Hannah G Yevick

M Eric

M Sylvain

M Loic Le Goff

Mme Martine

Ben Amar

M Pascal Silberzan

In today's world measured in tweets, being able to think calmly about the same problem for a few years has been a joy and a privilege. It is also thanks to many people, who have accompanied me through the thesis, that these years proved to be as rich as they were.

I would like to thank Pascal for welcoming me into his lab, and for all the feedback and time he dedicated to my work especially during the final months. His mentorship has greatly helped me grow as a scientist. To Axel for his sharp questions and help with even the smallest difficulty on the bench. To Isabelle for her support, motivation and positive outlook over bumps along the way. To all the students in the team, past and present: Maxime, Olivier, Daniel, Simon, Guillaume and the other Guillaume.

Each one who was there to brain storm, answer a question, sing a duet, or share a laugh at any hour. To Sandrine and John for their friendship during this crazy experience. To Philip, Pierre, Jonas, and Nir, for the enthusiasm and insight they provided to my project. To Sylvie for her discussions and many gifted antibodys.

And to Olivier & Olivier the BDD imaging wizards for their microscope insight and generosity.

More personally, to my mother and father whom I will never be able to thank correctly. It is owing to the longest and hardest journeys they willingly traveled that I find myself here today. And to my father for sharing with me his love of science and teaching me the meaning of dedication and resilience through his continual example.

And finally, to Guillaume the most significant discovery of my thesis, for bringing meaning and happiness to every day.

Chapter 1 French abstract

Dans de nombreux tissus épithéliaux, les cellules ne migrent pas sur des substrats plats mais font au contraire partie d'une monocouche bidimensionnelle courbée. C'est le cas par exemple pour les tubules rénaux, les acini du sein, les alvéoles pulmonaires ou bien les cryptes du côlon et de l'intestin. Cependant, malgré l'omniprésence de cette courbure hors plan in vivo, peu d'études expérimentales s'interrogent sur son influence sur le développement et la migration cellulaire. En effet, le comportement collectif des cellules au sein d'un épithélium à deux dimensions a été principalement étudié sur des substrats plans, négligeant ainsi l'influence de la topologie de l'environnement de culture sur le développement cellulaire.

Dans ce manuscrit de thèse, nous exposons les différentes expériences menées afin de caractériser et de quantifier l'influence de cette courbure hors du plan sur le développement, la migration ainsi que les propriétés mécaniques des tissus épithéliaux.

Les cellules épithéliales de issues de rein de chien (Madin Darby Canine Kidney, MDCK) sont cultivées sur des fils en verre de rayon variable. Un dispositif expérimental a été mis au point afin d'obtenir des courbures et des conditions initiales reproductibles. Les cellules sont déposées à une extrémité du dispositif, se divisent et forment un tissu épithélial cohésif dont les cellules migrent collectivement sur les fils. En utilisant un microscope confocal, en marquant par fluorescence les différents composants cellulaires et en pratiquant des ablations laser sur le tissu, nous avons ainsi étudié la dynamique de migration collective, la morphologie ainsi que les propriétés mécaniques du tissu sur un substrat courbé de maniéré contrôlée.

Pour permettre la comparaison de ces expériences avec des résultats déjà publiés sur le développement spontané de tubules in vivo, nous avons utilisé des fils de rayons similaires, c'est-à-dire compris entre 1µm et 85µm. Afin de découpler l'effet du à la courbure de ceux dus au confinement latéral, nous avons reproduit les mêmes expériences sur des substrats plats où les cellules sont confinées dans des bandes adhésives de largueurs comparables au périmètre des tubes.

En mettant en parallèle nos résultats sur ces deux types de substrats, nous suggérons que forcer les cellules à croître sur des cylindres de diamètre pertinent biologiquement induit de nouvelles propriétés biologiques qui sont à dissocier de l'effet du au confinement latéral du tissu. Souvent observé lors du développement in vivo de tubes épithéliaux, nous montrons que la courbure hors du plan contrôle l'alignement transversal des fibres d'actine, un des composant du cytosquelette cellulaire, alors que le confinement latéral sur substrat plat induit un alignement longitudinal. La monocouche présente un câble de traction de l'actine à son bord avant. Des structures supra cellulaires similaires sont couramment observées lors de la cicatrisation de blessures circulaires dans des tissus épithéliaux plans. La méchanisme de cordon de bourse de ces câbles contractile permettant la fermeture de ces blessures circulaires tout comme la fermeture d'un porte-monnaie grâce aux cordons de bourse a récemment été minimisée. Dans cette situation, le câble d'actine a surtout un rôle de régularisation de la pointe et ce sont principalement les protrusions qui contribuent à la fermeture de la blessure [START_REF] Anon | Cell crawling mediates collective cell migration to close undamaged epithelial gaps[END_REF][START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF]. Notre situation où des cellules épithéliales migrent sur les fils est directement comparable à cette fermeture de blessure circulaire. Elles ne se distinguent que par une transformation topologique par laquelle la région exempte de cellules à l'intérieur de la plaie est équivalente à la section transversale du fil. Sur les fils, il est évident que le mécanisme en cordon de bourse n'est pas productif pour la migration car il induit une contrainte normale à la direction de migration.

Toutefois, il est, comme sur des surfaces planes, efficace pour maintenir l'intégrité de la frontière avant au cours de la migration. Afin de quantifier comment la courbure influence les propriétés mécaniques du tissue, nous avons effectué des ablations laser sur ces câbles d'actine, à la fois sur surface courbée et sur surface plane. L'effet sur la dynamique de migration a aussi été quantifié et montre que le confinement accélère la migration cellulaire collective dans les deux situations. Cette étude à l'échelle de la population met ainsi en lumière l'influence de la topologie sur le développement et la maintenance d'une large gamme de tissus courbés.

Forward

This following thesis describes a study dedicated to exploring the possible role outof-plane curvature plays on the development and migration of epithelia. Out-ofplane curvature is present at the scale of ∼ 1 -100µm in a wide range of epithelial tissues comprising many organs including the kidney, breast, lung and colon. Collective cell behaviors, however, have been largely studied in vitro on flat substrates neglecting completely the role of the three dimensional geometry.

To lay the groundwork for this study the reader will be walked through fundamental topics relating to the definition, function and architecture of epithelial cells.

Then, basic processes of epithelial tissue organization and tube morphogenesis will be covered. Finally, the state of art model systems used for the study of out-of-plane curvature will be presented.

Epithelial cells and their functions

To motivate the work done during this thesis, we will begin by introducing the biological system studied. In particular, in vitro cultures of epithelial cells were employed to model tissue organization and cell dynamics in vivo. In this section we will describe epithelial cells and their functions. Then we will present how they contribute to the CHAPTER 2. INTRODUCTION architecture of an epithelium. Epithelial cells form a major class of cells found in vivo, and are defined by their directional polarity and the specialized junctions they form to adhere to their neighbors.

Epithelial tissues line organs and cavities within the body. They act as a protective barrier, but can also serve to absorb, secrete and transport fluids and provide sensory responses. Epithelial cells are classified by their shape and the number of layers they form. As seen in Figure 2-1 an epithelium can be described as squamous, cuboidal, or columnar as well as simple, stratified, and pseudostratified [START_REF] Alberts | Molecular Biology of the Cell[END_REF]. Simple epithelia are single layered and stratified epithelial are multilayered. A pseudo-stratified epithelia has nuclei arranged at more than one height from the basal plane while maintaining all cells in contact with the basement membrane. In some cases, for example the urethra, an epithelium can be made up of a combination of these organizations in close proximity in which case it is termed a transitional epithelium. The organization of an epithelium inside a tissue isn't fixed and it can change dramatically during development. For example, the mammary gland is stratified during embryonic and postnatal branching stages but develops a simple columnar organization after branching morphogenesis [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF]. This thesis describes work carried out primarily on Madin-Darby canine kidney epithelial (MDCK) cells a common model cell line prototypical of epithelial tissues. Although the overarching aim of this work is to understand the dynamics and the collective organization of an epithelial tissue, in the following two sections characteristics of a single epithelial cell will be presented. Given that the epithelial cell is a building block of our multicellular system of interest, its internal properties closely inform the collective dynamics of the group.

Below the architecture of an epithelium at the scale of a single cell will be described and then the junctions and adhesions a cell forms with its environment will be detailed. Subsequently we return to our multicellular system of interest and discuss the supracellular architecture present in an epithelial tissue.

Single cell architecture: the cytoskeleton

The internal structure of an epithelial cell is comprised of a set of fibers which attach together to form a scaffold or cytoskeleton inside the cytoplasm that dynamically grows and rearranges through polymerization and depolymerization. The cytoskeleton attaches to its environment through substrate adhesions and cell junctions. Finally, molecular motors interact with the cytoskeleton to apply forces and transport cargo.

The cell cytoskeleton can be divided into three types of filaments: actin (or 'microfilaments' of diameter 5-9nm), intermediate filaments (diameter 10nm), and microtubules (diameter 25nm), each of which help build a rigid structure inside the cell.

In the case of microtubules and actin filaments, the fibers have molecular motors associated with them which can apply force inside the cell.

In the following subsections, the three types of filament will be presented with a particular focus on the actin filaments and their associated molecular motors, myosins, as they will be studied in depth during a large part of this thesis.

Actin filaments and their associated molecular motors: myosins

Actin filaments

Actin filaments (microfilaments) are approximately 7 nm in diameter and are formed through the polymerization of actin monomers, or G actin (aka globular actin) into a polar helical filamentous structure. The filamentous actin (F actin) has a polarity with monomers being added faster to their "+ plus end" than their " -minus end" or "barbed end" (fig 2 -2A). Each monomer is added through the hydrolysis of an adenosine triphosphate or ATP, attached to the monomer, to adenosine diphosphate or ADP [START_REF] Alberts | Molecular Biology of the Cell[END_REF]. Actin filaments are dynamic and can also shrink in size at their -end through depolymerization as the ADP-actin disassociates from the -end. A phenomenon called treadmilling occurs when actin monomers are being added to the + end at the same time that they are being simultaneously removed at the -end.

Steady state treadmilling occurs when these two rates match. The growth of an actin filament can also be stabilized by capping proteins which bind to the fast growing + end preventing other monomers to be added. The subsequent monomer, however, is more stable and subsequent additions are much more favorable. An actin filament has two ends the barbed (B) and the plus end (P). Actin monomers are added to the plus end and removed from the barbed end. B) Arp2/3 (orange) is an actin nucleator that binds to the side of a filament and creates a new branch at a 70 • angle. Repeated Arp2/3 branching forms a dendritic actin network. C) Formin (purple) nucleates a filament and can either move progressively with the elongating barbed end or bundle filaments together. [START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF] The polymerization of actin can be stimulated with the help of other proteins.

Formins are a family of proteins that regulates linear actin assembly. Formins move with the barbed end of the filament during elongation aiding in successive nucleation events. Formin can also bind multiple fibers together forming an actin bundle (Fig 2 -2C). The Arp2/3 complex, binds to the side of an actin filament or competes with capping proteins to bind to a barbed end. Once bound, Arp2/3 creates a new daughter branch at a 70 angle from the original one. Repeated actin branching is possible on both the mother and the new daughter branch resulting in a dense dendritic network of actin (Fig 2 -2B) [START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF] .

Actin filaments can also take shape into larger structures with the help of crosslinking proteins which further organize actin into gel-like networks and bundles. Actin bundles are commonly cross-linked together by fimbrin or α-actinin. Filamin crosslinks actin at large angles in a gel-like formation.

The different forms of actin work together during cell migration. As illustrated in Fig 2 -3 a migrating cell on a rigid flat surface often forms an elongated fan-like protrusion. The branched organization of actin created from actin polymerization catalyzed by the Arp2/3 complex is present in the protruding lamellipodium. The tight parallel actin bundles, protrude further forward in a crawling cell in the form of filopodium. The arrow indicates the direction of migration. [START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF] Myosin II is a molecular motor that functions with actin to produce force. Myosin II is composed of two heavy chains and two light chains which can be divided into a head, neck and tail domain (Fig 234). The heavy chains have head regions and long α-helical tails, which wrap around one another to form dimers. Myosin's head domain exerts force by binding to an actin fiber through ATP hydrolysis and it "walks" towards the '+' end of an actin filament through successive movements: the head domain binds, undergoes a conformational change, releases from the filament and finally undergoes a conformational reversal to prepare for another step cycle.

Myosin, an actin associated molecular motor

For each step, myosin can cause a displacement of ∼5-10nm and generate ∼1-5pN of force [START_REF] Alberts | Molecular Biology of the Cell[END_REF]. Myosin II can assemble together with the tail of one myosin II interacting with the tails of adjacent motors. Together the group of myosins can form a "thick filament" with many heads available for actin binding on both ends. [START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF] Figure 2-4: A) Myosin II: Myosin II is comprised of three domains, the head, neck and tail regions [START_REF] Alberts | Molecular Biology of the Cell[END_REF]. B) Actin stress fiber: Myosin II (blue) head domains bind to actin filaments (red) in a bipolar manner. ATPase activity results in the movement of actin fibers in an anti-parallel manner [START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF].

Stress Fibers

The actin stress fiber is a contractile structure composed of actin filaments and myosin II motors. The stress fiber is formed from bundles of actin filaments of alternating polarity cross linked by α-actinin (Fig 2 -4B) [START_REF] Cramer | Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force[END_REF]. Thick filaments of myosin bind to actin in a bipolar manner pulling fibers together in an antiparallel configuration.

The bundles, or stress fibers are commonly anchored to the cell plasma membrane through substrate adhesions or 'focal adhesions' (discussed further in section2.2.2) but their morphology and position in the cell can vary. Stress fibers inside a single cell are divided into four main categories: dorsal, ventral, transverse arcs and perinuclear actin cap. The dorsal stress fibers are connected to the substrate at a single end, ventral fibers possess two anchors while the transverse arcs lack a direct attachment (Fig 2 -5). The perinuclear actin cap forms a dome-like actin cap on top of the nucleus and has been shown to regulate nuclear shape, for example under cell confinement [START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF] by providing a lateral compressive force [START_REF] Versaevel | Spatial coordination between cell and nuclear shape within micropatterned endothelial cells[END_REF].

Stress fibers assemble or rearrange when the cell encounters a mechanical force and their thickness and orientation inside a cell has been found to depend on the rigidity of the substrate a cell is plated on [START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF]. Generally stress fibers are well defined in cells plated on stiff substrates and weakly defined or absent from cells grown on soft substrates [START_REF] Yeung | Effects of Substrate Stiffness on Cell Morphology, Cytoskeletal Structure, and Adhesion[END_REF].

Intermediate filaments

Intermediate filaments are the most diverse cytoskeletal component and are comprised of numerous polypeptides which can vary across cell type. Some common building blocks of intermediate filaments are lamins, vimentin, and keratins. In neurons and epidermal cells these are 10 times more abundant than actin filaments. Unlike other cytoskeletal filaments, intermediate filaments do not have a polarity. Intermediate filament associated proteins crosslink individual filaments into a staggered array which bundles into a larger fiber(Fig. 23456). Intermediate filaments can link to microtubules, actin filaments, the plasma membrane and the nuclear surface interconnecting parts of the cytoskeleton thus playing an integral role in the stability of the cytoskeleton [START_REF] Ingber | Tensegrity I. Cell structure and hierarchical systems biology[END_REF].

Microtubules

Microtubules are hollow cylinders formed from 13 profilament strands (in mammalian cells) which contain alpha and beta forms of the globular protein tubulin. Similar to actin filaments, microtubules are polar and dynamic polymerizing and depolymerizing at both ends to adjust their size (Fig. 234567). The tubules are typically nucleated from and attached to one end to the microtubule organizing center, or centrosome and while they grow to an average of 25µm in length their size varies between cell type [START_REF] Li | Estimating microtubule distributions from 2D immunofluorescence microscopy images reveals differences among human cultured cell lines[END_REF]. The tubules support the migration of kinesines and dyneines two molecular motors which can move organelles and vesicles through the cell. Microtubules also play a significant role in cell division as they form a major structural component of the mitotic spindle which segregates a cell's chromosomes. Microtubules are composed of α-and β-tubulin subunits that are assembled into profilaments. A single microtubule in a mammalian cell contains 13 profilaments that wind together to form a cylinder of 24nm in diameter. Microtubules are dynamic in structure and can grow through polymerization and shrink via depolymerization.

[http://www.nature.com/scitable/topicpage/microtubules-and-filaments-14052932]

Cell Junctions and Adhesions

After discussing the properties of a cell's cytoskeleton we now consider the manner in which the cytoskeleton and the cell in general connect to the surrounding environment.

These connections can appear as either adhesions to neighboring cells or as adhesions to a substrate.

EPITHELIAL CELLS AND THEIR FUNCTIONS

Cell-cell Junctions

Epithelial cells are joined to their neighbors in a manner that can be classified according to nature and function into three categories: anchoring junctions, occluding junctions and communicating junctions.

• Communicating junctions (gap junctions for epithelial cells) enable the electric and chemical cell-cell communication.

• Occluding junctions (tight junctions for vertebrates) seal the cells together, selectively inhibiting molecules from penetrating the epithelium or membrane proteins and lipids from mixing between different domains of the cell membrane. Tight junctions divide different membrane regions of an epithelial cell and their role in polarizing epithelial tissue is discussed further in section (2.2.3) on cell polarity.

• Anchoring junctions mechanically link the cytoskeleton of two neighboring cells.

Anchoring junctions are further subdivided into two categories according to the cytoskeleton filament they bind to. These are termed adherens junctions, that link to actin filaments and microtubules and desmosomes that link to intermediate filaments.

