Emma Stepinac

Nicolas Landrein

Daria Skwarzy Nska

Patrycja Wo ´jcik

Johannes Lesigang

Iva Lu Ci C,

Cynthia Y He

Me ´lanie Bonhivers

Derrick R Robinson

Gang Dong
email: gang.dong@meduniwien.ac.at

Structural studies of the shortest extended synaptotagmin with only two C2 domains from Trypanosoma brucei

Extended synaptotagmins (E-Syts) localize at membrane contact sites between the endoplasmic reticulum (ER) and the plasma membrane to mediate inter-membrane lipid transfer and control plasma membrane lipid homeostasis. All known E-Syts contain an N-terminal transmembrane (TM) hairpin, a central synaptotagmin-like mitochondrial lipid-binding protein (SMP) domain, and three or five C2 domains at their C termini. Here we report an uncharacterized E-Syt from the protist parasite Trypanosoma brucei, namely, TbE-Syt. TbE-Syt contains only two C2 domains (C2A and C2B), making it the shortest E-Syt known by now. We determined a 1.5-A ˚-resolution crystal structure of TbE-Syt-C2B and revealed that it binds lipids via both Ca 2+ -and PI(4,5)P 2 -dependent means. In contrast, TbE-Syt-C2A lacks the Ca 2+ -binding site but may still interact with lipids via a basic surface patch. Our studies suggest a mechanism for how TbE-Syt tethers the ER membrane tightly to the plasma membrane to transfer lipids between the two organelles.

INTRODUCTION

Eukaryotic cells are compartmentalized into membrane-bound organelles, which are defined by their unique membrane lipid composition and specific functions. Membrane trafficking acts to transfer materials between organelles over long distances, whereas closely apposed membranes from two organelles can form membrane contact sites (MCSs) to exchange lipids between them without undergoing membrane fusion [START_REF] Hayashi | Cell-and stimulusdependent heterogeneity of synaptic vesicle endocytic recycling mechanisms revealed by studies of dynamin 1-null neurons[END_REF][START_REF] Lahiri | Membrane contact sites, gateways for lipid homeostasis[END_REF][START_REF] Levine | Inter-organelle membrane contact sites: through a glass, darkly[END_REF]. Extended synaptotagmins (E-Syts) are a family of evolutionarily conserved proteins localizing at the MCS between the endoplasmic reticulum (ER) and the plasma membrane and mediate lipid transfer between them [START_REF] Fernandez-Busnadiego | Three-dimensional architecture of extended synaptotagmin-mediated endoplasmic reticulum-plasma membrane contact sites[END_REF][START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF]. E-Syts belong to the tubular lipid binding (TULIP) superfamily. Proteins from this group contain hydrophobic tunnels in their TULIP domains and often function in lipid traffic and signaling by carrying lipids through the aqueous phase of the cell [START_REF] Beamer | Crystal structure of human BPI and two bound phospholipids at 2.4 angstrom resolution[END_REF][START_REF] Kopec | Bioinformatics of the TULIP domain superfamily[END_REF][START_REF] Qiu | Crystal structure of cholesteryl ester transfer protein reveals a long tunnel and four bound lipid molecules[END_REF][START_REF] Wong | Tubular lipid binding proteins (TULIPs) growing everywhere[END_REF]. The name of E-Syt derives from synaptotagmin (Syt), which is a protein anchored on the membrane of secretory vesicles and acting as a tether between the vesicles and their target sites during exocytosis [START_REF] Brose | Synaptotagmin: a calcium sensor on the synaptic vesicle surface[END_REF][START_REF] Elferink | A role for synaptotagmin (p65) in regulated exocytosis[END_REF][START_REF] Perin | Structural and functional conservation of synaptotagmin (p65) in Drosophila and humans[END_REF]. However, E-Stys differ from Syts in both their localization and function. E-Syts are present in plants, fungi, and animals [START_REF] Craxton | Evolutionary genomics of plant genes encoding N-terminal-TM-C2 domain proteins and the similar FAM62 genes and synaptotagmin genes of metazoans[END_REF][START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF][START_REF] Toulmay | A conserved membrane-binding domain targets proteins to organelle contact sites[END_REF]. There are three E-Syts, E-Syt1, 2 and 3, in mammals [START_REF] Min | E-Syts, a family of membranous Ca2+-sensor proteins with multiple C2 domains[END_REF]. These E-Syts all have two tandem hydrophobic helices at their N terminus, which form a transmembrane (TM) hairpin anchoring them within the ER membrane [START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF]. The E-Syts also contain a central SMP (synaptotagminlike mitochondrial-lipid binding protein) domain and five (E-Syt1) or three (E-Syt2 and 3) C2 domains at their C terminus [START_REF] Min | E-Syts, a family of membranous Ca2+-sensor proteins with multiple C2 domains[END_REF]. The first two C2 domains, C2A and C2B, of human E-Syt2 (HsE-Syt2) form a rigid V-shaped conformation, with only C2A capable of binding Ca 2+ [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF]. HsE-Syt2 also forms a homodimer via its SMP domain, which generates a hydrophobic tunnel along the dimer for lipid binding and transfer between the ER and the plasma membrane [START_REF] Schauder | Structure of a lipid-bound extended synaptotagmin indicates a role in lipid transfer[END_REF].

Trypanosomes are kinetoplastids that are thought to be one of the earliest branching lineages of eukaryotes [START_REF] Simpson | The evolution and diversity of kinetoplastid flagellates[END_REF]. Consequently, they are among the most divergent eukaryotes on the planet.

Studies on conserved proteins in trypanosomes could thus help us understand the fundamental function and evolution of these proteins. Here we report our structural and functional characterization of a unique, single-copy E-Syt from Trypanosoma brucei.

Similar to all mammalian E-Syts, T. brucei E-Syt (TbE-Syt, Tb927.10.13740) is predicted to also have an N-terminal TM hairpin and a central SMP domain, which is a defining element of the E-Syt protein family. However, TbE-Syt contains only two C2 domains, which we named C2A and C2B based on their topological and structural similarities to their counterparts in mammalian E-Syts. We determined a 1.5-A ˚-resolution crystal structure of TbE-Syt-C2B, which revealed that it adopts a type II topology and has two tightly bound Ca 2+ ions. These Ca 2+ ions are coordinated by a few negatively charged residues from two extended loops. Additionally, the structure shows an extensive surface patch consisting of mostly basic residues. Our in vitro liposome-binding data demonstrated that TbE-Syt-C2B bound lipids via both Ca 2+ -dependent and phosphatidylinositol 4,5-bisphosphate [PI(4,5)P 2 ]-dependent means through these two sites. Homology modeling analyses showed that TbE-Syt-C2A lacks Ca 2+ -binding sites, which is distinct from the Ca 2+ -binding C2A in all mammalian E-Syts. However, TbE-Syt-C2A also contains a similar basic patch to that on TbE-Syt-C2B. Furthermore, our analyses suggest that TbE-Syt-C2A and C2B are connected by a flexible linker, which is also different from the rigid and compact V-shaped conformation of C2A-C2B in mammalian E-Syts. TbE-Syt localized to a specialized ER subdomain in T. brucei, and these distinct features of TbE-Syt may correlate with its functions there.

RESULTS

TbE-Syt localizes to the ER via its N-terminal transmembrane hairpin

The gene Tb927.10.13740 from T. brucei encodes a protein of 594 residues and was previously annotated as a putative synaptotagmin [START_REF] Aslett | TriTrypDB: a functional genomic resource for the Trypanosomatidae[END_REF]. Our preliminary bioinformatics analyses suggested that this protein contains two TM motifs (aa14À31 and 34-56), an SMP domain (aa100-280), and two C2 domains (C2A: aa290À420; C2B: aa474À594) (Figure 1A). Sequence alignment of homologs from various trypanosome species showed that all these domains, except for the first TM motif, are highly conserved, whereas the short N-terminal extension and the connecting loop between the two C2 domains are both divergent and variable in length (Figure 1B). Based on its similar overall domain organization to mammalian E-Syts and characteristic localization to the cortical ER revealed by our studies, we provisionally renamed this protein T. brucei E-Syt (TbE-Syt).

To assess the localization of TbE-Syt in T. brucei, we generated a cell line which inducibly overexpressed TbE-Syt-myc and domains and analyzed by western blotting (WB) the whole cell (WC) or the cytoskeletonassociated fraction of detergent-extracted cells (CSK). The expression level was different among the constructs preventing further WB quantitative comparison (Figures S1A andS1B). However, the analysis showed that both TbE-Syt (FL) and TbE-Syt deleted of the C2B domain (T1) co-purified with the CSK fraction, whereas both the C2B domain (T2) and the TM domain (T3) alone were only found in WC suggesting no or poor CSK association. Nevertheless, the TM domain is required for CSK association as TbE-Syt deleted of its TM (T4) or deleted of both TM and C2B domains (T5) were all soluble.

BiP, which is a molecular chaperone located in the ER lumen, was chosen as an ER marker (Bangs et al., 1993) (Figure 2A, panel a). Co-immunolabeling of BiP and TbE-Syt-myc demonstrated that TbE-Syt co-localizes with BiP at the ER with a Pearson's coefficient (PC) of 0.93 G 0.04 (Figures 2A,panel b,and S1C). Similarly, TbE-Syt-YFP also localized to the ER in the cell (Figure S2). The C2B domain was not involved in TbE-Syt localization as its deletion or mutation did not change the ER localization of the protein (the PCs were 0.89 G 0.06 and 0.89 G 0.10 for T1 and mutC2B, respectively) (Figures 2A,panel c,and S1C,T1 and mutC2B). As expected, when C2B was expressed alone, it was cytosolic (Figures 2A,panel d,and S1C,T2). Notably, although the TM alone co-localized with BiP at the ER (PC 0.96 G 0.02), it disappeared in the extracted cytoskeletons (Figures 2A,panel e,and S1C,T3). Conversely, the construct lacking the TM was completely cytosolic (Figures 2A,panel f).

Besides the central ER that is connected to the nuclear envelope, the same as in canonical eukaryotes, trypanosomes have an extra unique flagellar attachment zone (FAZ)-associated cortical ER [START_REF] Sherwin | The cell division cycle of Trypanosoma brucei brucei: timing of event markers and cytoskeletal modulations[END_REF][START_REF] Vickerman | On the surface coat and flagellar adhesion in trypanosomes[END_REF]. In detergent-extracted cells (i.e., cytoskeletons), labeling of full-length TbE-Sytmyc remained along the flagellum up to the anterior end of the cell body (Figure S1C) and was detected in the cytoskeleton fraction by WB (Figure S1B). We therefore further checked whether TbE-Syt localizes to the FAZ-associated ER using another T. brucei cell line stably expressing C-terminally YFP-tagged TbE-Syt. Two antibodies, anti-PFR2 (L8C4) and anti-FAZ1 (L3B2), were chosen to mark the whole flagellum and the FAZ, respectively [START_REF] Gadelha | Cryptic paraflagellar rod in endosymbiont-containing kinetoplastid protozoa[END_REF][START_REF] Kohl | Assembly of the paraflagellar rod and the flagellum attachment zone complex during the Trypanosoma brucei cell cycle[END_REF]. Our immunofluorescence data showed that TbE-Syt overlapped with PFR2 along the flagellum, but the signal did not reach the flagellar tip (Figure 2B). TbE-Syt overlapped with FAZ1 along the entire FAZ, however (Figure 2C). This is consistent with the FAZ localization of TbE-Syt reported in a high-throughput screening database where the majority of C-terminally mNeonGreen-tagged TbE-Syt was observed in the FAZ area, with some weak signals forming reticulated patches in the cytoplasm [START_REF] Dean | TrypTag.org: a trypanosome genome-wide protein localisation resource[END_REF] (Figure S3).

