Ana Joaquina Jimenez

Alexandre Schaeffer

Chiara De Pascalis

Gaëlle Letort

Benoit Vianay

Michel Bornens

Matthieu Piel

Laurent Blanchoin

Manuel Théry
email: manuel.thery@cea.fr

Acto-myosin network geometry defines centrosome position

Introduction

The centrosome position is intimately associated to polarized cell functions such as adsorption and secretion, motility and mitosis [START_REF] Tang | Centrosome positioning in vertebrate development[END_REF]. Its position is characteristic and indicative of polarized cell functions [START_REF] Bornens | Cell polarity: having and making sense of direction-on the evolutionary significance of the primary cilium/centrosome organ in Metazoa[END_REF]. It is found at the cell center in proliferating cells in culture, while it presents a peripheral position in differentiated cells in tissues, where it loses part or all of its functions in microtubule organization [START_REF] Burakov | Centering and Shifting of Centrosomes in Cells[END_REF][START_REF] Sanchez | Microtubule-organizing centers: from the centrosome to non-centrosomal sites[END_REF][START_REF] Vallee | How dynein helps the cell find its center: a servomechanical model[END_REF]. During several cellular events essential to development, and organism homeostasis, the centrosome position undergoes a shift from the center to periphery of the cell, notably during ciliogenesis [START_REF] Pitaval | Microtubule stabilization drives 3D centrosome migration to initiate primary ciliogenesis[END_REF], neuronal developement [START_REF] Shao | Centrosome anchoring regulates progenitor properties and cortical formation[END_REF], immune synapse formation [START_REF] Stinchcombe | Communication, the centrosome and the immunological synapse[END_REF] or epithelial-to-mesenchymal transition [START_REF] Burute | Polarity Reversal by Centrosome Repositioning Primes Cell Scattering during Epithelial-to-Mesenchymal Transition[END_REF]. However the mechanisms that regulate the stability of central and peripheral states and those that allow a rapid switch between two states have not yet been fully understood.

Previous in vivo, in vitro and in silico studies suggest that centrosome position is the outcome of a balance of pulling and pushing forces applied on microtubules and transmitted to the centrosome [START_REF] Kimura | A novel mechanism of microtubule length-dependent force to pull centrosomes toward the cell center[END_REF][START_REF] Zhu | Finding the Cell Center by a Balance of Dynein and Myosin Pulling and Microtubule Pushing : A Computational Study[END_REF]. Overexpression or depletion of dynein heavy chains or its partners, and injections of dynein blocking antibodies suggest cortical and cytoplasmic dynein play a role in the production of pulling forces for the centrosome position [START_REF] Burakov | Centrosome positioning in interphase cells[END_REF][START_REF] Koonce | Dynein motor regulation stabilizes interphase microtubule arrays and determines centrosome position[END_REF][START_REF] Nguyen-Ngoc | Coupling of cortical dynein and G alpha proteins mediates spindle positioning in Caenorhabditis elegans[END_REF][START_REF] Tanimoto | Shape-motion relationships of centering microtubule asters[END_REF][START_REF] Wu | Effects of dynein on microtubule mechanics and centrosome positioning[END_REF]. Besides, microtubule polymerization against spatial boundaries have been shown to be responsible for the production of pushing forces [START_REF] Brito | Pushing forces drive the comet-like motility of microtubule arrays in Dictyostelium[END_REF][START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF][START_REF] Pinot | Effects of confinement on the self-organization of microtubules and motors[END_REF]. The exact role of actomyosin contration is unclear. The inhibition of actomyosin contraction had no visible effect on centrosome position in isolated cells or in monolayers [START_REF] Hale | SMRT analysis of MTOC and nuclear positioning reveals the role of EB1 and LIC1 in single-cell polarization[END_REF], however it was found capable to counteract the centrosome shifting due to local microtubule disassembly [START_REF] Burakov | Centrosome positioning in interphase cells[END_REF] and to perturb centrosome repositioning at the cell center after mitosis [START_REF] Chevrier | The Rho-associated protein kinase p160ROCK is required for centrosome positioning[END_REF].

In non-differentiated cells, and notably in cells proliferating in culture, the force balance is believed to set the centrosome position at the cell geometrical center, also called center of mass or centroid [START_REF] Graham | Enucleated cells reveal differential roles of the nucleus in cell migration, polarity, and mechanotransduction[END_REF][START_REF] Hale | SMRT analysis of MTOC and nuclear positioning reveals the role of EB1 and LIC1 in single-cell polarization[END_REF]Théry et al., 2006a;[START_REF] Vallee | How dynein helps the cell find its center: a servomechanical model[END_REF]. Microtubule-based forces in an in vitro reconstituted system also position the MTOC at the centroid of their confinement area [START_REF] Laan | Cortical Dynein Controls Microtubule Dynamics to Generate Pulling Forces that Position Microtubule Asters[END_REF] but in silico simulation suggested this mechanism may depend on the shape and physical properties of the boundaries [START_REF] Letort | Centrosome centering and decentering by microtubule network rearrangement[END_REF][START_REF] Pavin | Positioning of microtubule organizing centers by cortical pushing and pulling forces[END_REF]. Indeed, in cultured cells, the centrosome has been observed at the cell geometrical center in relatively isotropic boundary conditions (e.g. non polarized cells) but can be off-centered in the front or in the back of migrating cells [START_REF] Luxton | Orientation and function of the nuclearcentrosomal axis during cell migration[END_REF][START_REF] Pouthas | In migrating cells, the Golgi complex and the position of the centrosome depend on geometrical constraints of the substratum[END_REF][START_REF] Zhang | Centrosome defines the rear of cells during mesenchymal migration[END_REF], or toward intercellular junction in epithelial cells [START_REF] Burute | Polarity Reversal by Centrosome Repositioning Primes Cell Scattering during Epithelial-to-Mesenchymal Transition[END_REF][START_REF] Rodriguez-Fraticelli | Cell confinement controls centrosome positioning and lumen initiation during epithelial morphogenesis[END_REF]. As a result, there is no generic definition of the centrosome position and the key parameters involved in the regulation of this positioning are still unclear.

One limitation for the identification of the forces exerted on the centrosome is that the mechanism of centrosome positioning is hardly distinguishable from nucleus positioning. It has been a considerable limitation for the study of centrosome positioning in anisotropic conditions such as in migrating cells [START_REF] Dupin | Classical cadherins control nucleus and centrosome position and cell polarity[END_REF][START_REF] Gomes | Nuclear movement regulated by Cdc42, MRCK, myosin, and actin flow establishes MTOC polarization in migrating cells[END_REF]. Both the nucleus and the centrosome have their own self-centering properties [START_REF] Dupin | Nuclear positioning: mechanisms and functions[END_REF][START_REF] Kimura | A novel mechanism of microtubule length-dependent force to pull centrosomes toward the cell center[END_REF][START_REF] Reinsch | Mechanisms of nuclear positioning[END_REF]. But the physical links that connect them hinder their respective contributions in regards to their final position [START_REF] Bornens | Is the centriole bound to the nuclear membrane?[END_REF][START_REF] Burakov | Association of nucleus and centrosome: magnet or velcro?[END_REF][START_REF] Malone | The C. elegans Hook Protein, ZYG-12, Mediates the Essential Attachment between the Centrosome and Nucleus[END_REF][START_REF] Salpingidou | A novel role for the nuclear membrane protein emerin in association of the centrosome to the outer nuclear membrane[END_REF][START_REF] Zhang | SUN1/2 and Syne/Nesprin-1/2 Complexes Connect Centrosome to the Nucleus during Neurogenesis and Neuronal Migration in Mice[END_REF]. In addition, the nucleus also constitutes a dead volume microtubules don't have access to, which biases the spatial distribution of microtubules and their associated forces [START_REF] Luxton | Orientation and function of the nuclearcentrosomal axis during cell migration[END_REF]. Furthermore, centrosomal microtubules push and pull on the nuclear envelop [START_REF] Biedzinski | Microtubules control nuclear shape and gene expression during early stages of hematopoietic differentiation[END_REF][START_REF] Burke | Nuclei Take a Position: Managing Nuclear Location[END_REF][START_REF] Starr | Interactions between nuclei and the cytoskeleton are mediated by SUN-KASH nuclear-envelope bridges[END_REF] adding more complexity to the force balance in the centrosome-microtubule network. For these reasons, enucleated cells -here referred as cytoplasts -offered an interesting possibility to untangle the geometrical and molecular cues that specifically control centrosome position [START_REF] Karsenti | Role of the centrosome in organizing the interphase microtubule array: Properties of cytoplasts containing or lacking centrosomes[END_REF]. Plating them on adhesive micropatterns revealed that centrosome self-positions at the geometrical center of the cytoplasts suggesting that its off-centering in cells is due to microtubule interaction with the nucleus [START_REF] Dupin | Classical cadherins control nucleus and centrosome position and cell polarity[END_REF][START_REF] Graham | Enucleated cells reveal differential roles of the nucleus in cell migration, polarity, and mechanotransduction[END_REF]. However, the centrosome often detaches from the nucleus when moving to the cell periphery during the migration of neuroblasts [START_REF] Umeshima | Microtubule-based nuclear movement occurs independently of centrosome positioning[END_REF] or epithelium formation [START_REF] Strzyz | Interkinetic Nuclear Migration Is Centrosome Independent and Ensures Apical Cell Division to Maintain Tissue Integrity[END_REF] for example. This might indicate that the centrosome-microtubule network could be empowered of active off-centering properties independently of the nucleus, although this has not yet been demonstrated.

Here, we show that actin contractile network plays an important role in the confinement of the microtubule networks while the positioning of the centrosome at the center of this actin-based boundary is achieved by dynein-based forces on microtubules.

