Fabien Caillé
email: fabien.caille@cea.fr

Philippe Gervais

Sylvain Auvity

Christine Coulon

Solène Marie

Nicolas Tournier

Bertrand Kuhnast

Automated two-steps manufacturing of [ 11 C]glyburide radiopharmaceutical for PET imaging in Humans

Keywords: Glyburide, carbon-11, radiosynthesis, PET imaging, radiopharmaceutical

Glyburide is an approved anti-diabetes drug binding to the sulfonylurea receptors-1 (SUR-1) and substrate of solute carrier (SLC) transporters, which can be isotopically radiolabelled with carbon-11 for PET imaging. The aim of this work is to present an original and reproducible automated radiosynthesis of [ 11 C]glyburide and a full European Pharmacopeia 9.7 compliant quality control to use [ 11 C]glyburide in PET imaging clinical trials. Different conditions were explored to afford non-radioactive glyburide by one-step methylation. These experiments monitored by UPLC-MS revealed regioselectivity issues for this approach as methylation occurred preferentially on the sulfonylurea moiety. Therefore, a two-steps process was developed using sulfonamide 3 as precursor, synthesized in 79% yield. Methylation under nonradioactive conditions followed by reaction with cyclohexyl isocyanate in one pot afforded glyburide without formation of methylated side products. The optimized process was applied to the automated radiosynthesis of [ 11 C]glyburide from [ 11 C]MeOTf using a TRACERlab ® FX C Pro. Ready-to-inject [ 11 C]glyburide was obtained in 5% non-decay corrected radiochemical yield and 110 ± 20 GBq/µmol molar activity within 40 minutes (n = 8). A full quality control according to the European Pharmacopeia 9.7 guidelines was realized including organoleptic test, pH measurement, chemical identification with chemical and radiochemical purity assessment by analytical HPLC, residual solvents determination by gas chromatography, radionuclide purity and half-life measurement by gamma-spectrometry, bubbling point filter integrity test, sterility check by incubation in growth media and bacterial endotoxins measurement using the limulus amebocyte lysate test. [ 11 C]Glyburide was compliant with all requirements and can be used as a PET radiopharmaceutical in clinical trials.

INTRODUCTION

Glyburide, also named glibenclamide, is a second-generation sulfonylurea approved by the Food and Drug Administration and the European Medical Agency to treat type 2 diabetes mellitus. Glyburide increases the pancreatic production of insulin by binding to the ATPsensitive potassium channels (KATP) subunit sulfonylurea receptor 1 (SUR-1, ABCC8) of ßcells, allowing the control of glucose levels in blood. [START_REF] Gribble | Sulphonylurea Action Revisited: The Post-Cloning Era[END_REF] With widespread overexpression of SUR-1 in the central nervous system in co-association with transient receptor potential melastatin 4 (trpm4) after brain injury, [START_REF] Simard | Sulfonylurea Receptor 1 in Central Nervous System Injury: A Focused Review[END_REF] glyburide also proved to reduce edema, haemorrhage and tissue damage in preclinical models of numerous CNS injuries. [START_REF] Simard | Protective Effect of Delayed Treatment With Low-Dose Glibenclamide in Three Models of Ischemic Stroke[END_REF][START_REF] Simard | Endothelial Sulfonylurea Receptor 1-regulated NCCa-ATP Channels Mediate Progressive Hemorrhagic Necrosis Following Spinal Cord Injury[END_REF][START_REF] Simard | Glibenclamide Reduces Inflammation, Vasogenic Edema, and Caspase-3 Activation after Subarachnoid Hemorrhage[END_REF] More recently, the Glyburide Advantage in Malignant Edema and Stroke (GAMES-RP and GAMES-PILOT) clinical trials demonstrated that intravenous injection of glyburide was associated with improvements in midline shift, level of alertness, and NIH stroke scale in Humans. [START_REF] Kimberly | Analysis of Adjudicated Edema Endpoints in the Glyburide Advantage in Malignant Edema and Stroke (GAMES-RP) Trial (S23.003)[END_REF][START_REF] Sheth | Pilot Study of Intravenous Glyburide in Patients With a Large Ischemic Stroke[END_REF] Glyburide is also known to be a substrate of several membrane transporters that are key players in the distribution and elimination of drugs. In particular, glyburide is an avid substrate of some organic aniontransporting polypeptide (OATP, SLCO) transporters such as OATP1A2, OATP2B1 and OATP1B1 (Figure 1) [START_REF] Satoh | Citrus Juices Inhibit the Function of Human Organic Anion-Transporting Polypeptide Oatp-B[END_REF][START_REF] Koenen | Steroid Hormones Specifically Modify the Activity of Organic Anion Transporting Polypeptides[END_REF][START_REF] Marie | Imaging Probes and Modalities for the Study of Solute Carrier O (SLCO)-Transport Function In Vivo[END_REF] making an interesting probe to study the importance the OATPmediated influx at the blood-tissue interface. [START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] Glyburide is also carried by efflux ABC transporters such as the breast cancer resistance protein (BCRP, ABCG2), the P-glycoprotein (P-gp, ABCB1) and some multidrug resistance proteins (ABCC1 and 3). [START_REF] Hemauer | Role of Human Placental Apical Membrane Transporters in the Efflux of Glyburide, Rosiglitazone, and Metformin[END_REF][START_REF] Gedeon | Transport of Glyburide by Placental ABC Transporters: Implications in Fetal Drug Exposure[END_REF] Positron emission tomography (PET) is a powerful tool to quantitatively image at the molecular level and assess pharmacokinetic parameters of functional or pathological tissues. Therefore, PET imaging of SUR-1 using radiolabelled glyburide is an appealing approach supported by in vitro studies showing a saturable uptake of [ 3 H]glyburide proportional to the number of ßcells. [START_REF] Schmid-Antomarchi | The Receptor for Antidiabetic Sulfonylureas Controls the Activity of the ATP-Modulated K+ Channel in Insulin-Secreting Cells[END_REF] Unfortunately, PET imaging of SUR-1 at the pancreas level using [ [START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] C]glyburide [START_REF] Hwang | Synthesis and in vivo evaluation of [11C]glyburide for imaging pancreatic ß-cells. PO8 -Pharmacology General[END_REF] or fluorine-18 analogues [START_REF] Shiue | Synthesis of β-Cell Imaging Agents[END_REF][START_REF] Schmitz | Synthesis and Evaluation of Fluorine-18 Labeled Glyburide Analogs as β-Cell Imaging Agents[END_REF] only displayed a low radioactivity uptake in the pancreas and a rapid washout of the radiotracers through the liver and the small intestine. However, PET imaging of SUR-1 overexpression after CNS injuries remains promising to evaluate the recovery and detect possible residual damages. This approach is encouraged by recent results demonstrating a negligible brain penetration of [ 11 C]glyburide in a healthy human subject using PET imaging, allowing for a promising contrast between healthy/non-injured and blood-brain barrier (BBB)disrupted brain regions. [START_REF] Marie | 11 C-Glyburide PET Imaging Unveils the Negligible Brain Penetration of Glyburide in Humans[END_REF] The use of [ 11 C]glyburide PET imaging is also a powerful tool to assess non-invasively the functional activity of the transporters for which glyburide is a substrate. The study of P-gp at the BBB level has already been demonstrated with [ 11 C]glyburide. [START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] Glyburide can be radioisotopically labelled with carbon-11 (Figure 1), an extensively used positron emitter of 20.38 minutes half-life produced in cyclotron. Radioisotopic labelling does not modify the chemical structure and the radiotracer displays the exact same biological properties (binding to the receptors, selectivity, membrane permeation) as the original molecule. Radiolabelling of glyburide with carbon-11 has already been described by Hwand and co-workers in one step by methylation using O-desmethyl-glyburide as precursor and [ 11 C]methyl triflate in the presence of sodium hydroxide. [START_REF] Hwang | Synthesis and in vivo evaluation of [11C]glyburide for imaging pancreatic ß-cells. PO8 -Pharmacology General[END_REF] In those conditions, the authors reported a non-decay corrected radiochemical yield (n.d.c. RCY) of 3%. In our hands, those conditions gave the same results 11 but were unfortunately not reproducible. Aiming at investigating the use of [ 11 C]glyburide in a clinical trial, we needed a more reliable automated radiolabelling of glyburide with carbon-11. Therefore, we have developed an original one pot two-steps radiosynthesis of [ 11 C]glyburide by radiomethylation followed by urea formation inspired from the synthesis of the drug. [START_REF] Velingkar | Synthesis and Pharmacological Evaluation of Some Novel Potent Type Antidiabetic Agents[END_REF] We have finalized this radiosynthesis by a complete quality control compliant with to the European Pharmacopeia 9.7 guidelines for the manufacturing of [ 11 C]glyburide as a radiopharmaceutical preparation for Human injection.

