Mohyeddine Omrane

Amanda Souza Camara

Cyntia Taveneau

Nassima Benzoubir

Thibault Tubiana

Jinchao Yu

Raphaël Guérois

Didier Samuel

Bruno Goud

Christian Poüs

Amanda Souza Camara

Stéphane Bressanelli

Richard Charles Garratt

Abdou Rachid Thiam
email: thiam@ens.fr

Ama Gassama-Diagne

Septin 9 has Two Polybasic Domains Critical to Septin Filament Assembly and Golgi Integrity

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

Introduction

Septins form a GTPase protein family that are found in eukaryotes from yeasts to animals but are absent from higher plants and certain protists [START_REF] Pan | Analysis of septins across kingdoms reveals orthology and new motifs[END_REF][START_REF] Nishihama | New Insights into the Phylogenetic Distribution and Evolutionary Origins of the Septins[END_REF]. In mammals, thirteen septins have been identified and placed in four classes (the septin 2, 3, 6 and 7 subgroups) [START_REF] Peterson | Conquering the complex world of human septins: implications for health and disease[END_REF]. Septins assemble into apolar complexes that are able to form high order structures such as filaments and rings [START_REF] Weirich | The septin family of GTPases: architecture and dynamics[END_REF]. Each septin has at least two interfaces: one interface contains GTP-binding domain motifs, referred to as the G-interface, and the other contains the N and C termini of the protein, called the NCinterface. Thus, two septin proteins can develop G/G or NC/NC interactions with neighboring septins. Septins thereby form hetero-oligomeric complexes made up of hexameric subunits with the following sequence: (G7NC/NC6G/G2NC/NC2G/G6NC/NC7G) [START_REF] Sirajuddin | Structural insight into filament formation by mammalian septins[END_REF]. Septin 9 assembles at the extremities of the hexamer to generate an octamer [START_REF] Kim | SEPT9 occupies the terminal positions in septin octamers and mediates polymerizationdependent functions in abscission[END_REF]. This octamer has the NC interface of septin 9 at its ends, i.e. NC9G/G7NC/NC6G/G2NC/NC2G/G6NC/NC7G/G9NC, and is the building block for higher order septin structures [START_REF] Sirajuddin | Structural insight into filament formation by mammalian septins[END_REF][START_REF] Sellin | Deciphering the rules governing assembly order of mammalian septin complexes[END_REF][START_REF] Kim | SEPT9 occupies the terminal positions in septin octamers and mediates polymerizationdependent functions in abscission[END_REF]. During membrane remodeling processes, these structures can act as a diffusion barrier or scaffolds that recruit cytosolic proteins and other cytoskeletal elements such as microtubules or actins [START_REF] Tanaka-Takiguchi | Septinmediated uniform bracing of phospholipid membranes[END_REF][START_REF] Fung | Cell and molecular biology of septins[END_REF][START_REF] Bridges | Micron-scale plasma membrane curvature is recognized by the septin cytoskeleton[END_REF][START_REF] Mostowy | Septins: the fourth component of the cytoskeleton[END_REF].

Septins bind specifically to phosphoinositides (PIs) via a polybasic domain (PB1) located at the N-terminus of their GTP-binding domain. This interaction with PIs supposedly mediates septin membrane association, which is a determinant factor for the structural and functional features of the protein [START_REF] Pan | Analysis of septins across kingdoms reveals orthology and new motifs[END_REF][START_REF] Zhang | Phosphatidylinositol polyphosphate binding to the mammalian septin H5 is modulated by GTP[END_REF][START_REF] Tanaka-Takiguchi | Septinmediated uniform bracing of phospholipid membranes[END_REF][START_REF] Casamayor | Molecular dissection of a yeast septin: distinct domains are required for septin interaction, localization, and function[END_REF]. Septins associate with a variety of PIs at different intracellular membranes [START_REF] Zhang | Phosphatidylinositol polyphosphate binding to the mammalian septin H5 is modulated by GTP[END_REF][START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5-phosphate and microtubuledependent mechanism hijacked by HCV[END_REF][START_REF] Dolat | Septins promote macropinosome maturation and traffic to the lysosome by facilitating membrane fusion[END_REF][START_REF] Pagliuso | A role for septin 2 in Drp1-mediated mitochondrial fission[END_REF] and control numerous cellular functions such as cytokinesis, cilogenesis, vesicular trafficking, cell polarity and lipid droplet formation [START_REF] Fung | Cell and molecular biology of septins[END_REF][START_REF] Oh | Septin structure and function in yeast and beyond[END_REF][START_REF] Song | Septins As Modulators of Endo-Lysosomal Membrane Traffic[END_REF][START_REF] Balla | Phosphoinositides: tiny lipids with giant impact on cell regulation[END_REF][START_REF] Gassama-Diagne | Phosphoinositide signaling pathways: promising role as builders of epithelial cell polarity[END_REF][START_REF] Gassama-Diagne | Phosphatidylinositol-3,4,5-trisphosphate regulates the formation of the basolateral plasma membrane in epithelial cells[END_REF][START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5-phosphate and microtubuledependent mechanism hijacked by HCV[END_REF][START_REF] Schink | Phosphoinositides in Control of Membrane Dynamics[END_REF].

The morphology and positioning of intracellular organelles such as the Golgi and endoplasmic reticulum (ER) are critical for the proper transport and delivery of vesicles to maintain cell polarity, tissue homeostasis and functions [START_REF] Lavieu | The Golgi ribbon structure facilitates anterograde transport of large cargoes[END_REF]de Forges et al., 4 2012;[START_REF] Van Bergeijk | Right Time, Right Place: Probing the Functions of Organelle Positioning[END_REF]. Such morphological arrangements are often ensured by cytoskeleton factors such as microtubules and actins, which are in part recruited by septins [START_REF] Tanaka-Takiguchi | Septinmediated uniform bracing of phospholipid membranes[END_REF][START_REF] Fung | Cell and molecular biology of septins[END_REF][START_REF] Bridges | Micron-scale plasma membrane curvature is recognized by the septin cytoskeleton[END_REF][START_REF] Mostowy | Septins: the fourth component of the cytoskeleton[END_REF]. However, whether septins directly affect organelle morphology and function is poorly understood [START_REF] Gurel | Connecting the Cytoskeleton to the Endoplasmic Reticulum and Golgi[END_REF][START_REF] Weirich | The septin family of GTPases: architecture and dynamics[END_REF].

Here, by using septin 9 crystal structures and simulations of the molecular dynamics (MD) of the septin 9 monomer and dimer, we have identified the existence of a second polybasic domain (PB2). The deletion of PB2 phenocopied PB1 deletion by reducing the binding capacity of septin 9 to PI lipids and impairing the formation of septin filamented structures, hereinafter referred to simply as filaments. However, in vitro flotation assays revealed that the PB domains are not required for septin 9 membrane binding but proffer specificity to PIcontaining membranes. These findings prompted us to identify amphipathic helices that are adjacent to the PB domains and possibly mediate the physical association of septin 9 with membranes. We studied the importance of the PB domains on organelles and determined their critical role in Golgi assembly and functionality.

5

Results

Septins have a second polybasic domain PB2 that forms with PB1 a basic cluster at the

NC interface

Septins bind to PI lipids via a polybasic domain (PB1) located at the N-terminus of their GTPbinding domain [START_REF] Zhang | Phosphatidylinositol polyphosphate binding to the mammalian septin H5 is modulated by GTP[END_REF][START_REF] Pan | Analysis of septins across kingdoms reveals orthology and new motifs[END_REF]. However, we recently found that the deletion of PB1 in septin 9 reduces but does not abolish the interaction between septin 9 and monophosphorylated PIs [START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5-phosphate and microtubuledependent mechanism hijacked by HCV[END_REF]. This observation prompted us to look for the presence of additional PI-interacting domains. We aligned the sequences of septin 9 and other human septins and identified a second motif enriched in basic amino acids (aa399-402 of human septin 9 isoform 1; 586 residues) (Figure 1A). This second polybasic domain, which we termed PB2, contains a variable number of basic amino acids (2 to 4) but is conserved in all human septins (Figure 1A).

We next generated and purified a PB2-deleted mutant (septin 9_del2), a PB1-deleted mutant (septin 9_del1) [START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5-phosphate and microtubuledependent mechanism hijacked by HCV[END_REF], and a mutant lacking both PB1 and PB2 (septin 9_del1,2) (Figure S1A). These proteins displayed band profiles similar to septin 9_i1 (Figure 1B, Figure S1B), which was in a monomeric form based on migration on a native gel (Figure S1C). We then used a PIP strip overlay assay to determine the affinity of septin 9_i1 and its mutant forms with different phospholipid headgroups. As expected, we found a specific interaction between septin 9_i1 and PtdIns monophosphates (Figure 1C). The interaction signal with PIs was decreased in septin 9_del1 and septin_del2, and was almost abolished in septin 9_del1,2 (Figure 1C). This result supports the idea that both PB domains can mediate the interaction of septin 9 with phosphoinositides.

