Joël Bockaert
email: joel.bockaert@igf.cnrs.fr.

Sylvie Claeysen

Valérie Compan

Aline Dumuis

5-HT4 receptors: History, molecular pharmacology and brain functions

Keywords: Serotonin 5-HT4 receptor, Memory Feeding, Mood Depression

Twenty years ago, we started the characterization of a 5-HT receptor coupled to cAMP production in neurons. This receptor obviously had a different pharmacology to the other 5-HT receptors described at that time, i.e. the 5-HT1, 5-HT2, 5-HT3 receptors. We proposed to name it the 5-HT4 receptor. Nowadays, 5-HT4 receptors are one of the most studied GPCRs belonging to the "rhodopsin" family. Thanks to the existence of a great variety of ligands with inverse agonist, partial agonist, agonist and antagonist profiles, the pharmacological and physiological properties of this receptor are beginning to emerge.

Although some 5-HT4 partial agonists have been on the market for gastro-intestinal pathologies, 5-HT4 receptor drugs have still to be commercialized for brain disorders. However, since 5-HT4 receptors have recognized effects on memory, depression and feeding in animal models, there is still hope for a therapeutic destiny of this interesting target in brain disorders.

Introduction

In July 1990, at the Second IUPHAR satellite meeting on Serotonin, held by the Serotonin Club in Basel, Switzerland, began a series of "Serotonin Club Irvine H. Page Lectures". S.J. Peroutka, a wellknown and appreciated expert in the serotonin field gave a tribute to Dr. Irvine H. Page [START_REF] Peroutka | Serum vasoconstrictor (serotonin): isolation and characterization[END_REF]. S.J. Peroutka reminded younger colleagues that 5-hydroxytryptamine (5-HT) was successively called "vasotonin" (1933 -Bayliss and Ogden), "Enteramine" (1933 -Vialle and Erspamer), but that the modern name "serotonin" can be dated to Dr. Page's Science paper in 1948(Rapport et al., 1948).

In 1985, Irvine H. Page wrote "A long life has taught me that the natural history of one's active participation in a discovery is about 5-10 years. Then the subject grows complicated, new young faces appear with their better methods and they take over" [START_REF] Page | The Neonatology of Serotonin[END_REF].

Thus, I was very honoured when I received the Serotonin Club's invitation to give the Irvine H.

Page Lecture, especially since we discovered the 5-HT4 receptors (5-HT4Rs) (Dumuis et al.,1988a) 20 years ago with A. Dumuis and are still working on them, using, we hope, effective methods. The aim of this paper is to review 20 years of research on 5-HT4Rs.

The pre-history of 5-HT4Rs

My interest in neurotransmitter sensitive adenylate cyclase began more than 40 years ago when I came back to the Collège de France in Paris after post-doctoral training at Northwestern University in Chicago, where I was already working on G-protein coupled receptor desensitization. Paul Greengard had just published a paper on a dopamine sensitive adenylate cyclase in striatal membranes [START_REF] Kebabian | Dopamine-sensitive adenylate cyclase in caudate nucleus of rat brain, and its similarity to the "dopamine receptor[END_REF]. The possibility of using cAMP production, following receptor activation, to discover new neurotransmitter receptors and analyse their pharmacology, brain distribution and regulation was fascinating. I decided to interact with my new neighbouring neuroscientists and fantastic colleagues J.

Glowinski and M. Hamon. In 1978, with M. Hamon, we described a post-synaptic 5-HT sensitive adenylate cyclase in different brain areas of rat and guinea-pig brain [START_REF] Enjalbert | Post-synaptic serotonin-sensitive adenylate cyclase in the central nervous system. I. Development and distribution of serotonin and dopamine-sensitive adenylate cyclases in rat and guinea-pig[END_REF] (Fig. 1A).

Of course, due to a lack of specific drugs, we were unable to pharmacologically characterize the receptors involved.

When I moved to Montpellier in 1982, I decided to use primary cultures of neurons and glial cells to follow up my work on neurotransmitter receptors coupled to second messengers (cAMP, IP3, Ca 2+ , etc.). This was a very productive period since we discovered the metabotropic glutamate receptors in striatal neurons [START_REF] Sladeczek | Glutamate stimulates inositol phosphate formation in striatal neurones[END_REF] and 5-HT4Rs in colliculi neurons (Fig. 1B) (Dumuis et al., 1988a).

History

3.1. From the "Naughty but nice period" [START_REF] Clarke | The 5-HT4 receptor: naughty but nice[END_REF] to "A place in the sun" period [START_REF] Bockaert | The 5-HT4 receptor: a place in the sun[END_REF] In the 1980s, thanks to binding techniques, the molecular classification of 5-HT receptors took a definitive pathway. Three receptor classes were recognized at that time, the 5-HT1, the 5-HT2 and the 5-HT3 [START_REF] Bradley | Proposals for the classification and nomenclature of functional receptors for 5-hydroxytryptamine[END_REF]. We decided that it was timely to characterize the 5-HT receptors positively coupled to an adenylate cyclase in primary cultures of colliculi neurons. We immediately noticed that the receptor involved was insensitive to 5-HT1 and 5-HT2 antagonists (Fig. 1C see also Dumuis et al., 1988a) and that the only active antagonist was a 5-HT3 antagonist (Tropisetron: ICS 205930) although with an IC50 being incompatible with a 5-HT3 receptor interaction (Fig. 1C). Interestingly, 5carboxamidotryptamine (5-CT) was 50 times less potent than 5-HT (Fig. 1B). This incited us to replicate (Fig. 1D) the work of [START_REF] Shenker | Pharmacological characterization of two 5hydroxytryptamine receptors coupled to adenylate cyclase in guinea pig hippocampal membranes[END_REF] who described, in guinea-pig hippocampal membranes, two 5-HT sensitive adenylate cyclases. One stimulated with high potency by 5-CT, 5-HT (and 8-OH-DAPT) that was identified at that time as "5-HT1A receptor"-mediated (we now know that a 5-HT7 receptor was involved) and the other stimulated with lower potency by 5-HT and 5-CT (Fig. 1D). We found that this latter was inhibited, like the 5-HT-sensitive adenylate cyclase of colliculi neurons, by high concentrations of Tropisetron but not by a specific 5-HT3 antagonist MDL 72222 (Dumuis et al.,1988b) (Fig. 1E). We concluded, in the 1988 Molecular Pharmacology paper (Dumuis et al., 1988a) that until further classification of the 5-HT receptors is available, we propose to associate these receptors (in colliculi neurons and guinea-pig hippocampal membranes) with a novel category of receptors: the 5-HT4.

In 1989, at the International Symposium on "Serotonin from cell biology to pharmacology and therapeutics" in Firenze, we presented these results that were received with scepticism by the serotonin nomenclature committee. Benzamides, such as metoclopramide, renzapride, cisapride and zacopride were rapidly recognized as potent agonists [START_REF] Bockaert | Pharmacological characterization of 5hydroxytryptamine4 (5-HT4) receptors positively coupled to adenylate cyclase in adult guinea pig hippocampal membranes: effect of substituted benzamide derivatives[END_REF]. This was important because this formed a link between the 5-HT receptor coupled to adenylate cyclase and an unclassified prokinetic 5-HT receptor in guinea-pig ileum, insensitive to classical 5-HT1-3 antagonists, stimulated by benzamides and blocked by high concentrations of Tropisetron [START_REF] Clarke | 5-HT4 receptor: an overview[END_REF]. This was "nice" (a new 5-HT receptor expressed both in brain and gastro-intestinal organs was likely to exist), but "naughty" because we named it 5-HT4 without permission. Very rapidly, new specific antagonists were discovered, such as the benzamide SDZ 205557 and the benzimidazolone DAU 6215. The use of functional assays associated with the availability of these new drugs led to the characterization of the new 5-HT4 receptor in rat oesophagus, guinea-pig colon, human and pig atrium and adrenocortical cells.

