Jing Xie

Javad Najafi

Rémi Le Borgne

Jean-Marc Verbavatz

Catherine Durieu

Jeremy Sallé

Nicolas Minc
email: nicolas.minc@ijm.fr

Nenad Pavin

Anne-Marie Tassin

Jérémy Sallé

Dmitry Ershov

Milan Lacassin

Serge Dmitrieff

Nicolas Minc

Contribution of cytoplasm viscoelastic properties to mitotic spindle positioning

Keywords: Cell division, Mitotic spindles, Forces, Cytoplasm, Flows, Mechanobiology Cell division, Mitotic spindles, Forces, Cytoplasm, Flows forces, microtubules, actin, cytoplasm, cytoskeleton

Living cells are filled with macromolecules and polymer networks that set scale-dependent viscous and elastic properties to the cytoplasm. Although the role of these physical parameters in regulating molecular diffusion, reaction kinetics and cellular biochemistry is being increasingly recognized, their contributions to the motion of larger organelles, such as mitotic spindles, microtubule asters or nuclei for cell division and organization remain unknown. In this thesis, I implemented in vivo magnetic tweezers to apply calibrated forces and torques that displace and rotate mitotic spindles in live dividing sea urchin embryos. I uncovered that the cytoplasm matrix can impart large viscoelastic reactive forces that bring back spindles, or large passive objects like oil droplets to their original position. These forces are independent of cytoskeletal force generators, yet reach hundreds of piconewtons and scale with cytoplasm crowding. Spindle motion under force, also causes the cytoplasm to shear and rearrange, to eventually yield and fluidize, a process which dissipate elastic energy and limits spindle recoils. Such fluidization or plastic yield under force has functional implications for asymmetric and oriented divisions, as it allows spindles to maintain an offset position or tilt in cells. I also uncovered that the mechanical contribution of cytoplasm properties to mitotic spindle positions exhibits shape and size dependence, which may be of fundamental importance for early embryo development and morphogenesis. Thus, these findings suggest that bulk cytoplasm material properties may constitute important control elements for the regulation of division positioning, cellular organization and early embryo development.

du cytoplasme. Les flux de cisaillement induits par la contrainte et le mouvement du fuseau induisent un réarrangement du cytoplasme et dissipent l'énergie élastique, limitant le retour du fuseau avec des implications fonctionnelles pour les divisions asymétriques et orientées. Les forces réactives du cytoplasme dépendent de la forme et de la taille cellulaire avec des conséquences sur la stabilité de la machinerie de division pendant l'embryogénèse. Ces résultats suggèrent que les propriétés matérielles du cytoplasme peuvent constituer des éléments de contrôle importants pour la régulation du positionnement des divisions, de l'organisation cellulaire et du développement des embryons.

Mots clés :

Division cellulaire, Fuseau mitotique, Forces, Cytoplasme, Flux, Mécanobiologie

INTRODUCTION

In my thesis, I studied mechanisms of mitotic spindle/division positioning in large sea urchin embryos. In particular, I revealed the role of cytoplasm material properties to spindle positioning. Before diving into my results, I will introduce some important notions of the cell cycle, cytoskeleton regulation, division positioning and physico-chemical properties of the cytoplasm.

I. The cell cycle

Life is a continuous process that is passed from one generation to the next. The life cycle of a cell is called the cell cycle, and begins with the birth of a parent cell, ending with the formation of its daughter cells. During the cell cycle, cells are prepared for the future divisions consisting of a repartition of duplicated chromosomes into two daughter cells, in a process called karyokinesis, coordinated with a cytoplasm repartition called cytokinesis. In order to avoid a decrease of cell size and/or genetic material in the daughter cells, cell growth and DNA synthesis are necessary [START_REF] Ohkura | Meiosis: an overview of key differences from mitosis[END_REF]. To accomplish these processes, cells need to undergo different phases [START_REF] Mcintosh | Mitosis[END_REF][START_REF] Yanagida | The role of model organisms in the history of mitosis research[END_REF]. The cell proceeds through a cycle of DNA replication (S phase), gaps (G1 and G2 phases) and mitosis (M phase). The S phase and gap phases compose interphase. The M phase undergoes 5 stages: prophase, metaphase, anaphase, telophase, and cytokinesis, which is a continuous process from one parent cell to two daughter cells (Figure .I.1).

The entry and exist of these phases are regulated by a molecular trigger, called maturationpromoting factor (MPF). MPF is a protein complex that was identified from experiments on the development of frog eggs [START_REF] Masui | Cytoplasmic control of nuclear behavior during meiotic maturation of frog oocytes[END_REF][START_REF] Smith | The interaction of steroids with Rana pipiens Oocytes in the induction of maturation[END_REF]. Its activity oscillates with the cell cycle: it peaks at mitosis, then dramatically drops (Figure .I.1, top left).

Thus, injection of MPF into cells can promote their entry into mitosis [START_REF] Adhikari | The regulation of Maturation Promoting Factor during prophase I arrest and meiotic entry in mammalian oocytes[END_REF][START_REF] Kishimoto | Entry into mitosis: a solution to the decades-long enigma of MPF[END_REF][START_REF] Lohka | Nuclear responses to MPF activation and inactivation in Xenopus oocytes and early embryos[END_REF]. An intense investigation of MPF revealed that it is composed of two subunits: cyclin and cyclin-dependent kinase (Cdk). The cyclin level varies during the cell cycle and the entry into S phase and/or M phase is triggered by the activation of Cdk, which is dependent on the cyclin level. Mitotic-cyclin (M-cyclin) and Mitotic-Cdk (M-Cdk) serve to regulate the entry and exit of M phase. M-cyclin concentration constantly increases during interphase and peaks right before mitosis, when M-Cdk is activated, driving the cell into the M phase (Figure .I.1) [START_REF] Evans | Cyclin: a protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division[END_REF][START_REF] Hégarat | Cyclin A triggers Mitosis either via the Greatwall kinase pathway or Cyclin B[END_REF]. In addition to the binding of cyclin, M-Cdk must be activated by phosphorylation. The M-Cdk/cyclin complex remains inactive after phosphorylation by both activating and inactivating kinases. Thus, a specific activating phosphatase is needed to remove the inhibitory phosphate group (Figure.I.2). Active M-Cdk triggers the phosphorylation of a variety of proteins, including the protein Condensin.

Condensin associates with DNA in the chromosomes and mediates their condensation in prophase, and with proteins in the nuclear lamina to trigger nuclear envelope breakdown in prometaphase [START_REF] Beaudouin | Nuclear Envelope Breakdown Proceeds by Microtubule-Induced Tearing of the Lamina[END_REF]Wang et al., 2020b). It also impacts the dynamic behavior of the microtubule cytoskeleton to promote the formation of a mitotic spindle. As M-Cdk is activated, cyclin will be degraded; thus, high activity of M-Cdk results in its own inactivation due to the cyclin lysis. This accounts for the rapid drop in cyclin levels at the end of mitosis, triggering mitotic exit. Similarly during S phase, the activity of S-cyclin/Cdk complex regulates the entry and exit of S phase (Figure .I.1). One activity of the S-Cdk is to phosphorylate and activate proteins associated with the origin of replication (ORI) to trigger the initiation of DNA replication at the origin [START_REF] Heller | Eukaryotic origindependent DNA replication in vitro reveals sequential action of DDK and S-CDK kinases[END_REF][START_REF] Tanaka | The role of CDK in the initiation step of DNA replication in eukaryotes[END_REF].

During the gap phases, the cell continues to grow and to monitor intracellular and environmental conditions in order to meet certain requirements before proceeding to the S or M phases. If these criteria are not achieved, the cell will be arrested at points in the gap phases, which are called checkpoints. At the G1/S checkpoint, a cell must ensure the integrity of the DNA prior to replication and monitor cell's size and environmental conditions. At the G2/M checkpoint, a cell must ensure all the chromosomes have been replicated before entering into mitosis. The length of the cell cycle varies widely between cell types, from 2-3 hours in yeast cells to 12-24h or even more for some somatic animal cells.

In my project, I worked on the early cleavage of sea urchin embryos, which undergo synchronous and rapid cell cycles (~ 1 hour). These cycles differ from the standard four-phase cell cycle as they lack real G1 and G2 phase, thus producing smaller and smaller nucleated blastomeres [START_REF] Belisle | The Cell Cycle in Early Embryonic Development[END_REF]. These short cycles also occur in early development of many organisms, like frogs and zebrafish embryos with the cell cycle around 20-30 min [START_REF] Siefert | Cell cycle control in the early embryonic development of aquatic animal species[END_REF]. Since my work is on cell division, here I precisely describe two associated processes of the cell cycle, mitosis and cytokinesis.

Figure I.1:

The cell cycle and associated Maturation-promoting factor (MPF) activity. The cell cycle is composed of the S phase (DNA synthesis), M phase (Mitosis) and two gap phases (G1 and G2) in between. Mitosis is divided into five stages: prophase, prometaphase, metaphase, anaphase and telophase (inset at left bottom). The cell cycle is regulated by MPF activity. When the mitotic cyclin-dependent kinase (M-Cdk) is activated, the cell enters into mitosis. As a result, the Mitotic-cyclin (M-cyclin) is degraded inducing the inactivation of M-Cdk, thus cell exits mitosis. Analogous to mitosis, the entry and exit of S phase are regulated by S-cyclin and S-Cdk. M-cyclin and M-Cdk concentration during cell cycle is presented in the left top inset (adapted from Biol.Penn.State©2004).

Mitosis

Prior to mitosis, chromosomes duplicate with pairs of sister chromatids bound together at centromeres. Each chromatid has a protein complex called kinetochore at the centromere region. Kinetochores are composed of a permanent part bound to centromere referred to as inner kinetochore and a dynamic part referred to as outer kinetochore only assembled for mitosis that will be bound to kinetochore microtubule (MTs) of the spindle. A MT-organizing organelle called the centrosome is also duplicated before mitosis.

In the first stage of mitosis, prophase, the duplicated centrosomes move apart to opposite sides, and the mitotic spindle with highly dynamic MTs growing from the pair of centrosomes (referred to as spindle poles) begins to appear. Then in prometaphase, the nuclear envelope breaks down and spindle MTs capture the X shape chromosomes by connecting to the outer kinetochores. As metaphase proceeds, the tension exerted by MTs align the chromosomes at the midpoint plate of the centrosome axis referred to as the spindle equator (Figure.I.3). Just before anaphase, the spindle assembly checkpoint checks that all chromatids are attached to MTs and under bipolar tension. Chromosome segregation happens during anaphase, the cohesion-made bond between the sister chromatids breaks, and kinetochore MTs shrink to pull sister chromatids apart towards opposite poles (anaphase A). The poles are displaced further apart from pushing forces exerted by polar MTs growing and sliding past each other, and pulling forces by astral MTs contacting the cortex near the poles (anaphase B). As a result, the chromatids are displaced to the opposite poles and partitioned into two future daughter cells.

In telophase, the two new nuclei are reformed by enveloping each set of fragments and chromosomes start to decondense [START_REF] Batty | Mitotic Chromosome Mechanics: How Cells Segregate Their Genome[END_REF].

Figure.I.2: Activation of M-Cdk.

The activation of mitotic cyclin-dependent kinase (M-Cdk) is mediated through phosphorylations. The protein complex is first phosphorylated by an activating kinase and an inhibitory kinase. Then the inhibitory phosphate is canceled by a phosphatase, leading to the activation of the M-Cdk. This activation triggers the mitosis entry as presented in Fig. I.1 (from Biol.Penn.State©2004).

Cytokinesis

The cell cycle is completed by cytokinesis, which is the partitioning of the cytoplasm and other organelles into two daughter cells. Cytokinesis begins towards the end of mitosis such that telophase and cytokinesis partially overlap. Once the sister chromatids have reached the opposite poles, the cell starts to divide. In animal cells, a contractile ring forms just below the cell membrane at the position of the mitotic spindle midzone. The contractile ring consists of actin filaments, myosin II, septins (a protein interacting between the plasma membrane and the cortex) and other conserved proteins organizing these cytoskeletal elements. When it contracts

Figure.I.3:

The mitotic stages. Mitosis includes 5 stages: prophase when centrosomes start to move to opposite poles to form a spindle; prometaphase when nuclear envelope breaks down and chromosomes are attached to MTs through kinetochores; metaphase when chromosomes align on the metaphase plate; anaphase when chromosomes segregate by moving each sister chromatids and two pole towards opposite periphery; telophase when nucleus envelops reform and cell starts to divide at the position of metaphase plate (adapted from Cheeseman and Desai, 2008). inwards, a crack, called cleavage furrow is created, that drags the plasma membrane and eventually pinches the cell into two daughter cells (Figure.I.4,top).

Remarkably, the position of the cleavage furrow as well as its angle are determined by the position/orientation of the mitotic spindle. The first evidence suggesting the role of mitotic spindle to cleavage site came from early experiments by Conklin [START_REF] Conklin | Effects of centrifugal force on the structure and development of the eggs of Crepidula[END_REF]. By moving the mitotic spindle with centrifugal forces in crepidula eggs, he found that the cleavage furrow can occur in different regions on the cortex and its position is determined by the mitotic spindle.

Thus, a signal from the mitotic spindle must be transmitted to the cellular cortex to assemble the actin cytoskeleton and lead to formation of an actomyosin-based contractile ring. These local changes on the cell surface in the form of either relaxation or contraction of the cell membrane initiate the cleavage furrow. Which spindle portion determines the cleavage plane is still not fully understood and depends on cell types. There are three proposed hypothesis by which elements of the mitotic spindle could signal to the cell cortex to position the cleavage furrow (Figure .I.5) [START_REF] Field | Cytokinesis in eukaryotes: a mechanistic comparison[END_REF][START_REF] Gatti | Relationships between the central spindle and the contractile ring during cytokinesis in animal cells[END_REF]Kaltschmidt and Brand, 2002;[START_REF] Oegema | Rappaport rules: Cleavage furrow induction in animal cells[END_REF]. The first one is the astral relaxation model; the MT asters near opposite poles signal to the cell cortex, causing it to relax (Figure .I.5A) [START_REF] White | On the mechanisms of cytokinesis in animal cells[END_REF].

Alternatively, the astral MTs in the equatorial region (Figure .I.5B) or the overlapping MTs of the spindle mid-zone (Figure .I.5C) [START_REF] Devore | A model for astral stimulation of cytokinesis in animal cells[END_REF][START_REF] Rappaport | Establishment of the mechanism of cytokinesis in animal cells[END_REF] may send signals to The cell cycle is completed by cytokinesis, which partially overlaps with telophase and divides the cytoplasm and other organelles into two daughter cells. In animal cells, the contractile ring is composed of acto-myosin which squeezes inward to form a cleavage furrow, separating the cell into two daughter cells (adapted from Pollard, 2010).

mediate contraction in the cell equator. It is also possible that both models act together as redundant mechanisms.

In large cells, like early amphibian, fish and sea urchin embryos, the cleavage plane determination may differ from classical current models. This is because these cells are large with zygotes having sizes ranging from ~100 to ~1200 μm in diameter and their spindles are small to contact the cellular cortex, lacking important interaction to induce the cleavage furrow.

For instance, the preceding interphase asters center and orient a pair of centrosomes prior to NEB and determine the division plane orthogonal to the centrosome axis even before the spindle assembles. The orientation of the centrosomes is preserved by the mitotic spindle, then asters regrow and position the centrosomes to specify the next cleavage plane even before cytokinesis is completed (Figure .I.5) [START_REF] Rappaport | Experiments concerning the cleavage stimulus in sand dollar eggs[END_REF]Wuhr et al., 2010). B) or MTs at the spindle midzone (white lines in C) can signal to the equatorial region of the cell (red region), leading to ring assembly and furrow contraction (from Kaltschmidt and Brand, 2002).

II. Division positioning 1. Cytoskeleton

To study mechanisms of division positioning, we need to first understand the cytoskeleton, which is a complex, dynamic networks of polymers located in the cytoplasm of eukaryotic cells. Indeed the cytoskeleton can generate forces that are essential to position centrosomes nuclei and spindles. It is also involved in many cellular activities, like transporting intracellular material [START_REF] Boyle | Molecular biology of the cell, 5th edition by[END_REF][START_REF] Rogers | Membrane trafficking, organelle transport, and the cytoskeleton[END_REF][START_REF] Samaj | Endocytosis, actin cytoskeleton, and signaling[END_REF], participating in cell signaling pathways [START_REF] Colin | Triggering signaling pathways using F-actin self-organization[END_REF][START_REF] Moujaber | The Cytoskeleton as Regulator of Cell Signaling Pathways[END_REF], and contributing to cellular migration (de Mattos [START_REF] De Mattos Coelho-Aguiar | The Role of the Cytoskeleton in Cell Migration, Its Influence on Stem Cells and the Special Role of GFAP in Glial Functions[END_REF][START_REF] Fletcher | Cell mechanics and the cytoskeleton[END_REF] Seetharaman and Etienne-Manneville, 2020; [START_REF] Tang | The roles and regulation of the actin cytoskeleton, intermediate filaments and microtubules in smooth muscle cell migration[END_REF]. Moreover, it contributes to cell division, by segregating chromosomes and performing cytokinesis, and as a major effector of spindle positioning [START_REF] Kotak | Mechanisms of Spindle Positioning: Lessons from Worms and Mammalian Cells[END_REF][START_REF] Kunda | The actin cytoskeleton in spindle assembly and positioning[END_REF][START_REF] Pearson | Dynamic microtubules lead the way for spindle positioning[END_REF].

The cytoskeleton has very different structures, functions and dynamic behaviors inside cells, depending on the organism and cell type. Some specialized structures, such as flagella, cilia, lamellipodia and podosomes are formed by the cytoskeleton to serve various functions. In eukaryotes, it is composed of three main types of polymers, which are actin filaments, intermediate filaments (IFs) and microtubules (MTs).

Actin

Structure

G-actin is a free globular monomer and F-actin is the polymerized filamentous polymer. Gactin has a length of ~6 nm and a mass of 42kDa [START_REF] Collins | The primary structure of actin from rabbit skeletal muscle. Completion and analysis of the amino acid sequence[END_REF]. It is composed of 4 subdomains and a nucleotide binding cleft located between the subdomains 2 and 4 (Figure .II.1A) [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF]. G-actin monomers assemble linearly to form F-actin polymers with two intertwined right-handed helical strands (Figure .II.1B, C). The helix twists once every ~37 nm, and each monomer has the same orientation within the helix [START_REF] Holmes | Atomic model of the actin filament[END_REF]. Factin is the thinnest filament as compared with the two other cytoskeleton polymers, with a helical diameter around 8 nm (2000;[START_REF] Egelman | The structure of F-actin[END_REF]. Its persistence length is ~10 μm, which makes it more softer than MTs [START_REF] Wisanpitayakorn | Measurement of the Persistence Length of Cytoskeletal Filaments using Curvature Distributions[END_REF].

Dynamics

Actin monomers can self-assemble under physiological salt conditions, and cations are required to promote subunits binding [START_REF] Kang | Site-specific cation release drives actin filament severing by vertebrate cofilin[END_REF][START_REF] Kang | Identification of cation-binding sites on actin that drive polymerization and modulate bending stiffness[END_REF]. A polymerized actin filament has an arrowhead like structure with two ends, which are the barbed end (+ end), and the pointed end (-end). As actin filaments are polar, actin assembly rates at the two different ends are different, with a higher assembly rate at the barbed end than at the pointed end. Actin monomers preferentially bind adenosine triphosphate (ATP) than adenosine diphosphate (ADP), and ATP bound actin monomers initiate filament polymerization, while ADP bound monomers mediate its depolymerization. Upon actin assembly, because of its ATPase property [START_REF] Oda | The nature of the globular-to fibrousactin transition[END_REF], monomers quickly hydrolyze ATP into ADP, followed by a release of an inorganic phosphate (Pi) (Figure .II.2) [START_REF] Carlier | Direct evidence for ADP-inorganic phosphate-F-actin as the major intermediate in ATP-actin polymerization. Rate of dissociation of inorganic phosphate from actin filaments[END_REF][START_REF] Jégou | Individual Actin Filaments in a Microfluidic Flow Reveal the Mechanism of ATP Hydrolysis and Give Insight Into the Properties of Profilin[END_REF]. After incorporation, monomers will twist ~20 degrees between the subdomains 1 and 2 to change conformation. The assembly or disassembly rate of an actin filament depends on the monomer concentration. Once a critical threshold concentration has been exceeded, assembly of the polymeric form is favored. Otherwise, the filament tends to depolymerize with a monomer concentration below the threshold [START_REF] Uzman | Molecular Cell Biology[END_REF]. Monomers can add on and/or detach from both ends, and a steady-state happens when the net monomer addition rate (k+on -k+off) at the barbed end balances the net monomer loss rate (k-off -k-on) at the pointed end.

In this regime, actin filaments appear to move forwards at their plus end and retract at their minus end [START_REF] Wegner | Head to tail polymerization of actin[END_REF]. This process is called "treadmilling". Remarkably, although the filament appears to move, the individual monomers remain stationary (Figure. II.2,Figure.II.3A,and Figure.II.5).

Actin binding proteins

The basic behavior of actin is greatly modified by actin-binding proteins (ABPs), which have a different affinity for actin as a function of the actin nucleotide state. F-actin rigidity also depends on this nucleotide state, with a higher actin rigidity in the ADP-Pi state [START_REF] Isambert | Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins[END_REF]. There are many types of ABPs, such as actin capping proteins which control the length of actin filaments; severing proteins which break actin filaments; and other binding proteins which can stabilize or destabilize actin filaments (Figure .II.3B-D).

Figure.II.2: F-actin assembly and disassembly.

F-actin is polar and can add on or loss monomers from both ends. ATP bound actin monomers start the polymerization, while ADP bound monomers mediate the depolymerization. The ATP is transferred to ADP by hydrolysis upon filament assembly. When the polymerization rate is balanced with depolymerization rate, the actin filament reached an equilibrium state called "treadmilling" (adapted from lessons of Kosmrlj, 2015).

Actin networks

In cells, actin filaments assemble networks, which are involved in many important cellular processes, like cell shape changes, cytokinesis and migration. These networks are nucleated and linked in different ways (Figure.II.3E,Figure.II.4). Many of actin studies have focused on the cellular cortex, a thin contractile actomyosin network layer underneath the plasma membrane which may dominate the surface mechanics of many animal cells. However actin filaments deeper in the cytoplasm is much less studied, as F-actin in bulk is often less dense and thus harder to detect and study than at the cortex. Using confocal imaging and detectors with a large dynamic range, and live fluorescence probes, the study and visualization of bulk F-actin has improved and some of its functions begun to be understood. A number of recent papers have revealed its function in meiosis of oocytes and mitosis of early embryos. For instance, chromosomes congression is mediated by a contractile F-actin meshwork in starfish oocytes, meiotic spindle is moved towards the cortex by an F-actin mesh in mouse oocytes, and bulk F-actin stabilizes cytoplasm and limits MT-driven cytoplasmic streaming in Drosophila eggs [START_REF] Field | Bulk Cytoplasmic Actin and Its Functions in Meiosis and Mitosis[END_REF]. [START_REF] Field | Bulk Cytoplasmic Actin and Its Functions in Meiosis and Mitosis[END_REF] revealed changes in bulk actin meshwork during the cell cycle, with dense and contractile actin meshworks formed in mitosis and sparse, non-contractile meshworks in interphase in Xenopus egg extracts. This suggest that such bulk actin networks could contribute to mechanisms of spindle positioning for instance.

F-actin nucleation determines where and when actin polymerizes and has a strong influence on the structure of actin networks. There exists many different nucleators. For example, the Arp2/3 complex nucleates actin branched networks of short filaments at angles of 70 degree (Ichetovkin et al., 2002), while formins typically nucleate long linear actin cables [START_REF] Campellone | A nucleator arms race: cellular control of actin assembly[END_REF]. Arp2/3 usually works for actin nucleation at cortex and seems to be involved in specific bulk actin nucleation during mitosis. The Formin-2-Spire complex has been recently shown to nucleate cytoplasmic F-actin networks of long filament bundles in Drosophila and mouse oocytes [START_REF] Quinlan | Drosophila Spire is an actin nucleation factor[END_REF]. Actin polymerization may be responsible for the generation of large forces to deform the plasma membrane during cell locomotion or to move organelles and bacteria in the cytoplasm of living cells [START_REF] Mitchison | Actin-Based Cell Motility and Cell Locomotion[END_REF]Svitkina, 2018;Theriot et al., 1992;Theriot et al., 1994;Tilney and Portnoy, 1989).

In addition to the diversity of nucleators, many crosslinkers are also implicated in the formation, stabilization and force generation of different actin networks (Figure.II.4). For example, actin filaments are cross-linked antiparallel by α-actinin to from bundles with relatively large open intervals (Figure.II.4A). This provides access for myosin to intercalate and engage with actin, to form stress fibers that generate forces [START_REF] Feng | α-actinin1 and 4 tyrosine phosphorylation is critical for stress fiber establishment, maintenance and focal adhesion maturation[END_REF]. Fimbrin connects actin filaments in parallel arrays with short intervals, producing tight bundles, such as those found in microvilli (Figure .II.4B) [START_REF] Bretscher | Fimbrin is a cytoskeletal protein that crosslinks F-actin in vitro[END_REF]. Another type of cross-linkers which act in a different fashion is filamin. Filamin dimers produce flexible cross-links to link filaments in loose three-dimensional bundles (Figure.II.4C,D). This allows the formation of actin gels, which are typically found beneath the plasma membrane and are required for the formation of lamellipodia [START_REF] Venkatareddy | Nephrin regulates lamellipodia formation by assembling a protein complex that includes Ship2, filamin and lamellipodin[END_REF].

Functions

Actin networks are located at different positions in a cell to participate to many important cellular processes. It is present as an actomyosin meshwork at the cell cortex, generating contractile forces to deform the cell surface, contributing to processes including cell migration, division or differentiation (Chugh and Paluch, 2018). Actin also exists in the nucleus as monomers and filaments and play an important role in the maintenance of nuclear integrity, DNA repair and gene expression [START_REF] Plessner | Dynamizing nuclear actin filaments[END_REF][START_REF] Virtanen | Diverse functions for different forms of nuclear actin[END_REF].

Besides, actin-based stress fibers, which are contractile structures of antiparallel actin filament bundles, contribute to cell contractility, enabling tissue and extracellular matrix reshaping [START_REF] Pellegrin | Actin stress fibres[END_REF]. Actin can also interact with the plasma membrane to form membrane protrusions [START_REF] Jacquemet | Filopodia in cell adhesion, 3D migration and cancer cell invasion[END_REF][START_REF] Wang | Exchange of actin subunits at the leading edge of living fibroblasts: possible role of treadmilling[END_REF]. Moreover, actin is involved in other important mechanisms, such as muscle contraction, cell division and cytokinesis, vesicle and organelle movement, cell signaling and cell junctions (Gardel et al., 2010;Green et al., 2012;Munjal and Lecuit, 2014;Svitkina, 2018). Mutations in alleles of the genes that regulate the production of actin and/or its associated proteins cause various diseases such as muscular diseases, heart defects and deafness [START_REF] Parker | Actin Mutations and Their Role in Disease[END_REF].

In large oocyte, eggs and early blastomeres, their spindles are relatively small and lack astral MT contact with the cortex, which calls for different mechanisms for division positioning.

Although some researches show that their large interphase asters can position correctly nucleus/centrosome before mitosis (see Chapter II.3), bulk actin could play a role in spindle positing in large cells. 2) push the membrane forward through actin polymerization at plus end, (3) which is terminated by stochastic capping. ( 4) Exchange of ATP to ADP through hydrolysis. ( 5) ADF/cofilin binding and unbinding to ADP-F-actin subunits. (6) Tropomyosin irreversible binding to ADP-Factin subunits. (7) Branched filaments can detach from the Arp2/3 binding site, (8) promoting the main filament depolymerization from their minus-end. (9) The detached actin monomers will diffuse to the leading edge to participate for actin polymerization via ADP to ATP exchange by profilin (from Nonaka, 2011).

Myosin

Actin is responsible for the generation of large forces either from their polymerization dynamics of from their interaction with motors of the myosin family. This is a superfamily composed of 15 to 20 classes, but with similar structures. Myosins contain one or two heavy chains organized into three structurally and functionally different domains and several light chains (Figure.II.6). The globular head has the ATP-and actin-binding sites, which is conversed among all myosins serving to generate forces. Adjacent to the head binds the lever arm that acts as the neck interacting with helical calmodulin light chains. The part after the level arm is the tail, and is composed of a coiled coil region which has a dimerization function, and a C-terminal region that allows the attachment to subcellular structures, like cargos transported along actin strands [START_REF] Sweeney | Structural and functional insights into the Myosin motor mechanism[END_REF]. Myosins such as Myosin I, Myosin II and Myosin V, usually walk towards the plus ends of actin filaments. But some myosin move to the minus ends, like Myosin VI, while some others can move in both directions, like Myosin IX [START_REF] Wells | Myosin VI is an actin-based motor that moves backwards[END_REF]. In physiological conditions, myosin molecules assemble tail to tail with heads pointing outwards to form filaments, allowing myosin to become more effective, as well as to cross-link and contract actin filamnets (Figure .II.7) [START_REF] Craig | Structure and function of myosin filaments[END_REF].

In addition to transporting elements inside cells, myosin walking along the actin filaments can generate mechanical forces. Myosin II is known to generate forces in muscle cells. For this, actin and myosin filaments are organized in parallel arrays and their ends are bound together on a z-disk via actin filament plus ends and titin. As Myosin II walks towards the plus ends, it exerts contractile forces to move microfilaments towards their minus ends. This actomyosin active contractile structure is referred to as a sarcomere, which is the basic contractile unit of a muscle fiber (Figure .II.7A). Myosin II also powers cytokinesis ring contraction that squeezes cells into two new cells, and sets cortex tension that shapes the cell surface (Chugh and Paluch, 2018;[START_REF] Henson | The ultrastructural organization of actin and myosin II filaments in the contractile ring: new support for an old model of cytokinesis[END_REF]. In these processes, actin forms an actin cortex which is an isotropic crosslinked network. In the network, myosin filaments slide actin filaments past each other and can generate contractile tension as these filaments are connected (Figure .

Intermediate Filaments

Structure

Intermediate filaments (IFs) have a diameter of ~10 nm, which is larger than actin filaments but smaller than MTs. The fibrous IF monomers are composed of a large family of proteins with a head (N-terminal) and a tail (C-terminal) region bound together via a central α-helical rod domain. They form a coiled-coil dimer by assembling two monomers that interact through their rod domains. In dimers, the heads and tails can display wide variations in their sequences and length. Then, identical dimers are arrayed in an antiparallel fashion to form tetramers, which form the protofilaments by assembling linearly head to tail. An IF is made of eight parallel protofilaments held together by lateral hydrophobic and electrostatic interactions, and a hierarchy of inter-subunit interactions (Figure .II.8) [START_REF] Cooper | The Cell: A Molecular Approach[END_REF][START_REF] Herrmann | Intermediate Filaments: Structure and Assembly[END_REF].

Dynamics

When IF proteins fold into a conserved alpha-helical rod shape, their assembly initiates. This process happens spontaneously in physiological salt solutions and does not require ATP or proteinaceous cofactors. Filaments are formed following a series of polymerization and annealing events, and different combinations are found in different cell types. In contrast to actin filaments and microtubules, IFs lack polarity and cannot guide motor protein-driven

Figure.II.8: Assembly of intermediate filaments (IFs).

Two polypeptides wind around each other with their central rod domains to form a dimer. Two dimers assemble in an antiparallel fashion to form a tetramer. Tetramers connect end to end to make a protofilament. Around eight protofilaments bind laterally to construct an IF (from Physics of Cancer, 2nd Edition, 2018).

directional transport. However they can construct a dynamic network possibly through their interactions with actin-based and MT-based motor proteins [START_REF] Helfand | Intermediate filaments are dynamic and motile elements of cellular architecture[END_REF].

Mechanical properties

IFs are found in metazoans and they can be at least 10 times more abundant than other cytoskeleton filaments in some cell types like epidermal cells and the axons of neurons. They are present in particularly stiff tissues/organs such as hair, scales and fingernails, because IFs are the most stable cytoskeleton with a high tensile strength which is provided by the tight association between protofilaments [START_REF] Uzman | Molecular Cell Biology[END_REF]. These extensive interactions enhance the resistance of IFs to compression, twisting, stretching and bending forces, thus allowing cells to have elastic properties and to withstand tension like in epithelial cells [START_REF] Flitney | Insights into the mechanical properties of epithelial cells: the effects of shear stress on the assembly and remodeling of keratin intermediate filaments[END_REF][START_REF] Sanghvi-Shah | Intermediate Filaments at the Junction of Mechanotransduction, Migration, and Development[END_REF]. The organization and structure of IFs are drastically rearranged during mitosis. In baby hamster kidney (BHK-21) cells, IF networks are disassembled into cytoplasmic aggregates of protofilaments through phosphorylation upon entering mitosis [START_REF] Chou | Phosphorylation and disassembly of intermediate filaments in mitotic cells[END_REF]. In mitotic Vero cells, the keratin and vimentin filaments maintain their filamentous structure and form a cage around the mitotic spindle [START_REF] Cai | Changes of intermediate filament during mitosis in two epithelial cell lines[END_REF].

Functions

IFs are usually separated in nuclear IKs, like the nuclear lamina and those that form a cytoskeleton in the cytoplasm. Cyto-IFs such as keratin filaments provide internal support and cohesion to epithelial cell sheets; Neurofilaments help stabilize the extended axons in nerve cells; Vimentin and desmin filaments maintain the cell structural and mechanical integrity in mesenchymal and muscle cells, respectively (Table.II.1) [START_REF] Charrier | Mechanical Properties of Intermediate Filament Proteins[END_REF][START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF] al., 2019;[START_REF] Toivola | Intermediate filaments take the heat as stress proteins[END_REF]. In general, their primary role is to provide physical strength to cells to maintain cell shape and rigidity, and hold several organelles in place, such as the nucleus and desmosomes. Mutations in IF genes lead to a host of rather uncommon diseases.

For instance, as keratin is important in epithelial cells, its mutations lead to disorders in skin tissue, such as epidermolysis bullosa simplex, where the skin is very fragile and can blister easily even with a slight mechanical stress [START_REF] Goldfarb | Intermediate filament diseases: desminopathy[END_REF].

Although IFs are found as networks spanning the cytoplasm, their contribution to nuclear/spindle positioning is still unclear (Figure .II.9) [START_REF] Herrmann | Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular Scaffolds[END_REF]. Recent experiments from [START_REF] Pelletier | Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm[END_REF] reveals that the cytokeratin moves outward the aster together with the MTs, ER, mitochondria, acidic organelles, F-actin and soluble fluorescein during the anaphase aster separation in Xenopus egg extracts. This co-movement is mediated by dynein and actomyosin forces and suggests another mechanism that could position the aster/spindle [START_REF] Pelletier | Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm[END_REF].

Table.II.1: The major classes of intermediate filaments in mammals.

Keratin filaments are present in epithelial cells, providing tissue strength and integrity. Desmin, GFAP (Glial fibrillary acidic protein) and vimentin are mostly found in muscle, glial cells and mesenchymal cells, respectively. Neurofilaments play an important role in axon organization, and lamins interact with nucleus inner membrane to contribute to the surface mechanics of the nucleus (from lessons of Dr. Mamoun Ahram).

Microtubules

Microtubules (MTs) are the stiffest filaments of the cytoskeleton with a diameter of ~24nm.

Their main function is to form the mitotic spindle and segregate chromosomes during cell division, and to organize intracellular trafficking. They also play a fundamental role in centrosome, nucleus or spindle positioning.

Structure

Microtubules are hollow cylinders constructed through the polymerization of two globular proteins, α-tubulin and β-tubulin (Figure .II.10). These two monomers bind each other to form an α-β tubulin dimer. These dimers assemble protofilaments in a linear head-to-tail fashion.

Thus, protofilaments are polar with an α-tubulin at one end (the minus end) and β-tubulin at another end (the plus end). Then, thirteen protofilaments arrange themselves parallel to form a microtubule with a cylindrical pattern. MTs are polar, with the plus ends always having beta subunits exposed, and the minus ends alpha subunits exposed. The plus ends grows relatively fast and the minus end relatively slow. This polarity is important in determining the direction of molecular transports along microtubules, and for positioning centrosomes at the cell center.

The connection between adjacent protofilaments is formed by two α-tubulin subunits or two βtubulin subunits, yielding a left-handed helical inner structure. To close the helix, the last lateral connection at the seam is made by pairs of α-tubulin and β-tubulin [START_REF] Uzman | Molecular Cell Biology[END_REF].

Dynamics

In animal cells, MTs radiate outwards from an organelle called the centrosome, which is a microtubule organizing center (MTOC). It is composed of two centrioles, positioned orthogonally, and surrounded by the pericentriolar matrix (PCM). In the PCM, the γ-tubulin interacts with other PCM proteins to form a γ-tubulin ring complex (γ-TuRC), which nucleates and tethers MTs from their minus ends. Plant, yeast and fungal cells do not have centrosomes, but instead, spindle pole body (SPB) which concentrate γ-tubulin and serve as MTOC [START_REF] Kilmartin | Lessons from yeast: the spindle pole body and the centrosome[END_REF][START_REF] Marc | Microtubule-organizing centres in plants[END_REF].

MTs are often capped and anchored at MTOC by their minus ends, which restrict MT dynamics at the minus ends. MT polymerization initiate from the MTOC via the addition of dimers at both ends but with faster polymerization rate at the plus ends. MT filaments can grow/shrink rapidly through a cycle of guanosine triphosphate (GTP) hydrolysis to guanosine diphosphate (GDP), which functions as the ATP/ADP cycle for actin. Before polymerization, each subunit of the α-β tubulin heterodimer is bound to GTP. When incorporated on the MT plus ends, GTP is hydrolyzed to GDP which weakens the binding affinity of tubulin for adjacent molecules, thereby favoring depolymerization. MTs grow when the GTP hydrolysis rate is lower than the addition rate of dimers. Usually a GTP cap forms at the plus tip to stabilize the MT and favor continuous growth. MTs shrink when the plus tip is exposed with GDP-bound dimers, which destabilizes the structure and causes a rapid depolymerization, known as catastrophe. This situation can be "rescued" when MTs assemble a large amount of GTP-bound dimers along the lattice [START_REF] Dimitrov | Detection of GTP-tubulin conformation in vivo reveals a role for GTP remnants in microtubule rescues[END_REF]. MTs usually undergo cycles of catastrophe and rescue, and reach a dynamic equilibrium like actin treadmilling, when in a MT filament, GDP bound dimers are continually lost from the minus end and replaced by the addition of GTP-bound dimers to the plus end [START_REF] Waterman-Storer | Microtubule dynamics: treadmilling comes around again[END_REF]. switch from growth to shrinkage by a process called catastrophe or from shrinkage to growth by a process called rescue. Upon polymerization, MTs grow by adding GTP-bound heterodimers at the plus end, which are later hydrolyzed to GDP-bound subunits. Depolymerization occurs when the addition of subunits slows and the GDP-bound tubulin dimers are predominant on the MT lattice (adapted from Lasser, 2018).

MT associated proteins

MT associated proteins (MAPs) regulate single MT nucleation dynamics, and the assembly of MT-based higher order structures (Figure .II.11A). These proteins include many types and interact with MTs along their lattice and/or of their tips. Some proteins act to destabilize MTs, by severing MTs like katanin and spastin, or promoting depolymerization like stathmin, or suppressing rescue like some members of kinesin-8 and kinesin-14 family [START_REF] Goodson | Microtubules and Microtubule-Associated Proteins[END_REF]. Some proteins increase their stability, like Tau that stabilizes MTs [START_REF] Kar | Repeat motifs of tau bind to the insides of microtubules in the absence of taxol[END_REF], Cap-Gly family that promotes rescue [START_REF] Arnal | CLIP-170/tubulin-curved oligomers coassemble at microtubule ends and promote rescues[END_REF], HURP [START_REF] Silljé | HURP is a Ran-importin beta-regulated protein that stabilizes kinetochore microtubules in the vicinity of chromosomes[END_REF] that slows down MT depolymerization, the EB plus-end tracking proteins [START_REF] Tirnauer | EB1-microtubule interactions in Xenopus egg extracts: role of EB1 in microtubule stabilization and mechanisms of targeting to microtubules[END_REF] and structural MAPs [START_REF] Ichihara | Visualization of the stop of microtubule depolymerization that occurs at the high-density region of microtubule-associated protein 2 (MAP2)[END_REF] that can suppress catastrophe. And some like XMAP215/TOG family which promote MT dynamics and mitotic spindle formation [START_REF] Byrnes | TOG-tubulin binding specificity promotes microtubule dynamics and mitotic spindle formation[END_REF]. Thus, these regulations are crucial to the organization of MT assemblies (Figure .II.11B).

Organization

In animal cells, MTs are primarily nucleated from the centrosomes with their minus ends anchored inwards. Their plus ends thus extend outwards, forming a radial star-like structure called a MT aster. In interphase, centrosomes duplicate adjacent to the nucleus and form asters which are commonly thought to fill the whole cytoplasm and contact the cell cortex, to sense cell shape and position centrosomes accordingly, or to signal to the cortex for cytokinesis. The standard model is that MTs are all nucleated from the centrosomes and extend outward to reach the cell surface, so that the MT density decreases with aster radius. However asters can also fill the whole volume in cells as large as a mm in diameter, for example in frog or fish embryos a distance much larger the length of single MTs inside the aster. In addition, asters in these cells have constant or even increased MT density at the cell periphery to communicate to the cortex. These observation suggest that MT must also be nucleated away from the centrosome (Figure.II.12). Some of the plausible mechanisms include the branching of MTs from the side of pre-existing ones at γ-tubulin complex satellites, or nucleation from γ-tubulin complex at Golgi membranes within the aster (Efimov et al 2007, Rivero et al 2009). Another possibility is that MTs are continually released from centrosome and slide outwards by dynein pulling forces. A last model is that non astral MTs are captured and accumulated in the aster. This models is currently disfavored as rare MTs were observed between the expanding aster tips and the cortex in early frog and fish embryos (Mitchison et al., 2012). There exists some other models, like autocatalytic MT growth [START_REF] Decker | Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles[END_REF], MT spread by satellites and the nucleation near the cortex observed in plants, yeast and oocytes [START_REF] Gard | Gamma-tubulin is asymmetrically distributed in the cortex of Xenopus oocytes[END_REF][START_REF] Lüders | Microtubule-organizing centres: a re-evaluation[END_REF][START_REF] Maro | Fertilization and the cytoskeleton in the mouse[END_REF]. Thus, MT asters can grow to span the cytoplasm across distances ranging from few micron up to millimeters, a property which places them as essential cell shape sensors and force generation unit for nucleus/centrosome positioning (see Chapter II.3). Alfaro-Aco, 2015).

Figure.II.11: Microtubule organization with MT associated proteins (MAPs). (A) Schematics of different classes of MAPs activities. (B) Different combinations of MAPs induce different MT networks that determine cell organization and dynamics (from

During mitosis, MT asters shrink and become more dynamic to form a mitotic spindle. Plus tips are oriented either towards the cortex or the chromosomes (see Chapter II.2). MT depolymerization is mediated by Cdk1 kinase which promote MT catastrophe through MAPs regulation [START_REF] Belmont | Real-time visualization of cell cycle-dependent changes in microtubule dynamics in cytoplasmic extracts[END_REF][START_REF] Niethammer | Discrete states of a protein interaction network govern interphase and mitotic microtubule dynamics[END_REF]. MT nucleation at the existing spindle is found to speed up the spindle assembly [START_REF] Petry | Augmin promotes meiotic spindle formation and bipolarity in Xenopus egg extracts[END_REF]. The kinetochore MTs are stabilized by MAPs. Spindles typically form around duplicated centrosomes, but can also assemble without centrosomes, with MTs being nucleated from chromosomes and arranged by motors such as kinesins and dyneins. In anaphase, the chromosomes are separated by the depolymerization of kinetochore MTs from their plus ends, while MT-based motors at kinetochores drag the chromosome along the MT lattice towards the centrosome (anaphase A).

The remaining polar MTs overlapping at the center are crosslinked by Eg5 kinesin, a MT plusend directed motor, causing them to slide apart, which pushes the centrosomes towards opposite poles (anaphase B) and elongates the spindle length [START_REF] Brust-Mascher | Mitotic motors and chromosome segregation: the mechanism of anaphase B[END_REF]. Astral MTs regrow to fill again the cytoplasm during anaphase, as the levels of Cdk1 decrease [START_REF] Wheatley | CDK1 inactivation regulates anaphase spindle dynamics and cytokinesis in vivo[END_REF].

Motors

MT motor proteins can be either plus end directed or minus end directed. There are two main groups: dynein, walking towards MT minus ends, and kinesins, mostly walking towards MT plus ends. These motors transport cargos and generate forces on MTs. MTs, thus promoting their walking without completely detaching from MTs. Mechanisms which control stepping and directionality of dynein motion are still not clear, but could be partially stochastic [START_REF] Reck-Peterson | Singlemolecule analysis of dynein processivity and stepping behavior[END_REF]. Various proteins are required for dynein recruitment and motor activity. One major dynein regulator is the dynactin complex. The dynactin complex is composed of more than 20 subunits. The two main functions of dynactin is to activate dynein processivity towards the minus ends, and to mediate cargo attachment. For instance, its p150 subunit targets the MT plus end and tyrosinated α-tubulin, initiating dynein movements along MTs (Barbosa et al., 2017), while Arp1 interacts with spectrins, promoting the attachment of endomembrane vesicles [START_REF] Holleran | Centractin (ARP1) associates with spectrin revealing a potential mechanism to link dynactin to intracellular organelles[END_REF].

Kinesin

Kinesins have a more diverse family and include many plus end directed kinesins, few minus end directed kinesins, and several both ends directed kinesins. Kinesin structures vary, but generally contain two globular heads formed from heavy chains that are responsible for MT binding and motor activity, an α-helical coiled-coil neck that links heads and c-ternimal tails to mediate dimerization. The tail with light chains is responsible for cargo binding. But in some cases, cargos can directly bind to kinesin c-terminal tails.

Kinesin has a typical unidirectional movement along MTs, by hydrolyzing one molecule of ATP at each step (Figure.II.13). In most cases, the motor domain located at the N-terminus, known as N-kinesins, exhibit plus end directed motions. These kinesins walk along MTs with a hand-over-hand mechanism and do not completely detach from them, which is called neck linker zippering. The step size is the length of an α-β dimer. When a motor domain is located at the C-terminus, known as C-kinesin, it exhibits minus end directed motions. Such C-kinesins are able to rotate round MTs toward the minus tips, due to the different architecture of necks [START_REF] Endow | Determinants of kinesin motor polarity[END_REF]. In addition, these movements are usually non-processive, detaching from MTs after advancing one step. M-kinesins with motor domain located in the middle, are usually non-motile and have the ability to promote MT depolymerization [START_REF] Howard | Microtubule polymerases and depolymerases[END_REF].

Figure.II.13: Dynein and Kinesin transport of organelles along Microtubules (MTs). (Left)

Cytoplasmic dynein carries cargos by minus ends movement along MTs whereas (right) kinesin walks towards the plus ends. An important protein complex on dynein is dynactin, which is associated to the load of cargos and promotes dynein processivity. The largest dynactin subunit is p150 glued (turquoise), which is linked to cargos through p50 (pink) and extends to bind MTs via a CAP-Gly motif at the tips (adapted from Duncan, 2006).

The mitotic spindle

Structure and dynamics

The mitotic spindle is a highly dynamic assembly made of MTs, motors, centrosomes and other molecules. Centrosomes are duplicated in interphase, then they separate and move to opposite Xenopus and zebrafish embryos (Wuhr et al., 2010). But in embryos like sea urchin, nematodes and ascidians, cortex contact recovers progressively in subsequent smaller blastomeres through development. Mitotic spindle length is defined by the distance from the two centrosomes. It is regulated by MAPs and correlates with cell size to adapt to cellular functions. However, the mechanisms for this scaling remain unclear. During C.elegans and sea urchins embryonic cleavage, spindles shorten in subsequent smaller blastomere cells through a mechanism, where the growth rate of spindle microtubules scales with cell volume, but spindle assembly timing is constant throughout successive divisions [START_REF] Lacroix | Microtubule Dynamics Scale with Cell Size to Set Spindle Length and Assembly Timing[END_REF].

In addition to MTs, endomembrane and IFs are also important components of the spindle, known as a spindle matrix, participating in important processes to ensure proper division. The spindle matrix was initially proposed by studies of isolated mitotic spindles from synchronized sea urchin eggs in the 1960s. They observed non-MT materials surrounding mitotic spindles with the shape of spindle even after MTs were disassembled [START_REF] Goldman | The structure and some properties of the isolated mitotic apparatus[END_REF]. Some of these non-MT materials are passive passengers transported by MTs into daughter cells, some function as a spindle matrix to tether mitotic regulators and/or as a mechanical element to hold the spindle structure. The existence of a spindle matrix is further supported by recent mechanical perturbation experiments (Figure.II.15). When several kinetochore microtubules in one half of a spindle were ablated or depolymerized with ultra violet microbeams or caged MT inhibitor 105D [START_REF] Mitchison | Roles of polymerization dynamics, opposed motors, and a tensile element in governing the length of Xenopus extract meiotic spindles[END_REF], the spindle pole moved towards the kinetochores and the remaining intact kinetochore microtubules bent or buckled (Figure .II.15A) [START_REF] Pickett-Heaps | Traction fibre: toward a "tensegral" model of the spindle[END_REF]. These experiments suggests that spindle MTs are under compression of a continuous and elastic spindle matrix, covering the spindle, called external spindle matrix. Another type of spindle matrix align inner spindle microtubules, called internal spindle matrix. When a kinetochore MT is severed by irradiation, the kinetochore can [START_REF] Pickett-Heaps | Traction fibre: toward a "tensegral" model of the spindle[END_REF]. For my project, the notion of a spindle matrix should be considered as it could contribute to improve the viscoelastic interaction of spindles with the surrounding cytoplasm, or provide mechanical forces and contribute to chromosome segregation during cell divisions.

Advanced techniques to probe spindle structure

Spindle dynamics and mechanical properties lacked phenomenological and quantitative understanding until the development of recent advanced quantitative methods. Here, we focus ). From the data, they found that rare kinetochore MTs are connected to the centrosomes, with most of them being anchored to the entire spindle network [START_REF] Redemann | C. elegans chromosomes connect to centrosomes by anchoring into the spindle network[END_REF].

Spindle mechanical properties were studied using force calibrated glass microneedles (Figure .II.15B). [START_REF] Shimamoto | Insights into the micromechanical properties of the metaphase spindle[END_REF] designed a force measurement system with two types of glass needles, a stiff needle controlled by a piezo actuator to apply calibrated forces and a flexible needle to measure forces in the spindle. Combining with high-resolution microscopy and biochemical perturbations, he found that metaphase spindles in Xenopus egg extracts exhibit anisotropic viscoelastic properties [START_REF] Shimamoto | Insights into the micromechanical properties of the metaphase spindle[END_REF].

Mechanics of spindle positioning

Spindle positioning is crucial for cell division as it determines the position of the cleavage plane, and thus the size and position of daughter cells in tissues. When the spindle is located in the cell center, cellular components are equally distributed on the two sides of the spindle, inducing a symmetric division. Otherwise, division is asymmetric with one daughter cell larger than another. The spindle orientation decides the relative locations of the daughter cells and a mistake in orientation could cause disorders in embryo development, cell differentiation and tissue organization. Thus, the accurate positioning and orientation of the spindle is required for cell division and tissue development in all eukaryotes. Spindle positioning has been studied in diverse systems, and here I introduce some standard models.

