not for 19th and 20th c. texts, which do not require any spelling normalisation.

We observe that accuracies on normalised-spelling out-of-domain testing data are relatively similar for both the model trained on normalised data and the one trained on original data. The fact that the main difference are observed for theatrical plays could imply that the model trained on normalised data has been tailored for this genre. Without surprise, regarding non-normalised out-of-domain testing data, the accuracy of the model diminishes with centuries as we go back in time.

Results regarding POS annotation are relatively similar to the one of lemmatisation, and we observe again a significant impact of the theatrical genre on the accuracy.

INTERPRETATION

Interestingly, none of the most important errors are linked to graphematic polymorphism. Most of the problems are linked to homographs: le pronoun (il le veut) vs determiner (le château), the verb a (il a) vs the preposition (à Genève) when it does not have the grave accent (a Genève), the determiner des (il fait des ronds) vs the enclise de+le (le père des enfants). If such results confirm those obtained on normalised data, the presence of noise in the Presto core corpus could explain some errors.

FURTHER WORK

The next step, already in preparation, is the extension of the annotation to named entities to train a NER for EMF. With texts published on three centuries, and especially with a long excerpt of the Encyclopédie (c. 1,500,000 tokens), we do believe that our corpus is rich enough to carry preliminary tests. The presence of already corrected lemmas and POS tags for proper nouns (to which a special attention was given during the correction of the corpus) should dramatically ease the annotation process.

Regarding lematisation and POS-tagging, the most important task will be the extension of the training data for 16th c., and even 15th c. French, which is clearly underrepresented in our corpora: the complexity of middle French would certainly require more data, and new strategies to maintain the interoperability between medieval and (early) modern datasets.

CONTRIBUTIONS

This project is a follow-up to another one designed by Florian Cafiero, J.

DATA

The most up-to-date version of the models can be easily obtained and used thanks to the pie-extended Python package, available on Pypi (https://pypi.org/project/pie-extended/), with the command pie-extended download freem. All the data are available online at https://github.com/e-ditiones/LEM17.

APPENDIX

The full breakdown of the CornMol and FranText Open Access corpora can be found in [START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]. We therefore describe only the Presto data we have used.

Presto Gold

  -B. C. and S.G. It has been led by S.G., who prepared the data and the final article, with the help of many: J.-B. T. for the conversion of Presto gold from MULTEX to CATTEX, Lucence Ing for the annotation of Presto gold, and Matthias Gille Levenson for the correction of Presto core. Trainings have been configured and executed by T.C. J.-B. C. has accompanied the entire process, providing technical guidance and philological feedback on the compatibility with medieval data. All authors discussed the results and contributed to the final manuscript.

Table 1 : Available training data

 1

	Name	Gold Norm. Tokens	POS	Morph
	CornMol	Yes	Yes	90,000	CATTEX	Yes
	FranText OA	No	Yes	2 400,000	EAGLES	No
	Presto gold	Yes	Yes	60,000	MULTEXT No
	Presto core	No	Yes	6,820,000	MULTEXT No
	Presto controlled No	Yes	11,636,000 MULTEXT No
	Presto extended	No	Yes	28,309,000 MULTEXT No

Table 2 : Breakdown of the tokens per set (numbers are rounded)

 2

		set	Dev set	Test set	Total
	POS	132,905	9,733	15,303	157,941
		84%	6%	10%
	Lemma	6,666,473 70,009	352.482	7,088,964
		94%	1%	5%

Table 3 : Scores (normalised spelling data only

 3

			LEMMA
	Lemma	M2	M3	M3+NFKD	support
	In-domain	99.09	99.12		99.28	4,181
	Out-of-domain	97.92	98.59		98.67	13,497
			POS
	POS	M1	M1+aux M2	M2+aux support
	All	96.72	96.51	96.84	97.01	4,181
	Ambiguous token 91.86	91.43	92.40	92.29	934
	Unknown tokens	86.24	86.24	78.44	81.65	218

). M1 is the basic Pie configuration, M2 adds word embeddings to M1 architecture, and +aux indicates the use of auxiliary tasks -these architectures being fully described in

[START_REF] Camps | Corpus and Models for Lemmatisation and POS-tagging of Classical French Theatre[END_REF]

as base (sent-lm) and wembs. M3 uses a bigger number of dimensions (400) for the RNN than for the M1 configuration (150), and +NFKD indicates the additional use of unicode normalisation.

Table 4 : Lemmas (normalised+original spelling)

 4

Table 5 : POS (normalised+original spelling)

 5

		1 layer	2 layers	support
	all	97.09	97.18	14,303
	unknown tokens	87.57	88.4	724
	ambiguous tokens 93.81	94.11	4,281

Table 6 : Lemmatisation accuracies of the best model on out-of- domain data.

 6 The scripts for this particular evaluation are available on: Thibault Clérice and Jean-Baptiste Camps, PonteIneptique/classique_variante, Github, 8 sept. 2020, https://github.com/PonteIneptique/classique_variante. Test 1 tests our best model trained on normalisedspelling data on normalised out-of-domain data. Test 2 tests our best model trained on original-spelling data on normalised out-ofdomain data. Test 3 tests our best model trained on original data on original out-of-domain original data.

	Corpus	16th 17th 18th 19th 20th All cent.
		Test 1
	Drama	97.6 98.10 98.88 98.34 98.00	98.19
	Not drama 97.78 98.02 98.06 96.97 97.39	97.65
	Both	97.69 98.06 98.46 97.66 97.70	97.92
		Test 2
	Drama	96.65 97.42 97.69 98.2	97.5	97.51
	Not drama 97.48 98.24 98.27 97.12 96.79	97.59
	Both	97.08 97.83 97.99 97.66 97.15	97.55
		Test 3
	Drama	93.93 96.36 96.95 98.2	97.5	96.64
	Not drama 96.23 97.25 98.2 97.12 96.79	97.13
	Both	95.12 96.8 97.59 97.66 97.15	96.89
	Corpus	16th 17th 18th 19th 20th All cent.
		Test 1
	Drama	95.05 96.59 95.98 94.81 93.57	95.18
	Not drama 92.89 94.27 96.53 91.87 91.35	93.42
	Both	93.93 95.44 96.27 93.36 92.48	94.30
		Test 2
	Drama	93.53 95.68 95.01 93.37 93.42	94.19
	Not drama 92.75 94.5 95.21 92.09 93.59	93.64
	Both	93.12 95.09 95.12 92.74 93.5	93.92
		Test 3
	Drama	89.3 92.72 94.49 93.37 93.49	92.72
	Not drama 89.42 92.6 95.49 92.09 93.59	92.67
	Both	89.36 92.66 95.01 92.74 93.5	92.69

Table 7 : POS accuracies of the best model on out-of-domain data

 7

ACKNOWLEDGMENTS

We would like to thank Lucence Ing and Frédéric Duval for their help regarding complicated annotation choices.