EXPERIMENTAL SECTION

Chemistry

Chemicals were purchased from Aldrich (France) and used as received. Compound 1 was purchased from Eras Labo (France). Unless otherwise stated, non-radioactive reactions were monitored by ultra-performance liquid chromatography -mass spectroscopy (UPLC-MS). Chromatography was realized on a Ultimate 3000 (Thermo Scientific, USA) device equipped with an Acquity BEH 2.1 x 50 mm, 1.7 µm column (Waters, USA). A gradient of water with 0.1% of formic acid and acetonitrile with 0.1% of formic acid (3% of CH3CN/HCHO for 2 minutes, then rising to 100% during 7 minutes then decreasing to 3% during 1 minute then keeping 3% for 2 minutes) at a flowrate of 0.3 mL/min was used. Mass spectroscopy was performed with a Linear Trap Quadripole Orbitrap Velos (Thermo Scientific, USA) equipped with an electron spray ionization (ESI) chamber. Spectra were recorded between 100 and 1000 m/z. Melting point (M.p.) was measured with an Electrothermal IA9200 and is reported in °C. [START_REF] Gribble | Sulphonylurea Action Revisited: The Post-Cloning Era[END_REF] H and [START_REF] Gedeon | Transport of Glyburide by Placental ABC Transporters: Implications in Fetal Drug Exposure[END_REF] C NMR spectra were recorded on a Bruker Advance 400 MHz apparatus using DMSOd [START_REF] Kimberly | Analysis of Adjudicated Edema Endpoints in the Glyburide Advantage in Malignant Edema and Stroke (GAMES-RP) Trial (S23.003)[END_REF] as solvent. The chemical shifts (δ) are reported in ppm, downfield from TMS (s, d, t, q and m for singlet, doublet, triplet, quadruplet and multiplet respectively) and referenced with the solvent residual chemical shift. Coupling constants (J) are expressed in Hertz (Hz). High resolution mass spectroscopy (HRMS) was performed by the Institut de Chimie Organique et Analytique of Orléans (France).

General procedure for the one-step non-radioactive methylation of 1.

To a solution of 1 (2 mg, 1.0 equiv.) in the appropriate solvent (DMF, DMA or butanone, 300 µL) was added the appropriate base (sodium hydroxide, sodium hydride, DBU or potassium fluoride). The solution was stirred at room temperature for 2 minutes and a solution of methyl iodide in the corresponding solvent (1 M, 4 µL, 1.0 equiv.) was added. The solution was stirred for 30 minutes at the appropriate temperature (70 °C or 110 °C). An aliquot (10 µL) of the solution was withdrawn, diluted in CH3CN/H2O (1/1 v/v, 1 mL) and analysed qualitatively by UPLC-MS.

5-chloro-2-hydroxy-N-(4-sulfamoylphenethyl)benzamide (3).

To a cooled (-10 °C) suspension of compound 4 (200 mg, 1.0 equiv.) in anhydrous dichloromethane (2 mL) was added dropwise boron tribromide (1 M in CH2Cl2, 0.81 mL, 1.5 equiv.). The solution was stirred under argon for 1 h at 0 °C followed by 3 h at room temperature and monitored by thin layer chromatography on aluminum pre-coated plates of silica gel 60F254 (VWR, France). The compounds were localized at 254 nm using a UV-lamp. Water (5 mL) was added at 0 °C and the precipitate formed was filtrated, washed with ethanol (2 x 5 mL) and diethyl ether (2 x 5 mL) to afford compound 3 (150 mg, 79%) as a white solid. M.p.: 187.2-187.5 °C. [START_REF] Gribble | Sulphonylurea Action Revisited: The Post-Cloning Era[END_REF] H-NMR (DMSO-d 6 , 400 MHz) δ 12.50 (s, 1H, OH), 8.96 (t, J = 5.6 Hz, 1H, NH), 7.90 (d, J = 2.6 Hz, 1H, HAr), 7.75 (d, J = 8.3 Hz, 2H, HAr), 7.43 (m, 3H, HAr), 7.30 (s, 2H, NH2), 6.93 (d, J = 8.8 Hz, 1H, HAr), 3.55 (q, J = 6.0 Hz, 2H, CH2), 2.94 (t, J = 7.0 Hz, 2H, CH2) ppm. [START_REF] Gedeon | Transport of Glyburide by Placental ABC Transporters: Implications in Fetal Drug Exposure[END_REF]

Two-steps non-radioactive synthesis of glyburide from 3.

To a solution of 3 (2 mg, 1.0 equiv.) in butanone (300 µL) was added an aqueous solution of sodium hydroxide (1 M, 7 µL, 1.2 equiv.). The solution was stirred at room temperature for 2 minutes and a solution of methyl iodide in butanone (1 M, 6 µL, 1.0 equiv.) was added. The solution was stirred at 70 °C for 30 minutes. An aliquot (10 µL) of the solution was withdrawn, diluted into CH3CN/H2O (1/1 v/v, 1 mL) and analysed qualitatively by UPLC-MS. To the remaining solution, cyclohexyl isocyanate (7 µL, 10.0 equiv.) and an aqueous solution of sodium hydroxide (3 M, 19 µL, 10.0 equiv.) were added. The solution was stirred at 70 °C for 30 minutes. An aliquot (10 µL) of the solution was withdrawn, diluted into CH3CN/H2O (1/1 v/v, 1 mL) and analysed qualitatively by UPLC-MS.

Radiochemistry

Radiosynthesis of [ 11 C]glyburide.

Automated radiosynthesis with carbon-11 was performed using a TRACERlab ® FX C Pro (GE Healthcare, Uppsala, Sweden). No carrier-added [ 11 C]CO2 (18-37 GBq) was produced via the 14 N(p, α) [START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] C nuclear reaction by irradiation of a [ 14 N]N2 target containing 0.15 -0.5% of O2 on a cyclone 18/9 cyclotron (18 MeV, IBA, Belgium). [ 11 C]CO2 was subsequently reduced to [ 11 C]CH4 and iodinated to [ 11 C]CH3I following the process described by Larsen et al. [START_REF] Larsen | A New Method for Production of 11C-Labelled Methyl Iodide from 11C-Methane[END_REF] and finally converted to [ 11 C]CH3OTf according to the method of Jewett. 21 [ 11 C]CH3OTf was bubbled into a solution of compound 3 (1 mg) and aqueous sodium hydroxide (1 M, 3.5 μL) in butanone (200 μL) at -20 °C for 3 min. The mixture was heated at 70 °C for 3 min and a solution of cyclohexyl isocyanate (4 µL) and aqueous sodium hydroxide (3 M, 7 µL) in butanone (200 µL) was added. The mixture was heated at 70 °C for 3 min under a stream of helium (7 mL/min). Upon cooling to 50 °C, a mixture of water / acetonitrile / trifluoroacetic acid (TFA) (45/55/0.1 v/v/v, 1 mL) was added. Purification was realized by reverse phase semi-preparative HPLC (Waters Symmetry ® C18 7.8 x 300 mm, 7 μm) with a 515 HPLC Pump (Waters, USA) using a mixture of water / acetonitrile / TFA (45/55/0.1 v/v/v, 5 mL/min) as eluent. UV detection (K2501, Knauer, Germany) was performed at 220 nm. The purified compound was diluted with water (20 mL) and passed through a Sep-Pak ® C18 cartridge (Waters, USA). The cartridge was rinsed with water (10 mL), eluted with ethanol (2 mL) and the final compound was diluted with saline (0.9% w/v, 18 mL) before filtration under a laminar flow hood using a 0.22 µm Millex ® GV filter (Merck, USA). Ready-to-inject [ 11 C]glyburide (1.1 -1.5 GBq) was obtained in 5% non-decay corrected radiochemical yield (n.d.c. RCY) within 40 minutes. Automated process with module synopsis are presented in supporting information (Figure S7).

Quality Control

The quality control was realized on three consecutive productions of [ 11 C]glyburide.

Organoleptic test

The final preparation was visually examined behind a lead-shielded glass window.

pH measurement

The pH value was determined using a pH paper.

Chemical identification, chemical and radiochemical purities determination and molar activity measurement.

Identification, purities and molar activity were assessed according to the "Liquid chromatography" monograph n°01/2019:20229 of the European Pharmacopeia 9.7 by analytical reverse phase HPLC equipped with a 717plus Autosampler system, a 1525 binary pump, a 2996 photodiode array detector (Waters, USA) and a Flowstar LB 513 (Berthold, France) gamma detector. The system was operated with the Empower 3 (Waters) software. HPLC were realized on a reverse phase analytical Symmetry C18 (150 x 3.9 mm, 5 μm, Waters) column using a mixture of H2O/CH3CN/PicB7 ® (55/45/0.1 v/v/v, 2 mL/min) as eluent. UV detection was performed at 230 nm. The chemical identification of the peak was assessed by comparing the retention time of [ 11 C]glyburide with the retention time of the non-radioactive glyburide reference (tR ref ). For acceptance, the retention time must be within the tR ref ± 10% range. Radiochemical and chemical purities were calculated as the ratio of the area under the curve (AUC) of the glyburide peak over the sum of the AUCs of all other peaks on gamma and UV chromatograms respectively. Radiochemical and chemical purities are the mean values of three consecutive runs. Molar activity was calculated as the ratio of the activity of the collected peak of [ 11 C]glyburide measured in an ionization chamber (Capintec ® , Berthold) over the molar quantity of glyburide determined using calibration curves. Molar activity is calculated as the mean value of three consecutive runs.

