Keywords:

A huge thank you to Anne-Sophie Macé, for the interest in the project and being able to simply answer and solve all of my analysis problems and maneuver the complicated world of pixels.

Thank you to Aude Battistella, for her love of experiments, a thirst for new techniques and her expertise.

Thank you to William Beng, my first student, for perfecting the cellular dancing moves and methods to follow them.

Thank you to Jean de Sèze

Abstract

When cells migrate, they need to coordinate multiple signaling pathways in space and time to orchestrate the dynamics of their cytoskeleton and the distribution of their internal organelles. Yet, it remains unclear how the different signaling programs are coupled, and to what extent a proper cell polarity is required for migration. More specifically, is the orientation of the nucleus-Golgi axis a necessary directional cue for persistent migration? Is a sustained local activation of RhoGTPase signaling sufficient to establish a functional polarized cellular state? Does the nucleus-Golgi axis position create a bias in vesicle traffic? Such questions are difficult to answer because of the numerous feedbacks in the cell signaling circuitry.

During my thesis, using dynamic micropatterning, optogenetics, pharmacological and trafficking assays, and live-cell imaging, I found that a feedback between RhoGT-Pases' biochemical gradients -that dictate local membrane activity-and cell internal organization -that defines the global polarity axis of the cell-allows cell migration to be persistent. I first demonstrated that Golgi complex positioning is instructive for the selection of the direction of movement using a well-controlled dynamic micropatterning assay. Second, by pharmacologically dispersing Golgi complex and disrupting polarized secretion, I showed that persistent migration breaks down and becomes random. Third, I found evidence that the Golgi orientation biases protruding activity, most likely by directing the secretion of adhesive molecules. Fourth, by applying sustained optogenetic perturbations, I proved that a localized Cdc42 RhoGTPase gradient is able to orient the Golgi complex. Taken together, I propose a model of persistent cell migration based on the coupling between protrusion dynamics, driven by RhoGTPases' activities, and polarized secretion, biased by organelle positioning. i

Résumé

Lorsque les cellules migrent, elles doivent coordonner de multiples voies de signalisation dans l'espace et le temps pour orchestrer la dynamique de leur cytosquelette et la distribution de leurs organites internes. Cependant, on ne sait pas encore très bien comment les différents programmes de signalisation sont couplés, ni dans quelle mesure une polarité cellulaire globale est nécessaire pour la migration. Plus précisément, est-ce que l'orientation de l'axe joignant l'appareil de Golgi et le noyau est un repère directionnel nécessaire pour une migration persistante ? Est-ce que l'orientation de cet axe génère un biais dans le trafic vésiculaire ? Est-ce qu'une activation locale et maintenue de signalisation en RhoGTPase est suffisante pour établir un état cellulaire polarisé fonctionnel ? Il est difficile de répondre à de telles questions en raison des nombreuses boucles de rétroaction dans les circuits de signalisation cellulaire.

Au cours de ma thèse, en utilisant des expériences de micropatterning dynamique, d'optogénétique, de perturbations pharmacologiques, de trafic, ainsi que d'imagerie des cellules vivantes, j'ai découvert qu'une boucle de rétroaction entre les gradients biochimiques des RhoGTPases -qui dictent l'activité membranaire locale -et l'organisation interne de la cellule -qui définit l'axe de polarité global de la cellule -permet à la migration cellulaire d'être persistante.

Premièrement, j'ai d'abord démontré que le positionnement de l'appareil de Golgi est instructif pour la sélection de la direction du mouvement à l'aide d'une système expérimental contrôlé de micropatterning dynamique. Deuxièmement, en dispersant l'appareil de Golgi et en perturbant la sécrétion polarisée à l'aide de drogues, j'ai montré que la migration perd sa persistante et devient aléatoire. Troisièmement, j'ai avancé des preuves que l'orientation de l'appareil de Golgi biaise l'activité des protrusions membranaires, très probablement en dirigeant la sécrétion des protéines d'adhésion. Quatrièmement, en appliquant des perturbations optogénétiques maintenues, j'ai prouvé qu'un gradient localisé de la RhoGTPase Cdc42 est capable d'orienter l'appareil de Golgi. Au final, je propose un modèle de migration cellulaire persistante basé sur le couplage entre la dynamique des protrusions membranaires, induite par les activités des RhoGTPases, et la sécrétion polarisée, biaisée par le positionnement des organelles.

• A-P: Anterior-Posterior.

• APC: Adenomatous polyposis coli.

• APP: azido-PLL-g-PEG.

• Arf1: ADP-ribosylation factor 1.

• BIG1: Bad in glucose protein 1.

• BIG2: Bad in glucose protein 2.

• Arp2/3: Actin-Related Proteins 2/3.

• AsLOV2: Avena sativa light-oxygen-voltage-sensing domain 2.

• ATP: Adenosine triphosphate.

• BCN-RGD: Bicyclo[6.1.0]non-4-yn-9-ylmethyl-Arg-Gly-Asp.

• Bem1: Bud emergence protein 1.

• BFA: Brefeldin A.

• CCW: Counter-clockwise.

• Cdc42: Cell division control protein 42.

• ChR: Channelrhodopsins.

• Cla4: CLn Activity dependant.

• CLASPs: cytoplasmic linker associated protein 1.

• Clip-170: Cytoplasmic linker protein-170.

• CMSC: Cortical microtubule stabilization complex.

• ColX, Col10A: Collagen type X.

• COPI, COPII: coat protein complex I or II.

vii viii

Abbreviations

• CRISPR: Clustered regularly interspaced short palindromic repeats.

• Crb-PALS-PATJ): Crumbs; Protein containing ALS2cr12 (ALS2CR12) signature; PALS1-Associated Tight Junction Protein.

• Cry2/CIBN: Cryptochrome2/CIB N-terminal.

• CW: Clockwise.

• DH-PH domain: Dbl homology-pleckstrin homology domain.

• DIC: Differential Interference Contrast.

• Dlg1: Disks large 1.

• DMD: Digital Micromirror Device.

• DMEM: Dulbecco's Modified Eagle Medium.

• DNA: Deoxyribonucleic acid.

• EB1: End-binding 1.

• ECM: Extracellular matrix.

• EE: Early endosome.

• ELKS proteins: ERC (abbreviation for ELKS, Rab6IP2, and CAST).

• EMT: Epithelial-to-mesenchymal transition.

• Ena/VASP: Ena/Vasodilator-stimulated phosphoprotein.

• ER: Endoplasmic Reticulum.

• ERGIC: ER-Golgi intermediate compartment.

• ERM: ezrin, radixin, moesin.

• FAK: Focal adhesion kinase.

• FA: Focal adhesion.

• FMN: Flavin mononucleotide.

• FMNL: Formin-Like.

• FRET: Förster resonance energy transfer.

• GAP: GTPase activating protein.

• GBF1: Golgi-specific brefeldin A-resistance guanine nucleotide exchange factor 1.

• GCA: Golgicide A.

• GDF: GDI displacement factor.

• GDI: GDP Dissociation Inhibitor.

• GDP: Guanosine diphosphate.

• GEF: Guanine nucleotide exchange factor.

• GFP: Green fluorescent protein.

• GKAP: Guanylate kinase-associated protein.

• GMAP210: Golgi-Microtubule-Associated-Protein Of 210 KDa.

• GOLPH3: Golgi phosphoprotein 3.

• GPCR: G-protein coupled receptor.

• GRAF1: GTPase Regulator Associated with Focal Adhesion Kinase.

• GRASP55 and GRASP65: Golgi reassembly-stacking protein of 55 kDa and 65 kDa.

• GSK3B: Glycogen synthase kinase 3 beta.

• GTP: Guanosine triphosphate.

• GTPase: Enzyme hydrolyzing GTP.

• GUI: Graphical user interface.

• HEK: Human embryonic kidney.

• HILO: Highly inclined and laminated optical sheet.

• iLID: improved light-induced dimer.

• IM-LARIAT: light-activated reversible inhibition by assembled trap of intracellular membranes.

• IQGAP1: IQ Motif Containing GTPase Activating Protein 1.

• iRFP: near-infrared red fluorescent protein.

• ITSN: Intersectin.

• KASH: Klarsicht, ANC-1, Syne homology.

• KIF5B, KIF13B or KIF20A: Kinesin Family Member 5B, 13B or 20A.

• LED: Light-emitting diode.

• LEGI: Local excitation/global inhibition.

• LINC: Linker of nucleoskeleton and cytoskeleton.

• LOV: Light-oxygen-voltage-sensitive domain.

• MAP: Microtubule associated protein.

• mDia: mouse Diaphanous-related formin-1.

• MICAL3: Microtubule Associated Monooxygenase, Calponin And LIM Domain Containing 3.

• miRNA: micro RNA.

x

Abbreviations

• MLC: Myosin-II light chain.

• MRCK: Myotonic dystrophy kinase-related Cdc42-binding kinase.

• MSD: Mean square displacement.

• MT: Microtubule.

• MTOC: Microtubule organizing center.

• MVB: Multivesicular body.

• myr: myristoylated.

• NG-axis: Nucleus-Golgi axis.

• NPF: Nucleation promoting factor.

• NZ: Nocodazole.

• CDC42-PAR3-PAR6-aPKC: Cell division control protein 42; Partitioning defective 3; Partitioning defective 6, Atypical protein kinase C.

• PBS: Phosphate-buffered saline.

• PCB: Phytochromobilin.

• PhyB/PIF: PhytochromeB/Phytochrome-interacting protein.

• PI: Phosphoinositide.

• PI(3,4,5)P 3 or PIP 3 : Phosphatidylinositol [START_REF]1 Persistence time phase diagram[END_REF]4,5)-trisphosphate.

• PI(4,5)P 2 or PIP 2 : Phosphatidylinositol (4,5)-diphosphate.

• PI(4)P 2 or PIP: Phosphatidylinositol 4-phosphate.

• PI3K: Phosphoinositide 3-kinase.

• PLL-g-PEG: Poly(L-lysine)-graft-poly(ethylene glycol).

• PM: Plasma membrane.

• PTM: Post-translational modification.

• Rab: Ras-related protein in brain.

• Rab6A: Ras-related protein in brain 6A.

• RabGGT: Rab geranylgeranyl transferase.

• Rac1: Ras-related C3 botulinum toxin substrate 1.

• Ras: Rat sarcoma related.

• RE: Recycling Endosome.

• REP: Rab escort protein.

• Rho: Ras homolog.

Abbreviations xi

• ROCK: Rho-associated protein kinase.

• RPE1: Retinal pigmented epithelium 1.

• RTK: Receptor Tyrosine Kinase.

• RUSH: Retention Using Selective Hooks.

• SBP: Streptavidin-binding protein.

• Scrib-Dlg-Lgl): Scribble; Disks large; Lethal giant larvae protein.

• Sec3: Secretory 3.

• SFK: Src family tyrosine kinase.

• siRNA: Small interfering RNA.

• SNARE: SNAP REceptor.

• SNR: Signal-to-noise ratio.

• SPI: Selective protein immobilization.

• SspB: Stringent starvation protein B.

• TAN lines: Transmembrane actin-associated nuclear lines.

• TGN: Trans-Golgi Network.

• TIRF: Total Internal Reflection Fluorescence.

• TULIP: Tunable, light-controlled interacting protein.

• UV: ultraviolet light.

• VIF: Vimentin intermediate filament.

• WASP: Wiskott-Aldrich Syndrome protein.

• WAVE: WASP-family verprolin-homologous protein.

List of Figures

Introduction

A migrating cell reorganizes its cytoskeleton, changes the positioning of its organelles, adapts the trafficking needs and coordinates all these structural and molecular changes on the way. In the introduction chapter I will delve into the dynamics of cell migration, describing the main players in the actin cytoskeleton reorganization, adhesion, force generation and its regulation by Rho GTPases in the first part. Then, I will focus on cellular trafficking, changes in the microtubule (MT) network and control of membrane trafficking by Rab GTPases in the second part. Finally, I will combine the two parts together and discuss their connections, while describing the establishment of cell polarity in the third part, and present a recent biological technique, called optogenetics, which has proven to be instrumental in dissecting coordination in complex processes, such as cell migration.

Cell migration

Cell migration is a phenomenon that is crucial for the living organisms to survive. Simple bacterial organisms can propel themselves by moving a flagellum, a motor structure that can generate propulsive force that pushes the cell forward [START_REF] Nakamura | Flagelladriven motility of bacteria[END_REF]. This helps the bacterium to avoid repellents (danger) and follow attractants (find food) [START_REF] Nakamura | Flagelladriven motility of bacteria[END_REF]]. If we scale up, and go to eukaryotes, we can also find single-celled organisms using flagellar propulsion [Mitchell, 2007]. However, another mode of movement has evolved and became more evident as the cellular environment had changed. Instead of swimming in the liquid, cells started to crawl across and between solid surfaces [START_REF] Fritz-Laylin | Our evolving view of cell motility[END_REF]. To achieve that, they use various different structures and can either move forward by forming adhesions with the substrate, or by using friction or topographical cues of the surrounding environment [START_REF] Reversat | Cellular locomotion using environmental topography[END_REF]. One common feature is the need of constant force generation to push forward, as inertia is insignificant in the low Reynold's number environments [Purcell, 1976]. In this part of introduction, I will focus on how a eukaryotic cell can crawl on the surface. I will look into the structure of the cell and the generation of force and cytoplasmic flows within it, how a cell is able to adhere to the surface and explore the surroundings, and the molecular players relaying signals from outside to the inside of the cell.

Movement of cell body

A eukaryotic cell is separated from the external environment by a double-layered lipid membrane called plasma membrane, which encloses the cytoplasm with different organelles and the nucleus [de la Serna et al., 2016]. In order to move in any direction, it needs to push its membrane to that side. It can be pushed by hydrostatic pressure of the moving fluid [START_REF] Paluch | The role and regulation of blebs in cell migration[END_REF] or by solid push of filamentous structures built inside [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. These filamentous structures are a part of the cytoskeleton of the cells. The cytoskeleton consists of three filamentous structuresactin filaments, intermediate filaments and microtubules [START_REF] Huber | Cytoskeletal crosstalk: When three different personalities team up[END_REF]. All of them help to maintain the cell shape, but actin and microtubules also have dynamic and polar properties in addition to that [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF]. Microtubules are essential for trafficking and signalling factor distribution in cells, and I will come back to them in the following part of Introduction, but now I will focus on actin microfilaments, which are the main force generator in cell migration [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF].

Crawling eukaryotic cell migration was first described by Abercrombie in 1970s in a series of papers describing different aspects of cell movement [START_REF] Abercrombie | The locomotion of fibroblasts in culture[END_REF]. He has used fibroblast-like cells from embryonic chick heart and neonatal mouse muscle as his model. In multicellular eukaryotic organisms collective migration plays a very important role in the germ layer establishment in the developing embryo [START_REF] Scarpa | Collective cell migration in development[END_REF] or in wound healing in adult organisms [Shaw andMartin, 2009, Ilina andFriedl, 2009], and these phenomena have been widely researched, but I will focus on single-cell migration, which is similar to what Abercrombie described 50 years ago, as the mechanism is not completely understood. A concept of a single migrating cell can help us understand how immunity cells patrol our organisms looking for invaders [START_REF] Moreau | Integrating Physical and Molecular Insights on Immune Cell Migration[END_REF] and how cells escape primary tumours to form metastases elsewhere in the body [Van Zijl et al., 2011, Bravo-Cordero et al., 2012].

As mentioned before, a cell can move by deforming and pushing its membrane. The plasma membrane mainly consists of phospholipid molecules packed together in a double layer, with their hydrophilic heads facing outside and hydrophobic tails facing inside of the membrane [Singer andNicolson, 1972, Helfrich, 1973]. This type of structure makes them insensitive to lateral shear strain, as the membrane can easily flow in this direction. On the contrary, the membrane is very susceptible to bending and stretching, as this would expose the hydrophobic tails hidden inside. This produces tension and any bending or stretching of the membrane requires a certain amount of energy spent to deform it [START_REF] Sens | Membrane tension and cytoskeleton organization in cell motility[END_REF]. Having this in mind, to push the membrane, actin filaments need to overcome a certain membrane tension [START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF]]. An actin filament can polymerize at both sides with a preference for the barbed end, and as ATP brought with a monomer is hydrolysed, the monomer detaches [START_REF] Pollard | Cellular Motility Driven by Assembly and Disassembly of Actin Filaments[END_REF]]. If actin is polymerizing facing the membrane without being attached, the polymerizing barbed end at the front is being pushed backwards and no effective protrusion is produced, instead a backwards flow of actin is visible, which is called actin retrograde flow [Cramer, 1997]. However, if an adhesion is formed with a substrate and if the adhesion is mechanically linked to the actin meshwork, the force of actin polymerization can be translated to traction forces that would lead to a membrane protrusion being formed [Sixt, 2012, Vicente-Manzanares andHorwitz, 2011]. Still, this is not enough to move the full cell body.

For a cell body of a crawling cell to move, it needs to go through a cycle of protrusion-adhesion-retraction [START_REF] Reig | Cell migration: from tissue culture to embryos[END_REF], Le Clainche and Carlier, 2008, Ananthakrishnan and Ehrlicher, 2007,Gupton and Waterman-Storer, 2006,Vicente-Manzanares, 2005]. Once a protrusion is formed, it needs to adhere to the substrate and, thanks to the myosin II and actin depolymerization, retract its back [Cramer, 2013]. The process continues all over again, making the cell move forwards (see Figure 1.1 for a scheme). If protrusions are coordinated and are generated in the same spot, protruding in the Figure 1.1: Cell migration in in vitro 2D culture environments. A current view of Abercrombie's cell migration cycle, highlighting actin polymerisation-dependent processes (red), cell-substrate adhesive structures (purple) and myosin II-dependent events (green). Cells moving on 2D surfaces undergo repeated steps of: (1) extension of the leading edge and formation of immature cell-substrate adhesions; (2) maturation of cell-substrate adhesions; [START_REF]1 Persistence time phase diagram[END_REF] forward translocation of the cell body; and (4) disassembly of focal adhesions coupled to retraction of the rear edge. Taken from [START_REF] Reig | Cell migration: from tissue culture to embryos[END_REF].

same direction, the cell body moves directionally [START_REF] Petrie | Random versus directionally persistent cell migration[END_REF]. The coordination of protrusive membrane areas is still not completely understood, and multiple processes could be taking part in it, including external cues and related signalling pathways [START_REF] Reig | Cell migration: from tissue culture to embryos[END_REF], actin retrograde flow [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF], cytoplasmic flows [START_REF] Keren | Intracellular fluid flow in rapidly moving cells[END_REF] and membrane tension [START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF].

Most of the cell migration studies have been focused on mesenchymal cell migration in 2D, where a cell is crawling on the substrate [Vicente-Manzanares, 2005]. Recently, new modes of cell migration were described, where a cell moves without creating strong adhesions with the substrate and instead using either friction [START_REF] Paluch | The role and regulation of blebs in cell migration[END_REF] or topography of the environment [START_REF] Reversat | Cellular locomotion using environmental topography[END_REF]. Interestingly, it was shown, that the same cell could switch between these apparently different modes of migration [Liu et al., 2015, Friedl andWolf, 2010]. Moreover, the connecting link between these modes was revealed to be the actin retrograde flow [START_REF] Callan-Jones | Actin flows in cell migration: From locomotion and polarity to trajectories[END_REF], Maiuri et al., 2015, Reversat et al., 2020]. The mechanism of cell migration is still actively studied, with more and more modelling approaches being used, mainly focusing on cell migration in 1D and 2D (a substantial list of models can be found in [Lavi, 2019]). Together with in vitro [START_REF] Garcia-Arcos | Reconstitution of cell migration at a glance[END_REF] and in vivo [START_REF] Reig | Cell migration: from tissue culture to embryos[END_REF] experimental studies it helps us solve the outstanding biological questions. To delve more into the process of cell migration, in the next sections I will focus on actin cytoskeleton, cell adhesion and signaling proteins that regulate the process of cell migration.

Actomyosin network

Figure 1.2: Properties of actin filaments. Actin filaments are composed of subunits that are oriented in the same direction, which results in a polarized surface lattice and two structurally distinct ends (barbed and pointed). Motor proteins (myosins) move in a unidirectional manner along the filament surface owing to repeated interactions with the subunits in consistent orientations. The barbed and pointed ends of an actin filament exhibit different monomer association and dissociation rates. They also exhibit different critical concentrations for the assembly of ATP-actin as a result of ATP hydrolysis and phosphate release soon after monomer incorporation into the filament. Asymmetry in the state of the nucleotide that is bound along the filament, and structural differences between the two ends enable many actin-binding proteins to differentially regulate their dynamics and stability in vivo. Taken from [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF].

Actin filaments are one type of cytoskeletal structures that play a crucial role in cell migration. Composed of 42 kDa actin monomers, they can polymerize and form linear filaments (F-actin) [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. F-actin filaments are inherently polar, and polymerization rates are different at their two ends. The "barbed" end polymerizes faster than the "pointed" end [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF],Pollard and Borisy, 2003,Zsolnay et al., 2020]. The filaments have a tendency to age as well. New polymers are added in complex with ATP, and slowly hydrolyse it after they become a part of the filament. Once ATP hydrolysis is complete and the phosphate group dissociates, the actin monomer detaches as well. The combined action of polymerization and detachment at the two opposite ends is called is called actin treadmilling (see Figure 1.2) [START_REF] Pollard | Cellular Motility Driven by Assembly and Disassembly of Actin Filaments[END_REF], Li and Gundersen, 2008, Neuhaus et al., 1983]. For a filament to start forming, it needs nucleators, as the biochemical reaction itself is very slow. Moreover, actin monomers in physiological conditions are normally bound by a protein profilin, to prevent unwanted actin polymerization. In this case, a nucleator is essential to start the process [Blanchoin et al., 2014, Pollard andBorisy, 2003]. This role is mainly played by an Arp2/3 complex and formins, and can be enchanced by several different families of NPFs ("nucleation-promoting factors") like WASP and WAVE [Campellone andWelch, 2010,Cotteret andChernoff, 2002]. Arp2/3 complex is known to form branched actin networks. Actively polymerizing filaments are stopped by capping proteins, controlling their length. Polymerization is happening all over the network and if not capped, the filaments start to grow side by side and start forming linear bundles [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF], Yang and Svitkina, 2011, Raz-Ben Aroush et al., 2017]. Actin filaments have multiple binding sites and can form multivalent interactions with crosslinking proteins, that help to form different types of networks -isotropic, branched and bundled [START_REF] Braun | Cytoskeletal organization through multivalent interactions[END_REF], Pollard, 2016, Blanchoin et al., 2014]. Actin networks can be disassembled fast by ADF/cofillin protein, which decorates aging actin filaments and changes their rigidity, making them more flexible. Finally, at the limit of aging and new actin monomers the local stress makes a part of a filament detach [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. Another way to disassemble an actin network is by motor protein non-muscle myosin II. It binds to actin filaments and can contract the network [START_REF] Reymann | Actin network architecture can determine myosin motor activity[END_REF]. At a certain configuration, myosin II generated force might be too high, leading the actin filaments to buckle and break [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF], Vogel et al., 2013, Murrell and Gardel, 2012]. On the other hand, myosin II initiated actin network contractility can help in forming bundled actin structures and create cytoplasmic flows [START_REF] Murrell | Forcing cells into shape: The mechanics of actomyosin contractility[END_REF]. The dynamics of an actomyosin network are so complex, that it led to a creation of a new area in physics, called active gel theory [START_REF] Prost | Active gel physics[END_REF]. There the dynamics of the network are analysed as an active material, composed of molecules which use chemical energy to perform mechanical work [START_REF] Foster | From cytoskeletal assemblies to living materials[END_REF].

Nucleators, promoting factors and motor proteins lead to establishment of different cytoskeletal structures made of actin, and cell migration is an extreme example relying on at least five different structures -protrusive filopodia and lamellipodia, transverse arcs, stress fiber formation in focal adhesions and actin cortex (see Figure 1.3) [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. I am going to focus on the formation of cell protrusions, the initiating step for cell body movement in the next section.

Actin retrograde flow

The cytoskeleton of the cell is a dynamic structure and one of the most interesting phenomena arising out of this dynamic system are actin flows, generated inside cells [START_REF] Callan-Jones | Actin flows in cell migration: From locomotion and polarity to trajectories[END_REF]. These actin flows travel from the edge of the cell towards the center and are generally referred to as "actin retrograde flow". These retrograde flows can be described according to two reference points -relative to the cell or relative to the substrate [Cramer, 1997]. The flow arise from the simple fact of actin polymerization [van Goor et al., 2012, Babich et al., 2012]. As mentioned before, an actin filament can grow from both sides, but the polymerization is favoured at i) The actin cortex is anchored to the plasma membrane through ERM proteins and is contractile via myosin activity. ii) One category of contractile bundles, the stress fibers, are found spanning the cell body, usually oriented parallel to the direction of movement. They are attached to focal adhesions and involve a specific set of regulatory intracellular factors. iii) Transverse arcs are specific antiparallel actin filament formations found at the back of the lamellipodium. They are contractile through myosin activity. iv) The lamellipodium, hosts rapid, massive, and localized polymerization of branched actin networks. A: initiation of this dendritic network occurs via locally activated Arp2/3 complex binding to the side of an actin filament "primer" and by interaction with members of the WAVE family of proteins. Elongation of the network occurs by addition of the profilin/actin complex (black arrows) to the barbed ends of actin filament in close contact with the plasma membrane. B: Ena/VASP proteins, the formin FMNL2 and capping proteins control the elongation of the network by modulating the dynamics at filament barbed ends (right zoom inset). Ena/VASP and FMNL2 favor barbed end elongation whereas capping protein blocks it. v) The filopodia, are filled with parallel actin bundles elongated by the actin polymerases, Ena/VASP and formins, and tightly packed by the short bundler fascin. Taken from [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. the barbed end. So, depending on the concentration of free actin monomers around, the barbed end could be polymerizing and the pointed end shrinking [START_REF] Neuhaus | Treadmilling of actin[END_REF]. If an actin filament is polymerizing with its barbed end facing the membrane, it is pushed back and appears to be moving backwards in the reference of the cell [Wang, 1985]. However, if the actin filament is attached to the substrate, it can generate force and push the membrane it's facing [START_REF] Horwitz | Interaction of plasma membrane fibronectin receptor with talin -A transmembrane linkage[END_REF], Jurado et al., 2005]. This leads to a cell forming protrusions (see Figure 1.4) [START_REF] Pollard | Cellular Motility Driven by Assembly and Disassembly of Actin Filaments[END_REF]. In mesenchymal type of migration, where the cell is crawling on the substrate, two functionally distinct actin networks were described -a lamellipodium, assembled at the leading edge, and a lamella, 1-3 µm further from the edge [START_REF] Ponti | Two distinct actin networks drive the protrusion of migrating cells[END_REF]. A lamellipodium promotes random protrusion generation, while the lamella is where the cytoskeleton attaches to the substrate. These two networks are also distinct in their actin retrograde flow -very fast in lamellipodium and slow in lamella [START_REF] Alexandrova | Comparative dynamics of retrograde actin flow and focal adhesions: Formation of nascent adhesions triggers transition from fast to slow flow[END_REF]. Indeed, the formation of structures adhesive to the substrate at the lamella slows down the actin retrograde flow by converting the actin polymerization force to the traction force, letting the protrusion advance forward [START_REF] Alexandrova | Comparative dynamics of retrograde actin flow and focal adhesions: Formation of nascent adhesions triggers transition from fast to slow flow[END_REF], Ponti et al., 2004].

Additional retrograde pull on the actin cytoskeleton deeper in the cell body is generated by myosin II motor protein [START_REF] Henson | Two components of actin-based retrograde flow in sea urchin coelomocytes[END_REF], Lin et al., 1997], which can contract the network by attaching to adjacent actin filaments [Betapudi, 2014]. Myosin II concentration is increased at the end of the lamella, where anti-parallel actin bundles are formed and contractile force is generated [START_REF] Small | The comings and goings of actin: Coupling protrusion and retraction in cell motility[END_REF]. The formation of anti-parallel actin bundles is helped by the ruffling lamellipodium and protruding filopodia, when the ruffles and the filopodia fold back on the lamella, providing the source of actin filaments of different polarity [Small andResch, 2005,Nemethova et al., 2008]. The retrograde flow could also be involved in formation of actin stress fibers at the adhesion points [START_REF] Yamashiro | A new link between the retrograde actin flow and focal adhesions[END_REF].

The flows generated by actomyosin network might affect the process of cell polarity establishment as well. A recent study of significant number of migrating cell types has shown that the faster the cell was, the more directional and persistent was its trajectory [START_REF] Maiuri | The first World Cell Race[END_REF]. Cells appeared to be faster if the actin retrograde flow was higher, which lead to a proposition of a universal law relating actin retrograde flow and cell persistence [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF]. Molecules, directly or indirectly interacting with actin, could be advected and transported together with the retrograde flow. This could affect the concentrations of polarity factors at the other side of the leading edge and create their concentration gradient [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF].

Retrograde actin flows is a characteristic, which is conserved in all types of cell migration, from adhesive crawling to topographical propelling [START_REF] Reversat | Cellular locomotion using environmental topography[END_REF]. Though it might span different length scales. In mesenchymal cell migration it only covers the protruding part of the cell, while it encompasses the full cell body, when it moves in an amoeboid mode [START_REF] Renkawitz | Adaptive force transmission in amoeboid cell migration[END_REF]. Curiously, it was proven that a specific type of cell is not restricted to one type of movement, but can switch between the different modes, depending on its surroundings. In other words, slow mesenchymal type cells can switch to fast amoeboid-like migration [START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF],Renkawitz et al., 2009]. The switch can also be initiated by the change in the actomyosin contractility [START_REF] Ruprecht | Cortical contractility triggers a stochastic switch to fast amoeboid cell motility[END_REF]. Even epithelial cells can become migratory, if the contractility of actomyosin network is relaxed, releasing actin from actin bundles and freeing it for polymerization [START_REF] Lomakin | Competition for actin between two distinct F-actin networks defines a bistable switch for cell polarization[END_REF].

Cells can couple retrograde actin flows to transmit force and initiate movement by specific adhesion receptors, unspecific friction or by shape change and all these mechanisms can alternate from one to another [Reversat et al., 2020,Callan-Jones andVoituriez, 2016], but I am going to focus on adhesive cell migration and the players involved.

Adhesion

Cells can adhere to their environment and to one another using specialised transmembrane receptor proteins. There are four classes of them -integrins, cadherins, selectins and immunoglobulins [START_REF] Janiszewska | Cell adhesion in cancer: Beyond the migration of single cells[END_REF]. Each class is specialised for specific functions ranging from adhesion to the extracellular matrix (ECM) to interacting with cells of the immune system [START_REF] Janiszewska | Cell adhesion in cancer: Beyond the migration of single cells[END_REF]. I will focus here on a class that is involved in cellular adhesion to substrates -integrins. Integrins are heterodimers, with large multidomain extracellular portions and small cytoplasmic tails, consisting of α and βchains, of which there are 18 α-chains and 8 β-chains known to this day that can combine to form 24 different integrins [START_REF] Gahmberg | Regulation of cell adhesion: a collaborative effort of integrins, their ligands, cytoplasmic actors, and phosphorylation[END_REF]. This variety of integrins might be useful for cells to interact with multiple different substrates, but so far, αvβ3 and α5β1 pairs and their adhesion to fibronectin are the most researched [Huveneers andDanen, 2009, White et al., 2007]. These two integrin heterodimers are known to have distinct localization in the cell, with αvβ3 found at the leading edge of migrating cells and α5β1 in the cell body [START_REF] Huveneers | Adhesion signaling -Crosstalk between integrins, Src and Rho[END_REF].

Figure 1.6: Cartoon depicting the serial connection between the extracellular matrix, integrins, mechanosensitive adaptor proteins, and actin. As myosin pulls on actin filaments, force is transmitted to the different elements, leading to conformational changes in adaptor proteins and affecting unbinding events. Taken from [START_REF] Elosegui-Artola | Control of Mechanotransduction by Molecular Clutch Dynamics[END_REF].

Cells can translate the force of actin retrograde flow, generated by actin polymerization at the leading edge, to traction forces through their integrin adhesions (see Figure 1.6) [START_REF] Elosegui-Artola | Control of Mechanotransduction by Molecular Clutch Dynamics[END_REF], Alexandrova et al., 2008]. They form a "molecular clutch", which leads to a cell being able to protrude and move forward [START_REF] Elosegui-Artola | Control of Mechanotransduction by Molecular Clutch Dynamics[END_REF]. Adhesions first form at the leading edge, a few micrometres away from the cell boundary and mature as the cell moves over them in a sequence from nascent adhesions through focal complexes, focal adhesions, fibrillar adhesions and disassemble once they reach the rear of the cell [START_REF] Vicente-Manzanares | Adhesion dynamics at a glance[END_REF]. Nascent adhesions are small punctate structures [START_REF] Choi | Actin and α-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF]. They form when integrins attach to the substrate and get activated [START_REF] Sun | Nascent adhesions: From fluctuations to a hierarchical organization[END_REF]. Integrins can be activated either by "outside-in" activation by the substrate ligands or by "inside-out" activation through intracellular signaling [START_REF] Gahmberg | Regulation of cell adhesion: a collaborative effort of integrins, their ligands, cytoplasmic actors, and phosphorylation[END_REF]. Then follows the attachment of talin and kindlin, integrins start to cluster, and SFKs ("Src family of tyrosine kinases") are recruited. SFKs induce more actin polymerization around the adhesion through formin activation [START_REF] Iskratsch | Appreciating force and shape-the rise of mechanotransduction in cell biology[END_REF]. Several other proteins, like FAK ("Focal adhesion kinase"), paxillin and vinculin, are recruited [START_REF] Vicente-Manzanares | Adhesion dynamics at a glance[END_REF], which leads to Rac1 activation and even more actin polymerization [START_REF] Huveneers | Adhesion signaling -Crosstalk between integrins, Src and Rho[END_REF]. Nascent adhesions are short lived (∼60 s) and either disassemble or start to mature into focal complexes once they reach the boundary between the lamellipodium and the lamella (see Figure 1.7) [START_REF] Choi | Actin and α-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF]. Focal complexes are twice bigger than nascent adhesions and keep recruiting more proteins [START_REF] Choi | Actin and α-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF]. Once myosin II is recruited, it starts contracting actin bundles to form stress fibers [START_REF] Tojkander | Actin stress fibers -Assembly, dynamics and biological roles[END_REF] and generates force [START_REF] Choi | Actin and α-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF] (see Figure 1.7). This leads to a change in talin conformation, revealing cryptic adhesion sites for more vinculin molecules to bind -the focal adhesion gets reinforced [START_REF] Rio | Stretching Single Talin Rod[END_REF]. Fibrillar adhesions are the endpoint of maturation and are long lived (∼2h) [START_REF] Vicente-Manzanares | Adhesion dynamics at a glance[END_REF]. They disassemble once they reach the cell rear in a microtubule dependent process [START_REF] Ezratty | Microtubule-induced focal adhesion disassembly is mediated by dynamin and focal adhesion kinase[END_REF], Kaverina et al., 1999].

Figure 1.7: Schematic of adhesion assembly, turnover and maturation. Taken from [START_REF] Choi | Actin and α-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF].