Here, focus will be placed specifically on the anchoring junctions as they are attached to the cytoskeleton and the thesis also focuses on unraveling the complexity of the multicellular cytoskeletal organization.

Adherens junctions

Adherens junctions (Fig. 2345678) contribute to the strength of the mechanical link between neighboring cells in the epithelium and aid establishing apical-basal polarity across a cell sheet. Adherens junctions are more basal than tight junctions and in some epitheliums adherens junctions completely enclose the circumference of the cell and are thus associated with an actin belt of F-actin that also surrounds the cell. An important component of adherens junctions is a family of cadherin transmembrane, calcium dependent proteins. In epithelial cells E-cadherin together with the cytoplasmic molecule catenin forms the basis of mature adherens junctions. The cadherin-β-catenin complex binds to α-catenin which subsequently binds either directly to actin or to actin associated proteins [START_REF] Baum | Dynamics of adherens junctions in epithelial establishment, maintenance, and remodeling[END_REF].

In addition to connecting with actin, an adherens junction protein also associates with microtubules [START_REF] Franz | p120 catenin associates with microtubules: inverse relationship between microtubule binding and Rho GTPase regulation[END_REF]. The plus end of radially extending microtubules can therefore be targeted to adherens junctions and the presence of microtubules at the junctions aids in the further accumulation of junctional E-cadherin [START_REF] Meng | Adherens Junction : Molecular[END_REF].

Desmosomes

Desmosomes link intermediate filaments to the plasma membrane and are crucial in maintaining the mechanical integrity of an epithelium. Desmosomes assist cells in relieving mechanical stress as they support "hyperadhesive" junctions, namely junctions that remain intact during calcium depletion. The strength of these junctions, however, can be modulated through intracellular signaling and desmosomes strength is often varied over the course of wound healing and some parts of development. In MDCK cells for example, calcium independent desmosomes are never present before confluence, while after confluence nearly all the cells develop such junctions over a period of days [START_REF] Garrod | Desmosome structure, composition and function[END_REF].

Cell-substrate adhesion

In order to move in vivo, a cell must form adhesions with a surrounding scaffold called the extra-cellular matrix (ECM). The main components of the ECM are collagen I and IV, laminin and fibronectin. When a tissue is grown on a virgin substrate, the cells must first produce ECM on the substrate and then build adhesion between it and its basal membrane. These cell-substrate adhesions can be classified into two 2.2. EPITHELIAL CELLS AND THEIR FUNCTIONS categories: focal adhesions and hemidesmodomes each of which link actin filaments and intermediate filaments to ECM. Properties of focal adhesions will be presented here as these adhesions are studied during the thesis.

Focal adhesions

Focal adhesions tie a cell to a substrate by linking actin stress fibers to the extra cellular matrix via transmembrane integrin receptors. In a migrating cell, focal adhesions are preceded by focal complexes. Focal complexes are formed toward the leading edge of the migrating cell and are smaller protein complexes comprised mainly of vinculin and talin which aggregate near the membrane on the cytoplasm side and link the actin filament to an integrin. The integrin spans the membrane and attaches to the extracellular matrix outside the cell (Fig. 23456789). Focal adhesions are matured focal complexes and are more stable structures comprised of vinculin, and talin but also other proteins such as paxillin, filamin, alpha-actinin, and zyxin. Similarly to stress fibers, focal adhesions react to externally applied force and respond by growing in size [START_REF] Riveline | Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism[END_REF]. Focal adhesions are clearly defined on 2d cultures and their size is correlated with cell migration speed [START_REF] Kim | Focal adhesion size uniquely predicts cell migration[END_REF]. Cells migrating in 3d environments, such as gels, have been observed to possess a diffuse distribution of focal adhesion proteins unlike in 2d where they self-assemble. The presence of these proteins, however, has been found to regulate migration dynamics by controlling cell protrusions and the ability of a cell to deform the surrounding matrix [START_REF] Fraley | A distinctive role for focal adhesion proteins in threedimensional cell motility[END_REF]. Here, the basolateral surface of is at higher curvature than its apical membrane. [START_REF] Nelson | Epithelial Cell Polarity From the Outside Looking In[END_REF]

Cell Polarity

Tight junctions

Apical and basolateral domains are separated by ring of tight junctions located towards the upper part of the lateral cell surface. Tight junctions constitute a physical boundary between the two parts of the membrane preventing the diffusion of specific proteins and lipids.

Proximal-distal

Although not present in in vitro epithelial monolayers, epithelial tissues also can be defined by a planar cell polarity (PCP) in vivo. The PCP is perpendicular to the apical basal polarity and parallel to the plane of the tissue (Fig 2 -11B). Planar cell polarity results from both local and global signals or gradients which guide differentiation of the composition of the two sides of the cell cortex and therefore establish a preferred direction along the proximal-distal axis. Planar cell polarity is important in the correct morphogenesis of many tissues as it has been found to govern cilia function and structure and to orient cell division [START_REF] Simons | Planar Cell Polarity Signaling: From Fly Development to Human Disease[END_REF]. Directional cues from planar cell polarity also orient cell migration for example during during development and tissue repair [START_REF] Vladar | Planar cell polarity signaling: the developing cell's compass[END_REF].

Multicellular architecture

As this thesis focuses on the architecture of an epithelium at the tissue level, we will discuss in this section some aspects of multicellular architecture and demonstrate how multiple identical building blocks together can result in complex multicellular structures such as supracellular actin cables. Such multicellular structures are crucial in multiple in vivo processes to drive shape change and shape maintenance. Of particular interest to this thesis, multicellular actomyosin cables can guide the formation and maintenance of curvature in epithelial tissues. Below actin cables present in tissue morphogenesis will be discussed and illustrated through a range of in vivo examples.

Supracellular actin cables

Stress fibers not only give rise to forces inside a single cell, but actomyosin cables are also present in many multicellular systems driving collective movements. During development supracellular actin cables can be divided into three categories. Each case is illustrated in figure 2-12. Circumferential cables can be found during wound closure of an embryonic epithelium (Fig. 2-12A) during dorsal closure of a drosophila embryo (Fig. 2-12B), and in the salivary gland placode to aid the forming tube(Fig. 2-12C).

Circumferential cables often act using a "purse string" mechanism where contractions of the circular cable present at a epithelial boundary provide a centripetal force which drives epithelial closure.

In the drosophila epidermis and wing, actin forms boundary cables that impede the mixing of cells between spatially differentiating regions. These cables are under tension but they do not shorten in length (Fig. 2-12D-F). Finally, dynamic cables assist the rearrangement and reorientation of cells during development by constricting and changing shape (Fig. 2-12G-I). They are commonly present along the aligned boundary of 3-6 neighboring cells arranged in a vertical formation on either side of the cable. The cable's tension increases with decreased length which can alter a vertical cluster of neighboring cells into a horizontal one by contracting down to a single point or rosette while maintaining contact with the same cells throughout. [START_REF] Röper | Supracellular actomyosin assemblies during development[END_REF]. Cables are divided into three categories: circumferential cables closing the epidermis, static cables at boundaries and dynamic cables in morphogenesis. A) An actomyosin 'purse string' is responsible for closure of epithelial wounds for example in the drosophila and zebrafish. B) A similar actomyosin cable guides dorsal closure, helping the epidermis close in the drosophila. C) A cable in the salivary gland placod contracts to aid tube formation through invagination. D) Cables for static boundaries to prevent cell division and mixing across boundaries E) A cable creates a physical boundary between the ventral and dorsal segment of the fly wing. F) Rhombomere maintenance and ventricle formation are assisted through regional differences in myosin II . G) Convergent extension of the germ band occurs through a dynamic cable which pulls neighboring cells along one axis into a rosette and then extends them perpendicularly H) Kidney tubules elongate through a similar convergent extension driven by dynamic cables along their length. I)The neural tube is folded and extended with the help of circumferential cables that rearrange cells in the tissue through neighbor exchanges . In A-C) red arrows indicate the direction of the applied centripetal force. D-I) Double arrows indicate the line tension generated from the cables. [START_REF] Röper | Supracellular actomyosin assemblies during development[END_REF]

In vitro models of epithelia

Epithelial tissue formation is a complex collective process of cell growth, rearrangement and migration, as presented briefly above (sec. 2.2.4) and further in the following chapter (2.4). Much work has been dedicated to understanding the mechanics of how groups of epithelial cells interact and move together collectively. However, given the many challenges associated with monitoring and quantifying epithelial tissues in vivo, in vitro systems have been extensively employed.

The following discussion consequently focuses on in vitro studies of two dimensional flat epithelial tissues. The goals of this presentation are twofold. First, to demonstrate important information can be extracted from 2d in vitro models which mimic many characteristics of in vivo tissues and secondly, to present the limitations these systems have on describing some aspects of three dimensional tissue, for example its out-of-plane curvature.

Examples of two dimensional assays that expose some properties of epithelial tissue are discussed below. These assays applied on MDCK cells reveal spatial correlations during migration, the dependency of wound geometry on the formation and function of actin cables during re-epithelization, and effects of population confinement on epithelial tissues.

Collective cell migration, tissue dynamics, fingers and complex flow patterns

Collective cell migration has been widely studied in 2d epithelial tissue since the presence of strong junctions between cells help form complex correlated movements.

The scratch wound assay is the traditional technique employed to study collective migration. Cells are grown to confluence and then a portion of the monolayer is scraped away using a pipette tip or another sharp object [START_REF] Liang | In vitro scratch assay: a convenient and inexpensive method for analysis of cell migration in vitro[END_REF]. Cells migrate to close the wound and migration parameters can be measured [START_REF] Farooqui | Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement[END_REF]. Scratching, however, does not yield reproducible wound geometries and damaged border cells not mechanically removed introduce changes in the local signaling environment [START_REF] Yin | Wound-induced ATP release and EGF receptor activation in epithelial cells[END_REF].

To isolate the role of wound geometry in wound healing, MDCK cells were grown to confluence inside a PDMS micro-stencil. The stencil was removed and cells migrated outward into the newly created free space (Fig. 2345678910111213). Clusters of cells migrated together creating flows inside the monolayer, with a correlation length of typically 10 cell sizes [START_REF] Petitjean | Velocity fields in a collectively migrating epithelium[END_REF][START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF]. In addition to velocity correlations inside the tissue, multicellular digitations or fingers form at the leading edge guided by a wide "leader" cell (Fig. 234567891011121314) moving almost two times as fast as the mean border speed [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF]. The cells inside a finger have a preferential orientation and polarity compared to cells inside the monolayer [START_REF] Reffay | Orientation and polarity in collectively migrating cell structures: statics and dynamics[END_REF]. Finally, collective patterns were also observed in the mechanics of the migrating tissue. Traction force microscopy on a migrating monolayer revealed mechanical waves driven by tissue expansion. These waves demonstrated that (at least for substrates of rigidity 3kPa) traction forces involved in migration originate across large distances in the tissue and not just at the leading fingers (Fig. 23456789101112131415) [START_REF] Serra-Picamal | Mechanical waves during tissue expansion[END_REF].

The dynamics and force patterns of collective cell migration can provide information on the supracellular strategies used in vivo when cells crawl on a relatively flat substrate like during tissue repair. Two dimensional assays also provide information on tissue dynamics, tissue architecture and reveal the bio-mechanical processes that [START_REF] Trepat | Physical forces during collective cell migration[END_REF] are at play in tissue morphogenesis. Multicellular actin cables formed in 2D are one such example. The in vitro studies of actin cables can recapitulate elements of their structure, physical characteristics and functions in developing tissues.

Actin cables during re-epithelialization

Actomyosin cables, present in vivo as discussed above (section 2.2.4), can be recapitulated in vitro. Cells were seeded around PDMS pillars of radius 25-100µm pressed onto a glass coverslip, confining their growth. Upon removal of the pillars at confluence, an actomyosin cable assembled in minutes around the wound edge [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF][START_REF] Anon | Cell crawling mediates collective cell migration to close undamaged epithelial gaps[END_REF]. The actomyosin cable was present during the entire closure and ablation of the cable confirmed that it was exerting a centripetal force towards the center of the wound. However despite the elastic tension stored in the circular cable, it does not pull the wound closed using an in-vivo-like purse string mechanism described above. Inhibition experiments and analysis of the dynamics of the closure revealed that for wounds of diameter larger than a cell size the cable plays predominantly a regularization role at the front edge and active crawling of protrusive cells at the boundary is the principle propeller of closure. When a monolayer of MDCK cells migrates into a free space larger than the size of the small 40000µm 2 circular patches discussed above, the finger-like protrusions mentioned above develop. These migrating fingers are also bound by a multicellular actomyosin cable on their two sides (Fig. 234567891011121314151617) whose presence, similar to that of the cable around circular wounds, acts as a structural barrier preventing the formation of new leader cells [START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF]. Studies of monolayer dynamics, fingers, and actomyosin cables highlight the ability of in vitro assays to mimic some aspects of in vivo development. Nevertheless other in vivo characteristics of the cell micro environment are absent from these two dimensional flat assays. As mentioned earlier, out-of-plane curvature is one of them. Cellular confinement is another one. Although primary focus was given to out-of-plane curvature, work was done on the latter on a recently published study on the emergence of collective modes and tri-dimensional structures from epithelial confinement.

The main results of this project will be briefly detailed as the project motivated our present examination of complex out-of-plane environments. Indeed variations in the cell microenvironments and the in vitro culture conditions can lead to the emergence of complex patterns that were unpredicted by infinite 2D assays.

Population confinement

In certain in vivo configurations epithelial tissues are confined spatially. In the case of a tube, for example, cells are laterally confined. Such spatial confinement can be simulated by micropatterned two dimensional assays. One such study restricted populations of MDCK cells for several days within circular patches of radius 50-200µm formed from a strongly cell-repellent surface treatment (Fig. 2-18A) [START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF]. After confluence was reached, angle averaging the velocity of the cells in the patches revealed confinement-induced radial oscillations of cell displacements at the half-radius of the circular patch with a period of typically 7h (Fig. 2-18B). As well, the orthoradial component of the angle averaged velocity demonstrated that the cells rotated together with random angular velocity reversals. [START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF] Two dimensional confinement of a cell population can also affect the growth of the epithelium and lead to the development of tri-dimensional structures, a phenomenon of particular interest to this thesis. The presence of a, here circular, confining boundary can trigger MDCK cells which normally form a two dimensional monolayer to develop a peripheral three dimensional rim along the majority of the boundary between the adhesive and nonadhesive area(Fig. 2345678910111213141516171819). The polarity of the 3d structure is defined at the scale of the entire rim with the external rim surface apically polarized on the top where cells are in contact medium and basally polarized when in contact with the substrate. The inhomogeneous polarization of a continuous 3d epithelium illustrates that adding complexity to a flat cell assay, in this case through confinement, can yield new unpredicted cellular behaviors. This thesis accordingly explores out-of-plane curvature to alter the geometry of the cell microenvironment a logical progression from this work. A final example of 2D confinement relevant to our own work is illustrated in the recent work of Vedula et al. where MDCK cells are confined to migrate in tracks of widths 20-400µm (Fig. 2-20A) [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF]. Cells confined to tracks of width w have the same lateral confinement as cell in tubes of radius R where w = 2πR. The front progression inside the tracks increased for narrow widths below 100µm. This trend, however, disappeared when the cells were treated with blebbistatin, an inhibitor of myosin II.

In this case the migration speed of the front increased for large widths and decreased for a width of 20µm (Fig. 2-20C). Velocity field and traction force measurements also revealed differences between wide and narrow tracks with velocity vortices present on wide tracks and 'contraction-elongation' process driving migration in narrow tracks.

The migration mode in narrow tracks required a higher average traction in contrast to wide tracks where the force decayed by half over ∼100µm, the force spiked over time behind the leading edge during contraction-elongation cycles. Again, confining cells revealed new behaviors not present in 2D infinite conditions. This thesis will further explore lateral confinement in the context of curved epithelial tubes and will use a similar track assay as a method of comparing cells under lateral confinement, with and without out-of-plane curvature. The velocity of the cell front for different widths for untreated, and blebbistatin treated conditions. The speed of the untreated front increases with confinement below 100µm. [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF] Although two dimensional studies provide relevant insight into aspects of epithelial tissue properties there are other properties of in vivo tissue that are not replicated.

In the remainder of this section, some limitations of the two dimensional flat models in mimicking properties of in vivo tissue are described. These limitations are then further developed in the subsequent section where the differences between flat assays and in vivo epithelia are exposed by detailing the formation and regulation of curved epithelial tubes.

Limitations on 2D models

The in vitro systems discussed above (with exception of the rim formation) can be classified as 2D assays. Although some properties of in vivo tissues can be investigated in 2d assays, some significant differences exist between 2d assays and real 3d conditions. Below important differences are summarized.

Differences between 3D in vivo conditions and 2D culture [START_REF] Zegers | Epithelial polarity and tubulogenesis in vitro[END_REF] 1. Cells in 3D can migrate into the ECM in all directions while cells in a 2D culture can only move laterally, or crawl above their neighbors 2. Many supports used in 2D are far more rigid than the in vivo environments.

3. The localization and expression of some proteins changes between apical and basolateral surfaces when cells are cultured in 2D vs 3D.

4. Cells grown in 3D are more resistant to apoptotic signals.

5. Cell secretions (for example growth factors, ECM, proteins. . . ) can interact with the surrounding ECM in vivo thereby influencing cell behavior.

