Louis Bunel

Lancelot Pincet

Vivek Malhotra

Ishier Raote
email: ishier.raote@ijm.fr

Frédéric Pincet
email: frederic.pincet@ens.fr

A model for collagen secretion by intercompartmental continuities

Keywords: procollagen transport, TANGO1, ER exit sites, protein condensates, force generation

Newly synthesized secretory proteins are exported from endoplasmic reticulum (ER) at specialized subcompartments called exit sites (ERES). Cargoes like procollagen are too large for export by the standard COPIIcoated vesicle of 60 nm average diameter. We have previously suggested that procollagen is transported from the ER to the next secretory organelle, the ERGIC, in TANGO1-dependent inter-organelle tunnels. In the theoretical model presented here, we suggest that intrinsically disordered domains of TANGO1 in the ER lumen induce an entropic contraction, which exerts a force that draws procollagen towards the ERES. Within this framework, molecular gradients of pH and/or HSP47 between the ER and ERGIC create a force in the order of tens of femtoNewtons (fN). This force is substantial enough to propel procollagen from the ER at a speed of approximately 1 nm.s -1 . This calculated speed and the quantities of collagen secreted are similar to its observed physiological secretion rate in fibroblasts, consistent with the proposal that ER export is the rate limiting step for procollagen secretion. Hence, the mechanism we propose is theoretically adequate to explain how cells can utilize molecular gradients and export procollagens at a rate commensurate with physiological needs.

Significance Statement

Procollagen cannot be exported from the endoplasmic reticulum (ER) by standard COPII-coated vesicle of 60 nm average diameter. We have previously suggested that collagen is transported from the ER to the next secretory organelle, the ERGIC, in TANGO1-dependent inter-organelle tunnels. ER and ERGIC differ in molecular composition including their pH and protein composition. We propose a mechanical/entropic ratchet model whereby molecular gradients of pH and the collagen chaperone HSP47, provide the energy to propel procollagen from the ER at a speed that matches the physiological rate of collagen secretion.

Introduction

Secretory proteins are co-translationally inserted into the endoplasmic reticulum (ER), folded, and then collected at specialized domains called ER exit sites (ERES) for their transfer to the next station of the secretory pathway, the ER-Golgi Intermediate compartment (ERGIC). ERES are marked by COPII proteins, which are required for the export of secretory cargoes. COPII proteins assemble into a lattice on ER membranes to generate cargo-filled vesicles of 60 nm average diameter. Recent data suggest that COPIIdependent ER export can also happen through direct tunnels between ERES and the ERGIC, though the mechanistic details are rather scant [START_REF] Weigel | ER-to-Golgi protein delivery through an interwoven, tubular network extending from ER[END_REF][START_REF] Shomron | COPII collar defines the boundary between ER and ER exit site and does not coat cargo containers[END_REF]. Secretory cargo capture into COPII-dependent vesicles is either through bulk flow or signal-mediated export. Bulk flow export occurs without signals, relying on passive cargo diffusion into an ERES. Signal-mediated export involves recognition of specific signals in cargo proteins by the COPII coat, leading to cargo concentration at ERES. Transmembrane proteins directly interact with Sec24 of the COPII inner coat, while soluble proteins or those without cytoplasmic signals require cargo receptors to facilitate an interaction with Sec24. Receptor and cargo exit the ER together. COPII protein assembly into a lattice or coat provides the motive force to concentrate cargoes into the export carrier for transport to the next secretory compartment [START_REF] Tabata | Visualization of cargo concentration by COPII minimal machinery in a planar lipid membrane[END_REF][START_REF] Miller | Regulation of coat assembly--sorting things out at the ER[END_REF]. Compartmental identity changes gradually along the secretory pathway. There are differences in membrane lipid composition, soluble and membrane protein content, and ionic concentrations -including Ca 2+ (5) and Zn 2+ [START_REF] Kowada | Imaging of Labile Zn(2+) in the Golgi Apparatus Using a Localizable Small-Molecule Fluorescent Probe[END_REF]. Importantly, secretory organelle pH drops, from ~7.4 in the ER to ~6.5 at the ERGIC and cis-Golgi, to ~5 in post-Golgi secretory granules [START_REF] Paroutis | The pH of the secretory pathway: measurement, determinants, and regulation[END_REF]. Stable gradients can also be maintained within micrometer long tubular organelles over time [START_REF] Suresh | Tubular lysosomes harbor active ion gradients and poise macrophages for phagocytosis[END_REF]. It is not known if this electrochemical proton gradient contributes to the concentration and flow of secretory cargoes out of the ER. A procollagen molecule has an extended, rigid, trimeric (triple-helical) region, which can reach 300 nm in length in the ER lumen, i.e. too long to fit in a COPII vesicle [START_REF] Beck | Triple helix formation of procollagen type I can occur at the rough endoplasmic reticulum membrane[END_REF][START_REF] Bachinger | Folding mechanism of the triple helix in type-III collagen and type-III pN-collagen. Role of disulfide bridges and peptide bond isomerization[END_REF]. While it is clear that COPII proteins are required for procollagen export, no dedicated conventional cargo receptors have been identified yet. Procollagens are recruited to ERES by the ERES-resident protein TANGO1, which links procollagens to the COPII inner coat protein Sec23A. However, TANGO1 is unique among cargo receptor-like proteins in that it does not leave the ER along with the cargo -instead collagen moves forward, while TANGO1 is retained at the ERES. It remains unclear how procollagens are exported from the ER and whether factors other than cargo-receptor-COPII lattice assembly could provide a motive force. An informative set of data that casts light on these questions comes from a final step in procollagen folding prior to its export from the ER. Once formed, the triple helical structure is unstable at ~37°C. To stabilize collagen at these physiological temperatures, triple helical regions are held together by 'clamps' formed by Heat Shock Protein 47 (HSP47) dimers that can bind at several sites along the procollagen triple helix [START_REF] Nagata | A major collagen-binding protein of chick embryo fibroblasts is a novel heat shock protein[END_REF][START_REF] Widmer | Molecular basis for the action of the collagen-specific chaperone Hsp47/SERPINH1 and its structure-specific client recognition[END_REF]. The binding of HSP47 to collagen exhibits exquisite pH sensitivity, almost completely bound at the nearneutral pH found in the ER (~7.4) and almost completely dissociated by the lower pH found in the ERGIC [START_REF] Oecal | The pH-dependent Client Release from the Collagen-specific Chaperone HSP47 Is Triggered by a Tandem Histidine Pair[END_REF]. Live video microscopy of the ER-Golgi interface during procollagen secretion, at high spatiotemporal resolution, revealed that HSP47 dissociates from procollagen at the ERES and is retained at the ER [START_REF] Omari | Mechanisms of procollagen and HSP47 sorting during ER-to-Golgi trafficking[END_REF]. In the lumen of the ER, HSP47 binds an SH3-like domain (SLD) of TANGO1 to recruit triple helical (fully folded) procollagen to the ERES. In addition to the SLD, the lumenal portion of TANGO1 (TANGO1LUM) comprises a large region of ~1000 amino acids, most of which is predicted to be an intrinsically disordered region (TANGO1LUM IDR). On the cytoplasmic side of the ERES, TANGO1 is composed of (Fig. 1A) two coiled-coil (CC) domains and a proline rich domain (PRD). Raote et al. showed that TANGO1 molecules can self-arrange into a ring at the ERES [START_REF] Raote | Protein transport by vesicles and tunnels[END_REF][START_REF] Raote | Tunnels for Protein Export from the Endoplasmic Reticulum[END_REF][START_REF] Raote | A physical mechanism of TANGO1-mediated bulky cargo export[END_REF]. Cytoplasmic domains also facilitate the formation of a tunnel between the ER and the ERGIC. An unusual combination of an intramembrane helix and a transmembrane helix (IM-TM) isolate the ERES membrane from the rest of the ER, acting as a partial diffusion barrier for lipids between the fusing ERGIC and the bulk of the ER [START_REF] Raote | TANGO1 membrane helices create a lipid diffusion barrier at curved membranes[END_REF]. TANGO1LUM along with the recruited collagen cargo, would form a densely packed protein network, perhaps functioning as a partial physicochemical barrier between the ERES and the ERGIC. The starting point of our model is based on the idea that this barrier maintains molecular gradients. Specifically, such a partial barrier could stabilize electrochemical gradients of pH or HSP47 content. The molecular gradients favor the binding of TANGO1LUM IDR to procollagen in the ER lumen compared to the ERGIC. Tethering TANGO1LUM IDR to procollagen reduces the number of accessible conformations, lowering the ensemble's conformational entropy, and generates an effective entropic force that pulls away from the point of tethering. This entropic collapse resembles what was observed with transiently unstructured protein domains that provide sufficient forces to bring vesicles together [START_REF] Murray | An endosomal tether undergoes an entropic collapse to bring vesicles together[END_REF]. Here, we show that the molecular gradients can induce a total entropic motive force for secretory cargo transfer between the organelles. This force is sufficient to export procollagen from the ER at a physiological rate, even in the absence of a cargoreceptor.