To study the involvement of PB2 in the structural organization of septin 9, we opted for an MD simulation approach using the most resolved septin 9 crystal structure (aa 293-564), PDB code 5cyp. In this structure, the missing residues and side chains were added and completed by amino acids from 276 to 292 (see Methods), which included those of PB1. Regardless of the initially folded state of these added residues, we found one single final equilibrium conformation of the protein where the N-terminal region was pre-folded into an α-helix around PB1 (Figure 1D, Figure S1D). This equilibrated monomer was then superimposed on the crystal structure of septin 9 (PDB code 5cyp) to build a tetramer that contains the NC-NC interface (Figure 1E). At this interface, PB2 and PB1 appeared to make numerous salt bridges between septin monomers (Figure 1E, black dots in the inset) we found optimal distances 6 between amino acids of the PB domains and those of the adjacent septin. These interactions involved the R399 and R402 residues of PB2, interacting respectively with E477' and D484', and the R289 residue of PB1 interacting with D538'. The main chain atoms of R289 and A292 in PB1 made hydrogen bonds with R542' and T543' of the neighboring septin (Figure 1E). This structural analysis indicates that the PB2 domain forms an extended basic cluster with PB1 at the NC interface of septin 9.

Contribution of PB domains to septin 9 membrane association

To determine whether the PB domains are equally involved in septin 9-membrane interactions, we first performed MD simulations of the interaction between the monomeric structure of the protein shown in Figure 1D and membranes devoid of PtdIns4P (Figure S2A).

The simulations were made by leaving the protein close to a dioleoylphosphatidylcholine (DOPC) membrane, thus offering it the opportunity to change conformation over time. We simulated three conditions by changing the initial protein conformation and velocity (Figure S2A, MD1-3). In all cases, septin 9 was recruited to the membrane. However, we found that PB1 was always in contact with the membrane (Figure S2A)(see experimental procedure), while PB2 was not, under one of the conditions (Figure S2A,MD1). This observation suggests that PB1 may be better positioned to interact with membranes.

To further clarify the involvement of PB1 and PB2 in septin 9 interactions with PI lipids, we took advantage of the recently resolved crystal structure of septin 3 [START_REF] Macedo | The structure and properties of septin 3: a possible missing link in septin filament formation[END_REF], which belongs to the same subgroup as septin 9 (Figure 1A). By using homology modeling, we built a septin 9 monomer and tetramer (Figure S2B,C), and used the tetramer to determine its spatial organization on a DOPC/DOPE bilayer containing PtdIns5P [START_REF] Lomize | OPM database and PPM web server: resources for positioning of proteins in membranes[END_REF].

In the membrane-proximal PB1-PB2 cluster of the tetramer, we found that the basic residues R 289 , R 290 , K 291 and K 400 were particularly well positioned to interact with the phosphate headgroup of the phosphoinositides (Figure 2A). Three of these residues, namely R289, R290, and K291, belong to PB1, and K400 to PB2. This analysis also supports the idea that PB1 is more closely involved in regulating septin 9 membrane binding than PB2, which was consistent with the previous MD results (Figure S2A).

Septin 9 interactions with membranes in vitro do not require any of the PB domains

We decided to study the contribution of PB domains to septin association in vitro. Large and small liposomes (e.g. above 300 nm and below 200 nm), containing PtdIns4P or not, were respectively generated by vortex and high power sonication, so as to mimic flat and curved membranes. The liposomes were then mixed with septin 9_i1, and septin 9_del1,2. A sucrose gradient flotation assay was subsequently performed (Figure 2B), during which only bound proteins would float up with the liposomes to the top fraction (Figure 2B). The supernatant fraction was collected and the amount of bound proteins determined by Western blotting (Figure 2C).

As expected, septin_i1 bound more strongly to liposomes containing PtdIns4P than to those which lacked PtdIns4P (Figure 2C-F). However, binding was reduced on smaller liposomes S2D), which suggests that the binding capacity of septin 9 was better with flat rather than positively curved membrane regions. Surprisingly, we found that septin 9_del1,2, which lacked both PB domains, bound efficiently to all membranes (Figure 2C-F), despite the fact that it also had a slight preference for flatter membranes (Figure S2D). This efficient binding of septin 9_del1,2 was not detected in the PIP strip overlay assay because perfect membrane bilayers are not generated using this method (Figure 1C); it was however consistent with the binding of septin 9 to membranes devoid of PI lipids obtained by MD simulations (Figure S2A). Finally, the binding of septin 9_del1 and septin 9_del2 was not enhanced by the presence of PtdIns4P, and it was almost lost on small liposomes (Figure S2E). These results suggest that PB1 and PB2 are both required for the specific and efficient binding of septin 9 to PI-containing membranes.

(Figure 2C-F, Figure
In conclusion, our data described above, and particularly those obtained with septin 9_del1,2, suggest that septin 9 can bind bilayer membranes without involving its PB domains. Both PB domains seem to be necessary to provide septin 9 binding selectivity to PI-containing membranes, and especially to flat membranes or at least to those which are not positively curved.

Septins have PB-adjacent amphipathic helices (AH)

We next tried to determine how septin 9 was able to interact directly with membranes in the absence of PI lipids and without its PB domains (Figure 2). Many soluble proteins bind membranes using amphipathic α-helix motifs (AHs), which are moreover able to detect subtle differences in membrane curvature and charges [START_REF] Bigay | Curvature, Lipid Packing, and Electrostatics of Membrane Organelles: Defining Cellular Territories in Determining Specificity[END_REF], as is the case for septin 9. We therefore performed a bioinformatics screening for AHs in the full sequence of septin 9. Two striking sequences emerged from our analysis as being the most prominent AHs (aa274 to 294 and aa370 to 402). Surprisingly, these AHs were directly adjacent to PB1 and PB2, respectively (Figure 3A). The sequence close to PB1 corresponded to a flexible strand that can fold into an AH, which is probably why it is missing from the septin 9 crystal structure. MD simulation showed that this portion of the protein indeed folded as an α-helix (Figure S1D) and was well positioned to bind membranes (Figure 3A). The AH close to PB2 was folded but oriented toward the interior of the protein, unless a conformational switch occurred. These AHs contain very hydrophobic residues, such as tyrosine, tryptophan and phenylalanine, a feature that enhances membrane association. Our analysis therefore suggested that septin 9 has at least one PB-adjacent AH associated with PB1 that can mediate its physical association with membranes. In other septins, we also found flagrant AHs juxtaposed with the PB2 of septin 2, 6, and 7 with which septin 9 interacts to form the octamer. We took advantage of the existence of a crystal structure of the trimer formed by septin 2-6-7 to verify the orientation of the AHs. We found that the AH-PB2 of septin 6 was suitably oriented to bind membranes (Figure 3B). The AH feature at the PB1 domain of these septin 9 counterparts was less pronounced (Figure 3B, Figure S3A-D).

Septin 9 PB domains are essential for the formation of septin filaments

Our data supported the idea that the AHs of septin 9 are probably the membrane binding motifs which are restricted to PI-containing membranes by the PB domains. Under this scenario, the PB domains would be more available to participate in the NC/NC interactions that mediate the formation of septin high order structures.

We transfected HeLa cells with septin 9_i1, which we found was incorporated in high order filamentous structures that also contained endogenous septin 9 and septin 2 (Figure 4A,B).

However, the strong expression of septin 9_i1 seemed to displace endogenous septin 9 from the filaments, while septin 2 remained recruited at a similar level (Figure 4B,C). Our overexpressed septin 9 construct thus had a dominant negative effect on endogenous septin 9 (Figure S4E). When cells were transfected with the PB-deleted constructs (Del1, Del2, Del1,2), the filamentous structures were lost (Figure 4D,E,F) despite the presence of endogenous septin 9. Here also, these constructs displayed the dominant negative effect of septin 9 (Figure S4E), and septin 2 was not present in the filaments (Figure 4D). These results suggest that both PB domains are involved in septin 9 assembly, in line with our previous results from the structural analysis (Figure 1E, Figure S2C).

To avoid possible conformational changes to the protein and its dysfunction because of the deletion of PB domains, we performed simple point mutations. We substituted the basic lysine and arginine amino acids (K and R) with glutamine (Q), which is a non-charged but polar amino acid that has a long side chain as in K and R; this substitution was therefore optimal to minimize possible conformational changes in the protein. For example, in septin 9_Q1, the R and K residues of PB1 were not deleted as in septin 9_del1 but replaced by Q. We observed that cells transfected with septin 9_Q1, septin 9_Q2 or septin 9_Q1,2 were unable to form septin filaments (Figure S4A-C), in the same way as with the deletion (Figure 4D-F). We next performed simple mutations by substituting one or two R with alanine (A) within PB1, and the filaments were lost once again (Figure S4D). None of these constructs affected the normal expression of endogenous septin 9 (Figure S4E).

In conclusion, the point mutant phenocopied the deletion constructs and the results suggest that the positively charged PB cluster at the NC/NC interface is essential to the formation of septin filaments.

Septin 9 PB domains are critical for Golgi assembly

Septin 9 binds mainly to PtdIns3P, PtdIns4P and PtdIns5P which are primarily detected in early endosomes (EE), the Golgi apparatus and the endoplasmic reticulum (ER), respectively [START_REF] Pendaries | PtdIns5P activates the host cell PI3-kinase/Akt pathway during Shigella flexneri infection[END_REF][START_REF] Kutateladze | Translation of the phosphoinositide code by PI effectors[END_REF][START_REF] Sarkes | A novel HPLC-based approach makes possible the spatial characterization of cellular PtdIns5P and other phosphoinositides[END_REF]. We thus wanted to probe whether PB1 and PB2 contribute to the organization of these endomembrane compartments. We expressed septin 9_i1 and the mutant constructs in HeLa cells and then studied the morphology of these organelles.