Cortical forces

Cortical MT pushing

Astral MTs exert pushing forces on centrosomes when MTs polymerize against the cell cortex. This pushing model arise in two conditions, MTs need to contact the cortex and the cortex should behave as a stiff enough obstacle [START_REF] Inoué | Force generation by microtubule assembly/disassembly in mitosis and related movements[END_REF]. Astral MT pushing forces are involved in nuclear centration in fission yeast (Tran et al., 2001) and some aster centration in chambers in vitro or Xenopus egg extract [START_REF] Sulerud | Microtubule-dependent pushing forces contribute to long-distance aster movement and centration in Xenopus laevis egg extracts[END_REF], suggesting their possible contributions to spindle positioning. According to MT bending ability, there are two types of cortical pushing models (Figure .II.16A, B). When MTs are not easily bent against the cortex, each MT pushing force is assumed to be the same, thus total pushing forces only depend on the numbers of MTs contacting the cortex. As shown in Figure .II.17A, when the spindle is decentered toward the posterior, some MTs are not long enough to push the anterior cortex, causing more pushing forces from the posterior side. Thus, spindle is pushed towards the anterior until the total forces are balanced again in the cell center. Another model is when MT bending forces are smaller than MT pushing forces, meaning MTs are easy to bend or buckle. Thus, MT polymerization forces are length dependent, as longer MTs are easier to buckle yielding less pushing forces. As shown in Figure .II.17B, shorter MTs at the posterior induce more pushing forces which yields to spindle centration. Simplified in the model, the density of astral MTs contacting the cortex also need to be taken account, but it is associated with MT polymerization/depolymerization rate and stabilization. Finally, the MT pushing forces may rely on angles of MTs connecting to the cortex. Those MTs perpendicular to the cortex are expected to generate the highest pushing forces before buckling while MTs parallel to the cortex may provide little pushing forces. Both cortical pushing mechanisms can be length dependent, providing a spring-like behavior for spindle displacement. In the straight MT model, the more the spindle moves towards the posterior, the larger the pushing forces are generated towards the anterior. This is because more potentially short MTs can contact the posterior cortex while less MTs can reach the anterior cortex. In the buckled MT model, pushing force scales with the MT length to provide the length dependence.

Cortical MT pulling

Another scenario for cortical forces is that astral MTs generate pulling forces from the cortex to maintain spindle position. This mechanism requires that MTs extending from the spindle [START_REF] Henson | The ultrastructural organization of actin and myosin II filaments in the contractile ring: new support for an old model of cytokinesis[END_REF].

reach and attach to motors or other proteins to the cortex, and the cortex is rigid enough so that it does not invaginate. Thus, pulling forces are produced either through depolymerization of MTs from their plus tips, or by the pulling generated by the motion of dynein anchored at the cortex. Many cortical force-generating regulators are found to interact with dynein to generate cortical pulling forces, such as LGN/NuMA/Gαi in human cells (Figure .II.18) [START_REF] Kiyomitsu | Chromosome-and spindle-pole-derived signals generate an intrinsic code for spindle position and orientation[END_REF], and GPR-1,2/LIN-5/Gα in C.elegans [START_REF] Panbianco | A casein kinase 1 and PAR proteins regulate asymmetry of a PIP(2) synthesis enzyme for asymmetric spindle positioning[END_REF][START_REF] Srinivasan | A complex of LIN-5 and GPR proteins regulates G protein signaling and spindle function in C elegans[END_REF], and Gαi/Pins/Mud in Drosophila.

One experimental evidence for the cortical linkage comes from experiments in oocytes of the marine annelid, where meiotic spindles were pulled away from the cortex by a glass needle, causing the cortex to invaginate. This linkage can be broken via MT depolymerization after further pulling on spindle, leading to a recovery of the cortical shape [START_REF] Lutz | Micromanipulation studies of the asymmetric positioning of the maturation spindle in Chaetopterus sp. oocytes: I. Anchorage of the spindle to the cortex and migration of a displaced spindle[END_REF]. Laser ablation of the central spindle in an early anaphase C.elegans embryo, revealed that spindles are pulled by astral MTs during posterior spindle displacement (Grill et al., 2001). And laser ablation at the centrosome, showed free astral MTs from a spindle moved towards the cortex probably by pulling forces [START_REF] Grill | The distribution of active force generators controls mitotic spindle position[END_REF]. One limit of these experiments is that they did not perfectly separate cortical pulling vs cytoplasmic pulling. However, inhibition of cortical proteins like GPR-1,2 [START_REF] Grill | The distribution of active force generators controls mitotic spindle position[END_REF] and LET-99 [START_REF] Krueger | LET-99 inhibits lateral posterior pulling forces during asymmetric spindle elongation in C. elegans embryos[END_REF] caused the symmetric distribution of centrosome fragment velocities, suggesting the asymmetric spindle positioning requires cortical pulling forces. A key experiment supporting the cortical pulling is that the plasma membrane invaginates by MTs when the cortical stiffness is partially reduced in C.elegans [START_REF] Redemann | Membrane Invaginations Reveal Cortical Sites that Pull on Mitotic Spindles in One-Cell C. elegans Embryos[END_REF]. Cortical pulling forces can also promote pronuclear centration. Enrichment of LET-99 proteins on the posterior cortex near the division plane in C.elegans may inactivate cortical dynein thus promoting pronuclear centration and rotation through large anterior pulling force.

The cortical pulling model has two possible mechanisms to center spindles. The first one is that the anchors are limited but evenly distributed on the cortex (Figure .II.17C, orange stars). When the spindle is not centered, longer astral MTs spread on more surface space than shorter ones, reaching more cortical anchors and generating more pulling forces. Spindle is then pulled to the center until the force is balanced. The second one is that the cortical anchors are not limited but we assume longer MTs have more branches. In this situation, pulling forces scale with the number of MTs reaching the cortex. Thus spindle is pulled by longer MTs towards the center, as longer MTs have more branches attaching to the cortex (Pierre et al., 2016). Both cortical pulling models are length dependent, and promote centration, as long MTs have more chance to attach cortical sites, either through their spatial occupancy or branching, yielding more pulling forces.

Cytoplasmic pulling forces (See Annexe 1)

Although MT cortical forces are typically considered as the dominant modes of force generation (Tolić, 2008), experiments based on the local manipulation of MTs in asters, support that MTs can also pull directly from the cytoplasm without contacting the cell surface (Mitchison et al., 2012;Reinsch and Gönczy, 1998;[START_REF] Wuhr | How does a millimeter-sized cell find its center?[END_REF]. This mechanism is associated with cytoplasmic dynein transport. As the cytoplasm is viscoelastic, the moving cargos carried by dynein are under friction forces, which are transmitted to MTs. These tensile forces on astral MTs are opposite to the direction of dynein movement, and are transferred to the centrosomes, thereby pulling upon aster/spindle. This model thus requires active cytoplasmic dyneins transporting cargos along the MTs and a viscous or visco-elastic medium like the cytoplasm (Palenzuela et al., 2020b).

The first important support for MT pulling force exertion in bulk comes from seminal Colcemid-UV experiments by Hamaguchi and Hiramoto in the 80s (Figure .II.19A) (Hamaguchi and Hiramoto, 1986). During sperm aster centration in sand dollar embryos, MTs are depolymerized with Colcemid. By using local UV inactivation to repolymerize MTs, they found that asters can move to the center of the UV region, similar as the nucleus centering in the whole cell (Chambers, 1939), through cytoplasmic pulling forces. Then an experiment supporting cytoplasmic pulling for anaphase asters motion in large zebrafish blastomeres, used an inverse approach based on a caged MT depolymerizing drug Combretastatin 4A (Figure .II.19B) (Wuhr et al., 2010). By locally depolymerizing a fraction of MTs, the spindle moved toward the sides of longer MTs by cytoplasmic forces as MTs had not reached the cortex. Local laser ablation on parts of a centering aster in sea urchin also suggested a cytoplasmic pulling mechanism (Figure .II.19C) (Tanimoto et al., 2016). Organelle transport along MTs is another feature to indirectly demonstrate cytoplasmic pulling as it is dynein-cargo dependent. Depletion of one of these proteins (dyrb-1, RAB-5, RAB-7, or RILP-1) in C.elegans, decreased dynein dependent organelle transport and slowed aster centering motion (Kimura and Kimura, 2011). However, depletion of GPR-1,2 that eliminates cortical pulling also slows pronuclear centration [START_REF] Park | Dynamic localization of LIN-5 and GPR-1/2 to cortical force generation domains during spindle positioning[END_REF], which suggests that cortical pulling and cytoplasmic pulling may contribute together to pronuclear aster centration, at least in this relatively small embryo.

Position vs orientation

The three types of mechanisms proposed above can center as well as maintain the mitotic spindle position in the cell center. In all of these models, astral MTs are required to generate length-dependent pushing or pulling forces on centrosomes. Although which force dominates remains controversial, all of these force could operate together in maintaining spindle position (Figure .II.21A). Notably, these mechanisms also serve to orient the spindle in anisotropic cell shapes along their longest axis, but not in isotropic shapes as forces equalize in all orientations.

As demonstrated in Minc et al., 2011, when symmetric sea urchin zygotes were manipulated in different shapes by microfabricated chambers, the nucleus/spindle was positioned at the center of mass and stretched along the longest axis, which was predicted through a computational model based on MT length dependent pulling forces (Minc et al., 2011a). This suggests that cell shape is crucial for division plane positioning in symmetric cells by MT shape sensing ability. In addition to the geometry, another mechanism to orient the spindle is the cell polarization, which can be regulated by the asymmetrical distribution of MT associated motors, proteins, RNAs and cargos [START_REF] Panbianco | A casein kinase 1 and PAR proteins regulate asymmetry of a PIP(2) synthesis enzyme for asymmetric spindle positioning[END_REF].

Direct force measurement of spindle positioning in vivo

MT generated forces have been measured mostly in vitro, from single MT pushing force against a barrier (Dogterom and Yurke, 1997) or pulling force by bulk dynein (Palenzuela et al., 2020b), to aster positioning forces (Laan et al., 2012) or spindle rheological forces in egg extract [START_REF] Kiyomitsu | Chromosome-and spindle-pole-derived signals generate an intrinsic code for spindle position and orientation[END_REF]. However, the in vivo measurement of aster/spindle forces remains very difficult, because of the difficulties of exerting and measuring forces in intact cells. The first direct force measurement on spindle in vivo comes from experiments of Nicklas, 1983. He used microneedle to measure forces associated with mitotic spindle elongation during anaphase (Nicklas, 1983). Based on this pioneering work, recent experiments used microneedle to exert local forces on kinetochore MTs in mammalian spindles [START_REF] Suresh | Microneedle manipulation of the mammalian spindle reveals specialized, short-lived reinforcement near chromosomes[END_REF]. In addition, nuclear/aster centering forces have been recently measured in sea urchin zygotes using magnetic tweezers (Salle et al., 2019;Tanimoto et al., 2018).

However, the forces that maintain the spindle position and orientation had never been measured, until the study of Garzon-Coral, 2016, where magnetic tweezer were used to perturb mitotic spindle position during metaphase and anaphase in C.elegans embryos. These experiments start with the microinjection of magnetic beads into the worm's gonad, then an embryo with a bead inside is selected and placed on a microscope equipped with calibrated magnetic tweezers. Embryo development was followed and a constant force was applied at the right moment. When a magnetic force is applied to push one centrosome of the spindle via 1 µm magnetic bead away from the AP axis (Figure .II.21B, C), the displacement follows a typical viscoelastic behavior and reaches an equilibrium plateau once the magnetic forces and pushing forces are equals. Furthermore, upon stopping the magnetic force, the spindle recoils back to the center, much like a spring (Figure .II.21E). This suggests that forces are continually exerted by MTs to hold the spindle in the cell center. MT cortical pushing forces are argued to account for this viscoelastic behavior for spindle centering. Spindle displacement curves are well fitted by a Voigt model with a spring (elastic element) and a dashpot (viscous element) in parallel (Figure .II.21D). From the curves, the spindle centering stiffness, viscous drag and viscoelastic timescales can be computed [START_REF] Pecreaux | The Mitotic Spindle in the One-Cell C. elegans Embryo Is Positioned with High Precision and Stability[END_REF]. The Voigt model is also suitable for other mechanisms such as cytoplasmic pulling forces involved in pronuclear centration in sea urchin zygote (Tanimoto et al., 2018). Pécréaux, 2016, Howard, 2017[START_REF] Wu | Forces positioning the mitotic spindle: theories, and now experiments[END_REF].

Non-astral MT forces

Previous mechanisms presented forces exerted by astral MTs either from the cortex or the cytoplasm that contribute to center, maintain or orient the mitotic spindle. However, spindles in several animal oocytes like mouse, chordata, nematoda, and arthropoda, and cells of flowering plants do not have obvious astral MTs. Thus, other mechanisms must be at play for spindle positioning in these cell types. In oocytes, female meiotic spindles are localized in an extremely asymmetrical position with one spindle pole contacting the oocyte cortex. This position allows the elimination of three fourths of the chromosomes into two tiny polar bodies, so that most of the cytoplasm in the egg is kept for the future developing zygote [START_REF] Fabritius | Nuclear and spindle positioning during oocyte meiosis[END_REF]. ) oocytes, the meiotic spindle is positioned at the cortex in a parallel orientation with equal distances from two poles to the cortex. In C.elegans, this parallel cortical positioning is MT and kinesin-1 dependent [START_REF] Yang | Kinesin-1 mediates translocation of the meiotic spindle to the oocyte cortex through KCA-1, a novel cargo adapter[END_REF][START_REF] Yang | MEI-1/katanin is required for translocation of the meiosis I spindle to the oocyte cortex in C elegans[END_REF], as they move the nucleus towards the cortex before germinal vesicle breakdown and induce a circular streaming pattern through inward yolk transport. Probably an unknown pathway then move and rotate the spindle adjacent to the cortex with parallel orientation [START_REF] Mcnally | Kinesin-dependent transport results in polarized migration of the nucleus in oocytes and inward movement of yolk granules in meiotic embryos[END_REF]. The mechanism is different in mouse, meiosis II spindle is pushed/pulled to the cortex in a parallel position through an F-actin streaming driven by ARP2/3 complex (Figure .II.22B) [START_REF] Yi | Dynamic maintenance of asymmetric meiotic spindle position through Arp2/3-complex-driven cytoplasmic streaming in mouse oocytes[END_REF].

Pole-first migration of meiotic spindle

In mouse, the germinal vesicle is centered in the egg at its breakdown, assembling the meiosis I spindle near the center. The spindle moves to the closet cortex with a pole-first migration (Figure .II.22C). Although this migration has been studied and found associated with F-actin [START_REF] Verlhac | Asymmetric division in mouse oocytes: with or without Mos[END_REF], Formin 2 [START_REF] Dumont | Formin-2 is required for spindle migration and for the late steps of cytokinesis in mouse oocytes[END_REF], Spire 1 and 2 [START_REF] Pfender | Spire-type actin nucleators cooperate with Formin-2 to drive asymmetric oocyte division[END_REF], and ARP2/3 [START_REF] Sun | Arp2/3 complex regulates asymmetric division and cytokinesis in mouse oocytes[END_REF], its mechanism remains unclear. Some proposed models are shown in Figure .II.22C-F. First two pulling models suppose that the spindle movement is mediated by pulling forces either from myosin II transport on F-actin, or by myosin II-based actin contraction (Figure .II.20C, D). The actin bundles found in between the spindle pole and the cortex, as well as the cortical invagination support these models (Schuh and Ellenberg, 2008).

After the observation of an actin cloud behind the moving spindle and surrounded formin2, two pushing models were also proposed (Li et al., 2008). One is that the spindle is pushed by the formin-nucleated actin cloud, which polymerizes F-actin on the spindle (Figure .

II.22E).

This mechanism is similar to the comet-like propulsion of Listeria monocytogenes [START_REF] Lambrechts | Listeria comet tails: the actin-based motility machinery at work[END_REF]. Another is that formin localizes asymmetrically on the cortex behind the moving spindle, which polymerizes F-actin against the cortex to push the spindle forward (Figure .II.22F) [START_REF] Azoury | Symmetry breaking in mouse oocytes requires transient F-actin meshwork destabilization[END_REF].

III. Cytoplasm

The cytoplasm is defined as a jelly-like substance including all the materials between the nuclear membrane and the plasma membrane. In prokaryotes without nucleus, the cytoplasm is referred to as all the materials within the plasma membrane. It suspends various organelles and molecules, and allows many important cellular activities to take place inside cells, including organelle transport, cell division and many metabolic pathways. The cytoplasm has two regions, an inner region called endoplasm and an outer layer called the cell cortex or ectoplasm. The major components of the cytoplasm are the cytosol, the organelles and the cytoskeleton (see ChapterII.1).

In my project, I observed that the cytoplasm in sea urchin zygotes may provide important mechanical forces to maintain mitotic spindle position in the cell center. To understand from where cytoplasmic mechanical properties may emerge, I here describe some important components which could confer elasticity/viscosity.

Components 1.1 Cytosol

The cytosol refers to the liquid part of the cytoplasm, which is also known as groundplasm or intracellular fluid (ICF). It contains mostly water and ions, but has a semi-solid, jelly-like consistency as a great variety of proteins and small molecules are suspended inside, including protein kinases, amino acids, nucleic acids, fatty acids, glucose, other simple sugars and polysaccharides. Dissolved ions such as sodium, potassium, calcium are also found in cytosol and allowed to bicarbonate. The integrity of these elements confers some viscoelastic properties to the cytosol and serves several functions within a cell. These functions include metabolic reactions such as protein biosynthesis, signal transduction between organelles, nucleus and cell membranes, and cytokinesis [START_REF] Shaiken | Dissecting the cell to nucleus, perinucleus and cytosol[END_REF].

Organelles

Mitochondria

Mitochondria were first observed as granule-like structures in the muscle cells of insects in 1857 by Kolliker, and was named as mitochondria when similar objects were found in cells in 1897 by Benda. They appear singly or in groups inside the cytoplasm, and have diameters ranging from 0.2 to 2.0 µm and length ranging from 0.3 to 40 µm. They have fibrillar, spherical, rod and oval shapes, and the shapes change depending on the physiological conditions of the cells. Their number also varies from cell to cell. A mitochondria has a double layer membrane of lipoproteins. The outer layer forms a smooth bag-like structure covering the inner layer with finger-like invaginations in the lumen of the mitochondrion, which are called cristae or mitochondrial crests. Various enzymes, coenzymes, ATP, phosphate molecules and components for the transport of substrates are found on the cristae. The fluid filled within membranes is the mitochondrial matrix, which contains oxidative enzymes, coenzymes and single or double-stranded DNA (mtDNA) that is responsible for 10% of protein production in the mitochondria (Figure .III.2).

The mitochondria is regarded as the "power house" of the cell, because it is the principal location of oxidation that provides usable energy for cell activities. Energy production occurs in the cristae through biochemical reactions performed by a series of proteins, enzymes, and other molecules. These reactions convert energy stored in nutrient molecules like glucose to high energy phosphate compounds like ATP, accompanied with a reaction from O2 to CO2 and H2O via cellular respiration. Thus, mitochondria is required in all the aerobic cells.

Golgi complex

Electron micrographs of cellular thin sections revealed the existence of Golgi complex in all eukaryotes in 1950s. It is formed by a stack of flattened membranes of lipoproteins (known as cisternae), which are arranged parallel and associated with the endoplasmic reticulum (ER) in the cytoplasm. In addition to cisternae, the Golgi typically contains other membrane structures like tubules and vesicles [START_REF] Huang | Golgi structure formation, function, and post-translational modifications in mammalian cells[END_REF]. Tubules are tubular and branched structures extending from the cisternae to the periphery. The vesicles are spherical bodies that can be grouped into three types: transitional vesicles, secretory vesicles, and clathrin-coated vesicles. The Golgi complex is regarded as the "traffic police" of a cell as it secretes important materials such as lysosomes and cell wall materials and is involved in their transports trough processes like exocytosis. Further, the Golgi complex is responsible for the storage of proteins and enzymes which are secreted by ribosomes and transported by the ER (Figure .III.3).

The Golgi complex is found as a satellite organelle that can act as a non-centrosomal MT organizing center (MTOC) in vivo and in vitro [START_REF] Chabin-Brion | The Golgi complex is a microtubule-organizing organelle[END_REF][START_REF] Valenzuela | Golgi Outposts Nucleate Microtubules in Cells with Specialized Shapes[END_REF]. As mentioned before, it is involved in MT aster growth or branching, as it nucleates MTs at distances far from the nucleus or cell body through a subset of γ-tubulin. In addition, the Golgi-derived vesicles may serve as cytoplasmic anchors for dynein pulling forces on MTs [START_REF] Reck-Peterson | The cytoplasmic dynein transport machinery and its many cargoes[END_REF].

Lysosomes and endosomes

Lysosomes were first reported by de Duve in 1955. They are tiny spherical or irregular-shaped and single membrane bounded vesicles in the cytoplasm of animal cells. The lysosomes originate from the Golgi complex and contain hydrolytic enzymes, such as lipases, amylases, proteases, and nucleases. These enzymes are surrounded by the lysosomal membrane and are released to work when a certain cellular component is damaged or unneeded.

Figure.III.3: Schematics of interactions between the Golgi complex and the endoplasmic reticulum (ER).

The ER sends protein and other materials to the Golgi complex, which will organizes, modifies, packages, and tags them. These materials are then transported to other areas of the cell or are exported from the cell through exocytosis. Some of these are enzymatic proteins which will be packaged in the Golgi complex to send as new lysosomes or send for fusion with existing lysosomes (adapted from the Regents of University of Michigan Medical School © 2012).

In eukaryotic cells, endosomes are a collection of intracellular sorting organelles. These membrane-bound vesicles internalize molecules or other substances which come from either the cell exterior by the endocytosis or the Golgi complex. They will be delivered to lysosomes for degradation, or be recycled back to the cell membrane in the endocytic cycle or to the Golgi complex. According to their stage after internalization, endosomes can be classified as early, late or recycling endosomes.

Both lysosomes and endosomes are Golgi-associated vesicles transported by cytoplasmic dyneins through their dynactin complex. The movements of these cargos could exert pulling forces on the centrosome, thus bringing an aster to the cell center (Kimura and Kimura, 2011).

Endoplasmic reticulum (ER)

The endoplasmic reticulum (ER) is a large, dynamic structure, involved in calcium storage, protein synthesis, lipid metabolism and interactions with other organelles (Figure .III.3). These diverse functions are performed through its complex architecture. The ER is a continuous membrane network with distinct domains, the nuclear envelope (NE) covering the nucleus, and the peripheral ER defined by flat sheets and branched tubules (Figure .III.4) [START_REF] Schwarz | The endoplasmic reticulum: structure, function and response to cellular signaling[END_REF]. The rough ER (RER) is involved in protein synthesis as ribosomes, particles composed of ribonucleic acid (RNA) and proteins, are embedded on its membrane. The smooth ER (SER) lacks ribosomes and serves for lipid synthesis. The ER in different structures plays different functions in the cytoplasm and their amount varies depending on the cell types. The NE is connected to the peripheral ER through flat sheets which contains an intervening lumen (Figure .III.4C, D). The tubular network is very dynamic and interconnected by three-way junctions (Figure .III.4C). The sheets and tubules have different functions. Sheets, for instance, synthesize secreted proteins in pancreatic secretory cells and B cells, while tubules are involved in lipid synthesis, calcium signaling and sites of contact with other organelles in liver and muscle cells [START_REF] Baumann | Endoplasmic reticulum of animal cells and its organization into structural and functional domains[END_REF].

Changes of ER structure during mitosis

During mitosis, all organelles change shapes and functions to facilitate their proper segregation for cell division. In mammalian cells, the ER is present as a network of abundant sheets within the cytoplasm in interphase, then transforms into a dense tubular network with more branches during mitosis. The ER is excluded from the region of the nucleus or spindle during the cell cycle (Figure .III.5) [START_REF] Puhka | Endoplasmic reticulum remains continuous and undergoes sheet-to-tubule transformation during cell division in mammalian cells[END_REF]. This structural changes occur differently in cells. For example, in sea urchin and Xenopus zygotes, the ER accumulates at the spindle poles during mitosis, which is probably associated with the cytoplasmic dynein transport on MT asters. In addition, no obvious transformation from sheets to tubules is observed [START_REF] Terasaki | Dynamics of the endoplasmic reticulum and golgi apparatus during early sea urchin development[END_REF]Terasaki and Jaffe, 1991;[START_REF] Terasaki | Changes in organization of the endoplasmic reticulum during Xenopus oocyte maturation and activation[END_REF]. In the early C.elegans embryo and Drosophila melanogaster syncytial embryos, the ER forms sheets during mitosis (Poteryaev et al., 2005). The mechanism for these ER morphological evolutions is still unclear. Some linked regulators have been proposed, like the calcium regulation [START_REF] Terasaki | Dynamics of the endoplasmic reticulum and golgi apparatus during early sea urchin development[END_REF], the ribosomal action on the ER membranes [START_REF] Puhka | Endoplasmic reticulum remains continuous and undergoes sheet-to-tubule transformation during cell division in mammalian cells[END_REF] and ER membrane proteins REEP3 and REEP4 [START_REF] Kumar | REEP3 and REEP4 determine the tubular morphology of the endoplasmic reticulum during mitosis[END_REF]. The partitioning of perinuclear ER volume during division has been revealed to scale the nucleus size, which in independent with the cell size in early embryos [START_REF] Mukherjee | The Perinuclear ER Scales Nuclear Size Independently of Cell Size in Early Embryos[END_REF].

In addition, these changes suggest possible contribution of ER to cell division or nucleus/spindle positioning, such as acting as the spindle matrix to provide mechanical support to spindle (see ChapterII.2) or conferring cytoplasm elastic properties through its skeletal membrane network. In sea urchin zygotes, for example, the ER accumulates around the nucleus and centrosome during sperm aster centration, which is possibly transported by dynein and considered as a sign for cytoplasmic pulling mechanism (Terasaki and Jaffe, 1991). In early ascidian embryos, spindle asymmetric positioning is driven by a large subdomain of cortical ER where MT depolymerase Kif2 localizes, causing asymmetric cell divisions (Costache et al., 2017a). The ER is also involved in spindle movements in the C.elegans embryo by its associated TCC-1 protein [START_REF] Berends | F-actin asymmetry and the endoplasmic reticulum-associated TCC-1 protein contribute to stereotypic spindle movements in the Caenorhabditis elegans embryo[END_REF]. Recent experiments observed only minor inward movement of ER relative to asters during dynein mediated aster movement in Xenopus egg extracts, putting in questions the standard pulling model with ER as a cytoplasmic anchor [START_REF] Pelletier | Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm[END_REF].

Yolk

In the cytoplasm of oocytes, eggs or some growing embryos, nutritional materials are stored in the form of yolk, which is rich in water, lipids, proteins and polysaccharides. It is classified as "protein yolk" when it has more proteins than lipids, or "fatty yolk" when it has more fat than proteins. Both kinds of yolk are present in the cytoplasm with two structures, either granular yolk (Figure.III.6) or yolk platelets (Figure .III.7). The granular yolk forms fine particles usually found distributed in the eggs of invertebrates and lower chordates such as Amphioxus and tunicates. Yolk platelets are found in most vertebrates like cyclostomes, amphibians, birds and lung fishes, which usually form large concentrated granules [START_REF] Anton | Egg yolk: structures, functionalities and processes[END_REF]. These aggregates account for a large volume of the cell, which exclude other cytoplasmic components, thus influencing cell polarity and cytoplasm organization (Figure .III.7A) [START_REF] Mauch | Developmental Biology. Sixth Edition. By Scott F. Gilbert[END_REF][START_REF] Wallace | Studies on Amphibian Yolk. Iii. A Resolution of Yolk Platelet Components[END_REF].

Yolk induced cytoplasmic exclusion indirectly change the cytoskeleton forces by modulating aster shape, thus regulating the nucleus/spindle positioning (Figure .III.7A) (Belousov, 2011;Pierre et al., 2016;Wuhr et al., 2010). For instance, in zebrafish embryo, most of the cytoplasm is occupied by yolk, and embryo divisions only occur in a fine layer, called the blastodisc. In Xenopus embryos, MTs density has been proved anti-proportional to the yolk concentration, thus pushing asters position towards the animal pole (Figure .III.7B). Accordingly, computational simulations can predict division positioning during early cleavage in Xenopus embryos with a yolk exclusion model. These simulations work with both MT cytoplasmic pulling mechanism (Figure .III.7C) (Pierre et al., 2016), or cortical pushing mechanism where the yolk-cytoplasm interface is supposed as a rigid membrane [START_REF] Bjerknes | Physical theory of the orientation of astral mitotic spindles[END_REF].

Cytoplasm physical properties

Cytoplasm density

As detailed above, the cytoplasm is crowded with components ranging from small globular proteins to extended endomembranes and cytoskeletal networks. The density of the cytoplasm is defined by its dry mass and water content. The dry mass ranges from 20%-40% of the total cellular mass depending on cell types and conditions [START_REF] Albe | Cellular concentrations of enzymes and their substrates[END_REF][START_REF] Delgado | Intracellular Water Exchange for Measuring the Dry Mass, Water Mass and Changes in Chemical Composition of Living Cells[END_REF][START_REF] Illmer | A practicable and accurate method to differentiate between intra-and extracellular water of microbial cells[END_REF]. The cytoplasm density and how these components interact are important for many cellular processes like metabolism, organelle transports and cell division.

The density gradient centrifugation is a well-known method to measure the density [START_REF] Hartwell | Periodic Density Fluctuation During the Yeast Cell Cycle and the Selection of Synchronous Cultures[END_REF][START_REF] Novick | Identification of 23 complementation groups required for post-translational events in the yeast secretory pathway[END_REF]. Recently, a number of developed methods have provided precise measurement of cell density, such as suspended microchannel resonators (SMRs) which allows to measure the buoyant mass of a cell in suspension [START_REF] Burg | Weighing of biomolecules, single cells and single nanoparticles in fluid[END_REF], cryoelectron tomography which allows to construct a 3D electron density map [START_REF] Delarue | mTORC1 Controls Phase Separation and the Biophysical Properties of the Cytoplasm by Tuning Crowding[END_REF], indirect measurements like particle tracking through the diffusion of macromolecules [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF], or fluorescence correlation spectroscopy (FCS) [START_REF] Elson | Fluorescence Correlation Spectroscopy: Past, Present, Future[END_REF] and fluorescence recovery after photobleaching (FRAP) [START_REF] Lippincott-Schwartz | Studying protein dynamics in living cells[END_REF] through the diffusion of small particles, and the stimulated Raman scattering (SRS) microscopy which allows to identify spatial density of macromolecules [START_REF] Cheng | Vibrational spectroscopic imaging of living systems: An emerging platform for biology and medicine[END_REF].

The cell density is not constant in a cell and changes in response to environmental or developmental cues. Researchers have shown that these changes occur under a number of physiological conditions. For instance, it changes during the cell cycle in the fission yeast where density decreases during G2 and increases in mitosis and cytokinesis [START_REF] Odermatt | Variations of intracellular density during the cell cycle arise from tip-growth regulation in fission yeast[END_REF]. In budding yeast, the density is highest in late G1 and early S phase and lowest in early G1 [START_REF] Bryan | Measurement of mass, density, and volume during the cell cycle of yeast[END_REF]. In human cells, the density remains constant until it decreases during mitosis [START_REF] Son | Resonant microchannel volume and mass measurements show that suspended cells swell during mitosis[END_REF]. These changes are relatively small, around 0.5% [START_REF] Son | Resonant microchannel volume and mass measurements show that suspended cells swell during mitosis[END_REF].

The regulation of the density change remains poorly understood and possibly due to the uncoupling rate of the protein synthesis and cell volume growth. Some potential explanations have been proposed, such as volume expansion during mitosis and post-cytokinesis in fission yeast [START_REF] Odermatt | Variations of intracellular density during the cell cycle arise from tip-growth regulation in fission yeast[END_REF], or the synthesis of different classes of macromolecules in the cell cycle of budding yeast [START_REF] Blank | Translational control of lipogenic enzymes in the cell cycle of synchronous, growing yeast cells[END_REF] or mitotic swelling mediated by Na-H ion-exchange pumps in human cells [START_REF] Son | Resonant microchannel volume and mass measurements show that suspended cells swell during mitosis[END_REF].

The cell density also correlates with altered metabolic activity. An increase in cell density is usually accompanied by reduced metabolic activities, such as in unicellular organisms, where carbon starvation and energy shut-down increase the density [START_REF] Neurohr | Relevance and Regulation of Cell Density[END_REF][START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF]. In addition, cell density changes also occur during cell differentiation [START_REF] Grover | Measuring single-cell density[END_REF][START_REF] Zipursky | Leukocyte Density and Volume in Normal Subjects and in Patients With Acute Lymphoblastic Leukemia[END_REF], apoptosis [START_REF] Maeno | Normotonic cell shrinkage because of disordered volume regulation is an early prerequisite to apoptosis[END_REF], and cellular senescence [START_REF] Neurohr | Excessive Cell Growth Causes Cytoplasm Dilution And Contributes to Senescence[END_REF].

Intracellular density fluctuations affect the physical nature of the cytoplasm, such as macromolecular crowding, viscoelasticity and poroelasticity. These properties will in turn affect a number of cellular processes, such as protein-protein associations, phase transitions, and enzymatic fluxes. Thus, it is important to understand how physical properties affect cellular reactions. Molecular crowding is defined as a property emerging from the dense packing of macromolecules inside the cytoplasm. It can reduce the volume occupied by a molecular, called the volume exclusion (Figure .III.8A), thus increasing the effective molecular concentration and accelerating biochemical reactions [START_REF] Rivas | Macromolecular Crowding In Vitro, In Vivo, and In Between[END_REF]. Molecular crowding also promotes the formation of large molecular complex and promotes phase separation [START_REF] Delarue | mTORC1 Controls Phase Separation and the Biophysical Properties of the Cytoplasm by Tuning Crowding[END_REF], which could contribute to DNA damage repair and mRNA translation (Figure .III.8B) [START_REF] Boija | Transcription Factors Activate Genes through the Phase-Separation Capacity of Their Activation Domains[END_REF][START_REF] Kilic | Phase separation of 53BP1 determines liquid-like behavior of DNA repair compartments[END_REF]. Another effect from crowding is to restrict organelle diffusion in a size-dependent manner, which favors small organelle motions over that of larger ones (Figure .III.8C) [START_REF] Neurohr | Relevance and Regulation of Cell Density[END_REF].

To test how cytoplasm density and its physical properties could affect cell function, a common method to alter the density is to manipulate its water content through a dilution in vitro or an osmotic shock in vivo. In cell-free extracts, the dilution causes rapid loss of extract function [START_REF] Lohka | Induction of nuclear envelope breakdown, chromosome condensation, and spindle formation in cell-free extracts[END_REF]. Hypotonic shock reduce the density and crowding effect because of the water influx. Conversely, hypertonic shocks deplete water in the cytoplasm thereby increasing its density, but a strong desiccation can be detrimental for most cells. Using these shocks, some cytoplasm density functions have been discovered. For example, budding yeast cells accumulates glycerol after hypertonic stress and releases glycerol following the hypotonic shock [START_REF] Hohmann | An integrated view on a eukaryotic osmoregulation system[END_REF]. In fission yeast, moss and mammalian cells, higher cytoplasm density freezes MT dynamics such as polymerization and depolymerization [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization[END_REF]. In mammalian cells, water loss induces the activation of a set of MAP kinase, which serves the adaptation to hypertonic stress through for example, rapid ion influx [START_REF] Zhou | Mitogen-activated protein kinases as key players in osmotic stress signaling[END_REF].

Cytoplasm mechanical properties

The cytoplasm is a complex mechanical entity consisting of both solid (crowed macromolecular, endomembranes and cytoskeleton polymers), and fluid (cytosol) properties.

Its rheological behavior depends on the amplitude, frequency and spatial location of loads [START_REF] Fletcher | Active biological materials[END_REF] and have been explained by different rheological models. In general, three prominent models have been proposed. The viscoelastic model defines the cytoplasm as the single phase material where its rheology is represented by a network of springs and dashpots [START_REF] Crick | The physical properties of cytoplasm: A study by means of the magnetic particle method Part I[END_REF]Hiramoto, 1969a, b). The poroelastic model describes the cytoplasm as a biphasic material where a porous elastic solid meshwork is penetrated by an

Figure.III.8: Cytoplasm crowding effect. (A) Crowding reduced the accessible volume

VAccessible for other molecules in a size dependent manner, where large macromolecules are excluded from the cytoplasm (left) but small molecules can enter (right). The effective concentration (cEff) of molecules in the cytoplasm is higher than the total concentration (c) of the cell. n, number of molecules; V, volume; c, concentration. (B) Molecular crowding promotes the generation of phase-separated condensates, thus increasing VAccessible for other molecules (right). (C) Crowding restricts lateral diffusion in a size dependent manner. Large molecules cannot move close to other particles (left) while small molecules can pass through their intervals (right) (adapted from [START_REF] Neurohr | Relevance and Regulation of Cell Density[END_REF]. interstitial fluid [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF]. Finally, the soft glassy rheology model defines the cytoplasm as a glass-like material [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF]. Here, I will introduce all these models and their applications to cell biological phenomena, such as organelle positioning, blebbing and cell motility.

Poroelasticity

Researchers have revealed that cytoplasm constituents form a poroelastic material that allows small molecules to diffuse but restricts the motion of larger molecules [START_REF] Luby-Phelps | Probing the structure of cytoplasm[END_REF][START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF]Xiang et al., 2020). The cytoplasm poroelasticity thus depend on the pore and mesh sizes. The virtue of this model is that it can account for dilatational changes in the cytoplasm such as blebbing, cell oscillations or cell movement (Charras et al., 2005a;[START_REF] Keren | Intracellular fluid flow in rapidly moving cells[END_REF] and capture the crowding effect and active processes in cells. This model is a minimal physical model for a cell when it sticks, moves, blebs, or divides, as the cytoplasm heterogeneity and its relative motion between solid and fluid phase are considered Mitchison, 2008).

One prominent characteristic of the poroelastic model is a non-equilibration of internal pressure. When a poroelastic material is under a constant load, initially the liquid flows though the elastic mesh and continues over longer and longer distances. This creates a heterogeneous pressure over the material, where the pressure is the highest near the load and reduces over the distance. The pressure will equilibrate diffusively over time and finally vanish. Similar to the mesh deformation, which initially squeezes near the load, then becomes uniform over the material when the flow slows down and elastic stresses balance the external load (Figure .III.10) [START_REF] Dembo | Cell motion, contractile networks, and the physics of interpenetrating reactive flow[END_REF][START_REF] Gu | A triphasic analysis of negative osmotic flows through charged hydrated soft tissues[END_REF].

Some experiments indirectly support the poroelastic model for the cytoplasm from documenting the non-equilibration of pressure in blebbing cells [START_REF] Charras | Nonequilibration of hydrostatic pressure in blebbing cells[END_REF], in moving cells [START_REF] Keren | Intracellular fluid flow in rapidly moving cells[END_REF] and during the cell protrusion [START_REF] Zicha | Rapid actin transport during cell protrusion[END_REF]. These pressure will slowly equilibrate, possibly due to the intracellular flows of cytosol. In the poroelastic model, the cytoplasm deformation is limited by the redistribution rate of the liquid.

Thus, rheological properties of the cell can be simply predicted by the poroelastic diffusion constant, Dp, which is proportional to Eξ 2 /μ with E the elastic modulus of the elastic mesh, ξ the radius of pores, and μ the viscosity of the liquid. By probing Dp in mechanical, chemical With time, the liquid flow through pores in the gel over longer and longer distances, slowing equilibrating the pressure in the gel. Eventually, the deformation of the mesh becomes uniform and pressure vanishes (adapted from Mitchison, 2008). and genetic conditions, a series of direct experiments validated the poroelastic model at a physiological relevant timescale of ~10s in different cell types (Charras et al., 2005a).

According to the poroelastic model, hydrodynamic forces are proposed to be generated from the cooperation between osmotic and cytoskeletal dynamics. If the pore size is small ~30-60nm, the pressure equilibrates slowly through cells, causing local higher pressure to drive blebbing, protrusion, locomotion and division. These processes could be mediated by actomyosin contractility, or by local activation of some osmogenic ion transporters on the plasma membrane [START_REF] Mitchison | Implications of a poroelastic cytoplasm for the dynamics of animal cell shape[END_REF]. However, it remains difficult to test these hypothesis, given the difficulty of properly tracking the water flux, the complexity of ion homeostasis, the changes of ion concentrations in the cytoplasm and the plausible dynamic localization of ion transporters from the cytoskeleton [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF].

Glass-like properties

Many essential cellular processes involving shape deformations such as cell contraction, spreading, crawling, invasion, extravasation, division and wound healing are highly associated with mechanical stresses. These cannot be explained by a simple elastic cytoplasm where the mechanical stress is balanced over the cell to maintain its structural integrity. To achieve these processes, the cytoplasm needs to have liquid properties. Thus, many physical descriptions of the cytoplasm have been proposed and one of them is the soft glass rheology (SGR) [START_REF] Sollich | Rheology of soft glassy materials[END_REF], where the cytoplasm constituents go through a glass transition which is mediated by the volume fraction to exhibit both solid and liquid properties (Figure.III.11). The frequency dependency of the storage (elastic) modulus G'(ω) and the loss (viscous) modulus G"(ω) has been used to test SGR. Classes of soft glass materials (SGMs) including foams, emulsions, slurries and pastes have been studied for their rheological properties (Mackley et al., 1994;Khan et al., 1988a, Khan et al., 1988b;[START_REF] Mason | Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids[END_REF], Panizza et al., 1996, Hoffman and Rauscher, 1993[START_REF] Mason | Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids[END_REF]. SGMs should respect four properties: Their mechanical moduli is in the range of Pa to kPa; Their loss tangential modulus ( G"(ω) / G'(ω) ) is nearly constant to ~0.1 as a function of the frequency of the stress applied [START_REF] Sollich | Rheology of soft glassy materials[END_REF]; Their moduli are frequency dependent which are weak power laws as a function of the frequency of the applied stress; They exhibit aging behavior on certain conditions [START_REF] Mandadapu | On the cytoskeleton and soft glassy rheology[END_REF].

Many experiments show similar features of SGMs, such as structural disorder and metastability [START_REF] Sollich | Rheology of soft glassy materials[END_REF][START_REF] Weeks | Subdiffusion and the cage effect studied near the colloidal glass transition[END_REF]. Another key feature of glassy materials is the glass transition temperature, Tg, which is the temperature at which a liquid transits to a solid.

Below Tg, the liquid material is frozen with a high viscosity behaving as a solid, and is in a metastable state. An increasing pressure can also transit fluids to glasses (Figure .III.11) [START_REF] Hunter | The Physics of the Colloidal Glass Transition[END_REF][START_REF] Roland | Supercooled dynamics of glassforming liquids and polymers under hydrostatic pressure[END_REF]. Some experiments probed the rheological properties of the cytoplasm of eukaryotic cells and proposed that the cytoskeleton can be modeled with a SGR model, because of the similar rheological responses as compared with SGMs [START_REF] Bursac | Cytoskeletal remodelling and slow dynamics in the living cell[END_REF][START_REF] Deng | Fast and slow dynamics of the cytoskeleton[END_REF][START_REF] Fabry | Scaling the Microrheology of Living Cells[END_REF]. In bacteria, the cytoplasm lacks a pervasive cytoskeletal meshwork and its associated motors. However, it also exhibits glass-like properties, as demonstrated by singleparticle tracking of its components with different sizes. In particular, these properties are sizedependent with small particles perceiving more the liquid-like property and large macromolecular sensing the glassy property [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF]. This could explain previous findings of normal and anomalous diffusion in dense colloidal suspensions, where small size particles are mobile but larger ones can be restricted (Zaccarelli et al., 2005). These glassy behaviors are likely associated to the cellular metabolism, which could enhance the fluidity of the cytoplasm [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF].

Cytoplasm rheology in cells vs in bulk extracts

Cytoplasm rheology has been studied in early micro-rheology experiments performed in chick and sea urchin cells using injecting magnetic particles moved by magnetic tweezers as probes (Figure .III.12A) [START_REF] Crick | The physical properties of cytoplasm: A study by means of the magnetic particle method Part I[END_REF]Hiramoto, 1969a, b). The solid and fluid properties of the cytoplasm were quantified with bulk elastic moduli on the order of ~1-10 Pa, typical of soft gels and viscosities 100-1000 times that of water. Similar properties were also found in the cytoplasm of starfish oocytes using the tracking of cytoplasmic granules under pressure [START_REF] Shôji | Mechanical properties of the endoplasm in starfish oocytes[END_REF].

In cells, cytoplasm rheological properties could be influenced by many cellular processes, such as the metabolism [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF], the motor-driven organelle movements or fluctuations [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF] and the cell cycle [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF]. For example, recent work, using optical tweezers-based microrheology, revealed cytoplasm softening and fluidification during mitosis in MDCK cells. Remarkably, these softening and fluidification of the bulk cytoplasm during mitosis contrast with the cell cortex stiffening typical of mitotic cells [START_REF] Fischer-Friedrich | Rheology of the Active Cell Cortex in Mitosis[END_REF][START_REF] Sorce | Mitotic cells contract actomyosin cortex and generate pressure to round against or escape epithelial confinement[END_REF][START_REF] Stewart | Hydrostatic pressure and the actomyosin cortex drive mitotic cell rounding[END_REF]. This processes is possibly due to a switch of the dominating component for cytoplasm mechanical properties from MTs to F-actin during mitosis [START_REF] Hurst | Intracellular softening and fluidification reveals a mechanical switch of cytoskeletal material contributions during division[END_REF].

The cytoplasm of living cells is very dynamic and subjected to a number of forces [START_REF] Howard | Mechanics of Motor Proteins and the Cytoskeleton[END_REF]. These forces are usually associated with the activity of molecular motors needed to transport organelles or organize cell divisions (Vale, 2003). Recent work revealed that the aggregate activity of molecular motors could create randomly fluctuating forces, yielding diffusive-like active (non-thermal) motion of the cytoplasm. These fluctuating forces promote intracellular movements from small proteins to large organelles. These cytoplasmic forces are found to be three times higher in malignant cancer cells as compared to benign cells, suggesting cytoplasm activity and/or rheological properties may be a hallmark of cancer cells (Figure .III.12B) [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF].

More recent studies have established the rheological characteristics of the cytoplasm. For instance, size and speed dependent mechanical properties has been documented by moving probes with different sizes and speeds in living mammalian cytoplasm [START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF]. These size dependent properties are similar to those reported for the bacterial cytoplasm with a SGR model [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF] and in mammalian cells with a poroelastic model [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF]. In addition, the cytoplasm of living cells could exhibit force and frequency dependent mechanical properties [START_REF] Chaubet | Dynamic actin cross-linking governs the cytoplasm's transition to fluid-like behavior[END_REF][START_REF] Hoffman | Cell Mechanics: Dissecting the Physical Responses of Cells to Force[END_REF][START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF][START_REF] Tseng | Micromechanical Mapping of Live Cells by Multiple-Particle-Tracking Microrheology[END_REF][START_REF] Zhu | Cell Mechanics: Mechanical Response, Cell Adhesion, and Molecular Deformation[END_REF].

Xenopus extracts have also been used as a model system to dissect elements in the cytoplasm which regulate viscosity, elasticity or other rheological properties [START_REF] Valentine | Mechanical Properties of Xenopus Egg Cytoplasmic Extracts[END_REF]. In extract, like in cells, cytoplasm properties were also shown to exhibit the size dependence. The cytoplasm of extract behaves as a soft viscoelastic material at macroscopic length scales with an elastic modulus of ~2-10 Pa and a viscous modulus of ~0.5-5 Pa, which are consistent with values in live cells (Hiramoto, 1969a). Yet, at a length scales smaller than an estimated mesh size in the cytoplasm, the cytoplasm responds predominantly as a viscous liquid with a viscosity of ∼20 mPa-s. Importantly, elasticity in the extract is mostly associated with networks B) Schematic of an optical tweezer setup used to probe the rheology of the mammalian cytoplasm. A probe bead is moved at a control speed toward the boundary to obtain a force-displacement curve. The crowed bulk cytoplasm around the bead is depicted in the inset (adapted from Hiramoto, 1969 and[START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF].

of F-actin and MTs, but not Ifs like cytokeratin, suggesting that MTs and actin polymers may form a composite network with a mesh size of several microns [START_REF] Valentine | Mechanical Properties of Xenopus Egg Cytoplasmic Extracts[END_REF].

The viscoelasticity of the cytoplasm has been simply modeled with 1D linear viscoelastic models such as the Kelvin-Voigt model (see chapter II.3) or three-element models like the Jeffreys model [START_REF] Khadrawi | Basic viscoelastic fluid flow problems using the Jeffreys model[END_REF]. There also exists more refined non-linear viscoelastic models given the potential heterogeneous mechanical properties of the cytoplasm [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF][START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF]Mittasch et al., 2018b;[START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF][START_REF] Mogilner | Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel[END_REF][START_REF] Tseng | Micromechanical Mapping of Live Cells by Multiple-Particle-Tracking Microrheology[END_REF]. Jeffreys model appears more realistic than the Voigt model as it includes a dissipation term which accounts for potential fluidification of the material typical of weak elastic solid [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF]. It comprise an elastic spring (κ the stiffness) and two viscous dashpots with one which is purely viscous corresponding to the instantaneous shear relaxation (γ1 the drag coefficient), and another corresponding to the shear relaxation with an exponential function of time (γ2 the drag coefficient) [START_REF] Zhou | Viscoelasticity of biomolecular condensates conforms to the Jeffreys model[END_REF]. The elastic component κ and the viscous component γ1 are in parallel, functioning as a Voigt model, and the other viscous component γ2 is in series with them (Figure. III.13,left). When a force is applied suddenly to a Jeffreys element, the spring will not stretch and the two dashpots initially take up the force. Thus the creep curve starts with a linear displacement with a slope associated with γ1 and γ2. Then a part of the force is transferred to the spring, so that the creep curve flattens. When the spring reaches its maximum displacement, the first dashpot stops elongating, and the creep curve becomes linear again, only depending on the second dashpot with a slope of F/ γ2. Upon force cessation, only the displacement produced by "Voigt model" is restored, thus causing a partial recovery with a dissipation of the elastic energy from the second dashpot. viscoelasticity timescales (adapted from Hiramoto, 1969).

Role of MTs, actin and IFs

The cytoskeleton polymers establish the meshwork in the cytoplasm but they play different roles in bulk rheology. In Xenopus crude interphase egg extracts, using pharmacological and immunological disruption methods, F-actin and MT were found to confer mechanical strength, while the IFs (cytokeratin) did not contribute to bulk viscoelasticity [START_REF] Valentine | Mechanical Properties of Xenopus Egg Cytoplasmic Extracts[END_REF].

The mechanical role of these filaments and their different functions were also assayed in the cytoplasm of living cells. In early Drosophila embryos, high-speed video microrheology revealed that MTs contribute to the viscoelasticity inside the embryo while F-actin only plays a minor role towards the periphery [START_REF] Wessel | The Mechanical Properties of Early <em>Drosophila</em> Embryos Measured by High-Speed Video Microrheology[END_REF]. Swiss 3T3 fibroblasts exhibit higher stiffness and more mechanical heterogeneity upon injecting α-actinin, a cross linker of actin filaments. This suggests that the cross-linked state of actin filament network may be a sensitive parameter for cytoplasm elasticity [START_REF] Tseng | Micromechanical Mapping of Live Cells by Multiple-Particle-Tracking Microrheology[END_REF]. Cytoplasmic F-actin mesh could drive the random diffusion while MTs are more associated to the advection for the bulk mobility in Drosophila oocytes [START_REF] Drechsler | Active diffusion and advection in Drosophila oocytes result from the interplay of actin and microtubules[END_REF]. IFs could also confer cytoplasmic elasticity. For instance, the presence of vimentin IFs (VIFs) doubles the cytoplasmic shear modulus in mouse embryonic fibroblasts (mEFs) [START_REF] Guo | The role of vimentin intermediate filaments in cortical and cytoplasmic mechanics[END_REF]. Besides, VIFs could dominate cytoplasmic mechanics and maintain cell viability when cells are under severe deformation [START_REF] Hu | High stretchability, strength, and toughness of living cells enabled by hyperelastic vimentin intermediate filaments[END_REF].

