Benjamin Vallin

Yohan Legueux-Cajgfinger

Nathalie Clément

Martine Glorian

Laurent Duca

Pierre Vincent
email: pierre.vincent@upmc.fr

Isabelle Limon
email: isabelle.limon@upmc.fr

Régis Blaise

Novel short isoforms of adenylyl cyclase as negative regulators of cAMP production

Keywords: adenylyl cyclase 8E, cAMP signaling, dominant-negative, heterodimerization, vascular smooth muscle cells

Here, we cloned a new family of four adenylyl cyclase (AC) splice variants from transdifferentiated vascular smooth muscle cells (VSMCs) encoding short forms of AC8 that we have named "AC8E1-4" in accordance with the nomenclature of those previously identified. Using biosensor imaging and biochemical approaches, we showed that AC8E isoforms have no cyclase activity and act as dominant-negative regulators by forming heterodimers with other full-length ACs, impeding the traffic of functional units towards the plasma membrane. The existence of these dominant-negative isoforms may account for an additional unsuspected degree of cAMP signaling regulation. It also reconciles the induction of an AC in transdifferentiated VSMCs with the vasoprotective influence of cAMP. The generation of alternative splice variants of ACs may constitute a generalized strategy of adaptation to the cell's environment whose scope had so far been ignored in physiological and/or pathological contexts.

Introduction

Cells responses to their environment depend on the expression and membrane localization of adenylyl cyclases (ACs), which, together with cyclic nucleotide phosphodiesterases, are the principal enzymes controlling the cAMP signal. Nine membrane forms of adenylyl cyclases (ACs) have been identified in mammals, with discrete tissue distributions and unique regulatory properties, providing a potential focal point within the cell for the integration of diverse stimuli [START_REF] Defer | Tissue specificity and physiological relevance of various isoforms of adenylyl cyclase[END_REF][START_REF] Sunahara | Complexity and diversity of mammalian adenylyl cyclases[END_REF]. In vascular smooth muscle cells (VSMCs), it has been shown that i) changes in the AC population expressed in cells derived from hamster vas deferens smooth muscle modify the processing of stimulatory and inhibitory input [START_REF] Marjamaki | Factors determining the specificity of signal transduction by guanine nucleotidebinding protein-coupled receptors. Integration of stimulatory and inhibitory input to the effector adenylyl cyclase[END_REF], ii) differences between the Ca 2+ -sensitive AC isoforms of SMCs determine the effect of a vasopressin agonist on isoproterenol-stimulated cAMP [START_REF] Webb | Adenylyl cyclase isoforms and signal integration in models of vascular smooth muscle cells[END_REF], iii) the cAMP produced by AC isoform 6 (AC6) specifically enhances cAMP-mediated cytoskeletal reorganization without affecting cell growth due to its precise location within the membrane [START_REF] Gros | Adenylyl cyclase isoform-selective regulation of vascular smooth muscle proliferation and cytoskeletal reorganization[END_REF], iv) AC6 causes hyaluronan-mediated intimal thickening of the ductus aerius, whereas AC2 inhibits AC6induced hyaluronan production [START_REF] Yokoyama | Differential regulation of vascular tone and remodeling via stimulation of type 2 and type 6 adenylyl cyclases in the ductus arteriosus[END_REF].

We have shown in vitro that the full transition of rat VSMCs towards a migratory/inflammatory phenotype (referred to as a transdifferentiation process) is dependent on the de novo expression of AC8 [START_REF] Clément | PGE2 amplifies the effects of IL-1beta on vascular smooth muscle cell de-differentiation: a consequence of the versatility of PGE2 receptors 3 due to the emerging expression of adenylyl cyclase 8[END_REF][START_REF] Keuylian | The Notch pathway attenuates interleukin 1β (IL1β)mediated induction of adenylyl cyclase 8 (AC8) expression during vascular smooth muscle cell (VSMC) trans-differentiation[END_REF]. By contrast, in a non-inflammatory context, differentiated/contractile VSMCs mostly express AC isoforms 3, 5, and 6 [START_REF] Webb | Adenylyl cyclase isoforms and signal integration in models of vascular smooth muscle cells[END_REF][START_REF] Ostrom | Localization of adenylyl cyclase isoforms and G protein-coupled receptors in vascular smooth muscle cells: expression in caveolin-rich and noncaveolin domains[END_REF]. In a mouse model of atherosclerosis, knocking out the AC8 gene decreases the inflammation of the abdominal aorta (Limon unpublished) and atherosclerotic lesions [START_REF] Gueguen | Adénylyl cyclases et transdifférenciation des cellules musculaires lisses vasculaires : rôle dans le remodelage vasculaire pathologique[END_REF]. We have expanded these in vivo findings by showing, on human samples, that the neointimal VSMCs have high levels of AC8, whereas very few AC8-positive VSMCs are detected in the medial layer in either atherosclerotic or healthy arteries [START_REF] Gueguen | Implication of adenylyl cyclase 8 in pathological smooth muscle cell migration occurring in rat and human vascular remodelling[END_REF]. The causal relationship between AC8 expression and the migratory response of transdifferentiated VSMCs (tdVSMCs) is associated in the rat in vivo model of post-angioplasty restenosis with a marked transient upregulation of AC8 expression in VSMCs migrating to form the intimal cushion [START_REF] Gueguen | Implication of adenylyl cyclase 8 in pathological smooth muscle cell migration occurring in rat and human vascular remodelling[END_REF]. This increase in adenylyl cyclase expression was surprising. Indeed, increases in intracellular cAMP concentration ([cAMP] i ) have been shown to inhibit the migratory [START_REF] Mckean | The cAMP-producing agonist beraprost inhibits human vascular smooth muscle cell migration via exchange protein directly activated by cAMP[END_REF], proliferative [START_REF] Hewer | PKA and Epac synergistically inhibit smooth muscle cell proliferation[END_REF] and inflammatory [START_REF] Chatterjee | The proresolving lipid mediator maresin 1 (MaR1) attenuates inflammatory signaling pathways in vascular smooth muscle and endothelial cells[END_REF] properties of tdVSMCs. In addition, many studies have shown that increases in [cAMP] i in tdVSMCs antagonize pathological vascular remodeling [START_REF] Cai | Role of cAMP-phosphodiesterase 1C signaling in regulating growth factor receptor stability, vascular smooth muscle cell growth, migration, and neointimal hyperplasia[END_REF][START_REF] Douglas | Cilostazol for Restenosis Trial (CREST) Investigators, Coronary stent restenosis in patients treated with cilostazol[END_REF][START_REF] Indolfi | 8-chloro-cAMP inhibits smooth muscle cell proliferation in vitro and neointima formation induced by balloon injury in vivo[END_REF][START_REF] Inoue | Suppression of arterial intimal hyperplasia by cilostamide, a cyclic nucleotide phosphodiesterase 3 inhibitor, in a rat balloon double-injury model[END_REF][START_REF] Katakami | The phosphodiesterase inhibitor cilostazol induces regression of carotid atherosclerosis in subjects with type 2 diabetes mellitus: principal results of the Diabetic Atherosclerosis Prevention by Cilostazol (DAPC) study: a randomized trial[END_REF].

human, mice and/or rat so far [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF][START_REF] Defer | Molecular cloning of the human type VIII adenylyl cyclase[END_REF][START_REF] Delmeire | Type VIII adenylyl cyclase in rat beta cells: coincidence signal detector/generator for glucose and GLP-1[END_REF][START_REF] Muglia | The 5'flanking region of the mouse adenylyl cyclase type VIII gene imparts tissue-specific expression in transgenic mice[END_REF]. AC8A-D all display different structure, subcellular location and enzymatic activity [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF][START_REF] Delmeire | Type VIII adenylyl cyclase in rat beta cells: coincidence signal detector/generator for glucose and GLP-1[END_REF].

We show here that the AC expressed de novo in tdVSMCs correspond to a family of short AC8 proteins derived from new AC8 splice variantsthe AC8 gene by alternative splicing, that we have named "E" in accordance with the nomenclature of previously identified variants [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF][START_REF] Delmeire | Type VIII adenylyl cyclase in rat beta cells: coincidence signal detector/generator for glucose and GLP-1[END_REF]. AC8E isoforms are catalytically inactive and act as dominant-negatives by dimerizing with endogenous full-length adenylyl cyclases and retaining them in the rough endoplasmic reticulum (RER), thereby reducing global cAMP production within the cell. The existence of these dominant-negative isoforms may account for an additional, unsuspected degree of cAMP signaling regulation, and reconcile the de novo expression of an AC with the transdifferentiation process of VSMCs.

Materials and methods

Reagents

Dulbecco's modified Eagle's medium (DMEM), type I collagen from calf skin, poly-L-lysine, L-glutamine, penicillin, streptomycin, thapsigargin and 3-isobutyl-1-methylxanthine (IBMX) were purchased from Sigma-Aldrich, Saint Quentin Fallavier, France. We obtained fetal calf serum (FCS) and collagenase from Gibco BRL, Cergy-Pontoise, France and G418 from InvivoGen, San Diego, CA, USA. Elastase and the LightCycler 480 SYBR Green I Master mix were obtained from Roche Diagnostics, Meylan, France. Recombinant human interleukin-1β (IL-1β) was purchased from PeproTech, Neuilly-sur-Seine, France, and forskolin (fsk) was obtained from Tocris Bioscience, Bristol, UK. Opti-MEM, Lipofectamine RNAiMAX, M-MLV reverse transcriptase, oligo(dT) primers, RNaseOUT recombinant ribonuclease inhibitor, NuPAGE LDS sample buffer and polyacrylamide gels were obtained from Invitrogen, Life Technologies, Saint-Aubin, France. We purchased the QIAquick gel extraction kit from Qiagen, Les Ulis, France. FuGENE HD, the ReliaPrep RNA Cell Miniprep System and GoTaq DNA polymerase were purchased from Promega, Charbonnières-les-Bains, France.

Control and AC8 small interfering RNAs (siRNAs) were obtained from siTOOLs Biotech GmbH, Planegg, Germany. ArrayScript reverse transcriptase, Platinum SuperFi DNA polymerase, Halt protease inhibitor cocktail, EZ-Link Sulfo-NHS-SS-Biotin and streptavidin agarose resin were obtained from Thermo Fisher Scientific, Villebon sur Yvette, France. We purchased GelRed from Biotium, Fremont, CA, USA and oligonucleotides from Eurofins Genomics, Les Ulis, France. The DC protein assay and the Clarity western ECL substrate were purchased from Bio-Rad, Marnes-la-Coquette, France. Protein G PLUS-Agarose was obtained from Santa Cruz Biotechnology, Inc., Dallas, TX, USA and nitrocellulose membranes were purchased from Amersham, Courtaboeuf, France. N-glycosidase F was obtained from New England Biolabs, Évry, France. We obtained the cAMP -Gs HiRange kit from Cisbio Bioassays, Codolet, France and the Dako fluorescence mounting medium from Dako, Carpinteria, CA, USA.

Cell culture

by an intraperitoneal injection of pentobarbital (300 mg.kg -1 ) and VSMCs were isolated from thoracic aortas as previously described [START_REF] Clément | PGE2 amplifies the effects of IL-1beta on vascular smooth muscle cell de-differentiation: a consequence of the versatility of PGE2 receptors 3 due to the emerging expression of adenylyl cyclase 8[END_REF], according to European Directive 2010/63/EU and the rules laid down by the university ethics committee. Primary VSMC cultures were subcultured from passages 1 to 3 in culture dishes coated with type I collagen from calf skin.