Results

Presentation of the model

We begin at a stage where a tunnel has formed between the ER and ERGIC with TANGO1LUM located at its base, facing into the lumen of the tunnel (Fig. 1B-C). A procollagen trimer spans the tunnel from the ER lumen to the ERGIC lumen, aligned along the axis of the tunnel. Procollagen contains binding sites for the chaperone-like protein HSP47, which is found in the ER lumen. Two HSP47 binding sites are located approximately every 10 nm on the procollagen molecule [START_REF] Widmer | Molecular basis for the action of the collagen-specific chaperone Hsp47/SERPINH1 and its structure-specific client recognition[END_REF][START_REF] Koide | Xaa-Arg-Gly triplets in the collagen triple helix are dominant binding sites for the molecular chaperone HSP47[END_REF][START_REF] Abraham | Collagen's primary structure determines collagen:HSP47 complex stoichiometry[END_REF]. HSP47 can simultaneously bind the SLD at the N-terminal region of TANGO1 [START_REF] Ishikawa | Intracellular mechanisms of molecular recognition and sorting for transport of large extracellular matrix molecules[END_REF][START_REF] Fujii | Lowering the culture temperature corrects collagen abnormalities caused by HSP47 gene knockout[END_REF]. This dual binding of HSP47 ensures a mechanical coupling between procollagen and some TANGO1 proteins of the ring. The affinities, on-rates and off-rates of HSP47 to procollagen have previously been measured at various pH [START_REF] Oecal | The pH-dependent Client Release from the Collagen-specific Chaperone HSP47 Is Triggered by a Tandem Histidine Pair[END_REF][START_REF] Natsume | Interactions between collagen-binding stress protein HSP47 and collagen. Analysis of kinetic parameters by surface plasmon resonance biosensor[END_REF]. These pH-dependent kinetics have been proposed to be a binding switch, such that HSP47 binds to procollagen at the neutral pH in the ER and then unbinds as the pH drops in the early secretory pathway [START_REF] Widmer | Molecular basis for the action of the collagen-specific chaperone Hsp47/SERPINH1 and its structure-specific client recognition[END_REF]. There is a considerable change in HSP47 affinity for collagen observed at the pH values as seen in these secretory compartments, from 6 to 7.5. For instance, the off-rate of HSP47 is 0.192 s -1 at pH 6 and 0.028 s -1 at pH 7.5. The affinity and rate constants between HSP47 and SLD do not vary with pH. We use the previously measured affinity 0.26 µM [START_REF] Ishikawa | Intracellular mechanisms of molecular recognition and sorting for transport of large extracellular matrix molecules[END_REF] and a dissociation rate of 0.03 s -1 . The establishment and maintenance of specific molecular content in the ER and ERGIC, and their use by TANGO1LUM at the base of the tunnel, is key in our study. Two main gradients would be relevant for procollagen transport between ER and ERGIC -gradients of pH, and HSP47. These gradients define a zone of collagen binding at ER/ERES, and reduced binding in the tunnel/ERGIC. We will show that the gradients are sufficient to generate polarized and transient TANGO1/procollagen links, which produce enough force to propel procollagen from the ERES towards the ERGIC. We will evaluate the impact of these two gradients on the anterograde movement of procollagen. In the main text, we only consider a step-wise variation of pH and HSP47, while results of continuous gradients are presented in the supplementary information. It is well established that pH continuously decreases from ~7.4 in the ER to ~6 at the trans Golgi [START_REF] Paroutis | The pH of the secretory pathway: measurement, determinants, and regulation[END_REF]. Here, we will consider that the pH in the ERGIC and cis Golgi is ~6.5. There are a total of ~172,000 TANGO1 molecules per cell [START_REF] Itzhak | Global, quantitative and dynamic mapping of protein subcellular localization[END_REF], and ~300 ERES per cell [START_REF] Hammond | Dynamics of transitional endoplasmic reticulum sites in vertebrate cells[END_REF], i.e., an average of 500-600 TANGO1 per ERES. Also, there are ~8 million copies of HSP47 [START_REF] Itzhak | Global, quantitative and dynamic mapping of protein subcellular localization[END_REF] in HeLa cells, located in the ER. Hence, at a first approximation, we estimate the concentration of HSP47 in the ER at ~50 µM (see Materials and Methods). Based on these data, we will study the exit of procollagen over a range of TANGO1 molecules per procollagen varying from 10 to 600 and a local concentration of HSP47 in the ER varying from 1 to 500 µM.

TANGO1 is a long protein that contains an ~1000 residue long intrinsically disordered TANGO1LUM IDR in the ER lumen, an intra-membrane domain (IM) followed by a transmembrane domain (TM) and two coiled-coil regions on the cytosolic side (CC1 and CC2). An SH3-like domain (SLD) is located at the N-terminus. B. The C-terminal cytosolic coiledcoil regions of TANGO1

were suggested to open a tunnel between the ER lumen and the ERGIC. The lumenal portion of TANGO1 could separate the lumenal content of the ER and the ERGIC, creating a gradient of HSP47 and pH between the ER lumen and the tunnel. Some TANGO1LUM SLDs can bind to HSP47, which in turn binds to triple helical procollagen-generating a mechanical link that exert a force on procollagen. Because of the molecular gradients, this force is asymmetrical and drives procollagen movement. HSP47binding sites are located per pair every ~10 nm on the procollagen. All quantities are defined along the x-axis representing the center of the tunnel. The junction between the tunnel and the ER is placed at x=0; x<0 is in the lumen of the ER and x>0 is in the tunnel towards the ERGIC. Gradients of pH and [HSP47] are maintained, possibly by a network of TANGO1LUM IDRs.

A single TANGO1 generates force to propel procollagen

The long TANGO1LUM IDR at the base of the tunnel is largely disordered. Each IDR 'thread' can therefore be described as a polymer anchored at the membrane by the TANGO1 transmembrane domain and extending randomly on either side of the tunnel. The probability density of the position of the SLD depends on the persistence length, 𝜉, typically 4 residues (𝜉 1.4 𝑛𝑚) and the number 𝑁 of monomers, i.e. the number of repeats of this persistence length over the contour length of the TANGO1LUM IDR, here 𝑁 264. This probability density also varies with the accessible space. In a tunnel, the geometry resembles a one-dimensional space while a fully open space is in three dimensions. The expression of the probability density (per unit volume) along the axis of procollagen, 𝑥-axis, in a space of dimension 𝑑 is:

𝑝 𝑥 𝑒𝑥𝑝 𝑑𝑥 2𝑁𝜉 (1)
This symmetrical normal probability distribution is displayed in Fig. 2A for 𝑑 3.

Because of the pH and HSP47 gradients, the binding affinity of SLD to procollagen is different in the ER lumen and in the ERGIC. Convolving this difference and the SLD position distribution, provides the relative probability of a procollagen binding site to be occupied by an SLD (see Eq. 7 and associated text in the Materials and Methods). The examples presented in Fig. 2B display this asymmetric probability distribution and show limited variations with HSP47 concentration in the ER. When a TANGO1LUM stretches, it will try to retract, so that it can return to the relaxed conformation preferred by TANGO1LUM IDR. If the TANGO1LUM binds to a procollagen when it is stretched, its tendency to retract will generate a force that pulls procollagen towards the base of the tunnel. TANGO1LUM will never stretch beyond 150 nm (probability < 10 -12 ). Over this range, the extension of the TANGO1LUM is equally modeled as a worm-like chain (WLC, ( 27)) or a freely-jointed chain (FJC ( 28)). Both models (WLC or FJC) predict the same pulling force, within a 1% margin. The force probability displayed in Fig. 2C is obtained by combining the position probability in Fig. 2B and the force associated with each position. The asymmetry of the curves in Fig. 2C shows that the resulting force tends to pull procollagen towards the ERGIC. The mean force per procollagen occupied by an SLD is presented in Fig. 2D, for HSP47 concentrations between 0.1 nM and 1 mM assuming 1 nM HSP47 in the tunnel on the ERGIC side and 40 Tango1. There is a change in direction of the asymmetry, i.e., the resulting force propels procollagen towards the ER, when HSP47 concentrations is in the mM range, which is non-physiological. This shift in direction occurs because all the collagen binding sites and SLDs are bound to HSP47 in the ER, precluding the formation of a bond between procollagen and Tango1. This large range of HSP47 concentrations over which the force favors a movement towards the ERGIC shows the versatility of the system -it is insensitive to large fluctuations in concentrations. We now evaluate how several TANGO1 can collectively propel procollagen and induce procollagen movement. We present two approaches. In the first one, we assume all TANGO1 are at equilibrium. We studied the collective force generated by up to 600 TANGO1 per procollagen. The second approach presents simulations in which procollagen is completely unconstrained and movement occurs out of equilibrium. Because of the long simulation time, we could not go beyond 40 TANGO1 molecules per procollagen. Both approaches are complementary as they represent opposite situations (equilibrium vs. out of equilibrium) and provide similar quantitative result, showing the confidence in the conclusion.

Force induced by several TANGO1 at equilibrium

To understand how movement can be triggered with several TANGO1 acting in parallel, we start with a procollagen molecule extending from the ER into the tunnel. The model considers procollagen and TANGO1 are at equilibrium. Under these conditions, all TANGO1 molecules anchored at the ring can randomly bind to procollagen via HSP47, as described in the previous section. The probability of how many TANGO1 molecules are bound to specific procollagen HSP47-binding sites can be calculated. Each given configuration of procollagen interacting with some molecules of TANGO1, is associated with a certain force experienced by procollagen. The mean force can be computed by summing over all such possible configurations (Fig. 3A, see Materials and Methods for detailed calculation). As in the case of a single TANGO1, because of the pH and HSP47 gradients, the net mean force is positive and propels procollagen into the tunnel. Because the contributions of all TANGO1 are additive, this mean force is larger than that produced by a single TANGO1 and can reach up to 2 pN. To release the force, procollagen moves to a new position where there is no net force. The associated step size depends on the specific configuration of how many TANGO1 are interacting with procollagen at that moment. The mean step, presented in Fig. 3B for various HSP47 concentrations and numbers of TANGO1procollagen interactions, remains in the range 10 -30 nm (see Materials and Methods for detailed calculation). The procollagen displacement time can be estimated from the force it experiences and the equivalent viscosity of the medium (see Materials and Methods). This time is extremely short, less than 100 µs. Hence, when procollagen is unconstrained, it is unlikely that there is no time to reach equilibrium because procollagen moves too quickly compared to the kinetics of Tango binding and unbinding. Equilibrium can be reached if procollagen movement is retarded, e.g., by locally high viscosity, or transiently clamped by interactions with the membrane opposing the movement or by slow association of the procollagen trimer. In the latter case, movement will only occur when the clamp is released (growth of the tunnel or formation of the trimer) in the two examples), procollagen moves with a speed that varies linearly with the frequency of clamp release. This frequency must be slower than or commensurate with that of TANGO1 detaching from procollagen which is approximately the product of the off-rate of HSP47, 0.1 s -1 , and the number of HSP47-procollagen interactions (below 10, see Fig. 3C). Hence the speed would be less than 20 nm.s -1 .

It is worth noting that Eq. 1 assumes the TANGO1LUM IDR can freely access the whole space. In reality, the ER side is fully accessible but the protein cannot enter a large fraction of the volume on the tunnel side because the tunnel is narrow. This effect will amplify the probability of a TANGO1LUM IDR to be on the ER side and, thus, will accelerate the movement.