To further verify its association with the ER, we checked TbE-Syt localization at the ultrastructural level by immuno-gold labeling. The results showed that TbE-Syt localized to both the FAZ-associated ER beneath the flagellum and the central ER around the nuclear envelope (Figure 2D). Overall, our data confirm that TbE-Syt localizes primarily to the FAZ-associated ER in T. brucei, and correct localization is mainly mediated by its N-terminal TM domains.

Homology modeling suggests that TbE-Syt-SMP is capable of binding lipids

The SMP domain is the signature element of all E-Syts. However, none of the TbE-Syt constructs containing the SMP domain we generated produced soluble recombinant protein, which prevented us from carrying out in vitro biochemical and structural studies on this critical domain. To understand the structure and function of TbE-Syt-SMP, we turned to bioinformatics analyses to generate a homology model for it. The top hit (B) Sequence alignments of TbE-Syt homologs from various trypanosome species. Boundaries of the predicted domains are marked by arrows above the sequences with the same color schemes as in (A). The alignments were carried out using the option of ''Muscle with defaults'' in Jalview, with shading indicating the degree of conservation.

identified by the protein structure homology-modeling program SWISS-MODEL Workspace [START_REF] Waterhouse | SWISS-MODEL: homology modelling of protein structures and complexes[END_REF] was the crystal structure of the SMP domain of HsE-Syt2, which was solved to 2.4 A ˚resolution with bound phospholipids (PDB: 4P42) [START_REF] Schauder | Structure of a lipid-bound extended synaptotagmin indicates a role in lipid transfer[END_REF]. We chose this crystal structure, which shares 20.45% identity with TbE-Syt-SMP, as the template for our homology modeling (Figures 3A andS4A).

The resulting homodimeric model was of high quality based on the confidence evaluation and local similarity to the template (Figures S4B andS4C). Superimposing the TbE-Syt-SMP model onto the template structure of HsE-Syt2-SMP showed an excellent agreement (Figure 3B). The homodimeric TbE-Syt-SMP model, which was generated using the quaternary structure prediction option of SWISS-MODEL [START_REF] Bertoni | Modeling protein quaternary structure of homo-and hetero-oligomers beyond binary interactions by homology[END_REF] with lipids extracted from the superimposed template structure, predicted that the lipid molecules would bind in a deep cleft between the long a helix and the edge of the extended b sheet (Figure 3C). This cleft consists almost exclusively of hydrophobic residues that are highly conserved in all trypanosomes, which suggests that TbE-Syt-SMP has the capability of binding lipids in a similar fashion to the SMP domain of HsE-Syt2 (Figures 3D and3E).

The TbE-Syt C2B domain contains a conserved Ca 2+ -binding site

In contrast to mammalian E-Syts that have at least three C2 domains, TbE-Syt contains only two C2 domains. To further characterize the structure and function of TbE-Syt, we first determined a crystal structure for its C2B domain (Figure 4A). The structure was solved to 1.5 A ˚resolution using the selenium single-wavelength anomalous diffraction de novo phasing method (Table 1). There are two molecules per asymmetric unit, both of which contain aa474-594 of TbE-Syt. The two molecules are essentially identical, with an average root-mean-square deviation (RMSD) of 0.25 A ˚for all aligned backbone atoms.

The structure showed that TbE-Syt-C2B adopts a type II topology, consisting of eight b strands that form two sheets and a short a helix in the loop connecting b6 and b7 (Figure 4B). Additionally, there are two tightly bound Ca 2+ ions, which are coordinated by a few charged residues in two extended loops on the opposite end from the helix (Figure 4C). The interaction is mediated by a network of hydrogen bonds between the Ca 2+ ions and the side-chain oxygens of residues E492, D498, D545, and N547, which are all highly conserved in trypanosomes (Figure 4D). The main-chain carboxyl oxygens of residues V496 and K546 also form hydrogen bonds with either of the two Ca 2+ ions. Additionally, there are four stably bound water molecules hydrogen bonded to these two Ca 2+ ions (Figure S5).

TbE-Syt-C2B binds lipids in both Ca 2+ -and PI(4,5)P 2 -dependent manners

Similar to the Ca 2+ -binding site in the C2A domain of HsE-Syt2, TbE-Syt-C2B also has an extremely acidic ''crater'' on its surface (Figure 5A). Previous studies showed that the C-terminal C2 domain of mammalian E-Syt2 and E-Syt3 interacts with the plasma membrane via a basic surface patch [START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF]. In the TbE-Syt-C2B structure there is also a basic patch on b2 and b3, which contains residues K502 and K511 at its center (Figure 5B). Additionally, there is a highly conserved aromatic residue, Y500, at the deepest point of this curved patch. Both the basic patch and the conserved Y500 residues are reminiscent of the C2 domain of PKCa that associates with PI(4,5)P 2 via a similar basic patch [START_REF] Guerrero-Valero | Structural and mechanistic insights into the association of PKCalpha-C2 domain to PtdIns(4,5)P2[END_REF].

To check whether TbE-Syt-C2B interacts with lipids through either or both the Ca 2+ -binding site and the basic patch, we generated two types of mutations. In one mutant, we abolished Ca 2+ binding by mutating residues E492 and D498, which are simultaneously hydrogen bonded with both Ca 2+ ions, to alanine (E492A/D498A). In another mutant, we changed the two lysine residues at the center of the basic patch to opposite charges, i.e., K502E/K511E. Additionally, we generated a combined mutant for all these residues, E492A/D498A/K502E/K511E.

We used in vitro liposome binding assays to investigate whether TbE-Syt-C2B binds liposomes and, if so, whether any of the mutants affect this interaction. Purified wild-type and mutant proteins were incubated with sucrose-loaded vesicles containing different molar ratios of lipids and pelleted at high speed to separate the liposome-bound and unbound fractions of the proteins. SDS-PAGE analyses of the supernatant (unbound) and pellet (liposome-bound) fractions showed that wild-type TbE-Syt-C2B bound liposomes very weakly in the absence of both Ca 2+ and PI(4,5)P 2 (Figure 5C, WT: lane 4). However, addition of either Ca 2+ or PI(4,5)P 2 to the reaction showed robust binding (Figure 5C, WT: lanes 6 and 8). Notably, protein bound to liposomes was slightly more abundant when both Ca 2+ and PI(4,5)P 2 were present (Figure 5C, WT: lane 10). The mutant E492A/D498A abolished only the Ca 2+ -dependent lipid binding, but not PI(4,5)P 2 -mediated binding (Figure 5C, lane 6 versus lane 8). Interestingly, addition of Ca 2+ abolished the PI(4,5)P 2 -mediated liposome binding of this mutant even though PI(4,5)P 2 was present on the liposomes (lane 10). This was probably because excessive Ca 2+ ions would bind to the negatively charged head groups of PI(4,5)P 2 and thus shielded the interaction of the basic patch with the lipid. The converse effect was observed for the basic patch mutant (K502E/K511E), which retained the Ca 2+ -dependent liposome binding while completely losing PI(4,5)P 2 -lipid binding ability (Figure 5C, lane 6 versus lane 8). This indicated that TbE-Syt-C2B binds liposomes in two different fashions. Indeed, only upon mutating both Ca 2+ -binding and the central basic patch residues (E492A/D498A/K502E/ K511E) was the liposome binding of TbE-Syt-C2B completely abolished. (D) Hydrogen bonds between the Ca 2+ ions and coordinating residues in TbE-Syt-C2B. The plot was generated using LigPlot+ [START_REF] Laskowski | LigPlot+: multiple ligand-protein interaction diagrams for drug discovery[END_REF]. See also Figure S5.

TbE-Syt-C2A lacks the Ca 2+ -binding site but retains the PI(4,5)P 2 -binding patch

Previous studies have shown that the C2A domain in all mammalian E-Syts binds Ca 2+ and is involved in lipid interaction [START_REF] Min | E-Syts, a family of membranous Ca2+-sensor proteins with multiple C2 domains[END_REF][START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF]. We wondered whether TbE-Syt-C2A functions similarly. We tried to express recombinant TbE-Syt-C2A, either alone or together with C2B, SMP, or both, but did not succeed in obtaining soluble proteins. We thus tried to understand its structure and function by homology modeling. One of the top hits recognized by SWISS-MODEL [START_REF] Waterhouse | SWISS-MODEL: homology modelling of protein structures and complexes[END_REF] was the crystal structure of HsE-Syt2-C2A (PDB: 4NPK) [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF], which shares $17% identity with TbE-Syt-C2A. High local similarity of the final model and consistent alignment of secondary structures between the model and the template suggested that it is a convincing homology model (Figures 6A andS6). Superimposing the TbE-Syt-C2A model onto the HsE-Syt2-C2A crystal structure also showed an overall very good agreement (Figure 6B). The previously reported crystal structure of HsE-Syt2-C2A contains three tightly bound Ca 2+ ions coordinated by six Asp residues from two connecting loops via an extensive hydrogen bond network. This site is responsible for the binding of HsE-Syt2-C2A to lipids [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF]. Surprisingly, close examination of the putative Ca 2+ -binding site of TbE-Syt-C2A in the superimposed structures revealed that five of the six Asp residues in HsE-Syt2-C2A are substituted by hydrophobic residues in TbE-Syt-C2A (Figure 6C). Consequently, the concave acidic patch for Ca 2+ binding present in HsE-Syt2-C2A (Figure 6D) was replaced by a saddle-like hydrophobic area in TbE-Syt-C2A (Figure 6E). This suggests that the C2A domain in TbE-Syt is unlikely to bind Ca 2+ .

Previous studies showed that C2A and C2B of HsE-Syt2 share a similar conformation [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF]. We superimposed the homology model of TbE-Syt-C2A onto the crystal structure of TbE-Syt-C2B and found that not only was their overall conformation very similar but also the PI(4,5)P 2 -binding site was present in both C2 domains (Figures 6F and6G). As shown above, we have found that TbE-Syt-C2B interacts with lipids in both Ca 2+ -and PI(4,5)P 2 -mediated fashions (Figure 5C). The highly conserved basic patch on TbE-Syt-C2A suggests that, despite lacking a Ca 2+ -binding site, it might be still involved in lipid binding via the PI(4,5)P 2 -dependent mode (Figure 6H).

TbE-Syt-C2A and C2B are connected by a long flexible loop

Previous structural studies revealed that the first two C2 domains, i.e., C2A and C2B, of HsE-Syt2 shares high structural similarities with each other [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF]. A high-resolution NMR structure of the last C2 domain of HsE-Syt2, i.e., C2C, has also been determined (PDB: 2DMG). We therefore compared the structure of TbE-Syt-C2B with that of the three C2 domains of HsE-Syt2. TbE-Syt-C2B adopts the same topology as HsE-Syt2-C2A and C2B, i.e., type II, whereas HsE-Syt2-C2C has a distinct type I topology (Figure S7A). Superimposing TbE-Syt-C2B onto each of the three C2 domains of HsE-Syt2 showed that it is very similar to HsE-Syt2-C2A and C2B, with average RMSDs of 1.05 A ˚and 0.75 A ˚, respectively, but substantially deviated from C2C, with an RMSD of 3.57 A ˚(Figures S7B andS7C). This further confirms that the C2A and C2B domains in TbE-Syt are equivalent to C2A and C2B of HsE-Syt2.