Results

Centrosome is off-centered in cells plated on anisotropic adhesion pattern

The centrosome of mouse embryonic fibroblasts (MEF) was located at the geometrical center of cells plated on relatively isotropic adhesive patterns such as equilateral triangles (Figure 1A), as previously described [START_REF] Hale | SMRT analysis of MTOC and nuclear positioning reveals the role of EB1 and LIC1 in single-cell polarization[END_REF]. However, it appeared shifted from the geometrical center when cells were plated on isosceles triangle, despite the fact that in these conditions cells were not migrating nor forming contact with any adjacent cells (Figure 1B). With that micropattern, the actin-network architecture was polarized, and not just a homothetic transformation of the cell contour. The width of the network was greater along the triangle's base and the arrangement of actin bundles differed between the larger vertices and the smaller apex (Figure 1B). This suggested that the centrosome positioning away from the geometric center could be due to the asymmetry in the actin network. To further investigate this possibility, actin-network asymmetry was re-inforced. Previous work has shown that the distribution of the cell's adhesions to a substrate can direct the architecture of the actin network [START_REF] Chen | Large-scale curvature sensing by directional actin flow drives cellular migration mode switching[END_REF][START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF][START_REF] Théry | Cell distribution of stress fibres in response to the geometry of the adhesive environment[END_REF], and this can be achieved by plating a cell on a micropattern such that the cell adopts a convex edge and a concave edge. In this situation, the actin network tends to flow from sites of cell-substrate adhesions at the convex edge, towards sites between cell-substrate adhesion at the concave edge where stress fibers tend to form. Thus, cells were plated on L-shaped or C-shaped micropatterns to impose asymmetric actin network architecture. With both micropatterns, the actin network displayed a marked asymmetry and the centrosome was significantly shifted from the geometric center, in the direction of the actin-network retrograde flow towards the edge harboring contractile stress fibers (Figure 1C, D). Similar shift was observed in human retinal pigment epithelial (RPE1) cells and mouse muscle myoblast (C2C12) (Figure S1). This supported the idea that centrosome positioning is affected by the pattern of cell adhesions and the architecture of the actin network.

However, the nucleus position was also shifted from the cell geometrical center when cells were plated on anisotropic micropatterns (Figure 1E). So it was unclear whether the centrosome was off-centered because it was attached to an off-centered nucleus or whether the microtubule-centrosome network was not self-centering with respect to cell shape in those conditions.

Centrosome is off-centered in cytoplasts plated on anisotropic adhesion pattern

Cell enucleation allows the study of centrosome-microtubule network interaction with cell peripheral boundary without the bias of the interaction with the nucleus. Cytoplasts, i.e. enucleated cells, were produced by centrifugation of attached cells on ECM-coated plastic slides [START_REF] Piel | The Respective Contributions of the Mother and Daughter Centrioles to Centrosome Activity and Behavior in Vertebrate Cells 7[END_REF]. They were then detached and plated on large 2000µm2 disc-shaped micropatterns, in order to maximize their spreading and the available space for centrosome positioning in 2D. However, we found that the major network of vimentin intermediate filament in fibroblasts and RPE1 cells forms a dense network around the nucleus [START_REF] Patteson | Vimentin protects cells against nuclear rupture and DNA damage during migration[END_REF], which can resist enucleation, maintain its perinuclear architecture and affect microtubule network organization (Figure S2B). To avoid any geometrical bias due to intermediate filaments we further worked with vimentin-KO MEF [START_REF] Patteson | Vimentin protects cells against nuclear rupture and DNA damage during migration[END_REF]. In these cells, centrosomes were found to precisely position at the cell geometrical center of isotropical shapes: 84% were found in a 5µm wide region at the center of the disc (Figure 2A) or of equilateral triangles (Figure 2B). On discs, centrosomes displayed similar centering efficiency in cells and cytoplast, with or without the vimentin network (Figure S2C).

In order to investigate centrosome positioning in anisotropic conditions, we plated cytoplasts expressing EGFP-Centrin1 on a variety of triangular geometries. We first chose triangles of similar area but different height to bases ratio: equilateral, short isosceles (ratio 7/4) and isosceles (ratio 9/2) (Figure 2B, C and Figure S3). Thousands of different geometrical centers have been described in triangles (Kimberling). We measured centrosome position relative to some centers that are interesting because their definition presumes simple relationship with the sides or the vertexes of the triangle. Those are the circumcenter (equidistant to the triangle vertexes), the incenter (equidistant to the triangle sides), the geometrical center (which reflects the entire area of the triangle) and the orthocenter -which minimizes the sum of its distances to the triangle vertexes and to those of its pedal triangle. The distances between these centers increase with the height to base ratio of the triangle (Figure S3A), reflecting the variations of the contributions of their definition parameters (distance to vertex, distance to sides, distance to the middle of sides). To evaluate centrosome positioning, a triangular contour was fitted to the edges of the plated cytoplast (Figure S3B) to evaluate the position of all centers of the triangles (Figure S3C). With a greater height-to-base ratio, the centrosome was more distant from all pre-defined centers except the geometric center, or center of mass, to which it remained in close proximity (Figure S3D,E). This was in agreement with the accepted understanding of centrosome positioning, in that the entire area of the cytoplast, ie the entire cell mass, was implicated in its positioning, rather than the cell periphery alone [START_REF] Kimura | A novel mechanism of microtubule length-dependent force to pull centrosomes toward the cell center[END_REF]. The robustness of the prediction that the centrosome is positioned at the geometric center was confirmed in cytoplasts plated on more exotic geometries (Figure S4).

The centrosome sits at the center of the actin network

Interestingly, the centrosome and the geometric center were found to be separated by a small distance in the cytoplasts plated on short isosceles triangles (Figure 2C), as it was observed in nucleated cells (Figure 1). To further explore the conditions leading to centrosome off-centering cytoplasts were plated on L-shaped or C-shaped micropatterns shapes to impose asymmetric actin network architecture. With both micropatterns, the actin network was asymmetric and, as in the case of nucleated cells, the centrosome was significantly shifted from the geometric center, away from actin transverse arcs and towards peripheral stress fibers (Figure 2D). A similar shift was observed in cytoplast obtained from C2C12 (Figure S5). This supported the idea that centrosome positioning is affected by the pattern of cell adhesions and the architecture of the actin network, independently of the position of the nucleus.

Interestingly, we noted that a central zone in the cell was devoid of actin bundles, an observation that has been made by others as well [START_REF] Dong | Chiral geometry regulates stem cell fate and activity[END_REF], and we termed this region the Actin Inner Zone (AIZ). We manually detected the contour of this zone and its geometrical center: the Actin Inner Center (AIC) (Figure 3A). Our measurements revealed that the centrosome was closer, or equally distant, to the AIC than to the cell geometrical center in all the conditions we tested (Figure 3B, see Figure S6 and S7 for representative examples of centrosome positioning with respect to the AIZ). Therefore, the AIC appeared to be a better descriptor of centrosome positioning than the cell geometrical center

The centrosome position adapts to changes in the architecture of the actin network

The association between the architecture of the actin network and centrosome positioning was further examined by plating cytoplasts on various sizes of disks ranging from 500 to 3000 µm2. Surprisingly, we found that the extent of the distribution of centrosome positions was independent of the size of the disk (Figure S8A,B). However, the size of the averaged AIZ was also relatively independent of the size of the disk (Figure S8C) in line with the idea that centrosome positioning was sensitive to the AIZ.

To modulate the shape and position of the AIZ, cytoplast were plated on short isosceles triangles as those shapes were shown to shift centrosome position away from the geometric center (Figure 2C), and because cytoplast spreading was more efficient on triangles than on L-or C-shapes. Accurate analysis of centrosome positioning was not practical through chemically inhibiting actin assembly, Arp2/3 or formin because of the detachment of cytoplasts from adhesive micropatterns in those conditions. However, inhibiting Rho kinase ROCK with Y27632 resulted in a regular, homogeneous and homothetic network of thin and loose actin bundles along all cell edges (Figure 4A). In particular, the width of the network along the short edge of the triangle was lower than in the control condition, and was similar to those along the two longer edges (Figure 4B,C). In cytoplasts treated with the ROCK inhibitor, the center of the AIZ, the AIC, and the centrosome positioned in close proximity to the geometric center, unlike in the control condition, where the AIC and centrosome were positioned further from the short edge of the triangle than the geometric center (Figure 4D and4E). Noteworthy, in cells displaying a poorly contractile actin network, no transverse arcs and, therefore, no asymmetric AIZ like PtK2 cells, the centrosome was found precisely at the cell geometrical center (Figure 4F), as in MEF cytoplasts treated with ROCK inhibitor (Figure 4E). Altogether these results showed that the actomyosin network acts as a spatial boundary for the microtubule network and thereby affects centrosome position

Microtubules orientation adapts to the architecture of the actin network

Centrosome positioning is known to depend on the mechanical forces exerted on the microtubule network [START_REF] Kimura | A novel mechanism of microtubule length-dependent force to pull centrosomes toward the cell center[END_REF][START_REF] Wu | Effects of dynein on microtubule mechanics and centrosome positioning[END_REF]. We thus investigated whether microtubules inside of the AIZ engaged specific and distinct interactions from those on the outside. To quantify how microtubule organization is effected by the AIZ in comparison with the actin-dense region (termed the Actin Peripheral Zone; APZ), we analyzed local variations in microtubule morphologies and orientations in MEF cytoplast plated on disc-shaped micropattern (Figure 5A, 5B, see examples of segmented networks in Figure S9). The orientations were clustered into two categories; radial (<45°) and tangential (>45°), in relation to the angle in which the microtubule at a given point (pixel) crosses a straight line originating from the centrosome. The averaged local orientation was further described by the orientation ratio, which was defined as the ratio of pixels with radial orientations over those with tangential orientations. Based on orientation ratios, microtubules were more radially oriented in the AIZ than in the APZ (Figure 5C). Moreover, by performing a linescan along a cytoplast radius (Figure 5D), we found that the transition between radial to tangential orientations occurred precisely at the transition between the AIZ and the APZ (Figure 5E, see examples of linescans in Figure S10). From these results, we concluded that the architecture of the actin network acts locally on the shape and orientation of microtubules.

Microtubule disassembly perturbs centrosome positioning independently of its impact on actin network contraction.

