Ulloa-Aguirre Al

M.D Alfredo Ulloa-Aguirre

Eric Reiter
email: eric.reiter@inra.fr

Pascale Crépieux
email: pascale.crepieux@inra.fr

Follicle-stimulating Hormone Receptor Signaling: Complexity of Interactions and Signal Diversity

Keywords: FSH, follitropin, follicle-stimulating hormone receptor, GPCR, cell signaling network, reproduction

Follicle-stimulating hormone (FSH) is synthesized in the pituitary by gonadotrope cells. By binding to and interacting with its cognate receptor (FSHR) in the gonads, this gonadotropin plays a key role in the control of gonadal function and reproduction. Upon activation, the FSHR undergoes conformational changes leading to transduction of intracellular signals, including dissociation of G protein complexes into components and activation of several associated interacting partners, which concertedly regulate downstream effectors. The canonical Gs/cAMP/protein kinase A pathway, considered for a long time as the sole effector of FSHR-mediated signaling, is now viewed as one of several mechanisms employed by this receptor to transduce intracellular signals in response to the FSH stimulus. This complex network of signaling pathways allows for a fine-tuning regulation of the gonadotropic stimulus, where activation/inhibition of its multiple components vary depending on the cell context, cell developmental stage, and concentration of associated receptors and corresponding ligands. Activation of these multiple signaling modules eventually converge to the hormone-integrated biological response, including survival, proliferation and differentiation of target cells, synthesis and secretion of paracrine/autocrine regulators and, at the molecular level, functional selectivity and differential gene expression. In this minireview, we briefly discuss the complexity of FSHR-mediated intracellular signals activated in response to ligand stimulation. A better understanding of the signaling pathways involved in FSH action might potentially influence the development of new therapeutic strategies for reproductive disorders.

Introduction

Follicle-stimulating hormone or follitropin is synthesized in the anterior pituitary gland by gonadotrope cells. By binding to its cognate receptor in the female and male gonads, this gonadotropin plays a central role in the control of gonadal function and reproduction [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF][START_REF] Walker | FSH and testosterone signaling in Sertoli cells[END_REF]. The follicle-stimulating hormone receptor (FSHR) belongs to the highly conserved subfamily of the GPCR superfamily, the so-called Rhodopsin family and, more specifically, to the d-group of this large class of GPCRs [START_REF] Fredriksson | The G-protein-coupled receptors in the human genome form five main families. Phylogenetic analysis, paralogon groups, and fingerprints[END_REF]. As other structurally related glycoprotein hormone receptors [the LHCGR and the TSH receptor (TSHR)], the FSHR is composed of a large NH2-terminal extracellular domain (ECD), where recognition and binding of its cognate ligand occur. The ECD is structurally linked by the so-called hinge region to the transmembrane domain (TMD), which is composed of seven a-helices connected by alternating intracellular and extracellular loops, and that is involved in the activation and signaling functionality of the receptor. The FSHR ends with a COOHterminus (or C-tail) at the intracellular side, which contains important functional motifs of the receptor (Fig. 1).

The FSHR is primarily expressed by the gonads [START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF]. In the testis, this receptor is located at the basolateral Sertoli cell surface, where it supports cell growth and maturation, and thereby spermatogenesis [START_REF] Huhtaniemi | A short evolutionary history of FSH-stimulated spermatogenesis[END_REF]; in the ovary, the FSHR is expressed in the granulosa cells where FSH stimulation regulates growth and maturation of ovarian follicles and estrogen production [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF]. For many years the FSHR was thought to be localized exclusively in the gonads; nevertheless, new evidence from studies in experimental animals and in humans have suggested that this receptor may also be present in extragonadal tissues where FSH may have distinct physiological roles [START_REF] Kumar | Extragonadal Actions of FSH: A Critical Need for Novel Genetic Models[END_REF]. Nonetheless, some of these extragonadal tissues as targets for FSH action have been recently questioned [START_REF] Stelmaszewska | Revisiting the expression and function of follicle-stimulation hormone receptor in human umbilical vein endothelial cells[END_REF], indicating that further studies are still required to validate the existence of extragonadally-expressed FSHRs.

Studies on other GPCRs as well as on the FSHR, have shed some light on the mechanisms that presumably lead to FSHR activation and signal transduction. It appears that FSH primarily binds to the large ECD and that extracellular loops 1 and 3, which are extracellular projections of the TMD, represent potential secondary gonadotropin binding sites [START_REF] Jiang | Structural biology of glycoprotein hormones and their receptors: Insights to signaling[END_REF]. Upon FSH binding, the transmembrane helices (particularly the TMD helices 5, 6, 3, and 7) present a series of conformational changes and rearrangements that are transmitted down the intracellular extensions of the a-helices and associated intracellular domains (loops and C-tail; Fig. 1). This reorganization in intracellular domains in turn allows accommodation and activation of a number of effectors, including several receptorcoupled G proteins and other associated proteins and interacting partners, triggering the activation of a number of downstream signaling cascades that will eventually lead to a biological effect. An interesting nuance of this and other GPCRs is that the a-helices conforming the TMD may oscillate between multiple conformations, that will define activation of several or distinct signaling pathways and account for biased signaling [START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Reiter | Molecular mechanism of beta-arrestinbiased agonism at seven-transmembrane receptors[END_REF][START_REF] Reiter | betaarrestin signalling and bias in hormone-responsive GPCRs[END_REF][START_REF] Ulloa-Aguirre | Novel pathways in gonadotropin receptor signaling and biased agonism. Reviews in endocrine & metabolic disorders[END_REF]. These multiple mechanisms explain the recruitment of manifold signaling molecules to the complex signaling network activated by the FSHR during follicular and Sertoli cell maturation.

In this review, we provide a brief overview of the multifaceted aspects of FSHR transduction, signaling and biological actions.

Signal transduction at the FSHR: signaling pathways, interacting partners, and networks.

Most investigators agree that the effects of gonadotropins on the differentiated function of their target cells are mainly mediated by the activation of the canonical Gs/adenylyl cyclase/cAMP/PKA pathway, which subsequently leads to CREB phosphorylation and modulation of gene transcription [START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Dattatreyamurty | Physical and functional association of follitropin receptors with cholera toxin-sensitive guanine nucleotide-binding protein[END_REF][START_REF] Means | Testicular adenosine 3':5'monophosphate-dependent protein kinase. Regulation by follicle-stimulating hormone[END_REF][START_REF] Dias | Molecular, structural, and cellular biology of follitropin and follitropin receptor[END_REF][START_REF] Simoni | The follicle-stimulating hormone receptor: biochemistry, molecular biology, physiology, and pathophysiology[END_REF][START_REF] Ulloa-Aguirre | Role of the intracellular domains of the human FSH receptor in G(alphaS) protein coupling and receptor expression[END_REF][START_REF] Hunzicker-Dunn | FSH signaling pathways in immature granulosa cells that regulate target gene expression: branching out from protein kinase A[END_REF]. Nevertheless, it is now clear that this particular signaling cascade is not the only one activated by the action of these hormones. As detailed below, gonadotropins activate additional pathways that are involved in several cellular processes as proliferation and/or differentiation and, at the molecular level, functional selectivity and differential gene expression [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF][START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Reiter | betaarrestin signalling and bias in hormone-responsive GPCRs[END_REF][START_REF] Ulloa-Aguirre | Novel pathways in gonadotropin receptor signaling and biased agonism. Reviews in endocrine & metabolic disorders[END_REF][START_REF] Gloaguen | Mapping the folliclestimulating hormone-induced signaling networks[END_REF][START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF][START_REF] Ulloa-Aguirre | Multiple facets of follicle-stimulating hormone receptor function[END_REF][START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF].

The FSHR is connected via conformational selectivity to a nonlinear and complex signaling network. This network can involve either several G protein subtypes, including the Gs, Gi, and Gq/11 proteins (25-30), interaction with other receptors [e.g. the IGF-1R