HsE-Syt2-C2A and C2B fold into a compact V-shaped conformation, which is stabilized by the antiparallel interaction of the C termini of the last b strands on these domains [START_REF] Xu | Structure and Ca(2)(+)binding properties of the tandem C(2) domains of E-Syt2[END_REF] (Figure 7A). Structural comparison with HsE-Syt2-C2A-C2B showed that the last b strands of both TbE-Syt-C2A and C2B are too short to allow similar inter-strand interaction between them (Figures 7B and7C). Therefore, the linker between TbE-Syt-C2A and C2B, which consists of 55 residues (aa419À473), likely forms a long flexible loop.

The predicted flexibility of the loop is supported by the folding analysis on TbE-Syt (Figure S8). Local dynamic state of each residue in TbE-Syt was quantitatively evaluated using ODiNPred, which uses a deep neural network trained on experimental NMR-derived Z scores and has been shown superior in predicting disordered loops [START_REF] Dass | ODiNPred: comprehensive prediction of protein order and disorder[END_REF]. ODiNPred strongly suggests that the region spanning aa418À474 in TbE-Syt is exclusively disordered (Figure S8A).

DISCUSSION

We report here our structural characterizations of an uncharacterized E-Syt from T. brucei. Our bioinformatics analyses showed that, similar to all known mammalian E-Syts, TbE-Syt also has two TM motifs at its N terminus and a central SMP domain (Figure 1). However, it contains only two C2 domains, in contrast to at least three C2 domains in all other reported E-Syts in animals, plants, and yeast [START_REF] Craxton | Evolutionary genomics of plant genes encoding N-terminal-TM-C2 domain proteins and the similar FAM62 genes and synaptotagmin genes of metazoans[END_REF][START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF][START_REF] Min | E-Syts, a family of membranous Ca2+-sensor proteins with multiple C2 domains[END_REF][START_REF] Toulmay | A conserved membrane-binding domain targets proteins to organelle contact sites[END_REF]. This makes TbE-Syt the shortest E-Syt identified to date. (H) Dual plots of TbE-Syt-C2A in the same orientation as (F). The putative Ca 2+ -binding site is hydrophobic and not able to bind Ca 2+ , the PI(4,5)P 2 -binding site is highly conserved. This suggests that TbE-Syt-C2A could potentially binds lipids in the PI(4,5)P 2 -mediated manner. See also Figure S6.

Despite testing several RNAi constructs, RNAi against TbE-Syt in both procyclic and bloodstream forms of T. brucei did not decrease the expression of the protein (data not shown), which prevented us from further analyzing its cellular function. Previous systematic high-throughput RNAi screening data showed that depletion of TbE-Syt had no significant effect in bloodstream form T. brucei, but deleteriously affected procyclic forms (Figure S9) [START_REF] Alsford | High-throughput phenotyping using parallel sequencing of RNA interference targets in the African trypanosome[END_REF]. This suggests that TbE-Syt might play a vital role under certain conditions. Indeed, whereas no severe defects were observed upon their deletion in many organisms [START_REF] Manford | ER-to-plasma membrane tethering proteins regulate cell signaling and ER morphology[END_REF][START_REF] Saheki | Control of plasma membrane lipid homeostasis by the extended synaptotagmins[END_REF][START_REF] Sclip | Extended synaptotagmin (ESyt) triple knock-out mice are viable and fertile without obvious endoplasmic reticulum dysfunction[END_REF][START_REF] Toulmay | A conserved membrane-binding domain targets proteins to organelle contact sites[END_REF][START_REF] Tremblay | Loss of all 3 Extended Synaptotagmins does not affect normal mouse development, viability or fertility[END_REF], some specific defects have been observed in yeast, plants, and animals [START_REF] Aguilar | The plasma membrane proteins Prm1 and Fig1 ascertain fidelity of membrane fusion during yeast mating[END_REF][START_REF] Levy | Synaptotagmin SYTA forms ER-plasma membrane junctions that are recruited to plasmodesmata for plant virus movement[END_REF][START_REF] Saheki | Control of plasma membrane lipid homeostasis by the extended synaptotagmins[END_REF]. It is noteworthy that orthologs of TbE-Syt show high synteny in all pathogenic trypanosomes, further suggesting that it is an important gene that has been conserved over evolutionary time.

It was shown previously that in other organisms, including yeast and mammals, E-Syts are selectively concentrated in the cortical ER adjacent to the plasma membrane. This localization can be either constitutive or under the control of the cytosolic Ca 2+ level [START_REF] Chang | Feedback regulation of receptorinduced Ca2+ signaling mediated by E-Syt1 and Nir2 at endoplasmic reticulum-plasma membrane junctions[END_REF][START_REF] Giordano | PI(4,5)P(2)-dependent and Ca(2+)-regulated ER-PM interactions mediated by the extended synaptotagmins[END_REF][START_REF] Idevall-Hagren | Triggered Ca2+ influx is required for extended synaptotagmin 1-induced ER-plasma membrane tethering[END_REF][START_REF] Manford | ER-to-plasma membrane tethering proteins regulate cell signaling and ER morphology[END_REF][START_REF] Toulmay | A conserved membrane-binding domain targets proteins to organelle contact sites[END_REF]. Our in vivo localization data showed that TbE-Syt localizes to both the central ER close to the nuclear envelope and the FAZ-associated cortical ER beneath the flagellum (Figure 2D). Localization to the central ER was mediated exclusively by the TM motifs as the TM region itself was sufficient to target to the central ER (Figures 2A andS1). However, the TM motifs alone did not localize to the FAZ area and, unlike other longer constructs including full-length and TM-SMP-containing TbE-Syt, were removed in the extracted cells (Figure S1C, T3 construct). It is noteworthy that most tagged TbE-Syts used in our studies were overexpression constructs, which often yield a much higher expression level than that of the endogenous proteins. Notably, the expression levels were also different among constructs, preventing quantitative comparison in WB and immunofluorescence experiments. Tube-like connections have been observed between the FAZ-associated ER and the central ER around the outer nuclear membrane [START_REF] Lacomble | Three-dimensional cellular architecture of the flagellar pocket and associated cytoskeleton in trypanosomes revealed by electron microscope tomography[END_REF]. At an elevated expression level, a fraction of TbE-Syt might also redistribute to the central ER through such tube-like connections. Notably, TbE-Syt has been independently found to localize to the FAZ area and associate with CIF1, a protein present at the distal tip of the newly assembled FAZ [START_REF] Zhou | The CIF1 protein is a master orchestrator of trypanosome cytokinesis that recruits several cytokinesis regulators to the cytokinesis initiation site[END_REF]. Therefore, under physiological conditions TbE-Syt likely localizes only to the FAZ-associated cortical ER apposed to the plasma membrane.

It was reported previously that inter-membrane lipid transfer by HsE-Syt2 is through its SMP domain as the carrier of phospholipids [START_REF] Schauder | Structure of a lipid-bound extended synaptotagmin indicates a role in lipid transfer[END_REF]. Homology modeling analyses showed that TbE-Syt-SMP has a similar deep hydrophobic cleft that could accommodate lipid molecules as in HsE-Syt2 (Figure 3). Similar to HsE-Syt2, the SMP of TbE-Syt could also form an end-to-end homodimer based on our bioinformatics analyses. Both the putative lipid-binding cleft in TbE-Syt-SMP and the hydrophobic dimeric interface are highly conserved in all trypanosome homologs, suggesting that TbE-Syt might employ a similar mechanism to carry and transfer lipids as that reported for HsE-Syt2.

We have determined a high-resolution crystal structure for the C-terminal C2 domain of TbE-Syt (Figure 4), which was designated as C2B based on its high structural similarity to HsE-Syt2-C2B (Figure S7). Our structure-based mutagenesis studies revealed that TbE-Syt-C2B bound lipids in both Ca 2+ -and PI(4,5)P 2dependent manners via an acidic patch and an extended basic patch, respectively (Figure 5). Although disruption of one site did not abolish lipid binding of the other, wild-type protein bound liposomes much more abundantly than either mutant that abolished one of the two binding sites. Therefore, the two sites seem to work cooperatively in lipid binding, similar to what was reported for C2 domains of Syt1 [START_REF] Li | Phosphatidylinositol phosphates as co-activators of Ca2+ binding to C2 domains of synaptotagmin 1[END_REF][START_REF] Radhakrishnan | The Ca2+ affinity of synaptotagmin 1 is markedly increased by a specific interaction of its C2B domain with phosphatidylinositol 4,5-bisphosphate[END_REF][START_REF] Van Den Bogaart | Phosphatidylinositol 4,5-bisphosphate increases Ca2+ affinity of synaptotagmin-1 by 40-fold[END_REF]. For TbE-Syt-C2A, homology modeling suggested that it lacks nearly all acidic residues at the putative Ca 2+ binding site. However, TbE-Syt-C2A retains a conserved basic patch similar to that on TbE-Syt-C2B (Figure 6). This suggests that TbE-Syt-C2A may use only the basic patch to interact with the negatively charged head groups of PI(4,5)P 2 enriched on the plasma membrane.

With only two C2 domains, TbE-Syt is the shortest E-Syt identified to date. This may correlate with the unique MCS between the FAZ-associated ER and the plasma membrane in T. brucei. The FAZ in trypanosomes forms an adhesion structure between the flagellar and the plasma membrane, with one portion of the FAZ filament tightly associated with the cortical ER [START_REF] Lacomble | Three-dimensional cellular architecture of the flagellar pocket and associated cytoskeleton in trypanosomes revealed by electron microscope tomography[END_REF][START_REF] Vickerman | On the surface coat and flagellar adhesion in trypanosomes[END_REF]. The specialized FAZ in trypanosomes makes the FAZ-associated ER in a close and constitutive contact with the plasma membrane. In such a case, a short tether like TbE-Syt would be sufficient to bridge the two apposed membranes to allow efficient lipid transfer between the FAZ-associated cortical ER and the plasma membrane. Furthermore, in contrast to other organisms, including yeast, plants, and animals, which all have several types of E-Syts, trypanosomes have only a single copy of E-Syt. This might also correlate with the specialized function of TbE-Syt at the MCS between the FAZ-associated ER and the plasma membrane in trypanosomes.

