Florence Gaven

Lucie P Pellissier

Emilie Queffeulou Abc

Maud Cochet

Joël Bockaert Abc

Aline Dumuis

Sylvie Claeysen
email: sylvie.claeysen@igf.cnrs.fr

Pharmacological profile of engineered 5-HT4 receptors and identification of 5-HT4 receptor-biased ligands 1

Keywords: 5-HT4 receptor, G protein-coupled receptor, biased ligand, cyclic AMP, inositol phosphate RASSL, Receptor Activated Solely by Synthetic Ligand, DREADD, Designer Receptors

G protein-coupled receptors (GPCRs) can activate simultaneously multiple signaling pathways upon agonist binding. The combined use of engineered GPCRs, such as the Receptors Activated Solely by Synthetic Ligands (RASSLs), and of biased ligands that activate only one pathway at a time might help deciphering the physiological role of each G protein signaling. In order to find serotonin type 4 receptor (5-HT4R) biased ligands, we analyzed the ability of several compounds to activate the Gs and Gq/11 pathways in COS-7 cells that transiently express wild type 5-HT4R, the 5-HT4R-D 100 A mutant (known also as 5-HT4-RASSL, or Rs1) or the 5-HT4R-T 104 A mutant, which modifies agonist-induced 5-HT4R activation. This analysis allowed completing the pharmacological profile of the two mutant 5-HT4Rs, but we did not find any biased ligand for the mutant receptors. Conversely, we identified the first biased agonists for wild type 5-HT4R. Indeed, RS 67333 and prucalopride acted as partial agonists to induce cAMP accumulation, but as antagonists on inositol phosphate production.

Moreover, they showed very different antagonist potencies that could be exploited to study the activation of the Gs pathway, with or without concomitant block of Gq/11 signaling.

Introduction

G protein-coupled receptors (GPCRs) convert extracellular messages into intracellular signals to trigger the appropriate cellular responses. As GPCRs can induce multiple pathways at the same time [START_REF] Rajagopal | Teaching old receptors new tricks: biasing seventransmembrane receptors[END_REF], it is very difficult to decipher the consequences of the activation of a precise G protein in a physiological context. To overcome this problem, different GPCRs have been engineered over the last decade. First, Receptors Activated Solely by Synthetic Ligands (RASSLs) were generated by site-directed mutagenesis and Gq-, Gs-and Gi-coupled RASSLs are now available [START_REF] Conklin | Engineering GPCR signaling pathways with RASSLs[END_REF][START_REF] Coward | Controlling signaling with a specifically designed Gi-coupled receptor[END_REF][START_REF] Scearce-Levie | Engineering receptors activated solely by synthetic ligands (RASSLs)[END_REF]. These GPCRs are insensitive to their endogenous ligand and can be activated only by specific synthetic ligands. Then, Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) were produced [START_REF] Dong | Directed molecular evolution of DREADDs: a generic approach to creating next-generation RASSLs[END_REF] by artificially evolving the M3 and M4 muscarinic receptors to respond only to a silent drug (clozapine-N-oxide, CNO), and not to their endogenous ligand acetylcholine [START_REF] Armbruster | Evolving the lock to fit the key to create a family of G protein-coupled receptors potently activated by an inert ligand[END_REF]. A panel of DREADDs was thus created to control all the G-protein signaling pathways [START_REF] Conklin | Engineering GPCR signaling pathways with RASSLs[END_REF].

Moreover, as GPCRs bind not only to G proteins but also to arrestin family members, the group of J.

Wess developed recently an arrestin-biased DREADD [START_REF] Nakajima | Design and functional characterization of a novel, arrestin-biased designer g protein-coupled receptor[END_REF].

We engineered the first Gs-coupled RASSL, derived from the serotonergic type 4 receptor (5-HT4R), about ten years ago [START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF]. This RASSL was obtained by mutating a single aspartate residue (D 100 ) in the transmembrane domain 3 of 5-HT4R, a residue that is well conserved in GPCRs and particularly in biogenic amine receptors. The 5-HT4R-D 100 A mutant has lost the ability to bind to serotonin (5-hydroxytryptamine; 5-HT); however, it can be fully activated by a wide variety of highly specific 5-HT4R agonists [START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF]. Later, we identified a secondary coupling of 5-HT4R to the Gq/11 pathway, leading to inositol 3-phosphate (IP3) production [START_REF] Barthet | 5-hydroxytryptamine 4 receptor activation of the extracellular signal-regulated kinase pathway depends on Src activation but not on G protein or beta-arrestin signaling[END_REF]. Therefore, in collaboration with B. Conklin's group, we optimized the 5-HT4R-D 100 A mutant by inserting the additional point mutation D 66 N or D 66 A that suppresses 5-HT4R-induced IP3 production, in order to obtain a pure Gs-coupled receptor [START_REF] Chang | Modifying ligand-induced and constitutive signaling of the human 5-HT4 receptor[END_REF]. Biased agonism has been described for many GPCRs. Indeed, a wide range of ligands can promote different signaling events downstream of a particular GPCR [START_REF] Gesty-Palmer | Distinct beta-arrestin-and G protein-dependent pathways for parathyroid hormone receptor-stimulated ERK1/2 activation[END_REF][START_REF] Rajagopal | Teaching old receptors new tricks: biasing seventransmembrane receptors[END_REF][START_REF] Thomsen | Biased agonism of the calcium-sensing receptor[END_REF][START_REF] Wei | Independent beta-arrestin 2 and G protein-mediated pathways for angiotensin II activation of extracellular signal-regulated kinases 1 and 2[END_REF]. A ligand that acts as an agonist for one pathway can behave as an antagonist, an inverse agonist or be without effect on the secondary pathway engaged by the same GPCR. We hypothesized that 5-HT4R ligands that could differentially activate Gs and Gq/11 could help deciphering the roles of these different signaling pathways and could also represent new ligands for RASSLs. Thus, from a wide panel of potential 5-HT4R ligands we selected 22 compounds that belong to different chemical classes in order to cover almost all the different 5-HT4R ligand families. We then assessed whether these compounds could induce cAMP production upon activation by wild type 5-HT4R (WT), the 5-HT4R-D 100 A mutant (5-HT4R-RASSL or Rs1) [START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF] or the 5-HT4R-T 104 A mutant (the T 104 A mutation modifies agonist-induced 5-HT4R activation) [START_REF] Pellissier | Conformational toggle switches implicated in basal constitutive and agonist-induced activated states of 5-hydroxytryptamine-4 receptors[END_REF]). We then measured the ability of 10 of these compounds to induce IP3 production by quantifying IP1 accumulation. Finally, we thoroughly characterized the two more interesting 5-HT4R-biased ligands.