A significant increase in EE and ER markers was observed in the perinuclear region of septin 9_i1-expressing cells when compared to EV and septin 9 mutants, which were similar (Figure S5A-E). The most striking observation of the deletion of PB domains was on the Golgi structure (Figure 5A,B). In cells expressing septin 9_i1, we found the normal phenotype of a compact Golgi embedded in high order structures of septin 9_i1 filaments (Figure 5A,C), which contained septin 2, 6 and 7 (Figure S5F). Strikingly, the deletion or mutation of any of the PB domains led to Golgi fragmentation (Figure 5A, B, Figure S5G).

Assembly of the Golgi apparatus is dependent on microtubule polymerization [START_REF] Miller | Golgi-derived CLASP-dependent microtubules control Golgi organization and polarized trafficking in motile cells[END_REF]. The depolymerization of microtubules, typically under nocodazole treatment, results in Golgi fragmentation; removal of the nocodazole enables the re-polymerization of microtubules and Golgi reassembly. We thus took MDCK cells stably expressing septin 9_i1 and septin 9_del1,2 and treated them with nocodazole to induce Golgi fragmentation. The 10 nocodazole was then washed out and Golgi reassembly monitored (Figure 5D). In septin 9_i1 cells, the scattered Golgi elements reassembled normally within 20 min (Figure 5D,E) but not in septin 9_del1,2 cells (Figure 5D,E), even after much longer periods of time (Figure S5H).

The above observations suggest a function for septin filaments in Golgi assembly that is dependent on septin 9 PB domains.

Mutations of PB domains cause Golgi fragmentation but not Septin 9 dissociation from the membrane

Our data suggested that a lack of PB domains might cause a loss of the specific binding of septin 9 to PtdIns4P (Figure 2). We decided to monitor the interaction between septin 9 and PtdIns4P within cells. HeLa cells were therefore transfected with cDNAs of EV, septin 9_i1 and Del1, Del2 or Del1,2, and stained for V5 tag, TGN46 (Golgi marker) and PtdIns4P (Figure 6A and Figure S6A).

PtdIns4P was strongly co-localized with compact Golgi in EV and septin 9_i1, as had been expected [START_REF] Dippold | GOLPH3 Bridges Phosphatidylinositol-4-Phosphate and Actomyosin to Stretch and Shape the Golgi to Promote Budding[END_REF]. In cells transfected with the Del1, Del2 or Del1,2 constructs (Figure 6A), the Golgi was fragmented, as seen previously, but no significant difference in colocalization between TGN and PtdIns4P was noted (Figure 6B). However, we observed a nonsignificant decrease in the co-localization of septin 9 with PtdIns4P (Figure 6C) that varied between the different transfected constructs. PB-deleted mutants still displayed strong signals on small spherical compartments which were possibly Golgi ministacks, vesicles or other structures (Figure 6A, Figure S6A). To determine whether the mutant septin 9 proteins were associated with these membrane structures, we permeabilized the cells and removed the soluble proteins prior to fixation. We observed that the septin 9 mutated protein signal remained on intracellular structures (Figure 6D). This observation suggests that a lack of PB domains does not prevent the binding of mutant proteins to possible membrane structures, in line with our in vitro assays which revealed the ability of the mutants to bind to membranes (Figure 2). To further test this finding, a subcellular fractionation assay was performed (Figure S6B) and showed that septin 9_i1 always peaked with the Golgi marker, while septin 9_del1,2 had a more spread out signal, suggesting that it probably bound to other membranes, including fragmented Golgi elements (Figure S6B).

Taken together, our results suggest that PB1 and PB2 restrict septin 9 binding to PIcontaining membranes, such as PtdIns4P on Golgi, but are not directly responsible for septin 11 membrane association. They play a major function in septin complex assembly and subsequent organelle structuration.

Endogenous septin 9 localizes to Golgi and regulates its compactness and functionality

The transfection of our septin 9 mutant constructs, which had a dominant negative effect on endogenous septin 9, could be the reason for Golgi fragmentation. We therefore studied this endogenous septin 9 and found that it also co-localized with Golgi (Figure 7A). This observation was likewise supported by a subcellular fractionation assay (Figure 7B) in which both septin 2 and septin 9 peaked with GM130 (Figure 7B). These results suggest that endogenous septin 9 is present in septin structures associated with the Golgi apparatus.

We next worked with a cell line stably transfected with septin 9 siRNA (Figure 7C). In control cells, Giantin, which is also a Golgi marker, displayed polarized and compact features, i.e. enriched on one side of the nucleus (Figure 7C). However, in the septin 9 siRNA cells, we observed a fragmentation of the Golgi (Figure 7C). Interestingly, this fragmentation could be rescued by transfection with septin 9_i1 (Figure 7 E,F), but not with the PB-deleted constructs (Figure S7A,B). Here again, we performed the nocodazole washout assay which confirmed that Golgi reassembly is dependent on endogenous septin 9 (Figure S7C), which therefore plays an important role in maintaining the compact structure of the Golgi.

Our overall data suggest that septin 9 (endogenous and septin 9_i1) is incorporated into filaments which are critical to the Golgi structure. Since septin 2 and Septin 6 are involved in these filaments, they should also control Golgi compactness. We accordingly found that their depletion by a specific siRNA promoted Golgi fragmentation (Figure 7G, H, Figure S7E). This data reinforced our model in which septin complexes are incorporated into the filament structures which are associated with the Golgi membrane and control its compactness.

Finally, fragmentation of the Golgi apparatus is known to impede secretory pathways [START_REF] Xiang | Regulation of protein glycosylation and sorting by the Golgi matrix proteins GRASP55/65[END_REF][START_REF] Lavieu | The Golgi ribbon structure facilitates anterograde transport of large cargoes[END_REF][START_REF] Joshi | Golgi fragmentation in Alzheimer's disease[END_REF]. We thus probed whether septin 9 depletion (Figure S8A,B) impeded these pathways. We first used a Venus-tagged Neuropeptide Y construct (NPY-Venus) as a model of a secreted protein; we determined its level of secretion in the cell culture medium and lysates. We found that septin 9 depletion resulted in a significant decrease of secreted NPY-Venus (Figure S8C). We next studied the trafficking of a temperature-sensitive variant of the vesicular stomatitis virus G protein tagged with GFP 12 (tsVSVG-GFP) (this protein remains in the ER at 40°C but enters the secretory pathway when the temperature is lowered to 32°C [START_REF] Presley | ER-to-Golgi transport visualized in living cells[END_REF]. Control and septin 9-depleted cells were transfected with tsVSVG-GFP and fixed at different time points after the temperature was lowered from 40°C to 32°C (Figure S8D). After 2 hours, the protein signal in the Golgi area was greatly reduced in control cells whereas it remained intact in septin 9-depleted cells, suggesting a defect in intracellular trafficking. Taken together, these data indicate that septin 9 plays a critical role in Golgi compactness and its subsequent function in cellular trafficking.

Discussion

Septins belong to the family of GTPase proteins that assemble into macrostructure filaments which are important to the membrane remodeling processes. Here we have shown that septin 9 is particularly necessary for Golgi structure and function, as the absence of septin 9 provokes Golgi dissociation and impairs secretory pathways. Our results support the idea that septin 9 and other septins (such as septin 2 and septin 6) form a filament matrix which harbors Golgi stacks.

The association of septins with membranes was previously thought to be specifically mediated by an interaction between their polybasic domain PB1 and PI lipids [START_REF] Pan | Analysis of septins across kingdoms reveals orthology and new motifs[END_REF][START_REF] Zhang | Phosphatidylinositol polyphosphate binding to the mammalian septin H5 is modulated by GTP[END_REF][START_REF] Tanaka-Takiguchi | Septinmediated uniform bracing of phospholipid membranes[END_REF][START_REF] Casamayor | Molecular dissection of a yeast septin: distinct domains are required for septin interaction, localization, and function[END_REF]. Here we found that septin membrane association was much more subtly regulated. First, we identified the presence of a second polybasic domain (PB2) in septin 9, which is conserved among the different human septins and regulates the interaction between septin and PI lipids.

Second, we identified AH structures adjacent to PB1 and PB2 which probably mediate the physical association of septin 9 with membranes. Our result support the idea that PB1 and PB2 may act together to restrict the binding of these AHs of septin 9 to PI-containing membranes, and particularly to non-positively curved membranes. This conclusion is in line with the in vivo accumulation of septins in specific plasma membrane ingressions or concavities, such as cleavage furrows [START_REF] Spiliotis | Here come the septins: novel polymers that coordinate intracellular functions and organization[END_REF]. Finally, based on our in vitro observations, MD (Figure S2A) and modeling of the interaction between the septin 9 complex and PtdIns(4)P containing membranes (Figure 2A), PB1 appears to be more closely involved in regulating septin 9 membrane binding specificity than PB2, but both are critical for septin filament assembly.