Microtubule disassembly is known to impair centrosome positioning [START_REF] Burakov | Centrosome positioning in interphase cells[END_REF][START_REF] Dupin | Classical cadherins control nucleus and centrosome position and cell polarity[END_REF][START_REF] Hale | SMRT analysis of MTOC and nuclear positioning reveals the role of EB1 and LIC1 in single-cell polarization[END_REF]. Cytoplasts were plated on ice (2 hours) and treated with 10µM nocodazole to induce a complete disassembly of microtubules (Figure 6A, middle). As expected, this treatment induced a dispersion of centrosome positions (Figure 6B, middle). However, and in accordance with previous studies, microtubule depletion also increased cell contractility and induced the formation of large actomyosin bundles (Figure 6B, middle) [START_REF] Chang | GEF-H1 Couples Nocodazoleinduced Microtubule Disassembly to Cell Contractility via RhoA[END_REF][START_REF] Krendel | Nucleotide exchange factor GEF-H1 mediates cross-talk between microtubules and the actin cytoskeleton[END_REF]. The shape of the AIZ was severely deformed and was shifted asymmetrically with respect to the overall cytoplast shape (Figure 6C, middle). The centrosome mis-positioning appeared aligned with the shift of the AIZ (see examples in Figure S11).

The distortion of the AIZ in response microtubule disassembly could also be detected in cytoplasts plated on disks. Centrosome positioning was not completely random throughout the cytoplast, even after 20 hours of nocodazole treatment (Figure S12A,B), but limited to the AIZ (Figure S12C). Therefore, and importantly, both experiments suggested that the wellknown mispositioning of the centrosome in response to microtubule disassembly resulted not only from the absence of microtubules but also from the deformation of actin-based spatial boundaries through increased actin-network contractility.

To counterbalance the increase of contractility associated to microtubule disassembly, high doses of the ROCK inhibitor Y27632 (100 or 200 µM) were also added to nocodazoletreated cytoplasts (Figure 6A,right). In these conditions, the shape of the AIZ was similar to that in cytoplasts treated with Y27632 alone (at 20 µM); i.e. the AIZ formed a regular, homothetic peripheral band along the cell edges (Figure 6C, right). The lateral shift in the position of the AIZ was less than that in cytoplasts treated with nocodazole alone and the distribution of centrosomes followed the same trend (Figure 6B). Notably, in response to either nocodazole alone or nocodazole and Y27632, the centrosome-AIC distances were higher than those in the control cytoplasts (Figure 6D), showing that although centrosome positioning was coordinated with AIZ displacement, centrosomes were dispersed within the AIZ in the absence of microtubules. This suggested that microtubules direct centrosome positioning to the center of the AIZ.

Dyneins position the centrosome at the center of the actin network

Dyneins have been shown to be involved in centrosome positioning in eggs [START_REF] Tanimoto | Shape-motion relationships of centering microtubule asters[END_REF], embryos [START_REF] Nguyen-Ngoc | Coupling of cortical dynein and G alpha proteins mediates spindle positioning in Caenorhabditis elegans[END_REF][START_REF] De Simone | Dynein Transmits Polarized Actomyosin Cortical Flows to Promote Centrosome Separation[END_REF], unicellular eukaryotes [START_REF] Koonce | Dynein motor regulation stabilizes interphase microtubule arrays and determines centrosome position[END_REF][START_REF] Rehberg | Dictyostelium LIS1 Is a Centrosomal Protein Required for Microtubule/Cell Cortex Interactions, Nucleus/Centrosome Linkage, and Actin Dynamics[END_REF][START_REF] Vogel | Selforganization of dynein motors generates meiotic nuclear oscillations[END_REF] and mammalian cells [START_REF] Burakov | Centrosome positioning in interphase cells[END_REF][START_REF] Wu | Effects of dynein on microtubule mechanics and centrosome positioning[END_REF]. The two dynein inhibitors we tested, ciliobrevin D and dynarrestin, had no clear effect on the dispersion of the Golgi apparatus, which is a classic readout for dynein inactivation. Therefore we chose to inhibit dynein activity by expressing a dominant negative form of the dynactin subunit p150glued (p150-DN) [START_REF] Wu | Nesprins and opposing microtubule motors generate a point force that drives directional nuclear motion in migrating neurons[END_REF]. For these experiments we worked with WT MEF to detect the GFP signal of p150-DN without being perturbed by the centrin1-GFP signal in the vimentin-KO line with used before. In cytoplast of WT MEF plated on isoceles triangle, the centrosome was off-centered relative to cell geometrical center as in vimentin-KO cytoplasts (Figure S13). In dyneininactivated cytoplasts, the centrosomes were more dispersed than in control cytoplasts but still biased towards the apex of the triangle and the position of the AIZ (Figure7A). Similar observations were made upon dynein inactivation in RPE1 cytoplasts (Figure S14). In these conditions, microtubules were curvy all over the cell (Figure 7B) and the networks were highly asymmetric (Figure S14). However, the position of the centrosome remained limited by the actin bundles (Figure 7B) suggesting that dyneins were involved in centrosome positioning with respect to this network.

To further test this hypothesis we used the same experimental strategy as before to anihilate actin network asymmetry by relaxing acto-myosin contractility. In dyneininactivated cytoplasts treated with the ROCK inhibitor Y27632, centrosomes were then dispersed all over the cell and around the geometric center, corresponding to the shifted position of the AIZ (see the positions and angular distributions of centrosome in Figure 7A second and fourth columns). This showed that dyneins directed centrosome positioning to the center of the AIZ rather than to the geometric center of the cell.

To better understand how dyneins could direct centrosome position at the center of the AIZ, we performed a co-labelling of actin filaments, microtubules and p150glued (Figure 7C). p150Glued labeling revealed that dyneins were not evenly distributed throughout the entire cell and were concentrated within the AIZ (Figure 7D). Furthermore, the variations of size and symmetry of the AIZ were correlated to the same changes in the spatial distributions of p150Glued (Figure S15).This suggested that, in addition to the peripheral pushing forces exerted by contractile actin bundles deforming microtubules out of the AIZ (Figure 5), microtubules were put under higher tension in the AIZ by the concentrated distribution of dyneins in this region.

Conclusion

Centrosome, nucleus and the cell geometrical center.

The mechanism which specifically regulates the positioning of the centrosome in mammalian cells has long been confused with the mechanism that regulates the position of the nucleus, and notably the actomyosin network acting on the nucleus [START_REF] Burakov | Association of nucleus and centrosome: magnet or velcro?[END_REF][START_REF] Burke | Nuclei Take a Position: Managing Nuclear Location[END_REF][START_REF] Luxton | Orientation and function of the nuclearcentrosomal axis during cell migration[END_REF]. The consensus has been that the centrosome positions at the cell's geometric center, either autonomously [START_REF] Dupin | Classical cadherins control nucleus and centrosome position and cell polarity[END_REF][START_REF] Graham | Enucleated cells reveal differential roles of the nucleus in cell migration, polarity, and mechanotransduction[END_REF] or in association with the nucleus [START_REF] Hale | SMRT analysis of MTOC and nuclear positioning reveals the role of EB1 and LIC1 in single-cell polarization[END_REF]. Here, we established an in vitro cell system to study centrosome positioning in which a number of parameters were controlled. This system included cytoplasts devoid of nuclei and the major intermediate filament, vimentin, and cytoplasts of defined shapes dictated by the micropatterned substrates onto which they were plated. We showed that the centrosome position is defined by the architecture of the actin network. It is located at the center of the actin network; more precisely, it is positioned at the geometric center of an inner space that is devoid of actin bundles. This position can correspond or not to the cell's geometric center, depending on the anisotropy of the actin network, which in turn depends on the geometry of cell's adhesion.

Furthermore, our experiments in nucleated cells showed that centrosome off-centering is also active in cells but that it can be perturbed by the mechanism of nucleus positioning. In poorly contractile cells like PtK2, the centrosome distribution was well clustered around cell geometrical center and the nucleus distribution was spread around it (Figure 4). By contrast, in more contractile cells like fibroblasts, RPE1 cells or C2C12 myoblast, the distribution of centrosomes were more dispersed than the distribution of nuclei (Figure S1), and the distribution of centrosomes were more clustered in cytoplast than in cells (Figure S5); suggesting that the nucleus position is strongly determined by the contraction of the actomyosin network and that the nucleus can displace the centrosome from its position at the center of the actin network. These data showed that both organelles have independant selfcentering properties [START_REF] Reinsch | Mechanisms of nuclear positioning[END_REF][START_REF] Vallee | How dynein helps the cell find its center: a servomechanical model[END_REF] and that the level of acto-myosin contraction defines which of the two will dominate the competition.

Microtubule and actin.

Microtubules interact with actin via specific crosslinkers or non-specific steric interactions [START_REF] Dogterom | Actin-microtubule crosstalk in cell biology[END_REF]. In particular, a dense and growing actin network can apply pushing forces on microtubules [START_REF] Colin | Actin-Network Architecture Regulates Microtubule Dynamics[END_REF][START_REF] Gupton | Converging populations of f-actin promote breakage of associated microtubules to spatially regulate microtubule turnover in migrating cells[END_REF]. Here, we found that the actomyosin network constitutes the actual spatial boundary to which the microtubules are sensitive. Disrupting or modifying the geometry of the actin network via the pattern of cell adhesions, altered the spatial boundary and changed centrosome position accordingly (Figure 2, 3, 4). Microtubules appeared more bent within the actomyosin network at the cell periphery, and straighter in the central part devoid of actin (Figure 5). These results suggested that centrosome positioning is mainly ensured by a combination of peripheral pushing and central pulling forces along microtubules.

Dyneins.

Dynein have long been known to apply pulling forces on microtubules and to be thus involved in MTOC positioning. By acting at the periphery or throughout the cytoplasm in round eggs, dyneins are thought to position the centrosome at the egg geometrical center [START_REF] Kimura | A novel mechanism of microtubule length-dependent force to pull centrosomes toward the cell center[END_REF]. We found here that in adherent mammalian cells, the activity of dynein is not evenly distributed all over cell periphery but rather restricted to specific regions of the cell cortex. Indeed, the linear shape and radial orientation of microtubules and the increased amount of dynein within the central part of the basal cortex devoided of actin bundles suggest that dyneins put microtubules under tension in a subcellular pattern defined by the geometry of the contractile actin network (Figure 4B-E,7C, Figure S10). Consistent with this view, the microtubules are not able to interact with cell periphery in aged cytoplasts but the centrosome remains well positioned, suggesting that the inner part of the cell cortex is sufficient to ensure centrosome position at the cell center [START_REF] Brodsky | Microtubules ' Interaction with Cell Cortex is Required for Their Radial Organization, but Not for Centrosome Positioning[END_REF]. Dynein activity requires dynactin to be coupled to a cargo or any other substrate supporting the force load. In large and round embryos, dyneins have been proposed to act as a coupling device that transmits contractile forces from the actomyosin network onto microtubules [START_REF] De Simone | Dynein Transmits Polarized Actomyosin Cortical Flows to Promote Centrosome Separation[END_REF]. Whether this applies to spread cells, and how it sets and organizes tensional forces in these conditions where the microtubule network lies along the actin network remains to be investigated.