Integrins are the sites for adhesion, but also for signal transduction [START_REF] Elosegui-Artola | Control of Mechanotransduction by Molecular Clutch Dynamics[END_REF]. Multiple integrin complexes binding to the surrounding area let cells explore the environment and adapt [START_REF] Humphries | Signal transduction via integrin adhesion complexes[END_REF]. Super-resolution imaging of a focal adhesion revealed a structure of three layers -"integrin signalling", "force transduction" and "actin-regulatory" [Burridge, 2017,Kanchanawong et al., 2010]. Recent systems biology studies have identified 156 components that interact with integrin adhesive complexes and form the so called "adhesome" of the cell [START_REF] Zaidel-Bar | Functional atlas of the integrin adhesome[END_REF], later enlarged to 2,412 proteins, which are now selected into a "consensus ad-hesome" of 60 proteins, thought to represent a core cell adhesion machinery [START_REF] Horton | Definition of a consensus integrin adhesome and its dynamics during adhesion complex assembly and disassembly[END_REF]. From those, talin and vinculin are specifically involved in mechanotransduction, a process that lets the cell react to the physical properties (e.g. stiffness) of the surroundings and pass the signal deep inside the cell [START_REF] Mathieu | Intracellular mechanics: connecting rheology and mechanotransduction[END_REF]. Integrin adhesions can also serve as a hub for cytoskeleton remodelling [START_REF] Parsons | Cell adhesion: Integrating cytoskeletal dynamics and cellular tension[END_REF] and an end-point for vesicle secretion, which is largely regulated by small GTPases [START_REF] Eisler | A Rho signaling network links microtubules to PKD controlled carrier transport to focal adhesions[END_REF]. [START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF].

Rho GTPases

Rho GTPases is a family of small (∼21 kDa) G proteins and it belongs to a Ras superfamily of proteins [START_REF] Wennerberg | The Ras superfamily at a glance[END_REF]. Rho GTPases are molecular switches, shifting between their "on" (Rho-GTP) and "off" (Rho-GDP) conformations and relaying signals in multiple pathways [Jaffe andHall, 2005,Etienne-Manneville andHall, 2002]. First described as remodellers of actin cytoskeleton and amplification hubs to convert extracellular signals from surface receptors into cellular effects [START_REF] Raftopoulou | Cell migration: Rho GTPases lead the way[END_REF], now Rho GTPases are also known to play an important role in the endomembrane system [Phuyal andFarhan, 2019, Ridley, 2006].

There are 20 Rho GTPases in the human family, of which three Rho GTPases -Rac1, Cdc42 and RhoA -are considered canonical and are studied the most [START_REF] Vega | SnapShot: Rho Family GTPases[END_REF]. The whole family evolved from an ancestral Rac protein and are now distributed into 8 subfamilies [START_REF] Boureux | Evolution of the Rho family of Ras-like GTPases in eukaryotes[END_REF]. Rho GTPases are slow to hydrolyse and exchange GDP with GTP, thus, they are helped and regulated by multiple GEFs ("Guanine nucleotide exchange factors") and GAPs ("GTPase-activating proteins") [Rossman et al., 2005, Cherfils andZeghouf, 2013]. Interestingly, only 5% of Rho GTPases are active in the cell at a time [Pertz, 2010a, Benard et al., 1999, Ren et al., 1999]. Developments in the Rho GTPase biosensor field let us describe Rho GTPase activity patterns and their modular nature [Pertz, 2010a, Pertz et al., 2006]. A recent systems biology study explored the interactions of 141 known GEFs and GAPs with the 20 described human Rho GTPases and uncovered several tendencies of Rho signaling patterns. Most of the GEFs and GAPs are autoinhibited, which allows for local regulation, and they forme complexes in specific locations in the cell, permitting the recruitment of different Rho GTPases and their effectors locally [START_REF] Müller | Systems analysis of RhoGEF and RhoGAP regulatory proteins reveals spatially organized RAC1 signalling from integrin adhesions[END_REF]. In addition to that, it was shown that RhoGAPs were more promiscuous (could interact with multiple targets instead of being specific to one) than RhoGEFs, which makes it easier to confine Rho GTPase activity to specific spots in the cell, as whenever a Rho GTPase would diffuse away, it would be inactivated by a GAP [START_REF] Müller | Systems analysis of RhoGEF and RhoGAP regulatory proteins reveals spatially organized RAC1 signalling from integrin adhesions[END_REF]. Rho GTPases act at the membrane and on top of the GEF/GAP regulation, they are controlled by another group of proteins -RhoGDIs ("Guanosine nucleotide dissociation inhibitors") [START_REF] Cherfils | Regulation of small GTPases by GEFs, GAPs, and GDIs[END_REF], Garcia-Mata et al., 2011, Dovas and Couchman, 2005]. It extracts a RhoGTPase from the membrane, sequestering it to the cytosol and making it inactive. It has recently been shown that RhoGDIs can extract not only inactive RhoGTPases, but active ones as well, rendering them active players in Rho GTPases activity pattern formation [START_REF] Golding | Extraction of active rhoGTPases by rhoGDI regulates spatiotemporal patterning of rhogtpases[END_REF]. This is a known description of Rho GTPase regulation, but at least 10 of the known mammalian GTPases are not regulated in this way, and instead of hydrolysing GTP, they are able to quickly exchange GDP with GTP, making them constitutively active. These atypical Rho GTPases are called "fast-cycling" Rho GTPases and instead of being regulated by GEFs and GAPs, they might be regulated transcriptionally [Aspenström, 2018,Tao et al., 2001]. Furthermore, Rho GTPases can also be post-translationally modified by phosphorylation, ubiquitylation and sumoylation, changing their interaction with their regulators and effectors (see Figure 1.9). Rho GTPases can also be differentially lipidated, which would alter their interaction with membranes [START_REF] Hodge | Regulating Rho GTPases and their regulators[END_REF].

Figure 1.9: Overview of Rho GTPase regulation. The route from Rho GTPase protein expression to effector protein activation is tightly regulated. GEFs, GAPs and GDIs constitute the classic regulatory proteins that regulate the GTPase cycle. GEFs activate Rho GTPases by catalysing the exchange of GDP for GTP, whereas GAPs greatly stimulate the intrinsic GTPase activity of Rho GTPases and inactivate them. GDIs extract prenylated Rho GTPases from the membrane by binding the isoprenoid moiety and sequester them away in the cytoplasmic compartment. Unconventional mechanisms of regulating Rho GTPases are becoming more apparent. (a) Rho GTPase expression can be controlled at the transcriptional level by epigenetics and at the translational level by the action of microRNAs (miRNAs). (b) Post-translational covalent modifications of Rho GTPases, including phosphorylation and sumoylation, can result in the activation or inactivation of Rho GTPases, depending on the cellular context. (c) Protein levels of Rho GTPases can be acutely regulated by the ubiquitin-proteasome system. (d) The combination of classical and unconventional regulatory mechanisms ensures the appropriate spatiotemporal activation of the Rho GTPases during various cellular processes, including regulation of cytoskeletal dynamics, cell polarity and survival. Taken from [START_REF] Hodge | Regulating Rho GTPases and their regulators[END_REF].

The classical view of the mode of action of the three canonical Rho GTPases (Rac1, Cdc42 and RhoA) was that they were regulating actin remodelling in the cell and they were each responsible for one type of structure -Rac1 for formation of lamellipodia [START_REF] Michiels | Regulated membrane localization of Tiam1, mediated by the NH2-terminal pleckstrin homology domain, is required for Rac-dependent membrane ruffling and c-Jun NH2-terminal kinase activation[END_REF], Cdc42 for initiation of filopodia [START_REF] Nobes | Rho, Rac, and Cdc42 GT-Pases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamellipodia, and filopodia[END_REF] and RhoA for stress fibers [START_REF] Burridge | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF]. However, once it was possible to spatiotemporally map Rho GTPase activation [START_REF] Fritz | The dynamics of spatiotemporal Rho GTPase signaling: formation of signaling patterns[END_REF],Pertz, 2010a,Machacek et al., 2009,Pertz et al., 2006], it became clear that the "Rho GTPasecentric" view, where one Rho GTPase is sequentially regulated by GEFs, GAPs and GDIs and is responsible for singular functions, is too simplified. Instead, Rho GTPases' signalling dynamics occur on micrometer length scales and subminute timescales [Pertz, 2010a]. Rho GTPases activate and inhibit one another and, thanks to their spatial distribution, can actuate different effectors depending on their localisation [START_REF] Byrne | Bistability in the Rac1, PAK, and RhoA Signaling Network Drives Actin Cytoskeleton Dynamics and Cell Motility Switches[END_REF], Guilluy et al., 2011] and can initiate different cellular response depending on the shape of their gradient [de Beco et al., 2018]. An interesting example is RhoA, which was initially though to be found in the body and the back of a migrating cell, and thought to be excluded from the leading edge [START_REF] Raftopoulou | Cell migration: Rho GTPases lead the way[END_REF]. However, recent studies have found that RhoA is active in the leading edge as well [START_REF] Martin | Spatio-temporal co-ordination of RhoA, Rac1 and Cdc42 activation during prototypical edge protrusion and retraction dynamics[END_REF], Machacek et al., 2009, Pertz et al., 2006], but it's function is completely opposite to the one it exerces at the back of the cell [START_REF] Bolado-Carrancio | Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration[END_REF]. In the back, RhoA activates a kinase ROCK, which phosphorylates the myosin-II light chain (MLC) and promotes cell contractility (helping to retract the cell rear), while in the front, at the leading edge of the cell, its effector is mDia, which activates Rac1 and actin polymerization, and drive cell protrusion [START_REF] Bolado-Carrancio | Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration[END_REF].

Cdc42

Cdc42 ("Cell Division Cycle 42") is a protein that belongs to a Rho family of small GTPases. Two isoforms are known in humans -Cdc42u ("ubiquitous") and Cdc42b ("brain"), that both have a molecular mass of ∼21 kDa. The main difference between the two isoforms is their lipidation at the C-terminus CAAX box. Cdc42u is prenylated (geranylgeranylated), and Cdc42b is palmitoylated in addition to that [START_REF] Wirth | Dual lipidation of the brain-specific Cdc42 isoform regulates its functional properties[END_REF]. Both protein modifications are important for Cdc42 affinity to membranes, as a lipid tail allows protein's attachment to the membrane. Cdc42u is a ubiquitous isoform described in multiple cellular processes, while the functional studies of Cdc42b isoform are just starting to uncover its specific roles and importance of dual lipidation [START_REF] Endo | The two splice variant forms of Cdc42 exert distinct and essential functions in neurogenesis[END_REF], Bekhouche et al., 2020].

Cdc42 cycles between two conformations: active (with GTP bound) and inactive (with GDP bound). Its usual place of action is at the membrane. Cdc42's function can be activated by GEFs, that accelerate GDP exchange with GTP; inhibited by GAPs, that boost protein's GTPase activity; and regulated by GDI proteins, that can extract Cdc42 from membranes and prevent their reinsertion [START_REF] Hodgson | FRET binding antenna reports spatiotemporal dynamics of GDI-Cdc42 GTPase interactions[END_REF]. So far, there are 22 GEFs, 8 GAPs and 3 GDI proteins known to be linked to Cdc42 in vertebrates [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF].

Recent development of FRET biosensors for visualization of active RhoGTPases has lead to a deeper understanding of RhoGTPase dynamics. We have learned that active Cdc42 forms a sharp, fast-decaying gradient at the leading edge of migrating adherent cells [Nalbant, 2004, Machacek et al., 2009, Yamao et al., 2015, Yang et al., 2015a, de Beco et al., 2018]. One of the mechanisms leading to this pattern could be differential GEF/GAP concentrations along the perimeter of the cell. Cdc42 gradient could be shaped by a decaying distribution of GEFs, peaking at the leading edge, and a uniform GAP activity [de Beco et al., 2018,Brown andKholodenko, 1999]. Activated Cdc42-GTP form is known to cluster and become less mobile, while a RhoGDI-bound Cdc42-GDP remains dynamic and diffuses 30 times faster, as experimentally measured in human colon adenocarcinoma (Ls174T:W4) cells [START_REF] Bruurs | A Two-Tiered Mechanism Enables Localized Cdc42 Signaling during Enterocyte Polarization[END_REF]. This might be another way to control Cdc42 activity in the cell. Different mobility of active and inactive forms can lead to polarized distribution and symmetry breaking, as described by Turing-type reaction-diffusion mechanism [START_REF] Turing | The chemical basis of morphogenesis[END_REF]. This mechanism was already used to mathematically describe Cdc42 polarization in yeast [Goryachev andPokhilko, 2008, Wu andLew, 2013].

First described in yeast as a protein involved in budding and establishment of cell polarity [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF], Adams et al., 1990, Johnson and Pringle, 1990], Cdc42 and its homologs are now described as a signalling hub, or a "center of polarity", with many features conserved in all eukaryotic cells, from yeast to mammals [Etienne- Manneville, 2004]. It functions in processes ranging from cell migration to vesicle trafficking, and is known to be related to at least 45 different effector proteins encoded in human genome [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF]. How this multiplex signaling is achieved is not yet clear.

Cdc42 involvement in polarity establishment in yeast (budding in budding yeast S.cerevisiae and division in fission yeast S.pombe) is highly researched, described and mathematically modelled [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF], Miller et al., 2020, Chiou et al., 2017, Wedlich-Soldner et al., 2003, Khalili et al., 2020]. Cdc42 is initially activated by its GEF Bud3 [START_REF] Miller | Regulation of Cdc42 for polarized growth in budding yeast[END_REF], which gives way to a GEF Cdc24 later in the cell cycle. Active Cdc42 starts to cluster with a help of a positive feedback loop, as an effector Cla4 (PAK) and adapter molecule Bem1 get recruited by Cdc24. The trio Cla4-Bem1-Cdc24 acts as an effector-scaffold-GEF hub, to increase the local concentration of active Cdc42 [START_REF] Bendezú | Spontaneous Cdc42 Polarization Independent of GDI-Mediated Extraction and Actin-Based Trafficking[END_REF]. As mentioned before, active Cdc42 is less mobile than inactive Cdc42 bound to a GDI Rdi1, which increases its spatial segregation [START_REF] Hoffman | Structure of the Rho family GTP-binding protein Cdc42 in complex with the multifunctional regulator RhoGDI[END_REF] (see Figure 1.10). In addition to local clustering, Cdc42 is promoting formation of actin tracks towards the bud to increase vesicle trafficking [START_REF] Wedlich-Soldner | Spontaneous cell polarization through actomyosin-based delivery of the Cdc42 GTPase[END_REF], Wedlich-Soldner et al., 2004], and promoting polarized secretion by interacting with the exocyst component Sec3 [START_REF] Zhang | Membrane association and functional regulation of Sec3 by phospholipids and Cdc42[END_REF]. All in all, local polarity at the membrane is coupled with polarized cargo delivery to establish cell polarity [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF], Miller et al., 2020].

Figure 1.10: The Cdc42 GTPase and its regulators in budding yeast. Cdc42 activity is regulated by at least three types of regulators: the GEFs, Cdc24 and Bud3; the GAPs, Rga1, Rga2, Bem2, and Bem3; and the GDI Rdi1. These regulators are likely to mediate the regulation of Cdc42 in response to internal and external signals. Cdc42 regulates the organization of the actin and septin cytoskeletons and polarized secretion via its downstream effectors including PAKs. Taken from [START_REF] Miller | Regulation of Cdc42 for polarized growth in budding yeast[END_REF].

Another facet of Cdc42 signaling was uncovered while studying the embryos of C.elegans worms, where it is involved in the establishment of Anterior-Posterior (A-P) polarity axis before the first embryonic cleavage. There Cdc42 interacts with the Par complex, consisting from PAR-3, PAR-6 and PKC-3 (known as PKCζin vertebrates and aPKC in Drosophila). Cdc42 stabilizes the complex at the actomyosin cortex by binding to PAR-6 and helping to recruit the kinase PKC-3. PKC-3 then starts phosphorylating its targets, including posterior PAR proteins, which keeps them at the posterior side [START_REF] Rodriguez | aPKC Cycles between Functionally Distinct PAR Protein Assemblies to Drive Cell Polarity[END_REF]. As the Cdc42-PAR-6-PKC-3 complex clusters, it is displaced towards the anterior side of the embryo by actomyosin cortical flows [START_REF] Goehring | Polarization of PAR proteins by advective triggering of a pattern-forming system[END_REF]. This signaling pathway is also conserved in the process of polarization of epithelial cells [Rodriguez-Boulan andMacara, 2014, St Johnston andAhringer, 2010]. There, active Cdc42 accumulates at the junction-free apical side of the membrane [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF], Anderson et al., 2008]. This is a result of a Cdc42 inhibition by a GAP PAC-1 localized at the junctions. Another polarity complex called Crumbs (Crumbs-PALS1-PATJ) is found in epithelial cells. It interacts with the Par complex in a dynamic fashion and is involved in regulating junction maturation. Cdc42 might be involved in changing the binding affinity and how these complexes interact [START_REF] Pichaud | Regulation of Cdc42 and its effectors in epithelial morphogenesis[END_REF]. Therefore, Cdc42 is involved not only in establishment of polarity axis, but also in junction maturation in epithelial cells.

Another important area of research related to Cdc42 functions is cell migration. For a cell to move in one specific direction, it needs to polarize and break symmetry. Therefore, the processes of polarity establishment in budding yeast, roundworm embryos and fruit fly or mammalian epithelia are of great interest and relevance to understand the process of cell migration. In all of these cases Cdc42 forms activity patterns. Cell migration is normally triggered by external cues, and the signal is detected by three different inlets -GPCRs ("G-protein coupled receptors"), RTKs ("Receptor Tyrosine Kinases") and integrins [START_REF] Maldonado | Targeting Rac and Cdc42 GEFs in Metastatic Cancer[END_REF],Warner et al., 2019a,Etienne-Manneville, 2004]. In the first two cases the cue would be soluble, while the cell would detect substrate-bound cues in the latter case. From all of these receptors the signal is transferred to Cdc42 via different GEFs. In addition to that, Cdc42 can generate random internal activity bursts without any external cues [Yang et al., 2015a]. One of the first Cdc42 functional descriptions in migrating 3T3 fibroblasts was achieved by injecting cells with active Cdc42. Within 5 min cells started forming filopodia -long, finger-like actin protrusions [START_REF] Nobes | Rho, Rac, and Cdc42 GT-Pases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamellipodia, and filopodia[END_REF]. Cdc42 would signal the formation of filopodia through its effectors -formin families mDia and FMNL, and TOCA-1-N-WASP complex [START_REF] Kühn | Formins as effector proteins of rho GTPases[END_REF], Kühn et al., 2015, Watson et al., 2017, Bu et al., 2009]. Cdc42 can also induce branched actin formation through its already mentioned direct effector N-WASP (if PIP 2 is present [START_REF] Higgs | Activation by Cdc42 and PIP2 of Wiskott-Aldrich Syndrome protein (WASp) stimulates actin nucleation by Arp2/3 complex[END_REF]) signalling to an actin nucleator Arp2/3 complex [Ridley, 2006, Goley andWelch, 2006]. It was later shown that the generation of cellular protrusions -filopodia and lamellipodia -is a more complex process, and all three major RhoGTPases (Cdc42, Rac1 and RhoA) are a part of a dynamic network, which is hard to dissect and no one RhoGTPase is responsible for one specific type of protrusion, though, they provide different input in regulating cytoskeletal remodelling and adhesion [START_REF] Kühn | Formins as effector proteins of rho GTPases[END_REF],Pertz, 2010a, Ridley, 2006, Machacek et al., 2009, Martin et al., 2016, de Beco et al., 2018]. Different RhoGTPases can be affected by the same activators and can pass the signal towards same effectors [START_REF] Nouri | New model for the interaction of IQGAP1 with CDC42 and RAC1[END_REF]. On the other hand, there is strong evidence that Cdc42 signals upstream of Rac1, which enhances the signal of lamellipodial protrusion formation [O' Neill et al., 2016, Mitsushima et al., 2009, Nishimura et al., 2005, Etienne-Manneville and Hall, 2001].

Cdc42 acts not only in actin remodelling for generating protrusions, but is also involved in vesicle formation both at the leading edge and at the membranous compartments of the cell. It can act in plasma membrane compensation by regulating the amount of exocytosed and endocytosed membrane [START_REF] Harris | Cdc42 and Vesicle Trafficking in Polarized Cells[END_REF]]. On the one hand, Cdc42 promotes exocytosis, by interacting with the exocyst complex and facilitating vesicle fusion with the membrane [START_REF] Rossi | Exocyst structural changes associated with activation of tethering downstream of Rho/Cdc42 GTPases[END_REF], Pichaud et al., 2019, Mohammadi and Isberg, 2013]. On the other hand, Cdc42 signals through N-WASp to Arp2/3 to form branched actin structures that seal the exocytic pores by turning them into reinforced endocytic vesicles [START_REF] Sokac | Cdc42dependent actin polymerization during compensatory endocytosis in Xenopus eggs[END_REF],Garrett et al., 2000]. It was also described to directly interact with a GAP GRAF1 and facilitate rapid cell surface turnover and recycling at the leading edge [START_REF] Francis | Endocytic membrane turnover at the leading edge is driven by a transient interaction between Cdc42 and GRAF1[END_REF]. In addition to that, Cdc42 can also act at the internal membranes of the cell and regulate polarized trafficking in this way. The polarized Cdc42-dependent traffic is well described in yeast (see beginning of the section). A similar, though more complex, polarized trafficking regulation is being uncovered in higher eukaryotes as well. Several pools of Cdc42 were discovered with the main concentration being in the Golgi complex, where Cdc42 is thought to control Golgi tubulation process, which enhances the anterograde cargo trafficking [START_REF] Park | Coordinated regulation of bidirectional COPI transport at the Golgi by CDC42[END_REF]. Cdc42 was also described to interfere with the retrograde vesicle transport by binding to immature COPI vesicles through γ-subunit of COPI, and interfering with their association with the motor protein dynein [START_REF] Hehnly | Cdc42 regulates microtubule-dependent golgi positioning[END_REF], Harris and Tepass, 2010, Chen et al., 2005]. Most of the vesicle traffic is guided by microtubules in eukaryotic cells, and Cdc42 plays one more role in polarizing the trafficking system. It is proved to anchor the microtubule "+" ends at the plasma membrane and reorient the MTOCs (microtubule organizing centers -centrosome and Golgi) and the whole microtubule array towards the leading edge of the cell [Etienne- Manneville, 2004, Cau andHall, 2005]. The two signalling pathways of action include: recruitment of IQGAP1, which interacts with microtubule "+"-endassociated protein Clip-170 [START_REF] Fukata | Rac1 and Cdc42 capture microtubules through IQGAP1 and CLIP-170[END_REF],Watanabe et al., 2004], and activation of Par6-PKCζcomplex, which then inhibits GSK-3βkinase, and with that promotes the microtubule "+"-end association of APC and Dlg1 proteins, which in turn capture microtubules and pull on them with the help of a motor protein dynein [START_REF] Cau | Cdc42 controls the polarity of the actin and microtubule cytoskeletons through two distinct signal transduction pathways[END_REF],Etienne-Manneville et al., 2005,Etienne-Manneville and Hall, 2003,Palazzo et al., 2001, Etienne-Manneville and Hall, 2001]. It also enhances the traffic of Cdc42 itself towards the leading edge [START_REF] Shim | Rab35 Mediates Transport of Cdc42 and Rac1 to the Plasma Membrane during Phagocytosis[END_REF].

To sum up, Cdc42 functions in multiple signalling pathways -from actin remod-elling to endo/exocytosis compensation, to favoring anterograde trafficking of endomembranes, to microtubule capture -all leading to establishment of cell polarity.

Cellular trafficking

Cellular trafficking involves the movement of membranous vesicles carrying cargo in eukaryotic cells and maintains exchange of materials between organelles. Cells sort their newly synthesized proteins, secrete molecules, recycle receptors and engulf particles from outside using double-membrane vesicles of distinct identity [START_REF] Yarwood | Membrane trafficking in health and disease[END_REF]. While maintaining homeostasis of the cell, membrane trafficking plays a significant role in establishing cell polarity and migration. In this section, I will introduce the membrane trafficking machinery and then focus on polarized secretion and vesicle movement towards the plasma membrane of the cell. Starting with the Golgi complex as a vesicle sorting hub, I will introduce the important players of vesicular secretion from the microtubules and motor proteins that move the vesicles, to Rab GTPases that form membrane identity. Finally, I will specifically focus on Rab6 GTPase -an important regulator of polarized secretion.

Membrane trafficking system

Figure 1.12: Overview of intracellular trafficking pathways. Once internalized from the plasma membrane (PM), membrane-bound vesicles that carry receptors from the cell surface fuse with the early endosomes (EEs, light orange structure in the middle). The EE serves as a sorting station from which either tubulo-vesicular carriers deliver cargo to the endolysosomal system for degradation, or cargoes are recycled directly (fast recycling) or indirectly (slow recycling) to the plasma membrane via the endocytic recycling compartment (ERC). Cargoes leave the Golgi complex by anterograde transport and secretion, and can also be sent back towards the Golgi complex via retrograde transport. Adapted from [START_REF] Naslavsky | The enigmatic endosome -Sorting the ins and outs of endocytic trafficking[END_REF].

Eukaryotic cells have developed an intracellular membrane system in order to segregate different cellular processes in separate compartments and control reactant concentrations [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. A dynamic and complex membrane trafficking machinery allows the communication and exchange between these membrane enveloped organelles [START_REF] Dacks | Evolution of the eukaryotic membrane-trafficking system: Origins, tempo and mode[END_REF] and regulates the flows of proteins and lipids, otherwise called "cargo", inside cells [START_REF] Naslavsky | The enigmatic endosome -Sorting the ins and outs of endocytic trafficking[END_REF]. Cargo can enter the intracellular membrane system in two ways -by endocytosis from the cell surface or via a biosynthetic pathway [START_REF] Simonetti | Actin-dependent endosomal receptor recycling[END_REF]. In the first case, cargo enters through inward folding of plasma membrane, as it forms vesicles, when extracellular receptors and adhesion molecules are internalized [Simonetti andCullen, 2019, Wang et al., 2018]. In the second case, newly translated proteins are guided to the Endoplasmic Reticulum (ER) and enter its lumen or its membrane. They become cargo once they fission from ER inside vesicles [START_REF] Herrmann | Intracellular Parcel Service: Current Issues in Intracellular Membrane Trafficking[END_REF].

Vesicles entering by endocytosis (1.12, "Internalization") first fuse with the early endosome (EE), which serves as a sorting hub in the endocytic pathway [Naslavsky andCaplan, 2018,Huotari andHelenius, 2011]. From there the cargo can have four different fates: (i) it can be sent towards the lysosomes and get degraded (1.12, "Degradation"), (ii) sent straight back to the plasma membrane (1.12, "Fast recycling"), (iii) travel to the plasma membrane through the recycling endosome (RE) (also called ERC -"endocytic recycling compartment") (1.12, "Slow recycling") [Goldenring, 2015] or (iV) to the Golgi complex (1.12, "Retrograde transport") [START_REF] Naslavsky | The enigmatic endosome -Sorting the ins and outs of endocytic trafficking[END_REF], O'Sullivan and Lindsay, 2020,Hsu et al., 2012]. Cargo entering from the ER is first sent to the Golgi complex, from where it can be secreted to the extracellular environement (1.12, "Secretion") or move towards the EE (1.12, "Anterograde transport") [Naslavsky andCaplan, 2018, Herrmann andSpang, 2015].

Figure 1.13: General principles of membrane trafficking. Transport of proteins between compartments is initiated by (1) selection of cargo and its segregation from resident proteins of the donor compartment by the action of 'adaptors'; (2) encapsulation of cargo-bound adaptors within a protein scaffold or 'coat', which drives membrane deformation and ultimately scission to form a transport vesicle, or in some cases a tubular transport intermediate; [START_REF]1 Persistence time phase diagram[END_REF] uncoating and ( 4) movement of the vesicle to the target compartment; (5) membrane tethering, in which the vesicle is drawn towards the target membrane by extended proteins/protein complexes that work in conjunction with Rab GTPases; and (6) docking and membrane fusion, in which the vesicle is first tightly attached to the target membrane, followed by merging of the lipid bilayers, both processes being mediated by SNARE protein complexes and supported by accessory factors. Taken from [START_REF] Yarwood | Membrane trafficking in health and disease[END_REF].

When travelling between different membranous compartments, cargoes need to go through an established sequence of steps [START_REF] Yarwood | Membrane trafficking in health and disease[END_REF]. First, vesicles bud from the donor compartment, with the help of coat and adaptor proteins (1.13, "Budding") [START_REF] Faini | Vesicle coats: Structure, function, and general principles of assembly[END_REF]. Once a vesicle fissions off the donor membrane (1.13, "Scission") [START_REF] Mcmahon | Membrane curvature at a glance[END_REF], it starts to uncoat (1.13, "Uncoating"). Then, the vesicle is picked up by a motor protein and transported towards another membranous compartment following cytoskeletal tracks (1.13, "Transport") [Goldenring, 2015,Anitei andHoflack, 2012]. Once close to the acceptor compartment, vesicles are tethered through long protruding protein tethers on the acceptor membrane (1.13, "Targeting and tethering") [Spang, 2016] and fuse with the acceptor compartment with the help of SNARE proteins (1.13, "Docking and fusion") [START_REF] Han | The multifaceted role of SNARE proteins in membrane fusion[END_REF]. It has been proposed that the components involved are specific to each compartment, which ensures transport fidelity [START_REF] Yarwood | Membrane trafficking in health and disease[END_REF]. Cargoes can be sorted by specific proteins, like the retromer complex [Burd andCullen, 2014, Bonifacino andRojas, 2006] or just by localized actin polymerization, restricting protein lateral movement [START_REF] Simonetti | Actin-dependent endosomal receptor recycling[END_REF]. Vesicle membranes can change their identities by modifying their phospholipid composition [Waugh, 2019, von Blume and Hausser, 2019, Johansen et al., 2012], which would then lead to recruitment of different adaptor and regulator proteins, like Rabs [Stenmark, 2009], that by itself lead to binding to a different set of motor and tethering proteins [Hirokawa et al., 2009, Mallik andGross, 2004] -a process called vesicle "maturation". The complexity of intracellular membrane trafficking is just getting revealed and the amount of different trafficking pathways that exist is still not clear, but the concerted action of molecular players is able to generate polarized and directional flows of both lipids and proteins inside the cell. In the next section I will get into more details of the secretion pathways that go through the Golgi complex and discuss its importance as an organelle.

The Golgi complex and secretion

The Golgi complex serves as a sorting hub in eukaryotic cells [START_REF] Boncompain | Transport and sorting in the Golgi complex: multiple mechanisms sort diverse cargo[END_REF]. Its structure varies from organism to organism, but the features of a stacked membranous organelle are evolutionary conserved [START_REF] Klute | Evolution and diversity of the Golgi[END_REF]. Proteins synthesized in the ER enter at the Golgi's cis side, pass through the medial parts and exit at the trans side [START_REF] Glick | Models for Golgi traffic: A critical assessment[END_REF]. The proteins are sequentially modified on the way by glycosylation or proteolitic cleavage by the Golgi resident proteins, which is needed for their sorting and biological function [START_REF] Papanikou | Golgi compartmentation and identity[END_REF]. Once they reach the trans-Golgi network (TGN), they are sorted into carriers that would transport them to their final destination [START_REF] Papanikou | Golgi compartmentation and identity[END_REF]. The structure of the Golgi complex is inherently polar and provides directional movement to the biosynthetic pathway [START_REF] Glick | Models for Golgi traffic: A critical assessment[END_REF].

Figure 1.14: Two models of protein trafficking through the Golgi. (a) In the cisternal maturation model, vesicles derived from the ER fuse to form the cis cisternae of the Golgi (dark green). This cisterna then transforms into the medial cisterna (outlined in red) by a maturation process, possibly via an intermediate (striped yellow). Finally, the medial cisterna matures into the trans face of the Golgi (blue), to be consumed during secretory traffic to the cell surface. Sorting proteins for different destinations is accomplished by dividing cargo into different regions of the trans compartment of the Golgi before it fragments to generate vesicles for different destinations. COPI vesicles would retrieve and recycle resident Golgi proteins at each step. (b) In the vesicular transport model, the cis, medial and trans cisternae of the Golgi remain in place, without maturing, and COPI vesicles deliver cargo between cisternae. At the trans compartment, vesicles containing different secretory cargoes bud off to deliver their contents to distinct destinations. Taken from [START_REF] Malhotra | Cell biology: The Golgi grows up[END_REF].

The Golgi has been studied for more that 100 years by now, but, so far, a clear consensus of how this organelle forms and works has not been reached [START_REF] Glick | Models for Golgi traffic: A critical assessment[END_REF], Pfeffer, 2010, Saraste and Prydz, 2019]. The two main models were proposed -"cisternal progression/maturation" and "anterograde vesicular transport between stable compartments" [Glick andLuini, 2011, Malhotra andMayor, 2006]. In the cisternal maturation model, vesicles, pinching out of the ER, fuse together and form cis Golgi cisterna, which then moves forward and matures into the medial and trans cisterna together with its cargo, while Golgi resident proteins are moved backwards with the help of vesicles. The mature compartments are then sorted out as carriers and move to their destination (see Figure 1.14, a). In the vesicular transport model, stable Golgi cis, medial and trans compartments are formed and cargo moves between the cisternae through vesicles, while the resident Golgi proteins stay inside the stable cisternae. Once at the trans side, the cargo moves out by vesicular carriers (see Figure 1.14, b) [Glick andLuini, 2011, Malhotra andMayor, 2006]. In the last 15 years, the cisternal maturation model was gaining weight and importance in the field [START_REF] Malhotra | Cell biology: The Golgi grows up[END_REF], Matsuura-Tokita et al., 2006, Losev et al., 2006, Rivera-Molina and Novick, 2009, Kurokawa et al., 2019]. However, it cannot explain all the experimental data, e.g. different speed of small soluble cargo and large cargoes travelling through the Golgi [START_REF] Beznoussenko | Transport of soluble proteins through the Golgi occurs by diffusion via continuities across cisternae[END_REF]. To resolve that, it was proposed that heterotypic tubules could be connecting the different cisternae, to facilitate the movement of small soluble cargoes [START_REF] Beznoussenko | Transport of soluble proteins through the Golgi occurs by diffusion via continuities across cisternae[END_REF], Glick and Luini, 2011, Boncompain and Weigel, 2018] (see Figure 1.15, (B)).

Newly synthesized proteins enter the Golgi complex from the ER via COPII coated vesicles [START_REF] Béthune | Assembly of COPI and COPII Vesicular Coat Proteins on Membranes[END_REF]. Once reaching the Golgi area, the cargo has four options -(1) return to the ER, (2) stay in the Golgi complex, (3) get delivered to the endolysosomal compartment and (4) get delivered directly to the plasma membrane [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Taking into account the modified cisternal maturation model, the Golgi complex can be divided into three stages of maturation -cisternal assembly, carbohydrate synthesis and carrier formation [START_REF] Papanikou | Golgi compartmentation and identity[END_REF] (see Figure 1.15, (B)). The cargoes coming from the ER by COPII vesicles form the early cis cisterna. The cargoes that need to be recycled back to the ER (like trafficking proteins and ER resident proteins), pinch off at this stage by coated COPIa vesicles. The rest of the cargoes stay in the maturing medial and, later, trans cisternae, while [START_REF] Saraste | A New Look at the Functional Organization of the Golgi Ribbon[END_REF]. (B) Golgi complex can be divided into three stages of maturation. During the cisternal assembly stage, COPII vesicles bud from the ER and fuse with one another to generate a new Golgi cisterna, while COPIa vesicles bud from this nascent cisterna to recycle trafficking proteins and resident ER proteins to the ER. This stage includes cis Golgi cisternae, as well as ERGIC ("ER-Golgi intermediate compartment") membranes in animal cells. During the carbohydrate synthesis stage, most of the glycosylation reactions take place, and resident Golgi proteins are transferred between cisternae by COPIb vesicles. This stage includes cisternae that are often designated medial and trans. During the carrier formation stage, the cisterna disintegrates to produce cargo carriers that include secretory and clathrin-coated vesicles. This stage includes cisternae that are traditionally designated as TGN. Adapted from [START_REF] Papanikou | Golgi compartmentation and identity[END_REF].

being modified in the carbohydrate synthesis stage. Resident Golgi proteins move backwards to the earlier cisternae via COPIb vesicles. Small soluble cargoes, that don't need modification, can move fast through the maturing cisternae by tubular connections between them, while larger cargoes mature together with the cisternae [Glick andLuini, 2011, Boncompain andWeigel, 2018]. Next, the cisterna enters into a carrier formation stage, where it disintegrates to produce cargo carriers -secretory or clathrin-coated vesicles [START_REF] Papanikou | Golgi compartmentation and identity[END_REF] (see Figure 1.15). The efficient intra-Golgi transport of vesicles is achieved with the help of large coiled-coil tethering proteins, called golgins, protruding from each cisternae [START_REF] Muschalik | Golgins[END_REF], Lowe, 2019, Kulkarni-Gosavi et al., 2019, Ravichandran et al., 2020]. They are specific to a maturation stage of the cisternae and they can catch the passing vesicles according to their membrane identity and biophysical properties, and help them fuse with the Golgi membranes [START_REF] Wong | The specificity of vesicle traffic to the Golgi is encoded in the golgin coiled-coil proteins[END_REF], Lowe, 2019, Muschalik and Munro, 2018].