Whether septin 9 acts in a cellular context in a monomeric form is not known. Apart from the septin 9 isoform septin 9_i4, which has been found in non-filament structures [START_REF] Chacko | SEPT9_v4 expression induces morphological change, increased motility and disturbed polarity[END_REF], most septins have been so far been reported as being incorporated in filamentous structures, and whether they exist under monomeric form is also unknown. Despite our in vitro studies having been performed with the monomeric septin 9, our results provided information on how septin 9 membrane binding determinants might influence the localization of septin oligomers to membranes. These results are consistent with a recent report on the presence of AH structures in oligomeric septin filaments, capable of sensing macroscopic curvatures [START_REF] Cannon | An amphipathic helix enables septins to sense micrometer-scale membrane curvature[END_REF].

14

Based on our results, we propose that septin 9 binds membranes with AHs that can strongly associate to the membrane. In this setting, PB domains may interact with PI lipids to dock the protein on specific organelles, thereby preventing non-specific binding. This mechanism would enrich the protein on the membrane thanks to the PBs, and stabilize it through the action of AHs.

It is not yet clear how septins control the Golgi structure. One hypothesis is that the PB domains contribute to enriching septin 9 or octameric complexes in Golgi elements. Assembly of the octamers would form the septin filaments, which will meantime have brought different Golgi elements close enough to promote their fusion, e.g. by SNARE proteins. Under this hypothesis, a septin matrix will form a structure embedding the Golgi elements. This model is consistent with our experiments on Golgi reassembly after nocodazole treatment: this reassembly occurred with septin 9_i1, whereas with Del1,2 (Figure 5D, E, Figure S5H) or septin 9 depletion (Figure S7C) it did not. Consistent also with our model, the Golgi is fragmented by the depletion of septin 2 or 6. Hence, our study has revealed the importance of high order septin structures to Golgi homeostasis. Since microtubules and actin filaments are also known to maintain Golgi structure and interact with septins [START_REF] Miller | Golgi-derived CLASP-dependent microtubules control Golgi organization and polarized trafficking in motile cells[END_REF][START_REF] Egea | Actin dynamics at the Golgi complex in mammalian cells[END_REF][START_REF] Kondylis | The golgi comprises a paired stack that is separated at G2 by modulation of the actin cytoskeleton through Abi and Scar/WAVE[END_REF][START_REF] Fung | Cell and molecular biology of septins[END_REF], it is plausible that septins are engaged in hybrid filaments with microtubules and actin in order to maintain Golgi structure.

On other organelles, we observed that PB1 and PB2 affected ER and EE organization, which was reminiscent of the role that we described for septin 9 in lipid droplet dynamics; interestingly, septin filaments have been seen to be prominent around large lipid droplets [START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5-phosphate and microtubuledependent mechanism hijacked by HCV[END_REF]. This particular localization of septin high order structures to sites of micron-scale membrane curvature is emerging as an important feature of organelle dynamics [START_REF] Cannon | An amphipathic helix enables septins to sense micrometer-scale membrane curvature[END_REF].

Finally, septin structures have been proposed to act as a physical barrier against the nonspecific docking of vesicles on the active zone of the synapse [START_REF] Yang | Septins regulate developmental switching from microdomain to nanodomain coupling of Ca(2+) influx to neurotransmitter release at a central synapse[END_REF]. Thus septin structures may also behave as physical barriers that prevent the collapse of Golgi stacks or their connection to other organelles. Our findings on the role of septin 9 in the Golgi apparatus could probably be extended to other organelles and offer a paradigm for the structural and biological functions of septins. C. PIP strip overlay assay: PIP strips were incubated with either purified septin 9_i1 (I1), septin 9_del1 (Del1), septin 9_del2 (Del2) or septin 9_del1,2 (Del1,2) proteins at 0.5 0.5 µg.ml -1 or with the V5 tag peptide as a negative control, and analyzed using the anti-V5 antibody. LPA (lysophosphatidic acid), LPC (lysophosphocholine), PtdIns The cells were then extracted using cold PBS buffer containing triton X100 at 0.1% for 30 seconds then fixed and stained for V5tag (green) and GM130 (red). Scale bar:

Figure legends

10µm.

Figure 1 :

 1 Figure 1: Septin 9 and human septins have two polybasic domains

Figure 2 :

 2 Figure 2: PBs are required for specific interactions between septin 9_i1 and PIs and

Figure 3 :

 3 Figure 3: Septin 9 has putative PB-associated amphipathic helices mediating its

Figure 4 :

 4 Figure 4: Overexpressed septin 9_i1 replaces indigenous septin 9 in septin filaments while PB-mutated septin 9 expression impairs them

Figure 5 :

 5 Figure 5: Septin 9 localizes to Golgi and is required to ensure its compact morphology

Figure 6 :

 6 Figure 6: PBs are required for the specific recruitment of septin 9_i1 to the Golgi

Figure 7 :

 7 Figure 7: Septin 9 localizes to Golgi and in the same way as septins is required to ensure its compact morphology

Acknowledgements

This work received support in the form of a grant from the Association pour la Recherche sur le Cancer (ARC/SUBV/CKLQ6) for AGD, and from the ANRS (France Recherche Nord & sud SIDA -hiv Hépatites: FRENSH) through a grant to SB and a PhD fellowship for CT.

A.R.T is supported by the ANR-TERC (LDEN), Paris Sciences et Lettres, and ATIP-Avenir.

We would like to thank H. Russell (Queen's University, Belfast, UK.) for providing the septin 9_i1 construct. We also thank A. Baillet (Université Paris-Sud, UMR-S 1193, Villejuif, France) for access to live cell imaging facilities.

Limitation of the study

One limitation of this study is that the septin 9 protein studied in vitro is in monomeric form while it is unknown whether it can exist in such form in cells.

Author contributions

Declaration of Interests

The authors declare no competing interests.


Abstract-This paper addresses the problem of interaction between short run and long run locational signals and the coordination between generation investments and lumpy transmission investments. The short run locational signals we evaluate are sent by nodal pricing and the long run ones are sent by the average participation use-of-the-network tariff. Their joint implementation is also deemed. Numerical simulations are performed on a two-node network evolving during twenty years with increasing demand. The efficiency of these locational signals to coordinate the location of generation with lumpy transmission investments is measured. An independent Transmission System Operator invests to minimize the total cost of the network, that is to say the sum of the cost of congestion with the cost of transmission investments. And a unique generator behaving competitively chooses the location of her investments depending on two elements: the locational difference in generation investment costs and the costs of the network she may pay with short run nodal prices and with the long run average participation tariff. The network tariff varies with the transmission investments. And the transmission capacity greatly influences nodal prices. We find out that neither short run nodal prices nor long run average participation tariffs can thoroughly coordinate efficiently generation and transmission investments because of the lumpiness of transmission line capacities.

Index Terms-generation investment, lumpy transmission investment, long run coordination, locational signals, efficiency evaluation

The efficiency of short run and long run locational signals to coordinate generation location with lumpy transmission investments Vincent Rious, Philippe Dessante, Yannick Perez

Introduction

O ensure a non-discriminatory third party access to the network, the competitive reforms of the power sector have required to unbundle the network infrastructures from the competitive activities such that generation [START_REF] Ferc | Promoting Transmission Investment through Pricing Reform[END_REF]European Commission, 2007;[START_REF] Pollitt | The arguments for and against ownership unbundling of energy transmission networks[END_REF]. In this context, a monopoly called Transmission System Operator (TSO) manages the transmission network. The TSO and the generators invest then depending on their own objective function. The generators maximize profit. The TSO maximizes the social welfare if she is perfectly regulated. Despite network unbundling, the location of new generators remains highly dependent on transmission investments and vice versa. In this context, pricing schemes must be implemented to coordinate generation and transmission investments.

One could think of relying on the well-known marginal pricing to expand both generation and transmission capacity [START_REF] Crew | The theory of peak-load pricing: a survey[END_REF][START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. One invests so as to equalize short run and long run marginal costs of both generation and transmission. If these convenient assumptions prevailed in the power system, the generator would invest so as to equalize the marginal generation capacity cost with marginal generation cost. And the TSO would do the same equalizing the marginal transmission capacity cost with marginal congestion cost. Nodal pricing as market-based pricing of transmission service could then govern transmission investment and the location of generation (Hogan, 1992;[START_REF] Bushnell | Electric grid investment under a contract network regime[END_REF], 1997;[START_REF] Chao | A Market Mechanism for Electric Power Transmission[END_REF].

Applying this principle to the coordination of generation and transmission investments is not possible. The transmission of electricity suffers from many undesirable economic properties that make the direct application of these principles impossible. It combines both economies of scale and especially lumpiness of capacity [START_REF] Brunekreeft | Market-based investment in electricity transmission networks: controllable flow[END_REF]. [START_REF] Joskow | Merchant Transmission Investment[END_REF] show that lumpiness combined with the short run locational signals from nodal pricing result in an underincentive for a merchant investor to reinforce the network. Even if the transmission investment is optimal, nodal pricing can lead to inefficient location of generation because of the economic properties of the transmission of electricity [START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. Besides, some other less efficient options to operate the system are often implemented, although they send less short run locational signals [START_REF] Green | Nodal pricing of electricity: How does it cost to get it wrong[END_REF]. In brief, not only system operation may not send short run locational signals but also these signals are not sufficient to coordinate the location of generation with lumpy transmission investments.