Implications for centrosome positioning in differentiated/polarized cells.

The centrosome-positioning forces mediated via the actin network appeared potent and relevant for the cell in vivo because highly asymmetric actin networks, such as those developed on C-shaped micropatterns, brought the centrosome into contact with cell periphery, potentially reflecting the peripheral positioning mechanism in migrating or polarized cells [START_REF] Bornens | Cell polarity: having and making sense of direction-on the evolutionary significance of the primary cilium/centrosome organ in Metazoa[END_REF][START_REF] Tang | Centrosome positioning in vertebrate development[END_REF]. Hence, a change in actin contractility and actin-network asymmetry (due to changes in adhesion geometry) could be the initial step affecting the organization of microtubules and the distribution of dyneins, which, by repositioning the centrosome, could further bias internal traffic and reinforce the directional bias of the cell's polarization.

Methods

Cell Culture

Cell culture, cell lines, plasmids and transfection and drug treatment. MEF WT and KO for Vimentin cell lines (received from Robert Goldman), C2C12 and PTK2 cells were cultured in Dulbecco's Modified Eagle Medium (31966, Gibco) supplemented with 10% FBS (50900, Biowest) and 1% antibiotic-antimycotic (15240-062, Gibco). RPE1 cells were cultured in Dulbecco's Modified Eagle Medium Nutrient Mixture F-12 (31331-093, Gibco) supplemented with 10% FBS and 1% antibiotic-antimycotic. MEF KO Vimentin EGFP-Centrin 1 were made by transient transfection of pEGFP-C1-Centrin1 (kindly provided by James Sillibourne) with lipofectamine LTX (15338100, Invitrogen) in Opti-MEM (11058, Gibco) according to the procedure described by the manufacturer. Selection was performed with G418 at 0.5mg/ml and sorted by FACS twice with one month interval. They were posteriorly cultured with 0.2mg/ml. For p150 inhibition assay on cytoplasts, we used WT MEF instead of vimentin KO MEF to avoid confusion between GFP from centrin1 and from the p150 construct, or RPE1 cells. Centrosome positioning was similar in both cells lines (Supplemental Figure S13). Cells were electroporated with NEPA21 electroporator (from Nepa Gene) with the plasmid expressing GFP-p150-CC1 (214-548 aa of p150Glued) obtained from Mineko Kengaku (Kyoto University) and according to the manufacturer's protocole for MEF cells. Cells were then sorted by FACS 24h after electroporation and plated directly on slides for enucleation and enucleated 48h after electroporation. Living cells were incubated and imaged at 37°C with 5% CO2 in a humidified environment.

Enucleation

Cells were seeded the night before, 12h before enucleation on RINZL plastic micro-slides (71890-01, Delta Microscopies) precoated with Collagen I Rat Protein, Tail (A1048301, Gibco) at 12µg/ml and Fibronectin from bovine plasma (F1141, Sigma) at 1µg/ml for 1 hour. Cells were seeded to achieve a 90 % confluence by the time of the enucleation. Cells were put on 50ml tubes resistant to high-speed centrifugation (339652, Nunc) in complete medium with Cytochalasin D (C8273, Sigma) at 3µg/ml for 30min at 37°C, then centrifuged at 15'000 g for 1h at 37°C. Cytoplasts were then washed twice with pre-warmed DMEM then let them to rest for 30min at 37°C before detachment for seeding on micropatterns. An alternative protocole was used for C2C12 cells. In this case, cells were seeded the night before on RINZL slides pre-coated with Fibronectin (at 10µg/ml for 40min). On the day of the experiment, cells were incubated with Cytochalasin D at 2µg/ml for 45min at 37°C, then centrifuged at 10'000rpm at 37°C using an ultra-centrifuge (Avanti JXN-26, Beckman Coulter) equipped with a swinging rotor (JS-13.1, Beckman Coulter).

Drug treatment

Microtubules were removed by incubating cells in HBSS (14025092, Gibco) on ice and in a cold room at 4°C for 2 hours then warmed up to 37°C in complete medium with 10µM Nocodazole (M1404, Sigma) and incubated until fixation. Rock inhibition was achieved with Y27632 (Y0503, Sigma) at 20µM. Rock inhibition in the absence of microtubules was achieved with cold incubation as described above and warming up with complete medium with 10µM Nocodazole and Y27632 at 100 or 200µM as specified for 2h at least.

Fixation and Immunostaining

Cells plated on coverslips were fixed with Paraformaldehyde (15710, Euromedex), Glutaraldehyde (G5882, Sigma) or a mixture of both depending on the antibodies used. All fixation mixtures were done in Cytoskeleton Buffer supplemented with Sucrose (CBS, see below) with 0.1% Triton X-100 (T8787, Sigma) with either 3% Paraformaldehyde, 3% Paraformaldehyde + 0.025% Glutaraldehyde or 0.5% Glutaraldehyde. Fixation mixture was added to the cells for 10 min at room temperature. Glutaraldehyde related autofluorescence was quenched with a solution of PBS and 1mg/ml sodium Borohydride for 10 min at room temperature. Cells were then re-permeabilised with Triton 0.1% in PBS for 10 min at room temperature, then blocked with Bovine Serum Albumin (BSA, A2153, Sigma) at 1.5% in PBS for 10 min. Antibodies were diluted in PBS containing 1.5% BSA and both incubation with primary or secondary antibodies was made for 1 hour. Microtubules were stained with MCA77G from Abd serotec, ab18251 from Abcam or A-R-H#02 from Tab-IP (Curie Institute antibody platform). Centrosome staining was performed with anti-gamma Tubulin (T6557,Sigma), anti-pericentrin (ab4448, Abcam ; 611815, BD Biosciences) or antipolyglutamylated Tubulin (A-R-H#04, TabIP platform, Institut Curie). Vimentin was stained with 5741S from Cell Signaling using methanol fixation for 5min at -20°C . Dynein was stained with anti-p150glued antibodies (612709, BD Biosciences). A particular protocole was used for Dynein staining with an extra step of pre-permeabilisation using 0.025% Triton X-100 in CBS for 30 seconds followed by fixation in 4% PFA + 0.05% Glutaraldehyde + 0.1% Triton X-100 in CBS for 10 min. Actin filaments were stained with Phalloidin-A555 (A34055, Life Technologies) or Phalloidin-A568 (A12380, Life Technologies) together with secondary antibodies. Staining with DAPI (D9542, Sigma) was performed systematically with secondary antibodies to stain the nucleus or to control proper enucleation. Coverslips were mounted with Mowiol 4-88 (81381, Sigma). Cytoskeleton Buffer supplemented with Sucrose (CBS): A stock solution containing 10 mM HEPES (H3375, Sigma) at pH 6.1, 138 mM KCl (P3911, Sigma), 3 mM MgCl2 (208337, Sigma) and 2 mM EGTA (E3889, Sigma) was made. Sucrose was added extemporaneously before use at 0.32M (10%).

Micropatterning

Micropattern prototyping using Primo

The micropatterning protocol was adapted from [START_REF] Strale | Multiprotein Printing by Light-Induced Molecular Adsorption[END_REF]. Micropattern were obtained by shining a pattern of UV light through the microscope objective on a PEGylated glass coverslip covered with a liquid containing a photo-initiator. To limit the volume of liquid to use for the process (here choose at 30 µl), a custom silicone chambers was assembled using two sandwiched 250µm silicon sheets, cut with a plotter-cutter (GRAPHTEC CE-6000-40). For the bottom layer a millimeter pear shape in-between inlet and outlet channels (0.5 um wide), and for the top layer, holes upward the end of the inlet and outlet channels. 18x18 SCHOTT NEXTERION Coverslips #1.5H "High Performance" were used for prototyping steps. Coverslips were handles under a laminar flux hood. To promote attachment of PDMS chambers then attachment of Poly-l-Lysine-Polyethylenglycol/PLL-PEG, the surface of the coverslips was oxidized 40 seconds by exposure to air-plasma (PE-30, Plasma Etch) at 30W, under vacuum and with an air flow rate of 10 cc/minute. Then the silicone chamber was put onto the activated side followed by the introduction of PLL-PEG solution from the inlet channel. The PLL-PEG solution (PLL(20)-g[3.5]-PEG(2), SurfaceSolutionS, Switzerland), at a concentration of PLL-PEG at 0.1mg/ml in 10mM HEPES at pH7.4, was incubated for 30 minutes at room temperature. This step was performed extemporaneously, right before patterning. The coverslip was avoided to dry after this step and during and between all following steps. The coverslip was washed once with of PLPP (4benzoylbenzyl-trimethylammonium chloride, 14.5 mg ml-1) then fresh PLPP was added, by removing most of the liquid at the outlet with a highly absorbant precision paper (Kimwipes, Kimtech). Surface patterning was performed right after on an inverted Nikon microscope Ti-E equipped with a CFI Super Plan Fluor 20× ELWD (NA 0.45) objective capable of high UVtransmission, a Perfect Focus System 3, an ORCA-Flash 4.0 LT CMOS camera (Hamamatsu), a motorized stage (Märzhäuser) and the Primo module containing a DMD illumination with a 375 nm (4.5 mW) laser (Alvéole Lab). The microscope was controlled with the ImageJ µmanager software and the Primo module was controlled with the µManager-Leonardo plugin (Alvéole Lab). Micropattern shapes were designed using ImageJ, as an 8bit image with patterns filled in white on a black background. Each field was exposed for 25 seconds at 100% UV power corresponding to a 900 mJ/mm2 UV energy dose. The coverslips were washed 3 times with PBS by pipetting 100ul in the inlet while aspirating at the outlet using a high absorbant precision paper to create a flow within the chamber. Coverslips were then incubated with Fibronectin at 20µg/ml in PBS for 20 min by flowing 100µl of the solution, and then washed 3 times with PBS as described above. The silicone chamber assembly can be detached at this step by immersing coverslips in PBS and using tweezers. Patterned sample were kept at 4°C in PBS and used the next day. Cells were plated as described bellow for deep UV patterning.