Residual solvents

Content of ethanol and residual acetone, acetonitrile and butanone were determined according to the "Identification and control of residual solvents" monograph n°01/2017:20424 of the European Pharmacopeia 9.7. A gas chromatography system (Clarus 580, Perkin Elmer, USA) equipped with headspace injector (Turbomatrix 40, Perkin Elmer, USA), a woot fused silica column (CP select 624 CB 30 m x 0.53 mm 3µm, Varian, France) and a flame ionization detector was used. The system was monitored with the TotalChrom v6 (Pekin Elmer, USA) software. Chromatographic conditions were: headspace oven temp. 80°C, needle temp. 120°C, transfer line temp.: 180°C, oven temp. from 40 to 140°C, detector temp.: 250°C, gas flow (helium): 5 mL/min. Standard solutions of ethanol (5 mg/mL), acetone (5 mg/mL), acetonitrile (4.1 mg/mL) and butanone (5 mg/mL) were injected to calibrate the measured areas under the curve at known concentrations. The maximum authorized concentrations were calculated for a 10 mL injection and compared to the results observed on the chromatogram of the [ 11 C]glyburide preparation.

Radionuclide purity and half-life determination

Radionuclide purity and half-life determination were realized according to the "Radiopharmaceutical preparations" monograph n°07/2016:0125 of the European Pharmacopeia 9.7 by -ray spectrometry and radioactive decay measurement (Gamma ray spectrometry, gamma vision-32 V6.07 software, Ortec, France). Purity was assessed by the detection of the 511 keV -ray (> 99.9%) on the -spectrum (up to a total peak energy of 1022 keV) and half-life was calculated by decay measurement during a 2 minutes period.

Filter integrity

The filter integrity was determined by the "bubble point" test according to the "Radiopharmaceutical preparations" monograph n°07/2016:0125 of the European Pharmacopeia 9.7. The sterile filter was connected at the inlet side to a compressed air supply. A needle dipped in water was connected at the outlet side. The air pressure is gradually increased. The "bubble point" refers to the pressure producing a continuous stream of air bubbles in the water.

Sterility

The sterility was assessed according to the "Sterility" monograph n°04/2011:20601 corrected 7.7 of the European Pharmacopeia 9.7 by direct inoculation of resazurin thioglycolate, trypcase soy agar and sabouraud agar (Biomérieux, France) with an aliquot of the decayed preparation and incubation for 13 days at 32.5 °C for the first medium and 22.5 °C for the two others. Cultures were visually inspected and compared with positive and negative controls. Negative controls should be clear of any growth while positive cultures should present growth.

Bacterial endotoxins

The Endosafe ® Portable Testing System ™ (PTS ™ ) LAL assay (Charles River, Wilmington, USA) is composed of four channels containing LAL reagent and a chromogenic substrate. Two of the four channels contain an endotoxin spike and serve as the positive control. Each channel ends in an optical cell where the samples are analysed. The sample (25 µL) is mixed with the LAL reagent alone or with the LAL reagent and positive control (spike channels). Each sample is then combined with the chromogenic substrate and incubated for 15 min. at 37 °C. The colour intensity directly related to the endotoxin concentration. Readouts between 50% and 200% spike recovery are considered to be acceptable. The sensitivity of the assay was 0.025 EU/mL. The samples were diluted at 1/100 before analysis.

RESULTS AND DISCUSSION

Chemistry

One-step radiosynthesis of [ 11 C]glyburide using O-desmethyl-glyburide 1 as precursor and sodium hydroxide showed poor n.d.c. RCY and reproduciblity. [START_REF] Hwang | Synthesis and in vivo evaluation of [11C]glyburide for imaging pancreatic ß-cells. PO8 -Pharmacology General[END_REF][START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] Indeed, side products resulting from methylation reactions at other positions were observed. We have therefore decided to investigate different conditions (temperature, solvents, bases) for the one-step methylation of 1 under non-radioactive set up (Scheme 1 and Table 1). The crude reaction was analysed by UPLC-MS (see supporting information, Figures S1 to S5). A stronger base like sodium hydride resulted in the degradation of the starting material at high temperature (110 °C, entry 1) whereas lower temperature (70 °C, entry 2) afforded compound 2a where the methylation occurs preferentially on the sulfonylurea moiety, as shown by MS 2 experiments (see Figure S2D). This result is consistent with the similar pKa value of this moiety (~ 16.1 in DMSO [START_REF] Bordwell | Acidities of Carboxamides, Hydroxamic Acids, Carbohydrazides, Benzenesulfonamides, and Benzenesulfonohydrazides in DMSO Solution[END_REF] ) compared to the p-chlorophenol (~ 16.7 in DMSO [START_REF] Bordwell | Acidities and Hydrogen Bonding of Phenols in Dimethyl Sulfoxide[END_REF] ). No reaction occurred with a softer base like 1,8-diazabicyclo(5.4.0)undec-7-ene (DBU, entry 3). Cork and Hayashi reported the radiomethylation of phenols with [ 11 C]CH3I using a large excess of potassium fluoride and kryptofix-222 (K222) in dimethylacetamide (DMA) which afforded much higher yields compared to sodium hydroxide. [START_REF] Cork | Evidence for Charge Localisation by Strong Hydrogen Bonding in Fluoride-phenol Complexes and Its Effects on Reactivity/selectivity[END_REF] Following those experimental conditions, only the formation of the dimethylated product 2b was observed (entry 4). Finally, reproducing the radiomethylation conditions using sodium hydroxide in butanone afforded a mixture of glyburide and compound 2a (entry 5). It appeared from those experiments that selectively alkylating the phenol moiety of compound 1 from the sulfonylurea was difficult. These results can be explained by the high capacity of sulfonylurea to deprotonate at pH above 7. [START_REF] Grey | Sulfonylurea Herbicides' Fate in Soil: Dissipation, Mobility, and Other Processes[END_REF][START_REF] Renström | Sulfonylurea-Mediated Stimulation of Insulin Exocytosis via an ATP-Sensitive K+ Channel-Independent Action[END_REF] a All reactions were carried out for 30 minutes with 1.0 equiv. of methyl iodide compared to 1 b The crude reaction was analysed qualitatively by UPLC-MS Given the non-orthogonality of a one-step methylation with the sulfonylurea, a two-steps approach was considered. Bormans and Verbruggen reported the radiomethylation of numerous phenol derivatives with sulfonamides using [ 11 C]CH3I. 27 In this case, a phenol moiety could be methylated regioselectively regarding the sulfonamide. Inspired from this approach, nonradioactive glyburide was synthesized in two steps by methylation of the phenol 3 followed by reaction of the sulfonamide moiety with cyclohexyl isocyanate as described in the literature (Scheme 2). [START_REF] Velingkar | Synthesis and Pharmacological Evaluation of Some Novel Potent Type Antidiabetic Agents[END_REF] Firstly, compound 3 was synthesized from commercially available derivative 4 in one step and 79% yield by demethylation using boron tribromide. Methylation of compound 3 was realized using 1.0 equivalent of methyl iodide and a slight excess (1.2 equivalents) of sodium hydroxide in butanone at 70 °C for 30 minutes. The reaction was monitored by UPLC-MS (see Figure S6 in supporting information). In those conditions, methylation only occurred at the phenol moiety and no side product was observed. In parallel, reaction of sulfonamide 4 with cyclohexyl isocyanate in the presence of sodium hydroxide in butanone at 70 °C for 30 minutes was explored. The reaction afforded glyburide without formation of side products except for the hydrolysis of a part of the isocyanate into urea. Therefore, a large excess of cyclohexyl isocyanate and sodium hydroxide (10 equivalents each) were necessary to optimize the conversion into glyburide. Under those optimized conditions, the two steps were carried out sequentially in one pot (Scheme 2). At the end of the methylation reaction from 3, cyclohexyl isocyanate and sodium hydroxide were directly added to the reaction mixture and reaction proceeded for 30 minutes at 70 °C. This two-steps one pot sequence afforded a mixture of 5 compounds, including glyburide (tR = 7.52 min.) as observed by UPLC-MS (Figure 2). Some remaining starting material 3 was observed (tR = 6.63 min.). Compound 4 (tR = 6.79 min.) resulting from the methylation of 3 which was not fully converted into glyburide during the second step was also detected. Compound 1 (tR = 7.71 min.) resulting from the reaction of remaining starting material 3 with the excess of cyclohexyl isocyanate was also present in the mixture. Finally, di(cyclohexyl)urea (tR = 7.00 min.) was observed as a side product resulting from the hydrolysis of the isocyanate. This one pot approach demonstrated the orthogonality of the sequence as no other methylated products were observed, which would be detrimental when moving to radiomethylation with carbon-11. In the course of translating this methodology to radiochemistry, the side products observed for the one pot sequence will not be problematic. Indeed, the conversion of 4 into glyburide is expected to be total thanks to the particular stoichiometry of carbon-11 reactions (typically 100 to 1000 fold excess of chemical precursors compared to the isotope). Remaining starting material 3, compound 1 and di(cyclohexyl)urea will be present as non-radioactive side products which will not influence the radiochemical yield of [ 11 C]glyburide. They will be discarded during purification.