2D vs 3D Migration

Because of the many differences between the cell's microenvironments in 2D and 3D it isn't surprising that cell migration in 2D fails to capture many aspects of actual 3D cell migration in vivo.

In particular, during single cell migration in 2d, cells are commonly well spread and develop a fan-like lamellipodial protrusion and movement results from a combination of cell polarization, membrane extension via protrusion, formation of substrate adhesion, contractile force, followed by a release of attachment (section2.2.1) [START_REF] Lauffenburger | Cell Migration : A Physically Integrated Molecular Process[END_REF]. Cell migration in three dimensions is considerably different. The cell body is either more rounded (for amoeboid migration) or spindle shaped with elongated lamellipodia or filopodia which propels a rapid directional migration as schematized in figure 2-21 [START_REF] Friedl | Plasticity of cell migration: a multiscale tuning model[END_REF][START_REF] Petrie | At the leading edge of three-dimensional cell migration[END_REF]. The 3D migration rate is ligand density independent whereas in 2D the migration speed is ligand dependent. As well, cells migrating in 3D exhibit a contractility dependent migration and a posterior centrosome orientation. Conversely, cells in 2D display a contractility independent movement with a frontal centrosome [START_REF] Doyle | Onedimensional topography underlies three-dimensional brillar cell migration[END_REF].

Other differences to 2d migration are that cells migrating collectively through a 3D matrix often degrade and rearrange their environment creating tubelike tracks for the moving bulk [START_REF] Wolf | Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion[END_REF]. For epithelial cells, this type of migration is typically observed during collective cancer cell invasion. Out-of-plane curvature Finally, a critical difference between cells in 2D and in vivo conditions is that 2D cells lack out-of-plane curvature which is present often at the scale of one to ten cells in epithelial tubes and cysts. As depicted in figure 2-10 the apical and basolateral face of a cell comprising a tube or cyst is curved, a geometry that is not accessible on a rigid substrate. A curved geometry is not only important to mimic the shape of epithelia in vivo but curvature has also been shown give mechanical feedback to a cell. Studies of MDCK cysts developing in gels (section 2.2.3) confirmed that curvature of the apical or basolateral membrane can in fact activate stretch-induced ion channels which affect signaling inside the cell and increase cell proliferation or fluid exchange [START_REF] Tanner | An In Vitro Test of Cell Stretch-Proliferation Hypothesis of Renal Cyst Enlargement[END_REF]. To further present how ubiquitous of out-of-plane curvature is in tissue shape and morphogenesis, we will introduce the reader to the mechanisms of epithelial tubulogenesis and tube shape regulation.

Assembling epithelial tissues in vivo: tubulogenesis

Tissues exhibit an intermediary level of organizational complexity between a cell and an organ. Epithelial cells organize into tissues of tubes or cysts which function inside larger organs. Some organs, for example the kidney, possess a tubule network of varying diameters in different regions. Other epithelial tissues, for example the breast, bronchioles, pancreas, salivary glands, are formed from shorter tubular networks that finish in spherical acini as seen in figure 2-22c.Since this thesis focuses on work carried out on a cell line derived from kidney cells, below we will focus on the mechanisms of in vivo tube formation and acinus formation will not be discussed. As well, even though some mechanisms of tubulogenesis apply to both epithelial tissue as well as tubular endothelial vessels found throughout the body, focus will be placed on epithelia as endothelia are beyond the scope of this thesis. In all these cases the polarity of the inner surface is apical (red) and the basement membrane faces the outside of the tissue (green). [START_REF] Wang | Normal morphogenesis of epithelial tissues and progression of epithelial tumors[END_REF] Epithelial tubes can be regarded as polarized epithelia enclosing a central lumen.

The apical surface of tubes is directed towards the lumen and the basement membrane covers their outer surface Fig. 2-22. The apical side of epithelial cells can filter fluid or absorb gas from the lumen. In other instances, for example in glandular epithelium, fluid (ex. mucus, saliva, oil, milk,) is secreted in the opposite direction across the apical side into the lumen. The architecture of epithelial tubes can vary greatly in size ranging from tubes with a cross section comprised of many or down to two polarized cells connected by adherens junctions (Fig. 2-23a). In some instances tubes are formed from a single cell. Single cell tubes can either form when a cell makes an autocellular adherens junction (Fig. 2-23b) or, in the most extreme case, (Fig. 2-23c) when a lumen clears through the inside of a single cell.

Tube formation

Different epithelial tubes are formed from each germ layer. For example mammary glands originate from the ectoderm, the kidney from the mesoderm and the liver from the endoderm. As a consequence of the varying cell types, and microenvironment many different genetic pathways are implicated. Still, the basic physical shape changes that cells undergo during tube formation can be grouped into 6 general processes.

Each will be described in further detail below.

Wrapping and budding are two processes in which tubes are formed from already polarized epithelia.

Wrapping

Wrapping, or 'invagination', occurs when a sheet of cells forms a lumen through apical constriction driven by myosin mediated contractions in the apical F-actin meshwork (section 2.2.4). The cells along an axis narrow apically and widen basally to create a wedge shape. When the sheet is fully wrapped the cells pinch off forming a new tube above the basal plane. Wrapping invagination is the process used to form the neural tube (Fig. 2-24B-C). Wrapping can also occur in the opposite direction, with reversed polarity, creating an evagination or a tube pushed out of a monolayer down below the apical plane. Evagination happens, for example, in the leg imaginal disk epithelium in the drosophila [START_REF] Fristrom | The Mechanism of Evagination of lmaginal Discs of Drosophila melanogaster[END_REF]. Similar to invagination, evagination also relies on myosin mediated contractions [START_REF] Aldaz | Dual role of myosin II during Drosophila imaginal disc metamorphosis[END_REF].

Budding/branching

Budding/branching occurs when a small tubule is formed from an existing polarized tube. Reiterated budding, in a controlled spatio-temporal pattern, is the basis of branching morphogenesis. Tubes typically bifurcate during branching although in some instances trifurcation is possible [START_REF] Watanabe | Real-time analysis of ureteric bud branching morphogenesis in vitro[END_REF]. Budding/branching: a lumen is formed off an existing tube. apical surface (green), basal surface (blue) [START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]. Branching morphogenesis in various epithelial tissues in a mouse at embryonic day 13.5-15. A) salivary gland B) lung C) kidney. Immunofluorescent labeling of E-cadherin (green). D) mammary epithelium marked with red and green fluorescent proteins. [START_REF] Lu | Patterning Mechanisms of Branched Organs[END_REF] Epithelial tube branching architecture and function are closely related. In tissues limited by space, branching is highly regulated whereas less restrained branching can become more stochastic. In the lung, for example, tubes are highly branched to obtain a high surface area for gas absorption. In contrast, the many secretory organs, for example the salivary glands do not require large contact surface areas and therefore are much less branched.

Branching cues:

Correct branching is crucial in ensuring tissue function. Some examples of branching cues and control mechanisms used to regulate tissue packing and overall shape will be presented below.

The leading edge of the branching epithelium can contain small branch tips of one or two cells (Fig. 2-26). The tips are often highly dynamic with protrusive filopodia. More commonly, however, the branching tip of an epithelium consists of a heterogeneous and often multilayered cell population (Fig. 2-26C). In the breast, for example, this multilayered tip is the location of high cell proliferation, reorganization, and migration without the guidance of a leading cell extension [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF]. The location of a tip cell is determined by mutual inhibition in which cells compete to become a tip. Two proteins involved in tip cell competition are notch, a transmembrane receptor protein, and TGF-β, a growth factor protein (Fig. 2-26). Local secretions of notch in the drosophila trachea and TGF-β in the mammary gland create an inhibitory morphogen gradient for mutual tip cell inhibition ensuring that two buds do not form close together. A similar mechanism of self-avoidance drives some growing tubes to turn sharply away from neighboring branches upon approach establishing a minimal spacing between segments [START_REF] Silberstein | Postnatal mammary gland morphogenesis[END_REF].

Although local gradients provide some control of branching, highly stereotyped tissues rely strongly on gene networks to further control branching events [START_REF] Metzger | Genetic Control of Branching Morphogenesis[END_REF]. An intensive study of the mouse bronchial tree reconstructing the developmental history of ∼ 5000 branches revealed that the patterning can be divided into three genetically controlled subroutines which yield unique branching shapes. The subroutines are then repeated in different sequences to rendering the final complex tissue pattern. In addition to regulating the specificity of the three branching modes, genetic controls define a master routine that dictates the branching hierarchy by fixing the location and timing of the subroutines [START_REF] Metzger | The branching programme of mouse lung development[END_REF] .

Finally some branching cues can be triggered through external signals. In the secondary branching stage at the end of embryogenesis and during larval stages the drosophila trachea development is in fact controlled by local demands for oxygen which stimulate specific gene expression that guides new branch formation [START_REF] Jarecki | Oxygen regulation of airway branching in Drosophila is mediated by branchless FGF[END_REF].

Budding in unicellular tubes

Budding is employed to make tubes with autocellular adherens junctions as depicted in figure 2-23B. These types of tubes have been reported in the drosophila tracheal tube during tube elongation. In an elongating tube, autocellular junctions are formed through the intercalation of stalk cells present just below the migrating tip cells. Initially stalk cells are side by side, forming adherens junctions with their neighbors behind one or two tip cells encapsulating a central lumen (Fig. 2-27A). Individual cells reach around the lumen to form the initial autocellular adherens junction (Fig. 2-27B). Subsequently intercellular adherens junctions between neighboring cells progressively transform into autocellular junctions until only a small ring remains connecting each cell longitudinally at its two extremities to its neighbors (Fig. 2-27C-D) [START_REF] Ribeiro | Genetic Control of Cell Intercalation during Tracheal Morphogenesis in Drosophila[END_REF]. Unlike intercalation through convergent extension as discussed in section 2.2.4

where actin cables can rearrange cells, here one or two tip cells apply enough force to intercalate the lagging stalk cells [START_REF] Caussinus | Tip-cell migration controls stalkcell intercalation during Drosophila tracheal tube elongation[END_REF].

Cord hollowing

Cord hollowing creates a lumen inside a group of cells aggregated into a cord shaped mass. In instances of cord hollowing, in contrast to cavitation, the principle contributor to lumen creation is provided by the development of apical-basal polarity in the cells, not cell clearing [START_REF] Belting | It takes guts to make a single lumen[END_REF]. Apical basal polarity is established through the recruitment of apical proteins to multiple positions that are either randomly located, or along the midline of the cord. With the recruitment of apical markers, lumens form locally. Over time the lumens expand and fuse forming a single, central lumen. Cell hollowing, cell assembly and cell wrapping form the 3 smallest kinds of tubes.

Cell hollowing

Cell hollowing forms a lumen inside a single cell thus forming an intracellular tube (Fig. 2-30) without adherens junctions along the circumference. Hollowed cells, however, form junctions with their neighbors longitudinally connecting them to a larger tube network. The hollowing process is driven by small intracellular cytoplasmic vesicles that fuse to produce a larger lumen [START_REF] Lubarsky | Tube Morphogenesis : Making and Shaping Biological Tubes[END_REF]. As seen above, a wide variety of mechanisms can lead to the formation of tubes of the same final shape. The radius and length of the tubes once formed are not fixed and can continue to be adjusted as will be presented below.

Tube elongation

Once the cellular tubes are formed, their length can continue to progress through five different methods of elongation summarized in Figure 2

Cell elongation and cell rearrangement

Cell elongation and rearrangement occur when there are no further cells joining the system through division and recruitment. In these cases tube elongation is often associated with the regulation of molecular and cellular events that affect apical membrane mechanics [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF]. As well, convergent extension driven by a supracellular actin cable has been associated with cell rearrangement through the narrowing and elongating the epithelial tube. As discussed previously (section 2.2.4) neighboring cells along one dimension are connected by an actin cable. The cable contracts down to a point, and then re-extends in a perpendicular direction while continually remaining in contact with the same cells changing the shape of the tissue without an increase in cell number.

Proliferation

Generalized proliferation is a significant aspect of tube elongation especially during the initial formation of organs. Other forms of proliferation can occur at later stages.

For example during puberty, high proliferation during branching morphogenesis in the mammalian ducts enlarges the tissue size over length scales, from millimeters to centimeters [START_REF] Andrew | Morphogenesis of epithelial tubes: Insights into tube formation, elongation, and elaboration[END_REF].

Cell recruitment

Cell recruitment elongates some tubes by engaging cells in the local environment.

The classical example of cell recruitment is the drosophila malpighian tubes which are tubes present at the interface between the midgut and hindgut. These tubules initiate with only 6-10 cells and they grow in size through the addition of stellate cells that intercalate into an already polarized tube epithelium. Similarly in the kidney the nephron tubule is formed from mesenchymal cells that are recruited and coalesce together [START_REF] Costantini | Patterning a complex organ: branching morphogenesis and nephron segmentation in kidney development[END_REF].

Tube diameter regulation

Maintaining a controlled tube diameter enables a tissue to perform its required functions. Once fully formed, oriented cell divisions significantly affect tube diameter preservation. Regulation of division direction is related to planar cell polarity (PCP) signaling and the overexpression of many genes related to PCP have been shown to cause tube defects, for example, a deregulation of apical domain size and tube length in the drosophila trachea [START_REF] Maruyama | Drosophila as a model for epithelial tube formation[END_REF]. Division orientation, however, isn't always controlled. In the kidney divisions during development were measured to be randomly distributed, and it was convergent extension that brought the tube to the correct adult diameter. Subsequently the divisions became highly oriented to regulate the adult size [START_REF] Karner | Wnt9b signaling regulates planar cell polarity and kidney tubule morphogeneis[END_REF]. Epithelial tube size is also often maintained through fluid flow and pressure which is sensed by cilia on the apical surface of tube facing the lumen. Pathologies affecting cilia have therefore been linked to a deregulation in tube size [START_REF] Wilson | Cystic disease of the kidney[END_REF].

Two case studies of in vivo curvature

Supracellular actin alignment inside curved tissues

The discussion of tubulogenesis above emphasized the wide variety of curved epithelial tissue present in vivo. In this thesis, out-of plane curvature is studied in a controlled manner by growing epithelial cells on curved substrates. Before describing such in vitro studies, two in vivo tissues will be presented: the drosophila trachea and the drosophila egg chamber, both examples of epithelia that develop on curved rigid extracellular matrix whose presence guides the alignment of actin across the tissue.

Although the polarity and localization of the actin is different in the two cases, each generates aligned actin fibers on their surface facing the ECM. In the trachea, fibers

TWO CASE STUDIES OF IN VIVO CURVATURE

align on the the apical surface which is in contact with a luminal chitinous ECM while in the egg chamber fibers orient on the basal side that contacts the layer of collagen IV ECM.

Drosophila trachea

The drosophila trachea originates as approximately 80 cells and sprouts and fuses into a complex tubular network [START_REF] Samakovlis | Development of the Drosophila tracheal system occurs by a series of morphologically distinct but genetically coupled branching events[END_REF]. The final size of the epithelial tube is reached through an expansion driven by luminal chitin, a rigid cylindrical extra cellular matrix secreted below the apical surface (Fig. 2-34A-C).

Luminal chitin first appears during stage 13 of embryogenesis which occurs ∼9-10h after the start of a developmental process of ∼24 hours when the embryo is kept at 25

• C [START_REF] Wang | Septate-junction-dependent luminal deposition of chitin deacetylases restricts tube elongation in the Drosophila trachea[END_REF]. Circumferentially arranged apical actin rings form into parallel bundles during this stage of embryogenesis (Fig. 2-34E, yellow arrow) [START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF]. In fact, the cylindrical chitin scaffold is directly related to the formation of actin rings in the tube and the absence of chitin has been found to disrupt the apical cytoskeletal arrangement and the tube shape [START_REF] Tonning | A transient luminal chitinous matrix is required to model epithelial tube diameter in the Drosophila trachea[END_REF]. Chitin mutants show irregular cyst formation together with tube constrictions along its length. Although the chitin cylinder is needed for the actin ring formation it isn't clear what role it actually plays in organizing the actin. In relation to this project, we question if the cylindrical geometry of the chitin could alone drive the actin organization. This hypothesis will be explored during the course of this thesis. [75] E) A drosophila trachea ∼9h-10h after fertilization when circumferential apical actin bundles begin to form. The yellow arrow points to one such oriented bundle. (actin-GFP marking, scale bar=10µm) F) A confocal projection of an adult, wild type, trachea. The circumferential actin rings are far more well defined than in the embryonic tube. Adherens junctions marked in green delineate the boundaries between the tube cells. Actin(red) DE-cadherin(green) bar=50µm [START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF] When the tissue matures to adulthood, a corrugated rigid cuticle forms across the apical surface of the cells facing the lumen and the chitin core of the tube clears.

The cuticle prevents the lumen from collapsing during changes in pressure inside the hollow tube while allowing the tube to expand and contract along its length. In this final state, actin rings are still present and even more defined along the cuticle ridges (Fig. 2-34B) [START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF].

Drosophila egg chamber

The drosophila egg chamber is another example where actin aligns across a tissue. At stage 3 of egg chamber development 16 germline cells are encapsulated by a cuboidal epithelium. At this point F-actin is highly concentrated at the apical surface (Fig. 2-35A) which contacts the germline but it is also present throughout the cortex. In the following stages the chambers elongate altering the epithelial layer from cuboidal to squamous. Parallel actin fibers form at the basal surface of the follicle cells during elongation.