Large scale micropatterning with deep UV and cell seeding

The micropatterning protocol was adapted from [START_REF] Azioune | Protein micropatterns: A direct printing protocol using deep UVs[END_REF]. Polystyrene coating : 20x20 Coverslips (1304369, Schott) were cleaned for 10min in acetone then for 10min in isopropanol in a bath sonicator and then dried with compressed-clean air under a laminar flow hood. They were coated with adhesion promoter Ti-Prime (MicroChemicals) using a spin-coater (WS-650m2-23NPPB, Laurell) at 3000 rpm for 30s and baked on top heater for 2min at 120°C. Then a 1% polystyrene (MW 260,000, 178891000, Acros Organic) solution in toluene (179418, Sigma) was spin-coated on the coverslip at 1000 rpm. Plasma treatment and micropatterning : Polystyrene layer was oxidized by exposure to airplasma as described above to promote the attachment of PLL-PEG to the surface, which was diluted as described above and incubated for 30min at room temperature. PLL-PEG was removed and coverslips room air dried before putting them in tight contact with a chromed printed photomask (Toppan Photomask). Tight contact was maintained using a vacuum holder. The PLL-PEG layer was burned with deep UV (λ=190nm) through the non-chromed windows of the photomask, using UVO cleaner Jelight), at a distance of 1cm from the UV lamp with a power of 6mW/cm2, for 4 min. Cell seeding : Coverslips were washed once with distilled water then incubated with a solution of 40µg/ml Fibronectin (F1141, Sigma) in PBS (14190169, GIBCO) for 30min at room temperature. Coverslips were then washed, in a sterile 6-well dish with one coverslip per well and under the laminar flow hood, 3 times with 3ml sterile PBS, once with 3ml DMEM and once with 3ml DMEM-10%FBS-1%Antibiotic-Antimycotic (complete medium). Cells/cytoplasts were detached with TrypLE (12605036, Gibco), centrifuged and resuspended in complete medium at 100'000 cells/ml. Most medium was removed for each well containing a coverslip and 1ml of cell suspension was added. Cells were left for spreading for 1 hour at 37°C before washing-out non-attached cells with pre-warmed complete medium. Cells were incubated for at least one more hour at 37°C to promote correct spreading and polarisation, before further treatments.

Imaging

Microscopy

Most fixed and fluorescently labelled cells were imaged using an up-right epi-fluorescence microscope (Olympus up-right BX61 equipped with a CoolSnapHQ2 camera) monitored by Metamorph. Samples were scanned for cell selection with dry objectives 10x or 20x using a Metamorph plugin developped by Céline Labouesse and Benoît Vianay. Cells were chosen so that they were well spread on sharp patterns and that they do not had a nucleus in the case of conditions with cytoplasts. Cells were imaged with a 100x NA 1.4 oil objective, with 0.5µm spacement between z planes in a range of 15µm. When patterned cells did not fit in one camera field, overlapping images were taken for further stitching. An inverted spinning disk microscope (Nikon Ti2 equipped with a Retiga R3 camera), monitored by Metamorph was used for Figure 7C and Figure S2B using a 60X objective.

Image analysis

For patterned cells that could not fit in one camera field, ImageJ macros using Stitching plugin were used. Images were then processed the same than single images. Centrosome positioning analysis was performed with homemade ImageJ suite of macros. The closest plane to the coverslip (cell bottom) was determined creating a band ROI on the actin image, as an expansion of a rough cell border determined by threshold filtering. This ROI was applied to the microtubule channel where the z-plane with the highest Standard Deviation within the band was chosen as cell bottom. Cell Top was determined using the standard deviation of the whole image. Firsts and lasts superfluous z-planes were that way removed to lighten calculations.

Threshold filtering in actin cell bottom plane was performed to determine cell edges and centroid was calculated. Similar method was used to determine nucleus edges and centroid in the case of conditions with nucleated cells. Scanning the Prominence parameter of the "Find Maxima" plugin from imageJ was performed to determine the prominence value where the number of found maxima was closest to one. Scanning for maxima within the region around this principal centriole was performed to find eventual extra-centrioles. Cells with more than 4 centrioles were discarded. The centroid of the polygon defined after connecting all centrioles 3 by 3 into triangles and adding all areas was used for the calculation of the distances to the cell, and nucleus if applicable, centroids. All steps contained a quick-scanning verification and assisted-correction module to make sure the analysis was correct for all cells.

Centrosome positioning compared triangle characteristic centres

In the case of triangle-patterned cytoplasts, the contour defined previously was smoothened by converting curve into a spline defined by a discrete number of close points. The curve defined by the distance of each point from the spline to the previously calculated centroid was smoothened by quadratic regression until the curve presents only 3 maxima, corresponding to the 3 triangle vertexes. The indexes of these three points were used to find the 3 corresponding points the contour-spline. The coordinates of theses 3 points were used to fit the contour of the cell to a triangle. Geometrical calculations were performed to determine the coordinates of 4 characteristic centres of that triangle (centroid, incentre, circumcenter and orthocentre). Distances from the centrosome to these centres were calculated.

Actin inner zone (AIZ) and actin inner centre (AIC)

Actin inner zone was determined manually on projected and denoised (rolling ball filtering) actin images. The coordinates centroid of the zone was determined and the distance to cell and centrosome centroids was calculated.

Dot plots and plots of AIZs

An angle correction was determined for all cells in a semi-automatic way. The coordinates of all centres were redressed according to the correction angle and relative coordinates to cell or actin centroid were calculated and plotted. Similar procedure was performed for the regions defining AIZs. Either all contours of AIZs were drawn, or one black 8-bit image was created for each cell and the AIZs was drawn and filled in white. A sum of all the images was made and a Royal LUT was applied.

Microtubule orientations

Microtubule stacks were skeletonized using a homemade Java plugin. A sum projection was made before a homemade orientation filter was applied to determine the angle made by each pixel of the skeletonized microtubule network. The calculation of a relative angle to the centrosome was performed. This angle corresponds to the angle made locally by a portion of microtubule around a given pixel and the radius defined by the line passing by both the studied pixel and the centrosome. The distribution of relative angle value as a function of the distance to the centrosome was determined and plotted with R. This distribution was also performed this time limiting the considered values to a band as shown in the figures or to a given zone like the AIZ.

Statistical Analysis

Mann-Whitney non-parametric test was used to compare samples using GraphPad Prism software (Version 6.0). Bars in all figures correspond to the median except on Figure 3D. Error bars on Figure 3D correspond to standard error mean (SEM). A. Mouse embryonic fibroblast (MEF) vimentin-knockout (KO) cytoplasts expressing EGFP-Centrin1 were plated on short isosceles triangles, fixed and stained with phalloidin-A555. The scheme shows the analysis performed to study the AIZ and AIC. The red dot represents the geometric centers of the cytoplasts and the green dots the AICs. B. For a variety of shapes, the distance of the centrosome to the cytoplast's geometric center was compared with the distance of the centrosome to the AIC. Scale bars: 10µm.

Cytoplasts plated on 2000µm2

Isosceles "Short" triangles were plated for 2 hours then treated for 2 hours with Y27632 at 20µM. Analysis was performed as described before. A. Microtubule and actin staining as in Figure 1. One representative example is given for each condition. B. Plots of all the contours of AIZs relative to the cell center. C. The distance from the centrosome to the triangle basis and the distance from the lowest point of the AIZ to the triangle basis (upper panel) were calculated and plotted (lower panel) as well as the difference between these two distances. D. Plots of all AICs relative to the cell centroid and of centrosomes relative to the AIC. E. Plots of all centrosomes relative to the cell center and the respective angle distribution of the population, and its distance to cell centroid along indicated axis. F. PTK2 cells were platted on isotropic and anisotropic shapes and for each of them one example is given. The plots show centrosome and nucleus centroid distributions relative to cell centroid, and their distance to cell centroid along the axis indicated by dashed-black arrows. The red dots represents cell geometrical center, the dark-green dots represents the AIC, the light-green and yellow dots represent the centrosome. Blue dots represent the nucleus centroid. Dashed red line represents cell centroid position at the graph origin. Scale bars: 10µm.

Figure 5. Analysis of microtubule orientation in and outside the AIZ.

Cytoplasts were plated on 2000µm2 disks and stained for Actin and Microtubules like in Figure 1. A. Overview of the microtubule network analysis. The Orientation Ratio or "OR" is the ratio of the number of non-null pixels with an orientation <45°C and the number of non-null pixels with an orientation >45°C. B. Example of analyzed cytoplast C. Overview of the microtubule-AIZ cross-analysis: microtubule network analysis was performed along a radial band and in the AIZ and in the APZ. D. Results of cross-analysis plotting the "OR". The microtubules within AIZ are preferentially oriented radially and the ones outside the AIZ (in the APZ) are preferentially oriented tangentially. E. The independently determined AIZ boundary matches the boundary of two zones defined by a clear majority of radial or tangential microtubules respectively

Cytoplasts plated on 2000µm2

Isosceles "Short" triangles were treated with Ice-Nocodazole 10µM or Ice-Nocodazole 10µM/Y27632 100µM in order to uncouple the effect of contractility and the one of microtubules depletion. A. Representative images of cytoplasts from both conditions. In the absence of microtubules, actin contractility is highly increased. In cells depleted for microtubules and treated with Y27632 at 20µM, contractility was still abnormally high (not shown). A higher concentration of Y27632 (100-200µM) was then used. As observed in the example cell, this concentration was sufficient to inhibit contractility in the absence of microtubules. B. Plots of all centrosomes relative to the cell center, distance to cell centroid along indicated axis and the angle distribution of the population. C. Plots of all the contours of AICs relative to the cell centroid and of centrosomes relative to the AIC. D. Plots of all AICs relative to the cell centroid and of centrosomes relative to the AIC. E. Plot of the distance between the centrosome and the cell centroid or the AIC for the indicated conditions. Red dots represents cell geometrical center and dark-green dots represent the AIC. The lightgreen and yellow dots represent the centrosome. Scale Bars: 10µm. Green arrow points at the centrosome. C. Co-staining for microtubules and dyneins. Arrow heads point at dynein dots co-localizing with microtubules. D. Examples of cytoplasts stained for actin and for dynein using anti-p150glued antibodies. The images were processed with an unsharp mask for better visualization. The AIZ was determined and represented by purple dashed lines. The maximum projection of the dynein images shows a higher overall amount of dynein inside the AIZ. Scale bars: 10µm.