However VIFs do not contribute to myosin II driven random fluctuations in the cytoplasm, rather they act globally as structural polymers to anchor organelles against randomly fluctuating forces and contribute to cytoplasm stiffness [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF]. Finally, recent work discovered that cytoplasm transition from elastic to viscous material is controlled by the dynamic of actin cross-linking, which allows the viscoelastic cytoplasm to flow at long timescales [START_REF] Chaubet | Dynamic actin cross-linking governs the cytoplasm's transition to fluid-like behavior[END_REF].

Active vs passive rheological properties

The cytoplasm rheological properties could result from the mechanical nature of bulk material like entangled cytoskeletal polymers [START_REF] Kröger | The Structure and Rheology of Complex Fluids[END_REF], endomembranes, macromolecules and cytosol (Verdier, 2003), or from active processes like metabolism [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF] or motor driven flows [START_REF] Kimura | Endoplasmic-reticulum-mediated microtubule alignment governs cytoplasmic streaming[END_REF], cytoskeleton reorganization [START_REF] Hurst | Intracellular softening and fluidification reveals a mechanical switch of cytoskeletal material contributions during division[END_REF] and random fluctuations [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF]. These properties are thought as mechanical resistances that active forces need to overcome to transport organelles or position asters and spindles for instance (Hu et al., 2017a). In addition to the passive mechanics, living cells are dynamic with various active processes, which could affect bulk rheology. For example, the cellular metabolism could fluidize the cytoplasm to permit the movement of large cytoplasmic components [START_REF] Parry | The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity[END_REF]. Recent experiments reveal that epithelial cells are fluidized and softened during mitosis due to a cell controlled active mechanical switch of cytoskeletal material contributions [START_REF] Hurst | Intracellular softening and fluidification reveals a mechanical switch of cytoskeletal material contributions during division[END_REF]. Passive and active rheological properties may be distinguished by comparing their energy to that predicted from Brownian motion [START_REF] Mason | Particle Tracking Microrheology of Complex Fluids[END_REF][START_REF] Mason | Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids[END_REF][START_REF] Schnurr | Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations[END_REF]. However, it remains challenging to experimentally separate these properties as living cells need metabolism and motors to maintain their basic physiology.

Cytoplasm rheology affects fundamental processes ranging from the kinetics of biochemical reactions to vesicular transport and cell shape control (Delarue et al., 2018a;[START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF]Palenzuela et al., 2020a). However, many studies of bulk cytoplasm properties and their functions have focused on relatively small objects and active processes. Thus, how cytoplasm material properties impact the movement of large organelles like nuclei or spindle, and contribute to nucleus centration and spindle positioning remain poorly understood.

Cytoplasmic flows

As mentioned in Chapter III.2, the cytoplasm has fluid-like properties, which allow it to flow. These intracellular flows are responsible for molecular transport throughout the cell and their distributions in space. There exists various types of flows inside cells, including for example filament treadmilling driven flux, cortical flows and cytoplasmic streaming (Figure.III.14). The treadmilling of actin and MT filaments could drive a rearward flux of subunits by their growing ends when they elongate against a barrier (Figure .III.14A) [START_REF] Hill | Subunit treadmilling of microtubules or actin in the presence of cellular barriers: possible conversion of chemical free energy into mechanical work[END_REF]. This process has been observed during organelle partitioning [START_REF] Toro-Nahuelpan | Segregation of prokaryotic magnetosomes organelles is driven by treadmilling of a dynamic actin-like MamK filament[END_REF], intracellular virus particle trafficking [START_REF] Gardet | Role for Actin in the Polarized Release of Rotavirus[END_REF] and the transport of signaling receptors in filopodia [START_REF] Jacquemet | Filopodia in cell adhesion, 3D migration and cancer cell invasion[END_REF]. In most cells, cortical flows are generated by contractile actomyosin network (Munro et al., 2004). For instance in C.elegans, local actomyosin cortical contraction induces the movement of the network towards the anterior pole of the embryo, yielding a long range flow of associated materials towards the anterior pole (Figure .III.16B) (Mayer et al., 2010;[START_REF] Mcfadden | Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex[END_REF][START_REF] Wilson | Myosin II contributes to cell-scale actin network treadmilling through network disassembly[END_REF]. These cortical flows have also been documented during cell division to displace actomyosin networks towards the cleavage furrow [START_REF] Bray | Cortical flow in animal cells[END_REF] and cell migration like in amoeboid cells (Reymann et al., 2016). The cytoplasmic streaming or cyclosis (in plant cells) is usually observed in large cells where bulk effect dominates, like in mouse oocytes, algae, plants [START_REF] Houtman | Hydrodynamic flow caused by active transport along cytoskeletal elements[END_REF], amoebae, nematode embryos [START_REF] Kimura | Endoplasmic-reticulum-mediated microtubule alignment governs cytoplasmic streaming[END_REF] and fly embryos (Figure .III.14B) [START_REF] Ganguly | Cytoplasmic streaming in Drosophila oocytes varies with kinesin activity and correlates with the microtubule cytoskeleton architecture[END_REF][START_REF] Goldstein | A physical perspective on cytoplasmic streaming[END_REF]. It often initiates from cytoskeletal activity at the cell cortex such as the cortical actomyosin flows [START_REF] Mogilner | Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel[END_REF] or motor-mediated organelle transport along the cortical cytoskeleton (Goldstein and van de Meent, 2015a). These cortical activities create shear forces on the surrounding cytoplasm, thus entraining flows through the cytoplasm. Cytoplasmic streaming can also be induced by pressure gradients generated from the actomyosin contraction, the cell deformation and the osmotic shock [START_REF] Abadeh | Mass flow and velocity profiles in Neurospora hyphae: partial plug flow dominates intra-hyphal transport[END_REF]. These bulk flows transport molecules within the cytoplasm by advection, or from one cell to another, with important functions such as oocyte growth and physiology [START_REF] Quinlan | Cytoplasmic Streaming in the Drosophila Oocyte[END_REF]. Importantly not all molecules will follow the flow [START_REF] Sheetz | Nanometre-level analysis demonstrates that lipid flow does not drive membrane glycoprotein movements[END_REF]. Molecules could be governed by advection or diffusion in the cytoplasm, depending on their Peclet number, the contribution of advection over diffusion. It is dimensionless with Pe = Lu/D, where L is the typical length scale, u is the velocity, and D is the effective diffusion coefficient. The flow dominates particle motion when Pe ≫ 1, and may be negligible if Pe ≪ 1. Thus, larger organelles or molecular assemblies (small D) in a fast flow (high u) may be transported by cytoplasm flows over a long distance (large L).

Cytoplasmic flows may be important for cell migration (Etienne-Manneville, 2008; [START_REF] Keren | Intracellular fluid flow in rapidly moving cells[END_REF] and long-range molecular transports [START_REF] Pickard | The role of cytoplasmic streaming in symplastic transport[END_REF]. They also contribute to the spatial organization inside cells. For instance, kinesin-dependent cytoplasm streaming promotes the mixing of the oskar mRNA and RNA-binding proteins in the cytoplasm of Drosophila melanogaster embryos [START_REF] Krauss | Myosin-V regulates oskar mRNA localization in the Drosophila oocyte[END_REF]. The geometry of flows could also explain the asymmetric compartmentalization of nuclei in filamentous fungi (Pieuchot et al., 2015a) (Pieuchot et al., 2015b;[START_REF] Saturno | Sustained centrosome-cortical contact ensures robust polarization of the one-cell C. elegans embryo[END_REF] and the establishment of cell polarity in C.elegans zygotes [START_REF] Saturno | Sustained centrosome-cortical contact ensures robust polarization of the one-cell C. elegans embryo[END_REF]. Cytoplasmic flows were found to drive the asymmetric positioning of meiotic spindle in mammalian oocytes (Yi et al., 2011a), spindle rotation (Wang et al., 2020a) and uniform nuclear positioning in Drosophila embryos [START_REF] Deneke | Self-Organized Nuclear Positioning Synchronizes the Cell Cycle in Drosophila Embryos[END_REF], Many advanced methods have been implemented to study cytoplasmic flows, including FRAP (Fluorescence Recovery After Photobleaching), single molecule tracking, FCS (Fluorescence correlation spectroscopy), differential dynamic microscopy [START_REF] Drechsler | Active diffusion and advection in Drosophila oocytes result from the interplay of actin and microtubules[END_REF] and imagebased flow analysis of molecule movements inside cells [START_REF] Jacobson | The Lateral Organization and Mobility of Plasma Membrane Components[END_REF]. Besides, optical, magnetic, and hydrodynamic traps have been used to apply forces on cytoplasm elements to generate controllable flows [START_REF] Monachino | Watching cellular machinery in action, one molecule at a time[END_REF]. Finally, optogenetics and photo-switchable reagents are used to manipulate the flow generation pathways [START_REF] Hoorens | Reversible, Spatial and Temporal Control over Protein Activity Using Light[END_REF]Maiuri et al., 2015;[START_REF] O'neill | Membrane Flow Drives an Adhesion-Independent Amoeboid Cell Migration Mode[END_REF], while FLUCS (focused-lightinduced cytoplasmic streaming) could induce local and directional thermo-viscous flows to control or redirect intracellular flows (Mittasch et al., 2018a).

Aims of the thesis

The current standard model for mitotic spindle positioning arise from spindle astral MTs contacting the cell cortex. These astral MTs exert pushing or pulling forces from the cortex or the cytoplasm to position and align spindles according to cell shapes (Garzon-Coral et al., 2016;[START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF][START_REF] Pecreaux | The Mitotic Spindle in the One-Cell C. elegans Embryo Is Positioned with High Precision and Stability[END_REF]Salle et al., 2019;Tanimoto et al., 2018). However, in large cells, like zygotes and early blastomeres of several animal embryos, mitotic spindles are small compared to cell size. This is because in small cells, spindle size scales to cell size, but there is an upper limit of spindle length in large cells which prevents MT asters to reach the cortex and sense cell shape [START_REF] Rieckhoff | Spindle Scaling Is Governed by Cell Boundary Regulation of Microtubule Nucleation[END_REF]). Yet, these spindles can stay very stable in the center of large cells for a duration up to few tens of minutes. Thus, the aim of my thesis is to understand the mechanics of mitotic spindles positioning in large cells in the absence of cytoskeletal connections to the cortex. This study could bring new mechanisms that control the position of mitotic spindles and potentially other large organelles.

To achieve this aim, I focused on 3 objectives: 1. To determine if spindles are under viscoelastic forces without astral MTs contacting the cortex.

 I used large sea urchin zygotes as a model system and applied external forces or torques to move or rotate spindles in intact cells with magnetic tweezers to compute viscoelastic parameters like stiffness and drag on spindles.

2. To determine the origins of these viscoelastic forces.

 Probe and characterize cytoplasm material properties, and assay the role of crowding and cytoskeleton meshworks like F-actin in bulk.

To understand the implications of cytoplasm viscoelastic properties on division phenotypes.

 Probe impacts of cytoplasm rheology on asymmetric and oriented divisions.

During early sea urchin embryo development, cells divide into blastomeres which decrease in sizes and have different shapes. At the same time, spindle sizes decrease with cell sizes, leading to the absence of MT cortical contact until around the eight-cell stage. Based on my results from the first project, my data suggest that cytoplasm material properties could contribute to spindle positioning in these early blastomeres. From the literature, when astral MTs reach the cell cortex, they exert cell shape or cell size-dependent forces that position centrosomes or mitotic spindles in the cell center, and orient along the long cell shape axis, or maintain their positional stability as cell size decreases (Garzon-Coral et al., 2016;[START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF]Tanimoto et al., 2016;Tanimoto et al., 2018). Thus, my second project aims to understand if cytoplasm rheology exhibit shape or size sensing properties to maintain spindle position and orientation. To achieve that, I determined cytoplasm restoring stiffness on spindles in blastomeres with changing sizes and shapes, and in cells shaped in chambers. In parallel my colleagues Javad Najafi and Serge Dmitrieff in the team developed 3D simulations in COMSOL Multiphysics to understand the dependence of cytoplasm viscoelasticity on cell shapes and cell sizes for spindle positioning.

RESULTS

Contribution of cytoplasm viscoelastic properties to mitotic spindle positioning

Jing Xie, Javad Najafi, Rémi Le Borgne, Jean-Marc Verbavatz, Catherine Durieu1, Jeremy Sallé and Nicolas Minc

Paper in revision

Main Text

Introduction

The cytoplasm is a heterogeneous composite material crowded with large macromolecular complexes, endomembranes, and entangled cytoskeletal networks (1)(2)(3). These set a hierarchy of pore and mesh sizes which define rheological properties, such as viscosity and elasticity, that impact fundamental processes ranging from the kinetics of biochemical reactions to vesicular transport and cell shape control (4)(5)(6). The importance of cytoplasm material properties for cellular physiology has been recognized and studied for decades, starting from early micro-rheology experiments by Crick or Hiramoto (7)(8)(9). These showed that injected micrometric beads displaced in the cytoplasm exhibit typical viscoelastic responses, with partial positional feedback that move them back towards their initial position. Thus, the cytoplasm features both solid-like and fluid-like behavior, with bulk elastic moduli on the order of ~1-10 Pa, typical of soft gels and viscosities 100-1000 times that of water. More recent studies have now established that these rheological characteristics exhibit size, force or frequency dependence, and provided more refined descriptions of the cytoplasm using frameworks of non-linear viscoelasticity or poroelasticity (3,5,(10)(11)(12)(13). Object size is of particular relevance, given that components floating in the cytoplasm may range over 4-5 orders of magnitudes. Indeed, cytoplasm rheology has been proposed to transit from that of a Newtonian fluid for small particles to that of a more glassy or elastic solid for larger elements (12,14). To date, however, many studies of bulk cytoplasm properties and their functions have focused on relatively small objects, leaving the fundamental problem of how they impact the motion of large organelles, like nuclei or cytoskeletal assemblies poorly explored.

The mitotic spindle is one such large assembly that resides at a precise location in the cytoplasm to specify cytokinesis, and thus the size and position of daughter cells in tissues (15)(16)(17). Spindles are built from dynamic microtubules (MTs) and motors and can take up significant portions of cellular space.

They are commonly associated with networks of nuclear intermediate filaments and endomembranes that form a so-called spindle matrix (18,19). These considerations suggest that their motion in the dense cytoplasm matrix could be associated with large viscous and elastic drags, with potential implications for division positioning and chromosome segregation. Until now however, the literature covering the mechanics of spindle positioning has been dominated by the role of active directed forces from polar cytoskeletal networks. Spindles may for instance decenter or rotate, during asymmetric or oriented divisions, a process typically associated with forces generated by contractile acto-myosin networks (20,21) or astral microtubules (MTs) and associated motors like dynein (22). For symmetric divisions, mitotic spindles reside stably in the cell center. This is thought to be regulated by MTs that grow to contact cell boundaries and exert length-dependent pushing and/or pulling forces on the spindle: when spindles become off-centered, asymmetries in MT lengths and forces act as an effective spring related to cell shape to re-center spindles (23)(24)(25)(26)(27). Net forces applied by MT asters or actomyosin networks may range from few tens to hundreds of piconewtons (pN) (28)(29)(30). A displacement of an impermeable objects with the radius of a spindle of R= 5 µm by a distance d=5 µm, typical of many asymmetric divisions, in a matrix with an elastic modulus of G=1 Pa, like the cytoplasm, would generate a reactive force F=6πR*G*d ~500 pN. Thus, viscoelastic properties of the cytoplasm could in principle be highly relevant to the mechanics of spindle positioning. To date, however, the lack of proper assays to probe cytoplasm rheology at the scale of a moving spindle has impaired testing this fundamental problem for cell organization.

Here, by exploiting large sea urchin cells, where mitotic asters are too short to reach the cell surface, we establish and quantify the direct contribution of bulk cytoplasm viscoelasticity to the mechanics of spindle positioning. We use spindles or large passive oil droplets moved and rotated by calibrated magnetic tweezers in intact cells to probe cytoplasm viscosity and elasticity, at time and length scales representative of spindle movements commonly observed in asymmetric or oriented divisions. We find that the stress exerted by the spindle on the cytoplasm matrix causes it to flow and deform, and exert large reactive spring-like forces that move back this large organelle towards its initial position. Cellularscale flows also shear and rearrange the cytoplasm matrix, dissipating elastic energy and rendering spindle repositioning time-dependent which facilitates rotational over translational spindle motions. Our results place cytoplasm rheology as a hitherto unappreciated element in the force balance that controls the positioning of mitotic spindle and potentially other large organelles.

Results

Viscoelastic forces maintain metaphase spindle position even in the absence of astral MTs contacting the cortex

In many small cells, mitotic spindles are connected to the cell cortex by dynamic MTs which act as dominant force generators to maintain or modulate spindle position (31). In larger cells, limits in spindle size may prevent bounded metaphase mitotic asters from reaching the cell surface (32)(33)(34)(35). Using immunofluorescence and Airy-scan confocal microscopy to detect individual astral MTs around metaphase spindles of 95 µm-sized sea urchin zygotes, we computed a mean distance from astral MTs +tips to the actin-rich cortex of 14.5 +/-0.2 µm (+/-SEM), which corresponds to ~15 % of egg size. Out of ~4000 MTs tracked we found a mean of only 3.35 +/-0.74 MTs/cell that came within 5 µm of the egg surface, a distance typically larger than the actin cortex in these eggs (Fig 1A -1B) (36). These results were confirmed by visualizing MTs in live cells with different probes, as well as with transmission electron microscopy of eggs fixed with optimized methods to reveal MTs (Fig S1A -S1D) (37). In sharp contrast, and as previously reported, interphase and anaphase/telophase asters spanned the whole cell with a mean of 373 +/-7 and 408 +/-24 MTs/cell reaching a distance less than 5 µm to the surface, respectively (Fig 1C and Fig S1E) (32,35). In spite of lacking MT contact with the cell surface, the spindle appeared largely static at the cell center in both position and orientation, over the typical ~10 min duration of metaphase, or over longer time-scales when metaphase was prolonged with the proteasome inhibitor MG132 (Movie S1). Thus, metaphase spindles can robustly maintain their position and orientation for long periods of times, even in the absence of astral MTs contacting the cell cortex.

To directly modulate spindle position and orientation, we implemented in vivo magnetic tweezers to apply forces and torques to spindles in live cells (28). We injected a specific type of magnetic beads in unfertilized eggs, and added sperm to trigger fertilization (30,38). These beads exhibit spontaneous centripetal motion along MT asters and form compact aggregates that stay attached to centrosomes through the cell cycle in these cells, allowing to apply calibrated magnetic forces on centrosomes by approaching a magnet tip. The presence of beads at spindle poles did not affect spindle dimensions, and had no notable effect on cell cycle progression (Fig S1F -S1G). In some embryos, beads often split into two aggregates, following centrosome duplication in interphase or early prophase. In others, the beads only tracked one centrosome, allowing a point force application at a single spindle pole (Fig S1H -S1I). Using those, we applied external forces ranging from ~70 to 700 pN along different axis, and monitored resultant spindle motion. Pulling the spindle with an external force parallel to its long axis, caused the spindle to translate towards the magnet tip, while a force applied orthogonal to the spindle axis caused both translational and rotational motions that tended to align the spindle along the magnetic force axis Movie S2 and S3). Therefore, these experiments allowed to recapitulate spindle movements typically observed in asymmetric or oriented divisions with calibrated forces and torques in intact cells.

Astral MTs that grow to the cortex, to push or pull on spindles, may act effectively as an active elastic system related to cell shape that brings back a spindle to the cell center if its position is perturbed (23,25). In our system, where spindles lack MTs reaching the cell boundaries we anticipated a viscous response to applied forces with no elastic positional feedback. Strikingly, however, the displacementtime curve of spindles moved parallel or orthogonal to their long axis by external forces, exhibited a typical viscoelastic response: spindle motion was first linear at short time-scales below 10-30s, following a viscous regime, but then slowed down, yielding an inflection in the displacement-time curve indicative of internal elastic forces that push or pull back the spindle to oppose external forces (Fig 1F and 1J).

Accordingly, larger forces yielded larger displacement at a fixed time point, and when the force was released, the spindle recoiled back (Fig 1G,1K and Fig S1J). We also noted that at longer time scales above ~100-200 s the curve tended to converge onto another linear regime. In addition, recoils were only partial, with spindles recovering ~ 40-60 % of their initial displacements, often yielding a small asymmetry in division plane positioning (Fig 1G and 1K). These behaviors reflect significant dissipations in the stored elastic energy.

Rotational dynamics of spindles submitted to magnetic torques also exhibited a viscoelastic response, but elastic recoils appeared less pronounced than in translation, causing spindles to tilt and mostly maintain their final orientation at the time of force release (Fig 1L and 1M). Importantly, similar responses were obtained in cells arrested in metaphase with MG132, ruling out putative contributions of aster regrowth and initial cortex contact in late metaphase. Spindle pulling assays were also limited to a small enough displacement that ensured that mitotic asters did not contact the cortex, and spindle re-centering did not exhibit any correlation with the final distance to the cortex . Thus, although these data cannot firmly reject a minor role of MTs contacting the cortex, they suggest that most of this viscoelastic response may be attributed to elements in the cytoplasm. Together these results suggest the existence of viscoelastic restoring forces that maintain spindle positon and orientation, even in the absence of MTs reaching the cell cortex.

Spindle repositioning is caused by viscoelastic restoring forces from bulk cytoplasm material.

To understand the origin of these viscoelastic restoring forces, we tested the role of MTs and dynein as prominent force-generating systems for mitotic spindle positioning. We displaced spindles with magnetic tweezers, and rapidly rinsed cells with Nocodazole or Ciliobrevin D, to affect MTs or dynein motor activity respectively, and monitored the ability of spindles to recoil back (Fig 2A). In controls, the positional recovery followed a single exponential with a decay time-scale of 103 +/-41s and an offset of 43 +/-11%. Nocodazole treated spindles shrank in size to eventually disassemble, over a period of ~5-10 min, but recovered their positions with similar dynamics and offsets as controls. Ciliobrevin D treatment yielded similar response as Nocodazole but with less drastic effect on spindle shape (Fig 2B -2D and Fig S2A -S2F). Therefore, in agreement with the lack of MTs reaching cell boundaries, astral MT polymerization pushing or pulling forces mediated by dynein at the cortex or in the cytoplasm appear to be dispensable for repositioning spindles to the cell center.

To more directly establish that viscoelastic repositioning forces are independent of spindle associated cytoskeletal elements, we sought to recapitulate early micro-rheology assays performed by Crick or Hiramoto (7)(8)(9), but using objects that have similar sizes as mitotic spindles. Inspired by experiments performed in mouse oocytes and in Xenopus extracts (29,39), we embedded hydrophobic magnetic beads in soybean oil, and injected large 30-35 µm oil droplets to move them in the cytoplasm with magnetic tweezers. We purposely used unfertilized eggs, to circumvent the presence of large asters or spindles that could affect droplet motion in the cytoplasm from steric hindrance or by generating active flows and stresses (40) (Fig 2E -2F). In the absence of external forces, oil droplets were immobile in the cytoplasm for long durations of up to 1h, much like female nuclei in these unfertilized eggs (Fig S2G -S2L). Remarkably, droplets exhibited a viscoelastic response to external forces similar to spindles, with a rapid initial constant velocity followed by a saturating elastic regime. Upon force cessation, droplets moved back towards their initial position with similar positional offsets as spindles, but shorter timescales. Droplets viscoelastic recoil occurred independently of whether the droplet had a more centered or off-centered position suggesting that restoring forces are independent of the initial location of the object in the cytoplasm . These data suggest that elements in bulk cytoplasm may generate viscoelastic reactive forces that move spindles or similar-sized passive objects back to their initial positions.

While mitotic spindles are often pictured as polar networks made of MT filaments, the accumulation of membranous organelles or other nuclear intermediate filaments on their MT network has suggested the existence of a spindle matrix, which could render them more physically akin to an impermeable droplet (18,41). Accordingly, by performing Serial Block Face electron microscopy, we found that spindles were covered by packed endomembranes, with an "onion peel arrangement" typical of mitotic endoplasmic reticulum (ER) networks ( 42) (Fig 2L and Movie S5). This endomembrane accumulation is readily evident in DIC images as a smooth area around spindles (Movie S1-S3). Immunofluorescence further validated this accumulation, and segmentation of ER membranes provided an estimate of an upper-bound pore size of 0.2-0.5µm between membranes (Fig 2L -2M). Thus, metaphase spindles may be impermeable to relatively large objects and networks, a property which like oil droplets, allows them to be dragged by viscoelastic flows and forces from bulk cytoplasm.

The cytoplasm applies large elastic and viscous drags to the mitotic spindle.

To quantify restoring stiffness and viscous drags, we fitted experimental data with a three-element Jeffreys' model, which provided the simplest 1D linear model for the observed rising and relaxation curves (43). This model has been employed to describe, among others, the rheology of suspensions of elastic spheres, polymeric liquids, and was previously used to understand viscoelastic properties of the cytoplasm (8,44,45). This model features an elastic spring of stiffness κ, in parallel with a dashpot of viscosity γ1, in series with a second dashpot of viscosity γ2, defining two characteristic time-scales. The first one, τ1= κ/γ1 is the time-scale needed for spindle associated flows to charge the elastic elements in the material. The second, τ2=κ/γ2 sets the rate of plastic yield of these elements or fluidization of the material, which limit elastic restoration and generates an offset in the relaxation (43) (Fig 3A -3B).

Using this model, we computed a restoring stiffness for spindles pulled along their long axis of κ = 55 +/-6 pN/µm (n=19 cells) and 54 +/-6 pN/µm for orthogonal pulls (n= 21 cells). This shows that a displacement away from the cell center of 5% of the cell diameter (~4 µm), generates a restoring force of ~250 pN. These are forces equivalent to that generated by hundreds of molecular motors (46). The stiffness measured for oil droplets was twice higher than for spindles, accounting for their shorter relaxation time-scales (Fig 3C and Fig 2J). One possible interpretation is that oil droplets are actuated in an unfertilized cytoplasm previously reported to be twice stiffer than the mitotic cytoplasm (8,9). An alternative, is that the spindle may be porous to smaller elastic elements in the cytoplasm. These numbers amount to a lower-bound value of the effective bulk modulus, G=κ/6πR, with R the size of spindles, to be on the order of 0.2-0.3 Pa. This is smaller, but in the same range as previous rheological measurements of cytoplasm stiffness in different cell types and extracts (9,11,47). Spindle viscous drags were unexpectedly high with a parallel drag of 4493 +/-847 pN.s/µm and an orthogonal drag of 4498 +/-771 pN.s/µm (Fig 3D). Considering reported values of cytoplasm viscosity in these cells (8), they amount to the drag of an object typically ten times larger than the spindle. This enhanced drag could be explained by the confinement of the spindle by cell boundaries which couples hydrodynamically the spindle with the surface and reduces spindle mobility (48,49). Accordingly, theoretical predictions for a solid object moving in a viscous fluid contained in a sphere, with a radius twice that of the object, yield to a 10-20 fold increase of the object's drag coefficients (50). This suggests that spindle large drags could primarily result from its interaction with the cytoplasm fluid confined by cell boundaries. Overall, these analyses support that the response of spindles to external forces are primarily associated to the viscoelastic properties of the cytoplasm matrix (Fig S3A -S3D).

To compare the efficiency of bulk cytoplasm viscoelastic properties to that of active MT asters and motors, we next measured centering stiffness in anaphase, which follows metaphase by only few minutes. In anaphase, asters regrow to fill the whole cell volume, with an estimate of several hundreds of MTs contacting the cortex (Fig 1C and Fig S1E). Anaphase is thought to imply the largest MT based forces along the cell cycle, as MTs engage with dynein motors at the surface or in the cytoplasm, to separate chromosomes and move asters apart (28,40,51,52). Here, magnetic forces were only applied orthogonal to the spindle axis, as parallel pulls interfered with chromosome force-separation systems (Fig S3E -S3G). While the drags of anaphase spindles were similar to that found for metaphase spindles, a net difference was obtained in term of elastic behavior, with a restoring stiffness for anaphase spindles of 150 +/-14 pN/µm, nearly three times higher than during metaphase (Fig 3E -3G). These results suggest that bulk cytoplasm restoring forces can amount to an equivalent of ~30% of the maximum MT/dynein based pulling system in these cells.

Cytoplasm forces depend on cytoplasm crowding and bulk F-actin meshworks.

Crowding agents in bulk cytoplasm, that contribute to set elastic and viscous properties may include among others, cytoskeletal networks, endomembranes like Yolk granules and mitochondria, or ribosomes which are highly abundant in the cytoplasm (Fig 2L). As a general assay to affect cytoplasm crowding, we immersed cells ~5 min prior to mitosis in diluted or concentrated artificial sea water (ASW) and pulled spindles at metaphase onset. We limited the amplitude of these shocks to a range in which mitotic spindles length, anaphase and cytokinesis were unaffected, but we noted delays in metaphase in hypertonic treatments (Fig S4A -S4D). A hypotonic treatment in 80% ASW caused water to flow into the cells with a minor cell size increase, and reduced spindle restoring stiffness and drags in this diluted cytoplasm to 50.2% and 49.6% of control values respectively. Conversely, a hypertonic treatment in 110% ASW, shrank cells by ~6% and concentrated the cytoplasm, increasing spindle restoring stiffness and drags to 151.4% and 114.4% of control values, respectively . These results demonstrate that viscoelastic reactive forces applied on spindles are directly related to cytoplasm crowding. Furthermore, as one element which has been shown to contribute to bulk cytoplasm material properties we tested the role of F-actin (11,47). Imaging injected labelled utrophin, that binds F-actin, we detected a significant amount of disordered bulk F-actin meshes that surrounded the spindle, though unsurprisingly, the cortex was the most abundant part of the cell. Similar results were obtained with phalloidin staining (Fig S4I). To affect F-actin, we treated cells with Latrunculin B, which disassembled F-actin within minutes, causing the cell surface to soften and shrivel . In Latrunculin B treated cells, spindle repositioning stiffness was 34 +/-5 pN/µm, 1.6 times lower than controls and viscous drags were also significantly lower, and in proportion more reduced than elastic values (2 times lower than controls). As a consequence, the time-scales for both rising and relaxing phases in Latrunculin B were shorter than in controls, so that the re-centering dynamics, converged

Functional implications of cytoplasm mechanics for asymmetric and oriented divisions.

We next investigated an important feature of spindle response, which is the linear rising phase at long time-scale and the offset in the relaxation, which reflect progressive plastic rearrangements or fluidization of elastic elements in the cytoplasm. A prediction of this effect is that a longer force application should dissipate more elastic energy, allowing spindles to stay further from their initial position when the force is released. Accordingly, in the Jeffrey's model, the relaxation offset, a, depends mostly on the ratio of τ2 to the duration of force application, T, with 𝑎 = Therefore, elastic restoration by the cytoplasm may be very effective at short-time scales to stabilize spindles against random thermal or active forces, but vanishes over longer time-scales to facilitate spindle decentration during asymmetric divisions.

As another important read out of this effect, we found that τ2 was significantly smaller in rotation than in

Discussion

Function of bulk cytoplasm rheology in the mechanics of spindle positioning.

How spindles are positioned and oriented in embryos and tissues is a fundamental problem for cell and developmental biology highly relevant to the emergence of developmental disorders and cancer (17,53). One current dogma in many animal cells, is that spindles are placed with respect to cell boundaries by active forces from astral MTs that grow to the cell cortex. Here, by exploring a regime where mitotic MT asters do not reach out to the cortex, we demonstrate that the cytoplasm matrix acts as a viscoelastic medium that hold spindles or other large objects in place, and moves them back if their position is perturbed. Restoring forces are large and shall participate in the force balance positioning spindles and asters, by for instance opposing asymmetric cytoskeleton forces during nuclear or spindle decentration and asymmetric division, or those needed to center asters at fertilization (22,38,49). Our findings also suggest that restoring forces vanish faster in rotation than in translation, which we attribute in part to the geometry of rotational shear flows, and anisotropies in plastic yields in the cytoplasm material. Therefore a tilt acquired during force exertion is better maintained than a positional offset. This could allow an asymmetric cortical domain enriched in motors to reorient spindles without creating an asymmetric division, a phenotype commonly observed in many tissues (17,54,55).

It is important, however, to outline that at rest, the cytoplasm does not apply any net force, and cannot a priori center or decenter spindles, asters or nuclei. In large cells, this is achieved earlier in the cell cycle by interphase MT asters that reach to the cell boundaries, and pre-position centrosomes before metaphase (56). We propose that the cytoplasm matrix holds these prepositioned centrosomes in place [START_REF] Chaigne | F-actin mechanics control spindle centring in the mouse zygote[END_REF]. As spindles scale with cell size, cytoplasm rheology could very well be also relevant to spindle positioning in smaller cells lacking proper mitotic asters, or in which astral MTs do not reach the cell surface [START_REF] Lancaster | Mitotic rounding alters cell geometry to ensure efficient bipolar spindle formation[END_REF][START_REF] Stevens | From stem cell to embryo without centrioles[END_REF][START_REF] Khodjakov | Centrosome-independent mitotic spindle formation in vertebrates[END_REF]. However, an important open question, is how much these properties contribute in cells where numerous MTs clearly contact the cortex to exert forces that stabilize asters or spindles (28,38).

One possibility is that the impact of cytoplasm elasticity is reduced as astral MTs and motors push back organelles and network away from spindles, effectively confining elastic elements to a zone much closer to the cortex. Another possibility, which we favor, is that transport by motors along MTs could fluidize the cytoplasm space occupied by mitotic asters, effectively decreasing the elastic response of the cytoplasm [START_REF] Carlini | Microtubules Enhance Mesoscale Effective Diffusivity in the Crowded Metaphase Cytoplasm[END_REF]. Further work will be required to understand how active polar cytoskeleton forces and material properties of bulk cytoplasm are integrated to regulate cell division and organization.

Probing cytoplasm material properties at the scale of mitotic spindles.

The cytoplasm is a complex material, whose rheological properties and their impact on cellular functions are emerging as important concepts in cell biology. Here, we probed cytoplasm rheology at scales and speeds, typical of physiological mitotic spindle repositioning and reorientation. In line with previous rheological description of the cytoplasm for small objects (8,9), we find that a simple linear 1D viscoelastic Jeffreys' model can predict key rheological behavior including rising and relaxation curves, and time-dependent elastic dissipation. Although this suggests that we can treat the effect of the cytoplasm as that of an "inert" Jeffreys' material, these physical properties, are likely dictated and regulated by energy-driven active metabolic processes and random motor motion (4,11,13,14). We also envision that more advanced non-linear viscoelastic or poroelastic description of the cytoplasm could capture many of the features we report in here. Elasticity could for instance be graded, being stiffer close to the cortex and softer in the cell interior, due to the progressive stacking of organelles and networks. Inspections of electron micrographs do not immediately support this view, at least in this system. In addition, viscoelastic recoils of droplets moved from different initial locations in the cell (not only the cell center) suggest a more homogenous elasticity (Fig 2K). Poroelasticity would picture the cytoplasm matrix as a porous elastic solid, with a small pore size bathed in cytosolic liquid (5,[START_REF] Mitchison | Implications of a poroelastic cytoplasm for the dynamics of animal cell shape[END_REF]. As spindles would compress this poroelastic matrix, slowly dissipating pressure gradients would form and push back spindles in place.

Beyond physical frameworks to describe cytoplasm rheology, another important question is which elements define relevant material properties of the cytoplasm at the spindle scale. Meshworks of bulk F-actin filaments contributed to a fraction of ~40-50% of viscous and elastic behavior, acting as one important crowding agent at this scale. Intermediate filaments, like keratin or vimentin could not be tested here, but have been proposed to influence elastic properties of egg cytoplasm extracts (47). In addition, we propose that organelles like mitochondria, yolk granules or lysosomes could behave as dense suspensions of small elastic colloids, which generate mesoscopic elasticity as is known for classical suspension such as paints or bitumen (44). Further experiments of cytoplasm reconstitution will be required to determine which of these elements are dominant or dispensable at the spindle scale, or assay the role of their potential interactions.

Finally, our experiments comparing spindles and oil droplets, raise interesting questions on the physical nature of the mitotic spindle itself. In the context of our assays, we propose that spindles behave as objects impermeable to components larger than a fraction of a micron. Recent report suggest that small particles of ~10nm in size can diffuse in and out of spindles [START_REF] Carlini | Microtubules Enhance Mesoscale Effective Diffusivity in the Crowded Metaphase Cytoplasm[END_REF]. Spindles may thus be largely porous to proteins and molecular complexes such as ribosomes, so that elastic and viscous forces they experience may only arise from the response of larger organelles and networks in the cytoplasm. Mitotic spindles also feature important elastic properties, with axial stiffness measured in vitro to range around 80-900 pN/µm [START_REF] Shimamoto | Insights into the micromechanical properties of the metaphase spindle[END_REF]. In our experiments, we detected minor lengthening of mitotic spindles under force, which amounted to similar values (data not shown). Recent experiments on MT asters also support models of more porous or elastic structures with important implications for mechanisms of centrosome movement (40). By bringing numbers which have been largely missing in the literature, force measurements within live cells will strongly impact our understanding of the very basic mechanisms of cell organization and morphogenesis.

Material and Methods

Sea urchin gametes

Purple sea urchins (Paracentrotus lividus) were obtained from Roscoff Marine station (France) and maintained at 16°C in aquariums of artificial sea water (ASW; Reef Crystals, Instant Ocean). Gametes were collected by intracoelomic injection of 0.5 M KCl. Sperm was collected dry and kept at 4°C and used within 1 week. Eggs were rinsed twice with ASW, kept at 16 °C, and used on the day of collection.

Unfertilized eggs were transferred and adhered on protamine-coated glass-bottom dishes (MatTek Corporation) after removing the jelly coat through an 80-μm Nitex mesh (Genesee Scientific), injected and fertilized under the microscope.

Chemical inhibitors

Inhibitors were prepared in 100X stock aliquots in dimethyl sulfoxide (DMSO). To block metaphase, eggs were incubated for 30 min in 50 μM MG132 (Sigma-Aldrich) before fertilization. Nocodazole (Sigma-Aldrich) and Ciliobrevin D (EMD Millipore), were respectively applied ~3 min and ~5 min before spindle relaxation at a final concentration of 20 µM and 50 μM, respectively. Latrunculin B (Sigma-Aldrich) was added ~5 min before pulling the spindle at a final concentration of 20 μM. Blebbistatin (Sigma-Aldrich) was added 15 min post fertilization at a final concentration of 100 μM.

Hypotonic and Hypertonic shocks

To manipulate cytoplasm density with hypotonic or hypertonic shocks, ASW was prepared to 80% or 110% of its normal content, respectively, by adjusting the amount of DI water to salts mixtures. Eggs were rinsed with these different water at prometaphase, typically 5 min before force application. At these sea water concentrations, cells formed normal spindles and underwent a normal cytokinesis.

Metaphase was longer in concentrated ASW. Much lower concentration of 50% ASW were also assayed, but led to large leaks of cytoplasm from the site of injection that dragged spindles out of cells.

Higher concentration of 120% or 150% ASW led to cytokinesis failure.

Immunostaining

Immunostaining was performed using procedures described previously (35). Samples were fixed for 70 min in 100 mM Hepes, pH 6.9, 50 mM EGTA, 10 mM MgSO4, 2% formaldehyde, 0.2% glutaraldehyde, 0.2% Triton X-100, and 400 mM glucose. To reduce autofluorescence, eggs were then rinsed 3 times in PBS and placed in 0.1% NaBH4 in PBS freshly prepared, for 30 min. Eggs were rinsed with PBS and PBT (PBS + 0.1% TritonX) and blocked in PBT supplemented with 5% goat serum and 0.1% bovine serum albumin (BSA) for 30 min. Samples were rinsed with PBT before adding primary antibodies. For MT staining, cells were incubated for 48 h at 4°C with a mouse anti-α-tubulin (DM1A;

Sigma-Aldrich) primary antibody at 1:5,000 in PBT, rinsed 3 times in PBT and incubated for 4 h at room temperature with anti-mouse secondary antibody coupled to Dylight 488 (Thermo Fisher Scientific) at 1:1,000 in PBT for 4-5h. For ER staining, samples were treated with a rabbit anti-KDEL (Invitrogen) primary antibody at 1:2,000 in PBT, for 48h, rinsed in PBT and incubated with an anti-rabbit secondary antibody coupled to Dylight 650 (Thermo Fisher Scientific) at 1:1,000 in PBT. To stain F-actin, samples were incubated for 1h in a solution of Rhodamine Phalloidin at 4U/ml in PBT. Eggs were washed three times in PBT then twice in PBS, transferred in 50% glycerol in PBS, and finally transferred into mounting medium (90% glycerol and 0.5% N-propyl gallate PBS). Fixations of cells treated with Nocodazole, Ciliobrevin D, and Latrunculin B were performed 10 min after adding the drug (Fig S2F ).

Fixation for electron microscopy

To visualize astral MTs around spindles, one cell stage zygotes were fixed in metaphase (1h postfertilization) in 0.4M sodium acetate, 2% glutaraldehyde (Electron Microscopy Sciences) during 30sec and in 0.4M sodium acetate, 2% OsO4 (Electron Microscopy Sciences) during 30min [START_REF] Asnes | Cell cleavage. Ultrastructural evidence against equatorial stimulation by aster microtubules[END_REF], and transferred for 1h to 2% glutaraldehyde, 1% Osmium, then washed 15 min with the same buffer and 2 x 15 min in water. Dehydration was performed using graded concentrations of ethanol in water for 10 min each. Resin infiltration was performed by incubating 30 min in a 30% Agar low viscosity resin (Agar Scientific Ltd), then 30 min in a 50% Agar low viscosity resin, 30 min in a 75% resin followed by a 1h and overnight incubation in pure resin. The resin was then changed twice and the samples were incubated for 1 hour prior to inclusion in BEEM capsules and 18 hours polymerization at 60 °C. 70 nm sections were obtained using an EM UC6 ultramicrotome (Leica), and post-stained in 4% aqueous uranyl acetate followed by lead citrate.

For , 190215).

Live-probe for the cytoskeleton

TauMBD-mCherry constructs were expressed in BL21 (DE3)-RIL (Agilent) cells, purified on a Ni-NTA resin (Invitrogen) and dialyzed with PBS buffer using a 10000MWCO dialysis cassette (ThermoScientific). Tubulin-Atto565 was a gift from Benjamin Lacroix. Tubulin was purified from pig brains and labelled with NHS-ester-ATTO 565 (ATTO-TEC) [START_REF] Lacroix | Microtubule Dynamics Scale with Cell Size to Set Spindle Length and Assembly Timing[END_REF]. UtrCH-AlexaFluor488 was a gift from Peter Lenart. UtrCH recombinant protein was expressed in E.coli, purified on a Ni-NTA resin (Qiagen), and labelled with AlexaFluor 488 succinimidyl ester (Invitrogen) [START_REF] Bun | A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes[END_REF].

Magnetic force application

Magnetic tweezers were implemented as described previously (30,38). The magnet probe used for force applications in vivo was built from three rod-shaped strong neodymium magnets (diameter 4 mm; height 10 mm; S-04-10-AN; Supermagnet) prolonged by a sharpened steel piece with a tip radius of ~50 μm to create a magnetic gradient. The surface of the steel tip was electro-coated with gold to prevent oxidation. The probe was controlled with a micromanipulator (Injectman 4, Eppendorf), mounted on an inverted epifluorescent microscope.

Super-paramagnetic particles (diameter 800nm; NanoLink; Solulink) with spontaneous minus enddirected motion were used to apply magnetic forces on the spindles (30,38). To prepare beads for injection, a solution of 10 µl of undiluted streptavidin-beads was first washed in 100 μL of washing To image spindle displacement and rotation under force, unfertilized eggs stuck on protamine-coated glass dishes were incubated in 10 μg/ml Hoechst (Sigma-Aldrich) and subsequently injected with magnetic beads, and fertilized. At metaphase, chromosomes marked with Hoechst, lined up along the metaphase plate, and the spindle was easily visible as a dumbbell-shaped smooth region in DIC (Differential Interference Contrast), presumably because of its association with the ER (Movie S1).

These DIC images allowed to select spindles that were planar and to define the long and short axis directions for force applications. The magnet was then rapidly moved close to the eggs and held at a fixed position either at a position along the spindle axis (for parallel pulls) or orthogonal to the axis for orthogonal pulls (see Movie S2-S3). The end of metaphase was captured as the first time-point when chromosome separated, and the end of anaphase as the first time-point of cleavage furrow ingression.

For experiments implicating long force application (Fig 5 ), the magnet was progressively moved away from the egg using the automatic stage of the microscope.

To actuate oil droplets, unfertilized eggs were placed on protamine-coated glass-bottom dishes. To pull the oil droplets in the cytoplasm, a suspension of 10 µl of 1.2 µm hydrophobic superparamagnetic beads (magtivio, MagSi-proteomics C18) was washed in 100 µl of 30, 50, and 70 percent ethanol solution. It was then dried in vacuum for 20 minutes and re-suspended in 5 µl soybean oil (Naissance; Huile de soja). Preparation of glass capillaries and injection were done with the same methods as for other beads injection described above. All the injected eggs in each sample were surveyed to select the oil droplets with a sufficient amount of beads for pulling. After approaching the magnet, beads inside the oil formed aggregates and slowly moved toward the magnet while the oil droplet was stationary, until the aggregate contacted the oil-cytoplasm interface at the side facing the magnet tip. Large aggregates could not usually cross the interface due the oil surface tension, aggregate size, and hydrophobic properties of the beads, and were used to pull oil droplet in the cytoplasm. Upon force application, the magnet was quickly retracted when the oil distance to the cell cortex was ~10 µm, which caused the aggregate to detach from the oil/cytoplasm interface and the droplet to relaxed backward along the previous pulling force axis (Supplementary Fig 2K and 2L).

Imaging

Time-lapses of spindles and oil droplets moving under magnetic force were recorded on two inverted microscope set-ups equipped with a micromanipulator for magnetic tweezers, at a stabilized room temperature (18-20°C). The first set-up was an inverted epifluorescence microscope (TI-Eclipse, Nikon) combined with a complementary metal-oxide-semiconductor (CMOS) camera (Hamamatsu), using a 20X dry objective (Apo, NA 0.75, Nikon) and a 1.5X magnifier, yielding a pixel size of 0.216 μm.

The second one was a Leica DMI6000 B microscope equipped with an A-Plan 40x/0.65 PH2 objective yielding a pixel size of 0.229 µm, equipped with an ORCA-Flash4.0LT Hamamatsu camera. Both microscopes were operated with Micro-Manager (Open Imaging).

To visualize MTs or bulk F-actin with live probes, live imaging was performed on a spinning-disk confocal microscope (TI-Eclipse, Nikon) equipped with a Yokogawa CSU-X1FW spinning head, and an EM-CCD camera (Hamamatsu), using a 60X water-immersion objective (Apo, NA 1.2, Nikon), equipped with a 3D micromanipulator. Imaging of immunostained cells was performed on a confocal microscope (Zeiss, LSM980) coupled with an Airyscan 2 module in confocal mode with a 63X water immersion objective (NA, 1.4; C-Apo; Zeiss).

Electron Microscopy

Thin sections of eggs fixed as described above were observed by transmission electron microscopy (TEM) at 120 kV with a Tecnai12 transmission electron microscope (Thermo Fischer Scientific) equipped with a 4K Oneview camera (Gatan). For Serial Block Face scanning electron microscopy (SBF-SEM), samples mounted on aluminum pins were trimmed and inserted into a TeneoVS SEM (Thermo Fisher Scientific). Acquisitions were performed with a beam energy of 2.7kV, a current of 400pA, in LowVac mode at 40Pa, a dwell time of 1µs per pixel and sections of 100nm. The pixel size was 20nm.

Magnetic force calibration

Magnetic forces were calibrated in vitro following procedures described previously (30,38). The magnetic force field created by each magnet tip used was first characterized by pulling 2.8 μm monodispersed magnetic beads (Dynal) in a viscous test fluid (80% glycerol, viscosity 8.0×10-2 Pa sec at 22°C) along the principal axis of the magnet tip. Small motion of the fluid was subtracted by tracking 4 μm non-magnetic tracer fluorescent in the same solution. The speed of a magnetic bead V was computed as a function of the distance to the magnet, representing the decay function of the magnetic force, and fitted using a double exponential function.

To compute the dependence of the force on aggregate size, bead aggregates from the same beads as those used in vivo in sizes ranging from 2 to 8 μm, similar to that observed in cells, were pulled in the same fluid as above. The speed Va was measured and translated into a force using Stokes' law F=6πηRVa, where η was the viscosity of the test fluid, R the aggregate effective radius defined using the longest length L1 and the length perpendicular to the longest axis, L2, as R= 1 2 √𝐿 1 𝐿 2 . The force-size relationship at a fixed distance from the magnet was well represented and fitted by a cubic function.

These speed-distance and force-size relationships were combined to compute the magnetic forces applied to spindles inside cells as a function of time, from the size of aggregates at spindle poles and their distance to magnet tips.

Magnetic force calibration for oil droplets experiments followed the exact same procedure as above but establishing the force-size relationships for aggregates of hydrophobic beads used in oil droplets (Fig S2H). In live-cell experiments the sizes of the bead aggregates inside the oil droplets were measured at three different positions in the oil in the bright field, and were averaged.

Analysis of spindle position, orientation, and oil droplets position

Spindle displacement and rotation time-lapses were rotated to align the initial spindle axis to the horizontal X-axis. Magnet tip position was recorded in DIC and the position of bead aggregates were tracked from their fluorescence signal. Spindle position and orientation were processed manually in Fiji by tracking the centers of two smooth disks, which correspond to spindle poles in the DIC channel. This allowed to compute spindle length, center as well as angles with the magnetic force axis. Spindle displacements and magnetic forces were then projected along the horizontal X-axis for parallel pulling or along the Y-axis for orthogonal pulling. Chromosome plate position was also tracked but we often noticed some small delay in the motion of chromosomes as compared to that of spindle poles, presumably caused by some time-scales associated with internal elastic structures that hold chromosomes. Oil droplets were tracked using the TrackMate plugin in Fiji [START_REF] Tinevez | TrackMate: An open and extensible platform for single-particle tracking[END_REF] when the contrast was sufficient, and were checked and corrected manually in some cases. Displacement of the oil droplet was corrected when the egg had displaced during the pulling.

Tracking of MT distance to the cortex

Airyscan confocal images stained for MTs and F-actin were projected on a mid-section 2 μm thick, and planar spindles were selected. The horizontal distance between MT ends to the actin cortex was measured, by tracing lines along each MTs to the first border of the F-actin signal using Fiji.

MTs contacting the cortex were also counted from confocal images without F-actin staining in larger zsections of ~30 μm in thickness and the distance between their ends and the closest surface was measured.

Segmentation of endomembranes from SBF-SEM images

SBF-SEM images were processed using Ilastik a machine-learning-based interactive tool [START_REF] Berg | ilastik: interactive machine learning for (bio)image analysis[END_REF]. The Pixel classifier was trained iteratively with 3 labels (ER; yolk & mitochondria; cytosol) on a cropped image until a satisfying accuracy was reached for endomembrane compartments. Pixel classification maps were then extracted from the full scale dataset.