These bundles are oriented perpendicular to the anterior-posterior axis (the elongation direction) of the egg chamber [START_REF] Baum | Spatial control of the actin cytoskeleton in Drosophila epithelial cells[END_REF]. As for the drosophila trachea, the actin alignment requires the presence of an ECM. Here the ECM is comprised of a fibrillar collagen IV matrix which is polarized perpendicular to the anterior-posterior axis by follicle rotations around the long axis beginning at stage 3 to stage 13 [START_REF] Haigo | Global tissue revolutions in a morphogenetic movement controlling elongation[END_REF]. The aligned actin bundles were found to to be under tension through laser nano surgery and the focal adhesion protein zyxin, shown to be present all along actin bundles, demonstrated that they are attached to the substrate beneath them (Fig. 2-36C-E) [START_REF] Colombelli | Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization[END_REF].

Employing collagenase on a stage 12 elongated follicle led to a shape deformation, causing follicle rounding. In contrast, a Latrunculin A treatment to disrupt actin organization during the same elongated stage left the follicle shape undistorted [START_REF] Haigo | Global tissue revolutions in a morphogenetic movement controlling elongation[END_REF].

This demonstrates that despite the actin stress fibers being under tension, it is the ECM that forms a "molecular corset" stabilizing its shape. Thus, similarly to the drosophila trachea, the presence and geometry of the ECM in the egg chamber plays an essential role in both shape development and actin organization.

As described above, the drosophila trachea and the egg chamber are two examples of epithelia growing on a rigid curved ECM. The presence of the ECM is in both cases is indispensable for the alignment of the actin fibers within the cells. It isn't understood, however, what role curvature might play in the alignment. This thesis will explore the possibility that actin rearrangement at the scale of a tissue could be driven solely by the curvature of a substrate.

In vitro studies of curvature

Given the ubiquity and significance of epithelial tubes in vivo this thesis seeks to understand the possible influence of their out-of-plane curvature on collective epithelial cell properties. Before discussing assays employed to deconstruct the effect of curvature on epithelial cells, curvature will be defined and a convention provided for positive and negative curvature.

Definition of terms: curvature

In 2d the curvature κ is defined for every point s on a line as κ(s) = dφ/ds where φ denotes the angle of the tangent to the line at the point while s represents the arc length. The radius of curvature, r is then given by r = 1/κ and corresponds to the radius of a circle that would have the same tangent at a given point. For a point p on the surface of a three dimensional object the two principle curvatures are defined as c 1 = 1/R 1 and c 2 = 1/R 2 which are the maximum and minimum of the normal curvatures at a given point (Fig. 2-37). A curvature can also be defined at a point on the surface along any tangent to the surface. This thesis focuses on cylindrical epithelial tubes. The two principle curvatures of a cylinder of radius R, are 0 and 1/R . In this thesis positive and negative out-of-plane curvatures are defined to those of the outside and inside of a sphere, respectively.

A range of assays have been developed in 2D and 3D to explore the influence of curvature on cells. The role of curvature in 2D will be discussed and then assays to study out-of-plane curvature will be covered in greater detail.

Two dimensional in-plane curvature assays

Although out-of-plane curvature is inaccessible on two dimensional assays, in-plane curvature is relevant for single cells as well as expanding monolayers. On the scale of a single cell, the curvature imposed through geometrical constraints influences cytoskeletal organization [START_REF] Brock | Geometric determinants of directional cell motility revealed using microcontact printing[END_REF][START_REF] Théry | Micropatterning as a tool to decipher cell morphogenesis and functions[END_REF]. For example, NIH3T3 fibroblast cells seeded on micro-patterned squares spread across the entire pattern and take on its shape. The high curvature corner regions of the confined cell have been shown to correspond to the positions of lamellipodia formation (Fig. 2-38). In a similar muticellular study, Rolli et al. [START_REF] Rolli | Switchable adhesive substrates : Revealing geometry dependence in collective cell behavior[END_REF] plated groups of MDCK cells on adhesive circular micropatterns of radii 44-142µm. The non adherent zone was photoswitchable and could be rendered adherent through a UV flood exposure (Fig. 2-39).

This study demonstrated that as the radius of the island decreased the frequency of leader cell appearance increased. Thus similarly to single cells confinement, mul-

Three dimensional curvature assays

Curvature in vitro A large range of epithelial and endothelial cells can self organize into curved, three dimensional structures when seeded inside gels. For example, MDCK cells form spherical cysts in gels, which can branch into tubules when stimulated with growth factor [START_REF] Zegers | Epithelial polarity and tubulogenesis in vitro[END_REF]. Curved structures can also be formed in prepatterned gels. Seeding cells into round or even rectangular channels inside gels is now a standard procedure to engineer endothelial tubule networks [START_REF] Chrobak | Formation of perfused, functional microvascular tubes in vitro[END_REF] [86] [START_REF] Golden | Fabrication of microfluidic hydrogels using molded gelatin as a sacrificial element[END_REF].

Similarly to the 2D in plane experiments of the previous section, curvature has also been found to be relevant in some three dimensional gel assays. Nelson et al. engineered curved epithelial tubules of various shapes (eg. 'Y' and 'C' shapes (Fig. 2-41A-B)) inside gels and demonstrated that the local 3D curvature of the tubules can define the site of epithelial branching [START_REF] Nelson | Tissue geometry determines sites of mammary branching morphogenesis in organotypic cultures[END_REF]. In this system, however, the curvature does not initiate branching directly but rather the geometry of the tubule defines the geometry of the local inhibitory morphogen gradient. As a result, tubules branch preferentially at their convex side where concentration of inhibitory morphogens is lower.

Later studies of epithelial cells embedded into patterned gels found that curvature significantly affects the local mechanics of the epithelium. Regions of high curvature exert higher traction forces on the surrounding gel. High convex curvature yields inward traction forces whereas regions of high concave curvature results in outward pushing forces [START_REF] Gjorevski | Mapping of mechanical strains and stresses around quiescent engineered three-dimensional epithelial tissues[END_REF]. C) respectively. Branching occurred on the fractal tree at positions where the inhibitor was at a local minimum (scale 50µm) [START_REF] Nelson | Tissue geometry determines sites of mammary branching morphogenesis in organotypic cultures[END_REF] Studies such as those on gel-embedded tubules illustrate the influence of curvature on epithelia but moving from flat assays to the three dimensional environment of a gel introduces numerous free parameters beyond out-of-plane curvature (section 2.3.4:"limitations on 2D models") . For example, cells in 3D environments display different protein localization, resistance to apoptosis and/or available space for invasion compared to 2D assays [START_REF] Zegers | Epithelial polarity and tubulogenesis in vitro[END_REF]. In contrast, cell seeded on rigid surfaces, curved out of the plane, provide a controlled manner in which curvature can be incrementally added into the system while keeping other parameters identical to well studied 2D environments. Such surfaces were therefore chosen for this thesis to isolate the influence of out-of-plane curvature on epithelial cells. To further motivate the choice of rigid out-of-plane surfaces, two examples of cells growing on rigid curved surfaces in vivo will be presented.

Out-of-plane curvature assays

The remainder of the introduction will introduce studies performed on rigid surfaces with out-of-plane curvature. Seminal studies highlighting the pioneering approach of the British school in the 70's of cells on such surfaces will be presented followed by a summary of more recent work.

Historical background of out-of-plane curvature studies

The effect of curved substrates on cells was first examined by Paul Weiss [START_REF] Weiss | Experiments on cell and axon orientation in vitro: The role of colloidal exudates in tissue organization[END_REF] who observed Schwann cells oriented along the long axis of a wire of r=13µm inside a plasma medium. Weiss did not conclude that the substrate geometry determined the cell orientation but rather hypothesized that an oriented "colloidal exudate" from the explant that guided the cells. A study refuting the hypothesis of exudate was carried out almost 20 years later by Curtis and Varde who cultured chick embryonic heart fibroblasts on silica fibers of radius 5-15µm [START_REF] Curtis | Control of Cell Behavior : Topological Factors[END_REF]. They failed to see aligned residue on the wires which could guide the cells. Also the exudate hypothesis seemed doubtful as the cell alignment was modulated by the radius of curvature of the wire. Curtis and Varde also documented that on undulating fibers(r=4µm) (Fig. 2-42D), fibroblasts accumulated on the concave but not the convex curvature regions: a curvature response which could not have been guided by a uniformly aligned "exudate" on the wires. Dunn and Heath [START_REF] Dunn | A new hypothesis of contact guidance in tissue cells[END_REF] offered an alternate hypothesis for topological alignment of cells on curved substrates. They suggested that a cell might sense the curvature of a substrate below a diameter of 200µm by comparing the surface curvature with a rigid linear reference element inside its cytoplasm. In fact a microfilament candidates of ∼15µm in length, had previously been imaged with transmission electron microscopy in migrating chick heart fibroblasts by Abercrombie [START_REF] Abercrombie | The location of fibroblasts in culture[END_REF]. Abercrombie described microfilaments extending from possible substrate adhesions at the leading zone of the lamella backwards, and upwards by ∼ 1.2 µm at an angle of sin -1 (1/15) ∼4 degrees, towards the cortical meshwork of microfilaments at the rear of the lamella.

The filaments were assumed to be contractile and responsible for displacing the cell towards its anterior adhesions. These microfilaments were subsequently identified as actin stress fibers moving from focal adhesions at the leading edge backwards towards the center of the cell. In particular these actin fibers in fibroblasts are now known to be especially prominent and rigid [START_REF] Tojkander | Actin stress fibers-assembly, dynamics and biological roles[END_REF].

The leading filament was therefore hypothesized to restrict the bending angle of the leading protrusion to less than 4 • . From this model they concluded that a cell would be unable to traverse a substrate ridge above 4 • (Fig. 2-43). Indeed their experiments confirmed that cells seeded on a prism of 4 • exhibited a discontinuity in their migration when encountering the ridge however it was above an angle of 8 • that almost all fibroblasts were deflected while crossing the ridge, reorienting more parallel to it. Above 32 • degrees the lamella of the cells terminated abruptly at the ridge. The existence of a microfilament bundle was further corroborated by a study from Fisher & Tickle that employed normal and virally transformed hamster cells which did not contain organized microfilament bundles [START_REF] Fisher | Differences in alignment of normal and transformed cells on glass fibres[END_REF]. The normal cells unlike the transformed cells aligned on thin glass fibers with radii (r<100µm) whereas the transformed cells did not.

In a final set of experiments by Dunn [START_REF]Cell behaviour: A tribute to Michael Abercrombie[END_REF] chick heart fibroblasts were seeded on spherical beads (Fig. 2-42A,B). Here the cells experienced high positive curvature in all directions, unlike cells in a cylindrical geometry. Indeed timelapse microscopy revealed that cells on small beads with a radius less than 50µm exhibited lower motility and spreading than cells on larger beads. This experiment suggested that if a fibroblast cannot relax along a low curvature direction as on a wire they limit their motion and adhesions. However, since cells can spread and move to some extent called into question the suggestion that a microfilament precludes completely motion in the presence of a sufficiently curved surface.

State of the art : Single cell studies:

Despite their elegance the studies presented above left unanswered several aspects of the nature and possible role of microfilaments or other cell components in curvature sensing and cell reorientation. Advances in biotechnology since the early 80's have provided additional tools for establishing the role of curvature on cells. Newer studies, however, have concentrated on the single cell response to curvature ignoring the behavior of entire tissues.

In the following section state of the art of out-of-plane curvature studies on rigid substrates will be summarized. Since this thesis primarily examines positive outof-plane curvature the discussion concentrates on cells grown in positive curvature environments, for example, the surface of cylinders and glass spheres. Although the thesis is dedicated to the study of epithelial cells here we overview as well studies of fibroblasts, neurons, epithelial, endothelial and glioma cells as these provide additional information regarding the mechanisms that affect curvature sensing.

In this section the morphological response of single cells to curvature are first considered. The, collective response of monolayers of cells is discussed in the final section of the chapter.

Cell body orientation

That the body of some cells reorient with curvature was known since the seminal study of Weiss [START_REF] Weiss | Experiments on cell and axon orientation in vitro: The role of colloidal exudates in tissue organization[END_REF]. This observation has since been reproduced and further quantified in investigations of various cell types. For example, measurements of cell orientation at different radius of curvature quantified the increased alignment of L929 fibroblasts (Fig. 2 The study of L929 fibroblasts measured cell orientation 3 days after seeding and therefore did not incorporate the dynamics of alignment. In fact, further studies demonstrated that if cells are seeded on wires, their orientation can change over time. In the case of mouse embryonic fibroblasts (MEF) on wires of R=25µm they showed weak orientation after 2 hours of culture but at 8h the orientation increased twofold before diminishing by 24h [START_REF] Rovensky | Morphogenetic response of cultured normal and transformed fibroblasts, and epitheliocytes, to a cylindrical substratum surface. Possible role for the actin filament bundle pattern[END_REF]. The cells were seeded at very low densities so the decrease of alignment at 24h is observed in preconfluent conditions when the cells are still isolated or only weakly interacting with neighbors. The change of cell orientation with time cannot therefore be linked to a large increase in density. In the case of NIH-3T3 fibroblasts, orientation and elongation were also time dependent, occurring earlier on smaller fibers than large ones [START_REF] Hidai | Self-standing aligned fiber scaffold fabrication by two photon photopolymerization[END_REF] Cytoskeleton arrangement When the microtubules were depolymerized with colcemid the actin in the cells was aligned in both directions [START_REF] Svitkina | Transverse pattern of microfilament bundles induced in epitheliocytes by cylindrical substrata[END_REF]. A further study extends the investigation of actin orientation to Ras transform and demonstrates that cancerous mutations can change the way cells respond to curvature [START_REF] Levina | Cylindrical Substratum Induces Different Patterns of Actin Microfilament Bundles in Nontransformed and in ras-Transformed Epitheliocytes[END_REF]. IAR-2 and IAR-ras-c4 cells transformed by the expression of the N-ras oncogene were compared. The Ras transform is a common mutation found in human tumors [START_REF] Bos | ras Oncogenes in Human Cancer : A Review[END_REF] and it can drive an epithelial to mesenchymal (EMT) transition in cells. EMT causes cells to lose their apical-basal polarity and cell-cell adhesions and to develop a fibroblast-like independent migration. Interestingly, IAR-ras-c4 epithelial cells aligned their actin in longitudinal bundles similar to the fibroblasts, perpendicular to their untransformed IAR-2 counterparts. Smeal et al. grew neurons on both flat surfaces and glass wires of r=17.5-250µm [START_REF] Smeal | Substrate Curvature Influences the Direction of Nerve Outgrowth[END_REF]. Neurons on a cylindrical substrates demonstrated a higher sensitivity to curvature than that reported for fibroblasts [START_REF] Hwang | Controlled cellular orientation on PLGA microfibers with defined diameters[END_REF]. L929 fibroblasts sense substrate curvature below a fiber diameter of 250µm. DRG neural outgrowths, however, already reacted to curvature on wires of diameter 500µm (Fig. 2-49). This suggests To reproduce the experimental observations of cytoskeletal organization under curvature Biton et al. [START_REF] Biton | The cellular response to curvature-induced stress[END_REF] modeled cell reorientation on cylindrical substrates by assuming that the curvature generates both shear stress, derived from the cell's active contractility, and anisotropic bending of rigid stress fibers. The shear stress aligns the cell preferentially along directions of high curvature, while the anisotropic bending tends to align the cell longitudinally along the wire to counteract deformation. The cell realignment under curvature then resulted from a competition between these two opposing effects. This model suggests that the actin filaments of single epithelial cells align in the circumferential direction since contractility is dominant in this cell type while fibroblasts aligned their actin filaments along the longitudinal axis since stress-fiber bending energy dominates. Biton et al. predict a continuum of possible orientations between longitudinal and transverse alignments on a wire of a given radius depending on the ratio of bending stress and contractility for a given cell.

A
Only the longitudinal orientation, however, is predicted to be stable for any value of bending and contractility. This model only pertains to a single cell and thus lacks a description of cellcell adhesions. Accordingly, it is not fully adapted to our problem of interest. The number and orientation of cell-cell junctions around a single cell adds further layers of complexity which would need to be balanced with internal bending and contractility.

Blebbing

In addition to organizing the cytoskeleton and morphology of a static cell, curvature has been found to influence the mode of migration of single glioblastoma cells moving along cylindrical geometries in vivo. Glioblastoma cells are a type of cancerous glial cells, a non-neuronal cell found in the central nervous system [START_REF] Jessen | Glial cells in the enteric nervous system contain glial fibrillary acidic protein[END_REF]. In vivo, these cells move along highly aligned white matter, a component of the central nervous system made up of bundled myelinated axons which range in diameter from below 500nm-7µm.

Glioblastoma cells seeded on flat substrates exhibit relatively continuous blebbing.

Blebs are cell membrane protrusions that are generated when actomyosin contractions of the cell cortex temporarily either rupture the or detach the membrane from the cell cortex. Cytosol streams out from the cell inflating small portions of cell membrane [START_REF] Charras | A short history of blebbing[END_REF]. Polarized blebbing can be used as a propulsive method of migration as has been observed in migrating cancer cells [START_REF] Friedl | Plasticity of cell migration: a multiscale tuning model[END_REF]. Blebbing decreased in size and count as the cell elongated and was inhibited completely with spreading above 1400µm 2 on the wire. When the cell retracted during migration, blebs began to reform. The ability of cylindrical geometry to cause cells to cycle in and out of blebbing phases is possibly relevant in the context of cancer since blebs have been linked to a drug resistance and cell survival [START_REF] Babiychuk | Blebbing confers resistance against cell lysis[END_REF].