Movement of unconstrained procollagen

To obtain quantitative information on the movement of unconstrained out-of-equilibrium procollagen, the best approach is to perform simulations. We chose to start with a procollagen that is initially positioned at the base of the tunnel. TANGO1 molecules can bind randomly to procollagen, inducing a force thereby generating a step-wise movement. Thus, the first step occurs when the first TANGO1 binds. The binding and the subsequent movement bring this site of TANGO1/procollagen interaction to the base of the tunnel where the net force on procollagen is zero. The length of the second step, which occurs when a second TANGO1 binds, depends on the distance between the two TANGO1/procollagen bonds (see Fig. 4A for description). The direction and amplitude of the subsequent steps depend on the type of event (TANGO1 binding or unbinding), and location (ER or ERGIC lumen). Examples are shown of traces that represent a single run of simulation showing fiber displacement with time (Fig. 4B) and their means (Fig. 4C). Because of the increase of computation time with the number of TANGO1, we limited the simulations to a maximum of 40 TANGO1 per procollagen.

Despite the fact that both forward and backward movements of the procollagen occur within the 60 seconds simulations, the general features of the movement forward are reproducible between the various traces Fig. 4C. There are three phases. The first phase is a lag phase, waiting for the first TANGO1/procollagen bond to form. It lasts for a 3-4 seconds, when there are only 15 TANGO1 (Fig. 5C). The lag phase reduces as the number of TANGO1 molecules is increased. Fewer than 40 TANGO1 molecules are sufficient to make this lag phase disappear (Fig. 4B).

During the second phase, only one or two TANGO1 are bound to procollagen. These bonds are almost exclusively in the ER. They need to be moved to the base of the tunnel or inside the ERGIC, i.e. over a large distance to dissipate the force. The resulting steps are large, ~ 10 nm and the movement is fast, 10 to 20 nm.s - 1 , see for instance the fast movement between 2 and 3 s for 15 TANGO1 (Fig. 4C).

During the third phase, a steady-state is reached and procollagen advances at a uniform speed. The step size and their frequency depend on the number of TANGO1 molecules and the HSP47 concentration. Their variations are displayed in Fig. 5. Varying the number of TANGO1 or HSP47 concentration significantly changes the step size and frequency, between 1 and 10 nm and 0.1 and 1.2 s -1 , respectively. However, these variations in TANGO1 numbers and HSP47 concentration almost cancel each other out, making the speed of procollagen movement almost uniform in the ranges investigated here, between 1 and 2 nm.s -1 , with a maximum observed for 40 TANGO1 and 40µM unbound HSP47.

Figure 4: Movement of unconstrained procollagen. A. Schematic of the first events leading to procollagen movement. The first TANGO1 binds to procollagen (top panel), it applies a force that propels the procollagen until the force disappears (second panel, the arrow indicates the length of the step). A second TANGO1 binds (third panel) leading to a second step (bottom panel) and the cycles continue by attachment and detachment of TANGO1. B. Examples of trajectories (displacement of procollagen) in time for 8 simulations per conditions. C. Mean of the displacements over 15 trajectories. The blue shaded area corresponds to the standard deviation.

In A and B, left panels are for 15 TANGO1, right panels for 30 TANGO1, top for 5 µM HSP47 in the ER lumen and bottom panels for 40 µM HSP47 in the ER lumen.

Discussion

Energetic principle underlying the model

Our model suggests that collagen export from the ER is carried out by a mechanochemical ratchet brought about by the entropic contraction of TANGO1LUM IDRs surrounding the ERES. When the disordered region is partially extended it increases the probability of the SLD capturing a trimeric procollagen in the ER lumen at a distance away from the ERES. As one end of the TANGO1LUM IDR is connected to the TANGO1 transmembrane and therefore attached to the ER membrane, this reduces the ensemble's conformational entropy, generating an effective entropic force that pulls the SLD toward the ER membrane and propels procollagen from the ER to the ERGIC. The model, based on this principle, is summarized in Fig. 6. HSP47 binds procollagen and TANGO1 in the ER lumen and dissociates in the tunnel connecting them. TANGO1LUM IDR that stretch in the ER lumen and are attached to procollagen exert a force that propels procollagen towards the ERGIC. Molecular gradients, e.g., pH and/or HSP47 concentration, are required to polarize the movement (Fig. 6). Hence, at least one of these gradients must be maintained for sustainable procollagen transport. This is actively achieved by mechanisms that recycle HSP47 towards the ER lumen and keep a constant pH in the ER and in the ERGIC. These mechanisms are an indirect energy source of procollagen movement.

Stability of the system

Secretory traffic itself is pH-dependent, an effect that has been attributed to pH-sensitivity of processes and proteins involved in membrane fusion or fission. Here we show that a pH gradient between two compartments in the early secretory pathway could produce sufficient motive force to export cargoes from the ER without a need for a bona fide cargo receptor to drive cargo concentration. Both the equilibrium and unconstrained models predict similar speed of procollagen transport, ~1-10 nm.s -1 . The wide range of HSP47 concentrations and TANGO1 copy number over which the speed remains constant shows the flexibility and stability of the system. ERES do not need to always contain exactly the same number of TANGO1 molecules per procollagen and the HSP47 concentration can vary over several orders of magnitude without affecting the efficiency of procollagen transport. The mean number of TANGO1/procollagen links varies (Fig. 5D) but always remains between 10 and 30% of the total number of TANGO1 per procollagen. On the ER side, only a small number of TANGO1 are bound to procollagen and are sufficient to produce significant movement. When there are more links between TANGO1 and procollagen, the movement is smoother but the speed remains the same. Typically, 70-90% of the TANGO1LUM are not bound to procollagen and can maintain any other inter-TANGO1 cohesion. The results presented here are based on the assumption that there is a stepwise variation of both HSP47 and pH at the base of the tunnel because of the TANGO1LUM that can physically separate the ER lumen and the tunnel/ERGIC content. If only one of these two gradients actually exists, the conclusions remain qualitatively, as shown in Fig. 2D when the HSP47 concentration is the same in the ER and in the tunnel (data point for 1nM of HSP47in the ER). Similarly, a situation of a slow gradient of HSP47 concentration or pH would not affect the outcome significantly (see Supplementary information).

Origin of molecular gradients at the ERES and experimental tests

In this study we have used pH and HSP47 as representative molecular gradients, but the outcome will hold true for any gradients that affect TANGO1procollagen binding / unbinding in the ER and ERGIC. To study the putative origin of these gradients, HSP47 and protons are to be considered separately because they have very different properties: HSP47 is large, several nm in size, and diffuses slowly essentially following Stokes-Einstein equation for diffusion. Protons on the other hand are very small (~0.1 nm) and diffuse in water according to the Grotthuss mechanism. In the following we will model the compartment that encompasses the tunnel and part of ERGIC as a 500 nm long tubule with a diameter of 100 nm. Regarding HSP47: it is easy to envision its distribution as a gradient. This type of protein gradient is observed in several systems including at the ERES. Such gradients of predominantly ER-resident proteins have already been described that are COPII-dependent [START_REF] Ma | ER retention is imposed by COPII protein sorting and attenuated by 4-phenylbutyrate[END_REF] or cargo-dependent [START_REF] Gomez-Navarro | Cargo crowding contributes to sorting stringency in COPII vesicles[END_REF]. It is also reasonable to consider that very high density of TANGO1LUM IDR, cargo proteins, and cargo receptors, at the base of the tunnel creates a tight spaghetti-like network of disordered chains that may completely prevent HSP47 from entering the tunnel, or, at least significantly retard its diffusion towards the tunnel, thereby generating a gradient. It is worth noting that HSP47 bound to SLD and procollagen is brought in the tunnel by collagen. Because the affinity between HSP47 and SLD is ten times stronger than that between HSP47 and procollagen sites (260 nM vs. 2.25 µM), an HSP47 arriving in the ERGIC detaches primarily from procollagen. If it is also released from SLD, a single free HSP47 corresponds to a concentration of ~500 nM in the tubule. Hence, this free HSP47 quickly rebinds to an SLD and is brought back to the ER by the spontaneous random movement of the corresponding TANGO1 molecule. Regarding the proton gradient: the tubule contains ~0.7 proton at pH 6.5. A freely diffusing proton would leave the tubule in approximately 10 µs, which is equivalent to a flow of 70,000 protons per second. Secretory pathway membranes are enriched in V-ATPase, Na/H exchange (NHE) pumps, and other proteins that import protons into organelles. It is well-established that each V-ATPase consumes ~30 ATP.s -1 and 10 protons are pumped for 3 ATP [START_REF] Abbas | Structure of V-ATPase from the mammalian brain[END_REF][START_REF] Zhao | Molecular basis for the binding and modulation of V-ATPase by a bacterial effector protein[END_REF][START_REF] Maxson | Detection and quantification of the vacuolar H+ATPase using the Legionella effector protein SidK[END_REF]. Thus, a single V-ATPase can pump up to 100 protons per second. Hence, 70,000 protons per second is 700 times the proton influx from a single V-ATPase, meaning it is unlikely that proton pumps will be sufficient to compensate for the protons freely exiting this tubule. However, pH gradients have been visualized in smaller tubular extensions in individual lysosomes [START_REF] Suresh | Tubular lysosomes harbor active ion gradients and poise macrophages for phagocytosis[END_REF]. it is very possible that protons cannot freely diffuse out of the tunnel because the Grotthuss mechanism is based on local water organization that may easily be disrupted by the presence of the dense protein network of at the base of the tunnel. We assume that this impaired Grotthuss mechanism likely retards proton diffusion by several order of magnitude. For instance, if the diffusion is reduced 100 times, the influx of protons will be sufficient to maintain a pH on the ERGIC side of the tunnel. In terms of number of V-ATPase involved, this reduced diffusion would imply that 7 V-ATPases would be necessary on the ERGIC to maintain the pH, which is reasonable. This calculation does not include the action of other proteins such as NHE pumps that may even amplify the process. In summary, a protein gradient has been demonstrated for other similar proteins, and realistic within this context. A proton gradient maintained by proton pumps and sodium-proton exchange pumps has also been observed in similar geometries and is achievable by altering proton diffusion. Even though the it is reasonable to consider molecular gradients maintained by dense protein networks of TANGO1LUM IDR, cargo proteins, and cargo receptors, it has yet to be shown experimentally. Optical approaches seem the most likely to succeed as pH-sensitive variants of GFP have been directed to specific organelles [START_REF] Llopis | Measurement of cytosolic, mitochondrial, and Golgi pH in single living cells with green fluorescent proteins[END_REF]. Sensitive measurements can be performed by using signal sequence-tagged GFP variants, including pHluorin [START_REF] Miesenbock | Visualizing secretion and synaptic transmission with pH-sensitive green fluorescent proteins[END_REF] and dual-emission GFP (deGFP). More recent DNA-based sensors [START_REF] Chakraborty | Nucleic Acid-Based Nanodevices in Biological Imaging[END_REF], such as CalipHluor (8) provide simultaneous quantitative information about both Ca 2+ and pH, if they could be appropriately targeted to ERES The main difficulty is to visualize the tiny volume of the tubule at the time when it is assembled. High spatio-temporal resolution of the site using such reagents, could provide quantitative insights into a proton gradient.