and the EGFR [START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF][START_REF] Baumgarten | IGF1R signaling is necessary for FSH-induced activation of AKT and differentiation of human Cumulus granulosa cells[END_REF][START_REF] Zhou | Cellular pattern of insulin-like growth factor-I (IGF-I) and IGF-I receptor gene expression in the developing and mature ovarian follicle[END_REF][START_REF] Zhou | IGF-I signaling is essential for FSH stimulation of AKT and steroidogenic genes in granulosa cells[END_REF]] and proteins [e.g. b-arrestins, APPL1, FOXO1a, and 14-3-3t] (34-39), or heterodimerization with the LHCGR [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF][START_REF] Feng | Heterodimerization between the lutropin and follitropin receptors is associated with an attenuation of hormone-dependent signaling[END_REF][START_REF] Mazurkiewicz | Single-molecule analyses of fully functional fluorescent protein-tagged follitropin receptor reveal homodimerization and specific heterodimerization with lutropin receptor[END_REF][START_REF] Urizar | Glycoprotein hormone receptors: link between receptor homodimerization and negative cooperativity[END_REF]. These mechanisms have been reported to regulate a number of intertwined signaling pathways, including engagement of distinct kinases (such as PKA, PKC, PI3K, PKB/Akt, p70S6K and ERK1/2) [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF][START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Ulloa-Aguirre | Novel pathways in gonadotropin receptor signaling and biased agonism. Reviews in endocrine & metabolic disorders[END_REF][START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF][START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF][START_REF] Zeleznik | Protein kinase B is obligatory for folliclestimulating hormone-induced granulosa cell differentiation[END_REF][START_REF] Crepieux | The ERK-dependent signalling is stage-specifically modulated by FSH, during primary Sertoli cell maturation[END_REF][START_REF] Fan | MAPK3/1 (ERK1/2) in ovarian granulosa cells are essential for female fertility[END_REF] (Fig. 2). This complex signaling network allows for a fine-tuning regulation of the gonadotropic stimulus, where activation/inhibition of its multiple components will vary depending on the cell context, developmental stage of the host cells, and concentration of receptors and ligands [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF][START_REF] Kumar | Extragonadal Actions of FSH: A Critical Need for Novel Genetic Models[END_REF][START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF][START_REF] Crepieux | The ERK-dependent signalling is stage-specifically modulated by FSH, during primary Sertoli cell maturation[END_REF][START_REF] Casarini | LH and hCG action on the same receptor results in quantitatively and qualitatively different intracellular signalling[END_REF][START_REF] Donadeu | The differential effects of the gonadotropin receptors on aromatase expression in primary cultures of immature rat granulosa cells are highly dependent on the density of receptors expressed and the activation of the inositol phosphate cascade[END_REF][START_REF] Musnier | Developmental regulation of p70 S6 kinase by a G protein-coupled receptor dynamically modelized in primary cells[END_REF]. Furthermore, preferential activation of distinct signaling modules by the FSHR occurring through stabilization of distinct FSHR conformations in response to binding of particular ligands or receptor mutations may also occur (Figs. 1 and3) [START_REF] Ulloa-Aguirre | Novel pathways in gonadotropin receptor signaling and biased agonism. Reviews in endocrine & metabolic disorders[END_REF][START_REF] Wehbi | Selective modulation of follicle-stimulating hormone signaling pathways with enhancing equine chorionic gonadotropin/antibody immune complexes[END_REF][START_REF] Wehbi | Partially deglycosylated equine LH preferentially activates beta-arrestin-dependent signaling at the folliclestimulating hormone receptor[END_REF], paving the way for designing drug candidates that may elicit selective signaling at the gonadal level [START_REF] Dias | A negative allosteric modulator demonstrates biased antagonism of the follicle stimulating hormone receptor[END_REF][START_REF] Dias | Inhibition of Follicle-Stimulating Hormone Induced Preovulatory Follicles in Rats Treated with a Nonsteroidal Negative Allosteric Modulator of Follicle-Stimulating Hormone Receptor[END_REF]. Let us briefly dissect the complex signaling network turned on by the activated FSHR.

Signaling through G proteins

As mentioned previously, FSH binding triggers a sequence of conformational changes within the receptor, which promotes activation of intracellular signaling pathways. The primary transduction effectors described for the FSHR are heterotrimeric G proteins [START_REF] Dattatreyamurty | Physical and functional association of follitropin receptors with cholera toxin-sensitive guanine nucleotide-binding protein[END_REF][START_REF] Abou-Issa | Modulation of follicle-stimulating hormone-sensitive rat testicular adenylate cyclase activity by guanyl nucleotides[END_REF][START_REF] Ayoub | Assessing Gonadotropin Receptor Function by Resonance Energy Transfer-Based Assays[END_REF]. Upon Gs interaction with intracellular loops 2 and 3 of hormonebound FSHR on the ERW and BBXXB (B: basic residue and X: non-basic residue) motifs (Fig. 1) [START_REF] Ulloa-Aguirre | Role of the intracellular domains of the human FSH receptor in G(alphaS) protein coupling and receptor expression[END_REF], adenylate cyclase is stimulated and cAMP-dependent intracellular targets are activated. One main target of cAMP is protein kinase A (PKA) that mediates FSHdependent signaling including the ERK MAPK cascade that controls Sertoli cell mitotic phase [START_REF] Crepieux | The ERK-dependent signalling is stage-specifically modulated by FSH, during primary Sertoli cell maturation[END_REF]. In preantral granulosa cells, FSH-dependent activation of ERK is mediated through PKA-dependent destabilization of a constitutive 100 kDa MEK phospho-tyrosine phosphatase [START_REF] Cottom | Follicle-stimulating hormone activates extracellular signal-regulated kinase but not extracellular signal-regulated kinase kinase through a 100-kDa phosphotyrosine phosphatase[END_REF], identified recently as dual specificity phosphatase 6 or DUSP6 [START_REF] Law | How Protein Kinase A Activates Canonical Tyrosine Kinase Signaling Pathways To Promote Granulosa Cell Differentiation[END_REF]. In fact, activation of phosphatases by PKA appears to be a general mechanism whereby FSH stimulates components not only of MAPK cascades, but also of PI3K-dependent signaling, by indirectly enabling IGF-1R-transduced insulin receptor substrate 1 phosphorylation in granulosa cells [START_REF] Law | G protein-coupled receptors (GPCRs) That Signal via Protein Kinase A (PKA) Cross-talk at Insulin Receptor Substrate 1 (IRS1) to Activate the phosphatidylinositol 3-kinase (PI3K)/AKT Pathway[END_REF]. In these cells, FSH-dependent PKA activation also stimulates p38 MAPK, likely involved in Sgk activation [START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF] and in modeling granulosa cell shape [START_REF] Maizels | Follicle stimulating hormone (FSH) activates the p38 mitogen-activated protein kinase pathway, inducing small heat shock protein phosphorylation and cell rounding in immature rat ovarian granulosa cells[END_REF]. However, the relationship between FSH/PKA and p38 MAPK phosphorylation has been recently questioned by studies in which expression of a constitutively active form of PKA in granulosa cells was not sufficient alone to activate this particular pathway [START_REF] Puri | Protein Kinase A: A Master Kinase of Granulosa Cell Differentiation[END_REF]. Protein kinase A is considered as the master regulator of transcription factors of the cAMP response element-binding protein (CREB)/activating transcription factors (ATF) family (60) (Fig. 2). Nonetheless, in FSH-stimulated Sertoli cells, PKA regulates the activity of other nuclear targets, such as the retinoic acid receptor α (61), an important modulator of male germ cell development. More generally, PKA activity could be involved in global chromatin remodeling, as illustrated by H3 histone phosphorylation in FSHstimulated granulosa cells [START_REF] Salvador | Follicle-stimulating hormone stimulates protein kinase A-mediated histone H3 phosphorylation and acetylation leading to select gene activation in ovarian granulosa cells[END_REF]. Noteworthy, the requirement of CREB itself on FSHdependent transcriptome also needs to be reconsidered because genome-wide sequencing technologies combined with bioinformatics analyses have recently underlined that FSH-responsive genes in human granulosa cells are notably enriched in binding motifs for GATA family of transcription factors, whereas the frequency of CREBdependent genes is much scarcer than initially anticipated [START_REF] Perlman | Transcriptome analysis of FSH and FSH variant stimulation in granulosa cells from IVM patients reveals novel regulated genes[END_REF]. Scrutinizing FSHregulated promoter regions at the systems level will certainly bring to light the involvement of unexpected transcriptional regulators and upstream kinases in the future.

In addition to PKA, FSH-stimulated cAMP rise also activates the exchange proteins directly activated by cAMP or EPACs, that enhance small RAS-like GTPase Rap1 activity [START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF]. EPAC is presumably involved in the activation of PKB/Akt [START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF], a PI3K target whose activity is counteracted by PTEN to cease Sertoli cell proliferation [START_REF] Dupont | FSH-stimulated PTEN activity accounts for the lack of FSH mitogenic effect in prepubertal rat Sertoli cells[END_REF]. Likewise, in granulosa cells, Akt neutralizes the anti-proliferative effect of AMP-activated protein kinase (AMPK) [START_REF] Cunningham | FoxO1a can alter cell cycle progression by regulating the nuclear localization of p27kip in granulosa cells[END_REF][START_REF] Cunningham | Follicle-stimulating hormone promotes nuclear exclusion of the forkhead transcription factor FoxO1a via phosphatidylinositol 3-kinase in porcine granulosa cells[END_REF] and promotes the phosphorylation and nuclear exclusion of FOXO1a, one of its prominent substrate that also hampers the G1/S phase transition.

Interestingly, recent work has revealed that FOXO1a controls the expression of most FSH-responsive genes in these cells [START_REF] Herndon | Forkhead box O member FOXO1 regulates the majority of follicle-stimulating hormone responsive genes in ovarian granulosa cells[END_REF]. Many of these genes correspond to those involved in autophagy [START_REF] Herndon | Forkhead box O member FOXO1 regulates the majority of follicle-stimulating hormone responsive genes in ovarian granulosa cells[END_REF][START_REF] Shen | Protective mechanism of FSH against oxidative damage in mouse ovarian granulosa cells by repressing autophagy[END_REF], and recent studies suggest that FSH might protect granulosa cells from atresia in part by preventing mitophagy [START_REF] Shen | FSH protects mouse granulosa cells from oxidative damage by repressing mitophagy[END_REF]. The mechanisms involved encompass FOXO1a nuclear exclusion via PI3K/Akt/mTOR activation and inhibition of E3 Ubiquitin ligase Parkin recruitment in the outer membrane of damaged mithochondria by PTEN-induced putative kinase 1 (PINK1) [START_REF] Shen | FSH protects mouse granulosa cells from oxidative damage by repressing mitophagy[END_REF]. Not only Gs-but also βarrestin-dependent signaling might transduce the anti-atretic protective effect of FSH, as

shown recently in granulosa cells [START_REF] Casarini | beta-arrestins regulate gonadotropin receptormediated cell proliferation and apoptosis by controlling different FSHR or LHCGR intracellular signaling in the hGL5 cell line[END_REF].

Both PKA and Akt-dependent pathways cooperatively interact to stimulate the mTOR and p70S6 kinase, ultimately leading to mRNA translation (48,71,72) (73)(Fig. 2).