Once the cargo reaches TGN, it can be either delivered to the endolysosomal compartment or sent directly to the plasma membrane for secretion (or plasma membrane integration) [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Carriers destined for the endolysosomal compartment are structured, clathrin-coated vesicles [START_REF] Kirchhausen | Molecular structure, function, and dynamics of clathrin-mediated membrane traffic[END_REF], while secretory carriers tend to be tubular and unstructured, as they don't have any associated coat proteins [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. With the advancement of experimental techniques [Boncompain et al., 2012, Boncompain andWeigel, 2018], more and more players of the secretion process from the Golgi are being discovered [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Several different types of carriers have been characterized so far(see Figure 1.16). Some of the molecular players involved might be common to several carriers, yet a consensus for a general mechanism for the post-Golgi carrier formation has not been reached [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Cargo proteins vary in size, membrane association, destination and modification, therefore, it is possible that different sorting rules may apply to different classes of cargo [START_REF] Boncompain | Transport and sorting in the Golgi complex: multiple mechanisms sort diverse cargo[END_REF]. Carriers are characterized by distinct small GTPases, phospholipids or motor proteins involved in their formation [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Rab6 GTPase is an abundant Rab GTPase at the Golgi complex [START_REF] Gilchrist | Quantitative Proteomics Analysis of the Secretory Pathway[END_REF] and is involved in two proposed classes of post-Golgi carrier formation [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF]. Having its abundance in mind, I will focus on Rab6-positive post-Golgi carriers later in this chapter.

In vertebrate cells, membrane trafficking is performed on cytoskeleton tracks, especially on microtubules (MTs), with the help of their associated motor proteins [START_REF] Anitei | Bridging membrane and cytoskeleton dynamics in the secretory and endocytic pathways[END_REF]. The main microtubule organizing center (MTOC) is the centrosome, but MTs were found to be nucleated at the Golgi complex as well [START_REF] Rivero | Microtubule nucleation at the cis-side of the Golgi apparatus requires AKAP450 and GM130[END_REF]. Considered to be an evolutionary adaptation for transporting membranes and cargo in long distances, MTs serve as directional tracks for cargo secretion. A possibility to nucleate MTs at the Golgi itself, makes it possible to polarize secretion and affect cell polarity [Sanders andKaverina, 2015, Meiring et al., 2020].

Figure 1.16: Proteins associated with tubular carriers in mammalian cells. Models from experimental data on different types of secretory tubular carriers that bud towards the plasma membrane in mammalian cells. The carriers have been drawn as separate entities unless there is strong experimental evidence to combine the carriers. Some of the machinery described here might be overlapping on the same carriers, for example the SM carriers and CARTS, and the LAMP1-RUSH carriers, Rab6 carriers and the Arf1 carriers. Protein cartoons are not to scale and do not meaningfully reflect protein structure. Taken from [START_REF] Stalder | Direct trafficking pathways from the Golgi apparatus to the plasma membrane[END_REF].

Microtubules

Microtubules (MTs) make up a part of the cytoskeleton of a eukaryotic cell in addition to actin and intermediate filaments [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF]. Composed of αtubulin and β-tubulin heterodimeric subunits with GTP attached, they form cylindrical tubules of ∼25 nm in diameter [START_REF] Janke | The tubulin code and its role in controlling microtubule properties and functions[END_REF] (see Figure 1.17). Their structure makes them polar, as the subunits connect to each other in the same direction [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF]. The two ends of a MT are denoted as minus ("-") end and plus ("+") end. MT structure also makes them stiff, with the persistence length in the order of millimeters [START_REF] Huber | Cytoskeletal crosstalk: When three different personalities team up[END_REF]. The persistence length is a stiffness parameter of a microtubule and roughly reflects the distance over which a filament is straight [Van Mameren et al., 2009]. Both polarity and stiffness of MTs make them instrumental as tracks for directed vesicle movement, which is carried out by associated motor proteins -dynein and kinesins (Figure 1.17, top panel) [Meiring et al., 2020, Li andGundersen, 2008]. The minus end is usually nucleated at a microtubule organizing center (MTOC), while the plus end grows by polymerization (1.17, top panel). Once incorporated into a polymer, tubulin hydrolyses GTP attached to it. This means that along the length of a MT, most of the subunits are GDP-tubulin, with only a GTP-tubulin cap at the active polymerizing plus end. Once the active polymerization stops, the monomers dissociate and the MT starts to shrink (Figure 1.17). This process of shifting between MT growth and shrinkage is called dynamic instability [Janke andMagiera, 2020, Li andGundersen, 2008].

Figure 1.17: Properties of microtubules. Microtubules are composed of α-tubulin and βtubulin heterodimeric subunits that are oriented in the same direction, which results in a polarized surface lattice and two structurally distinct ends (plus and minus ends). The minus ends of microtubules are often anchored at the centrosome or other MTOCs. Motor proteins (kinesins and dynein) move in a unidirectional manner along the filament surface owing to repeated interactions with the consistently oriented subunits. Tubulin hydrolyses GTP shortly after assembly, resulting in a cap of GTP-containing tubulin subunits on growing plus ends. Because GTP-tubulin and GDP-tubulin have different dissociation rates, MTs depolymerize rapidly following the loss of the GTP cap. The alternation between growth (top panel) and shrinkage (botton panel) of MTs, with infrequent transitions, is known as dynamic instability and contributes to the ability of microtubules to search for polarity factors. Taken from [START_REF] Li | Beyond polymer polarity: How the cytoskeleton builds a polarized cell[END_REF].

The dynamics of microtubules can be regulated by inserting different isotypes of tubulins or by their post-translational modifications (PTMs). These MT changes make up the "tubulin code" [START_REF] Janke | The tubulin code and its role in controlling microtubule properties and functions[END_REF]. The most usual and best explored PTMs include acetylation, tyrosynation and detyrosination, phosphorylation, polyglutamylation, polyglycylation and polyamination (see Figure 1.18). Most of them occur at the C-terminal tails of tubulin subunits, but some of them, like acetylation, can even be found in the lumen of MTs [START_REF] Janke | The tubulin code and its role in controlling microtubule properties and functions[END_REF]. For a long time it was questioned, if PTMs can stabilize MTs, or if stable MTs just accumulate modifications. Now, it seems that at least a few of PTMs, like acetylation (increases bending without breaking) [START_REF] Eshun-Wilson | Effects of α-tubulin acetylation on microtubule structure and stability[END_REF], Xu et al., 2017, Portran et al., 2017] and polyamination (reduces depolymerization) [START_REF] Song | Transglutaminase and Polyamination of Tubulin: Posttranslational Modification for Stabilizing Axonal Microtubules[END_REF] have direct effect on either the mechanical properties or dynamics of MTs, respectively [START_REF] Janke | The tubulin code and its role in controlling microtubule properties and functions[END_REF]. The tubulin code can affect the MT properties directly and, also, be read by the microtubule associated proteins (MAPs). This can lead to changes in MT stiffness, speed of MT polymerization, attachment of motor proteins, MT guiding to specific locations in the cell and other outcomes, depending on the nature of the MAP [Janke andMagiera, 2020, Bodakuntla et al., 2019].

Figure 1.18:

The elements of the tubulin code. Microtubules dynamically assemble from dimers of α-tubulins and β-tubulins. Tubulins are highly structured proteins, forming 'tubulin bodies', whereas their C-terminal amino acids form unstructured tails that protrude from the microtubule surface. The tubulin code refers to the concept that different tubulin gene products, together with a variety of post-translational modifications (PTMs), modulate the composition of individual microtubules. Tubulin isotypes (α-tubulins, dark grey and brown; β-tubulins, light grey and pink) are encoded by different tubulin genes and can mix during microtubule assembly. Tubulin PTMs are catalysed by a range of enzymes and are located either at the globular, highly structured tubulin bodies (for example, acetylation (Ac), phosphorylation (P) and polyamination (Am)), or at the unstructured C-terminal tails of tubulin (for example, glutamylation, glycylation, tyrosination, detyrosination and removal of glutamate residues to produce Δ2-tubulin and Δ3-tubulin). Tubulin PTMs can generate binary switches (on-off signals) by adding or removing single functional residues (acetylation, phosphorylation or detyrosination) or can gradually modulate the strength of their signals by adding different numbers of residues (polyamination, polyglutamylation and polyglycylation). Polymodifications are initiated by the generation of a branching point, from which side chains are further elongated. Taken from [START_REF] Janke | The tubulin code and its role in controlling microtubule properties and functions[END_REF].

MTs are essential for efficient trafficking in large eukaryotic cells. They are involved in almost every step of secretion process, where they are used as tracks for vesicle transport from ER to the Golgi complex, and for post-Golgi trafficking towards the membrane [START_REF] Fourriere | The role of microtubules in secretory protein transport[END_REF]. Recent discoveries point to MT involvement in the turnover of focal adhesions (FAs) [START_REF] Seetharaman | Microtubules at focal adhesions -a double-edged sword[END_REF]. MTs are guided towards the FAs by MAPs interacting with actin cytoskeleton [START_REF] Seetharaman | Microtubules at focal adhesions -a double-edged sword[END_REF]. Next, MTs are caught at the plasma membrane, creating cortical microtubule stabilization complexes (CMSCs) close to FAs [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF]. This MT stabilization creates tracks for targeted secretion [Akhmanova andNoordstra, 2017, Meiring et al., 2020]. Selective MT stabilization and biased enrichment (by reorientation of the MT network and nucleation at the Golgi) at the leading edge of a migrating cell leads to more persistent cell migration (Figure 1.19) [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF], Hao et al., 2020]. Directed secretion requires motor proteins to carry the vesicles, which I will introduce in more detail in the next section. In a polarized mesenchymal cell migrating on a 2D substrate, the Golgi complex and the centrosome are positioned on one side of the nucleus and promote the formation of a polarized microtubule array oriented in the direction of migration (arrow) (right panel). Taken from [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF].

Motor proteins

Three types of cytoskeletal motors participate in membrane trafficking [START_REF] Akhmanova | Linking molecular motors to membrane cargo[END_REF]. They can transport different types of cargoes, from vesicles targeted for secretion to whole organelles. Two types of motors -dynein and kinesinsassociate to microtubules and use them as tracks for unidirectional transport [Olenick andHolzbaur, 2019, Hirokawa et al., 2009]. Dyneins move towards the minus end of MTs, while most of the kinesins move towards the plus end [START_REF] Fourriere | The role of microtubules in secretory protein transport[END_REF], Olenick and Holzbaur, 2019,Hirokawa et al., 2009]. The third type of motors is myosins, which move on actin cytoskeleton [START_REF] Hartman | The myosin superfamily at a glance[END_REF]. All three types of motors use ATP as their source of energy and step forward on their tracks thanks to conformational changes enabled by ATP hydrolysis [START_REF] Xiao | Cytoskeleton molecular motors: Structures and their functions in neuron[END_REF]. Adapted from [START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF].

Motors can bind to cargoes directly, but most of the time require specific adaptors [Akhmanova andHammer, 2010, Cross and[START_REF] Cross | Motor-cargo adaptors at the organelle-cytoskeleton interface[END_REF]. The activation of dynein requires even more molecular players, as it is active only in complex with its cofactor dynactin and a cargo specific activator protein [Olenick andHolzbaur, 2019, Reck-Peterson et al., 2018] (see Figure 1.20). In the abscence of binding partners, dynein is found in its auto-inhibited state and has low affinity for microtubules [START_REF] Zhang | Cryo-EM Reveals How Human Cytoplasmic Dynein Is Auto-inhibited and Activated[END_REF]. Before the interaction with cargo, kinesins and myosins are found in their inactive folded position as well [START_REF] Akhmanova | Linking molecular motors to membrane cargo[END_REF]. The huge variety of possible cargoes in the cell imposes the necessity of cargo adaptors. These are molecules that can directly interact with a motor protein and directly or indirectly with the cargo [START_REF] Cross | Motor-cargo adaptors at the organelle-cytoskeleton interface[END_REF]. The adaptors themselves usually interact with cargo through their membrane lipids or are recruited by Rab GTPases. Motors, on their side, recognize their adaptor proteins by short peptide motifs or coiled-coil structures [START_REF] Cross | Motor-cargo adaptors at the organelle-cytoskeleton interface[END_REF]Dodding, 2019, Reck-Peterson et al., 2018]. The interaction between the cargo and its motor protein can be regulated by a few other processes as well, including phosphorylation of the motor, inactivation of recruiting Rab GTPases or increase in local calcium concentration. It leads to the detachment of cargo or to the motor detachment from the track [START_REF] Hirokawa | Kinesin superfamily motor proteins and intracellular transport[END_REF]. Adapted from [START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF].

Interestingly, multiple different motor proteins can be attached to the same cargo. This leads to a certain tug-of-war as dynein and kinesin motors are pulling the cargo in opposite directions [START_REF] Derr | Tug-of-war in motor protein ensembles revealed with a programmable DNA origami scaffold[END_REF],Monzon et al., 2020]. It was proposed that it is regulated by certain adaptor proteins that could interact with both dynein and kinesin motor proteins. They serve as bidirectional switches, reacting to intracellular changes (Figure 1.21) [START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF]. This bidirectional motility was shown to be important for motor protein activation [START_REF] Ally | Opposite-polarity motors activate one another to trigger cargo transport in live cells[END_REF] and might be helpful to avoid "roadblocks" on crowded microtubules, to optimize the coupling and proofread the direction of cargo movement [Stephens, 2012]. As mentioned before, motor proteins need to recognize their cargoes and this is done either directly or through adaptor proteins, according to the membrane identity of the vesicles and organelles. This identity is largely formed by Rab GTPases [START_REF] Horgan | Rab GT-Pases and microtubule motors[END_REF].

Rab GTPases

Rab GTPases ("Ras-related protein in brain") are a family of small GTPases, which belongs to a Ras superfamily of proteins [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF], Homma et al., 2020]. Its members are involved in all the different steps of intracellular membrane trafficking [Stenmark, 2009, Galvez et al., 2012]. It is the largest small GTPase family with ∼70 members described in humans [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF], with five of its members (Rab1, Rab5, Rab6, Rab7 and Rab11) being found in all eukaryotic genomes, which confirms its ancient evolutionary roots and importance [Pereira-Leal andSeabra, 2001, Klöpper et al., 2012]. Targeting of the Rab/REP (or Rab/GDI) complex to specific membranes is mediated by the interaction with a membrane-associated GEF, which stimulates GDP to GTP exchange of Rab; or in few cases by interaction with a GDF first, followed by GEF stimulated activation. The GTP-bound (active) Rab conformation is recognized by multiple effector proteins, which then carry out their specific functions. GAP stimulates Rab GTPase activity and converts Rab back to the inactive, GDP-bound form, resulting in the dissociation of effectors. GDI regulates the cycling of Rab between the membranes by extracting inactive Rab from a membrane into the cytosol and subsequently delivering it back to a donor membrane compartment. Taken from [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF].

Rab GTPases are prenylated and, like this, can insert into membranes, where they perform their function [START_REF] Seabra | Controlling the location and activation of Rab GTPases[END_REF]. As the other small GTPases, they act as switches, and recruit effectors in their active Rab-GTP form [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF]. Like previously described Rho GTPases, they can be regulated by GEF activators, GAP inhibitors and GDI proteins, which extract them from membranes and keep them inactive in cytosol [START_REF] Homma | Rab family of small GTPases: an updated view on their regulation and functions[END_REF], Voss et al., 2019]. However, a large pool of inactive Rho GTPases are found in the membranes, while inactive Rab GTPases are efficiently extracted from the membranes. Another difference is a chaperone protein REP ("Rab escort protein") that interacts with Rab proteins right from their translation and brings them to RabGGT ("Rab geranylgeranyl transferase") for, mostly double, prenylation at their C-terminus CXC group [START_REF] Goody | Mechanisms of action of Rab proteins, key regulators of intracellular vesicular transport[END_REF],Seabra and Wasmeier, 2004, Alexandrov et al., 1994]. Prenylated Rabs can then be inserted into membranes. Different Rabs are described to associate to specific organelles and membranes [Pfeffer, 2017, Chavrier et al., 1990]. It is not completely clear how certain Rabs are recruited to distinct membranes, but there is proof that they could be localized either by their GEFs or GDF ("GDI displacement factor") proteins [Pfeffer, 2017]. Once activated, Rabs start recruiting their effectors [START_REF] Zhen | Cellular functions of Rab GTPases at a glance[END_REF]. Recently, a mechanism of Rab activation ultrasensitivity and bistability was described, proposing that Rab proteins get activated after a certain threshold of GEF concentration and stay active despite the varying concentration of GEFs. The activity is switched off efficiently by a GAP [Barr, 2013, Bezeljak et al., 2020]. The activity of Rabs is also controlled by their intrinsic ability to hydrolyse GTP, which is very low for certain Rabs like Rab6, which stays active longer and can ensure long-range vesicular transport, and high for others like Rab5, which acts in fast fusion events [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF]. Because Rabs, their effectors and membrane phosphoinositides create the membrane identity of different organelles, it ensures correct intracellular membrane trafficking [Pfeffer, 2017, Barr, 2013, Stenmark, 2009].

Rab GTPases are essential regulators of all different aspects of membrane trafficking, from the sorting of components to a vesicle at the donor membrane, to fission, uncoating of that vesicle, vesicle transport, tethering to the acceptor membrane and vesicle fusion with it [Stenmark, 2009,Galvez et al., 2012,Zhen and Stenmark, 2015]. A multitude of Rab GTPase effectors include phosphoinositide kinases or phosphatases, which affect the lipid composition of membranes and sorting, coat recruitment and uncoating processes (see Figure 1.23, (a) and (b)). Rab GTPases can also bind motor proteins or their adaptors, enabling vesicle loading on the cytoskeletal tracks and movement along them (see Figure 1.23, (c)). Rabs can interact with tethers, ensuring the docking of a vesicle (Figure 1.23, (d)) and facilitate vesicle fusion by recruiting effectors, which interact with SNARE proteins (Figure 1.23, (e)) [Stenmark, 2009, Pylypenko et al., 2018]. (a) Active GTP-bound Rab activates a sorting adaptor to sort a receptor into a budding vesicle. (b) Through recruitment of phosphoinositide (PI) kinases or phosphatases, the PI composition of a transport vesicle is altered (the conversion of PI-x into PI-y) and thereby causes uncoating through the dissociation of PI-binding coat proteins. (c) Rab GTPases mediate vesicle transport along actin filaments or microtubules (collectively referred to as cytoskeletal tracks) by recruiting motor adaptors or by binding directly to motors (not shown). (d) Rab GTPases mediate vesicle tethering by recruiting rod-shaped tethering factors that interact with molecules in the acceptor membrane. Such factors interact with SNAREs and their regulators to activate SNARE complex formation, which results in membrane fusion. (e) Following membrane fusion and exocytosis, the Rab GTPase is converted to its inactive GDP-bound form through hydrolysis of GTP, which is stimulated by a GTPase-activating protein (GAP). Targeting of the Rab-GDP dissociation inhibitor (GDI) complex back to the donor membrane is mediated by interaction with a membrane-bound GDI displacement factor (GDF). Conversion of the GDP-bound Rab into the GTP-bound form is catalysed by a guanine nucleotide exchange factor (GEF). Taken from [Stenmark, 2009].

Certain Rabs localize and are associated to specific organelles, and distinct steps in membrane trafficking pathway [START_REF] Nassari | Rabs in signaling and embryonic development[END_REF], Galvez et al., 2012]. Rab5 is related to early endosomes, Rab6 -with Golgi and secretion pathway, Rab7 -with late endosomes and lysosomes, Rab11 -with recycling endosomes [START_REF] Nassari | Rabs in signaling and embryonic development[END_REF],Zhen and Stenmark, 2015, Galvez et al., 2012]. However, the actual membrane maturation process is not that simple. Rab GTPases interact with each other directly or through their effectors and can even recruit each other's activators -a process called the Rab cascade [START_REF] Galvez | SnapShot: Mammalian Rab Proteins in Endocytic Trafficking[END_REF], Pylypenko et al., 2018]. Some Rabs are able to simultaneously bind two effectors, and some effectors are able to bind multiple Rabs at a time [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF], Rai et al., 2019]. These interactions can lead to signal propagation or signal stopping and change in membrane identity [Pfeffer, 2017]. Two interesting examples of the Rab cascade were found between Rab11 and Rab8, [Py-lypenko et al., 2018], and Rab5 and Rab7 [START_REF] Galvez | SnapShot: Mammalian Rab Proteins in Endocytic Trafficking[END_REF], Rink et al., 2005]. In the first case, Rab11 binds Rabin8, which is a GEF for Rab8, and recruits it in this way. Both Rabs are then present on the membrane [START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF]. In the second case, Rab5 recruits a complex, which removes its own GEF and recruits a GEF for Rab7. Furthermore, Rab7 is proposed to recruit a still unknown GAP for Rab5, inactivating it and removing Rab5 from the membrane [START_REF] Galvez | SnapShot: Mammalian Rab Proteins in Endocytic Trafficking[END_REF]. Both of these mechanisms are generalized in Figure 1.24.

Rab cascades can introduce polarity into the system, while reassuring a one way membrane flow. In the next paragraph I will focus on the most abundant Rab GTPase in cells -Rab6 -and its involvement in the secretion pathway [START_REF] Gilchrist | Quantitative Proteomics Analysis of the Secretory Pathway[END_REF]. Here GAP proteins are included to remove a previous-acting Rab from a specific membrane domain. The presence of the GAP will sharpen the boundaries between individual Rab domains. Taken from [Pfeffer, 2017].

Rab6

Rab6A (Ras-related protein in brain 6A) is a small GTPase protein that belongs to Rab family of GTPases. Two main isoforms have been described -Rab6A and Rab6A , which differ from one another just by three amino acids and both have molecular mass of ∼24 kDa. They are generated by alternative splicing [START_REF] Echard | Alternative splicing of the human Rab6A gene generates two close but functionally different isoforms[END_REF]. Both isoforms are expressed at a similar level and, though, very similar in sequence, the difference in their functionality is still on debate [START_REF] Echard | Alternative splicing of the human Rab6A gene generates two close but functionally different isoforms[END_REF], Young et al., 2005, Del Nery et al., 2006]. Rab6 is twice geranylgeranylated at it's C-terminus CXC motif, which makes this protein able to be anchored in membranes and is instrumental for its targeting to the Golgi complex [START_REF] Beranger | The effector domain of Rab6, plus a highly hydrophobic C terminus, is required for Golgi apparatus localization[END_REF], Goud et al., 1994, Goud et al., 1990]. Rab6 is found in medial and trans-Golgi cisternae, the TGN and post-Golgi vesicles [START_REF] Goud | Study of Rab6, a Ras-like GTP-binding Protein Associated with the Golgi Complex[END_REF]. Although the activity of Rab6 should be regulated by GEFs and GAPs (like other small GTPases) only a few were identified so far [START_REF] Pusapati | Ric1-Rgp1 complex is a guanine nucleotide exchange factor for the late Golgi Rab6A GTPase and an effector of the medial Golgi Rab33B GTPase[END_REF], Cuif et al., 1999].

Rab6 protein is involved in multiple processes related to membrane trafficking -from Golgi-to-ER recycling [START_REF] White | Rab6 coordinates a novel Golgi to ER retrograde transport pathway in live cells[END_REF], Echard et al., 2000, Young et al., 2005, Matsuto et al., 2015], to dynactin recruitment to Golgi membranes [START_REF] Short | The Rab6 GTPase regulates recruitment of the dynactin complex to Golgi membranes[END_REF], Bergbrede et al., 2009] to retrograde trafficking [START_REF] Mallard | Early/recycling endosomes-to-TGN transport involves two SNARE complexes and a Rab6 isoform[END_REF], Shafaq-Zadah et al., 2016, Carpier et al., 2018], but here, I will focus on its role as a general regulator of post-Golgi secretion [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF].

It was shown that Rab6-positive vesicles fission out of the Golgi complex at specific places and not all over the Golgi surface. These locations are called Rab6 hotspots and in HeLa cells the average number was 6 hotspots per Golgi [START_REF] Miserey-Lenkei | Coupling fission and exit of RAB6 vesicles at Golgi hotspots through kinesin-myosin interactions[END_REF]. Rab6 is known to interact with a kinesin KIF20A [START_REF] Echard | Interaction of a Golgi-associated kinesin-like protein with Rab6[END_REF], Echard et al., 2001], which helps to accumulate Rab6 in microtubule nucleation sites at the Golgi complex and restricts its diffusion inside the Golgi, which might lead to a formation of a hotspot [START_REF] Miserey-Lenkei | Coupling fission and exit of RAB6 vesicles at Golgi hotspots through kinesin-myosin interactions[END_REF]. Both Rab6 and KIF20A have myosin II binding sites and recruit it to the Rab6 fission hotspots [START_REF] Miserey-Lenkei | Rab and actomyosin-dependent fission of transport vesicles at the golgi complex[END_REF], Miserey-Lenkei et al., 2017]. Myosin II is necessary for the fission of Rab6-positive vesicles from the Golgi/TGN membranes [START_REF] Miserey-Lenkei | Rab and actomyosin-dependent fission of transport vesicles at the golgi complex[END_REF] and, together with KIF20A, provides the link between actin and microtubule cytoskeletons in the vesicle fission out of the Golgi [START_REF] Miserey-Lenkei | Coupling fission and exit of RAB6 vesicles at Golgi hotspots through kinesin-myosin interactions[END_REF].

Rab6-positive vesicles are carried out of the Golgi on microtubule tracks by kinesin KIF5B [START_REF] Grigoriev | Rab6 Regulates Transport and Targeting of Exocytotic Carriers[END_REF] and can transport various types of cargo [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF]. Though not essential for secretion, Rab6 controls the organization of exocytosis [START_REF] Grigoriev | Rab6 Regulates Transport and Targeting of Exocytotic Carriers[END_REF], Fourriere et al., 2019]. During or just after the fission, Rab6 recruits another Rab GTPase Rab8, which is required for the vesicle docking [START_REF] Grigoriev | Rab6, Rab8, and MICAL3 cooperate in controlling docking and fusion of exocytotic carriers[END_REF]. Rab6-positive vesicles were shown to target the plasma membrane sites enriched in ELKS protein [START_REF] Grigoriev | Rab6 Regulates Transport and Targeting of Exocytotic Carriers[END_REF], Nyitrai et al., 2020]. Interestingly, microtubules are attached to the cell cortex by CLASPs through a complex including LL5βand ELKS, which usually forms in the vicinity of focal adhesions (FAs) [START_REF] Lansbergen | CLASPs Attach Microtubule Plus Ends to the Cell Cortex through a Complex with LL5β[END_REF], Meiring et al., 2020]. To support that, it was recently reported that Rab6-positive vesicles fuse with the plasma membrane close to the area of FAs [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF]. Rab6 interacts with ELKS directly, while Rab8 does it through a protein MICAL3 [START_REF] Grigoriev | Rab6, Rab8, and MICAL3 cooperate in controlling docking and fusion of exocytotic carriers[END_REF]. MICAL3 belongs to MICAL family of redox proteins, known for F-actin depolymerization [Ortegón Salas et al., 2020], though its function in helping vesicles fuse with the plasma membrane is not known yet. It is plausible, that MICAL3 could be involved in the reorganization of the complex or actin depolymerization, to make plasma membrane more accessible for fusion [START_REF] Grigoriev | Rab6, Rab8, and MICAL3 cooperate in controlling docking and fusion of exocytotic carriers[END_REF], Bance et al., 2019].

A recent study has hypothesized that Rab6-positive vesicles might be using direct microtubule tracks to FAs, using just a subset of microtubules available [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF]. It is not well known how the affinity of Rab6-positive vesicles to microtubule tracks is regulated in the long-distance range, however several studies have pointed to a few mechanisms of local regulation. In a study by [START_REF] Bance | Microtubule acetylation but not detyrosination promotes focal adhesion dynamics and astrocyte migration[END_REF] it was revealed that microtubule αTAT1-mediated acetylation increases in the vicinity of FAs, thus promoting MICAL3-dependent Rab6-positive vesicle fusion at FAs. A recent pre-print proposes a role for kinesin KIF13B, which has a high affinity to freshly polymerized microtubule ends [START_REF] Serra-Marques | Concerted action of kinesin-1 KIF5B and kinesin-3 KIF13B promotes efficient transport of exocytotic vesicles to microtubule plus ends[END_REF]. KIF13B can bind Rab6positive vesicles, and take over kinesin KIF5B, which carries the vesicles initially. Both of the studies share the idea that Rab6-vesicles are delivered towards the FAs, promoting focal adhesion turnover and cell migration [START_REF] Bance | Microtubule acetylation but not detyrosination promotes focal adhesion dynamics and astrocyte migration[END_REF],Serra-Marques et al., 2020]. You can see a proposed model of the role of Rab6 in post-Golgi secretory pathway in Figure 1.25. Nonetheless, the positive Rab6 role in cell migration was contested by a recent study, where depletion of Rab6 was shown to promote Cdc42 activity and actin polymerization, establishing Rab6 as a negative regulator of cell migration [START_REF] Vestre | Rab6 regulates cell migration and invasion by recruiting Cdc42 and modulating its activity[END_REF].

All in all, Rab6 is a major secretion regulator, responsible for targeted exocytosis and involved in FA turnover and cell migration processes. RAB6 is present on CD59-, TNFα-, and ColX-containing vesicles exiting the Golgi complex. Myosin II is implicated in the fission of these vesicles from Golgi membranes. Vesicles are transported to the plasma membrane in a KIF5B-dependent manner, and ELKS ensures their docking to exocytic hotspots close to FAs. Taken from [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF].

Cell polarity

Cell polarity manifests as intrinsic asymmetry in the cell either in shape, structure, or organization of intracellular components [START_REF] Campanale | Development and dynamics of cell polarity at a glance[END_REF]. In this section I will describe how cell polarity emerges from different cellular asymmetries. Then I will focus on a specific case of polarity that emerges in migrating cells -front-rear polarity -and the Nucleus-Centrosome-Golgi axis that marks it. I will delve deeper into the functional role of Golgi positioning in the cell and describe several models proposed to explain persistent cell migration.

Polarity emerges from cellular asymmetries

A cell is able to create gradients of molecules and structural asymmetry, which is essential for multiple processes, like asymmetric cell division, tissue formation, immune response and cell migration. These asymmetries let the cell localize different activities to distinct regions of the cell [START_REF] Mellman | Coordinated protein sorting, targeting and distribution in polarized cells[END_REF]. These asymmetries of intracellular components and the feedback loops maintaining them, if coordinated along an axis, give rise to the emergence of a polarized state [Etienne- Manneville andArkowitz, 2020, Vaidziulyte et al., 2019]. Elementary processes: (top) gradients of proteins or activity of proteins, (right) anisotropy of cell shape and cytoskeleton, (bottom) asymmetric distribution of vesicles and organelles, (left) oriented transport of material. A functional polarized state is achieved when these elementary processes are properly coupled (arrows 1-6). Taken from [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF].

Cellular asymmetries can be broken down into four elementary processes -(i) gradients of proteins or activity of proteins, (ii) anisotropy of cell shape and cytoskeleton, (iii) asymmetric distribution of vesicles and organelles and (iv) oriented transport of material (see Figure 1.26) [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF]. Now, I am going to describe the actual asymmetries and precise molecular mechanisms that couple them. Rho GTPases build gradients along the perimeter of the cell [de Beco et al., 2018, Pertz, 2010b] and interact with the conserved polarity protein complexes Par (CDC42-PAR3-PAR6-aPKC), Crumbs (Crb-PALS-PATJ) and Scribble (Scrib-Dlg-Lgl) at the cell cortex [START_REF] Riga | New insights into apical-basal polarization in epithelia[END_REF], Peglion and Goehring, 2019, Pichaud et al., 2019, Campanale et al., 2017], and locally remodel the actin cytoskeleton [Warner et al., 2019b, Lawson and Ridley, 2018, Molinie and Gautreau, 2018]. These Rho GT-Pase gradients form cell protrusions and an asymmetric cell shape (see Figure 1.26, arrow 1). The action of Rho GTPases also leads to the remodelling of the MT network, affecting the positioning of organelles, which rely on the MT and actomyosin networks for their transport (Figure 1.26, arrows 2 and 4) [Etienne-Manneville, 2013, Barlan andGelfand, 2017, van Bergeijk et al., 2016]. The mitochondria can be localized to the areas of higher energy consumption [START_REF] Schuler | Miro1mediated mitochondrial positioning shapes intracellular energy gradients required for cell migration[END_REF]] and the endomembrane system, with its key organelle, the Golgi complex, can be positioned for polarized secretion with the help of these cytoskeletal networks [Meiring et al., 2020, Yadav andLinstedt, 2011]. Organelle positioning is also affected by the cytoplasmic flows, generated by actin polymerization (actin retrograde flow), contraction of actin cortex or movement of motor proteins [START_REF] Illukkumbura | Patterning and polarization of cells by intracellular flows[END_REF]. Differential localization of organelles and, specifically, the endomembrane system enhances polarized protein trafficking (Rho GT-Pases and proteins from polarity complexes among them) and generates asymmetric lipid distribution in the form of vesicle trafficking, exocytosis and endocytosis (Figure 1.26, arrows 6 and 2) [START_REF] Fourriere | The role of microtubules in secretory protein transport[END_REF], Xing et al., 2016, Etienne-Manneville, 2013, O'Neill et al., 2018a, Malinverno et al., 2017]. Organelles are of different lipid composition, which means that their asymmetrical positioning leads to distinct redistribution of lipids in the cell as well [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF]. Rho GTPases, for example, are able to interact with membrane phospholipids like PI(4,5)P 2 and PI [START_REF]1 Persistence time phase diagram[END_REF]4,5)P 3 and changing the distribution of these lipids affects Rho GTPase localization (Figure 1.26, arrow 3) [Senju andLappalainen, 2019, Remorino et al., 2017]. In addition to that, some organelles can act as mobile platforms for local activation. For example, a Rho GTPase Rac1 can be activated on early endosomes [START_REF] Palamidessi | Endocytic Trafficking of Rac Is Required for the Spatial Restriction of Signaling in Cell Migration[END_REF],Malinverno et al., 2017], or changes in actin cytoskeleton can be induced by releasing Ca 2+ and activating myosin motor-dependent contractility (Figure 1.26, arrow 5) [START_REF] Sáez | Role of calcium permeable channels in dendritic cell migration[END_REF].