The 5-HT4 receptors earned a "place in the sun" in 1992 [START_REF] Bockaert | The 5-HT4 receptor: a place in the sun[END_REF]. (1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) From 1990 onwards, most pharmaceutical companies and some academic groups synthesized a wide series of 5-HT4 agonists and antagonists (for reviews see [START_REF] Bockaert | 5-HT4 receptors[END_REF]Bockaert et al., , 1997)). Among the agonists, the first class includes substituted tryptamines as well as indole carbazimidamides (including maleate tegaserod "Zelnorm") which is prescribed for women suffering from irritable bowel syndromes with constipation, but recently withdrawn from the market because of possible cardio-vascular problems. The second class includes a long series of 2-methoxy-4-amino-5-chloro benzamides, such as metoclopramide, zacopride and cisapride. The latter has been on the market for gastro-oesophageal diseases and is still used with certain restrictions in some countries. A benzodioxane derivative the SL65.0155 is particularly potent for learning and memory [START_REF] Moser | SL65.0155, a novel 5-hydroxytryptamine( 4) receptor partial agonist with potent cognition-enhancing properties[END_REF] and has reached phase IIb for Alzheimer's disease. The third class includes the benzimidazolones, such as BIMU8 and the fourth aryl ketones which has a compound, RS 67333 with a large alkyl group, known to easily cross the blood brain barrier. Another interesting agonist is a pyridine carboxamide, a very recently described procognitive drug (VRX-03011) that is in phase II for Alzheimer's disease. Among the antagonists, GR 113808 was the first 5-HT4R antagonist with a low affinity for 5-HT3R and was used under a tritiated form [ 3 H]GR 113808 for binding studies. Antagonist classes include benzoates (such as SDZ 205557), benzoate dioxane (such as SB 204070 and SB 207710) in which the 5-chloro has been substituted for a radioactive iodine 125 I, an excellent ligand for binding studies [ 125 I]SB 207710, benzimidazolones (DAU 6285) and aryl ketones. Finally, with Roche Laboratories, we found very potent inverse agonists (RO 116-0086 and RO 116-1148) which are des-amino, des-chloro benzoate dioxanes [START_REF] Joubert | A 5-HT4 receptor transmembrane network implicated in the activity of inverse agonists but not agonists[END_REF]. Using either form [ 3 H]GR 113808 and [ 125 I]SB 207710 brain distribution has been studied (for a review see Bockaert and Dumuis, 1997). The receptor is localized on neurons, the highest densities being in olfactory bulb, islands of Calleja, basal ganglia and accumbens, hippocampus, substantia nigra.

Pharmacology and molecular biology periods

Within the nigro-striatal pathway the receptor is localized both in cell bodies and terminals of GABA neurons. In the cortex, the hippocampus and the amygdala, 5-HT4Rs are likely localized on cholinergic neurons (5-HT4Rs stimulate acetylcholine release) but also on glutamatergic neurons [START_REF] Bockaert | 5-HT4 receptors[END_REF]Bockaert and Dumuis, 1997;[START_REF] Huang | 5-Hydroxytryptamine induces a protein kinase A/ mitogen-activated protein kinase-mediated and macromolecular synthesisdependent late phase of long-term potentiation in the amygdala[END_REF].

The 5-HT4R gene is the longest among the GPCR genes (700 kb) and consists of 38 exons (Bockaert et al., 1997). Its 5' non-translated region is exceptionally long (>500 kb) and complex. The coding sequence includes at least 14 exons. To date, 10 functional splice variants have been described.

For 9 of them, splicing gives rise to alternate C-terminal domains after a single position (L358) named a, b, c. One splice variant (h) is generated in the second extracellular loop. As some (such as h or i) do not present any frame stop codons, additional combinations probably remain to be discovered (Bockaert et al., 2006b).

G protein-dependent and -independent signalling and interacting proteins

G protein dependent

Since 5-HT4Rs were discovered following their capacity to activate adenylate cyclase, the 5-HT4R-mediated Gs/cAMP/PKA signalling pathway is evidently the best studied (Fig. 2). In transfected cell lines, several other couplings have been found (see Bockaert et al., 2006b) including coupling to Gq and G13. However, such couplings have not yet been found in native cells. Following PKA activation, a series of ionic currents are modulated. These include a long-lasting inhibition of K + currents (mediated by a PKA-dependent inhibition of phosphatases) which generates neuronal excitability and a decrease in spike accommodation [START_REF] Ansanay | A cyclic AMPdependent, longlasting inhibition of a K. current in mammalian neurons[END_REF]Bockaert et al., 2006b). cAMP produced by 5-HT4Rs also activates the exchange factor Epac which activates a-secretase and the release of sAPPa (soluble amyloid precursor protein) via an Epac/Rap1/Ras pathway [START_REF] Lezoualc'h | The serotonin 5-HT4 receptor and the amyloid precursor protein processing[END_REF].

G protein-independent

In cell lines as well as in colliculi neurons in culture, 5-HT4Rs activated the extracellular signalregulated kinase (ERK) [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][START_REF] Mohler | VRX-03011, a novel 5-HT4 agonist, enhances memory and hippocampal acetylcholine efflux[END_REF][START_REF] Restivo | The promnesic effect of G-protein-coupled 5-HT(4) receptors activation is mediated by a potentiation of learning-induced spine growth in the mouse hippocampus[END_REF]. Curiously, we recently found that this activation was mostly Gs/cAMP/PKA-independent. Using pharmacological, genetic and molecular tools, we also demonstrated that the classical G proteins (Gq, Gi, Go) and associated downstream messengers were not involved. In contrast, the 5-HT4R-mediated ERK activation was dependent on Src tyrosine kinase and interestingly not dependent on b-arrestin which is found to mediate many G protein-independent ERK activations by GPCRs [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]. We found that a 5-HT4R/Src complex was formed which persisted upon endocytosis [START_REF] Barthet | Uncoupling and endocytosis of 5-HT4 receptors: distinct molecular events with different GRK2 requirements[END_REF]. The 5-HT4R-mediated ERK stimulation may be important for 5-HT4R-mediated long-term potentiation (LTP) (Bockaert et al., 2006b;[START_REF] Huang | 5-Hydroxytryptamine induces a protein kinase A/ mitogen-activated protein kinase-mediated and macromolecular synthesisdependent late phase of long-term potentiation in the amygdala[END_REF]. The 5-HT4R-dependent, cAMP/PKAindependent, activation of Src has also been found in intestinal cell lines (CaCo-2 and T84) 5-HT4Rs [START_REF] Gill | Serotonin inhibits Naþ/Hþ exchange activity via 5-HT4 receptors and activation of PKC alpha in human intestinal epithelial cells[END_REF]. In these cells, Src seems to activate a PLC/Ca 2+ /calmodulin pathway and finally controls the Na + /H + exchanger [START_REF] Gill | Serotonin inhibits Naþ/Hþ exchange activity via 5-HT4 receptors and activation of PKC alpha in human intestinal epithelial cells[END_REF].