Viscoelastic parameter calculation

Spindle displacement and rotation were fitted with a Jeffreys' model using a custom code written in Matlab (Mathworks) to compute viscoelastic parameters. For the rising phase, the spindle position was fitted using:

𝑑(𝑡) 𝐹(𝑡) = 1 𝜅 [1 -𝑒 -𝑡 𝜏1 ] + 𝑡 𝜅𝜏2 , ( Equation 1)
where d is the displacement along the X-axis or Y-axis (for parallel or orthogonal pulling respectively), and F is the magnetic force. These fits allowed to compute the restoring stiffness, κ, and the viscoelastic time-scales, τ1 and τ2 corresponded to the Jeffreys' viscoelastic timescales, allowing to compute viscous drags on spindles as 𝛾 = κ𝜏 1

Spindle orientation was fitted similarly, using:

𝜃(𝑡) 𝑇(𝑡) = 1 𝜅 [1 -𝑒 -𝑡 𝜏1 ] + 𝑡 𝜅𝜏2
(Equation 2)

where θ, is the spindle axis angle and T the torque computed as the force projected orthogonal to the spindle long axis and multiplied by half the spindle length. This allowed to compute a rotational stiffness, κ, and viscoelastic time-scales corresponding to rotational behavior under force.

Spindle relaxation dynamics was fitted using:

𝑑(𝑡) 𝑑 (0)
= (1 -𝑎)𝑒 -𝑡 𝜏1 + 𝑎 (Equation 3)

where t = 0 corresponds to the time of the end of force application, to compute the relaxation offset a and the decay time-scale τ1. The same equation was used for rotational relaxation but replacing d by θ.

To estimate the enhanced drag of spindles associated with the confinement by the cell boundaries, we used an effective spindle radius defined as: 𝑅 𝑠 = 1 2 √𝐿 𝑠 𝑊 𝑠 , where Ls and Ws the length and the width of the spindle. The enhanced drag of a rigid sphere inside a spherical confinement, is computed as 𝛾 𝑐 = 𝐾𝛾 , were K is a wall correction factor and γ=6πηR the drag in an infinite medium (50). K is computed as

𝐾 = 1-𝜆 5 1- 9 4 𝜆+ 5 2 𝜆 3 - 9 4
𝜆 5 +𝜆 6 (Equation 4)

With λ was the ratio between the spindle radius and that of the egg.

Fit of the data were obtained for each single force experiment, for spindles or oil droplets, using Nonlinear least squares method in Matlab curve fitting. Various combinations of start points of fit parameters were tried and chosen in a way that maximum R-square and tighter confidence interval were achieved. Curves were also visually inspected to ensure that they passed through more points and were not biased with respect to the data points. Finally, other 2 or 3-element models than Jeffreys' were also tested, but failed to provide better fit of all behaviors than this model.

Flow analysis

The recorded spindle pulling images in DIC were analyzed using the particle image velocimetry PIVlab tool in Matlab [START_REF] Thielicke | PIVlab -Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB[END_REF]. The exterior of the egg was masked to be excluded from the analysis. Contrast limited adaptive histogram equalization (CLAHE) and two dimensional Wiener filter with accordingly windows of 20 and 3 pixels widths were applied on the images in the pre-processing steps for denoising.

Image sequences were investigated in the Fourier space by three interrogation windows with 64, 32, and 16 pixels widths and 50% overlapped area. The spline method was used for the window deformation and subpixel resolution obtained by two-dimensional Gaussian fits. The distribution of the velocity components of the vectors for each set was visually inspected and restricted to remove the outliers in the post-processing stage. Moreover, two other filters based on the standard deviation and local median of velocity vectors were applied to validate the vector fields. The output vector fields after smoothing were used for the analysis. The vector field was temporally averaged over the pulling or relaxation phase except when tracking imaginary tracers.

For measuring the shear rate in the pulling phase, the vector field on the half side of the egg close to the magnet was spatially averaged along the pulling axis (Fig S6B andS6G). Shear rate was calculated as the ratio of the maximum of the velocity component in the direction of pulling divided by the distance taken for the velocity component to drop to zero. Maximums of the velocity components were obtained by a one dimensional Gaussian fits. Spatial autocorrelation in direction was computed as c(r) = <ŝ(r+r0).ŝ(r0)>, where ŝ and r were the unit vector in the direction of velocity and distance, respectively, and the results were averaged over initial positions r0. The crossing point of the spatial autocorrelation function with the x axis was considered as the vortex size. Divergence of the vector field was calculated by summation of partial derivatives of its components using central difference. Vorticity was measured as ω= ∇×v where v was the vector field. Vector fields were also used to follow the path of 100 equally spaced tracers along the line perpendicular to the spindle axis by excluding the spindle itself [START_REF] Zhang | Swarming dynamics in bacterial colonies[END_REF]. To this aim, the corresponding velocity vector in the selected point was obtained based on bilinear interpolation. The interpolated velocity vector and initial position were used to solve the ordinary differential equation by Euler's method and find the position of the tracer in the next frame. This procedure was continued through all pulling frames.

To compare advection by flows and diffusion, the Peclet number was calculated as Pe=Lu/D with L, u, and D the characteristic length, flow speed, and diffusion coefficient, respectively. Taking the viscosity of the cytoplasm to be 1,000 times that of the water ( 8), an effective temperature for the active cytoplasm of ~10 times that of room temperature [START_REF] Egelman | Comprehensive Biophysics[END_REF], we computed a diffusion coefficient of ~10 -2 µm 2 /s for a 1 µm radius vesicle. Measured flow speeds in the cytoplasm was in the order of 10 -2 µm/s and eggs of ~100 µm diameter. This leads to the Peclet number ~10 2 indicating that advection dominates over diffusion for objects of this size.

Statistical analysis

All experiments presented in this MS were repeated at least twice and quantified in a number of cells or events detailed in each figure legend. Statistical and correlation analyses were carried out using

Cytoplasm viscoelastic properties as a shape-sensing system for mitotic spindle positioning

Jing Xie, Javad Najafi, Serge Dmitrieff and Nicolas Minc

Manuscript in preparation

Cytoplasm viscoelastic properties as a shape-sensing system for mitotic spindle positioning Summary:

Global astral microtubule forces that position centrosomes or mitotic spindles, have been shown to exhibit cell size or cell shape-dependence, allowing spindles for instance to orient along the long cell shape axis, or to maintain their positional stability as cell size decreases [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF]Tanimoto et al., 2016;Tanimoto et al., 2018). As shown in Result.1, I found that the cytoplasm material may serve to maintain the mitotic spindle in the center of large cells by opposing its displacement with elastic drags, which restore spindle centered position. To test if the effect of cytoplasm properties may exhibit size or shape dependence, I initiated a series of experiments to manipulate cell shape and size independently and compute cytoplasm viscous and elastic drags on moving spindles with magnetic tweezers. In parallel my colleagues Javad Najafi and Serge Dmitrieff in the team developed 3D simulations in COMSOL Multiphysics in which a solid body with the shape of the spindle is moved by external forces in a viscoelastic fluid confined by boundaries of different shapes and sizes.

Initial experiments and simulations suggest that cytoplasm restoring stiffness on spindles is highly dependent on cell shape, but not on cell size (will be proved with precise experiments).

Cytoplasm restoring stiffness increases with the cell aspect ratio, and is also higher orthogonal to the long cell shape axis. We propose that these effects emerge from the hydrodynamic coupling of the spindle with cell boundaries, which increases viscous and elastic drags imparted by the cytoplasm on a moving spindle.

Results:

As embryogenesis progresses sea urchin embryos transit from a spherical one-cell zygote to two hemispherical blastomeres and then four elongated ellipsoidal blastomeres. We first displaced and rotated spindles in 2-cell stage blastomeres with magnetic tweezers. These cells have half the volume of zygotes, but exhibit hemi-spherical shapes, with spindles that are assemble aligned along the long flat dimension (Fig. 1). The 2-cell stage cell long axis is similar as that at the one cell stage but spindles are smaller, likely scaled to cell volume (Fig. 2C), and still lacked prominent MT contact with the cortex. Magnetic beads were injected before fertilization and partitioned in different blastomeres during centrosome duplication and cell division. Similar as pulls in the one-cell stage, spindles with beads bound to one spindle pole were displaced and/or rotated by magnetic forces applied parallel or orthogonal to the spindle axis (Fig. 1 A-B, E-F). As documented in the one cell stage, the spindle exhibited a viscoelastic response that was well fitted by a Jeffreys 3-element fluid model. Interestingly, in parallel pulls, both spindle drags and restoring stiffness were slightly increased by ~a factor of 1.2X as compared to the one cell stage. In addition, in contrast with the one cell stage in which stiffness and drags are nearly equal in parallel and orthogonal pulls, in these hemispherical cells, orthogonal restoring stiffness was ~1.4X higher than parallel stiffness (Fig. 1 C-D, G-H). As a consequence, a displacement orthogonal to the long axis was much better restored than a displacement along the long axis (Fig. 1K). These results suggest that, much like for positioning systems based on astral MT pushing or pulling forces, cytoplasm elastic restoring forces may be highly dependent on cell shape.

Similar experiments were performed on spindles at the four cell stage where cells have one quarter the volume of zygotes and exhibit ellipsoidal shapes with spindles aligning along the long axis (Fig. 2A-B). Spindle length decreased again presumably scaling with the cell volume.

In parallel pulls, we found that cytoplasm restoring stiffness increased again at the four cell stage (Fig. 2D-2G). Together, although cellular dynamics or other properties could change among different cell stages, these results suggest that elastic drags may be highly dependent on the short axis and/or the aspect ratio of the cell. In order to directly assay the impact of cell shape or aspect ratio on cytoplasm viscoelastic forces, we designed micro-chambers made in SU8 Resin with various dimensions and shapes.

These chambers allow to control the shape of zygotes, as well as to inject magnetic beads and to apply magnetic forces to spindles. Cells are maintained/attached in the chamber with protamine coating. I provide below preliminary experiments which suggest that we can combine magnetic tweezers assays with cell shape manipulation. In the near future I will To understand if and how cytoplasm material viscoelastic properties may confer shapedependent restoring stiffness to mitotic spindles, Javad Najafi and Serge Dmitrieff implemented finite-element simulations in COMSOL Multiphysics. We simulate the translation and rotation of spindles embedded in a viscoelastic fluid under an applied constant force in different boundary conditions. The spindle is modeled as a rigid object and cytoplasm as a viscoelastic fluid with viscosity values similar to those measured by us or found in the literature, and two time-scales which represent the viscoelastic behavior. Importantly, the fluid is assumed to obey no-slip conditions at the interface with the spindle and with the "cell" boundaries. These simulations use the module CFD (Computational Fluid Dynamics) and solid-liquid interface, and describe the material using an Oldroyd-B model, which is equivalent to the Jeffreys model used to analyze our experiments, provided proper conversion between the viscoelastic constant used between the two models.

A time dependent model was implemented and a constant step force was applied to one half of an ellipsoid (the spindle) using a boundary load. The ellipsoid was placed in the center of mass of the geometry which coincides with the origin of the coordinate system. The cell shape and size in two and four cell stages were respectively half and one fourth of the single cell (Fig. 4). The force was applied along the x direction to translate the ellipsoid for a certain time and then released. The same force was applied along the z direction to rotate the ellipsoid. All the parameters for the different runs were kept identical and only the geometry of the external boundary conditions was changed (Table 1). The spindle displacements under force/torque and their relaxations were predicted from the simulations and accounted for most of the observed experimental results (Fig. 5). First, in a normal spherical cell, the simulations reproduced the viscoelastic behavior and partial recoils of spindles, with well-matched viscous and elastic drags, and recovering offsets. Second, as cell shape was changed either to reproduce the geometry of 2-cell or 4-cell blastomeres, the restoring stiffness gradually increased as in experiments. Further a simulation of a cell with same size as the zygote but shaped in a rectangle (to reproduce experiments in micro-chambers)

showed that changing cell shape or aspect ratio is sufficient to modulate restoring stiffness. In the simulations, this effect was most likely caused by an enhanced hydrodynamic coupling between the spindle and the boundary as the short axis of the cell is reduced, and thus the spindle becomes closer to the cell surface. Finally, we also simulated the response of the spindle to a parallel or orthogonal pull at the two-cell stage blastomeres. As in experiments, we found that in rotation the stiffness was higher than in translation, presumably again, because as spindles approach the surface when pulled orthogonal to their long axis the effective stiffness increases because of proximity of the surface and the no-slip condition of the fluid.

Discussions/future directions

These experiments and models suggest that the impact of the cytoplasm viscoelastic properties will greatly vary with cell shape. In more elongated cells, with a constant volume, the stiffness along the long axis will increase with the aspect ratio. We interpret this effect as a result of the reduced distance between the spindle and the cell surface which increases the coupling of the spindle with the fixed boundary condition by the viscoelastic cytoplasm. In effect, this will tend to reduce the positional fluctuations along the long axis as cells become more and more elongated, potentially limiting errors in size repartition between the two daughter cells at cell division. A second interesting output is that stiffness becomes anisotropic when a cell is elongated. The stiffness along the short axis being high than along the long axis. This effect could allow positional fluctuations to be smaller in the transverse direction as compared to the longitudinal direction, which when normalized to cellular dimension allows to maintain a nearisotropic positional stability of the spindle. It is important to stress that these findings are still preliminary, and in a near future, I will complete data sets on manipulated cell shapes and simulations, to provide a more complete work on how the cytoplasm may contribute to positon or stabilize spindles in cells with varying shapes and dimensions. and orient the mitotic spindle in large cells, which is different from the current dogma in many cell types where spindles are placed by active forces from astral MTs that reach to the cell cortex. These viscoelastic properties come from cytoplasm materials, for instance, the bulk factin meshworks account for ~40%-50% of the cytoplasm elastic and viscous behavior at the scale of spindles. This suggests the existence of other elastic elements in the cytoplasm.

Intermediate filaments, like keratin and vimentin could be good candidates, as they have been reported to contribute mechanical strength in vivo in nerve cell axons, muscle cells, and epithelial cells (Andra et al., 1997;Alberts et al., 2002). However, their functions for the elasticity of Xenopus egg cytoplasmic extracts seemed to be minor [START_REF] Valentine | Mechanical Properties of Xenopus Egg Cytoplasmic Extracts[END_REF]. In the lab, we still need to image intermediate filaments in sea urchin embryos and test their mechanical functions by, for example, the injection of the anti-cytokeratin antibody C11 which could block the cytokeratin mechanical properties [START_REF] Valentine | Mechanical Properties of Xenopus Egg Cytoplasmic Extracts[END_REF]. In addition, the cytoplasm is filled with particles like yolk and mitochondria, as shown in the EM image (Figure 1). I anticipate that these suspending particles could behave as small elastic colloids to generate mesoscopic elasticity in the cytoplasm [START_REF] Frohlich | Theory of the rheological properties of dispersions[END_REF]. This hypothesis could be tested in vitro with egg extracts by assaying elasticity with different concentration of particles.

In my model, where MT asters do not grow to the cortex, cytoplasm viscoelasticity is sufficient to hold mitotic spindles or other large objects in place and move them back if their positions are perturbed. These restoring forces are large and of similar magnitude as the MT forces measured during sperm aster centration in the same model system (Tanimoto et al., 2018), and ~3X higher than the MT forces associated to metaphase spindle maintenance at the cell center in C.elegans (Garzon-Coral et al., 2016). The cytoplasmic elastic forces could be highly relevant to spindle positioning in smaller cells lacking astral MTs or where mitotic asters do not contact the cell surface [START_REF] Khodjakov | Centrosome-independent mitotic spindle formation in vertebrates[END_REF][START_REF] Stevens | From stem cell to embryo without centrioles[END_REF]. But how much these forces contribute to cells where numerous MTs clearly contact the cell cortex remains unclear [START_REF] Pecreaux | The Mitotic Spindle in the One-Cell C. elegans Embryo Is Positioned with High Precision and Stability[END_REF]Tanimoto et al., 2018a). My previous data showed that cytoplasm restoring stiffness in metaphase accounts for around 30% of that in anaphase, where asters regrow to fill the whole cell volume and to imply the largest MT/dynein based forces along the cell cycle. This is very interesting as it suggests that the cytoplasm elastic contributions could be unexpectedly high in cells where mitotic asters can reach the cortex and stabilize spindles.

To test this hypothesis, one could promote spindle growth to reach the cortex in sea urchin zygotes with MT stabilizer Hexylene glycol (HG) or Paclitaxel (Taxol), and compare the elastic contribution between cytoplasm and MTs. In addition, I could shorten but not completely depolymerize mitotic asters in smaller blastomeres where MTs reach the cell surface. This is an opposite way to quantify cytoplasm elastic contribution in a cortical-contacting model and could be achieved with the MT inhibitor urethane [START_REF] Costache | Kif2 localizes to a subdomain of cortical endoplasmic reticulum that drives asymmetric spindle position[END_REF][START_REF] Lee | Astral microtubules determine the final division axis of cells confined on anisotropic surface topography[END_REF][START_REF] Strickland | Induction of Cytokinesis Is Independent of Precisely Regulated Microtubule Dynamics[END_REF].

One important feature of cytoplasmic forces is that there are not net forces. These are reactive forces in response to spindle motions and cannot actively center or decenter large organelles like spindles, asters and nuclei. These forces could oppose the motions of large organelles, as small particles are allowed to pass through the pores of cytoplasm meshworks. This is interesting as this behavior could participate in the force balance during some important processes, for instance, aster centration at fertilization (Figure 2), spindle decentration for asymmetric divisions and aster separation during anaphase (De [START_REF] Simone | Uncovering the balance of forces driving microtubule aster migration in C. elegans zygotes[END_REF][START_REF] Grill | The distribution of active force generators controls mitotic spindle position[END_REF]Tanimoto et al., 2018a). This hypothesis could be tested in vitro by monitoring aster/spindle motions in the egg cytoplasm extract of reduced/enhanced elasticity. In vivo, Latrunculin B cannot be used in the situation, as bulk F-actin meshworks contribute to both cytoplasm elasticity and viscosity. The reduced viscosity mediates lower dynein pulling forces that will compensate with the lower reactive forces from cytoplasm, thus causing similar aster centration speed (Tanimoto et al., 2016).

From my thesis, the cytoplasm emerges as a complex material, whose rheological behaviors can be predicted by a simple 1D viscoelastic Jeffreys' model (Hiramoto, 1969a, b). The key difference of Jeffrey model from Voigt model is the existence of the second dashpot, which causes an incomplete recovery and a partial dissipation of elastic energy. This dissipation could come from the fluidization or plastic rearrangements of cytoplasm elastic elements. We suppose that when spindles move to compress the cytoplasm, elastic materials will restore elastic energy, but at the same time, they rearrange to fluidize and dissipate elastic energy.

Cytoplasm fluidization or rearrangement was also observed in the region of MTs growth during anaphase (Figure 3A). Bulk F-actin meshworks were aligned along MTs and became more diluted compared to regions without MTs. This suggests that MTs could rearrange cytoplasm elastic elements and locally fluidize the cytoplasm to facilitate organelle transports or protein diffusions (Figure 3B). This hypothesis could explain the reduced cytoplasm elastic modulus in metaphase as compared with that in non-fertilized eggs, and is supported by recent findings from [START_REF] Huang | Cytoplasmic organization promotes protein diffusion[END_REF], where organized MTs promote protein diffusions. In the lab, we could study the MT-mediating cytoplasm fluidization with the diffusion of injected tracers in and out of MT regions. From the literature, when astral MTs reach the cortex, they exert length-dependent forces which could orient spindles/centrosomes along the long cell axis [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF] and maintain their positional stability with enhanced centering stiffness in small cells (Garzon-Coral et al., 2016). My second project studied the shape or size dependence of the cytoplasm rheology on mitotic spindle positioning and found the cytoplasm viscoelastic properties greatly vary with cell shapes. In more elongated cells, with a constant volume, the stiffness along the long axis may increase with aspect ratio. This result was predicted from the simulation and may be further proven using experiments on shaped cells in chambers. I hypothesize that this effect could come from an increased hydrodynamic coupling between the spindle and the cell surface of the short axis. This shape dependent property could on one side reduce spindle positional fluctuations along the long axis when cells become more and more elongated, thus limiting errors in size repartition between the two daughter cells at cell division. On the other side, the increased reactive forces along the long axis could oppose motions of large organelles like asters and spindles. This is interesting as it could explain the increased difficulty of aster centration in elongated cells after fertilization. In addition, it could potentially suggest a new function of cell rounding during mitosis. As cytoplasm restoring stiffness on spindles reduces in rounded shapes, this could allow spindles to move or rotate to the correct position or orientation. One possible support for this hypothesis is that elongated shapes induce asymmetric divisions of HeLa cell under confinement [START_REF] Cadart | Exploring the Function of Cell Shape and Size during Mitosis[END_REF][START_REF] Taubenberger | The Mechanics of Mitotic Cell Rounding[END_REF]. It could be another project to study cytoplasm viscoelastic properties during cell rounding and their implications for the symmetry/asymmetry of cell division.

Another interesting result from my second project is that the cytoplasm stiffness becomes anisotropic when the cell is elongated. The stiffness is higher along the short axis than along the long axis, allowing even lower positional fluctuations at the short axis. But when normalized to the cellular dimension, these fluctuations are near-isotropic, thus maintaining spindle stability in all directions. This anisotropic stiffness could also maintain spindle orientation along the long axis and rotate back the spindle if the orientation is perturbed. All these findings are still preliminary, and in a near future, I will complete these data sets on manipulated cell shapes and cell sizes. For instance, cytoplasm restoring stiffness on spindles will be essayed in the cells in chambers, and in smaller blastomeres with round shapes (using Ca 2+ free sea water). At the same time, 3D simulations will be used to help better understand how the cytoplasm may contribute to positon or stabilize spindles in cells with varying shapes and dimensions.

INTRODUCTION

The actin and microtubule (MT) cytoskeletons are universal force-generating machineries. They can deform and move organelles, cells and tissues on length scales spanning 3-4 orders of magnitude. Accordingly, the forces they produce vary in amplitude, from few pN for individual polymers and motors, up to tens of nN for larger assemblies [START_REF] Howard | Mechanics of Motor Proteins and the Cytoskeleton[END_REF]. A large part of our current understanding of force generation comes from in vitro studies using purified filaments and motors. Those served to delineate the minimal organizational principles supporting force generation, and compute typical magnitudes. In general, one could segregate force generation into two simple classes: protrusive (pushing) and contractile (pulling) forces [START_REF] Tolić-Nørrelykke | Push-me-pull-you: how microtubules organize the cell interior[END_REF]Svitkina, 2018). For example, MT and actin filaments typically produce pushing forces in the sub-pN range, when polymerizing against a barrier (Dogterom and Yurke, 1997;[START_REF] Footer | Direct measurement of force generation by actin filament polymerization using an optical trap[END_REF]. Conversely, filament shortening by depolymerization [START_REF] Grishchuk | Force production by disassembling microtubules[END_REF][START_REF] Jegou | Formin mDia1 senses and generates mechanical forces on actin filaments[END_REF], or their association with molecular motors, like dynein for MTs [START_REF] Mallik | Cytoplasmic dynein functions as a gear in response to load[END_REF][START_REF] Gennerich | Forceinduced bidirectional stepping of cytoplasmic dynein[END_REF] and myosin for actin [START_REF] Finer | Single myosin molecule mechanics: piconewton forces and nanometre steps[END_REF] entail significant modes of pulling force exertion. Integration of these force-generation units into larger networks with defined polarities, turn-over and organization allows to scale up force amplitude [START_REF] Parekh | Loading history determines the velocity of actin-network growth[END_REF][START_REF] Laan | Force-generation and dynamic instability of microtubule bundles[END_REF][START_REF] Thoresen | Reconstitution of contractile actomyosin bundles[END_REF]Laan et al., 2012;[START_REF] Bieling | Force feedback controls motor activity and mechanical properties of selfassembling branched actin networks[END_REF], as well as generate a plethora of remarkable network shape changes and movements, including contraction [START_REF] Reymann | Actin network architecture can determine myosin motor activity[END_REF][START_REF] Foster | Active contraction of microtubule networks[END_REF], growth [START_REF] Loisel | Reconstitution of actin-based motility of Listeria and Shigella using pure proteins[END_REF][START_REF] Ishihara | Microtubule nucleation remote from centrosomes may explain how asters span large cells[END_REF], translation [START_REF] Holy | Assembly and positioning of microtubule asters in microfabricated chambers[END_REF][START_REF] Telley | Aster migration determines the length scale of nuclear separation in the Drosophila syncytial embryo[END_REF], rotation [START_REF] Schaller | Polar patterns of driven filaments[END_REF][START_REF] Sanchez | Spontaneous motion in hierarchically assembled active matter[END_REF], or oscillations [START_REF] Placais | Spontaneous oscillations of a minimal actomyosin system under elastic loading[END_REF], akin to in vivo situations. Model systems, on the other hand, have defined the role and molecular regulation of cytoskeletal force generation in vivo, for key processes like spindle positioning, cell migration or tissue morphogenesis [START_REF] Cramer | Actin-dependent motile forces and cell motility[END_REF]Gardel et al., 2010;[START_REF] Mcnally | Mechanisms of spindle positioning[END_REF]Munjal and Lecuit, 2014;Svitkina, 2018). Cell division, for instance, which is the particular focus of this review, relies on a thorough spatio-temporal regulation of force-generation by both actin and MTs. In late prophase/metaphase, the mitotic spindle needs to be accurately positioned and oriented to specify the division plane [START_REF] Morin | Mitotic spindle orientation in asymmetric and symmetric cell divisions during animal development[END_REF]Minc and Piel, 2012). In many cells, this process is orchestrated by astral MTs that push and/or pull onto spindle poles, to move and rotate the spindle into place [START_REF] Mcnally | Mechanisms of spindle positioning[END_REF]. Spindle assembly and chromosome segregation are also heavily dependent on MT-based forces [START_REF] Dumont | Force and length in the mitotic spindle[END_REF]. These forces contribute to shape and elongate the spindle, as well as move and position chromosomes in the metaphase plate and pull them apart later in anaphase. For cytokinesis, signals emanating from the spindle drive the assembly of a cytokinetic acto-myosin ring, which will contract to deform the plasma membrane, leading to the physical separation of daughter cells (Green et al., 2012). Thus, in a typical time of few minutes, MTs, actin, and their associated motors, can create a remarkable multitude of forces varying in amplitude and directions, that coexist in a cytoplasm as small as few microns.

Our appreciation of the importance of force generation by the cytoskeleton for cell and tissue behavior, contrasts with our current knowledge of the directionality and magnitudes of those forces in vivo. For instance, to date, only few reports have provided direct force measurements within live cells. These include measurements of contractile stresses generated by acto-myosin rings [START_REF] Rappaport | Cell division: direct measurement of maximum tension exerted by furrow of echinoderm eggs[END_REF], forces associated with chromosome segregation (Nicklas, 1983), intracellular vesicle transport [START_REF] Hendricks | Force measurements on cargoes in living cells reveal collective dynamics of microtubule motors[END_REF][START_REF] Rai | Molecular adaptations allow dynein to generate large collective forces inside cells[END_REF] and MT aster or spindle positioning (Garzon-Coral et al., 2016;Tanimoto et al., 2018). Whether cytoskeleton polymers apply pushing vs. pulling forces, to move or position nuclei or spindles, is also still surprisingly a matter of intense debate in many model systems (Grill et al., 2001;[START_REF] Bezanilla | Spindle positioning: actin mediates pushing and pulling[END_REF]Garzon-Coral et al., 2016).

Another important conceptual notion in cytoskeleton force exertion is to distinguish between the role of forces applied from the cell surface vs. those applied directly from bulk cytoplasm. Because biological research has made a powerful use of model systems like yeast and adherent animal cells, which are small cells dominated by surface effects, the largest body of the literature has so far covered cytoskeletal force exertion at, or close to the cell surface. Examples range from actin polymerization for lamellipodium protrusion, contractile forces that regulate the actin cortex, or forces on astral MTs pulled by dynein anchored to the cortex during spindle positioning. Similarly, the proximity of glass coverslips in most in vitro assays, has limited our appreciation of the role of viscous or viscoelastic interactions of cytoskeleton filaments and motors with elements in bulk. Force exertion from bulk cytoplasm, may represent another important class of cytoskeletal regulation, which remains poorly appreciated and documented. We will review evidences supporting force exertion in bulk for both MTs and actin, discuss molecular and physical mechanisms, limits and relevance to organelle positioning and cell division.

MICROTUBULE FORCES IN BULK CYTOPLASM Experimental Evidences Supporting the Existence of MT Forces in the Cytoplasm

MTs are long and rigid polymers which grow from within the cytoplasm. In animal cells, MTs are dominantly nucleated from the centrosome, and radiate to form star-shape structures, called MT asters [START_REF] Bornens | The centrosome in cells and organisms[END_REF]. The net forces and torques exerted by astral MTs are instrumental to move, position, and orient centrosomes and associated nuclei and spindles [START_REF] Morin | Mitotic spindle orientation in asymmetric and symmetric cell divisions during animal development[END_REF]Minc and Piel, 2012;[START_REF] Mcnally | Mechanisms of spindle positioning[END_REF]. Many seminal studies have clearly demonstrated that MTs can generate significant pushing forces in vivo to promote nucleus or spindle centration (Tran et al., 2001;[START_REF] Tolić-Nørrelykke | Positioning and elongation of the fission yeast spindle by microtubule-based pushing[END_REF]. Astral MTs interaction with cortical dynein is also widely accepted to create pulling forces that position and orient spindles in a multitude of cell types (Grill et al., 2001;Gönczy, 2008). Although such MT cortical forces are typically considered as dominant modes of force generation [START_REF] Tolić-Nørrelykke | Push-me-pull-you: how microtubules organize the cell interior[END_REF], experiments based on the local manipulation of MTs in asters, support that MTs can also pull directly from the cytoplasm without contacting the cell surface (Reinsch and Gönczy, 1998;[START_REF] Wühr | How does a millimeter-sized cell find its center?[END_REF]Mitchison et al., 2012).

The seminal Colcemid-UV experiments by Hamaguchi and Hiramoto in the 80s, constitute the first important support for MT force exertion in bulk (Hamaguchi and Hiramoto, 1986) (Figure 1A). Using the centration of sperm asters in large Sand dollar (echinoderm) embryos, they depolymerized all MTs with Colcemid, a powerful MT inhibitor which can be inactivated with UV light. Local UV-based inactivation allows MTs to regrow in defined sub-cellular regions. Importantly, as long as the UV light is on, those regions remain stable against diffusion of inactivated molecules, given the large excess of Colcemid in the medium. Thus, this assay allows to create asymmetric asters with MTs differing in length. Remarkably, asters moved to the center of UV zones, following the direction of longer MTs, much like they normally do when migrating to the center of the whole cell (Chambers, 1939). Importantly, multiple modulations of this Colcemid-UV assay clearly ruled out any requirements for a contact between MTs and the cortex, demonstrating that MT forces exerted in bulk can displace asters and centrosomes (Hamaguchi and Hiramoto, 1986).

Recent experiments in large zebrafish blastomeres, used an inverse approach based on an engineered caged version of the MT drug Combretastatin 4A (Wuhr et al., 2010; Figure 1B). Local and transient UV-based uncaging of the drug allows for depolymerizing a fraction of MTs, creating asymmetric asters that again moved toward the sides of longer MTs. Net motion occurred long before MTs reached the cortex, supporting that MT forces exerted in bulk can displace large asters. A last version of those experiments, involved UV laser-based ablation of parts of centering sperm asters in sea urchin embryos (Tanimoto et al., 2016; Figure 1C). Cutting MTs along a line parallel to the aster centering path, yielded a systematic deviation away from the ablation line, suggesting that uncut MTs predominantly exert pulling forces. Soon after ablation, MTs regrowth and restored the position of the centrosome on the centered path. Similarly, cutting MTs at the aster front caused aster to transiently stop or even step back toward the cortex. Thus, at least in large eggs and blastomeres, those different assays provide strong evidence that MT cytoplasmic forces are dominant in driving the motion of centrosomes, nuclei, and asters.

Mechanisms Supporting Microtubule Force Generation in the Cytoplasm

In the systems mentioned above, as well as in many other cell types, the main motor driving centrosome motion is dynein [START_REF] Gönczy | Cytoplasmic dynein is required for distinct aspects of MTOC positioning, including centrosome separation, in the one cell stage Caenorhabditis elegans embryo[END_REF][START_REF] O'connell | Mammalian spindle orientation and position respond to changes in cell shape in a dynein-dependent fashion[END_REF]Wuhr et al., 2010;Tanimoto et al., 2016;[START_REF] Cheng | Spontaneous emergence of cell-like organization in Xenopus egg extracts[END_REF]. Dynein anchoring and activation at the cortex have been extensively documented, but how this minus-end directed motor may load onto MTs and pull them in bulk is less well understood. One possibility is that dynein could be anchored on relatively static structures in bulk, like a stiff actin or intermediate filament network (Reinsch and Gönczy, 1998). Although actin appears to be dispensable for MT bulk force exertion in some systems (Tanimoto et al., 2016;[START_REF] Cheng | Spontaneous emergence of cell-like organization in Xenopus egg extracts[END_REF], the role of intermediate filaments has not been tested thoroughly to date. An alternative scenario, introduced in another classical paper by Hamagushi and Hiramoto is that small objects like vesicle cargos moving along MTs, could interact hydrodynamically with the viscous cytoplasm, and yield frictional forces that pull onto MTs (Hamaguchi et al., 1986; Figure 2A). This hypothesis was based on the observation that some particles like polystyrene beads injected in eggs, may exhibit highly persistent minus-end (B) Specific subunits of the dynein-dynactin complex and adaptors thought to mediate dynein-cargo loading as well as cargo motion, during C. elegans pro-nuclear centration. The cytoplasmic dynein-cargo is loaded onto MTs by interacting with EB proteins at the plus end or tyrosinated α-tubulin along the MTs. Modified according to Kimura and Kimura (2011) and Barbosa et al. (2017). Scale bar, 20 µm.

motions along astral MTs. Because vesicle-cargos like endosomes, lysosomes, mitochondria or yolk granules, as well as larger endomembranes of the endoplasmic reticulum, are typically transported by dynein along MTs, they could provide natural viscous anchors for MTs to pull in bulk (Terasaki and Jaffe, 1991;Reinsch and Gönczy, 1998; Figure 2A).

This model received the best support from genetic functional analyses in the model C. elegans one-cell embryo (Figure 2B). Upon fertilization, much like in echinoderms mentioned above and most animal eggs, the male pro-nucleus moves to the cell center guided by centering sperm asters. Building on large-scale protein knock-down analyses, Kimura and colleagues defined the role of the dynein light chain subunit dyrb-1, as well as adaptors RILP and Rab7 that connect dynein to vesicle cargos for centrosome centration (Kimura and Kimura, 2011). RNAi of those factors significantly reduced endosomes and lysosomes minus-end directed motion and net aster centration speed, bringing key molecular insights into how organelle motion could mediate dynein force exertion from the cytoplasm. Recent studies of the dynein-dynactin complex in the same system, revealed mechanisms controlling the loading of vesicle cargodynein complexes onto MTs. These showed interactions between the dynactin subunit p150 GAP-Gly domain with MT +TIP EB proteins, as well as with tyrosinated α-tubulin. Specific mutants of this domain yielded concomitant defects in endosome motion and aster centration, giving further support to the vesicle-based pulling model in C. elegans (Barbosa et al., 2017). Because organelle trafficking along MTs is a feature of all eukaryotic cells, this mechanism could potentially influence nuclear or spindle positioning in many cells, not only zygotes. However, it remains unclear whether the prominent -end directed motion of endosomes and lysosomes reported in C. elegans represents a conserved feature, or if competing activities with +end directed kinesins could cancel out this effect in other cell types.

Implications of MT Cytoplasmic Forces for Aster Positioning

How might dynein pulling in bulk cytoplasm influence the stereotypical centering motion of asters? The most-accepted design is that longer MTs should accumulate more dyneins and cargos, allowing them to exert more pulling forces on centrosomes [START_REF] O'connell | Mammalian spindle orientation and position respond to changes in cell shape in a dynein-dependent fashion[END_REF][START_REF] Vallee | How dynein helps the cell find its center: a servomechanical model[END_REF]Wuhr et al., 2010;Minc et al., 2011). This design provides a robust mean to convert aster shape into a net force, and account for aster centration, as well as all above-mentioned experiments where MTs are locally depleted (Tanimoto et al., 2016;Haupt and Minc, 2018). This design received important support from multiple theoretical modeling work (Kimura and Onami, 2005;[START_REF] Hendricks | Force measurements on cargoes in living cells reveal collective dynamics of microtubule motors[END_REF]Letort et al., 2016;Tanimoto et al., 2016). Hydrodynamic simulations even allowed to account for the resultant flows and forces in the fluid associated with lengthdependent MT pulling in bulk [START_REF] Shinar | A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo[END_REF][START_REF] Nazockdast | Cytoplasmic flows as signatures for the mechanics of mitotic positioning[END_REF]. Yet, to date, there is no experimental or theoretical validation that vesicle transport will be an efficient mean for force exertion on MTs, nor that vesicles actually accumulate onto MTs in a length-dependent manner.

One important mean to connect the length-scales of single force-generation events to that of whole asters, is to compute the net forces associated with centering asters in vivo [START_REF] Wu | Forces positioning the mitotic spindle: theories, and now experiments[END_REF]De Simone et al., 2018). Building on injected magnetic beads which exhibit persistent minus-end directed motion and stick to centrosomes, we recently used in vivo magnetic tweezers, to derive force-velocity relationships for centering sperm asters in sea urchin eggs (Tanimoto et al., 2018; Figure 3A). These allowed to extract a stall force that equilibrates the endogenous aster net centering force of ∼600 pN. This force is equivalent to a net excess of hundreds of motors, or tens of vesicle cargos at the aster front [START_REF] Rai | Molecular adaptations allow dynein to generate large collective forces inside cells[END_REF]. While this may seem realistic, the lack of understanding on how much of the vesicle force is actually transmitted to single MTs or to the centrosome, precludes any firm conclusion for the exact mechanism that generates such large forces. Asters are bushy, with MTs often unconnected to the rest of the network, and whether vesicle motion will just transport MTs to the periphery of the aster, promoting aster expansion, drive network rearrangements, or actually pull on the centrosome is not clear (Mitchison et al., 2012;[START_REF] Ishihara | Microtubule nucleation remote from centrosomes may explain how asters span large cells[END_REF]; Figure 2A). In addition, the motion of vesicle cargos in dense asters, is a sophisticated hydrodynamic problem, resembling that of a sphere moving in a closed pipe, which could significantly limit dynein force transmission to MTs [START_REF] Happel | Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media[END_REF][START_REF] Nazockdast | Cytoplasmic flows as signatures for the mechanics of mitotic positioning[END_REF].

In vivo magnetic forces can also serve to move the centrosome away from the cell center, and assay their ability to re-find the cell center. Such experiments were first performed on centered mitotic spindles in C. elegans zygotes (Garzon-Coral et al., 2016). They revealed the existence of MT-dependent visco-elastic forces, which maintain the spindle in the cell center that were proposed to emerge from astral MT pushing forces on the cortex. During aster centration in sea urchin embryo, applying magnetic forces orthogonal to the centering axis, also yielded similar MT viscoelastic forces, which maintain the centrosome along the centering path (Figure 3B). The centering stiffness provided by MTs is ∼60 pN/µm. Thus, a displacement 1 µm away from the centering path, creates a net imbalance of 60 pN in MT forces from the two sides on the centrosome. We interpreted this imbalance as a natural consequence of the length-dependent MT pulling model: as the aster is moved away from the center MTs become longer in the other direction, exerting a net restoring force proportional to the net displacement of the aster center (Tanimoto et al., 2018;[START_REF] Dmitrieff | Scaling properties of centering forces[END_REF]. Remarkably, this MT-based centering stiffness becomes gradually smaller as the sperm aster approaches the cell center (Salle et al., 2019). This reduction could also be a mere consequence of the cytoplasmic pulling model. As vesicles and/or endomembranes are transported to the aster center by dynein, they become gradually depleted from the rest of the cytoplasm, thereby reducing the amount of viscous anchors for dynein to pull on MTs (Figure 3C). Accordingly, the endoplasmic reticulum exhibits a massive accumulation around centering sperm asters (Terasaki and Jaffe, 1991). Whether other cargos exhibit similar accumulation remains to be determined, and could represent a qualitative criteria to identify the specific dynein cargos supporting bulk pulling.

Finally, in addition to centering asters and promoting symmetric division, length-dependent bulk MT forces may also influence division orientation. During early embryonic cell cycles, asters duplicate and orient to specify the geometry of early division patterns. One remarkable properties of those divisions, is that they usually orient along the long axis of the cell. This process, which is thought to be a general property of many cells, was first reported in the nineteenth century in Oskar Hertwig's classical rules [START_REF] Hertwig | Das Problem der Befruchtung und der Isotropie des Eies, Eine Theory der Vererbung[END_REF]Minc and Piel, 2012). Length-dependent MT forces allow to orient aster pairs along the long axis of cells, thereby explaining those centuryold division rules (Wuhr et al., 2010;Minc et al., 2011;Pierre et al., 2016;Haupt and Minc, 2018). In different embryos, aster geometries may be influenced not only by cell shape, but also by the presence of neighboring asters, or yolk layers which affect MT growth. Combinations of those factors ultimately dictate aster shapes and consequent position and orientation, accounting for a large part of the diversity of cleavage patterns seen in different embryos (Pierre et al., 2016). Thus, MT length-dependent bulk pulling forces constitutes a generic design which may account for essential self-organizing properties of asters and early embryos.

ACTIN-BASED FORCES IN BULK CYTOPLASM The Actin Comet-Tail Model

Actin is also responsible for the generation of large forces, in essential instances like cell migration, cytokinesis, and shape changes (Gardel et al., 2010;Green et al., 2012;Munjal and Lecuit, 2014;Svitkina, 2018). The largest part of F-actin in animal cells resides in the cell cortex, underneath the plasma membrane. As a consequence, addressing the role of bulk F-actin has long remained difficult, in part because the visualization of filaments (A) External calibrated magnetic forces applied with magnetic tweezers on the aster center, through minus-end accumulated beads in sea urchin embryos. Forces applied along the centering axis serve to derive force-velocity relationships for centering asters. This relationships is mostly linear supporting a motion limited by viscous interactions, with the slope allowing to compute an effective drag. The intersection of the line with the x-axis yields estimates of the aster endogenous force of ∼600 pN. Modified according to Tanimoto et al. (2018). (B) Forces applied orthogonal to the centering axis serve to characterize MT-based visco-elastic forces stabilizing the centered position of the aster in the transverse axis during centration. Blue curve: Typical experimental displacement-time curve, allowing to compute visco-elastic parameters of MT-based centering system. Upon force application, the aster moves toward the magnet until reaching an equilibrium plateau, and recoils back to the center after releasing the force, behaving as a spring. Computation of the centering stiffness and the drag from the plateau and the slope of the curve. Modified from Tanimoto et al. (2018). (C) Successive force measurements showed that aster centering stiffness becomes reduced during aster centration (Salle et al., 2019). Proposed model for how cytoplasmic forces may become less efficient during centration, and yield to this stiffness reduction: As the aster centers, dynein drags endomembranes to the cell center, depleting the rest of the cytoplasm, and thereby rendering cytoplasm force exertion less efficient. Modified from Terasaki and Jaffe (1991) and Salle et al. (2019).

deep in the cytoplasm is often obscured by the very bright cortex [START_REF] Field | Bulk cytoplasmic actin and its functions in meiosis and mitosis[END_REF]. The development of actin live probes including life-act and Utrophin has allowed important new discoveries on the specific function of bulk actin (Li et al., 2008;Field et al., 2011;[START_REF] Almonacid | Active diffusion positions the nucleus in mouse oocytes[END_REF][START_REF] Shamipour | Bulk actin dynamics drive phase segregation in zebrafish oocytes[END_REF].

One well documented class of mechanism for force exertion by F-actin in bulk cytoplasm, comes from studies of the propulsion of the pathogenic bacterium Listeria monocytogenes (Figure 4A). Upon infection, this microbe hijacks the actin cytoskeleton machinery of the host cell to grow a long "comet tail" made of highly reticulated actin filaments that propel the bacterium in the cytoplasm (Tilney and Portnoy, 1989;Theriot et al., 1992;[START_REF] Tilney | How Listeria exploits host cell actin to form its own cytoskeleton. I. Formation of a tail and how that tail might be involved in movement[END_REF]. At the surface of bacterial poles, a nucleation promoting factor called ActA recruits and activates host Arp2/3 complex that promotes branched actin growth [START_REF] Welch | Actin polymerization is induced by Arp2/3 protein complex at the surface of Listeria monocytogenes[END_REF]. Multiple seminal studies reconstituted actin comets at the surface of beads, vesicles, droplets, in cytoplasmic extracts, or in minimal solutions (Theriot et al., 1992;[START_REF] Cameron | Motility of ActA protein-coated microspheres driven by actin polymerization[END_REF][START_REF] Loisel | Reconstitution of actin-based motility of Listeria and Shigella using pure proteins[END_REF][START_REF] Pantaloni | Mechanism of actin-based motility[END_REF][START_REF] Bernheim-Groswasser | The dynamics of actin-based motility depend on surface parameters[END_REF][START_REF] Giardini | Compression forces generated by actin comet tails on lipid vesicles[END_REF][START_REF] Trichet | VASP governs actin dynamics by modulating filament anchoring[END_REF][START_REF] Delatour | Arp2/3 controls the motile behavior of N-WASP-functionalized GUVs and modulates N-WASP surface distribution by mediating transient links with actin filaments[END_REF]. Those served to draw a large part of our current understanding of actin assembly and force generation, needed for other processes like lamellipodium based migration (Theriot et al., 1994;[START_REF] Laurent | Role of proteins of the Ena/VASP family in actin-based motility of Listeria monocytogenes[END_REF][START_REF] Pantaloni | Mechanism of actin-based motility[END_REF]. In addition, comet tails also form around other pathogens including viruses [START_REF] Welch | Arp2/3-mediated actin-based motility: a tail of pathogen abuse[END_REF], as well as at the surface of endosomes, lysosomes or yolk granules [START_REF] Taunton | Actin-dependent propulsion of endosomes and lysosomes by recruitment of N-WASP[END_REF][START_REF] Shamipour | Bulk actin dynamics drive phase segregation in zebrafish oocytes[END_REF], suggesting that they could promote the intracellular motion of many types of cargos in the cytoplasm.

The forces developed by actin comet-tails can be enormous, ranging from hundreds of pN to few nN [START_REF] Giardini | Compression forces generated by actin comet tails on lipid vesicles[END_REF][START_REF] Mcgrath | The force-velocity relationship for the actin-based motility of Listeria monocytogenes[END_REF][START_REF] Upadhyaya | Probing polymerization forces by using actin-propelled lipid vesicles[END_REF][START_REF] Marcy | Forces generated during actin-based propulsion: a direct measurement by micromanipulation[END_REF][START_REF] Plastino | The actin slingshot[END_REF]. In addition to propelling the bacterium, those forces may help the microbe to eventually deform and breach the host membrane for propagation to neighboring cells [START_REF] Portnoy | The cell biology of Listeria monocytogenes infection: the intersection of bacterial pathogenesis and cell-mediated immunity[END_REF][START_REF] Pizarro-Cerda | Subversion of cellular functions by Listeria monocytogenes[END_REF]. The propulsive speeds of Listeria are also impressive, reaching up to ∼1 µm/s, and are nearly equal to that of actin tail growth speeds [START_REF] Dabiri | Listeria monocytogenes moves rapidly through the host-cell cytoplasm by inducing directional actin assembly[END_REF]. In the absence of external forces, the ensemble cargo (e.g., bacteria, beads. . . ) plus actin tail is an isolated system [START_REF] Prost | The physics of listeria propulsion[END_REF]. Consequently, which of the cargo or the tail will move in the laboratory frame is dictated by the ratio of the viscous drags of each object. Those drags depend on their respective geometries and the viscosity of the cytoplasm. Given the large density of filaments in the actin tail, its drag may be well approximated with that of a solid cylinder, which increases linearly with the tail length [START_REF] Happel | Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media[END_REF]. Thus, if the tail is much shorter than the cargo radius, it will elongate with no net displacement of the cargo. Once the tail reaches a similar length than the cargo, they will move in opposite directions at similar speeds. However, when the length of the tail exceeds the radius of the cargo, the drag of the tail will dominate and propel the cargo at a speed that is linked to that of actin tail growth, by: V cargo = V actin (1+γ cargo /γ tail ) [START_REF] Prost | The physics of listeria propulsion[END_REF]. In vivo, actin tails are typically 20-30X longer than their cargos, and thus the speed of the cargos, can be very well approximated with that of actin growth (Theriot et al., 1992). Thus, as for MTs and vesicles moved by dynein discussed above, the comet tail-based motion exemplifies how a pure viscous interaction with bulk cytoplasm, can support force exertion and rapid net motion of cargos.

However, the bacterium or other cargos are often subjected to external forces, when encountering other organelles or cellular networks, or when pushing against the membrane. For instance, Listeria's speed depends on its location within the host cells, which has been used to argue for an influence of the local density of cytoskeletal networks of actin, MTs or intermediate filaments [START_REF] Giardini | Effects of intermediate filaments on actin-based motility of Listeria monocytogenes[END_REF][START_REF] Giardini | Compression forces generated by actin comet tails on lipid vesicles[END_REF]. During microbe escape, actin tails also appear to connect to the cortex of evaginating membranes, raising the possibility that the tail could push on more elastic or viscoelastic elements to support forward progression of the bacterium against load [START_REF] Sechi | The isolated comet tail pseudopodium of Listeria monocytogenes: a tail of two actin filament populations, long and axial and short and random[END_REF]. Because some actin tails appear smaller than their cargos, it is likely that visco-elastic interactions of the tail with other elements may be required in some instances [START_REF] Shamipour | Bulk actin dynamics drive phase segregation in zebrafish oocytes[END_REF].

In the context of cell division, the comet-tail pushing mechanism has been used to account for the decentration of the meiotic spindle in mouse oocytes (Figure 4B). Meiotic spindle displacement from the cell center to the nearest cortex, has been the subject of significant debates, arguing for the prominence of contractile forces from an acto-myosin network connected to the cortex vs. pushing from an actin cloud [START_REF] Azoury | Spindle positioning in mouse oocytes relies on a dynamic meshwork of actin filaments[END_REF]Li et al., 2008;Schuh and Ellenberg, 2008;[START_REF] Bezanilla | Spindle positioning: actin mediates pushing and pulling[END_REF]. The pushing mechanism is based on the observation of a large formin-nucleated F-actin cloud surrounding spindles and chromosomes, which breaks symmetry to become asymmetric at the onset of spindle displacement (Li et al., 2008). Notably, the cloud lagging the spindle has a size that roughly equals or is smaller than the spindle. Thus, following above arguments, whether the cloud solely uses viscous interaction with the cytoplasm to move spindles and chromosomes, or if it pushes on other bulk visco-elastic networks remains an interesting open question.