These asymmetries are closely interdependent and lead to a robust maintenance of cell polarity, demonstrating that cell polarity cannot be reduced to the function of a few selected molecular players [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF], Freisinger et al., 2013].

Front-Rear polarity axis

The four elementary processes generating cell polarity are recapitulated in the polarized mesenchymal migrating cell (see Figure 1.27) [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF]. A crawling mesenchymal cell is asymmetrically shaped with a protruding front, which moves forward and a retracting back (Figure 1.27, top panel). Rho GTPases generate gradients of activity along the perimeter of the cell. Rac1 and Cdc42 gradients peak at the leading edge of the cell, while RhoA is enriched at the contractile rear (Figure 1.27, (A)). Controlled by Rho GTPases, actin structures create asymmetry with branched actin structures at the lamellipodium and bundled actin in filopodia of the protruding front that attach to the substrate through focal adhesions (FAs). Another actin structure -stress fibers -made of thick actin bundles, forms at FAs and stretches towards the rear of the cell, connecting to FAs there and keeping the back of the cell under tension (Figure 1.27, (B)). The organelles of the endomembrane system and mitochondria are often positioned between the nucleus and the protruding front, supported by the microtubule network (Figure 1.27, (C)). Phospholipids like PIP 2 and PIP 3 also form a gradient along the polarity axis of the cell (Figure 1.27, (D)) [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF]. This asymmetry of migrating cells can be defined with a front-rear polarity axis [START_REF] Llense | Front-to-Rear Polarity in Migrating Cells[END_REF]. This polarity axis was indicated to coincide with the axis going through the center of the nucleus and the centrosome of the cell, making it a hallmark of cell polarity [Luxton andGundersen, 2011, Orlofsky, 2019].

The function of the Nucleus-Centrosome axis positioning is still not completely understood [Orlofsky, 2019], but multiple studies have been conducted to figure out how does it align with the front-rear polarity axis. Two separate pathways, one controlling the positioning of the centrosome and another, controlling the positioning of nucleus have been dissected [START_REF] Elric | Centrosome positioning in polarized cells: Common themes and variations[END_REF]. Scratch wound healing assays, where the monolayer of cells is physically scratched and the cells are left to fill the gap, were an instrumental technique to investigate how cells polarize towards the wound [START_REF] Liang | In vitro scratch assay: A convenient and inexpensive method for analysis of cell migration in vitro[END_REF]. These experiments, conducted on fibroblast and astrocyte cells, showed that Cdc42, its interaction with Par polarity complex (Par6-aPKC-Par3) and subsequent recruitment of dynein motor to the cell cortex was responsible for keeping the centrosome in the center of the cell [Gomes et al., 2005a] or its repositioning [Etienne- Manneville et al., 2005, Cau andHall, 2005]. In migrating astrocytes, the signalling pathway involved anchoring of MT plus ends at the cell cortex at the leading edge via Dlg1 recruitment of APC and recruitment of motor protein dynein The polarized migrating cell. Top, cartoon of a canonical polarized mesenchymal migrating cell. The cell presents a front-rear organization, with a protruding front and a retracting rear. (A-D) Subsets of elements that compose a canonical polarized cell. (A) Signaling gradients of RhoGTPases: Rac1 and Cdc42 are mainly activated in the protruding region of the cell, whereas RhoA is responsible for the rear retraction. RhoA is also transiently activated in the front of the cell (not shown). (B) The actin cytoskeleton (red) and focal adhesions (FA, light orange). At the protruding front, in the lamellipodia, branched actin pushes the PM and is subjected to a retrograde flow. In filopodia, actin is bundled. Actin arcs can be present in the lamella, behind the lamellipodia. Stress fibers are observed along the quiescent edges of the cell, in the retracting rear, and in the lamella. Nascent FAs (not shown) are observed in the lamellipodia, and mature FAs are observed at the end of stress fibers, in the lamella and in the rear. (C) The microtubule (MT) network and organelles. The MTOC or centrosome (yellow) and the Golgi complex (light pink) are aligned and organized along the rear-to-front polarity axis. MTs span the whole cell with a radial organization centered on the MTOC. The endoplasmic reticulum (green, ER) and mitochondria (purple) are scattered in perinuclear regions assuming an asymmetric distribution towards the front. Endosomes (big pink circles), recycling endosomes (amorphous shape), and secretory vesicles (small pink circles) are observed all across the cell. Their trafficking routes depend on MTs and molecular motors. (D) Asymmetric distribution of lipids both at the PM and in endomembranes. At the cell scale, lipid gradients, such as the PI(4,5)P 2 -PI(3,4,5)P 3 gradients, are distributed along the rear-to-front axis (green to pink). Organelles are also defined by specific lipid compositions (not shown) that depend on complex lipid trafficking and spatially restricted reactions. Adapted from [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF].

at the same spot via Dlg1 and GKAP interaction. By walking on a MT towards its minus end, but being attached to the cell cortex at the protruding edge, dynein creates a pulling force and recenters the MTOC towards the leading edge of a migrating cell (Figure 1.28, red box) [Etienne- Manneville et al., 2005, Manneville andEtienne-Manneville, 2006]. In fibroblasts, MTOC is recentered through Par3 interacting with dynein directly (Figure 1.28, grey box) [START_REF] Schmoranzer | Par3 and Dynein Associate to Regulate Local Microtubule Dynamics and Centrosome Orientation during Migration[END_REF]. Alternative models of centrosome repositioning by cytoplasmic MT pulling and MT pushing were proposed and modelled as well [Orlofsky, 2019, Kimura and Kimura, 2011, Zhao et al., 2012, Letort et al., 2016]. While centrosome positioning is regulated by MT network, nucleus responds to the changes in actomyosin network and is pushed back by the actin retrograde flow, though in both cases the initiating molecular player is Cdc42. It activates serine/threonine-protein kinase MRCK, which promotes myosin II generated flow of actin fibers. Nucleus is moved backwards by its attachments to those actin fibers. The links are generated through the LINC (linker of nucleoskeleton and cytoskeleton) complex components TAN (transmembrane actin-associated nuclear) lines either directly [Gant Luxton et al., 2011] or through intermediate filaments [START_REF] Dupin | Cytoplasmic intermediate filaments mediate actin-driven positioning of the nucleus[END_REF] (Figure 1.29, right). Nucleus and centrosome positioning are regulated by two different mechanisms, but they are usually seen migrating together [Orlofsky, 2019,Burakov andNadezhdina, 2013]. This might as well be just a result of being regulated by the same initial trigger (e.g. Cdc42) or being driven by the same forces, but it could also mean a physical connection [Burakov andNadezhdina, 2013, Janota et al., 2017]. Two mechanisms have been proposed -"magnet-like" and "velcro-like" [START_REF] Burakov | Association of nucleus and centrosome: Magnet or velcro?[END_REF]. In the first one, nucleus is brought close to the centrosome along the MTs by the motor proteins and its position is kept stable by the interplay of kinesin and dynein action [START_REF] Burakov | Association of nucleus and centrosome: Magnet or velcro?[END_REF], Splinter et al., 2010, Zhang and Han, 2010, Janota et al., 2017] (Figure 1.29, middle). Dynein motors are also responsible for nuclear rotation [Wu et al., 2011,Levy andHolzbaur, 2008]. A strong physical link between the nucleus and centrosome is contradicted by the nuclear rotation phenomenon [START_REF] Burakov | Association of nucleus and centrosome: Magnet or velcro?[END_REF]]. However, the LINC complex proteins can also bind to the actin cytoskeleton, which could serve as a "velcro-like" connection [START_REF] Tzur | SUNdomain proteins: 'Velcro' that links the nucleoskeleton to the cytoskeleton[END_REF], Janota et al., 2017] (Figure 1.29, left).

Figure 1.29: The LINC complex connects the cytoskeleton to the nuclear envelope. The linker of cytoskeleton and nucleoskeleton (LINC) complex consists of the outer nuclear membrane KASH proteins (including Syne/nesprins in mammals), which interact in the perinuclear space with the inner nuclear membrane SUN proteins. Outer nuclear membrane proteins bind components of the cytoskeleton in order to implement force transmission, and the inner membrane proteins interact with the nuclear lamina to effect this force into the nucleus. These complexes are arranged along the nuclear envelope in transmembrane actin-associated nuclear (TAN) lines to couple the nucleus to dorsal, rearward-moving actin cables in migrating fibroblasts. Alternatively, LINC complexes can interact with the microtubule cytoskeleton via molecular motors such as dynein and kinesin to enable nuclear positioning and centrosomal interaction. The nuclear envelope can also bind to the intermediate filaments using these complexes, through proteins such as plectin. Taken from [START_REF] Barker | Centrosome positioning in non-dividing cells[END_REF].

Nucleus-centrosome axis position was shown to depend on cell-cell adhesions, based on interaction of N-cadherins [START_REF] Dupin | Classical cadherins control nucleus and centrosome position and cell polarity[END_REF], and adhesions to the substrate, formed through FAs [START_REF] Théry | Anisotropy of cell adhesive microenvironment governs cell internal organization and orientation of polarity[END_REF], Ladoux et al., 2016]. Its repositioning during epithelial-to-mesenchymal transition (EMT) was shown to promote cell scattering, priming a cell to move out of the organized epithelial tissue [START_REF] Burute | Polarity Reversal by Centrosome Repositioning Primes Cell Scattering during Epithelial-to-Mesenchymal Transition[END_REF]. Once reoriented towards the extracellular matrix (ECM) it seems to promote the asymmetry and completely switch from apico-basal to front-rear polarity, possibly promoting material exchange with the newly forming FAs [START_REF] Burute | Polarity Reversal by Centrosome Repositioning Primes Cell Scattering during Epithelial-to-Mesenchymal Transition[END_REF], Etienne-Manneville, 2013, Vaidziulyte et al., 2019]. In vertebrate cells, the centrosome is spatially related to another organelle, which is highly involved in material exchange and intracellular trafficking -the Golgi complex [Rios, 2014, Sütterlin andColanzi, 2010]. This link proposes a role for polarized trafficking and a function for nucleus-centrosome-Golgi axis [Orlofsky, 2019, Barker et al., 2016].

Golgi positioning

Golgi positioning at the center of the cell close to the centrosome is a feature of vertebrate cells [START_REF] Wei | Unraveling the Golgi ribbon[END_REF]. Its multiple stacks connect laterally and form a "ribbon" structure (Figure 1.30, (B)) [Wei andSeemann, 2010, Gosavi andGleeson, 2017]. In yeast, plant and invertebrate cells Golgi stacks are dispersed in the cytoplasm (Figure 1.30, (A)), suggesting that Golgi positioning in the center of the cell is not essential for the Golgi complex function in global cargo sorting and trafficking [START_REF] Fourriere | Microtubule-independent secretion requires functional maturation of Golgi elements[END_REF]. However, the ribbon structure in vertebrate cells is recognized to play a role in additional cellular functions, like signalling, MT nucleation and polarized trafficking [Gosavi andGleeson, 2017, Luini andParashuraman, 2016]. In vertebrates, the Golgi is organized as a ribbon structure in the perinuclear region of most cells, maintained close to the centrosome (small red oval) by interactions with microtubules (blue). Taken from [START_REF] Gosavi | The Function of the Golgi Ribbon Structure -An Enduring Mystery Unfolds![END_REF].

The Golgi complex is positioned and assembled in the center of the cell in two stages, dependent on two discrete MT subsets [START_REF] Miller | Golgi-derived CLASP-dependent microtubules control Golgi organization and polarized trafficking in motile cells[END_REF], Vinogradova et al., 2012]. First, centrosomal MT array positions the Golgi membranes in the center. The Golgi protein golgin-160 recruits dynein motors, which drag them towards the MT minus ends and the main MTOC -the centrosome [START_REF] Yadav | Article Golgin160 Recruits the Dynein Motor to Position the Golgi Apparatus[END_REF]Linstedt, 2011]. The Golgi membranes are able to nucleate MTs [START_REF] Wu | Molecular Pathway of Microtubule Organization at the Golgi Apparatus[END_REF], Rivero et al., 2009, Efimov et al., 2007], and so, the second stage leads to the assembly of a more compact Golgi complex via Golgi nucleated MTs drawing the stacks together laterally [START_REF] Miller | Golgi-derived CLASP-dependent microtubules control Golgi organization and polarized trafficking in motile cells[END_REF]. The compact structure in the cis-totrans direction is maintained by GRASP65 and GRASP55 proteins, helping to form the Golgi stacks [START_REF] Zhang | GRASPs in Golgi Structure and Function[END_REF].

As mentioned before, the Golgi complex, as well as the centrosome, are able to nucleate MTs and can serve as microtubule organizing centers [START_REF] Wu | Microtubule Organizing Centers[END_REF]. While the centrosome nucleates MTs radially, inherently polarized Golgi complex creates an asymmetric MT array, growing outwards in front of it (Figure 1.19) [START_REF] Efimov | Asymmetric CLASP-Dependent Nucleation of Noncentrosomal Microtubules at the trans-Golgi Network[END_REF], Meiring et al., 2020]. This asymmetry was proposed to create a bias in the trafficking direction of cargoes leaving the Golgi complex (Figure 1.31) [START_REF] Yadav | Golgi positioning[END_REF]. The Golgi positioning close to the centrosome is dynamic and the Golgi complex was shown to reorient towards the leading edge of most of the mesenchymal migrating cells [START_REF] Millarte | The Golgi in cell migration: Regulation by signal transduction and its implications for cancer cell metastasis[END_REF], Yadav et al., 2009, Kupfer et al., 1982], making a part of the Nucleus-Centrosome-Golgi polarity axis [START_REF] Yadav | Golgi positioning[END_REF]. Dispersing the Golgi complex and changing its localization in the cell perturbed directed cell migration [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF],Miller et al., 2009,Hurtado et al., 2011]. These results indicate that the main function of Golgi positioning in the centrosomal region is to support cell polarity by asymmetric vesicular trafficking [Orlofsky, 2019]. The polarity factors themselves (like Cdc42 and its activators) were shown to be present in the cargo vesicle [START_REF] Osmani | Cdc42 localization and cell polarity depend on membrane traffic[END_REF]. Moreover, Golgi-associated MTs were reported to work as "fast-tracks" for vesicle cargo [START_REF] Hao | Golgi-associated microtubules are fast cargo tracks and required for persistent cell migration[END_REF]. Golgi-associated MTs were shown to have less MT lattice repair sites and MT intersections, which made the cargoes stop less and move more straight [START_REF] Hao | Golgi-associated microtubules are fast cargo tracks and required for persistent cell migration[END_REF].

Figure 1.31: Golgi positioning directs secretion to cell leading edge. Extracellular signals, such as wounding, trigger actin assembly and reorientation of the centrosome, the Golgi apparatus, and the microtubule array (A). As a consequence, secretion is directed to the leading edge. Once initiated, maintenance of polarity requires directed secretion toward the leading edge by the pericentrosomally positioned Golgi apparatus (B). Taken from [START_REF] Yadav | Golgi positioning[END_REF].

There are a few mechanisms describing how the Golgi complex reorients towards the leading edge in migrating cells. The Golgi complex is spatially close to the centrosome, making it susceptible to each other's movement. The centrosome cannot be repolarized if Golgi repolarization is blocked [START_REF] Bisel | ERK regulates Golgi and centrosome orientation towards the leading edge through GRASP65[END_REF] and the Golgi moves together with the centrosome when it is pulled towards the leading edge by the MTs [START_REF] Yadav | Golgi positioning[END_REF]. In addition to that, it was shown that The Golgi complex could be regulated separately from the centrosome by an actin-dependent mechanism [START_REF] Magdalena | Microtubule involvement in NIH 3T3 Golgi and MTOC polarity establishment[END_REF]. This regulation pathway involves PI(4)P, GOLPH3, MYO18A and F-actin (Figure 1.32). GOLPH3 is a protein that can bind PI(4)P at the Golgi and bridge it to the actin cytoskeleton [START_REF] Dippold | GOLPH3 Bridges Phosphatidylinositol-4-Phosphate and Actomyosin to Stretch and Shape the Golgi to Promote Budding[END_REF]. In a polarized migrating cell, actin polymerization is the most active at the leading edge and creates a gradient of F-actin. It was proposed that increased density of F-actin leads to an increased chance of interaction with MYO18A, an unconventional myosin motor. This motor protein interacts with the Golgi localized GOLPH3 protein and pulls on it. As the F-actin and MYO18A concentration is higher on one side of the Golgi, it creates and imbalance in the pulling force, which equalizes once the Golgi complex reorients and faces the leading edge [START_REF] Xing | GOLPH3 drives cell migration by promoting Golgi reorientation and directional trafficking to the leading edge[END_REF], Xie et al., 2018]. It shows that both MT and actin cytoskeletons act in the Golgi reorientation process. The importance of Golgi's close physical proximity to the centrosome has been recently questioned [START_REF] Tormanen | Function of Golgi-centrosome proximity in RPE-1 cells[END_REF], pointing to the fact that the most important element for polarized secretion and cell migration is the Golgi complex positioning in the cell center [START_REF] Hurtado | Disconnecting the Golgi ribbon from the centrosome prevents directional cell migration and ciliogenesis[END_REF]. A large part of cell migration experiments are conducted on cells moving in 2D, crawling on a substrate. It was suggested that Golgi positioning in front or behind the nucleus is dependent on the geometry of the cell. When put on one dimensional tracks, the same cells could migrate with their Golgi behind the nucleus, while switching to 2D made the Golgi complex reorient in front of it. Golgi position seemed to clearly depend on the width of the path [START_REF] Pouthas | In migrating cells, the Golgi complex and the position of the centrosome depend on geometrical constraints of the substratum[END_REF]. In another example migrating cells seemed to commit to Golgi position either in the rear or the front of the cell and had persistently kept it, making stabilization the most important property of the Nucleus-Golgi axis [START_REF] Natividad | Golgi Stabilization, Not Its Front-Rear Bias, Is Associated with EMT-Enhanced Fibrillar Migration[END_REF].

Figure 1.32: Model for GOLPH3-dependent Golgi reorientation and directional trafficking in wound healing. After cell monolayer wounding, an imbalance across the Golgi in the GOLPH3/MYO18A/F-actin machinery pulls the PI(4)P-rich Golgi to reorient toward the leading edge. As a functional consequence of Golgi polarization, directional trafficking occurs toward the leading edge, which is required for cell migration. Taken from [START_REF] Xing | GOLPH3 drives cell migration by promoting Golgi reorientation and directional trafficking to the leading edge[END_REF].

Persistent migration

Migrating cells react to external cues and choose the direction of movement accordingly. The gradients of external cues can manifest as soluble molecules (chemotaxis), substrate adhesivity (haptotaxis), surface stiffness (durotaxis) and even electric current (galvanotaxis) [START_REF] Petrie | Random versus directionally persistent cell migration[END_REF]. More evidence is accumulating that cells can also recognize topographic patterns of their surroundings [START_REF] Caballero | Ratchetaxis: Long-Range Directed Cell Migration by Local Cues[END_REF], Lo Vecchio et al., 2020]. However, besides external regulation, cells also have an intrinsic directionality, and are able to move persistently even without a directional external cue or under uniform stimulation [START_REF] Petrie | Random versus directionally persistent cell migration[END_REF]. Cells retain a certain type of "memory" that enhances persistence in cell migration. Four informative parameters can be extracted from the trajectory of the migrating cell, that would help to quantify its directionality. They are -(i) centre of the cell mass at each time point, (ii) the distance travelled between positions (path length), (iii) the turning angle (Θ) and (iv) the net displacement (see Figure 1.33 [START_REF] Petrie | Random versus directionally persistent cell migration[END_REF]. Having these, cell directional persistence can be measured in several different ways -directionality ratio, mean square displacement (MSD) and direction auto-correlation [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF]. Each one of these methods has its advantages and disadvantages and complement each other in the information provided. Directionality ratio compares the ratio of cell displacement over the sum of path lengths between different positions (path 1 + path 2 + ...) (Figure 1.33). The closer the ratio is to 1, the more directional a cell is moving. MSDs give us information about the area explored by the cell over time, which describes the efficiency of migration. The MSD slope ratio of 2 means that a cell is moving in a straight line and 1 is for randomly moving cells. Direction auto-correlation compares how the turning angle (Θ in this case) correlates in different timescales. Its decaying slope instructs us about the persistence time of a moving cell [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF]. At each time point, the migration can be defined by the centre of the cell mass, the distance travelled between positions (path length), the turning angle (Θ) and the net displacement. This information can be used to describe the rate and directionality of migration. Adapted from [START_REF] Petrie | Random versus directionally persistent cell migration[END_REF].

A "protrusion-based" general model of mesenchymal cell migration converges on a mechanism where a cell achieves persistent migration by stabilizing protrusions and maintaining the orientation of the leading edge [Petrie et al., 2009, Andrew andInsall, 2007]. Cells generate protrusions stochastically by local excitation of either PI3K [Weiger et al., 2009,Arrieumerlou andMeyer, 2005] or Cdc42 [START_REF]Locally excitable Cdc42 signals steer cells during chemotaxis[END_REF]. Both of these signals are able to activate Rac1 and actin polymerization that creates a local protrusion [START_REF] Bosse | Cdc42 and Phosphoinositide 3-Kinase Drive Rac-Mediated Actin Polymerization Downstream of c-Met in Distinct and Common Pathways[END_REF]. These locally created protrusions are then stabilized, leading to directional persistence in cell migration. Multiple different models have been proposed to describe the mechanism of protrusion stabilization and persistent cell migration, implicating differential Rho GTPase activity [START_REF] Pankov | A Rac switch regulates random versus directionally persistent cell migration[END_REF], directed trafficking and secretion [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF], Shafaq-Zadah et al., 2016, Hao et al., 2020], internal retrograde flows [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF], Yolland et al., 2019, Zhang et al., 2014, Zhang et al., 2017], structural changes [START_REF] Gan | Vimentin Intermediate Filaments Template Microtubule Networks to Enhance Persistence in Cell Polarity and Directed Migration[END_REF] and membrane tension [START_REF] Batchelder | Membrane tension regulates motility by controlling lamellipodium organization[END_REF], Houk et al., 2012] or adhesions [START_REF] Hennig | Stick-slip dynamics of cell adhesion triggers spontaneous symmetry breaking and directional migration of mesenchymal cells on one-dimensional lines[END_REF], Sens, 2020, Ron et al., 2020], to mention just a few.

Pankov et al. reports that persistent cell migration depends on total Rac1 activity. If Rac1 expression in cells is high, they form multiple lateral protrusions, lowering the migration persistence. Decreasing Rac1 activity leads to a formation of one stable protrusion and directionally persistent migration (see Figure 1.34) [START_REF] Pankov | A Rac switch regulates random versus directionally persistent cell migration[END_REF]. Rac activation that is too low or too high leads to immobilization, with stunted lamellae at low levels and continuous, circumferential lamellae or cell rounding at very high levels. The cells shown in the examples were primary human fibroblasts stained for Rac1 after culturing on a 2D substrate (state III) or in a 3D matrix (state II) compared with effects of extensive knockdown of Rac1 using 200 nM Rac siRNA (state I) or overexpression of constitutively activated Rac QL after transient transfection (state IV). Taken from [START_REF] Pankov | A Rac switch regulates random versus directionally persistent cell migration[END_REF].

Yadav et al. presents a model where directed secretion from the pericentrosomally positioned Golgi complex is facing the leading edge and plays the central role in stabilizing the front protrusion and promoting cell migration. Dispersal of the Golgi by depleting golgins golgin-160 and GMAP210, disturbs polarized secretion, while keeping global secretion kinetics normal. This abolishes cells' ability to polarize and migrate directionally (Figure 1.31) [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF]. Hao et al. further develops the idea of directed secretion from the leading edge facing Golgi complex. They propose that Golgi-associated MTs are enriched at the cell area facing the leading edge and serve as "fast tracks" for the secreted cargo. Golgi-associated MTs are shown to have less lattice repair sites and MT intersections, which makes anterograde cargo vesicle movement faster [START_REF] Hao | Golgi-associated microtubules are fast cargo tracks and required for persistent cell migration[END_REF]. Shafaq-Zadah et al. demonstrates the importance of retrograde transport of adhesion proteins β1-integrins. They are transported from the plasma membrane back to the TGN and resecreted towards the leading edge of a migrating cell in a polarized manner. This process helps to relocalize integrins from the previous sites of function towards the leading edge and promote persistent cell migration (Figure 1.35) [START_REF] Shafaq-Zadah | Persistent cell migration and adhesion rely on retrograde transport of β 1 integrin[END_REF]. Maiuri et al. has revealed the importance of actin retrograde flows and their relation to cell speed and persistence. A universal relationship was revealed: the faster a cell goes, the more persistent it is. Actin retrograde flow is generated by actin polymerization at the leading edge and actomyosin contraction at the trailing edge, and is directly translated to cell speed via cellular attachments to the environment (adhesion or friction) and turned into traction forces, which pull the cell forward. The retrograde flows are able to transport polarity cues by advection, enhancing cellular asymmetry. With this mechanism, for example, polarity cues that would reduce cell migration are fast depleted from the leading edge, stabilizing cell polarity and increasing migration persistence (Figure 1.36) [START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF]Voituriez, 2016]. Actin flows were also proposed to play the role of "cellular memory". Actin flows were shown to be stable for longer than fluctuating edge protrusions and correlated better with cell directionality. This feature might be cell-type specific and necessary for cells to efficiently explore their environment, without losing their movement direction [START_REF] Yolland | Persistent and polarized global actin flow is essential for directionality during cell migration[END_REF]. A somewhat similar model for persistent migration generated by the transport of polarity cues was proposed by Zhang et al. In their model the inhibitory cues are transported via microtubules, instead of actin retrograde flow. The disruption of MTs by Nocodazole lead to oscillatory cell movement and decrease in persistence (Figure 1.37) [START_REF] Zhang | Microtubules stabilize cell polarity by localizing rear signals[END_REF]. This proposition was followed by a report showing that it is the position of the centrosome that regulates transport in inhibitory cues along MTs and defines the rear of the cell. Inhibitory cues are transported from the leading edge towards the centrosome and are concentrated there, which gives rise to the retraction of the rear of the cell (Figure 1.38) [START_REF] Zhang | Cryo-EM Reveals How Human Cytoplasmic Dynein Is Auto-inhibited and Activated[END_REF]. Another "cellular memory" mechanism was proposed by Gan et al., where it is structured by intermediate filaments. While the propulsion of the migrating cell is generated by a short lived dynamic actomyosin network (∼30s), spatiotemporal orchestration of signalling cues largely depends on dynamic MT network (3-5 min). Vimentin intermediate filaments (VIFs) closely interact with MTs and create a structural copy of the previously polarized MT network. VIF network is long lived compared to MTs (>10 min) and can serve as a template for the new MT growth, stabilize the position of a protrusion and enhance cell's directional persistence (Figure 1.39) [START_REF] Gan | Vimentin Intermediate Filaments Template Microtubule Networks to Enhance Persistence in Cell Polarity and Directed Migration[END_REF].

Figure 1.39: Vimentin and Microtubule interactions. Left: hierarchy of events leading to cell polarization and directed migration. The vimentin (VIF) network, which constitutes the third cytoskeleton component in mesenchymal cell migration, assembles along microtubules. Hence, VIFs establish a structure copy of the microtubule network with 4-to 5-fold slower turnover (>10 min for VIFs, 3-5 min for microtubules). Right: schematic of cytoskeleton organization in a polarized, migrating cell with and without vimentin. Propulsion of the cell front is driven by polymerization of a dense network of actin filaments. Net traction of the cell body is enabled by a front-rear gradient in adhesion and contraction of cortex and actomyosin bundles aligned with the axis of migration. The vectorial asymmetry of the actomyosin and adhesion machineries depends on spatiotemporal orchestration of many signaling cues, which are organized to a large extent by a dynamic microtubule network, partly in response to extracellular guidance cues. Taken from [START_REF] Gan | Vimentin Intermediate Filaments Template Microtubule Networks to Enhance Persistence in Cell Polarity and Directed Migration[END_REF]. Houk et al. proposes that membrane tension could work as a long-range inhibitor of lateral lamellipodia formation and keep one stable protrusion. Membrane tension doubles during a leading edge protrusion, and increased tension is transmitted through the full perimeter of the cell, inhibiting actin assembly and protrusion formation elsewhere (Figure 1.40) [START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF], Batchelder et al., 2011]. Protrusion at the leading edge generates mechanical tension (T, depicted as red springs) in either the plasma membrane or the underlying cytoskeleton. This tension acts as a long-range inhibitor of protrusion. Taken from [START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF]. Hennig et al. has presented a model where cells can break symmetry by stochastically detaching adhesive contacts on one side. This results in a migration initiation on the other side. Longer cells were shown to be slower. It correlated with larger spreading and more adhesions formed, which are hard to break, so the movement is slowed (Figure 1.41) [START_REF] Hennig | Stick-slip dynamics of cell adhesion triggers spontaneous symmetry breaking and directional migration of mesenchymal cells on one-dimensional lines[END_REF]. The model, relying on stick-slip dynamics, was further developed theoretically to explain the persistence of migration, by coupling cell polarization state to cell length [START_REF] Ron | One dimensional cell motility patterns[END_REF] and adding a membrane tension component [Sens, 2020].

Figure 1.41: Deduced scheme of the proposed stick-slip migration mechanism: During nonmotile spreading (stick), the cell builds up a high traction force that eventually will overcome adhesion strength in the perspective rear of the cell. Upon the retraction of the rear, the cell shortens and lowers its mechanical interaction with the substrate to initiate migration (slip). Taken from [START_REF] Hennig | Stick-slip dynamics of cell adhesion triggers spontaneous symmetry breaking and directional migration of mesenchymal cells on one-dimensional lines[END_REF].

All in all, direction persistence in migrating cells is possibly regulated by multiple mechanisms increasing cellular asymmetry and stabilizing the movement direction. As this process involves several different feedback loops, it is sensitive to perturbations where one or another protein is overexpressed or depleted. It is important to perturb the system locally and transiently, to be able to dissect these complex processes. Recently, a new technique called optogenetics was put to use in cell biology. It applies light to perturb cell function of interest in a localized and timely manner.

Optogenetics

Optogenetics is a biological technique, which involves any genetically encoded protein system designed to accomplish a specific light-mediated task [START_REF] Wittmann | Lights, cytoskeleton, action: Optogenetic control of cell dynamics[END_REF]. Its application spans from neuroscience [START_REF] Kim | Integration of optogenetics with complementary methodologies in systems neuroscience[END_REF], Boyden, 2015] to embryonic development [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF], Hartmann et al., 2020] and allows us to study complex signalling networks with precise perturbation. Inhibiting a protein or changing gene expression are comparably slow processes and can't give us an accurate representation of rapid intracellular dynamics. A slow perturbation gives the system time to reach a new steady state or compensate for the lost function, which makes it difficult to interpret [START_REF] Wittmann | Lights, cytoskeleton, action: Optogenetic control of cell dynamics[END_REF],Krueger et al., 2019,Hartmann et al., 2020]. Conversely, optogenetic activation can be controlled in time and space, in different patterns. Moreover, it can be applied with subcellular precision, in this case activating only one specific part of the cell [START_REF] Kichuk | Lights Up on Organelles: Optogenetic Tools to Control Subcellular Structure and Organization[END_REF],Krueger et al., 2019,Meshik et al., 2018, Rost et al., 2017, Karunarathne et al., 2015].

Optogenetic tools

Optogenetics relies on naturally found photoresponsive protein domains, that undergo conformational changes in response to light [START_REF] Hartmann | Using optogenetics to tackle systems-level questions of multicellular morphogenesis[END_REF]. This protein type is abundant in light-reactive forms of life, like plants and cyanobacteria [Hegemann andNagel, 2013, Yizhar et al., 2011]. When introduced into animal cells, they work in an orthogonal manner and can be engineered to excite different systems in a cell [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF], Liu and Tucker, 2017, Tischer and Weiner, 2014]. Optogenetics started as a technique to activate neuron signalling in animals in vivo, and the first tools were channelrhodopsins (ChRs) [START_REF] Kim | Integration of optogenetics with complementary methodologies in systems neuroscience[END_REF], Hegemann and Nagel, 2013, Yizhar et al., 2011]. These are channel proteins, which open upon activation with light. When introduced into a neuronal membrane, they cause and influx of ions to the cell and a change in membrane potential, which translates into a neuronal signal [Hegemann andNagel, 2013, Kim et al., 2017].

A second generation of optogenetic tools was based on the ability of proteins to dimerize (1.42, (A)), cluster (1.42, (B) and (C)) or unfold (1.42, (D)) upon the ilumination with light [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF],Johnson and Toettcher, 2018,Tischer and Weiner, 2014]. The modular nature and variability of these systems enables the control of multiple signalling pathways in the cell. The activation is possible by localizing signals to a specific part in the cell, increasing local concentration by clustering or revealing active protein sites by uncaging parts of the protein [START_REF] Guntas | Engineering an improved light-induced dimer (iLID) for controlling the localization and activity of signaling proteins[END_REF], Taslimi et al., 2014, Wu et al., 2009]. It is also possible to inhibit the activity by trapping and sequestering a protein from its place of function [START_REF] Niopek | Optogenetic control of nuclear protein export[END_REF], Lee et al., 2014].

Three most commonly used dimerizing optogenetic modules are: light-oxygenvoltage (LOV) domain (e.g. iLID [START_REF] Guntas | Engineering an improved light-induced dimer (iLID) for controlling the localization and activity of signaling proteins[END_REF], TULIPs [START_REF] Strickland | TULIPs: tunable, light-controlled interacting protein tags for cell biology[END_REF]), Cryptochrome (Cry2/CIBN [START_REF] Kennedy | Rapid blue-light-mediated induction of protein interactions in living cells[END_REF]) and Phytochrome based systems (PhyB/PIF [START_REF] Levskaya | Spatiotemporal control of cell signalling using a light-switchable protein interaction[END_REF]) (see Figure 1.43). These modules vary in several different parameters -activation wavelength, activation reversal time, cofactors, molecular size. While iLID and Cry2/CIBN systems are activated by blue light (450 nm), with reversal time of ∼20 s and ∼3 min, respectively, the PhyB/PIF system is activated by red light (660 nm) and stays stable for ∼20 hours. However, it can be inactivated by far-red light (750 nm) [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF], Wittmann et al., 2020]. All three modules need co-factors to be activated. LOV domain of iLID system binds FMN, while Cry2 binds FAD and ATP. Both are readily available inside the cells. The co-factor for PhyB/PIF system Phytochromobilin (PCB) needs to be administered exogenously, which makes it a little harder to implement. Finally, the size of the modules are important to have in mind, when considering steric hindrance. iLID is the smallest (AsLOV2: 16 kDa, SspB: 13 kDa), Cry2 is almost 4 times as large (Cry2: 57 kDa, CIBN: 20 kDa) and PhyB comes as largest (PhyB: ∼100 kDa, PIF: 11,5 kDa) [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF], Wittmann et al., 2020].

Figure 1.42: Approaches to controlling protein activity using optogenetics. In all panels, photoreceptors are depicted in blue, their binding partners in green and proteins of interest in gray. (A) Light-induced protein dimerization can be used to recruit a protein of interest to a specific intracellular location, where it can pursue its function. (B) Light-dependent oligomerization (clustering) can induce active functional signaling hubs or inhibit protein function. (C) Light-induced dimerization can also be adopted to sequester a protein of interest away from its site of action. (D) Photo-uncaging based on LOV domains can be used to directly control protein activity with light. Taken from [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF].