Comparison with physiological procollagen secretion

The predicted speed of a few nm.s -1 for transport of procollagen from the ER to the ERGIC can be compared to the physiological rate of procollagen secretion in cells. It was recently established that fibroblasts secrete ~100,000 procollagen molecules per hour [START_REF] Pickard | ER-Golgi and lysosomal pathways together drive fibrous tissue formation[END_REF]. Procollagen is roughly 300 nm long. Hence, fibroblasts secrete a quantity of approximately 30 mm procollagen per hour, i.e., 10,000 nm procollagen per second. There are about 180,000 TANGO1 per cell. Assuming, 60 TANGO1 propel procollagen any time translates to export of 3,000 procollagen molecules from the ER. This corresponds to a speed of ~3. nm.s -1 , which is consistent with the predicted value. This model is based on the ER-ERGIC transport of procollagen in a vertebrate system, but represents a general mechanism where electrochemical gradients of ions and proteins can be used to provide the motive force to transfer components from one compartment to another.

Building the ER/ERGIC tunnel

As a final comment, it is worth noting that the TANGO1induced force presented here may facilitate the initial formation of the ER/ERGIC tunnel. Before the two compartments are connected, there is no pH or HSP47 gradient. However, TANGO1 will still bind to procollagen up to 60 nm away from the membrane. Since procollagen is exclusively in the ER, there is a "gradient" of procollagen binding sites and the global force generated will push on the membrane, starting a bud on the cytoplasmic face that may extend 60 nm towards the ERGIC to balance the pulling and pushing force. This deformation of the ER membrane can act synergistically with COPII proteins to build an export route. Once the transport step is concluded and collagen has been transferred to the ERGIC, it is conceivable that ERES machinery disengage to separate the ERES and ERGIC continuity for a subsequent round of cargo transport. Alternatively, when there is no cargo to contribute to the ER-ERGIC diffusion barrier, then these local ionic gradients are abolished. While the mechanism presented here relates to vertebrate TANGO1 / HSP47 -dependent procollagen export, the SLD could bind to other chaperones or cargo receptors that have similar pH-dependent activity profiles to utilize the same principle to export not only collagens, but also other secretory cargoes.

Materials and Methods

Procollagen modeling

Procollagen triple helices are rod-like complexes that are ~300 nm long. In our model, a triple helical procollagen is transported through a tunnel generated by the function of TANGO1 from the ER to ERGIC. We have assumed that there is an infinite supply of procollagen. The movement of procollagen can thus be considered unidimensional. The origin of the movement axis, 𝑥 0, is chosen at the position of the TANGO1 ring. Negative 𝑥 values are located in the ER while positives are in the ERGIC. HSP47 binding sites are found in pairs, distributed evenly at 10nm intervals along the axis of procollagen. We represented this arrangement by modeling procollagen as a rigid long rod with dual HSP47 every 10 nm. The affinity, and on-and off-rates of HSP47 to procollagen binding have previously been measured and depend on the pH.

HSP47 concentration in the ER

HSP47 is only located in the ER. There are ~8 million copies of HSP47 per cell. Each cell has a volume of 2.5.10 3 µm 3 and the ER occupies 10% of the cell volume. Hence 8 million copies of HSP47 are randomly distributed in 2.5.10 2 µm 3 which corresponds to ~50 µM.

Binding procollagen and TANGO1

TANGO1 binds procollagen with low affinity (3.3 µM for procollagen IV (38)), which is neglected in our modelling. They can be indirectly connected by a shared HSP47 protein that is simultaneously attached to the SH3-like domain (SLD) of TANGO1 and one of the binding sites of procollagen. The probability that an SLD or a binding site on procollagen located at 𝑥 is occupied by a HSP47 protein is respectively:

𝑝 𝑥 / (2a) 𝑝 𝑥 / (2a)
Where 𝐾 𝑥 , 𝐾 𝑥 and 𝑐 𝑥 are the affinities of HSP47 binding with SLD, with procollagen and the HSP47 concentration at 𝑥 (as defined is Fig. 1).

Force of TANGO1 on procollagen

When TANGO1 is connected to procollagen, it has to remain at that location, preventing its natural movement thereby generating a force pulling the procollagen towards the tunnel at 𝑥 0. The value of this force, 𝑓 𝑥 , is very well characterized and can also be obtained using the WLC [START_REF] Bouchiat | Estimating the persistence length of a worm-like chain molecule from force-extension measurements[END_REF] or the FJC (28) model over the distance range we used here (between 3√𝑁𝜉 and 3 √𝑁𝜉 .

Procollagen movement modeling

Procollagen can be approximated as a cylinder of length 300 nm and diameter between 1.5 nm when HSP47-free and 8 nm when bound to HSP47. Following Broersma [START_REF] Broersma | Viscous Force and Torque Constants for a Cylinder[END_REF], we find that for a medium with the viscosity of water and a force of 50 fN, the initial speed of procollagen movement is between 10 and 60 µm/s. This speed vanishes exponentially with time during the displacement because of the fast decrease in force. The characteristic time for a 5 nm displacement is between 40 and 80 µs. As indicated in the main text, each step of the procollagen movement occurs with a frequency of 0.1 Hz or less, which shows that the displacement upon force can be considered as instantaneous. It could be argued that TANGO1LUM locally increase the viscosity. However, this will impact the global movement only if the resulting viscosity is greater than 1,000 -10,000 that of water.

Equilibrium

In the equilibrium section, we assume that procollagen has already entered the tunnel and a pair of HSP47 binding sites is located at 𝑥 0. Within the distance considered, there are 12 HSP47 binding sites in the ER and in the ERGIC. Hence, we consider 26 binding sites (13 pairs). Our goal here is to find the probability of all possible configurations in which some TANGO1 are connected to procollagen. Using the force corresponding to each configuration, we will obtain the mean force applied on procollagen. To compute all configurations, we assumed that TANGO1-SLD has full access to the whole space, as shown in Eq. ( 1) that is used in a three-dimensional system. In reality the dimensionality is probably lower, which will favor more bond formations, suggesting an underestimation of the force. The local concentration of SLD along the axis is:

𝑐 𝑥 𝑁 𝑝 𝑥 𝑁 𝑒𝑥𝑝 𝑑𝑥 2𝑁𝜉 /𝑁 (3)
Where 𝑁 is the Avogadro constant.

Hence the concentration of HSP47-bound SLD is:

𝑐 𝑥 𝑝 𝑥 𝑐 𝑥 / (4)
the probability of having a collagen binding site located at 𝑥 is bound to Tango1 can be written as:

𝑃 𝑥 〈𝐶𝐻𝑆〉 〈𝐶𝐻𝑆〉 〈𝐶𝐻〉 〈𝐶〉 1 1 〈𝐶𝐻〉 〈𝐶𝐻𝑆〉 ⁄ 〈𝐶〉 〈𝐶𝐻𝑆〉 ⁄ (5)
Where 〈𝐶〉, 〈𝐶𝐻〉 and 〈𝐶𝐻𝑆〉 are respectively the fractions of the time a collagen site is unbound, bound to HSP47 alone and bound to SLD via a shared HSP47. The ratios 〈𝐶𝐻〉 〈𝐶𝐻𝑆〉 ⁄ and 〈𝐶〉 〈𝐶𝐻𝑆〉 ⁄ are equivalent to ratios of effective concentrations. Thus:

〈 〉 〈 〉 6a 〈 〉 〈 〉 6b
Where 𝑐 𝑥 is the local concentration of HSP47 and 𝐾 𝑥 is the affinity between a collagen binding site and HSP47. The first equation assumes 𝐾 𝑥 is the same whether HSP47 is bound to SLD or not. The second equation is the equilibrium between C, CHS and bound SLD. Hence, the resulting probability is: 𝑃 𝑥 𝑐 𝑏𝑇 𝑐 𝑏𝑇 𝑐 𝐻𝑆𝑃47 𝐾 𝐶 [START_REF] Paroutis | The pH of the secretory pathway: measurement, determinants, and regulation[END_REF] The mean force can now be expressed as:

∑ ∑ ∏ 𝑃 𝑥 ∏ 1 , 𝑃 𝑥 ∑ 𝑓 𝑥 ( 8
)
Where 𝑙 is the number of occupied collagen sites in each combination 𝑥 , 𝑥 (𝑗 𝑙) is the list of occupied sites and 𝑥 (𝑗 𝑙) the unoccupied sites. 𝑁 is the number of collagen sites (here, we set it to 26). When a force is applied and freely moves, a displacement will occur to bring the force to zero. Noting 𝛿 the displacement associated with configuration 𝑥 , we obtain the mean displacement per step:

𝛿 𝑃 𝑙 𝛿 𝑥 𝑖 ( 9 ) Where 𝑃 is the probability of combination 𝑥 .