Results

Pharmacological screening of the functional coupling between 5-HT4R ligands and WT 5-HT4R, 5-HT4R-D 100 A or 5-HT4R-T 104 A

To identify 5-HT4R ligands that could differentially activate Gs and Gq/11, COS cells were transiently transfected with the WT 5-HT4(a)R, 5-HT4R-D 100 A or 5-HT4R-T 104 A cDNA plasmids (100 ng cDNA / 10 7 cells, corresponding to 9.5 ± 0.9, 9.2 ± 0.7 and 8.7 ± 0.6 pmol/mg proteins, respectively). Cells were then incubated with each ligand and cAMP and IP1 (a breakdown product of IP3) accumulation were quantified using the specific CisBio HTRF kits (see Experimental Procedures). The maximal responses above basal (expressed as percentage of BIMU8 maximal response) are summarized in Tables 123. Supplementary Figure 1 shows the raw data in which the basal cAMP or IP1 accumulation was not subtracted.

cAMP accumulation

As previously described, cAMP accumulation was more strongly induced following binding of 5-HT4R agonists to 5-HT4R-D 100 A than to WT 5-HT4R, except for 5-HT and related molecules that belong to the indole class, such as HTF919 [START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF] (Table 1 and Supplemental Figure 1B).

Conversely, signaling transduction through 5-HT4R-T 104 A resulted in reduced activation of cAMP production, except with the 5-HT4R agonists of the indole class (5-HT, HTF919) and the benzimidazolones (BIMU1 and BIMU8) (Table 1 and Supplemental Figure 1B).

Compounds that are classically described as 5-HT4R antagonists or weak, partial agonists acted as partial agonists (GR 113808, GR 125487, for example) or even as full agonists (ML10375, SB 204070) when coupled to 5-HT4R-D 100 A (Table 2 and Supplemental Figure 1A). Inverse agonists, such as RO 116 2617 or RO 116 1148, behaved as neutral antagonists when interacting with this RASSL.

Antagonists and inverse agonists did not activate cAMP production via 5-HT4R-T 104 A. Tropisetron, which acts as a 5-HT4R antagonist or week partial agonist, was the only drug that retained some activity with the T 104 A mutant (Table 2 and Supplemental Figure 1A).

IP1 accumulation

Receptor-induced IP1 accumulation (Table 3 and Supplemental Figure 1C) was assessed using nine compounds that were classified as 5-HT4R agonists based on their ability to induce cAMP accumulation and ML 10375 that acts as a 5-HT4R antagonist. Dose-response curves were generated to analyze precisely the Gq/ 11 activation profiles (Figure 1). For WT 5-HT4R, the EC50 values of all the tested ligands were shifted to the right compared to Gs activation (for instance, 5-HT EC50 = 4.2 ± 0.8 x 10 -9 M for cAMP production and 1.9 ± 0.3 x 10 -7 M for IP1 accumulation) (Tables 1,3). Molecules of the indole class (5-HT, HTF919) and benzimidazolones (BIMU8) were the most potent and effective activators of the Gq/ 11 pathway via WT 5-HT4R (Figure 1A,B). The Gq/ 11 activation pattern following coupling of 5-HT4R-D 100 A with the different ligands was comparable to the Gs activation profile obtained for the same molecules (Figure 1C, D and Supplementary Figure 1B,C). Indeed, the majority of the tested compounds could induce IP1 accumulation upon 5-HT4R-D 100 A stimulation, except molecules belonging to the indole class (5-HT, HTF919). Similarly, RS 67333 was much less efficient in stimulating Gq/ 11 signaling than in activating Gs via 5-HT4R-D 100 A (Table1). Finally, 5-HT4R-T 104 A could stimulate IP1 production only very weakly (Figure 1E, F and Supplemental Figure 1C) and ML 10302 acted as an inverse agonist with this receptor mutant (Table1, Figure 1F and Supplemental Figure 1C).

Characterization of biased ligands for WT 5-HT4R

The results of the functional screening indicated that, among the tested compounds, RS 67333, prucalopride and ML 10302 acted as partial agonists for the Gs pathway and induced only weakly IP1 accumulation following interaction with WT 5-HT4R (Figure 2A, B andC). Specifically, doseresponse curves showed that the EC50 values for RS 67333-mediated Gg/11 activation were strongly shifted to the right in comparison to those concerning Gs activation (EC50 = 8.4 ± 1.1 x 10 -10 M for cAMP and 2.0 ± 0.7 x 10 -7 M for IP1 accumulation) with a significant loss of efficacy (from 49 ± 2% for cAMP to 19 ± 1% for IP1 accumulation at 10 -5 M) (Figure 2C and Tables 1 and3). Prucalopride and ML 10302 could not induce IP1 accumulation (Figure 2B, C and Table 3).

In competition experiments, RS 67333 could efficiently inhibit BIMU8-induced IP1 accumulation with an IC50 of 3.4 ± 0.8 x 10 -9 M, similar to the IC50 of GR 113808 (3.8 ± 1.1 x 10 -9 M) (Figure 2D). However, RS 67333 could not completely reverse IP1 production, as this drug possesses a weak partial agonist activity towards the Gq/11 pathway (Figure 2B,D). Prucalopride was much less potent than RS 67333 in competing with BIMU8-induced IP1 accumulation (IC50 = 6.2 ± 1.7 x 10 -6 M) (Figure 2D).

Finally, the efficacy bias factor (eBF) was calculated as the ratio between the maximal response (Rmax) of the two signaling pathways (cAMP/IP1 ratio), as described by H. Bräuner-Osborne's group [START_REF] Thomsen | Biased agonism of the calcium-sensing receptor[END_REF]. Taking BIMU8 as the reference, the eBF for 5-HT and HTF919 were 1.1 ± 0.2 and 0.9 ± 0.1, respectively, whereas the eBF value for RS 67333 was 2.6 ± 0.3.

Discussion

In order to find pharmacological tools to decipher the role of the different G protein-linked signaling pathways engaged by 5-HT4R, we tested the ability of several specific compounds to induce cAMP and IP1 accumulation following coupling with wild type 5-HT4R and with two previously described receptor mutants (5-HT4R-D 100 A and -T 104 A). Our results confirm that a wide range of ligands stimulate more efficiently 5-HT4-D 100 A-than WT 5-HT4R-mediated signaling; however, we could not identify a molecule that selectively activates only Gs (and not Gq/11) upon stimulation of 5-HT4-D 100 A or of 5-HT4R-T 104 A. ML 10302 was the only drug that acted as a weak partial agonist for the WT receptor, a full agonist for the D 100 A mutant and an inverse agonist for 5-HT4R-T 104 A concerning IP1 production.

Nevertheless, as recently highlighted by Tschammer et al [START_REF] Tschammer | Histidine 6.55 is a major determinant of ligand-biased signaling in dopamine D2L receptor[END_REF] who found that a specific residue in the Dopamine D2L receptor is a major determinant of ligand-biased signaling, our analysis revealed that the D 100 residue and to a lesser extent the T 104 residue are crucial elements that have to be taken into account when designing new 5-HT4R-biased ligands.