Associated proteins

Although some differences in signal transduction between the C-termini splice variants have been reported, this was found exclusively in cell lines but not in native cells. The physiological relevance, if any, of the splice variants remains to be elucidated (Bockaert et al., 2006b). In an effort to make some progress in the possible different signalling of 5-HT4R splice variants, we used a fishing and proteomic approach to define the composition of the "receptosome" associated with the C-termini of three 5-HT4R splice variants [START_REF] Joubert | New sorting nexin (SNX27) and NHERF specifically interact with the 5-HT4a receptor splice variant: roles in receptor targeting[END_REF] Two of them, 5-HT4a, and 5-HT4e express a canonical recognition motif for PDZ domains at their C-termini. SCF, the C-terminal of 5-HT4a may interact with class I PDZ domains, whereas VPV, the C-terminal of 5-HT4e may interact with class II PDZ domains.

The 5-HT4b C-terminal (-SDT) shows no consensus interaction motif. Ten proteins have been found to interact with 5-HT4aRs. Among them, seven encompass one or several PDZ domains (Bockaert et al., 2006a;[START_REF] Joubert | New sorting nexin (SNX27) and NHERF specifically interact with the 5-HT4a receptor splice variant: roles in receptor targeting[END_REF]. The two more interesting ones were (i) SNX27 (sortin nexin 27) that belongs to the huge nexin family implicated in the regulation of membrane protein trafficking and (ii) NHERF (Na + /H + exchanger regulatory factor). In fact, two splicing forms of SNX27 (a and b, also called Mrt1a and Mrtb) interact with 5-HT4Rs and are localized in early endosomes. SNX27a is constitutively expressed, whereas SNX27b is induced by methamphetamine treatment [START_REF] Kajii | A developmentally regulated and psychostimulant-inducible novel rat gene mrt1 encoding PDZ-PX proteins isolated in the neocortex[END_REF]. NHERF interacts with the FERM domain of activated ezrin. In fibroblast cells expressing NHERF and 5-HT4Rs, ezrin was redistributed from the cytoplasm to microvilli and was co-localized with NHERF and 5-HT4Rs [START_REF] Joubert | New sorting nexin (SNX27) and NHERF specifically interact with the 5-HT4a receptor splice variant: roles in receptor targeting[END_REF].

Mechanisms of 5-HT4R desensitization

Many years ago, we described in colliculi neurons [START_REF] Ansanay | Characterization of homologous 5-HT4 receptor desensitization in colliculi neurons[END_REF] and rat oesophagus [START_REF] Ronde | Homologous desensitization of 5hydroxytryptamine4 receptors in rat esophagus: functional and second messenger studies[END_REF] that 5-HT4Rs rapidly desensitized (more than 60% in 5 min). The desensitization (uncoupling) was homologous and not reproduced by cAMP. We recently decided to further analyse the mechanisms involved [START_REF] Barthet | Uncoupling and endocytosis of 5-HT4 receptors: distinct molecular events with different GRK2 requirements[END_REF]. However, in HEK 293 and COS-7 cells transfected with 5-HT4Rs, we found that no significant uncoupling of the receptor occurred upon stimulation [START_REF] Barthet | Uncoupling and endocytosis of 5-HT4 receptors: distinct molecular events with different GRK2 requirements[END_REF]. We found that this was due to the low concentration of theGRK2 in HEK293 andCOS-7 cells, a GPCR kinase which is highly expressed in neurons and brain. Co-transfection of HEK 293 or COS-7 cells with GRK2 was sufficient to reproduce the rapid and profound 5-HT4R uncoupling [START_REF] Barthet | Uncoupling and endocytosis of 5-HT4 receptors: distinct molecular events with different GRK2 requirements[END_REF]. In contrast, the endocytosis of 5-HT4R which is a phenomenon dissociated from uncoupling required only "low concentrations" of GRK2 found in HEK 293 and COS-7 cells. The uncoupling and endocytosis were independent and dependent on GRK2 kinase activity, respectively. Thus, phosphorylation of a Ser/Thr cluster, in the C-terminal, and common to all splice variants was required for endocytosis but not for uncoupling. Endocytosis of 5-HT4Rs required both b-arrestin and dynamin.

We found no difference in uncoupling and endocytosis among the different 5-HT4R splice variants.

We recently found (manuscript in preparation) that desensitization of the G-protein-independent 5-HT4R-stimulated Src kinase activation required GRK5 instead of GRK2.

From constitutive activity (CA) to receptor activation

The molecular mechanism by which agonists, antagonists and inverse agonists activate and inactivate GPCRs is a key question in pharmacology. 5-HT4Rs are particularly interesting for such studies because of the long series of compounds of different chemical classes which are available.

Another interesting and almost unique property of 5-HT4Rs is their high CA [START_REF] Claeysen | Novel brainspecific 5-HT4 receptor splice variants show marked constitutive activity: role of the C-terminal intracellular domain[END_REF][START_REF] Bockaert | Molecular and cellular determinants of GPCR splice variant constitutive activity[END_REF].

Compared to b2-adrenergic receptors (b2-ARs), all C-termini splice variants of 5-HT4R have a very high CA (Fig. 3A). The shorter is the C-terminal, the higher is the CA. Thus, the C-terminal is a key regulator of the CA. Truncation of the C-terminus further increases the CA. The C-termini of 5-HT4Rs are key element of activation, but certainly not the only one. Comparison of the crystal structures of inactive rhodopsin (bound by the inverse agonist cis-retinal) and partially active rhodopsin (metarhodopsin I) [START_REF] Ruprecht | Electron crystallography reveals the structure of metarhodopsin I[END_REF], as well as site-directed mutagenesis of histamine H1 associated with molecular modelling [START_REF] Jongejan | Linking agonist binding to histamine H1 receptor activation[END_REF], proposed that activation of GPCRs includes the disruption of a hydrogen bond between two well-conserved residues W6.48 and D2.50. This disruption triggers the conformational transition of N7.49 towards D2.50 and ultimately, leads to the disruption of the "ionic lock" between R3.50 and D/E3.49 as well as with additional D/E 6.30 (Fig. 3C).

The W6.48 which is in the gauche + (g + ) rotamer pointing toTM 7 (TM = transmembrane) in the inactive state is submitted to a "toggle switch" and is in the trans (t) rotamer conformation pointing to TM5 in the activated state. Studies on histamine H1 [START_REF] Jongejan | Linking agonist binding to histamine H1 receptor activation[END_REF] and 5-HT4Rs (manuscript in preparation) indicate that T3.36 is also submitted to a "concerted toggle switch" with W6.48.

Interestingly, among the amine receptors, only very few receptors have a Threonine at position 3.36 (1%), all other 5-HT receptors have a Ser or a Cys at that 3.36 location. b2-AR has an alanine (Fig. 3B), which may account for the low basal activity of this receptor.