Out of equilibrium simulations

To study the displacement of procollagen in HSP47 and pH gradients, we used stochastic simulation algorithm considering the displacement of a single procollagen along the tunnel. At the start of each simulation, the procollagen is positioned at the entrance of the tunnel. HSP47 molecules are randomly bound to SLDs and procollagen sites according to the associated chemical reaction. The movement of procollagen is implemented in 10 ns steps. At each step, the SLD and HSP47 proteins freely diffuse (see Supplementary information), SLD/HSP47, HSP47/procollagen and SLD/HSP47/procollagen randomly bind or unbind and the procollagen moves by diffusion and under the force applied by TANGO1. Each simulation lasted an equivalent of 60 seconds. We tracked the position of procollagen extremity and of the force applied by TANGO1 on procollagen over the simulation time. Simulations were run for a number of TANGO1 in [START_REF] Bachinger | Folding mechanism of the triple helix in type-III collagen and type-III pN-collagen. Role of disulfide bridges and peptide bond isomerization[END_REF][START_REF] Raote | Protein transport by vesicles and tunnels[END_REF][START_REF] Koide | Xaa-Arg-Gly triplets in the collagen triple helix are dominant binding sites for the molecular chaperone HSP47[END_REF][START_REF] Itzhak | Global, quantitative and dynamic mapping of protein subcellular localization[END_REF][START_REF] Gomez-Navarro | Cargo crowding contributes to sorting stringency in COPII vesicles[END_REF][START_REF] Miesenbock | Visualizing secretion and synaptic transmission with pH-sensitive green fluorescent proteins[END_REF]40] and an external concentration of HSP47 in [START_REF] Weigel | ER-to-Golgi protein delivery through an interwoven, tubular network extending from ER[END_REF][START_REF] Pezzati | High-resolution calcium mapping of the endoplasmic reticulum-Golgiexocytic membrane system. Electron energy loss imaging analysis of quick frozen-freeze dried PC12 cells[END_REF][START_REF] Bachinger | Folding mechanism of the triple helix in type-III collagen and type-III pN-collagen. Role of disulfide bridges and peptide bond isomerization[END_REF][START_REF] Koide | Xaa-Arg-Gly triplets in the collagen triple helix are dominant binding sites for the molecular chaperone HSP47[END_REF][START_REF] Gomez-Navarro | Cargo crowding contributes to sorting stringency in COPII vesicles[END_REF]40,50,100,500]. Fifteen trajectories were run for each pair of TANGO1 number and HSP47 concentration.

We assumed that binding of the reactants does not happen in any specific sequential order and that no cooperativity exists between the reactants, procollagen, HSP47 and TANGO1. We also assumed that HSP47 in solution is constant over the simulation time, meaning that the simulated system is in contact with an infinite reservoir of HSP47. Free HSP47 molecules diffusing in the ER compartment are restricted to diffuse within the ER interval. Only HSP47 bound to procollagen or TANGO1 is allowed to cross the TANGO1 diffusion barrier. Whenever an HSP47 molecule in the ERGIC dissociates from both TANGO1 and procollagen, the HSP47 is removed from the ERGIC. Such immediate removal is abrupt, however live video microscopy, with high spatio-temporal resolution showed that HSP47 does not leave the ERES, suggesting that a removing and/or inactivation mechanism locally exists [START_REF] Omari | Mechanisms of procollagen and HSP47 sorting during ER-to-Golgi trafficking[END_REF]. Details of the simulation procedure are presented in the Supplementary text. The python codes for the Equilibrium and Out of equilibrium cases are provided in the Supplementary text. awarded to V.M. and F.P. V.M. acknowledges the support of the Spanish Ministry of Science and Innovation to the EMBL partnership, the Centro de Excelencia Severo Ochoa and the CERCA Programme / Generalitat de Catalunya. I.R. acknowledges the support of Fondation pour la Recherche Médicale (grant AJE202210016216).

Figure 1 :

 1 Figure 1: Model of procollagen transport by TANGO1. A. TANGO1 is a long protein that contains an ~1000 residue long intrinsically disordered TANGO1LUM IDR in the ER lumen, an intra-membrane domain (IM) followed by a transmembrane domain (TM) and two coiled-coil regions on the cytosolic side (CC1 and CC2). An SH3-like domain (SLD) is located at the N-terminus. B. The C-terminal cytosolic coiledcoil regions of TANGO1 were suggested to open a tunnel between the ER lumen and the ERGIC. The lumenal portion of TANGO1 could separate the lumenal content of the ER and the ERGIC, creating a gradient of HSP47 and pH betweenthe ER lumen and the tunnel. Some TANGO1LUM SLDs can bind to HSP47, which in turn binds to triple helical procollagen-generating a mechanical link that exert a force on procollagen. Because of the molecular gradients, this force is asymmetrical and drives procollagen movement. HSP47binding sites are located per pair every ~10 nm on the procollagen. All quantities are defined along the x-axis representing the center of the tunnel. The junction between the tunnel and the ER is placed at x=0; x<0 is in the lumen of the ER and x>0 is in the tunnel towards the ERGIC. Gradients of pH and [HSP47] are maintained, possibly by a network of TANGO1LUM IDRs.

Figure 2 :

 2 Figure 2: TANGO1 extension, binding probability and force. A. Because the TANGO1LUM IDR is intrinsically disordered, the location of the SLD follows the symmetric gaussian distribution presented in Eq. 1. The case of a three-dimensional space is displayed here. B-C. Probability of the location (B) and force (C) of a TANGO1/procollagen link assuming 40 Tango1 molecules overall, a 1 nM HSP47 concentration, and pH 6.5 in the tunnel, and 1 µM (orange) or 50 µM (blue) and pH 7.4 in the ER lumen. Positive forces are towards the ERGIC and negative forces are towards the ER. These distributions are asymmetric as a result of the HSP47 and pH gradient. Regions shaded in green or red are in the ER or ERGIC, respectively in panels A, B and C. D. Mean force per bound procollagen site, obtained as the sum of the product of the force (panel A) and force probability (panel C) at each concentration for 40 Tango1.

Figure 3 :C

 3 Figure 3: Equilibrium: force, displacement, occupied sites. A. Mean force on procollagen when several TANGO1 (10 to 40, right axis) are acting at equilibrium and for HSP47 concentrations varying from 1 µM to 500 µM in the ER lumen (front axis). B. Mean procollagen displacement (step) to dissipate the force exerted by TANGO1 on the procollagen. HSP47 concentration in the ERGIC is set at 1 nM. C. The number of occupied sites, i.e., bound to SLD via HSP47, depends on

Figure 5 :

 5 Figure 5: Physical characteristics of the trajectories. A, B, C and D display respectively the mean step size, step frequency, speed and TANGO1/procollagen links for 15 to 40 TANGO1 copy numbers and 1 to 500 µM HSP47 in the ER lumen.

Figure 6 :

 6 Figure 6: Diagram depicting how procollagen movement is achieved

Acknowledgements

We thank Prof. Andreas Ernst and Prof. Felix Campelo for useful discussion. This work was supported by the LiquOrg synergy grant, ERC-2020-SyG-951146,


Dong-Ming Yan

Julien Wintz

Bernard Mourrain

Wenping Wang

Frédéric Boudon

Christophe Godin

Efficient and robust tree model reconstruction from laser scanned data points

This paper presents a reconstruction pipeline for recovering a tree model from laser scanned data points. The process is made up of three main steps: segmentation, reconstruction and modeling. Based on a variational k-means clustering algorithm, cylindrical components and ramified regions of data points are identified and located. An adjacency graph is then built from neighborhood information of components. Simple heuristics allow us to extract a tree structure and identified branches from the graph. Finally, a B-spline model is computed to give a compact and accurate reconstruction of the branching system. I.3.3Computer GraphicsMethodology and Techniques

Introduction

Due to the complexity and the diversity of plant shapes, the construction of plant geometric models is still a challenging problem for both computer graphics and biology. Two major approaches have been developed so far.

On the one hand, plant models can be simulated by procedural methods. With various degrees of realism these methods can mimic the development of plant axes to create complex branching structures as an emerging property of prescribed developmental rules. Global constraints can be added to these local-to-global procedures to control the overall shape of the resulting models [WP95,PHHM97,SRDT01,BPF * 03]. These methods have proved very successful to build up various types of plant models ranging from herbs to trees. However, these procedural methods have two important limits. First, modelers must have some expertise about the growth of the plant they want to model in order to design the developmental rules or tune the parameters. Second, if one wants to build up a model corresponding to the exact 3D structure of a plant, these methods do not give any hint on how to organize measurements on the observed plant to build up an accurate computer representation.

Figure 1: Tree model reconstruction. From left to right: 1) Scanned data of an apple tree; 2) Segmentation result, different colors for different clusters; 3) Branch identification result. The color of each branch is the same as its starting cluster; 4) Final B-spline surface representation of tree branches.

Data acquisition

To address the latter issue, researchers in both biology and computer graphics have designed methods to directly capture the 3D plant structures in computers using different types of sensors and adapted measurement protocols. Contact methods were initially developed by agronomists and plant modelers to digitize moderate size plants. Magnetic [START_REF] Sinoquet | Assessment of the threedimensional architecture of walnut trees using digitising[END_REF] or sonic [?, ?] devices were used to allow the observer to get the position and orientation of each plant organ using a 3D pointer. These methods make it possible to create 3D branching models faithful to the observed plant topology and geometry [START_REF] Godin | A method for describing plant architecture which integrates topology and geometry[END_REF]. However, they are extremely time-consuming (the digitizing of a single tree contained in a 3m3 bounding box takes 1 day for 2 persons on average). To alleviate this difficulty, researchers have considered the use of other types of sensors. The possibility to reconstruct plant structures using digital cameras was tested in different works [SRDT01, RMD04, PS05]. One or several photographs are taken around the plant from different viewing angles which make it possible to extract geometric and optical characteristics of the plant structure using image analysis techniques. In general, the global 3D silhouette of the plant is first extracted. Then, depending on the application, additional traits are extracted from the images: local opacity and texture of elementary cell volumes [START_REF] Reche | Volumetric reconstruction and interactive rendering of trees from photographs[END_REF], foliage characteristics such as crown volume or total leaf area of the plant [START_REF] Phattaralerphong | A method for 3d reconstruction of tree crown volume from photographs: assessment with 3D-digitized plants[END_REF] or even approximations of the plant branching system using a procedural method to grow a plant within the bounding volume [START_REF] Shlyakhter | Reconstructing 3D tree models from instrumented photographs[END_REF]. These approaches are easy to apply to medium-size isolated plants, and give good results for inferring global characteristic of plant foliage. However, identifying individual organs from 2D photographs (trunk, branches or individual leaves) is still a limiting issue [START_REF] Hsu W.-H | Constructing a 3D trunk model from two images[END_REF].

More recently, to capture accurately the geometry of individual plants, researchers developed techniques based on 3D laser scanners. The additional depth information associated with each pixel of the scanned image makes it possible to recover the position of the plant structure in 3D and some of its optical properties. This information has been recently exploited at the organ level to reconstruct leaf surfaces with accuracy and provide parameters that can be further exploited in light interception models, [CAD * ar]. At plant level, first tests for the reconstruction of simple branching systems were carried out by [START_REF] Pfeifer | Automatic reconstruction of single trees from terrestrial laser scanner data[END_REF]. A more complete method was proposed by [START_REF] Xu | Knowledge and heuristic-based modeling of laser-scanned trees[END_REF] who introduced a method for reconstructing complete plant models from 3D scans. This method makes it possible to infer the topology and the geometry of the plant structure with accuracy. However, if the main branching system (trunk and low order branches) is usually accurately reconstructed, the rest of the branching system (finer branch of high order) is inferred via an additional stochastic procedural method. The result was assessed via visual inspection.