Although this section has been dedicated to cells on positive curvature assays, one notable model of cell migration subject to negative curvature is interesting to note here.

Negative curvature: migration velocity

Although this section primarily considers cells on positive curvature assays one model of cell migration subject to negative curvature is of particular relevance to note here. A simulation of the migration dynamics of cells inside a lumen was performed by Kim et al. to [START_REF] Kim | Integrating focal adhesion dynamics, cytoskeleton remodeling, and actin motor activity for predicting cell migration on 3D curved surfaces of the extracellular matrix[END_REF]. Cells confined to migrate on the inside surface of a lumen (of diameter larger than the cell's cross section) has the same lateral confinement as a cell on the outside of a wire. This study, therefore, could be related to work discussed in this thesis on migration under positive curvature.

A cell migration simulation procedure was formulated by modeling focal adhesion dynamics, cytoskeleton and nucleus remodeling, and actin motor activity through a double membrane model of the cell and nucleus which progressed through with distinct simulated adhesion node positions. The velocities and trajectories of cells in rectangular lumen obtained from the calculation were fit with previously published data from Irimia et al [START_REF] Irimia | Spontaneous migration of cancer cells under conditions of mechanical confinement[END_REF] which described the migration of 7 types of cancerous cells confined in rectangular microchannels of height 3 or 12 µm and widths between 6-100µm. The model was then employed to explore the migrational properties of cells in curved lumens. Adding curvature to the system predicted an increase in velocity with decreasing lumen radius above a critical diameter of ∼7µm (Fig. 2-53). For smaller diameters the cell was confined to a lumen with a size less than its dimensions and had to constrict to migrate.

The increase in migration speed with increased confinement, is reminiscent of the study of cells confined laterally in 2D tracks (sec. 2.3.3) [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF]. This thesis will study the collective migration of cells under simultaneous lateral confinement and positive curvature. The dynamics will be compared to the migration in tracks and lumen to distinguish the influence of confinement and curvature.

State of the art: Multicellular studies

While the multiple studies summarized above principally examined the response of single cells to curved substrates, less work exists involving cell populations. One relevant study, however, was very recently published on endothelial cells grown on the outside of wires of varying radii. Although, as mentioned above, there is a large body of work on endothelial cells forming confluent tubes of negative geometry, specifically inside gels this is the first study of endothelial monolayers on positively curved rigid substrates.

Endothelial monolayers

In vivo endothelial cells arrange in tubes of diameter from 8µm -1cm in the largest arteries [START_REF] Aird | Spatial and temporal dynamics of the endothelium[END_REF]. Inside these vessels, cells elongate longitudinally away from branch points [START_REF] Reidy | The effect of local blood flow patterns on endothelial cell morphology[END_REF]. Recently Ye et al. explored the role of shear stress and curvature in regulating cell elongation inside two cell lines commonly used to model different types of vasculature [START_REF] Ye | Brain microvascular endothelial cells resist elongation due to curvature and shear stress[END_REF]. Human umbilical vein endothelial cells (HUVEC) arrange into large vessels whereas human brain microvascular endothelial cells (HBMEC) form smaller vessels with sometimes only a single cell around the perimeter.

HUVEC and HBMEC cells lines were grown to confluence on the outside of glass wires ranging from radius of 5-250µm. HBMEC cells displayed insensitivity to substrate curvature for radii above r= 12.5 µm. Below this critical value the average orientation of the cell body decreased quickly to around 15 degrees since the circumference of the wire was smaller than the cell length, forcing the cells to align (Fig. 2-54A). On wires of diameter 10µm HBMEC wrap fully around the wire forming a junction with themselves. In fact, the number of cells around the wire as the diameter decreased closely fit a power law N ∝ d α , with α = 0.86 down to a single cell (Fig. 2-54B).

In contrast, a confluent HUVEC monolayer was highly sensitive to curvature already exhibiting an orientation of 15 0 at R=100µm. The orientation was nearly longitudinal for r=5.5µm (Fig. 2-54A). At small radii, unlike HBMEC cells, the number of cells around the perimeter were never fewer than 3 cells. The number of cells around the wire however, still scaled as a power law with diameter above ∼ 30µm , with α = 0.80 (Fig. 2-54B).

Ye et al also reported a difference in the actin orientation inside the monolayers.

For HBMEC, actin aligned more preferentially in the circumferential direction while HUVEC favors a longitudinal alignment. Before this study, the cell type (fibroblasts, epithelial, neural) was thought to control the response of the actin cytoskeleton to cur-vature with fibroblasts and neural cells favoring longitudinal alignment and epithelial cells favoring transverse alignment. The varying response to curvature between two endothelial cells seen here questions ones ability to predict one unique actin response for an entire cell type. Another possibility is that the varying actin alignment of HBMEC and HUVEC cells on curved substrates is actually a collective effect and the actin of both cells would align similarly under curvature as single cells. Further study is necessary to understand the rearrangement of actin in an entire curved monolayer. For HBMEC α = 0.86 and the x-axis intercept where N=1 is at d=9.8µm. For HUVEC, however, α = 0.80 and the x-axis intercept where N=1 is at d=4.4µm. The dotted line shows α = 1 E) Parallel and F) perpendicular indices for actin fiber distribution in confluent monolayers of HBMEC and HUVEC cells in 2D on large and small wires under static conditions and for large wires under shear stress (SS). Error bars are the SE. [START_REF] Ye | Brain microvascular endothelial cells resist elongation due to curvature and shear stress[END_REF] Chapter 3

Materials and Methods

A rigid curved substrate had to be selected for the in vitro study of epithelial tissues subject to out-of-plane curvature . The surface needed to possess a well defined profile at every point across an area of hundreds of microns squared, a surface large enough to study a population of cells. The substrate also need curved features that could be rescaled to yield curvatures between ∼0.5 µm and ∼100µm.

Particular advantages of a cylindrical shape are that a single value of the radius determines the global curvature which can be adjusted from infinity to a value smaller than the curvature of a typical cell.

As well, collective cell migration under high curvature over large distances can be characterized in long cylinders while monolayers on the outside of small radius glass balls, for example, rapidly cover the spherical surface through division and migration limiting the available time to determine the migration parameters.

Finally, cell growth on the outside of cylinders mimics the geometry of in vivo tubes. We avoided growing cells inside capillaries since although this also replicates the geometry of epithelial tubes, fluid flow would be necessary to refresh the medium inside the lumen and flow has been demonstrated to alter the orientation and response of cells [START_REF] Meer | Analyzing shear stressinduced alignment of actin filaments in endothelial cells with a microfluidic assay[END_REF][START_REF] Simmers | Arterial shear stress regulates endothelial cell-directed migration , polarity , and morphology in confluent monolayers[END_REF][START_REF] Praetorius | Bending the MDCK Cell Primary Cilium Increases Intracellular Calcium[END_REF]. Out-of-plane curvature in capillaries could therefore not be directly compared to 2d conditions without simultaneously considering flow.

The three methods used to fabricate cylindrical substrates will be detailed below.

Surface fabrication

Pillar assays

The first technique to fabricate cylinders was through photolithography. A plastic mask with arrays of transparent circles of diameter 100µm and 200µm was designed using the L-edit software package. The pattern on the plastic mask was moved to a chrome glass mask to improve its optical transfer function. SU8 (Microchem), a negative photoresist, was spin coated on a silicon wafer which was then exposed to a UV lamp through a chrome mask and developed to create a mold with round cylindrical pillars. The mold was covered in PDMS to form the negative pattern.

Glass wires

Glass wires were the primary substrates used. Wires of radius larger than 20µm were made by heating glass pipettes with a hand-held blow torch and pulling each end manually. As well, glass wires of radius (R) 40µm and 85µm were purchased (CM Scientific). Finally, small glass wires of R below 20µm as well as tapered cones were manufactured from glass pipettes of R = 500µm (WPI Inc) with a pipette puller (Sutter Instruments P-2000). The surfaces of the glass wires were inspected with a SEM microscope and a surface was smooth down to less than half a micron was

SURFACE FABRICATION

Polystyrene (PS) wires

In addition to cones drawn from a pipette puller, wires with radii below 10µm were manufactured from a solution of 25% polystyrene (PS) dissolved in N,N'-dimethyl formamide (DMF) (Fluka Analytical) (With the help of Sisi Lee from the Yong Chen laboratory, ENS Chemistry department). DMF-PS solution is commonly employed for electrospinning thin fibers, a procedure employing electrical fields to draw thin micron or nano-scale fibers from a solution [START_REF] Huang | A review on polymer nanofibers by electrospinning and their applications in nanocomposites[END_REF]. Here, however, the solution was drawn by hand through a syringe tip and weaved between two PDMS supports. After drawing a row of wires, the Gel-Pak was covered with PDMS that was subsequently cured to fix the wires in place. Although PS wires can be conveniently produced in large quantities at radii below 10µm, such wires have a rough surface as a result of residual solvent trapped inside the newly formed fibers [START_REF] Kim | Unique Surface Morphology of Electrospun Polystyrene Fibers from a N,N-Dimethylformamide Solution[END_REF] and were therefore not employed. As well, PS wires are fragile and thus break far more easily than glass during immunofluorescent staining. Finally, if not drawn quickly enough the fibers would be loosely suspended between the supports and would therefore oscillate during time-lapse acquisitions.

SURFACE COATING

Surface coating 3.2.1 Fibronectin

All three assay structures mentioned above, namely, PDMS pillars, glass wires, and PS wires were activated in a oxygen plasma cleaner (Harrik Plasma) and then coated with bovine plasma fibronectin (Life Technologies) at 10µg/ml in PBS, an extra cellular matrix protein to which the cells attach. By employing fluorescent Cy3-fibronectin, it was confirmed that the fibronectin attached evenly on the cylindrical substrates. The structures were subsequently transferred to either six well plates or culture dishes.

Pll-Peg

The types of cells used in this work easily adhere to glass or polystyrene bottomed culture dishes. During long experiments cells developed and migrated down the sides of the PDMS supports and onto the flat dish bottom. With time, the cells could reach the surface between the objective of the inverted video microscope and the glass wire, reducing the quality of the image of the cells on the wire. To prevent cells from growing onto the dish's glass bottom, the wells were pretreated with a 0.1mg/mL cell-repellant solution of Poly L-lysine-PolyEtheylene Glycol (Pll PEG, Susos) before wire assays were incorporated.

Micropatterning

Growing cells on cylindrical wires intrinsically induces a lateral, although borderless, confinement; therefore we compared our results with experiments conducted on confining tracks micropatterned on a flat substrate. These experiments allowed us to uncouple effects of confinement from those resulting from curvature.

Adhesive tracks of width 20µm-500µm were micropatterned on clean glass slides (Fig. 3-5a) using a highly resistant surface treatment [START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF][START_REF] Duclos | Perfect nematic order in confined monolayers of spindle-shaped cells[END_REF][START_REF] Tourovskaia | Long-term microfluidic cultures of myotube microarrays for high-throughput focal stimulation[END_REF]. A protein-repellant layer of polyacrylamide and polyethylene glycol were coated on piranha cleaned glass (Fig. 3-5b) followed by a photoresist layer (Fig. 3-5c). After exposure through a mask the photoresist was developed (Fig. 3-5d) and an oxygen plasma was employed to locally remove the protein repellent layer on the exposed areas (Fig. 3-5e). Finally, the undeveloped photoresist was dissolved with acetone(Fig. 3-5f). The resulting surface (Fig. 3-5g) consists of a patterned protein-repellant layer with virgin glass exposed for cell culture. Cells can be seeded over the entire slide and allowed to adhere for 3 hours. Washing with PBS leaves cells attached exclusively to the adhesive part of the patterns.

Ibidi culture inserts

Ibidi culture inserts (Biovalley) were employed to seed cells into onto the micropatterned tracks in a controlled location (Fig. 3456). The inserts contained two wells of volume 70µl and outer dimension 8.4x8.4x5µm. Cells were added to either side of the two well chambers and were grown to confluence. The inserts were removed and the cells migrating in the confining micropatterns were observed. • MDCK MDCK or Madin-Darby canine kidney cells are an immortalized simple epithelial cell line which forms monolayers in culture. Depending on the substrate they are seeded on, their height can vary between cuboidal and columnar with heights that are larger on permeable substrates than on ridged plastic or glass surfaces [START_REF] Zuk | Type I collagen gel induces Madin-Darby canine kidney cells to become fusiform in shape and lose apical-basal polarity[END_REF].

MDCK wild type (MDCKwt) cells were used along with a stable MDCK LifeAct-GFP cell line created in the team by Olivier Cochet [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF]. The cells were transfected using the LifeAct-GFP plasmid (Ibidi) and their filamentous actin tagged with a GFP protein. Additionally, MDCK E-cadherin-GFP histone-mCherry cells transfected by Myriam Reffay in the team, were employed for preliminary tests [START_REF] Reffay | Orientation and polarity in collectively migrating cell structures: statics and dynamics[END_REF].

• HEK-HT-GFP Finally, immortalized HEK-HT-GFP (Human Embryonic Kidney cells) from the team of Jacques Camonis: U830, Insitut Curie were used. The closure dynamics of round circular wounds formed in HEK-HT-GFP monolayers has been quantified [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF] and a circular wound and a migrating front fully wrapped around a wire differ by a topological transformation in which the cell-free region within the closing wound is the equivalent of the wire cross-section. HEK-HT-GFP cells were therefore selected for comparison to wound healing studies.

HEK-HT-GFP cells have enforced expression of hTERT (human telomerase

reverse transcriptase) a catalytic subunit of telomerase [START_REF] Nakamura | Reversing time: origin of telomerase[END_REF]. The cell line was also transfected to express GFP by Lynda Latreche (U830, Institut Curie).

Culture protocols

MDCK and NIH3T3 cells were passed at 10% in DMEM GlutaMax (Dulbecco's Modified Eagle Medium) (Gibco) and supplemented with 10% FBS (Gibco) and 1% antibiotics (penicillin: 1000units/mL , streptomycin 10mg/mL). The two fluorescent MDCK cell lines were also cultured in geneticin at 0.4µg/mL (Gibco). HEK-HT cells were cultured in DMEM GlutaMax (Gibco) supplemented with 10% FBS, 100µg/mL hygromycin and 50mg/mL geneticin. Cells were incubated in an environment containing 37 • C at 5% CO 2 and saturated in humidity. All cells were passed at 10% using trypsin-EDTA (0.5mL) every 3-4 days and maintained for experiments to a maximum of 25 passages. Cells were seeded on the fibronectin coated PDMS supports and allowed to adhere for 2h. The substrates were then washed with PBS and medium was added to the entire dish. The cells were cultured for 3-5 days allowing them time to divide and migrate onto the wires before being put under the microscope.

Microscopy

Imaging cells migrating on glass cylinders introduced complexities not present on flat glass slides. The wire acts like an optical lens, distorting the light that passes through it. As well, because of the height of the structures, a microsope objective with a sufficiently large working distance had to be selected. On this microscope the wires were illuminated from above and imaged from below, therefore the the light illuminating the cells facing the objective had to travel through the wire's distorting optical lens. The cells on the two sides of the wire (Fig. 345678, red arrows), however, were illuminated from light which only passed through the culture medium and were therefore viewed clearly. Resolving the location of the cell front at these two sides was sufficient to measure its progression over time. High magnification images of fluorescently marked cells were therefore observed under an upright spinning disk microscope (Zeiss, CoolSnapHQ2: PICT-IBISA BDD imaging platform, Institut Curie). Water immersion objectives allowed the lens to be lowered as close as required to the sample. Further, the 40x and 63x water immersion objectives possessed working distances of 2500µm and 2100µm respectively enabling the imaging of the sides of large wires. This procedure removed the working distance restrictions, but environment regulation still proved difficult under an upright microscope as the local environment is normally controlled by capping the top of the stage with a cover which regulates humidity and CO 2 while the live sample is observed from the bottom. A cap, however, cannot be used if the objective is submerged in the dish.

Video microscopy

The entire box around the microscope was heated to 37 • but medium rapidly evaporates at this temperature. To image cells in live under this microscope we developed a home-made system where the sample dish was put in a bag which was fastened around the immersion objective and an incoming tube carrying humidity and CO 2 .

Two photon laser ablation

Photoablation employs a high power laser to make selective cuts. This technique is commonly employed inside a cell or tissue to probe for regions under tension [START_REF] Kumar | Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics[END_REF][START_REF] Colombelli | Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization[END_REF][START_REF] Reffay | Orientation and polarity in collectively migrating cell structures: statics and dynamics[END_REF][START_REF] Bonnet | Mechanical state, material properties and continuous description of an epithelial tissue[END_REF]. In this thesis photoablation experiments were performed with a Zeiss LSM 710 NLO microscope (PICT-IBISA BDD imaging platform, Institut Curie). The confocal microscope was equipped with a MaiTai laser (Spectra Physics) scalable between 690-1040nm with a pulse width <100fs. The microscope contains 4 lasers with emission wavelengths of 405/457/488/514/561/633nm. The laser and acquisition electronics were controlled with Zen2010 software (Zeiss). Both the stage and a box around the microscope were incubated at 37 • C. An environment of saturated water vapor and 5% CO2 was maintained around the sample.

An unconventional 63x water objective with a working distance 2100µm was selected for the inverted microscope to address the challenge posed by the limited, 190µm distance associated with the the oil objective. A finger of a laboratory latex glove was employed to form an elastic tube wrapped around the objective to prevent liquid spillage into the microscope. A large drop of water was then placed on the lens and brought into contact with the glass bottomed dish to create a meniscus with the water. The Mai-Tai laser was used at 85% power and at a wavelength of 890nm, with a bleach time of .156s and 1.8s between image acquisitions. Laser ablation was used to cut portions the fluorescent actin cytoskeleton of Life-Act GFP cells without harming other parts of the cell. Specifically, ablation was used for precision cutting of actin fibers inside the cell and actin cables along cell boundaries in both flat and curved conditions.