Based on the unique domain organization and distinct structure of TbE-Syt compared with mammalian E-Syts and Syt1 (Figure 8A), we propose a working model for how TbE-Syt might mediate lipid transfer between the cortical ER and the plasma membrane in trypanosomes (Figure 8B). Two TbE-Syt molecules form a homodimer through the end-to-end interaction of their SMP domains. The C2A domain is connected to the SMP via a short linker (aa280À290), which is predicted to be ordered by ODiNPred (Figure S8A). Consistently, homology modeling based on the crystal structure of HsE-Syt-SMP-C2A (PDB: 4NPK) generated a compact structure of TbE-Syt-SMP-C2A (Figure S8B). To generate MCSs between the ER and the plasma membrane, the dimeric TbE-Syt is first anchored on the ER membrane via the N-terminal TM domains. The two C2B domains at the distal end of the structure would make initial contact with the plasma membrane both via the acidic patch in a Ca 2+ -dependent manner and via the basic patch to interact with PI(4,5)P 2 . It is noteworthy that the basic residues (K502, K511) in the PI(4,5)P 2 -binding site on TbE-Syt-C2B are not as conserved as those acidic residues in the Ca 2+ -binding site in other trypanosome species (Figure 1B), suggesting that the Ca 2+ -binding site is the major and universal element for TbE-Syt-C2B to interact with the plasma membrane.

In contrast, the basic patch on TbE-Syt-C2A is highly conserved throughout all trypanosomes. Given that it lacks the Ca 2+ -binding site, TbE-Syt-C2A would dock onto the plasma membrane solely in a PI(4,5)P 2 -dependent fashion. Interestingly, the putative PI(4,5)P 2 -binding site in the homologous model of TbE-Syt-C2A is orientated inward facing the tubular SMP (Figure 8B, left). In such case the hinge between the SMP and C2A domains would have to be partially opened to allow the exposure of the basic patch on the C2A domain to interact with the acidic head groups of PI(4,5)P 2 molecules on the plasma membrane. Notably, the linker connecting C2A and C2B contains a couple of conserved positively charged residues (Figure 1B), whereas high-throughput proteomics studies revealed six phosphorylation sites in this loop, i.e., S437, S441, S443, S447, S459, T460 [START_REF] Alsford | High-throughput phenotyping using parallel sequencing of RNA interference targets in the African trypanosome[END_REF]. These suggest that the linker between TbE-Syt-C2A and C2B may play a regulatory role in fine-tuning the interaction between TbE-Syt and the plasma membrane. Altogether, TbE-Syt could thereby tether and staple the FAZ-associated cortical ER onto the plasma membrane to allow the dimeric SMP domains, which could carry multiple lipid molecules in their hydrophobic clefts, to shuttle lipids originating from the ER membrane through their hydrophobic tunnels to the plasma membrane.

Figure 1 .

 1 Figure 1. Domain arrangement and conservation analyses of TbE-Syt (A) Schematic illustration of the predicted domains in TbE-Syt. Amino acids in primary structure are shown above the schematic.(B) Sequence alignments of TbE-Syt homologs from various trypanosome species. Boundaries of the predicted domains are marked by arrows above the sequences with the same color schemes as in (A). The alignments were carried out using the option of ''Muscle with defaults'' in Jalview, with shading indicating the degree of conservation.

Figure 2 .

 2 Figure 2. TbE-Syt localizes to the ER (A) TbE-Syt colocalizes with BiP at the ER via its N-terminal transmembrane domain. T. brucei procyclic form cells (parental, a) and those expressing various truncations of myc-tagged TbE-Syt (bÀf) were probed by immunofluorescence with BiP (red) and anti-myc (green) antibodies. Kinetoplasts and nuclei were stained with DAPI. Scale bar, 5 mm. (B and C) Cells stably expressing TbE-Syt-YFP were stained with DAPI for DNA and labeled with anti-PAR (a-PAR) antibodies for the entire flagellum (B) or with anti-FAZ1 (a-FAZ1) for the FAZ (C). Images were acquired with an LSM510 Meta confocal microscope. The tips of the FAZ and the flagellum are marked by arrows and arrowheads, respectively. Scale bars, 5 mm. (D) Immunogold labeling of TbE-Syt-YFP cells using anti-GFP antibodies. Gold particles were associated both with the central ER around the nuclear envelope (open arrowheads) and with the FAZ-associated ER beneath the flagellum (arrowheads). Scale bar, 200 nm. See also Figures S1-S3.

Figure 3 .

 3 Figure 3. Homology modeling of the SMP domain of TbE-Syt (A) Modeling of the SMP domain (aa100À280) by SWISS-MODEL using the crystal structure of HsE-Syt2 (PDB: 4P42) as the template. (B) TbE-Syt-SMP model (orange) superimposed onto the modeling template (marine). The lipid molecules in the HsE-Syt2 structure are shown as red sticks. (C) Inferred dimeric assembly of TbE-Syt-SMP based on the crystal structure of HsE-Syt2. (D) End view of TbE-Syt-SMP in (A) seen from the right side. The interior of the structure (purple circle) contains mostly hydrophobic residues. (E) Electrostatic surface of TbE-Syt-SMP in the same orientation as in (D). Lipid molecules extracted from the superimposed HsE-Syt2 structure are shown as orange sticks. All images were prepared using PyMOL. See also Figure S4.

Figure 4 .

 4 Figure 4. Crystal structure of the C2B domain of TbE-Syt (A) Ribbon diagram of the TbE-Syt-C2B crystal structure color-ramped from blue at the N terminus to red at the C terminus. Secondary structures and the two bound Ca 2+ ions (gray spheres) are labeled. The two molecules in the asymmetric unit are shown superimposed in the lower right corner. (B) Secondary structure diagram of TbE-Syt-C2B, with the residue ranges of each structural element indicated. (C) Stereo view of the 2Fo-Fc map around the Ca 2+ -binding site contoured at 2 s level. Electron densities around the Ca 2+ ions are highlighted in purple. The plot was produced using CCP4mg (McNicholas et al., 2011).(D) Hydrogen bonds between the Ca 2+ ions and coordinating residues in TbE-Syt-C2B. The plot was generated using LigPlot+[START_REF] Laskowski | LigPlot+: multiple ligand-protein interaction diagrams for drug discovery[END_REF]. See also FigureS5.

Figure 5 .

 5 Figure 5. TbE-Syt-C2B binds lipids using two distinct sites (A) Ribbon (left) and electrostatic (right) plots of the Ca 2+ -binding acidic patch in the TbE-Syt C2B domain. The three highly conserved acidic residues in the core of the patch are shown as sticks and labeled. Ca 2+ ions are omitted for clarity. (B) Side view of TbE-Syt-C2B with the two basic residues in the center of the positively charged patch labeled. (C) Liposome pelleting assays of wild-type (WT) and three mutants of TbE-Syt-C2B in the presence or absence of PI(4,5)P 2 and/or CaCl 2 . S: supernatant; P: pellet.

Figure 6 .

 6 Figure 6. Homology modeling of the TbE-Syt C2A domain (A) Modeling of TbE-Syt-C2A (aa290À420) by SWISS-MODEL using the homologous structure of the HsE-Syt2-C2A (PDB: 4NPK) as the template. (B) TbE-Syt-C2A model (cyan) superimposed onto the modeling template (yellow). The three Ca 2+ ions in the template structure are shown as pink spheres. (C) Close-up view of the Ca 2+ -binding site of the superimposed structures in (B). Residues in HsE-Syt2 coordinating Ca 2+ ions (pink spheres) are shown as orange sticks, and corresponding residues in TbE-Syt are shown as teal sticks. (D) Electrostatic plot of the Ca 2+ -binding site of HsE-Syt2, with the three Ca 2+ ions shown as labeled spheres. (E) Corresponding region in TbE-Syt-C2A in the same orientation as in (D) and with the same electrostatic scale. The putative Ca 2+ -binding site is mostly hydrophobic in TbE-Syt-C2A. (F) Superimposed ribbon diagrams of the C2A model and the C2B crystal structure of TbE-Syt. The three critical residues in the patches for PI(4,5)P 2 -mediated lipid binding are shown as sticks. (G) Electrostatic plot and ribbon diagram of TbE-Syt-C2B. Ca 2+ ions bind to the acidic patch at the top end, and the PI(4,5) P 2 -binding site is encircled in orange.(H) Dual plots of TbE-Syt-C2A in the same orientation as (F). The putative Ca 2+ -binding site is hydrophobic and not able to bind Ca 2+ , the PI(4,5)P 2 -binding site is highly conserved. This suggests that TbE-Syt-C2A could potentially binds lipids in the PI(4,5)P 2 -mediated manner. See also FigureS6.

Figure 7 .

 7 Figure 7. The C2A and C2B domains of TbE-Syt are connected by a long flexible loop (A) Ribbon diagram of HsE-Syt2-C2A-C2B (PDB: 4NPK), shown in two orientations. The anti-parallel interaction of the last b strand from both domains is indicated with a dashed oval in the lower orientation. (B) Ribbon diagrams of TbE-Syt-C2A-C2B in the same orientations as in (A). TbE-Syt-C2A is the homology model, and C2B is the crystal structure. H594 is the last residue at the C terminus of TbE-Syt. The last b strands in both TbE-Syt-C2A and C2B are much shorter than those in HsE-Syt2-C2A and C2B and thus not able to make an inter-strand interaction as in HsE-Syt2-C2A-C2B. The long flexible linker is shown as a dashed line. (C) TbE-Syt-C2A-C2B and HsE-Syt2-C2A-C2B as shown in (A) and (B), superimposed. See also Figures S7 and S8.

Figure 8 .

 8 Figure 8. Structural comparison and hypothetical working model of TbE-Syt in lipid transferring (A) Comparison of the domain arrangement of TbE-Syt and mammalian E-Syts and Syt1. All C2 domains in Syt1 bind Ca2+ , whereas only some of the C2 domains in the E-Syts bind Ca 2+ . TbE-Syt is distinct from all known mammalian E-Syt1, 2, and 3 in that it contains only two C2 domains. Furthermore, TbE-Syt-C2B binds Ca 2+ but TbE-Syt-C2A does not, which is the opposite of E-Syt1-3. (B) Hypothetical model illustrating how the ER-anchored TbE-Syt might attach to the plasma membrane via both Ca 2+and PI(4,5)P 2 -mediated interactions. This would tether the cortical ER to the plasma membrane to allow the lipid-carrying SMP dimer to shuttle lipids between the two apposed membranes. See also FigureS9.

Figure S1 .

 S1 Figure S1. Localization of TbE-Syt at the ER. Related to Figure 2. (A) Schematic representations of the C-terminally myc-tagged TbE-Syt constructs, including full-length (FL), mutC2B (E492A/D498A), and five truncations (T1-T5), expressed in procyclic form T. brucei. (B)Western blot analysis of the level of expression of TbE-Syt-myc constructs in whole cells (WC) and their association with the cytoskeleton in detergent-extracted cells (CSK). Anti-TbSAXO antibodies were used as a loading control. (C) Labeling of BiP and myc-tagged TbE-Syt, mutC2B, and truncations T1-T5 in whole cells (WC) and cytoskeletons (CSK). The kinetoplasts and nuclei were stained with DAPI. Scale bar, 5 µm.

Figure S2 .Figure S3 .

 S2S3 Figure S2. TbE-Syt-YFP localized to both the FAZ-associated ER and the central ER. Related to Figure 2. Note: YFP fluorescence (A) gave slightly weaker but sharper signals than anti-GFP immunofluorescence (B). Scale bar, 10 µm.

Table 1 .

 1 Data collection and refinement statistics

	Data collection
	Space group

a Values in parentheses are for the highest resolution shell.