A-RPE1 and B-C2C12 cells were seeded on 2000µm2 equilateral triangles, isosceles "short" triangles, L-shapes or U-Shapes. Cells were stained for actin using Phalloidine-A555 and with anti-Pericentrin to label the centrosome. The centrosome position distribution is shifted from the cell centroid in anistropic shapes but centered in isotropic shapes (equilateral triangles). Plots show centrosome and nucleus centroid distributions relative to cell centroid, as indicated. Scale bars: 10 µm.

Figure S2. Vimentin filaments bias microtubule organisation in cytoplasts.

A. Cytoplasts protocole overview. B. Cytoplasts made with MEF WT cells plated on disks (area: 1200µm2, radius: 11.0µm) and stained with anti-tubulin and anti-vimentin antibodies. An unsharp mask filter was applied to both channels and an enhance contrast was applied to the vimentin images before projection for better visualisation. Cells present Vimentin cage-like structures displacing microtubules, which surround the Vimentin, pointed by red arrows. These cages most likely explain differences in centrosome position distribution between cells and cytoplasts revealed in C. C. Quantification of centrosome position for three cell lines plated in 2000µm2 disks (Radius, 14.2 µm): RPE1, MEF WT or MEF KO for Vimentin. RPE1 cells (which contain high levels of Vimentin) and cytoplasts present very different distribution of centrosome positioning. On the other hand, MEF WT and KO for Vimentin and their respective cytoplasts present very similar distribution, also similar to RPE1 cells. The lack of difference between MEF WT and its corresponding cytoplasts may be due to the natural low levels of Vimentin present in MEF WT cells compared to RPE1 cells. Scale bars : 10µm.

Figure S3. Triangle analysis

A. Description of the triangle centers used for calculations of distances to the centrosome. B. Automatic analysis overview: contour and cell centroid were determined with actin staining. The contour ROI was converted into a spline. The distance between of each vertex of the spline and the cell centroid was calculated to create the "Plot of Distances" curve. The curve was smoothened with linear regression so limit the maxima to three (as for the three triangle vertexes). Maximas were found by calculating the derivative and its sign. The corresponding vertex coordinates were used to construct the triangle fit. Cytoplasts of C2C12 cells were seeded on 2000µm2 isosceles "short" triangles, L-shapes or U-Shapes. Cytoplasts were stained for actin using Phalloidine-A555 and with anti-Pericentrine to label the centrosome. The centrosome position distribution is shifted from the cell centroid. Green arrows point at the centrosome. Scale bars : 10 µm. Cytoplasts were seeded on a variety of 2000µm2 shapes presented in Figure 3. Cytoplasts were stained for actin using Phalloidine-A555. AIZ were determined. The centrosome pointed by green arrows is centered inside the AIZ. Scale bar : 10µm.

Figure S9. Analysis of microtubule orientation

Several examples of the analysis of microtubule network orientation are presented. Cytoplasts spread on 2000µm2 disks were fixed and stained for microtubules and centrosome. Image stacks were taken and analyzed using as described in Figure 4 and in the materials and methods section, using the centrosome coordinates as the center for the calculation of the relative orientation. Best plane of microtubules in shown on the left columns and the orientation map is shown on the right columns. Scale bars : 10µm.

FiguresFigure 1 .

 1 Figures

Figure 1 .

 1 Figure 1. Centrosome is shifted from the geometrical center in cells plated on anisotropic adhesion micropatterns.

Figure 2 .

 2 Figure 2. Centrosome positioning at and away from the cell geometrical center in enucleated cells.

Figure 2 .

 2 Figure 2. Centrosome positioning at and away from the cell geometrical center in enucleated cells.

Figure 3 .

 3 Figure 3. Centrosome positioning close to the actin inner center (AIC).

Figure 3 .

 3 Figure 3. Centrosome positioning close to the actin inner center (AIC).

Figure 4 .

 4 Figure 4. Role of contractility in the architecture of the AIZ and centrosome positioning.

Figure 4 .

 4 Figure 4. Role of contractility in the architecture of the AIZ and centrosome positioning.

Figure 6 .

 6 Figure 6. Effect of microtubule disassembly on AIZ and centrosome positioning.

Figure 6 .

 6 Figure 6. Effect of microtubule disassembly on AIZ and centrosome positioning.

Figure 7 .Figure 7 .

 77 Figure 7. Role of dyneins in centrosome positioning in the AIZ

  Geometrical definitions were used to calculate the characteristic lines and centers of each cell fitted as a triangle. All geometrical elements are plotted on the right panel in the centrosome picture. The centrosome (or centrioles) is outlined and pointed by a black arrow. C. Several examples of the analysis are shown. Scale Bar : 10µm. D. Distance between the centrosome and the different triangle centers for three types of triangles, of 2000µm2: equilateral, isosceles 7/4 ratio (Short), isosceles 9/2 ratio (Long).

Figure S5 .

 S5 Figure S5. Centrosome is also off-centered in C2C12 cytoplasts platted in anisotropic shapes.

Figure S7 .

 S7 Figure S7. Centrosome positions at the center of the AIZ in different shapes.

Figure S10 .

 S10 Figure S10. Analysis of microtubule orientation with respect to AIZ and APZ.

Figure S14 .

 S14 Figure S14. Spatial distributions of dyneins in response to AIZ geometry

Acknowledgements

We thank Robert Goldman for sharing the MEF WT and vimentin-KO cell lines, Hiroki Umeshima for sending us the plasmid p150glued DN, Franck Perez, Sandrine Moutel and the plateform TabIP for sharing their electroporator and antibodies, the cytometry plateforme of the Institute for Research of Saint-Louis Hospital, as well as Tanguy Chocat and Esteban Beuve Helissey for their assistance in performing experiments. This work was supported by the European Research Council (ERC Adv 741773 to L.B., ERC CoG 771599 to M.T.) and a post-doctoral fellowship from La Ligue contre le cancer (FFJL14157 to A.J.J.).

Author contributions

Conceptualization : M.T., L.B., M.P., M.B.; Funding Acquisition, M.T., L.B., A.J.J.; Methodology : M.T., L.B., M.P., M.B., A.J.J., A.S.; Investigation : A.J.J., A.S., C.D., G.L., B.V.; Analysis : M.T., L.B., A.J.J., G.L.; Supervision : M.T., L.B. Writing : M.T., A.J.J..

Declaration of interest

The authors declare no conflict of interest. Cytoplasts were seeded on 2000µm2 micropatterns with a variety of shapes. They were stained for microtubules and actin, and centrosome positioning was assed and plotted relative to the cell geometrical center calculated by the contour found with the actin channel. Overlapping images were taken and stitched for D,E,G and H before image processing. Scale bars : 10µm. A. Efficient removal of microtubules is achieved by incubation on ice for 2 hours followed by warming up in the presence of 10µM Nocodazole and incubation for different lapses of time. This treatment allowed to efficiently remove all microtubules (Lower left panels). B. Plots of all centrosomes relative to the cell center and quantification of the distance between the centrosome and the cell centroid for different time points of nocodazole treatment. C. Averages AIZs for the indicated conditions and quantification of the AIZ area for different time points of nocodazole treatment. Red dot represents cell geometrical center or the AIC as indicated by the graph title. In C, the red dot represents the cell geometrical center and the blue cross represents the averaged relative AIC. The light-green dots are the centrosomes. Green arrows point at the centrosome. Scale bars : 10µm.

Figure S13. Centrosome and AIC positioning in WT and Vimentin-KO cells seeded in triangles.

Cytoplasts were seeded in "short" 2000µm2 isosceles triangles and stained for centrosome and actin. A. The centrosome position in both cell lines present the same asymmetry towards the cell apex although it is slightly more dispersed in WT derived cytoplasts. B. A less centered AIZ seems to be responsible for this mild difference. This off-centering could be due increased contractility or the presence of Vimentin cages. The red dots represent the cell centroid. Scale bar : 10µm.


Madhukar Bhat

Jean-Marc Thiesse

Patrick Le Callet

A CASE STUDY OF MACHINE LEARNING CLASSIFIERS FOR REAL-TIME ADAPTIVE RESOLUTION PREDICTION IN VIDEO CODING

Keywords: Machine learning, Real-time delivery, Resolution prediction, Random Forest(RF), MLP

At lower bit-rate encoding video in real-time with a reasonable viewing quality is challenging. Content adaptive per-title encoding is usually leveraged for OTT/VOD delivery by selecting the optimal resolutions and qualities of a given video using multiple encodings. Built on such powerful resolution selection principles, this paper introduces an on the fly resolution prediction without requiring multiple encoding with the help of machine learning which is suitable for real-time video delivery. Two machine learning networks are defined based on the resolution of the previous decision period. Three types of machine learning classifiers: weighted SVM, Random Forests (RF), and custom-designed Multi-Layer Perceptron (MLP) are tested. Suitability of classifiers for real-time resolution prediction is discussed based on the accuracy, BDrate performances, and impact of misclassification on encoding performance and hardware implementability. The proposed solution offers a promising average bit-rate savings upto 12.6%.

INTRODUCTION

Video delivery optimization is thriving in this day and age to address rapid expansion in video consumption. There are several types of video consumption in different scenarios. Applications such as On-demand service, point-to-point communication has been an integral part of modern-day Internet usage. Depending on usage scenarios, real-time (live) video delivery is challenging, considering many network conditions and user consumption methods [START_REF] Mukerjee | Practical, real-time centralized control for cdn-based live video delivery[END_REF].