Cells were grown at 37°C, under an atmosphere containing 5% CO 2 , in DMEM containing 1 g.L -1 glucose, 4 mM L-glutamine, 10% FCS, 100 U.mL -1 penicillin, and 100 µg.mL -1 streptomycin. VSMCs were starved by incubation for 12 h in serum-free DMEM before treatment with IL-1β (10 ng.mL -1 ) for 72 h. HEK-293 cells were grown at 37°C, under an atmosphere containing 5% CO 2 , in DMEM containing 4.5 g.L -1 glucose, 4 mM L-glutamine, 5% FCS, 100 U.mL -1 penicillin, and 100 µg.mL -1 streptomycin.

Transfection

Before transfection with siRNAs, VSMCs at 80% confluence were incubated for 2 h in antibiotic-free DMEM containing 1 g.L -1 glucose, 4 mM L-glutamine and 10% FCS. Cells were then transfected by adding 0.25% Lipofectamine RNAiMAX and 5 nM siRNAs diluted in 12.5% final Opti-MEM. The AC8 siRNA is a mixture of 30 different siRNAs directed against mRNA regions conserved in all AC8 splice variants (reference sequence: NM_017142.1). Cells were transferred, 24 h after transfection, to starvation (serum-free) medium for 12 h.

Plasmid transfection was systematically performed with HEK-293 cells at 80% confluence in complete growth medium, in the presence of FuGENE HD and Opti-MEM, according to the information provided in the FuGENE HD Protocol Database (Promega). Cells were systematically used 48 h post-transfection. Stable transfection was performed in the same complete growth medium supplemented with 0.8 µg.mL -1 G418 antibiotic for one week, and monoclonal cell populations were generated by limiting dilution.

Cloning strategies

To clone the AC8 splice variants expressed in tdVSMCs, cells were treated with IL-1β (10 ng.mL -1 ) for 72 h and total RNA was extracted with the ReliaPrep RNA Cell Miniprep System. Total RNA (1 µg) was then reverse-transcribed with ArrayScript reverse transcriptase and 2.5 µM oligo(dT) primers. The cDNAs encoding the rat AC8 were amplified with Platinum SuperFi DNA polymerase, using phosphorylated forward and reverse primers (Table S1) binding to the 5'-untranslated region and the 3'-untranslated region of the rat AC8A cDNA (NM_017142.1), respectively. The final PCR products were visualized by electrophoresis in a 1% agarose gel. Amplicons of the expected size were purified with the QIAquick gel extraction kit and blunt-cloned into the EcoRV site of pcDNA3. Positive clones were sequenced and four cDNAs encoding AC8 were identified and named AC8E1, E2, E3 and E4.

We obtained pcDNA3-VSV by inserting a double-stranded HindIII/KpnI-compatible end oligonucleotide adaptor (Table S1), including the vesicular stomatitis virus glycoprotein tag sequence (VSV), between the HindIII and KpnI restriction sites of pcDNA3. AC8A, AC8E1 and AC8E4 coding sequences were amplified by PCR with primers deleting the start codon (Table S1). The purified PCR fragments were inserted between the KpnI and XbaI restriction sites of pcDNA3-VSV to generate plasmids encoding N-terminally VSV-tagged AC8A, AC8E1 and AC8E4.

We generated the HA-AC3-expressing vector by inserting a double-stranded EcoRI/BamHIcompatible end oligonucleotide adaptor (Table S1), including the human influenza hemagglutinin (HA) epitope sequence, in frame with the first 26 coding bases of the rat AC3 sequence (from +3 to +29, including the internal rAC3 BamHI site), in place of the EcoRI/BamHI fragment of pcDNA3-rAC3 (a generous gift from C. Dessauer).

All clones and constructs were sequenced on both strands, by dye-labeling chain-terminator chemistry methods, with an ABI 3730xl DNA Analyzer (Thermo Fisher Scientific, Villebon sur Yvette, France).

PCR

Total RNA was extracted with the ReliaPrep RNA Cell Miniprep System, according to the manufacturer's protocol. After annealing oligo(dT) primers (1 µM) to template RNAs (0.5-1 µM) at 70°C for 5 min, we initiated primer extension by adding M-MLV reverse transcriptase plus 0.5 mM dNTPs, 1 unit of RNaseOUT recombinant ribonuclease inhibitor and 20 mM DTT, and incubated the reaction mixture for a further 60 min at 37°C.

Quantitative PCR was performed with a LightCycler 480 instrument as described previously [START_REF] Blirando | The stellate vascular smooth muscle cell phenotype is induced by IL-1β via the secretion of PGE2 and subsequent cAMP-dependent protein kinase A activation[END_REF]. The forward and reverse primers used for selective amplification of the cDNAs encoding rat cyclophilin A and ACs are presented in Table S1. Real-time quantitative PCR data are presented as the amount of each target mRNA relative to the amount of mRNAs for the cyclophilin A housekeeping reference gene.

For the relative quantification of the various AC8 transcripts, cDNAs from IL-1β-treated VSMCs (equivalent to 50 ng of total RNA) were amplified in a Prime Full Size Thermal Cycler (Techne, UK) with 1.25 U of GoTaq DNA polymerase, 1.5 mM MgCl 2 , 0.2 mM of each dNTP, and 0.5 µM of forward and reverse primers. Primer pairs for RT-PCR analysis were tested for self-complementarity, dimer formation and melting temperature with Serial Cloner 2-6-1 software. PCR was performed with the following thermal settings: denaturation and enzyme activation at 95°C for 2 min, with 25 to 33 cycles of 95°C for 1 min, 58 to 64°C for 1 min, and 72°C for 1 min, followed by a final extension at 72°C for 5 min. The sizes of the amplified fragments were determined by GelRed staining after electrophoresis in a 2% agarose gel. The PCR fragments were visualized with a E-BOX VX5 digital image processor (Vilber Lourmat, Collégien, France) and signal intensity was determined with Image J software. The forward and reverse primers used for selective amplification of the cDNAs encoding AC8 variants are presented in Table S1.

Preparation of cell lysates

HEK-293 cells were washed with ice-cold phosphate-buffered saline (PBS), scraped into RIPA lysis buffer (25 mM Tris-HCl, pH 7.5, 150 mM NaCl, 1% NP40, 1% sodium deoxycholate, 0.1% SDS, Halt protease inhibitor cocktail) and subjected to three five-second bursts of sonication with a Sonifier 150 (Branson Ultrasonics, Danbury, CT, USA). The resulting cell lysates were briefly incubated on a rotating wheel for 15 min at 4°C and then cleared by centrifugation (13,000 x g for 15 min at 4°C). Protein concentrations were determined with the DC protein assay. Proteins were then mixed with the NuPAGE LDS sample buffer and denatured for 1 h at 37°C before SDS-PAGE analysis.

When indicated, whole-cell lysates were treated with N-glycosidase F before electrophoresis.

Briefly, proteins (20 µg) were denatured by heating at 100°C for 10 min in 0.5% SDS and 40 mM DTT. Denatured proteins were incubated with 500 units of N-glycosidase F or the same volume of 50% glycerol (controls) in 20 mM Tris-HCl pH 7.5, 50 mM NaCl, 5 mM EDTA and 1% NP-40 for 1 h at 37°C. Proteins were then mixed with the NuPAGE LDS sample buffer and incubated for 5 min at 100°C before SDS-PAGE analysis.

Subcellular fractionation

HEK-293 cells grown in 10-cm dishes were washed with ice-cold PBS and lysed by passing 10 times through a 26-gauge needle in fractionation (F) buffer containing 20 mM HEPES pH 7.4, 250 mM sucrose, 10 mM KCl, 1.5 mM MgCl 2 , 1 mM EDTA, 1 mM EGTA, 1 mM DTT and Halt protease inhibitor cocktail. The lysate was first centrifuged at 600 x g for 10 min.

The supernatant (supernatant 1) was then centrifuged at 10,000 x g for 15 min to isolate the heavy membrane pellet. The resulting supernatant 2 was centrifuged at 100,000 x g for 1 h in an Optima MAX-XP ultracentrifuge (Beckman Coulter, Brea, CA, USA) to separate the light membrane pellet from the cytoplasmic fraction. The heavy and light membrane pellets were then resuspended in F buffer, passed through a 26-gauge needle 10 times and recentrifuged at the speeds indicated above. The resulting pellets, corresponding to the heavy membrane and light membrane fractions, were washed twice with PBS and resuspended in a final PBS buffer supplemented with 2% SDS.

Cell surface biotinylation

HEK-293 cells grown in 6-cm dishes were biotinylated in the presence of PBS+ (0.1 mM CaCl 2 , 1 mM MgCl 2 , pH 8.0) supplemented with 1.5 mg.mL -1 sulfosuccinimidyl-2-(biotinamido) ethyl-1,3-dithiopropionate (EZ-Link Sulfo-NHS-SS-Biotin) for 45 min at 4°C. Cells were then incubated for another 45 min at 4°C with a quenching solution containing PBS+ supplemented with 100 mM glycine. Cells were washed with PBS and solubilized in lysis buffer (20 mM Tris HCl pH 7.4, 2 mM EDTA, 2 mM EGTA, 0.1% SDS, 1% Triton, Halt protease inhibitor cocktail). Biotinylated proteins were precipitated with streptavidin agarose resin suspended in 50 mM Tris HCl pH 7.4, 100 mM NaCl, 50 mM EDTA, Halt protease inhibitor cocktail. Precipitated proteins were resuspended in 2X NuPAGE LDS sample buffer, denatured for 30 min at 37°C and subjected to western blot.

Co-immunoprecipitation

HEK-293 cells grown in 10-cm dishes were washed with ice-cold PBS and lysed in 1 mL of solubilization (S) buffer (50 mM Tris pH 7.4, 1 mM EDTA, 150 mM NaCl, 0.3% (v/v) NP40, and Halt protease inhibitor cocktail). After incubation for 15 min on a rotating wheel, the cell suspension was passed 10 times through a 21-gauge needle and centrifuged at 10,000 x g for 10 10 min. The supernatant was then harvested, incubated on a rotating wheel for 1 h with 5 µl of anti-HA or anti-VSV antibody (Table S2) and then incubated overnight with 40 µL of 50% Protein G PLUS-Agarose bead slurry. Beads were washed five times in S buffer and complexes were eluted in 2X NuPAGE LDS sample buffer. The final eluate was vortexed vigorously and incubated for 1 h at 37°C before western blot analysis.

Western blot

Proteins were subjected to SDS-PAGE and transferred onto nitrocellulose membranes.

Membranes were blocked by incubation for 1 h at room temperature with Tris-buffered saline supplemented with 0.1% Tween 20 and 5% non-fat dried milk. Then, membranes were successively incubated with the primary antibodies indicated in Table S2 and horseradish peroxidase (HRP)-conjugated secondary antibodies. Signals were detected by enhanced chemiluminescence using the Clarity western ECL substrate, on Fujifilm LAS-300 (Fujifilm Medical Systems, Standford, CT, USA). When indicated, we used β-actin detection to control for equal protein loading and transfer efficiency.

Immunocytochemistry

HEK-293 cells were grown to subconfluence on poly-L-lysine-coated coverslips and fixed by incubation with 4% PFA for 30 min. PFA was then neutralized by incubation for 10 min with 50 mM NH 4 Cl at room temperature. Cells were then permeabilized by incubation with 0.2% Triton X-100 in PBS for 5 min. Before immunodetection, non-specific sites were blocked by incubating cells in PBS supplemented with 5% donkey serum, 0.2% Triton X-100. Then, cells were successively incubated with primary antibodies directed against AC8 or the HA and VSV tags (Table S2) and Alexa Fluor conjugated secondary antibodies diluted in PBS supplemented with 5% donkey serum. The coverslips were mounted in Dako fluorescence mounting medium. Images were acquired with a Leica SP5 confocal microscope (Leica Microsystems, Wetzlar, Germany).