Actin-Based Pulling in Bulk

Acto-myosin based contraction is the main force that drives cell shape changes, cytokinesis, and many tissue rearrangements (Green et al., 2012;Munjal and Lecuit, 2014;Chugh and Paluch, 2018). Acto-myosin networks are most prominent at the cortex, and their local contraction can yield actin flows that concentrate actin and myosin toward the site of highest contractility [START_REF] Callan-Jones | Actin flows in cell migration: from locomotion and polarity to trajectories[END_REF]. Provided balanced disassembly at this site, the network can exhibit steady state gradients in actin density and flows, which are thought to contribute to cell polarization, as well as multiple aspects of cell migration (Mayer et al., 2010;[START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF]Maiuri et al., 2015;[START_REF] Ruprecht | Cortical contractility triggers a stochastic switch to fast amoeboid cell motility[END_REF]. Can similar mechanisms organize the bulk cytoplasm in such events as nuclear or spindle positioning? Bulk cytoplasmic extracts can exhibit massive acto-myosin dependent contractility [START_REF] Field | Bulk cytoplasmic actin and its functions in meiosis and mitosis[END_REF]Field et al., 2011), suggesting that those types of forces exist in the cytoplasm and could contribute to organize the cell interior. Recent in vitro studies provide important support for the relevance of bulk actin flows to cellular spatial organization (Figure 4C). These are based on the encapsulation of crude frog extracts supplemented with energy mix in water-in-oil celllike droplets [START_REF] Pinot | Confinement induces actin flow in a meiotic cytoplasm[END_REF][START_REF] Tang | Cytoplasmic self-organization established by internal lipid membranes in the interplay with either actin or microtubules[END_REF][START_REF] Malik-Garbi | Scaling behaviour in steady-state contracting actomyosin networks[END_REF]. Remarkably, those extracts rapidly self-organize to create sustained gradients of acto-myosin contractility with actin flowing from the droplet surface to its center [START_REF] Pinot | Confinement induces actin flow in a meiotic cytoplasm[END_REF][START_REF] Malik-Garbi | Scaling behaviour in steady-state contracting actomyosin networks[END_REF]. Flow properties depend on factors which control actin assembly and disassembly, as well as network connectivity [START_REF] Malik-Garbi | Scaling behaviour in steady-state contracting actomyosin networks[END_REF].

Remarkably, this network self-organizes around an aggregate of vesicles, which are dragged by actin flows, and locates to the precise droplet center. When this vesicle aggregate is moved away from the droplet center with magnetic tweezers, acto-myosin flows exert a net centering force, which moves the aggregate back to the droplet center. Thus, much like MT asters, disordered acto-myosin networks can act as elastic springs related to cell geometry. Their restoring elastic forces also emerge from a shape anisotropy of the network. When the network center is close to the cortex, the network grows larger away from the cortex, and drags more fluid, thereby creating a pressure gradient that pushes it back to the droplet center. This pressure gradient depends on the permeability of the network as well as fluid flow speeds and organization. Thus, this mechanism may have similarities with MT aster centering from bulk dynein forces. Whether this mechanism directly contributes to center organelles like the nucleus in cells remains to be tested, but similar bulk actin flows, have been shown to exist in fish embryos and influence the organization of their cytoplasm [START_REF] Shamipour | Bulk actin dynamics drive phase segregation in zebrafish oocytes[END_REF].

DISCUSSION

Several decades after the pioneering experiments by Hamaguchi and Hiramoto (1986), our appreciation of cytoskeleton force exertion in bulk remains narrow. This in part because those effects are best studied in large cells, such as eggs and blastomeres, which are less studied than yeast or adherent vertebrate cells. However, vesicles trafficking along MTs or actin growth in bulk are highly conserved processes, and thus it is likely that such forces exist even in small asters and cells [START_REF] Telley | Aster migration determines the length scale of nuclear separation in the Drosophila syncytial embryo[END_REF][START_REF] Wu | Investigation of in vivo microtubule and stress fiber mechanics with laser ablation[END_REF]. Whether their impact remains negligible as compared to surface forces is an exciting question for the future of the field. The physical mechanisms supporting force exertion from the cytoplasm are also still in their infancy. For instance, it is not clear if the radial organization in the standard model is actually required for aster motion based on cytoplasmic forces. Recent data with in vitro frog extracts actually suggest that asters can self-organize, center nuclei and organize cleavage patterns, even in the absence of centrosomes [START_REF] Cheng | Spontaneous emergence of cell-like organization in Xenopus egg extracts[END_REF]. Akin to the situation depicted in Figure 4C for bulk acto-myosin networks, a disordered MT network with a rough polarity and front-rear asymmetry, could in principle propel itself to the cell center by moving fluid through it using dynein-powered organelle/endomembrane transport. The efficiency of such self-propulsion would depend on parameters such as network permeability and density of viscous pullers, which are parameters difficult to map directly in vivo [START_REF] Nazockdast | Cytoplasmic flows as signatures for the mechanics of mitotic positioning[END_REF]Tanimoto et al., 2018;[START_REF] Ierushalmi | Centering and symmetry breaking in confined contracting actomyosin networks[END_REF]. Finally, whether cytoplasm viscosity is sufficient for significant force exertion, or if cytoskeleton polymers take support on more elastic or viscoelastic elements is not known. Although actin is not required for aster motion based on cytoplasmic pulling (Kimura and Kimura, 2011;Minc et al., 2011;Tanimoto et al., 2016), it may potentially influence their motion properties, by modulating the viscosity of the cytoplasm. Future work integrating the physical properties of the cytoplasm with cytoskeletal forces, to understand the motion of large objects like asters, spindles or nuclei shall strongly impact the field of cell division.

Introduction

During cell division, multiple cues are integrated to determine the relative position and size of daughter cells. Cell geometry, polar domains, or sites of cell-cell adhesion may, for instance, influence microtubule (MT) aster forces, which move and orient centrosomes, nuclei, and spindles to generate the wide variety of division types observed in different cells and tissues (Grill et al., 2001;[START_REF] Théry | The extracellular matrix guides the orientation of the cell division axis[END_REF]Minc et al., 2011). One of the most striking examples of division positioning control is asymmetric division. During this process, asters, nuclei, and spindles are usually first centered in the cell and then become displaced to one side, leading to the unequal segregation of cytoplasmic and cortical contents and producing cells with distinct sizes [START_REF] Dan | Studies on unequal cleavage in sea urchins I. Migration of the nuclei to the vegetal pole[END_REF][START_REF] Kaltschmidt | Rotation and asymmetry of the mitotic spindle direct asymmetric cell division in the developing central nervous system[END_REF]Kaltschmidt and Brand, 2002;[START_REF] Kimura | Local cortical pulling-force repression switches centrosomal centration and posterior displacement in C. elegans[END_REF]. Asymmetric division is a common mechanism to generate fate diversity from yeast to humans, particularly well-studied in lineage progenitors, in stem cells, and in the Caenorhabditis elegans zygote (Gönczy, 2008;[START_REF] Morin | Mitotic spindle orientation in asymmetric and symmetric cell divisions during animal development[END_REF]. Upstream signals responsible for asymmetry have been largely identified in such model cell types, but how downstream mechanical forces can orchestrate a robust and reproducible asymmetric division still remains unclear.

In animal cells, aster positioning is dynamically controlled by MT forces (Reinsch and Gönczy, 1998;Minc and Piel, 2012;Mitchison et al., 2012). Cytoplasmic dynein is one of the main MT-associated motors responsible for aster positioning. Dynein may generate cytoplasmic pulling forces, from the viscous drag created by the motion of endomembranes, such as the endoplasmic reticulum, or other vesicle cargos, it drives toward asters' centers (Hamaguchi et al., 1986;Kimura and Kimura, 2011). This process may result in MT forces that scale to their length, and ensure aster centration and orientation with respect to cell geometry (Hamaguchi and Hiramoto, 1986;Kimura and Onami, 2005;[START_REF] Wühr | A model for cleavage plane determination in early amphibian and fish embryos[END_REF]Minc et al., 2011;De Simone et al., 2018;Haupt and Minc, 2018). Dynein motors may also be anchored at the cell cortex within specific polar domains to generate asymmetric pulling forces that decenter asters for asymmetric division (Grill et al., 2001;[START_REF] Colombo | Translation of polarity cues into asymmetric spindle positioning in Caenorhabditis elegans embryos[END_REF]. Regulation of the balance between cytoplasmic and cortical dynein forces is most likely at the heart of most division geometries, like those found during cleavage or stem cell lineage (Kaltschmidt and Brand, 2002;Mitchison et al., 2012;Pierre et al., 2016). However, given the difficulty of manipulating an inherently asymmetric division in a controllable and quantitative manner, the generic mechanisms regulating this competition remain mostly unexplored.

We implemented magnetic cortical domains that spontaneously cluster dynein minus end activity in sea urchin (Paracentrotus lividus) zygotes. These domains transform the first symmetric cleavage typical of those cells into a marked asymmetric division. We find that centering asters are relatively insensitive to the domain and can be decentered only after they reach the cell center. Combined in vivo force measurements and computer simulations support a novel paradigm in which asymmetric divisions may be triggered by a reduction in centering forces under constant cortical pulling forces.

Results and discussion

Magnetic cortical pulling domains to control the asymmetry of cell division Certain particles injected into neurons or marine embryos may spontaneously exhibit minus end-directed movement to cluster around centrosomes [START_REF] Adams | Rapid transport of foreign particles microinjected into crab axons[END_REF]Hamaguchi et al., 1986). By screening magnetic particles injected into sea urchin zygotes, we found one type of particle displaying highly persistent MT minus end motion that formed compact aggregates at the aster center in a dynein-dependent manner (Fig. S1, A-C; Tanimoto et al., 2018). Using calibrated magnetic probes, we assembled, relocated, and retained cortical domains made of those beads of ∼5-10 µm in size (Fig. S1 D and Video 1). To test whether these domains loaded with dynein activity could pull on MTs to drive asymmetric divisions, we assembled them in nonfertilized eggs and added sperm. Strikingly, ∼20-30 min after fertilization, the zygote nucleus, which is normally maintained in the cell center, became attracted by the domain and exhibited a net asymmetric displacement. As occurs during symmetric divisions in those cells, the mitotic spindle formed after the asymmetric location and elongation of the interphase nucleus (Minc et al., 2011) and was thus well aligned with the domain, thereby driving cytokinesis that cleaved the cell in a marked asymmetric manner (Fig. 1, A andB; and Video 2). Asymmetric cleavages were never observed in un-injected eggs, in injected eggs in which the magnetic probe was removed after fertilization allowing the cap to move toward the center, or in eggs in which the cap was formed with another type of magnetic beads devoid of minus end activity (Fig. 1, C-G; and Videos 3 and 4).

Interestingly, the size of the cap appeared to control divided blastomere size asymmetry in a nonlinear manner. As measured by the angle formed by the edges of the cap and the cell center, a narrow cap (below ∼10°) had little effect on the nucleus and subsequent division position, whereas a wider cap (above ∼15°) tended to move nuclei to a point at which they were in near contact with the cortex, generating a strong asymmetric division (Fig. 1 H). We also noted that a small, ineffective cap at the onecell stage could offset the nucleus and consequent division plane in subsequent smaller blastomeres, suggesting that the size of the cap relative to that of the cell could be a critical factor in controlling the asymmetry of division (Fig. S1 E).

MT visualization with immunostaining revealed that asters were organized around decentering nuclei as in normal cells (Minc et al., 2011), filling the whole cytoplasm and contacting cortical caps (Fig. S1, F andH). Closer inspection of MT organization suggested that MTs did not fully penetrate magnetic caps, but rather interacted with the beads in a lateral configuration (Fig. S1, I-K). Importantly, we did not note any specific change in local MT arrangement and density at the cap, which suggested that those caps may not primarily influence MT forces by modulating MT stability or dynamics (Fig. S1, F and G; Laan et al., 2012). Finally, asymmetric nuclear displacement toward the cap strictly required both MTs and dynein activity (Fig. S1, L andM; and Video 5). Thus, it was possible to relocate a fraction of endogenous dynein activity into tunable cortical domains that pull on astral MTs to control the asymmetry of cell division.

Cortical pulling drives aster decentration only after asters have reached close to the cell center

We next addressed how cortical caps affect aster positioning dynamics by tracking centering and decentering nuclei marked with Hoechst. When fertilization occurred opposite the cap, the male pronucleus moved to the cell center, where it fused with the female, and the zygote nucleus then decentered along a trajectory reoriented toward the cap (Fig. S2 A and Video 6, i and ii). This behavior was not unexpected, because MTs nucleated from the male pro-nucleus may not reach the opposite cortex before the end of centration (Tanimoto et al., 2016). Accordingly, in such situations, released caps only started to detach from the cortex when the aster had reached close to the cell center (Fig. S2 E and Video 7).

Strikingly, however, when the sperm entered the side containing the cap, asters still migrated toward the cell center, ignoring the cap, and then stepped back to decenter toward the cap (Fig. 2 A; Fig. S2, B andC; and Video 6, iii and iv). This switch in aster directionality was observed in 100% of cases (n = 11 events), independent of the distance between the cap and the site of sperm entry (Fig. 2, A andB; and Video 6). In such eggs, immunostaining confirmed a clear interaction between centering asters and magnetic domains. In addition, cap release assays yielded a near-immediate centripetal motion of cortical magnetic beads (Fig. S2, D and F;and Video 7). This demonstrates that asters that begin centration close to caps can efficiently pull on them as early as few minutes after fertilization. Finally, aster centration speed in the presence of a domain was only slightly lower than controls, but was typically 3.5 times higher than decentration speeds (Fig. 2, C andD). Together, these results indicate that a change in the imbalance between centering and decentering forces may take place when asters are close to the cell center.

Requirement for an evolution of centering or decentering forces in asymmetric divisions

To understand the key elements driving consecutive centration and decentration phases, we developed a minimal 1D model (Fig. 2 E and Materials and methods). The aster was represented as a frontal MT of length L f , and a rear MT of length L r . Center- ing MT forces were scaled to the segment length through a constant a, and MT lengths were assumed to be limited by the cortex (Kimura and Onami, 2005;Tanimoto et al., 2016). The position x of the aster center evolved with time following an overdamped force balance equation, with γ the effective drag of the aster:

γ x ˙ = a ( L f -L r ) -F cap in
which F cap is the decentration force ex- erted by the cortical cap (Fig. 2 E). In the absence of a cap (F cap = 0), the aster centered at a speed bounded by MT polymerization rate and stopped at the cell center (x = 0), with no decentering motion. When F cap > 0, asters moved toward the center, but stopped before reaching the center at a final position given by x = F cap /2a and did not exhibit any decentering movement (Fig. 2 F). Allowing the drag γ to change over time affected the kinetics of centering, but not the final position, and did not account for the net change in aster directionality. Therefore, to account for the observed successive centering and decentering phases, we allowed forces to vary over time. Accordingly, increasing F cap , or decreasing the centering constant a after the aster had reached the cell center could account for both the successive centering and decentering phases and the reduction in aster speed during decentration (Fig. 2 G and Fig. S3, A andB). This simple analysis suggests that, during asymmetric divisions, cortical pulling forces may increase in strength over time, or alternatively, that the centering forces become weaker.

Cortical pulling forces remain constant during and after centration

To address putative time-dependent variations of cortical forces, we set out to directly compute the net decentering force exerted by the domain during and after aster centration. For this, we progressively moved back the magnetic probe away from the egg surface (Fig. 3 A). When the endogenous force from MTs on the cap became larger than the decreasing magnetic force, the cap detached from the cortex and moved to the cell center (Fig. 3,B and C;and Video 8).

The distance between the magnetic probe and bead domain was converted into a force and served to extract a "take-off " force, corresponding to the moment when the pulling force on the domain overcomes the magnetic force (see Materials and methods). To compute asymmetric forces on the domain during centration, we used a set of caps located close to the site of sperm entry (Fig. S2 F). This analysis revealed similar mean "take-off " profiles during and after centration, with mean cortical forces of 293.9 and 287.4 pN, respectively (Fig. 3 D). Finally, in agreement with the influence of cap size on division asymmetry, larger caps appeared to exert more pulling forces (Fig. 1 H and Fig. 3 E). These results suggest that magnetic domains pull with near constant force and that changes in aster directionality and speed cannot be readily accounted for by a significant evolution of cortical forces.

Centering cytoplasmic pulling forces become weaker after centration

A second, less intuitive prediction of our 1D model is that a reduction in MT centering forces per unit length may account for changes in both aster directionality and aster speed. To test this possibility, we directly measured the time evolution of aster centering forces in vivo. We injected magnetic beads and let them aggregate to the aster center, and applied calibrated forces (Tanimoto et al., 2018). Aster responses at different time points were compared within the same cell and under the same magnetic force by applying consecutive pulls orthogonal to the centering path. During centration, this caused the aster to deviate from its centering path toward the magnet probe and to recoil back to its normal centered path upon force cessation. After centration, force exertion displaced asters and attached nuclei away from the center, which also recoiled back upon force cessation (Garzon-Coral et al., 2016;Tanimoto et al., 2018;Fig. 4, A and B;and Video 9).

Strikingly, the amplitude of the deviation away from the cell center was much larger after the aster had reached the center as compared to during centration, indicating that centered asters are easier to decenter (Fig. 4, A andC; and Video 9). To quantify those effects, we fitted the displacement time curves by using a viscoelastic Kelvin-Voigt model, in which an elastic spring and a dashpot act in parallel. We computed the aster centering spring (B) Time-lapse of aster centration, and concomitant reduction of the magnetic force holding the cap. Top: Low-magnification view of the embryo moving away from the probe (left). Bottom: Details of cap detachment dynamics. Yellow stars: the aster center; arrowheads: the cap. (C) Typical example of the evolution of the distance between the cell cortex and the cap (gray), and of the magnetic force (red), as a function of the distance between the egg and magnet. Arrowhead: the cap "take-off." (D) Average distance between cap and cortex plotted as a function of the magnetic force, during centration (in green; n = 16) and after centration (in red; n = 18). Dashed lines are SD. Take-off forces (arrows) correspond to cortical forces exerted by domains onto asters and were determined using the fits (continuous lines; see Materials and methods). constant (κ, also called centering stiffness), which reflects the strength of length-dependent MT forces, and the aster drag (γ; Garzon-Coral et al., 2016;Tanimoto et al., 2018). Individual fitting of paired experimental curves performed in the same egg and under the same force showed that aster centering stiffness was systematically lower after centration, with a mean ratio before/after centration of ∼2.9 (Fig. 4 D). At the population level, the mean spring constant during centration was κ 1 = 61.48 pN/ µm and κ 2 = 18.10 pN/µm after centration (Fig. 4 F). Individual force measurements after centration yielded similar spring constant values, ruling out potential caveats of altering aster integrity after force application (Fig. 4 D). This lower value, reached early after centration, was also similar at later time points in interphase (Fig. S3, C andD). Interestingly, aster drags did not appear to be significantly modified, suggesting that the reduction in aster speed after centration may primarily arise from an alteration in the force imbalance on the aster (Fig. 4 E). Together, these quantitative measurements strongly support that a significant reduction in aster centering stiffness occurs as asters approach the cell center.

A 3D force competition model for aster positioning

To provide a faithful representation of the geometry of the system, we then developed a 3D model, in which we could input the respective 3D positions of the cap and site of sperm entry, for a direct comparison with individual experiments (see Materials and methods). Importantly, parameters were implemented using measured values for γ, κ, and F cap , and not adjusted further. The decrease in aster centering stiffness κ was represented by a linear decay over a 1-min period, at a fixed time after fertilization, but slower decays could also account for experimental behavior (Fig. S3, F andG). The model was compared with individual experiments, and accounted for the complex 3D trajectories of asters and yielded similar values for centered and final decentered aster positions, as well as centration-versus-decentration speeds (Fig. 5, A-E; and Video 10). Therefore, a model based on the quantified reduction of centering stiffness accounts for the inversion of aster directionality and net changes in speed and strongly supports a hitherto unappreciated mode of regulation of asymmetric division.

Conclusions

By developing a novel approach based on magnetic domains that can efficiently pull on MTs in a symmetrically dividing cell, we recapitulated most generic features of asymmetric divisions, including a dose-dependent effect of domain size and strength on daughter size asymmetry and a centering phase followed by a decentering one. One key finding is that a reduction in aster centering stiffness (forces/per unit MT length) provides the trigger for the prevalence of asymmetric forces from the domain needed for asymmetric division (Fig. 5 F). Although our experimental data do not allow us to clearly resolve the decay time of the centering stiffness (Fig. S3, C and D), they suggest a relatively rapid decay over a traveling distance of ∼20-30% of the egg radius close to the cell center (Fig. S3, F andG).

An important question these findings pose is what molecular reorganization may drive a weakening in the cytoplasmic MT pulling system. One possibility is that dynein activity becomes globally reduced in the cytoplasm, through time-dependent exhaustion or cell cycle progression. This hypothesis does not readily agree with experimental findings, as bead aggregates moving to the aster center exhibit similar centripetal speeds during or after aster centration (Fig. S3 E). A second plausible hypothesis is that gradual changes in aster structure, through the promotion of MT branching and/or densification, for instance, alter cytoplasmic force transmission to the centrosome in a timedependent manner [START_REF] Dan | Studies of unequal cleavage in molluscs II. Asymmetric nature of the two asters[END_REF]Mitchison et al., 2012). Although we cannot firmly reject a contribution from this effect, we note that MT radial arrangements remain roughly similar during the few minutes corresponding to the decay in centering stiffness (Minc et al., 2011;Tanimoto et al., 2016). A last model, which we favor most, is that cargos and/or endomembranes pulled by dynein to support MT cytoplasmic pulling may accumulate at the aster center, which could cause a gradual depletion of available cytoplasmic anchors. Accordingly, structures such as the endoplasmic reticulum progressively concentrate around the sperm nucleus toward the end of aster centration, at timings that match our measured decay in centering stiffness (Terasaki and Jaffe, 1991;Reinsch and Gönczy, 1998;[START_REF] Audhya | A role for Rab5 in structuring the endoplasmic reticulum[END_REF].

Finally, we foresee that our model, based on a global rather than local regulation, could serve as a major mechanism regulating asymmetric centrosome positioning and divisions in many cell types. In C. elegans zygotes, asters also exhibit a net change in directionality, essentially recapitulated in experiments presented here in Fig. 2 A and Fig. S2 C [START_REF] Kimura | Local cortical pulling-force repression switches centrosomal centration and posterior displacement in C. elegans[END_REF]. Interestingly, time-resolved analyses of cortical forces in these cells suggest that they also act upon mitotic asters much before the onset of decentration [START_REF] Labbé | The forces that position a mitotic spindle asymmetrically are tethered until after the time of spindle assembly[END_REF]. In other cell types, the modulation of centering forces could also emerge from time-dependent changes in MT pushing forces (Tran et al., 2001;[START_REF] Tolic-Nørrelykke | Nuclear and division-plane positioning revealed by optical micromanipulation[END_REF]Garzon-Coral et al., 2016). Pushing, which promotes aster centering, could become less efficient as a result of aster size increase or changes in MT polymerization rate, all resulting from a global rather than local regulation at cortical domains (Letort et al., 2016;[START_REF] Howard | Physical limits on the precision of mitotic spindle positioning by microtubule pushing forces: Mechanics of mitotic spindle positioning[END_REF][START_REF] Pitaval | Microtubule stabilization drives 3D centrosome migration to initiate primary ciliogenesis[END_REF]. Further quantitative mapping of the evolution of centering and decentering forces will be instrumental for understanding asymmetric divisions.

Materials and methods

Sea urchin maintenance and gametes collection

Purple sea urchins (P. lividus) were obtained from the Roscoff Marine station (France) and kept at 16°C in an aquarium for several weeks in artificial sea water (Reef Crystals; Instant Ocean). Gametes were collected by intracoelomic injection of 0.5 M KCl. Sperm was collected dry and kept at 4°C for 1 wk. Eggs were rinsed twice, kept at 16°C, and used on the day of collection. The jelly coat of unfertilized eggs was removed by passing them three times through an 80-µm Nitex mesh (Genesee Scientific) to facilitate egg adhesion on protamine-coated glass-bottom dishes (MatTek Corporation). Eggs were transferred on protamine-coated dishes for a maximum time of 15 min before injection, and were injected and fertilized under the microscope.

Magnetic particles preparation and injection

The spontaneous minus end-directed motion of specific superparamagnetic particles (NanoLink; Solulink) was used to both create cortical pulling caps and to apply forces on MT aster centers (Tanimoto et al., 2018). To prepare beads for injection, a solution of 10 µl of undiluted beads functionalized with streptavidin was first washed in 100 µl washing solution (1 M NaCl with 1% Tween-20) and sonicated for 5 min. The beads were then rinsed in 100 µl PBS, incubated in 100 µl 2 µg/ml Atto488-biotin (Sigma-Aldrich), rinsed again in 100 µl PBS, and finally resuspended in 20 µl PBS and kept on ice until use. Fluorescent and magnetic MyQuVigen Beads (Nvigen) served as control nonpulling beads, and were prepared according to the same protocol except for the incubation with fluorophores.

Unfertilized eggs were placed on a protamine-coated glassbottom dish. The bead solution was injected using a microinjection system (FemtoJet 4; Eppendorf) and a micromanipulator (Injectman 4; Eppendorf ). Injection pipettes were prepared from siliconized (Sigmacote; Sigma-Aldrich) borosilicate glass capillaries (1-mm diameter). Glass capillaries were pulled with a needle puller (P-1000; Sutter Instruments) and ground with a 30° angle on a diamond grinder (EG-40; Narishige) to obtain a 5-10-µm aperture. Injection pipettes were back-loaded with 2 µl bead solution before each experiment and were not reused.

Magnetic tweezers

The magnetic probe was built from three rod-shaped, strong neodymium magnets (diameter, 4 mm; height, 10 mm; S-04-10-AN; Supermagnet) prolonged by a sharpened steel piece with a tip radius of ∼50 µm to create a magnetic gradient. The surface of the steel tip was electrocoated with gold to prevent oxidization. Magnetic probes were calibrated by tracking the velocity of single magnetic beads in a medium of known viscosity, as a function of the distance to the magnet, and by using the Stokes relationship to compute the net magnetic force. The same experiment performed on bead aggregates of various sizes at a given distance allowed us to establish force-size relationships. For this part, the drag of bead aggregates was assayed by measuring sedimentation speed in a medium of known viscosity, and found to be well represented by the drag of a spherical particle with a radius equal to the geometrical mean of the aggregate size (Tanimoto et al., 2018). The magnetic tweezers position was controlled with the injection micromanipulator (Injectman 4; Eppendorf). To assemble the pulling cortical cap, we injected the beads and aggregated them at the cell cortex ∼10-20 min before fertilization by positioning the magnetic tip at 50-100 µm from the egg and maintaining it during all the experiment. Step-like motion during time-lapse acquisition, used for measuring cortical forces, was achieved with a home-built Micro-Manager (Open Imaging) script piloting the microscope stage (MS-4400; ASI) to move the sample relative to the fixed magnetic tweezers, with step sizes of 5 µm spaced by 30-s intervals.

Microscopy and image analysis

Injections, magnetic tweezer manipulations, and time-lapse acquisitions were performed on a wide-field fluorescence microscope (TI-Eclipse; Nikon) equipped with a complementary metal oxide-semiconductor camera (Orca-flash4.0LT; Hamamatsu). Samples were filmed with a 20× dry objective (NA, 0.75; Apo; Nikon) and a 1.5× magnifier (final pixel size, 0.217 µm). The microscope was operated with Micro-Manager (Open Imaging). Live imaging was carried out in artificial sea water at a stabilized room temperature (18-20°C). Immunostained samples were imaged with a confocal microscope (LSM780; Zeiss) with a 63× water immersion objective (NA, 1.4; C-Apo; Zeiss). Images were processed with Fiji (ImageJ; National Institutes of Health) and assembled in Photoshop (Adobe). Noise was reduced by using a median filter (1-pixel width) for the DNA (Hoechst) channel. Aster and bead trajectory tracking was performed with a custom code written in MatLab (MathWorks). Centration and decentration speed measurements were computed from a linear fit on 70% of the centration trajectory centered around the midpoint of the centration trajectory and during the 5 min after centration, respectively, by using a representative subset of 18 individual trajectories. The centration position was defined as the position with the shortest distance to the center. The decentration position was obtained by fitting a decreasing exponential to the trajectory after centration. To represent the effect of magnetic forces on the position of aster centers during and after centration (Fig. 4, B andC), we used a simple time-lapse projection that highlights the deviation from the centering path during centration (Fig. 4 B) and a kymograph to visualize the deviation of an already centered aster along the pulling axis (Fig. 4 C).

Drug treatments

Drugs were prepared as 100× stock aliquots in DMSO. Nocodazole (Sigma-Aldrich) was used at a final concentration of 20 µM. Ciliobrevin D (EMD Millipore) was used at a final concentration of 50 µM. Drugs were rapidly added (within less than a minute) when aster centration was completed and maintained until the end of the experiment.

Immunostaining

Immunostaining was performed by using procedures similar to those described previously [START_REF] Foe | Stable and dynamic microtubules coordinately shape the myosin activation zone during cytokinetic furrow formation[END_REF]Minc et al., 2011). Embryos were fixed in the same glass-bottom dish, after filming centration or decentration, for 70 min in 100 mM Hepes, pH 6.9, 50 mM EGTA, 10 mM MgSO 4 , 2% formaldehyde, 0.2% glutaraldehyde, 0.2% Triton X-100, and 800 mM glucose. To limit autofluorescence, samples were rinsed in PBS and placed in 0.1% NaBH 4 in PBS made fresh 30 min before use. Samples were then rinsed in PBS and PBT (PBS 0.1% Triton X-100) and incubated for 24 to 48 h in mouse anti-tubulin (DM1A; Sigma-Aldrich) primary antibody at 1:5,000 in PBT. After three washes of 1 h in PBT, samples were incubated for 12 h in goat anti-mouse secondary antibody coupled with Dylight 550 (Thermo Fisher Scientific) at 1:1,000 in PBT. Samples were then washed three times for 1 h in PBT, transferred in 50% glycerol PBS, and finally transferred into mounting medium (90% glycerol and 0.5% N-propyl gallate PBS).

Cortical force measurement

To compute the cortical force exerted by the cap, we fitted the binned distance-force curves (Fig. 3 D) with a simple model, assuming that the cap takes off at a critical force (when the magnet is far enough) and then moves at constant speed toward the center. A more complete model including a small decreasing force from the magnet after takeoff could not be reliably fitted to the data because of experimental noise. This model yields a simple relationship between the distance of the aggregate to the cortex, x c , and the magnetic force, F mag :

x c = x 0 + β ( 1 _ √ _ F mag -1 _ √ _ F cap )
.

We fitted the binned force-distance curves (Fig. 3 D) to this model by minimizing the absolute orthogonal error on (x c , F mag ) as a function of β and F cap , using MatLab's fminsearch function. This analysis yielded a force of F cap = 293.9 pN during centration and of F cap = 287.4 pN after centration. Fitting individual force-dis- tance curves by minimizing the absolute orthogonal error led to comparable mean values, and allowed us to estimate an SD (248.76 ± 206 pN and 291.27 ± 152 pN during and after centration, respectively). Statistical analysis on those two sets of data yielded a t test P-value of 0.1435, suggesting they are not significantly different from each other.

Computing aster drag and spring constant

To compute aster drags and centering spring constants from individual experiments (Fig. 4, D and E), we fitted each displacement curve by using a Kelvin-Voigt model, in custom-made MAT LAB scripts, as previously described (Garzon-Coral et al., 2016),

x _ F = 1 _ κ [ 1 -exp ( -tκ _ γ ) ] ,
where κ is the aster centering stiffness (or centering spring constant) and γ the drag coefficient. In experiments, the duration of force application was adjusted to allow the aster to reach the plateau when magnetic forces equilibrate MT centering forces (Garzon-Coral et al., 2016;Tanimoto et al., 2018). Mean values reported in the text correspond to fits of binned data (Fig. 4 F). We note that this method allowed us to reliably compare drag values before and after centration, but most likely correspond to a lower bound of the actual values of the drag (Garzon-Coral et al., 2016;Tanimoto et al., 2018).

Theoretical models

1D model

In the 1D model, the aster was represented by one frontal MT segment (directed toward the center) of length L f , and one rear MT segment (directed toward the nearest cortex) of length L r (Fig. 2 E; Tanimoto et al., 2016). In sea urchin zygotes, as in other embryos, centering forces have been found to be predominantly associated with MT length-dependent pulling, mediated by dynein pulling in bulk cytoplasm (Hamaguchi and Hiramoto, 1986;Kimura and Onami, 2005;[START_REF] Wühr | A model for cleavage plane determination in early amphibian and fish embryos[END_REF]Tanimoto et al., 2016). MT pulling forces were thus scaled to segment lengths through a constant a, yielding a net centering force:

F c = a ( L f -L r ) . (1)
Position x of the aster was set close to the center initially and evolved with time after an overdamped force balance equation, with γ the effective drag of the aster,

γ x ˙ = F c -F cap , (2)
in which F cap is the decentration force applied by the cortical do- main on the aster (Fig. 2 E). Finally, the lengths of the front and rear segments increase with time as a consequence of MT polymerization, at a rate v p , so that

L ˙ r = L ˙ f = v p . (3)
A key assumption of this model and similar previous ones is that MT length is limited by the cortex (Kimura and Onami, 2005; Minc et al., 2011; Tanimoto et al., 2016), which implies that -R < x -L r and R > x + L f , with R the radius of the cell. Eqs. 1, 2, and 3 were integrated by using a custom MatLab script. In this 1D model, the parameter a can be converted into a centering spring constant κ, with κ = 2a. The default parameter values for this model were κ 1 = 61.48 pN/µm (our measurement), F cap = 293.9 pN (our measurement), and γ = 140 pN min/µm, as computed in Tanimoto et al. ( 2018), and v p = 8.25 µm/min (fitted and adjusted, and consistent with measurement from Tanimoto et al., 2016). In Fig. 2 F, we changed the value of F cap = 0 pN, 100 pN, and 1,000 pN. In Fig. 2 G, we started the simulation with F cap = 293.9 pN and κ 1 = 61.48 pN/µm, and we then either decreased κ to κ 2 = 18.01 pN/µm or increased F cap to 1,003.27 pN at t = 11 min, by using a linear decay/increase over a 1-min period. In Fig. S3 B, we varied the final value of κ after centration from 5 to 60 pN/µm. In Fig. S3 A, we varied the final value of F cap from 300 to 800 pN using similar decay/increase times.

3D model

For the 3D model, the aster was represented with a constant angular distribution of MTs, ρ(θ,φ) = N/4π (with N the number of MTs), of length L(θ,φ) (Minc et al., 2011;Tanimoto et al., 2016).

The net centration force on the aster thus reads:

F c = ρ ∫ 0 2π ∫ 0 π a u(θ, ϕ ) L(θ, ϕ ) sin(ϕ ) dθdϕ, (4)
in which u(θ,φ) is the unit vector oriented with angles θ and φ and a is the pulling force per unit length of an MT computed from the values of κ measured in experiments (see below). The dynamic equations for MT lengths and aster position r are similar to those in the 1D model,

γ r ˙ = F c + F cap (5) L ˙ ( θ, ϕ ) = v p , (6)
with MT length limitation by the cortex implying

R > | | r + u(θ, ϕ ) L(θ, ϕ ) | | .
Eqs. 4, 5, and 6 were integrated by using a Euler scheme, implemented through a MatLab script. For this process, we discretized L(θ, ϕ) using a uniform range of θ and φ, spherical coordinates with the aster center as the origin, and verified that this distribution was homogeneous and did not induce a systematic bias. The integral in Eq. 4 was accordingly replaced by a discrete sum of the n = 28,654 discrete elements,

F c = k ∑ i=1 N L i u i
in which L i and u i are the length and orientation of MTs for the orientation i. The force per MT unit length a was computed from the experimental measurement of the aster centering spring constant κ. A Taylor expansion of Eq. 4 around x = 0 leads to

a = 3 _ N κ,
in which κ is the centering spring constant measured experimentally.

Once a MT contacted the cap, the full pulling force from the cap was added to that force balance and assumed to be F cap = F cap u d , in which u d is the unit vector directed from the aster center to the cap position. As a consequence, although the cap had a fixed size, this size had little influence on the model prediction. To incorporate the decrease of κ after centration, we used a linear decrease between two time points t 1 and t 2 from a spring constant value κ 1 to a value κ 2 . Positions and speeds extracted from model results were computed in the same manner as for the experiments. The parameter values used were the same as in the 1D model, with additional parameters κ 2 = 18.01 pN/µm (measurement), cap size = 5 µm (close to measurement values), t 1 = 10 min, and t 2 = 11 min (best-fitting values; see influence in Fig. S3, F andG).

Online supplemental material Fig. S1 includes the characterization of bead aggregates motion; an example of cap formation and relocation; an example of the long-term effect of a small pulling cap during embryonic cleavages; details of the MT network under cortical pulling; and control experiments demonstrating the requirement of MTs and dynein for cortical pulling. Fig. S2 shows other examples of aster centration/decentration trajectories; the details of MT networks during centration under cortical pulling; and a characterization of the relationship between aster size and cortical pulling. Fig. S3 includes the effect of increasing cap force and decreasing centering constant on aster position in the 1D model; the evolution of measured spring constants and released cap velocities before and after centration; and the simulated aster positions from different profiles of centering force reduction. Video 1 is an example of cortical cap assembly and relocation. Video 2 shows an asymmetric division induced by an artificial cortical pulling domain (Fig. 1 B). Video 3 is a control embryo with a "nonmaintained" cap (Fig. 1 D). Video 4 is a control embryo containing a "nonpulling" cap (Fig. 1 E). Video 5 shows decentration failures upon dynein inhibition and MT depolymerization (Fig. S1 L). Video 6 shows aster centration and decentration under cortical pulling (Fig. 2 A and Fig. S2, A-C). Video 7 shows examples of "free-cap" motions when fertilization occurs close to or far from the cap. Video 8 is a magnetic force reduction experiment during aster centration under cortical pulling (Fig. 3 B). Video 9 is an aster pulling experiment during and after centration (Fig. 4 A). Video 10 shows a 3D simulation of aster centration and decentration under cortical pulling (Fig. 5 A).

Bioelectric signaling and the control of cardiac cell identity in response to mechanical forces

Hajime Fukui, Renee Wei-Yan Chow, Jing Xie, Yoke Yin Foo, Choon Hwai Yap, Nicolas Minc, Naoki Mochizuki and Julien Vermot

Paper published in Science

DEVELOPMENTAL BIOLOGY Bioelectric signaling and the control of cardiac cell identity in response to mechanical forces Hajime Fukui 1,2 , Renee Wei-Yan Chow 1 , Jing Xie 3 , Yoke Yin Foo 4 , Choon Hwai Yap 4,5 , Nicolas Minc 3 , Naoki Mochizuki 2 , Julien Vermot 1,5 * Developing cardiovascular systems use mechanical forces to take shape, but how ubiquitous blood flow forces instruct local cardiac cell identity is still unclear . By manipulating mechanical forces in vivo, we show here that shear stress is necessary and sufficient to promote valvulogenesis. We found that valve formation is associated with the activation of an extracellular adenosine triphosphate (ATP)-dependent purinergic receptor pathway, specifically triggering calcium ion (Ca 2+ ) pulses and nuclear factor of activated T cells 1 (Nfatc1) activation. Thus, mechanical forces are converted into discrete bioelectric signals by an ATP-Ca 2+ -Nfatc1mechanosensitive pathway to generate positional information and control valve formation. T he cardiovascular system is continuously exposed to mechanical forces such as fluid shear stresses and stretching forces generated by blood flow and heartbeat. In the heart, the mechanotransduction cascade translates forces into cellular biochemical signals in the endocardial cells (EdCs) to shape valves (1 2 , ). These cell types present unique functional properties and are thought to differentially respond to forces depending on the heart regio ns to which th ey belong ( , 3 4). Here, we examined the ability of mechanical forces to modulate specific endocardial fate toward valvulogene sis. We found that valvular cell identity is directed by mechanical forces through different mechanosensitive pathways: transient receptor potential (TRP)mediated klf2a activation and adenosine triphosphate (ATP) mediated Ca -2+ oscillations leading to Nfatc1 signaling in response to local high shear stresses.

Using zebrafish to allow for high-precision control of spatiotemporal mechanical parameters, we analyzed Ca 2+ dynamic patterns by live imaging of the fluorescent Ca 2+ -sensor protein GCaMP7a expressed in EdCs using Tg (fli1a:galff);(uas:GCaMP7a) (5). We found that EdCs displayed Ca 2+ oscillations almost exclusively in the EdCs of the atrioventricular canal (AVC) that will form the AV valve (Fig. 1,A to C; fig. S1,A to E; and movies S1 and S2) between 32 and 102 hours postfertilization (hpf). To verify that the Ca 2+ oscillations were associated with valvulogenic differentiation, we searched for the decoder and the effector of Ca 2+ signaling. Nuclear factor of activated T cells 1 (Nfatc1) is an established Ca 2+ -sensitive transcription factor known to modulate the endocardial-to-mesenchymal transition and subsequent heart valve morphogenesis (fig. S2, A andB) (6)(7)(8)(9)(10)(11). We generated a Nfat binding element reporter line, Tg(4xnfbr:d2EGFP), which expresses d2EGFP in response to the binding of nuclear-localized Nfat protein (fig. S2, C andD). Nfat reporter expression was observed in EdCs of the AVC from 34 hpf onward (Fig. 1, and E, and fig. S2E), with a similar time course observed for the Ca 2+ response (Fig. 1, C andE). We confirmed these results by tracking Nfat nuclear relocalization of an endothelialand endocardial-specific green fluorescent protein (GFP)-Nfatc1 reporter (fig . S2F). Thus, both spatial and temporal regulation of Ca 2+ signaling and Nfat activation are features of the valvulogenic EdCs.

To determine whether the observed Ca 2+ oscillations in EdCs are force responsive, we assessed the Ca 2+ signals in hearts stopped by MS-222 or p-amino blebbistatin treatment. We found tha t Ca 2+ oscillations were abrogated in EdCs when the hear t stopped and recovered after the heartbeat was restarted (fig. S3, A to C). Because lower hematocrit affects shear stress and flow profile in the AVC ( , 12 13), we analyzed the bloodless mutant Vlad Tepes (gata1a) (14). Both gata1a mutants and morphants exhibited fewer Ca 2+ spikes and a decrease in Nfat activity (fig. S3, D to G). Thus, both Ca 2+ oscillations and Nfat activation are stimulated in response to mechanical forces generated by the beating heart.

We next changed the mechanical force distribution in the living heart by artificially changing the boundary conditions and thus the flow forces in the system (Fig. 2A). We inserted a 30-to 60-mm-diameter agarose-based magnetic bead into the cardiac lumen by microsurgery without perturbing heart function (Fig. 2, A and B, and movie S3). To quantify the force generated around the bead, we performed a three-dimensional (3D) simulation of the wall shear stress and pressure around the bead using an image-based computational fluid dynamics simulation with dynamic wall motion ( ) (Fig. 2C and fig. S4, A to C). Shear stress 15 and pressure were increased in the vicinity of the bead (movie S4) and were close to the endogenous forces generated where the valve normally forms (15)(16)(17). In vivo, we observed Ca 2+ spikes in the EdCs next to the bead when trapped in the atrium or in the ventricle (Fig. 2D; fig. S4,D to G; and movies S5 and S6). To more precisely control shear forces, we directly manipulated the bead within the heart using magnetic tweezers (Fig. 2E). The force generated ranged from 100 to 2000 pN (fig.

S4, H and I), a stimulus that is slightly higher than endogenous wall shear stresses generated in the AVC ( ). Although the mag-15 17

net probe alone did not affect Ca 2+ influx in EdCs, direct pulling of the magnetic bead led to the generation of Ca 2+ influx in the EdCs of the arrested heart (Fig. 2, F to H; fig. S4,J and K; and movie S7). Thus, Ca 2+ fluxes are induced in the EdCs by wall shear stress and associated wall pressure, whereas cardiac contractility is not necessary. We assessed the biological relevance of the localized response initiated by bead grafting to find out whether it is associated with the formation of ectopic valves. Sixteen to 20 hours after bead grafting in the atrium, valve-like EdC clusters were observed near the bead. The valve-like structures were visible in the atrial region that protruded from the atrial surface to the atrial cavity or the cardiac jelly (Fig. 3A and fig. S5A). A grafted bead triggered the mislocalized protrusions into cardiac jelly (fig. S5A), which constitutes the first sign of v alve morphogenesis in zebrafish ( ). We 18 additionally found that the grafted bead induced the expression of in the valve-twist1b like structures (Fig. 3B and fig . S6,A to D) and the ectopic expression of klf2a, , klf4a and wnt9b in the EdCs surrounding it (fig . S7, A to C and F). These observations indicate that ectopic valve like structures share sim-ilarities with endogenous valves. In addition, Nfat activity was ectopically induced in EdCs located near the bead (fig. S5, B andC), which is consistent with the fact that Nfatc1 nuclear localization is activated in response to ectopic forces and reduced when heart contractility is affected (fig. S5, D to G). Nuclear translocation of Nfatc 1 was inhibited by a chemical blocker of calcineurin (FK506) acting on the Ser/Thr dephosphorylation site of Nfat (fig . S5D). Thus, the nuclear localization of Nfatc1 is promoted by increased mechanical force in a Nfatc1 Ser/Thr dephosphorylation-dependent manner. Neither klf2a nor klf4a expression was affected when calcineurin was inhibited by either FK506 or VIVIT, a sel ective peptide inhibitor of Nfat ( ) (fig. S7, C to F), 19 suggesting that the Ca 2+ -Nfat signaling path-way acts independently of the klf2a mechanotransduction pathway. Conversely, egr1, a known mechanosensitive gene expressed in the AVC (20), was down-regulated by calcineurin inhibition (fig. S7, G andH), suggesting that egr1 acts downstream of Nfatc1. Thus, mechanical forces are key to specifying heart valve position during development b y modulating both the Klf2a-a nd the Nfatc1-signaling pat hways.

To characterize the factors responsible for the force-dependent Ca 2+ -Nfat signal activation, we first focused on established mutant lines for the stretch-sensitive channels Trpp2,Trpv4,Piezo1,Piezo2a,and Piezo2b (17,21 22 , ) and for ciliogenesis (iguana, Dzip1) (23), which have been implicated in flow sensing in the cardiovascular system (24). We found that all of these mutants showed normal Ca 2+ activation (fig. S8, A andB) as well as for embryos treated with gadolinium io n (Gd 3+ ), a nonspecific stretch-sensitive channel blocker (fig. S8C). Alternatively, ATP is released in cultured endothelial cells in response to mechanical stimuli ( ). As a response, ATP activates Ca 252+ signaling through the purinergic receptor P2X channels (26) (Fig. 4A). Accordingly, Ca 2+ influx in EdCs of the AVC was abolished when cytosolic ATP levels were depleted by oligomycin A, a mitochondrial ATP synthase inhibitor (fig . S8D). We investigated whether extracellular ATP alters Ca 2+ influx in EdCs by microinjecting oligomycin A, apyrase (an ATPase), and ATP S g (an ATP analog) into the cardiac lumen (Fig. 4B, and movie S8), and found that the Ca 2+ influx was significantly affected in response to changes in extracellular ATP levels (Fig. 4C and fig. S8,E to I). Transcripts of the ATP receptors p2rx1, p2rx4a, and p2rx7 were present in EdCs of the heart (fig. S9, A andB). Embryos treated with antagonists of P2X1, P2X4, and P2X7; embryos overexpressing a dominant-negative form of either human P2X4 (hP2X4C353W) or zebrafish p2rx4a (zP2rx4aC365W) mRNA; and p2rx4a morphants displayed a significant reduction of Ca 2+ spikes in EdCs (Fig. 4D and fig. S9, C to G and I). These results show that the Ca 2+ influx in EdCs is modulated by P2X channels in response to changes in extracellular ATP levels.

We next assess ed whether the activation and inhibition of P2X-mediated ATP signaling affected valve formation. Embryos treated with a combination of P2X1, P2X4, and P2X7 antagonists; a combination of P2X4 with P2Y2 antagonists; a P2X4 antagonist; or a P2Y2 antagonist suppressed Nfat reporter activation, whereas the other P2X or P2Y antagonists had no effect (fig. S10, A andB). Furthermore, overexpression of a dominant-negative form and knock-down of p2rx4a did not affect klf2a and klf4a expression but significantly suppressed Nfat reporter expression (Fig. 4E and fig. S9, H, J, andK), correlating well with the abnorm al Ca 2+ activation (Fig. 4D and fig. S9G). In addition, embryos displayed abnormal valve st ructures with incomplete morphogenesis of the valve, absence of leaflet formation (Fig. 4F), and mislocalized Twist1b-positive cells in the endocardium when p2rx function was inhibited (Fig. 4F and fig. S11, A to C). EdCs were excluded from the luminal part of the valve when Nfat activity was suppressed in these cells (fig. S11, D andE), consistent with the fact that Nfatc1 is necessary for valve development in zebrafish (7). Although vascular endothelial growth factor (Vegf) signaling is known to activate Nfat signaling (27), a Vegfr2 inhibitor had no effect on either Nfat reporter expression or Ca 2+ activation in the EdCs (fig. S10, A to D). These results suggest that P2X and P2Y receptors coordinately modulate Nfat activity in the EdCs independently of VEGF signaling. In addition, we found that Nfat activity in the endocardium seemed to be unrelated to tyrosine phosphoryla tio n (28) (fig. S10, A andE). Altogether, these results confirm that P2X functions act upstream of Nfat activity to control valve development in response to mechanical stimuli. Mechanical forces have been implicated in a broad range of events during embryonic development (29 31 -). The presented work reframes our view of how EdCs interpret mechanical forces (Fig. 4G) and supports the intriguing possibility that valve formation is mainly defined by the mechan osensitive inputs resulting from the local tissue constraints and flow forces ( , ,

). Piezo and Trp channels 7 18 32 34 are well-established stretch-sensitive channels involved in cardio vascular morphogenesis and valve development (17, , 21 35-37). Our work identifies ATP as an additional mechanosensitive paracrine signal by which hemodynamic forces can direct heart valve development. Therefore, it is a compound that could be used to help grow heart valves in vitro and may be involved in congenital heart valve defects. More generally, this work shows that biological systems rely on multiple mechanosensitive pathways to precisely control morphogenetic processes. ATP release and stretch-sensitive channels are activated in response to discrete mechanical stimuli to precisely generate the permissiv e signal contr olling the localization and timing of valve morphogenesis. We view this as a safeguard mechanism that increases the robustnes s of the mechanose nsitive process to avoid ectopic valve formation in other regions of the heart where mechanical forces are also at work. [0001] La présente invention se rapporte au domaine de la biologie, en particulier de la mécanobiologie, et concerne plus particulièrement une méthode de caractérisation des propriétés mécanobiologiques d'une cellule ou de l'un de ses éléments ou compartiments.

ARRIERE PLAN TECHNOLOGIQUE

[0002]

La mécanobiologie est un domaine de recherche émergent visant à comprendre comment la mécanique des organites cellulaires, des cellules, des tissus, et/ou de leur environnement influence la physiologie des organismes. Un des socles de ce domaine de recherche et de ses applications biomédicales est de pouvoir mesurer et appliquer de manière précise des forces mécaniques à la surface des organites et des cellules dans des environnements tissulaires complexes.

[0003]

Les forces mécaniques au sein et autour des cellules peuvent influencer des processus clés comme la différentiation, la division ou encore la migration cellulaire (Engler et al., 2006;[START_REF] Ladoux | Mechanobiology of collective cell behaviours[END_REF]. De manière importante, de nombreuses maladies comme le cancer, les maladies cardiovasculaires, les maladies génétiques et malformations développementales, sont typiquement associées à des changements drastiques de propriétés mécaniques des cellules et tissus (Carey et al., 2012;[START_REF] Makale | Cellular mechanobiology and cancer metastasis[END_REF][START_REF] Murthy | Piezos thrive under pressure: mechanically activated ion channels in health and disease[END_REF] . Au sein des cellules, le noyau possède aussi une forme et une rigidité de surface, essentiel à l'intégrité de l'enveloppe nucléaire et à la préservation de l'information génétique. Ainsi, la forme, la taille et la mécanique du noyau sont très souvent utilisées comme marqueurs de la progression de cancer [START_REF] Jevtic | Mechanisms of nuclear size regulation in model systems and cancer[END_REF].