Max Perutz Labs, Vienna Biocenter, Center for Medical Biochemistry, Medical University of Vienna, 1030 Vienna, Austria

iScience 24, 102422, May 21, 2021

iScience 24, 102422, May 21, 2021

ACKNOWLEDGMENTS

We thank Drs. K. Ersfeld, J. Bangs, K. Gull, and P. Bastin for the antibodies of anti-myc, anti-BiP, L8C4, and L3B2, respectively. We also thank Dr. J. Sunter for sharing the raw imaging data of TbE-Syt that initially appeared on the TrypTag.org website. We are grateful to the staff at the beamline of ID23-2 at the European Synchrotron Radiation Facility (ESRF) for their help with X-ray diffraction, to Y. Zhang for generating the

Data and code availability

The accession number for the crystal structure of TbE-Syt-C2B reported in this paper is PDB: 7A1R.

Limitations of the study

Although we have characterized the structure and membrane binding of the C2B domain of TbE-Syt, we could not express and purify its two other domains, i.e., SMP and C2A. This prevents us from revealing their atomic structures and carrying out lipid transfer assays as those previously reported for mammalian E-Syt2.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Gang Dong (gang.dong@meduniwien.ac.at).

Materials availability

All unique/stable reagents generated in this study are available from the lead contact without restriction.

METHODS

All methods can be found in the accompanying transparent methods supplemental file.

SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.isci.2021.102422.

AUTHOR CONTRIBUTIONS

G.D. and D.R.R. conceived the project. J.L., D.S., and P.W. cloned the gene, expressed the proteins, and grew crystals. G.D. collected the diffraction data and carried out crystal structure determination and all bioinformatics analyses. E.S. and I.L. carried out liposome-binding assays. C.Y.H. coordinated immunofluorescence and immuno-EM analyses of TbE-Syt. N.L., D.R.R. and M.B. carried out all other in vivo analyses. G.D. wrote the manuscript with help of other authors.

DECLARATION OF INTERESTS

The authors declare no competing interests. https://tritrypdb.org/tritrypdb/app/record/gene/Tb927.10.13740

Transparent Methods

Cloning and site-directed mutagenesis

For in vivo assays, the TbE-Syt ORF (Tb927.10.13740) was amplified by PCR from T. brucei TREU927/4 GUTat10.1 genomic DNA [START_REF] Berriman | The genome of the African trypanosome Trypanosoma brucei[END_REF] and cloned into modified pLew100 vector containing the puromycin resistance gene [START_REF] Wirtz | A tightly regulated inducible expression system for conditional gene knock-outs and dominant-negative genetics in Trypanosoma brucei[END_REF]. This allowed tetracycline-inducible expression of 3xmyc C-terminal tagged TbE-Syt and various trucations ( C2B: aa1-473; C2B: aa474-594; TM: aa1-96; TM: aa97-594; C2A-SMP: aa97-473). The mutant E492A/D498A (mutC2B) was generated in pLew100-TbE-Syt-myc subsequently by site-directed mutagenesis using a QuikChange kit (Stratagene) according to the manufacturer's instructions. For the RNAi experiments in procyclic form and bloodstream form, a TbE-Syt fragment (bp 957-1581) was cloned into the double promoter p2T7 TiB -GFP vector (LaCount et al., 2002), and the pLew100 for stem-loop construct [START_REF] Wirtz | A tightly regulated inducible expression system for conditional gene knock-outs and dominant-negative genetics in Trypanosoma brucei[END_REF]. All cloned constructs were verified by DNA sequencing.

For bacterial purification, full-length TbE-Syt (aa1-594) was amplified by PCR from the T. brucei genomic DNA and ligated into the expression vector pET15b (Novagen) between the NdeI and BamHI sites. Various truncations of TbE-Syt, including TM-SMP-C2A-C2B (aa60-594), TM-SMP-C2A (aa60-422), TM-SMP (aa60-285), SMP-C2A-C2B (aa94-594), SMP-C2A (aa94-422), SMP (aa94-285), C2A-C2B (aa282-594), C2A (aa282-422), and C2B (aa459-594), were subcloned from the full-length construct into both pET15b (Novagen) and a custom vector MalpET that provides a fusion tag of maltose-binding protein (MBP) to the N-terminus of the truncated fragments. However, except for the construct of C2B (aa459-594), none of the other truncations yielded soluble proteins.

TbE-Syt-C2B (aa459-594) cloned into pET15b yielded protein with an N-terminal His6 tag that was cleavable by thrombin. The three mutants, E492A/D498A, K502E/K511E and E492A/D498A/K502E/K511E, were subsequently generated based on this construct by site-directed mutagenesis using the QuikChange kit (Stratagene) according to the manufacturer's instructions. Incorporations of mutations were confirmed by DNA sequencing.

Trypanosome cell lines, growth conditions and transfection

The TbE-Syt ORF (Tb927.10.13740) was amplified by PCR from genomic DNA of T. brucei TREU927/4 GUTat10.1 [START_REF] Melville | The molecular karyotype of the megabase chromosomes of Trypanosoma brucei stock 427[END_REF]. The trypanosome cell lines T. brucei 427 procyclic form 29-13 and bloodstream form 90-13 co-expressing the T7 RNA polymerase and tetracycline repressor [START_REF] Wirtz | A tightly regulated inducible expression system for conditional gene knock-outs and dominant-negative genetics in Trypanosoma brucei[END_REF] were grown and transfected as described before [START_REF] Pradel | NIMA-related kinase TbNRKC is involved in basal body separation in Trypanosoma brucei[END_REF]. After transfection, the cells were selected with puromycin (1 g/ml) and phleom cin 5 g/ml (proc clic form) and 2.5 g/ml (bloods ream form) as appropriate. Clones were selected after serial dilutions. Ectopic expression and RNAi were induced with tetracycline at 10 ng/ml (except TbE-Syt TM::myc expression that was induced at 100 ng/ml) and 1-10 g/ml, respectively.

Protein expression and purification

Recombinant His6-TbE-Syt-C2B and the three mutants were expressed in the E. coli strain BL21(DE3). The bacterial cells transformed with individual constructs were grown in Luria-Bertani (LB) medium at 37°C with continuous agitation to an OD600 of 0.6-0.8, and then placed on ice for 30 min (cold shock). Induction of protein expression was done by addition of 0.5 mM isoprop l -D-1-thiogalactopyranoside (IPTG), and the cells were further incubated at 16°C overnight (14-16 h) with continuous agitation. Bacterial cells were harvested by centrifugation in a Sorvall GS3 rotor (6,000×g, 12 min, 4°C), and the pellet was resuspended in 20 ml of lysis buffer (20 mM Tris-HCl pH 8.0, 100 mM NaCl, 20 mM imidazole, 5% (v/v) glycerol) per liter of cell culture.

Harvested cells were lysed in an EmulsiFlex-C3 homogenizer (Avestin) and cell debris was removed by centrifugation (40,000×g, 40 min, 4°C). The resulting supernatant was filtered (0.45-µm, Amicon) and loaded onto a 5-ml Ni-HiTrap column (GE Healthcare) that was pre-equilibrated with the same lysis buffer. The column was washed with 5 × column volume (cv) of lysis buffer, and bound protein was subsequently eluted using a linear gradient concentration of imidazole (20 -500 mM, 20×cv) in the same lysis buffer.

The N-terminal His6 tag was removed by incubating the pooled fractions containing wildtype or mutant TbE-Syt-C2B with ~2% (w/w) of thrombin (4°C, overnight). Target proteins were further purified on a Superdex-200 16/60 column (GE Healthcare), which was preequilibrated with buffer containing 20 mM Tris-HCl (pH 8.0) and 100 mM NaCl. The eluted proteins were pooled and concentrated using the centrifugal filters (MWCO 3,000, Amicon), and protein concentration was determined using ultraviolet (UV) absorbance at 280 nm and double-checked on SDS-PAGE gels for quality control.

Se-Met-substituted TbE-Syt-C2B was expressed following previously reported protocols [START_REF] Doublie | Preparation of selenomethionyl proteins for phase determination[END_REF]. Purification was carried out using the same protocol as for the wild-type pro ein, e cep ha 15 mM -mercaptoethanol and 10 mM DTT was added to the lysis buffer and the gel filtration buffer, respectively. The purified protein was concentrated to ~15 mg/ml for crystallization trials.

Crystallization, data collection and structure determination

Small clustered crystals of TbE-Syt-C2B were originally obtained in a large-scale crystallization screening trial using native protein and commercial crystallization screening kits (Hampton Research). Rod-shaped crystals of Se-Met-substituted TbE-Syt-C2B were subsequently obtained upon extensive optimization tests. The final crystallization conditions contained 0.1 M sodium cacodylate (pH 6.5), 0.15 M sodium acetate, and 28%

(v/v) polyethylene glycol 8,000. Crystals were harvested by sequentially soaking in the same reservoir solution with 5%, 10% and 15% (v/v) glycerol, loop mounted, and then flash frozen in liquid nitrogen. Diffraction data were collected at the beamline ID23-2 of the European Synchrotron Radiation Facility (ESRF), which ran at the fixed wavelength of 0.873 Å (14.2 keV). To minimize radiation damage, the data used for final structure determination were collected using the helical data acquisition mode to scan along the long axis of the crystal rod. All data were integrated and scaled using XDS [START_REF] Kabsch | Xds[END_REF].

Structure determination was carried out using the single-wavelength anomalous diffraction method. Selenium sites were located and experimental electron density maps calculated using the program AutoSol within the Phenix suite [START_REF] Terwilliger | Decisionmaking in structure solution using Bayesian estimates of map quality: the PHENIX AutoSol wizard[END_REF]. Partially built models were checked and missing loops were manually added in COOT [START_REF] Emsley | Coot: model-building tools for molecular graphics[END_REF]. Refinement was done using phenix.refine [START_REF] Afonine | Towards automated crystallographic structure refinement with phenix.refine[END_REF].

Liposome pelleting assay with sucrose-loaded vesicles

Sucrose-loaded vesicles were prepared as follows: all lipids were reconstituted in chloroform and mixed in molar ratio of 20% cholesterol, 15% DOPS, 35% DOPE, and 30% DOPC, with 60 µM rhodamine dye. PI(4,5)P2-containing vesicles had 5% of PI(4,5)P2 and 25% of DOPC. The lipid mixture was dried to a thin film under weak nitrogen stream, hydrated in 20 mM HEPES (pH 7.5), 0.3 M sucrose and vortexed vigorously for 1 min at RT. The multilamellar vesicles created by this process were then subjected to four cycles of freezing in liquid nitrogen followed by thawing in a sonicating water bath at RT. This mixture of small unilamellar vesicles was diluted with 20 mM HEPES (pH 7.5), 100 mM KCl and pelleted at 230,000 × g for 30 min at RT. The pelleted vesicles were resuspended in 20 mM HEPES (pH 7.5), 100 mM KCl and incubated with purified protein at a 1:1 ratio for 30 min at RT. For Ca 2+ -mediated liposome binding tests, proteins were incubated with 2 mM CaCl2 for 5 min at RT prior to mixing with the vesicles. To separate soluble and sucrose-loaded vesicles-bound proteins, the mixtures were pelleted at 8000 × g for 30 min at RT, and equal volumes of supernatant and resuspended pellets were analyzed on SDS-PAGE gels.