Scheme 2. Two-steps non-radioactive synthesis of glyburide by methylation of 3 followed by formation of the sulfonylurea moiety. Compound 3 was synthesized from commercially available derivative 4 by demethylation using boron tribromide.

Radiochemistry

The previous optimized conditions were applied to the one pot two-steps automated radiosynthesis of [ 11 C]glyburide from precursor 3 using a TRACERlab ® FX C Pro module (Scheme 3). Automated process is depicted in supporting information (Figure S7). [ [START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF]

Quality Control

Quality control of [ 11 C]glyburide was achieved on three consecutive batches of the radiopharmaceutical preparation following the European Pharmacopeia 9.7 general monograph on radiopharmaceutical preparations n° 07/2016:0125 (Table 2). [START_REF]Radiopharmaceutical Preparations In European Pharmacopoeia[END_REF] The representative analysis of the quality control of [ 11 C]glyburide are presented in supporting information (Figure S9 to S13). The final solution was considered limpid and colourless with a pH of 6.2. The identity of [ 11 C]glyburide confirmed by reverse phase analytical HPLC was within the acceptable range of retention time (tR ± 10%) compared to the non-radioactive glyburide reference. The chemical and radiochemical purities also determined by HPLC with UV and gamma detections respectively were above 99.9%. Acetonitrile, acetone and butanone were investigated as residual solvents using a static headspace gas chromatography and the quantities detected were compliant with the specification of the European Pharmacopeia 9.7. The quantity of ethanol as excipient was also evaluated by static headspace gas chromatography at 0.21 g/inj., below the acceptable limit of 0.79 g/inj. A radionuclide purity above 99.9% (energy of photons at 511 keV) and a half-life of 20.38 minutes were measured by gamma spectrometry, within the acceptable range of 19.9 -20.9 minutes for carbon-11. At the end of synthesis, the radiopharmaceutical preparation was sterilized by filtration through a 0.22 µm filter under a grade A laminar flow hood. The bubble point test showed that the integrity of the filter was conserved up to 60 psi. The sterility of the radiopharmaceutical preparation was checked by incubation of the final [ 11 C]glyburide preparation for 13 days in resazurin thioglycolate, trypcase soy agar and sabouraud agar for aerobic and anaerobic bacteria, aerobic bacteria and fungi respectively. The radiopharmaceutical preparation was considered sterile as no germs aggregates could be observed. The bacterial endotoxins were measured quantitatively in the [ 11 C]glyburide preparation according to the Endosafe ® test using limulus amebocyte lysate (LAL). 3.5 EU/inj. of endotoxins were measured in the preparation, below the acceptable limit of 50 EU/inj.. Overall, the quality control of the [ 11 C]glyburide preparation proved to be compliant with the European Pharmacopeia 9.7 guidelines, making of [ 11 C]glyburide a radiopharmaceutical preparation suitable for human injection.

CONCLUSION

We have described a highly reproducible and automated two-steps synthesis for the isotopic radiolabelling of glyburide with carbon-11. This original two-steps approach avoids the formation of methylated side products experienced in previously reported radiosynthesis to regioselectively radiolabel glyburide at the expected position. Optimized automated conditions afforded ready-to-inject [ 11 C]glyburide which was obtained in sufficient activity to perform PET images. A complete quality control was realized to qualify this tracer as a radiopharmaceutical for Human injection according to the European Pharmacopeia 9.7 guidelines. This whole manufacturing process is currently being integrated into an investigational medicinal procedure dossier (IMPD) aiming at conducting a clinical trial using [ 11 C]glyburide to elucidate the hepatic transport of drugs.

Figure 1 .

 1 Figure 1. Glyburide is a substrate of SUR-1 and different transporters at the cell membrane which can be isotopically radiolabelled with carbon-11 at the methoxy position.

  C-NMR (DMSO-d 6 , 100 MHz) δ 167.4 [C], 158.5 [C], 143.5 [C], 142.2 [C], 133.3 [CH], 129.2 [2CH], 127.3 [CH], 125.8 [2CH], 122.4 [C], 119.4 [C], 116.9 [CH], 40.2 [CH2], 34.5 [CH2] ppm. HR-ESI(+)-MS m/z calcd for C15H16ClN2O4S: 355.0514 [M+H] + , found 355.0513.

Scheme 1 .

 1 Scheme 1. Non-radioactive methylation of O-desmethyl glyburide 1 under different conditions

Figure 2 .

 2 Figure 2. UPLC-MS analysis of the two-steps one pot non-radioactive synthesis of glyburide from 3 after 1 hour. A) Full chromatogram; B) Mass spectrum of the 6.63 min. peak; C) Mass spectrum of the 6.79 min. peak; D) Mass spectrum of the 7.00 min. peak; E) Mass spectrum of the 7.52 min. peak; F) Mass spectrum of the 7.71 min. peak.

  C]Methyl triflate was prepared from cyclotron produced [ 11 C]CO2 according to the gaseous method described by Larsen[START_REF] Larsen | A New Method for Production of 11C-Labelled Methyl Iodide from 11C-Methane[END_REF] and Jewett.[START_REF] Jewett | A Simple Synthesis of [11C]methyl Triflate[END_REF] [ 11 C]Methyl triflate afforded better RCY in a shorter reaction time than [ 11 C]methyl iodide for the synthesis of [11 C]4 (28% in 2 minutes and 9% in 5 minutes respectively). In agreements with results obtained in non-radioactive conditions, no side product was observed during the methylation step, underlining the orthogonality of the method under radioactive conditions too. The large excess of precursor 3 compared to [ 11 C]MeOTf prevented from possible poly-methylation reactions and the phenol moiety proved to be more reactive than the sulfonamide in those conditions. Following the previous observations, a large excess of cyclohexyl isocyanate and sodium hydroxide (10 equivalents regarding 3 for both) were used to fully convert [[START_REF] Tournier | Effects of Selected OATP And/or ABC Transporter Inhibitors on the Brain and Whole-Body Distribution of Glyburide[END_REF] C]4 into [ 11 C]glyburide within 3 minutes at 70 °C. A stream of helium (7 mL/min) was used during to second step to ensure the homogeneity of the reaction mixture. Lower amounts of cyclohexyl isocyanate or sodium hydroxide during the second step resulted in a mixture of [ 11 C]4 and [ 11 C]glyburide, thus decreasing the radiochemical yield. Purification by reverse phase semi-preparative HPLC followed by reformulation by solid-phase extraction and sterilization afforded ready-to-inject [ 11 C]glyburide in 5% n.d.c. RCY (n = 8) and a molar activity of 110 ± 20 GBq/µmol within 40 minutes. This fully automated procedure afforded up to 1.5 GBq of [ 11 C]glyburide with high reproducibility. This amount of activity is sufficient enough to produce PET images in Humans as 300-400 MBq are typically injected. No radioactive side products were observed during the semi-preparative HPLC (see Figure S8 in supporting information), except for unreacted [ 11 C]methyl triflate, facilitating the purification of the radiotracer which was submitted to a complete quality control to aim at Human injection.

Scheme 3. Automated two-steps radiosynthesis of [ 11 C]glyburide.

Table 2 .

 2 Quality control on a [ 11 C]glyburide preparation according to the specifications of the European Pharmacopeia 9.7[START_REF]Radiopharmaceutical Preparations In European Pharmacopoeia[END_REF]

	Test	Specifications 28	Results
	Organoleptic test	Limpid colourless liquid	Compliant
	pH	5.0 -8.0	6.2
	Chemical identification	tR ± 10 %	Compliant
	Chemical purity	≥ 95%	≥ 99%
	Radiochemical purity	≥ 95%	≥ 99%
		Ethanol ≤ 0.79 g/inj.
	Residual solvents	Acetone ≤ 50.00 mg/inj. Acetonitrile ≤ 4.10 mg/inj.	Compliant
		Butanone ≤ 50.00 mg/inj.
	Radionuclide purity	Photons energy : 511 keV Half-life : 19.9 -20.9 min.	≥ 99% 20.3 min.
	Filter integrity	≥ 50 psi	60 psi
	Sterility	Sterile	Sterile
	Bacterial endotoxins	≤ 50 EU/inj.	3.5 EU/inj.

Acknowledgments

The authors thank Françoise Hinnen and Stéphane Demphel for technical assistance, and the CEA intramural research funding for financial support.