[0004]

Ces découvertes récentes ont conduit au développement d'une nouvelle discipline pluridisciplinaire, la mécanobiologie, à l'interface entre l'ingénierie, la biologie et la médecine, qui consiste à étudier la régulation et le rôle des forces nucléaires, cellulaires et tissulaires pour caractériser le comportement des systèmes vivants et leur dérégulation dans différentes maladies [START_REF] Lim | Mechanobiology[END_REF]. La mécanobiologie implique l'application et la mesure de forces sur les cellules et/ou tissus vivants [START_REF] Roca-Cusachs | Quantifying forces in cell biology[END_REF]. A ce jour, deux méthodes commerciales sont disponibles : (i) les pinces optiques et (ii) la microscopie par force atomique.

[0005]

La méthode de pinces optiques est une méthode proposée pour appliquer des forces ou sonder les propriétés mécaniques de la surface ou de l'intérieur des cellules. Cette méthode possède une gamme de forces typiquement comprise entre 0.01 pN et 10 pN, et s'applique à des problématiques moléculaires (moteurs ou filaments biologiques uniques). Elle est en revanche inadaptée à des mesures en volume, puisque la force devient trop faible dès que l'on s'éloigne du plan focal du laser, et sa gamme de forces ne correspond pas aux forces typiques cellulaires et tissulaires (10-1000 pN). Cette méthode nécessite par ailleurs l'utilisation de laser infrarouge coûteux et dont l'alignement doit systématiquement être calibré, impliquant souvent des protocoles longs et dépendant de l'utilisateur.

[0006]

La méthode de microscopie par force atomique (AFM) consiste à indenter, à l'aide d'une pointe couplée à un déflecteur calibré, la surface de cellules ou tissus pour en mesurer par exemple la rigidité. Elle ne peut pas être appliquée à des mesures au sein du volume des cellules ou tissus, et créé des dommages conséquents sur les cellules, notamment dans les gammes de forces intéressantes pour étudier la mécanobiologie d'une cellule. Elle est donc limitée dans sa compatibilité avec des échantillons vivants. Elle est aussi associée à un montage complexe, nécessitant des calibrations précises et souvent débattues dans les communautés (différents modèles d'interprétation des courbes distances-forces).

[0007]

Ainsi, les méthodes disponibles à ce jour sont largement limitées à l'application de forces sur échantillons fins, et la gamme de forces utilisable dans ces techniques reste limitée à quelques piconewton (pN) au maximum sur des échantillons vivants. Elles sont par ailleurs coûteuses et difficiles à implémenter en routine, et peu compatibles avec l'imagerie dynamique.

[0008]

Ainsi, il existe un besoin de développer de nouvelles stratégies permettant d'étudier et de caractériser les propriétés mécanobiologiques cellulaires, et notamment de mettre à disposition une méthode permettant d'apporter des informations précises sur la biomécanique cellulaire et tissulaire et pouvant s'utiliser dans une gamme d'applications large.

Résumé de l'invention

[0009] L'invention a pour but de pallier au manque de méthodes robustes, versatiles et précises d'application et de mesures de forces dans des échantillons biologiques. Les inventeurs proposent ici une méthode fondée sur l'utilisation de pointes magnétiques adaptées à la mécanique de surface tissulaire, cellulaire et nucléaire, permettant d'appliquer des forces dans des gammes allant du pN jusqu'au nN, et ce au sein de tissus profonds ou d'embryons multicellulaires non humains en développement. Cette méthode s'appuie sur des micro-pointes aimantées qui appliquent des forces magnétiques sur des microparticules paramagnétiques fonctionnalisées pour se lier spécifiquement à des éléments et/ou compartiments cellulaires. Cette approche permet notamment des applications localisées de forces : (i) au sein des cellules, pour des applications par exemple pour l'étude de la mécanique du noyau (ii) à la surface d'une cellule unique ou au sein de tissus ou embryons multicellulaires de grandes tailles (iii) avec une gamme de forces surpassant de 2-3 ordres de grandeurs la gamme des méthodes commerciales courantes comme les pinces optiques et la microscopie par force atomique et/ou (iv) avec une compatibilité optimale avec les cellules et tissus vivants. Les inventeurs démontrent ici la versatilité, la robustesse et l'applicabilité de la méthode selon l'invention au sein de cellules et tissus invertébrés et vertébrés, dans le cadre d'une déformation du noyau au sein d'une cellule vivante, d'application de force de surface sur cellules uniques ainsi qu'au sein de la lumière de larges ensembles multicellulaires.

[0010]

La méthode a été validée dans plusieurs types cellulaires et différents embryons multicellulaires en développement. Ceux-ci incluent des embryons d'échinodermes (oursins), d'insectes (drosophiles), de vertébrés (Poisson zèbre) et des cellules mammifères en culture.

[0011]

Les deux principales techniques concurrentes pour sonder la mécanique de cellules et tissus sont les pinces optiques, et la microscopie par force atomique. Par rapport à l'invention, ces méthodes sont : (i) limitées à des mesures en surface d'échantillons fins (cellules adhérentes ou monocouches), (ii) limitées à une gamme de forces faible, peu compatible avec les forces nécessaires à l'étude de la plupart des cellules et tissus, (iii) invasives, et donc peu compatibles avec la physiologie et l'imagerie de cellules vivantes sur de longues périodes, (iv) très difficiles d'implémentation et (v) beaucoup plus couteuses.

[0012] L'invention se démarque des autres méthodes de mesure et d'application de forces, par sa versatilité en termes d'applications pour étudier des propriétés mécanobiologiques concernant les organites cellulaires, les propriétés du cytoplasme cellulaire, les forces de surface, et ce, au sein de cellules uniques ou de cellules insérées dans un tissus complexe et profond. En outre, cette approche est entièrement compatible avec des échantillons vivants et avec le développement et la prolifération de cellules et tissus vivants, et permet une gamme de force bien plus large que les méthodes de pinces optiques.

[0013]

Au-delà des informations sur la physiologie de nombreux tissus et embryons, la versatilité et la simplicité d'implémentation de la méthode, promet une application dans des contextes de recherches industrielles biomédicales. Par exemple l'invention pourra servir de standard pour une classification rapide et précise des propriétés mécaniques de tissus dans des contextes de diagnostic de maladies, pour établir des essais rapides pour cribler les réponses mécanobiologiques d'organes et de tissus sains et malades, pour établir des signatures mécaniques utiles dans le diagnostic de tissus malsains dans le domaine de la santé, ou pour développer des criblages chimiques spécifiquement liés à la mécanobiologie tissulaire, en particulier pour évaluer l'effet de médicaments ou de petites molécules sur des réponses mécanobiologiques (rigidité d'un tissu ou d'une cellule saine ou tumorale, propriétés structurales du noyau, etc.).

[0014] L'invention a pour objet une méthode, de préférence in vitro ou ex vivo, pour caractériser au moins une propriété mécanobiologique d'un élément ou compartiment cellulaire dans un échantillon biologique, ladite méthode comprenant :

[0015] a) l'introduction de billes superparamagnétiques dans l'échantillon biologique lesdites billes comprenant un revêtement biologique apte à adresser de manière spécifique les billes superparamagnétiques à un élément ou compartiment cellulaire d'intérêt, [0016] b) l'application d'un champ magnétique sur lesdites billes superparamagnétiques de manière à appliquer une force sur l'échantillon biologique, [0017] c) la mesure d'au moins une propriété mécanobiologique de l'élément ou compartiment cellulaire dans l'échantillon biologique.

[0018]

En particulier, le champ magnétique est appliqué par une pointe magnétique, ladite pointe magnétique comprenant préférentiellement au moins un aimant millimétrique ou submillimétrique prolongé par une pointe métallique, ladite pointe métallique étant préférentiellement usinée avec un rayon de courbure compris entre 5 et 100 micromètres.

[0019]

Selon un aspect, la méthode selon l'invention comprend en outre (i) une étape préalable dans laquelle le revêtement biologique des billes est sélectionné en fonction de l'élément ou compartiment cellulaire d'intérêt, (ii) une étape préalable de préparation de la pointe et/ou des billes superparamagnétiques et/ou (iii) une étape de calibration de la pointe et des billes.

[0020]

De préférence, l'échantillon biologique est choisi parmi une cellule, un tissu, un organe et un embryon non humain, préférentiellement préalablement obtenu par échantillonnage. En particulier, l'échantillon biologique est vivant et/ou non fixé.

[0021]

Selon un aspect, l'élément ou compartiment cellulaire est choisi parmi : la membrane cellulaire, la membrane nucléaire, la membrane d'un organite, tel que la mitochondrie, le réticulum endoplasmique ou l'appareil de golgi, les lysosomes, les peroxysomes ainsi que leur contenu, tel que le cytoplasme, les microtubules et/ou les centrioles, de préférence la membrane cellulaire ou la membrane nucléaire.

[0022]

De préférence, les propriétés mécanobiologiques sont choisies parmi : la rhéologie, la cinématique, la résistance mécanique, l'élasticité, la rigidité, la plasticité et les propriétés visco-élastiques, et toutes combinaisons de celles-ci.

[0023]

Le revêtement biologique des billes superparamagnétiques peut être un revêtement protéique, comprenant au moins une protéine appât apte à reconnaitre une protéine proie sur l'élément ou compartiment cellulaire d'intérêt, de préférence un anticorps ou une lectine, préférentiellement un anticorps choisi parmi un anticorps anti Sodium Potassium ATPase, anti PMCA1, anti Pan Cadherin, anti E Cadherin, anti N Cadherin, anti ADAM22, anti LRP4, anti Fas (APO-1, CD95), anti CD27, anti EGFR, anti NPC et anti NUP98. Les billes superparamagnétiques ont de préférence une taille comprise entre 100 nm et 100 µm, de préférence entre 100 nm et 50 µm, préférentiellement entre 100 nm et 1 µm.

[0024]

En particulier, la force appliquée sur l'échantillon biologique est comprise entre 0.,001 pN et 200 nN, de préférence entre 0,5 pN et 1,5 nN.

[0025]

Les méthodes selon l'invention permettent notamment de (i) L'invention concerne également l'utilisation du kit selon l'invention, pour (i) caractériser les propriétés mécanobiologiques d'un échantillon biologique, et/ou (ii) caractériser l'impact d'une drogue ou d'un médicament sur un échantillon biologique, et/ ou (iii) identifier les cellules tumorales dans un échantillon biologique.

DESCRIPTION DES DESSINS

[0029]

[fig. 1] représente le principe de pointe magnétique pour l'application de force à la surface du noyau, de cellules uniques et de tissus multicellulaires. A. Schéma présentant le dispositif de pointe magnétique : un aimant permanent prolongé d'une pointe métallique est monté sur un micromanipulateur 3D. La pointe est approchée d'un échantillon vivant placé dans un milieu de culture et observé au microscope. B.

Exemple schématique d'application de force sur une culture cellulaire contenant des particules magnétiques spécifiquement adressées à la membrane plasmique ou à l'enveloppe nucléaire. C. Exemple schématique d'application de forces sur un tissu contenant des particules magnétiques associées à la membrane plasmique ou piégées dans la lumière de l'épithélium.

[0030]

Figure 2 représente la calibration des forces magnétiques appliquées.

[0031]

[fig. 2A] Les billes magnétiques placées dans un milieu visqueux se déplacent vers la pointe et leur vitesse instantanée (représentée avec un gradient de gris) permet de calibrer la force en fonction de la distance avec la pointe magnétique.

[0032]

[fig. 2B] Force magnétique créée par la pointe sur des particules magnétiques (1μm de diamètre) dans des milieux de viscosités différentes (viscosité indiquée dans la légende). La modulation de la viscosité permet d'établir de manière plus précise la force sur une gamme de distances plus grande.

[0033]

Figure 3 [fig. 4] représente la mesure de la rigidité du noyau au sein d'une cellule intacte. Des billes magnétiques couvertes d'anticorps dirigés contre les protéines de surfaces du noyau (anti-NPC), injectées au sein d'une cellule vivante d'oursin, se lient spécifiquement à la surface nucléaire et permettent de tirer et de déformer le noyau. La déformation et la valeur de la force appliquée permettent de calculer la rigidité de la surface nucléaire.

[0039]

[fig. 5] représente la mesure de la rigidité de la surface d'une cellule unique. Des billes magnétiques ont été injectées dans un embryon d'oursin au stade 1 de de développement. La présence de l'aimant provoque l'agrégation des billes magnétiques et la déformation de la membrane cellulaire. La déformation et la valeur de la force appliquée (ici ≈ 660pN) permettent de calculer la rigidité de la surface cellulaire.

[0040]

[fig. 6] représente la mesure des propriétés mécaniques d'un tissu au sein d'un système multicellulaire 3D. Une large bille magnétique injectée au sein de l'endocardium du coeur d'un poisson zèbre vivant permet d'appliquer des forces calibrées sur les tissus de surface et de calculer la rigidité de compression et de déformation des tissus.

DESCRIPTION DETAILLEE DE L'INVENTION

[0041]

La méthode selon l'invention s'appuie sur l'utilisation de billes superparamagnétiques et de pointes magnétiques pour évaluer les caractéristiques mécanobiologiques d'une cellule, d'un élément, ou d'un compartiment de celle-ci. Ces différents éléments sont plus particulièrement décrits ci-après.

Billes superparamagnétiques [0042] La méthode selon l'invention est compatible avec toutes sortes de particules ou billes superparamagnétiques. Il en existe commercialement un grand nombre, présentant une gamme de chimie de surface modulable. Les inventeurs ont testé et validé la méthode selon l'invention avec une dizaine de billes de marques différentes, sans aucun signe de défaut ou de limite de l'approche.

[0043]

Tel qu'utilisé ici, le terme « paramagnétisme » concerne le comportement d'un matériau qui ne possède pas d'aimantation spontanée mais qui, sous l'effet d'un champ magnétique extérieur, acquiert une aimantation orientée dans le même sens que le champ magnétique appliqué, par exemple un champ tel qu'appliqué par une pointe magnétique. Un matériau paramagnétique possède une susceptibilité magnétique de valeur positive. L'aimantation de ces matériaux peut également se renverser spontanément sous l'influence de la température, notamment à la température de Curie du matériau. Une interaction d'échange entre les moments magnétiques existe qui, en dessous d'une certaine température, conduit à un ordre magnétique (ferromagnétique, ferrimagnétique ou antiferromagnétique). Au-dessus de cette température, les moments fluctuent et ces matériaux se caractérisent par une susceptibilité magnétique scalaire positive de l'ordre de 10 -5 à 10 -3 . Par « supraparamagnétisme » ou « superparamagnétisme » est entendu un comportement des matériaux paramagnétiques de dimensions micrométriques ou nanométriques.

[0044]

Selon un mode de réalisation particulier, les billes superparamagnétiques sont constituées de coeurs d'oxydes de fer tel que de la magnétite, de taille micrométrique ou nanométrique, et généralement enrobés dans une enveloppe de polymère. Le moment magnétique des billes dépend du nombre de coeurs ou domaines magnétiques. Les billes constituées par un grand nombre de domaines ont un fort moment magnétique et sont donc facilement attirées par un aimant permanent. Comme elles sont superparamagnétiques, les billes acquièrent rapidement une aimantation sous l'effet d'un champ magnétique. Cette aimantation disparaît immédiatement avec la suppression du champ. Selon un mode de réalisation, le coeur superparamagnétique des billes est inclus dans une couche de polymère (par exemple des polysaccharides) fonctionnalisé avec un domaine de liaison (par exemple de la streptavidine). Ce domaine de liaison est utilisé pour la fixation du revêtement qui va assurer l'adressage des billes à un élément ou compartiment cellulaire particulier.

[0047] L'« adressage » est entendu ici comme un mécanisme permettant le transport des billes superparamagnétiques vers leur destination intra ou extracellulaire d'intérêt. Par exemple, lorsque les billes ont un revêtement constitué par des anticorps anticadhérine, une protéine de la membrane plasmique, les billes sont adressées (i.e. transportées/localisées puis fixées) au niveau de la membrane plasmique après leur injection.

[0048]

Par « revêtement » est entendu ici une couche déposée à la surface d'un matériau, ici une bille superparamagnétique, pour lui conférer des propriétés particulières. Notamment, le revêtement présent à la surface des billes paramagnétiques permet l'adressage spécifique des billes à un compartiment ou élément cellulaire et éventuellement leur fixation sur celui-ci. Le revêtement peut notamment être un revêtement protéique, peptidique ou lipidique.

[0049]

De préférence, le compartiment ou élément cellulaire est choisi parmi : la membrane cellulaire, la membrane nucléaire, la membrane d'un organite, tel que la mitochondrie, le réticulum endoplasmique ou l'appareil de golgi, les lysosomes, les peroxysomes ainsi que leur contenu, tel que le cytoplasme, les microtubules et/ou les centrioles. De préférence, le revêtement présent à la surface des billes permet leur adressage et leur fixation à la membrane cellulaire ou à la membrane nucléaire, ou à d'autres organites cellulaires.

[0050]

De préférence, la fixation des billes à un compartiment ou élément cellulaire est réalisée par liaison non-covalente, notamment une liaison de type protéine-protéine, en particulier de type protéine appât-protéine proie, ou de type anticorps-antigène.

[0051]

Par « protéine proie » est entendu ici une protéine cellulaire d'intérêt, que l'homme du métier souhaiterait cibler pour évaluer des caractéristiques mécanobiologiques d'une cellule, d'un compartiment ou élément de celle-ci.

[0052]

Par « protéine appât » ou « protéine hameçon » est entendu ici une protéine capable de reconnaitre, d'interagir et de se lier à la protéine proie, en particulier ayant une affinité spécifique à un compartiment/structure cellulaire.

[0053] L'homme du métier sait identifier des couples protéine appât-protéine proie d'intérêt. Par exemple, pour adresser spécifiquement les billes superparamagnétiques à la membrane nucléaire, une protéine proie peut être une protéine constituant les pores nucléaires et la protéine appât un anticorps reconnaissant spécifiquement cette protéine des pores nucléaires.

[0054]

Selon un mode de réalisation, le revêtement des billes superparamagnétiques est un revêtement protéique, de préférence un anticorps, un peptide ou une lectine.

[0055]

Des billes magnétiques fonctionnalisées avec des protéines telles que des anticorps sont disponibles commercialement. Alternativement, des méthodes et kits de fonctionnalisation sont disponibles afin de recouvrir les billes d'un composé d'intérêt. Ces méthodes et kits sont bien connus de l'homme du métier. Par exemple, la réaction entre les groupes ester sulfonique et acide carboxylique permet de créer des liaisons covalentes entre les billes et le composé d'intérêt, tandis que les billes-streptavidine sont fonctionnalisées via l'interaction biotine-streptavidine par des anticorps ou autres protéines préalablement couplés de façon covalente à de la biotine.

[0056]

Pour les anticorps n'étant pas disponibles en version biotinylée, leur biotinylisation préalable est possible, notamment via l'utilisation de méthode et de kit de biotinylation, par exemple le kit EZ-link NHS-biotin commercialisé par Sigma.

[0057]

Selon un mode de réalisation, le revêtement des billes super-paramagnétiques est un anticorps, de préférence choisi parmi un anticorps anti Sodium Potassium ATPase, anti PMCA1, anti Pan Cadherin, anti E Cadherin, anti N Cadherin, anti ADAM22, anti LRP4, anti Fas (APO-1, CD95), anti CD27, anti EGFR, anti NPC et anti NUP98.

[0058]

De manière préférée, les protéines « hameçons » utilisées pour adresser spécifiquement les particules à la membrane plasmique ou l'enveloppe nucléaire sont choisies parmi le tableau suivant : [0059] [0060] De préférence, les billes superparamagnétiques ont une taille comprise entre 100 nm et 100 µm, de préférence entre 100 nm et 50 µm, préférentiellement entre 100 nm et 1 µm.

[0061] L'homme du métier sait choisir la taille des billes ainsi que leur revêtement selon l'utilisation envisagée, en tenant compte de l'élément ou compartiment cellulaire visé.

[0062]

Selon un mode de réalisation particulier, les billes utilisées sont choisies parmi : [0063] (i) des billes de 800 nm, en particulier couvertes de streptavidine, présentant des propriétés d'agrégation et de collages aspécifiques à différentes structures biologiques comme le noyau, les centrosomes du fuseau mitotique ou la surface de certaines cellules.

[0064]

(ii) des billes de 100 nm couvertes de streptavidine ne présentant pas d'interactions spécifiques avec les structures cellulaires utilisées pour la calibration et les expériences contrôles.

[0065]

(iii) des billes magnétiques de 200 nm incluant une couche fluorescente de type « quantum dots » recouverts par des moteurs moléculaires purifiés (dynéines), permettant en particulier un adressage plus précis à certaines structures intracellulaires.

[0066]

(iv) des billes passivées à la BSA (Bovine Serum Albumin) de 1µm de diamètre, permettant en particulier un déplacement inerte dans le cytoplasme des cellules.

[0067] (v) des billes de 30-50 µm, en particulier couvertes d'une couche d'agarose, permettant notamment de déformer des portions larges d'un tissus, par exemple au sein du coeur d'un embryon.

[0068]

(vi) Des billes de 1µm de diamètre (Dynabeads) associées à un anticorps anti-pores nucléaires (anti-NPC) permettant l'adressage à l'enveloppe nucléaire et la déformation du noyau.

[0069]

De préférence, les particules superparamagnétiques utilisées sont des billes fluorescentes. Ainsi, les billes supraparamagnétiques selon l'invention peuvent comprendre en outre une ou plusieurs molécules fluorescentes, tel qu'un fluorophore, permettant leur visualisation en microscopie.

[0070]

Ainsi, facultativement, pour les particules non fluorescentes, une incubation avec un fluorophore biotynilé (Atto-biotin, Sigma) peut être réalisée si la visualisation des particules en microscopie à fluorescence est nécessaire. L'aimant du coeur magnétique est de préférence en néodyme, en ticonal, en alnico, en Neodyme Fer Bore (NdFeB) ou en Samarium Cobalt (SmCo). De manière préférée, les aimants du coeur magnétique sont en néodyme.

Pointe magnétique

[0079]

Les aimants en néodyme peuvent particulièrement être recouverts d'une fine couche de nickel-cuivre-nickel afin de les protéger contre la corrosion.

[0080]

Le coeur magnétique est prolongé à son extrémité proximale par une pointe métallique présentant un rayon de courbure compris entre 5-100 micromètres, de préférence entre 10 et 90 micromètres, 20 et 70 micromètres, 5 et 50 micromètres, 10 et 50 micromètres, 25 et 50 micromètres.

[0081]

De préférence, la pointe métallique a une forme tubulaire cylindrique. Le diamètre de la pointe métallique peut notamment être compris entre 0.5 et 1 millimètre. Les pointes plus fines permettent une précision spatiale plus fine, et les plus larges une gamme de forces plus large.

[0082]

Selon un mode de réalisation, la pointe métallique peut présenter une extrémité proximale effilée ou biseautée, permettant de faciliter le passage de la pointe magnétique dans un tissu.

[0083] Par « extrémité proximale », on entend la portion de la pointe magnétique la plus rapprochée des billes et/ou de la cellule, du tissu, de l'élément ou compartiment cellulaire d'intérêt. Inversement, par « extrémité distale », on entend la portion de la pointe magnétique la plus éloignée de ces éléments.

[0084]

De préférence, la pointe métallique surplombant le coeur magnétique est en acier, fer, nickel ou cobalt ou l'un de leur alliage, préférentiellement en acier.

[0085]

Selon un mode de réalisation, la pointe métallique surplombant le coeur magnétique est recouverte d'une couche d'or. En particulier, la couche d'or est appliquée par « electrosputting » pour améliorer la stabilité de la pointe vis-à-vis de l'oxydation dans les milieux de cultures, permettant notamment d'abolir les effets toxiques sur les cellules, et de conserver les pointes pour des durées d'utilisation de plusieurs mois/ années.

[0086]

Selon un mode de réalisation particulier, la pointe magnétique comprend un coeur magnétique composé de trois aimants en néodyme prolongés par une pointe d'acier aiguisée présentant un rayon de courbure d'environ 50 µm, apte à créer un gradient magnétique. La surface de la pointe en acier peut notamment être recouverte d'une couche d'or par électrolyse pour éviter l'oxydation.

[0087]

Les pointes magnétiques sont de préférence calibrées en suivant la vitesse de chacune des billes magnétiques dans un milieu de viscosité connue, en fonction de la distance à la pointe magnétique, et en utilisant la relation de Stokes pour calculer la force magnétique nette. La même expérience réalisée sur des agrégats de billes de tailles différentes à une distance donnée a permis d'établir des relations force-taille. La traînée des agrégats de billes peut être testée en mesurant la vitesse de sédimentation dans un milieu de viscosité connue, et est représentée par la traînée d'une particule sphérique de rayon égal à la moyenne géométrique de la taille de l'agrégat (Tanimoto et al., Nature Physics 2018). Une méthode de calibration de la pointe et des billes est particulièrement décrite ci-après.

[0088] La force résultante de l'application de la pointe magnétique sur les billes dépend en particulier de trois facteurs : (i) des propriétés magnétiques de la pointe et sa courbure (ii) de la susceptibilité magnétique des particules et de leur volume et/ou (iii) de la distance entre la pointe et la particule magnétique.

Méthode et Utilisation

[0089] L'invention concerne particulièrement une méthode pour étudier la mécanique cellulaire et intracellulaire, notamment au sein d'un échantillon biologique, notamment un tissu et ou un embryon multicellulaire, préférentiellement un embryon non humain.

[0090]

La méthode selon l'invention comprend une étape d'injection de billes superparamagnétiques, l'injection pouvant être réalisée à l'aide de systèmes d'injection commerciaux (par exemple l'InjectMan Eppendorf) des particules ou billes magnétiques soit au sein du cytoplasme de la cellule, soit à la surface de la cellule, soit au sein de la lumière d'un tissu ou d'un embryon. Par exemple, par le biais d'un micromanipulateur 3D, on approche la pointe magnétique à une distance contrôlée de la cellule et des billes superparamagnétiques, pour pouvoir appliquer une force précise sur la structure d'intérêt. Cette application de force peut être répétée plusieurs fois au cours d'un cycle cellulaire, maintenue, ou modulée en changeant la position de la pointe magnétique.

[0091] L'invention concerne plus particulièrement une méthode permettant de caractériser une ou plusieurs propriétés mécanobiologiques d'une cellule ou de l'un de Les différentes étapes de la méthode selon l'invention sont plus particulièrement décrites ci-après.

[0095]

Echantillon biologique et caractéristiques mécanobiologiques étudiés

[0096] L'échantillon sur lequel est appliquée la méthode peut être un organisme, un embryon, un organe, un tissu ou une cellule.

[0097] L'échantillon sur lequel est appliquée la méthode est de préférence sélectionné parmi une cellule, un tissu ou un organe préalablement obtenu par échantillonnage, ou un embryon préférentiellement non-humain.

[0098]

De préférence, l'échantillon est sous forme vivante et/ou non fixé.

[0099] L'échantillon peut être préalablement traité, par exemple en utilisant une solution d'eau de javel 50%. L'échantillon peut également être légèrement asséché puis collé sur une lamelle de verre et immédiatement recouvert d'une goutte d'huile perméable à l'oxygène (par exemple avec l'Oil 10S Voltalef).

[0100] L'échantillon testé peut provenir d'un sujet ou être issu d'une culture cellulaire, notamment en utilisant des lignées cellulaires disponibles commercialement.

[0101] L'échantillon peut être notamment une biopsie, réalisée sur un sujet préalablement à la méthode selon l'invention. Les termes « individu », « hôte », « sujet » et « patient », sont utilisés ici de manière interchangeable, et désignent un mammifère, plus particulièrement un sujet animal et plus particulièrement encore un humain. Lorsqu'il s'agit d'un animal, l'animal peut être un animal domestique tel qu'un chat ou un chien, un animal d'élevage tel qu'un cheval ou une vache, ou un animal de laboratoire, tel qu'une souris, une drosophile, etc.

[0102]

Selon un mode de réalisation, la méthode selon l'invention est réalisée sur une cellule. De préférence, la cellule étudiée est une cellule unique ou une cellule isolée, une cellule comprise dans un tissu pluricellulaire ou multicellulaire, une cellule comprise dans un embryon, ledit embryon étant de préférence non-humain, ou une cellule comprise dans un échantillon biologique, tel qu'une biopsie ou un explant. La cellule peut autrement être un microorganisme, tel qu'une bactérie, une levure ou un champignon unicellulaire.

[0103]

En particulier, la cellule étudiée est une cellule humaine, animale ou végétale. Selon un mode de réalisation, la cellule est une cellule non humaine.

[0104]

Selon un mode de réalisation particulier, la cellule est une cellule tumorale ou cancéreuse. La cellule peut être issue d'une tumeur primaire, une cellule cancéreuse circulante ou une métastase.

[0105]

Selon un mode de réalisation particulier, l'échantillon sur lequel est réalisé la méthode selon l'invention est un embryon, de préférence un embryon non humain.

[0106]

En particulier, l'embryon est choisi parmi un embryon d'oursin (Paracentrotus lividus), de drosophile (Drosophila melanogaster) ou de poisson Zèbre (Danio Rerio).

[0107]

De préférence, le compartiment ou l'élément cellulaire ciblé par les billes superparamagnétiques est choisi parmi : la membrane cellulaire, la membrane nucléaire, la membrane d'un organite, tel que les mitochondries, le réticulum endoplasmique ou l'appareil de golgi, les peroxysomes, les lysosomes ainsi que leur contenu, le cytoplasme, les microtubules et/ou les centrioles.

[0108]

De préférence, le compartiment ou l'élément cellulaire ciblé est la membrane cellulaire ou la membrane nucléaire.

[0109]

La méthode selon l'invention permet d'évaluer les caractéristiques mécanobiologiques de ces différents éléments.

[0110]

Les termes « caractéristiques mécanobiologiques » et « propriétés mécanobiologiques » sont utilisés ici de manière interchangeable et concernent les effets des contraintes mécaniques (étirements, compressions, cisaillements...) sur les cellules ou les tissus vivants. La mécanobiologie englobe la rhéologie, la cinématique, la résistance mécanique, l'élasticité, la plasticité, la rigidité, la flexibilité et les propriétés viscoélastiques, ou toute combinaison de celles-ci.

[0111]

Selon un mode de réalisation, les propriétés mécanobiologiques sont choisies parmi : la rhéologie, la cinématique, la résistance mécanique, l'élasticité, la plasticité, la rigidité, la flexibilité et les propriétés viscoélastiques, ou toute combinaison de cellesci. De préférence, la propriété mécanobiologique mesurée est la rigidité ou l'élasticité.

[0112] La « rhéologie » est la science qui étudie les déformations et l'écoulement de la matière. Elle a pour objet d'analyser les comportements mécaniques des substances et d'établir leurs lois de comportement. Elle englobe de nombreuses disciplines fondamentales telles que la résistance des matériaux, la mécanique des fluides, la plasticité et l'élasticité. Les propriétés rhéologiques d'une matière ou d'un élément cellulaire correspondent au comportement mécanique et aux relations entre les déformations et les contraintes de la matière. La rhéologie du fluide cytoplasmique d'une cellule ou de la lumière d'un tissu peut être mesurée par la méthode de pointe magnétique proposée. Pour cela des billes de tailles différentes peuvent être déplacées par l'application d'une force magnétique, permettant de déterminer la viscosité du cytoplasme, la dépendance de cette viscosité suivant la taille de l'objet déplacé, ou la force de cisaillement. Les viscosités typiques du cytoplasme s'étendent entre 10-1000 cP, et dépendent de la taille de l'objet déplacé dans le fluide ainsi que du type cellulaire.

[0113]

La « résistance mécanique » d'un élément est son comportement global (relation entre sollicitations -forces ou moments -et déplacements) et son comportement local (relation entre contraintes et déformations). Lorsque l'intensité de la contrainte augmente, il y a d'abord déformation élastique (l'élément se déforme proportionnellement à l'effort appliqué et reprend sa forme initiale lorsque la sollicitation disparaît), suivie parfois d'une déformation plastique (l'élément ne reprend pas sa forme initiale lorsque la sollicitation disparaît, il subsiste une déformation résiduelle), et enfin rupture (la sollicitation dépasse la résistance intrinsèque du matériau). La résistance mécanique de la membrane cellulaire ou nucléaire, ou d'une couche tissulaire peut être sondée par l'application des pointes magnétiques selon l'invention. Notamment l'application précise de forces de surface, et la mesure concomitante de la déformation, permet de déterminer les relations contraintes déformations de ces surfaces biologiques, et de calculer par exemple des constantes d'élasticité, s'échelonnant depuis 10 à 1000 pN/µm, des modules de Young de l'ordre de 1-100 MPa ou des déformations seuil de ruptures pour ces surfaces de 5-50%.

[0114] La « viscoélasticité » est la propriété de matériaux qui présentent des caractéristiques à la fois visqueuses et élastiques, lorsqu'ils subissent une déformation. Les matériaux élastiques se déforment lorsqu'ils sont contraints, et retournent rapidement à leur état d'origine une fois la contrainte retirée. En rhéologie, le comportement d'un matériau viscoélastique linéaire est ainsi intermédiaire entre celui d'un solide élastique idéal symbolisé par un ressort de module E (ou G) et celui d'un liquide visqueux newtonien symbolisé par un amortisseur de viscosité η. L'élasticité d'un matériau traduit sa capacité à conserver et restituer de l'énergie après déformation. La viscosité d'un matériau traduit sa capacité à dissiper de l'énergie. Les propriétés viscoélastiques de la membrane cellulaire ou nucléaire, ou d'une couche tissulaire peuvent être testées par l'application des pointes magnétiques selon l'invention. Notamment l'application précise de forces de surface, et la mesure en dynamique de la déformation résultante, permet de caractériser les échelles de temps viscoélastiques, et les constantes visqueuses et élastiques associées. Certains matériaux peuvent notamment exhiber des propriétés élastiques à temps courts et visqueuses à temps long (matériaux de type Maxwell) ou à l'inverse ils s'écoulent à temps courts et se comportent comme un solide élastique à temps longs (Matériaux de type Kelvin Voigt). Les échelles de temps viscoélastiques pour les matériaux biologiques considérés par l'invention peuvent varier entre 0.1-1000s ; les constantes de frictions visqueuses entre 100-10000 pN/μm, et les constantes élastiques de 10 à 1000 pN/µm.

[0115]

La « rigidité » ou « raideur » est la caractéristique qui indique la résistance à la déformation élastique d'un corps. Plus un élément est rigide, plus il faut lui appliquer une force importante pour obtenir une déformation donnée. A contrario, la « flexibilité » désigne la propriété selon laquelle un matériau souple peut être aisément courbé ou plié sans se rompre.

[0116]

La « résistance mécanique » d'un matériau est caractérisée par sa limite d'élasticité et/ou sa résistance à la traction.

[0117]

Les propriétés mécanobiologiques peuvent notamment être évaluées par la mesure du module de Young. Un élément ayant un module de Young (ou module d'élasticité) élevé (> à 50 GPa) est dit rigide, celui dont le module de Young est faible est au contraire souple, élastique ou flexible.

[0118] Préparation de la pointe magnétique et des billes paramagnétiques

[0119] Selon un mode de réalisation, la méthode selon l'invention peut comprendre en outre une étape de préparation de la pointe et/ou des billes paramagnétiques.

[0120]

Selon un mode de réalisation, la méthode selon l'invention comprend en outre la préparation ou fabrication d'une pointe comprenant ou consistant en l'assemblage d'éléments nécessaires et adaptés à son utilisation magnétique.

[0121]

La fabrication de la pointe comprend principalement l'assemblage d'un coeur magnétique et d'une pointe métallique tels que décrits ci-dessus dans le paragraphe « pointe métallique ».

[0122]

Ainsi l'homme du métier pourra optimiser les caractéristiques de la pointe selon l'échantillon à évaluer.

[0123]

Selon un mode de réalisation, la pointe magnétique est une pince magnétique.

[0124]

Selon un mode de réalisation, la méthode selon l'invention comprend en outre le choix et la préparation des billes superparamagnétiques préalablement à leur introduction dans la cellule, tissu, organe ou embryon.

[0125] L'adressage des particules magnétiques à une localisation subcellulaire spécifique peut être contrôlé par l'ajout de protéines « hameçons » à la surface des particules.

Dans la plupart des cas ces protéines sont biotynilées pour un couplage efficace avec le groupement streptavidine présent à la surface des particules magnétiques.

[0126]

En pratique, dans un premier temps, les particules sont lavées dans une solution saline ou une solution tampon, par exemple du tampon phosphate (PBS). Les particules sont ensuite incubées dans une solution contenant la protéine « hameçon ». Par exemple, pour un adressage à l'enveloppe nucléaire, un anticorps biotinylé dirigé contre les pores nucléaires tel que l'anticorps anti-NPC (SantaCruz sc-58815) peut être utilisé.

[0127]

De préférence, l'excès de protéines « hameçons » est éliminé par un lavage dans une solution tampon, par exemple du PBS.

[0128]

Les particules fonctionnalisées sont finalement re-suspendues dans du PBS à une concentration adaptée pour l'injection.

[0129]

De préférence, la concentration des billes paramagnétiques fonctionnalisées est comprise entre 0.5 et 5 mg/ml dans la solution d'injection.

[0130]

Pour les anticorps n'étant pas disponibles en version biotinylée, leur biotinylation peut être réalisée, notamment par l'utilisation préalable d'un kit de biotinylation (ex : EZ-link NHS-biotin, Sigma).

[0131]

Facultativement, lorsque les billes utilisées sont non fluorescentes, une seconde incubation avec un fluorophore biotynilé, par exemple le fluorophore Atto-biotin (Sigma) peut être réalisée à cette étape si la visualisation des particules en microscopie à fluorescence est nécessaire.

[0132]

De préférence, l'excès de fluorophore est éliminé par un lavage dans une solution tampon, par exemple du PBS.

[0133]

Les particules fonctionnalisées sont finalement re-suspendues dans du PBS à une concentration adaptée pour l'injection.

[0134]

De préférence, la concentration des billes paramagnétiques fonctionnalisées est comprise entre 0.5 et 5 mg/ml dans la solution d'injection.

[0135] Il est possible de vérifier la fonctionnalisation des billes, par diffusion dynamique de la lumière (DLS pour « Dynamic Light Scattering ») qui permet de mesurer la distribution en taille d'objets en suspension dans une solution. Ainsi il est possible de comparer la taille des billes initiales et la taille des billes fonctionnalisées, les billes fonctionnalisées ayant une taille supérieure aux billes non fonctionnalisées.

[0136]

Selon un mode de réalisation, la méthode selon l'invention comprend en outre une étape de vérification de la fonctionnalisation des billes avant injection, par exemple par la technique de DLS.

Calibration

[0137]

Pour connaitre la force précise appliquée sur une bille par la présence de la pointe magnétique et évaluer ainsi les propriétés mécanobiologiques de l'élément ou com-

Introduction des billes magnétiques [0141]

La méthode selon l'invention comprend une étape comprenant ou consistant en l'introduction de billes superparamagnétiques dans une cellule, un tissu, un organe ou un embryon, notamment tel que décrit ci-dessus, lesdites billes comprenant un revêtement permettant d'adresser spécifiquement les billes superparamagnétiques à un élément ou compartiment donné.

[0142]

Cette étape peut notamment s'appuyer sur l'utilisation de micro-injecteurs classiques, disponibles dans les laboratoires de biologies, tel que des micro-injecteurs 3D.

[0143]

Pour injecter des billes au sein d'une cellule ou d'un tissu, les éléments à optimiser incluent, par exemple, la taille de l'ouverture du micro-capillaire, la pression d'injection, la pression de compensation et la durée d'injection. Par exemple, l'injection in vivo d'une solution de billes magnétiques de 800nm à 5mg/ml est réalisée avec les paramètres suivants : Ouverture du capillaire : 5 à 15 micromètres, Pression de compensation : 5 à 30 hectoPascals, Pression d'injection : 15 à 90 hectoPascals, et durée d'injection : 100 à 500 millisecondes. Ces protocoles ont été affinés dans le cadre de cette invention.

[0144]

Pour les mesures en surfaces des cellules, l'adressage des billes est réalisé le plus souvent en ajoutant les particules magnétiques dans le milieu et en les laissant se coller à la surface cellulaire externe.

[0145]

Selon un mode de réalisation l'injection des billes dans la cellule est réalisée par biolistique ou bombardement. Cette technique consiste à propulser les billes superparamagnétiques d'intérêt dans les cellules à l'aide d'un canon à particules (par exemple Biolostic -Biorad PDS-1000/He).

[0146]

Selon un mode de réalisation, l'introduction des billes dans l'échantillon d'intérêt est réalisée par l'introduction d'une aiguille d'injection.

[0147]

Les aiguilles d'injection sont de préférence préparées à partir de capillaires en verre borosilicaté en utilisant une étireuse, par exemple l'étireuse P-1000 de Sutter Instruments. Les capillaires peuvent être traités au préalable avec une solution de siliconisation, par exemple la solution Sigmacote de Sigma.

[0148]

De préférence, les aiguilles ont un diamètre compris entre 1 µm et 1 mm de diamètre et sont particulièrement adaptées au diamètre des billes à injecter. Les aiguilles sont de préférence aiguisées selon un angle de 10°à 30°+/-2°, de préférence d'environ 30°j usqu'à obtenir une ouverture, par exemple à l'aide d'une biseauteuse (EG-40, Narishige). Le diamètre de l'ouverture de l'aiguille d'injection peut être comprise entre 1 µm et 1 mm, de préférence entre 5 et 15 micromètres.

[0149]

De préférence 1 à 5 microlitres de solution d'injection comprenant les billes superparamagnétiques sont introduits, à l'arrière de l'aiguille, juste avant le montage sur le système d'injection.

[0150]

Application et mesure de forces au sein d'échantillons vivants.

[0151] La méthode selon l'invention comprend une étape comprenant ou consistant en l'application d'un champ magnétique sur lesdites billes superparamagnétiques, de manière à appliquer une force sur l'échantillon biologique. Ceci permet d'évaluer et/ou mesurer des propriétés mécanobiologiques de l'élément ou compartiment cellulaire dans l'échantillon biologique.

[0152]

Le système de pointe magnétique est compatible avec différents types de microscopie, permettant de visualiser l'application de la pointe magnétique à proximité des billes et le déplacement des billes superparamagnétiques.

[0153]

Le tissu ou la cellule en question sont imagés sur un système de microscopie inversé ou droit, et après injection ou positionnement des billes magnétiques, la pointe magnétique est amenée dans le voisinage de l'échantillon pour appliquer une force et un champ magnétique. La position et/ou l'orientation de la pointe sont contrôlées par le biais d'un micromanipulateur, par exemple tel qu'un micromanipulateur 3D commercial. Les images de microscopie prises doivent contenir la pointe et la ou les particules magnétiques et permettent par le biais de scripts informatiques, de calculer la force exacte en fonction de la taille de la particule, de la distance entre la pointe magnétique et les billes, et de la calibration mentionnée ci-dessus. Suivant le procédé, le suivi par vidéomicroscopie de la déformation de la surface tissulaire, cellulaire ou nucléaire, ou du mouvement d'une organite, permet de calculer in fine, les propriétés mécanobiologiques de l'élément étudié (constante de rigidité élastique, seuil de rupture, friction visqueuse, ou échelle de temps visco-élastique).

[0154]

Selon un mode de réalisation, le microscope utilisé est un microscope fluorescent à champ large ou un microscope confocal. Le microscope peut être équipé d'une caméra. Le microscope peut également être piloté par Micro-Manager (Open Imaging).

[0155]

De préférence, les images sont prises à température ambiante (18-20°C). [0156] Afin d'obtenir les informations les plus robustes possible, la force appliquée sur la cellule par le biais de la pointe magnétique et des billes superparamagnétiques doit être constante et stable pendant un instant t. La position de la pointe doit ainsi être maintenue de façon stable à proximité des billes.

[0157]

Selon un mode de réalisation, la pointe est positionnée entre 10 et 500 µm de la cellule ou de l'élément ou compartiment cellulaire d'intérêt. Selon un mode de réalisation, la pointe est positionnée entre 10 et 500 µm à distance de la surface des billes superparamagnétiques.

Champ d'application de la méthode

[0158] L'utilisation des billes superparamagnétiques et de la pointe magnétique permettent d'explorer l'impact de l'environnement mécanique (stimulus) sur les cellules, d'étudier la perception de stimulus et les mécanismes de réponse des cellules et leur participation aux processus mécaniques et biologiques.

[0159] L'invention concerne l'utilisation de la méthode selon l'invention pour : [0160] (i) caractériser les propriétés mécanobiologiques d'une cellule ou de l'un de ses éléments ou compartiments, et/ou [0161] (ii) caractériser l'impact d'une drogue ou d'un médicament sur une cellule, un tissu, un organe ou un embryon ou de l'un de ses éléments ou compartiments, et/ou [0162] (iii) identifier et caractériser des cellules ou tissus endommagés, par exemple des cellules cardiaques endommagées dans le cadre de maladies cardiaques ou génétiques, et/ou [0163] (iv) identifier et caractériser des cellules tumorales dans un échantillon, lesdites cellules tumorales présentant des caractéristiques mécanobiologiques différentes des cellules normales, et/ou [0164] (vi) comprendre l'interaction mécanique des cellules entre elles ou avec la matrice qui les entoure qui leur permet de former des tissus cohérents, et/ou [0165] (vii) étudier la mécanotransduction, c'est-à-dire la façon dont la cellule intègre le signal mécanique et le transforme en signal biochimique lui permettant de réagir, de s'adapter et même de modifier l'expression de ses gènes. La mécanotransduction est impliquée dans de nombreuses fonctions cellulaires comme le changement de forme, la différenciation, la croissance, la prolifération et l'apoptose. Trois types de mécanotransduction sont actuellement décrits en fonction de la transduction qu'emploie la cellule pour adapter sa réponse aux facteurs environnementaux. La première est l'ouverture de canaux ioniques suite au stress mécanique, la seconde est l'initiation d'une cascade de signalisation et la troisième emprunte un pont physique entre les points focaux et la chromatine.

Kit et utilisation du kit

[0166]

La présente invention concerne finalement un kit permettant de réaliser la méthode selon l'invention.

[0167]

En particulier, le kit comprend : [0168] a) une pointe magnétique, de préférence telle que décrite ci-dessus dans le paragraphe « pointe magnétique », [0169] b) des billes superparamagnétiques adaptées à l'adressage spécifique et à la fixation desdites billes superparamagnétiques à un élément ou compartiment cellulaire donné, de préférence telles que décrites ci-dessus dans le paragraphe « billes superparamagnétiques », [0170] c) optionnellement une solution permettant la fonctionnalisation des billes superparamagnétiques, par exemple comprenant des anticorps ou une protéine appât, [0171] d) optionnellement, une ou plusieurs solutions destinées à la calibration des billes et de la pointe magnétique, [0172] e) optionnellement une solution permettant la mise en suspension et l'injection des billes superparamagnétiques dans une cellule ou un tissu cellulaire ;

[0173] f) optionnellement, un instrument permettant l'injection des billes, de préférence une aiguille d'injection préparée à partir de capillaires en verre borosilicaté.

[0174]

Les kits selon l'invention peuvent en outre comprendre un ou plusieurs consommables tels qu'un milieu de culture ou un milieu de préservation pour les tissus ou cellules, ou encore une notice explicative. L'invention concerne finalement l'utilisation du kit tel que décrit ci-dessus, pour (i) caractériser les propriétés mécanobiologiques d'une cellule ou de l'un de ses éléments ou compartiments, et/ou (ii) caractériser l'impact d'une drogue ou d'un médicament sur une cellule ou de l'un de ses éléments ou compartiments, et/ou (iii) identifier les cellules tumorales dans un échantillon, lesdites cellules tumorales présentant des caractéristiques mécanobiologiques différentes des cellules normales.

EXEMPLES MATERIEL ET METHODES Fabrication des pointes magnétiques [0181]

Les pointes magnétiques sont composées d'un coeur magnétique fait d'une superposition d'aimants submillimétriques ou millimétriques en néodyme, dont la géométrie et la magnétisation peuvent être modulées. Ce coeur est prolongé par une pointe d'acier usinée avec un rayon de courbure pouvant aller de 5-100 micromètres. Les pointes plus fines permettent une précision spatiale plus fine, et les plus larges une gamme de forces plus grandes. Pour stabiliser les pointes vis-à-vis de l'oxydation dans les milieux de cultures, et ainsi abolir les effets toxiques sur les cellules, les pointes sont recouvertes d'une fine couche d'or, en particulier d'une épaisseur de 0.5 à 1 micromètre par « electrosputting ». Les paramètres « d'electrosputting » sont à adapter pour chaque taille de pointes et chaque alliage métallique utilisés afin d'obtenir une couche d'or continue. Les pointes peuvent notamment être en acier. Des pointes ainsi fabriquées peuvent être conservées à l'abri de la poussière pendant plusieurs années.

Préparation et choix des particules magnétiques.

[0182]

La méthode est compatible avec toutes sortes de particules super-paramagnétiques, présentant une gamme de chimie de surface modulable, exploitant notamment des liaisons avidin-biotin, ou des réactions de sulfonation de groupement carboxyle. Les inventeurs ont notamment testé et validé la méthode de l'invention avec une dizaine de marques de billes différentes, sans aucun signe de défaut ou de limite de l'approche. Le choix des particules et de la modification de leur chimie de surface permettant un champ très large d'applications.

[0183] L'adressage des particules magnétiques à une localisation subcellulaire spécifique peut être contrôlé par l'ajout de protéines « hameçons » (ayant une affinité spécifique à un compartiment/structure) à la surface des particules. Dans la plupart des cas ces protéines sont biotynilées pour un couplage efficace avec le groupement streptavidin présent à la surface des particules magnétiques. [0184] En pratique, dans un premier temps, les particules sont lavées dans une solution à 1M NaCl, 1% Tween puis re-suspendues dans du PBS (Phosphate Buffer Saline). Si nécessaire, les particules sont ensuite incubées de 15 à 60 min dans une solution contenant la protéine « hameçon » requise. Par exemple, pour un adressage à l'enveloppe nucléaire, un anticorps biotinylé dirigé contre les pores nucléaire (mouse anti-NPC antibody -SantaCruz sc-58815) a été utilisé et validé ([fig.5]). L'excès de protéine est éliminé par un lavage dans du PBS. Facultativement, pour les particules non fluorescentes, une seconde incubation avec un fluorophores biotynilé (Atto-biotin, Sigma) peut être réalisée à cette étape si la visualisation des particules en microscopie à fluorescence est nécessaire. Les particules sont finalement re-suspendues dans du PBS à une concentration comprise entre 0.5 et 5 mg/ml. Cette solution d'injection peut être utilisée pendant plusieurs heures.

[0185]

Des exemples de protéines « hameçons » pouvant être utilisées pour adresser les particules à la membrane plasmique ou l'enveloppe nucléaire sont notamment décrits dans le Tableau 1.

[0186]

Pour les anticorps n'étant pas disponibles en version biotinylés, l'utilisation préalable d'un kit de biotinylation est requise (ex : EZ-link NHS-biotin, Sigma).