The reconstruction problem

In this paper, we consider the problem of reconstructing complete branching systems faithful to observed tree from 3D laser scans. Since branches may be hidden by leaves, we restrict our approach to trees without leaves (e.g. temperate species observed in winter for example). Our goal is to obtain a compact model that reflects with accuracy the observed branching system. In particular, from the clouds of points obtained from the 3D laser scans, the method should be able to:

• identify the different plant axes. Ambiguity in axis recognition may come from two main phenomena i) different axes may have parts that are close to each other in the 3D space, ii) parts of the axes may be hidden by other axes.

• identify axis connections. Connections between axes may also be hidden or partially sampled, making it difficult to guess the correct hierarchy of axes.

• estimate axis geometry. One key issue of the reconstruction is to recover the axis diameter variation from the partial sampling of the axis surface (each scanned imaged only contains a part of this surface).

We propose hereafter a chain of algorithms that is aimed to meet these requirements. First, the main trunk and branch structures of the tree are identified during the reconstruction process. Each branch is represented by a sweeping surface along its skeleton, with various radius determined from scanned data. We choose this parametric representation since it is compact, efficient to manipulate and easy to edit. The overall reconstruction process is illustrated on an apple tree in Fig. 1.

The main contributions of this paper include:

• A complete framework for tree structure reconstruction from scanned point cloud.

The reconstructed model is represented by a set of sweeping surfaces along the skeleton of the tree;

• A new variational point cloud segmentation framework is proposed (Section 2), which locates the cylindrical and branching regions efficiently;

• Simple heuristics are proposed to reconstruct branching structure of trees from segmentation result (Section 3);

Related work

Recently, with the increasing requirements for the realism of the visual effect, researchers begin to integrate computer vision techniques with computer graphics for tree modeling and rendering. A lot of works have been done on image based [RMD04, QTZ * 07, NFD07, TZW * 07, TCH07] and sketch based plant modeling [START_REF] Okabe | Interactive design of botanical trees using freehand sketches and example-based editing[END_REF][START_REF] Ijiri | Seamless integration of initial sketching and subsequent detail editing in flower modeling[END_REF][START_REF] Ijiri | The sketch l-system: Global control of tree modeling using free-form strokes[END_REF]. The input data could be a sequence of photographs, two images of different views or some simple 2D sketches, and the output is a 3D tree model, which has similar visual effect with the input images. Image based modeling techniques are usually used for realistic rendering purpose. Since the output model is synthesized instead of reconstructed from real data, which is different from the real geometry of a tree. It cannot be used for agronomy or biology analysis and simulation.

Relatively little work has been done on tree reconstruction from scanned point data in literature. Pyysalo et al. [START_REF] Pyysalo | Reconstructing tree crowns from laser scanner data for feature extraction[END_REF] propose a method to reconstruct tree crowns from scanned data for feature extraction. But their purpose is to compute statistic information of forest, which is far from the real branch structure of a tree. Gorte and Pfeifer [START_REF] Gorte | Structuring laser-scanned trees using 3D mathematical morphology[END_REF] use a 3D morphology method to segment and extract the skeleton from point data. As reported by the authors, the space and time become the bottleneck of their method, which increases with the third power of the resolution. It becomes impossible for large point sets with millions of points. Based on the segmentation method of [GP04], Pfeifer et al. [START_REF] Pfeifer | Automatic reconstruction of single trees from terrestrial laser scanner data[END_REF] present a method to reconstruct tree models by fitting cylinders for segmented data. Because the incompleteness of the scanned data, the fitted cylinder can be far from the real branch. Instead of fitting, we use bounding cylinder to approximate the radius of the branches, which is more efficient and more robust than cylinder fitting.

The most related work to our approach is [START_REF] Xu | Knowledge and heuristic-based modeling of laser-scanned trees[END_REF]. In this work, the input scanned data are first connected together to form a graph. The main skeleton of the tree is produced by clustering points with same quantized distance to the root and the clusters are used to generate skeleton of tree. The other small branches and leaves are synthesized then. But the topology of the skeleton of their method may not be a tree structure, which often contain loops, as we will discuss later, and the resulting skeleton is not geometric faithful since only the distance to the root is used for segmentation.

In our work, a novel skeletonisation method based on variational geometric clustering is proposed. Further more, the main trunk and branches are identified and we produce a more compact and topological correct representation of branch structure of the tree. We refer the reader to [START_REF] Boudon | Survey on Computer Representations of Trees for Realistic and Efficient Rendering[END_REF] for a survey on computer representation and efficient rendering techniques of trees.

Outline

Our approach is composed of three main steps: segmentation, branch reconstruction and modeling. Section 2 introduces a new variational approach for point cloud data segmentation. Section 3 presents an efficient algorithm for reconstructing branches from the clusters obtained in the segmentation phase. Finally, a flexible interactive modeling system is introduced in Section 4. Experimental results are given in Section 5 before we draw our conclusions in Section 6.

Segmentation

Laser scanned real trees produce a huge amount of unstructured data, which naturally feature many cylindrical shapes -the branches -see Fig. 1 (left) for example. The aim of the segmentation step is to partition the data into connected sub clusters, each cluster being bounded by a circular cylinder as tightly as possible. We will first give the problem definition and then explain our variational point cloud segmentation algorithm in detail.

Let P = {p i , i = 1, . . . , N} be a dense point set of a tree model. A segmentation

C of P is a set of clusters {C i , i = 1, . . . , n}, such that S n i=1 C i = P, where (n ≪ N),
and C i ∩ C j = ∅, for any i = j. Each cluster C i contains a sub set of the point set, i.e.

C i = {p i k , k = 1, . . . , n i }, where n i = |C i |.
We propose a hybrid approach to segmenting the point set and detecting cylinder components at the same time. The following are the main steps of our segmentation algorithm:

1. Preprocessing: A kd-tree representation of the point set P is constructed to facilitate the retrieval of neighboring points of any data point in the point set P.

K-means clustering:

The preprocessed point set is segmented into clusters using the Lloyd iteration [START_REF]Least square quantization in PCM[END_REF], which minimizes the energy function defined in Eqn. 1 below. Each cluster is a connected sub-graph of the kd-tree.

3. Cylinder detection: For each cluster C i obtained from the k-means clustering, a minimal bounding cylinder is computed to measure the tightness of the bounding volume. If the bounding volume satisfies some criteria, the cluster C i is flagged as fixed and will not change anymore.

4. Subdivision: If there remain clusters that cannot be bounded by a cylinder tightly or the number of points in these clusters is more than a user specified value, then they are subdivided and the process goes back to step 2. Otherwise, the algorithm terminates.

Preprocessing

Since a point set features no adjacency relationship, the neighborhood of a point p i is represented by its k-nearest neighbor points, N k (p i ). A kd-tree data structure is constructed for efficient neighborhood search. We use ANN library [START_REF] Mount | ANN: A library for approximate nearest neighbor searching[END_REF] for kdtree construction in our implementation and choose k = 8 in all our experiments.

K-means clustering

In this step, we want to segment the input point cloud P into a set of clusters C, reflecting the main structure of the tree, where all points belonging to a cluster form a connected component.

To this end, we propose a variant of the well known k-means clustering technique, which efficiently segments the point set while keeping the connectivity of neighborhood at the same time. The clustering algorithm is adapted from the distortion minimization flooding algorithm used for mesh segmentation [START_REF] Cohen-Steiner D | Variational shape approximation[END_REF]. The Lloyd iteration [START_REF]Least square quantization in PCM[END_REF] is used to repeat between clustering and centroid replacement. The energy

E(P, C) = n ∑ i=1 E(P i , C i ) = n ∑ i=1 n i ∑ j=1 d(p j , c i ) 2 , ( 1
)
where c i is the center of the cluster C i and d(p j , c i ) is the Euclidean distance between the point p j and the center c i . The following is the detailed description of our variational segmentation algorithm. 1. Initialization: To start the algorithm, we randomly select n points {s i , i = 1...n} as initial seeds to define n clusters {C i , i = 1...n}, where n is a user input parameter.

2. Clustering: Once a seed point is found for each cluster, we segment the point set by growing a region for each cluster according to these seeds. Each point p i is equipped with a flag to indicate whether this point is selected or not. The flag of each seed point is set to selected and the flags of all other points are set as unselected at beginning. The implementation of the clustering algorithm is similar to that proposed in [START_REF] Cohen-Steiner D | Variational shape approximation[END_REF]. We use kd-tree instead of the connectivity information of triangle mesh. The reader is referred to [START_REF] Cohen-Steiner D | Variational shape approximation[END_REF] for details.

3. Updating: Once the clusters C i have been identified, a new seed point s i needs to be selected from C i in order to compute the next generation of clusters. This is done as follows. First the center c i of each cluster C i is computed. We choose

s i = arg min p j ∈C i d(c i , p j )
, as the new seed point; that is, we use the data point p j in C i that is closest to c i as the new seed. Next the total error E iter (P, C) of the energy function is evaluated, where iter is the number of iterations done so far. Should a maximal number of iteration be reached or should the error between two iterations be smaller than a user defined threshold (i.e. |E iter -E iter-1 | < ε), the iteration stops; otherwise we go to step 2.

Cylinder detection

The k-means clustering terminates when it has produced a well shaped partition of the input point cloud. Since the shape of branches is naturally cylindrical (at least locally), we consider extracting cylinder components from the partition.

In order to compute bounding cylinders, the principle direction of each cluster C i is computed. The eigenvector of the covariance matrix of C i with largest eigenvalue is selected as the z-direction (i.e. central axis) of the cylinder. Each point of C i is projected onto the plane passing through center of the cluster C i and having the z-direction as its normal vector. A minimal bounding circle [Gär99] of projected 2-dimensional points is computed, and the radius of this circle is used as the radius of the bounding cylinder. The tightness of the bounding cylinder is measured by evaluating the root mean square (RMS) error between the data points and the bounding cylinder of C i . If the RMS error is smaller than a threshold δ, the cluster C i is flagged as fixed and will not be changed any further.