Etienne Thoret
email: thoret@prism.cnrs.fr

Mitsuko Aramaki

Lionel Bringoux

Sølvi Ystad

Richard Kronland-Martinet

Hearing elliptic movements reveals the imprint of action on prototypical geometries

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

Introduction

Our perceptual system stores and categorizes objects from our surroundings around canonical items, called prototypes, that are the most representative of their category. Geometric prototypes have been viewed as mainly emerging from visual experiences [START_REF] Rosch | Natural categories[END_REF][START_REF] Rosch | Family resemblances: Studies in the internal structure of categories[END_REF][START_REF] Feldman | Bias toward regular form in mental shape spaces[END_REF][START_REF] Kalénine | The visual and visuo-haptic exploration of geometrical shapes increases their recognition in preschoolers[END_REF][START_REF] Theurel | The haptic recognition of geometrical shapes in congenitally blind and blindfolded adolescents: is there a haptic prototype effect[END_REF], via the haptic sensory channel [START_REF] Theurel | The haptic recognition of geometrical shapes in congenitally blind and blindfolded adolescents: is there a haptic prototype effect[END_REF][START_REF] Kalénine | The visual and visuo-haptic exploration of geometrical shapes increases their recognition in preschoolers[END_REF]) and via a motor restitution [START_REF] Feldman | Bias toward regular form in mental shape spaces[END_REF][START_REF] Kalénine | Adults and 5-year-old children draw rectangles and triangles around a prototype but not in the golden ratio[END_REF]. Alternatively, the possibility to recall prototypes through visual and haptic modalities or motor output may suggest common processing of these specific shapes. Whether such prototypes only rely on spatial cues that are present in the visual, haptic, and kinetic domains is still questioned. Could such geometric prototypes also be recalled through auditory stimuli that are solely based on dynamic motor cues? Answering this question would provide a new path to understanding the influence of the motor system on human learning, memory, and cognition. This would indeed suggest that human movement dynamics and more generally the sensory-motor contingencies influence the structuration of geometric shape categories during development.

Interestingly, studies revealed the proficient role of the auditory modality to perceive movements and shapes through timbre variations of monophonic sounds [START_REF] Merer | Semiotics of sounds evoking motions: Categorization and acoustic features[END_REF]2013). More strikingly, [START_REF] Thoret | From sound to shape: auditory perception of drawing movements[END_REF] demonstrated that auditors listening to synthesized monophonic friction sounds corresponding to those produced by the pencil of someone drawing on a paper, were able to recognize specific kinematics characterizing biological motion, in particular the 1/3 power law linking the tangential velocity of the hand movement to the curvature of the drawn shape [START_REF] Lacquaniti | The law relating the kinematic and figural aspects of drawing movements[END_REF]. In addition, they were even able to discriminate geometric shapes, such as a circle, an ellipse, and a line, simply by listening to synthetic friction sounds in which timbre variations revealed the velocity profile of the drawing movement. In follow-up studies, we demonstrated that these acoustic variations may even distort the visuomotor coupling of biological motions (Thoret et al, 2016a[START_REF] Thoret | When eyes drive hand: Influence of non-biological motion on visuo-motor coupling[END_REF]. Taken together, these studies suggest that simple geometric shapes can be evoked through the auditory channel and that the auditory modality may play a significant role in the perception and production of geometric shapes.

Here we investigated the hypothesis that geometrical prototypes can be recalled through the auditory modality employing timbre variations of friction sounds evoking the velocity of biological movements. We focused on a particular shape category, ellipses, that encompass any closed shape of a conic section contained between a line and a circle. From a geometric point of view, an ellipse is principally described by its eccentricity representing its flatness. The eccentricity is a number comprised between 0 and 1: the flatter the ellipse, the higher the eccentricity. The line and the circle are two specific cases which eccentricities equal 1 and 0 respectively. From a dynamic point of view and concerning the 1/3 power law, the accelerations of an elliptic movement increase as the distance between the focal points of the ellipse increases (i.e., when the ellipse tends towards a line). Ellipses can be distinguished by ear from circles and lines and do not involve discontinuity movements. Hence, this geometric shape has been chosen for the present study.

Based on the dynamic model of biological motion described below, four experiments were designed to examine how participants assessed the prototypical ellipse through different modalities. The first three experiments aimed at highlighting the geometric prototype from visual and motor restitutions. The fourth experiment was the cornerstone of this series of experiments and focused on sounds' ability to evoke an elliptic prototype based on the kinematics underlying the drawn ellipse. Consistency between this auditory prototypical ellipse and the visual and motor prototypes would support a common encoding of prototypical shapes.

Before presenting the four experiments, the dynamic model of elliptic motions used in the four experiments will be described in the following section. The results of these experiments are presented together.

A model of biological elliptic motor dynamics

Biomechanical mechanisms involved in graphical production as handwriting have been extensively investigated. It has been shown that dynamic and geometric properties of elliptic motions can be modeled by explicit equations. The dynamic approach of movement production supports the idea that planar hand movements can be modeled by two harmonic oscillators (x(t), y(t)) whose frequencies, amplitudes and phases evolve over time [START_REF] Hollerbach | An oscillation theory of handwriting[END_REF]) with the following system:

! 𝑥(𝑡) = 𝐴 ! (𝑡)cos (𝜔 ! (𝑡) + 𝜙 ! (𝑡)) 𝑦(𝑡) = 𝐴 " (𝑡)cos (𝜔 " (𝑡) + 𝜙 " (𝑡))
where Ax and Ay are the amplitudes, and wx and wy the frequencies, and fx and fy the phases of the two oscillators. In the case of periodic elliptic motions, this model can be simplified by equaling the amplitudes and frequencies of the oscillators (A(t) = Ax = Ay = A and w(t) = wx = wy = w):

! 𝑥(𝑡) = 𝐴 𝑐𝑜𝑠(𝜔𝑡) 𝑦(𝑡) = 𝐴 𝑐𝑜𝑠(𝜔𝑡 + 𝑅𝑃) (1)
where A is the amplitude, 𝜔 = #$ % the frequency with T the period of the motion, and RP = fx fy the relative phase between the oscillators x(t) and y(t).

Hence, this system co-defines the motion dynamics and the geometry, but may also be used to parameterize only the geometry of the entire ellipse whether or not the ellipse is considered dynamically. Practically, the eccentricity e of the ellipse and the relative phase RP are linked by the following relations:

5 𝑅𝑃 = 2 𝑎𝑟𝑐𝑡𝑎𝑛√1 -𝑒 # 𝑒 = >1 -𝑡𝑎𝑛 # ? &' # @
(2)

It should be noted that this model complies with the biological rules, namely the 1/3 power law [START_REF] Lacquaniti | The law relating the kinematic and figural aspects of drawing movements[END_REF].

This model then enables the generation of biological elliptic motions whose trajectory can be continuously morphed from a line (RP = 0°) to a circle (RP = 90°) by simply acting on RP (see Figure 1). It will be used in the four following experiments in order to generate visual and auditory stimuli complying with biological motion. Motor productions of Experiment 2 will also be analyzed regarding this model.

Finally, the tangential velocity profile was generated according to the equations (1) and can be explicitly written as follows:

𝑣(𝑡) = 𝐴 #$ % >𝑠𝑖𝑛 # ? #$ % 𝑡@ + 𝑠𝑖𝑛 # ? #$ % 𝑡 + 𝑅𝑃@ (3)
Although the mapping was arbitrarily fixed during the experiment, it is noticeable that it also varied according to the period T and the amplitude A of the motion.

Experiment 1 -Static Visual Output

The first experiment aimed to evaluate the prototype of the ellipse from visual restitution (i.e., visual output). To that aim, an adjustment protocol was established. Participants were asked to adjust the eccentricity of static ellipses on a screen to evoke the most representative shape of this geometric category.

Methods

Participants. Twenty right-handed participants (8 women) with an average age of 30.6 years (SD = 12.8) voluntarily took part in the experiment. All the participants were naive to the purpose of the experiment. As in all the following experiments, participants gave their informed consent before the study, and the experiment was approved by the Aix-Marseille University ethical committee. For this experiment and the three subsequent ones, participants were selected from various groups, including personal acquaintances, students, engineers, researchers, and professors at the CNRS Campus Joseph Aiguier in Marseille, as well as individuals from the Sport Science Faculty of Aix-Marseille University in Marseille, France.

Stimuli. The visual stimuli were white static ellipses displayed on a black background with different sizes and eccentricities according to the dynamic model previously introduced (equations ( 1)). Three sizes defined by the amplitudes A1 = 3cm, A2 = 5cm, A3 = 10cm were chosen. The ellipses were rotated counterclockwise by 45° to conform to the preferential drawing inclination of an ellipse for right-handed persons [START_REF] Danna | Coordination dynamics of elliptic shape drawing: Effects of orientation and eccentricity[END_REF].

Apparatus. The participants sat in front a computer screen (DELL 1907fp) with a resolution of 1280 x 1024 pixels and a frame rate of 60 Hz. The ellipses were displayed at the center of the screen and the interface was programmed with Max/MSP software (http://cycling74.com/). Participants modified the ellipse eccentricities by using a MIDI AKAY MPK keyboard. The experiment took place in a lighted room.

Task. The participants were asked to adjust the eccentricity of the static ellipse displayed on the screen so as to set the most representative geometric shape of this category. The notion of the most representative ellipse was explained in French to the participants by the following sentences (here translated in English): Ellipses correspond to any closed shape between a line and a circle. When you imagine an ellipse, you may have one particular elliptic shape in mind.