The most interesting finding of this study is the identification of two biased ligands (RS 67333 and prucalopride) for wild type 5-HT4R. Indeed, these two ligands acted as partial agonists for the Gs pathway and as antagonists for the Gq/11 pathway. Moreover, RS 67333 potently reversed BIMU8induced IP1 production. This drug has already been used in vivo to promote learning and memory in rodents, passes well through the blood brain barrier and has a good bioavailability [START_REF] Freret | Synergistic effect of acetylcholinesterase inhibition (donepezil) and 5-HT(4) receptor activation (RS67333) on object recognition in mice[END_REF][START_REF] Marchetti | Differential modulation of the 5-HT(4) receptor agonists and antagonist on rat learning and memory[END_REF][START_REF] Marchetti | Modulation of memory processes and cellular excitability in the dentate gyrus of freely moving rats by a 5-HT4 receptors partial agonist, and an antagonist[END_REF]. Therefore, RS 67333 could be an interesting tool for studying the effect of Gs activation in vivo, while selectively blocking coupling of 5-HT4R to Gq/11.

Multiple signaling pathways are linked to 5-HT4R activation. This receptor is also coupled to G13 and RhoA activation and it has been involved in RhoA-dependent neurite retraction [START_REF] Ponimaskin | 5hydroxytryptamine(4a) receptor is coupled to Ga subunit of heterotrimeric G13 protein[END_REF]. Moreover, 5-HT4R stimulates the extracellular signal-regulated kinase (ERK) pathway via Src activation and independently of G proteins or b-arrestins [START_REF] Barthet | 5-hydroxytryptamine 4 receptor activation of the extracellular signal-regulated kinase pathway depends on Src activation but not on G protein or beta-arrestin signaling[END_REF]. It would be interesting to study biased agonism of these additional pathways.

From a therapeutic point of view, 5-HT4 agonists have been developed and commercialized for gastrointestinal disorders (cisapride, tegaserod, prucalopride, mosapride…). However, some were later withdrawn, as their administration was associated with cardiovascular or other adverse events. These side-effects could be ascribed to the lack of selectivity of the first commercialized drugs for 5-HT4R and to their affinity also for other molecules, such as the hERG K + channel and the 5-HT1 receptor [START_REF] De Maeyer | 5-HT4 receptor agonists: similar but not the same[END_REF][START_REF] Tack | Systematic review: cardiovascular safety profile of 5-HT(4) agonists developed for gastrointestinal disorders[END_REF]. Thus, highly specific synthetic agonists are urgently needed.

Biased agonism and development of ligand-directed signaling can also help circumventing these adverse effects and thus it could be useful to have ligands that activate the Gs pathway, without triggering Gq/11 signaling. Indeed, cAMP production has been linked to neuroprotective effects [START_REF] Michel | Chronic activation of the cyclic AMP signaling pathway promotes development and long-term survival of mesencephalic dopaminergic neurons[END_REF][START_REF] Silveira | Neuroprotection by cAMP: Another brick in the wall[END_REF], whereas sustained IP3 production has been associated with tumor formation via PKC activation.

In conclusion, RS 67333 and prucalopride, which belong respectively to the aryl-ketone and benzofuran families, are two 5-HT4R biased ligands that activate Gs signaling and cAMP production, while blocking the Gq/11 pathway and constitute promising tools for analyzing the role of Gs activation in vivo. Moreover, this study provides important insights for designing new drugs that could be used to treat various disorders related to 5-HT4R signaling [START_REF] Bockaert | 5-HT(4) receptors, a place in the sun: act two[END_REF].

Experimental procedures

Plasmid Constructs

Wild type 5-HT4(a)R, 5-HT4R-D 100 A (D 100 A) and 5-HT4R-T 104 A (T 104 A) cDNA plasmids in pRK5 were previously described in [START_REF] Barthet | Uncoupling and endocytosis of 5-hydroxytryptamine 4 receptors. Distinct molecular events with different GRK2 requirements[END_REF][START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF][START_REF] Pellissier | Conformational toggle switches implicated in basal constitutive and agonist-induced activated states of 5-hydroxytryptamine-4 receptors[END_REF].

Drugs

The following compounds were used: BIMU8

(endo-N-(8-methyl-8-azabicyclo[3.2.1]oct-3-yl)-2-oxo- 3-isopropyl-2,3-dihydro-1Hbenzimidazole-1-carboxamide),

Cell Cultures and Transfections

COS-7 cells were grown in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% dialyzed fetal calf serum (dFCS) and antibiotics. Cells were transfected at 60-70% confluence by electroporation as described previously [START_REF] Claeysen | Novel brain-specific 5-HT4 receptor splice variants show marked constitutive activity: role of the C-terminal intracellular domain[END_REF] and then processed for subsequent experiments.

Determination of cAMP or Inositol Phosphate (IP1) production in transfected cells

COS-7 cells were transfected with the appropriate plasmids and then seeded in 24-well plates (100 000 cells/well for cAMP and 500 000 cells/well for IP1 measurement). Twenty-four hours after transfection, cells were incubated with the appropriate drug concentration for 10 min (cAMP) or 30 min (IP1), as previously described [START_REF] Barthet | Uncoupling and endocytosis of 5-hydroxytryptamine 4 receptors. Distinct molecular events with different GRK2 requirements[END_REF]. cAMP or IP1 accumulation was quantified by HTRF ® using the cAMP Dynamic kit or the IP-One kit (Cisbio International, Bagnols-sur-Cèze, France), according to the manufacturer's instructions.

Membrane preparation and radioligand binding assay

Membranes were prepared from transiently transfected COS-7 cells plated in 15-cm dishes and grown in DMEM with 10% dFCS as described in Claeysen et al. [START_REF] Claeysen | A Single Mutation in the 5-HT4 Receptor (5-HT4-R D100(3.32)A) Generates a Gs-coupled Receptor Activated Exclusively by Synthetic Ligands (RASSL)[END_REF]. Membranes were homogenized in 50 mM HEPES (pH 7.4; 5 mg of proteins in 1 ml of solution) and stored at -80°C until use. Membrane suspensions (about 10 µg), diluted in 100 µl of 50 mM HEPES containing 10 mM pargyline and 0.01% ascorbic acid, were incubated with 100 µl

Data Analysis

The dose-response curves were fitted using GraphPad Prism and the following equation for monophasic dose-response curves: y = (ymax -ymin) / 1 + [(x / EC50) nH] + ymin, where EC50 is the concentration of the compound needed to obtain 50% of the maximal effect and nH is the Hill coefficient. Competition and saturation experiments were evaluated by non-linear regression analysis using GraphPad Prism. All represented data correspond to the mean ± SEM of three independent experiments performed in triplicate. Statistical significance was determined with the Student Newman Keul's test using GraphPad Prism.