[0187]

Les inventeurs ont notamment utilisé et validé des protocoles utilisant (i) des billes de 800nm de la marque NanoLink (Solulink), qui présentent des propriétés d'agrégation et de collages aspécifiques à différentes structures biologiques comme le noyau, les centrosomes du fuseau mitotique ou la surface de certaines cellules ([fig. 3A] -3B). (ii) Des billes de 100nm couverte de streptavidine (Chemicell) ne présentant pas d'interactions spécifiques avec les structures cellulaires utilisé pour la calibration et les expériences contrôles. (ii) Des Quantum dots magnétiques streptavidine de 200nm (Nvigen) recouverts par des moteurs moléculaires purifiés (dynéines) permettant un adressage plus précis à certaines structures intracellulaires. (iii) Des billes passivées à la BSA (Bovine Serum Albumin) de 1 µm de diamètre (Dynabeads) permettant un déplacement inerte dans le cytoplasme des cellules ([fig.3C]). (iv) Des billes de 30-50 µm (Magne) permettant de déformer des portions larges d'un tissus au sein du coeur d'un embryon de poisson zèbre ([fig.3D]). (v) Des billes de 1 µm de diamètre (Dynabeads) associées à un anticorps anti-pores nucléaires (anti-NPC) permettant l'adressage à l'enveloppe nucléaire et la déformation du noyau ([fig.4]).

Calibration de la force appliquée

[0188]

Pour connaitre la force précise appliquée sur une bille par la présence de la pointe magnétique, il est nécessaire de calibrer le couple pointe magnétique-billes (Figure 2). Cette calibration permet de connaitre la force exacte en fonction de la distance entre la bille et la pointe magnétique. Pour cela une suspension de billes diluée (

Injection des billes magnétiques

[0189] Cette étape implique l'utilisation de micro-injecteurs classiques disponibles dans les laboratoires de biologie. Pour injecter des billes au sein d'une cellule ou d'un tissu, les éléments à optimiser incluent, la taille de l'ouverture du micro-capillaire d'injection, les pressions et durée d'injection. Pour les mesures en surface des cellules ou tissus, les méthodes sont plus directes et consistent le plus souvent à ajouter les particules magnétiques dans le milieu et les laisser se coller à la surface cellulaire.

[0190]

Les aiguilles d'injection sont préparées à partir de capillaires en verre borosilicaté (diamètre 1 mm) en utilisant une étireuse (P-1000 ; Sutter Instruments). Les capillaires sont traités au préalable avec une solution de siliconisation (Sigmacote, Sigma). Les aiguilles sont aiguisées selon un angle de 30°jusqu'à obtenir une ouverture de 5-10 micromètres à l'aide d'une biseauteuse (EG-40, Narishige). 2 à 3 microlitres de solution d'injection sont introduits, à l'arrière de l'aiguille, juste avant le montage sur le système d'injection.

[0191] L'injection de larges billes (20-60µm) au sein des tissus cardiaques de l'embryon de poisson zèbre se fait en incisant les tissus entre le sinus et l'atrium et en poussant la bille au sein de l'atrium à l'aide d'une aiguille placée sur micromanipulateur sous le microscope.

[0192]

Les embryons d'oursin sont injectés dans une chambre à fond en verre contenant de l'eau de mer. Le verre est préalablement traité avant une solution de protamine 1% (Sigma) pour assurer l'adhésion de l'échantillon. L'aiguille d'injection est contrôlée par un micromanipulateur motorisé (Injectman 4, Eppendorf) et une pompe d'injection (FemtoJet, Eppendorf).

[0193]

Les embryons de drosophile sont récoltés 1h maximum après la ponte et dechorionés dans une solution d'eau de javel 50%. Ils sont ensuite légèrement asséchés puis collés sur une lamelle de verre. Ils sont immédiatement recouverts d'une goutte d'huile perméable à l'oxygen (Oil 10S Voltalef). L'injection est réalisée grâce à un micromanipulateur hydraulique (Narishige) à l'extrémité antérieure de l'embryon avant la phase de cellularisation. Le contrôle de la pression d'injection est effectué manuellement à l'aide d'un micro-injecteur (CellTram, Eppendorf).

Culture cellulaire et tissulaire [0194] Les oursins adultes (Paracentrotus lividus) proviennent des stations marines de Roscoff et Villefranche sur mer (France) et sont conservés plusieurs semaines dans des aquariums d'eau de mer artificielle maintenus à 16C°. Les gamètes sont obtenus par injection intracoelomique de KCL 0.5M. Les oeufs sont conservés dans l'eau de mer à 16C°pendant maximum 12h. Le sperme peut être conservé non dilué pendant 1 semaine à 4C°. La gangue des oeufs est retirée en les passant dans un maillage de 80 micromètres. Avant chaque expérience le sperme est activé par dilution et mis en contact avec les oeufs pour la fécondation.

[0195]

Les Drosophiles (Drosophila melanogaster) sont maintenues à 25C°dans des tubes contenant un milieu nutritif. Pour la collecte des embryons, les drosophiles sont transférées dans des pondoirs contenant un milieu gélosé supplémenté en levure fraiche. Les pondoirs sont remplacés toutes les 30-60 minutes et les embryons sont collectés en rinçant les pondoirs à l'eau et en séparant les embryons de la levure à l'aide d'un tamis. Les embryons étant en cours de développement, ils sont préparés pour l'injection immédiatement.

[0196]

Les embryons de Poisson Zèbre (Danio Rerio) sont cultivés dans un milieu standard enrichi (https://zfin.org/zf_info/zfbook/chapt1/1.3.html); pendant 2-3 jours après fertilisation à ~28˚C et préparés pour l'injection de billes (voir ci-dessus). Ils sont retournés pour que le coeur soit face à la lamelle sous une binoculaire, puis imagés directement au microscope muni de pointes magnétiques. (ii) Injection et déplacement de particules magnétiques couplées à des Quantum dots et à la streptavidine de 200 nm (Nvigen) recouvertes par des moteurs moléculaires purifiés (dynéines) permettant un adressage aux microtubules et au centrosome.

Protocoles testés et validés

[0199]

(iii) Injection et déplacement de particules passivées à la BSA (Bovine Serum Albumin) de 1 µm de diamètre (Dynabeads) permettant un déplacement inerte dans le cytoplasme des cellules (Figure 3).

[0200]

(iv) Injection et déplacement de billes de 1µm de diamètre (Dynabeads) associées à un anticorps anti-pores nucléaires (anti-NPC) permettant l'adressage à l'enveloppe nucléaire et la déformation du noyau. Elles ont notamment été utilisées pour déformer la membrane nucléaire et mesurer ses propriétés ([fig.4]).

[0201] (v) Injection et déplacement de billes de 800 nm de la marque NanoLink (Solulink), qui présentent des propriétés d'agrégation et d'adhésion aspécifiques à différentes structures biologiques. Elles ont notamment été utilisées pour déformer la membrane cellulaire et mesurer ses propriétés ([fig.5]).

[0202]

(vi) Injection et déplacement de très larges billes de 30-50µm (Magne) permettant de déformer des portions larges d'un tissus au sein du coeur d'un embryon de poisson zèbre ([fig.6]).

Imagerie [0203]

Le système de pointes magnétiques est compatible avec différents types de microscopie. Les images présentées Figures 2A, 3A

RESULTATS [0204]

Une nouvelle méthode pour appliquer de larges forces aux surfaces cellulaires ou nucléaires au sein de tissus vivants.

[0205]

A ce jour, les méthodes commerciales d'applications de forces sur cellules vivantes, telles que l'AFM (Microscopie à Force Atomique) ou les pointes optiques, restent peu adaptées à des échantillons profonds, comme des tissus ou des embryons, notamment à cause d'une gamme de force limitée (souvent en dessous ou autour du pN), et du manque d'accès en profondeur des échantillons. Les inventeurs proposent ici une méthode fondée sur l'utilisation de pointes magnétiques, permettant d'appliquer des forces calibrées sur des particules magnétiques associées à la surface d'un tissu, d'une cellule unique, ou d'un noyau au sein d'une cellule ([fig.1]).

[0206]

Pour établir les possibilités d'application du système de pointes magnétiques, les forces applicables ont été calibrées en fonction de différentes billes magnétiques, pour des distances allant de la dizaine à la centaine de microns, correspondant aux échelles associées aux échantillons biologiques, depuis la cellule unique jusqu'aux ensembles multicellulaires. Pour cela, une pointe magnétique est couplée à un micromanipulateur en 3D et immergée dans un liquide visqueux de viscosité connue. Des billes magnétiques fluorescentes sont mises en solution, et des séquences d'images (films) sont enregistrées pour mesurer la vitesse des particules en fonction de leur distance à la pointe magnétique ([fig.2A]). Différents milieux avec des valeurs de viscosité différentes, permettent d'étendre la gamme de calibration sur des distances allant jusqu'à plusieurs centaines de microns ([fig.2B]). La vitesse de la particule en fonction de sa distance à la pointe est extraite par le biais d'un script d'analyse d'image ad-hoc, et permet de calculer la force magnétique en utilisant la loi de Stokes : F=6πηRV, avec η la viscosité du liquide, R, le rayon de la bille et V la vitesse de la bille. En utilisant différentes billes ayant des tailles allant de 1-50 µm, une gamme de force allant de la fraction du pN jusqu'à la centaine de nN, couvrant une gamme d'amplitude sur 5-6 ordres de grandeur, est démontrée, établissant ainsi la versatilité en termes d'amplitude de forces applicables par ce système (Tableau 1).

[0207]

Pour valider l'applicabilité de cette méthode au sein d'échantillon profond, des billes magnétiques ont ensuite été injectées au sein d'échantillons unicellulaires et multicellulaires ayant des tailles caractéristiques de l'ordre de 100 microns ([fig. 3A]-3B). Ces expériences montrent que des billes injectées au sein de ces cellules ou dans le lumen de larges embryons peuvent être déplacées facilement. Par ailleurs, en suivant par vidéomicroscopie les divisions cellulaires ou le développement des embryons sur plusieurs heures ([fig. 3C]-3D), les cellules injectées vont pouvoir se diviser, et les tissus se développer normalement, suggérant que l'injection et la manipulation de billes n'affectent pas la physiologie des cellules et tissus.

[0208]

Application à des mesures mécaniques de la surface du noyau cellulaire.

[0209] Une des premières applications de la méthode selon l'invention est d'aller sonder les propriétés mécaniques de la surface du noyau, au sein d'une cellule vivante. Cette application de force en profondeur est totalement incompatible avec les méthodes commerciales disponibles mentionnées ci-dessus. Ces informations quantitatives sont pourtant très précieuses, car les propriétés du noyau ont été suggérées comme marqueurs de nombreux processus comme la différentiation cellulaire, fortement dérégulées dans les cellules cancéreuses [START_REF] Kirby | Emerging views of the nucleus as a cellular mechanosensor[END_REF]. Néanmoins, mesurer ces propriétés au sein d'une cellule vivante est une tâche difficile et n'a jamais été rapportée dans la littérature. Pour valider cette approche, un protocole a été établi pour attacher à la surface des billes magnétiques des anticorps contre les pores nucléaires, des protéines hautement conservées chez les eucaryotes. Ces billes injectées au sein d'une cellule peuvent se lier et s'accumuler spécifiquement à la surface du noyau et permettent par l'approche d'une pointe magnétique de déformer le noyau. La mesure de la déformation en fonction de la force appliquée permet de calculer directement une élasticité (rigidité) de l'enveloppe nucléaire. Ainsi, par exemple, dans l'expérience présentée dans la [fig. 4], une force de 560.4 pN est appliquée et la déformation résultante est de ~8.7μm ; ce qui permet d'obtenir une rigidité effective de l'enveloppe nucléaire 62.2 pN/ μm directement au sein d'une cellule vivante.

[0210]

Application à des mesures mécaniques sur la surface cellulaire sur cellule unique.

[0211]

Une seconde application de la méthode est dans le calcul de la rigidité de la surface cellulaire. La surface cellulaire est limitée par la membrane plasmique qui contient en dessous un cortex fait d'actine et de myosine qui est important pour l'intégrité de surface. Les propriétés de ce cortex sont également essentielles pour des processus comme la migration ou la division cellulaire qui peuvent être dérégulés dans les cellules tumorales et métastatiques, par exemple. A ce jour, les propriétés mécaniques du cortex constituent ainsi une cible d'étude de la mécanobiologie fondamentale et appliquée à la médecine. Ces propriétés restent difficiles à mesurer précisément, notamment au sein de tissus profonds. En injectant des billes magnétiques au sein d'une cellule et en les approchant de la surface cellulaire, des forces peuvent être directement appliquées pour déformer le cortex et en mesurer ses propriétés viscoélastiques. Ainsi, à partir de l'expérience présentée dans la [fig. 5], une rigidité de 16.7 pN/μm et une viscosité effective de 1008,5 pN/μm de la membrane cellulaire sont mesurées.

[0212]

Application à des mesures mécaniques de tissus multicellulaires.

[0213] Une autre application importante du système de pointe magnétique est de pouvoir aller sonder des forces au sein de tissus à des profondeurs de l'ordre de la centaine de micromètres. Cet aspect est essentiel, car les modèles modernes d'étude de maladies (e.g. organoïdes, embryoïdes, sphéroïdes cancéreux) sont des modèles 3D avec des échelles de tailles de centaines de microns, où le besoin de sonder les propriétés des tissus en profondeur est important. Pour cela, les inventeurs démontrent ici la possibilité d'injecter de larges billes magnétiques au sein du lumen des tissus cardiaques d'un embryon de modèle vertébré (Poisson zèbre). Ces billes permettent d'appliquer des forces de tension de l'ordre de plusieurs dizaines de nN. Lorsque les billes sont déplacées par la pointe magnétique, elles viennent compresser le tissu et aussi le déformer. Ces expériences permettent ainsi de mesurer des constantes mécaniques de rigidité de compression de 16.3 mN/m et une élasticité de surface du tissu de 12.1 mN/ m, correspondant à une élasticité de ~1.7 kPa, correspondant à un ordre de grandeur typique pour des tissus cardiaques mesuré par d'autres moyens [START_REF] Kshitiz | Matrix rigidity controls endothelial differentiation and morphogenesis of cardiac precursors[END_REF].

DISCUSSION

[0214]

Les inventeurs présentent ici une méthode simple, versatile et robuste d'application de forces magnétiques adaptée à des échantillons larges comme des tissus ou des embryons. Le premier avantage de cette méthode par rapport aux méthodes commerciales actuelles, est qu'elle est à priori compatible avec tous types de microscopes et de micromanipulateurs disponibles dans des laboratoires standards de recherche et développement. Le second avantage est qu'elle couvre une gamme de forces et de distances bien supérieure aux autres approches, s'étalant sur 5-6 ordres de grandeur, et avec des distances de travail allant jusqu'à plusieurs centaines de micromètres. Ce point donne une unicité à l'approche présentée ici, car elle ouvre l'accès à des mesures dans le volume d'échantillons profonds comme les embryons en développement, les explants de tissus et les organoïdes qui servent de nouveaux standards dans la recherche biomédicale [START_REF] Simian | Organoids: A historical perspective of thinking in three dimensions[END_REF].

[0215]

Les inventeurs démontrent une série d'applications potentielles pour mesurer et étudier la mécanique de la surface d'un noyau d'une cellule, d'une cellule individuelle et celle d'un tissu. Cette versatilité est rendue possible par l'utilisation de différentes particules magnétiques de tailles différentes, et par des modulations de leur recouvrement de surface. Ces méthodes apportent des quantifications au sein de cellules ou de tissus vivants, qui ne peuvent pas être obtenues par les méthodes disponibles dans le commerce. La simplicité et la versatilité du système promet son application dans des criblages thérapeutiques ou du diagnostic de routine. Par exemple, dans le cadre de criblages thérapeutiques, il est possible de mesurer directement l'effet d'un composé ou d'une drogue sur la mécanobiologie d'un échantillon cellulaire vivant. Pour conclure, cette méthode de mesure, au vu de sa gamme d'applicabilité, sa souplesse et sa simplicité, pourrait servir en routine autant pour étudier les fondamentaux de la mécanobiologie que pour le développement de méthodes de diagnostics standards pour la médecine.

BILBLIOGRAPHIE

Abrégé

La présente invention concerne une méthode pour caractériser des propriétés mécanobiologiques d'un élément ou compartiment cellulaire, ladite méthode reposant sur l'utilisation d'une pointe magnétique et de billes superparamagnétiques.

Figure

  Figure.I.4: Cytokinesis.The cell cycle is completed by cytokinesis, which partially overlaps with telophase and divides the cytoplasm and other organelles into two daughter cells. In animal cells, the contractile ring is composed of acto-myosin which squeezes inward to form a cleavage furrow, separating the cell into two daughter cells (adapted fromPollard, 2010).

Figure.I. 5 :

 5 Figure.I.5: Three models for the formation of the cleavage furrow. (A) The astral MTs in red regions signal the cell cortex to relax, thus inducing the contraction at the equator. (B) and (C) show two equatorial models where the astral MTs at the center (white arrows in B) or MTs at the spindle midzone (white lines in C) can signal to the equatorial region of the cell (red region), leading to ring assembly and furrow contraction (fromKaltschmidt and Brand, 2002).

Figure.II. 1 :

 1 Figure.II.1: The structure of G-actin and F-actin. (A) The structure of a globular monomer of actin (G-actin) with a nucleotide (either ATP or ADP) bound in the center. (B) The structure of an actin filament (F-actin) assembled from monomers with a plus end (barbed end) and a minus end (point end). F-actin filaments have helical shapes with two parallel strands held together by lateral contacts and a twist repeating every 37 nm. (C) Electron microscopy of negatively stained F-actin (from Zelinski, 2014).

Figure.II. 3 :

 3 Figure.II.3: F-actin dynamics with binding proteins. (A) F-actin polymerizes at its barbed end and depolymerizes at its pointed end. (B) A capping protein bound to barbed end to block filament dynamics at the barbed end. (C) Arp2/3 bound to F-actin pointed end to terminate the polymerization and de-polymerization at this end. (D) Severing of F-actin is mediated by Cofilin binding. (E) Arp2/3 nucleated branched networks of F-actin with attachments at sides and angles around ±70° (from Nonaka, 2011).

Figure.II. 4 :

 4 Figure.II.4: Actin networks with different cross-links. (A) The crosslinker α-actinin, usually found in stress fibers, connects actin filaments in an antiparallel fashion with large intervals which enable access to myosin II. (B) Fimbrin makes tight crosslinks of parallel filaments. (C) and (D) Filamin dimer makes a flexible cross-link and induces a gel-like actin network, which are typically found beneath the plasma membrane (adapted from www.open.edu).

Figure.II. 5 :

 5 Figure.II.5: A model of f-actin treadmilling induced cell front protrusion. (1) Actin filaments are branched by Arp2/ 3 next to the plasma membrane and (2) push the membrane forward through actin polymerization at plus end, (3) which is terminated by stochastic capping. (4) Exchange of ATP to ADP through hydrolysis. (5) ADF/cofilin binding and unbinding to ADP-F-actin subunits. (6) Tropomyosin irreversible binding to ADP-Factin subunits. (7) Branched filaments can detach from the Arp2/3 binding site,(8) promoting the main filament depolymerization from their minus-end.(9) The detached actin monomers will diffuse to the leading edge to participate for actin polymerization via ADP to ATP exchange by profilin (from Nonaka, 2011).

Figure.II. 6 :

 6 Figure.II.6: Myosin structures. (A) Schematic representation of myosin structure for myosin I, myosin II and myosin V (from Molecular Cell Biology, 4th edition). (B) A zoom structure of myosin II, with the head, neck and tail domains. The heads serve as actin binding sites while the long rigid coiled-coil tail functions in muscle contraction (adapted from Walsh, 2011).

  II.7B) (Soares e Silva et al., 2011).

Figure.II. 7 :

 7 Figure.II.7: Myosin II generating contraction. (A) Representation of the force generation by myosin II in a sarcomere, which is the contractile unit of the muscle fiber. Myosin molecules forms more effective filaments to contract the sarcomere towards each other through their plus end movements. (B) Schematic of myosin contraction in an actin cortex. Myosin filaments produce contractile tension by sliding crosslinked actin filaments (adapted from M. Soares e Silva 2011).

Figure.II. 9 :

 9 Figure.II.9: The keratin network inside a PtK2 cell. An immunofluorescent image of labeled keratin filaments in rat kangaroo kidney epithelial cells (PtK2 line) (from Microscopyu website).

Figure.II. 10 :

 10 Figure.II.10: Microtubule (MT) structure and dynamics. MTs are polar filaments composed of α-β tubulin heterodimers. They usually grow from plus ends and can rapidly

Figure.II. 12 :

 12 Figure.II.12: Models for aster growth. (A) Standard model with MTs nucleated at the centrosome (red) and elongating radially. (B) Nucleation of MTs from the side of preexisting MTs (yellow dots), or from Golgi membranes (blue). (C) MTs release from centrosome and slide outward. (D) Capture of non-astral MTs. MT density decreases with radius only in model A, other models exhibit constant, or even increase density at the periphery (from Mitchison, 2012).

  sides of the nucleus, forming future spindle poles. Spindle MTs are of three distinct types: kinetochore microtubules, polar microtubules, and astral microtubules. They play different roles and generate forces to maintain the spindle structure and participate in the division processes. During prophase, a kinetochore MT grows from a centrosome, and encounters a kinetochore on one of the sister chromatids of a chromosome by prometaphase. It binds the kinetochore protein with its plus tip to capture the chromosome. Sister chromatids of a chromosome are thereby bound to MTs from opposite poles. During metaphase, forces from opposite kinetochore MTs on a chromosome are balanced, resulting in the alignment of the chromosomes at the spindle equator (Figure.II.14). Polar MTs growing from two opposite poles overlap their plus ends at the spindle equator without attaching to the kinetochores, and are stabilized by MAPs. Astral MTs extend outward from the centrosomes to the cell periphery and have freely exposed plus ends. Both polar and astral MTs contribute to chromosome segregation by pushing or pulling the centrosomes apart. Astral MTs are thought to reach the cell cortex in most cells, but may not contact the cortex in extremely large cells, like in early

Figure.II. 14 :

 14 Figure.II.14: The mitotic spindle at metaphase. (A) An immunofluorescent image of a metaphase spindle in a tissue-culture cell. MTs in green and chromosomes in blue (adapted from Wittmann, 2001). (B) Schematics of a mitotic spindle at metaphase and its associated components. At metaphase, the chromosomes align at the spindle equator through kinetochore MTs (green) emanating from the centrosomes at spindle poles. The polar MTs (red) grow from centrosomes and overlap antiparallel at the spindle equator. The astral MTs (blue) extend from centrosomes to reach the cell cortex (adapted from Biol.Penn.State, 2004).

Figure.II. 15 :

 15 Figure.II.15: Two types of spindle matrix proved by physical perturbations. (A) Elastic external spindle matrix is stretched by the spindle, thus the spindle shrinks after cutting a few kinetochore MTs via UV irradiation (arrows present the direction of compression). (B) Internal spindle matrix aligns along kinetochore MTs and pulls kinetochore to spindle poles during anaphase. The supported experiment is that kinetochore can still move towards the spindle pole during anaphase after cutting the indicated kinetochore MT by UV irradiation (arrow presents the movement of the kinetochore after cutting the linked MT) (adapted from Zheng, 2010).

Figure.II. 16 :

 16 Figure.II.16: Advanced techniques for quantitative measurements of the metaphase spindle. (A) 3D reconstruction of a C.elegans metaphase spindle using electron tomography. (B) (i) Schematic of experiment using glass microneedles to pull MTs on a metaphase spindle. (ii) Confocal and (iii) bright-field images of an X.laevis spindle with arrowheads indicating the tips of the needles, and the arrow indicating the force direction (adapted from Oriola, 2018).

Figure.II. 17 :

 17 Figure.II.17: Schematics of different spindle centering mechanisms. Red arrows indicate forces. (A) Cortical pushing mechanisms with non-buckled MTs. The MT elastic forces Fe (bending) are much larger than the polymerization stall force Fs (pushing), thus MTs remain straight against the cortex. Spindle moves towards the anterior as more MT pushing forces are generated at the posterior cortex. (B) Cortical pushing mechanisms with buckled MTs. The MT elastic forces Fe (bending) are smaller than the polymerization stall force Fs (pushing), thus MTs bend against the cortex. Shorter MTs are less bent and can exert more pushing forces. (C) Cortical pulling mechanism with stars indicating the motors anchored at the cell cortex. (D) Cytoplasmic pulling mechanism with stars indicating the cytoplasmic motors and grey spheres indicating the transported cargos along MTs (adapted from Wu, 2017).

Figure.II. 18 :

 18 Figure.II.18: Cytoplasmic pulling with cortical regulators. Schematics of metaphase spindle centration in a HeLa cell. (A) Spindle moves to the right as higher concentration of LGN-NuMA complexes are on the right cortex. (B) Spindle is balanced in the center. (C) Spindle moves to the left as higher concentration of LGN-NuMA complexes are on the left. When the left spindle pole is close to the cortex, Plk1 dissociate dynein from LGN-NuMA complexes, thus spindle moves to the right like (A) (adapted from McNally, 2013).

  Figure.II.17D, given the spindle is moved backward, front longer MTs can load more cargocarrying dyneins, yielding more pulling forces at front. The spindle is pulled in the direction of longer MTs, forming a length dependent mechanism.

Figure.II. 19 :

 19 Figure.II.19: Experimental evidences of MT cytoplasmic pulling mechanism for aster motion. (A) Aster movements towards the regions of MT polymerization in a Sand dollar embryo with drug Colcemid. (B) Anaphase spindle in Zebrafish 2-cell stage blastomeres moves following their longer MTs after a local MT depolymerization in asters with caged combretastatin 4A. (C) Aster movements in sea urchin embryos after UV-laser cutting along the indicated lines (red dotted lines) during aster centration. Laser ablation on the side of asters causes a transient deviation toward the top of the cell, supporting MT bulk pulling. Then MT regrowth promote a return of the aster to the centration path. Similarly, laser cuts at aster front cause aster to transiently step back, and move again to the cell center upon MT regrowth (from Xie, 2020).

Figure.II. 20 :

 20 Figure.II.20: Model for cleavage plane determination in large cells. Length dependent cytoplasmic pulling forces are used in the model. (A) Aster centration with length asymmetric sperm asters. (B) Sperm asters break down, small first mitotic spindle forms. (C) Anaphase asters expand but do not grow into each other and orient centrosome pairs to determine the 2nd division plane. (D) Metaphase spindles at two cell stage. MTs are in red and centrosomes in green (from Wuhr, 2010).

Figure.II. 21 :

 21 Figure.II.21: Direct force measurement of spindle positioning by Garzon-Coral et al. (A) Schematic of spindle positioning in a C.elegan embryo with different force generating mechanisms. (B) Experiment using magnetic tweezer to apply forces on one centrosome of the metaphase spindle and (C) the centrosome deviates away from the A-P axis. (D) Viscoelastic model of the spindle centering machinery using the Voigt element. (E) Spindle displacement upon magnetic force application and cessation, well represented by Voigt element (adapted fromPécréaux, 2016, Howard, 2017[START_REF] Wu | Forces positioning the mitotic spindle: theories, and now experiments[END_REF].

Figure.II. 22 :

 22 Figure.II.22: Mechanisms of non-astral spindle positioning. (A) Metaphase C.elegans meiotic spindles are positioned in a parallel orientation at the cortex by MTs and kinesin-1. (B) The mouse meiosis II spindle is positioned parallel by actin-dependent cytoplasmic streaming. (C) Pole-first migration of the mouse meiosis I spindle to the cortex is driven by myosin II cargo transport, (D) myosin II contraction of anti-parallel F-actin, or (E) forminnucleated pushing from the spindle or (F) from the cortex. Red arrows indicate the pointed ends of F-actin (adapted from McNally, 2013).

Figure.III. 1 :

 1 Figure.III.1: Schematics of a cell containing organelles and structures (from courses of lumenlearning).

Figure.III. 2 :

 2 Figure.III.2: Schematic of a mitochondrion. The mitochondria are the energy-conversion factories of the cell containing two separate lipid bilayer membranes and various molecules located on the inner membrane (adapted from Yusoff, 2015).

Figure.III. 4 :

 4 Figure.III.4: ER structure in different spices. (A) Nuclear envelope of ER in a HeLa cell transfected with GFP-Sec61β and (B) imaging of the peripheral ER closer to the coverslip. (C) ER network in Xenopus egg extracts with (D) large ER sheets containing ribosomes. (E) Electron micrograph (EM) of rough ER from guinea pig pancreas. (F) EM of smooth ER from ocular rabbit muscle (adapted from Schwarz, 2016).

Figure.III. 5 :

 5 Figure.III.5: Confocal images of ER throughout the cell cycle. (A) The ER structure of a CHO-K1 cell at interphase. White arrow heads point the ER structure at periphery. (B)-(E) ER structure during mitosis with (B) prometaphase, (C) metaphase, (D) anaphase and (E) telophase. (F) ER in metaphase with another labeling marker. ER is excluded in the region of spindle (adapted from[START_REF] Puhka | Endoplasmic reticulum remains continuous and undergoes sheet-to-tubule transformation during cell division in mammalian cells[END_REF].

Figure.III. 6 :

 6 Figure.III.6: Structure of yolk granules (adapted from Anton, 2013).

Figure.III. 7 :

 7 Figure.III.7: Yolk exclusion and influence to spindle position in early amphibian division. (A) Early Xenopus embryo division pattern with aster organization against yolk granules. (B) Immunostaining image along the A-V axis in a Xenopus 2-cell stage embryo, presenting MT density decreases as yolk concentration increases. Scale bar, 40 mm. (C) Model predictions of spindle positioning for (A) with black lines indicating the position and orientation of spindles (adapted from Pierre, 2016).

(

  Figure.III.9).

Figure.III. 9

 9 Figure.III.9 Comparison of three cytoplasm models. Cytoplasm is a homogeneous liquid in the viscous model. In the viscoelastic model, cytoplasm is a homogeneous network immersed in a fluid. The poroelastic model differentiates the two phases that allows the liquid to move relative through the network during shape change (adapted fromMitchison, 2008).

Figure.III. 10

 10 Figure.III.10 Pressure equilibration in the poroelastic model. Upon a constant load, pressure and deformation initiate near the plunger, where water flows through its porous membrane. With time, the liquid flow through pores in the gel over longer and longer distances, slowing equilibrating the pressure in the gel. Eventually, the deformation of the mesh becomes uniform and pressure vanishes (adapted from Mitchison, 2008).

Figure.III. 11

 11 Figure.III.11 Transition of liquid, glassy and solid phases with the volume fraction, φ. Top: Solid arrows indicate equilibrium states, whereas dashed arrows are non-equilibrium states. The glass transition volume fraction φg ~0.58. Bottom: Confocal images of the analogous phases in a colloidal suspension with 5% polydispersity (adapted from Hunter, 2012).

Figure.III. 12 :

 12 Figure.III.12: Probing cytoplasm properties in living cells. (A)Experimental image of an injected particle moving under a constant force inside the egg (left). The corresponding displacement of the particle as a function of time. The black line on the top represents the application of the magnetic force to the particle (right). (B) Schematic of an optical tweezer setup used to probe the rheology of the mammalian cytoplasm. A probe bead is moved at a control speed toward the boundary to obtain a force-displacement curve. The crowed bulk cytoplasm around the bead is depicted in the inset (adapted fromHiramoto, 1969 and[START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF].

Figure.III. 13 :

 13 Figure.III.13: Viscoelastic properties of the cytoplasm. The Jeffreys model (left) and the corresponding curves during force application and cessation (right). G1, elastic modulus; η1 and η2, viscosity, τ1 and τ2

Figure.III. 14

 14 Figure.III.14 Types of cytoplasmic flows. (A) Treadmilling driven transport with the flux of subunits during Pseudomonas phage infection. PhuZ polymerization at the cells poles drives treadmilling and flux of subunits, which transport and distribute viral capsids (blue) to the nuclear membrane by rotating the phage nucleus (dark blue). (B) Long range cortical flow in C. elegans zygotes, which is induced by anisotropy contractility of cortical actomyosin network. (C) Cytoplasmic streaming in C.elegans embryo (top) with asymmetric myosin-II localization (green) and mouse oocyte (bottom) with actin cap (green). Flow directions are shown near the cortex (blue arrows) and at the center (red arrows) and the meiotic spindle is shown in orange (adapted from Illukkumbura, 2020 and Niwayama, 2016).

Figure 1 .

 1 Figure 1. Viscoelastic forces hold spindles in the center of large cells even in the absence of astral Microtubules contacting the cell cortex. (A) (Left) Airy-scan confocal image of a sea urchin zygote in metaphase fixed and stained for Microtubules (MTs), DNA and F-actin. (Right) Close up view on + Ends of microtubules, marked with white arrowheads, and the actin-rich cortex. (B) Quantification of the distance from MT+ TIPS to the actin cortex (n= 168 MTs from 4 eggs). (C) Number of MTs reaching a distance less than 5 µm from the cortex in different phase of the first cell cycle (n= 3, 20, 5 and 2 cells respectively). Error bars correspond to +/-SEM. (D-E) Time-lapse of metaphase spindles with magnetic beads bound to one spindle pole, displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip, and recoiling upon force cessation. (F) Time evolution of the displacement measured from the initial centered position of the spindle normalized by the applied force for metaphase spindles in normal cells (n=11) and in cells treated with MG132 to arrest cells in metaphase (n=9). (G) Time evolution of the displacement back to the cell center when the external force is released, normalized to that at the moment of force cessation, for the same cells and conditions as

Figure 2 .

 2 Figure 2. Visco-elastic restoring forces on spindles are associated to the material properties of bulk cytoplasm. (A-B) Metaphase spindles are displaced with magnetic tweezers and treated with either DMSO as controls (n=5), Nocodazole to affect microtubules (n=5 cells) or Ciliobrevin D to inhibit Dynein activity (n=5 cells), and their recoiling behavior to the cell center is assayed. (C-D) Quantification of the positional offsets to the cell center, a, and decay time-scales τ1 of relaxation curves plotted in B, using a single exponential model as indicated in the inset in B. (E) Scheme representing injected oil droplets containing hydrophobic magnetic beads used to actuate large objects with magnetic tweezers in the cytoplasm. (F) Time-lapse of a magnetic oil droplet displaced with an external magnetic force and

Figure 3 .

 3 Figure 3. Cytoplasm material generates large elastic and viscous drags on mitotic spindles of similar magnitude as those applied by active microtubule arrays. (A) Scheme of metaphase spindles held in the cell center by viscoelastic elements in the cytoplasm. (B) Scheme of Jeffreys 3element model made of a spring and a dashpot in parallel and another dashpot in series, and typical creep and relaxation behavior of this element. (C-D) Cytoplasm restoring stiffness and viscous drags on mitotic spindles moved parallel or orthogonal to the spindle axis (n= 18 and 19 respectively) and for oil droplets (n=7), computed using fits to the Jeffreys' models represented in B. Open and closed dots correspond respectively to data obtained in control or MG132 treated cells. (E) Time evolution of the displacement measured from the initial centered position of the spindle and normalized by the applied force in metaphase and anaphase. (F-G) Restoring stiffness and viscous drags of metaphase and anaphase spindles moved orthogonal to the spindle axis (n=19 and 17 respectively). Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a twotailed Mann-Whitney test. n.s, P > 0.05, **, P < 0.01, ****, P < 0.0001.

  onto a similar positional offset, but occurred faster. Importantly, this effect did not implicate putative acto-myosin contractile forces, as treatment with Blebbistatin to inhibit Myosin II did neither alter restoring stiffness and drags nor spindle repositioning dynamics. These data suggest that bulk F-actin meshworks may act as important crowders that contribute to ~40-50% of cytoplasm elastic and viscous drags on pulled spindle.

Figure 4 .

 4 Figure 4. Influence of cytoplasm crowding and F-actin meshwork on spindle restoring stiffness and drags. (A) Scheme representing experiments to change cytoplasmic density by placing eggs in hypotonic or hypertonic artificial sea water (ASW). (B) Displacement normalized by applied force of metaphase spindles in control (n=10), hypotonic (n=6) and hypertonic (n=7) sea water. (C-D) Cytoplasm resorting stiffness and viscous drags on mitotic spindles moved parallel to the spindle axis, in controls, hypotonic or hypertonic sea water. (E) Confocal images of eggs injected with Utrophin-488 to visualize F-actin at metaphase in bulk cytoplasm (top) and ~5 min after treating the same cell with Latrunculin B (bottom). The two images are treated with the same contrast to compare F-actin signals. (F) Displacement normalized by applied force of metaphase spindles in control (n=10), cells treated with Latrunculin B (n=13) and cells treated with Blebbistatin (n=6). (G-H) Cytoplasm restoring stiffness and viscous drags in controls, cells treated with Latrunculin B and cells treated with Blebbistatin. Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a twotailed Mann-Whitney test. n.s, P > 0.05, *, P < 0.05. Scale bars, 20 µm.

  (Fig 5A). To test this, we arrested cells in metaphase with MG132, pulled spindles and held them for increasing periods of time(Fig 5B). Practically, this implied decreasing the pulling force gradually by progressively distancing the magnet, to avoid spindles moving onto the cortex.Remarkably, spindles held longer progressively lost their recoiling behavior with a well-matched alignment of experimental data on the predicted theoretical curve.

  translation. This was reflected both in the more linear shape of the rising curve under force and in the higher values in the angular relaxation offset as compared to translation for the same spindles. Thus, rotating spindles appear to dissipate faster rotationally stored elastic energy, causing spindle reorientation to be less-well restored by the cytoplasm than translation. This effect will tend to favor spindle rotation over translation, allowing for instance active force generators to easily tilt spindles, without translating it. We conclude that the dissipation of spindle elastic restoration by plastic rearrangements in the cytoplasm and their time-dependence may be highly relevant to understand spindle positioning phenotypes.

Figure 5 .

 5 Figure 5. Dissipation of stored elastic energy and implications for asymmetric and oriented divisions. (A) Theoretical curve of creep and relaxation curves for different force application times in the Jeffreys' model. Note how longer force applications tend to dissipate positional memory during relaxation. (B) Scheme explaining the assay to test the influence of force application time on relaxation. (C) Relaxation responses of metaphase spindles pulled and held with magnetic tweezers for increasing durations. (D) Relaxation offset, a, plotted as a function of force application duration, overlaid with the predicted theoretical curve form Jeffreys' model, a =

Figure 6 .

 6 Figure 6. Large-scale flows of cytoplasm elements associated with spindle motions. (A-D) Cytoplasm streamlines averaged on a duration of 60 s and size of 50 µm during parallel force application on spindles (A) and during spindle recoils (B), or during orthogonal force applications averaged on a duration of 100 s and size of 90 µm (C) and relaxation (D). Streamlines are superimposed onto a color map of local flow vorticities, ω. (E) Quantification of flow vortices size during parallel or orthogonal pulls (n=8 and 13 cells respectively). (F) Proposed models based on flow map analysis and force response of metaphase spindles.In parallel pulls, the cytoplasm matrix made of relatively large objects including cytoskeletal elements and endomembranes (Yolk, mitochondria or ER), is compressed at the spindle front and stretched at the rear, which causes it to push or pull back the spindle with elastic restoring forces. At the same time, this matrix is sheared along the spindle. In orthogonal pulls, compression of the cytoplasm may be prominent at the spindle front, like in parallel pulls, but in rotation, the broken symmetry causes shear to dominate over compression. Shear stresses fluidize or plastically rearrange the cytoplasm faster than in compression potentially accounting for reduced elastic restoring of spindle

solution ( 1 M

 1 NaCl with 1% Tween-20), and sonicated for 5 min. The beads were then rinsed in 100 µl PBS, incubated 15 min in 100 µl 2 µg/ml Atto565-biotin (Sigma-Aldrich), rinsed again in 100 µl PBS, and finally re-suspended in 20 µl PBS and kept at 4°C until use. Unfertilized eggs were placed on a protamine-coated glass bottom dish. The bead solution was injected using a micro-injection system (FemtoJet 4, Eppendorf) and a micro-manipulator (Injectman 4, Eppendorf). Injection pipettes were prepared from siliconized (Sigmacote) borosilicate glass capillaries (1 mm diameter). Glass capillaries were pulled using a needle puller (P-1000, Sutter Instrument) and ground with a 40° angle on a diamond grinder (EG-40, Narishige) to obtain a 10 µm aperture. Injection pipettes were back-loaded with 2 µl of bead solution before each experiment, and were not re-used. After fertilization, beads were spontaneously transported along MTs and formed a large aggregate at the center of the aster. This aggregate stayed stably at the centrosome and occasionally split at centrosome duplication. Thus at metaphase, beads sometimes ended up on one or the two spindle poles (FigS1H and S1I). The targeting of beads towards the centrosomes presumably occurred in a dynein-and microtubuledependent manner. Thus in the presence of 20 µM Nocodazole or 50 µM Ciliobrevin D, beads could detach from the spindle pole under external forces (Fig S2A and S2B, red arrow heads).

Figure S1 .

 S1 Figure S1. Metaphase astral MTs do not reach the cortex, yet spindles can recoil back to the cell center upon force-induced displacement. (A) Number of astral MTs reaching a distance less than 5µm to the cortex in metaphase as assayed by Immunofluorescence (IF), Transmission electron microscopy (TEM), or live-imaging of injected TMBD-mCherry or Tublin-Atto-565. (B-C) Representative images of metaphase spindles in live cells with MTs labelled by injecting the indicated probes. (D) Transmission electron microscopy using fixation methods to reveal the presence of MTs, and close up view with green arrowheads pointing at MT + TIPs, and yellow arrowheads pointing at yolk granules. (E) Immunofluorescence of MTs imaged with confocal microscopy in different indicated phases of the cell cycle. The time below the images correspond to the average duration of the cell cycle phases. (F) Duration of metaphase in normal zygotes and in zygotes injected with magnetic beads that attach to mitotic spindles. (G) Spindle polar length in controls, cells injected with magnetic beads or in cells treated with MG132. (H) Example image of an egg in which bead aggregates have split and accumulated on the two spindle poles. (I) Time-sequence of a bead aggregate that accumulates at one spindle pole from interphase to metaphase. (J) Displacement after 100s of force application plotted as a function of the applied force for both orthogonal and parallel pulls (n=32). The line is a linear fit, and correlation coefficients and corresponding P-values are indicated in the plot. (K) Relaxation offset during spindle recoils is independent of the distance of the spindle to the cortex. The line is a linear fit, and correlation coefficients and corresponding P-values indicated in the plot. Error bars correspond to +/-S.E.M. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05.

Figure S2 .

 S2 Figure S2. Viscoelastic spindle recoils are independent of MTs and dynein, and occur with similar characteristics for a passive oil droplet. (A) Time-lapse of a spindle pulled with magnetic tweezers and treated during the pull with Nocodazole to depolymerize MTs, and monitor recoils in the absence of MTs. Note the disappearance of MTs. (B) Egg treated with Ciliobrevin D to inhibit dynein activity and pulled and let to recoil. Note the progressive shrinking of the spindle caused by dynein inhibition. In these two sets of experiments the drugs were added at different timings to ensure that the effect was maximum at the end of the pulling phase, based on multiple optimization assays (see Methods). (C) Time evolution of the normalized displacement back to the cell center in orthogonal pulls when the external force is released in cells treated with the indicated chemicals (n=4 for DMSO, 6 for Nocodazole, 6 for Ciliobrevin D). (D-E) Quantification of the positional offsets to the cell center, and decay time-scales of relaxation curves plotted in C, using a single exponential model. (F) Confocal images of zygotes after treatment of indicated chemicals. (G) Scheme of the assay used to move magnetized oil droplets in cells with magnetic tweezers. (H) Close up view of hydrophobic beads aggregates within oil droplets, used to quantify the size of the aggregates, and calibration curve linking the force at 70 µm from the magnet tip to the center of the aggregate. (I) Quantification of spindle (n=6) and oil droplets sizes (n=8). (J) Tracking of oil droplet centers in the absence and in the presence of external forces. (K) Displacement vectors of oil droplets center during the relaxation after force cessation. (L) Quantification of the deviation angle between the pulling and relaxation trajectories in individual magnetic oil droplets experiments (n=8). Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05, *, P < 0.05. Scale bars, 20 µm, unless otherwise indicated.

Figure S3 .

 S3 Figure S3. Comparison of metaphase and anaphase spindles pulls and relaxation. (A) Viscoelastic timescales, τ1 measured during the rising pulling phase or the relaxation phase. (B) Relaxation offsets for metaphase spindles pulled parallel or orthogonal. (C) Restoring stiffness measured for the indicated conditions in parallel and orthogonal pulls. (D) Viscoelastic time-scales for metaphase (n=18 for parallel and 19 for orthogonal pulls) and anaphase spindles pulls (n=17). (E) Timelapse of a representative pulling and relaxing experiment on anaphase spindles. (F) Anaphase duration for control eggs vs eggs injected with magnetic beads. (G) Time-evolution of anaphase spindle length. Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05, **, P < 0.01, ****, P < 0.0001. Scale bars, 20 µm.

Figure S4 .

 S4 Figure S4. Impact of cytoplasm density, F-actin and myosin II on viscoelastic forces on spindles from bulk cytoplasm. (A) Confocal images of eggs treated 5min with normal ASW (Artificial Sea Water), 80% ASW or 110%ASW, fixed and stained for MTs and DNA. (B-D) Diameter, metaphase duration and spindle length of eggs in ASW (n=8) or 5 min after treatment in 80% ASW (n=8) and 110% ASW (n=8). (E) Time evolution of the normalized displacement back to the cell center in controls (n=10) and in cells treated with 80% ASW (n=6) and 110% ASW (n=7). (F-G) Viscoelastic timescale, τ1 measured during the rising pulling phase or the relaxation phase, in controls and cells treated with 80% ASW and 110% ASW. (H) Relaxation offset for controls and cells treated with 80% ASW and 110% ASW. (I) Confocal images of eggs treated with DMSO or Blebbistatin, fixed and stained for MTs, DNA and F-actin. (J) Scheme representing F-actin structures and in vivo force application on metaphase spindles in the presence of Latrunculin B. (K) Time-lapse of eggs treated with Latrunculin B to depolymerize F-actin and assayed for spindle displacement under force and relaxation. (L) Time evolution of the normalized displacement back to the cell center in controls (n=10), in cells treated with Latrunculin B (n=13) and in cells treated with Blebbistatin (n=6). (M) Relaxation offset for controls and cells treated with Latrunculin B and Blebbistatin. (N-O) Viscoelastic timescale, τ1 measured during the pulling phase or the relaxation phase, in controls and cells treated with Latrunculin B and Blebbistatin. Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05, *, P < 0.05, **, P < 0.01, ***, P < 0.001. Scale bars, 20 µm.

Figure S5 .

 S5 Figure S5. Role of the duration of force application in the dissipation of elastic energy, and differences between translational and rotational behavior. (A-D) Kymographs following beads and DNA overtime for the relaxation phases upon force applications of varying durations. The dotted arrowhead marks the initial position of spindle centers at the onset of the relaxation phase, and the filled arrowhead indicates the final position after 300s. (E) Comparison of translational and rotational creep behavior using the arc length tracking the spindle pole displacement as a measurement of effective displacement during rotational motion. (F-H) Restoring stiffness, drags and decay times measured for translation vs rotation. Open and closed dots correspond respectively to data obtained in control or MG132 treated cells. Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Wilcoxon test. n.s, P > 0.05. Scale bars, 20 µm.

Figure S6 .

 S6 Figure S6. Flows of cytoplasm elements and associated analysis during spindle translational and rotational motions. (A) Flow maps of a representative spindle pulled with magnetic forces parallel to its axis, superimposed with a color map of the flow velocity projected along the x-axis. (B) Averaged velocity component in the horizontal direction (x) in the box indicated in A, plotted as a function of the vertical distance (y), used to compute shear rates. (C) Spatial autocorrelation averaged on 8 individual experiments and flow analysis used to compute flow vortex sizes. (D) Color maps of the divergence of the velocity used to locally map zones where the cytoplasm matrix may compress (indicated with arrows). (E) Trajectories of imaginary flow tracers placed along the direction orthogonal to the spindles used to visualize net displacement of cytoplasm material as a function to the distance to the spindle. (F-J) Similar analysis as in (A-E) for spindles pulled orthogonal to the spindle axis. (K) Viscoelastic timescales τ1 and τ2 extracted for spindles from rising curves and compared to a time-scale calculated from the inverse of the shear rate from the flow maps. Error bars and shades correspond to +/-S.E.M and +/-S.D respectively. Scale bars, 20 µm.

Figure1:

  Figure1: Cytoplasm elasticity exhibits both shape and size dependence. (A-B) Time-lapse of metaphase spindles at the two cell stage with magnetic beads bound to one spindle pole, displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip, and recoiling upon force cessation. (C) Time evolution of the displacement measured from the initial centered position of the spindle normalized by the applied force for metaphase spindles at the one cell stage (n=11) and at the two cell stage (n=12). (D) Time evolution of the displacement back to the cell center when the external force is released, normalized to that at the moment of force cessation, for the same cells and conditions as in C. (E-F) Experiments of metaphase spindles displaced and rotated by magnetic forces applied orthogonal to the spindle axis, and spindle recoiling upon force cessation. (G-H) Similar analysis as (C-D) for orthogonal pull of spindles in one cell stage (n=14) and in two cell stage (n=11). (I-L) Comparison of restoring stiffness, drags, relaxation offsets and decay times in indicated conditions. (M-N) Viscoelastic timescales τ1, τ2 in both one cell and two cell stages during spindle parallel and orthogonal pulls. In C-D, and G-H, the bold lines correspond to fits of the data using general creep or relaxation equations of the Jeffreys' viscoelastic model. Error bars and shades represent +/-S.E.M and +/-S.D/2 respectively. Results were compared using a two-tailed Mann-Whitney test. n.s, P > 0.05, *, P<0.05, **, P<0.01. Scale bars, 20 µm.

Figure2:

  Figure2: Cytoplasm elastic drags vary with cell shape. (A-B) Images and scheme of metaphase spindles at the four cell stage with magnetic beads bound to one spindle pole, displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip (top). Upon releasing the force, the spindle recoiled back and the embryo was divided into eight cell stage (bottom right). Two orientations of four cell stage were shown, and we focused on the right one. (C) Spindle polar length from one cell to four cell stages. (D) Time evolution of the displacement measured from the initial centered position of the spindle normalized by the applied force for metaphase spindles in one cell stage (n=11), two cell stage (n=12) and four cell stage (n=9). (E) Time evolution of the displacement back to the cell center when the external force is released, normalized to that at the moment of force cessation, for the same cells and conditions as in D. (F-G) Comparison of restoring stiffness and drags in indicated conditions. Error bars and shades represent +/-S.E.M and +/-S.D/2 respectively. Results were compared using a two-tailed Mann-Whitney test. n.s, P > 0.05, *, P<0.05, ***, P<0.001. Scale bars, 20 µm.

Figure3:

  Figure3: A new assay to directly test the impact of cell shape on cytoplasm viscoelastic restoring forces on spindles. (A-B) Schematics of a cell shaped in a U chamber. Metaphase spindles are pre-positioned in the cell center and oriented along the long axis of the rectangular cuboid. Spindles with magnetic beads bound to one spindle pole were displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip. (C) An example of a cell at metaphase shaped in a U chamber. (D) Time-lapse of metaphase spindles in shaped cells with magnetic beads bound to one spindle pole, displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip, and recoiling upon force cessation. Scale bars, 20 µm.

Figure 4 :

 4 Figure 4: Simulations of spindle positioning in different cell morphology. The geometries used were respectively (A) sphere as a one cell stage embryo, (B) rectangular cuboid as a cell in a micro chamber, (C) Hemi-sphere as a two cell stage, and (D) one quarter of a sphere as at the four cell stage. The spindle is placed in the origin of the coordinate system and center of mass of the geometry. The cell dimensions can be read out from the axis.

Figure 5 :F

 5 Figure 5: Pulling and releasing curves from simulations. (A) Scaled translational displacement curve for the one, two, and four cell stage along with the one-cell stage in a rectangular cuboid geometry. (B) Scaled translational and rotational displacement for the parallel and perpendicular pulling of the spindle in the two cell stage. To orthogonal displacement was computed from the arc length of the spindle pole motion, and the force as the perpendicular component to the radial axis at each step. (C) Normalized relaxation curve of all the simulations after setting the external force to zero.