Point-to-point video streaming methods deliver video to its members at a given bit-rate in real-time. In this scenario, Constant Bit-Rate (CBR) video encoding methods are applied. Depending on bit-rate, Quantization Parameter (QP) is derived using pre-analysis. Delivery of a video below a specific bit-rate for a particular resolution introduces significant distortion resulting from high QP. One option to achieve acceptable encoding at such resolution is to send a lower number of pixels through resolution or frame-rate down-sampling [START_REF] Segall | Improved high-definition video by encoding at an intermediate resolution[END_REF]. The bit-rate below which switching to a lower resolution is better depends on the temporal and spatial features of video content. The newest video standard in progress Versatile Video Coding (VVC) [START_REF] Ohm | Versatile video codingtowards the next generation of video compression[END_REF] incorporates an option to select a resolution in a normative way through Reference Picture Resampling (RPR) [START_REF] Luo | Summary report on reference picture resampling filters[END_REF] considering these factors.

Content adaptive encoding techniques have been widely adapted to account for network conditions and video characteristics. Typically, adaptive streaming techniques such as DASH [START_REF] Sodagar | The mpeg-dash standard for multimedia streaming over the internet[END_REF] and HLS [START_REF] Pantos | Http live streaming draft-pantoshttp-live-streaming-13[END_REF] provide a multi-representation delivery framework for video depending on network conditions. In [START_REF] Weinberger | Choosing the right video bitrate for streaming hls and dash[END_REF], recommendations are provided on ranges of bit-rates for different resolutions for the OTT scenario. While these applications focus on general thumb rule, it is asserted that some contents can have a different complexity of scenes that might behave differently.

Professional solutions such as [START_REF] Ateme | The single critical factor for high-quality streaming, now and forever[END_REF] are already leveraging such principle, based on the creation of a bit-rate/resolution ladder for various video profiles maximizing quality for VOD applications. Netflix, a popular OTT content provider, proposed dynamic optimizer in video coding [START_REF] Katsavounidis | Dynamic optimizer -a perceptual video encoding optimization framework[END_REF]: each scene is encoded at multiple down-scaled resolutions and a range of bit-rates. The convex hull of bit-rate/qualities is produced to select the best operating resolution at a given scene using metrics such as PSNR and VMAF [START_REF] Li | Vmaf-video quality metric alternative to psnr[END_REF] after up-scaling all encoded videos to the full resolution. In [START_REF] Bourtsoulatze | Deep video precoding[END_REF], deep video pre-coding is performed with a design of CNN based multiple downscaling filter network operating before video transmission. Resolution selection is carried out based on the precoding network-based single RD point of different scales. It has reduced complexity compared to Netflix based optimizer, which needs several rate-distortion points per scale factor.

The above methods encode the source video at many different resolutions and bit-rates before transmission. Then RD-based selection of the best quality video at a given network condition is selected. These techniques are designed for on-demand delivery. In the case of a point-to-point live delivery system, it would be computationally expensive and introduce unmanageable latency to encode the video at different bit-rates and then select the best resolution based on the convex hull.

There are solutions [START_REF] Wien | Real-time system for adaptive video streaming based on svc[END_REF][13] based on scalable video cod-ing (SVC) [START_REF] Schwarz | Overview of the scalable video coding extension of the h. 264/avc standard[END_REF] by encoding multiple layers of resolution to deliver video at suitable resolution for different network conditions. In these methods, instead of optimizing the encoding resolution, the SVC framework is used for the selection of suitable resolution based on general thumb rule for delivery.

To practically find better-performing resolution for a realtime video delivery system, particularly at a given lower bitrate scenario, a potential solution would be to have a priory decision based on pre-analysis to predict the best encoding resolution for the decision period. Considering potential VVC's support of switching to a lower resolution, it is more relevant than ever to have a simple but effective method guiding switching to lower resolution with pre-analysis of initial frames in the live point-to-point video coding scenario.

This paper proposes a novel on the fly adaptive resolution prediction for a decision period before encoding process without the RD-score requirement for each resolution allowing the saving of multiple resolution encodings. Then, computationally less expensive real-time and hardware friendly machine learning, weighted SVM, RF's, and custom-designed MLP, are studied. Features from the first few frames are used to predict better performing resolution for a decision period. In this paper, we consider two resolutions, the original resolution, and down-scaled resolution by a factor of 4 in terms of area. This prediction is interpreted as a binary classification problem in the context of machine learning. Depending on the resolution of the previous decision period, two separate classifiers Network-HR and Network-LR, are employed. During training, a weight-based label is proposed to avoid misclassification resulting in quality loss. A professional HEVC encoder is employed for testing in this paper. Labeling can be formulated for any codec, including VVC in the future. Accuracy of classifiers on these algorithms is discussed, and respective BD-rate comparison to reference without adaptive resolution selection is carried out. Finally, the impact of misclassification is analyzed.

The paper is organized as follows. Section 2 details the Real-time resolution selection algorithm. Section 3 explains the learning algorithms and optimization process. The results are discussed in Section 4. Section 5 details the conclusion drawn.

REAL-TIME RESOLUTION SELECTION

This section introduces the proposed adaptive real-time resolution selection as a binary classification problem. Two machine learning networks are employed, depending on the resolution of the previous decision period. One of these networks predicts a suitable resolution for the current decision period.

Resolution selection as a classification problem

Prediction of better resolution on the fly for a decision period in a video is challenging. The difficulty arises mainly due to the unavailability of every frame of a decision period of a video for pre-analysis. A general thumb-rule in terms of bitrate, QP, or any other parameter for resolution selection would miss content-based adaptation. Hence, alternative solutions such as machine learning algorithms are better to approach to predict operating resolution for the current scene in real-time scenarios.

Key questions addressed in this paper are when to change the resolution, how often to check for resolution change, and how to change resolution. Real-time implementations in HEVC, CBR encoding mode, employs a speedy real-time compatible pre-analysis step to guide the encoding process. Features derived from pre-analysis before the main encoder begins for the current decision period is utilized for predicting better resolution. On how often to change resolution, a caveat needs to be addressed for codecs that do not support normative Reference Picture Resampling. Codecs other than VVC consider resolution change as starting of new bit-streams. The decision period is set as the Intra period or scene change in this paper to avoid potential playback issues. The downsampling filter applied in this paper is a professional three taplinear filter. Since the upscaling happens at decoder end and the majority would do linear filtering, the same is assumed for ground truth formation for the dataset.

Machine learning Networks for classification

In this paper, two machine learning networks are proposed. One of the networks is used depending on the resolution of the previous decision period. Fig. 1 describes these networks. Two machine learning networks are used mainly to address potential adaptive rate-control interference. This interference would potentially happen if we assume original resolution at the starting of each decision period and then decide to switch to a lower resolution or not. Consider lower resolution is selected multiple times in a row, utilization of encoder preanalysis data used for resolution selection from original resolution has to be re-scaled or re-calculated. Two learning networks are used so that the re-calculation of rate control preanalysis is required only during resolution change.

Resolution selection mechanism

If the previous decision period resolution was original (HR) resolution, learning Network-HR is employed. Network-HR works as a classifier, which could predict to retain resolution (R HR ) or downscale the resolution (D HR ). Learning Network-LR is employed if the previous decision period resolution was the downscaled resolution. Network-LR would work as a classifier that would predict to retain lower resolution (R LR ) or upscale to a higher resolution (U LR ).

Classification labels

The selection of best resolution for the training process, i.e., label formation required for supervised classification methods, could be made in many ways. One way is to measure the quality (Q) of upscaled LR and HR against the source and select a better one for the label (L i ) formation in-terms of PSNR. Label L i , for a sample, is given as,

L i = 0, if Q HRi -Q LRi ≤ 0 1, if Q HRi -Q LRi > 0 (1)

LEARNING ALGORITHM DESIGN

In this section, dataset creation and training processes for learning algorithms are detailed.

Training and testing samples

Data selection for training samples for a machine learning algorithm needs to be plentiful and diverse. In the case of resolution prediction, only one sample is available for each Intra period. Compared to other machine learning proposals for video compression, which mostly operate at CTU level, the amount of samples available for resolution selection is sparse by orders of magnitudes. With the consideration of data sparsity, videos are collected from Xiph [START_REF]Xiph, Xiph.org video test media[END_REF] for CIF, and Full HD and open-source Vimeo videos listed in [START_REF] Vatolin | Hevc video codecs comparison 2018[END_REF] are selected for both full HD and 4K.

CIF

Full-HD 4K Bit-rates 2-20 kbps 0.2-1 Mbps 1-5Mbps Table 1. Bit-rate ranges for CIF, Full-HD and 4K For a specific operating resolution, bit-rates are selected in such a way that there is a benefit in resolution selection. Fig. 2 shows the probability of retaining original resolution of video p HR for bit-rates given in Table 1. It shows selected bitrates are most useful for each operating resolution in-terms of having the ability to choose LR or HR.

Dataset creation, training, and testing are performed separately for each resolution. The selected Intra period is 2 seconds. Labels are formed at each Intra period. A total of 8 In addition, testing samples are created for measuring the performance of machine learning algorithms. The following sequences are tested for each resolution. For CIF, SVT videos [START_REF] Haglund | The svt high definition multi format test set[END_REF] combined to form 2000 frames with 5 different scenes is tested. For full-HD SVT video combined to form 1000 frames with five different scenes, three full-HD videos from JCT-VC common conditions [START_REF] Jctvc-L | Common test conditions and software reference configurations[END_REF] are tested. For 4K videos, five videos from JCT-VC common conditions are tested.

Feature selection

Features selected for a learning algorithm needs to be representative of the purpose. In this paper, it is an adaptive resolution prediction for a decision period. It is important to select minimal features that successfully select a better resolution to avoid an increase in complexity leading to an implementation difficulty in the real-time encoding scenario. The objective is to use features from the first few frames to decide a resolution for the whole decision period. Available features are evaluated as follows.