EC50

Serotonin (5-HT) 88 ± 5 4.2 ± 0.8 x 10 -9 -1.9 ± 0.9 x 10 -6 107 ± 4 7.0 ± 1.2 x 10 -8 BIMU8 100 1.9 ± 0.3 x 10 -8 100 6.3 ± 0.5 x 10 -9 100 8.5 ± 0.6 x 10 -8

AGONISTS

Indoles and Indole Carboxylates HTF919 65 ± 5 5.0 ± 0.4 x 10 -9 20 ± 3 1.0 ± 0.2 x 10 -6 57 ± 5 1.2 ± 0.2 x 10 -7

Benzamides Zacopride 91 ± 4 1.6 ± 0.4 x 10 -7 75 ± 4 2.1 ± 0.8 x 10 -7 8 ± 3 2.9 ± 0.9 x 10 -5 SC 53116 72 ± 3 85 ± 4 35 ± 4 Cisapride 61 ± 3 7.8 ± 1.2 x 10 -9 72 ± 5 7.4 ± 0.5 x 10 -9 21 ± 2 2.0 ± 0.6 x 10 -6

Benzoates ML10302 34 ± 3 1.4 ± 0.2 x 10 -9 60 ± 2 7.7 ± 1.0 x 10 -9 -N.D.

Benzodioxanes

Benzofurans

Prucalopride 50 ± 7 2.1 ± 0.8 x 10 -8 83 ± 6 5.3 ± 1.1 x 10 -8 28 ± 1 1.0 ± 0.5 x 10 -6

Aryl ketones RS 67333 49 ± 2 8.4 ± 1.1 x 10 -10 90 ± 6 1.2 ± 0.6 x 10 -9 -N.D.

Naphtalimides

RS 56532 58 ± 3 1.4 ± 0.3 x 10 -7 68 ± 3 1.9 ± 0.5 x 10 -7 20 ± 5 1.2 ± 0.7 x 10 -5

Benzimidazolones

EC50

Serotonin (5-HT) 82 ± 7 1.9 ± 0.3 x 10 -7 -6.2 ± 0.2 x 10 -10 60 ± 7 1.2 ± 0.9 x 10 -5 BIMU8 100 7.8 ± 1.0 x 10 -8 100 2.3 ± 0.9 x 10 -8 100 6.7 ± 0.6 x 10 -7

AGONISTS

Indoles and Indole Carboxylates HTF919 73 ± 4 6.9 ± 0.3 x 10 -8 -N.D. 10 ± 4 1.9 ± 0.7 x 10 -5

Benzamides Zacopride 25 ± 3 1.4 ± 0.8 x 10 -6 71 ± 4 5.4 ± 1.0 x 10 -7 3 ± 2 N.D. Cisapride -N.D. 97 ± 2 2.0 ± 0.3 x 10 -7 14 ± 3 1.6 ± 0.5 x 10 "agonists" with WT 5-HT4R, 5-HT4R-D 100 A and 5-HT4R-T 104 A concerning cAMP accumulation.

EC50 and Rmax for cAMP accumulation in COS-7 cells that were transiently transfected with the different 5-HT4R plasmids (50 ng) following incubation with 5-HT4R "agonists" (10µM for 10 minutes). Rmax was calculated by removing the basal response and is expressed as a percentage of the BIMU8 maximal response (6.7 ± 0.3 pmol of cAMP/100,000 cells for WT 5-HT4R, 5.0 ± 0.2 pmol for 5-HT4R-D 100 A and 4.4 ± 0.3 pmol for 5-HT4R-T 104 A). -, no significant effect above basal. Data represent the mean ± SEM of at least three independent experiments performed in triplicate.

Table 2: Maximal response (Rmax) above basal of the tested 5-HT4R "antagonists" and "inverse agonists" with WT 5-HT4R, 5-HT4R-D 100 A or 5-HT4R-T 104 A concerning cAMP accumulation.

Rmax for cAMP accumulation in COS-7 cells that were transiently transfected with the different 5-HT4R plasmids (50 ng) following incubation with 5-HT4R "antagonists" and "inverse agonists" (10µM for 10 minutes). Rmax was calculated by subtracting the basal response and is expressed as a percentage of the BIMU8 maximal response (6.7 ± 0.3 pmol of cAMP/100,000 cells for WT 5-HT4R, 5.0 ± 0.2 pmol for 5-HT4R-D 100 A and 4.4 ± 0.3 pmol for 5-HT4R-T 104 A). -, no significant effect above basal. --, inverse agonist effect. Data the mean ± SEM of at least three independent experiments performed in triplicate. EC50 and Rmax for IP1 accumulation in COS-7 cells that were transiently transfected with the different 5-HT4R plasmids (100 ng) following incubation with 5-HT4R ligands (10µM for 30 minutes). Rmax was calculated by removing the basal response and is expressed as a percentage of the BIMU8 maximal response (53.8 ± 6.0 pmol of IP1/250,000 cells for WT 5-HT4R, 42.7 ± 6.9 pmol for 5-HT4R-D 100 A and 40.8 ± 4.2 pmol for 5-HT4R-T 104 A). Data represent the mean ± SEM of at least three independent experiments performed in triplicate.

  pentyl-iminosemicarbazone), (S)-zacopride ((S)-N-(1-azabicyclo[2.2.2]oct-3-yl)-4amino-5-chloro-2-methoxy-benzamide monohydrochloride), SC 53116 (4-Amino-5-chloro-N-[[(1S,7aS)-hexahydro-1H-pyrrolizin-1-yl]methyl]-2-methoxy-benzamide), cisapride (cis-N-[1-[3-(4fluorophenoxy)propyl]-3-methoxy-4-piperidinyl]-4-amino-5-chloro-2-methoxy-benzamide, ML 10302 (2-(1-piperidinyl)ethyl-4-amino-5-chloro-2-methoxybenzoate), SL 65.0155 (5-(8-Amino-7-chloro-2,3dihydro-1,4-benzodioxin-5-yl)-3-[1-(2-phenylethyl)piperidin-4-yl]-1,3,4-oxadiazol-2(3H)-one hydrochloride), Prucalopride (4-Amino-5-chloro-N-[1-(3-methoxypropyl)piperidin-4-yl]-2,3dihydrobenzofuran-7-carboxamide), RS 67333 (1-(4-amino-5-chloro-2-methoxy-phenyl)-3-(1-butyl-4piperidinyl)-1-propanone), RS565324-amino-4-chloro-N-(quinuclidin-3-yl)-1methyl-indole-3-carboxylate), Tropisetron (ICS 205 930; [(3a tropanyl)-lH-indole-3carboxylic acid ester]), GR 125487 ([1-[2(methylsulphonyl-amino)ethyl]4-piperidinyl]methyl-5fluoro-2-methoxy-1-H-indole-3-carboxylate, hydrochloride), SDZ 205557 (2-methoxy-4-amino-5chlorobenzoic acid 2-(diethylamino) ethyl ester, hydrochloride), ML 10375 (2-(cis-3,5-dimethyl-1piperidinyl)ethyl4-amino-5-chloro-2-methoxybenzoate), SB 204070 ((1-butyl-4-piperidinyl)methyl 8amino-7-chloro-1,4-benzodioxane-5-carboxylate), RS 39604 (1-[4-amino-5-chloro-2-(3,5dimethoxybenzyl-oxy)phenyl]-3-[1-[2-[(methylsulfonyl)amino] ethyl]]-4-piperidinyl]]-1-propanone hydrochoride), Pimozide (2H-Benzimidazol-2-one, 1-(1-(4,4-bis(4-fluorophenyl)butyl)-4-piperidinyl)-1,3-dihydro-), RO116-1148 2,3-dihydrobenzo-(1,4)-dioxine-5-carboxylic acid 1-butylpiperidin-4ylmethylamide hydrochloride.