The segmentation should finish whenever all clusters are flagged as fixed. But this case seldom happens in practice, since clusters including intersection regions of different branches are hardly bounded by a cylinder appropriately. This kind of clusters need to be further subdivided in the next step.

Cluster subdivision

Deciding how many cluster should be created at the beginning is not an easy task. Moreover, the segmentation result after only one k-means iteration cannot be used to produce a skeleton of the tree. In this step, each unfixed cluster is subdivided into two clusters if the number of points of this cluster is larger than a user defined number. One sub-cluster uses the seed of its parent cluster as its own seed, the seed of the other is chosen as the parent cluster's point with maximal distance to its seed. After subdivision, the process starts back at the clustering step.

The algorithm terminates when no cluster can be subdivided anymore or the total number of clusters exceeds a maximum user specified value. Note that we also provide the user the ability to stop the algorithm whenever current results are deemed satisfactory. The segmentation result of the apple tree is shown in Fig. 2

(middle left).

Other operations are provided for convenience such as inserting one new cluster or merging a pair of two clusters but we will not detail this anymore in the paper.

Branch reconstruction

After the segmentation step, most of cylindrical regions of the input data are grouped together, and the intersecting regions of branches are also located progressively. The aim of this step is to extract the skeleton of the tree from segmented clusters. We further detect all the branches from the skeleton of the tree.

Building adjacency graph

First, an adjacency graph is built from the clusters by detecting the neighborhood information for each cluster. This is achieved by checking each point p i and its k-nearest neighbors p j ∈ N k (p i ): if p i and p j belong to different clusters C i and C j , then C i and C j are flagged as neighbors. The adjacency graph G is obtained by defining a node for each cluster and an edge for each pair of neighboring clusters.

Skeleton extraction

The next step is to construct the skeleton from the adjacency graph G. Due to the definition of neighboring cluster, the adjacency graph may not be a tree, that is because three mutually meeting clusters form a loop, as shown in Fig. 3 (left), which causes problems in later processing. We resolve this problem by reducing the adjacency graph into a tree as follows. First, the root node is selected as the node contains the point with the lowest z position. Once the root node is found, we compute the shortest paths from the root to all the other nodes in the graph. The shortest paths are then converted into a tree structure, representing the skeleton of the tree, see Fig. 3 (right).

The only issue requiring explanation here is the definition of the weight for each edge in the graph. In order to achieve high geometric fidelity, we use a more elaborate method in our framework to measure the distance between two neighboring clusters, instead of using the distance between the center of adjacent clusters as a weight for the edge connecting these cluster in the skeleton, as done in [START_REF] Xu | Knowledge and heuristic-based modeling of laser-scanned trees[END_REF]. For each pair of neighboring clusters, we define a junction point, extracted by traversing all the points included in two connected clusters C i and C j . If a point p belongs to C i and one or more of its neighbors belong to C j , then this point p is classified as a boundary point of C i and C j , and vice versa. The position of a junction point is computed as the center of all the boundary points between C i and C j . Fig. 4 (upper left) shows the definition of such a junction point. Then the distance of two clusters is measured as the sum of the distances from the junction point to the centers of the two clusters. This distance is used as the edge weight for skeleton extraction from the adjacency graph.

In addition to the definition of junction points for each adjacent cluster, we also compute an extra junction point for each leaf node, including the root, to better approximate the real structure of the tree. Fig. 4 (lower left) illustrates this simple idea for creating junction points for leaf nodes. This new point is computed as the symmetric junction point about the center of this cluster. All the edges that do not belong to the shortest paths to the root cluster are removed.

Branch identification

Once the skeleton of the tree is computed, identifying all the branches becomes necessary for a tree modeling and simulation system. We propose a simple and intuitive method for detecting longest possible branches, which we call distance based method.

A branch is defined as a sequence of nodes, which starts from a node of intersecting branches, i.e. the valence of the node val(N i ) ≥ 3 and ends with a leaf node. The main trunk starts from the root, which is a special case. To identify all the branches, we first detect the main trunk of tree, then identify all the other branches recursively.

Starting from the root node, we first compute the longest distance for each node to the leave nodes recursively. We select the longest path as the main branch, and the other branches are detected recursively as following.

Detection of a branch is finished when a leaf node is reached. We use an FIFO queue to facilitate the branch detection procedure. The queue is initialized by pushing the root in the queue. The node on the top of queue is popped out repeatedly, and a branch with longest distance from this node to a leave node is detected. Each time when we find a branch, we check all the children of each node of this branch. If all the children of the node are already assigned to a branch, then this node is flagged as inactive, otherwise it is marked as active and pushed to the end of queue. The algorithm ends when the queue is empty. Algorithm 3.1 outlines the algorithm. The branch identification result of the apple tree is shown in Fig. 1 (middle right).

Tree modeling

The final step of our pipeline aims at providing a compact and smooth surface representation of tree models not only for visualization but also for modeling and simulation, since further processing of tree models include intersection, self intersection, curvature or distance computation. We use the B-spline surface representation.

The B-spline surface not only offers high accuracy of representation but also supports interactive shape manipulation by a designer using the B-spline control points. Another important advantage of the B-spline representation is that it comes together with a bunch of tools that allow to make it grow. This is especially useful when biologists want to simulate e.g. the growth of trees.

The modeling of the tree is performed in two steps. First, the skeletons of tree branches are transformed into a set of B-spline curves. Second, these B-spline curves are used as paths to generate surface patches in a process called lofting [?].

B-spline fitting

The reconstruction step provides us with a structural description of the input data set that will serve as input to the modeling phase. Following this description, the output model will be a set of B-spline surface patches for all the branches of the tree. Algorithm 3.1: Branch identification algorithm.

Input: S, the skeleton of the tree Output: B, the set of branches of the tree Create a queue Q ;

Q ← root(S) ; while Q = ∅ do Create a branch b ; Node t = pop(L) ; Node c = t ; b ← c ; while !leaf(n =next(c)) do c = n ; b ← c ; end foreach n ∈ b do foreach c ∈ children(b) do if !selected(c) then Q ← n ; end end B ← b ; end return B ;
First, we fit a B-spline curve to the set of vertices of a branch skeleton. Recall that a vertex is either the center of a cluster or a junction point on the skeleton.

Given a set of m data points, {p 1 , . . . , p m }, we compute a B-spline curve of order 4 (i.e. degree 3) with uniform knots and n control points to approximate all the skeleton vertices in the given order, and express this curve as

c(t) = n ∑ i=1 c i B i,k,t (t).
(2)

B-spline lofting

After we have obtained a B-spline curve as the central path, the radii of a tree branch along its central path can be obtained by linearly interpolating the radii of the bounding cylinders along its skeleton. Next we will explain how to use the lofting technique to define the control point of a B-spline sweep surface approximating a tree branch from the control points of the B-spline central path and the radius information of the branch. First we sample a sequence of n points v i on the central path c(t) and construct normal planes N i of c(t) passing through the point v i . Here n is a user-specified parameter. On each plane N i , we need to define a 2D local ortho-normal coordinate frame F i with the v i as the origin such that the sequence of the frames F i exhibits no twist about the central curve of the tree branch. We compute these frames using the method in [START_REF] Jüttler | Computation of rotation minimizing frame[END_REF] for computing a rotation minimization frame (RMF).

Then on each plane N i , we position a regular polygon H i with fixed orientation with respect to the frames F i on the successive planes N i , as shown in Fig. 5. Here the size of the polygon on each plane N i is scaled by the radius of the tree branch that we computed earlier. Denote the vertices of the polygon H i by c i, j , i = 1, 2, . . . , n 1 , j = 1, 2, . . . , n 2 . We choose n 2 = 10 in our implementation. Then we obtain a tensor product B-spline surface

s(u, v) = n 1 ∑ i=1 n 2 ∑ j=1 c i, j B i,k 1 ,u (u)B j,k 2 ,v (v) (3)
Fig. 5 shows the process of lofting operation. We note that the use of rotation minimization frame (RMF) here is critical to the quality of the B-spline surface representation, since the commonly used Frenet frame is unstable on a general curve in 3D; for instance, its normal vector flips at inflection points of the central path [START_REF] Jüttler | Computation of rotation minimizing frame[END_REF]. This work has been implemented as a plugin in the algebraic geometric modeling environment, which allows the visualization and manipulation of geometric objects with algebraic representation such as implicit or parametric curves or surfaces.

Results and discussion

The input point cloud is normalized into the unit cube [0, 1] 3 at the initialization stage. The threshold ε for clustering is set to 1e -5 and the maximal number of iterations is set to 30 in all our experiments (Section 2.2). The error threshold δ (Section 2.3) is different for models with different noise level, which varies in the interval [1e -3 , 1e -2 ]. Fig. 1, 2, 3 and 4 give the detailed description of each step in our modeling process.

Fig. 6 shows a testing result on a noisy model which is not well aligned after multiview scan. Our algorithm can still produce a result which is similar to its original structure. More testing results of complex models are given in Fig. 7 and Fig. 8. Table 1 lists the timing statistic of our algorithm tested on various scanned point models. The lofting time depends on the number of sample points used to create the Bspline surface. The default number is 30.

At last, we give a comparison between our approach and Xu et al. 's work [START_REF] Xu | Knowledge and heuristic-based modeling of laser-scanned trees[END_REF].

Firstly, they compute shortest paths on input point data directly. Then all the points are clustered into bins after quantification of the shortest distance to the root. This does not consider any geometric information of the input data. In contrast, our variational segmentation approach tries to isolate the cylindrical regions from input data, and we compute the shortest paths for segmented clusters, which is more efficient. We also introduce junction points for skeleton extraction, which yield better results than only use the centers of each cluster, as shown in Fig. 3. In addition, the branch structure is constructed from the skeleton, which is needed by tree grown simulation. A comparison of generated skeleton of Xu et al. 's method and ours is given in Fig. 9, which indicates that, using the same number of clusters, our method yields a more efficient and more faithful representation of a reconstructed tree.

Summary and outlook

In this paper, we present an efficient framework for reconstructing ramified tree structure from scanned point cloud data. Our segmentation algorithm is simple and easy to implement. The whole process is automatic but can also be dynamically controlled by the user easily. The result model can be used not only for simulation but also for rendering. The output branches can easily be converted into a piecewise linear mesh representation by sampling the B-spline representation of our surface patches. However, the algebraic representation we provide has important applications in many fields such as agronomy and botany, enabling many algorithms to analyze the growth of trees in different stages. In the future, we plan to improve our reconstruction pipeline so that we could deal with the scanned point data with leaves.