Western blotting

Cells (2×10 7 ) were split for whole cells (WC) and cytoskeleton (CSK) samples and processed for western blotting analysis as described before [START_REF] Florimond | BILBO1 is a scaffold protein of the flagellar pocket collar in the pathogen Trypanosoma brucei[END_REF]. Briefly, protein samples (equivalent to 5×10 6 trypanosomes whole cell or cytoskeletons) were separated on 15% (w/v) SDS-PAGE gels and transferred by semi-dry (BioRad) blotting to PVDF membranes. After blocking, the membranes were incubated overnight at 4°C with the anti-myc (9E10 mouse monoclonal, 1:10,000) primary antibody. After washes in 1 M NaCl and in blocking solution, the membranes were incubated for 1 h at RT with the secondary antibody [anti-mouse HRP-conjugated (Jackson, 1:10,000)]. Blots were visualized using the Clarity Western ECL Substrate kit (Bio-Rad) on an ImageQuant LAS4000. After stripping in 100 mM glycine (pH 2.3), 0.1% (v/v) IGEPAL CA-630 and 1% (w/v) SDS, the membranes were processed as above with anti-TbSAXO (mAb25) antibodies as a loading control [START_REF] Dacheux | A MAP6-related protein is present in protozoa and is involved in flagellum motility[END_REF].

Immunofluorescence and microscopy

Wide-field fluorescence microscopy on T. brucei cells were processed for whole cell (WC) or detergent-extracted cytoskeletons (CSK) immunolabeling as described before [START_REF] Florimond | BILBO1 is a scaffold protein of the flagellar pocket collar in the pathogen Trypanosoma brucei[END_REF]. Briefly, the slides were incubated with primary antibodies [anti-BiP (Bangs et al., 1993) 1:4,000, anti-myc (monoclonal 9E10) 1:20, L8C4 neat, and L3B2 1:25] and washed 2 x 5 min in PBS, then incubated with the secondary antibodies [antirabbit Alexa594-conjugated (Fischer A11012) 1:100; anti-mouse FITC-conjugated (Sigma F-2012)]. After DAPI staining (5 min, 10 µg/ml in PBS), the slides were mounted with SlowFAde Gold Antifade reagent. Images were acquired on a Zeiss Imager Z1 microscope with a Zeiss 100x objective (NA 1.4), using a Photometrics Coolsnap HQ2 camera and Metamorph software (Molecular Devices), and processed with ImageJ.

Pearson s correla ion coefficien s ere calc la ed (n = 22) for he TbE-Syst constructs FL, T1, T3, and mutC2B using the imageJ JaCoP plugin [START_REF] Bolte | A guided tour into subcellular colocalization analysis in light microscopy[END_REF]) and Cos es s randomi a ion [START_REF] Costes | Automatic and quantitative measurement of protein-protein colocalization in live cells[END_REF]. The large cytosolic pool of T4 and T2 prevented the analysis.

Immuno-cryoEM was performed by Dr. Wandy Beatty (Washington University) as described previously [START_REF] Zhou | A coiled-coil-and C2-domain-containing protein is required for FAZ assembly and cell morphology in Trypanosoma brucei[END_REF]. Briefly, cells stably expressing TbE-Syt-YFP were fixed with 4% (w/v) paraformaldehyde solution and 0.2% (w/v) glutaraldehyde (EMS) in 100 mM phosphate buffer (pH 7.2) for 1 h at 4 C. The fixed cells were embedded in 10% gelatin and infiltrated with 2.3 M sucrose, 20% polyvinyl pyrrolidone in PIPES-NaOH (pH 6.9) containing 1 mM MgCl2. Liquid nitrogen frozen sections were obtained using a Leica Ultracut UCT cryoultramicrotome (Leica Microsystems, Bannockburn, IL), and processed for immunolabeling with anti-GFP antibodies (Abcam, UK), followed with secondary antibodies conjugated to colloidal gold (Jackson ImmunoResearch Laboratories). Labeled sections were visualized with a JEOL 1200 EX electron microscope (JEOL). GCAGCTGCATATGAGCACTCGCTCGACGGT GCC

Supplemental References


Mathieu Serrurier
email: serrurie@irit.fr

Didier Dubois
email: dubois@irit.fr

Henri Prade
email: prade@irit.fr

Super increasing sequences and learning of default rules

Keywords: Super increasing sequence, default rules, learning

This paper points out that the same mathematical structure, called "superincreasing sequence" appears in various disguises in different areas such as nonmonotonic reasoning (in relation with the probabilistic representation of default rules), cryptography (as an application of the knapsack problem), or uncertainty modeling (when dealing with probability/possibility transformations). Apart from bridging research trends, which are usually considered separately, this note takes advantage of this parallel for discussing different approaches to the learning of default rules.

Introduction

Default reasoning, as a way of handling if-then rules with potential exceptions, is a basic form of reasoning for dealing with commonsense knowledge. As such, it has been extensively studied in the last 25 years in AI, and applied to inference from expert rules, e.g. [START_REF] Morgenstern | An expert system using nonmonotonic techniques for benefits inquiry in the insurance industry[END_REF]. However, it is worth noticing that default rules can be encountered in other contexts such as algorithmic procedures, or machine learning. Indeed, this note starts from the remark that greedy algorithms are very close in spirit to default reasoning. This can be emphasized on the basis of a classical example of a greedy procedure, namely the one for giving the change for a given amount of money. The efficiency of greedy methods on this problem (which would be NP-complete in the general case) relies on a particular mathematical property of the distribution of the values of the money units (coins or banknotes) that are available. Interestingly enough, a similar mathematical structure, known as "super-increasing sequence" is at work in the knapsack crypto-systems used for key encoding, and is also underlying a finite probabilistic semantics, called big-stepped probabilities, in nonmonotonic reasoning.

The paper is organized as follows. The next section provides a short background on superincreasing sequences and its link with greedy algorithms, while Section 3 gives a brief reminder on big-stepped probabilities, linear possibilities, and their role in nonmonotonic reasoning semantics. Section 4 illustrates the parallel between the two contexts by presenting different approaches to the learning of default rules either based on the identification of a big stepped probability distribution, or on the use of possibilistic layered rules.

Super increasing sequences and greedy algorithms

Optimization algorithms usually go through a series of steps, where choices between different options must be made. Greedy algorithms always choose the best local option with the hope that the algorithm will lead to an optimal solution. These algorithms are very efficient, from a computational point of view, but do not find the global optimum in general. Let us consider, as an example, the standard versions of the knapsack problem. Given an increasingly ordered sequence X = x 1 , .

δ i * x i = v.
This problem is NP-complete. The search one is to determine a collection of p binary variables δ 1 , ..., δ p ∈ {0, 1} such that

p i=1 δ i * x i ≤ v and p i=1 δ i * x i
is maximal. In general, this problem is NP hard, and then greedy algorithms are not optimal for any of the two problems. It is known that with some particular sequences X, called super increasing sequences, the complexity of the decision problem becomes polynomial and even linear. These sequences are defined by : Definition 1 Let X = x 1 , ..., x p be a sequence of real numbers. X is a super increasing sequence iff

∀1 < i ≤ p, x i > i-1 j=1 x j .
In this case, the greedy procedure consists, at each step, in choosing δ i = 1 for i such that the value x i that is immediately lower than the rest of the value of v to be covered. At the end, if an i is selected twice or no x i is lower than the rest of the value of v there is no solution. Otherwise, the greedy algorithm find the unique solution.

There are two well-known uses of super increasing sequences for the knapsack problem. The first one corresponds to the knapsack public key crypto-system [START_REF] Merkle | Hiding information and signatures in trapdoor knapsacks[END_REF]. The designer publishes a public key that is composed by a sequence X = x 1 , . A second application is based on the unbound search knapsack problem. In this case, we consider an increasingly ordered sequence X = x 1 , ..., x p and a value v and we search a collection of integers n 1 , ..., n p such that v = p i=1 n i * x i and p i=1 n i is minimal. The problem is NP-hard in general, be it can be polynomially resolved by the same kind of greedy algorithm than the one described previously when X is a complete super increasing sequence, whose definition is now recalled.

Definition 2 Let X = x 1 , ..., x p be a sequence of real numbers. X is a complete super increasing sequence iff x 1 = 1 and X is a super increasing sequence and it exists no x and i such that X = x 1 , ..., x i , x, x i+1 , ..., x p is still a super increasing sequence.

The direct application of complete super increasing sequences corresponds to the problem of giving the change for a given amount of money v with a minimum number of money units. This problem is a typical unbound search knapsack problem. It is the reason why, in general, money units constitute complete super increasing sequences. Other classical examples of the use of super increasing sequences is the writing of numbers in base 2, 10,...Each step of a greedy algorithm can be represented as a set of default rules. Conversely, reasoning with sets of default rules can be viewed as a greedy procedure, since it consists in always applying the most specific applicable rule. Let us take the example of a machine providing change. Let X = x 1 , ..., x p be the complete increasing sequence of values of the money units that are available and v be the change to give back.

while v>0 v>xp -> give back xp and v=v-xp ... v>xi -> give back xi and v=v-xi ... v>x1 -> give back x1 and v=v-x1 end

Clearly the rules are presented here in a decreasing specificity ordering. If x 1 = 1 the algorithm terminates for any integer v. If X is a super increasing sequence, as it is the case in practice for money, the above algorithm always provides an optimal solution in terms of a minimal number of money units that are given back. For instance, with the non super increasing sequence X = {300, 250, 249, 1} and v = 499, the above algorithm gives back 200 money units (one time 300 + 199 times 1), while the optimal solution only uses 2 money units (250 and 249).

Big-stepped probabilities and nonmonotonic reasoning

Kraus, Lehmann and Magidor [START_REF] Kraus | Nonmonotonic reasoning, preferential models and cumulative logics[END_REF] have proposed an approach to nonmonotonic reasoning based on postulates that a nonmonotonic consequence relation should satisfy. On the basis of these postulates, a preference entailment system has been defined (called system P ). Several semantics have been proposed for this system. Among them, a probabilistic, finite semantics, and a possibility theory-based one have been provided in [START_REF] Benferhat | Possibilistic and standard probabilistic semantics of conditional knowledge bases[END_REF].

More precisely, it has been proved that a default rule α → β belongs to the inference closure of system P iff for all probability measures P rob belonging to a set of a so-called big-stepped probabilities we have P rob(β ∧ α) > P rob(¬β ∧ α)(or equivalently P rob(β/α) > 1 2 ). Big-stepped probabilities are defined by Definition 3 P rob is a big-stepped probability distribution on the ordered set of mutually exclusive events ω 1 , ..., ω n iff

∀1 ≤ i < p, P rob(ω i ) > p j=i+1 P rob(ω j )
In fact, it is allowed that the two last non-zero terms be equal, when representing a nonmonotonic consequence relation. Big-stepped are also known as atomic-bound probabilites [START_REF] Snow | Diverse confidence levels in a probabilistic semantics for conditional logics[END_REF].

Clearly, big-stepped probabilities corresponds to a super increasing sequence in the sense of the previous section (X = P rob(ω p ), ..., P rob(ω 1 )).