The usual way to comply with these difficulties is to implement a two-part tariff. The first part of this tariff should be nodal prices. The second part is network tariffs. These later aim at sharing the cost of transmission infrastructures among the network users, especially the generators, in the most cost-reflective way. Well-designed network tariffs incentivise the generators to locate efficiently on the network and thus to maximize social welfare [START_REF] Pérez-Arriaga | Guidelines on tariff settings[END_REF]. But network tariffs are hard to design. A lot of different network tariffs have then been proposed [START_REF] Camacho | Diseño regulatorio de la actividad de transporte en mercado de electricidad regionales[END_REF]. But there may be no network tariffs that achieve the same coordination between generation and transmission investment as a vertically integrated utility does.

This paper only focuses on the average participation tariff for the three following reasons. First it has been extensively studied from a static point of view [START_REF] Kirschen | Contributions of individual generators to loads and flows[END_REF]1996[START_REF] Bialek | Topological generation and load distribution factors for supplement charge allocation in transmission open access[END_REF][START_REF] Rubio | Marginal Pricing of Transmission Services: A Comparative Analysis of Network Cost Allocation Methods[END_REF] and we are going to study it in the dynamic interaction of generation and transmission investments. Second the average participation tariff has an interesting property. It coincides with the Shapley values. This guarantees that the average participation tariff is a fair, symmetric, stable and acceptable allocation of cost for all the "players" [START_REF] Bialek | Proportional sharing assumption in tracing methodology[END_REF]2004).

T

Third network tariffs can send long run locational signals that should overcome the difficulty to incentivise the location of generation when transmission investment is lumpy. But the efficiency of the average participation tariff for coordinating generation and transmission investments has never been studied whether it is implemented with or without short run locational signals [START_REF] Camacho | Diseño regulatorio de la actividad de transporte en mercado de electricidad regionales[END_REF][START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF].

This paper investigates the efficiency of the average participation tariff to coordinate transmission and generation investments whether it is implemented with or without nodal pricing. The model used in this paper is similar to the model of Sauma-Oren (2006a, b) but they differ on some points. Sauma and Oren do not consider network tariffs and nodal pricing is the unique locational signals that they study. The simulations of Sauma and Oren take into account lumpiness of transmission investment while their model does not. Sauma and Oren consider uncertainty and imperfect competition of generation. They consider that the TSO acts under the constraints of generation investments and their optimization problem is an Equilibrium Problem with Equilibrium Constraints (EPEC).

Our paper considers network tariffs and studies their efficiency to locate generation investments. The model used to carry out this study includes lumpiness of transmission investments. These two points make the optimization problem non-convex and hard to solve. The following simplifications are then made. There is no uncertainty. The TSO and the generators have perfect information on investments, capacities and value of short run and long run locational signals. The TSO is perfectly regulated. The generators behave competitively. This paper does not assume the TSO acts under the constraints of the generation investments because the transmission investments may face local opposition and not be built. The generators may then locate their plants under the constraints of impossible transmission investments. The coordination problem studied in this paper is not an EPEC. It is a double optimization one, to maximize the generation profit and to minimize the cost of the network.

The rest of the paper is organised as follows. Section 2 presents the options of locational signals that will be studied in the following sections, that is to say, for the short run locational signals 1° nodal pricing and 2° redispatch (that sends no locational signal), and for the long run ones, 1° the average participation tariff or 2° no tariff. Section 3 models a liberalised system where a TSO and a generator must coordinate to minimize their own costs. The TSO invests to minimize the sum of the congestion cost and of the cost of the network investments. The generator minimizes the sum of investment costs, operation costs taking into account or not the network congestions and the tariff she may have to support. To evaluate the efficiency of coordination achieved by these options and their combination, the investments made by a benevolent integrated utility define a benchmark. Section 4 analyzes the results of simulations. And section 5 concludes on the limited efficiency of short and long run locational signals to coordinate generation and transmission investment.

Locational signals between transmission and generation investments in a liberalised power market

In the liberalised system, generation and transmission need signals to coordinate the location and timing of their investments. The system operation and the network tariffs can send such locational signals. Some options to operate the power system signal congestion. Similarly, some options of network tariffs are designed for the generators to take into account the cost of the network and the reinforcements that may result from their investment decisions. But other options of network tariffs or system operation do not send any locational signals and are nevertheless implemented. This section presents what seems to us, the most and the least efficient options of short and long run locational signals and their theoretical effects on coordination between generation and transmission investments.

Short run system operation and coordination of investments

Different options to operate the power system are possible. The most efficient option is nodal pricing. This option gives a different price to power depending on the network congestion and on the node where power is generated or consumed [START_REF] Schweppe | Spot Pricing of Electricity[END_REF]. The nodal price is the local economic value of power and includes the generation cost and the congestion cost. Recurring differences in nodal prices reveal the structural network congestions. Nodal pricing incentivises the generators to use efficiently the available transmission capacities. Thus nodal prices are short run locational signals and participate in coordinating generation and transmission investments.

But nodal pricing or even its zonal version is not always implemented. Although redispatch is the least efficient option to operate the system, the TSO may have to implement it (Green 1997a[START_REF] Bompard | A comparative analysis of congestion management schemes under a unified framework[END_REF]. In this case, after the energy market closed, the TSO modifies the generation scheduling to manage congestion. The congestion cost following the change in generation scheduling is then generally socialised. In this means of managing network congestion, the electricity market receives no locational signal containing information on the constraints on the grid, and the market for power continues to operate as if there were no constraints on it. The generators do not take into account the network constraints in the location of their new plants.

Besides, short run locational signals alone cannot coordinate efficiently generation and transmission investments. Owing the volatility of nodal prices, one usually relies on transmission rights to distinguish a long run locational signal among the short run ones. The most used ones are the Financial Transmission Rights (FTRs). The FTRs send distorted locational signals for three reasons. First the market participants do not correctly anticipate the economic value of FTRs and add them an excessive risk premium [START_REF] Siddiqui | Efficiency of the New York Independent System Operator Market for Transmission Congestion Contracts[END_REF]. Second the FTRs are allocated assuming the system operation is simpler than in reality (O'Neill et al., 2006). These simplifications also distort the locational signals of FTRs [START_REF] Lesieutre | Convexity of the set of feasible injections and revenue adequacy in FTR markets[END_REF][START_REF] Joskow | Merchant Transmission Investment[END_REF]. Third lumpiness of transmission reinforcements depreciates the short locational signals from nodal pricing [START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. Long run locational signals must then complete the short run ones to overcome these three difficulties.

Long run network tariffs and coordination of investments

Different designs of network tariffs are possible. The simplest option of network tariff is called generation-spur only (CER, 2004). The generators are then required to pay only for the line that connects them to the network and not for any other lines of the network. This method has a weak theoretical efficiency. It only incentivises the generators to be close to the network. An efficient network tariff would incentivise the generator to locate plants while taking into account the available transmission capacity and the transmission upgrading that may be needed to accommodate them. However, at least half of the European TSOs apply generation-spur only [START_REF] Etso | Overview of transmission tariffs in Europe: Synthesis[END_REF].

The TSO can also implement network tariffs that vary between locations. These locational differences of tariff incentivise the generators to connect in areas where it does not create too much congestion or in areas where it relieves congestion [START_REF] Pérez-Arriaga | Guidelines on tariff settings[END_REF]. This paper studies such a network tariff called the average participation tariff. The average participation tariff allocates the cost of the network depending on the total use of the network by each generator. To calculate the network used by each generator, the power flows are traced from generation to load to identify the lines and the share of their capacity used by each generator to supply load. The tracing rule used to calculate the average participation tariff links the inflows and the outflows in each node such that the inflows equally distribute in the outflows as illustrated by fig. 1 [START_REF] Bialek | Topological generation and load distribution factors for supplement charge allocation in transmission open access[END_REF]. The flow through the node i is 100 MW. 40% come from line j-i and 60% from line k-i. The sharing principle states that the outflow of 70 MW of line i-m comes from 40% of the line j-i that is to say 28MW and from 60% of the line k-i that is say 42 MW. Similarly, the outflow of 30 MW of the line i-l comes from 40% on line j-i that is to say 12 MW and from 60% of the line k-i that is to say 18 MW.

Different approaches have been proposed to calculate the average participation tariff. [START_REF] Bialek | Topological generation and load distribution factors for supplement charge allocation in transmission open access[END_REF] proposes a matrix approach to calculate the average participation tariff. [START_REF] Kirschen | Contributions of individual generators to loads and flows[END_REF] proposes a graph approach where the network and the power flows describe an oriented graph. The cost allocation consists then in following the power flows from generators to consumers respecting the sharing principles. Other studies have applied the average participation tariff to real networks and compared the resulting network tariffs with other cost allocation principles [START_REF] Camacho | Diseño regulatorio de la actividad de transporte en mercado de electricidad regionales[END_REF][START_REF] Camacho | Comparison of several inter-TSO compensation methods in the context of the internal electricity market of the European Union[END_REF]. The coordination provided by the average participation tariff has never been studied from the point of the view of the investment dynamics [START_REF] Camacho | Diseño regulatorio de la actividad de transporte en mercado de electricidad regionales[END_REF][START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. The following sections aim at evaluating the efficiency of the average participation tariff to coordinate generation and transmission investments.

More generally, the following model evaluates the efficiency of different combinations of options to operate the system (redispatch and nodal pricing) and of network tariffs (no tariff1 or the average participation tariff).

Model of transmission and generation investment in a liberalised power system

In a liberalised power system where the TSO and the generator are unbundled, they both invest to maximize their own objective. However the transmission investments and the location of generation remain strongly interdependent. They must coordinate to maximize the social welfare. Locational signals implements this coordination.