Translational regulation of mRNA in response to FSH has been proposed initially in granulosa cells [START_REF] Alam | Follicle-stimulating hormone activation of hypoxia-inducible factor-1 by the phosphatidylinositol 3-kinase/AKT/Ras homolog enriched in brain (Rheb)/mammalian target of rapamycin (mTOR) pathway is necessary for induction of select protein markers of follicular differentiation[END_REF][START_REF] Kayampilly | Follicle-stimulating hormone increases tuberin phosphorylation and mammalian target of rapamycin signaling through an extracellular signal-regulated kinase-dependent pathway in rat granulosa cells[END_REF]. During granulosa cell proliferation, hormone-bound FSHR leads to Gs-dependent and ERK-mediated phosphorylation of TSC2 (tuberin), a mTOR effector that stimulates p70S6K activity, ultimately leading to enhanced cyclin D2 expression [START_REF] Kayampilly | Follicle-stimulating hormone increases tuberin phosphorylation and mammalian target of rapamycin signaling through an extracellular signal-regulated kinase-dependent pathway in rat granulosa cells[END_REF][START_REF] Meroni | FSH activates phosphatidylinositol 3-kinase/protein kinase B signaling pathway in 20-day-old Sertoli cells independently of IGF-I[END_REF]. Via the PI3K/Akt mTOR pathway, FSH stimulates the expression of hypoxiainducible factor-1 (HIF-1) mRNA, encoding a transcription factor that regulates the expression of vascular endothelial growth factor (VEGF) [START_REF] Alam | Follicle-stimulating hormone activation of hypoxia-inducible factor-1 by the phosphatidylinositol 3-kinase/AKT/Ras homolog enriched in brain (Rheb)/mammalian target of rapamycin (mTOR) pathway is necessary for induction of select protein markers of follicular differentiation[END_REF]. Furthermore, activation of FSH-mediated mTOR pathway also induces the expression of some follicular differentiation markers, such as the LHCGR, inhibin-α, P450AROM, or the βII-subunit of PKA. In the testis, cAMP-and PI3K/mTOR-dependent pathways also cooperate in the activation of p70S6K by inducing phosphorylation profiles that differ according to the development stage of Sertoli cells [START_REF] Musnier | Developmental regulation of p70 S6 kinase by a G protein-coupled receptor dynamically modelized in primary cells[END_REF][START_REF] Musnier | mRNA-selective translation induced by FSH in primary Sertoli cells[END_REF][START_REF] Lecureuil | Follicle-stimulating hormone activates p70 ribosomal protein S6 kinase by protein kinase A-mediated dephosphorylation of Thr 421/Ser 424 in primary Sertoli cells[END_REF]. This developmentally regulated phosphorylation profile of p70S6K is supported by the observation that during the Sertoli cell differentiation phase, Akt is phosphorylated directly by FSHR signaling and not via transactivation of the IGF-1R as shown in the mitotic phase [START_REF] Meroni | FSH activates phosphatidylinositol 3-kinase/protein kinase B signaling pathway in 20-day-old Sertoli cells independently of IGF-I[END_REF][START_REF] Khan | Follicle-stimulating hormone amplifies insulin-like growth factor I-mediated activation of AKT/protein kinase B signaling in immature rat Sertoli cells[END_REF], suggesting different properties of the PI3K-regulated network at both stages [START_REF] Musnier | Developmental regulation of p70 S6 kinase by a G protein-coupled receptor dynamically modelized in primary cells[END_REF][START_REF] Musnier | mRNA-selective translation induced by FSH in primary Sertoli cells[END_REF][START_REF] Lecureuil | Follicle-stimulating hormone activates p70 ribosomal protein S6 kinase by protein kinase A-mediated dephosphorylation of Thr 421/Ser 424 in primary Sertoli cells[END_REF]. By using these PI3Kdependent signaling mechanisms, FSH may promote rearrangements and posttranslational modifications of initiation and elongation factors that form the translational machinery at the 5′ untranslated region (UTR) of mRNAs. For example, in Sertoli cells FSH stimulates the phosphorylation of eukaryotic translation initiation factor 4 (eIF4) G and eIF4B, a cofactor of the eIF4A RNA helicase, via mTOR and p70S6K respectively.

In only a few minutes, all these molecular events induce cap-dependent translation of mRNAs such as VEGF and c-fos [START_REF] Musnier | mRNA-selective translation induced by FSH in primary Sertoli cells[END_REF], as well as Internal Ribosome Entry Site (IRES)dependent mRNA translation [START_REF] Leon | Activation of a GPCR leads to eIF4G phosphorylation at the 5' cap and to IRES-dependent translation[END_REF]. Cell responsiveness to FSH is not limited to the regulation of mRNA transcription and translation, and recent data have proposed that a complex miRNA network orchestrates the stability, and hence the dynamics, of various components of the FSH signaling network [START_REF] Ayoub | Computational modeling approaches in gonadotropin signaling[END_REF][START_REF] Leon | Integrating microRNAs into the complexity of gonadotropin signaling networks[END_REF]. For example, the stabilization of PTEN would occur through hormone-induced degradation of miRNAs complementary to the PTEN mRNA [START_REF] Nicholls | Hormonal regulation of sertoli cell micro-RNAs at spermiation[END_REF]. PTEN is required for Sertoli cells to achieve terminal differentiation [START_REF] Dupont | FSH-stimulated PTEN activity accounts for the lack of FSH mitogenic effect in prepubertal rat Sertoli cells[END_REF] and its mRNA is spatially restricted at spermiation in the adluminal region of Sertoli cells [START_REF] Nicholls | Hormonal regulation of sertoli cell micro-RNAs at spermiation[END_REF].

Like many other GPCRs, the FSHR receptor exhibits some tendency to promiscuity with other G proteins. For example, the FSHR has been reported to interact with Gi when activated by particular glycosylated variants of FSH [START_REF] Arey | Induction of promiscuous G protein coupling of the follicle-stimulating hormone (FSH) receptor: a novel mechanism for transducing pleiotropic actions of FSH isoforms[END_REF][START_REF] Arey | Are circulating gonadotropin isoforms naturally occurring biased agonists? Basic and therapeutic implications[END_REF][START_REF] Babu | Activation of extracellularregulated kinase pathways in ovarian granulosa cells by the novel growth factor type 1 follicle-stimulating hormone receptor. Role in hormone signaling and cell proliferation[END_REF]. Likewise, in Sertoli cells at early stages of maturation, cyclin-D1 expression depends in part on Gi FSHR coupling [START_REF] Crepieux | The ERK-dependent signalling is stage-specifically modulated by FSH, during primary Sertoli cell maturation[END_REF]. Further studies are needed to determine whether the FSHR variant expressed at this stage matches with the alternative splicing product of the FSHR identified previously in granulosa cells that stimulates Pertussis toxin-sensitive ERK phosphorylation but is unable to enhance cAMP levels [START_REF] Babu | Activation of extracellularregulated kinase pathways in ovarian granulosa cells by the novel growth factor type 1 follicle-stimulating hormone receptor. Role in hormone signaling and cell proliferation[END_REF]. An analogous phenomenon of signaling dichotomy has been observed in cultured rat granulosa cells when the FSHR is occupied simultaneously by FSH and FSHR negative allosteric modulators, which promote persistent FSH-stimulated estradiol biosynthesis in the face of inhibited cAMP production [START_REF] Dias | A negative allosteric modulator demonstrates biased antagonism of the follicle stimulating hormone receptor[END_REF]. Besides, at supraphysiologic concentrations (>200 ng/ml), FSH also mediates FSHR coupling to Gq/11 [START_REF] Quintana | Follitropin (FSH) and a phorbol ester stimulate the phosphorylation of the FSH receptor in intact cells[END_REF][START_REF] Conti | Specificity of the cyclic adenosine 3',5'-monophosphate signal in granulosa cell function[END_REF] leading to increased IP3 levels.

Role of FSHR associated partners, b-arrestins, Ca 2+ mobilization, and cross-talk

with other plasma membrane receptors in FSHR signaling APPL1, FOXO1a, and 14-3-3t. In addition to signaling through G proteins, the FSHR also directly interacts with a number of partners that elicit particular signaling mechanisms.

These partners include, among others, the APPL1 adapter, the above-mentioned FOXO1a, and 14-3-3t [START_REF] Cohen | Human follitropin receptor (FSHR) interacts with the adapter protein 14-3-3tau[END_REF][START_REF] Dias | Emerging roles for the FSH receptor adapter protein APPL1 and overlap of a putative 14-3-3tau interaction domain with a canonical G-protein interaction site[END_REF][START_REF] Nechamen | Human follicle-stimulating hormone (FSH) receptor interacts with the adaptor protein APPL1 in HEK 293 cells: potential involvement of the PI3K pathway in FSH signaling[END_REF][START_REF] Nechamen | APPL1, APPL2, Akt2 and FOXO1a interact with FSHR in a potential signaling complex[END_REF][START_REF] Dias | Identifying protein interactors in gonadotropin action[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF][START_REF] Reiter | GRKs and beta-arrestins: roles in receptor silencing, trafficking and signaling[END_REF]. The APPL1 adapter is an important regulator of signaling and trafficking events within cells, and is expressed in many tissues, including the testis and the ovary [START_REF] Diggins | APPL1 is a multifunctional endosomal signaling adaptor protein[END_REF]. In fact, this adapter interacts with many signaling proteins in a cell type-dependent manner. APPL1 may govern signal specificity and trafficking by interacting with PI3K and Akt (88) that in turn phosphorylates FOXO1a, as well as with the small GTPase Rab5 (89), a mediator of fusion of clathrin-coated vesicles with early endosomes [START_REF] Zerial | Rab proteins as membrane organizers[END_REF]. Studies employing a yeast interaction trap, identified APPL1 as an important interacting protein with the FSHR [START_REF] Dias | Emerging roles for the FSH receptor adapter protein APPL1 and overlap of a putative 14-3-3tau interaction domain with a canonical G-protein interaction site[END_REF][START_REF] Nechamen | Human follicle-stimulating hormone (FSH) receptor interacts with the adaptor protein APPL1 in HEK 293 cells: potential involvement of the PI3K pathway in FSH signaling[END_REF][START_REF] Nechamen | APPL1, APPL2, Akt2 and FOXO1a interact with FSHR in a potential signaling complex[END_REF]; furthermore, it has been found that linking between this adapter and the FSHR occurs at the intracellular loop (IL) IL1, specifically at Lys393, Leu394 and Phe399 (39) (Fig. 1). In HEK293 cells stably expressing the FSHR, APPL1 and 2 appear to be associated with each other via the NH2terminus of APPL1 in a FSH-independent manner [START_REF] Dias | Emerging roles for the FSH receptor adapter protein APPL1 and overlap of a putative 14-3-3tau interaction domain with a canonical G-protein interaction site[END_REF][START_REF] Nechamen | Human follicle-stimulating hormone (FSH) receptor interacts with the adaptor protein APPL1 in HEK 293 cells: potential involvement of the PI3K pathway in FSH signaling[END_REF][START_REF] Nechamen | APPL1, APPL2, Akt2 and FOXO1a interact with FSHR in a potential signaling complex[END_REF]. Given that the FSHR associates with APPL1 and interacts with FOXO1a (which does not interact with APPL1