We found that binding of 5-HT and other indole-amine derivatives was totally dependent on the ionic interaction between the protonated amine of the side chain and the aspartate (A) at position 3.32 (D.32). In contrast, binding and activation of benzamides, such as S-zacopride, and benzimidazolones, such as BIMU8, did not depend on the presence of D3.32. Thus, the D3.32A mutant was the first RASSL (receptor activated solely by synthetic ligands) coupled to Gs [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]. Interestingly, some neutral or weak partial agonists were almost full agonists on the RASSL. Site-directed mutagenesis and molecular modelling, performed in collaboration with L. Pardo (manuscript in preparation), indicate that the BIMU8 agonist triggers the concerted toggle switch of T3.36 and W6.48 by forming a hydrogen bond with W6.48, whereas the benzamides induced this concerted switch by forming a hydrogen bond with T.3.36.

Brain functions

Although 5-HT4Rs control many important functions at the periphery, including those of the gastro-intestinal and urinary tracts, human heart and adrenal gland, we will focus this review on three brain functions which are emerging and could be relevant in therapy: memory and cognition, mood, behaviour and feeding.

Learning and memory

A great number of studies indicate pro-cognitive effects of 5-HT4R agonists both on short-term memory (such as social olfactory memory) (Fig. 4A) or long-term olfactory memory (such as olfactory associative memory) (Fig. 4B) (for a review see [START_REF] Bockaert | 5-HT4 receptors[END_REF]. Increase in memory acquisition also includes auto-shaping task, object recognition, Morris water-maze task when the inter-trial intervals were high (2 h), delayed matching performance and impeded spontaneous alteration scores. In addition, 5-HT4R activation reduces deficit in memory induced by atropine, scopolamine and 5-HT4R antagonists (for a review see [START_REF] Bockaert | 5-HT4 receptors[END_REF].

The cellular basis of such learning and memory effects may be an increase in acetylcholine release found in frontal cortex and hippocampus and an increase in LTP which has been described in hippocampus and amygdala [START_REF] Bockaert | 5-HT4 receptors[END_REF][START_REF] Huang | 5-Hydroxytryptamine induces a protein kinase A/ mitogen-activated protein kinase-mediated and macromolecular synthesisdependent late phase of long-term potentiation in the amygdala[END_REF]. Moreover, other recent reports further support this notion that 5-HT4Rs play a role in memory. They reported an association between 5-HT4R mRNA and protein expression in cortical areas, hippocampus, olfactory tubercles on one hand and memory consolidation on the other hand [START_REF] Pérez-García | An mRNA expression analysis of stimulation and blockade of 5-HT7 receptors during memory consolidation[END_REF][START_REF] Manuel-Apolinar | Modifications of 5-HT4 receptor expression in rat brain during memory consolidation[END_REF].

In addition to these effects on learning and memory, an effect of 5-HT4Rs on non-amyloidogenic metabolism pathway of APP via stimulation of the a-secretase has been described [START_REF] Lezoualc'h | The serotonin 5-HT4 receptor and the amyloid precursor protein processing[END_REF][START_REF] Cachard-Chastel | 5-HT4 receptor agonists increase sAPPalpha levels in the cortex and hippocampus of male C57BL/6j mice[END_REF]. In correlation with the precedent data, a recent report by [START_REF] Cho | Activation of 5-HT4 receptors inhibits secretion of beta-amyloid peptides and increases neuronal survival[END_REF] demonstrated that a selective 5-HT4 partial agonist, RS 67333, inhibits the generation of the b-amyloid peptide (Ab) in primary cortical neurons.

Interestingly, two 5-HT4R partial agonists, the SL 65.0155 from Sanofi-Aventis [START_REF] Moser | SL65.0155, a novel 5-hydroxytryptamine( 4) receptor partial agonist with potent cognition-enhancing properties[END_REF] and VRX-03011 (Epix Pharmaceuticals;[START_REF] Mohler | VRX-03011, a novel 5-HT4 agonist, enhances memory and hippocampal acetylcholine efflux[END_REF] which have high pro-mnesic properties in rodents have reached clinical phase II for the treatment of Alzheimer's disease. Both compounds act synergically with cholinesterase inhibitors on rodent memory. All these data are in perfect correlation with previous reports showing that there is indeed a marked loss of 5-HT4R binding sites in cortical and hippocampal regions in the Alzheimer brain [START_REF] Reynolds | 5-Hydroxytryptamine (5-HT)4 receptors in post mortem human brain tissue: distribution, pharmacology and effects of neurodegenerative diseases[END_REF][START_REF] Wong | Characterization of [ 3 H]GR-113808 binding to 5-HT4 receptors in brain tissues from patients with neurodegenerative disorders[END_REF].

Finally, we have recently found, in collaboration with French and Italian colleagues, that SL65.0155 enhances simultaneously olfactory discrimination performance and associated spine growth an effect blocked by the RS 39604 antagonist (Fig. 4B). SL65.0155 has no effect alone [START_REF] Restivo | The promnesic effect of G-protein-coupled 5-HT(4) receptors activation is mediated by a potentiation of learning-induced spine growth in the mouse hippocampus[END_REF]. Spine growth and density have been found to be associated with LTP induction and are considered to be a possible cellular basis of memory formation (for a review see [START_REF] Alvarez | Anatomical and physiological plasticity of dendritic spines[END_REF]. It is also tempting to make a link between 5-HT4R-induced cAMP formation and spine density. Indeed, cAMP reduces phosphorylation of cyclin-dependent kinase 5 (cdk5) site in the Wiskott-Aldrich syndrome protein (Wave1) and increases spine density in a Wave1-dependent manner [START_REF] Kim | Phosphorylation of WAVE1 regulates actin polymerization and dendritic spine morphology[END_REF].

Control of mood, putative antidepressant role of in 5-HT4R agonists

All antidepressant treatments and especially serotonin reuptake inhibitors (SSRIs) increase the efficacy of 5-HT transmission at the post-synaptic levels and finally induce post-synaptic 5-HT receptors activation. Unfortunately, the initial elevation of 5-HT concentration triggered by SSRIs induces the stimulation of 5-HT1A receptors localized on cell bodies of 5-HT neurons in the raphe, inhibiting their firing and counteracting the facilitation of 5-HT transmission (Fig. 5A). Thus, the 3-6 weeks delay before the onset of the therapeutic action of the antidepressant corresponds to the time needed for 5-HT1A receptor desensitization. Compounds that directly and rapidly stimulate the firing activity of 5-HT neurons are expected to be swiftly acting antidepressants. In fact, 5-HT4R agonists have been found to exert positive tonic and phasic effects on the firing of a sub-population of 5-HT neuron of the dorsal raphe nucleus (DRN) when injected at the periphery but not directly at the raphe level [START_REF] Lucas | Frontocortical 5-HT4 receptors exert positive feedback on serotonergic activity: viral transfections, subacute and chronic treatments with 5-HT4 agonists[END_REF][START_REF] Lucas | 5-HT4 receptors exert a frequency-related facilitatory control on dorsal raphe nucleus 5-HT neuronal activity[END_REF][START_REF] Conductier | Adaptive changes in serotonin neurons of the raphe nuclei in 5-HT(4) receptor knock-out mouse[END_REF]. This suggests that the effect was mediated by 5-HT4Rs localized elsewhere. Note also that 5-HT4R knock-out mice have reduced spontaneous activity of 5-HT dorsal neurons. Injection of the herpes simplex virus (HSV) coding for 5-HT4Rs increased DRN 5-HT neuronal mean activity when injected in the medial pre-frontal cortex (mPFC) but not in the striatum or hippocampus [START_REF] Lucas | Frontocortical 5-HT4 receptors exert positive feedback on serotonergic activity: viral transfections, subacute and chronic treatments with 5-HT4 agonists[END_REF] (Fig. 5B). Thus, 5-HT4Rs of the mPFC, probably localized on some pyramidal neurons known to innervate the DRN, exert a tonic and phasic stimulatory action on DRN which surprisingly did not seem to desensitize (Fig. 5A). Thus, as expected citalopram, a SSRI, was far more potent in inhibiting DRN firing in 5-HT4R knock-out mice than in WT mice [START_REF] Conductier | Adaptive changes in serotonin neurons of the raphe nuclei in 5-HT(4) receptor knock-out mouse[END_REF].