Measurement of cAMP dynamics

Cells on collagen (VSMCs) or poly-L-lysine (HEK-293)-coated coverslips were infected with the T Epac VV -encoding adenoviral vector (~100 particles per VSMC) or transfected with the T Epac VV -encoding vector (HEK-293) for 24 h. The generation of the T Epac VV -encoding adenovirus has been described elsewhere [START_REF] Blirando | The stellate vascular smooth muscle cell phenotype is induced by IL-1β via the secretion of PGE2 and subsequent cAMP-dependent protein kinase A activation[END_REF]. Coverslips were placed in a microscope chamber continually perfused (2 mL.min -1 ) with a buffer containing 125 mM NaCl, 2 mM CaCl 2 , 1 mM MgCl 2 , 1.25 mM NaH 2 PO 4 , 26 mM NaHCO 3 , 25 mM glucose, maintained at 32°C and saturated with 95% O 2 -5% CO 2 . Ratiometric analyses were performed as follows:

fluorescence was excited with a LED source at 435 nm, and fluorescence emission was monitored with a dichroic mirror (T450LPXR) and alternating emission filters for the donor (HQ480/40) and acceptor (D535/40). Pairs of images were recorded with a Orca-ER CCD camera (Hamamatsu Photonics, Japan), at 20-second intervals. Changes in [cAMP] i are expressed as the ratio of donor fluorescence (F480) to acceptor fluorescence (F535). The ratios were multiplied by a same constant for all experiments, such that the baseline ratio was 1 in basal conditions. The maximum ratio change (Rmax) was obtained by stimulating cells with 10 µM fsk and 200 µM IBMX. Filters and mirrors were obtained from AHF analysentechnik AG, Tübingen, Germany.

cAMP accumulation assay

cAMP accumulation in whole-cell lysates was measured with the cAMP -Gs HiRange kit after incubation for 60 minutes with the phosphodiesterase inhibitor IBMX (500 µM) and the general AC activator forskolin (10 µM), according to the manufacturer's instructions.

Statistics

All data are presented as the means ± SEM of at least three independent experiments. The statistical significance of differences between groups was assessed with GraphPad Prism 6 (Graphpad Software Inc., La Jolla, CA, USA). The nonparametric two-tailed Mann-Whitney test was used for pairwise comparisons. The nonparametric two-tailed Kruskal-Wallis test and Dunn's post test were used for multiple comparisons. Differences were considered significant if P < 0.05.

Results

The AC8 molecules expressed in transdifferentiated VSMCs belong to a novel family of AC8E isoforms, all lacking the first five transmembrane domains

We previously showed that the de novo expression of AC8 is a key feature of rat VSMCs undergoing transdifferentiation (tdVSMCs) in response to interleukin-1β (IL-1β) [START_REF] Clément | PGE2 amplifies the effects of IL-1beta on vascular smooth muscle cell de-differentiation: a consequence of the versatility of PGE2 receptors 3 due to the emerging expression of adenylyl cyclase 8[END_REF][START_REF] Keuylian | The Notch pathway attenuates interleukin 1β (IL1β)mediated induction of adenylyl cyclase 8 (AC8) expression during vascular smooth muscle cell (VSMC) trans-differentiation[END_REF][START_REF] Gueguen | Implication of adenylyl cyclase 8 in pathological smooth muscle cell migration occurring in rat and human vascular remodelling[END_REF].

Four different splice variants of AC8, encoding the AC8A-D isoforms, have been identified [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF][START_REF] Defer | Molecular cloning of the human type VIII adenylyl cyclase[END_REF][START_REF] Delmeire | Type VIII adenylyl cyclase in rat beta cells: coincidence signal detector/generator for glucose and GLP-1[END_REF][START_REF] Muglia | The 5'flanking region of the mouse adenylyl cyclase type VIII gene imparts tissue-specific expression in transgenic mice[END_REF]. AC8A is the full-length isoform. AC8B, C and D variants lack exon 11, exon 8 and both these exons, respectively. We cloned the AC8 cDNAs from rat VSMCs stimulated with IL-1β (10 ng.mL -1 ) for 72 hours. All 13 clones sequenced displayed a non-frameshift 414 bp deletion at the end of the exon 1, termed c.538_951del. They also displayed two other minor substitutions: a CG to GC missense mutation affecting bases 74 and 75 in exon 1 and resulting in the replacement of a glycine residue by an alanine residue in the protein, and a silent G to C mutation at base 3171 in exon 18 (Fig. 1A). The non-frameshift deletion stretches from a canonical alternative 5' donor site in exon 1 (E5SS, changing the 3' boundary of exon 1) to the 3' acceptor splice site (3SS) of intron 1. Some cDNAs lack exon 8 and/or exon 11 (Fig. 1A andS1). Thus, tdVSMCs express a new family of four splice variants of the AC8 primary mRNA named AC8E1 to 4: the AC8E1 mRNA lacks only the end of exon 1, whereas the AC8E2, 3 and 4 mRNAs also lack exon 8, exon 11, and both these exons, respectively (Fig. 1A).

We then determined the relative abundances of AC8E1-4 transcripts and AC8A-D messengers (pooled together). We distinguished between these two pools of variants by amplifying cDNAs generated from tdVSMC mRNAs with forward (F) and reverse (R) primers annealing on either side of c.538_951del (Fig. 1B, left), assuming that the AC8E1-4 PCR products would be 395 bp long whereas the AC8A-D PCR products would be 800 bp long. We used cDNAs from contractile VSMCs and rat brain as negative and positive controls, respectively, for AC8 expression. As expected (Fig. 1B, middle) [START_REF] Conti | Distinct regional and subcellular localization of adenylyl cyclases type 1 and 8 in mouse brain[END_REF], an intense 800 bp band was detected in brain samples, in which the 395 bp band was barely visible; neither of these two bands was detected in contractile VSMC samples, confirming the lack of AC8 expression in these cells.

In tdVSMC samples, the 395 bp PCR products relating to AC8E1-4 were highly abundant, whereas the 800 bp PCR products corresponding to AC8A-D were barely detectable. Based on a densitometric analysis of fluorescent amplicons, AC8Es accounted for more than 90% of total AC8 transcripts in tdVSMCs (Fig. 1B,right).

The amounts of the various AC8E mRNA subvariants were determined with forward (F) and reverse (R) primers binding to exons 7 and 12, respectively (Fig. 1C, left and middle). These amounts are expressed as a percent of total AC8E mRNAs: 15.5% for AC8E1, 18% for AC8E2 , 30.5% for AC8E3 and 36% for AC8E4 in tdVSMCs (Fig. 1C,right). All the AC8E transcripts lack the 414 bp region encoding the putative first five transmembrane domains (TM), three extracellular and two intracellular loops of the enzyme (Fig. S1 andS2). The AC8E2 and AC8E3 mRNAs additionally lack either exon 8 (198 bp) encoding a 66-amino acid cytoplasmic domain corresponding to almost the entire C1b region, or exon 11 (90 bp) encoding a 30-amino acid extracellular domain corresponding to the TM9-10 loop, with two functional sites for N-linked glycosylation, respectively [START_REF] Pagano | Insights into the residence in lipid rafts of adenylyl cyclase AC8 and its regulation by capacitative calcium entry[END_REF]. AC8E4 displays all three deletions. ------------------------------------------------------ ------------------------------------------------------ ------------------------------------------------------ ------------------------------------------------------ -------------------------------------------------- -------------------------------------------------- ----------------------------------------------------------------------------------TACTTTGTCTTCA 1784: TAAATATT ---------------------------------------------------------------------------------- Results are expressed in % of total AC8E transcripts and represent the means ± SEM of 5 independent experiments.

The de novo expression of AC8Es in transdifferentiated VSMCs downregulates cAMP production

We then investigated a possible change in the dynamics of cAMP production associated with the de novo expression of AC8Es in VSMCs, using the FRET-based biosensor T Epac VV [START_REF] Klarenbeek | A mTurquoisebased cAMP sensor for both FLIM and ratiometric read-out has improved dynamic range[END_REF].

Rat VSMCs were transdifferentiated by IL-1β treatment (10 ng.mL -1 ) for 72 hours. Relative changes in [cAMP] i in response to the AC activator forskolin (fsk, 10 µM) were monitored over time, by calculating the ratio R of donor (F480 nm) to acceptor (F535 nm) fluorescence. cAMP level is reported as a percentage of the maximum ratio change (Rmax), corresponding to saturation of the biosensor. Rmax was systematically determined at the end of the experiment, by adding 200 µM 3-isobutyl-1-methylxanthine (IBMX), a broad-spectrum phosphodiesterase inhibitor, in the presence of 10 µM fsk. In contractile VSMCs, fsk addition increased the mean fluorescence ratio to 96.9 ± 1.7% of the Rmax (Fig. 2A). By contrast, cAMP responses barely reached 53.3 ± 6.6% of the Rmax in tdVSMCs. At the start of the experiment, the baseline ratio was similar for contractile VSMCs and tdVSMCs (Fig. S3A).

We used a siRNA strategy to investigate whether the smaller increase in [cAMP] i in tdVSMCs was due to the de novo expression of AC8Es (Fig. 2B). As expected, in tdVSMCs transfected with the control siRNA, the response to forskolin was similar to that of untransfected tdVSMCs (46.0 ± 6.1 vs. 53.3 ± 6.6% of the Rmax, Fig. 2A vs. Fig. 2B).

However, a partial recovery of the cAMP responses was observed in tdVSMCs transfected with the AC8 siRNA: in these cells, forskolin increased the fluorescence ratio to a significantly higher level than in tdVSMCs transfected with the control siRNA (65.5 ± 6.7 vs.

46.0 ± 6.1% of the Rmax, Fig. 2B). Baseline ratios were similar in tdVSMCs transfected with the control siRNA and in tdVSMCs transfected with the AC8 siRNA (Fig. S3B). The efficacy and specificity of the AC8 siRNA were demonstrated by real-time PCR 48 h post-transfection (Fig. S4). Together, these data demonstrate that the de novo expression of AC8Es profoundly affects cAMP dynamics by reducing the increase in [cAMP] i in tdVSMCs. This reconciles the increased expression of AC8 in atherosclerotic vessels with the reduced cAMP levels required for the pathological proliferation and migration of inflammatory VSMCs. for contractile VSMCs: 96.9 ± 1.7%, N = 5; for tdVSMCs: 53.3 ± 6.6%, N = 4, P = 0.0159. In (B), fsk responses were as follows: for Ctrl siRNA-transfected tdVSMCs: 46.0 ± 6.1%, N = 10; for AC8 siRNA-transfected tdVSMCs: 65.5 ± 6.7%, N = 10, P = 0.0288. Side-by-side comparisons were performed with the Mann-Whitney test for unpaired data. *: P < 0.05.

Expression and localization of AC8E isoforms

The lack of the TM9-10 loop with two functional sites for N-linked glycosylation in AC8B reduces its expression relative to that of AC8A and AC8C [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF]. Since AC8E3 and 4 both miss this N-glycosylated extracellular domain, we next analyzed in western blot the protein expression of each AC8E isoform from four different clones of stably transfected HEK cells (Fig. 3A). The antibody we used was raised against the C2b terminal domain, a region that remains present in all AC8E isoforms. AC8E1 and AC8E2 clones expressed high protein levels. Consistently with the study of Cali et al. [START_REF] Cali | Splice variants of type VIII adenylyl cyclase. Differences in glycosylation and regulation by Ca2+/calmodulin[END_REF], we found that AC8E3 and AC8E4 are very poorly expressed.