or 2) [START_REF] Nechamen | APPL1, APPL2, Akt2 and FOXO1a interact with FSHR in a potential signaling complex[END_REF][START_REF] Cunningham | Follicle-stimulating hormone promotes nuclear exclusion of the forkhead transcription factor FoxO1a via phosphatidylinositol 3-kinase in porcine granulosa cells[END_REF] and that APPL1 interacts with Akt [START_REF] Nechamen | Human follicle-stimulating hormone (FSH) receptor interacts with the adaptor protein APPL1 in HEK 293 cells: potential involvement of the PI3K pathway in FSH signaling[END_REF], it has been proposed that the interplay between a FSHR-FOXO1a complex with an activated FSHR-APPL1-Akt complex leads to FOXO1a phosphorylation and abrogation of apoptosis [START_REF] Ulloa-Aguirre | Multiple facets of follicle-stimulating hormone receptor function[END_REF][START_REF] Dias | Emerging roles for the FSH receptor adapter protein APPL1 and overlap of a putative 14-3-3tau interaction domain with a canonical G-protein interaction site[END_REF]. In fact, as described above, FSH stimulation results in rapid FOXO1a phosphorylation and its exclusion from the nucleus in granulosa cells [START_REF] Cunningham | Follicle-stimulating hormone promotes nuclear exclusion of the forkhead transcription factor FoxO1a via phosphatidylinositol 3-kinase in porcine granulosa cells[END_REF]. In the same vein, association of the FSHR with 14-3-3t has been mapped to the IL2, overlapping with the canonical G protein binding sites, specifically the ERW motif (Fig. 1) (35). 14-3-3 proteins are involved in a number of biological processes and play an important role in regulating signaling pathways by interacting with phosphorylated signaling proteins [START_REF] Tzivion | 14-3-3 proteins: active cofactors in cellular regulation by serine/threonine phosphorylation[END_REF]. In HEK293 cells, overexpression of 14-3-3t led to decreased cAMP levels [START_REF] Cohen | Human follitropin receptor (FSHR) interacts with the adapter protein 14-3-3tau[END_REF] suggesting a role of 14-3-3t in FSHR/Gs-mediated signal transduction. The association of APPL1, 14-3-3t, and

FOXO1a with the FSHR suggests that FSH causes phosphorylated FOXO1a to be sequestered to the cytosol by 14-3-3t, with APPL1 facilitating this process.

b-arrestins. Besides evoking ERK1/2 phosphorylation through the Gs pathway, FSHR activates this particular signaling cascade through b-arrestins [START_REF] Crepieux | The ERK-dependent signalling is stage-specifically modulated by FSH, during primary Sertoli cell maturation[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF], which in addition to their well-recognized role in GPCR desensitization, internalization, and recycling (see below), have also emerged as important players in the regulation of GPCR signaling [START_REF] Reiter | betaarrestin signalling and bias in hormone-responsive GPCRs[END_REF][START_REF] Reiter | GRKs and beta-arrestins: roles in receptor silencing, trafficking and signaling[END_REF]. The FSHR has been reported to be phosphorylated by PKA and PKC second messenger-dependent kinases but also by G protein-coupled receptor kinases (GRK) 2, 3, 5, and 6 in various cell culture models [START_REF] Marion | G protein-coupled receptor kinase 2 and beta-arrestins are recruited to FSH receptor in stimulated rat primary Sertoli cells[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF][START_REF] Krishnamurthy | The association of arrestin-3 with the follitropin receptor depends on receptor activation and phosphorylation[END_REF][START_REF] Lazari | Role of G protein-coupled receptor kinases on the agonist-induced phosphorylation and internalization of the follitropin receptor[END_REF][START_REF] Nakamura | Signaling and phosphorylationimpaired mutants of the rat follitropin receptor reveal an activation-and phosphorylation-independent but arrestin-dependent pathway for internalization[END_REF][START_REF] Troispoux | Involvement of G protein-coupled receptor kinases and arrestins in desensitization to follicle-stimulating hormone action[END_REF]. mobilization by interacting with PLCd-1 [START_REF] Lin | A novel follicle-stimulating hormone-induced G alpha h/phospholipase C-delta1 signaling pathway mediating rat sertoli cell Ca2+-influx[END_REF]. Moreover, studies in human granulosa cells revealed that in addition to the regulatory roles of APPL1 described above, interaction of this adapter with the FSHR also leads to IP3 production and release of Ca 2+ from intracellular stores [START_REF] Thomas | The adapter protein APPL1 links FSH receptor to inositol 1,4,5-trisphosphate production and is implicated in intracellular Ca(2+) mobilization[END_REF]. On the other hand, it has been shown that exposure of swine granulosa cells or rat Sertoli cells to FSH leads to a rapid increase in intracellular Ca 2+ accumulation, which may occur in a cAMP-dependent (e.g. via stimulation of PLCe) and -independent (e.g. via the Gq/11 bg complex) manner [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF][START_REF] Gorczynska | The relationship between 3',5'cyclic adenosine monophosphate and calcium in mediating follicle-stimulating hormone signal transduction in Sertoli cells[END_REF]106,107,110,111).

Whatever the mechanism(s) involved in Ca 2+ mobilization, it seems that Ca 2+ -mediated signaling is important for FSH-regulated functional differentiation of granulosa and Sertoli cells (112-114).

Cross-talk with other plasma membrane receptors in FSHR signaling. Among the mechanisms contributing to GPCR signal pleiotropy is receptor cross-talk, which may occur either via intracellular effectors or through heterodimerization. In this regard, the tyrosine kinase receptors IGF-1R and EGFR have emerged as important functional partners of the FSHR. Regarding the former, it has been shown that ligand-activated IGF-1R and FSHR act synergistically to enhance steroidogenesis, LHCGR and inhibin-a expression, and cell proliferation in different cell contexts and species, albeit with some differences [START_REF] Zhou | IGF-I signaling is essential for FSH stimulation of AKT and steroidogenic genes in granulosa cells[END_REF]115,116). In addition, both FSH and locally produced IGF-1 are essential for granulosa cells differentiation, follicle survival and fertility [START_REF] Zhou | IGF-I signaling is essential for FSH stimulation of AKT and steroidogenic genes in granulosa cells[END_REF]117). Signaling mediated by both receptors converge and overlap in activating distinct signaling cascades downstream of adenylyl cyclase, mainly the PI3K/Akt pathway [START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF][START_REF] Baumgarten | IGF1R signaling is necessary for FSH-induced activation of AKT and differentiation of human Cumulus granulosa cells[END_REF]. Furthermore, female mice with conditional knockdown of the IGF-1R in granulosa cells or exposed to IGF-1R inhibitor, exhibited defective FSH-stimulated Akt activation and steroidogenesis, indicating the key role played by the IGF-1R on FSHR-regulated cell proliferation and differentiation [START_REF] Gonzalez-Robayna | Follicle-Stimulating hormone (FSH) stimulates phosphorylation and activation of protein kinase B (PKB/Akt) and serum and glucocorticoid-lnduced kinase (Sgk): evidence for A kinase-independent signaling by FSH in granulosa cells[END_REF][START_REF] Baumgarten | IGF1R signaling is necessary for FSH-induced activation of AKT and differentiation of human Cumulus granulosa cells[END_REF]. The molecular mechanism(s) proposed for the synergic effects of FSH and IGF-1 at the receptor level include the ability of activated FSHRs to inhibit dephosphorylation of the IGF-1R by protein kinase phosphatases, such as PTP-1B and Src homology 2 domain-containing phosphatase 2 (SHP-2), both expressed in granulosa cells (118-120). Alternatively, the interaction between molecular chaperones and IGF-1R may be enhanced, as suggested by the prevention of cyp19 and P450scc expression in response to FSH by HSP90 (heat-shock protein 90) inhibition [START_REF] Zhou | IGF-I signaling is essential for FSH stimulation of AKT and steroidogenic genes in granulosa cells[END_REF].