Note that the following inequalities can be derived from definition 3

∀i = 1, . . . , n -2, P rob(ω i |A i ) > 0.5 (1)
with

A i = {ω i , . . . , ω n }.
Moreover, Π(ω i+1 ) = p j=i+1 P rob(ω j ) for 1 ≤ i < p and Π(ω p ) = P rob(ω p ) defines a basic probability/possibility transformation, first introduced in [START_REF] Dubois | On several representations of an uncertain body of evidence[END_REF], such that Π(ω i ) > P rob(ω i ) for all i. Thus, we have the following bounds

Π(ω i ) > P rob(ω i ) > Π(ω i+1 ).
Then, the Π(ω i )'s form a linear possibility distribution, which is the basis of another equivalent semantics for system P , namely we have

Π(α ∧ β) > Π(α ∧ ¬β) for any default rule α → β (with Π(α) = max{π(ω), ω |= α}).
Thus, a set of default rules can be equivalently viewed as : i) associated with big stepped probability distributions, which provide a statistical flavor to them;

ii) associated with a layered possibilistic [START_REF] Benferhat | Representing default rules in possibilistic logic[END_REF] logic base, which may be assimilated to a greedy reasoning procedure, viewing the clauses as rules.

This provides two directions for learning or mining default rules

Learning

Let us now consider the problem of finding of set of default rules that cover a finite number of examples.

We first recall a data mining approach based on the building of big stepped probabilities from the data. In this context, we can associate a default rule with the probability corresponding to the proportion of examples covered by the rule. A default set of rules is optimal if the rules cover all the examples and they are underlain by big stepped probability distributions. In this case, these rules are genuine default rules in the sense of system P . This is the base for the data mining algorithm described in [START_REF] Benferhat | A big-stepped probability approach for discovering default rules[END_REF]. We consider a set of examples E = {w 1 , ..., w n } where each w i =< l 1 , . . . , l q > is a binary vector corresponding to q different attributes under consideration. First, the algorithm determines a partition of The "if then" rule associated with the subset E i is such that the attributes involved in its antecedent are discriminant with respect to the examples in E j , j > i, while the attributes appearing in conclusion are those which are identically valued in E i . By using a super increasing sequence (which corresponds to a big stepped probability when reasoning with proportion of examples), the set of default rules found is granted to satisfy the requirements of the system P . It means in practice that the new default that could be deduced from the found default rules, using system P would still agree with the database it start from.

E = E 1 ∪ . . . ∪ E p such that |E 1 |, . . .
The use of super increasing sequences would be also worth investigating in the scope of machine learning. In particular, it could be interesting in relation with the recently developed algorithms [START_REF] Serrurier | Possibilistic inductive logic programming[END_REF][START_REF] Serrurier | Coping with exceptions in multiclass ILP problems using possilistic logic[END_REF] based on possibilistic logic in the framework of inductive logic programming (ILP) [START_REF] Nienhuys-Cheng | Foundations of Inductive Logic Programming[END_REF]. However in the ILP settings, all the rules forming the hypotheses to be induced are supposed to be Horn clauses with the same predicate in their head. It is still interesting to layer the rules in order to handle inconsistency, even if it correspond to a very special type of set of default rules.

Learning from a set examples to be stratified

The authors of the present paper have proposed an algorithm for learning from a possibilistic database [START_REF] Serrurier | Possibilistic inductive logic programming[END_REF] They may be obtained from a set ∆ of expert default rules (if available), by computing the level of inconsistency of each example with the set of stratified rules associated with ∆ using the ranking procedure in [START_REF] Benferhat | Representing default rules in possibilistic logic[END_REF]. Then, the priority of the example would be all the greater as the level of inconsistency is low.

In case no expert knowledge is available, as often, it would be interesting to assess the necessity levels of the examples by determining a partition associated with a super increasing sequence. This would ensure, with a correct and complete ILP algorithm, to find an hypothesis made of genuine default rules. In this scope, the ideal partition of the set of examples is the one that describes a partition that corresponds to a super increasing sequence, with respect to the number of examples in each set of the partition. Moreover, the idea is also to build a partition E = E 1 ∪ . . . ∪ E p of the examples, where the example in E 1 are as similar as possible, and then the examples in E 1 ∪ E 2 remain similar as much as possible, and so on for all i j=1 E j . Formally, let consider

E = E 1 ∪ . . . ∪ E p such that |E p |, . . . , |E 1 | is a super increasing sequence (i.e. ∀j, |E j | ≥ p i=j+1 |E i | and d is a distance
between examples (in the case of relational learning some distances have been proposed, see [START_REF] Emde | Relational instance-based learning[END_REF] for instance). Given a set of example E i = {e 1 , . . . , e n }, the average value of the distance between examples in E i is

D(E i ) = n k=1 n j=k+1 d(e k , e l ) |E i | * (|E i |-1) 2
.

According to the above discussion, a good partition for the sets of examples may be the super increasing one that minimizes the value

p i=1 |E i | * D( i j=1 E j ). (2)
It is obvious that, without any information, finding an optimal solution is a N P -complete problem. A possible heuristics may be first to fix the shape of the super increasing sequence as the "extremal" one in the sens of equation 1, i.e,

|E i | = [ |E-i-1 j=1 E j | ] 2 + 1
where [ ] denotes the integer part. Then, as long as the criterion (eq. 2) decrease, we swap pairs of examples in between two subsets of the partition (Alg 1). Remark that this approach is not optimal. Better results with respect to the criterion could be achieved by also allowing the move of an example from one subset to another subset; this will require the use of metaheuristics such as simulated annealing or genetic algorithms.

Alg

f (h i ) = supp(h i ) -suppEf f (h i-1 ) with suppEf f (h 1 ) = supp(h 1 ).
Thus, a stratified hypothesis will be considered as acceptable from the non monotonic reasoning point of view, if the sequence {suppEf f (h 1 ), . . . , suppEf f (h n )} is a super increasing sequence. In order to guide the algorithm toward stratified hypothesis that describes a super increasing sequence and that have an high accuracy, we need to measure the distance between the sequence of the effective supports and the closest super increasing sequence (as define in algorithm 2). Then the function to maximize is

val(H p ) = acc(H p ) -c * distIS(H p )
where acc(H p ) is the accuracy of H p and c is a constant. The constant c is used for the control of the relative weight of accuracy vs. the distance of the hypothesis to the closest super increasing sequence. We consider that the most general hypothesis H g (i.e. the hypothesis that classes all examples in the majority class) is as acceptable as the most specific hypothesis H s (i.e. E). Thus c = acc(Hs) * distIS(Hg)-acc(Hg) * distIS(Hs) distIS(Hs)-distIS(Hg)

. Since distIS(H g ) = 0, we can take c such as c = acc(H g ).

Alg. 2 distIS

Require: H p = h 1 , ..., h n a stratified hypothesis 1: cumulsupport = 1 2: dif f = 0 3: ǫ = 1

Conclusion

In this paper, we have outlined the links that exists between non-monotonic reasoning and greedy algorithms by pointing out the similarity of the two mathematical structures underlying them : super increasing sequences and big-stepped probabilities. This link echoes the two-sided nature of the representation of default rules either in statistical terms or as properly layered sets of classical formulas. It suggests that learning a minimal default rules coverage of a set examples amounts to identify hypotheses that induce super increasing sequences of subsets of examples.

|E| 4 :if i > 0 then 7 :i

 47 i = n 5: while cumulsupport > 0 do 6: currentsupport = suppEf f (h i ) = i -1 17: end while 18: return dif f

  .., x p and a value v, We can define two different knapsack problems. The decision one consists in determining if it exists a collection of p binary variables δ 1 , ..., δ p ∈ {0, 1} such that

	p
	i=1

  ., x p . A message binary (δ 1 , ..., δ p ) is encoded by mes = x 1 * δ 1 + ... + x p * δ p .

	is a knapsack problem which is NP-complete.
	But the designer, who may receive such a
	message, possesses two secret keys (obeying
	some technical constraints) M and W such that
	M * x 1 , ..., M * x p mod W is a super increasing
	sequence. Then, the designer can easily decode
	the message.
	So, knowing mes and X, decoding the message

  , |E P | is a super increasing sequence (where || means cardinality). The partition must be minimal, i.e. any subset of E cannot be split while keeping the super increasing properties. A partial order on partitions is defined in order to express preference for partitions that group examples having a maximal number of identically valued attributes. When a partition has been discovered, a set of default rules can be identified. For identifying rules, the subsets of E are considered from E p to E 1 .

  . A possibilistic ILP database is composed of two sets : B p and E p . B p is named background knowledge and contains ground facts and formulas associated with necessity degrees. E p is the set of examples that describes the concept to be learnt. It contains ground facts pertaining to the same predicates (the one that appears in the head of the rules to be induced), and are also associated with necessity levels. Theses necessity levels are supposed to reflect the importance of the example with respect to is nature, namely it is more important to cover typical examples rather than exceptional ones. The goal is then to find a possibilistic hypothesis H p such that B It starts with E αp and B αp for computing H p , then it computes H p-1 from E αp ∪ E α p-1 and B αp ∪ B α p-1 and so on. The hypotheses found are merged and necessity levels are associated with rules with respect to the levels of their exceptions. This allows the algorithm to learn both general rules with some exceptions with respect to the less prioritized examples, and more specific rules without exceptions. The major limitation of this method is that we have to have assigned the necessity levels of the examples.

p ∪ H p |= p E p ,

where |= p is the possibilistic entailment. Then, the necessity levels on the examples correspond to priority levels for covering them. The examples that have the highest level must be covered in priority. On the contrary, the examples with a low level of necessity are not covered in priority and the rules may make error on them. The necessity levels make a partition of E (and B in the same way). Namely we have E = E α i ∪ . . . ∪ E αp where α 1 < . . . < α p and E αp contains all examples that have α i as necessity level. The method is based on a classical ILP algorithm that learns hypotheses from increasing sets of examples.

  for all possible pairs of examples (e i ∈ E i , e j ∈ E j ) do Given a stratified hypothesis H p = h 1 , ..., h n (h 1 is the most prioritized rule), we note supp(h) the proportion of examples to which the rule apply (even it leads to wrong classification). We call effective support of a rule the proportion of examples to which the rule effectivelly apply when considering the priorities in possibilistic logic. More formally, the effective support is then suppEf

	and to compensate the errors of a rule at a given
	level by rules at higher levels. The possibilistic
	hypothesis are learned directly by adapting an
	ILP algorithm based on simulated annealing [12].
	The stratification is induced in maximizing the	. 1 Building a partition
	accuracy and does not take into consideration an	Require: E the set of examples
	intended default rule meaning. In order to do that,	Require: d a distance between examples
	a measure could be introduced for guiding the	1: let E = E 1 ∪ . . . ∪ E p a random "extremal"
	learning process in order to induce hypotheses		sequence
	that describe super increasing sequences of	2: improvement=true
	examples.	3: while improvement do
		4:
		5:	if it exists a pair (e i , e j ) that decreases
			the criterion when they are swapped
			then
		6:	choose the pair (e i , e j ) that minimizes
			the criterion
		7:	swap e i and e j
		8:	else
		9:	improvement=false
		10:	end if
		11:	end for
		12: end while
		4.2 Learning stratified set of rules from
			classical examples
		In [10], possibilistic logic is used for dealing with
		exceptions, assimilated as inconsistency, in a clas-
		sical ILP setting. Due to the monotonicity of first
		order logic consequence relation, hypotheses in
		ILP cannot deal with exceptions (misclassifica-
		tion). In particular, classical hypotheses accumu-
		late all exceptions of the rules that appear in them
		and if a rule has an exception, there is no way
		to compensate by with another rule. In [10], We
		have proposed to use possibilistic logic in order
		to manage the exceptions. Thus, given a classical
		background knowledge B and a set of examples
		E, a stratified set of rules H p is to be induced such
		that it exists a stratification of E, named E p , such
		that
			B ∪ H p |= p E p .
		By contrast with the previously described ap-
		proach, the stratification of the examples is
		not given and depends on the hypothesis. The
		stratification of rules allows the algorithm to
		deal with multiple classification of examples


Thomas Poulard

Quentin Fosse

Jean-Yves Hogrel

Marie-Cécile Niérat

Thomas Similowski

Martin Dres

Damien Bachasson

Jean-Luc Gennisson

Ultrasound shear wave elastography for assessing diaphragm function within the intensive care unit

Keywords: diaphragm, ultrafast ultrasound imaging, shear wave elastography, mechanical ventilation, intensive care unit, muscle

Availability of robust non-invasive tools for assessing diaphragm function is clinically relevant in a variety of clinical settings. Diaphragm shear modulus (SMdi) assessed by using ultrasound (US) shear wave elastography (SWE) can be used as a surrogate of transdiaphragmatic pressure (Pdi) that is considered as the most specific approach to assess diaphragm function. Here, we investigated the ability of SWE to reveal changes in transdiaphragmatic pressure for assessing diaphragm function within an ICU setup. SWE was performed in 22 mechanically ventilated patients within varying breathing conditions to induce changes in Pdi. Eight patients displayed a significant correlation between changes in Pdi (ΔPdi) and changes in SMdi (ΔSMdi). An absence of correlation was associated with a significantly higher respiratory rate. These findings highlight the need to increase SWE sampling rate to improve the applicability of SWE for diaphragm monitoring.