Subcellular fractionation experiments demonstrated that AC8E isoforms still insert into cellular membranes (Fig. 3B). Indeed, AC8E1-4 and the full-length AC8A mainly concentrated in the heavy membranes fraction and were absent from the cytosolic fraction.

Heavy membranes include the plasma, endoplasmic reticulum and mitochondrial membranes, as attested by the levels of markers for these membranes, β1-integrin, calnexin and cyclooxygenase IV (COX IV), respectively, and the absence of β-actin, a cytosolic marker. In AC8A HEK samples (Fig. 3B), the immunoreactive bands between the 180 and 250 kDa molecular mass markers are of the size expected for AC8A monomers; the bands above 300 kDa are compatible with the predicted size of AC8A homodimers. In the samples derived from AC8E1-4 HEK, bands at or below 130 kDa and those around 300 kDa correspond to the monomeric and dimeric AC8E species, respectively (Fig. 3A and3B). The anti-AC8 antibody does not cross-react with any endogenous AC, as no bands were detected in the control HEK samples (Fig. 3B).

Immunocytochemistry showed AC8A at the plasma membrane whereas AC8E1-4 were intracellular and extranuclear (Fig. 3C). Hence, AC8A but not AC8E1 was detected when purifying biotinylated cell surface proteins (Fig. 3D). AC8E1 is unlikely targeted to mitochondria since it lacks the characteristic specific sequences (TargetP1.1, WoLF PSORT and Predotar 1.04 software). Consistent with AC8Es progressing through the RER, the migration profile of AC8E1 was efficiently altered by the exposure of cell lysates to Nglycosidase F (Fig. S5). Interestingly, the migration patterns of AC8A and AC8E1 were differently sensitive to N-glycosidase F: whereas AC8A showed a continuum of molecular species indicative of partial deglycosylation, the treatment had a less pronounced effect on AC8E1. Thus, AC8E1 likely possesses less diversified N-glycans motifs, in line with AC8E isoforms being, to some extent, stuck in the RER during the maturation process. In addition to demonstrating that AC8E1 and AC8E2 are the two most strongly expressed AC8E isoforms, these results indicate that all AC8Es are retained in the RER during the maturation process and form intermolecular dimers.

D

Western blot analysis of cell surface biotinylated proteins purified from HEK-293 cells transfected with the empty vector or with AC8E1-or AC8A-encoding plasmids and inputs.

Data information: In (A-D), the western blot and immunofluorescence images shown are representative of at least 3 independent experiments. All AC8 immunodetections were performed with the anti-AC8 (R20) antibody.

The AC8E isoforms are catalytically dead and lower intracellular cAMP concentration

Consistently, only the expression of AC8E1 and AC8E2 in HEK cells significantly limits the increase in [cAMP] i in response to forskolin as compared to mock-transfected cells (Fig. 4A).

Indeed, the mean fluorescence ratio was 51.1 ± 4.1% and 57.2 ± 2.8% of the Rmax in AC8E1-and AC8E2-transfected cells, respectively, whereas in control HEK cells or in AC8E3-and AC8E4-expressing cells it reached 87.8 ± 6.1%, 75.5 ± 2.5% and 76.6 ± 4.0% of the Rmax, respectively. In AC8A-expressing HEK cells, forskolin alone leads to biosensor saturation (101.0 ± 0.6% of the Rmax); the basal ratio in AC8A HEK was higher than that in control HEK and AC8Es-transfected cells, consistent with the overexpression of AC8A increasing basal and induced cAMP production.

As shown previously [START_REF] Martin | Capacitative Ca2+ entry via Orai1 and stromal interacting molecule 1 (STIM1) regulates adenylyl cyclase type 8[END_REF], AC8A is activated by capacitative calcium entry (CCE). We next passively depleted calcium stores with the SERCA inhibitor thapsigargin (500 nM) in the absence of extracellular calcium (1 mM EGTA), and AC activity was jump-started with a low dose of forskolin (10 nM). The addition of extracellular calcium (2 mM CaCl 2 ) led to CCE, which increased intracellular cAMP levels in AC8A-but not in AC8E1-expressing cells (Fig.

The AC8E isoforms have dominant-negative effects on endogenous AC activity

We hypothesized that AC8E expression reduced cAMP synthesis. We tested this hypothesis by stimulating ACs with a low dose of forskolin (1 µM) while blocking phosphodiesterases with IBMX (200 µM) to monitor the speed of cAMP synthesis with the FRET-based biosensor T Epac VV (Fig. 5A). The ratio increase depends on the buffering effect of the biosensor on cAMP, and a slower onset is expected when the biosensor is present at a higher concentration. Therefore, for each cell, we plotted the slope at the origin of the ratio increase as a function of fluorescence intensity, used as a proxy for biosensor concentration.

Regardless of fluorescence intensity, the initial slope of the ratio curve was shallower in AC8E1 HEK than in control HEK for a same amount of biosensor (Fig. 5B). In contrast and as expected, cells expressing AC8A showed a dramatically fast response onset. Similar results were obtained when performing cAMP accumulation assays in whole-cell lysates. AC8E1 significantly downregulated, by more than three times, whereas AC8A increased, by the same factor, the accumulation of cAMP after a 60-minute period of incubation with forskolin (10 µM) plus IBMX (500 µM) as compared to control HEK cells (Fig. 5C). Altogether, these data demonstrate that the inactive AC8E1 isoform acts as a dominant-negative on endogenous AC activity. 336.2 ± 46.5%, P = 0.0079; for AC8E1 HEK: 37.8 ± 2.6%, P = 0.0079. Side-by-side comparisons were performed with the Mann-Whitney test for unpaired data. **: P < 0.01.

The dominant-negative effect of AC8E1 combines with direct AC interaction and the blocking of functional AC trafficking

Previous studies have shown that heteromeric complexes assemble between full-length ACs and engineered deletion mutants [START_REF] Ding | Isoformspecific regulation of adenylyl cyclase function by disruption of membrane trafficking[END_REF][START_REF] Gu | Dimerization of mammalian adenylate cyclases[END_REF]. We next explored whether the dominant-negative AC8E1 isoform directly influenced AC activity through heterodimer formation. We first assessed the ability of AC8E1 to interact with AC3, a major AC isoform expressed in contractile and transdifferentiated VSMCs [START_REF] Webb | Adenylyl cyclase isoforms and signal integration in models of vascular smooth muscle cells[END_REF]. HEK cells were transfected with VSV-tagged AC8E1 or HA-tagged full-length AC3 or both (Fig. 6A), and the interaction between these two proteins was assessed by co-immunoprecipitation. On western blots (Fig. 6B, upper left), after immunoprecipitation of the VSV-tagged AC8E1, we detected an immunoreactive band with the anti-HA antibody above 270 kDa in samples from cells transfected with both the VSV-and HA-tagged constructs (lane 4). It corresponds to AC heterodimers containing glycosylated AC3 molecules. No bands were observed in the corresponding negative controls empty vector alone (lane 1)]. As expected, the anti-VSV antibody gave a similar pattern (Fig. 6B, lower left, lanes 3 and 4). Reverse co-immunoprecipitation with the anti-HA antibody for precipitation and the anti-VSV antibody for immunoblotting was just as effective (Fig. 6B, upper right).

This physical interaction translated into significantly lower levels of cAMP synthesis in response to forskolin in cells co-expressing AC3 and AC8E1 than in cells expressing AC3 only (Fig. 6C, 4 vs. 3). Again, the expression of AC8E1 alone decreased the forskolin-induced production of cAMP observed in pcDNA3 (control)-transfected cells (Fig. 6C, 2 vs. 1).

In addition, HA-AC3 was clearly present within the cell when co-expressed with VSV-AC8E1, whereas it reached the plasma membrane when expressed with VSV-AC8A (Fig. 6D). The Pearson's colocalization coefficients with Costes'automatic thresholding (Fiji software Coloc2 plugin) were r = 0.86 for AC8A/AC3 and r = 0.84 for AC8E1/AC3.

Overall, these data demonstrate a dominant-negative effect of AC8E1 on AC3 function associated with a physical interaction between these two proteins, and they suggest that the AC8Es-dependent decrease in cAMP synthesis is due to a loss of AC trafficking to the plasma membrane.

Discussion

The transdifferentiation process of medial VSMCs, which allows them to proliferate and migrate towards the intima, is a major cause of atherosclerosis and post-angioplasty restenosis. It has become clear that the contribution of VSMCs to atherosclerotic lesions has been greatly underestimated, because these cells may express macrophage, mesenchymal stem cell and/or myofibroblast markers in lesions [START_REF] Shankman | KLF4-dependent phenotypic modulation of smooth muscle cells has a key role in atherosclerotic plaque pathogenesis[END_REF]. Identification of the molecular mechanisms and entities driving changes in VSMC phenotype is therefore crucial for future drug development programs. We show here that VSMC transdifferentiation is associated with the de novo expression of a new family (the E family) of AC8 isoforms. These isoforms are catalytically inactive and have dominant-negative effects, decreasing total cAMP production.

The inhibitory effect of AC8E1 on AC activity is accompanied by the formation of heterodimers between functional ACs and AC8E1. The de novo expression of members of the AC8E family may constitute a novel strategy of cellular desensitization to cAMP signaling distinct from those involving phosphodiesterases and multidrug resistance-associated proteins [START_REF] Bautista Niño | Phosphodiesterase 1 regulation is a key mechanism in vascular aging[END_REF][START_REF] Rybalkin | Cyclic nucleotide phosphodiesterase 1C promotes human arterial smooth muscle cell proliferation[END_REF][START_REF] Sassi | Multidrug resistance-associated protein 4 regulates cAMP-dependent signaling pathways and controls human and rat SMC proliferation[END_REF][START_REF] Tilley | Vascular smooth muscle cell phenotype-dependent phosphodiesterase 4D short form expression: role of differential histone acetylation on cAMP-regulated function[END_REF].

The lack of enzymatic activity of AC8E1 is consistent with the notion that the C1/C2 interaction forming the catalytic site is not the only one interaction required for cyclase activity, instead being promoted by an intramolecular interaction between intact M1 and M2

transmembrane cassettes [START_REF] Gu | Persistent interactions between the two transmembrane clusters dictate the targeting and functional assembly of adenylyl cyclase[END_REF][START_REF] Seebacher | An isoform-specific interaction of the membrane anchors affects mammalian adenylyl cyclase type V activity[END_REF]. The need of this intramolecular interaction also accounts for improper transfer of AC8E isoforms towards the plasma membrane [START_REF] Gu | Persistent interactions between the two transmembrane clusters dictate the targeting and functional assembly of adenylyl cyclase[END_REF].