Another receptor modulating FSH-stimulated granulosa cell proliferation and differentiation in the developing follicle is the EGFR, which participates in phosphorylation of ERK1/2 and p38MAPK in granulosa and cumulus cells of preovulatory follicles (121-123). Thus, in addition to EPAC and Rap1 in promoting p38MAPK phosphorylation (see above), FSH-stimulated induction of EGF-like factors, like AREG, appears as well to play an important role in the PKA-independent activation of MAPK signaling in developing granulosa cells [START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF]124,125). Additional studies have further indicated that besides promoting activation of the MAPK cascade, AREG and FSH stimulate Akt and FOXO1a phosphorylation through activation of members of the Src family of tyrosine kinases or SFKs [START_REF] Wayne | Follicle-stimulating hormone induces multiple signaling cascades: evidence that activation of Rous sarcoma oncogene, RAS, and the epidermal growth factor receptor are critical for granulosa cell differentiation[END_REF]. As in the case of the IGF-1/IGF-1R pathway described above, it appears that the AREG/EGFR/RAS and FSH/FSHR signaling pathways converge on common downstream targets, mainly ERK1/2, p38MAPK and Akt phosphorylation, leading to upand downregulation in the expression of different genes that impact on both follicle maturation and granulosa cell differentiation into granulosa-lutein cells exhibiting functional and steroidogenic profiles that differ from those exhibited by maturing granulosa cells [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF]123,(126)(127)(128). The importance of the EGF/EGFR pathway in follicular maturation and ovulation is emphasized by studies in mice showing that the absence of Areg results in subfertility and decreased response to exogenous gonadotropin treatment (129).

In addition to cross-talk with the IGF-1R and EGFR, the FSHR interacts with the structurally-related LHCGR. Although the functional relationship between these two gonadotropin receptors had been well recognized for a long time, it was only recently that functional cross-talk and physical interaction between gonadotropin receptors were reported [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF][START_REF] Feng | Heterodimerization between the lutropin and follitropin receptors is associated with an attenuation of hormone-dependent signaling[END_REF][START_REF] Mazurkiewicz | Single-molecule analyses of fully functional fluorescent protein-tagged follitropin receptor reveal homodimerization and specific heterodimerization with lutropin receptor[END_REF]. Hetero-oligomerization of the FSHR and LHCGR has been demonstrated using BRET, fluorescence correlation spectroscopy, and more recently, photoactivatable-localization microscopy (PALM) (<10 nm resolution) [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF]130,131).

Biochemical studies in HEK293 cells, showed that when heterodimerized, FSH and LHCG receptors exhibited cross-inhibitory effects on Gs signaling: heterodimerization of LHCGR with FSHR led to attenuation of LH-stimulated cAMP production, whereas when FSHR heterodimerized with LHCGR, FSH-stimulated second messenger production was mitigated [START_REF] Feng | Heterodimerization between the lutropin and follitropin receptors is associated with an attenuation of hormone-dependent signaling[END_REF]. More recently, Jonas and colleagues [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF] employed PALM to detect physical and functional interaction between the FSH and LHCG receptors in human granulosa-lutein cells. They found that both receptors associate as functionally asymetric heteromers, and that this association leads to prolonged LH-stimulated Ca 2+ signaling via influx of extracellular calcium in a Gaq/11-and Gbg-dependent manner [START_REF] Jonas | Temporal reprogramming of calcium signalling via crosstalk of gonadotrophin receptors that associate as functionally asymmetric heteromers[END_REF].

Concurrently, these data demonstrate that gonadotropin receptors, when heterodimerized, may undergo allosteric regulation, with one receptor impacting on cell signaling triggered by the other as previously suggested [START_REF] Urizar | Glycoprotein hormone receptors: link between receptor homodimerization and negative cooperativity[END_REF]. Cross-talk between gonadotropin receptors may be potentially important for reproductive function, given that in vivo both receptors coexist in granulosa cells, particularly during the last stages of follicle development prior to ovulation [START_REF] Richards | The ovary: basic biology and clinical implications[END_REF].

Signal termination and biased agonism

Signal termination at the FSHR is a tightly regulated multistep process known as homologous desensitization. First, GRKs rapidly phosphorylate serine/threonine residues of the FSHR COOH-terminus [START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Marion | G protein-coupled receptor kinase 2 and beta-arrestins are recruited to FSH receptor in stimulated rat primary Sertoli cells[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF][START_REF] Lazari | Role of G protein-coupled receptor kinases on the agonist-induced phosphorylation and internalization of the follitropin receptor[END_REF][START_REF] Nakamura | Signaling and phosphorylationimpaired mutants of the rat follitropin receptor reveal an activation-and phosphorylation-independent but arrestin-dependent pathway for internalization[END_REF][START_REF] Troispoux | Involvement of G protein-coupled receptor kinases and arrestins in desensitization to follicle-stimulating hormone action[END_REF]. Second, b-arrestins 1 and 2 are recruited and prevent Gs interaction with the core domain of the FSHR through steric hindrance [START_REF] Ulloa-Aguirre | The Follitropin Receptor: Matching Structure and Function[END_REF][START_REF] Ayoub | Assessing Gonadotropin Receptor Function by Resonance Energy Transfer-Based Assays[END_REF][START_REF] Nakamura | Signaling and phosphorylationimpaired mutants of the rat follitropin receptor reveal an activation-and phosphorylation-independent but arrestin-dependent pathway for internalization[END_REF][START_REF] Troispoux | Involvement of G protein-coupled receptor kinases and arrestins in desensitization to follicle-stimulating hormone action[END_REF]132). Third, the amount of intracellular cAMP decreases and the receptor becomes refractory to further FSH stimulation [START_REF] Reiter | betaarrestin signalling and bias in hormone-responsive GPCRs[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF][START_REF] Reiter | GRKs and beta-arrestins: roles in receptor silencing, trafficking and signaling[END_REF]133). Following desensitization, the FSHR is rapidly internalized and predominantly resensitized, with a minor fraction of the FSHR being degraded [START_REF] Ayoub | Assessing Gonadotropin Receptor Function by Resonance Energy Transfer-Based Assays[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF]134). Interestingly, the FSHR was recently reported to traffic to very early endosomes for its post-endocytic sorting rather than early endosomes like most GPCRs (135-137) (Fig. 2). In contrast with Gs, which leads to full cAMP response with less than 5% of FSHR occupancy, more than 90% of FSHR molecules need to be occupied to achieve maximal b-arrestin recruitment and internalization [START_REF] Ayoub | Assessing Gonadotropin Receptor Function by Resonance Energy Transfer-Based Assays[END_REF].

Major advances in GPCR structural biology over the last decade have profoundly changed the conceptual basis of receptor activation and pharmacological efficacy. In particular, it is now appreciated that GPCRs adopt multiple inactive and active conformations that are connected to distinct transduction mechanisms [START_REF] Reiter | Molecular mechanism of beta-arrestinbiased agonism at seven-transmembrane receptors[END_REF](138)(139)(140)(141)(142)(143)(144)(145)(146)(147).

Accordingly, it has been shown that a given ligand or receptor mutation can modify the stabilized conformation of the receptor-ligand complex, as compared to the wild-type receptor-reference-ligand complex (Fig. 3). This phenomenon is generally referred to as pharmacological bias [START_REF] Reiter | Molecular mechanism of beta-arrestinbiased agonism at seven-transmembrane receptors[END_REF]138,141,144). Practically, this conceptual framework delineates two levels of pharmacological bias. First, ligand bias that are elicited by certain ligands that stabilize a subset of the receptor conformations, leading to an imbalance between the signaling pathways activated when compared to the reference agonist. Second, receptor bias that can occur in the case of mutations [e.g. in the case of FSHR Met512Ile mutation at the second extracellular loop or Ala189Val mutation at the ECD] (7,148,149)

or of single nucleotide polymorphisms (e.g. the Asn680Ser polymorphism, Fig. 1) (150,151) at the receptor level, leading to imbalanced or impaired signaling compared to the wild-type receptor (Fig. 3). Different classes of small molecules capable of modulating FSHR have been identified (152-157), including three negative allosteric modulators (NAMs) [START_REF] Dias | A negative allosteric modulator demonstrates biased antagonism of the follicle stimulating hormone receptor[END_REF][START_REF] Dias | Inhibition of Follicle-Stimulating Hormone Induced Preovulatory Follicles in Rats Treated with a Nonsteroidal Negative Allosteric Modulator of Follicle-Stimulating Hormone Receptor[END_REF]158).

ADX61623 increased the affinity of FSH binding, yet blocked FSHR-mediated cAMP and progesterone but not estradiol production in rat primary granulosa cells, whereas in vivo, it did not affect FSH-induced preovulatory follicle development [START_REF] Dias | A negative allosteric modulator demonstrates biased antagonism of the follicle stimulating hormone receptor[END_REF]. Two other NAMs, ADX68692 and ADX68693, with structural similarities to ADX61623, were subsequently shown to exhibit biased NAM activities on FSHR in rat primary granulosa cells (52,158):

ADX68692 blocked FSHR-promoted cAMP, progesterone and estradiol production whereas ADX68693 inhibited cAMP and progesterone with the same efficacy as ADX68692 but did not block estradiol production. Importantly, ADX68692 but not ADX68693 decreased the number of oocytes recovered in the ampullae [START_REF] Dias | Inhibition of Follicle-Stimulating Hormone Induced Preovulatory Follicles in Rats Treated with a Nonsteroidal Negative Allosteric Modulator of Follicle-Stimulating Hormone Receptor[END_REF]. A positive allosteric modulator (PAM), Org 214444-0, has also been described (159); this PAM exhibited nanomolar FSHR agonistic effects and selectivity over the structurally related LHCGR and TSHR. When co-incubated with FSH, Org 214444-0 increased FSH binding and cAMP activation. Furthermore, in vivo, Org 214444-0 recapitulated the action of FSH in a model of fertility in rat. More recently, another series of small molecules acting as agonist-PAMs were reported (160-162). These thiazolidinone derivatives have been shown to activate FSHR signaling in CHO cells and to enhance estradiol production in cultured rat granulosa cells (161). In addition, optimization of substituted benzamides led to more FSHR-selective molecules (162). Small molecules have also been reported to behave as competitive antagonists. First, suramin has been shown to inhibit testosterone production and FSHR signaling (163,164). Another compound displaying similar antagonistic properties as suramin but with much better specificity for FSHR was later described (165). With the notable exception of the ADX series, whether these compounds lead to balanced or biased agonism/antagonism compared to FSH remains unknown and will need further investigation.