  [ 3 H]-GR 113808 (specific activity: 82 Ci/mmol) and 50 µl of buffer or competing drugs at 20°C for 30 min. For saturation analysis assays, various concentrations of [ 3 H]-GR 113808 (0.001-0.8 nM) were used. BIMU8 (10 µM) was used to determine specific binding. To quantify [ 3 H]-GR 113808 bound to WT receptors in cells co-expressing WT and D 100 A (or DD) 5-HT4Rs, experiments were performed in the presence of 10 µM 5-HT, which does not bind to the D 100 A or DD mutants. The difference between the total [ 3 H]-GR 113808 binding and the remaining binding measured in the presence of 5-HT corresponded to the [ 3 H]-GR 113808 binding to co-expressed D 100 A (or DD) receptors. Protein concentration was determined using the bicinchoninic acidic method.

3:

  Agonist potencies (EC50) and maximal response (Rmax) above basal of the tested 5-HT4R ligands with WT 5-HT4R, 5-HT4R-D 100 A or 5-HT4R-T 104 A concerning IP1 accumulation.

Figure 1 :

 1 Figure 1: Dose-response curves of IP1 accumulation following incubation with 5-HT4R ligands.COS-7 cells that transiently express WT 5-HT4R (A, B), 5-HT4R-D 100 A (C, D) or 5-HT4R-T 104 A (E, F) were incubated with the different 5-HT4R ligands and IP1 accumulation was expressed as the percentage of the IP1 production (60.5 ± 2.6 pmol/100,000 cells) induced by 10 -5 M 5-HT in cells transfected with 100 ng of WT 5-HT4R plasmid (A, B, E, F) or as a percentage of the IP1 production (49.6 ± 2.2 pmol/250,000 cells) induced by 10 -5 M BIMU8 in cells transfected with 100 ng of 5-HT4R-D 100 A plasmid (C, D). Data for each drug correspond to the mean ± SEM of three independent experiments performed in triplicate.

Figure 2 :

 2 Figure 2: Characterization of biased 5-HT4R ligands. COS-7 cells that transiently express WT 5-HT4R were incubated with the indicated ligands. (A-C) Dose-response curves for cAMP and IP1 accumulation. cAMP and IP1 values were expressed as a percentage of the cAMP or IP1 production (6.7 ± 0.3 pmol/100,000 cells or 53.8 ± 6.0 pmol/250,000 cells, respectively) induced by 10 -5 M BIMU8 in cells transfected with 50 ng (cAMP) or 100 ng (IP1) WT 5-HT4R plasmid. (D) Competition of BIMU8-induced IP1 response. IP1 values were expressed as a percentage of the IP1 production (42.2 ± 3.7 pmol/250,000 cells) induced by 10 -5 M BIMU8 in cells transfected with 100 ng WT 5-HT4R plasmid. Each point in the curve is the mean ± SEM of three independent experiments performed in triplicate.

  Figure1

Table 1

 1

	Drug (10µM)

Table 2

 2

	Drug (10µM)		cAMP
		WT 5-HT4R	5-HT4R-D 100 A	5-HT4R-T 104 A
		Rmax ± S.E.M.	Rmax ± S.E.M.	Rmax ± S.E.M.
		(%)	(%)	(%)
	Serotonin (5-HT)	88 ± 5	-	107 ± 4
	BIMU8	100	100	100
	ANTAGONISTS
	Indoles and Indole
	Carboxylates
	GR 113808	-	50 ± 4	7 ± 2
	Tropisetron	23 ± 2	51 ± 5	38 ± 4
	GR 125487	-	36 ± 5	-
	Pimozide	-	13 ± 3	-
	Benzamides
	SDZ 205557	22 ± 5	70 ± 3	-
	Benzoates
	ML 10375	9 ± 3	72 ± 2	-
	Benzoate dioxanes
	SB 204070	29 ± 4	88 ± 3	8 ± 2
	Benzoate Aryl Ketones
	RS 39604	19 ± 3	77 ± 5	-
	RS 100235	20 ± 2	56 ± 4	11 ± 3
	RS 67532	25 ± 2	91 ± 6	13 ± 2
	INVERSE AGONISTS
	Benzoate dioxanes
	RO 116 2617	--	-	--
	RO 116 1148	--	5 ± 3	6 ± 2

Table 3

 3

	Drug (10µM)

  -5

	Benzoates
	ML10302	-	N.D.	50 ± 4 1.3 ± 0.6 x 10 -7	--	N.D.
	Benzofurans
	Prucalopride	-	N.D.	70 ± 4 4.7 ± 0.6 x10 -7	-	N.D.
	Aryl ketones
	RS 67333	19 ± 1 2.0 ± 0.7 x 10 -7	38 ± 3 7.3 ± 0.7 x 10 -8	14 ± 2 2,3 ± 1.1 x 10 -6
	Naphtalimides
	RS 56532	17 ± 6 2.4 ± 0.2 x 10 -5	59 ± 3 1.1 ± 0.4 x 10 -6	22 ± 4 4.3 ± 0.7 x 10 -6

TABLE LEGENDS Table 1 : Agonist potencies (EC50) and maximal response (Rmax) above basal of the tested 5-HT4R

 LEGENDS1

ACKNOWLEDGMENTS

We are grateful to Philippe Marin for constructive discussion and constant support. This work was financially supported by grants from CNRS, INSERM, the French Minister of Research (ANR Blanc 2006, to AD and SC), the France Alzheimer association (to SC), the Soroptimist International (French Union, to SC) and the Languedoc Roussillon region ("Chercheuse d'Avenir" 2012, to SC). Binding experiments, cAMP measurements and ELISA were carried out using the ARPEGE Pharmacology Screening Interactome facility at the Institute of Functional Genomics (Montpellier, France).