AC molecules within homo-and heterodimers of ACs cross-regulate each other. This is well illustrated by i) the work of Baragli et al., showing that AC2 and 5 assemble in vivo and exhibit enhanced cyclase activity as compared to AC2/AC2 or AC5/AC5 homodimers [START_REF] Baragli | Heterodimers of adenylyl cyclases 2 and 5 show enhanced functional responses in the presence of Galpha s[END_REF], ii)

the study of Gu et al., demonstrating that the co-expression of a full-length AC8 together with an inactive engineered mutant (lacking part of the catalytic C1 domain) suppresses its activity [START_REF] Gu | Dimerization of mammalian adenylate cyclases[END_REF]. Therefore, the negative regulation, by AC8E isoforms, of cAMP production by tdVSMCs is likely due to the ability of these isoforms to form complexes with endogenous full-length ACs. The findings of previous mutagenesis studies suggest that the region involved is the second transmembrane (M2) cassette [START_REF] Gu | Dimerization of mammalian adenylate cyclases[END_REF][START_REF] Gu | Persistent interactions between the two transmembrane clusters dictate the targeting and functional assembly of adenylyl cyclase[END_REF]. The M2 hydrophobic cassette of AC8 contains seven SmxxxSm motifs (where Sm is a small residue: Gly, Ala, Ser or Thr) that have been proposed to drive TM helix dimerization in multi-pass proteins [START_REF] Senes | Statistical analysis of amino acid patterns in transmembrane helices: the GxxxG motif occurs frequently and in association with betabranched residues at neighboring positions[END_REF]. VSMCs mainly express AC3, 5 and 6 [START_REF] Webb | Adenylyl cyclase isoforms and signal integration in models of vascular smooth muscle cells[END_REF][START_REF] Ostrom | Localization of adenylyl cyclase isoforms and G protein-coupled receptors in vascular smooth muscle cells: expression in caveolin-rich and noncaveolin domains[END_REF], all of which being capable of forming heterodimers with AC8 (Fig. 6B; [START_REF] Gu | Dimerization of mammalian adenylate cyclases[END_REF]). Taking this supplementary information into account, we further propose that AC8Es inhibit cAMP synthesis within tdVSMCs by acting on AC isoforms 3, 5 and 6.

Intact M1 and M2 cassettes within a single unit are essential for the correct translocation of AC8A to the plasma membrane (Fig. 3C and3D; [START_REF] Gu | Persistent interactions between the two transmembrane clusters dictate the targeting and functional assembly of adenylyl cyclase[END_REF]). The overall decrease in cAMP production may, therefore, be due to AC8E isoforms retaining full length ACs in the RER.

Several lines of evidence suggest that this is probably the case: i) AC3 was excluded from the plasma membrane when co-expressed with AC8E1 (Fig. 6D); ii) Ding and collaborators have demonstrated that a truncated form of AC6, similar to the AC8E isoforms in the sense that it also lacks one of the two membrane cassettes, prevents full-length AC6 molecules from reaching the plasma membrane [START_REF] Ding | Isoformspecific regulation of adenylyl cyclase function by disruption of membrane trafficking[END_REF]. The RER is the seat of protein quality control, addressing misfolded proteins to the ubiquitin-proteasome system for degradation. We therefore hypothesize that the lower levels of cAMP production observed in AC8E-expressing cells might be due to the degradation of AC dimers. In favor of that, the truncated form of AC6 mentioned by Ding and collaborators, that alters the trafficking of full-length AC molecules, also decreases their protein expression level. This would amount to a hijacking of the RER protein quality control mechanism from its original purpose, as it would prevent the trafficking of normal proteins to the plasma membrane. Together with alternative splicing, this process may constitute a new type of mechanism for regulating protein levels and/or signaling in cells. Although such a regulatory mechanism has never been described before, a role of alternative RNA processing in specifying the post-endocytic sorting of G-proteincoupled receptors has already been established [START_REF] Tanowitz | Alternative splicing determines the postendocytic sorting fate of G-protein-coupled receptors[END_REF].

Our finding that AC8E1 is N-glycosylated suggests that the two unique functional glycosylation sites of the TM9-10 loop are located within the RER lumen during protein processing (Fig. S5). According to the charge balance rule [START_REF] Hartmann | Predicting the orientation of eukaryotic membrane-spanning proteins[END_REF][START_REF] Sato | Testing the charge difference hypothesis for the assembly of a eucaryotic multispanning membrane protein[END_REF], the net charge difference of the 15 amino acids surrounding each end of a transmembrane domain determines its orientation in the lipid bilayer, with the most positive neighboring region facing the cytosol. It has also been shown that i) predictive transmembrane domains with a low hydrophobicity may become extramembrane domains and ii) highly hydrophobic transmembrane domains stabilize neighboring transmembrane domains of low hydrophobicity [START_REF] Bogdanov | Lipids and topological rules governing membrane protein assembly[END_REF]. From the charge balance rule, the glycosylation status and the hydrophobic profile of AC8E1, one can assume that the remaining sixth transmembrane domain of the M1 cassette relocates to the cytosol and that the M2 cassette anchors to the RER membrane in the same orientation as AC8A. This is even more likely foreseen due to the fact that VSV-tagged AC8E1 molecules pulled-down endogenous AKAP79 in co-immunoprecipitation experiments, a cytosolic protein known to interact with the N-terminus of AC8A (Fig. S6). Based on that, and consistently with the study of Gu et al. [START_REF] Gu | Dimerization of mammalian adenylate cyclases[END_REF], the whole N-terminus/TM6/C1 region of AC8E isoforms may be close enough (< 5 nm) to inhibit their AC partners whether by direct interaction or by causing steric hindrance.

Finally, this discovery of novel AC splice variants specifically expressed in the pathological context of vascular remodeling is relevant to various diseases related to splicing defects, including cancers and neurological diseases [START_REF] Chabot | Defective control of pre-messenger RNA splicing in human disease[END_REF]. The generation of AC alternative splice variants may therefore be part of a more general strategy of cell adaptation to its environment, the scope of which was previously unknown. Consistent with this, Katsushika and collaborators have described an AC5-alpha subvariant in dog heart encoding the first half of the enzyme only [START_REF] Katsushika | In vivo generation of an 38 adenylylcyclase isoform with a half-molecule motif[END_REF]. This variant is of particular interest because the heterodimerization motifs of the AC6 isoform, which belongs to the same family as AC5, appeared to be located in the M1 cassette [START_REF] Ding | Isoformspecific regulation of adenylyl cyclase function by disruption of membrane trafficking[END_REF]. Evidence for a functional impact of splice variants is accumulating [START_REF] Kelemen | Function of alternative splicing[END_REF][START_REF] Pagliarini | Splicing Regulation: A Molecular Device to Enhance Cancer Cell Adaptation[END_REF], but the causal contribution of disease-associated splice variants to the disease remains unclear in most cases. The functional assessment of AC5 and 8 splice variants in the heart and vessels could pave the way for further studies of the splice variants specifically expressed in a pathological context.

Supplementary figures

Figure S1 -Exon organization of AC8E variants

AC8E1-4 mRNAs all share a 414 bp deletion at the end of exon ------------------------------------------------------------------VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL -------------------------------------------------------------------VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL -------------------------------------------------------------------VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL ------------------------------------------------------------------ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------FLHLDCAPSNSDFFLNGGYSYRGVIFPTLRNSFKSRDLERLYQRYFLGQRRKSEVVMNVLDVLTKLTLLVLHLSLASAPMDPLKGILLGFFTGIEVVICALVVVRKDTTSHTYLQYSGVVTWVAM --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------VVICALVVVRKDTTSHTYLQYSGVVTWVAM --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------TTQILAAGLGYGLLGDGIGYVLFTLFATYSMLPLPLTWAILAGLGTSLLQVTLQVLIPRLAVFSINQVLAQVVLFMCMNT ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------TTQILAAGLGYGLLGDGIGYVLFTLFATYSMLPLPLTWAILAGLGTSLLQVTLQVLIPRLAVFSINQVLAQVVLFMCMNT ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------TTQILAAGLGYGLLGDGIGYVLFTLFATYSMLPLPLTWAILAGLGTSLLQVTLQVLIPRLAVFSINQVLAQVVLFMCMNT ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

FLHLDCAPSNSDFFLNGGYSYRGVIFPTLRNSFKSRDLERLYQRYFLGQRRKSE----------------------------------------------------------------------- FLHLDCAPSNSDFFLNGGYSYRGVIFPTLRNSFKSRDLERLYQRYFLGQRRKSE----------------------------------------------------------------------- FLHLDCAPSNSDFFLNGGYSYRGVIFPTLRNSFKSRDLERLYQRYFLGQRRKSE----------------------------------------------------------------------- FLHLDCAPSNSDFFLNGGYSYRGVIFPTLRNSFKSRDLERLYQRYFLGQRRKSE----------------------------------------------------------------------- TTQILAAGLGYGLLGDGIGYVLFTLFATYSMLPLPLTWAILAGLGTSLLQVTLQVLIPRLAVFSINQVLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL -
FDNIVGKQNTLAALTRNSINLLPNHLAQALHVQSGPEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS FDNIVGKQN------------------------------------------------------------------YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS FDNIVGKQNTLAALTRNSINLLPNHLAQALHVQSGPEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS FDNIVGKQN------------------------------------------------------------------YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS TM7 PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS PEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS ALVLITTAEDYKCLPLILRK ALVLITTAEDYKCLPLILRK ALVLITTAEDYKCLPLILRK ALVLITTAEDYKCLPLILRK ALVLITTAEDYKCLPLILRK

TM8

TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA TCCWINETYLARNVIIFASILINFLGAVINI------------------------------TCCWINETYLARNVIIFASILINFLGAVINI--------------------------

TM9

TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA TCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA -----------------------------

Figure 1 - 1 :

 11 Figure 1 -Four AC8 splice variants are expressed in tdVSMCs A Alignment of AC8A-and AC8E1-4 encoding sequences. Red dotted lines represent the nucleotide regions deleted in AC8E variants; black arrows indicate the 5' donor sites (5SS) and the 3' acceptor site (3SS) involved in alternative splicing; point mutations relative to the AC8A sequence are marked in red.

  -GTCCTGGCCCAGGTGGTGC 556...1468 AACATCGT 529: AAATCGGAG -

  -GTCCTGGCCCAGGTGGTGC 556...1468 AACATCGT 529: AAATCGGAG -

  -GTCCTGGCCCAGGTGGTGC 556...1468 AACATCGT 529: AAATCGGAG -

  GGGCAAACAGAAT ACTCTGGCTGCCC 1915...2075 TTAAAGACTCCAGCCTGGAGCACAAG TATTCTCAAATGCG 2114...2384 TGGGAGCCGTCA 1476: GGGCAAACAGAAT ACTCTGGCTGCCC 1501...1661 TTAAAGACTCCAGCCTGGAGCACAAG TATTCTCAAATGCG 1700...1970 TGGGAGCCGTCA 1476: GGGCAAACAGAAT -

  -TATTCTCAAATGCG 1502...1772 TGGGAGCCGTCA 1476: GGGCAAACAGAAT -

  -TATTCTCAAATGCG 1502...1772 TGGGAGCCGTCA 1476: GGGCAAACAGAAT ACTCTGGCTGCCC 1501...1661 TTAAAGACTCCAGCCTGGAGCACAAG TATTCTCAAATGCG 1700...1970 TGGGAGCCGTCA TAAATATT CTGTGGTGTGATTTTGACAAGTCGATA 2430...2451 CAATTCCTCAGCTGTGTTTACAGATATCTGCTCCTACCCAGAG TACTTTGTCTTCA 1982: TAAATATT CTGTGGTGTGATTTTGACAAGTCGATA 2016...2037 CAATTCCTCAGCTGTGTTTACAGATATCTGCTCCTACCCAGAG TACTTTGTCTTCA 1784: TAAATATT CTGTGGTGTGATTTTGACAAGTCGATA 1818...1839 CAATTCCTCAGCTGTGTTTACAGATATCTGCTCCTACCCAGAG TACTTTGTCTTCA 1982: TAAATATT -

B

  CTGGGGTGTTGGCCATGGTGACGTGTGCAGT 2537...3571 GCAGTTGTCCTTGGGCTTGTCCAG 3594...3729 CAAATCCGATTTGCCATAA :3747 2093: CTGGGGTGTTGGCCATGGTGACGTGTGCAGT 2123...3157 GCAGTTGTCCTTGGCCTTGTCCAG 3180...3315 CAAATCCGATTTGCCATAA :3333 1895: CTGGGGTGTTGGCCATGGTGACGTGTGCAGT 1925...2959 GCAGTTGTCCTTGGCCTTGTCCAG 2982...3117 CAAATCCGATTTGCCATAA :3135 2003: CTGGGGTGTTGGCCATGGTGACGTGTGCAGT 2033...3067 GCAGTTGTCCTTGGCCTTGTCCAG 3090...3225 CAAATCCGATTTGCCATAA :3243 1805: CTGGGGTGTTGGCCATGGTGACGTGTGCAGT 1835...2869 GCAGTTGTCCTTGGCCTTGTCCAG 2892...3027 CAAATCCGATTTGCCATAA :3045 Abundance of AC8E transcripts relative to AC8A-D messengers. Left panel: diagram of the PCR strategy and resulting PCR products. Middle panel: agarose gel of the PCR products from rat brain, contractile (control) VSMC and tdVSMC cDNAs. Right panel: relative quantification of AC8A-D and AC8E1-4 mRNAs in brain and tdVSMCs, based on a densitometric analysis of fluorescent amplicons. Results are expressed in % of total AC8 transcripts and represent the means ± SEM of 4 independent experiments. C Relative abundance of the AC8E1 to 4 variants in tdVSMCs. Left panel: diagram of the PCR strategy and resulting PCR products. Middle panel: agarose gel of the PCR products from tdVSMC cDNAs. Right panel: relative quantification of AC8E1-4 mRNAs in tdVSMCs.