Recently, the group of G. Debonnel investigated the possibility that RS 67333 and prucalopride, two 5-HT4R agonists, could have antidepressant activity. They found that acute injection of both drugs, like citalopram, reduced the immobility time in the forced-swimming test, and that the inhibition of 5-HT neuron firing rate, by citalopram, was shifted to the right by RS 67333 (Fig. 5C,D). In addition, after 3 days of injection of RS 67333, an increase in 5-HT release in CA3 neurons of hippocampus, measured by the enhancement of post-synaptic 5-HT1AR activity, was observed. A 3-day treatment with RS 67333 significantly enhanced the mitogenesis in the sub-granular zone (SGZ) of the hippocampus, an effect also associated with long-term (3-6 weeks) SSRI treatment. A 3-day period of treatment with citalopram was insufficient to produce such an effect. Altogether, these findings illustrate that 5-HT4R agonists could be considered to be a putative class of antidepressants.

Feeding behavior

Looking for a phenotype associated with invalidation of 5-HT4Rs in mice, we first found that the absence of this receptor attenuated stress-induced hypophagia and novelty-induced exploratory activity [START_REF] Compan | Attenuated response to stress and novelty and hypersensitivity to seizures in 5-HT4 receptor knock-out mice[END_REF]. This suggests that 5-HT4Rs may be involved in stress-induced anorexia.

Following this idea and the observation that 5-HT4Rs are highly expressed in nucleus accumbens (NAc), we recently found that direct stimulation of 5-HT4Rs in the NAc reduced the physiological drive to eat and increased CART (cocaine-and amphetamine-regulated transcript) mRNA content in fed and fooddeprived WT but not knock-out mice (Fig. 6A-C). CART is an anorectic peptide. 5-HT4Rs control CART mRNA expression via a cAMP/PKA signalling pathway. We also found, using WT and knockout mice, that the anorectic effect of 3,4-N-methylene-dioxymethamphetamine (MDMA; the active principle of ecstasy) involves 5-HT4Rs (Fig. 6D). Finally, we found that the 5-HT4Rs and MDMAinduced anorexia were both reduced by injecting CART siRNA into the NAc (Fig. 6E). Collectively, these results demonstrate that the 5-HT4R-mediated up-regulation of CART in the NAc triggers the appetite-suppressant effects of ecstasy.

Conclusion

Twenty years after their first description, 5-HT4Rs still have some mysteries to be discovered and safe 5-HT4R drugs for clinical use are still to be developed. Among the mysteries, we can quote:

(1) The incredible length of the gene and the number of splice variants. Why is there such a diversity? (2) The high constitutive activity of 5-HT4Rs. Are 5-HT4Rs constitutively active in some neurons or neuronal compartments? If so, what roles do they play? Does an endogenous inverse agonist effectively exist?

The clinical use of 5-HT4R drugs has encountered some difficulties. Some drugs like cisapride or maleate tegaserod have been on the market for gastro-oesophageal reflux, constipation or irritable bowel syndromes, but were removed from the market because of their adverse cardiac problems, probably unrelated to their action on 5-HT4Rs. The tentative to use of 5-HT4R partial agonists for cognitive deficiencies particularly, but not exclusively, in Alzheimer's disease is still ongoing. The use of 5-HT4R ligands in feeding disorders (bulimia or anorexia) but also in depression is still an ongoing continual challenge. Finally, 5-HT4Rs constitute an excellent "model" of GPCR for molecular pharmacology studies. This is due to the great number of agonists, antagonists and inverse agonists of diverse chemical structures available, the generation of mutants, including a very simple and potent RASSL which may be used in gene therapy and the possibility of obtaining mg amounts of pure, native and functional 5-HT4R proteins [START_REF] Baneres | Molecular characterization of a purified 5-HT4 receptor: a structural basis for drug efficacy[END_REF].

Figure legends

Figure 1 Some historical experiments which have characterized a neuronal 5-HT receptor coupled to adenylate cyclase as new 5-HT receptors that we called 5-HT4Rs. (A) Dose-response curves for 5-HT sensitive adenylate cyclase in colliculi homogenates. Modified from [START_REF] Enjalbert | Post-synaptic serotonin-sensitive adenylate cyclase in the central nervous system. I. Development and distribution of serotonin and dopamine-sensitive adenylate cyclases in rat and guinea-pig[END_REF]. (B) Effects of various concentrations of 5-HT and 5-CT (5-carboxamidotryptamine) on cAMP production in colliculi neurons in primary cultures. Modified from Dumuis et al. (1988a). (C) Effect of a series of 5-HT antagonists on the 5-HT-stimulated cAMP production in colliculi neurons in primary cultures. The 5-HT concentration was 1 mM. Modified from Dumuis et al. (1988a). (D) Stimulation of adenylate cyclase activity of adult guinea-pig hippocampal membranes by 5-HT and 5-CT. Modified from Dumuis et al. (1988a). (E) Inhibition of 5-CT-stimulated adenylate cyclase activity in adult guinea-pig hippocampal membranes by Tropisetron at two 5-CT concentrations: 0.3 and 100 mM. Modified from Dumuis et al. (1988a).

Figure 2

A general schema of Gs-dependent and Gs-independent signalling and desensitization of 5-HT4Rs.

Figure 3

Constitutive activity and activation of 5-HT4Rs. (A) Mouse 5-HT4R (m5-HT4Rs) splice variants exhibited high but also different constitutive activities. Comparison with the constitutive activity of human b2-adrenergic receptors (b2). Modified from [START_REF] Claeysen | Novel brainspecific 5-HT4 receptor splice variants show marked constitutive activity: role of the C-terminal intracellular domain[END_REF]. (B) Nature of the residue at position 3.36 in amine receptors. The high constitutive activity of 5-HT4Rs may be due to the presence of a T at this position [START_REF] Jongejan | Linking agonist binding to histamine H1 receptor activation[END_REF]. (C) Proposed hydrogen bond network linking D2.50-W6.48 through two water molecules in the inactive conformation of rhodopsin. This link is disturbed during activation. Modified from [START_REF] Jongejan | Linking agonist binding to histamine H1 receptor activation[END_REF].

Figure 4

5-HT4Rs and memory. (A) Role of 5-HT4Rs in social memory. Social recognition of juvenile conspecifics by adult rat during 5 min (first exploration period (P1)) and at a delay of 30 (P2 = 30) and 120 (P2 = 120) min. At the 30 min delay between P1 and P2, adults recognized the juvenile as indicated by a reduction of the exploration period (P2/P1 <1), whereas after a 120 min delay, all adults have lost their memory of juveniles. The recognition of juveniles was individual-specific, a different juvenile was recognized as a new individual after 30 min (P2/P1 = 1). BIMU1 (10 mg/kg) injected after the first presentation enhanced short-term memory (i.e. recognition of the identical but not the different juvenile after a 2-h delay). Modified from [START_REF] Letty | 5-HT4 receptors improve social olfactory memory in the rat[END_REF]. (B) Involvement of 5-HT4Rs in olfactory memory.