In the same line, it has long been suggested that naturally occurring FSH glycoforms may also elicit distinct effects on target cells (166). The common α-subunit and FSHβ each contain two N-linked oligosaccharides (at positions Asn52 and Asn78 on FSHα and at Asn7 and Asn24 in FSHβ) that play a pivotal role in the functional properties of the hormone (167-170). Removal of the carbohydrate residue at position 78 on the αsubunit significantly increases receptor binding affinity of human FSH. Likewise, carbohydrate at position 52 on the α-subunit was found to play an essential role in signal transduction since its removal resulted in a significantly decreased potency. A hypoglycosylated FSH (FSH21/18) was 9-to 26-fold more active than fully-glycosylated FSH (tetra-glycosylated FSH24) in binding and functional assays (171,172). Another human FSH deglycosylated variant, which possesses only α-subunit oligosaccharides, was significantly more bioactive in vitro than the tetra-glycosylated form of the hormone (173,174). In contrast, hyperglycosylated FSH enhanced the number of ovulated eggs and subsequent in vitro embryo development (175). Interestingly, partially deglycosylated eLH (eLHdg) behaved as a biased agonist at the FSHR, eliciting β-arrestin recruitment to FSHR as well as ERK and rpS6 phosphorylation in a β-arrestin-dependent and Gs/cAMPindependent manner [START_REF] Wehbi | Partially deglycosylated equine LH preferentially activates beta-arrestin-dependent signaling at the folliclestimulating hormone receptor[END_REF].

The effects of FSH21/18 and FSH24 has further been studied in vivo (176).

Administration of these FSH glycoforms to Fshb null female mice induced expression of several FSHR downstream signaling pathway components, including phosphorylated forms of CREB, PKA, Akt, p38, and p42/44 ERK, and FSH-regulated genes (e.g. Cy19a, inha, and inhbb) in a similar manner, albeit with some differences in the kinetics of response between the two glycoforms. In contrast, when FSH21/18 or FSH24 was injected to Fshb null males, differential up-and down-regulation in expression of the nine FSH-responsive genes analyzed (e.g. in cdo1, Clu, Tbx22, Zic3, Car13, Amh and FSHr)

was observed, suggesting biased agonism of the FSH glycoforms at the Sertoli cell level in vivo (176). Whether the functional selectivity shown by hypo-and fully-glycosylated FSH is only due to differences in binding affinity or to stability of interaction with the FSHR (171,177), or actually to induction of distinctly different receptor conformations leading to selective activation of downstream signaling pathways, still remains to be analyzed in more detail. Another class of potential ligand bias comes from cases where structural constraints are conveyed on the hormone by an antibody, leading to the modification of its pharmacological properties [START_REF] Ulloa-Aguirre | Novel pathways in gonadotropin receptor signaling and biased agonism. Reviews in endocrine & metabolic disorders[END_REF]. Polyclonal anti-peptide antibodies against ovine

FSHβ subunit led to a significant enhancement of biological activity in vivo in mice (178).

Likewise, the use of a monoclonal antibody against bovine FSH in snell dwarf mice showed an increase in uterine weight (179). Studies also evaluated the impact of equine chorionic gonadotropin (eCG)/anti-eCG complexes on gonadotropin bioactivities. They showed that anti-eCG IgGs were either inhibitory or hyper-stimulatory on LH and FSH bioactivity (180). Furthermore, Wehbi and colleagues (49) discriminated the nature of these complexes on FSH signaling and revealed their biased properties.

Conclusions

From the above discussion, it is clear that FSH-stimulated intracellular signaling is mediated through an intricate network whose dynamic properties depends on the stage of target cell development and cell context, which may in turn be regulated by numerous factors intrinsic to the cell and by the ligand. These factors include changing ligand pulse frequency and local concentrations, particular structure (166,172,176,181-183), and interaction dynamics with the FSHR (177).

Since the multiple components of the FSHR-regulated signaling network (Fig. 2) are activated neither with the same amplitude nor at the same time, the temporal and dynamical aspects that govern the kinetics of the biochemical reactions involved has to be considered. These complex dynamics can be approached with computational modeling using ordinary differential equations, as proposed previously for the FSHR [START_REF] Ayoub | Computational modeling approaches in gonadotropin signaling[END_REF]184). For example, in granulosa cells, FSH-induced cAMP pathway dynamics has been modelled with careful examination of steady-states and parameter sensibility (184).

Dynamic interactions between cAMP and mTOR pathways, that converge onto p70S6 kinase activation by FSH or insulin was modelled using experimental data from primary Sertoli cells [START_REF] Musnier | Developmental regulation of p70 S6 kinase by a G protein-coupled receptor dynamically modelized in primary cells[END_REF]. This model provided clues on p70S6 kinase phosphorylation rates and was experimentally validated using pharmacologically perturbed conditions. Further developments of FSHR network modeling will help to fill the gap between detailed knowledge on molecular interactions and comprehensive understanding of hormonal dynamics. Functional interactions of the FSHR with several tyrosine kinase receptors other than the IGF-1R and EGFR described above, may further increase the landscape complexity. These include the neurotropic factors GDNF (glial cell line-derived neurotropic factor) (185) and BDNF (brain-derived neurotrophic factor) (186) receptors, as well as receptors of the TGFβ family members (187), known to potentiate the mitogenic action of FSH in Sertoli cells and/or granulosa cells. These aspects will require further investigation.

Since the first pioneering evidence that the gonads exhibit binding sites specific for the FSHR and respond to FSH by increasing intracellular cAMP levels [START_REF] Means | Testicular adenosine 3':5'monophosphate-dependent protein kinase. Regulation by follicle-stimulating hormone[END_REF](188)(189)(190)(191), significant advances in our understanding of the structure and function of the FSH/FSHR system has been achieved. Nonetheless, there are still important issues that remain to be elucidated and that will require the application of new experimental paradigms, "omic" technologies (genomic, transcriptomic, and proteomic techniques), and systems biology tools to facilitate this challenging task. These issues include, for example, a more detailed elucidation of the mechanisms underlying differential gene expression and protein phosphorylation during granulosa cell differentiation and follicle maturation under the influence of FSH variants, FSH analog compounds, and FSHR allosteric modulators, which may convey important therapeutic benefits to the clinical arena. To this end, in vitro experimental models such as intact follicle culture or three-dimensional bioprosthetic ovary models that may better reproduce the physiological environment of the developing follicle may be applied; these systems might allow to explore more deeply the signaling pathways and gene expression profile induced by FSH both in target cells in their in-situ arrangements and within different granulosa cell compartments throughout follicle maturation (192)(193)(194). As noted above, further studies are also needed not only to validate the existence of extragonadally-expressed FSHRs but also to dissect in more detail their corresponding signaling networks and pathways as well as gene expression profiles, which might eventually allow to assign them physiological roles according to their particular location. Integration of large-scale information obtained from these techniques will undoubtedly facilitate the building up of more integrative signaling framework models that may be applied to simulate in silico the biological consequences of intermittent FSH stimuli on its target cell in multiple-way combinations. Beyond any doubt, past and present studies may just represent the prologue to what remains to be unveiled.

  β-arrestins recruited to GRK2-or GRK5/6-phosphorylated FSHR have been shown to exert distinct intracellular functions in time and space: β-arrestin 1 and 2 binding to GRK2-phosphorylated FSHR leads to the internalization and recycling of the receptor, whereas phosphorylation of the FSHR by GRK5 and 6 is required for β-arrestin-dependent, heterotrimeric G protein-independent ERK signaling, as shown by other GPCRs[START_REF] Reiter | betaarrestin signalling and bias in hormone-responsive GPCRs[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF][START_REF] Heitzler | Competing G protein-coupled receptor kinases balance G protein and beta-arrestin signaling[END_REF][START_REF] Kim | Functional antagonism of different G protein-coupled receptor kinases for beta-arrestinmediated angiotensin II receptor signaling[END_REF][START_REF] Ren | Different G proteincoupled receptor kinases govern G protein and beta-arrestin-mediated signaling of V2 vasopressin receptor[END_REF][START_REF] Shenoy | beta-arrestin-dependent, G proteinindependent ERK1/2 activation by the beta2 adrenergic receptor[END_REF]. Concurrently, these findings are consistent with a model of phosphorylation bar code elicited by distinct GRKs that could control the conformation of β-arrestin recruited to the receptor and thereby its ability to interact with specific partners[START_REF] Reiter | Molecular mechanism of beta-arrestinbiased agonism at seven-transmembrane receptors[END_REF][START_REF] Heitzler | Competing G protein-coupled receptor kinases balance G protein and beta-arrestin signaling[END_REF][START_REF] Kim | Functional antagonism of different G protein-coupled receptor kinases for beta-arrestinmediated angiotensin II receptor signaling[END_REF][START_REF] Ren | Different G proteincoupled receptor kinases govern G protein and beta-arrestin-mediated signaling of V2 vasopressin receptor[END_REF][START_REF] Shenoy | beta-arrestin-dependent, G proteinindependent ERK1/2 activation by the beta2 adrenergic receptor[END_REF](100). A well-documented illustration is the temporal encoding of ERK activation: in contrast to G protein-mediated ERK activation, which is rapid and transient, ERK recruitment and signaling activated by β-arrestins is slower (~5-10 min to reach maximum), but protracted (t1/2 >1 hour)[START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF]. It has recently been demonstrated that the 5-hydroxytryptamine 2 receptor, β2-adrenergic receptor, CXC-chemokine receptor 4, and the FSHR activate the ERK pathway via a mechanism involving MEK-dependent β-arrestin 2 phosphorylation at Thr383. Importantly, this agonist-induced phosphorylation of b-arrestin 2 is a necessary step for ERK recruitment to β-arrestin complex and for ERK activation (101). More recently, Gs-dependent and βarrestin-dependent FSH signaling have been shown to cooperatively activate p70S6K, within a constitutively assembled β-arrestin/p70S6K/rpS6 module (72,102,103); this complex controls the translation of 5′ TOP mRNAs, a subset of mRNAs representing almost 20% of cellular mRNA abundance and that encode for ribosomal proteins, poly(A)binding protein, and factors of the translational machinery (102-104). The co-joined action of Gs-and β-arrestin-transduced signaling on p70S6K contrasts with the parallel action that both effectors have on the ERK MAPK, whose kinetics of phosphorylation differs depending on the transducer (Gs vs β-arrestins)[START_REF] Wehbi | Partially deglycosylated equine LH preferentially activates beta-arrestin-dependent signaling at the folliclestimulating hormone receptor[END_REF][START_REF] Kara | A phosphorylation cluster of five serine and threonine residues in the C-terminus of the follicle-stimulating hormone receptor is important for desensitization but not for beta-arrestin-mediated ERK activation[END_REF]103). Finally, the β-arrestindependent intracellular signaling may be preferentially activated when the FSHR is stabilized in distinct conformation(s) in response to particular ligands or receptor mutations, in a process known as biased agonism or functional selectivity (Fig.3), which is discussed below. Ca 2+ mobilization. FSH-stimulated Ca 2+ mobilization in both granulosa and Sertoli cells has been well recognized for a long time and it has been attributed to both rapid influx of Ca 2+ through T-type Ca 2+ channels as well as release from intracellular stores(28,30,105- 109), where Gi/Gbg/PI3K or Gs-and/or Gq-mediated activation of phospholipase C (PLC)b or other PLC isoforms appear to play an important role. In fact, in rat Sertoli cells, FSHR can signal through the transglutaminase Gah to promote extracellular Ca 2+