Figure 2 -

 2 Figure 2

20 Figure 3 -

 203 Figure 3 -Expression and localization of AC8E isoformsAWestern blot showing the stable expression of AC8E1, E2, E3 and E4 in HEK-293 cells. For each construct, four independent clones, numbered 1 to 4, were analyzed.BWestern blot showing the subcellular distribution of AC8A and AC8E1-4 in heavy membranes (HM), light membranes (LM) and the cytosol (C). β-integrin, calnexin, cyclooxygenase IV (COX IV), and β-actin are markers of the plasma, rough endoplasmic reticulum and mitochondrial membranes and the cytosol, respectively.CImmunostaining showing the subcellular distribution of AC8A, AC8E1-4 in HEK-293 cells. Slides were analyzed with a Leica SP5 confocal microscope (63x).

Figure 4 -B

 4 Figure 4 -The AC8E isoforms are inactive and prevent increases in cellular cAMP

Figure 5 -

 5 Figure 5

Figure 6 -BD

 6 Figure 6 -AC8E1 heterodimerizes and inhibits AC activity A Western blots showing AC8E1 (left panel) and AC3 (right panel) levels in HEK-293 cells transiently expressing VSV-AC8E1 and/or HA-AC3, probed with anti-VSV and anti-HA antibodies.

Figure

  Figure S2 -Multiple amino acid sequence alignment and structural domains of the AC8A and AC8E1-4 proteins A Schematic representation of AC8A.

  ----------------------------------------------------------------YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS FDNIVGKQNTLAALTRNSINLLPNHLAQALHVQSGPEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS FDNIVGKQN------------------------------------------------------------------YSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS ALVLITTAEDYKCLPLILRKTCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA ALVLITTAEDYKCLPLILRKTCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA ALVLITTAEDYKCLPLILRKTCCWINETYLARNVIIFASILINFLGAVINILWCDFDKSIPLKNLTFNSSAVFTDICSYPEYFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA ALVLITTAEDYKCLPLILRKTCCWINETYLARNVIIFASILINFLGAVINI------------------------------YFVFTGVLAMVTCAVFLRLNSVLKLAVLLIMIAIYALLTETIYA ALVLITTAEDYKCLPLILRKTCCWINETYLARNVIIFASILINFLGAVINI----------------------------

B

  Amino acid sequence alignment of Rattus norvegicus AC8A, AC8E1, AC8E2, AC8E3 and AC8E4. Structural domains are indicated beneath the sequences. The missing amino acids in each AC8E isoform are represented by dotted lines. In (A) and (B), the N-terminal domain is shown in red. M1 and M2 are the two transmembrane clusters composed of the membrane-spanning domains TM1-6 (green) and TM7-12 (purple), respectively. Membrane-spanning domains are linked by intracellular (IL) or extracellular (EL) loops. The C1 domain is subdivided into C1a (blue) and C1b (orange) domains. The C2 region is also subdivided in two regions, C2a (blue) and C2b (orange). The C1a and C2a regions (blue) form the catalytic core. M2 presents two N-glycosylation sites in extracellular loop 5, indicated by *.

Figure S3 -Figure S5 -

 S3S5 Figure S3 -Basal [cAMP] i in VSMCs A, B Baseline ratio (R basal) in contractile VSMCs and tdVSMCs (A) and in tdVSMCs transfected with control (Ctrl) or AC8 siRNA (B). Bars indicate the mean R basal ± SEM of at least N = 4 independent experiments performed on n = 10 to 20 individual cells. In (A), R basal values were as follows: for contractile VSMCs: 1.05 ± 0.02, N = 5; for tdVSMCs: 1.00 ± 0.01, N = 4, P = 0.1905. In (B), R basal values were as follows: for Ctrl siRNA-transfected tdVSMCs: 1.06 ± 0.01, N = 10; for AC8 siRNA-transfected tdVSMCs: 1.05 ± 0.02, N = 10, P = 0.5191. Side-by-side comparisons were performed with the nonparametric Mann-Whitney test for unpaired data. ns: not significant.

  1, corresponding to the light gray hatched box. Deletions of exon 8, exon 11 or both are represented by light gray boxes.

	AC8E1	E 1	E 2	E 3 E 4 E 5	E 6	E 7	E 8	E 9	E 10	E 11 E 12 E 13	E 14 E 15	E 16	E 17	E 18
	AC8E2	E 1	E 2	E 3 E 4 E 5	E 6	E 7	E 8	E 9	E 10	E 11 E 12 E 13	E 14 E 15	E 16	E 17	E 18
	AC8E3	E 1	E 2	E 3 E 4 E 5	E 6	E 7	E 8	E 9	E 10	E 11 E 12 E 13	E 14 E 15	E 16	E 17	E 18
	AC8E4	E 1	E 2	E 3 E 4 E 5	E 6	E 7	E 8	E 9	E 10	E 11 E 12 E 13	E 14 E 15	E 16	E 17	E 18

  -

			TM1	TM2
	TTQILAAGLGYGLLGDGIGYVLFTLFATYSMLPLPLTWAILAGLGTSLLQVTLQVLIPRLAVFSINQVLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL AGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL
				VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL AGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL
				VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL AGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL
				VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL AGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL
				VLAQVVLFMCMNTAGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL AGIFISYLSDRAQRQAFLETRRCVEARLRLETENQRQERLVLSVL
	TM3	TM4	TM5	TM6
	PRFVVLEMINDMTNVEDEHLQHQFHRIYIHRYENVSILFADVKGFTNLSTTLSAQELVRMLNELFARFDRLAHEHHCLRIKILGDCYYCVSGLPEPRQDHAHCCVEMGLSMIKTIRFVRSRTKHD
	PRFVVLEMINDMTNVEDEHLQHQFHRIYIHRYENVSILFADVKGFTNLSTTLSAQELVRMLNELFARFDRLAHEHHCLRIKILGDCYYCVSGLPEPRQDHAHCCVEMGLSMIKTIRFVRSRTKHD
	PRFVVLEMINDMTNVEDEHLQHQFHRIYIHRYENVSILFADVKGFTNLSTTLSAQELVRMLNELFARFDRLAHEHHCLRIKILGDCYYCVSGLPEPRQDHAHCCVEMGLSMIKTIRFVRSRTKHD
	PRFVVLEMINDMTNVEDEHLQHQFHRIYIHRYENVSILFADVKGFTNLSTTLSAQELVRMLNELFARFDRLAHEHHCLRIKILGDCYYCVSGLPEPRQDHAHCCVEMGLSMIKTIRFVRSRTKHD
	PRFVVLEMINDMTNVEDEHLQHQFHRIYIHRYENVSILFADVKGFTNLSTTLSAQELVRMLNELFARFDRLAHEHHCLRIKILGDCYYCVSGLPEPRQDHAHCCVEMGLSMIKTIRFVRSRTKHD
	VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP
	VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP
	VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP
	VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP
	VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP VDMRIGIHSGSVLCGVLGLRKWQFDVWSWDVDIANKLESGGIPGRIHISKATLDCLSGDYNVEEGHGKERNEFLRKHNIETYLIKQPEESLLSLPEDIVKESVSCSDRRNSGATFTEGSWSPELP
	FDNIVGKQNTLAALTRNSINLLPNHLAQALHVQSGPEEINKRIEHTIDLRSGDKLRREHIKPFSLMFKDSSLEHKYSQMRDEVFKSNLVCAFIVLLFITAIQSLLPSSRLMPMTIQFSILIMLHS

Table S2 -List of antibodies used in immunoblots, immunoprecipitation and immunofluorescence experiments

 S2

	Target proteins	Sources	Applications	Manufacturers	Catalog numbers
	AC8 (C-terminus)	goat polyclonal	IB, IF	Santa Cruz Biotechnology, Inc.	sc-1967
	AC3 (C-terminus)	rabbit polyclonal	IB	Santa Cruz Biotechnology, Inc.	sc-588
	GAPDH	rabbit monoclonal	IB	Abcam	Ab181602
	β-actin	mouse monoclonal [AC-15]	IB	Sigma-Aldrich	A5441
	β1-integrin	rabbit monoclonal [EP1041Y]	IB	Millipore	50-171-223
	Calnexin	rabbit polyclonal	IB	Santa Cruz Biotechnology, Inc.	sc-11397
	COX IV	goat polyclonal	IB	Santa Cruz Biotechnology, Inc.	sc-69359
	AKAP79	mouse monoclonal	IB	BD Biosciences	610314
	VSV tag	mouse monoclonal [P5D4]	IB	Abcam	ab50549
		goat polyclonal	IP, IF	Abcam	ab3861
	HA tag	mouse monoclonal [16B12]	IP, IF	Abcam	ab130275

4B). This additional experiment shows that AC8E1 does not exhibit the typical calciumactivated cyclase activity of AC8A. Overall, these results demonstrate that the c.538_951 deletion, despite lying outside the catalytic domains, kills the enzymatic activity of AC8Es while retaining the ability to lower cAMP responses in AC8E1-2.

Acknowledgments

We would like to thank S. Bolte and JF. Gilles from the imaging facility of the Paris-Seine Biological Institute (IBPS), C. Dessauer for providing the AC3 construct and JB. Klarenbeek for providing the T Epac VV expression plasmid. This work was supported by ANR grant 11BSV103401, the Lefoulon-Delalande Foundation, the French Federation of Cardiology (F.F.C), the Nouvelle Société Francophone d'Athérosclérose (NSFA), the Société Française de Cardiologie (SFC) and the Groupe de Réflexion sur la Recherche Cardiovasculaire (GRRC).

Conflict of interest

None declared.