In this task, rats deprived of water for 48 h were trained to make two odor-reward associations. One arbitrarily odor is designed as positive (S+) and the other as negative (S-). Rats had to approach the odor and water only when the odor was positive. Approach to the negative odor resulted in presentation of non-adversive light and water was not delivered. Individual trials were presented in a quasi-random fashion. Mean performance obtained across the five sessions of 60 trials by rats injected with BIMU1 (10 mg/kg) or saline (control) after the session 3 are indicated. In the reversal session, rats were tested 1 month after the injection of BIMU1 or saline (control) with reversal of the valence of the previous learned odors. Rats injected with BIMU1 are less efficient than naive rats in learning this reverse test likely because they still ''remember'' the previous odor association. Modified from [START_REF] Marchetti-Gauthier | BIMU1 increases associative memory in rats by activating 5-HT4 receptors[END_REF]. (C) Mice were trained to discriminate between two odors as in B. In the "trained" group the positive odor was associated with the reward (water) in 100% of the trials. In the "pseudo-trained group there was no positive odor as each odor was randomly associated with the reward on 50% of the trials". Golgi-Cox impregnated oblique dendrites of CA1 pyramidal neurons are shown. Statistical analysis [START_REF] Restivo | The promnesic effect of G-protein-coupled 5-HT(4) receptors activation is mediated by a potentiation of learning-induced spine growth in the mouse hippocampus[END_REF] indicates that the spine density was not different between control and pseudo-trained mice, whereas there was a difference between pseudo-trained and trained, between trained plus saline and trained plus SL65.0155. Modified from [START_REF] Restivo | The promnesic effect of G-protein-coupled 5-HT(4) receptors activation is mediated by a potentiation of learning-induced spine growth in the mouse hippocampus[END_REF]. (D) In food-deprived mice, the i.p. injection of MDMA decreased food intake of WT but not 5-HT4R knock-out mice. Food intake was measured for 3 h following the treatment. (E) The anorectic effects of BIMU8 and MDMA were reduced when CART was knocked down in the NAc using siCART. Food intake was measured for 1 h after treatment.

Figure 5 5-

 5 Figure 55-HT4Rs and depression. (A) Localisation of 5-HT receptors controlling activity of 5-HT dorsal raphe nucleus (DRN). 5-HT1ARs are on cell bodies of 5-HT neurons whereas 5-HT4Rs are not. We hypothesized that 5-HT4Rs which stimulate the activity of 5-HT neurons are localized in the medial prefrontal cortex (mPFC) (see[START_REF] Lucas | Frontocortical 5-HT4 receptors exert positive feedback on serotonergic activity: viral transfections, subacute and chronic treatments with 5-HT4 agonists[END_REF]. (B) Mean firing rate of DRN. Control: integrated firing rate histogram showing a sample of DRN in sham-operated rat. Herpes simplex virus (HSV) HSV-5-HT4Rs in mPFC: integrated firing rate histogram showing a sample of DRN in rats injected with coding 5-HT4Rs, in mPFC. The effect of various injections of the virus in the mPFC, striatum (Str), hippocampus (Hip) and with a virus coding Lac-Z in the mPFC. Modified from Lucas et al. (2005). (C) Effect of citalopram, a SSRI (10 mg/kg), and two 5-HT4Rs agonists, prucalopride (2.5 mg/kg) and RS 67333 (1.5 mg/kg) on the time spent immobile in the forced-swimming test. Modified from Lucas et al. (2007). (D) A 3-day treatment period with RS 67333 reduced the inhibition of 5-HT neuron firing induced by citalopram, via 5-HT1A receptor activation. Modified from Lucas et al. (2007).

Figure 6 5-

 6 Figure 65-HT4Rs and feeding (modified from[START_REF] Jean | Anorexia induced by activation of serotonin 5-HT4 receptors is mediated by increases in CART in the nucleus accumbens[END_REF]. (A) Coronal midbrain section showing the nucleus accumbens (NAc) in which drugs and siRNA were injected. A schematic signalling pathway showing the central role of 5-HT4Rs in MDMA (3,4-methylene-dioxymethamphetamine) (and likely cocaine) in inhibition of feeding via a cAMP/PKA synthesis of CART. (B) Direct injection of the 5-HT4R agonist BIMU8 in NAc inhibited food intake in food-deprived mice. The same injection stimulated CART synthesis. Food intake was measured between 1 and 3 h after treatment. (C) An i.p. injection of MDMA increased CART mRNA content in NAc of WT but not in 5-HT4R knock-out mice.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6

 123456 Figure 1


M Eletta Negretti

Jan-Bert Flòr

Emil Hopfinger

On gravity currents over changing topography

We present experimental results on continuously supplied and well developed gravity currents moving from horizontal to concave or constant-slope boundaries. Results show that the gravity current velocity is in continuous spatial development and approaches an equilibrium state velocity only when the slope change is small. Following closely the theory of Turner (1973) we derive a general equation for the depth-integrated velocity including a variable slope angle and all forcing and dissipation sources. The comparison of this equation with the experimental data reveals that bottom friction can be very large in the region of appearance of the KH billows and of the same order of magnitude as entrainment. The comparison with currents on straight slopes reveals that the results are independent of bottom curvature and demonstrates that the current continuously adjusts to the gradual slope changes.

Introduction

Gravity currents are key features that affect ocean, atmospheric and coastal circulation [START_REF] Baringer | Mixing and spreading of the Mediterranean outflow[END_REF]). Ambient water and sediment from the bottom are entrained and mixed thus changing the properties of water masses.

Laboratory studies of gravity currents have been essential in the understanding of the dynamics of gravity currents. Most of these studies focused on gravity currents on horizontal or slightly inclined boundaries, where the head is an essential feature of the flow. The first experiments on a steady downslope flow were conducted by [START_REF] Ellison | Turbulent entrainment in stratified flows[END_REF] who also developed the, now classical, similarity theory of these flows [START_REF] Turner | Buoyancy effects in fluids[END_REF]). The initial developing region of an accelerating current over linear inclines (4 • up to 15 • ), before reaching constant Richardson number conditions, was investigated by [START_REF] Pawlak | Mixing and entrainment in developing stratified currents[END_REF].

When there are rapid slope changes, the current may accelerate or decelerate which affects interfacial instability because of changes in the Richardson number and hence vertical mixing. In contrast with former studies, we consider a well developed horizontal flow, having a large Richardson number before reaching the concave or linear slope. The acceleration provoked by the abrupt slope change and consequent interfacial instabilities will cause strong entrainment of ambient fluid which rapidly slows down the current. The question is whether this flow still reach the expected equilibrium state on the slope, characterized by a nearly constant velocity due to a balance between buoyancy and total friction.