You will adjust the ellipse on the screen to display the ellipse you think is the most prototypical.

The adjustment protocol was based on the one proposed by [START_REF] Carlyon | Pitch Comparisons between Electrical Stimulation of a Cochlear Implant and Acoustic Stimuli Presented to a Normal-hearing Contralateral Ear[END_REF]. The ellipse eccentricity was adjusted thanks to 6 different keys defined on the keyboard: "<<<" -"<<" -"<" and ">" -">>" -">>>". Depending on the selected key, the ellipse eccentricity was modified with different step sizes. The higher the number of arrows the greater the step size,

i.e. the modification of the eccentricity. To avoid a possible non-sensorial bias due to the orientation of the arrows (right or left), the action of the keys on the eccentricity differed across participants. Hence, for half of the participants, arrows that pointed to the right increased the eccentricity and for the other half they had the opposite effect. In addition, the step sizes were not the same in both directions. Hence, for a given participant, all the arrows in one direction (right or left) increased for instance the eccentricity by steps of {.01; .02; .03} while the others (left or right) decreased the eccentricity by steps of {-.1; -.001; -.005}. Finally, 11 repetitions for each size starting from 11 different initial eccentricities equally distributed between 0 and 1 were executed. The experiment was then composed of 33 trials, i.e. 3 {Sizes} x 11 {repetitions}, presented according to two pseudo-random series counterbalanced across the participants. The participants were prompted to explore the whole range of possibilities with the large arrows and to refine their adjustment with the smaller ones. For each participant, 33 final eccentricities were collected and the median was computed.

Experiment 2 -Motor Output

The goal of this experiment was to evaluate whether a prototypical eccentricity of an ellipse can be elicited by a motor output. A motor production task was set up during which the participants were asked to draw the ellipse which best represents this geometric shape category.

Methods

Participants. Twenty participants (2 left-handed -5 women) with an average age of 39.6 years (SD = 11.5) voluntary took part in the experiment and were naive to the purpose of the study. None of them participated in Experiment 1.

Apparatus. The participants sat in front of a Wacom Intuos5 graphic tablet enabling to record graphic movements with a spatial precision of 5.10 -3 mm and a sample rate of 129 Hz.

The data were recorded and collected using an interface programmed with the Max/MSP software. The experiment was conducted in a lighted room.

Task. The participants were asked to repeatedly and continuously draw the most representative ellipse of this geometric shape category on the graphic tablet during 50 seconds.

The notion of the most representative ellipse was explained with the same sentence as in Data analysis. For each participant, recordings of the sampled coordinates (x(t), y(t)) of the stylus on the graphic tablet were collected. To eliminate the numerical noise, the raw data were smoothed with a Savitsky-Golay filter (Savitsky and Golay, 1964) with a 43 samples window and a 3 rd -order interpolation. This is equivalent to a low-pass filter with a cutoff frequency of 8 Hz. A high-pass filter (Butterworth) with a cutoff frequency of .2 Hz was also applied to eliminate the spatial drift of the participants' hands during their movements.

The geometric characteristics of the drawn ellipses were analyzed according to the relative phase. Computing the Hilbert transforms of x(t) and y(t) enabled to estimate the relative phase RP between two oscillators [START_REF] Panter | Modulation, Noise, and Spectral Analysis[END_REF][START_REF] Smith | Introduction to digital signal processing: a computer laboratory textbook[END_REF] with the following formula: 𝑅𝑃(𝑡) = |𝑥 )(𝑡) -𝑦 )(𝑡)|, where 𝑥 ) and 𝑦 ) are the unwrapped Hilbert transforms of x and y. The median of the relative phases RP were then computed for each recording and then transformed into eccentricity. For each participant, 3 final eccentricities were collected and the median was computed.

Experiment 3 -Dynamic Visual Output

Here, the Experiment 1 was reproduced with dynamic visual stimuli. The participants were asked to calibrate the eccentricity of the elliptic trajectory of a moving spotlight to create the most representative ellipse. Task. The adjustment protocol and the task were the same as in Experiment 1. For each (size) x (period) pair, 11 repetitions were performed starting from 11 different initial eccentricity values equally distributed between 0 and 1. The experiment was composed of 99 trials, i.e. 3 {sizes} x 3 {periods} x 11 {repetitions}, presented according to two pseudo-random series counterbalanced across the participants. For each participant, 99 final eccentricities were collected and the median was computed.

Methods

Apparatus. The apparatus was the same as in Experiment 1.

Experiment 4 -Auditory Output

Here, participants were submitted to auditory stimuli generated with the dynamic characteristics of the motor performances recorded in experiment 2 and were asked to modify this dynamic to evoke a friction sound that conveys the most representative elliptic movement exclusively from the auditory modality. By using monophonic sounds, only dynamic information was transmitted to the participants, as opposed to the visual cases in which both spatial and dynamic cues were contained in the stimuli. Hence, this experiment intended to show whether geometric prototypes could emerge from the auditory stimulations, which would signify that spatial information is not strictly needed to evoke a prototype.

Methods

Participants. Twenty participants (9 women) with an average age of 32.1 years (SD = 9.56) voluntary took part in the experiment. None of them participated to the experiments 1, 2 & 3.

Stimuli. Stimuli were monophonic synthetic friction sounds simulating the motion of a pencil on a rough surface, e.g., a piece of paper. A physically based model which simulates the physical sound source as the result of successive impacts of a plectrum, here a pencil nail, on the asperities of a surface, was used [START_REF] Conan | An Intuitive Synthesizer of Continuous-Interaction Sounds: Rubbing, Scratching, and Rolling[END_REF]. The surface roughness is modeled by a noise reflecting the different heights of the surface asperities. Movements on this surface is then simulated processing this noise according to the velocity profile of the movement: the faster the movement the more impacts there are. From a signal processing point of view, such an operation is equivalent to a low-pass filter on the noise with a central frequency directly linked to the movement velocity. The filtered noise is finally convolved with an impulse response simulating the resonance of an object such as a table . To control the synthesis model, we used the 60 motions (3 recordings x 20 participants) recorded in the motor experiment (Experiment 2).

Task. The participants were asked to modify the sound to evoke an elliptic motion for which the trajectory was the most representative of an ellipse. They were implicitly adjusting the delay between the recorded oscillators which implicitly modify the ellipse's roundness. For each of the 60 movements to adjust, 4 periods of the initial recording were used to generate the stimuli. The participants were informed when they reached limits, i.e. 0 or 1 eccentricity, and the adjustment protocol was inspired by one proposed by Carlyon and colleagues [START_REF] Carlyon | Pitch Comparisons between Electrical Stimulation of a Cochlear Implant and Acoustic Stimuli Presented to a Normal-hearing Contralateral Ear[END_REF]. The eccentricity of the ellipse could be modified either with a large or a small modification of the actual eccentricity by using top-down and left-right-arrows respectively, by steps of .10/.3 and .05/.2 respectively. In order to avoid an experimental bias, for each opposite key, e.g., left/right, the roundness was modified with a different step so that participants could not count the number of taps to adjust the friction sound. The participants were prompted to explore the whole range of possibilities with the large arrows and to refine their adjustment with the smaller ones.

Apparatus. Sounds were presented through Sennheiser HD650 headphones and the sample rate of the soundcard was 44100 Hz with 16-bit resolution. The friction sounds were real-time synthesized with MATLAB software. The experiment was carried out in a quiet room.

The sound was modified by the participants using the keyboard of the computer.

Data analysis. For each participant, 60 eccentricities values were collected and their median was computed to characterize the prototypical ellipse.

Results

Coherence between prototypes. We first investigated whether the four different experiments led to four different prototypes. 2a). These tests thus supported an absence of significant difference between the motor, the visual -static and dynamic -and the auditory prototypes.

Eccentricity of the prototypes. Secondly, we investigated the eccentricity of the prototypes for each experiment. 2a). We determined a statistically based confidence interval for each prototype, one in each experiment. We linearly sampled the eccentricity range between 0 and 1 with 1000 equally spaced eccentricity values. We then ran 1000 one sample t-tests between the data distribution of each experiment and the 1000 eccentricity values. The results of each of the 1000 tests characterizes whether the distribution is different from the candidate eccentricity. For each of the 1000 t-tests, the inverse of the bayes factor BF10,inverse=1/BF10 was stored. BF10,inverse can be interpreted exactly as BF10, but for no difference with the null hypothesis, the higher the BF10,inverse the less different the distribution with the candidate eccentricity. We here assume that BF10,inverse>3 characterizes a fair threshold for no difference with the null hypothesis, i.e. the eccentricity value can be considered in the prototype range [START_REF] Jeffreys | The theory of probability[END_REF][START_REF] Goodman | Toward evidence-based medical statistics. 2: The Bayes factor[END_REF][START_REF] Held | How the maximal evidence of p-values against point null hypotheses depends on sample size[END_REF]. As results distributions were globally localized, the 1/BF10 curve is an inverse U-shape. For each experiment, we therefore used BF10,inverse=3 as a threshold to determine the lower and upper bound of the confidence interval.