Though optogenetics is a versatile tool, it is important to know its limitations as well. The sharpness of optogenetic activation pattern depends both on the diffraction limit and photochemistry kinetics. If an optogenetic system reverts to its inactive state fast (seconds), its activation can be kept local, but if the inactivation kinetics extend to minutes and hours, the activated molecule would have enough time to diffuse and spread. In addition to that, fast reverting systems need to be activated frequently, to keep the signal on, which might be toxic for cells [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF]. Moreover, it needs to be taking into account that a certain base level of activation is possible in the system as well (leakiness). Finally, overlapping excitation spectra of fluorescent labels and optogenetic activation are of importance. Choosing an optogenetic system that is activated with blue light, leaves red and far-red parts of the spectrum for labelled proteins, if to avoid unwanted overactivation of the optogenetic system [START_REF] Wittmann | Lights, cytoskeleton, action: Optogenetic control of cell dynamics[END_REF].

In the last decade, the use of optogenetics have expanded into diverse fields of cell biology, from gene expression to organelle positioning to cell migration (Figure 1.44) [START_REF] Kichuk | Lights Up on Organelles: Optogenetic Tools to Control Subcellular Structure and Organization[END_REF]. Upon blue-light illumination, the photosensitive protein CRY2 undergoes a conformational change and binds to its interaction partner CIBN. (C) Phytochrome (PHYB/PIF). The phytochrome system consists of the PHYB photoreceptor, which binds to its interaction partner PIF upon red-light illumination. Far-red illumination causes the PHYB/PIF interaction to dissociate, making the optogenetic system reversible. PHYB activity depends on the plant-specific co-factor PCB. Adapted from [START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF].

Figure 1.44: Optogenetic control of subcellular structure and organization. Light-induced modules allow for photosensitive control over protein secretion, accumulation, and degradation in addition to nuclear import and export. Optogenetic systems also allow for manipulation of plasma membrane morphology, organelle transport, cell death signaling, and mitochondrial membrane potential. Taken from [START_REF] Kichuk | Lights Up on Organelles: Optogenetic Tools to Control Subcellular Structure and Organization[END_REF].

Optogenetics in cell migration

Cell migration emerges from a coordination of several signalling pathways and structural reorganizations in the cell. To better understand these processes, most of these steps can be controlled with optogenetics [START_REF] Wittmann | Lights, cytoskeleton, action: Optogenetic control of cell dynamics[END_REF], Meshik et al., 2018, Karunarathne et al., 2015].

Cell migration can be initiated by G-protein coupled receptors (GPCRs). Several approaches have been lead to activate cell migration at this step with re-engineered opsin proteins that are coupled to G-proteins [Ajith Karunarathne et al., 2013a[START_REF] Karunarathne | Optical control demonstrates switchlike PIP3 dynamics underlying the initiation of immune cell migration[END_REF]. Going one level downstream the signaling pathway, cell migration was triggered by locally controlling G-protein inhibition in spatially uniform chemoattractant environment using Cry2/CIBN system [O' Neill and Gautam, 2014]. Activating PI3K, the kinase responsible for PIP 3 generation, which recruits Rac1 Rho GTPase was also carried out with PhyB/PIF system [START_REF] Graziano | A module for Rac temporal signal integration revealed with optogenetics[END_REF]. Going even more downstream the signaling pathway of cell migration is the activation of Rho GTPases, through light-dependent recruitment of their GEFs. It is probably the most explored approach and multiple optogenetic systems were used to implement this [O' Neill et al., 2016, Guntas et al., 2015, Valon et al., 2015, Levskaya et al., 2009]. All three optogenetic dimerizers -iLID, Cry2/CIBN and Phyb/PIF -were used achieving spatiotemporal control Cdc42, Rac1 and RhoA small GTPases (Figure 1.45). Finally, uncaging technique of LOV domain was used to create a photoactivatable Rho GTPase Rac1, able to elicit direct actin remodelling and cell migration [START_REF] Wu | A genetically encoded photoactivatable Rac controls the motility of living cells[END_REF], Wang et al., 2010, Winkler et al., 2015]. Cellular trafficking and organelle positioning is closely related to cell migration and optogenetic methods have also been used to dissect these pathways [START_REF] Kichuk | Lights Up on Organelles: Optogenetic Tools to Control Subcellular Structure and Organization[END_REF], Wittmann et al., 2020]. MT tracks, used for trafficking, and MT dynamics were optogenetically controlled by crosslinking MT plus ends with F-actin [START_REF] Adikes | Control of microtubule dynamics using an optogenetic microtubule plus end-F-actin cross-linker[END_REF] or by EB1 photodissociation [Van Haren et al., 2018]. Optogenetic cargo recruitment and organelle repositioning by motor proteins was elegantly engineered with LOV2 module based TULIPs system [van Bergeijk et al., 2015] and later improved by using the iLID system and a photosensitive motor protein, which homodimerizes and becomes functional only upon illumination with blue light [START_REF] Nijenhuis | An optimized toolbox for the optogenetic control of intracellular transport[END_REF]. Another LOV-based system was created for light-controlled control of motor protein speed by changing the conformation of a motor's lever arm, comparable to "optical gearshifting" [START_REF] Nakamura | Remote control of myosin and kinesin motors using light-activated gearshifting[END_REF]. Finally, optogenetic perturbation, termed IM-LARIAT, was also used to reversibly oligomerize Rab GTPases and reveal their different functions in membrane trafficking [START_REF] Nguyen | Optogenetic oligomerization of Rab GTPases regulates intracellular membrane trafficking[END_REF].

PhD hypothesis

Single cells on 2D substrate perform random migration even in the absence of external cues. Depending on the cell type, cells are either staying in place or can move over relatively long distances of hundreds of micrometers per day. In the latter case, cells are able to polarize and perform stretches of persistent cell movement, which could be perceived as "efficient migration", as the cell is moving in a directional manner. In my thesis research, I hypothesized that this persistent cell migration emerges from the coordination between cell protrusions and intracellular organization. This coordination works like a feedback, and the two sides of it reinforce each other. Protrusions arise stochastically and can be stabilized by the asymmetric distribution of organelles and polarized trafficking that follows. I simplified the cell to a system of two parts -1) biochemical gradients, generating protrusions (Figure 1.46, "Biochemical gradients"), and 2) polarity axis, representing internal organization (Figure 1.46, "Cell internal organization"). To induce cell protrusions, I employed optogenetics to activate the RhoGTPase Cdc42, responsible for control of actomyosin cytoskeleton and enabling generation of stochastic protrusions. To quantify and analyze intracellular organizaton, I have chosen the axis going through the center of Nucleus and the center of the Golgi complex as a proxy for polarity axis (Figure 1.46). For a study model, I chose an hTERT RPE1 ("retinal pigment epithelial") immortalized cell line, as these cells are known to be persistent as mesenchymal-type cells [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF] and have reproducible internal organization [START_REF] Schauer | Probabilistic density maps to study global endomembrane organization[END_REF].

Results

Imaging feedback routine to follow a migrating cell

Cell migration is a dynamic process that requires a live imaging system, which is able to follow cells on time scales of hours and spatial scales of several millimeters. In order to image cell movement without the cell escaping the camera's field of view, we choose a low magnification objective (10x), with a field of view covering hundreds of micrometers. Unfortunately, in this case we lose the resolution and detailed appearance of cell protrusions and organelles (see Figure 2.1, A). Instead, we opted to keep the high resolution (60x) imaging (Figure 2.1, B), and add a possibility to move the microscope stage, once a cell starts moving out of the field of view. Together with an M1 student William Beng, we have developed a live-imaging feedback routine, which extracts the shape of the cell from the image taken in real time, finds the centroid of the shape and aligns it with the previous center (explained in more detail in Methods and Materials section 4.10.2). This routine keeps the cell in the middle of the field of view as long as the experiment runs, letting us follow the cell throughout it, and reconstruct its trajectory from the obtained coordinates.

Persistent protrusion forms in front of the Golgi complex

Mesenchymal cell migration is invariably related to membrane protrusions that are formed [START_REF] Dolati | On the relation between filament density, force generation, and protrusion rate in mesenchymal cell motility[END_REF]. First, we tested if the position of protrusive activity is geometrically related to the position of aforementioned polarity axis going through the centroids of the nucleus and the Golgi complex (Nucleus-Golgi axis). To visualize the Nucleus-Golgi axis, we have fluorescently labelled the nucleus, the Golgi complex and the membrane of the hTERT RPE1 cells. The membrane label provides high contrast imaging of cell borders and lets us quantify the shape of the cell, find its center of mass and follow the cell's position with our imaging routine mentioned in the paragraph above (see also 4.10.2). The other two labels let us quantify the positions of the nucleus and the Golgi complex. We were kindly provided with an RPE1 stable cell line overexpressing a GFP-Rab6A GTPase construct as a Golgi complex label. We infected this stable cell line with lentiviral particles of myr-iRFP construct and, like that, incorporated a label for the membrane (for protocol, see 4.4). We used a Hoechst 33342 (1 µM for 30 min) fluorescent stain to label the nucleus.

I imaged cells migrating in 2D on a fibronectin covered coverslip (for protocol, see 4.5) for 16h (Figure 2.2, A), plotted the trajectories and quantified the angle (α) between the direction of movement, which is defined as a vector between the center of mass of a cell in two consecutive time frames (Figure 2.2, B, black dashed arrow), and Nucleus-Golgi axis (Figure 2.2, B, orange dashed arrow). A polar histogram of averaged angles from the full dataset (n=17) shows that the angle between the two axes stays in the range of +/-30°from direction of movement (Figure 2.2, C). Thus, there is a correlation between the direction of movement and the Nucleus-Golgi axis (Figure 2.2). To evaluate protrusive cell activity, we further quantified it by constructing morphodynamic maps of cell shape changes. We have divided the border of the cell membrane to 100 markers and compared their position frame by frame (for detailed explanation see 4.11.5). From this information we were able to deduce, at which marker points the cell was protruding and where it was retracting. To simplify visualization, we have stretched the whole border to a line and, like this, were able to visually graph the evolution of membrane protrusions and retractions in time (Figure 2.3, (A)). We have normalized the map according to the position of the Nucleus-Golgi axis. The black line in the middle of the map depicts the point on the membrane, where Nucleus-Golgi axis is pointing to. Every point on the map corresponds to a particular distance travelled by the membrane in a timeframe (t=5 min) and can be expressed as protrusion speed (see Figure 2.3, (B)). If averaged over the full dataset (n=17), the peak of protrusion speed is localized close to the point were Nucleus-Golgi axis is crossing the membrane, indicating that position of Nucleus-Golgi axis correlates with the direction of protrusion activity (see Figure 2.3, (C)). We have also plotted morphodynamic maps normalized to the direction of movement. In this case, the highest protrusion speed is centered on the direction of movement (Figure 2.4, (A)). Because the peak of protrusion speed is thinner and exactly at the center line, our data indicate that the cell moves where it protrudes (Figure 2.4, (B)). Altogether, the directionality of cell movement is given by the protrusions, the Nucleus-Golgi axis points towards protruding activity, and thus, the Nucleus-Golgi axis position is correlated to the direction of movement.

Nucleus-Golgi axis and direction of movement align when a cell starts moving

We have seen that Nucleus-Golgi axis aligns to the direction of movement in a migrating cell, but, so far, it described migrating cells that have started the process of locomotion before the start of experiment. To investigate the process of initiation of cell migration and the position of Nucleus-Golgi axis before the cell starts moving, we used a dynamic micropattern assay (Figure 2.5, (A)). Cells are confined to round patterns of fibronectin (d=35 µm) that induce an isotropic shape. The advantage of a dynamic micropattern is a possibility to release the cells from a pattern at a given point of time, mimicking the start of migration (Figure 2.5, for the protocol, see 4.5).

We have noticed that after the release from the pattern, the cells did not move out for the first several hours, and were protruding in different directions without establishing a clear direction of movement (Figure 2.5, (B)). This is also visualized in several schematized examples, depicted in Figure 2.6, representing actual cells in the experiment, showing the movement of Nucleus-Golgi axis. The blue lines show the position of the Nucleus-Golgi axis at the start of the experiment and the color evolves towards the red lines, representing the position of the axis at the end of experiment. Looking at first example on the second row, it is visible that the cell was protruding in several different positions before moving out of the pattern (blue and red lines facing outward).

We have quantified the angle between the direction of movement (Figure 2.5, (B), orange dashed line) and Nucleus-Golgi axis (Figure 2.5, (B), black dashed line). As a point of reference for direction of movement, we took the time point when the center of nucleus crosses the border of the pattern (Figure 2.5, (B), "ESCAPE" and Figure 2.7) and drew a line through the center of nucleus and center of the pattern (Figure 2.5, (B), orange dashed line). We have quantified the angle between this axis and the initial position of Nucleus-Golgi axis (Figure 2.8, (A)) or its position at the moment of "escape" (Figure 2.8, (B)). The initial (t=0) Nucleus-Golgi axis position didn't correlate with direction of movement, but the two axes reproducibly aligned at the moment of "escape" (t=ESCAPE) (Figure 2.8, (A) and (B), respectively). This indicates that Nucleus-Golgi axis aligns to the direction of movement when the cell establishes its direction of migration and actually starts moving.

The question of causality remains open: is it the protrusion that defines the direction of movement, or is it the Nucleus-Golgi axis? To study this, we have examined the evolution of Nucleus-Golgi axis (Figure 2.9, black line) and cell movement (Figure 2.9, orange line) until the point when the cell "escapes" the pattern. We have plotted the evolution of the axes positions and found that the two events are concomitant. The two axes start converging towards the point of "escape" approximately at the same time (Figure 2.9, black and orange arrows). The fact that we cannot distinguish the order of events suggests that neither protrusion, nor Nucleus-Golgi axis defines the "escape". It seems that the processes are coordinated, rather than an ordered sequence of events.

To dissect this process, we decided to use a perturbative approach, trying to disconnect the protruding activity from the internal polarity axis.

Dispersing the Golgi complex diminishes persistence of migration

The Golgi complex is proposed to play an important role in polarized secretion [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF]. Interestingly, the compact Golgi complex is found behind the nucleus in amoeboid movement and in front of the nucleus in mesenchymal movement, but the functional importance of it is not yet fully understood [Orlofsky, 2019].

Following my PhD hypothesis that persistent cell migration emerges from the coordination between cell protrusions and intracellular organization, we conducted a series of experiments, where we disrupted the Golgi complex with the help of drugs in order to inhibit polarized transport. We have tested three different drugs known to interfere with the Golgi complex integrity -Brefeldin A [Fujiwara et al., 1988,Dinter andBerger, 1998], Golgicide A [START_REF] Sáenz | Golgicide A reveals essential roles for GBF1 in Golgi assembly and function[END_REF] and Nocodazole [START_REF] Dinter | Golgi-disturbing agents[END_REF]] (for a protocol see 4.6).

Brefeldin A (BFA) is a drug used to disperse the Golgi complex towards the ER exit sites [START_REF] Beck | The COPI system: Molecular mechanisms and function[END_REF]. It reversibly targets three GEFs of Arf1 GTPase -BIG1, BIG2 and GBF1 [START_REF] Niu | Dynamics of GBF1, a Brefeldin A-Sensitive Arf1 Exchange Factor at the Golgi[END_REF], Sáenz et al., 2009, Boal et al., 2010]. This GTPase is involved in recruiting the coat proteins required for COPI vesicle formation and is essential for proper vesicle budding at the Golgi complex cis side [START_REF] Kawamoto | GBF1, a guanine nucleotide exchange factor for ADP-ribosylation factors, is localized to the cis-Golgi and involved in membrane association of the COPI coat[END_REF]. If the process is inhibited, the vesicle exchange between ER and the Golgi complex and ER protein recycling is perturbed [Pelham, 1994]. Arf1 is also crucial for golgin-160 and dynein recruitment to Golgi membranes [START_REF] Yadav | Article Golgin160 Recruits the Dynein Motor to Position the Golgi Apparatus[END_REF].

First, we optimized the drug conditions for our experimental set-up according to [START_REF] Bershadsky | Disruption of the Golgi apparatus by brefeldin A blocks cell polarization and inhibits directed cell migration[END_REF], Alvarez and Sztul, 1999, Abraham et al., 2016]. We have performed cell migration experiments of 16h with addition of BFA at the beginning of the experiment. We have used three different BFA concentrations, going from 5 µg/mL (18 µM), through 1 µg/mL (3.5 µM), to as low as 0.2 µg/mL (1 µM). Using all three concentrations, the Golgi complex was successfully dispersed in the first 5 min of the experiment, but even the lowest BFA concentration induced a change in cell morphology. Instead of forming thin lamellipodial protrusions, cells switched to thick cylindrical-shaped lobopodia-type protrusions [Petrie et al., 2012, Sixt, 2012]. After a few hours (3-6h) with the drug, cells did not contract its protruding parts anymore, and eventually died (after ∼15h) (Figure 2.10). Golgicide A (GCA) is a drug with a very similar action mechanism as Brefeldin A, but, because of its structure, it targets GBF1, a GEF of Arf1, specifically [START_REF] Sáenz | Golgicide A reveals essential roles for GBF1 in Golgi assembly and function[END_REF]. GCA is a reversible inhibitor and degrades over time. Therefore, w have optimized the concentration of the drug, so that the effect of the Golgi complex dispersal stays for at least 6h (I used 35 µM concentration for further experiments, with Golgi dispersal duration of 6.2±0.9 h) (Figure 2

.11).

A similar effect on cell morphology could be visible as in the case of BFA addition. After the addition of GCA, lamellipodial protrusions would be exchanged with more cylindrical lobopodia-type protrusions, which would reversibly switch back to lamellipodial protrusions after the Golgi complex would reform (passing by a short episode of small blebs forming all through the cell) (Figure 2.12). Together with dispersal of the Golgi complex, GCA also affects the rate of secretion in cells [START_REF] Sáenz | Golgicide A reveals essential roles for GBF1 in Golgi assembly and function[END_REF], Ignashkova et al., 2017, Kaczmarek et al., 2017].

Nocodazole (NZ) is a drug, which inhibits microtubule (MTs) polymerization [De Brabander et al., 1976,Turner andTartakoff, 1989] and a drug that disperses the Golgi complex [Minin, 1997, Dinter andBerger, 1998], but, in low concentrations, does not affect the microtubule polymer level [START_REF] Liao | Low concentrations of nocodazole interfere with fibroblast locomotion without significantly affecting microtubule level: Implications for the role of dynamic microtubules in cell locomotion[END_REF], or the secretion process per se [Van De Moortele et al., 1993, Liao et al., 1995, Schmoranzer et al., 2003, Fourriere et al., 2016]. Low NZ concentration (0.1 µM) was described to induce slower MT growth and longer time spent pausing [START_REF] Mikhailov | Relationship between microtubule dynamics and lamellipodium formation revealed by direct imaging of microtubules in cells treated with nocodazole or taxol[END_REF]].

We hypothesized that the dispersal of the Golgi complex will inhibit polarized secretion and interfere with persistent migration. To quantify that we have constructed morphodynamic maps of the control cells and cells affected with Golgicide A (35 µM) or Nocodazole (0.1 µM). In all the cases cells show protrusive membrane activity (Figure 2.13, A-C). However, persistent protrusive activity, which is seen in control cells (Figure 2.13, A), is lost upon the addition of Golgicide A or Nocodazole (Figure 2.13,B and C,respectively). Protrusions seem to form randomly or travel around the perimeter of the cell as a wave. If the average protrusion speed is calculated from the morphodynamic maps, we can see that the speed is slightly reduced in the GCA experimental condition (12±2 µm/h), while in the NZ experimental condition (17±6 µm/h) cells protrude at the same speed as in control (16±5 µm/h) (Figure 2.14). The random protrusive membrane activity leads to loss of directionality in cell trajectories, as seen when trajectories are aligned to the same starting point in the x and y coordinates and plotted (Figure 2.15, A-C), while the average speed of movement remains the same in all conditions (Figure 2.16, A). We have measured the directionality of cell migration in two different ways, by calculating the directionality ratio and direction autocorrelation. Directionality ratio is calculated by dividing the shortest distance between the beginning and end points of a trajectory by the length of the actual trajectory of the cell. The closer the ratio is to 1, the more directional the cell is (Figure 2.16, (B)). However, the directionality ratio varies over the time course of cell trajectory and this is not captured in the standard end-point calculation. Direction autocorrelation analysis turns every move into a displacement vector and only takes into consideration the angle between the vectors at different time points. For each pair of vectors an autocorrelation coefficient is obtained, and varies from 1 (cell is moving directionally) to -1 (cell is moving to the opposite direction). After, coefficients are averaged and an autocorrelation curve decaying in time is obtained (Figure 2.17, (A)). The rate of decay gives us the cell persistence time and tells how prone a cell is to turn (Figure 2.17, (B)) [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF]. In our experiments both directionality ratio and direction autocorrelation give similar results. Control cells migrate with directionality ratio of 0.56±0.3, cells in GCA with 0.14±0.14 and in NZ with 0.08±0.03 (Figure 2.16, (B)). The persistence time is 2.3±1.4 h, 0.7±0.7 h and 0.3±0.3 h, for control cells, GCA and NZ respectively (Figure 2.17, (B)). In both cases, the experimental conditions with the drug show significantly lower directionality ratio and persistence time. Thus, after dispersing of the Golgi complex by two different mechanisms, the persistence of cell movement is impaired. We show that disrupting global secretion by Golgicide A and interfering with polarized trafficking by low concentrations of Nocodazole leads to loss of protrusion stabilization, as seen in the morphomaps (Figure 2.13) without severely affecting protrusion speed. Interestingly, our results show that dispersing the Golgi complex leads to the loss of a stably positioned protruding activity without affecting the cell ability to protrude. This suggests that an intact Golgi and aligned Nucleus-Golgi axis, is required for a persistently localized protruding activity. The N-G axis may serve as a "memory" or a "landmark" for protrusions to happen.

Trafficking from Golgi complex is biased towards the protrusion

We hypothesized that the persistence of cell migration is enhanced once protrusion activity is coordinated with internal organization (1.5). Hence, we tested if the flow of traffic is increased in front of the Golgi complex (towards the side where the Nucleus-Golgi axis is pointing), thus, creating a bias of polarized traffic. First, we have used the Retention Using Selective Hooks (RUSH) assay (for a detailed protocol, see 4.7) to test the pattern of cargo trafficking secretion from the Golgi complex. The RUSH assay lets us select a cargo and lock it in the ER by the interaction of streptavidin binding protein (SBP) in the ER and streptavidin on the engineered cargo construct. The release of the cargo can be easily controlled by addition of biotin, which has higher affinity to streptavidin and outcompetes the interaction with SBP. The cargo is released, and the process of trafficking towards its destination can be monitored thanks to the GFP labelled cargo construct, until all the labelled cargo is released. We chose a GFP labelled collagen X (Col10A), a secreted cargo, for our experiments. This cargo, once released is secreted and exposed to the outside of the cell. In order to measure the secretion localization of the cargo, we have coated the glass coverslips, on which we plated RPE1 cells, with anti-GFP antibodies (for protocol details, see 4.8). Once the cargo reaches the outside of the cell, it is captured by these antibodies, leaving a cumulative signature of all the cargo secreted during the assay. We have tracked secretion in 47 RPE1 cells and noticed that in 21 of them the secretion was not directed in front of the Nucleus-Golgi axis, but towards a newly formed protrusion (see Figure 2.18. More examples are seen in Figure 2.19, where cargo secretion is represented as secreted Col10A signature on a coverslip (Figure 2.19, (A)-(C)). These 21 cells, in which secretion was directed towards the protruson, were caught at the moment of turning, or generating a new protrusion. The other 26 cells from the dataset were more static. In these cells the trafficking pattern was spread through the whole cell, with a slight increase of secretion in the vicinity of the Golgi complex. Our experimental results suggest that secretion is directed to nascent protrusions and not necessarily in front of the Nucleus-Golgi axis. To test if secretion is perturbed in the presence of Golgicide A (GCA), we have conducted a RUSH experiment in presence of this drug. We have added GCA before releasing the RUSH cargo with biotin (Figure 2.20, (A) -the Golgi complex before addition of GCA, (B) -the Golgi complex is dispersed after addition of GCA). After the addition of biotin and Col10A cargo release, there was no noticeable secretion during the full period of 2 hours in the presence of the drug (Figure 2.20, (C) -cargo at the moment of release, (D) -cargo 2 h after release).

We have also looked at the trafficking of post-Golgi vesicles (Rab6A protein labelled with iRFP by using a CRISPR technique (4.4)) to quantify the trafficking pattern and its changes in a migrating cell in the period of hours. Thanks to our cell tracking routine (4.10.2), we were able to track cells in high resolution (60x) for long-term (16 h) live-cell imaging experiments. We were using TIRF microscopy (4.10.1), to image vesicles that are close to the substrate (Figure 2.21, A, upper panel). To investigate if vesicle trafficking is related to the forming cell protrusions, we have constructed morphomaps, showing plasma membrane protrusions over time (Figure 2.21, B, upper panel). To calculate the intensity of trafficking in every direction, we have divided the perimeter of a cell into 100 markers (similar to morphomap technique in 4.10.1) and drew straight lines towards the center of the Golgi complex from each one of them (Figure 2.21, A, lower panel). Then, we have calculated the fluorescence intensity along each line over time and constructed a trafficking morphomap, representing the traffic intensity (Figure 2.21, B, lower panel). We wanted to quantify, was it the protrusion forming first and the trafficking following, or was it the trafficking that initiated the protrusion? Following a technique from a recent paper [START_REF] Machacek | Coordination of Rho GTPase activities during cell protrusion[END_REF], we have calculated the temporal cross-correlation coefficient between protrusions and trafficking for each marker along the cell contour. Then, we averaged the cross-correlation for all markers (grey curves) and for all cells (red curve). The averaged cross-correlation presents a positive peak reaching 0.19±0.11 (n = 16 cells) for a positive lag of 21±13 min (Figure 2.21, C). This graph indicates that the protrusion is forming first and secretion follows with an average lag time of 21±13 min. This difference in timing is visible on the representative morphomaps as well (Figure 2.21, (B), dashed lines and the orange double arrow). The activity of membrane protrusions peaks (Figure 2.21, (B), upper panel) before the trafficking (Figure 2.21, (B), lower panel). Interestingly, we see that on this longer timescale of our experiment (16h), the traffic reorients towards the protrusion, then the reorientation of the Nucleus-Golgi axis follows and this intensified traffic continues in front of the Golgi complex (also visible in an example image in Figure 2.22, A, orange arrows). The visible flow of vesicles disappears after the addition of a Golgi complex disrupting drug Golgicide A (GCA) (Figure 2.22, B), correlating with a previously described result that GCA addition significantly decreases cell migration persistence (2.4). This suggests that the polarized flow of vesicles represents a platform for a reinforcement of the protrusion.

Biochemical gradient of Cdc42 activity reorients the Golgi complex

Our results show that polarized secretion is important for migration. Cellular protrusions that are needed for a cell to move are orchestrated by a network of RhoGT-Pases -proteins that are responsible for actin remodelling [Ridley, 2011, Warner et al., 2019c]. We chose to look at the gradients of one of the RhoGTPases -Cdc42. It is known not only for its involvement in actin remodelling, but also for its crucial role in establishing cell polarity [Etienne- Manneville, 2004]. We hypothesized that Cdc42 is involved in polarized secretion and reorientation of Nucleus-Golgi axis.

In order to experimentally control active Cdc42 localization and its activation levels, we used an optogenetic system described in [START_REF] Guntas | Engineering an improved light-induced dimer (iLID) for controlling the localization and activity of signaling proteins[END_REF]. In this system, Cdc42 is activated by bringing the catalytic DH-PH domain of one of its activators -GEF ITSN -at the plasma membrane, where it interacts with the pool of Cdc42 proteins and activate them. This optogenetic system is based on protein dimerization upon illumination with blue light. It comprises two protein parts -one is cytosolic (SspB) with a domain of ITSN attached, and the other is attached to the plasma membrane (iLID). When blue light is shone, the affinity of these two parts to each other increases, and the SspB is recruited to the plasma membrane. It carries the Cdc42 activator (ITSN DH-PH domain) with it and, thus, activates Cdc42 in the specified location (4.9). The place of activation can by controlled with engineered patterns of blue light, which can be applied either with a laser or with a LED light source (4.10.1). In our experimental set-up, we wanted to test if the position of Nucleus-Golgi axis can be controlled with an engineered biochemical gradient of Cdc42 and initiate Nucleus-Golgi axis reorientation. Using the previously described imaging routine (2.1), we added a possibility to induce Cdc42 activation, while imaging a migrating cell and adapt the activation pattern to the changing shape of the cell (see a detailed explanation in 4.10.3). Our previous experiments revealed that the sharp gradient of Cdc42 is the most effective to generate a protrusion [de Beco et al., 2018], therefore, we chose to activate a thin region along the border of the cell (Figure 2.23, first sketch on the left). We conducted 16 h live-cell imaging experiments, starting with the activation 90°away from the existing Nucleus-Golgi axis. We quantified the change in the angle between Nucleus-Golgi axis and optogenetic activation axis (going through the center of activation area and the center of nucleus) throughout the movie (Figure 2.24). The orientation can be appreciated in the excerpts of a movie in Figure 2.23. The Nucleus-Golgi axis is repositioning from 90°away towards the area of optogenetic activation, until it reaches it and stabilizes in that position (0°). We compared these results (n=19 cells) (Figure 2.25, (A)) with a control experiment (n=26 cells), in which ITSN is missing. The Nucleus-Golgi axis also moved in the control experiment, but, instead of stabilizing when it reached the point of optogenetic activation (0°), it kept turning (Figure 2.25, (B)). This data indicate, that biochemical Cdc42 activity reorients the Nucleus-Golgi axis towards it.

To confirm that the optogenetic activation is able to stabilize the Nucleus-Golgi axis, we have also conducted an experiment, where we optogenetically activate cells in front of existing Nucleus-Golgi axis (Figure 2.26, (A)). The axis was stabilized as the angle between Nucleus-Golgi axis and optogenetic activation stayed close to 0°during the full duration of the experiment (n=21 cells) (Figure 2.26, (B)).

A shape of a cell changes in response to cytoskeleton rearrangements, differences in osmotic pressure, cytoplasmic flows [START_REF] Chalut | The Actin Cortex: A Bridge between Cell Shape and Function[END_REF], Schakenraad et al., 2020, Illukkumbura et al., 2020, Mogilner and Manhart, 2018, Keren et al., 2009]. A change in the cell shape can also induce cytoplasmic fluid flows and organelle movement [START_REF] Koslover | Cytoplasmic Flow and Mixing Due to Deformation of Motile Cells[END_REF]. A changing shape of a cell can influence the position of Nucleus-Golgi axis. We have designed another experiment to test the reorientation of Nucleus-Golgi axis without the influence of cell shape changes. This time, we put cells on round patterns (d=35 µm). The pattern itself is covered with fibronectin (20 µg/mL) and the cell cannot escape out of it, as the outside is passivated with PLL-g-PEG, which is non-adhesive for cells (for a detailed protocol, see 4.5) (Figure 2.27).

In this set of experiments, optogenetic activation of Cdc42 induced membrane ruffles in the area of activation (Figure 2.27, movie excerpts), but the cell shape did not change, because the area around the pattern was non-adhesive. As expected, the reorientation of Nucleus-Golgi axis aligned with the activation area. We have compared the optogenetically activated cells (n=16 cells) (Figure 2.28, A) and control condition with ITSN missing (n=13 cells) (Figure 2.28, B). Thus, localized Cdc42 activation was sufficient to control the positioning of Nucleus-Golgi axis. Moreover, the Nucleus-Golgi axis reorientation happened faster in the cells grown on a pattern, in comparison to freely attached cells, with 50% of them reorienting in 1 h on a pattern, and in 3 h, when freely attached (Figure 2.29). Changing the direction of movement by 90°is considered a full change in direction of movement in 2D cell migration experiments [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF]], but we further tested if the Nucleus-Golgi axis position could be changed, if Cdc42 activation was triggered completely on the other side, 180°away from the existing position. We performed this experiment on patterned cells (Figure 2.30, (A)) and confirmed that complete change in Nucleus-Golgi axis direction can be achieved with local Cdc42 activation (Figure 2.30, (C)). Nucleus-Golgi axis was stabilized in the area of activation after reorienting (

External Cdc42 activation rescues cell migration

As shown in our previous experiments, in presence of low levels of the drug Nocodazole (NZ) (0.1 µM), the Golgi complex integrity and cell migration persistence are perturbed (2.4). As low concentrations of NZ perturb microtubule dynamics [Liao et al., 1995, Mikhailov andGundersen, 1998], we wanted to test, how this affects the reorientation of the Nucleus-Golgi axis. We have performed a set of experiments where we used optogenetic activation of Cdc42, but in presence of NZ (0.1 µM) (Figure 2.31, A). The Nucleus-Golgi axis reoriented in 77% of the cells (n = 13 cells) (Figure 2.31, (B)), which is slightly less than without NZ (95%, n = 19 cells) (see Figure 2.24). We have also quantified the migration directionality ratio of optogenetically activated cells in the presence of NZ (Figure 2.32). Interestingly, optogenetic Cdc42 activation has rescued the directionality of cell migration (Figure 2.32, "NZ" compared to "Opto NZ"). Directionality of cells in presence of NZ was drastically perturbed, reaching only 19% of directionality in control cells (directionality ratio of 0.11±0.04). Optogenetic Cdc42 activation restored the directionality to 0.4±0.2, a number comparable to freely migrating cells (0.59±0.31) and optogenetically activated cells without NZ (0.4±0.24) (Figure 2.32). The directionality of migration is also visible in the plotted trajectories, some of which are going out of the starting point in almost straight lines (Figure 2.31, (C)). Taking everything into account, it is notable that optogenetic Cdc42 activation is able to rescue migration directionality in the presence of Nocodazole.

Persistence arises from coupling between membrane protrusions and internal cell organization

We propose a working model that could describe our data. First, secretion of vesicles from the Golgi complex are directed towards the main protrusion (t = 20 min after protrusion forms) (Figures 2.18 and 2.21). A flow of vesicles is directed towards it (Figure 2.21) thanks to microtubule tracks from the Golgi to the nascent protrusions and forming FAs [START_REF] Dogterom | Actin-microtubule crosstalk in cell biology[END_REF], Bouchet et al., 2016, Margaron et al., 2013, Stehbens and Wittmann, 2012]. Second, new protrusions are more likely to form where the trafficking and secretion flows, such that persistent protrusion activity can be stabilized. Third, Nucleus-Golgi axis reorients towards the now sustained protrusion (t = 180 min) (Figure 2.29). If there is no directed traffic and secretion, the persistence time of cell migration drops from 140 min to 20 min (Figure 2.17, (B)), which is the duration of a protrusive event. The position of the Golgi complex then biases polarized secretion [START_REF] Hao | Golgi-associated microtubules are fast cargo tracks and required for persistent cell migration[END_REF] and promotes the initiation of new protrusions that sustain directional motility (see Figure 2.33).

Next, we establish a mathematical model based on our data to describe the process of persistent migration in randomly migrating mesenchymal cells (for details of the model see 4.12). It is a minimal effective model that implements the two sides of the feedback between polarity axis and protrusion dynamics, proposed in my PhD hypothesis (1.5). We intended to synthetically reproduce our main experimental observables -morphodynamic maps and directional persistence of cell trajectories. We have first reconstructed a morphodynamic map of a single protrusion. Then, we have built it up and expanded to full synthetic morphodynamic maps. These maps are constructed from the accumulation of protrusions, either appearing randomly along the cell edge or being biased towards a specific direction given by a simulated polarity axis. We have implemented the feedback by coupling the polarity axis to the protrusion dynamics and vice versa. First, secretion of vesicles (white dots) from the Golgi (yellow) are directed toward the main protrusion, thanks to microtubule tracks from the Golgi to the nascent adhesion points. Second, the Nucleus-Golgi polarity axis is reoriented towards a main protrusion, thanks to microtubules (purple), that are anchored to the protrusion by nascent focal adhesions (dark blue), being pulled, and to actin retrograde flow (green gradient and arrows), that pushes the nucleus backwards. The polarized secretion promotes the initiation of new protrusions that sustain directional motion (magenta arrows show the directionality of the interacting parameters -F basal , F prot , P rand and P polarized .)