Theoretical analysis

We considered the general governing equation and then proceeded with the depth integrated equations following closely the procedure given in [START_REF] Turner | Buoyancy effects in fluids[END_REF]. The flow has been considered two-dimensional and stationary. Using the boundary layer and Boussinesq approximations and making use of the similarity hypothesis as in [START_REF] Turner | Buoyancy effects in fluids[END_REF], after somme arrangements we obtain the following equation

U 3 B = S 2 sin θ C D + E 1 + 1 2 S 1 Ri + h U dU dx 1 + 1 2 S 1 Ri + 1 2 S 1 h dRi dx . (1)
Here, Ri = ḡ′ h cos θ/U 2 is the bulk Richardson number with ḡ′ cos θ the buoyancy force normal to the wall, B = ḡ′ hU is the buoyancy flux per unit width which is constant and equal to the buoyancy flux supplied at the gate B 0 = g ′ 0 h 0 U 0 , where U 0 and h 0 are the velocity and height at the gate. S 1 , S 2 are factors related to the shape of the velocity and density profiles. For currents on slopes, typical values are S 1 ≈ 0.3 and S 2 ≈ 0.8, as also estimated from the current experiments. The first two terms in the denominator of (1) represent the total friction due to bottom drag (C D ) and interfacial entrainment (E), while the last term in the denominator represents the pressure variation along the slope. The third term represents the acceleration along the slope. Herein, we define an acceleration parameter T a = (h/U)dU/dx, which can be either positive or negative as the pressure term.

A developed gravity current on constant slope moves at constant velocity [START_REF] Ellison | Turbulent entrainment in stratified flows[END_REF], [START_REF] Britter | The motion of the front of a gravity current travelling down an incline[END_REF]). In this case (1) reduces to

U 3 B = S 2 sin θ C D + E , (2)
where terms in Ri have been neglected because S 1 2 Ri ≪ 1. The entrainment coefficient is now a function of slope angle only and can be approximated by E = 9 • 10 -4 (θ + 5) and when the slope angle θ > 5 • bottom friction can be neglected. Thus, since S 2 sin θ/θ varies little in the range 10 • < θ < 50 • , the velocity is nearly the same on slopes in this range. This would suggest that on a varying slope boundary the velocity might remain constant provided it adjusts continuously to the varying acceleration.

Experimental set-up and inflow conditions

The experiments were conducted in an open glass-walled tank of approximately 6m long connecting two 800l reservoirs shown in figure 1. The channel cross section is reduced to 25cm wide and 20cm deep. The first section of the channel has a total length of roughly 2.3m (with the gate at 2m upstream), is horizontal and permits the boundary layer of the gravity flow to fully develop. The next section is a concave or linear slope and is free to pivot about O (see figure 1) to vary (H -H 0 ) and enables different starting angles θ 0 for the same radius of curvature R = 2m. The length S = Rθ 0 was varied in the experiments over concave slopes between 60cm, 80cm and 110cm resulting in θ 0 = 17 • (experiment C1), 23 • (experiment C2) and 31.5 • (experiment C3), respectively. On the concave wall the slope angle θ varies from the maximum θ 0 at the beginning of the slope to 0 at S (see figure 1). Additionally, two experiments over constant slopes with θ = 15 • and 22 • and lengths of respectively S = 104cm and S = 73cm have been performed.

The gravity current was generated pumping salt water at a given density (g ′ = 4.5cm/s 2 ) and flow rate (Q = 0.6l/s) from the first reservoir. The outlet is placed at the bottom of the downstream channel end to control the total water depth and allow to discharge the lower layer salty flow. Velocity measurements were made using the PIV technique with an acquisition frequency of 30 frames/s and a spatial resolution of 0.0435cm/pixel. Dye visualizations using Rhodamine 6G were used to estimate the density profiles and some averaged values of the density field by normalizing locally with the maximal value.

All averaged data presented are intended to be a time average over approximately 2,000 images except if specified differently.

The velocity and the current depth at 195cm downstream of the gate (5cm before the slope change) have reached U m ≈ 6cm/s and h ≈ 6cm respectively resulting in a bulk Reynolds number based on these scales of Re = 3500.

Figure 2a displays velocity profiles at 20cm, 85, 195cm and 199cm from the gate. With increasing distance the shape of the profile approaches that of a wall jet.

The shape of the density profile can be estimated from the dye visualizations with Rhodamine 6G and is displayed in figure 2b at 195cm from the gate showing a top hat shape with a thin interface of ≈ 2cm.

θ = 31 • 19.5 • 14.2 • 8.5 • 3 • 0 KH ↑ x(cm) U(cm/

Current on the concave slope

Figure 3 display the depth integrated experimental velocity (symbols) versus the downstream direction for respectively experiment C3 (a) and C1 (b). The dotted line represents the free fall velocity U f ree = 2S 2 Rg ′ 0 (cos θ 0 -cos θ) + U 2 0 , where the shape factor S 2 = 0.75 has been evaluated from the experimental data and U 2 0 is the velocity at the ridge x = 0. In experiment C3 the flow first accelerates, reaching a maximal value at x ≈ 17.5cm, which corresponds approximately to the location where KH billows first develop. The velocity then decreases due to interfacial and bottom friction. After a re-adjustement, the velocity increases again at x ≈ 50cm, where the slope is still 16 • . At x = 115cm (θ = 0) the velocity seems to reach a value of 9cm/s. At this location however, the flow has reached the end of the slope and it is expected to decelerate to find again the velocity ≈ 2g ′ h. This situation is very different from those normally described in previous studies of gravity currents: here, the flow, once on the slope, passes through acceleration-deceleration cycles before reaching the horizontal bottom at the end of the slope, where other conditions will dominate. The equilibrium state as in equation ( 2), in which the driving buoyancy force is balanced by the total friction (mainly due to entrainment), is here never reached. This is highlighted by comparing the measured velocities with the equilibrium state (2) indicated by the dash-dotted line in the figures 3a and b. Here the well-known entrainment law from [START_REF] Turner | Buoyancy effects in fluids[END_REF] which can be fitted by E ≈ (5 + θ • )9 • 10 -4 when θ > 5 • has been used. Similar arguments hold for experiment C2. For both experiments C3 and C2, the maximal velocity is roughly 2/3 of the predicted equilibrium state velocity.

Experiment C1 behaves somewhat differently. We see from figure 3c that the velocity increases more gently until x ≈ 31cm corresponding again to the onset of the KH instabilities for this experiment. Then the velocity decreases again after a passage at a maximal value of 7.5cm/s. This maximal velocity value is very close to the equilibrium state velocity of 8.4cm/s. For x > 50cm, we observe an agreement between the equilibrium state velocity and the experimental velocity, which are both decreasing rapidly.

θ = 26 • 19.5 • 14.2 • 8.5 • 2.7 • 0 KH ↑ x(cm) E = 1/
In summary, we can state that when the initial slope angle is large the development of the gravity flow happens through acceleration and deceleration cycles. When the initial slope angle is small as for experiment C1, the acceleration is less and there is nearly a smooth approach of an equilibrium state.

It is clear that a smooth transition to an equilibrium flow governed by (2) requires that the initial acceleration of the current, expressed by an acceleration parameter, remains below a certain value. The local value of T a ,is not appropriate because it depends on the flow behaviour. We can introduce an overall acceleration parameter in the form T a = h i ∆U/(U m x m ), where x m is the position of maximum velocity U m , ∆U = U m -U i and h i is the initial current height. In experiment C3, with x m = 17.5cm, U m = 8.5cm/s, ∆U = 2.5cm/s and h i = 5cm, the value of this acceleration parameter is T a = 0.07. For experiment C1, x m = 31cm, U m = 7.5cm/s, ∆U = 2.5cm/s and h i = 4cm, the value is T a = 0.05. These values are close to the local T a estimated from the experiments.The implication is that for a smooth transition from U i to an equilibrium velocity U m the acceleration parameter needs to be T a < 0.05 but no critical value can be given. Low acceleration requires either a small slope or/and an interfacial instability near the beginning of slope change.