We also computed the eccentricity eccmax leading to the highest BF10,inverse. This provides a third estimation of the elliptic prototype eccentricity for each experiment. This analysis provides the following results: motor: eccmax=.

General Discussion

In this study, we aimed at investigating whether a common prototype of elliptic shapes elicited across modalities, especially from auditory stimuli, could be identified. We compared the restituted geometry through different outputs (visual, motor and auditory) across a series of four experiments. A common elliptic prototype characterized by an eccentricity of .887 was uncovered, hence demonstrating the common encoding of this prototype.

This complements knowledge from previous studies on the existence of prototypical geometric shapes [START_REF] Rosch | Natural categories[END_REF][START_REF] Rosch | Family resemblances: Studies in the internal structure of categories[END_REF][START_REF] Feldman | Bias toward regular form in mental shape spaces[END_REF][START_REF] Kalénine | Adults and 5-year-old children draw rectangles and triangles around a prototype but not in the golden ratio[END_REF]. This is also in line with those from [START_REF] Wamain | Biological geometry perception": visual discrimination of eccentricity is related to individual motor preferences[END_REF], who highlighted that the ellipse drawn with those from pure motor experiments aiming at revealing the preferentially drawn ellipse [START_REF] Dounskaia | Interjoint coordination during handwriting-like movements[END_REF][START_REF] Sallagoïty | Stability of coordination patterns in handwriting: Effects of speed and hand[END_REF][START_REF] Danna | Coordination dynamics of elliptic shape drawing: Effects of orientation and eccentricity[END_REF] corresponding to stable states, so-called motor attractors [START_REF] Kelso | Pattern formation in speech and limb movements involving many degrees of freedom[END_REF]) (cf. Figure 2). Our results showed that the perceptual prototype -either visual or auditory -is coherent with the motor one, with an eccentricity value slightly below the intermediate ellipse of .91. This eccentricity difference may arise from the intention of the participants which were different because of a different task.

Here we asked them to draw the most prototypical ellipse, which wasn't present at all in the spontaneously drawn ellipses asked in [START_REF] Wamain | Biological geometry perception": visual discrimination of eccentricity is related to individual motor preferences[END_REF]. This slight difference suggests that we cannot obviously exclude that other cue also might have shaped the geometry of the prototype than motor constraint such as visual experience. Interestingly, when superimposing the prototypical ellipse obtained in the present study with the prototypical rectangle highlighted by [START_REF] Kalénine | Adults and 5-year-old children draw rectangles and triangles around a prototype but not in the golden ratio[END_REF], common proportions can be observed. The length to width ratio for prototypical rectangles and the semi-major to semi-minor axis ratio for prototypical ellipses are both close to 2.3, which corresponds to .9 in term of eccentricity.

Above all, these results suggest a common coding of prototypical shape geometry and more generally further support the role of the sensorimotor loop on our perceptual processes [START_REF] O'regan | A sensorimotor account of vision and visual consciousness[END_REF][START_REF] Varela | The embodied mind[END_REF][START_REF] O'regan | Why red doesn't sound like a bell: Understanding the feel of consciousness[END_REF]. Interestingly, neuropsychological studies demonstrated that motor schemes are re-activated during perceptual processes through different sensory modalities [START_REF] Chao | Representation of manipulable man-made objects in the dorsal stream[END_REF][START_REF] Creem-Regehr | Neural representations of graspable objects: are tools special?[END_REF][START_REF] Grafton | Premotor cortex activation during observation and naming of familiar tools[END_REF][START_REF] Grèzes | Does visual perception of object afford action? Evidence from a neuroimaging study[END_REF][START_REF] Kohler | Hearing sounds, understanding actions: action representation in mirror neurons[END_REF][START_REF] Bangert | Shared network for auditory and motor processing in professional pianists: evidence from fMRI conjunction[END_REF][START_REF] Zatorre | When the brain plays music: auditorymotor interactions in music perception and production[END_REF], and through motor imagery (for a review see Jeannerod, 1995 or Grosprêtre, Ruffino and[START_REF] Grosprêtre | Motor imagery and cortico-spinal excitability: A review[END_REF]. Concerning handwriting, it has been shown that seeing a letter activates the cortical processes involved when producing the corresponding script [START_REF] Longcamp | Visual presentation of single letters activates a premotor area involved in writing[END_REF][START_REF] James | Letter processing automatically recruits a sensory? Motor brain network[END_REF][START_REF] Longcamp | The imprint of action: Motor cortex involvement in visual perception of handwritten letters[END_REF]. Similarly, perceiving a geometric shape may share processes involved when we are drawing it. In Experiment 4, an elliptic prototype that did not differ from the visual and motor outputs was elicited from monophonic sounds that only carried dynamic cues. This salient result shows that the elliptic prototype is not only geometric but also can be transmitted through a dynamic dimension. Hence without rejecting the necessity of visual experience in the emergence of prototypical shapes (Theurel et al., 2011;[START_REF] Kalénine | The visual and visuo-haptic exploration of geometrical shapes increases their recognition in preschoolers[END_REF], our data suggest that the prototypical shape is encoded through a common process based on the underlying covariation between biological kinematics and shape geometry which characterizes the corresponding drawing movement [START_REF] Lacquaniti | The law relating the kinematic and figural aspects of drawing movements[END_REF] and its perception through several sensory channels (Viviani et al., 1992;[START_REF] Viviani | The effect of movement velocity on form perception: Geometric illusions in dynamic displays[END_REF][START_REF] Viviani | Visuo-manual pursuit tracking of human two-dimensional movements[END_REF][START_REF] Thoret | From sound to shape: auditory perception of drawing movements[END_REF]. This unified percept [START_REF] Hommel | Codes and their vicissitudes[END_REF] can then be recalled even through the auditory modality, which does not provide any spatial cues. Further experiments using the same auditory based paradigm, in particular with other geometric shapes, are needed to precisely assess the central role of the sensorimotor loop in the emergence of prototypical shape geometries.

Limitations & Perspectives

This study has mainly two methodological limitations. Firstly the investigation was made at group level and subjects were different in each experiment. This allowed us to strikingly highlight the existence of a common prototype between a set of different participants in each modality. This was the main hypothesis of this study and the reason why the elliptic prototype was primarily investigated at group level. It would be of interest to investigate this issue at subject level to exclude that such a prototype may vary across modalities for a given set of participants. However, such a subject level investigation would require a different experimental procedure as one experiment might influence the result of the others. In this case it would not be possible to completely disentangle a potential priming between them. Secondly, the experiment was performed in controlled laboratory experimental conditions with a population of N=80 (4x20). The generalizability of the result could be improved by running such a series of experiments on a larger number of participants with online testing platforms. Lastly, and this is probably the most important conceptual limitation of this study, we have here investigated the prototype of only one shape, the ellipse, which is a very specific shape without any discontinuities, and which moreover can be drawn continuously. To generalize our results, it would be relevant to run the experiment with a more complete set of shapes such as rectangles or triangles, that have been subject to a certain number of studies in the past. This would nevertheless require refinements in the sound modeling procedure due to the discontinuities in the drawing movement of such shapes.

Excellence Initiative of Aix-Marseille University (A*MIDEX). The authors would like to thank Thomas Bordonné and Joris Agator for their help running the experiments. E.T. is thankful to Jeremy Danna for his thoughtful suggestions and guidance at the very beginning of this project.

Figure 1 .

 1 Figure 1. Continuum of different ellipse shapes from a line (left) to a circle (right) with the

Experiment 1 .

 1 Participants saw their hands during the recording, but no trace was visible on the graphic tablet. The experiment comprised three sessions of 50 seconds. The participants were asked to draw small, intermediate, and large ellipses in two different orders counterbalanced across participants: 1) small -2) intermediate -3) large, or conversely. No template of the ellipses was presented, but the participants could train in advance by drawing the 3 different ellipses on the graphic tablet during a session preceding the experiment.

Participants.

  Twenty participants (1 left-handed; 3 women) with an average age of 32 years (SD = 11.4) voluntary took part in the experiment. None of these participants took part in Experiments 1 & 2.Stimuli. The visual stimuli were white spotlights displayed on a black background moving on elliptic paths of different sizes and with different periods according to the dynamic model defined in equation (1). As in Experiment 1, the elliptic paths were rotated counterclockwise by 45°. Three periods of the spotlight motion (T1 = 1.2s, T2 = 1.5s, T3 = 1.8s) inducing different spotlight speeds were chosen.

Figure 2 .