Ablation is commonly executed with a 2 photon MaiTai laser and imaged with a green laser. In this thesis a 2 photon laser was used for both ablation and image acquisition. The precision in z when ablating and imaging retraction on the curved surface of a wire of radius 10µm is of increased importance than when ablating on a flat substrate. Imaging with the MaiTai laser insured that the cable was imaged exactly at the ablation z plane.

Immunofluorescence

For the immunofluorescence reported in this thesis, cells were fixed in 4% PFA for 15 minutes, permeabilized in 0.1% Triton X-100 for 10 minutes and blocked in 10%FBS in PBS for 30 minutes. Ezrin was labeled with an anti-ezrin produced in rabbit (made by the team of Laurence Del Maestro, Institut Curie, 1:300) followed by an Alexa 488 chicken anti-rabbit (Molecular Probes, 1:500). Vinculin labeling was performed with a mouse Monoclonal Anti-Vinculin antibody (Sigma, 1:500) followed by Alexa 546 goat anti-mouse (Molecular Probes, 1:500). Actin was labeled using Alexa 488 phallodin (Molecular Probes, 1:1000). Hoescht (Sigma, 1:10000) was used to mark the nuclei. Phospho-Myosin Light Chain 2 (Cell Signaling, 1:200) marked myosin. Each antibody was diluted in 10%FBS in PBS and incubated in a moist, dark environment for 1 hour.

Mounting medium is commonly used to fix and preserve an immunofluorescence sample. A drop is placed on a glass coverslip and the glass slide with the newly fluorescent sample is carefully lowered on to it. In the case of wire assays, however, mounting medium was avoided because air bubbles which hindered imaging were easily trapped between the wires when they were being lowered onto mounting medium. Thus, upon completion of the immunofluorescence, wire assays were maintained in PBS and imaged immediately. This also allowed the wires to be imaged with the upright spinning disk microscope, discussed above, which had the largest working distance.

Ki67 antibody was used to mark cells cell proliferation. During active parts of the cell cycle (G1, S, G2, and mitosis) the protein is visible through immunofluorescence.

However, cells in a resting state or G 0 are not marked. The Ki67 antibody(rabbit), was used at a dilution of 1/200 and incubated for 3h at room temperature. The marking was followed by an Alexa 488 chicken anti-rabbit (Molecular Probes, 1:500)

DRUG INHIBITIONS

Drug Inhibitions

The factors influencing the migration of cells along the curved substrates were determined through inhibition experiments. Cells were initially observed through the microscope for 24 hours. The dish was removed and, after supplementing the culture medium with a inhibitory drug, replaced under the microscope. The cell behavior was subsequently recorded for several additional hours to observe the effects of the new conditions. Below are drugs used in this study are detailed:

• Blebbistatin (Sigma), an inhibitor of myosin II contractility was used at a concentration of 50µM. Blebbistatin increases the boundary velocity of collectively migrating MDCK cells on flat surfaces [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF][START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF].

• Hepatocyte growth factor human (HGF), was used at 10ng/mL, a sub-scattering concentration. In the case of wound healing experiments, HGF has been shown to accelerate re-epithelialization by ∼50% [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF].

• NSC-23766 (Tocris Bioscience), an inhibitor of Rac GEF was used at 50µM. NSC slows down the closure of small MDCK model wounds by inhibiting cell protrusions [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF].

• C3 transferease (Cytoskeleton Inc.) inhibits RhoA B and C proteins without inhibiting other related Rho family proteins , for example Cdc42 and Rac. C3 transferase was used at 1µg/mL. C3 transferase limits the contractility of actin cables [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF] and the formation of leader cells in MDCK wound healing [START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF].

• Mitomycin C (Sigma) an inhibitor of division was used at a concentration of 5µg/ml. Mitomycin C, however shows signs of toxicity on MDCK cells after 12h [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF]. Therefore, it could not be used for long term studies of cell migration on wires.

• Thymidine (Sigma) used at 2mM, is commonly used to synchronize cells to the same position in the cell cycle. When cells are exposed to thymidine they are held at the G1-S border. Cells, however, which are already in S, G2 or M phase will divide. Thymidine was used to slow cell proliferation in a less toxic manner than mitomycin C. Cells could be held in S phase using thymidine longer than the 12 hours possible with mitomycin C.

Image processing

Image projections

Confocal images were captured at different z positions along the side of the wire (Fig. 3-9A). A projection of images taken on the top half of the wire were used for some analysis(Fig. 3-9B). For example, the orientation of the actin cytoskeleton on the wires was measured from stack projections. The orientation of objects off axis in the projections, however, underestimates the actual angle on the surface of the wire.

The length of the longitudinal component of the object is conserved in the projection but the length of the circumferential component is shortened.

θ (t=0) = tan -1 tan θ b cos(sin -1 ( b r )) (3.1)
.

The term in the denominator b r = sin(α) where α is the opening angle of the cylinder (Fig. 3-10B). Hence the amount by which off-axis angles are underestimated does not depend on the radius of the cylinder but is instead related to the opening angle.

Plotting the measured angle θ b as a function of actual angle θ (t=0) for four different α the manner by which error made by neglecting this trigonometric correction increases with α increases(Fig. 3-11) for off-axis measurements. In other words, this error increases as the measurements are increasingly made off axis.

In the image analysis, we restricted ourselves to the z projections between ±α = 30, which for a wire of radius R corresponds to image widths 2Rsin(α) keeping the maximum error in the angles measured lower than 10%. No further correction was therefore afforded.

Image feature orientation

Algorithms to analyze image feature orientation were employed to quantify cytoskeleton arrangement inside monolayers. As well the orientation inside kymograph images of cell migration on wires were calculated to return the velocity profile inside the monolayer. Two different techniques were used to measure feature orientation: an adapted fast Fourier transform analysis Matlab code and an orientation plug-in for ImageJ. Whereas both can be tuned to measure the orientation for both situations, actin was quantified by FFT and the kymographs by the orientation plug-in. The FFT analysis was employed initially to analyze the actin orientation. Later, when the kymographs were to be quantified, the orientation plug-in was found to be more rapidly adaptable to the new image parameters. Below both techniques will be presented in further detail.

Fast Fourier Transform Image analysis

A FFT image treatment technique was adapted from the algorithm used by Bosveld et al. to measure orientation inside drosophila tissue [START_REF] Bosveld | Mechanical control of morphogenesis by Fat/Dachsous/Four-jointed planar cell polarity pathway[END_REF]. To determine the cytoskeleton alignment in the presence of curvature, actin fibers on the top portion of the wires were analyzed by summing consecutive confocal images around the upper wire surface.

The top region in focus was cropped and divided into square sub windows of width The green box is representative of the size of a single window which is of dimension 7µmx7µm. B) A subwindow image. C) A subwindows with a windowing mask applied over it D) The FFT norm of the windowed image. E) A threshold applied to the FFT. F) An ellipse is fit over the thresholded FFT in E. The major axis of the ellipse give the orientation of the subwindows. Ellipses of eccentricity above a threshold were used for analysis. 64 pixels, or 7µm which had an overlap of 0.6. Each sub image was filtered using a windowing function to minimize edge effect and the FFT was calculated. An ellipse was fit to the thresholded signal and its eccentricity and orientation were calculated.

The orientation of the FFT analysis was kept for sub windows whose anisotropy was above a fixed threshold value also of 0.6.

Velocity kymographs & OrientationJ

Kymographs of the velocity of cells migrating on wires represents the spatial location of the front over time(Fig. 345678910111213). The position of the migrating cell front is represented on the X axis and the time evolves on the Y axis of the image. The slope of the line (green dotted line in Fig. 3 Defining a structure tensor for the image :

J = ∇f, ∇f T w = f x , f x w f x , f y w f x , f y w f y , f y w (3.2)
where the weighted inner product is f,

g w = R 2 w(x, y)f (x, y)g(x, y)dxdy
The first eigenvalue of J gives the ROI orientation.

Orientation = θ = 1 2 arctan 2 f x , f y w f y , f y w -f x , f x w (3.3)
The OrientationJ algorithm on the kymograph image then returns an orientation at every point across the image. Thresholding the original image creates a binary mask divides the image into cell front and background noise regions. The profile of the longitudinal velocity of the cells moving down the wire at every point in time can be extracted for from the orientation field.Figure 3-14 illustrates each step in the analysis and the resulting velocity profiles for 8 time points. While the pillar assay didn't provide a method for clear investigation of the cell morphology or even behavior on a wire two conclusions could be drawn. Firstly, cells were able to migrate collectively under curvature of radius 50-100µm and secondly, MDCK cells could form protrusions over a ridge of 270 • an observation which deviates from the study of Dunn&Heath [START_REF] Dunn | A new hypothesis of contact guidance in tissue cells[END_REF] in which fibroblast cells fail to traverse a prism with a ridge of 32 • . Their measurement, therefore, is either cell type specific or it may reflect a single versus collective behavior and cannot be applied to our migrating epithelial monolayer of MDCK cells.

Cells seeded on wires laying on their side and suspended off a PDMS substrate allowed for better observation of the cellular monolayer covering its surface. Identical To begin, the polarity of monolayers grown on a cylindrical geometry was characterized. Identifying the polarity of our model system allowed for a comparison to be made with in vivo epithelial tubes and in vitro 2D monolayers.

Polarity

The cells migrating on wires were fixed for immunolabeling after the front had progressed for 48 hours. The polarity of this system was compared to that of a monolayer on a flat substrate. Staining the monolayers for ezrin, an apical marker, confirmed that both the apical surface of the cells on wires and flat substrates were in contact with the culture medium and their basal plane in contact with the wire (Fig. 4-3).

Therefore, the cell polarity seen on the 2d substrates(Fig. 4-3) was conserved on the curved surfaces down to wires of R=10µm. The polarity with respect to curvature was the inverse of what is seen in epithelial tubes in vivo where the apical side points into the lumen. Rather the polarity of our system compares to MDCK cysts grown in suspension. The polarity of MDCK cells was even conserved on wires at late stages of confluence. MDCK cells form domes or blister-like structures inside confluent monolayers when imbalances in pumping cause fluid to build up underneath the monolayer. The cells around the initiation point lift off the substrates forming a rounded dome which grows, bursts, and then returns to the substrate. Domes were routinely observed on curved surfaces as well and they maintained an apical polarity on their outer surface (Fig. 4-4).

Cell morphology

Fiber radius controls the cell's morphology

Similarly to the monolayer polarity, for radii above R=20µm the morphology of the migrating monolayer on curved wires was similar to cells on flat wires with finger cells developing on the leading edge. Cells cultured on wires below R=5µm, however, were observed to elongate up to 110µm, ∼2x longer than the elongation of leader cells along their migration direction when migrating on a flat substrate. Such elongation is reminiscent of a mode of 3D migration where cells develop a spindle morphology in the direction of motion [START_REF] Friedl | Plasticity of cell migration: a multiscale tuning model[END_REF](sec. 2.3.4).

As long as the wire radius was larger than 5µm, several cells were needed to circle the wire and cells in the monolayer maintained the classical 2D arrangement observed on flat surfaces, including the formation of migration fingers preceded by leader cells [START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF]. In contrast, single cells could wrap around thin wires (R<5µm) and formed chains in which adhesions were nevertheless maintained between the back edge of a cell and the front edge of its follower (Fig. 4-5C). Depending on the division events and on local cell density, individual cells either wrapped around the wire (as commonly observed at the leading edge where the cell density is lower) or clustered themselves around it. Very interestingly, no seam was observed on the cells that appeared as speared by the wire (Fig. 4-5B) while nevertheless maintaining adhesions with the cells preceding or following them.

The cells fully wrapped around the wire are morphologically similar to the in vivo unicellular tubes discussed in the introduction(sec. 2.4). In vivo, such tubes may form through intercalation, where two cells pair across a lumen, one reaches around to make an autoadherens junction at a single point, before elongating the junction with the zipping upward of one cell with respect to the other. The other in vivo methods of forming unicellular tubes are cell hollowing, or cell wrapping followed by self-fusion. Here, the dynamics of the formation of a unicellular MDCK tube was not followed but they could hypothetically develop either through the zipping mechanism or wrapping followed by a self fusion. In fact, MDCK cells seeded in 2D have been shown to continuously wrap around micropillars obstacles by plasma membrane fusion, suggesting that membrane fusion may be a mechanism behind the formation of small seamless capillaries [START_REF] Sumida | Self-contact elimination by membrane fusion[END_REF].

Despite the geometrical similarities between unicellular tubes in vivo and in this case, two differences between these tubes must be mentioned. Unicellular tubes are fluid or air filled in vivo, but here the tube lumen is filled with glass and the polarity in our experiment is inverted compared to in vivo conditions, with its basal, not apical surface facing the lumen. The rigid substrate in the lumen, and the polarity introduces cues that may alter the mechanisms of unicellular tube formation.

Density profiles

Cell density varies with radius

Despite the difference in elongation the cells exhibit on wires of different sizes, the density profiles of cells along the wire of R = 10µm and R = 40µm showed a The uniaxal migration mode of 1D cells is over 5x faster than the migrating front with the migration velocity of a cell front on a near flat substrate (r=80µm) where v =18.2µm/h ± 3.5 (n=13).

Confinement vs. curvature

If plating cells on cylindrical wires induced a curvature of the epithelium, it also intrinsically induced a lateral (although borderless) confinement over the perimeter of these wires. To differentiate which of these two effects is responsible for cell detachment from the front edge, cells were cultured in 2d micropatterned adhesive tracks of widths varying from 20µm to 500µm (Fig. 456789). These experiments showed that, at equivalent confinement, 94% of the the experiments show no detachment in tracks of width 50 -200µm (62 negative observations over 66 experiments). Furthermore, the rare detaching events, however, did not resemble the detachments on wires, and were instead spread not rounded cells that ripped away from the bulk before being reincorporated in under 2h, contrary to the situation on wires. These individual cells, did not undergo a uniaxial rapid migration but rather remained close to the front, or stretched along the edge of the track . We conclude that the cell detachment seen on wires is a unique curvature dependent mechanism that is not recapitulated by confinement on tracks. MDCK cells are prototypical of epithelial cells and grow in the form of a monolayer because of their strong cell-cell adhesions. This cell detachment is therefore particularly surprising. We propose here that this behavior is the signature of a new curvatureinduced Epithelial-Mesenchymal Transition (EMT). EMT is usually the result of an external biochemical stimulus, for example a hepatocyte growth factor (HGF) [START_REF] Lee | New insights into the regulation of epithelialmesenchymal transition and tissue fibrosis[END_REF].

Indeed HGF is a well-known scattering factor for MDCK cells [START_REF] Ridley | Regulation of scatter factor/hepatocyte growth factor responses by Ras, Rac, and Rho in MDCK cells[END_REF] and this system is routinely used to model EMT. However, mechanical cues have also been identified

as EMT effectors such as substrate rigidity [START_REF] Tilghman | Matrix rigidity regulates cancer cell growth and cellular phenotype[END_REF] or in-plane curvature [START_REF] Gomez | Tissue geometry patterns epithelial-mesenchymal transition via intercellular mechanotransduction[END_REF]. Out-of plane curvature is therefore a newly identified mechanical parameter that impacts this transition.

Monolayer molecular architecture

The properties of the cytoskeleton of cells inside curved monolayer were probed for changes with increasing curvature. Figure 4-2 illustrates the convention we adopted for θ. A θ = 0 describes an orientation along the wires long axis whereas θ = π/2 represents the circumferential direction.

Actin cytoskeleton alignment

Actin cytoskeleton align circumferentially at high curvatures Alexa Fluor 488 phallodin staining was employed to label the cytoskeleton and revealed that actin fibers were present on the basal surface of the cell(Fig. [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF][START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF][START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF][START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF][START_REF] Cramer | Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force[END_REF][START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF][START_REF] Versaevel | Spatial coordination between cell and nuclear shape within micropatterned endothelial cells[END_REF][START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF][START_REF] Yeung | Effects of Substrate Stiffness on Cell Morphology, Cytoskeletal Structure, and Adhesion[END_REF][START_REF] Pellegrin | Actin stress fibres[END_REF][START_REF] Ingber | Tensegrity I. Cell structure and hierarchical systems biology[END_REF][START_REF] Li | Estimating microtubule distributions from 2D immunofluorescence microscopy images reveals differences among human cultured cell lines[END_REF].

Even though the apical-basal polarity is inverted in comparison to epithelial tubes in vivo [START_REF] Little | Kidney development: two tales of tubulogenesis[END_REF], this study mimics the developing drosophila trachea (section 2.5) where the actin fibers are also localized at the plane in contact with the luminal, cylindrical chitin, at the apical side of the cells [START_REF] Massarwa | Apical secretion in epithelial tubes of the Drosophila embryo is directed by the Formin-family protein Diaphanous[END_REF].

The local in plane orientation of these fibers was quantified by local FFT analysis [START_REF] Bosveld | Mechanical control of morphogenesis by Fat/Dachsous/Four-jointed planar cell polarity pathway[END_REF] (section 3.7.2). The measurements were done using narrow crop around the center of the z projection made from images of half the wire. The width of the crop depended on the wire radius and was selected to minimize the angle estimation error of the z projection to under 10%. The algorithm disregarded subwindow that did not have a clear oriented feature by introducing an anisotropy threshold in the FFT. Because the images analyzed were marked for F-actin the cell boundary, which contains a belt of actin, was labeled along with the actin fibers. The orientation analysis run over the entire image counted the orientation of the boundaries along with the F-actin.