Evaluation of available features

Evaluation of useful features can be availed through methods such as a wrapper method [START_REF] Kohavi | Wrappers for feature subset selection[END_REF] based on F-score of the network for each and combinations of features, filter models [START_REF] Liu | Computational methods of feature selection[END_REF] such as mutual information [START_REF] Peng | Feature selection based on mutual information: Criteria of maxdependency, max-relevance, and min-redundancy[END_REF] and correlation and regularization of model during training process [START_REF] Ma | Penalized feature selection and classification in bioinformatics[END_REF].

In this paper, mutual information is used at first to minimize massive data such as motion vector, the histogram of pixels, and variance since its much faster than the wrapper method to select features. Then F-score for SVM is calculated for reduced features to verify the usefulness of features. After this analysis, the final selected features are listed below. They are divided into four categories Rate control based, Spatial features, Temporal features, Encoder pre-analysis based features. In total, 43 features are selected.

Rate-Control Based features: This section of features is relevant to the rate control algorithm to keep the encoded bit-stream under targeted bit-rate.

• X Rate-control-f eatures : Three features Initial QP, Frame rate and targeted bit-rate Spatial features: Spatial features such as histogram of pixel values and variance of CTU's of Intra frame are taken into account with mutual information in consideration.

• X var andX hist : Maximum, minimum and average of Variance of all CTU's and histogram of all pixels of the Intra frame respectively Temporal features: Temporal features are needed to determine temporal complexity of the scene. Motion vectors which can be made available from pre-analysis are extracted. Besides, the scene change index of each frame of the first GOP in the decision period is taken into account. The scene change index is derived from fast motion estimation of lowered resolution of the source video.

• X M vx and X M vy : Motion vectors in Horizontal and vertical direction of middle picture in first GOP for 16x16 block size. Ten maximum and the average motion vector in both horizontal and vertical directions are selected.

• X scene-change-score : Scene change score of each frame. Encoder pre-analysis based features: For the CBR mode of encoding, HEVC encoders have a very fast pre-analysis where QP estimation for all pictures in a GOP and overall probability of Intra is predicted.

• X QP -est : Estimated QP of all frames in the initial GOP

• X p-intra : Estimated Intra probability

Training process

A training process aims to maximize the accuracy of the classification rate on the test set of a training dataset. The training process for best resolution prediction for the decision period/scene is tested with three techniques: linear SVM, RF, and Multi-layer Perceptron (MLP) classifier. These three learning techniques are computationally less expensive and require no additional hardware requirement. Section 6 shows the performance of these classifiers with an angle to hardware implementation. The impact of misclassification on PSNR is considered as the sample weight to improve accuracy.

Sample weight generation for mis-classification

The impact on PSNR arising from misclassification is assessed using the difference in PSNR. Let R/C be the misclassification when the classifier chooses to retain resolution R instead of changing resolution C compared. In such case weight for that sample W si is defined as,

W si = R P SN R -C P SN R R P SN R * C rate R rate (2)
This weight account for the varying effect of misclassification and successfully avoids misclassification with very high PSNR differences. The ratio of bit-rate is to account for bit-rate difference induced by encoder control compared to the target rate. In case of Network-HR misclassification is retaining resolution instead of downscaling or vice versa (R HR /D HR ), (D HR /R HR ) and for Network-LR it is retaining resolution instead of upscaling and vice versa (R LR /U LR ), (U LR /R LR ) . In the next subsections design of learning algorithms is given in detail.

SVM and Random Forests

SVM tries to find a unique separating hyper-plane that maximizes the margin between two classes. In this paper, a nonlinear SVM is utilized with a polynomial kernel with a degree of 2, and a kernel coefficient of 1/n f eatures is applied. RF classifiers employ many single correlated decision trees, and the final decision is made by gathering results from all single decision trees and de-correlating them. In this paper, RF classifiers are used since they are lightweight and have a better trade-off with accuracy and over-fitting training data. The configuration adopted in the context of resolution prediction is: tree depth of 12, and the number of estimators is 25.

Multi-layer Perceptron (MLP) classifier design

The proposed MLP is designed in such a way that it is hardware friendly. For hardware, it is desirable to have similar mathematical operations for decisions coming from different networks. Hence, the target is to use the identical network topology for all resolution and both Network HR and LR. With this in mind and considering design guidelines are given in [START_REF] Karsoliya | Approximating number of hidden layer neurons in multiple hidden layer bpnn architecture[END_REF], an MLP network with four fully connected hidden layers with neuron sizes [START_REF]Xiph, Xiph.org video test media[END_REF][START_REF] Bourtsoulatze | Deep video precoding[END_REF][START_REF] Weinberger | Choosing the right video bitrate for streaming hls and dash[END_REF][START_REF] Sodagar | The mpeg-dash standard for multimedia streaming over the internet[END_REF] was selected for both Network-HR and Network-LR. The activation function used was the Rectified Linear Unit (RELU). The applied loss function was the mean squared error with sample weights derived in the last section. L1 regularization for the first layer was added to avoid over-fitting. Adam (Adaptive Moment Estimation) optimizer was adopted for weight update as it requires less memory and its easiness in handling hyper-parameter optimization. For hardware implementations MLP are better than RF as the same architecture for hardware computation remains for all resolutions. On the other hand, an RF classifier might have a different architecture for each update of a dataset and each resolution.

RESULTS

In this section, the performance of learning algorithms explained in the previous section is discussed in two contexts. At first, the accuracy of networks is analyzed. Then the BDrate performance of each network and the impact of misclassification on the performance of encoding is studied.

Accuracy of Networks

One can measure the accuracy of machine learning networks by calculating precision (P), Recall (R), and F1-score (F1) [START_REF] Goutte | A probabilistic interpretation of precision, recall and f-score, with implication for evaluation[END_REF]. Results for SVM, Random-forest, and MLP networks for each resolution are reported in Table 2 In this section, the BD-rate performance of each machine learning algorithm is tested against the reference encoding of high resolution. A comparison to ground truth resolution is reported in Table 3. Test sequences mentioned in the Section 3 are tested for BD-rate performance. Bit-rates tested were four bit-rates in the range of 5-20kbps for CIF, 0.1-1Mbps for Full-HD, and 1-5Mbps for 4K videos. Table 3 shows that dynamic resolution selection introduces bit-rate gain at the same quality. The potential to gain bit-rate at the same quality increases with the resolution. Overall BD-rate performance of MLP algorithm and RF are close, but SVM has lower BD-rate savings because of its lower accuracy. In some sequences, the BD-rate savings of learning algorithms are higher than ground truth. This is because, in some cases, even-though wrong decisions are made bit-rate of LR is much smaller than HR, and the difference in quality is small. Table 3. BD-rate at same quality compared to single higher resolution at CIF, FUll-HD and 4K

Impact of misclassifications

Misclassification of the trained network in resolution switch incurs a loss of quality compared to the ground truth. In the context of this paper, the main quality loss that is to be studied is when the lower resolution was falsely selected instead of the original resolution. This sub-section aims at analyzing maximum loss against a reference with only high resolution. The condition for this occurrence would be the false positive in Network-HR and false negative in Network-LR. In this analysis, maximum PSNR loss (dP SN R(C/R) max ) and BD-rate loss (BD loss(C/R) max ) due to misclassification in tested sequences are reported in Table 4. Overall performance analysis shows that MLP and RF classifiers perform better than SVM in resolution prediction at the starting of an intra-period. RF classifier sometimes edges MLP mainly due to similar architecture constraints put forward in designing MLP for its hardware friendliness. The same topology would have the same template of a code port for efficient weight multiplication for prediction. As mentioned earlier, RF classifier could pose challenges in hardware implementation by changing its tree architecture in case of updating algorithm with more data, which would require a change of the code suitable for hardware implementation.

CONCLUSION

In the context of real-time content-adaptive video encoding, this paper introduces an on the fly resolution prediction suitable for lower bit-rate scenarios where multiple encoding for selecting better resolution is not desirable. In the proposed framework, machine learning classifiers SVM, RF, and designed MLP are studied for different video resolutions. Depending on the resolution of the previous Intra-period, two machine learning networks are defined. Original resolution and downscaled resolution by a factor of 4 in terms of the area are tested in this paper. The performance of Learning algorithms has been evaluated in terms of accuracy, BD-rate, and misclassification impact for CIF, Full-HD, and 4K resolution. MLP and RF classifiers are better than SVM with MLP more suitable for hardware implementations. Adaptive resolution prediction using MLP introduces an average bitrate gain of 2.3% -12.6% depending on the resolution of the video.

Fig. 1 .

 1 Fig. 1. Two machine learning networks are used based on the resolution of previous decision period

of Higher resolution being better at a given bit-rate

  Probability of retaining higher resolution at tested bitrates.Point 2-9 in x-axis are in the range of selected bit rates in Table1. Point 10 and 1 are 10% higher and lower bit-rates than point 2 and 9 respectively different bit-rates are encoded for each video in the specified bit-rate range. Training samples are pre-processed to make the dataset at each resolution balanced for each class. In total, 9832 samples for CIF, 4464 samples for Full-HD, and 3624 samples for 4K are trained.

		0.9
		0.8
		0.7
	P	0.6
		0.5
		0.4
		0.3							CIF Full-HD
									4k
		0.2
		1	2	3	4	5	6	7	8	9
						Bit-rate points
	Fig. 2.

HR

Probability

Table 2 .

 2 . Each selected network achieved excellent overall accuracy. RF classifier outperforms both SVM and MLP in terms of its accuracy mainly due to similar topology constraint put-forward for MLP across all conditions. Accuracy of the network for both learning network-HR and LR based on resolution of previous period

		Precision(%)		Recall(%)		F1-score(%)
	Conditions	CIF FHD 4K CIF FHD 4K CIF FHD 4K
	SVM
	Network-HR 79	75	75	81	75	75	80	75	75
	Network-LR	79	76	72	80	76	75	79	76	74
	RF
	Network-HR 89	89	87	82	89	87	85	89	87
	Network-LR	85	86	87	82	86	85	83	86	86
	MLP
	Network-HR 86	85	87	84	87	87	86	86	87
	Network-LR	80	82	87	80	89	87	80	85	87
	4.2. BD-Rate performance

Table 4 .

 4 Maximum PSNR loss and Bit-rate loss during misclassification