  Loss ES, Jacobus AP, Wassermann GF. Rapid signaling responses in Sertoli cell membranes induced by follicle stimulating hormone and testosterone: calcium inflow and electrophysiological changes. Life Sci. 2011; 89:577-583. 110. Oestreich EA, Wang H, Malik S, Kaproth-Joslin KA, Blaxall BC, Kelley GG, Dirksen RT, Smrcka AV. Epac-mediated activation of phospholipase C(epsilon) plays a critical role in beta-adrenergic receptor-dependent enhancement of Ca2+ mobilization in cardiac myocytes. J Biol Chem. 2007; 282:5488-5495. 111. Sharma OP, Flores JA, Leong DA, Veldhuis JD. Cellular basis for folliclestimulating hormone-stimulated calcium signaling in single rat Sertoli cells: possible dissociation from effects of adenosine 3',5'-monophosphate. Endocrinology. 1994; 134:1915-1923. 112. Jayes FC, Day RN, Garmey JC, Urban RJ, Zhang G, Veldhuis JD. Calcium ions positively modulate follicle-stimulating hormone-and exogenous cyclic 3',5'adenosine monophosphate-driven transcription of the P450(scc) gene in porcine granulosa cells. Endocrinology. 2000; 141:2377-2384. 113. Seals RC, Urban RJ, Sekar N, Veldhuis JD. Up-regulation of basal transcriptional activity of the cytochrome P450 cholesterol side-chain cleavage (CYP11A) gene by isoform-specific calcium-calmodulin-dependent protein kinase in primary cultures of ovarian granulosa cells. Endocrinology. 2004; 145:5616-5622. 114. Wu JY, Gonzalez-Robayna IJ, Richards JS, Means AR. Female fertility is reduced in mice lacking Ca2+/calmodulin-dependent protein kinase IV. Endocrinology. 2000; 141:4777-4783.

Figure 1 .

 1 Figure 1. Schematic representation of the human FSHR with the cytoplasmic face

Figure 2 .

 2 Figure 2. A simplified overview of the FSHR signaling network. The color code,

Figure 1 Figure 2 Figure 3

 123 Figure 1

Acknowledgments

The authors thank Dr. Teresa Woodruff for her kind invitation to prepare this minireview, and to Ari Kleinberg from the RAI-UNAM for the artwork of figures 1 and 3.

Finantial support: Research in the authors' laboratories are supported by grants from CONACyT, Mexico (grant 240619) and the Universidad Nacional Autónoma de México (UNAM) (to A.U.-A.), ARD 2020 Biomédicament from Région Centre (to E.R and P.C.), and French National Research Agency under the program "Investissements d'avenir" Grant Agreement LabEx MabImprove: ANR-10-LABX-53 (to E.R. and P.C.).

note, the phosphorylation state of the FSHR conveyed by GIPC is not known. This network has been established by using the Cell Designer algorithm [START_REF] Kitano | Using process diagrams for the graphical representation of biological networks[END_REF]


Olivier Wittenberg
email: wittenberg@dma.ens.fr

CHOW GROUPS OF ZERO-CYCLES IN FIBRATIONS

HAL is

For rational surfaces, a more precise conjecture, which also predicts the kernel of the first map, appears in [3]. Even the case of cubic surfaces over Q is widely open.

A notable consequence of the exactness of this complex would be that X possesses a zero-cycle of degree 1 if and only if there exists a family (z v ) v∈Ω of local zero-cycles of degree 1 whose image in Hom(Br(X), Q/Z) vanishes.

Saito [START_REF] Saito | Some observations on motivic cohomology of arithmetic schemes[END_REF] proved the conjecture for curves, under the assumption that the divisible subgroup of the Tate-Shafarevich group of the Jacobian is trivial. (When the curve has a rational point, this assumption is in fact equivalent to the conjecture.) The aim of the talk was to discuss the following fibration theorem and its proof.

Theorem. Let f : X → C be a dominant morphism with rationally connected ( e.g., geometrically unirational) generic fiber, where C is a smooth, proper, irreducible curve with X(k, Jac(C)) div = 0. If the smooth fibers of f satisfy the conjecture, then so does X.

The oldest instance of a fibration argument establishing a particular case of the above conjecture is Hasse's proof of the Hasse-Minkowski theorem for quadratic forms in four variables with rational coefficients. It was based on Dirichlet's theorem on primes in arithmetic progressions and on the global reciprocity law. A delicate argument relying on the same two ingredients allowed Salberger [START_REF] Salberger | Zero-cycles on rational surfaces over number fields[END_REF] to settle the conjecture for conic bundle surfaces over P 1 k . His proof was later generalised in various directions (see [START_REF] Colliot-Thélène | Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties[END_REF], [START_REF] Colliot-Thélène | Rational points and zero-cycles on fibred varieties: Schinzel's hypothesis and Salberger's device[END_REF], [START_REF]Principe local-global pour les zéro-cycles sur les surfaces réglées[END_REF], [START_REF] Frossard | Obstruction de Brauer-Manin pour les zéro-cycles sur des fibrations en variétés de Severi-Brauer[END_REF], [START_REF] Hamel | The Brauer-Manin obstruction for zero-cycles on Severi-Brauer fibrations over curves[END_REF], [START_REF] Wittenberg | Zéro-cycles sur les fibrations au-dessus d'une courbe de genre quelconque[END_REF], [START_REF] Liang | Astuce de Salberger et zéro-cycles sur certaines fibrations[END_REF]). In all of these papers, Dirichlet's theorem on primes in arithmetic progressions for general number fields was used in the following form: given a finite subset S ⊂ Ω f and elements ξ v ∈ k * v for v ∈ S, there exists ξ ∈ k * arbitrarily Date: July 11th, 2014.

1 close to ξ v for v ∈ S such that ξ is a unit outside S except at a unique (unspecified) place v 0 , at which it is a uniformiser. (Strictly speaking, when k is not totally imaginary, a more general statement which incorporates approximation conditions at the real places, and which builds on results of Waldschmidt in transcendence theory, needs to be used.) Given a finite abelian extension L/k from which ξ v is a local norm for v ∈ S and which is unramified outside S, it then follows, in view of the global reciprocity law, that ξ is a local norm from L at v 0 too, and hence that v 0 splits in L.

The reciprocity argument we have just described fails when the extension L/k is not abelian. This failure has led to severe restrictions on the fibrations to which the previous methods could apply. In the proof of the above theorem, the following elementary lemma serves as a substitute for Dirichlet's theorem.

Lemma. Let L/k be a finite Galois extension. Let S be a finite set of places of

k. For each v ∈ S, let ξ v ∈ k * v . If ξ v is a local norm from L/k for each v ∈ S, there exists ξ ∈ k * arbitrarily close to ξ v for v ∈ S,
such that ξ is a unit outside S except at places which split in L.

Proof. Affine space minus any codimension 2 subset satisfies strong approximation off one place. The lemma is a consequence of this fact applied to (R L/k A 1 L ) \ D, where D denotes the singular locus of the complement of the torus

R L/k G m in R L/k A 1 L .
Another ingredient of the proof is an arithmetic duality theorem (obtained in [12, §5]) for a variant of Rosenlicht's relative Picard group, denoted Pic + (C), whose definition we briefly recall. Let M ⊂ C be the set of points over which the fiber of f is singular. For each m ∈ M , fix a finite extension L m /k(m). Then Pic + (C) is defined as the quotient of Div(C \ M ) by the subgroup generated by the principal divisors div(h) such that for each m ∈ M , the function h is invertible at m and h(m) is a norm from L m .