To remove completely the presence of cell boundaries, a double immunofluorescent staining for F-actin and E-cadherin, could have been carried out and then the two signals could have been subtracted to yield only the cell's internal F-actin. An orientation trend, however, was already well visible without removing the signal added by the cell boundaries so the full F-actin signal was kept.

We found that F-actin orientation was random inside monolayers on large radii as it is for flat substrates (Fig. 4-10). In contrast, actin fibers were highly oriented perpendicular to the wire's longitudinal axis below R=30µm(Fig. [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF][START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF][START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF][START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF][START_REF] Cramer | Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force[END_REF][START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF][START_REF] Versaevel | Spatial coordination between cell and nuclear shape within micropatterned endothelial cells[END_REF][START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF]. It worth noticing that the same transverse actin alignment was observed even for wires whose radius was small enough to be fully wrapped around by a single cell.

Order parameter

The orientation of these actin fibers can be better quantified by using the apolar order parameter S = cos(2θ) [START_REF] Reffay | Orientation and polarity in collectively migrating cell structures: statics and dynamics[END_REF][START_REF] Kemkemer | Cell Orientation Induced by Extracellular Signals[END_REF]. As previously, θ is the angle between the actin fiber's orientation and the wire's long axis (Fig. 4-2). S = 0 corresponds to a random orientation, S = 1 to a perfect alignment with the fiber main axis and S = -1 to an orientation perpendicular to the fiber main axis.

Basal actin fibers moves through cells

In addition to being aligned at a radius below ∼ 30µm, the same fiber often appeared to be continuous from cell to cell (Fig. 4-11 inset and Fig. [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF][START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF][START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF][START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF][START_REF] Cramer | Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force[END_REF][START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF][START_REF] Versaevel | Spatial coordination between cell and nuclear shape within micropatterned endothelial cells[END_REF][START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF][START_REF] Yeung | Effects of Substrate Stiffness on Cell Morphology, Cytoskeletal Structure, and Adhesion[END_REF][START_REF] Pellegrin | Actin stress fibres[END_REF][START_REF] Ingber | Tensegrity I. Cell structure and hierarchical systems biology[END_REF]. This observation implies a mechanical relay at the cell-cell adhesion sites [START_REF] Millán | Adherens junctions connect stress fibres between adjacent endothelial cells[END_REF] and it is a clear signature of local mechanical continuity (Fig. PS wires showed actin alignment in longitudinal and transverse direction PS wires were initially used to explore actin orientation on wires below a radius of 10µm. PS assays were adopted over glass wire for preliminary tests of high curvature as they were rapid to manufacture and easier to align on supports than small radius glass wires.

Circumferential actin fibers were present in MDCK Life-Act cell fronts migrating on PS wires. Longitudinal actin streaks, however, were simultaneously present as seen in figure 4-16. The longitudinal actin was an artifact of the rough lengthwise features on the wire surface formed from the evaporation of the solvent during fabrication [START_REF] Kim | Unique Surface Morphology of Electrospun Polystyrene Fibers from a N,N-Dimethylformamide Solution[END_REF]. Because of the influence these ridges had on the cytoskeleton of the cells, this assay was abandoned: the roughness of the surface could not be ignored and the PS wires therefore did not provide a satisfactory parallel to smooth flat glass substrates. Instead smooth glass wires were manufactured using a pipette puller and employed for all further studies.

Studies on PS wires also illustrated that thin wires trigger extreme cell elongations (Fig. 4-16A) but that at late stages of confluence, the monolayer densifies and multiple cells can wrap around the circumference of even wires of R=1µm (Fig. 4-16C)

Leading edge

actin cable present at leading edge Immunofluorescent staining demonstrated that myosin co-localizes with an accumulation of actin on leading edge of the migrating fronts (Fig. 4-17. This confirms the structure is indeed a pluricellular actin "cable" similar to the contractile cable present at the edge of a classical 2d closing wound [START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF][START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF][START_REF] Anon | Cell crawling mediates collective cell migration to close undamaged epithelial gaps[END_REF]. Confinement vs. curvature

Actin orients longitudinally on narrow tracks

Here again, to uncouple curvature effects from lateral confinement, we quantified the actin alignment on micro-patterned tracks. As seen in figure 4-18, the actin fiber orientation in small-width tracks tended to orient parallel to the tracks, further quantifying previous observations [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF]. MDCK cells in tracks aligned along the principal direction whereas on wires they oriented perpendicular to it.

Moreover, observations on tracks showed the strong influence of the borders with actin cables on the boundary lining the adhesive track's edge, introducing clear boundary effects not present on the wires. In confined adhesive islands of MDCK cells the presence of a nonadhesive boundary spurs collective displacement modes and the formation of three dimensional structures [START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF](section 2.3.3). A confining boundary also changes the velocity and traction force patterns of an advancing monolayer [START_REF] Kim | Propulsion and navigation within the advancing monolayer sheet[END_REF]. The actin alignment below 40µm as a result of curvature has previously observed for single epithelial cells [START_REF] Svitkina | Transverse pattern of microfilament bundles induced in epitheliocytes by cylindrical substrata[END_REF] on a radius of 16µm but no step transition had been reported for the actin alignment in epithelial cells at a critical radius. HBMEC brain endothelial cells plated on wires but not HUVECs also demonstrate a circumferentially aligned actin cytoskeleton at high curvature [START_REF] Ye | Brain microvascular endothelial cells resist elongation due to curvature and shear stress[END_REF] but the alignment at only two radii was reported, so no quantification in the orientation versus curvature can be deduced. Although the actin orientation versus radius trend has never been reported, single cell body orientation with varying radius had been quantified for fibroblasts [START_REF] Hwang | Controlled cellular orientation on PLGA microfibers with defined diameters[END_REF].

Both of these cell types give smooth transitions between aligned and random cell body Whereas the order parameter decreases linearly with increased track width, the order parameter of actin on wires transitions rapidly from oriented S ∼ -0.7 to random S = 0.

(n angles > 2500 per radius)

orientations(section 2.6.4). Given that fibroblasts have a well defined actin cytoskeleton on glass which aligns with its spindle morphology, we can deduce that their actin alignment transitions in a similar fashion. The histograms of the angle distribution widen with increased radius but the angles need to translated into the order parameter S to make a direct comparison with the present work. Because no order parameter is given in the study, this thesis is therefore the first report of a step function transition between ordered and unordered actin alignment driven by substrate curvature.

This perpendicular actin orientation is also observed in vivo in the morphogenesis of the drosophila trachea [START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF]. Indeed, in that case, cells grow on a rigid tubular chitin template [START_REF] Devine | Requirement for chitin biosynthesis in epithelial tube morphogenesis[END_REF]. The actin fibers orient perpendicularly to the tube main direction, suggesting, by comparison with the present experiments that this could be the result of having to grow on highly curved substrate. Interestingly, in the case of the drosophila trachea it is the apical side of the cells that faces the cuticle template. Therefore it appears that this organization of actin cytoskeleton is independent of cell polarity.

Aligned actin fibers begin to appear when the radius of the tube is below R=40µm although, unlike our system, aligned actin fibers remain after the tube is enlarged.

The adult tracheal tube, however, cannot be compared to our model system because a corrugated cuticle is secreted apically reinforcing the actin rings.

Focal adhesions

Cells under high curvature form more focal adhesions than cells on flat surfaces.

To investigate more closely this transverse alignment of the actin fibers, we characterized the system's focal adhesions which link actin fibers to the substrate of the wires. To that purpose, cells were stained simultaneously for vinculin and actin. In an attempt to better characterize the mechanics of these circumferentially oriented stress fibers, we undertook series of laser photoablation experiments. We observed almost no retraction after ablation for the fibers within the cells and when single fibers were cut on wires of radius R = 10µm and R = 40µm, the retraction was visible for only a maximum of 0.5 µm. This observation is consistent with the high density of FAs and their localization along the fibers previously mentioned. This situation is in sharp contrast with the control experiments where fibers were ablated in cells cultured on flat surfaces and where focal adhesions were located at the two extremities of the stress fibers. There, we routinely observed retractions of several microns, as previously reported [START_REF] Kumar | Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics[END_REF][START_REF] Colombelli | Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization[END_REF].

Actin cable ablation

Actin cables retract slower when ablated on highly curved surfaces The number of adhesions is much less along the circumferential cable present at the leading edge. In this case, retraction after the cut was much more significant (up to several micrometers), a clear signature of the elastic tension stored in this cable.

Upon ablation, the initial retraction speed was significantly smaller on small radii wires compared to flat surfaces of large radii wires (0.9 ±0.5 µm s -1 vs. 1.4 ± 0.6 µm s -1 , this last value being consistent with previous measurements [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF][START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF]). Whereas the difference in retraction confirms a difference in internal cytoskeletal properties of cells under high curvature to those on flat substrates, the reason for the difference is not certain without further experiments. The slower retraction of the actin cable on R ≤ 10µm can be attributed to either a decreased tension or to an enhanced friction with the surface compared to cables on flat substrates. The increase in focal adhesions seen on curved surfaces suggests that the actin meshwork inside the cell is more pinned down to the wire than when on a flat surface. We hypothesize that the change in the substrate attachment of the cell's actin meshwork may act as an added source of friction resisting cable retraction.

Collective migration 4.5.1 Front velocity vs. radius

Since curvature was shown to have a large influence on the cytoskeleton arrangement, we investigated the impact of the wire geometry on migration velocity. The velocity of the front was quantified for wires at different radii between R=2µm and R=85µm.

Cells on wires with a radius below R=20µm migrated collectively faster than cells on larger wires which had velocities comparable to those on a flat surface.

The cell fronts on wires above R=10µm migrated with a constant speed as evident from the kymographs (Fig. 4-24). Analyzing the slopes of features inside the kymographs formed from fronts migrating at R=40 and 20µm returns the velocity profile at every point along the front over time. These profiles are stable with time and can therefore be averaged. The average velocity profiles for R=40 and 20µm (Fig. 4-25) illustrate that with diminished radius the velocity increases not only at the leading edge but throughout the bulk. From these profiles, a decay length can also be defined, describing the distance it takes for the front velocity to diminish by half. Interestingly, although the profiles do not share the same magnitude they both decay by half around 200µm behind the leading edge (decay length of 193µm for R=40µm and 226µm for R=20µm). The length of 200µm is consistent with the velocity correlation length of migrating 2D monolayers of MDCK cells [START_REF] Petitjean | Velocity fields in a collectively migrating epithelium[END_REF] after the removal of a PDMS stencil. Oscillatory motion on wires R < 10µm

For smaller radii, the average progression was faster (up to 35 ± 4 µm/h) but it was also less regular as the cell front moved both forward and backward as it progressed.

This was due to cell divisions that interfered with the forward motion on the small wires (Fig. 4-26). When the cell rounded up before division, the free space created allowed the cells on either side to move together. After division the reintegration of the two daughter cells provided an outward pressure on their neighbors. This effect, also present on small width tracks [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF], became noticeable when the number of cells around the wire was very small (ie. for small radius wires). Surprisingly, despite the very different cytoskeletal organization on wires compared to that on tracks, the velocity-confinement relationship of the front progression in these two cases was very similar (Fig. . We therefore conclude that this velocity increase results from confinement and not curvature. Furthermore, the wire geometry allows the cells to migrate in a confined but boundary-free situation, we can therefore conclude that this increase in migration speed is truly a confinement effect and is not due to contact guidance by the edges of the tracks. Similarly, the oscillatory behavior at small radius is also observed with small width tracks [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF] and is therefore the consequence of confinement that makes these division events more noticeable.

Mechanisms governing collective migration

To identify the factors at play in the migrating front on the wires, inhibition experiments were conducted to explore the different components involved in the collective cell migration under curvature. Cell proliferation was inhibited using mitomycin [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF] and thymidine. The proliferation profiles were also measured using the ki-67 antibody.

Subsequently we focused on myosinII and Rho, both of which act on contractility [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF][START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF], and Rac [START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF] which controls protrusive activity. Finally HGF [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF] was employed at a concentration which is subscattering on flat surfaces to explore influence of collectivity on migration.

Cell proliferation

The migration of a cell front was observed typically for 24 hours and then cell proliferation was inhibited using mitomycin C. Figure 4-28 shows the front progression before and after the inhibition, with the introduction of the drug indicated with a blue dotted line. The addition of the mitomycin slows down drastically the migration in the bulk, but the front continues to migrate forward at the same velocity. The protrusive front migration of the leading cells is therefore independent of divisions for the 12 hour timescale of the experiment (before the drug showed signs of toxicity).

In contrast, the forward migration of the bulk was closely linked to cell division. If cells division could be completely arrested for long time scales it could be ascertained if the front speed decreases to remain cohesive with the slowly moving bulk or if the protrusive cells would split away form the monolayer.

The result obtained with mitomycin was confirmed with thymidine, another drug that inhibits division. Whereas mitomycin inhibits cells from dividing, thymidine arrests cells at the G1-S border and those which are past that point in the cycle still divide. The influence of thymidine was therefore more gradual than mitomycin but less toxic, and cells could be held back from dividing at least twice as long as with mitomycin which becomes toxic at 12 hours. There again, the front velocity and R=85µm suggesting that in this range, curvature does not play a role on cell division for R>40µm. Substrate mechanics [START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF] and geometry [START_REF] Nelson | Emergent patterns of growth controlled by multicellular form and mechanics[END_REF] has been shown to influence proliferation rate and the ki-67 treatment should be repeated at R=10µm

to explore a possible change in proliferation in this region where cells respond more strongly to curvature. To probe the different elements orchestrating collective cell migration on wires, and in particular the increase in front velocity at small radii, drug inhibitions were carried out to inhibit myosin II contractility along with Rho and Rac. HGF growth factor a drug which enhances epithelial motility and weakens cell-cell junctions [START_REF] Ridley | Regulation of scatter factor/hepatocyte growth factor responses by Ras, Rac, and Rho in MDCK cells[END_REF] was also employed to explore the influence of cell collectivity on the migration trend.

The results from these four drugs on wires of radius 10,40, and 85µm are displayed in two ways in figure 4

Myosin II contractility

Cell fronts treated with Blebbistatin migrated at a unique speed independent of radius When cells were treated with blebbistatin, the front velocity increased for R=40µm and 85µm (p< 0.01 , p< 0.001 respectively) but it decreased (p< 0.05) for R=10µm resulting in a migration velocity for all three cases around 25µm/h. The same trends have been reported for cells migrating in tracks [START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF]. In that case blebbistatin disrupted actin stress fibers, hindering cells from exerting traction forces even though cells maintained their cell-cell junctions. Cell junctions guide strong adhesive steering mechanism [START_REF] Anon | Cell crawling mediates collective cell migration to close undamaged epithelial gaps[END_REF] forming vortices in wide tracks and contraction elongation migration patterns, attributed to cell divisions, on narrow tracks in the control. These migration modes could not develop without traction forces, thus cells exhibited directional stream-like motion moving down the track with a long-range correlated velocity for all widths. Therefore the blebbistatin treatment results in the same change in velocity to that in tracks, confirming that confinement, not curvature, controls the velocity versus radius trend.

Rho and Rac

Rho and Rac are involved in the increase in velocity at small radii Both NSC-23766 inhibitor of Rac1 and C3-transferase inhibitor of Rho demonstrated a significant decrease in migration speed at R=10µm (p< 0.001). NSC hinders cells from making efficient protrusions and C3 inhibits the contractility of actin cables and the formation of leader cells on flat surfaces. The migration on small wires is therefore guided by both protrusive activity and contractility.

In contrast, on large wires of R=40 and 80µm NSC does not change the migration velocity (p=n.s.). While NSC diminishes protrusive activity it does not impair leader cells, suggesting that pulling at the front boundary and the divisions in the bulk are sufficient to propel migration at large radii. C3 transferase, which does impair leader cells, decreases the velocity at 40 and 85µm (p < 0.05, p < 0.05 respectively) but less dramatically than at R=10µm (p < 0.001).

For R=10µm cells fronts respond similarly to C3 and blebbistatin but it is not clear why C3 has an opposite effect to that of blebbistatin for large radii. Both C3 and blebbistatin act on the Rho pathway which controls the contractility of the cell and have been reported in many systems to induce similar responses [START_REF] Mih | Matrix stiffness reverses the effect of actomyosin tension on cell proliferation[END_REF]. We therefore

HGF growth factor

HGF increases the velocity of migrating fronts on large wires but not at small HGF at 10ng/ml increased the migration velocity at R=40µm and R=85µm (p< 0.001) but failed to influence the front speed at R=10µm (p=n.s). HGF weakens the collectivity of migration and at high concentrations (above what was used) can cause cell scattering on flat surfaces. The increase in front velocity at large radii is therefore not surprising. However, the inability for HGF to promote an increased migration at R=10µm (p=n.s.) suggests that cells cannot migrate collectively above a velocity of ∼40µm/h. Cells moving above this velocity are therefore forced to break away from the bulk and migrate independently in the one dimensional mode. Although the concentration of HGF employed was under the scattering limit on flat surfaces, it was observed that cells broke away from the monolayer much more frequently for R < 20µm when treated with the drug. The percentage of breaking events increased from 38% in the control to 77% with HGF (23 positive observations over 30 experiments) suggesting that HGF stimulates EMT at lower concentrations on curved surfaces.