The first part of this section presents the problem used to evaluate the efficiency of locational signals to coordinate generation and transmission investments. The second part of this section models for this simple case the objective function of the TSO and the generator to make investment decisions, and the interaction between the locational signals and their investment decisions.

Problem data

To evaluate the efficiency of the locational to coordinate the generation and transmission investments, the system of fig. 2 is studied for twenty years. Load has the five following characteristics. 1° It is located to the east. 2° Over the year, load is described by a linear load duration curve. 3° The first year, load varies between 1700 MW and 3400 MW. 4° Minimum and maximum loads increase by 2% each year. 5° It is inelastic. The last two assumptions about load are usual ones in investment planning.

Generation has the following characteristics. Base and peak plants (respectively indexed B and P) generate power. When the total generation capacity is not enough to supply demand, there is Energy Non Supplied (ENS). In the model, a plant located at the same node as load and with the same capacity as load stands for the ENS. This plant has a cost (C ENS ) of 10 000 €/MWh to reflect the economic loss of power for demand. The peak investments are decided by arbitrating between the opportunity to build a new peak plant and the opportunity to shed load and so to have a quantity of Energy Non Supplied [START_REF] Stoft | Power System Economics[END_REF].

The marginal cost of peak generation is 30 €/MWh. The investment cost of this generation type is 5.2 million euros 2 . The marginal cost of base generation to the east (indexed E) C BE is 18 €/MWh while to the west (indexed W) C BW is 18 €/MWh + ε, where ε is very small. Such a little difference ε between the base generation cost to the east and to the west avoids that there is an indetermination on the plant (to the west or to the east) that is first in the merit order. The generator can choose to invest in two types of base plants, both of them with a unit generation capacity Q B of 200 MW. The first type of base plants is located to the west and costs I BW . It is 5% cheaper than to locate a plant to the east with an investment cost I BE . The investment cost of a new base plant is 206 million euros to the east and 216 million euros to the west. But the plants to the west are far from load. Reinforcing the transmission network may then be needed to connect a plant to the west. The unit capacity of the network investment Q T is 400 MW and costs I T is 60 million euros. The generator can then have to pay for a share of the cost of the network if she connects to the west. The costs are discounted over years by a discount rate of 8%.

As load grows over time, the generator and the TSO could build no more than one investment each year for each type of investments. And these investments are lumpy with a capacity of (i.) 10 MW for a peak plant, (ii.) 200 MW for a base plant to the east, (iii.) 200 MW for a base plant to the west, or (iv.) 400 MW for a network investment. The initial transmission capacity is 2550 MW. The initial generation capacity of base plants is 2400 MW and the initial capacity of peak plants is 1000 MW.

The choice of marginal and investment costs for the base plants avoids that the decision to locate a plant modifies the energy mix (between base and peak plants and ENS), since this paper only focuses on the effect of short run and long run locational signals on the location of new plants. At the same time, the peak plant and the ENS give realism to our model. If there is congestion, the peak plants and the ENS substitute to base plants to the west.

General presentation of the model

The model measures the efficiency of different locational signals to coordinate generation and transmission investments in the liberalised power system. These investments must coordinate to minimize the social cost of the whole system.

In a vertically integrated utility, the location of generation obviously takes into account the constraints and the reinforcement projects of the network. Similarly, when reinforcing the network, the transmission investments of the integrated utility take into account not only the congestion cost but also the location of new plants. In a liberalised system, when the TSO and the generator are unbundled, the generator takes into account the network constraints and the network reinforcements to locate plants only through the short-run and long term locational signals if they are implemented. And the TSO reinforces the network to minimize the sum of the investment cost and of the congestion cost that result from the location of power plants.

The global problem of coordination between generation and transmission investments is split in four steps as shown on fig. 3.

The first step is the optimization problem of the system operation. The TSO operates the power system to minimize the short run generation cost while respecting the network capacity constraints. The TSO can send short-run locational signals depending on the implemented option to operate the system. Besides, the TSO uses this step to know the congestion cost. The subsection 3.3. presents this step of the model.

The second step deals with the long term optimization problem from the results of the system operation in the previous step. The TSO is assumed perfectly regulated and benevolent. She invests to minimize the sum of the network investment cost and the congestion cost. The TSO is also assumed to anticipate perfectly the generation investments. The subsection 3.4. presents this step.

In the third step, the TSO calculates the network tariffs. Depending on the implemented option, long term locational signals can then be sent. The subsection 3.5. presents this step.

The fourth and last step is the generation investment decision. The generator is assumed to have neither a short-run market power nor a long run one. Therefore, it is similar to consider a unique and benevolent generator or several competitive ones. To locate plants, the generator considers the locational signals from the system operation and the network tariffs. The generator is also assumed to anticipate perfectly the network capacity and the value of potential locational signals. The subsection 3.6. presents the problem of minimization of generation cost.

Model of system operation

This paper considers that only two options can be implemented to operate the power system. The system can be operated either by nodal pricing or with a one-price market followed by redispatch. This short-run step of the model calculates for each plant3 k the generated quantity S k . The constraints of the optimization problem are the maximal generation capacity max k S of each plant k, the balance between generation and load D. Depending on the option chosen to operate the system, these constraints may also include the maximal capacity F max of the unique transmission line in our example. C k is the short run generation cost function of each plant k. The generator is assumed to have no market power and bids in a competitive way. Transmission is assumed lossless. The generated quantities in a nodal market can be found solving the problem defined by the equations 1 to 4 [START_REF] Bompard | A comparative analysis of congestion management schemes under a unified framework[END_REF] and S* stands for these quantities.

( )      ∑ k k k S S C min (1) s.t. { } max 0 ; ; ; k k S S ENS P BE BW k ≤ ≤ ∈ ∀ (2) D S k k = ∑ (3) max F S BW ≤ (4)
If redispatch is implemented, the generator minimizes the generation cost under the constraints of its maximal capacity but without taking into account the network capacity constraints. Since the generator is paid or pays its marginal cost when redispatched, the redispatch does not change the profit maximization of the generator. Her profit is only related to the one-price energy market that precedes the redispatch step. The profit maximization of the generator when redispatch is implemented can be modeled by the equations 5 to 7 as follow. S** stands for the quantities that would be generated if congestion was not taken into account.

( )      ∑ k k k S S C min (5) s.t. { } max 0 ; ; k k S S P BE BO k ≤ ≤ ∈ ∀ (6) D S k k = ∑ (7)
Repeating the step of system operation for each hour h and each year y of the studied period, the TSO and the generator decide their investments.

Model of network investment

The TSO is assumed benevolent. She invests to minimize the sum of the network investment cost and the congestion cost [START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. Without market power from generators, this minimization is equivalent to the maximization of the social welfare for given generation investments (Pérez Arriaga-Smeers 2003). The TSO calculates the congestion cost for the studied period from the generated quantities S* k,y,h that take into account the network capacity constraints, and the generated quantities S** k,y,h that do not take into account these constraints. The quantities S* and S** are then deduced from the previous step.

The congestion cost CC y,h for an hour h of a year y is the sum for all the plants k of the variations in cost induced by the limited network capacity. The congestion cost can then be defined as follows:

( ) ( ) ( ) ∑ - = k h y k k h y k k h y S C S C CC , , , , , * * * (8)
For the two-node node network considered in this paper, the TSO increases the capacity of the unique transmission line to minimize the cost of investment and the congestion cost. The transmission investments are assumed lumpy and they all have the same capacity Q T . For each year y of the studied period, the decision variables of the network investment δ y are binary. If δ y equals one, the capacity of the line increases by Q T MW the year y. If δ y equals zero, the capacity of the line stays the same for the year y. Each network investment (with a capacity of Q T ) costs I T . The costs are discounted by a rate a.

The network investment problem for the TSO is the following one:

( ) ( ) ( ) ( ) ∑ ∑∑       - + + - y k h h y k k h y k k T y y S C S C I a y , , , , * * * 1 min δ δ (9)
Such that the system operation determines the generated quantities S* k,y,h that take into account congestion, and S** k,y,h that do not take into account congestion The solution of this optimization problem gives the moment when the network investments must be done given the congestion cost. The capacity of the line is calculated for each year y knowing the decision variables of network investment δ y . Assuming the initial transmission capacity of the line is F ini , the capacity F max,yc of the line for the year y c can be calculated as follows:

∑ = + = c c y y y T ini y Q F F 1 max, δ (10)
The constraints in the system operation then depend on network investment decisions. Because of vertical unbundling, the TSO can no more directly act on the location of generation. But she can influence it reinforcing the network and sending locational signals, especially long term ones.

Calculus of the average participation tariff

This paper considers only two options for the network tariff. When the first option is implemented, the generator does not pay any network tariff. When the second option is implemented, the generator pays an average participation tariff.

In the considered example, the average participation tariff can be easily calculated. The flow tracing is obvious because there is only one line. Only the power plants to the west use the transmission network to supply load to the east. Only these plants to the west pay a network tariff. The level of the tariff is calculated in three steps. The average participation tariff is calculated from the Maximum Allowed Revenue (MAR) and the MAR is calculated using the equations 11 to 13 [START_REF] Joskow | Incentive regulation in theory and practice: electricity distribution and transmission network[END_REF].

First, the Regulated Asset Base (RAB) is calculated from one year to another taking into account the investments of the last year and the depreciation of the existing lines that are not still completely depreciated.