In the very simple situation of a fibration over P 1 k with only two singular fibers, above 0 and ∞, each of which possesses an irreducible component of multiplicity 1, if we let L 0 = L ∞ = L and if we are given an adelic point (P v ) v∈Ω ∈ X(A k ) supported outside of f -1 (M ), it is easy to see that the class of (f (P v )) v∈Ω belongs to the image of the diagonal map Pic + (C) → v∈Ω Pic + (C ⊗ k k v ) if and only if there exists c ∈ k * such that ct v is a local norm from L for all v ∈ Ω, where t v ∈ k * v denotes the coordinate of f (P v ) ∈ P 1 (k v ). If this condition is satisfied, applying the lemma to ξ v = ct v and setting t = ξ/c yields a point t ∈ k * = G m (k) ⊂ P 1 (k) such that X t (A k ) = ∅, provided L and S were chosen large enough in the first place.

It is this argument, which bypasses any abelianness assumption, which forms the core of the proof of the theorem.


HAL is

ZERO-CYCLES ON HOMOGENEOUS SPACES AND THE INVERSE GALOIS PROBLEM

OLIVIER WITTENBERG

(report on joint work with Yonatan Harpaz)

Let Γ be a finite group and k be a number field. It has been understood since Hilbert and Noether that the problem of realising Γ as a Galois group over k is really a problem about the arithmetic of the unirational variety A m k /Γ, where Γ acts by permuting the coordinates once an embedding Γ ֒→ S m has been chosen. Equivalently, it is really a problem about the arithmetic of the homogeneous space SL n,k /Γ, where Γ acts by multiplication on the right, an embedding Γ ֒→ SL n (k) having been chosen. (Indeed, by Speiser's lemma, these two varieties are stably birational.) Letting X denote a smooth compactification of SL n,k /Γ, a positive answer to the inverse Galois problem for Γ would follow, in particular, from the density of X(k) in the Brauer-Manin set X(A k ) Br(X) . Theorem 1. Let X be a smooth compactification of a homogeneous space V of a connected linear algebraic group G over k. Let x ∈ V ( k) be a geometric point and let H x ⊆ G( k) denote its stabiliser.

(1) The image of the natural map CH 0 (X) → v∈Ω CH 0 (X ⊗ k k v ), where Ω denotes the set of places of k, consists of those families (z v ) v∈Ω in the kernel of the Brauer-Manin pairing such that deg(z v ) is independent of v.

In particular, if X(A k ) Br(X) = ∅, then X admits a zero-cycle of degree 1. Assume now that G is semi-simple and simply connected ( e.g., that G = SL n,k ) and that H x is finite.

(

) Assume that [4, Conjecture 9.1] is true. If H x is solvable, then X(k) is dense in X(A k ) Br(X) . (3) If H x 2
admits a filtration, with cyclic graded quotients, by normal subgroups of H x which are stable under the natural outer action of Gal( k/k), then

X(k) is dense in X(A k ) Br(X) .
The density of X(k) in X(A k ) Br(X) may well hold for all rationally connected varieties (a conjecture put forward by Colliot-Thélène) and was previously known for smooth compactifications of homogeneous spaces of linear algebraic groups with connected geometric stabiliser and for smooth compactifications of homogeneous spaces of semi-simple simply connected linear algebraic groups with finite abelian geometric stabiliser (Sansuc, Borovoi). Assertion (1) was previously known under these same assumptions (Liang). Furthermore, Neukirch had proved the density of X(k) in X(A k ) when V = SL n,k /Γ and the order of Γ and the number of roots of unity contained in k are coprime (a condition which excludes, e.g., 2-groups).

Assertion (3) applies to V = SL n,k /Γ when Γ is supersolvable (e.g., when it is nilpotent). Both ( 2) and ( 3) rely on an induction on the order of H x. Even if one Date: April 23rd, 2018.

focuses on the inverse Galois problem, and therefore on homogeneous spaces of the form SL n,k /Γ, it is an essential point for this induction that the theorem can be applied to homogeneous spaces of SL n,k which need not have a rational point and whose geometric stabiliser need not be constant.

Assertions ( 2) and (3) thus recover Shafarevich's theorem on the inverse Galois problem for finite solvable groups, in the supersolvable case (and, conditionally, in general). They also go further, as they yield answers to Grunwald's problem, which asks for Galois extensions of k with group Γ whose completions at a finite set S of places of k are prescribed. In particular, combining ( 2) and ( 3) with recent work of Lucchini Arteche on the bad places for the Brauer-Manin obstruction on such X shows that Grunwald's problem admits a positive answer when Γ is supersolvable (conditionally, when Γ is solvable) and S avoids the places dividing the order of Γ. We recall that some condition on S must appear even in the simplest situations: Wang gave a counterexample for k = Q, Γ = Z/8Z, S = {2}.

The strategy of the proof of Theorem 1 relies on a geometric dévissage of these homogeneous spaces, which we now explain. For the sake of simplicity, we focus on (2) and assume that G = SL n,k and that [4, Conjecture 9.1] holds. In this situation, we establish the following inductive step, which does not require any assumption on the finite group H x and which clearly implies (2

): if X ′ (k) is dense in X ′ (A k ) Br(X ′ )
for any smooth compactification X ′ of any homogeneous space of G with geometric stabiliser isomorphic to the derived subgroup of

H x, then X(k) is dense in X(A k ) Br(X) .
The starting point is a version, for rationally connected varieties, of the theory of descent that Colliot-Thélène and Sansuc developed in the 80's for geometrically rational varieties. Just as in the theory of descent for elliptic curves, the idea is to reduce questions about the rational points of a given variety X to the same questions for auxiliary varieties which lie above it. The auxiliary varieties we use are the universal torsors of Colliot-Thélène and Sansuc; for a smooth and proper variety X over k such that Pic(X ⊗ k k) is torsion-free, they are torsors Y → X under the torus over k whose character group is Pic(X ⊗ k k).

Proposition 2. If X is a smooth and proper variety over

k such that Pic(X ⊗ k k) is torsion-free, then X(A k ) Br(X) is contained in the union, over all universal torsors f : Y → X, of f ′ Y ′ (A k ) Br(Y ′ ) , where Y ′ denotes a smooth compactification of Y such that f extends to a morphism f ′ : Y ′ → X.
This statement, which can also be deduced from recent work of Cao, was first proved by Colliot-Thélène and Sansuc when X is geometrically rational, a generality which is insufficient for our purposes since there exist finite nilpotent groups Γ such that SL n,k /Γ fails to be geometrically rational (Saltman, Bogomolov). Here, the point is that the full Brauer group of X is taken into account. Dealing with the algebraic subgroup Br 1 (X) = Ker Br(X) → Br(X ⊗ k k) is not enough, as recent examples of transcendental Brauer-Manin obstructions to weak approximation on SL n,k /Γ for certain p-groups Γ show (Demarche, Lucchini Arteche, Neftin [START_REF] Demarche | The Grunwald problem and approximation properties for homogeneous spaces[END_REF]).

The next result elucidates the geometry of the universal torsors in our situation. Putting together the above two propositions, we see that in order to prove assertion (2) of Theorem 1, the only missing ingredient is a positive answer to the following question, where Z, B are smooth compactifications of W , Q such that π extends to a morphism p : Z → B. Question 4. Let p : Z → B be a dominant morphism between smooth and proper varieties over k. Assume that B and the generic fibre of p are rationally connected.

If B(k) is dense in B(A k ) Br(B) and Z b (k) is dense in Z b (A k ) Br(Z b ) for all rational points b of a dense open subset of B, is Z(k) dense in Z(A k ) Br(Z) ?
An answer in a very special case (the case in which B = P 1 k and in which for any b ∈ P 1 (k) \ {0, ∞}, the variety Z b is smooth and the map Br(k) → Br(Z b ) is onto) was a key step in Hasse's proof of the Hasse-Minkowski theorem on the rational points of quadrics-namely, the step which relies on Dirichlet's theorem on primes in arithmetic progressions (see [START_REF] Wittenberg | Rational points and zero-cycles on rationally connected varieties over number fields, to appear[END_REF]Proposition 3.17]). More general situations have been considered ever since. The general case, however, seems entirely out of reach. In [START_REF] Harpaz | On the fibration method for zero-cycles and rational points[END_REF], we provide a positive answer when B is rational over k, assuming the validity of [4, Conjecture 9.1], and we provide a positive answer to the analogous question for zero-cycles, under the same assumption on B, unconditionally.

As the torus Q is quasi-trivial, it is rational over k, and so is B. This completes the strategy for establishing the first two assertions of the theorem in the case of a homogeneous space of SL n,k with finite solvable geometric stabiliser. To deduce [START_REF] Demarche | Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis[END_REF] in full generality, a first reduction, using Sylow subgroups, allows us to deal with homogeneous spaces of SL n,k with arbitrary finite geometric stabiliser; the general case then follows thanks to the work of Demarche and Lucchini Arteche [START_REF] Demarche | Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis[END_REF]. The proof of (3) rests on a variant of this strategy. Universal torsors are replaced with torsors of a certain intermediate type built out of the cyclic quotients appearing in (3); they lead to fibrations π : W → Q admitting a rational section over k. On the other hand, for fibrations into rationally connected varieties which are smooth over a quasi-trivial torus and which admit a rational section over k, we provide an unconditional positive answer to Question 4, by performing a descent (in the form of a slight generalisation of Proposition 2) and applying the work of Harari [START_REF] Harari | Méthode des fibrations et obstruction de Manin[END_REF].

Proposition 3 .

 3 Let V and X be as in Theorem 1, with G = SL n,k and H x finite. Let f : Y → X be a universal torsor of X. There exist a dense open subset W ⊆ Y , a quasi-trivial torus Q and a morphism π : W → Q whose fibres are homogeneous spaces of G with geometric stabiliser isomorphic to the derived subgroup of H x.