Vladimir Gauthier

Aude Bolopion

Michaël Gauthier

Comparison of dynamic models for non-contact micromanipulation based on dielectrophoretic actuation

Several approaches are proposed in the literature to calculate the drag force, the electric field and the induced dielectrophoretic force. This paper analyzes the performances of various models for closed loop control of dielectrophoretic systems in comparison with experiments. This article compares their performance in terms of accuracy, computation time, and memory consumption. Four classical approaches are available to calculate the electric field. Their performances are analyzed in the paper. We have shown that combining the dipolar model of dielectrophoresis force with an anisotropic drag force (integrating the wall-effect) provides an interesting ratio precision/computation time. This paper provides an original comparison of several models described in literature whose performances have been compared with experiments.

I. INTRODUCTION

Manipulation of micro-objects in fluid is of great interest, especially in biological applications. In this framework, a great variety of systems has been developed [START_REF] Lee | Separation and sorting of cells in microsystems using physical principles[END_REF] which includes the dielectrophoresis (DEP) systems. The DEP physical principle enables to manipulate a dielectric microobject placed in an AC electric field [START_REF] Pethig | Review Article Dielectrophoresis: Status of the theory, technology, and applications[END_REF]. Under certain conditions, dielectric objects (including biological cells) are polarized and are attracted toward local extrema of the electric field. The electric field are commonly produced by electrodes sputtered on a substrate. Most of the systems are dedicated to statistical sorting of cells, but the new generation is focused on single cell positioning [START_REF] Zemánek | Feedback control for noiseaided parallel micromanipulation of several particles using dielectrophoresis[END_REF].

To guarantee that a single micro-object is positioned accurately, closed-loop control must be implemented. Along the trajectory, the micro-object positions can be measured with cameras [START_REF] Kharboutly | High speed closed loop control of a dielectrophoresis-based system[END_REF], event based sensors [START_REF] Ni | Visual tracking using neuromorphic asynchronous event-based cameras[END_REF] or by impedance spectrometry [START_REF] Brazey | Impedance-based real-time position sensor for lab-ona-chip devices[END_REF]. The control law requires a model of the system characterized by high non-linearities. This model is based on the forces applied on the particle (dielectrophoretic force, drag force, etc.). The first step of the model consists in the calculation of the electric field around the manipulated object. Different approaches have been proposed such as the electric field superposition [START_REF] Michálek | Dipole and multipole models of dielectrophoresis for a non-negligible particle size: Simulations and experiments[END_REF], the charge distribution superposition [START_REF] Kharboutly | Modeling the trajectory of a microparticle in a dielectrophoresis device[END_REF], the Green's function [START_REF] Gurtner | Green's functionbased control-oriented modeling of electric field for dielectrophoresis[END_REF] or the Fourier series Authors are with FEMTO-ST Institute, AS2M department, Univ Bourgogne Franche-Comté, CNRS, 24 rue Alain Savary, 25000 Besancon, France, vladimir.gauthier@femto-st.fr

This work has been supported by the EUR EIPHI program (Contract No. ANR-17-EURE-0002), by the French Agence Nationale de la Recherche and the Swiss National Science Foundation through the CoDiCell project (contract "ANR-17-CE33-0009-01"), by the MiMedi project funded by BPI France (grant No. DOS0060162/00) and the European Union through the European Regional Development Fund of the Region Bourgogne-Franche-Comte (grant No. FC0013440), by the French RENATECH network and its FEMTO-ST technological facility, by the Collegium SMYLE (SMart SYstems for a better LifE) and by the Region Bourgogne-Franche-Comte.

y x z u 0 u 1 F Drag F DEP u N -1
Fig. 1: Benchmark system used for the comparison: an array of parallel electrodes in a fluidic channel to control the lateral position of microparticles by applying a dielectrophoretic force. The electrode's width, l, is 5 µm or 10 µm and the particles have a radius, a, between 5 µm and 10 µm. [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF]. The calculation of the dielectrophoretic force depends on assumptions on the electric field's non-uniformity, leading to multipolar model. The other predominant force is the drag force induced by the liquid, and several expressions are also proposed in the litterature [START_REF] Ambari | Effect of a plane wall on a sphere moving parallel to it[END_REF], [START_REF] Ambari | Wall effects on a sphere translating at constant velocity[END_REF].

To use these models to perform closed-loop control they must meet several requirements in terms of accuracy, computation time and memory requirement. This article proposes to analyze and compare these models. Several experimental particle trajectories are taken as references. This article will thus provide a comprehensive analysis for people interested in implementing closed-loop control based on dielectrophoretic actuation.

This paper is organized as follows. Section II provides the quasi-static model of the system. Section III compares several models of drag and dielectrophoretic forces with experiments. Section IV analyses different approaches to compute the electric field. Section V concludes the paper.

II. MOTION OF A PARTICLE IN AN AC ELECTRIC FIELD

To compare different models of the drag and dielectrophoretic forces, as well as different approaches to compute the electric field, experimental data will be taken as references. They will be obtained from a benchmark described in Figure 1. It is composed of an array of parallel electrodes in a fluidic channel. This configuration is of interest for example to sort micro-objects, or biological cells. The microobjects flow through the channel along the x direction due to the fluid motion. The lateral position y of the micro-object is controlled by the electric potential on each electrode. TABLE I: Order of magnitude of the velocity induced by each force acting on the benchmark experiments. Those values ares comptuted for ethanol and water. For other liquids, refer to formula given in [START_REF] Castellanos | Electrohydrodynamics and dielectrophoresis in microsystems: scaling laws[END_REF]. Deviating the position of the objects enables to collect them in different reservoirs to sort them. This paper focuses on modeling the lateral displacement induced by the electrode array. In the benchmark experiments, the electrode's width, l, is 5 µm or 10 µm and the spherical micro-objects (particles) have a radius, a, between 5 µm and 10 µm.

A. Dynamic model

In the following, we consider that the liquid in the microchannel is static, and that the trajectory of the particule is consequently in the plane defined by ( y, z). In the general case, the forces applied on the particle are the fluid drag force, gravity-buoyancy, dielectrophoresis force and Brownian motion. Moreover, the medium can be subjected to AC electro-osmosis and electrothermal flow. Based on the work of Castellanos et al. [START_REF] Castellanos | Electrohydrodynamics and dielectrophoresis in microsystems: scaling laws[END_REF], it is possible to compute the relative importance of these forces on the velocity of the particle. Table I summarizes the order of magnitude of the particule velocity induced by each force.

AC electro-osmosis, Brownian motion and electrothermal flow are at least two orders of magnitude less than the dielectrophoretic force, and one order of magnitude less than the joint effect of gravity and buoyancy. According to this calculation, these three effects will be neglected in our case.

For a particle subjected to gravity-buoyancy F g , dielectrophoresis F DEP and fluid drag F drag , Kharboutly et al. demonstrated that the inertial term can be neglected in Newton's second law [START_REF] Kharboutly | Modeling the trajectory of a microparticle in a dielectrophoresis device[END_REF]. Thus, the motion of the particle can be deduced from:

0 = F g + F drag + F DEP . (1)
The gravity-buoyancy force is given by:

F g = 4 3 πa 3 (ρ m -ρ p )g z, ( 2
)
where a is the particle's radius, ρ m (resp ρ p ) is the fluid density (resp. particle density) and -g z the gravitational acceleration. The next sections present various expressions of the drag and dielectrophoretic forces proposed in the literature.

B. Model of the drag force

The classical model of the drag force applied on a spherical object is given by the Stockes' law. An extended version of this law has been proposed in [START_REF] Ambari | Effect of a plane wall on a sphere moving parallel to it[END_REF], [START_REF] Ambari | Wall effects on a sphere translating at constant velocity[END_REF]:

F drag = -6πµa(λ y ẏ y + λ z ż z), (3)
where µ is the dynamic viscosity and λ y and λ z are correction factors enabling to model the impact of the substrate close to the particle (wall effect). These correction factors are defined in [11, Eq. ( 1)] and [12, Eq. (3.

2)]:

λ y = 1 - 9 16 a z + 1 8 a z 3 - 45 256 a z 4 - 1 16
a z 5 -1 , (4)
λ z = 4 3 sinh α ∞ n=1 n(n + 1) (2n -1)(2n + 3) 2 sinh(2n + 1)α + (2n + 1) sinh 2α 4 sinh 2 (n + 1 2 )α -(2n + 1) 2 sinh 2 α -1 , (5)
where

α = cosh -1 (1 + (z -a)/a),
z is the altitude of the center of gravity of the particle above the substrate. As the drag coefficients are different along y and z, this general model is called "anistropic drag force" in the following of this paper. The isotropic classical Stockes' law represents the particular case of Eq 3 considering the assumption λ y = λ z = 1. This simplified model is called "isotropic drag force" in the following. Section III-B discusses the influence of the anistropy of the drag force on particle trajectories.

C. Model of the dielectrophoretic force

Close to the electrodes, the electric field is highly nonuniform. The force induced by a highly non-uniform electric field on a uniform spherical dielectric particle can be derived using Maxwell stress tensor [START_REF] Wang | General expressions for dielectrophoretic force and electrorotational torque derived using the Maxwell stress tensor method[END_REF] or effective multipole moment [START_REF] Washizu | Multipolar dielectrophoretic force calculation[END_REF]. Maxwell stress tensor approach is regarded as the most rigorous. However, Michálek [START_REF] Michálek | Dipole and multipole models of dielectrophoresis for a non-negligible particle size: Simulations and experiments[END_REF] shows that for a spherical particle over parallel electrode array the quadripolar approximation shows results similar to Maxwell stress tensors. Maxwell stress tensors being too long to compute for closed-loop control, effective multipole moment are usually used. The quadripolar approximation of the i component, i ∈ {y, z}, of the dielectrophoretic force induced by an electric field E can be found in [16, Eq. ( 8)] as:

F DEP,i = 4πε m a 3 K (1) E m ∂E i ∂x m + K (2) a 2 6 ∂E m ∂x n ∂ 2 E i ∂x n ∂x m . (6)
Equation ( 6) uses the Einstein summation convention: all repeated indexes are summed. The real part of the generalized Clausius-Mossotti factor K (n) is defined as: where ε * m and ε * p are the complex permittivities of the medium and the particle, respectively. These are defined as ε * = ε + σjω with ε the permittivity, σ the conductivity and ω = 2πf the angular frequency of the harmonic electric field. Equation ( 6) describes the quadripolar expression of the DEP force. The dipolar expression of the DEP force is obtained form Eq (6) by neglecting the terms ∂ 2 Ei ∂xn∂xm . The comparison between both expressions are defined in sec. III-C.

K (n) = Re n(ε * p -ε * m ) nε * p + (n + 1)ε * m , (7)
The next section discusses the model of the drag force, and in particular the drag force anisotropy (Eq. 4 and Eq. 5) as well as the model of the dielectrophoretic force (Eq. 6), difference between quadripolar and dipolar model, compared to experimental data. Section IV focuses on different approaches to compute the electric field.

III. COMPARISON BETWEEN MODELS AND EXPERIMENTS

Using equations ( 1) to ( 6) the trajectory of the particle can be defined considering its initial position and the electric field in the workspace. The objective of this section is to compare the computed trajectories of the models presented in the previous section with experiments. This comparison requires to compute the electric field in the workspace. Different methods to compute this electric field can be used providing a very similar computed electric field but requiring different calculation times and memory requirements. The comparison of the different ways to compute the electric field will be presented in section IV. In this section, the electric field in the workspace is calculated using the "Fourier Series method" [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF].