 2 Figure 2. Averaged eccentricities obtained from the four experiments. The boxplot represents

  relative phase slightly below 45°, i.e. an eccentricity slightly below.91, and

  For each experiment, we ensured the normality of the different distributions by using a Lilliefors test (all non-significant, Bonferroni corrected a=.05/4=.0125). It must be noted that for the auditory experiment the Lilliefors test was only marginally significant because of Bonferroni corrections (p=.0176). Therefore, in the following

	we used both parametric and non-parametric approaches. Two statistical tests were applied: (1)
	a non-parametric Kruskal-Wallis test with experiment as a factor (df=3; c 2 = 1.14; p=.76); (2)
	parametric Bonferroni corrected pairwise t-tests between the different experiments. Results
	were all non-significant (df=19, motor vs. visual static: p=.33, BF10=.35; motor vs. visual
	dynamic: p=.84, BF10=.23; motor vs. auditory: p=.92, BF10=.23; visual static vs. visual
	dynamic: p=.55, BF10=.27; visual static vs. auditory: p=.25, BF10=.42; visual dynamic vs.
	auditory: p=.82, BF10=.24) (Figure

Acknowledgments

This work was funded by the French National Research Agency (ANR) under the MetaSon:

Métaphores Sonores (Sound Metaphors) project (ANR-10-CORD-0003) in the CONTINT 2010 framework and the SoniMove Project (ANR-14-CE24-0018). E.T. was funded through an ILCB/BLRI grant no. ANR-16-CONV-0002 (ILCB), ANR-11-LABX-0036 (BLRI) and the

Authors contributions

Declaration of interests

The authors declare no competing interests.


Clément Aubert

Thomas Rubiano

Neea Rusch

Thomas Seiller

Realizing Implicit Computational Complexity

Originalities in Implicit Computational Complexity. Automatic performance analysis and optimization is a critical for systems with resource constraints. The field of Implicit Computational Complexity (ICC) [START_REF] Dal | A short introduction to implicit computational complexity[END_REF] pioneers in embedding in the program itself a guarantee of its resource usage, using e.g. bounded recursion [START_REF] Bellantoni | A new recursion-theoretic characterization of the polytime functions (extended abstract)[END_REF][START_REF] Leivant | Stratified functional programs and computational complexity[END_REF] or type systems [START_REF] Baillot | Light types for polynomial time computation in lambda-calculus[END_REF][START_REF] Lafont | Soft linear logic and polynomial time[END_REF]. It drives better understanding of complexity classes, but also introduces original methods to develop resourcesaware languages, static source code analyzers and optimizations techniques, often relying on informative and subtle type systems. Among the methods developed, the mwp-flow analysis [START_REF] Jones | A flow calculus of mwp-bounds for complexity analysis[END_REF] certifies polynomial bounds on the size of the values manipulated by an imperative program, obtained by bounding the transitions between states instead of focusing on states in isolation, and is not concerned with termination or tight bounds on values. It introduces a new way of tracking dependencies between "chunks" of code by typing each statement with a matrix listing the way variables relate to each others.

Having introduced such novel analysis techniques, and, as opposed to traditional complexity, by utilizing models that are generally expressive enough to write down actual algorithms [20, p. 11], ICC provides a conceivable pathway to automatable complexity analysis and optimization. However, the approaches have rarely materialized into concrete programming languages or program analyzers extending beyond toy languages, with a few exceptions [START_REF] Avanzini | Automating sized-type inference for complexity analysis[END_REF][START_REF] Hoffmann | Resource aware ML[END_REF]. Absence of realized results reduces ability to test the true power of these techniques, limits their application in general, and understanding their capabilities and potential expressivity remains underexplored.

We present an ongoing effort to address this deficiency by applying the mwp-flow analysis, that tracks dependencies between variables, in three different ways, at different stages of maturation, in their temporal order. The first and third projects bend this typing discipline to gain finer-grained view on statements independence, to optimize loops by hoisting invariant [START_REF] Moyen | Loop quasi-invariant chunk detection[END_REF] and by splitting loops "horizontally" to parallelize them [START_REF] Aubert | A Novel Loop Fission Technique Inspired by Implicit Computational Complexity[END_REF]. The second project refines, extends and implements the original analysis to obtain a fast, modular static analyzer [START_REF] Aubert | mwp-analysis improvement and implementation: Realizing implicit computational complexity[END_REF]. All three projects aim at pushing the original type system to its limits, to assess how ICC can in practice lead to original, sometimes orthogonal, approaches. We also discuss our intent and motivations behind formalizing this analysis using Coq proof assistant [START_REF] Kumar | The coq proof assistant[END_REF], in a spearheading endeavour toward formalizing complexity analysis.

1. Loop Quasi-Invariant Chunk Detection. Loop peeling for hoisting (quasi-)invariants can be used to optimize generated code [1, p. 641], and is implemented e.g. in LLVM as the licm pass. This work [START_REF] Moyen | Loop quasi-invariant chunk detection[END_REF] leverages an ICC-inspired dependency analysis to provide a transformation method to compilers. It enables detection of quasi-invariants of arbitrary degree in composed statements called "chunks". It reuses the mwp's matricial system and typed data flows to generate dependency graphs, to compute an invariance degree for each statement or chunks of statements. It then finds the maximum (worst) dependency graph for loops, and recognizes whether an entire block is quasi-invariant. If this block is an inner loop, it can be hoisted, and the computational complexity of the overall program can be decreased. A prototype analysis pass [START_REF] Aubert | Lqicm on c toy parser[END_REF] has been designed, proven correct and successfully implemented using a toy C parser, and as a prototype pass for the LLVM. This is the first known application of introducing ICC techniques in mainstream compilers.

2. Improved and Implemented mwp-Analysis. In an ongoing development, we improved and implemented the mwp-bounds analysis [START_REF] Jones | A flow calculus of mwp-bounds for complexity analysis[END_REF], which certifies that the values computed by an imperative program are bounded by polynomials in the program's input, represented in a matrix of typed flows, characterizing controls from one variable to another. While this flow analysis is elegant and sound, it is also computationally costly-it manipulates non-deterministically a potentially exponential number of matrices in the size of the program [6, 2.3]-and missed an opportunity to leverage its built-in compositionality. We addressed both issues by expanding the original flow calculus, and adjusting its internal machinery to enable tractable analysis [START_REF] Aubert | mwp-analysis improvement and implementation: Realizing implicit computational complexity[END_REF], and further extended the theory with analysis of function definitions and calls-including recursive ones, a feature not widely supported [14, p. 359]. Our effort and theoretical development is realized in an open-source tool pymwp [START_REF] Aubert | pymwp: MWP analysis in Python[END_REF], capable of automatically analyzing complexity of programs written in a subset of the C programming language.

3. Splitting Loops Horizontally to Improve Their Parallel Treatment. Our most recent effort is directed toward program optimization through loop parallelization. Using an ICC-inspired data flow-based variable dependency analysis, we can reproduce the tour de force of detecting opportunities for loop fission that have been missed by other standard analyses [START_REF] Moyen | Loop quasi-invariant chunk detection[END_REF]. In particular, the dependency analysis allows optimizing loops by splitting them "horizontally", e.g. from for (int i = 1; i < 10; i++){a

[i] = a[i-1] + i; b[i] = b[i-1] + i;} to: for ( int i = 1 ; i < 1 0 ; i ++){ a [ i ] = a [i -1 ] + i ;} for ( int i = 1 ; i < 1 0 ; i ++){ b [ i ] = b [i -1 ] + i ;}
Our approach can process loop-carried dependencies [11, 3.5.2]-such as the one illustrated above-and optimizes while loops [START_REF] Aubert | A Novel Loop Fission Technique Inspired by Implicit Computational Complexity[END_REF]Sect. 5].-and, more generally, loops whose trip-count cannot be known at compilation time-that are completely ignored by OpenMP [11, 3.2.2], and generally present great difficulty and often prevent optimization [5, Sect. A]. Combined with OpenMP pragma directives, this approach gives a speed-up "as good as" AutoPar-Clavawhich "compare[s] favorably with closely related auto-parallelization compilers" [2, p. 1]-when both are applicable that can be integrated in automatic parallelization pipelines [5, Sect. B]. Our benchmark, shared at https://github.com/statycc/icc-fission, substantiate experimentally those claims and provides further evidence.

. . . and Pushing Even Further. From there, many other directions can be explored. Since ICC techniques tend to be designed for simpler program syntax, compiler intermediate representations present an ideal location and point of integration for performing analyses. Implementing the analysis in certified tools such as the CompCert compiler [START_REF] Leroy | Formal verification of a realistic compiler[END_REF] (or, more precisely, its static single assignment version [START_REF] Barthe | Formal verification of an SSAbased middle-end for compcert[END_REF]) naturally necessitates certifying the complexity analysis, and we plan to pursue this effort using the Coq proof assistant [START_REF] Kumar | The coq proof assistant[END_REF]. The plasticity of both compilers and of the implemented analysis should facilitate porting our results to support fur-ther programming languages in addition to C. As complexity analysis is difficult in Coq [START_REF] Guéneau | Vérification mécanisée de la correction et complexité asymptotique de programmes)[END_REF], we believe a push would be welcome, and that ICC provides the necessary tools for it.

* This research is supported by the Th. Jefferson Fund of the Embassy of France in the United States and the FACE Foundation, and has benefited from the research meeting 21453 "Static Analyses of Program Flows: Types and Certificate for Complexity" in Schloss Dagstuhl. Th. Rubiano and Th. Seiller are supported by the Île-de-France region through the DIM RFSI project "CoHOp".