Membrane dynamics of a single activation of a RhoGTPase were experimentally computed in a recent paper [START_REF] Yamao | Distinct predictive performance of Rac1 and Cdc42 in cell migration[END_REF], where the authors compute the transfer function between a point-like Cdc42 pulse of activity at time 0 and position 0, and the membrane dynamics that follow (Figure 2.34, top left panel). To simulate the morphodynamic map following a single protrusion, we designed a synthetic Cdc42 pulse of activity (see Figure 2.34, bottom left panel) extended in space and time such that, when convoluted with the transfer function described above, it would lead to a signature of protrusive activity in the morphodynamic map, similar to the one seen in our data (see spatial and temporal extent for NZ and GCA in Figure 2.15, (B) and (C)). Next, we ensured that the protrusion frequency of our simulations matched the data (see Figure 2.34,right panel). Having this, we were able to simulate full morphodynamic maps by nucleating protrusive events, happening randomly in space (see Figure 2.35, for two values of protrusion frequencies) (for details see 4.12.1).

We have implemented the feedback between polarity axis and protrusion dynamics into the simulation. First side of the feedback takes into account the effect of the polarity axis on protrusions and describes the probability of protrusions forming in front of the Nucleus-Golgi (NG) axis (for details see 4.12.2). Second side of the feedback considers the effect of protrusions on the polarity axis and the bias with which the NG axis is pulled towards a protrusion (for details see 4.12.4). In our mathematical model, the initiation of protrusions is modeled by a probability of protrusion P polarized in front of the NG axis and P rand = 1 -P polarized elsewhere. When p polarized = 0, protrusions are happening randomly along the contour, and when p polarized = 1, protrusions are always happening in front of the Nucleus-Golgi axis. The pull of the NG axis towards the protrusion is parametrized by an effective force F prot that acts against F basal , which characterizes the random rotation of the NG axis. The force, pulling the NG axis towards a protrusion is, then, characterized by a value κ: d dt x N G = κF prot + (1 -κ)F basal . When κ = 0, the Nucleus-Golgi axis follows its natural evolution, and when κ = 1, the Nucleus-Golgi axis follows the protrusions. The strength of both feedbacks can, thus, be summarized by two numbers between 0 and 1: P polarized and κ = (F tot -F basal )/(F prot -F basal ). With the described feedback, we have produced realistic morphodynamic maps and tested all the different situations with both or only one side of the feedback on. For visualisation, we used the morphodynamic maps to simulate a full migrating synthetic cell (see Figure 2.36, A). The position of the cell centroid depends on the protrusive cell activity. Thus, the instantaneous movement of the cell centroid can be calculated as the sum of all the velocities of the markers along the cell contour, which means that the generated morphodynamic maps can be translated into cell trajectories. By running the synthetic morphomap simulation with different P polarized and κ values multiple times, we have generated trajectories of synthetic cell movement (see Figure 2.36, B), which we used for further analysis of persistent migration. The simulated trajectories were analyzed in the same way as the experimental ones. We have calculated their autocorrelation of direction and persistence times. Next, we have summarized the results of our mathematical model in a phase diagram of persistence time, where the strength of both sides of the feedback defines how persistent cell migration is (see Figure 2.37). Our simulation shows that if the feedback is one-sided, high persistence time (more than 1 h) cannot be achieved. This is visible going up along the left side and going right along the lower side of the diagram, where either the κ (left side) or P polarized (lower side) increases from 0 to 1. There is a sharp transition going to the optimal zone of persistence times (Figure 2.37, (b)). Here, migration is persistent, but susceptible to directional change. Once entering the upper right corner of the diagram, trajectories become very directional, a cell is moving almost in a straight line (see Figure 2.37, (c)). In addition to mapping of persistence time as a function of the strength of the two sides of the feedback, we developed two other independent measures aimed at quantifying cell polarity -Protrusion unicity index and Alignment index (Figure 2.38).

Protrusion unicity index shows how many simultaneous protrusions are generated in the cell (4.12.6), and the Alignment index describes how effectively the NG-axis aligns with the direction of mevement (4.12.7). As seen from the Figure 2.38, Protrusion unicity increases with the value of P polarized , while Alignment depends on both P polarized and κ. Altogether, the three "look-up tables" (Persistence time, Protrusion unicity, and Alignment) differ in their dependencies with regards to the two parameters κ and P polarized , and can be used to estimate their values independently. Each of these tables provides a range for the two parameters, and when combined they should converge to a single couple of values (Figure 2.39). If it is the case, it would be a signature of the consistency of our minimal model. With our data on RPE1 cells, we found a persistence time of 2.3±1.4 h, a protrusion unicity index of 0.63±0.12, and an alignment index of 0.72±0.21. Using these numbers and the tables to estimate the ranges for κ and P polarized , we observed that there is a region of the parameter space that is consistent and predict that κ = 0.9 and P polarized = 0.7 (Figure 2.40). Thus, our approach suggests that the high persistence of RPE1 cells can be explained by a relatively high values of the feedback strengths.

Discussion and Perspectives

Persistence of cell migration emerges from an interplay of several different signalling pathways [START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF]. Though it is hard to dissect a system relying on feedback loops, it is becoming possible with precise quantification of experimental data and newly developed experimental techniques. Using live-cell imaging and tracking, we describe the reorientation of the Nucleus-Golgi polarity axis during migration on a single-cell level without gradients of external cues (2.2). We have investigated the behaviour of cells at the start of migration, when being released from an isotropic pattern and correlated the position of the Nucleus-Golgi axis with the direction of movement (2.3). We have also pharmacologically disrupted the integrity of the Golgi complex, showing that this strikingly reduces the persistence of migration (2.4). While trying to understand if polarized secretion might arise from the biased traffic in front of the Golgi complex, we have conducted RUSH assays and tracked traffic of post-Golgi vesicles, which showed that in a turning (direction changing) cell, secretion is biased towards a newly forming protrusion. Then, a reorientation of the Nucleus-Golgi axis follows. The flow of traffic gets reinforced in front of the Nucleus-Golgi axis and new protrusions keep forming towards the same direction (2.5). In order to understand how the Nucleus-Golgi axis is reoriented, we used optogenetic tools to generate local RhoGTPase Cdc42 gradients and found that they are sufficient to reorient this axis of polarity (2.6). Summing up the experimental data, we have proposed an effective minimal model describing the role of a feedback between the Nucleus-Golgi polarity axis and protrusion dynamics. Our model has reproduced realistic simulations of migrating cells and showed that the ability of a cell to migrate persistently can be described by two parameters P polarized and κ, i.e. the efficiency of polarization and the strength of the bias to pull the polarity axis towards a forming protrusion.

In this PhD thesis, we have studied random single-cell migration on 2D substrates in a uniform external environment. We have proposed that the persistence of migration emerges from the coordination between stochastically generated plasma membrane protrusions and internal cell organization. We took the Nucleus-Golgi axis as a marker for internal cell polarity and investigated the importance of its position in cell migration. Nucleus-Golgi axis was described to reorient towards the protruding front of the migrating cells [START_REF] Millarte | The Golgi in cell migration: Regulation by signal transduction and its implications for cancer cell metastasis[END_REF], Yadav et al., 2009, Kupfer et al., 1982] and its position was proposed to be involved in polarized secretion [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF]Linstedt, 2011]. Most of these studies were done using a wound scratch healing assay and involved collectively moving cells at the border of the wound [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF],Osmani et al., 2006,Etienne-Manneville et al., 2005,Etienne-Manneville and Hall, 2001, Kupfer et al., 1982]. When the cells are moving collectively at the wound edge, the protruding edge of a cell is the only border that does not form junctions with neighbouring cells, which makes it hard to dissect the involvement of cell-cell junctions in the process of Nucleus-Golgi axis reorientation [START_REF] Barker | Centrosome positioning in non-dividing cells[END_REF], Luxton and Gundersen, 2011, Dupin et al., 2009]. We have confirmed that the Nucleus-Golgi axis reorients towards the protrusion even in the migrating single RPE1 cells (2.2 and 2.3).

Rho GTPase Cdc42 was proposed to play a role in the Nucleus-Golgi axis reorientation [Etienne- Manneville and Hall, 2001]. Several different pathways activated by Cdc42 could be working in the process -microtubules, that are anchored to the protrusion by the forming focal adhesions, being pulled towards the protrusion and reorienting the centrosome and the Golgi complex together [Etienne- Manneville et al., 2005], the Golgi complex being pulled by polymerizing actin forces via GOLPH3/MYO18A pathway [START_REF] Xing | GOLPH3 drives cell migration by promoting Golgi reorientation and directional trafficking to the leading edge[END_REF], and actin retrograde flow pushing the nucleus backwards [Gomes et al., 2005b]. We have used optogenetics to locally activate Cdc42 in single-cells and confirmed that subcellular Cdc42 activation is sufficient to reorient the Nucleus-Golgi axis (2.6). The axis orientation process was faster in cells on round fibronectin patterns than in freely migrating cells (50% of cells have reoriented in 60 min on the pattern vs. 180 min in freely moving cells) (Figure 2.29). In our experiments, freely migrating RPE1 cells were more stretched out than the cells on round micropatterns (d = 35 µm). This proposes involvement of actomyosin contractility and membrane tension in the reorientation process [Mathieu, 2020]. Interestingly, we have also noticed that instead of always taking the shortest path to reorient towards a newly forming protrusion, Nucleus-Golgi axis showed a bias of moving clockwise (CW) (for more details see Appendix A. The bias was enhanced if the cells were left to attach to the substrate for at least 16 hours. This bias might be pointing to actin structure that forms when the actin cytoskeleton matures during attachment to the substrate [START_REF] Tee | Cellular chirality arising from the self-organization of the actin cytoskeleton[END_REF]. A chiral structure might be formed, which facilitates Nucleus-Golgi axis reorientation in CW direction.

To investigate the function of Nucleus-Golgi axis and its reorientation, we have disrupted the Golgi complex and measured its effect on cell migration persistence (2.4). We have used three different drugs -Brefeldin A (BFA), Golgicide A (GCA) and Nocodazole (NZ). The effect of BFA was too disruptive for long-term experiments even in low doses. This might be because of its multiple targets in the cell. BFA inhibits three GEFs of Arf1 GTPase -BIG1, BIG2 and GBF1 [START_REF] Niu | Dynamics of GBF1, a Brefeldin A-Sensitive Arf1 Exchange Factor at the Golgi[END_REF], Sáenz et al., 2009, Boal et al., 2010]. This GTPase is involved in recruiting the coat proteins required for COPI vesicle formation and is essential for proper vesicle budding at the Golgi complex cis side [START_REF] Kawamoto | GBF1, a guanine nucleotide exchange factor for ADP-ribosylation factors, is localized to the cis-Golgi and involved in membrane association of the COPI coat[END_REF]. In addition to that, BFA was also described to disrupt the microtubule and actin cytoskeletons [Alvarez andSztul, 1999, Bershadsky andFuterman, 1994], TGN-to-cell surface transport [O' Neill et al., 2018b, Shen et al., 2012, Li et al., 2011, Strous et al., 1993, Miller et al., 1992] and protein synthesis [START_REF] Fishman | Brefeldin A inhibits protein synthesis in cultured cells[END_REF]. Golgicide A (GCA) is a drug with a very similar action mechanism as Brefeldin A, but, because of its structure, it targets GBF1, a GEF of Arf1, specifically [START_REF] Sáenz | Golgicide A reveals essential roles for GBF1 in Golgi assembly and function[END_REF]. Thanks to this, it is easier to predict its involvement in signaling pathways and its effect on cells. At the same time, it is less detrimental for cell viability and favourable in long-term experiments. We have seen an interesting effect on cell morphology after the addition of GCA. Lamellipodial protrusions have exchanged with more cylindrical lobopodia-type protrusions, which reversibly switches back to lamellipodial protrusions once GCA is degraded and after the Golgi complex reforms (passing by a short episode of small blebs forming all through the cell) (Figure 2.12). This might be caused by changes in cell contractility, as depletion of Arf1 from the leading edge of the cell by GCA might increase RhoA activity there, leading to a different type of protrusions formed [Petrie and Yamada, 2012, Petrie and Yamada, 2015, Rafiq et al., 2017]. GCA is known to affect the rate of secretion in cells as well [START_REF] Sáenz | Golgicide A reveals essential roles for GBF1 in Golgi assembly and function[END_REF], Ignashkova et al., 2017, Kaczmarek et al., 2017]. We have also used Nocodazole (NZ), which inhibits microtubule polymerization [De Brabander et al., 1976, Turner andTartakoff, 1989] and disperses the Golgi complex [Minin, 1997, Dinter andBerger, 1998], but doesn't interfere with protein secretion [Van De Moortele et al., 1993, Liao et al., 1995, Schmoranzer et al., 2003, Fourriere et al., 2016]. We have analysed the protrusive activity and migration of directionality of cells in the presence of GCA (35 µM) and NZ (0.1 µM) and noticed that the persistent migration was lost (Figure 2.17), but protrusions were still forming (Figure 2.13) and usually protruding in lateral waves. This phenomenon has been recently described in migrating fish keratocyte cells and results from actin anti-capping protein VASP depletion in the site of protrusion [START_REF] Barnhart | Adhesion-Dependent Wave Generation in Crawling Cells[END_REF]. Although the average protrusion speed in control cells and NZ affected cells was the same (16±5 µm/h and 17±6 µm/h, respectively), we have noticed a slightly reduced protrusion speed in GCA affected cells (12±2 µm/h), possibly owing to reduction in secretion. Reduced secretion is also visible in our trafficking experiments (Figure 2.20).

Since migration persistence was lost after disrupting the Golgi complex with GCA and NZ drugs, it indicates that the Golgi complex and trafficking from it is important for persistent migration. Several studies have proposed that disrupting microtubules and pericentrosomal Golgi position diminishes polarized long-range trafficking [START_REF] Fourriere | Microtubule-independent secretion requires functional maturation of Golgi elements[END_REF],Schmoranzer et al., 2003] and reduces cell migration [Etienne- Manneville, 2013, Schmoranzer et al., 2003, Etienne-Manneville and Hall, 2001, Liao et al., 1995]. Polarized trafficking towards the protruding front of the cell could be important for bringing GEFs of Rho GTPases and active GTPases themselves, such as Cdc42 [START_REF] Osmani | Cdc42 localization and cell polarity depend on membrane traffic[END_REF]. Our experiments, where we optogenetically activated Cdc42 in presence of NZ, have shown that persistent cell migration can be rescued by locally activating Cdc42 (see 2.7). Which points to a possibility that Cdc42 activators or Cdc42 itself could be brought to the leading edge by polarized trafficking. A similar mechanism has been described in yeast, where cell polarity is established by Cdc42, where it locally clusters and amplifies its activity by a positive feedback loop, while at the same time promoting the formation of actin tracks and polarized secretion towards the cluster [START_REF] Miller | Regulation of Cdc42 for polarized growth in budding yeast[END_REF], Pichaud et al., 2019]. The polarity establishment in bigger mammalian cells could be similar in a way that trafficking is used as one part of the feedback, but instead of actin tracks involve the MT network.

Our cargo trafficking experiments have indicated that the cargo is trafficked and secreted towards the newly forming nascent protrusions (see 2.5). This could be explained by the microtubules being guided towards the newly forming adhesions by the actin cytoskeleton [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF],Etienne-Manneville, 2013]. A study from Fourriere et al. has shown that Rab6 positive post-Golgi vesicles release their cargo in the vicinity of FAs [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF]. A question remains, how Rab6 positive vesicles are loaded onto microtubules and transported in a polarized manner. One hypothesis could be that the microtubule density is higher on the side of the protruding front of the cell [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF], Etienne-Manneville, 2013]. The Golgi complex is able to nucleate MTs and its inherently polarized stacked structure results in a polarized MT network [START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF], Vinogradova et al., 2009, Rivero et al., 2009, Miller et al., 2009]. Once the Nucleus-Golgi axis reorients towards the leading edge, the Golgi MT network is remodelled and is facing the leading edge [Etienne- Manneville, 2013]. Golgi-associated MTs were also shown to act as fast-tracks for cargo transport towards the leading edge, making polarized trafficking even more efficient [START_REF] Hao | Golgi-associated microtubules are fast cargo tracks and required for persistent cell migration[END_REF]. However, the higher density of microtubules in front of the Golgi does not explain, how the cargo is directed to the nascent protrusions in the first place, before the Nucleus-Golgi axis reorients. Another hypothesis, which takes trafficking towards nascent protrusions into account, would be that the MTs are selected and cargo is loaded on them specifically [START_REF] Miserey-Lenkei | Coupling fission and exit of RAB6 vesicles at Golgi hotspots through kinesin-myosin interactions[END_REF]. This could happen once the MTs are directed towards the leading edge by the actin cytoskeleton and are anchored there. Then, MT minus end directed motors could bring specific cues back towards the Golgi complex and initiate the loading of cargoes. We have quantified the cross-correlation coefficient between protrusion initiation and Rab6 positive post-Golgi vesicle traffic towards them, and found that trafficking followed the protrusive activity with a 20 min lag. The calculated cross-correlation coefficient of 0.19±0.11 was similar in range to the one calculated between Rho GTPase activation and plasma membrane dynamics from [START_REF] Machacek | Coordination of Rho GTPase activities during cell protrusion[END_REF], where it was ranging between 0.2-0.3. As Rho GTPase activation and plasma membrane dynamics are established to be causally related [Machacek andDanuser, 2006, Machacek et al., 2009], we consider that our calculated cross-correlation coefficient is substantial to claim that protrusion formation and trafficking are correlated.

Our proposed working model builds on the ideas that: (i) localized Cdc42 activity can polarize the cytoskeleton of the cell [Etienne- Manneville et al., 2005, Xing et al., 2016,Gomes et al., 2005b], (ii) the pericentrosomal position of the Golgi complex plays an important role in directed secretion [START_REF] Yadav | A Primary Role for Golgi Positioning in Directed Secretion, Cell Polarity, and Wound Healing[END_REF], and (iii) retrograde transport through the Golgi complex and polarized re-secretion in Rab6 post-Golgi vesicles is essential for persistent cell migration [START_REF] Shafaq-Zadah | Persistent cell migration and adhesion rely on retrograde transport of β 1 integrin[END_REF]. In our minimal model we propose a feedback between a probability of a cell to form a protrusion in front of the Nucleus-Golgi polarity axis (described by P polarized ) and the bias that the Nucleus-Golgi axis is pulled towards the forming protrusion (described by κ) to describe the main elements of persistent cell migration (see 2.8 and 4.12). The ability of a cell to polarize could translate to directed trafficking and stabilization of one leading protrusion. It can also be described with our proposed Protrusion unicity index, which takes into account the amount of protrusions present in a cell at a given time-point (see 4.17). After calculating the Protrusion unicity index (see 4.12.6) in the parameter space of P polarized and κ, we have noticed that the Protrusion unicity index increases together with P polarized . Thus, calculating the Protrusion unicity index can help to map the cell to the phase diagram of Persistence time along the P polarized axis. We have also calculated an Alignment index, as a measure of how well the NG-axis aligns with direction of cell movement (see 4.12.7). The values of the Alignment index show that it depends both on κ and P polarized (Figure 4.18). It can be explained by the fact that even when κ = 1, if P polarized is close to zero, protrusions are forming randomly and the NG-axis does not have enough time to align.

Our proposed model fits the data from migrating RPE1 cells, but it would be interesting to see, if our model could describe the persistent random migration of other cell types as well. To map any cell type on a phase diagram of Persistence time, only a few parameters are needed. Having access to cell trajectories enables the calculation of per-sistence time. Evaluating the average amount of protrusions during migration allows the calculation of the Protrusion unicity index, and, finally, quantifying the average angle between the Nucleus-Golgi axis and the direction of movement permits the calculation of the Alignement index (Figure 2.37). If it turns out that the three calculated parameters don't match, it will indicate that though our proposed feedback mechanism might be dominant in RPE1 cells, other feedbacks might be more prominent in the other cell types. A few different mechanisms for a cell to select one protrusion from several competing ones have been proposed, including membrane tension [Houk et al., 2012, Sens andPlastino, 2015], asymmetry of essential polarity components generated by actin retrograde flow [START_REF] Maiuri | Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence[END_REF] and polarized protein delivery [START_REF] Cheng | Centrosome guides spatial activation of Rac to control cell polarization and directed cell migration[END_REF]. A combination of the proposed mechanisms might be in play and result in varied persistence times in different cell types.

It would be informative to learn how polarized trafficking is directed towards the nascent protrusions and the leading edge. If it is delivered by Rab6 positive vesicles, how these vesicles are directed towards the vicinity of focal adhesions (FAs)? Can Rab6 vesicles be delivered to the nascent adhesions as well? What is the cargo delivered to the leading edge? The Nucleus-Golgi axis reorientation mechanism should be investigated in more detail, to determine the contribution of actin and microtubules in the process (for our short preliminary study see Appendix B).

Learning more about the molecular mechanism of the feedbacks that lead to persistent cell migration, might lead to a possibility to not only describe and map migrating cells to a phase diagram of Persistence time, but also change their position in it. Stronger coupling of the molecular players responsible for polarized trafficking and protrusive activity (e.g. certain Rab and Rho GTPases) could push the cell to the upper right corner of the Persistence time diagram and make them super-persistors, which move in a straight trajectory. However, becoming super-persistent might be deleterious to the sensitivity of cell migration and result in inability to turn. Interestingly, the values of κ and P polarized we have found for RPE1 cells are close to the limit where cells would move super-persistently (no turning at all). They might be at an optimum of robustness and sensitivity: cells are highly persistent, but not locked into a permanent polarized state, such that they can turn if needed (for example, to follow a stimulus). In this thesis, I show that by using quantitative data analysis and novel approaches to control cell behaviour, like optogenetics, micropatterning and trafficking assays, it is possible to construct minimal models to describe complex cell behaviour.

Materials and Methods

During my thesis, I used different techniques that perturb cellular processes in space and time in a controlled manner. These techniques include creation of stable cell lines, micropatterning, optogenetic activation, pharmacological and trafficking assays, live-cell imaging, and modelling. I employed image analysis and statistics techniques to extract the data from my experimental dataset.

Cell culture

hTERT RPE1 cells (CRL-4000 strain, ATCC, Manassas, VA) were cultured at 37 °C with 5% CO 2 in Dulbecco's modified Eagle's/F-12 medium supplemented with 10% fetal bovine serum, GlutaMAX (2 mM) and penicillin (100 U/mL)-streptomycin (0.1 mg/mL). Cells were passaged twice a week in a ratio of 1/10 by washing them with PBS (1x) solution and dissociating using TrypLE Express (Thermo Fisher Scientific, Waltham, MA) reagent for 5 min.

Plasmids

pLL7.0: hITSN1(1159-1509)-tgRFPt-SSPB WT (Plasmid #60419), pLL7.0: Venus-iLID-CAAX (from KRas4B) (Plasmid #60411), pMD2.G (Plasmid #12259), psPAX2 (Plasmid #12260) lentiviral plasmids were bought from Addgene (Watertown, MA). pHR: myr-iRFP plasmid was a gift from Simon de Beco (Institut Curie, France) and pIRESneo3: Str-KDEL-ST-SBP-EGFP (Plasmid #65264) was a gift from Gaëlle Boncompain (Institut Curie, France).

Transfection

Transfections were performed using X-tremeGENE 9 (Roche Applied Science, Penzburg, Bavaria, Germany) according to the manufacturer's instructions using an equal amount of plasmid DNA for each construct (1 µg) and a ratio of 3:1 of transfection reagent and DNA.

Stable cell lines

Stable cell lines were generated using two techniques -lentiviral infection and CRISPR cell line development.

Lentiviral.

For lentivirus production, packaging cell line HEK 293T cells were cotransfected with pMD2g (envelope), psPAX2 (packaging) and lentiviral (transfer*) plasmids in a 1:3:4 ratio, respectively (*pHR-, pLVX-or pLL7-based plasmids were used as transfer plasmids). Lentivirus was harvested 48 h after transfection and filtered from the supernatant of cell culture by passing it through 0.45 µm filter using a syringe. Next, the traget RPE1 cell line was transduced for 24 h with media containing lentiviral particles. Subsequently, RPE1 cells were selected by Fluorescence-activated Cell Sorting (FACS) according to the fluorescence level of transduced protein.

CRISPR.

A CRISPR cell line with a heterozygous iRFP-Rab6A knock-in as a Golgi complex label was kindly developed for my project by an engineer in the team Aude Battistella.

CRISPR sgRNAs were designed using the Optimized CRISPR Design tool (for sequences see Table 4.1). For sgRNA-encoding plasmids, single-stranded oligonucleotides (Eurofins Genomics, Germany) containing the guide sequence of the sgRNAs were annealed, phosphorylated and ligated into BbsI site in px335 plasmid, coding for Cas9 (kindly provided by M.Wassef, Curie Institute, Paris, France). Homology arms of ∼800bp were amplified from genomic DNA using PCR primers with 40 bp overhangs compatible with pUC19 backbone digested with Xba1 and Ecor1 (New England Biolabs, Ipswich, MA) (sequences in 4.1). Gibson reactions were performed using a standard protocol with home-made enzyme mix [START_REF] Gibson | Enzymatic assembly of DNA molecules up to several hundred kilobases[END_REF]. RPE1 cells were transfected with 90 µL of Polyethylenimine (PEI MAX #24765 Polysciences, Warrington, PA) and 15 µg of the pX335-gRNA and pUC19-homology arms-iRFP plasmids, both diluted in 240 µL NaCl 150mM. 7 days after transfection, positive cells were sorted with FACS for enrichment, and after additional 10 days FACS sorted again by single cell per well in a 96-well plate. All 96 clones were screened by PCR and 8 clones were selected for further verification by Western blotting, followed by sequencing.

Name

Guide sequence (5' to 3') gRNA-3-mACTB GTCTCCGCCCGTGGACATTG LeftArm fwd gaccatgattacgccaagcttgcatgcctgcaggtcgactGCCACAGTGCTCC GCTTTCC

LeftArm rev gcgacggatccttcagccatTGTGGAACTAGAGGAGCGGC

Linker-iRFP fwd gccgctcctctagttccacaATGGCTGAAGGATCCGTCGC Linker-iRFP rev ccgaagtctgcgcgcgtggaCCGGATTGGCCACTCTTCCAT

RightArm fwd tggaagagtggccaatccggTCCACGgGaGgAGACTTCGG

RightArm rev GggttttcccagtcacgacgttgtaaaacgacggccagtgCAGTGATGAAAG TCAAGAGAACAAAATGAGGTTTTCCG

Micropatterning

Coverslip preparation.

Coverslips for live-cell imaging were prepared by cleaning round glass coverslips (d=25 mm, 0.17 mm thickness) (Menzel Gläser, Thermo Fisher Scientific, Waltham, MA) for 1 min in O 2 plasma and incubating them with fibronectin (2 µg/mL) (Merck, Darmstadt, Germany) in 100 mM NaHCO 3 (pH 8.5) for 1 h in room temperature. Coverslips were washed with PBS (1x) three times and stored in +4°C in PBS (1x).

Static patterns.

Micropatterned coverslips were prepared as described by [START_REF] Azioune | Simple and rapid process for single cell micro-patterning[END_REF]: O 2 plasma-cleaned coverslips were incubated with 100 µg/mL of PLL-g-PEG (Surface Solutions, Switzerland) in 10 mM HEPES, pH 7.4 for 1 h. They were then exposed to deep UV through micropatterned quartz/chrome photomasks (Toppan, Round Rock, TX) for 5 min, and incubated with fibronectin (20 µg/mL) in 100 mM NaHCO 3 (pH 8.5) for 1 h.

Releasable (dynamic) patterns.

Releasable micropatterns were prepared similarly, with PLL-g-PEG being replaced by azido-PLL-g-PEG (APP) at 100 µg/mL and fibronectin used at lower concentration (10 µg/mL). Migration was released by addition of 20 µM BCN-RGD for 10 min (described in [Van Dongen et al., 2013]).

Drug assays

In drug assays, RPE1 cells were treated with Brefeldin A (0.2 µg/ml, 1 µg/ml and 5 µg/ml) (Sigma-Aldrich, St.Louis, MO), Golgicide A (0.7 µM, 7 µM, 10 µM, 14 µM, 35 µM and 70 µM) (Sigma-Aldrich, St.Louis, MO) and Nocodazole (0.1 µM) (Sigma-Aldrich, St.Louis, MO) in complete DMEM/F-12 medium at 37 °C in 5% CO 2 for the duration of the experiment. 30 min before the experiment and before addition of the drug, cells were incubated with Hoechst 33342 (1 µg/ml) dye (Thermo Fisher Scientific, Waltham, MA), to label cell nuclei. Then, the dye was washed with 1X PBS buffer (pH = 7.5) and a drug diluted in complete medium was added. Cells were imaged immediately after addition of a drug.

RUSH assay

Retention using selective hooks (RUSH) assay was performed as described in [Boncompain et al., 2012] and [Boncompain and Perez, 2012]. RPE1 cells were transfected with 2 µg of plasmid containing the RUSH system (Str-KDEL-SBP-EGFP-Col10A1) and a GFP labelled Collagen type X (ColX) cargo. 24 h after transfection, cells were put on anti-GFP antibody coated glass coverslips and let to attach (described in 4.8). After 2 h biotin was added (40 µM final concentration from 4 mM stock) to the full medium. Biotin's affinity for streptavidin is much higher than SBP's (straptavidinbinding protein's), thus it replaces the bound cargo, which leads to the cargo release. Cells were imaged for 2 h, until the ColX cargo passed from the endoplasmic reticulum (ER) to the Golgi complex and then was secreted (4.2). As the coverslip was covered with anti-GFP antibodies, it enabled the GFP-labelled ColX cargo capture upon secretion, which made the secretion localization clearly visible (imaging in TIRF mode 4.10.1) Col10A) is hooked in the donor compartment (ER in this case) and gets released upon addition of biotin and moves towards the acceptor compartment (plasma membrane in this case) (adapted from [Boncompain and Perez, 2012]).

SPI assay

Selective protein immobilization (SPI) assay was performed as described in [START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF]. Round glass coverslips (d = 25 mm) were either autoclaved and incubated in bicarbonate buffer (0.1 M pH 9.5) for 1 h at 37°C (300 µL, upside down) or plasma cleaned (2 min vacuum, 1 min plasma). Next, the coverslips were transferred to poly-L-lysine (0.01% diluted in water) and incubated for 1 h at 37°C (300 µL, upside down). After being washed in PBS and dried they were transferred to a solution of anti-GFP antibodies (diluted in bicarbonate buffer) and incubated for 3 h at 37°C (70 µL, upside down). After another wash with PBS, cells were seeded on top of coated coverslips in complete medium (at least 2 h given for cells to attach before conducting a RUSH assay (4.7)). Antibodies used for coating in this study were rabbit anti-GFP (A-P-R#06; Recombinant Antibody Platform of the Institut Curie; dilution 1:100).

Optogenetics

For local subcellular activation of a RhoGTPase Cdc42, we have used an optogenetic dimer iLID-SspB as described in [START_REF] Guntas | Engineering an improved light-induced dimer (iLID) for controlling the localization and activity of signaling proteins[END_REF]. The cytosolic part of the dimer has a DH-PH domain of ITSN attached to it, which serves as an activator of RhoGTPase Cdc42. The other iLID part of the dimer is attached to the plasma membrane via CAAX doamin, and changes its conformation upon illumination with blue light (440±10 nm). After the conformation change, the binding affinity of two parts of the dimer increases, iLID and SspB dimerizes and RhoGTPase activator gets recruited close to the plasma membrane, where it can activate Cdc42 (Figure 4.3).

RPE1 cells used in the optogenetic experiments were engineered to stably express the optogenetic dimer and selected for average-high fluorescence level by FACS (the highest expressing cells were discarded, as they were not responsive to optogenetic activation). Experiments were performed in live-cell imaging conditions described in the passage below (4.10.1), using a DMD projector and a blue (440±10 nm) LED illumination source (4.10.1). The projection of blue light was controlled with an interface of a MATLAB script and a microscope controlling MetaMorph software by sending a static pattern of light, or using the imaging routine described below (4.10.3). The illumination pattern was optimised for a local signal and weak illumination to reduce the phototoxicity and enable long-term experiments.

Imaging

Live-cell imaging

All imaging was performed at 37 °C in 5% CO 2 with an IX71 inverted fluorescence and Differential Interference Contrast (DIC) microscope (Olympus, Melville, NY), controlled with MetaMorph software (Molecular Devices, Eugene, OR). The microscope was equipped with a 60x objective (NA=1.45), motorized stage and filter wheel with SmartShutter Lambda 10-3 control system (Sutter Instrument Company, Novato, CA), a stage-top incubation chamber with temperature and CO 2 control (Pecon, Meyer Instruments, Houston, TX), ORCA-Flash4.0 V3 Digital CMOS camera (Hamamatsu Photonics K.K., Japan), z-axis guiding piezo motor (PI, Karlsruhe, Germany), CRISP autofocus system (ASI, Eugene, OR), a laser control system with azimuthal TIRF configuration (iLas2, Roper Scientific, Tucson, AZ) and a DMD pattern projection device (DLP Light Crafter, Texas instruments, Dalas, TX), illuminated with a SPEC-TRA Light Engine (Lumencor, Beaverton, OR) at 440±10 nm. Before imaging, cells were dissociated using Versene Solution (Thermo Fisher Scientific, Waltham, MA) and seeded for adhesion on previously mentioned prepared coverslips.

TIRF microscopy.

Total Internal Reflection Microscopy (TIRF) (also known as evanescent wave microscopy) is a widefield microscopy technique, which uses unique properties of evanescent wave of light, induced by bending the light of excitation laser to the point of total internal reflection, happening at the interface of two media with different refractive indices (usually, a specimen and a glass coverslip). This evanescent wave of light decays exponentially and can propagate only about ∼100-200 nm into the specimen. Thanks to this, the fluorophores are only excited in this thin band, while avoiding out-of-focus fluorescence. This technique is mainly used to explore processes happening close to the membrane of live adherent cells [START_REF] Mattheyses | Imaging with total internal reflection fluorescence microscopy for the cell biologist[END_REF].

In our experiments we used a variation of TIRF, called azimuthal TIRF. Instead of projecting at a single angle, the laser spins at the backfocal plane of the objective. It generates homogeneous illumination and, like this, avoids fringe interferences and imaging artefacts.

HILO microscopy.

With our TIRF system set-up, we could also easily switch to a Highly inclined and laminated optical sheet (HILO) microscopy, just by reducing the tilt of the laser. In this case, the laser goes through the sample at a sharp angle, and instead of illuminating the full volume as in wide-field epifluorescent imaging, it illuminates a fraction of it with a thin inclined beam (Figure 4.4). This increases the signal-to-noise ratio (SNR) of the image [START_REF] Tokunaga | Highly inclined thin illumination enables clear single-molecule imaging in cells[END_REF]. We used this type of imaging to get a better signal of the Golgi complex and nuclear markers in the cell. [START_REF] Tokunaga | Highly inclined thin illumination enables clear single-molecule imaging in cells[END_REF] and [START_REF] Mattheyses | Imaging with total internal reflection fluorescence microscopy for the cell biologist[END_REF]).