Mohammad Tavallaeinejad
email: mohammad.tavallaeinejad@mail.mcgill.ca

Michael P Païdoussis

Manuel Flores Salinas

Mathias Legrand

Mojtaba Kheiri

Ruxandra Mihaela Botez

Manuel Flores Salinas

Why inverted flags flap: An experimental study

Keywords: fluid-structure interactions, inverted flags, large-amplitude flapping, fluidelastic instability, flutter

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Introduction

This paper focuses the fluid-structure interaction (FSI) of a flexible thin plate in axial flow: a cantilevered thin plate (or flag) of length L and height H subjected to a fluid flowing axially with velocity U and directed from the free end towards the clamped one, otherwise known as an 'inverted flag;' see figure 1.

Inverted flags are known to exhibit large-amplitude periodic flapping around the undeflected equilibrium. A number of studies on the dynamics of inverted flags suggest that the physical mechanism underlying large-amplitude flapping may be Vortex-Induced Vibration (VIV) (e.g., [START_REF] Sader | Large-amplitude flapping of an inverted flag in a uniform steady flow -a vortex-induced vibration[END_REF]. In these studies, the flapping phenomenon is attributed to the periodic formation and synchronized shedding of trailing-edge vortices (TEV) and leading-edge vortices (LEV), which is a characteristic of VIV (see figure 1).

Although several aspects of the dynamics may be explained through the VIV mechanism, there are some circumstances where vortex shedding, which plays a central role in VIV, may not occur for a flapping inverted flag, hence posing a challenge to the credence of the VIV mechanism. For instance, in an experimental study, [START_REF] Pazhani | An experimental investigation of the dynamics of an inverted serrated flag[END_REF] investigated the effect of leading-edge serrations. They found that the serrated flag does display large-amplitude flapping, even though vortex formation and shedding from the leading edge was not observed. Moreover, via a scaling analysis, [START_REF] Sader | Large-amplitude flapping of an inverted flag in a uniform steady flow -a vortex-induced vibration[END_REF] predicted that VIV cannot occur for heavy flags or small mass ratios1 , yet large-amplitude flapping does. [START_REF] Goza | Global modes and nonlinear analysis of inverted-flag flapping[END_REF] explored computationally the physical mechanisms for large-amplitude flapping of inverted flags, concluding that for a specific set of system parameters, large-amplitude flapping cannot be attributed to classical VIV, and also for small-amplitude flapping. Finally, [START_REF] Gurugubelli | Large amplitude flapping of an inverted elastic foil in uniform flow with spanwise periodicity[END_REF] performed simulations in which a rigid splitter plate was attached to the flag trailing edge, thus suppressing trailing-edge vortex shedding; they found that inverted flags undergo large-amplitude flapping even though the interactions between vortices detached from the leading-edge at the cycle extremities were eliminated -a prediction not yet verified experimentally, which is one of the objectives of the present experiments.

The primary purpose of experiments described in this paper is to explore the correlation between vortex shedding and the flapping mechanism; specifically, the qualitative and quantitative effects of suppression of both LEV and TEV on the onset, frequency, and amplitude of flapping.

The paper is organized as follows. First, experiments with a rigid splitter plate attached to the trailing-edge of the inverted flag are described (see Figure 2), aiming to evaluate the importance of the existence of TEV and to examine the effects of forced disconnection between counter-rotating LEV on large-amplitude flapping. Second, experiments with inverted flags with a serrated leading-edge, similar to those used by [START_REF] Pazhani | An experimental investigation of the dynamics of an inverted serrated flag[END_REF], are described. These experiments explore the effects of simultaneous suppression of LEV and TEV. Finally, the synchronization of lift and displacement and phase dynamics are studied.

Rigid splitter plate

The experiments were conducted in a subsonic wind tunnel with a fairly large test-section. The flow velocity in the test-section was incremented in small steps, and the flag motion was recorded via a high-speed camera at each step. An image processing technique was then utilized to extract the time history of oscillations. Brass plates, i.e. 'flags' (H = 101 mm, L = 198 mm, and thickness h = 0.38 mm), as well as polycarbonate flags with different dimensions (see Table 1) were used in the experiments. Experiments have been conducted with and without a rigid splitter plate. The splitter plate was made from a plywood sheet of thickness h s = 10 mm, height H s = 610 mm, and length L s = 1800 mm, and was secured firmly to the walls of the test-section (see figure 3); no significant motion of the splitter plate was observed during the experiment, even at very high wind speeds.

Figure 4(a) shows bifurcation diagrams for the tip rotation of 160 × 160 mm polycarbonate flags C (circles) and flag D (diamonds), with the rigid splitter plate (filled symbols) and without it (empty symbols). A slight reduction is seen for the flapping amplitude of the flag with a splitter plate. This may be explained using observations made by [START_REF] Gurugubelli | Large amplitude flapping of an inverted elastic foil in uniform flow with spanwise periodicity[END_REF]. In their computational study, the inverted flag with the splitter plate exhibits only two counter-rotating vortices shed from the leading edge over the flapping cycle. The absence of the trailing edge vortices, and the inhibition of vortex-vortex interaction leads to a larger pressure distribution at the trailing edge and to a slightly smaller drag at the leading edge. This results in a smaller bending moment, which in turn leads to a reduction in the curvature along the flag.

The frequency of oscillation is also reduced slightly when the splitter plate is introduced, see Figure 4(b). For instance, the maximum reduction in flapping frequency for the h = 1.02 mm flag is at U ⋍ 20 m/s, where the frequency is reduced by almost 8%. This may also be associated with loss of the trailing edge vortices, caused by the rigid splitter plate. More specifically, the trailing edge vortex formation and shedding accelerates the drop in the pressure distribution over the flag, which consequently leads to a faster transition from maximum deflection from one side to the other, hence to a higher frequency (see [START_REF] Gurugubelli | Large amplitude flapping of an inverted elastic foil in uniform flow with spanwise periodicity[END_REF]). Figure 5 shows that the onset of large-amplitude flapping for all flags tested (except for flag B) is delayed when the splitter plate is added. This may be linked to the pressure reduction close to the leading edge of the inverted flag due to the splitter plate: the presence of the splitter plate introduces a small additional damping to the dynamical system; consequently, the critical flow velocity for large-amplitude flapping increases, and the flapping amplitude and frequency become smaller at the onset of large-amplitude flapping.

However, all these differences are very minimal. The main and most significant conclusion is that introducing a splitter plate has a minimal influence on the critical flow velocity for large-amplitude flapping, its amplitude and frequency. ] without the rigid splitter plate.

Flag

Serrated inverted flags

In order to further understand the effect of vortex shedding on the global dynamics of inverted flags, a serrated leading-edge geometry (chevron) with height H s = 10 mm and width W s = 10 mm was introduced to polycarbonate flags of different aspect ratios, see Figure 6 The observed behaviour shows that, for the range of parameters investigated in these experiments, the dynamical characteristics of inverted flags are not very sensitive to (i) the formation and periodic shedding of vortices from the leading and trailing edges, and (ii) vortexvortex interaction (if any exists). Hence, another mechanism must be the cause of large-amplitude flapping; namely, it may be a fluidelastic self-excited flutter.