RAB(n) = RAB(n -1) -Annuities(n -1) + Investments(n -1) (11)

The depreciation annuity is a simple division of the investment cost by the depreciation period decided by the regulator.

Annuity = Investment cost / Depreciation period (12)
For the considered two-node network, the depreciation annuity is calculated assuming that the new network investments are depreciated over forty years and the initial transmission capacity is depreciated over thirty years from the beginning of the study.

The MAR is calculated from the depreciation annuities, from the RAB and from the return on investment4 . In the present case, the return on investment WACC 5 is assumed to be equal to 7,5%.

MAR(n) = RAB(n) x WACC + Annuities(n) (13)
The average participation tariff is calculated from the MAR. Moreover, to allocate optimally the cost of transmission lines, only the cost of the used share of lines should be allocated to the users responsive to the locational signals. To the contrary, the cost of the unused share of lines should be allocated to the users the less sensitive to locational signals since the unused share of the line is linked to the lumpiness of the transmission capacity [START_REF] Pérez-Arriaga | Guidelines on tariff settings[END_REF]. These users of the network are a priori those that are already little responsive to price signals, that is to say consumers. As a result, the power plants that use the network are assumed to pay only 50% of the cost of the used share of the transmission capacity.

The calculation of the tariff has just been presented. Previous subsections modeled the objective function of the TSO and the main options of system operation. The following subsection presents the objective function of the generator.

Model of generation investment

The generator is assumed to have no market power. The objective of profit maximization is then similar to cost minimization. The generator invests in order to minimize the sum of short run generation cost and generation investment costs and of the network tariff.

As seen in 3.3, the generation operation cost can take into account congestion or not depending on the chosen option to operate the system. As seen in 3.5, the generator can also have to pay an average participation tariff, depending on the chosen option for network tariff and on its location.

To invest, the generator arbitrates between these two costs and the generation investment cost. The generation investments are assumed lumpy. The unit capacity of the base (respectively peak) investments is Q B (resp. Q P ). For each year y of the studied period, the decision variables of the generation investment δ k,y are binary. If δ k,y equals one, the generation capacity of the plant k increases by Q MW6 the year y. If δ k,y equals zero, the generation capacity of the plant k stays unchanged the year y. The investment cost of the plant k equals I k . The discount rate is a. Then the generation investment problem is as follows:

( ) ( ) ∑ ∑ ∑             + + + - y k h h y k k y k k y k y S C Tarif I a y k , , , , 1 min , δ δ (14)

Such that the system operation determines the generated quantities S k,y,h

The solution of this problem gives the moment when and the location where the generator must invest. The capacity of a generation plant k can be calculated for each year y from the decision variables of this investment δ k,y . Assuming the initial generation capacity of the plant k is S ini,k , the capacity S k,max,yc of this plant for the year y c can be calculated as follows:

∑ = + = c c y y y k k ini y k Q S S 1 , , , max, δ (15)
The constraints for the system operation then depend on generation investment decisions. The fundamental elements of the coordination problem are now defined. The following subsection models how they interact. Sauma-Oren (2006a, b) assume the investment decisions for generation and transmission are sequential with a priority given to the generation investments. With their assumption, the TSO must reinforce the network taking into account the investment decisions of generation.

Interaction between locational signals and transmission and generation investments

However, it is interesting to consider situations where the TSO cannot invest. It is a current situation because of the oppositions to building of new power transmission lines. In such situation, the generators must adapt the location of their new plant to supply load despite the network constraints.

As a result, we made no assumption about generation or transmission investing sequentially first. Different equilibriums can then be observed for the problem of generation and transmission investments in the liberalised power system. This assumption of non-sequential investments allows to highlight non-linear effects of network tariffs and of transmission capacity lumpiness7 .

The problem of coordinating generation and transmission investments is then a double minimization, respectively of the objective function of the TSO and of the generator, as follows: This optimization problem has three important features. First the investment variables are binary. Second the calculation of the tariff is an average one. These two first features create nonconvexity. Lastly, this problem is a double optimization. These features prevent us from solving this problem with analytical tools. That's why the equilibrium conditions of this problem are studied with numerical simlations. A genetic algorithm fits particularly well to solve investment problems in the power system [START_REF] Latorre | Classification of publication and models on transmission expansion planning[END_REF] and to solve a double optimization problem such as ( 18) by search of dominant point [START_REF] Srinivas | Multiobjective optimization using non-dominated sorting in genetic algorithm[END_REF].

( ) ( ) ( ) ( ) ( ) ( )              + + +       - + + ∑ ∑ ∑ ∑ ∑∑ - - yt k h h y k k y k k y k y y k h h y k k h y k k T
To define a set of dominant points, the following double optimization problem is deemed, ,

y k y δ δ if ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )      < ≤ ≤ < § , § * , * § , § * , * § , § * , * § , § * , * , , , , , , , ,
y k y y k y y k y y k y y k y y k y t y yt y k y G G and F F or G G and F F δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ (18)
The dominant points dominate all the other possible points in the meaning of ( 18). The set of dominant points is called the Pareto Front and they are the different equilibriums solutions to the problem of double optimization (17). Since the two criteria we want to optimize are contradictory, there exist several equilibriums. The example on fig. 4 illustrates such a situation, where the x-axis and the y-axis respectively stand for the value of the function F and G for the points ( )

y k y , ,δ δ . The
Pareto front is the set of points that are the nearest to the bottom left corner of fig. 4, that is to say the clear squares. The following section evaluates with this algorithm the efficiency of short run and long run locational signals to coordinate the generation and transmission investments on the example of a two-node network.

Results and analyses

This section presents the results and analyses of the simulations. First the generation and transmission investments of a benevolent integrated utility, her achieved coordination and social cost define a benchmark. Second this benchmark is compared to the social cost and the coordination achieved in a liberalised system where locational signals coordinate generation and transmission investments.

Benchmark of a benevolent integrated utility

The efficiency of locational signals is measured and compared to the optimal investment strategy of a benevolent integrated utility as a benchmark. Such a utility minimizes the total cost of the power system, that is to say the sum of the network investment cost, the generation investment cost and the short-run generation cost under the constraints of the network capacity.

( ) ( ) ∑ ∑ ∑             + + + - y k h h y k k k y k T y y S C I I a y k y , , , , * 1 min , δ δ δ δ (19)

Such that the system operation determines the generated quantities S* k,y,h

With the data presented in section 2., the social cost of the optimal solution of this problem is 6.05 billion euros8 . The most efficient location of generation is to the east near load.

System equilibrium without locational signals

To analyze the efficiency of locational signals to coordinate generation and transmission investments, the worst case is studied first, when neither short run locational signals nor long run ones are implemented. Congestion is managed with redispatch and the generator pays no network tariff.

Each equilibrium is characterized by the value that the objective functions of the TSO and the generator take. Each equilibrium is then positioned in the plan defined by these two objective functions (fig. 5). There are multiple equilibriums for this double minimization because the cost of the network can decrease if the generation cost ingeniously increases9 . This happens because the generator is not informed of the transmission cost her locational decision induces. The equilibrium circled at the bottom of fig. 5 is the same investment strategy as the optimal one. This equilibrium has the smallest cost of the network. The social cost of the other equilibriums is greater than the social cost of the optimum. In a liberalised system, the generator wants to minimize her costs. This equilibrium is the point the more to the left on fig. 5.

The locational signals coordinate efficiently generation and transmission when they penalise sufficiently the generator if she does not locate in accordance with the social cost minimization. For the generator to take optimal investment decisions, the suboptimal generation investments must be more expensive to her than the optimal ones. The locational signals must lead the suboptimal points to the right of the system optimum, in the hatched part of fig. 5. The effect of nodal pricing to coordinate the generation and transmission investments is now studied.

Efficiency of nodal pricing to coordinate generation and transmission

In this sub-section, the generator pays nodal pricing but no network tariff. As previously, the equilibriums of this problem are positioned in a plan defined by the objective function of the generator for the x-axis and by the objective function of the TSO for the y-axis. To evaluate the effect of nodal pricing, these equilibriums are compared with those without locational signal in fig. 6. Fig. 6. Equilibriums of the investment problem in a liberalised system without tariff.

Comparison of the equilibriums with and without nodal pricing.

The equilibriums reached with redispatch are the clear squares whereas those reached with nodal pricing are the dark crosses. Fig. 6 shows that only one of the suboptimal equilibriums with redispatch loses its quality of equilibrium when it is evaluated with nodal pricing. It is the only cross that is not inscribed in a circle.

The arrows between the equilibriums with redispatch and with nodal pricing stand for the effects of nodal pricing on the cost for the generator. Fig. 6 shows also that nodal pricing penalises the generator for all the equilibriums except for the optimal one (where there is no congestion givent the transmission investment in this case). The penalties are too small because all the equilibriums with redispatch except one are still equilibriums with nodal pricing.

Fig. 6 shows also that nodal pricing does not eliminate preferentially the equilibrium with the highest cost of the network. Nodal pricing penalises weakly this equilibrium. Lumpiness of the transmission capacity creates this effect. For this investment strategy, the generator builds all her base plants to the west far from the load. The TSO is forced to increase the transmission capacity. And the lumpiness of these network investments decreases the difference in nodal pricing so that the generator faces no price difference. The generator is then only partially informed of the consequences of her behavior, which induce network investment costs. For this example, we can conclude that nodal pricing poorly coordinates the location of generation and lumpy transmission investments. The two following subsections analyze now if long term locational signals increase coordination between generation and transmission investments.