A. Experimental data

The models discussed in this paper are compared with experimental data, considered as the reference. Four experiments listed in Table II are reported in this paper. The four experiments enable to test trajectories for various parameters such as different electrode width l, particle radius a and particle materials. The experiment are conducted in a petri dish with an open channel. To avoid bubble formation, ethanol is used. For each experiment the motion is recorded at 1000 frames per second with a pixel resolution of 1.44 µm allowing accurate off-line tracking. At t 0 , a step voltage of 5 V rms at 500 kHz is set on one electrode close to the object, the voltage of others electrodes are set to zero. when the particle goes close to the substrate, the correction factors increase and the drag force increases too Eq [START_REF] Zemánek | Feedback control for noiseaided parallel micromanipulation of several particles using dielectrophoresis[END_REF].

B. Impact of the drag force anisotropy

As λ z is always greater than λ y (e.g. λ z /λ y = 1.53 for d/a = 1), the drag coefficient along y is smaller than the one along z. This anisotropy induced by the substrate (walleffect) has a strong impact on the particle trajectory. Indeed, the same force amplitude along y and z induce a velocity along z smaller than the velocity along y. In other words, the wall-effect tends to favor the movements parallel to the plane. Figure 3 illustrates this effect. It shows the position of the particle (experiment 0) as a function of time. Figure 3(b) represents the altitude of the particle predicted by models. The models taking into account the drag force anisotropy predicts a trajectory with a lower height than the models based on isotropic drag force. Moreover, the height of the particle has a significant impact on the magnitude of the DEP force: the lower is the particle, the higher the electric field gradients are, the higher the DEP force is. Consequently, the anisotropic drag force model predicts a trajectory along y with a higher velocity than the isotropic model.

The anisotropic model shows a good coherence with the experimental measurement. All further simulations uses the anisotropic drag force model.

C. Multipolar dielectrophoresis

While computing the dielectrophoretic force, higher order terms are commonly neglected based on the dipole approximation. However, in theory, this dipole approximation is valid only if the spatial variations of the electric field are small compared to the particle size [START_REF] Washizu | Multipolar dielectrophoretic force calculation[END_REF]. In this section the influence of higher order multipoles (quadrupoles) is evaluated with respect to experimental data.

Figure 4 represents the position of the particle obtained both experimentally and using the proposed models with the dipolar and quadripolar approximations. Experimental conditions are the following. The electrode size is decreased to 5 µm and spherical particles with radius up to 10.2 µm are tested according to Table II. A step voltage of 5 V is applied on an electrode at t 0 = 10 µs. To compute the trajectories obtained from the model (Eq. 1) the anisotropic drag force is considered, as discussed in the previous section. To compute the dielectrophoretic force the electric field is obtained from the Fourier series method [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF]. This choice is discussed in Sec. IV. The trajectories of the particle obtained for both the dipolar and quadripolar approximations are plotted in Fig. 4 and compared with experiments.

According to Figure 4, even if the electric field is highly non-uniform, the trajectories obtained from the models and the experiments are very close. As expected, the quadripolar model is slightly more accurate when predicting the particle trajectory. However, it takes twice as long to compute. Since computation time is a critical issue for closed loop control the dipolar approximation is retained in the following.

IV. ELECTRIC FIELD COMPUTATION

The previous section analyzes the influence of different models of the dielectrophoretic force. However, it was assumed that the electric field was known. This section discusses different approaches to compute the electric field in terms of computing resources and accuracy.

There are three different approaches to compute the electric field: numerical models, semi-analytical models and analytical models. Numerical models, such as finite element methods, require too much computation time to be usable for closed loop control of a particle motion using dielectrophoresis. They are not considered in this paper.

A. Semi-analytical methods

Semi-analytical models use the superposition principle to extrapolate the electric field from a base of pre-computed numerical solution [START_REF] Kharboutly | Modeling the trajectory of a microparticle in a dielectrophoresis device[END_REF], [START_REF] Michálek | Dipole and multipole models of dielectrophoresis for a non-negligible particle size: Simulations and experiments[END_REF].

1) Superposition principle on the electric field: The superposition principle can be applied directly to the electric field and its derivative issued from each electrode, leading to:

E(x, y, z) = N n=1 E n (x, y, z) • U n , (8)
with E n the precomputed map considering an unitary potential on the electrode n and U n the potential applied on it. The dielectrophoretic force is then computed using Eq [START_REF] Brazey | Impedance-based real-time position sensor for lab-ona-chip devices[END_REF].

2) Superposition principle on the charge distribution: A second solution is to retrieve the electric field from the map of the charge accumulated on each electrode surface, leading to :

E(x, y, z) = 1 2πε m N n=1 U n K k=1 C n,k ---→ P k M ||P k M || 3 , (9)
where C n,k is the charge induced by the n th electrode on P k , an elementary point. M = (x, y, z) is the point of application.

B. Analytical methods

For particular geometry of electrodes, analytical formulations exist. For electrode arrays, Green's function [START_REF] Gurtner | Green's functionbased control-oriented modeling of electric field for dielectrophoresis[END_REF] and Fourier series [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF] have been recently studied.

1) Green's functions: The solution of the Laplace equation in a half-space, with Diriclet conditions, can be transformed, thanks to Green's theorem to:

φ(x, y, z) = z 2π ∞ -∞ h(x , y ) [(x -x ) 2 + (y -y ) 2 + z 2 ] 3 2 dx dy , (10)
with φ(x, y, z) the electric potential in the space and h(x, y) the electric potential on the boundary. Gurtner et al explicit the electric potential on the boundary as a sum of polynomial approximations induced by each electrode h(x, y) = n h n (x, y)U n [START_REF] Gurtner | Green's functionbased control-oriented modeling of electric field for dielectrophoresis[END_REF]. The electric field can be derived using: E(x, y, z) = -∇φ(x, y, z).

2) Fourier series: Fourier series can be used to approximate the electric potential on the electrode array as a sum of exponential. The electric field in the whole space can be expressed as:

E(x, y, z) = N n=1 p
U n a n,p e p (x, y, z), [START_REF] Ambari | Effect of a plane wall on a sphere moving parallel to it[END_REF] with a n,p the Fourier coefficient and e p (x, y, z) a combination of exponential. For the benchmark experiment, an analytical formulation of the a n,p coefficient is given in [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF].

For more general cases, a semi-artificial neural network can be used to pre-compute numerical value of a n,p coefficient [START_REF] Song | A semi-analytical approach using artificial neural network for dielectrophoresis generated by parallel electrodes[END_REF].

C. Comparison of electric field computation techniques for closed loop control

To be usable for closed loop control on an embedded platform, the approaches described above must provide accurate electric field computation while being resource efficient. In the following, the four previously presented methods are compared on the benchmark system presented in Figure 1. Since this system is invariant along the x direction, computation are reduced to (O, y, z) plan, significantly reducing the computation time. 1) Precision: Using the same scenario as in Section III, the trajectory obtained with the four approaches to compute the electric field, enumerated previously, are compared to experimental trajectories. As discussed in the previous sections the anisotropic drag force and the dipolar model of the dielectrophoretic force are selected. For the semianalytical methods, maps of the electric field, its derivatives and charge distributions are pre-computed using a finite element software (Comsol). The Green's method uses third order polynomial approximation given in [START_REF] Gurtner | Green's functionbased control-oriented modeling of electric field for dielectrophoresis[END_REF]. The Fourier method uses analytical formulation of the Fourier coefficients given in [START_REF] Gauthier | Analytical formulation of the electric field induced by electrode arrays: Towards automated dielectrophoretic cell sorting[END_REF].

Figure 5 shows the prediction of the particle position with respect to time versus the experiments described in Section III before the particle hits the electrode array (bottom of the channel) at t = 0.6 s. As dielectrophoresis is very sensitive to the voltage applied on each electrode, a quantitative study of the precision of each model requires comparison on a broad range of different electric fields in the whole space. For such exhaustive study, experimental data are hard to obtain. Thus, only qualitative conclusion is given here. The different model's trajectories laid on a bundle of 15 µm. This is less than twice the diameter of the particle. When performing closed loop control the inaccuracies in the model are handled by the feedback loop and can be considered as perturbations. Thus, the four models can be used to perform closed loop control. Computing resources, which are critical issues, are discussed in the next section.

2) Computing resources: The comparison of the computing resources required by these four approaches is been performed on three different arrays of respectively 8, 16 and 32 electrodes. In each case the electrode width is 10 µm. Thus, increasing the number of electrodes allows to compare the scale-up efficiency of each model. All models are run on the same desktop computer (Intel Core i5, 3.30 GHz, 8 GB RAM, 64-bit, Linux 3.10, CentOS 7) from C code. C code is chosen as a reference for real-time embedded applications. The C code is available on request for each model. Table III shows the computing time and the memory required by the four models for the three different electrode arrays.

Based on these comparisons the electric field superposition method is the fastest, as it requires almost no computation. However, it requires a large amount of data loaded in memory. The charge superposition approach reduces the precomputed map to the electrodes surface, but it requires more computation leading to longer computation time. Green's function leads to complex formula using inverse tangent and square root, with a third order polynomial. For this reason this method is the slowest to compute. Fourier series are a good option when the number of electrode increases.

V. CONCLUSIONS & PERSPECTIVES

This article aims at analyzing the performances of dynamic models usable for closed-loop control of dielectrophoretic systems. Dipolar model versus quadratic model of the dielectrophoretic force and isotropic versus anisotropic drag force model have been compared. We have shown that a model computing anisotropic drag force and dipolar dielectrophoretic force appears as the simplest model predicting trajectories close to the experiments. To compute the electric field, the method of superposition of the electrical field is the fastest to predict the electrical field. If memory consumption is an issue, Fourier series are a good option when the number of electrode increases.

The quadratic dependence of the dielectrophoretic force on the electric potential applied on each electrodes makes the inverse model hard to compute. Optimal closed-loop control will be investigated in future works.

Fig 2 Fig. 2 :

 22 Fig 2 describes the value of the factors λ y and λ z in function of the ratio d/a between d = z -a the particlesubstrate distance and a the particle radius. As expected,

Fig. 3 :

 3 Fig.3: Experiment 0: Position of the particle in response to a step voltage. Models computing dipolar and quadripolar expressions of the DEP force and isotropic and anisotropic drag forces are compared to experiments. As Eq (5) leads to infinite drag force at the initial position, particle-substrate distance d = 0, during the first five microseconds of simulation the following expression of α is considered in Eq (5): α d=0 = cosh -1 (1 + (z -0.99a)/a).

Fig. 4 :

 4 Fig. 4: Position of the particle in the channel with respect to time in response to a step voltage. The dipolar and quadripolar approximations are compared to experiments for particles having different radius.

Fig. 5 :

 5 Fig.5: Position of the particle in the channel in response to a step voltage, experiment 0. Different approaches to compute the electrical field are compared to experiment using dipolar approximation of the dielectrophoretic force and anisotropic drag force.

TABLE II :

 II Experiments performed to obtain reference data

		Electrodes width l	Part. radius a	Part. material
	Experiment 0	10 µm	5.1 µm	Borosilicate
	Experiment 1	5 µm	5.1 µm	Borosilicate
	Experiment 2	5 µm	8.7 µm	Borosilicate
	Experiment 3	5 µm	10.2 µm	Polystyrene

TABLE III :

 III Time & memory required to evaluate the dielectrophoretic force for different models on a 2D case

	Number of electrodes	Electric field superposition	Charge distribution superposition	Green's function	Fourier series
	8	515 ns,	7.78 MB	55.0 µs,	< 2 MB	326 µs,	< 2 MB	21.9 µs, < 2 MB
	16	605 ns,	30.0 MB	209 µs,	< 2 MB	616 µs,	< 2 MB	84.8 µs, < 2 MB
	32	908 ns,	60.5 MB	812 µs,	< 2 MB	1.21 ms, < 2 MB	335 µs,	< 2 MB