Synchronization of lift and displacement and phase dynamics

Several experiments were conducted to measure simultaneously the forces acting on the flag (i.e. lift and drag) and its motion. The phase difference between the time traces of the fluid forces and flag displacements were examined. Moreover, the dominant frequencies of the fluid forces were obtained. These experiments were motivated by the observation made by Goza et al. ( 2018) for large-amplitude flapping of heavy inverted flags. They reported that, compared to light flags, several additional vortices are shed per cycle for heavy (low µ) ones, resulting in additional peaks in the frequency spectrum of the lift signal. Moreover, the frequency associated with the largest peak in the lift spectrum was different from that of the displacement spectrum. This led Goza (2019) to refer to the large-amplitude flapping of massive flags as "not-classical VIV".

In order to investigate experimentally the existence of synchronization between the lift force and displacement for heavy inverted flags, stainless steel flags of varying length (hence, varying mass ratio) were tested (see Table 2). The transverse (lift) and streamwise (drag) components of the fluid flow force were simultaneously measured at the flagpole, utilizing an in-house built aerodynamic balance (A Mini45-E Array Technology Incorporated Inc). Time traces of the lift, F Z (0, t), and the drag, F X (0, t), components (see Figure 7) were collected at 1000 Hz; the sampling rate for the tip transverse displacement, w (L, t), was 160 -280 Hz.

Frequency characteristics

Figure 8 shows the time traces and PSDs of w (L, t) and the lift signals for a stainless-steel inverted flag with L = 100 mm. In the PSD plots for the lift signal, the peaks are labeled sequentially as f L1 , f L2 etc. from lower to higher frequencies. As seen from figures 8(b,d), higher harmonics of nearly the same magnitude as the main frequency, f 1 , appear in the PSD of the lift, while the motion is periodic, supporting the Goza et al. observations discussed above. By increasing the flow velocity, motion becomes chaotic-like at U = 8.3 m/s; the loss of synchronization with departure from a periodic behaviour can be seen in figures 8(e,f).

The spectrograms of the displacement and lift signals are presented in figures 8 (g) and (h), respectively, showing an increase in dynamic activity and the presence of additional frequency peaks in the lift dynamics with increasing U. The increase in number and the strength of higher harmonics in the lift frequency spectrum suggests that the conjectured VIV-associated oscillation is gradually replaced by another mechanism.

Figure 9 peak in the displacement PSD plot shown in figure 9(d) for L = 50 mm flag at U = 14.4 m/s is f 1 = 18 Hz, while the dominant peak in the lift PSD plot occurs at f L2 = 2f 1 = 36 Hz, and subdominant peaks occur at f L1 = f 1 = 18 Hz, f L3 = 3f 1 = 54 Hz, and f L4 = 5f 1 = 90 Hz, whereas the contribution of these harmonics in the flag oscillation is very weak. This indicates that vortex shedding may be synchronized to a higher displacement frequency; in the present case, the vortex shedding frequency is twice the flapping frequency, giving rise to a 1:2 synchronization.

Phase dynamics

It is known that in the case of VIV-driven motion of a circular cylinder in cross-flow, sharp changes occur in the phase angle between the fluid forces and cylinder motion at resonance, as the flow velocity is varied. In particular, the phase between the cross-flow force and the transverse displacement of the cylinder jumps from near 0 to near π (refer to Khalak and Williamson 1999, [START_REF] Zhao | Fluid-structure interaction of a square cylinder at different angles of attack[END_REF][START_REF] Seyed-Aghazadeh | Vortex-induced vibration and galloping of prisms with triangular cross-sections[END_REF]).

Here, the instantaneous phase difference between the time series obtained for the transverse displacement of the flag and the lift are calculated using the Hilbert transform [START_REF] Khalak | Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping[END_REF]Williamson 1999, Konstantinidis et al. 2019). The instantaneous phase is defined as φ w (t) = atan[w (L, t)/ ŵ (L, t)] and φ F (t) = atan[F L (0, t)/ FL (0, t)], where ŵ (L, t) and FL (0, t) are the Hilbert transforms of w (L, t) and F L (0, t), respectively. Next, the instantaneous phase lag, φ d (t), between the lift and the displacement is calculated as φ d (t) = φ F (t) -φ w (t).

Figure 10 shows the variation of the time-averaged phase lag, denoted by φ d , as a function of the dimensionless flow velocity for flags A-D (table 2). In all cases, the time-averaged phase difference never crosses 90 • and remains bounded in the [0 50] range over the large-amplitude flapping regime. The different values of the phase difference may well be due to the effect of different values of structural damping for the different flags. Similar observations have been made by [START_REF] Seyed-Aghazadeh | Vortex-induced vibration and galloping of prisms with triangular cross-sections[END_REF] for triangular prisms in cross-flow, reporting that the jump from ∼ 0 to ∼ 180 • in phase difference between flow forces and the body motion did not occur, and hence the oscillation was concluded to be of the galloping type.

The above observations suggest that flag motion and vortex shedding influence each other reciprocally; however, vortex shedding does not appear to be the cause for flapping. The large-amplitude flapping of short inverted flags accompanied by high-frequency vortex shedding suggests that a fluidelastic excitation mechanism may be involved, and hence time-averaged aerodynamic forces govern the motion. A similar conclusion has been reached for slender prismatic bodies with bluff cross-section and sufficiently long afterbody by [START_REF] Nemes | The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack[END_REF], [START_REF] Zhao | Fluid-structure interaction of a square cylinder at different angles of attack[END_REF] and [START_REF] Seyed-Aghazadeh | Vortex-induced vibration and galloping of prisms with triangular cross-sections[END_REF], among others. Additionally, these observations agree well with computational predictions of [START_REF] Goza | Global modes and nonlinear analysis of inverted-flag flapping[END_REF], reporting that the dominant frequency of lift (largest peak in the PSD plot) is higher than that of the tip displacement, suggesting that the motion is not "classical VIV".

Conclusions

Some experiments were described in this paper, aiming at examining the global dynamics of inverted flags and, in particular, at probing the impact of periodic vortex shedding from the leading and trailing edges thereon.

The effect of vortex shedding from both leading and trailing edges was investigated. It was shown that suppression of the leading and trailing edge vortices, and also inhibition of the interaction between the two counter-rotating vortices (if any exists), results in only minor changes in the critical velocity, amplitude and frequency. The overall dynamics and features of the system remained intact, and the large-amplitude flapping persisted for all flags tested in the experiments, with TEV and LEV present or suppressed.

Force measurements provided some insights into the relationship between vortex shedding and large-amplitude flapping; a difference between the dominant (peak) frequencies of the lift and flapping was found in some cases. Moreover, it was shown that for heavier inverted flags, additional frequency peaks appear in the lift frequency spectrum, with power as great as or larger than that matching the motion dominant frequency. In addition, the lift and tip displacements were found to be desynchronised in the chaotic-like flow regime for lighter flags.