Efficiency of the average participation tariff to coordinate generation and transmission

In this subsection, the generator must pay for the network she uses through the average participation tariff, whether there is congestion on the network or not. To analyze the effect of the average participation tariff, the system is first assumed to be operated with redispatch.

To evaluate the coordination reached with the average participation tariff, the related equilibriums are positioned in the same plan as before (objective function of the generator for the xaxis and objective function of the TSO for the y-axis -fig. 7). These equilibriums can then be compared with those without average participation tariff. The equilibriums reached with redispatch and without average participation tariff are the clear squares whereas those reached with redispatch and average participation tariff are the dark triangles. Fig. 7 shows that every investment strategy without the average participation tariff remains equilibrium with average participation tariff. The average participation tariff then fails in incentivising an efficient location of the generator, although with average participation tariff the inefficient equilibriums are now very close to the point where the generator finds it less profitable to choose these investment strategies.

The system is now assumed to be operated with nodal pricing and the generator must pay the average participation tariff for the power plant far from load to the west. To evaluate the coordination reached when nodal pricing and the average participation tariff are jointly implemented, the related equilibriums are positioned in the same plan as before and compared with the equilibriums calculated previously. The equilibriums reached with nodal pricing and without average participation tariff are 'x' crosses whereas those reached with nodal pricing and average participation tariff are '+' crosses.

Previously, we have shown that the implementation of one locational signal is not sufficient. Whereas now, fig. 7 shows that the joint implementation of nodal pricing and the average participation tariff constraints the generator to choose the generation investment strategy that minimizes the social cost. Therefore, the implementation of the short run and long run locational signals optimally coordinates the transmission and generation investments in this case.

A case of inefficient location of generation caused by the average participation tariff

The average participation tariff can also lead to inefficient location of generation in some particular situations. Consider a case where the initial transmission capacity is not 2550 MW anymore but 2700MW without modifying the other data of the problem. The optimal social cost (if a benevolent integrated utility were investing) is then 6.04 billion euros10 . The optimal set of generation and transmission investments is then the following one. The efficient location of generation is to the east, near load, except for the first investment of a base plant and no transmission is needed. Fig. 8. shows why this is the optimal set of generation investments. The initial transmission capacity is 2700 MW while the initial generation capacity to the west far from load is 2400 MW. As a consequence, there are 300 MW of available transmission capacity. It is a sufficient capacity to transmit generation of only one new base plant with a unit capacity of 200 MW (fig. 8.a. and b.). For the following generation investments, the investment cost is greater to the east than to the west. But the location of generation to the west would require to reinforce the network to ensure that generation can supply load. As a result, it is cheaper to locate generation near load (Fig. 8.c. and d.).

Consider now the same system when transmission and generation are unbundled. To evaluate the coordination reached with the average participation tariff in this case, the equilibriums of the investment problem are positioned in the same plan as before (objective function of the generator for the x-axis and objective function of the TSO for the y-axis -fig. 9). These equilibriums can then be compared with those without average participation tariff11 . The clear squares stand for the equilibriums with redispatch and without tariff. When the average participation tariff is implemented, the equilibriums become the dark triangles. And the circled triangles are the points that form part of the Pareto front in this case. The arrows between the equilibriums without tariff and those with the average participation tariff illustrate the effect of the network tariff on the cost for the generator.

When the generator pays the network tariff, there are only two equilibriums left, represented by the circled triangles on fig. 9. The three other equilibriums without tariff are no more equilibrium with the average participation tariff. Either the tariff makes these generation investment plans more expensive than those corresponding to the global optimum or the equilibriums with tariff now dominate the equilibriums corresponding to these generation investment plans. Fig. 9 shows that the average participation tariff generally incentivises the generator to invest near load, but not sufficiently in some situations. This simulation shows also that it is not sufficient to focus only on the equilibrium that minimizes the objective function of generator. Of course, this equilibrium without tariff is not an equilibrium anymore with tariff. But the tariff does not ensure that the generator chooses the generation investments that lead to the global optimum of the system. Besides, the equilibrium of lowest cost (dashed circled on fig. 9) does not correspond to the optimum reached by the benevolent integrated utility, because the network tariff penalises unfortunately the generator for the optimal generation investment. All the optimal base plant investments locate to the same node as load, except the first one because at the beginning of the studied period 300 MW of transmission capacity are available (fig. 8). But, the equilibrium of lowest cost when generation and transmission are unbundled does not correspond to the optimal investment plans, because the generator does not realize this first investment far from load. This investment far from load would be more expensive to her than to locate all her base plants to the same node as load. Locating one plant far from load would indeed force her to pay the network tariff. Of course, the network tariff improves the coordination between generation and transmission investments. But, there is no guarantee that it allows to reach the optimum of the system.

Conclusion

To show the interactions between the locational signals and the generation and transmission investments, this paper modeled a system where a TSO and a generator are unbundled and maximize their objective functions. The TSO upgrades the network to minimize the sum of the congestion cost and the investment cost, since she is perfectly regulated. The generator minimizes the sum of the investment cost, the short run generation cost taking into account network capacity constraints or not and the network tariffs she may have to pay.

Numerical simulations showed that the locational signals coordinate the generation and transmission investments with a variable efficiency because of lumpiness of transmission investment. The nodal pricing is seldom sufficient to coordinate the generation and transmission investments because lumpiness of transmission investment greatly decreases the differences in nodal prices that should signal congestion. The implementation of the average participation tariff does not ensure that the generation and transmission investments is eventually optimal, because it is hard to take into account the lumpiness of transmission investment while respecting cost reflectivity. The average participation tariff then includes lumpiness only imperfectly. But implementing this tariff signicatively improves the coordination between generation and transmission investments. The joint implementation of nodal pricing and the average participation tariff stays the best combination to coordinate as efficiently as possible the generation and transmission investments. The simulations show also that implementing locational network tariffs is prioritary over implementing nodal pricing to coordinate more efficiently the location of generation with lumpy transmission investment. In the considered examples, the average participation tariff allows a more efficient location of generation even when the congestion management scheme is redispatch.

Future researchs will have to confirm the results of this work. First one could extend the study of average participation tariff on larger and meshed network. One could then precise the effect of parallel flows in the coordination process between the location of generation and lumpy transmission investments. Besides, one could reproduce the work of this paper to study the interaction between investments and the marginal participation tariff, which is the network tariff applied in Great Britain (Green, 1997b). One could also compare the efficiency of average and marginal participation tariffs to extend the existing comparisons of these network tariffs [START_REF] Camacho | Diseño regulatorio de la actividad de transporte en mercado de electricidad regionales[END_REF][START_REF] Camacho | Comparison of several inter-TSO compensation methods in the context of the internal electricity market of the European Union[END_REF]. Moreover, to make the behavior of generators more realistic, one could consider market power and model the difficulty that they may feel to evaluate the evolution of nodal prices after investment of lumpy transmission capacity. One should also consider other investment situtations where the location of generation modifies not only the investment cost but also the marginal generation cost. Lastly, to exemplify the effect of network regulation, one should modify the objective function of the TSO to cost-of-service regulation or to implementable incentive regulation schemes [START_REF] Stoft | Problems of transmission investment in a deregulated power market[END_REF]. One could then evaluate the impact of regulation on the coordination between generation and transmission investments.

Fig. 1 .

 1 Fig. 1. Sharing principle.

Fig. 2 .

 2 Fig. 2. Modeled system.

Fig. 3 .

 3 Fig. 3. Box representation of the model.

  system operation determines the generated quantities S k,y,h

  where F and G respectively stand for the objective function of the TSO and of the generator in the present case.It is said that a point ( )

Fig. 4 .

 4 Fig. 4. Pareto front of a double minimization.

Fig. 5 .

 5 Fig. 5. Equilibriums of the investment problem in a liberalised system without locational signal.

Fig. 7 .

 7 Fig. 7. Equilibriums of the investment problem in a liberalised power system. Comparison of the equilibriums without tariff, with tariff, and with tariff and nodal pricing.

•

  Fig. 8. Optimal sequence of generation investments when the initial transmission capacity is 2700 MW

Fig. 9 .

 9 Fig. 9. Impact of the average participation tariff on the coordination between generation and transmission investments

The option with no tariff assumes that the generator is located exactly at the node where she must be connected. Then there is no need of a connection line.

For these numerical simulations, the data for the generation costs are similar to the data used byStoft (2002, page 124). The investment costs are then calculated assuming that the discount rate is equal to 8%.

Indexed BW for base investment to the west (far from load), BE for investment of base plant to the east (near load), P for investment of peak plant (to the east) and ENS for the Energy Non Supplied.

The regulator usually decides the return on investment.

Weighted Average Cost of Capital

Q being Q B or Q P depending on the plant k being a base or peak one.

The lumpiness of the generation investments induces nonlinearity too but to a lesser extent given the parameters of the numerical example (see 2.1.).

We obtain this result with a genetic algorithm too.

If the generator builds her base plants near load, her investment costs are greater but there is no need to reinforce the network.

This optimization was also realized with a genetic algorithm.

Only the equilibriums with redispatch are considered because there is no congestion on the transmission network, except a little one on one equilibrium only.