DMD pattern projection device.

A Digital Micromirror Device (DMD) is an array of microscopic mirrors (10 µm x 10 µm), that each can have an individually controlled tilt [Davis, 2013]. Different tilt affects the micromirror's ability to reflect light. The function of a DMD is equivalent to a projector. Every micromirror in the array corresponds to a pixel and by fast tilting the micromirrors to change the amount of reflected light (basically, by switching them "on" and "off"), we can control the amount of light projected out of the DMD. The longer the micromirror would stay "on", the higher grayscale value of a pixel we would get.

In our experiments we have used a DMD device with dimensions of 640 x 480, able to generate 8-bit grayscale patterns. We have generated custom made dynamic subcellular patterns for every cell during optogenetic experiments and projected them on cells using a DMD device and a blue LED illumination source (SPECTRA Light Engine (Lumencor, Beaverton, OR). For a scheme of our set-up, see Figure 4.5.

Imaging routine to follow migrating cells

Imaging routine to follow migrating cells with high magnification (60x) was established using a microscope imaging software MetaMorph and numerical computing environment MATLAB. Its goal is to move the microscope stage whenever a cell that is being imaged moves away from the center of the field of view, and realign it with the center of the imaged cell. Like this, we can keep the cell of interest in the field of view and follow it throughout the experiment.

The main script is written in MATLAB and commands to MetaMorph are given through calling its macros called 'journals'. Basically, MetaMorph software is used to communicate with the microscope and take images, while MATLAB governs the whole process of imaging. The user can control the routine with a generated graphical user interface (GUI), making it easier to navigate (Figure 4.6). The GUI displays a selected position and its coordinates and let's you choose a different pattern of activation for every cell. A window with segmentation preview lets you adjust the threshold parameters and the thickness of the pattern, while displaying and updating the changes in real-time. The choice of how many channels you want to use for acquisition and how often you want to image are global and are defined for the full set of cells in the experiment. A useful option is to adapt the imaging frequency for each channel separately, while choosing to aquire "Every n-th Time Point". The user can image multiple stage positions (i.e. multiple cells) in multiple wavelengths in one experiment. One specific wavelength is chosen as segmentation channel. The images from this channel would be used to segment the shape of the cell and to instruct its position. The segmentation threshold can be adjusted for every position and the watershed algorithms can be chosen to separate two touching objects (i.e. cells) in every case. The user can also choose to image in specific channels at different time intervals (Figure 4.6).

Optogenetic activation in the imaging routine

Local subcellular activation with light, required for optogenetic experiments, is tricky to achieve without an option to adjust the activation area for each cell. We have used the previously mentioned imaging routine to follow migrating cells and added a step, that would let us activate a specified area with blue light, needed for our optogenetic experiments. Having in mind our goal to activate protrusions in the cell, we needed to activate along the border of the cell. Using the fact that cell shape is already segmented in this case, we could use the contour and define the angle and thickness of activation along the contour (see Figure 4.8). An option to draw your own activation area, not related to the shape of the cell, also exists, though is not recommended in our case, as the shape of the cell can easily change during the experiment and it might move out of the independent pattern.

Image analysis 4.11.1 Image segmentation

Live-cell imaging data obtained using our cell tracking feedback routine (4.10.2) was analysed using a custom-built Matlab routine. Written with an easy to use Graphical User Interface (GUI) it would let us segment the shape of the cell, shape of the Golgi complex, shape of the nucleus, track their position and extract and visualise their trajectories.

All three structures of interest (cell membrane, the Golgi complex and the nucleus) were fluorescently labelled, so to find and segment their shape, we would use a Matlab function 'graythresh' to select the pixels over a certain threshold of fluorescence intensity. This threshold is adaptative and each image in the movie can have its individual threshold, even if in practice, the same threshold is used for several following images. Next, we would binarize the image with a function 'im2bw', delete the structures touching the image border with 'imclearborder', remove small objects from the image with 'bwareaopen', dilate-erode to close the structures with 'imclose', using a disk with a radius of 10 pixels as a structuring element, and fill the holes in the structure with 'imfill' function. This procedure would result in a segmented cell shape. After that, we would use the 'regionprops' function to get the 'centroid' of the cell. We would use a similar procedure for segmenting the Golgi complex and the nucleus shapes, but with slightly different threshold range. In addition to that, we would optimize the centroid search area by selecting the centroid closest to the centroid in the previous image, which is particularly useful when several regions of interest are found in the image.

The extracted centroids of all three structures would be concatenated into trajectories depicting the movement through the full experiment. Using our tracking routine implies that the microscope stage would move when a cell moves out of the defined field of view. In this case, the trajectory presents jumps, due to the stage movement. These jumps can be corrected using the recorded position of the stage and a defined scaling parameter. After this, we have corrected real trajectories that can be used for further analysis.

The full package of image segmentation was done with the help of an Image Analysis Engineer in the Institut Curie Imaging Platform Anne-Sophie Macé and Mathieu Coppey.

Nucleus tracking (semi-manual)

Experiments with the optogenetic system are sensitive to blue light and imaging in the green and blue channels need to be limited or, even better, avoided completely. We would normally use a Hoechst 33342 dye to label the nuclei, but we could not use it at all in our optogenetic experiments, as it was leading to overactivation of the optogenetic system.

In this case, we could not use the previously described image segmentation (4.11.1) and we used the DIC images to manually tag the nuclei. To make this process at least semi-automated, we have written another Matlab routine, that would let us click on the estimated center of nucleus, or position two intersecting lines that would mark the length and the width of the nucleus in 2D. From this information, the centroids of the nuclei would be recorded and concatenated to a trajectory, which would be corrected according to the stage movement.

Reorientation plot analysis

Evaluation of the Nucleus-Golgi axis reorientation requires two axes: one going through the centroid of the Nucleus and the centroid of the Golgi and another one going through the center of the Nucleus and the center of the optogenetic activation area. We used the previously described image segmentation techniques to segment the optogenetic activation area (4.11.1 and 4.11.2). Next, we would calculate the angle between the two axes (using centroid coordinates and an inverse tangent function 'atan' in Matlab). Then, we would wrap the angle in radians to [0 2π] , using the 'wrapTo2Pi' function, unwrap it with 'unwrap' function, convert the angle from radians to degrees and plot it. Examples can be seen in Figure 2.24.

Cumulative plot analysis

We used the data from the previously described reorientation analysis (see 4.11.3) to plot and compare how fast the reorientation process is happening in different experimental conditions. We chose and angle of 30°to delineate that the Nucleus-Golgi axis have reoriented and calculated the first timepoint, when the angle was <30°. Knowing the reorientation time points of all the cells in the dataset, we used the 'cumsum' function in Matlab to get the cumulative sum of how many cells have reoriented at a certain timepoint and normalized it to 1 (depicting 'all cells') by dividing by the total number of cells in the dataset (see Figure 2.29).

Morphodynamic map analysis

Morphodynamic map analysis was based on the similar analysis in [Yang et al., 2015a]. The cell displacement was followed from frame to frame, providing information, where cell plasma membrane was protruding and where it was retracting. In practise, the contour of the cell in each movie was equidistantly divided into 100 points, called markers. From one frame to another, the pairing of markers was chosen by minimizing the total square distances between makers at time t and t+dt by testing all possible circular shifts of the contour at t+dt. The position of the Nucleus-Golgi axis, calculated from the Golgi and nucleus centroid positions was plotted on top of the morphodynamic map, showing which way it was pointing (Figure 4.9). For further analysis and visualisation, obtained morphodynamic maps could be normalized according to the Nucleus-Golgi axis, cell trajectory or the x-axis of the image by using Matlab's 'circshift' function.

The Matlab script for morphodynamic map analysis was done with the help of an Image Analysis Engineer in the Institut Curie Imaging Platform Anne-Sophie Macé and Mathieu Coppey.

Autocorrelation plot

Autocorrelation data were plotted following the [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF] paper, but adapted from Excel to Matlab.

Traffic flow analysis

Image stacks in tiff format were adjusted using Fiji's 'Bleach correction -Histogram matching' function. Then, a previously described morphodynamic map of cell protrusions was recorded for every cell (4.11.5) and a Golgi mask was created using the segmentation algorithm (4.11.1). A line was drawn from every one of 100 points of the cell boundary in the morphomap towards the centroid of the Golgi mask. Using Matlab's function 'improfile', the mean of fluorescence intensity was calculated along every line. Using these calculations another morphomap, depicting the secretion pattern, was drawn and cross-correlation between the two morphomaps was calculated using 'xcov' function in Matlab.

The Matlab script for secretion analysis was done with the help of Mathieu Coppey.

Modelling

The model describing coupling between excitable protrusions and Nucleus-Golgi axis was developed by Mathieu Coppey. It consists of a minimal effective model of cell migration that implements the two sides of the feedback between polarity axis and protrusion dynamics. It is intended to reproduce and connect our main experimental observables, namely morphodynamic maps and directional persistence of cell trajectories. In this model, we considered the dynamics of the cell edge which ultimately dictates the movement of the cell. Indeed, considering that the cell area is constant (no elastic deformation), the displacement of the cell center of mass is given by the sum of all displacement of points along the edge.

Morphodynamic map of a single protrusion

As a first step, we implemented a Matlab code to simulate realistic morphodynamic maps. Similarly to our data, we considered the movement of 100 markers, x i with i ∈ 0..100, equally distributed along the contour of a synthetic cell. To simulate one protrusive event, we implemented numerically a transfer function such that it was similar to the experimental one reported in [START_REF] Yamao | Distinct predictive performance of Rac1 and Cdc42 in cell migration[END_REF]. This transfer function characterises the edge movement following a point-like activity of Cdc42. To build it, we summed four terms: i) a negative Gaussian function with a relatively large width to account for the initial lateral inhibition, ii) a positive Gaussian function with a relatively small width to account for the actual local protrusive event, iii) a positive Gaussian function with a mean moving forward and backward to account for the traveling wave, and iv) a negative Gaussian function in time centered on 0 to account for the central long-lasting inhibition. All those terms were combined with exponentially decaying function of time to account for the temporal "fading". This transfer function was further convolved with a synthetic Cdc42 signal to simulate a realistic protrusion. We assumed that Cdc42 activity for a single protrusion could be described by a "signaling puff" in space and time, made using a product between a Gaussian function (lateral extension of the puff) and an exponentially decaying function of time (duration of the puff). The resulting morphodynamic map then represents the edge dynamics following a single protrusive event (note that what we call a single protrusive event could be the outcome of several protrusions sustained by another feedback -for example between actin and Cdc42 or Rac1 activity). The duration of Cdc42 activity was chosen such that the duration of the protrusion event was similar to the one observed in our data. For that, we considered the experimental morphodynamic maps under Nocodazole and Golgicide A treatments to better isolate unique protrusive events. Experimental protrusions are extended over c.a. 10 frames, thus 50 minutes. We used this number such that our simulation time frame matches the experimental one. The single protrusion morphodynamic map was then normalized such that the integral (sum over space and time) was null (zero mean) to ensure a constant cell area. This morphodynamic map is shown in Figure 2.37.

First side of the feedback: effect of the polarity axis on protrusions

Next, we simulated a full morphodynamic map by introducing the random appearance of protrusion over time. We took a total duration of the simulation of 1000 frames, t tot = 1000, and the frequency at which protrusions happen was characterized by a probability of appearance per unit of time p rand = 0.5. The Figure 4.10 illustrates morphodynamic maps for different values of p rand . If for a given time a protrusion event happened, the position of this protrusion event along the contour was chosen either randomly (uniform distribution over all markers of the contour) or in the direction of the polarity axis (see bellow), given by the position of a specific marker x N G that corresponds to the intersection of the Nucleus-Golgi axis with the cell contour (whose dynamics are described in the next paragraph). The choice of a polarized protrusion was characterized by the probability p polarized (probability of a randomly placed protrusion is then 1 -p polarized ), which quantifies the strength of the feedback between the polarity axis and biased initiation of protrusions. When p polarized = 0, protrusions are happening randomly along the contour, and when p polarized = 1 protrusions are always happening in front of the Nucleus-Golgi axis (see Figure 4.11 for an example). To avoid a non-realistic perfectly straight movement, we introduced a low level of noise for polarized protrusions, namely the position of protrusion was drawn from a normally distributed function whose mean is x N G and standard deviation is σ N G = 5 (1/20 of the cell contour). Note that our main result does not depend on the exact value of σ N G . Indeed, this parameter plays a role only on the asymptotic value of the autocorrelation of direction when p polarized ∼ 1, but not on the actual characteristic decay time of the autocorrelation function (which characterizes the persistence time, our main observable). there is a weak tendency to form protrusion in the direction of the Nucleus-Golgi axis. In the bottom figure, there is a strong tendency to form protrusion in the direction of the Nucleus-Golgi axis. The x axis is time (1000 frames) and the y axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Natural dynamics of the polarity axis

As mentioned above, we also needed to explicitly model the evolution of the polarity axis. This polarity axis, specified by the position x N G , was defined as the pointing direction of the Nucleus-Golgi axis but it can also be thought as the direction of the polarized secretion. indeed, in the context of our model, this polarity axis should be taken as the effective bias of either Golgi positioning or directionality of secretion on the protrusive activity (both of them correlate, see our experimental data). In absence of any feedback of protrusions on the polarity axis, we could assume that this polarity axis remains at the same position. However, under this assumption, if we plug-in the second feedback (biased protrusions) the cell would move straight, which would not be realistic. We, thus, modeled a "natural" movement of the polarity axis that would mimic the random evolution of the Nucleus-Golgi axis when no protrusions affect it. The closest experimental data to infer this dynamic is found for cells plated on a round pattern (see Figure 2.28,control in B). In that situation, the Nucleus-Golgi axis moves as a correlated random walk whose span reaches 360 degrees in about 4 hours. We simulated such dynamics by assuming that the instantaneous speed of the Nucleus-Golgi axis was set by the derivative of a smoothed random function whose values over time are given by a random number between 0 and 10 times the number of markers. The overall natural evolution of the polarity axis, x natural N G , is depicted in Figure 4.12 for a timescale comparable to experiments and in Figure 4.13 for the total duration of the simulation. The actual model we chose for the natural evolution of the polarity axis is arbitrary, nonetheless the details do not matter for the outcome of our simulation. The only important effect is that this polarity axis gets reoriented randomly in about 4 hours.

Second side of the feedback: effect of protrusions on the polarity axis

To model the other side of the feedback, namely the reorientation of the polarity axis by protrusions, we assumed that an effective force was attracting the previously defined Nucleus-Golgi axis towards protrusions. This force was computed as the sum of membrane speed over all markers, F prot = 100 x i =0 v x i . The underlying assumption is that every protruding portion of the cell pulls on the Nucleus-Golgi axis with a force proportional to the protrusion speed and does this independently of the respective positions of protrusions with regards to the Nucleus-Golgi axis. This effective force is competing with the force corresponding to the natural evolution of the Nucleus-Golgi axis,

F basal = d dt x natural N G
. The strength of the feedback was implemented by introducing a linear combination between these two forces characterized by a value κ: d dt x N G = κF prot + (1 -κ)F basal . When κ = 0, the Nucleus-Golgi axis follows its natural evolution. When κ = 1, the Nucleus-Golgi axis follows the protrusions. This parameter κ can be expressed as the relative contribution of the effective force towards protrusions, κ = Ftot-F basal Fprot-F basal , where F tot is the total force acting on the Nucleus-Golgi axis. The Figure 4.14 shows an example of morphodynamic maps with two values of the strength of the feedback. As above, the rule chosen to implement the feedback is arbitrary (we could have taken a metric such that protrusions close to the Nucleus-Golgi axis matter more than the distant ones), but our goal was to implement a minimal model integrating the feedback. The details are not critical for the outcome of our modeling approach.

Full model with the two-sided feedback

Altogether, the two sides of the feedback can be implemented in our simulation to produce realistic morphodynamic maps, see Figure 4.15 for an example with a low frequency of protrusions and Figure 4.16 for an example with realistic protrusion frequency. These morphodynamic maps were then translated into cell trajectories, by noticing that the instantaneous movement of the cell centroid is simply the sum of all the velocities of the markers along the cell contour. These trajectories were analyzed in the same way as the experimental ones, to obtain the autocorrelation of direction and, then, the characteristic decay time of this function that we call the persistence time. By varying the strength of the two sides of the feedback, we were able to produce the phase diagram presented in Figure 2.37. For visualisation purposes, we also used the morphodynamic maps to produce synthetic movies of migrating cells. For this purpose, we inverted the process of morphodynamic map quantification and used a morphodynamic map to evolve an elastic contour over time.

Protrusion unicity index

In addition to the mapping of persistence time as a function of the strength of the two sides of the feedback, we developed two other independent measures aimed at quantifying cell polarity. First, to quantitatively assess the polarity of cells in terms of front-to-back polarity, we wanted to compute a number, characterizing the number of simultaneous protrusions. Indeed, cells presenting a single protrusion over time are monopolar and thus well polarized, whereas cells presenting several protruding fronts are multipolar and, thus, are lacking a single polarity axis. We introduced a Protrusion unicity index as the inverse average number of simultaneous protrusions to quantify this aspect of cell polarity. To compute this index, we used a sliding window of 10 frames (50 minutes) applied on the morphodynamic map and we segmented protrusions based on a threshold (70% of maximal protrusion speed). The number of competing protrusions, N p , was then obtained as the number of non-connected segmented objects and this number was averaged over the whole duration of the simulation (1000 frames) and over 20 realizations. The Protrusion unicity index for a given value of κ and P polarized was taken as 1/N p . This index is equal to one when a single protrusion is present, and goes to zero as more and more protrusions are competing. As seen from the Figure 4.17, the main parameter dictating this unicity index is P polarized . This is easily understood: no matter if the NG-axis follows protrusions or not, if P polarized is high, there will always be a single protrusive activity in front of the NG-axis.

Alignment index

To quantitatively assess the polarity of cells in terms of the alignment of their polarity axis with direction of movement, we wanted to compute how well the NGaxis aligns with cell movement. We, thus, introduced an Alignment index, as the standard deviation of the angle between the NG-axis and instantaneous direction of movement. In terms of circular statistics, this standard deviation is called the angular dispersion and is defined as r = ( 1 n × n i=1 sin θ i ) 2 + ( 1 n × n i=1 cos θ i ) 2 . The angular dispersion varies between 0 (uniform dispersion) and 1 (perfect alignment). As seen from the Figure 4.18, the Alignment index depends both on κ and P polarized . Indeed, when P polarized is close to zero, even if κ = 1 protrusions happen randomly all the time and the NG axis does not have time to follow them, thus leading to a low value of alignment. While conducting optogenetic activation experiments on freely moving cells on 2D substrate, I was randomly choosing on which side of the existing Nucleus-Golgi axis to induce optogenetic activation. I was activating either on the right (R) from the existing Nucleus-Golgi axis, or on the left (L). Interestingly, I observed a bias in the turning of this axis. I have found that turning clockwise (CW) towards the induced light happened more often than turning counter-clockwise (CCW) (87% from total cells that reoriented, Figure A.3, first group "Free 24h", n = 23 (R) and n = 17 (L) cells). Additionally, I noticed that if the activation spot was 90°to the left (L), the Nucleus-Golgi axis turned 270°to reorient, taking the longer path and going clockwise (CW) (24%, Figure A.3, first group "Free 24h", "L" stack, orange). This never happened if the activation area was 90°away to the right (R) (see in Figure A.3,first group,light blue). In addition to that, more than half of these cells failed to reorient at all (53%, Figure A.3,first group "Free 24h",grey). This phenomena of a bias of Nucleus-Golgi axis turning only one way might propose the existence of handedness, otherwise called -chirality [START_REF] Wan | Cell chirality: Emergence of asymmetry from cell culture[END_REF].

One must always be careful when involving chirality in its assumptions, as the asymmetric bias might arise from the differences in the substrate, in the substrate pattern, the shape of a cell or, even, the force of gravity [START_REF] Tamada | Autonomous right-screw rotation of growth cone filopodia drives neurite turning[END_REF], Wan et al., 2013, Wan et al., 2011, Tee et al., 2015]. In our experiments cells were free to move on fibronectin coated coverslips, thus, the substrate was homogenous. However, it is important to rule out the bias that might come from the membrane shape. For this, we looked at the results from my previously described experiment, where cells are put on an isotropic round pattern. In this case, the Nucleus-Golgi axis reorients, but the protrusions don't attach outside of the pattern, keeping the round symmetric shape. Curiously, in this case the amount of cells taking the short path if activated to the left (L) highly increased (from 24% to 67%, see A particular detail discerning the experiments with freely moving cells and cells on a pattern is the time given to attach to the substrate. It is twice shorter if cells are put on a pattern (<10h). This is to avoid cell division when the cell is already attached on the pattern, as this cell would need to be discarded from the analysis. To test the hypothesis that the difference in percentage of reorientation modes stems from attachment times, I performed another set of experiments, where freely moving cells were attached on the substrate for <10h instead of 24h as before. Interestingly, I did not observe the bias in Nucleus-Golgi axis turning when adhesion time of cells was reduced to <10h (Figure A.3, middle group "Free <10h", n = 17 (R) and n = 17 (L) cells).

A randomized selection of optogenetic activation position revealed a preference of Nucleus-Golgi axis movement in a clockwise (CW) direction instead of taking the shortest path to realign with the induced protrusion. The chirality of RPE1 cells was already proposed in literature before [START_REF] Duclos | Spontaneous shear flow in confined cellular nematics[END_REF], but mostly in the context of collective cell migration on micropatterns [START_REF] Wan | Micropatterned mammalian cells exhibit phenotype-specific left-right asymmetry[END_REF], Raymond et al., 2016]. It is hard to compare collective cell migration with the results in single cells, because chirality might be an emerging property of a system [START_REF] Wan | Cell chirality: Emergence of asymmetry from cell culture[END_REF]. The few proposed molecular candidates from which cellular chirality might arise are components of cytoskeleton [Pohl, 2015, Satir, 2016] -actin cytoskeleton [START_REF] Tee | Cellular chirality arising from the self-organization of the actin cytoskeleton[END_REF] and centrosome with microtubules [START_REF] Xu | Polarity reveals intrinsic cell chirality[END_REF]. Our results point to the involvement of maturation of cytoskeleton during attachment to the substrate [START_REF] Tee | Cellular chirality arising from the self-organization of the actin cytoskeleton[END_REF]. A chiral structure might be forming, which matures slowly and which would facilitate Nucleus-Golgi axis movement in one direction. All in all, optogenetic techniques that let us override intracellular biochemical gradients could be a good strategy to dissect complex pathways, like establishment of chirality, in a controlled manner. The reorientation of Nucleus-Golgi axis can be achieved by several different mechanisms, whose role is hard to separate from each other and hard to dissect. Three basic possibilities can be thought of: Golgi could be turning around Nucleus (Figure B.1,1), Nucleus could be turning around the Golgi (Figure B.1,2) or Nucleus-Golgi could move as a single block (Figure B.1,[START_REF]1 Persistence time phase diagram[END_REF]. Nucleus-Golgi axis reorientation has been proposed to be regulated either by microtubules or by actin cytoskeleton. One of the proposed pathways is MT capture at the cell cortex at the leading edge and pulling on the centrosome and the Golgi complex [Etienne- Manneville et al., 2005]. Another proposed pathway reorients the Nucleus-Golgi axis through actin polimerization and actin retrograde flow [Gomes et al., 2005b]. In this case, it is the nucleus that is moving away from the leading edge of the migrating cell, as it is pushed back with the actin retrograde flow. The actin retrograde flow directly depends on actin polimerization. As polimerization increases, the retrograde flow becomes stronger [START_REF] Ponti | Two distinct actin networks drive the protrusion of migrating cells[END_REF]. With optogenetic Cdc42 activation, we were directly increasing actin polimerization in the activated area, which might lead to nucleus being pushed back and Nucleus-Golgi axis reorienting. In all three aforementioned possibilities of how Nucleus-Golgi axis could be reorienting, the total distance travelled by each organelle (Nucleus or Golgi) is specific and could give us a clue, which model is correct. In the first model, where the Golgi is travelling around the nucleus, the Golgi would travel a longer distance. In the second model, where the nucleus is displaced and turns around the Golgi complex, it should be inverse and the total distance travelled by the Nucleus should be higher than distance travelled by Golgi. In the third model, where Nucleus and Golgi move together, we would expect the total displacement of each organelle to be similar ( . This suggests that Nucleus and Golgi might be moving together, and adding NZ, which prevents MT polymerization, doesn't disrupt the process. To be able to spot even smaller differences, we calculated the total difference between Nucleus and Golgi displacement, which did not show any difference either (Figure B.2,(B)).

The results indicate, that Nucleus and Golgi travel a similar distance in the process of Nucleus-Golgi axis reorientation. It proposes that either Nucleus and Golgi have a strong link and reorient as a single block, or that both the Nucleus and the Golgi are reoriented at the same time in a coordinated manner, but by different mechanisms. We have to keep in mind, that in these experiments, only low concentrations of NZ were used, affecting only the dynamic population of microtubules, and results might be different in the case of full microtubule depolymerization. The experimental conditions were not sufficient to dissect the different contributions of microtubule and actin networks to this complex process. A stronger perturbation might be needed to dissect the Nucleus-Golgi axis reorientation process.

1. 1

 1 Cell migration in in vitro 2D culture environments. . . . . . . . . . . . . 1.2 Properties of actin filaments. . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Specialized actin organizations in vivo. . . . . . . . . . . . . . . . . . . . 1.4 The force transmission by adhesion. . . . . . . . . . . . . . . . . . . . . 1.5 Plasticity of migration modes. . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Cartoon depicting the serial connection between the extracellular matrix, integrins, mechanosensitive adaptor proteins, and actin. . . . . . . 1.7 Schematic of adhesion assembly, turnover and maturation. . . . . . . . . 1.8 Nanoscale architecture of focal adhesions. . . . . . . . . . . . . . . . . . 1.9 Overview of Rho GTPase regulation. . . . . . . . . . . . . . . . . . . . . 1.10 The Cdc42 GTPase and its regulators in budding yeast. . . . . . . . . . 1.11 Multiple signalling pathways controlled by Cdc42. . . . . . . . . . . . . 1.12 Overview of intracellular trafficking pathways. . . . . . . . . . . . . . . . 1.13 General principles of membrane trafficking. . . . . . . . . . . . . . . . . 1.14 Two models of protein trafficking through the Golgi. . . . . . . . . . . . 1.15 Golgi complex structure and stages of maturation. . . . . . . . . . . . . 1.16 Proteins associated with tubular carriers in mammalian cells. . . . . . . 1.17 Properties of microtubules. . . . . . . . . . . . . . . . . . . . . . . . . . 1.18 The elements of the tubulin code. . . . . . . . . . . . . . . . . . . . . . . 1.19 Examples of microtubule geometries in mesenchymal cells. . . . . . . . . 1.20 Activation of dynein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.21 Possible regulation of cargo directionality. . . . . . . . . . . . . . . . . . 1.22 Rab functional cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.23 Scheme of Rab GTPase functions in vesicle trafficking. . . . . . . . . . . 1.24 Rab cascade model for the establishment and maintenance of the directionality of the secretory and endocytic pathways. . . . . . . . . . . . . 1.25 Proposed model to explain the role of RAB6 in post-Golgi secretory pathway. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.26 Cell polarity emerges from collective interconnection of cellular asymmetries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.27 The polarized migrating cell. . . . . . . . . . . . . . . . . . . . . . . . . 1.28 Actin and microtubule-dependent processes that control centrosome and nucleus positioning in cell migration. . . . . . . . . . . . . . . . . . . . . 1.29 The LINC complex connects the cytoskeleton to the nuclear envelope. . 1.30 The structure of the Golgi apparatus in different organisms. . . . . . . . 1.31 Golgi positioning directs secretion to cell leading edge. . . . . . . . . . . 1.32 Model for GOLPH3-dependent Golgi reorientation and directional trafficking in wound healing. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.33 Random and directional migration. . . . . . . . . . . . . . . . . . . . . . Chapter 1

Figure 1 . 3 :

 13 Figure 1.3: Specialized actin organizations in vivo. Motile cells have distinct actin organizations in different locations in the cell, specialized for precise functions. i) The actin cortex is anchored to the plasma membrane through ERM proteins and is contractile via myosin activity. ii) One category of contractile bundles, the stress fibers, are found spanning the cell body, usually oriented parallel to the direction of movement. They are attached to focal adhesions and involve a specific set of regulatory intracellular factors. iii) Transverse arcs are specific antiparallel actin filament formations found at the back of the lamellipodium. They are contractile through myosin activity. iv) The lamellipodium, hosts rapid, massive, and localized polymerization of branched actin networks. A: initiation of this dendritic network occurs via locally activated Arp2/3 complex binding to the side of an actin filament "primer" and by interaction with members of the WAVE family of proteins. Elongation of the network occurs by addition of the profilin/actin complex (black arrows) to the barbed ends of actin filament in close contact with the plasma membrane. B: Ena/VASP proteins, the formin FMNL2 and capping proteins control the elongation of the network by modulating the dynamics at filament barbed ends (right zoom inset). Ena/VASP and FMNL2 favor barbed end elongation whereas capping protein blocks it. v) The filopodia, are filled with parallel actin bundles elongated by the actin polymerases, Ena/VASP and formins, and tightly packed by the short bundler fascin. Taken from[START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF].

Figure 1 . 4 :

 14 Figure 1.4: The force transmission by adhesion. Actin filaments are constantly undergoing polymerization and depolymerization, resulting in retrograde flow. Actin filaments can connect to integrin to form focal adhesions. The resistance provided by the focal adhesions against retrograde flow promotes membrane protrusion. Also, contractile forces generated by myosin are converted by the focal adhesion into traction forces against the ECM. Combined, these forces drive forward movement by membrane protrusion. As the focal adhesions mature, the connection to actin is reinforced and become fully engaged. Taken from www.mechanobio.info page.

Figure 1 . 5 :

 15 Figure 1.5: Plasticity of migration modes. Mesenchymal migration can be characterized by specific adhesion complexes (focal adhesions), and polymerization induced actin flows. By lowering adhesion and increasing confinement, cells can switch to an amoeboid mode characterized by cortical actin flows driven by actin/myosin contractility. Taken from [Callan-Jones and Voituriez, 2016].

Figure 1 . 8 :

 18 Figure 1.8: Nanoscale architecture of focal adhesions. Schematic model of focal adhesion molecular architecture, depicting experimentally determined protein positions (not stoichiometry) and revealing several structural layers. Taken from [Kanchanawong et al., 2010].

Figure 1 . 11 :

 111 Figure 1.11: Multiple signalling pathways controlled by Cdc42. Cell polarization requires the spatial and temporal regulation of several cell components. Orientation of the actin and microtubule cytoskeletons, regulation of cell contacts and organization of membrane traffic occur in concert. Multiple signalling pathways downstream of Cdc42 regulate these different cellular components (black box). These signals are transduced by different Cdc42 direct (solid line) or indirect (dotted line) effectors (blue) and involve several intermediates (blue). Taken from [Etienne-Manneville, 2004].

Figure 1 .

 1 Figure1.15: (A) Building blocks of the Golgi apparatus. Adapted from[START_REF] Saraste | A New Look at the Functional Organization of the Golgi Ribbon[END_REF]. (B) Golgi complex can be divided into three stages of maturation. During the cisternal assembly stage, COPII vesicles bud from the ER and fuse with one another to generate a new Golgi cisterna, while COPIa vesicles bud from this nascent cisterna to recycle trafficking proteins and resident ER proteins to the ER. This stage includes cis Golgi cisternae, as well as ERGIC ("ER-Golgi intermediate compartment") membranes in animal cells. During the carbohydrate synthesis stage, most of the glycosylation reactions take place, and resident Golgi proteins are transferred between cisternae by COPIb vesicles. This stage includes cisternae that are often designated medial and trans. During the carrier formation stage, the cisterna disintegrates to produce cargo carriers that include secretory and clathrin-coated vesicles. This stage includes cisternae that are traditionally designated as TGN. Adapted from[START_REF] Papanikou | Golgi compartmentation and identity[END_REF].

Figure 1 . 19 :

 119 Figure 1.19: Examples of microtubule geometries in mesenchymal cells. An unpolarized mesenchymal cell containing both Golgi-and centrosome-anchored microtubules (left panel).In a polarized mesenchymal cell migrating on a 2D substrate, the Golgi complex and the centrosome are positioned on one side of the nucleus and promote the formation of a polarized microtubule array oriented in the direction of migration (arrow) (right panel). Taken from[START_REF] Meiring | Generation and regulation of microtubule network asymmetry to drive cell polarity[END_REF].

Figure 1 . 20 :

 120 Figure1.20: Activation of dynein. Dynein motor can function and transport cargo on microtubule tracks only in complex with dynactin and a coiled-coil activator protein. The formation of the complex leads to processive movement towards the minus end of the microtubule. Adapted from[START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF].

Figure 1 . 21 :

 121 Figure 1.21: Possible regulation of cargo directionality. Different regulatory proteins might activate dynein or kinesin motors that are attached to the same cargo. Distinct activation would result in movement either towards the minus end or the plus end of microtubule, respectively.Adapted from[START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF].

Figure 1 . 22 :

 122 Figure1.22: Rab functional cycle. The newly synthesized GDP-bound Rab is recognized by REP and presented to RabGGT, which geranylgeranylates the Rab on one or two C-terminal Cys residues. Targeting of the Rab/REP (or Rab/GDI) complex to specific membranes is mediated by the interaction with a membrane-associated GEF, which stimulates GDP to GTP exchange of Rab; or in few cases by interaction with a GDF first, followed by GEF stimulated activation. The GTP-bound (active) Rab conformation is recognized by multiple effector proteins, which then carry out their specific functions. GAP stimulates Rab GTPase activity and converts Rab back to the inactive, GDP-bound form, resulting in the dissociation of effectors. GDI regulates the cycling of Rab between the membranes by extracting inactive Rab from a membrane into the cytosol and subsequently delivering it back to a donor membrane compartment. Taken from[START_REF] Pylypenko | Rab GTPases and their interacting protein partners: Structural insights into Rab functional diversity[END_REF].

Figure 1 . 23 :

 123 Figure 1.23: Scheme of Rab GTPase functions in vesicle trafficking. Distinct membrane trafficking steps that can be controlled by a Rab GTPase and its effectors (indicated in orange).(a) Active GTP-bound Rab activates a sorting adaptor to sort a receptor into a budding vesicle. (b) Through recruitment of phosphoinositide (PI) kinases or phosphatases, the PI composition of a transport vesicle is altered (the conversion of PI-x into PI-y) and thereby causes uncoating through the dissociation of PI-binding coat proteins. (c) Rab GTPases mediate vesicle transport along actin filaments or microtubules (collectively referred to as cytoskeletal tracks) by recruiting motor adaptors or by binding directly to motors (not shown). (d) Rab GTPases mediate vesicle tethering by recruiting rod-shaped tethering factors that interact with molecules in the acceptor membrane. Such factors interact with SNAREs and their regulators to activate SNARE complex formation, which results in membrane fusion. (e) Following membrane fusion and exocytosis, the Rab GTPase is converted to its inactive GDP-bound form through hydrolysis of GTP, which is stimulated by a GTPase-activating protein (GAP). Targeting of the Rab-GDP dissociation inhibitor (GDI) complex back to the donor membrane is mediated by interaction with a membrane-bound GDI displacement factor (GDF). Conversion of the GDP-bound Rab into the GTP-bound form is catalysed by a guanine nucleotide exchange factor (GEF). Taken from[Stenmark, 2009].