The experimental results presented in Sections 2-4 suggest that a fluidelastic instability may be the underlying mechanism for the flapping motion of heavy inverted flags. The near-identical qualitative behaviour of normal inverted flags and those with a serrated leading edge and a splitter plate at the trailing edge suggests that the global (qualitative) dynamical characteristics of heavy inverted flags are not governed by the unsteady vortex shedding from the leading and trailing edges. In other words, periodic vortex shedding is not the cause, but an effect of large-amplitude flapping.

It is stressed that flow visualization was not carried out in the experiments with serrated flags and the splitter plate. The wake behind the flag may display three-dimensional characteristics; yet, as reported by [START_REF] Pazhani | An experimental investigation of the dynamics of an inverted serrated flag[END_REF], the dominant vortical features in the near wake is broken down and the coherent formation and shedding of vortices is disrupted.

There are definitely potential connections, yet to be discovered in the future, between the phase dynamics and the underlying mechanism for large-amplitude flapping. Further investigations would be desirable to better clarify the distinction between VIV and the underlying mechanism for large-amplitude flapping of heavy flags.

Figure 1 -

 1 Figure 1 -Inverted flag in large-amplitude regime, shedding leading-edge vortices (LEV) and trailing-edge vortices (TEV) in the wake.

Figure 2 -

 2 Figure 2 -Experimental set-up for a serrated inverted flag with the rigid splitter plate, showing the measured forces at the flagpole, utilizing a force balance.

Figure 3 -

 3 Figure 3 -Experimental set-up for the inverted flag (a) without and (b) with the rigid splitter plate.

Figure 4 -

 4 Figure 4 -Experimental results for inverted flags with L = H = 160 mm and [ ] h = 0.76 mm, [ ] h = 1.02 mm; (a) bifurcation diagram (b) variation of the dominant frequency in PSD with the flow speed. The empty and filled markers correspond to the flags with and without the splitter plate, respectively; the black and red symbols correspond to the wind speed sweep up and down, respectively.

AFigure 5 -

 5 Figure 5 -Critical flow speed for the onset of large-amplitude flapping of different inverted flags with sweeping up the wind speed; [ ] with and [] without the rigid splitter plate.

  (a). Using flow visualization techniques,[START_REF] Pazhani | An experimental investigation of the dynamics of an inverted serrated flag[END_REF] have shown that this serrated geometry produces small counter-rotating pairs of vortices, which suppresses the formation and periodic shedding of vortices from the leading edge. The Pazhani and Acharya (2019) experiments with serrated flags have been repeated in the present study, with wider flags -to minimize three-dimensionality of the flow caused by the side edges -also introducing a rigid splitter plate at the trailing edge of the flag to interrupt the communication of the separated shear layers. Mainly, qualitative experiments were conducted. Insofar as the onset and amplitude of large-amplitude flapping is concerned, the responses are similar to those of normal inverted flags. For instance, the experimental results for flags of A = 3.0 in figure 6(b) show no notable differences in the critical values of flow velocity and the amplitude of oscillation, with and without the splitter plate and serrations.

Figure 6 -

 6 Figure 6 -Experiments with serrated inverted flags: (a) specimens used in the experiments with a similar serration geometry but different flag dimensions, (b) bifurcation diagram for an inverted flag with flat leading edge and no splitter plate (filled circles) and a serrated flag with the splitter plate at the trailing edge (empty circles); both flags are of A = 3.0. The black and red symbols correspond to the wind speed sweep up and down, respectively.

Figure 7 -

 7 Figure 7 -Measured forces at the flagpole, utilizing a force balance.

Figure 8 -

 8 Figure8shows the time traces and PSDs of w (L, t) and the lift signals for a stainless-steel inverted flag with L = 100 mm. In the PSD plots for the lift signal, the peaks are labeled sequentially as f L1 , f L2 etc. from lower to higher frequencies. As seen from figures 8(b,d), higher harmonics of nearly the same magnitude as the main frequency, f 1 , appear in the PSD of the lift, while the motion is periodic, supporting the Goza et al. observations discussed above. By increasing the flow velocity, motion becomes chaotic-like at U = 8.3 m/s; the loss of synchronization with departure from a periodic behaviour can be seen in figures 8(e,f).The spectrograms of the displacement and lift signals are presented in figures 8 (g) and (h), respectively, showing an increase in dynamic activity and the presence of additional frequency peaks in the lift dynamics with increasing U. The increase in number and the strength of higher harmonics in the lift frequency spectrum suggests that the conjectured VIV-associated oscillation is gradually replaced by another mechanism.Figure9shows the time traces and PSDs for flags with (a,b) L = 70 mm, (c,d) L = 50 mm, and (e,f) L = 35 mm, respectively. Strikingly, the PSDs of lift and displacement show the same frequency peaks (i.e., f L1 = f 1 ), with the lift showing harmonics nearly equal or larger than the dominant frequency of the motion. For example, the frequency associated with the dominant

Figure 9 -

 9 Figure 9 -(Left) tip transverse displacement [ ] and the normalized lift [ ] for stainless-steel inverted flags with (a) L = 70 mm at U = 7.4 m/s, with (c) L = 50 mm at U = 14.4 m/s, and with (e) L = 35 mm at U = 19.0 m/s; (right) their associated PSDs.

Figure 10 -

 10 Figure 10 -Phase difference between transverse force (lift) and transverse displacement for stainless steel inverted flags with [ ] L = 100 mm, [ ] L = 70 mm, [ ] L = 50 mm, and [ ] L = 35 mm over the periodic large-amplitude flapping regime.

Table 1 -

 1

		Material	L × H(mm) h(mm)
	A	Polycarbonate 150 × 225	1.02
	B	Polycarbonate 150 × 600	0.76
	C	Polycarbonate 160 × 160	0.76
	D	Polycarbonate 160 × 160	1.02
	E	Brass	198 × 101	0.38

Labels and dimensions of pairs of inverted flags tested in experiments with and without the rigid splitter plate.

Table 2 -

 2 Stainless-steel inverted flags with H = 75 mm, h = 0.08 mm, and varying length utilized in experiments.

	Flag L(mm)	µ	A
	A	100	0.21 0.75
	B	70	0.15 1.07
	C	50	0.10 1.50
	D	35	0.07 2.14

The fluid-to-plate mass ratio is defined as µ = ρ f L/ρ p h; ρ f and ρ p being the mass density of the fluid and plate, respectively, and h is the thickness of the plate. Small µ is associated with "heavy flags".

Acknowledgements

The financial support by the Natural Sciences and Engineering Research Council of Canada, the Solution Mining Research Institute (SMRI) and Pipeline Research Council International (PRCI) is gratefully acknowledged.