Entrainment

Given the velocity fields data, we can obtain estimates of the entrainment rates. The entrainment rate can thus be calculated from the variation of the flow rate observed in the experiments normalized by a local velocity relevant for the layer, i.e. E = 1 U dU h dx = dh dx +T a . The experimental entrainment rates for experiment C3 are presented in figure 4a. An alternative estimate of the entrainment rate can be made using equation (1). We can obtain a total friction coefficient (C D + E) by rearranging (1) equation in the form where the acceleration term, T a , the change in Ri and the shape factor S 1 are determined from the experiments. The extrapolated total friction coefficient is plotted in figure 4b. The comparison between the two figures allows an estimate of the bottom friction coefficient C D and to verify the validity of the experimental entrainment coefficient E at the locations where T a = 0 (the term of the variation of Ri is generally one order of magnitude less than the other terms and can thus be neglected). In figure 4a, we see that at x ≈ 20cm corresponding approximately to the location of onset of the KH instabilities, the entrainment coefficient is E ∼ 0.05 and at the same location, the total friction coefficient is roughly the same. For 20cm < x < 30cm however, while the entrainment rates remain approximately E ∼ 0.05, the total friction coefficient (C D + E) increases significantly with the largest values approaching 0.18. This implies (besides any source of experimental error, as for instance the power of 3 of the velocity in (3), the difficulties in determining T a and the gradients of dRi/dx), that the bottom friction coefficient must become very large, of order 10 -1 (figure 4b).

C D + E = S 2 sin θ U 3 /B -T a 1 + 1 2 S 1 Ri - 1 2 S 1 h dRi dx (3) u ′ w ′ /U 2 m z/z 1/2 x = 23cm x = 35cm x =
An estimate of the bottom friction coefficient C D can be obtained from the velocity fluctuations in the boundary layer. Selected vertical profiles at different sections of the Reynolds stresses u ′ w ′ normalized using the local maximal velocity U m are presented in figure 5a for the three experiment C3. The dotted line represents the measured values from [START_REF] Zhou | The effect of excitation on the coherent and random motion in a plane wall jet[END_REF] obtained for a wall jet. We see that in experiment C3 the values are very large as compared to the classical wall jet, reaching 5% of the maximal velocity. This high shear stress is due to the particular development of the KH billows (merging process) which cause locally a significant decrease of the lower layer depth. Coupled with this phenomenon, we have also observed the generation of bottom billows in the bottom boundary layer rotating in opposite direction as compared to the KH billows. This is shown in figure 5b, which displays zoomed images of the dye visualizations in the regions of maximal bottom friction for one experiment over straight slope with θ = 15 • .

The question now is whether the current on straight slopes behaves similarly to that on curved bottom. The large angle at the beginning and its following rapid decrease could cause the overshoot as the acceleration is inhibited by both the decreasing angle and the unstable interface, generating KH billows. We performed two additional experiments with a mean constant slope angle of 22 • and of 15 • . A very similar behavior as compared to the experiments over the concave bottom has been noticed. The depth integrated velocity behaves also very similar as for the curved boundaryand we observed the same behavior for the bottom friction coefficient and Reynolds stresses which presents very high values.

From this comparison we conclude that the slope curvature has apparently no effect on the spatial flow development.

Conclusions

The main results that emerge from the present study are: (i) when a gravity current with an initially stable interface on horizontal or a nearly horizontal boundary moves onto a steep slope, it undergoes a cycle of accelerations and decelerations and does not reach the constant equilibrium velocity within a distance of about 30h 0 considered. (ii) The first KH billows cause boundary layer separation and reattachment that leads to a large boundary friction coefficient which is of the order of the interfacial drag due to entrainment. (iii) The spatial development on a concave boundary, more representative of natural slopes, is very similar to that on a constant slope boundary.

In order to make the results of more general interest, notably the velocity, it is appropriate to represent the development in terms of non-dimensional quantities. From (1) we get the velocity scale (B 0 sin θ) 1/3 . An appropriate length scale is the distance x c where KH instability is first observed and the current velocity reaches its maximum. This is related to a decrease in Richardson number down to a critical value Ri c

Ri

= g ′ h U 2 cos θ = B 0 U 3 cos θ = Ri c . (4)
Using the free fall velocity U f ree = 2g ′ 0 x c,th sin θ + U 2 0 , where U 0 is the velocity at slope begin, we get an equation for x c,th as a function of the known initial parameters B 0 , g ′ 0 , U 0 and θ

x c,th = B 0 Ric cos θ 2/3 -U 2 0 2g ′ 0 sin θ . ( 5
)
For the critical Richardson number we take the experimental value of Ri c = 0.13 at onset of KH instability and on the concave boundary we take for the slope angle θ = θ, that is a mean slope between x = 0 and x at KH instability onset. The theoretical predictions for x c,th are in good agreement with the experimental observations of x c,exp for all experiments.

In figure 6b the depth integrated velocities for all experiments using x c ≡ x c,exp to normalize the downstream direction x and using (B 0 sin θ) 1/3 to normalize the velocity U are plotted. We see that the velocity data nicely collapse on a single curve x/x c ≤ 1, with a non-dimensional velocity maximum of about 2.6. Different decays are observed for x > x c for the different experiments, including experiment C1, where an overlap between the equilibrium state velocity and the experimental velocity has been highlighted in § 4 (cf. figure 3b) close to the end of the slope, where bottom drag starts to be dominant. The first

Figure 1 :

 1 Figure1: Sketch of the experimental set-up and definition of notations. We recall that x = R(θ 0 -θ) and z = (Rr).

Figure 2 :

 2 Figure 2: Initial conditions of the gravity current flowing on the initial horizontal channel. (a) Mean velocity profiles at X = 20cm (....), 85 (-.), 195cm (--) and 199cm (-) from the gate; (b) vertical density profile obtained from the dye visualizations at D = 195cm from the gate for experiment C3.

Figure 3 :

 3 Figure 3: Comparison between experimental velocity (symbols) and the predictions of (2) (dash-dotted line) with C D = 2 • 10 -3 and E = 9 • 10 -4 (5 + θ) from Ellison and Turner (1959) for experiment C3 (a) and C1 (b). The dotted line represents the free fall solution neglecting friction and pressure variations.

Figure 4 :

 4 Figure 4: Entrainment coefficients E = 1/U d(U h)/dx and total friction (C D + E) determined from equation (1) using the experimental data for experiment C3. --E = (5 + θ)9 • 10 -4 .

  Figure 5: (a) Selected vertical velocity profiles of Reynolds stresses u ′ w ′ at three x positions on the concave slopes normalized with the maximal velocity U 2 m for experiment C3. .... plane wall jet Zhou et al. (1996). (b) Zoomed views of the current at onset of KH instability of one experiment over straight slope (θ = 15 • ), showing the development of large bottom billows coupled with the development of KH billows.

Figure 6 :

 6 Figure 6: Depth integrated velocity normalized by (B 0 sin θ) 1/3 along the downstream direction normalized by x c ≡ x c,exp for all experiments on concave and straight slopes.