Figure 1 . 24 :

 124 Figure 1.24: Rab cascade model for the establishment and maintenance of the polarity of the secretory and endocytic pathways. (A) In the first scenario, a Rab GEF specific for Rab A generates active Rab A. That Rab recruits a second GEF, which activates Rab B. Similarly, Rab B recruits a GEF to activate Rab C. In this model, a membrane could have Rabs A-C intermingled or at least on a single compartment. (B)Here GAP proteins are included to remove a previous-acting Rab from a specific membrane domain. The presence of the GAP will sharpen the boundaries between individual Rab domains. Taken from[Pfeffer, 2017].

Figure 1 . 25 :

 125 Figure1.25: Proposed model to explain the role of RAB6 in post-Golgi secretory pathway. All RAB6 effectors associated to post-Golgi secretion, myosin II, KIF5B, and ELKS/RAB6IP2, are involved in the secretion of various cargos. The different events can be envisioned as follows. RAB6 is present on CD59-, TNFα-, and ColX-containing vesicles exiting the Golgi complex. Myosin II is implicated in the fission of these vesicles from Golgi membranes. Vesicles are transported to the plasma membrane in a KIF5B-dependent manner, and ELKS ensures their docking to exocytic hotspots close to FAs. Taken from[START_REF] Fourriere | RAB6 and microtubules restrict protein secretion to focal adhesions[END_REF].

Figure 1 .

 1 Figure 1.26: Cell polarity emerges from collective interconnection of cellular asymmetries.Elementary processes: (top) gradients of proteins or activity of proteins, (right) anisotropy of cell shape and cytoskeleton, (bottom) asymmetric distribution of vesicles and organelles, (left) oriented transport of material. A functional polarized state is achieved when these elementary processes are properly coupled (arrows 1-6). Taken from[START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF].

Figure

  Figure1.27: The polarized migrating cell. Top, cartoon of a canonical polarized mesenchymal migrating cell. The cell presents a front-rear organization, with a protruding front and a retracting rear. (A-D) Subsets of elements that compose a canonical polarized cell. (A) Signaling gradients of RhoGTPases: Rac1 and Cdc42 are mainly activated in the protruding region of the cell, whereas RhoA is responsible for the rear retraction. RhoA is also transiently activated in the front of the cell (not shown). (B) The actin cytoskeleton (red) and focal adhesions (FA, light orange). At the protruding front, in the lamellipodia, branched actin pushes the PM and is subjected to a retrograde flow. In filopodia, actin is bundled. Actin arcs can be present in the lamella, behind the lamellipodia. Stress fibers are observed along the quiescent edges of the cell, in the retracting rear, and in the lamella. Nascent FAs (not shown) are observed in the lamellipodia, and mature FAs are observed at the end of stress fibers, in the lamella and in the rear. (C) The microtubule (MT) network and organelles. The MTOC or centrosome (yellow) and the Golgi complex (light pink) are aligned and organized along the rear-to-front polarity axis. MTs span the whole cell with a radial organization centered on the MTOC. The endoplasmic reticulum (green, ER) and mitochondria (purple) are scattered in perinuclear regions assuming an asymmetric distribution towards the front. Endosomes (big pink circles), recycling endosomes (amorphous shape), and secretory vesicles (small pink circles) are observed all across the cell. Their trafficking routes depend on MTs and molecular motors. (D) Asymmetric distribution of lipids both at the PM and in endomembranes. At the cell scale, lipid gradients, such as the PI(4,5)P 2 -PI(3,4,5)P 3 gradients, are distributed along the rear-to-front axis (green to pink). Organelles are also defined by specific lipid compositions (not shown) that depend on complex lipid trafficking and spatially restricted reactions. Adapted from[START_REF] Vaidziulyte | Intracellular organization in cell polarity -placing organelles into the polarity loop[END_REF].

Figure 1 . 28 :

 128 Figure1.28: Actin and microtubule-dependent processes that control centrosome and nucleus positioning in cell migration. Green curved lines represent microtubules, blue straight lines actomyosin fibers. The centrosome is shown as a purple dot and the nucleus is grey. Coordinated centrosome movements rely on microtubule-dependent as well as actin-dependent processes. The molecular mechanisms involved in centrosome and nucleus movement are depicted in the right panels, in colored boxes. Their polarized distribution at the cell cortex is shown with the corresponding color on the drawing on the left. Taken from[START_REF] Elric | Centrosome positioning in polarized cells: Common themes and variations[END_REF].

Figure 1 . 30 :

 130 Figure 1.30: The structure of the Golgi apparatus in different organisms. (A) Golgi ministacks (green) are dispersed throughout the cytoplasm in yeast, plants, and invertebrates. (B)In vertebrates, the Golgi is organized as a ribbon structure in the perinuclear region of most cells, maintained close to the centrosome (small red oval) by interactions with microtubules (blue). Taken from[START_REF] Gosavi | The Function of the Golgi Ribbon Structure -An Enduring Mystery Unfolds![END_REF].

Figure 1 . 33 :

 133 Figure 1.33: Random and directional migration. Part (a) of the figure depicts a cell at three time points as it migrates in a uniform concentration of external cue. Part (b) depicts a cell at three time points as it migrates in a gradient of increasing concentration of external cue.At each time point, the migration can be defined by the centre of the cell mass, the distance travelled between positions (path length), the turning angle (Θ) and the net displacement. This information can be used to describe the rate and directionality of migration. Adapted from[START_REF] Petrie | Random versus directionally persistent cell migration[END_REF].

Figure 1 . 34 :

 134 Figure 1.34: Four stages of Rac-GTP regulation of cell morphology and types of cell motility. The amount of Rac localized in lamellae as shown by anti-Rac1 antibody localization (left) and depicted schematically in the diagram (red) with increasing levels of Rac activation (broad gray arrow) from state I to state IV. Increased levels of total cellular active Rac produce characteristic increases in the extent of random cell motility accompanied by varying velocities of cell migration in 2D versus 3D culture or after experimental manipulations of Rac activity.Rac activation that is too low or too high leads to immobilization, with stunted lamellae at low levels and continuous, circumferential lamellae or cell rounding at very high levels. The cells shown in the examples were primary human fibroblasts stained for Rac1 after culturing on a 2D substrate (state III) or in a 3D matrix (state II) compared with effects of extensive knockdown of Rac1 using 200 nM Rac siRNA (state I) or overexpression of constitutively activated Rac QL after transient transfection (state IV). Taken from[START_REF] Pankov | A Rac switch regulates random versus directionally persistent cell migration[END_REF].

Figure 1 . 35 :

 135 Figure 1.35: Retrograde trafficking in distal tip cell migration in C.elegans.Non-ligand-bound β1-integrin is endocytosed and transported in a retromer-, Rab6-and syntaxin 16-dependent manner to the TGN. From the TGN, polarized secretion operates the targeted β1-integrin delivery to the leading edge of migrating cells, ensuring a topical supply of focal adhesion materials, thereby enabling persistent cell migration. Taken from[START_REF] Shafaq-Zadah | Persistent cell migration and adhesion rely on retrograde transport of β 1 integrin[END_REF].

Figure 1 . 36 :

 136 Figure 1.36: Actin flows couple cell speed and cell persistence. Taken from [Callan-Jones and Voituriez, 2016].

Figure 1 .

 1 Figure 1.37:A modified LEGI model. A diagram of the modified local excitation/ global inhibition (LEGI) model that involves the production of both excitation and inhibitory signals in the frontal region, followed by the transport of inhibitory signals away from the front to maintain frontal protrusions and cell polarity in control cells. In Nocodazole-treated cells, the impairment of the transport and the resulting accumulation of inhibitory signals at the front act against the excitation signals and cause the head to switch into a tail. Taken from[START_REF] Zhang | Microtubules stabilize cell polarity by localizing rear signals[END_REF].

Figure 1 . 38 :

 138 Figure 1.38: Effect of centrosome position on cell polarity through the distribution of inhibitory signals. (A) In a LEGI type model for controlling cell migration, both inhibitory (red dots) and excitation (green dots) signals are generated at the front. While excitation signals remain localized, inhibitory signals are transported along microtubules to reach a higher concentration near the centrosome (blue dot) than elsewhere, where they induce retraction in the region nearby (green star denotes the front and red star denotes the rear). (B) During directional reversal at the end of a strip (black bar), protrusion takes place at the original tail soon after the original front reaches the dead end, which causes a decrease in the generation of both excitation and inhibitory signals at the original front. As the new protrusion at the opposite end starts to send inhibitory signals to the centrosome, the stalled original front is initially unable to turn into a tail due to the long distance from the centrosome, where retraction signals are concentrated (Stage 1). The probability of retraction increases as the centrosome moves toward the stalled front end causing a corresponding shift of inhibitory signals (Stage 2), eventually turning it into a retracting tail (Stage 2, red star). (C) During symmetry breaking in one dimension, both ends protrude during early stages while sending inhibitory signals to the centrosome. As the cell spreads out, the end closer to the centrosome eventually receives a sufficient concentration of inhibitory signals to cause retraction. Taken from[START_REF] Zhang | Cryo-EM Reveals How Human Cytoplasmic Dynein Is Auto-inhibited and Activated[END_REF].

Figure 1 . 40 :

 140 Figure1.40: Conceptual mechanism for long-range inhibition by mechanical tension. Protrusion at the leading edge generates mechanical tension (T, depicted as red springs) in either the plasma membrane or the underlying cytoskeleton. This tension acts as a long-range inhibitor of protrusion. Taken from[START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF].

Figure 1 . 43 :

 143 Figure1.43: Optogenetic dimerization systems. (A) iLID. LOV domain, depicted in blue, reveals a SsrA peptide upon the illumination of blue light, which can be bound by a specific interactor SspB. (B) Cryptochrome (Cry2/CIBN). Upon blue-light illumination, the photosensitive protein CRY2 undergoes a conformational change and binds to its interaction partner CIBN. (C) Phytochrome (PHYB/PIF). The phytochrome system consists of the PHYB photoreceptor, which binds to its interaction partner PIF upon red-light illumination. Far-red illumination causes the PHYB/PIF interaction to dissociate, making the optogenetic system reversible. PHYB activity depends on the plant-specific co-factor PCB. Adapted from[START_REF] Krueger | Principles and applications of optogenetics in developmental biology[END_REF].

Figure 1 . 45 :

 145 Figure1.45: Example of a RAW macrophage cell undergoing optogenetically driven cell migration through Cdc42 activation. Note the accumulation of mCherry-tagged GEF at the leading edge. Scale bar is 10 µm. Time is in min:s. Taken from[START_REF] Meshik | Optogenetic control of cell migration[END_REF].

Figure 1 . 46 :

 146 Figure 1.46: Simplified sketch of a PhD hypothesis.

Figure 2 . 1 :

 21 Figure 2.1: Resolution in low vs. high magnification. Cells imaged with 10x magnification (A) and 60x magnification (B) (scale bar -50 µm.)

Figure 2 . 2 :

 22 Figure 2.2: Nucleus-Golgi axis aligns to direction of movement in a migrating cell. (A) Migrating RPE1 cell at different time points tracked (cyan: myr-iRFP, yellow: GFP-Rab6A, blue: Hoechst 33342, trajectory overlaid in orange, microscope stage movement represented by an arrow, scale bar -20 µm). (B) Full trajectory of a representative cell shown in (A) with Nucleus-Golgi axis (black dashed arrow) and direction of movement (orange dashed arrow) overlaid. (C) Polar histogram representing the averaged angle between Nucleus-Golgi axis and direction of movement, which is normalized to 0°(n=17 cells).

Figure 2 . 3 :

 23 Figure 2.3: Persistent protrusions form in front of the Golgi complex. (A) Explanatory sketch of how a morphodynamic map of cell shape changes is calculated. The contour of the cell is extracted and compared between frames, and stretched out to a line representation, where the distance travelled by a point in the contour is represented (red color meaning strong movement forward, blue -retraction). (B) Morphodynamic map of a representative cell normalized to Nucleus-Golgi axis (black). (C) Average protrusion speed over time (n=17 cells, dashed blue line -sd).

Figure 2 . 4 :

 24 Figure 2.4: Cell moves where it protrudes. (A) Morphodynamic map of a representative cell normalized to direction of movement (black). (B) Average protrusion speed over time (n=17 cells, dashed blue line -sd).

Figure 2 . 5 :

 25 Figure 2.5: Cell moving out of a dynamic micropattern. (A) Schematic representing a cell is confined on a round fibronectin pattern and after the addition of BCN-RGD is enabled to move outside and "escape" the pattern. (B) RPE1 cell "escaping" the pattern (transparent cyan: pattern, cyan dot: nucleus centroid, yellow: GFP-Rab6A, red dot: Golgi centroid, black dashed line: Nucleus-Golgi axis, orange dashed line: direction of movement, scale bar -20 µm).

Figure 2 . 6 :

 26 Figure 2.6: Several examples of Nucleus-Golgi axis positioning in cells while moving out of an isotropic pattern (white circle: pattern, a line represents evolution of Nucleus-Golgi axis position in time from blue (start of experiment) to red (end of experiment), movement aligned by the author for visual purposes).

Figure 2 . 7 :

 27 Figure 2.7: Distance of the nucleus centroid from the center of the pattern. The nucleus starts to move out of the center approximately 1h before the escape. Its movement clearly points to the moment when the cell goes out of the pattern (black arrow).

Figure 2 . 8 :

 28 Figure 2.8: Nucleus-Golgi axis and direction of movement align when a cell starts moving. Polar histograms representing the angle between Nucleus-Golgi axis at the beginning of experiment (t=0) (A) or at the time of "escape" (t=ESCAPE) (B) and direction of movement when the cell moves out of the pattern (n=36 cells).

Figure 2 . 9 :

 29 Figure 2.9: Nucleus-Golgi axis position is established at the same time as direction of movement. Evolution of Nucleus-Golgi axis position and cell movement (orange: Nucleus-pattern axis, black: Nucleus-Golgi axis, the position of both axes are normalized by the direction of movement at the time of "escape" from the pattern (orange curve goes to zero) (n=36 cells)).

Figure 2 .

 2 Figure 2.10: Migrating RPE1 cell at different time points in presence of BFA (0.2 µg/mL) (DIC images, orange arrows -forming lobopodia, scale bar -20 µm).

Figure 2 . 11 :

 211 Figure 2.11: Optimization of Golgicide A concentration for a long-term cell migration experiment. y-axis depicts how long the Golgi complex stays morphologically dispersed, x-axis shows concentrations used.

Figure 2 .

 2 Figure 2.12: Migrating RPE1 cell at different time points in presence of GCA (35 µM) (DIC images, dark orange arrows -forming lobopodia, light orange arrows -blebs, yellow arrowslamellipodium, scale bar -20 µm).

Figure 2 .

 2 Figure 2.13: Morphodynamic maps of freely moving cells in presence of drugs. (A-C) Representative morphodynamic maps of RPE1 cells freely moving on a fibronectin-covered coverslip in control condition (Ctrl) (A), with Golgicide A (GCA) (0.7 µM) (B) and with Nocodazole (NZ) (0.1 µM) (C).

Figure 2 . 14 :

 214 Figure 2.14: Average protrusion speed of migrating cells in presence of drugs. Control condition (Ctrl) compared with Golgicide A (GCA) (0.7 µM) and with Nocodazole (NZ) (0.1 µM) (unpaired two sample t-test, *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001).

Figure 2 .

 2 Figure 2.15: Dispersing the Golgi complex interferes with directionality of trajectory. (A-C) Trajectories of RPE1 cells in Ctrl (n=17) (A), with GCA (n=12) (B) and with NZ (n=14) (C).

Figure 2 .

 2 Figure 2.16: Dispersing the Golgi complex doesn't change the speed, but reduces migration directionality ratio. Average speed of the cell (A) and directionality ratio (B) compared in control (Ctrl), with Golgicide A (GCA) and with Nocodazole (NZ) (unpaired two sample t-test, *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001).

Figure 2 . 17 :

 217 Figure 2.17: Dispersing the Golgi complex reduces persistence of migration. Direction autocorrelation (A) and persistence time (B) compared in control (Ctrl), with Golgicide A (GCA) and with Nocodazole (NZ) (unpaired two sample t-test, *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001).

Figure 2 . 18 :

 218 Figure 2.18: Trafficking from Golgi complex is biased towards the protrusion. Collagen X cargo (labelled in black) is travelling from ER to the Golgi complex and secreted during a RUSH assay experiment (green dashed line: protrusions, black dashed line: Nucleus-Golgi axis, scale bar -20 µm).

Figure 2 . 19 :

 219 Figure 2.19: Examples of secreted cargo being trafficked towards cellular protrusions in RPE1 cells. (A)-(C) Secreted Col10A cargo signature on anti-GFP covered coverslip (green dashed line: protrusions, scale bar -20 µm).

Figure 2 . 20 :

 220 Figure 2.20: Secretion arrest in presence of GCA. (A)-(B) The Golgi complex visible in (A) is dispersed upon addition of GCA (35 µM) (B). (C)-(D) Biotin (40 µM) is added to release the cargo from the ER and start the RUSH assay (C). (D) Even after 2 h no noticeable cargo secretion is visible (a mid-section of the cell is shown, where the cargo is trapped) (black label: iRFP-Rab6A in (A) and (B) and Col10A in (C) and (D), black contour: cell borders, orange: contour of nucleus, scale bar -20 µm).

Figure 2 . 21 :

 221 Figure 2.21: Trafficking pattern follows protrusions. (A, upper panel) RPE1 cells expressing endogenous levels of a marker for post-Golgi vesicles (iRFP-Rab6A) (scale bar -20 µm). (A, lower panel) Cyan lines represent a line over which vesicle traffic intensity is calculated over time. (B, upper panel) A representative morphodynamic map representing plasma membrane protrusions in time. (B, lower pannel) A representative morphodynamic map representing the flow of post-Golgi vesicles from the Golgi complex along straight lines towards the surface over time (time period -6.5 h, black dashed lines represent the time difference between a spike in protrusions (upper panel) and a spike in secretion (lower panel)). (C) Correlation coefficient, comparing the time lag between plasma membrane protrusions and secretion (n = 16 cells, red line: average curve depicting the correlation coefficient, grey lines: single cell data).

Figure 2 .

 2 Figure 2.22: Post-Golgi vesicle traffic to the protrusion stops in presence of GCA. (A) Post-Golgi vesicles (GFP-Rab6A label) are trafficked towards a forming protrusion before addition of Golgicide A (GCA, 35 µM) (orange arrows point to vesicle accumulation). (B) Trafficking stops upon addition of GCA (excerpts from the same single-cell movie with constant image brightness parameters, scale bar -20 µm).

Figure 2 .

 2 Figure 2.23: Optogenetic activation of Cdc42 gradient. RPE1 cell, following the Nucleus-Golgi axis reorientation toward the optogenetically induced protrusion (yellow: iRFP-Rab6A (Golgi complex label), blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, scale bar -20 µm).

Figure 2 .

 2 Figure 2.24: Nucleus-Golgi axis reorients upon optogenetic activation. Optogenetic activation 90°away from Nucleus-Golgi axis leads to its reorientation in RPE1 cells freely moving on fibronectin covered coverslip (n=19 cells). A magnified inset shows the reorientation pattern in more detail (thin orange lines -single cell data, thick orange line -data average, dashed thick orange lines -standard deviation).

Figure 2 .

 2 Figure 2.25: Biochemical gradient of Cdc42 reorients the Golgi complex. Optogenetic activation of protrusion formation 90°away from Nucleus-Golgi axis leads to its reorientation in RPE1 cells freely moving on fibronectin covered coverslip (n=19 cells) (A) and is random in control condition (n=26 cells) (B) (corresponding optogenetic constructs used are depicted above the graphs).

Figure 2 . 26 :

 226 Figure 2.26: Gradient of Cdc42 stabilizes Nucleus-Golgi axis. (A) Excerpts from a movie where an RPE1 cell moves on a fibronectin covered coverslip with optogenetic activation in front of Nucleus-Golgi axis (0°). (B) Optogenetic activation induces protrusions and keeps the Nucleus-Golgi axis stabilized (n=21 cells). (C) Trajectories are directional in this condition (yellow: iRFP-Rab6A (Golgi complex label), blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, scale bar -20 µm).

Figure 2 . 27 :

 227 Figure 2.27: Optogenetic activation of Cdc42 gradient on a pattern. RPE1 cell on a round fibronectin pattern (d=35 µm), following the Nucleus-Golgi axis reorientation toward optogenetic activation of Cdc42 (yellow: iRFP-Rab6A, blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, scale bar -20 µm).

Figure 2 .

 2 Figure 2.28: Biochemical gradient of Cdc42 reorients the Golgi complex on a pattern. Optogenetic activation of protrusion formation 90°away from Nucleus-Golgi axis leads to its reorientation in RPE1 cells on round fibronectin micropatterns (n=16 cells) (A) and is random in control condition (n=13 cells) (B).

Figure 2 .

 2 30, (B)). The difference in average speed of reorientation (55±19 deg/h) compared to the previous experiment (37±23 deg/h) was insignificant (Figure 2.30, (D)).

Figure 2 .

 2 Figure 2.29: Cumulative reorientation time. This graph shows the ratio of cells, whose Nucleus-Golgi axis reorients, to total cell amount in time (reorientation threshold -30°, black: activation on pattern, orange: activation on free cells).

Figure 2 . 30 :

 230 Figure 2.30: Complete reorientation upon optogenetic activation. (A) Optogenetic activation of Cdc42 180°away from Nucleus-Golgi axis leads to its reorientation in RPE1 cells on round fibronectin micropatterns (n=5 cells) (B) (scale bar -20 µm). (C) Cumulative reorientation ratio, which shows the ratio of cells, whose Nucleus-Golgi axis reorients, to total cell amount in time (reorientation threshold -30°, black: activation 90°away on pattern, grey: activation 180°away on pattern). (D) Nucleus-Golgi axis reorientation speed, measured in degrees/h (black: activation 90°away, grey: activation 180°away, Wilcoxon rank sum test, n.s. -not significant).

Figure 2 . 31 :

 231 Figure 2.31: Optogenetic activation in presence of Nocodazole. (A) Excerpts from an experiment where an RPE1 cell moves on a fibronectin covered coverslip with optogenetic activation 90°away from existing Nucleus-Golgi axis in presence of Nocodazole (NZ) (yellow: iRFP-Rab6A (Golgi complex label), blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, scale bar -20 µm). (B) Optogenetic activation reorients Nucleus-Golgi axis (n=13 cells). (C) Trajectories of cells moving in this experimental condition.

Figure 2 .

 2 Figure 2.32: Directionality ratio comparison between optogenetically activated cells in presence of Nocodazole (NZ) (blue: freely moving cells ("Control"), black: freely moving cells in presence of NZ ("NZ"), orange: optogenetically activated cells ("Opto"), grey: optogenetically activated cells in presence of NZ ("Opto NZ"); Wilcoxon rank sum test, *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001).

Figure 2 . 33 :

 233 Figure2.33: Proposed model of persistent migration (sketch). First, secretion of vesicles (white dots) from the Golgi (yellow) are directed toward the main protrusion, thanks to microtubule tracks from the Golgi to the nascent adhesion points. Second, the Nucleus-Golgi polarity axis is reoriented towards a main protrusion, thanks to microtubules (purple), that are anchored to the protrusion by nascent focal adhesions (dark blue), being pulled, and to actin retrograde flow (green gradient and arrows), that pushes the nucleus backwards. The polarized secretion promotes the initiation of new protrusions that sustain directional motion (magenta arrows show the directionality of the interacting parameters -F basal , F prot , P rand and P polarized .)

Figure 2 . 34 :

 234 Figure 2.34: Simulated protrusion dynamics. Experimentally described membrane dynamics after a point-like Cdc42 activation (upper left panel) were convoluted with a RhoGTPases signal extended in space and time (lower left panel) to describe and depict membrane dynamics for a single protrusion (right panel).

Figure 2 .

 2 Figure 2.35: Simulated morphodynamic maps. Synthetic morphodynamic maps could be generated by varying the protrusive activity. The intensity of protrusive activity changes from one protrusion in every 20 frames in (A), to one in 5 frames in (B).

Figure 2 . 36 :

 236 Figure 2.36: Synthetic migrating cell. (A) A synthetic migrating cell is seen at different points during simulated migration. A corresponding morphodynamic map can be seen in the lower panel. (B) Running the synthetic cell migration simulation multiple times can generate trajectories for further analysis.

Figure 2 . 37 :

 237 Figure 2.37: Proposed model of persistent migration. In our mathematical model, the biased initiation of protrusions is modeled by a probability of protrusion P polarized in front of the Nucleus-Golgi (NG) axis and P rand = 1 -P polarized elsewhere. The attraction of the NG axis towards the main protrusion is parametrized by an effective force F prot that acts against F basal , which characterizes the random rotation of the NG axis. The strength of both feedbacks can, thus, be summarized by two numbers between 0 and 1: P polarized and κ = (F tot -F basal )/(F prot -F basal ). Examples of different positions in the Persistence time diagram are provided (a-c), depicting a synthetic morphomap, expected trajectories and a trajectory's autocorrelation of direction graph. The three sketches of a migrating cell next to the scale of persistence time represent the different values along the scale.

Figure 2 .

 2 Figure 2.38: Protrusion unicity and Alignment indices. The three sketches of a migrating cell next to the Protrusion unicity scale represent the different amount of protrusions along the scale and the three sketches of a migrating cell next to the scale of Alignment index represent the different angles of alignment between NG-axis and direction of movement along the scale.

Figure 2 . 39 :

 239 Figure 2.39: Persistence time, Protrusion unicity index and Alignment index as look-up tables. x-axis represents P polarized and y-axis represents κ in all three phase diagrams, area in inside of the white contour represents the value calculated for RPE1 cell line.

Figure 2 .

 2 Figure 2.40: RPE1 cell line the the phase diagram of Persistence time. Red area represents the converging point of three indices and predicted values of P polarized and κ.

Figure 3 . 1 :

 31 Figure 3.1: Persistence time phase diagram. The biased initiation of protrusions is modeled by a probability of a protrusion in front of the Nucleus-Golgi (NG) axis and the attraction of the NG axis towards the main protrusion. The strength of both feedbacks can, thus, be summarized by two numbers between 0 and 1: P polarized and κ. Optimal persistence time values are marked by the white dashed contour.

Figure 4 .

 4 Figure 4.1: A small part of a quartz/chrome photomask used for micropatterning.

Figure 4 . 2 :

 42 Figure 4.2: Working mechanism of the RUSH system. The cargo, consisting of a fluorescent protein GFP, SBP and a reporter (Col10A) is hooked in the donor compartment (ER in this case) and gets released upon addition of biotin and moves towards the acceptor compartment (plasma membrane in this case) (adapted from[Boncompain and Perez, 2012]).

Figure 4 . 3 :

 43 Figure 4.3: Optogenetic dimer system for Cdc42 activation. (A) A sketch of the iLID-SspB optogenetic dimer system with the fluorescent labels on both parts of the dimer and a RhoGTPase activator attached to the cytosolic part. (B) A sketch of the activation process upon illumination with blue light.

Figure 4 . 4 :

 44 Figure 4.4: TIRF vs. HILO vs. wide-field epifluorescence microscopy. Comparison of fluorescent molecule activation when imaging with different microscopy techniques (adapted from[START_REF] Tokunaga | Highly inclined thin illumination enables clear single-molecule imaging in cells[END_REF] and[START_REF] Mattheyses | Imaging with total internal reflection fluorescence microscopy for the cell biologist[END_REF]).

Figure 4 . 5 :

 45 Figure 4.5: Light activation with DMD projection device. Adapted from [Rullan et al., 2018].

Figure 4 . 6 :Figure 4 . 7 :

 4647 Figure 4.6: Feedback routine for moving the microscope stage to follow a migrating cell.

Figure 4 . 8 :

 48 Figure 4.8: Specific light activation included in the feedback routine.

Figure 4 . 9 :

 49 Figure 4.9: Parameters needed to construct a morphodynamic map. The small white circles represent the markers, red and blue lines represent the distance the cell boundary moved from one frame to another, showing protrusion in red and retraction in blue. Red contour represents the contour of the nucleus and the green contour represents the contour of the Golgi, with their centroids marked with squares, respectively. The black line represents the Nucleus-Golgi axis and the arrow is pointing to its position in the morphodynamic map.

Figure 4 . 10 :

 410 Figure 4.10: Example of morphodynamic maps without any feedback for varying frequencies of protrusions. The x-axis is time (1000 frames) and the y-axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Figure 4 . 11 :

 411 Figure 4.11: Example of morphodynamic maps with two extreme values of the feedback between polarity axis and protrusions. The direction of the Nucleus-Golgi axis is depicted by the central black line which corresponds to the position of x N G over time. In the top figure,there is a weak tendency to form protrusion in the direction of the Nucleus-Golgi axis. In the bottom figure, there is a strong tendency to form protrusion in the direction of the Nucleus-Golgi axis. The x axis is time (1000 frames) and the y axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Figure 4 . 12 :

 412 Figure 4.12: Natural evolution of the Nucleus-Golgi axis in the simulation for 150 frames (∼15 hours) for 20 repetitions.

Figure 4 .

 4 Figure 4.13: Natural evolution of the Nucleus-Golgi axis in the simulation for 1000 frames (∼80 hours) for 20 repetitions.

Figure 4 . 14 :

 414 Figure 4.14: Example of morphodynamic maps with two extreme values of the feedback between protrusions and polarity axis. The direction of the Nucleus-Golgi axis is depicted by the black line which corresponds to the position of x N G over time. In the top figure, there is a weak tendency of the Nucleus-Golgi axis to follow protrusions, whereas in the bottom figure, there is a strong tendency of the Nucleus-Golgi axis to align with every protrusion. The x-axis is time (1000 frames) and the y-axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Figure 4 . 15 :

 415 Figure 4.15: Example of morphodynamic maps with the two sides of the feedbacks in action. The direction of the Nucleus-Golgi axis is depicted by the black line, which corresponds to the position of x N G over time. The top figure corresponds to weak feedback, and the bottom figure to strong feedback. The x-axis is time (1000 frames) and the y-axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Figure 4 . 16 :

 416 Figure 4.16: Example of morphodynamic maps with the two sides of the feedbacks in action, for realistic frequencies of protrusion per unit of time. The direction of the Nucleus-Golgi axis is depicted by the black line which corresponds to the position of x N G over time. the top figure corresponds to intermediate feedback (κ = 0.5, p polarized = 0.5) that still leads to random migration. The bottom figure corresponds to strong feedback (κ = 1, p polarized = 1) that leads to very persistent migration. The x-axis is time (1000 frames) and the y-axis is the contour along the cell, x i , i ∈ 0..100. The color code represents membrane speed in arbitrary units, from deep blue (retraction) to deep red (protrusion).

Figure 4 . 17 :

 417 Figure 4.17: Protrusion unicity index. The three sketches of a migrating cell next to the scale represent the different amount of protrusions along the scale.

Figure 4 .

 4 Figure 4.18: Alignment index. The three sketches of a migrating cell next to the scale represent the different angles of alignment between NG-axis and direction of movement along the scale.

Figure A. 1 :

 1 Figure A.1: Reorientation modes with optogenetic activation. If optogenetic activation is imposed 90°away from existing Nucleus-Golgi axis, the axis can move in three different ways: (1) take the shortest path, (2) move only one-way, which sometimes imposes taking a longer path, (3) not move. All three situation can happen in both freely moving (A) and confined (B) cells (yellow: iRFP-Rab6A, blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, orange line: direction of axis movement).

Figure A. 2 :

 2 Figure A.2: Examples of Nucleus-Golgi axis reorientation from experiments in freely moving cells in 2D. Nucleus-Golgi axis moves along the shortest path in (A) and (B), takes the long path in (C) and doesn't move during the full experiment in (D) (yellow: iRFP-Rab6A, blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, orange line: direction of axis movement, scale bar -20 µm).

  Figure A.3, compare L column CCW (light blue) in the first and third group). There was no bias towards turning CW or CCW, and the orientation almost always happened following the shortest path (Figure A.4 and Figure A.3, third group "Pattern", n = 26 cells in total).

Figure A. 3 :

 3 Figure A.3: Frequency of reorientation modes in optogenetic activation experiments. Experiments are grouped by attachment type (free or on pattern) and timing (24h on substrate and <10h). Two columns in each group depict the side of optogenetic activation as on the right (R) or on the left (L) from the existing Nucleus-Golgi axis (see the inset on top right). The colors show the movement direction of N-G axis -clockwise (CW, orange), counter-clockwise (CCW, light blue), or if it doesn't move at all (grey).

Figure A. 4 :

 4 Figure A.4: Examples of Nucleus-Golgi axis reorientation in cells on a pattern. Nucleus-Golgi axis moves along the shortest path in (A) and (B) and doesn't move during the full experiment in (C) (yellow: iRFP-Rab6A, blue: optogenetic activation, black dashed line: Nucleus-Golgi axis, blue dashed line: optogenetic activation axis, orange line: direction of axis movement, scale bar -20 µm).

Figure B. 1 :

 1 Figure B.1: Nucleus-Golgi axis movement possibilities (yellow: the Golgi complex, light purple: Centrosome, grey: Nucleus, black arrow: turning direction).

  Figure B.1). To test which model is correct, we analysed and compared the positions of Nucleus and Golgi in three different experimental conditions -optogenetic activation in presence of NZ, optogenetic activation in normal conditions and freely moving cells (see Figure B.2). We have plotted the total displacement of Nucleus or Golgi over the first 100 min of the different experimental conditions and did not notice any significant difference between the displacements of Nucleus or Golgi in neither of the conditions (Figure B.2, (A))

Figure B. 2 :

 2 Figure B.2: Nucleus and Golgi displacement. (A) Total Nucleus and Golgi displacement over first 100 min of activation (black: Nucleus displacement ("N"), orange: Golgi displacement ("G")). (B) Total difference of displacement over first 100 min of activation (black: optogenetically activated cells in presence of NZ ("Opto NZ"), orange: optogenetically activated cells ("Opto"), blue: freely moving cells ("Ctrl"); Wilcoxon rank sum test, n.s. -not significant, *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001).

Table 4 . 1 :

 41 Rab6A sgRNA and linker-iRFP homology arm sequences.

Acknowledgements

First of all, I want to thank my two supervisors, Mathieu Coppey and Kristine Schauer, for taking this PhD quest with me and making it an interdisciplinary adventure. You have nurtured my experience as a budding scientist and gave me the freedom to explore and grow. I especially thank Mathieu for the feeling that everything is possible, and Kristine for seeing and establishing the link between cell biology and biophysics. Also, thank you to the members of my Thesis Advisory Committee, Pascal Hersen and Julie Plastino, who not only made my TAC meetings an exciting experience, but also advised me on all things professional and personal, painting a more vivid picture of the life of a scientist. I thank Louise Cramer and Lukas Kapitein, for kindly accepting to review my thesis, and to Raphaël Voituriez, Patrick Caswell and Ana-Maria Lennon-Dumenil for being a part of my PhD thesis jury, and kindly devoting their time.

I would also like to thank all the professors of the courses I took during my PhD thesis, from Epistemology of Science to Optical Imaging. These courses made me discover and delve deeper to the roots of science, both theoretical and experimental.

I thank the committee of the doctoral program Interfaces pour le Vivant (IPV) for selecting and funding my project, and the Fondation pour la Recherche Médicale (FRM), for funding the last year of my thesis, and letting me finalise my research.

I would also like to thank Simon de Beco, who was my supervisor and mentor during my first months in France and in the lab. Thank you for your care and for showing me how a biologist can find its way in biophysics.

Acknowledgements

A special thanks to my two sequential office mates -Amanda Remorino, who taught me to self-express, and Lorena Kolar-Znika, who is a perfect partner for an argument and a relentless seeker of the truth. :)

List of Tables