Figure 2 :

 2 Figure 2: Intermediate results of the hybrid segmentation algorithm. Top row: segmentation result. From left to right, the number of clusters is 19, 60, 96, 214, respectively. Bottom row: bounding cylinders of corresponding clusters. The green cylinders are fixed and those blue ones are unfixed.

Figure 3 :

 3 Figure 3: Skeleton generation. The background is the clustering result and the dash line means the branch connected to the root. Left: graph generated by connecting centers of neighboring clusters, which includes a loop in branching region (the triangle formed by three neighboring clusters). Right: skeleton generated by convert this graph into a tree.All the edges that do not belong to the shortest paths to the root cluster are removed.

Figure 4 :

 4 Figure 4: Definition of junction points. Upper left: the green spheres represent the center of each cluster, and the red spheres represent the internal junction points. Lower left: junction point definition of leaf node. Right: Skeleton generated by our method with junction points.

Figure 5 :

 5 Figure 5: Illustration of lofting operation.

Figure 6 :

 6 Figure 6: Reconstruction result of fagus. Top: Segmentation and branch detection result. Bottom: Skeleton and the lofting result.

Figure 7 :

 7 Figure 7: Reconstruction result of melgueil. Top: Segmentation and branch detection result. Bottom: Skeleton and the lofting result.

Figure 8 :

 8 Figure 8: Reconstruction result of walnut. Top: Segmentation and branch detection result. Bottom: Skeleton and the lofting result.

Figure 9 :

 9 Figure 9: Comparison of skeleton results. The background is the clustered point data overlayed with the skeleton. Left: Skeleton generated by Xu et al.'s method with 357 clusters. Right: skeleton of our method with 356 clusters. Our method produces a better clustering and produces geometric details more faithfully.

Table 1 :

 1 Timing Statistics in seconds. |P| is the number of points obtained from the scan, |C| is the number of computed clusters and |B| is the number of branches. Segmentation, branching and modeling are the time taken by clustering, branch reconstruction and B-spline lofting, respectively.

	Model	|P|	|C|	|B|	Segmentation	Branching	Modeling
	hetre	34542	80	26	5.94	0.015	1.1
	apple tree	60126	356	96	26.5	0.048	6.6
	melgueil	117601	370	103	73.4	0.078	9.255
	walnut	217187	1394	502	215.2	1.034	114.4


Managérialisme

Nino Tandilashvili

Le managérialisme est un concept central dans les débats autour de la gestion publique depuis des années 1990. Il imprègne à la fois une partie des réformes mondiales conduites dans le secteur public, qui ont pour objectif d'améliorer la performance des organisations et des services publics, et aussi un courant de littérature scientifique, qui critique la montée de l'importance du management dans le fonctionnement des organisations publiques.

Dans la littérature scientifique le managérialisme reste un concept polémique. A contrario d'autres concepts discutés de la gestion publique, tel que le néolibéralisme ou encore le New Public Management, le managérialisme n'a jamais bénéficié d'une description formelle. La divergence dans la littérature est fondée sur le fait que le managérialisme revêt une multitude de manifestations dans plusieurs disciplines et induit de perceptions variées.

L'analyse de la littérature permet d'identifier six approches différentes du concept de managérialisme : 1) l'assimilation du managérialisme à l'utilisation d'outils et de méthodes de gestion du service privé dans le service public ; 2) la perception du managérialisme comme une montée de classe des managers ; 3) la conceptualisation du managérialisme comme un nouvel archétype organisationnel adapté à tout type d'organisation visée ; 4) la conceptualisation du managérialisme comme un processus de réification ; 5) l'association du managérialisme au New Public Management ; et 6) la différenciation entre le managérialisme et le new managérialisme. Le point le plus saillant de ces interprétations est que, comme beaucoup de termes finissant en « isme », le managérialisme est utilisé dans un cadre idéologique (Enteman, 1993 ;Pollitt, 1990 ;Trow, 1994 ;Meek, 2003 ;Deem et Brehony, 2005) et montre des convictions personnelles des auteurs. Parallèlement, le suffixe « isme » montre une critique, voire même une attitude péjorative des auteurs. Le « managérialisme » est péjorative quand il décrit « la progression de la caste de management » (Locke, 2009) ou un nombre excessif de techniques de gestion (Dunand, 2011).

Les réformes basées sur l'idéologie du managérialisme ont pour objectif (tel qu'affiché par les réformateurs) améliorer la performance des organisations et des services publics et augmenter leur efficacité. L'objectif de la performance regroupe en deux points : 1) la qualité de service et la prestation produite -la qualité est souvent comprise comme étant la transparence des activités et la rapidité de service ; et 2) le bon fonctionnement des organisationsqui peut être garanti en se débarrassant de la lourdeur administrative traditionnelle. L'objectif de l'efficacité se traduit souvent par 1) la rationalité économique et 2) l'appropriation des valeurs du marché. Ainsi, les valeurs comme la productivité, la rentabilité ou la diminution des coûts sont promues par le concept. La culture de résultats et la mesure en chiffres sont également liées à l'objectif d'efficacité.

Plusieurs réformes françaises ont affiché des objectifs similaires depuis fin 1990. En modifiant profondément la logique de gestion financière du secteur public, la Loi Organique Relative aux Lois des Finances (LOLF) est incontestablement la plus grande manifestation du managérialisme dans la gestion publique française. Ce n'est pas uniquement une réforme budgétaire, c'est également un changement de culture profond qui substitue à la logique de moyens la logique de résultats. La loi met au coeur du fonctionnement administratif le triptyque « pertinence -efficacité -efficience », soubassement doctrinal du contrôle qui offre une analyse usuellement conduite a posteriori (Benzerafa Alilat, et al., 2016). Enfin, la LOLF, comme c'est souvent le cas des réformes managérialistes, a aussi l'impact sur la culture. Il s'agit de responsabiliser les gestionnaires sur l'atteinte des objectifs des politiques publiques (efficacité socio-économique), la satisfaction des usagers (qualité de service) au moindre coût (efficience). Pour ce faire, les managers publics disposent de marges de manoeuvre accrues en matière d'affectation des moyens à leur disposition.

  Bibliographie ENTEMAN Willard F. (1993), Managerialism: The Emergence of a New Ideology, Madison, The University of Wisconsin Press. HOOD Christopher (2000), Paradoxes of Public-Sector Managerialism, Old Public Management and Public Service Bargains, International Public Management Journal, Vol.1/3 p. 1-22. LOCKE Robert R. (2009), Managerialism and the Demise of the Big Three, Real-world economics review, N°51, p. 28-47. DUNAND Christophe (2011), Dépasser un Managérialisme insoutenable, Actualité Sociale, N°35, p.14-16. TANDILASHVILI Nino (2016), Le managérialisme et l'identité universitaire. Le cas de l'université française, Thèse de doctorat en gestion, sous la direction de Patrick Gibert, Université Paris Nanterre. BENZERAFA ALILAT Manel, GARCIN Laurent, GIBERT Patrick (2016), Le volet performance de la LOLF. Standardisation et résilience d'un genre entre rationalité politique et rationalité de gestion, Revue française de gestion, Vol. 260/7, p. 11-31. New public management Nouvelle gestion publique LOLF

Tableau 1 : Différentes approches de définition du managérialisme La conceptualisation du managérialisme La thèse centrale de l'approche Certains auteurs de référence

	L'utilisation d'outils et de		Des outils de gestion, TQM, reengineering, empowerment,
	méthodes de gestion du service		sont des solutions en soi.
	privé dans le service public
	La montée de classe des		Remplacement de professionnels et intellectuels par les
	managers		technocrates au sein des organisations et au niveau de la
			société.
	Le nouvel archétype		Le triomphe des organisations sur les individus.
	organisationnel
	Le processus de réification		Le remplacement de la subjectivité par l'objectivité dans les
			rapports sociaux.
	L'association du managérialisme	Le NPM est le processus de réforme de la gestion publique,
	au New Public Management		alors que le managérialisme -une approche idéologique de la
			gestion publique.
	La différentiation entre le		Le new managérialisme est le processus de managérialisation
	managérialisme et le new		dans le secteur public exclusivement, alors que le
	managérialisme		managérialisme s'applique à tous types d'organisation.
	L'utilisation d'outils et de	L'universalisme des outils de	Pollitt (1990), Boje (1991,
	méthodes de gestion du	gestion. TQM, reengineering,	1999), Boston et al. (1991),
	service privé dans le service	empowerment, sont des solutions	Terry (1998), Peters (1996,
	public	en soi.	2011), Blanchot et Padioleau
				(2003), Dunand (2011)
	La montée de classe des	Remplacement de professionnels	Pollitt (1990), Enteman (1993),
	managers	et intellectuels par les	Andrews (1998), Mulgan
		technocrates au sein des	(1998), Hoopes (2003), Deem
		organisations et au niveau de la	et Brehony (2005), Cunliffe
		société.	(2009), Locke (2009)
	Le nouvel archétype	Le triomphe des organisations sur	Pollitt (1990), Enteman (1993),
	organisationnel	les individus.	Seth (2001), Guiggin (2003),
				Smets (2005), Locke (2009)
	Le processus de réification	Le remplacement de la	Bourguignon (2007),
		subjectivité par l'objectivité dans	Gauléjac (2012)
		les rapports sociaux.
	L'association du	Le NPM est le processus de	Pollitt (1990, 1993, 2014),
	managérialisme au New	réforme de la gestion publique,	Hood (1995), Guiggin (2003),
	Public Management	alors que le managérialisme -une	Meek (2003), Deem et Brehony
		approche idéologique de la	(2005), Cunliffe (2009),
		gestion publique.	Dunand (2011), Fitzsimons
				(2012), Fortier (2013)
	La différentiation entre le	Le new managérialisme est le	Clarke et Newman (1994),
	managérialisme et le new	processus de managérialisation	Terry (1998), Saint-Martin
	managérialisme	dans le secteur public	(2000), Deem (2001) Maassen
		exclusivement, alors que le	(2003), Cunliffe (2009),
		managérialisme s'applique à tous	Fitzsimons (2012), Pick et al.
		types d'organisation.	(2012)
	La conceptualisation du		La thèse centrale de l'approche
	managérialisme