I. INTRODUCTION

The diaphragm being the main respiratory muscle, assessing its efficiency is of primary importance in various populations. Diaphragm dysfunction is highly prevalent in patients admitted in the intensive care unit (ICU) and is associated with prolonged ICU-stay, poorer prognosis and/or death [START_REF] Dres | Critical illness-associated diaphragm weakness[END_REF]. Diaphragm function may be estimated by measuring transdiaphragmatic pressure (Pdi). Pdi measurement requires the insertion of nasogastric catheters through the nose or mouth of the patient and is computed as the difference between the gastric pressure (Pga) and the esophageal one (Pes). Since the diaphragm is the only muscle responsible for a concomitant decrease in Pes and an increase in Pga, Pdi is considered as the gold standard method to assess diaphragm force generation. In addition to invasiveness, Pdi is also an indirect measure of diaphragm contractility [START_REF] American | ATS/ERS Statement on respiratory muscle testing[END_REF].

Ultrasound imaging of the diaphragm has been widely used to assess its function [START_REF] Nason | Imaging of the diaphragm: anatomy and function[END_REF]. Diaphragm may easily be imaged via an intercostal approach during which diaphragm thickness and thickening fraction can be measured, or via a subcostal approach to measure its excursion. The ease of use of diaphragm ultrasound has led to a vast body of research on this topic. However, equivocal relationships between Pdi and diaphragm thickening fraction have been reported [START_REF] Goligher | Measuring diaphragm thickness with ultrasound in mechanically ventilated patients: feasibility, reproducibility and validity[END_REF], supporting the need to investigate innovative techniques to improve diaphragm function assessment. Our group has recently shown in healthy subjects that inspiratory changes in diaphragm shear modulus (ΔSMdi) measured using ultrasound shear wave elastography (SWE) are strongly correlated to changes in Pdi (ΔPdi, [START_REF] Bachasson | Diaphragm shear modulus reflects transdiaphragmatic pressure during isovolumetric inspiratory efforts and ventilation against inspiratory loading[END_REF]). The aim of the present study was to investigate the suitability of SWE to assess diaphragm function in mechanically ventilated patients within the ICU.

II. MATERIAL & METHODS

A. Patients

All patients or their legal representative gave written informed consent. This study conformed to the Declaration of Helsinki and was approved by the local ethics committee. Patients had to be 18 and over, receiving mechanical ventilation for more than 24 hours and able to perform a spontaneous breathing trial (SBT, i.e. breathing while receiving no ventilator support). Out of the twenty-five patients, three of them were not considered for analysis (two for an incomplete set of data, one because of complete diaphragm paralysis). Patients were studied in a semirecumbent position (around 40 degrees).

B. Ultrasound recording

An ultrafast ultrasound scanner (Aixplorer, Supersonic Imagine, France) driving with a linear transducer array (SL10-2, Supersonic Imagine) was used to scan the right hemidiaphragm. The probe was placed on the anterior axillary line vertical to the chest wall, at the 8 th -11 th intercostal space. The ultrasound sequence was designed to optimize the pushing beam in the diaphragm. Briefly, ultrasounds were focused along one line to create radiation force that acted as a shear wave source. Then the propagating shear wave was captured using an ultrafast imaging sequence (3500 frames.s -1 ) allowing its velocity measurement. By using a Matlab interface, B-Mode images and SWE maps where retrieved. The conventional SWE framerate of the device is set to 1 Hz. The SWE sequence was then modified to reach 2 Hz and sometime decreased to 1.6 Hz depending on diaphragm depth.

C. Physiological parameters

Various physiological parameters were recorded simultaneously with the ultrasound acquisitions. Pga and Pes were measured using balloon catheters (NutriVent TM , Mirandola, Modena, Italy) inserted through the mouth or nose of the patient and connected to separated differential pressure transducers (model DP45-32, Validyne, Northridge, CA). Pdi was computed as the difference between Pga and Pes. Heart rate, breathing frequency, oxygen saturation and arterial blood pressure were continuously monitored using in-room monitoring systems. Flow was measured using a flow sensor (Hamilton Medical, Bonaduz, Switzerland) connected to a spirometer (ADInstruments, Bella Vista, Australia). All signals were analogue-to-digitally converted at a sampling rate of 1 kHz using a PowerLab system (16/35, ADInstruments, Bella Vista, Australia).

All signals (i.e. ultrasound data and physiological parameters) were synchronized using a trigger output sent by the ultrasound scanner to the PowerLab when the ultrasound acquisition started. The experimental setup is presented in Fig. 1.

D. Breathing conditions

Variations in diaphragmatic work during breathing was induced by changing ventilator parameters. Thirty seconds acquisitions were performed at 3 and 9 minutes after the start of each condition. Afterward, a SBT was performed during which the patient was breathing without receiving help from the ventilator. Thirty seconds recordings were performed every five minutes with a maximal duration set at 30 minutes.

E. Data processing and statistical analysis

All data were analyzed offline using standardized MATLAB scripts. Regarding SWE maps, a region of interest (ROI) was defined in the diaphragm for every tested condition in which shear modulus values were averaged. A shape preserving interpolation was then applied to transform shear modulus values at 1 kHz, so that diaphragm shear modulus (SMdi) could be easily compared to Pdi. ΔSMdi was computed as the difference between maximal SMdi minus minimal SMdi over the breathing cycle. ΔPdi was computed as the difference between maximal Pdi minus minimal Pdi over the breathing cycle Pearson's correlation (r), repeated measure correlation (R [START_REF] Bakdash | Repeated measures correlation[END_REF]) were performed to evaluate the relationship between ΔSMdi and ΔPdi. Differences between patients who failed and patients who succeeded the SBT were assessed through Student's t-test. All analysis were performed in the computing environment R (version 3.2.4, R Foundation for Statistical Computing, Vienna, Austria [START_REF] Team | A language and environment for statistical computing[END_REF]). Statistical significance was set at p<0.05.

III. RESULTS

A. Typical recording of diaphragm SWE

Fig. 2. displays a typical imaging of the diaphragm using SWE. The diaphragm is classically identified by the two echogenic pleural and peritoneal membranes bounding the muscular layer.

B. Relationship between ΔSMdi and ΔPdi

Relationship between ΔSMdi and ΔPdi are presented for two patients. One of them displayed a significant correlation (r = 0.88, p < 0.001), while the other showed no correlation (r = -0.05, p = 0.88).

The patient that displayed significant ΔSMdi-ΔPdi correlation had a significantly lower respiratory rate compared to the patient with no significant ΔSMdi-ΔPdi correlation (p<0.02).

IV. DISCUSSION AND PERSPECTIVES

This study investigated whether SWE could be reliably used to evaluate diaphragm contractility in critically ill patients. These preliminary findings are promising although the use of SWE for diaphragm assessment may not be generalized to all patients. Fig. 3. Variations of diaphragm shear modulus (SMdi, red), esophageal (Pes, green), gastric (Pga, yellow) and transdiaphragmatic (Pdi, blue) pressures over time, for a patient with a very strong correlation between ΔPdi and ΔSMdi (A, r = 0.88) and a patient with a null correlation (B, r = -0.05). Time-Motion imaging overlaid with shear modulus maps are also displayed.

The fact that absence of ΔSMdi-ΔPdi correlation was associated with a higher respiratory rate suggest that low SWE sampling rate hampers the ability of SWE to monitor diaphragm activity. As stated above, shear modulus values were acquired at 1.6-2 Hz. Therefore, an increased respiratory rate results in a decreased number of shear modulus values per breathing cycle while the probability to oversee within-cycle maximal and minimal shear modulus increases. Consequently, the risk to underestimate ΔSMdi is growing with respiratory rate. Fig. 3 shows typical recording of physiological parameters and SMdi over time in two patients with strong (Fig. 3A) and absent (Fig. 3B) ΔSMdi-ΔPdi correlation. One may clearly observe that an increased respiratory rate (Fig. 3B) negatively impacts SWE ability to monitor changes in SMdi. This supports that the low success rate of diaphragm SWE in patients is mainly related to technological limitations.

Conventional SWE sequences used in the present work involves four ultrasound pushing beams generated over multiple laterally-spaced spatial points for generating shear waves. To keep the sequence within the FDA guidance and to increase the framerate, a new sequence reducing the number of pushing lines to two was designed in order to obtain 4-Hz framerate. Then a multiple tracking location (MTL) algorithm allows the computation of shear wave velocity maps. A recent work reported that a two-point measurement of shear wave velocity can be reliably used to assess the mechanical properties of viscoelastic material [START_REF] Kijanka | Two Point Method For Robust Shear Wave Phase Velocity Dispersion Estimation of Viscoelastic Materials[END_REF]. This technique is very promising as a single (i.e. instead of four) ultrasound pushing beam would be sufficient to map a predefined area. This would lead to a four times higher sampling frequency than what is actually used while remaining within the limits of radiation exposure. However, its applicability to the skeletal muscle remains to be investigated.

These findings support that SWE is a promising noninvasive alternative for monitoring diaphragm function. However, the generalization of SWE for the diaphragm monitoring depends upon technological developments to overcome current limitation of commercially available SWE sequences.

Fig. 1 .

 1 Fig. 1. Experimental setup. All acquisitions were performed in the patient's room. The ultrasound device was connected to a controlling computer, which was synchronizing and recording ultrasound images (SWE and Bmode) and physiological data.

Fig. 2 .

 2 Fig. 2. Shear modulus (SMdi) map in kPa measured using shear wave elastography overlaid with standard B-Mode during intercostal scanning at the right zone of apposition.

Supported by the AFM "Association Française contre les Myopathies" jointly with "Fondation EDF".