Figure 1 :

 1 Figure 1: EM image of a fixed metaphase zygote (left) and corresponding classification of different endomembrane compartments in the cytoplasm (right). The chromosomes, ER membranes, yolk granules and mitochondria are in blue, purple, yellow and red, respectively. Scale bar, 20 µm.

Figure 3 :

 3 Figure 3: Cytoplasm fluidization with MTs and its implication for protein diffusion. (A) Confocal image of a fixed anaphase zygote with labeled F-actin (purple), DNA (cyan) and MTs (white). Bulk F-actin meshworks rearrange along MTs. (B) Organization of the cytoplasm (e.g. MTs) promotes protein diffusion (from Huang, 2021).

Figure 2 :

 2 Figure 2: Bulk dynein-mediated aster centration with opposing reactive cytoplasm viscoelastic forces. Aster movement pushes on the viscoelastic cytoplasm which generates both elastic and drag forces opposing on the aster (adapted from Xie, 2020).

FIGURE 1 |

 1 FIGURE 1 | Experimental evidences of the role of MT cytoplasmic pulling forces for aster motion. (A) A Sand dollar embryo is fertilized in the presence of the MT drug Colcemid. Using UV light, MTs are allowed to polymerize in specific regions. When moving the UV region, the sperm aster migrates to the center of the new region, following the direction of longer MTs. As MTs do not contact any cortex, those experiments support that forces exerted by MTs in bulk cytoplasm can drive aster motion and positioning. Modified from Hamaguchi and Hiramoto (1986). (B) Zebrafish 2-cell stage blastomeres are incubated in caged combretastatin 4A. Local UV-based uncaging allows for locally depolymerizing MTs in asters. Asters move following their longer MTs, long before those contact the cortex, supporting MT cytoplasmic force exertion. Modified from Wuhr et al. (2010). (C) Sea urchin embryos are fertilized, and MT centering asters are cut with a UV-laser along the indicated lines while they move to the cell center. Laser ablation on the side of asters causes a transient deviation toward the top of the cell, supporting MT bulk pulling. MT regrowth promote a return of the aster to the centration path. Similarly, laser cuts at aster front cause aster to transiently step back, and move again to the cell center upon MT regrowth. Modified from Tanimoto et al. (2016).

FIGURE 2 |

 2 FIGURE 2 | Mechanisms supporting dynein cytoplasmic pulling force exertion on MTs. (A) Aster centration by dynein-mediated forces in bulk. Dynein may transport vesicle-cargos (e.g., endosomes or lysosomes) or large endomembrane networks like the endoplasmic reticulum (orange insets). The motion of those cargos in the viscous cytoplasm creates flows and drag forces that pull on MTs and ultimately centrosomes. This module coupled to front-rear asymmetries in MT length in asters generates a net centering force. Similar cytoplasmic forces may also transport MTs to the periphery of the asters, contributing to aster expansion (purple insets).(B) Specific subunits of the dynein-dynactin complex and adaptors thought to mediate dynein-cargo loading as well as cargo motion, during C. elegans pro-nuclear centration. The cytoplasmic dynein-cargo is loaded onto MTs by interacting with EB proteins at the plus end or tyrosinated α-tubulin along the MTs. Modified according toKimura and Kimura (2011) andBarbosa et al. (2017). Scale bar, 20 µm.

FIGURE 3 |

 3 FIGURE 3 | Implications of MT cytoplasmic forces for aster centration. (A) External calibrated magnetic forces applied with magnetic tweezers on the aster center, through minus-end accumulated beads in sea urchin embryos. Forces applied along the centering axis serve to derive force-velocity relationships for centering asters. This relationships is mostly linear supporting a motion limited by viscous interactions, with the slope allowing to compute an effective drag. The intersection of the line with the x-axis yields estimates of the aster endogenous force of ∼600 pN. Modified according toTanimoto et al. (2018). (B) Forces applied orthogonal to the centering axis serve to characterize MT-based visco-elastic forces stabilizing the centered position of the aster in the transverse axis during centration. Blue curve: Typical experimental displacement-time curve, allowing to compute visco-elastic parameters of MT-based centering system. Upon force application, the aster moves toward the magnet until reaching an equilibrium plateau, and recoils back to the center after releasing the force, behaving as a spring. Computation of the centering stiffness and the drag from the plateau and the slope of the curve. Modified fromTanimoto et al. (2018). (C) Successive force measurements showed that aster centering stiffness becomes reduced during aster centration(Salle et al., 2019). Proposed model for how cytoplasmic forces may become less efficient during centration, and yield to this stiffness reduction: As the aster centers, dynein drags endomembranes to the cell center, depleting the rest of the cytoplasm, and thereby rendering cytoplasm force exertion less efficient. Modified fromTerasaki and Jaffe (1991) andSalle et al. (2019).

FIGURE 4 |

 4 FIGURE 4 | Some mechanisms for actin-based force exertion in bulk. (A) Actin comet tail model for actin based cytoplasmic pushing. Comet tails grow at the surface of different microbes, such as Listeria monocytogenes, or even at the surface of intracellular vesicles. Actin polymerization promoted by local actin regulators such as ActA for Listeria and Wasp for lysosomes promotes the growth of a branched actin network, by activating host arp2/3 complex. Assuming pure viscous interactions of both cargos and tails with the cytoplasm, the propulsive speed of the cargo is linked to that of actin growth speed by their drag ratio as indicated. (B) Meiotic spindle asymmetric displacement in mouse oocytes. An actin cloud forms around spindle and chromosomes as a result of formin-nucleation activity around spindles or chromosomes. This cloud breaks symmetry and pushes the spindle upward invoking similar physical principles as for comet-tails. Modified from Li et al. (2008). (C) Self-organized acto-myosin contractile networks in extracts encapsulated in droplets can drive actin and fluid flows. Darcy flows through the permeable network create a pressure gradient that pushes the network toward the cell center. Modified from Ierushalmi et al. (2019).

Figure 1 .

 1 Figure 1. Magnetic cortical pulling domains drive marked asymmetric divisions. (A) Magnetic beads injection, cap formation, and induced asymmetric division. (B-E) Time-lapse images of the cleavage of sea urchin zygotes. (B) The cap is formed with beads with strong MT minus end activity and maintained; (C) a noninjected control embryo; (D) the pulling cap is not maintained; and (E) a control using a cap formed with beads that do not interact with MTs. Yellow stars: female/zygote nucleus; red stars: blastomere nuclei after division. (F) Divided blastomere area ratio in conditions B to E (n = 10, n = 8, n = 11, and n = 10 cells). (G) Quantification of the angle (Δα) between the division axis and the axis from the cell center to the cap (n = 12, n = 17, and n = 10 cells). (H) Blastomere area ratio plotted as a function of the angle (β) formed by the edges of the pulling cap and the cell center. The dashed line is a visual guide. Results were compared by using a two-tailed Mann-Whitney test. ns, P > 0.05; ****, P < 0.0001. Error bars are SD. Bars, 20 µm.

Figure 2 .

 2 Figure 2. Consecutive aster centration and decentration. (A) Time-lapse of the consecutive centering motion of the male nucleus followed by a decentration of the zygote nucleus toward the cap. Arrowheads: nuclei at the aster center; red stars: blastomere nuclei. Contrast is adjusted to compensate for an increase in DNA labeling (Hoechst), and bright blobs correspond to excess sperm on the fertilization envelope. (B) Aster trajectories from fertilization to metaphase onset, aligned with the pulling cap (n = 32 cells). (C) Aster position with and without cortical caps (n = 18 and n = 9, respectively). (D) Aster velocity during centration and decentration (n = 18, n = 17, and n = 17 cells). (E) 1D force competition model with a pulling cap force (in red) and length-dependent pulling forces (in blue). (F) Simulated aster position under no, weak, or strong cortical forces. (G) Simulated aster position, with a decreasing centering constant, a (purple) or an increasing cap force, F cap , after centration (red). Results were compared by using a two-tailed Mann-Whitney test. ns, P > 0.05; ****, P < 0.0001. Error bars are SD. Bars, 20 µm.

Figure 3 .

 3 Figure 3. Cortical pulling forces remain constant during and after aster centration. (A) The method used to measure cortical pulling forces. (B) Time-lapse of aster centration, and concomitant reduction of the magnetic force holding the cap. Top: Low-magnification view of the embryo moving away from the probe (left). Bottom: Details of cap detachment dynamics. Yellow stars: the aster center; arrowheads: the cap. (C) Typical example of the evolution of the distance between the cell cortex and the cap (gray), and of the magnetic force (red), as a function of the distance between the egg and magnet. Arrowhead: the cap "take-off." (D) Average distance between cap and cortex plotted as a function of the magnetic force, during centration (in green; n = 16) and after centration (in red; n = 18). Dashed lines are SD. Take-off forces (arrows) correspond to cortical forces exerted by domains onto asters and were determined using the fits (continuous lines; see Materials and methods). (E) Cortical forces plotted as a function of cap volumes. Red dashed line: linear regression. Pearson r and P value are displayed on the graph. Bars, 20 µm.

  Figure 3. Cortical pulling forces remain constant during and after aster centration. (A) The method used to measure cortical pulling forces. (B) Time-lapse of aster centration, and concomitant reduction of the magnetic force holding the cap. Top: Low-magnification view of the embryo moving away from the probe (left). Bottom: Details of cap detachment dynamics. Yellow stars: the aster center; arrowheads: the cap. (C) Typical example of the evolution of the distance between the cell cortex and the cap (gray), and of the magnetic force (red), as a function of the distance between the egg and magnet. Arrowhead: the cap "take-off." (D) Average distance between cap and cortex plotted as a function of the magnetic force, during centration (in green; n = 16) and after centration (in red; n = 18). Dashed lines are SD. Take-off forces (arrows) correspond to cortical forces exerted by domains onto asters and were determined using the fits (continuous lines; see Materials and methods). (E) Cortical forces plotted as a function of cap volumes. Red dashed line: linear regression. Pearson r and P value are displayed on the graph. Bars, 20 µm.

Figure 4 .

 4 Figure 4. Aster centering stiffness decreases after centration. (A) Time-lapse of a centering aster subjected to two consecutive external magnetic forces. Top: Low-magnification views of the embryo and magnet tip. Bottom: Position of aster centers (nuclei) and beads aggregate. Orange line: the centration path (fertilization from the top); orange arrows: the direction of the magnetic forces. Bars, 20 µm. (B) Time-lapse projection of aster deviation from the centration path upon the first force application. (C) Kymograph of aster deviation from the cell center from the second force application. Black and white arrowheads: the initial centered position and the maximum deviation (plateau) during force application, respectively. Bars, 5 µm. (D) Quantification of paired aster centering spring constants (connected by gray dashed lines [n = 10]). The "single-pull" category corresponds to force measurement performed only once after aster centration (n = 15). (E) Quantification of paired aster drags. (F) Average displacement/force plotted as a function of time. Error bars are SEM. Dashed lines: Voigt model fit (see Materials and methods). Results were compared using a two-tailed Mann-Whitney test. ns, P > 0.05; **, P < 0.01.

Figure 5 .

 5 Figure 5. Reduction in aster centering stiffness drives aster decentration and asymmetric division. (A) Time-lapse of a 3D simulation with constant pulling cap and aster centering stiffness reduction. The red hemisphere is the cap, MTs are in green and the aster trajectory in blue. (B) Examples of comparisons between simulated (top) and experimental (bottom) aster trajectories. (C) Aster position relative to the cell center in 3D simulations using positions of caps and sperm entry from experiments (in blue; n = 18). Blue dashed lines: SD. The red dashed line: the experimental curve (shown in Fig. 2 B). (D and E) Comparison of aster distances from the cell center and aster speeds in simulations (blue) and experiments (red). Error bars are SEM. (F) Schematized consecutive aster centration and decentration and model for asymmetric division driven by a reduction in aster MT centering stiffness under constant cortical forces.

3

  Université de Paris, Centre National de la Recherche Scientifique UMR7592, Institut Jacques Monod, Paris, France.4 Department of Biomedical Engineering, National University of Singapore, Singapore, Singapore.5 Department of Bioengineering, Imperial College London, London, UK. *Corresponding author. Email: jvermot@ic.ac.uk

Fig. 1 .

 1 Fig. 1. Endogenous Ca 2+ influx and Nfat signal activation occur in EdCs of the AVC during valvulogenesis. A ( ) Representative single-scan beating heart images of the Tg(fli1a:galff);Tg(uas:GCaMP7a); Tg(kdrl:nls-mCherry) embryo. Panels are the heatmap-colored GCaMP7a images at the indicated time points. Arrowheads and dashed lines indicate GCaMP7a signal and outline of the endocardium, respectively. ( ) Normalized Ca B 2+ dynamics determined by F GCaMP7a /F nls-mCherry. Each colored line indicates the ratiometric change of individual cells (three cells) shown in movie S2. ( ) The number of Ca C 2+ spikes in EdCs of the indicated region from 32 to 150 hpf ( > 5). ( ) Confocal single-scanned heart images of n D Tg(4xnfbr:d2EGFP); Tg(fli1a:myr-mCherry) n embryo ( = 20). ( ) Number of Nfat reporter activated EdCs from 30 to 146 hpf E -( = 14). A, atrium; V, ventricle. Scale bars, 30 m. n m

Fig. 2 .Fig. 3 .

 23 Fig. 2. Mechanical forces directly trigger Ca 2+ influx in EdCs of zebrafish heart. ( ) Representative image of bead implantation into the heart. ( ) Schematics A B of bead retention. ( ) Force intensities from 3D dynamic mesh simulation C of wall shear stress with a bead (clear circle) c lose to the impact location. (D) Representative GCaMP7a image of embryo grafted with a bead (asterisk). (E) Schematic of magnetic tweezer-based force application to a zebrafish heart. ( ) Single-scan images of F Tg(fli1a:galff);Tg(uas:GCa MP7a);Tg(kdrl:nls-mCherry) grafted embryo (original bead position is indicated by dashed cyan c ircles) pulled by the magnetic probe (dotted magenta lines), left view (n = 6, yielding similar results). (G and H) Quantification of bead velocity (G) and shear stress (H) applied by the ma gnetic tweezer shown in movie S7. Gray shading indicates the period of activated GCaMP7a signal in EdCs. Arrowheads indicate the GCaMP7a signal and yellow dashed lines the endocardium. Scale bars, 15 mm in (C) and 30 m in (D) and (F). m

Fig. 4 .

 4 Fig. 4. Extracellular ATP and P2rx channels function for valve development. A ( ) ATP-dependent P2XRs Ca 2+ activation schematic. (B) Schematic of the microinjection approach to injecting drugs into cardiac lumen. (C) Number of Ca 2+ spikes in EdCs of the AVC for PBS-injected (n = 11), oligomycin A-inj ected (n = 7), apyraseinjected (n = 8), and ATPgS-injected (n = 9) embryos at 54 hpf. (D E and ) Number of Ca 2+ influxes (D) and Nfat reporter activation (E) in EdCs of the AVC for embryos injected with zp2rx4aWT [n = 9 in (D) and n = 16 in (E)] and zp2rx4aC365W mRNA [n = 10 in (D) and n = 18 in (E)] at 54 hpf. (F) Confocal images of TgBAC(twist1b:GFP);Tg(fli1a: lifeact-mCherry) embryo injected with zp2rx4aW T (n = 8) and zp2rx4aC365W mRNA (n = 18). Arrowheads and percentages indicate expression in the EdCs and occurrence of each representative valve structure, twist1b respectively. Asterisks indicate mislocalized EdCs with ectopic expression. ( ) Summary of endocardial twist1b G mechanosensitive signal pathways for valve development. Note that forces trigger the ATP-transducer (Ca 2+ )-decoder (NFAT) system, which is independent of the expression activation. Scale bars, 15 m. klf2a m

  [0045] De telles billes sont notamment commercialisée par Invitrogen (Dynabeads ™ MyOne ™ Streptavidin C1), Chemicell (nano-screenMAG-Streptavidin), Promega (High Capacity Magne ® Streptavidin Beads), Nvigen (MyQuVigen™ -Streptavidin) et Solulink (NanoLink™ Streptavidin Magnetic Beads). [0046]

  pointe magnétique comprenant un coeur magnétique comprenant une superposition d'aimants millimétriques ou submillimétriques en néodyme prolongé par une pointe d'acier usinée avec un rayon de courbure compris entre 5 et 100 micromètres, [0177] b) des billes superparamagnétiques comprenant un revêtement permettant d'adresser spécifiquement les billes superparamagnétiques à un élément ou compartiment cellulaire donné, le revêtement des billes superparamagnétiques étant un revêtement protéique, de préférence un anticorps ou une lectine, [0178] c) optionnellement une solution permettant la mise en suspension et l'injection des billes superparamagnétiques dans une cellule ou un tissu cellulaire, et [0179] d) optionnellement, un instrument permettant l'injection des billes, de préférence une aiguille d'injection préparée à partir de capillaires en verre borosilicaté. [0180]

  Injection et déplacement de particules de 100 nm couvertes de streptavidine (Chemicell) ne présentant pas d'interactions spécifiques avec les structures cellulaires utilisées pour la calibration et les expériences contrôles (Figures2 et 3).[0198]

  -3C, 4 et 6 ont été prises sur un microscope fluorescent à champ large (TI-Eclipse; Nikon) équipé d'un camera CMOS (Orca-flash4.0LT; Hamamatsu). Les échantillons ont été imagés avec un objectif 20× sec (NA, 0.75; Apo; Nikon) et un grossisseur 1.5×. Le microscope est piloté par Micro-Manager (Open Imaging). Les Figures 3B et 3C ont été prises sur un système de microscopie confocal à tête « spinning », yokogawa X1, monté sur un statif Nikon Ti, muni d'une caméra EM-CCD. Les cellules sont imagées avec un objectif Nikon 60X 1.4 NA Plan Apo à eau. Les images sont prises à température ambiante (18-20°C).

  4°C until processing. Samples were then prepared for Serial Block Face using the NCMIR protocol (https://ncmir.ucsd.edu/sbem-protocol). They were washed 3 times with cold cacodylate and post-fixed for 1 hour in a reduced osmium solution containing 1% osmium tetroxide, 1.5% potassium ferrocyanide in 0.15 mM sodium cacodylate buffer, followed by incubation with a 1% thiocarbohydrazide (TCH) solution in water for 20 min at room temperature (RT). Subsequently, samples were fixed with 2% OsO4 in water for 30 min at room temperature, followed by 1% aqueous uranyl acetate at 4 °C overnight.The samples were then subjected to en bloc Walton's lead aspartate staining (2) at 60 °C for 30 min. Then, samples were dehydrated in graded concentrations of ethanol for 10 min each. The samples were infiltrated with 30% Agar low viscosity resin (Agar Scientific Ltd) for 1 hour, 50% Agar low viscosity resin for 2 hours and 100% Agar low viscosity resin overnight. The resin was then changed and the samples further incubated during 3 hours prior to inclusion in BEEM capsule Bottle Neck tips (EMS) and polymerized for 18h at 60 °C. The polymerized blocks were mounted onto special aluminum pins for SBF-SEM imaging (FEI Microtome 8mm SEM Stub, Agar Scientific), with Two part conduction silver epoxy kit (EMS

ER endomembrane visualization by Serial Block Face electron microscopy , one cell stage zygote were fixed in metaphase in 0.2M cacodylate buffer, 0.25M sucrose, 2% paraformaldehyde, 2% glutaraldehyde during 1h and progressively transferred in 0.2M cacodylate buffer, 0.35M NaCl, and stored at

Table 1 : Parameters used in the COMSOL model.

 1

	Parameters	Physical Meanings	Values
	f0 (pN)	Pulling force	300
	tp (s)	Pulling time	150
	τ (s)	Viscoelastic characteristic time 88
	µs (Pa.s)	-	1.075
	Viscosity (Pa.s)	Viscosity of the fluid	10.75
	E (Pa)	Young modulus of spindle	3.2e5
	ν ρ (kg/m 3 ) ρs (kg/m 3 )	Poisson ratio of spindle Density of cytoplasm Density of spindle	0.35 1000 1190
	R (µm)	Cell radius	100
	a (µm)	Spindle long semi-axis	24
	b (µm)	Spindle short semi-axis	11

1

  Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Centre National de la Recherche Scientifique UMR7104, Institut National de la Santé et de la Recherche Médicale U1258 and Université de Strasbourg, Illkirch, France. 2 Department of Cell Biology, National Cerebral and Cardiovascular Center Research Institute, Suita, Japan.

  représente l'application de forces au sein de cellules et d'embryons et effet(s) sur la division cellulaire et le développement.

	[0034] [0035] [0036] [0037] [0038]	[fig.3A] Déplacement de particules magnétiques au sein d'une cellule vivante d'oursin. [fig.3B] Déplacement de billes magnétiques au sein d'un embryon de drosophile. [fig.3C] Divisions successives de cellules d'oursins injectées avec des billes fluo-rescentes. [fig.3D] Application de forces à la surface de cellule épithéliale unique au sein d'un tissu embryonnaire de Drosophile injecté avec des billes magnétiques.

  Par «pointe magnétique» est entendu une pointe comprenant un matériau qui est soit magnétisable, soit magnétisé. Le fonctionnement de la pointe magnétique repose sur un gradient de champ magnétique créé par une pointe comprenant au moins un aimant ou éléctro-aimant, destiné à créer une force sur une ou plusieurs billes magnétiques attachées à des structures spécifiques au sein ou à la surface de cellules.[0073]De préférence, l'aimant utilisé est un aimant permanent. Par « aimant permanent » est entendu un matériau magnétique dur, dont l'aimantation rémanente et le champ coercitif sont grands. Ce type d'aimant permet d'exercer une force d'attraction sur tout matériau ferromagnétique. Un aimant possède un pôle nord et un pôle sud. Les pôles de même nature se repoussent, ceux de natures différentes s'attirent.[0074]Selon un mode de réalisation, les pointes magnétiques sont composées d'un coeur magnétique fait d'une superposition d'aimants millimétriques ou submillimétriques, dont la géométrie et la magnétisation peuvent être modulées.[0075]En particulier, la pointe magnétique comprend un coeur magnétique composé d'au moins 1, 2, 3 ou 4 aimants superposés, de préférence 3 aimants superposés.[0076]De préférence, le ou les aimants forment le coeur magnétique et ont un diamètre compris entre 1 et 5 millimètres, de préférence entre 2 et 5 millimètres, entre 3 et 4 millimètres, notamment de 4 millimètres.[0077]De préférence, le coeur magnétique a une forme tubulaire cylindrique. En particulier, le diamètre du coeur magnétique est compris entre 1 et 5 millimètres, de préférence entre 2 et 5 millimètres, entre 3 et 4 millimètres, entre 2 et 3 millimètres, entre 1 et 2 millimètres, entre 1 et 3 millimètres, entre 3 et 5 millimètres, entre 4 et 5 millimètres.

	[0078]	La longueur du coeur magnétique est typiquement comprise entre 2 et 3 centimètres.
	[0071] [0072]	La présente invention propose l'utilisation d'une pointe magnétique permettant d'appliquer une force sur la cellule, l'élément ou le compartiment cellulaire d'intérêt, par l'application d'un champ magnétique sur les billes superparamagnétiques.

  1.25%) est placée dans une solution de viscosité connue. Les agents visqueux dilués dans l'eau ayant été testés et validés sont : Glycerol (Sigma) 60% de viscosité 15 cP (or mPa.s), sucrose (Sigma) 65%, viscosité 15cP ; Methycellulose15 2% (Fisherscientific); viscosité 15cP ; Glycerol 65% , viscosité, 20cP ; sucrose 80%, viscosité 20cP ; Polyethylèneglycol 8000 (Sigma), viscosité 20cP ; Methylcellulose 400 2% (Fisherscientific), 400cP([fig.2B]). Lorsque la pointe magnétique est placée dans la solution, les billes se déplacent à une vitesse qui permet de calculer la force de friction visqueuse de Stokes (F=6πηRV, η : viscosité du liquide, R rayon de la bille, V vitesse de la bille) qui équilibre la force magnétique. Un script d'analyse d'image développé sur le logiciel Matlab (Mathworks), permet : (i) le suivi dynamique de la particule, et le calcul de sa vitesse, et (ii) de positionner précisément le centre de la pointe comme référence. Ce script extrait ainsi directement la relation force magnétique-distance à la pointe magnétique, ainsi que des raffinements de cette force suivant l'angle entre la trajectoire de la bille et l'axe principale de rotation de la pointe magnétique. Pour une même pointe, cette calibration peut être effectuée pour différents types de billes. Ainsi, une fois la calibration effectuée, le script permet d'extraire la valeur et la direction de la force de manière automatique, pendant une expérience au sein d'échantillons vivants. Ceci est notamment décrit dans la publicationde Tanimoto et al., Nature Physics 2018.

  [0216] Carey, S.P., T.M. D'Alfonso, S.J. Shin, and C.A. Reinhart-King. 2012. Mechanobiology of tumor invasion: engineering meets oncology. Crit Rev Oncol Hematol. 83:170-183. [0217] Engler, A.J., S. Sen, H.L. Sweeney, and D.E. Discher. 2006. Matrix elasticity directs stem cell lineage specification. Cell. 126:677-689. Méthode in vitro ou ex vivo pour caractériser au moins une propriété mécanobiologique d'un élément ou compartiment cellulaire dans un échantillon biologique, ladite méthode comprenant : a) l'introduction de billes superparamagnétiques dans l'échantillon biologique lesdites billes comprenant un revêtement biologique apte à adresser de manière spécifique les billes superparamagnétiques à un élément ou compartiment cellulaire d'intérêt, b) l'application d'un champ magnétique sur lesdites billes superparamagnétiques de manière à appliquer une force sur l'échantillon biologique, c) la mesure d'au moins une propriété mécanobiologique de l'élément ou compartiment cellulaire dans l'échantillon biologique. [Revendication 2] Méthode selon la revendication 1, dans laquelle le champ magnétique est appliqué par une pointe magnétique, ladite pointe magnétique comprenant préférentiellement au moins un aimant millimétrique ou submillimétrique prolongé par une pointe métallique, ladite pointe métallique étant préférentiellement usinée avec un rayon de courbure compris entre 5 et 100 micromètres. [Revendication 3] Méthode selon la revendication 2, dans laquelle la méthode comprend en outre (i) une étape préalable dans laquelle le revêtement biologique des billes est sélectionné en fonction de l'élément ou compartiment cellulaire d'intérêt, (ii) une étape préalable de préparation de la pointe et/ou des billes superparamagnétiques et/ou (iii) une étape de calibration de la pointe et des billes. [Revendication 4] Méthode selon l'une quelconque des revendications 1 à 3, dans laquelle l'échantillon biologique est choisi parmi une cellule, un tissu, un organe et un embryon non humain, préférentiellement préalablement obtenu par échantillonnage. [Revendication 5] Méthode selon l'une quelconque des revendications 1 à 4, dans laquelle l'échantillon biologique est vivant et/ou non fixé. [Revendication 6] Méthode l'une quelconque des revendications 1 à 5, dans laquelle l'élément ou compartiment cellulaire est choisi parmi : la membrane cellulaire, la membrane nucléaire, la membrane d'un organite, tel que la mitochondrie, le réticulum endoplasmique ou l'appareil de golgi, les lysosomes, les peroxysomes ainsi que leur contenu, tel que le cytoplasme, les microtubules et/ou les centrioles, de préférence la membrane cellulaire ou la membrane nucléaire. [Revendication 7] Méthode selon l'une quelconque des revendications 1 à 6, dans laquelle les propriétés mécanobiologiques sont choisies parmi : la rhéologie, la cinématique, la résistance mécanique, l'élasticité, la rigidité, la plasticité et les propriétés visco-élastiques, et toutes combinaisons de celles-ci. [Revendication 8] Méthode selon l'une quelconque des revendications 1 à 7, dans laquelle le revêtement biologique des billes superparamagnétiques est un revêtement protéique, comprenant au moins une protéine appât apte à reconnaitre une protéine proie sur l'élément ou compartiment cellulaire d'intérêt, de préférence un anticorps ou une lectine, préférentiellement un anticorps choisi parmi un anticorps anti Sodium Potassium ATPase, anti PMCA1, anti Pan Cadherin, anti E Cadherin, anti N Cadherin, anti ADAM22, anti LRP4, anti Fas (APO-1, CD95), anti CD27, anti EGFR, anti NPC et anti NUP98. [Revendication 9] Méthode selon l'une quelconque des revendications 1 à 8, dans laquelle les billes superparamagnétiques ont une taille comprise entre 100 nm et 100 µm, de préférence entre 100 nm et 50 µm, préférentiellement entre 100 nm et 1 µm. [Revendication 10] Méthode selon l'une quelconque des revendications 1 à 9, dans laquelle la force appliquée sur l'échantillon biologique est comprise entre 0.001 pN et 200 nN, de préférence entre 0,5 pN et 1,5 nN. [Revendication 11] Méthode selon l'une quelconque des revendications 1 à 10, pour (i) caractériser l'impact d'une drogue ou d'un médicament sur un échantillon biologique, et/ou (ii) identifier des cellules tumorales dans un échantillon biologique. [Revendication 12] Kit comprenant : a) une pointe magnétique comprenant préférentiellement un coeur magnétique comprenant une superposition d'aimants millimétriques ou submillimétriques en néodyme prolongé par une pointe d'acier, la pointe d'acier étant préférentiellement usinée avec un rayon de courbure compris entre 5 et 100 micromètres, b) des billes super-paramagnétiques comprenant un revêtement biologique apte à adresser spécifiquement les billes superparamagnétiques à un élément ou compartiment cellulaire d'intérêt, le revêtement des billes superparamagnétiques étant de préférence un revêtement protéique, préférentiellement un anticorps ou une lectine, c) optionnellement une solution permettant la mise en suspension et l'injection des billes superparamagnétiques dans une cellule ou un tissu cellulaire, et d) optionnellement au moins une solution de calibration des billes superparamagnétiques et de la pointe magnétique. [Revendication 13] Utilisation du kit selon la revendication 12, pour (i) caractériser les propriétés mécanobiologiques d'un échantillon biologique, et/ou (ii) caractériser l'impact d'une drogue ou d'un médicament sur un échantillon biologique, et/ou (iii) identifier les cellules tumorales dans un échantillon biologique.

	[Revendication 1]	Revendications

Prism 6 (GraphPad Software, La Jolla, CA). Statistically significant differences and tests used depended on whether experiments were paired or not and are reported in figure legends.

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Acknowledgements I would like to thank the members of the jury for kindly accepting to evaluate my work: and the examiners Juliette Azimzadeh, Lea-Laetitia Pontani, Guillaume Charras, and Antoine Guichet and especially the reviewers Isabel Palacios and Jean-Léon Maître for reviewing my manuscript! I would like to thank Nicolas for his guidance and encouragement during my PhD. He is a really brilliant, talented, efficient and hardworking scientist and I learnt a lot from him for doing research in my carrier. I need to thank him pour pushing me to improve my skills for the research and spending a lot of time and energy on my project and papers! I thank all the collaborators who contributed to my PhD work: Javad for oil droplet experiments; Jeremy for image segmentation, taking care of urchins and including my data in his JCB paper; Rémi Le Borgne, Jean-Marc Verbavatz1and Catherine Durieu for electron microscopy images; Javad and Serge for excellent COMSOL simulation and physical advices and I thank Hajime Fuki and Julien Vermot for their shiny paper in Science! I would like to thank all the people in the lab for their help and support during my PhD: Louis, Javad, Ilaria, Celia, Magid, Amir and the new comer Aude. I also thank the former members: Hirokazu Tanimoto for setting up the magnetic tweezers; Valeria for kindly talking and teaching; Daria for suggestions and the recommendation letter for UNESCO; and Ramakanth for the Indian snacks! I thank also all the people in CRI, Camille, Elodie, Yaneth, David and Maria for supporting my thesis and helping in the administration part. I thank my TAC supervisors, Isabelle and Julien for kind advices and all the people that helped me in the IJM, a special thanks goes to Yan and Juanjuan. I thanks all my friends and a special thanks goes to Li Liu and Siyu for their talk and accompany Acknowledgment We thank P. Lenart, B. Lacroix and J. Dumont for sharing reagents, as well as our colleagues C. Leduc, S. Dmitrieff, G. Romet-Lemonne, Y. Bellaïche and J-L. Maître for carefully reading this MS. We gratefully thank all members of the Minc team for discussion and technical help. J.X. acknowledges the "École Doctorale FIRE -Program Bettencourt" and a fellowship from the Chinese Scholarship Council (201708070046). J.N. is supported by a Post-doc fellowship from the ARC foundation (PDF20191209818) and is an EMBO Non-Stipendiary Fellow (ALTF 881-2019). We acknowledge the ImagoSeine core facility of the Institut Jacques Monod, member of Infrastructure en Biologie Santé et Agronomie and France-BioImaging (ANR-10-INBS-04) infrastructures. This work was supported by the Centre National de la Recherche Scientifique (CNRS), the Université de Paris, and grants from La Ligue Contre le Cancer (EL2021.LNCC/ NiM), the Agence Nationale pour la Recherche (ANR, "TiMecaDev"), the Fondation Bettencourt Schueller ("Coup d'élan"), and the European Research Council (ERC CoG "Forcaster" no. 647073) to N.M.

ACKNOWLEDGMENTS

We thank Julie Plastino, Cécile Sykes, and Jacques Prost for discussions on comet-tail propulsion, as well as Jeremy Sallé, Javad Najafi, and Guillaume Romet-Lemonne, for carefully reading the manuscript. Sallé et al. Centering forces control asymmetric division Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Acknowledgments We thank K. Barett, B. Blanchard, H. Tanimoto, and other members of the Minc laboratory for help. J. Xie is funded by a fellowship from the Chinese Scholarship Council (201708070046) and is part of the Frontière du Vivant PhD Program. S. Dmitrieff is supported by a Momentum grant from the Centre National de la Recherche Scientifique. We acknowledge the ImagoSeine core facility of the Institut Jacques Monod, member of Infrastructure en Biologie Santé et Agronomie and France-BioImaging (ANR-10-INBS-04) infrastructures. This research was funded by the Centre National de la Recherche Scientifique and the European Research Council (CoG Forcaster no. 647073). The authors declare no competing financial interests. Author contributions: J. Sallé and J. Xie performed the experiments. D. Ershov developed the image analysis scripts. M. Lacassin and S. Dmitrieff designed and performed the models. J. Sallé, S. Dmitrieff, and N. Minc designed the research and wrote the manuscript. Submitted: 13 July 2018 Revised: 30 October 2018 Accepted: 30 November 2018 AC KN OW LE D GM E NT S We thank the members of J.V. 's and N.Mo. 's laboratories; the imaging and the fish facility staff of IGBMC; and M. Sone, A. Chiba, K. Hiratomi, and T. Babazono in N.Mo.'s laboratory for their assistance. F unding: This work was supported by the European Research Council (GA no. 682938), the Agence Nationale de la Recherche (ANR-15-CE13-0015-01, ANR-10-IDEX-0002 02, ANR-12-ISV2-0001-01, and -ANR-10-LABX-0030-INRT to J.V.), the University of Strasbourg (USIAS-2017-097), the Takeda Medical Research Foundation, the Uehara Memorial Foundation, the Cell Science Research Foundation (H.F.), and JSPS KAKENHI (21K 06764 to H.F.). R.W.-Y. C. was supported by a Fondation Lefoulon-Delalande fellowship. J.X. acknowledges a fellowship from the Chinese Scholarship Council (2017 08070046) and N.Mi grants from La Ligue Contre le Cancer (EL2021.LNCC/ NiM) and the European Research Council (ERC CoG Forcaster no. 647073). " " Author contributions: H.F. and J.V. conceived the project. H.F. designed the work and performed experiments. R.W.C. performed the analysis of Ca 2+ signaling normalization. H.F., J.X. and N.Mi. performed the magnetic tweezer experiments. Y.Y.F. and C.H.Y performed the analysis of 3D simulation. N.Mi. and N.Mo. provided reagents and suggestions. H.F. and J.V. wrote the manuscript. All authors interpreted the data, contributed to data analysis, and discussed the manuscript.

FUNDING

JX acknowledges support from a fellowship of the Chinese Scholarship Council (CSC). The Minc lab is currently funded by the CNRS and the European Research Council (CoG Forcaster No. 647073).

Centering forces control asymmetric division Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Centering forces control asymmetric division Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Centering forces control asymmetric division Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Journal of Cell Biology https://doi.org/10.1083/jcb.201807102 Journal of Cell Biology https://doi.org/10.1083/jcb.201807102

SUPPORTING INFORMATION

This supporting information file contains 6 Supplemental Figures and

Supporting movie legends

Movie S1. Metaphase spindles remain still in the cell center. Time-lapse of a zygote with DNA labelled with Hoechst, through metaphase, followed by a time-lapse of an egg treated with MG132 to prolong metaphase. Time is in min:sec. Movie S2. Metaphase spindle pulled parallel to their long axis with magnetic tweezers in live cells. Time-lapse of 2 metaphase spindles pulled with magnetic forces along their long axis and let to recoil and divide. Beads are labelled in red and DNA in blue. Time is in min:sec.

Movie S3

. Metaphase spindle pulled orthogonal to their long axis with magnetic tweezers in live cells. Time-lapse of 2 metaphase spindles pulled with magnetic forces orthogonal to their long axis, let to recoil and divide. Beads are labelled in red and DNA in blue. Time is in min:sec. Movie S4. Magnetized oil droplets pulled in the cytoplasm and let to recoil. Time-lapse of an egg injected with an oil droplet containing magnetic beads, pulled with magnetic tweezers and let to recoil. Time is in min:sec.

Movie S5. Serial Block Face images of metaphase cytoplasmic components with corresponding

3D pixel classification. Z-stacks of the metaphase cytoplasm with classified chromosomes (blue), ER (purple), Yolk (yellow) and Mitochondria (red). Close up views of the spindle region are presented at bottom. Movie S6. Cytoplasm flows during parallel and orthogonal pulls. Time-lapse of an egg in which the metaphase spindle was pulled parallel to its long-axis, superimposed by the flow vector maps in red; followed by a similar time-lapse for an orthogonal pull. Time is in min:sec.

ANNEXE 1 Cytoskeleton force exertion in bulk cytoplasm

Jing Xie and Nicolas Minc

Review published in Frontiers in Cell and Developmental Biology

AUTHOR CONTRIBUTIONS

JX and NM designed the content, made figures, and wrote text.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Pulling cap assembly and relocation. Unfertilized egg after magnetic bead injection. Embryos were visualized using differential interference contrast; beads are in green. The magnetic probe is used to assemble and relocate a cortical pulling cap. Images were obtained by wide-field time-lapse microscopy. Frames were taken every 30 s for 17 min.

Sallé et al.

Centering forces control asymmetric division

Video 2. Asymmetric division induced by artificial cortical pulling. A cortical pulling cap is maintained during the first cleavage in embryos by using a magnetic probe. Embryos were visualized using differential interference contrast; the beads forming the pulling cap are in green. Images were obtained by wide-field time-lapse microscopy. Frames were taken every 10 s for 98 min. Video 3. "Free cap" control embryo. First cleavage visualized in an embryo containing a free pulling cap (no magnet). Embryos were visualized using differential interference contrast; the beads are in green. Images were obtained by wide-field time-lapse microscopy. Frames were taken every 20 s for 63 min. Video 4. "Non-pulling cap" control embryo. First cleavage visualized in an embryo containing a nonpulling cap maintained at the cortex. Embryos were visualized using differential interference contrast; the beads forming the cap are in green. Images were obtained by wide-field time-lapse microscopy. Frames were taken every 30 s for 62 min.

Video 5. Decentration after dynein motors inhibition or MT depolymerization. Nucleus decentration after drug addition (white square at the bottom left corner of each video). From top to bottom: DMSO; 50 µM Ciliobrevin D; 20 µM Nocodazole. Embryos were visualized using differential interference contrast; the beads forming the cap are in green. Images were obtained by wide-field time-lapse microscopy. Frames were taken every 30 s for 15 min. -27. A. L. Armesilla et al., Mol. Cell. Biol. 19, 2032-2043(1999). 28. A. K. Patra ., , 127 135 (2013) The PDF file includes:

Materials and Methods

Figs. S1 to S11 References

Other Supplementary Material for this manuscript includes the following:

Movies S1 to S8 MDAR Reproducibility Checklist

Materials and Methods

Zebrafish (Danio rerio) strains, transgenic lines, and mutant lines

The experiments using zebrafish were approved by the animal experimentation committee of the institutional review board of the IGBMC (reference numbers MIN APAFIS#4669-2016032411093030 v4 and MIN 4669-2016032411093030 v4-detail of entry 1) and of the National Cerebral and Cardiovascular Center (permit number: 21055), and performed according to the guidelines of the Institute. Embryos were raised in E3 medium and incubated at 28.5 o C. Heart rate was analyzed at this condition from 32 hpf to 150 hpf as a control (Fig. S3H). Developmental staging was referred to chronological and morphological criteria (38). We used the AB strain as wild-type. The following zebrafish transgenic lines were used for experiments: Tg(fli1a:gal4ff) (39), Tg(uas:GCaMP7a) (40), Tg(kdrl:nls-mCherry) ncv5 (41), Tg(fli1a:lifeact-mCherry) ncv7 (42), Tg(fli1a:myr-mCherry) ncv1 (43), Tg(fli1a:h2b-mCherry) ncv31 (5), Tg(myl7:nls-mCherry) ncv11 (44), Tg(uas:RFP) (45), and TgBAC(nfatc1:gal4ff) (34). The Tg(4xnfbr:d2EGFP) ncv531 , TgBAC(twist1b:GFP) ncv534 , Tg(fli1a:GFP-nfatc1) ncv532 , and Tg(uas:VIVIT-mCherry) ncv533

were generated as described in the experimental procedures. We used FK506, a Calcineurin inhibitor, which is blocking valve morphogenesis to test the specificity in the Tg(fli1a:lifeact-GFP);Tg(kdrl:nls-mCherry) embryos (6,46) (Fig. S2B). Such treatment significantly suppressed the reporter expression of Tg(4xnfbr:d2EGFP) embryos (Fig. S10, A andB). In addition, VIVIT peptide overexpression using a selective inhibitor of Nfat dephosphorylation (19), using the TgBAC(nfatc1:galff) driver which is specific to EdCs (34) was used. Such treatment also led to the suppression of reporter activation (Fig. S2D), demonstrating that our reporter Tg(4xnfbr:d2EGFP) is indeed revealing Nfat activation. The following zebrafish mutants were used for experiments: The knockout alleles of m651 for gata1a ( 14), ts294e for dzip1 (23), tc321 for trpp2 (22), sa1671 for trpv4 (17) (Zebrafish International Resource Center [ZIRC]), sa12608 for piezo1 (European Zebrafish Resource Center [EZRC]), sa12414 for piezo2a (ZIRC), sa14724 for piezo2b (ZIRC).

Genotyping primers

The following genotyping PCR primers were used for amplification: piezo1 (5'-CTATTCCTTTGAGAGCCCTTTG-3' and 5'-GCATGTGGATACAGCAATGAC-3', for annealing); piezo2a (5'-AATGTGATGTGTTGCTCTGC-3' and5'-CTTTCAGCAAAGGCATCTCC-3', 60 o C for annealing, andfor sequence; 5'-TCAGTCTGTTCGGGATTTCTC-3'); piezo2b (5'-TGCTAGGTGGTTGGCTTTCTC-3' and5 GCaMP7a using a 488 nm wavelength laser line. Excitation of GFP and mCherry was done using 488 nm and 561 nm wavelength laser lines, respectively. Beating heart samples were taken every 10 msec exposure time unless otherwise described and the data were acquired by binning 2 x 2. Confocal images of 1.5 m steps were taken with an upright TCS SP8 confocal microscope system (Leica) equipped with a 25x water immersion objective (Leica HCX IRAPO L, 0.95 N.A.) and an upright FV3000 confocal microscope system (Olympus) equipped with a 20x water immersion objective (Olympus XLUMPlan FL_N, 1.0 N.A.). Dechorionated embryos were mounted in 1% low-melting agarose (Invitrogen-Thermo Fisher Scientific) dissolved in E3 medium. At early stages (30 hpf and 34 hpf), the pre-AVC region is defined as the middle area between arterial pole and venous pole. Furthermore, the tissue curvature is found in the pre-AVC region and used as morphological landmarks. After 48 hpf, the endocardial cells on the AVC region is defined by the area located between the superior and inferior region of the atrium and the ventricular chamber. Images were processed with a Las X software (Leica), Zen 3.1 software (Zeiss), FV31S-SW software (Olympus), ImageJ and Imaris 9.6 (Bitplane).

Chemical treatments

Embryos were treated with the following small molecule inhibitors: MS-222 (also known as tricaine, 2.0 mg/mL, Sigma-Aldrich) or BDM (2,3- were deposited on top of the agarose with E3 medium. A hole was created in the center of the yolk by forceps and the bead of roughly 30-40 m diameter was inserted into a hole.

The bead was pushed anteriorly by the tip of forceps. Once the bead reached the venous pole, suction caused by the heart contraction will move the bead into the cardiac lumen (47). Embryos then were released from agarose and allowed to develop in E3 medium at 28.5 o C. Approximately 30% embryos kept the bead move continuously in the atrium or the ventricle together with the blood flow were applied to the experiments. Whereas, the embryos with the bead sucked in the outflow tract were excluded for the experiments.

Simulation of influences in the grafted bead in the atrium

The dynamic geometry of the zebrafish cardiac atrium was approximated from a 2D fluorescent imaging video of the atrial chamber containing the moving magnetic bead. A fixed centerline was defined within the atrial chamber from inlet towards AV junction, defined by splines of several centerline points. The inner and outer radii of the atrium were manually traced over the cardiac cycle for every centerline point (Fig. S4A). A wall motion model was then curve-fitted to these measurements, where the radius dimension was described as the 2D Fourier of time and azimuthal angle at every centerline point, and the cubic Hermite function was used to interpolate between centerline points, similar to our previous methods (15). 3D dynamic wall computational fluid dynamics simulations of blood flow in the atrium were conducted with ANSYS Workbench 2019 (ANSYS Inc). A 30 m spherical bead was inserted into the atrium (Fig. S4, B and C), programmed to move according to a unidirectional oscillatory motion waveform traced from the above-mentioned 2D video, using ANSYS user-defined function. The atrial chamber was meshed with about 775k tetrahedral cells, and a zone of 30 m radius from the center of the bead was programmed to have an overset mesh with 506k tetrahedral cells that was superimposed onto the atrial chamber mesh, which were determined by a mesh convergence study. In both mesh, refined mesh at wall boundaries was achieved via about five inflation layers. The blood fluid in the atrial chamber was assumed to have a viscosity of 3.5 cP and density of 1060 kg/m 3 . The inlet and outlet boundary conditions were set to zero reference pressures. A total of 1050 time-steps per cardiac cycle was simulated, with results were extracted from the second cycle.

Magnetic tweezer

A magnetic tweezer was used to apply force to magnetic beads (PureCube Glutathione MagBeads, Cube Biotech) (48,49) where V is the velocity of the magnetic bead and x is the distance between the bead and the magnet tip. V300 is the bead velocity at a distance 300 m away from the magnet tip.

The same experiment performed on agarose magnetic beads with varying sizes at a fixed distance of 300 m then allowed to compute the net magnetic force, and establish forcesize relationships, using the Stokes equation.

where R is the bead radium (m). F300 is the magnetic force (pN) at a fix distance 300 m from the magnet tip.

According to velocity-distance and force-size relationships, we computed the final equation for calculating the magnetic force:

where F is the magnetic force (pN), and Vx (m/s) is the velocity at x m in the magnetic to make a pTol2-4xnfbr vector. The sequence of 4x tandem repeats was confirmed by DNA sequence. pTol2-4xnfbr vector was inserted with E1b minimal promoter and d2EGFP-polyA sequence to construct the pTol2-4xNfbr-E1b-d2EGFP-pA plasmid.

To monitor the nfat signal inhibition, we established a transgenic line expressing VIVIT-mCherry under the control of Gal4-UAS system; Tg(uas:VIVIT-mCherry) ncv533 .

We used a pmCherry-N1 vector as a template and VIVIT peptide Tol2-mediated zebrafish transgenesis was performed by injecting 30 pg of transgene plasmid together with 50 pg of tol2 transposase mRNA, followed by subsequent screening of F1 founders and establishment of stable transgenic strains through selection in F3 generations.

Ca 2+ influx normalization

To monitor the Ca 2+ signal during heart development, we crossed the Tg(fli1a:gal4ff);Tg(uas:GCaMP7a) line, where a fluorescent Ca 2+ sensor protein GCaMP7a is driven by endocardial gal4, with the Tg(kdrl:nls-mCherry) line, where kdrlpromoter drives nls-mCherry and thus labels endocardial nuclei. To measure the normalized Ca 2+ signal of a particular cell over time, we developed software in Matlab (Mathworks) to do the following: For each embryo, the cells imaged move in and out of the focus plane during heartbeat, causing fluctuations in the detectable Ca 2+ signal. Our first step was thus to transform our XYT movies into XYtR movies, where T is the timepoints acquired, t is the timepoint along the cardiac cycle, and R is the iteration of cardiac cycles. To do so, we must account for the changes in heartrate over the period of imaging. Using Matlab, we selected nine region of interests (ROIs) one tenth of the size of the whole image and measured the fluorescence intensity of the nuclear channel over time, Inuclear (T). We calculate the position of the intensity peaks based using ct_getpeaks (55) and select two ROIs where the fluctuations in nuclear channel intensity due to heartbeat are the clearest. Next, we averaged the peak positions acquired from the two ROIs iteratively. Each of these averaged peak positions are assumed to correlate to a specific position within the cardiac cycle. We then calculated the average number of timepoints between these peaks to get the average period of heartbeat tmax. We cut the XYT movie into sections with length of (tmax + 7 images); each centered around the image corresponding to the averaged peak position. We then recombined the sections into a XYtR movie.

For each cell of interest within the embryo, we created XYR movie: The XYtR movie is opened in FIJI, the timepoint along the cardiac cycle that best captures the cell of interest was manually identified, and an XYR movie was created for that timepoint.

Image of average signal: Importing the XYR movie back into Matlab, an image that showed the average Ca 2+ and average nuclear signal over the entire course of imaging was calculated. For both channels, each pixel in the final image is the sum of the signal intensity divided over the total number of images, Rmax. Normalized Ca 2+ signal: Using the image of the average signal as a guide, we manually drew around the cell of interest to generate the ROI. The normalized Ca 2+ signal for the ROI was then calculated using:

where Icalcium is the fluorescence intensity of the Ca 2+ signal, Inuclear is the fluorescence intensity of the nuclear signal, and the baseline is the minimum Icalcium/Inuclear over the entire XYR movie. Calculate peak position: The position of the peaks was calculated using ct_pulseanalysis (55) with the SMOOTH parameter set to 5. Note that Ca 2+

signaling in nearby cells could cause noise when measuring the normalized Ca 2+ signal in the cell of interest. Determination of which Ca 2+ peaks are truly associated with the cell of interest thus relies on viewing the phased-matched movie and the normalized Ca 2+ calculations side by side (Movie S2).

Whole-mount in situ hybridization (WISH)

The antisense klf2a, klf4a, egr1, p2rx1, p2rx4a and p2rx7 RNA probes labeled with digoxigenin (DIG) were prepared by using an RNA labeling kit (Roche). WISH was performed as previously described (56). Colorimetric reaction was carried out using BM purple (Roche) as the substrate. To stop the reaction, embryos were washed with PBS-T, fixed with 4% PFA for 20 min at room temperature and subsequently immersed in glycerol. Images were taken using a stereo microscope (Leica M165C).

RNAscope analysis

Embryos were fixed by 10% NBF for overnight at room temperature. After fixation, the solution was changed to 50% Methanol / PBBT (PBS with 2 mg/mL BSA and 0.1%