Surface defects on wires

Wire surface defects alter the front speed but its linear progression is maintained

A final insight into the mechanisms involved in the progression of the cell front came by accident. The glass wires were easily prone to collecting dust or other defects on their surface if not washed sufficiently before beginning an experiment, or if dust was present inside the culture medium during an acquisition. When the migrating front reached the dust or defect, it would slow down. Interestingly, the front would continue to migrate with a constant but diminished velocity tens of hours after the leading cell had passed the defect(Fig. . This provides evidence that the bulk's adhesion and friction with the wire plays a role in the linear displacement of the front, and the migration is not governed only by a protrusive leading edge and cell division.

Additional experiments, however, adding defects to wires in a controlled manner need to be done to further quantify this phenomenon. The speed of migrating fronts is disrupted when a defect on the wire or a dust particle is encountered. The leading front, moving on a wire of radius 10µm encounters a dust particle at t=35h. Defects cause the front to adopt a slower, linear trend over the span of tens of hours, long after the front has moved past the defect.

Theoretical models of migration

The linear progression of the cell front over time on wires or tracks and the increase of migration speed at small radii are two intriguing aspects that would need to be explained. We have identified migration and proliferation as key elements in the behavior of the migrating fronts of cells on wires.

Many models for the collective migration exist to describe migrating tissue using different balances of a few common ingredients, for example, proliferation, protrusive activity, tissue rheology, and substrate friction [START_REF] Arciero | Continuum model of collective cell migration in wound healing and colony expansion[END_REF][START_REF] Cochet-Escartin | Border forces and friction control epithelial closure dynamics[END_REF][START_REF] Mi | Onedimensional elastic continuum model of enterocyte layer migration[END_REF]. A relevant theoretical model similar to our system describes the linear progression of a cell front in a confined track [START_REF] Douezan | Spreading dynamics of cellular aggregates confined to adhesive bands[END_REF]. The model addresses an experiment in which spherical cellular aggregates of murine sarcoma (S-180) cells are deposited on adhesive tracks of width 100µm. To describe the linear trend, a 1D model of confined spreading was established.

We present here its major features. Three energies are defined for spreading on a band of width e.

First, the adhesive energy gain per unit time, Se L where S is the spreading parameter for the front moving a length L as seen on figure 4-33D.

Secondly the viscous dissipation is defined as keL L2 given a surface friction coef-ficient k.

Finally dissipation from permeation of cells moving from the aggregate onto the track is expressed as η( L/ξ) 2 ξ 2 e, with η representing the aggregate viscosity and ξ the breadth of permeation as seen illustrated in figure 4-33C [START_REF] Helfrich | Capillary flow of cholesteric and smectic liquid crystals[END_REF][START_REF] De Gennes | Spreading of a stratified incompressible droplet[END_REF].

Balancing the energy gained with the energy lost yields (η + keL) L = S (4.1)

Exploring the two extreme cases where permeation can be neglected (ie. η < kL) results in L 2 ∼ S/kt or the permeation is predominant (ie. η > kL) yields L ∼ S/ηt. Because experimentally the front progressed linearly, it is concluded that energy dissipation is predominantly from permeation.

Both the lateral confinement of the track, and cells fronts moving away from a reservoir of cells are reminiscent of the lateral confinement on wires and the confluent layer of cells on the PDMS substrate feeding the wires, respectively. Whereas in the wires experiment cells don't permeate from a stratified 3D aggregate, a similar mechanism in which cells from the bulk feed the migrating front may be at play.

Adapting the permeation term to our geometry and introducing the role of protrusions at the front could be a first step to model our system. However, a confinement or radius dependent term must be introduced as well to reproduce the increase in migration speed on small wires.

Extreme curvatures: cone tips

We now focus on the behavior of the cells at extremely small radii. To explore situations characterized by radii smaller than 1µm, we had to slightly alter our system since submicron wires cannot be easily handled. Here, we used tapered glass cones with opening angles down to 1.5 o , drawn from a pipette puller, with submicron radius tips.

Below R c =0.5µm cells can no longer migrate collectively We hypothesize that oscillations of the leading cell near the critical radius may be related to the cell failing to make stable adhesions with the surface. The lamellipodia of cells seeded on arrays of nanopatterned functionalized gold nanodots that are spaced too far apart also undergo periodic protrusion and retraction cycles [START_REF] Cavalcanti-Adam | Cell spreading and focal adhesion dynamics are regulated by spacing of integrin ligands[END_REF].

Whereas in this case the retraction cycles were of 3min -1 a similar mechanism might be at play in our case with the cell failing to adhere correctly to migrate forward at the critical radius. Additional experiments are needed to better comprehend the periodic behavior in our system. Live imaging of MDCK-vinculin GFP, for example, could follow the creation and stability of focal adhesions near the tips of cones. The influence of out-of-plane curvature on epithelial populations revealed in this thesis also has consequences on the way curved in vivo tissues below a certain size are (scale: 100µm) [START_REF] Alexander | Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model[END_REF] understood and modeled. Geometry may play a larger role in collective properties of tissue with high radius of curvature (for example small tubes) than currently understood. For example, the close comparison in the actin organization inside MDCK cells on glass wires and the drosophila tracheal cells on chitin tubes suggests that curvature may orchestrate cell architecture in association with genetic controls.

In addition to reconsidering the role of high curvature in vivo, the experimental substrate used in this thesis is transferable to in vitro studies of other epithelial or endothelial cell lines that form tubes. Preliminary experiments carried out on HEK-HT cells migrating on wires showed that this cell line was more susceptible to breaking away from the leading edge than MDCK cells. A velocity versus radius trend could not be cleanly measured as cells consistently broke off from the migrating front on small radius wires, thus continually redefining the location of the collectively migrating front.

A study of different cell lines could also reveal if the critical radius for actin alignment is shared across epithelial tissues. Minimal reconstituted systems can be similarly employed to provide insight into the mechanics of circumferential actin alignment. Using existing techniques [START_REF] Kron | Fluorescent actin filaments move on myosin fixed to a glass surface[END_REF] to attach myosin motors to cylindrical surfaces and adding purified actin can test if the interaction of F-actin and myosin motors with a curved substrate is enough to trigger alignment.

Whereas this thesis modulated the radius of curvature of a substrate by comparing monolayers on wires of different radii, the radius of the substrate was fixed for the entire experiment. A continuation of this thesis work could be to modulate the radius of a curved substrate over the course of an experiment. An enlarging substrate incorporating radial stretch would model more closely tissue development where curved epithelial tissues change shape. In the the drosophila trachea and egg chamber, for example, the curved epithelial tissue grow radially over the course of development.

For the egg chamber, as well, the tissue moves from a spherical to a ellipsoid shape.

An in vitro assay that could incorporate a changing radius of curvature would activate stretch induced ion channels, which are implicated in regulation of curvature in epithelial cysts [START_REF] Tanner | An In Vitro Test of Cell Stretch-Proliferation Hypothesis of Renal Cyst Enlargement[END_REF]. on wires and tracks. We therefore predict an increase in MDCK front velocity with decreased lumen radius. Small lumen radii, will likely be hard to test however, since for R<30µm, the transitional radius for positive curvature, lumen dimensions are close to the dimensions of a cell. Although the two curved conditions would form an epithelium of the same final shape, the apical basal polarity is inverted between the two: on wires the basal surface faces the tube's center whereas inside lumen the apical surface would point inward. As well, in one case the lumen is filled with glass, whereas in the other the lumen would be filled with medium.

Finally, conical substrates present an interesting new technique for engineering floating epithelial cysts in a controlled location. Cysts embedded in gels are fixed in space, but they have their apical side facing the cavity and their basal side facing outward. Floating cysts, however, have the inverted polarity but are hard to study in live as they develop in flasks that are continually stirred [START_REF] Wang | Steps in the morphogenesis of a polarized epithelium. II. Disassembly and assembly of plasma membrane domains during reversal of epithelial cell polarity in multicellular epithelial (MDCK) cysts[END_REF]. Being able to localize a floating cyst eases the study of cysts growth dynamics and polarity development in this geometry.

Figure 1 -

 1 Figure 1-1: A) Dispositif expérimental ou les fils en verre sont suspendus et alignés sur un support en PDMS. B) Convention utilisé pour l'angle.

Figure 1 - 2 :

 12 Figure 1-2: Tissu épithélial ou les filaments de F-actine sont marqués: R = 30, 20, 5µm. L'orientation perpendiculaire à la fibre apparait pour tous ces rayons.

Figure 1 - 3 :

 13 Figure 1-3: Confiner une monocouche épitheliale sur des bandes adhésives oriente le cytosquelette d'actine dans la direction de la piste. w=100 µm B) w=50µm (scale: 20µm)

Figure 1 - 4 :

 14 Figure 1-4: Parametre d'odre qui traduit la qualité de l'orientation collective des fibres d'actine, S = cos(2θ) .

Figure 1 -

 1 Figure 1-5: A) Ablation d'un cable d'actine sur un fil de rayon R=10µm B) Vitesse de retraction sur des fils compares au surfaces plats.

Figure 1 - 6 :

 16 Figure 1-6: Vitesse de la monocouche migrant collectivement sur les fils (noir) ansi que sur les bande adhesives (rouge). La dynamique du migration et controlée par le confinement plutôt que par le courbure.

Figure 2 - 1 :

 21 Figure 2-1: The seven subcategories of epithelial cells divided by individual cell geometry and overall tissue organization [http://cnx.org/content/m46048/latest/]

Figure 2 - 2 :

 22 Figure 2-2: Actin filament polymerization. During actin filament assembly monomers assemble through dimerization and trimerization, steps which are energetically unfavorable.The subsequent monomer, however, is more stable and subsequent additions are much more favorable. An actin filament has two ends the barbed (B) and the plus end (P). Actin monomers are added to the plus end and removed from the barbed end. B) Arp2/3 (orange) is an actin nucleator that binds to the side of a filament and creates a new branch at a 70 • angle. Repeated Arp2/3 branching forms a dendritic actin network. C) Formin (purple) nucleates a filament and can either move progressively with the elongating barbed end or bundle filaments together.[START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF]

Figure 2 - 3 :

 23 Figure 2-3: Structure of a migrating cell. Actin in the lamellipodium is arranged in a branched network while actin in protruding filopodium is organized into parallel bundles.The arrow indicates the direction of migration.[START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF]

Figure 2 - 5 :

 25 Figure 2-5: Actin stress fiber structure: A) U2OS osteosarcoma cell stained for F-actin.Three types of stress fibers are highlighted in this cell, dorsal stress fibers (red), arcs (yellow), and ventral stress fibers (green). Scale bar 10µm B) Ventral stress fibers are present on the bottom of the cell below the nucleus. Dorsal stress fibers connect the focal contacts along the cell edge up to the transverse arcs stress fibers present at the cell surface.[START_REF] Pellegrin | Actin stress fibres[END_REF]

Figure 2 - 6 :

 26 Figure 2-6:Intermediate filaments are formed of smaller filaments that align to form a staggered array and twist into a rope-like structure.[http://www.nature.com/scitable/content/the-structure-of-intermediate-filaments-14706444]

Figure 2 - 7 :

 27 Figure 2-7: A schematic of microtubules and their growth mechanism.Microtubules are composed of α-and β-tubulin subunits that are assembled into profilaments. A single microtubule in a mammalian cell contains 13 profilaments that wind together to form a cylinder of 24nm in diameter. Microtubules are dynamic in structure and can grow through polymerization and shrink via depolymerization.[http://www.nature.com/scitable/topicpage/microtubules-and-filaments-14052932]

Figure 2 - 8 :

 28 Figure 2-8: A schematic of adherens junctions between adjacent cells. Cadherins link neighboring cells as the extracellular domain of one cadherin dimer links to the extracellular domain of the cadherin in a neighboring cell. As well, rings of filamentous actin form a belt around the junctions inside the cell. [3].

Figure 2 -

 2 Figure 2-9: a) Structure of an focal complex in migrating cells b) Structure of a mature focal adhesion [http://www.reading.ac.uk/cellmigration/adhesion.htm]

  Apical-basalMost epithelial cells exist in cohesive sheets or monolayers with an asymmetric structural organization, or polarity. Polarized epithelial cells possess apical and basolateral domains each with a distinguished by domain-specific proteins that form an apicalbasal axis. The development of apical-basal cell polarity is a complex mechanism resulting in separated specialized domains on the plasma membrane and in the cytoplasm. Generally, an extrinsic cue from a cell's environment, for example an adhesion either to extra cellular matrix, or neighboring cells, initiates the development of cell polarity.A polarity axis inside a cell leads to directed behaviors such as fluid secretion and transport. In vivo the apical domain commonly faces the lumen of internal cavities or the outside surface of the body. The apical surface facing the cavity therefore possesses a higher positive curvature with respect to the external basal surface (fig 2-10A). When present, cilia, and microvilli localize on the apical surface and the basal surface binds to a basement membrane through focal adhesions. Cells can contribute to an existing basement membrane by secreting their own layer of extra cellular matrix entitled 'basal lamina' a layer 20-300nm thick comprised predominantly of laminin and type IV collagen[START_REF] Laurie | Localization of type IV collagen, laminin, heparan sulfate proteoglycan, and fibronectin to the basal lamina of basement membranes[END_REF].In vitro, MDCK cells embedded inside gels develop polarized cysts which can form tubular branches when stimulated with HGF[START_REF] Montesano | Identification of a fibroblast-derived epithelial morphogen as hepatocyte growth factor[END_REF]. These three dimensional structures have an apical-basal polarity similar to that of in vivo tubes with their apical side facing the lumen. The polarity of MDCK cysts in vitro, however, is reversed when they are grown in suspension. In this condition their basal surface faces the lumen, secreting basal lamina into the cavity Fig.(2-10B) [?].

Figure 2 -

 2 Figure 2-10: A) An epithelial tube with the polarity found either in vivo or in tubes and cysts grown in gels in vitro. The apical membrane faces the lumen of the tube and the basolateral membrane faces the exterior of the tube. In this geometry, the apical membrane is more curved than the basolateral surface. B) An example of inverted polarity seen in suspended epithelial MDCK cysts. Cells secrete ECM inside the cavity thus developing a basolateral membrane inside and an apical side on the outside of the cyst facing the medium.Here, the basolateral surface of is at higher curvature than its apical membrane.[START_REF] Nelson | Epithelial Cell Polarity From the Outside Looking In[END_REF]

Figure 2 -

 2 Figure 2-11: a) Morphology of a polarized epithelial monolayer. Vertical epithelial polarization is divided into distinct apical, basal, and lateral domains of the plasma membrane. Apical surfaces often contain microvilli which are used for absorption and excretion. The basal surface binds to a fibrous extracellular matrix (ECM) through transmembrane integrin which is part of focal adhesions. Lateral membranes are linked to adjacent cells through junctional complexes (tight junctions, adherens junctions, and desmosomes) and provide diffusion barriers. b) Horizontal epithelial polarization of planar cell polarity (PCP) proteins forms the proximal-distal axis in the plane of the epithelium.PCP can cause different proteins to localize to the proximal and distal cortical domains; here the differential protein localizations are illustrated in green and red.[START_REF] Wang | Normal morphogenesis of epithelial tissues and progression of epithelial tumors[END_REF]

Figure 2 - 12 :

 212 Figure 2-12: Instances of supracellular actomyosin cables during development.Cables are divided into three categories: circumferential cables closing the epidermis, static cables at boundaries and dynamic cables in morphogenesis. A) An actomyosin 'purse string' is responsible for closure of epithelial wounds for example in the drosophila and zebrafish. B) A similar actomyosin cable guides dorsal closure, helping the epidermis close in the drosophila. C) A cable in the salivary gland placod contracts to aid tube formation through invagination. D) Cables for static boundaries to prevent cell division and mixing across boundaries E) A cable creates a physical boundary between the ventral and dorsal segment of the fly wing. F) Rhombomere maintenance and ventricle formation are assisted through regional differences in myosin II . G) Convergent extension of the germ band occurs through a dynamic cable which pulls neighboring cells along one axis into a rosette and then extends them perpendicularly H) Kidney tubules elongate through a similar convergent extension driven by dynamic cables along their length. I)The neural tube is folded and extended with the help of circumferential cables that rearrange cells in the tissue through neighbor exchanges . In A-C) red arrows indicate the direction of the applied centripetal force. D-I) Double arrows indicate the line tension generated from the cables.[START_REF] Röper | Supracellular actomyosin assemblies during development[END_REF]

Figure 2 - 13 :Figure 2 - 14 :

 213214 Figure2-13: Velocity fields and phase contrast image of a migrating epithelial monolayer 2 hours after stencil removal. The velocity map demonstrates that the cell velocity is not always perpendicular to the border. Flows develop in the monolayer with a correlation length of 10 cell sizes. High velocity regions are located at the leading edge and further back in the monolayer and are not correlated with cell divisions which are distinguished as white dots in the phase-contrast image. (scale: 100µm, arrow 40µ/h)[START_REF] Petitjean | Velocity fields in a collectively migrating epithelium[END_REF]

Figure 2 - 15 :

 215 Figure 2-15: The traction forced generated by a collectively moving epithelium in a wound healing assay. The correlations between the complex forces patterns and velocity fields enabled Trepat et al. to deconstruct the contribution of the leading cell from that of the cells inside the tissue on the collective migration of an epithelial monolayer. A) Phase contrast image B) Traction forces normal to the wound edge. C) Traction forces perpendicular to the wound edge. (scale 200µm)[START_REF] Trepat | Physical forces during collective cell migration[END_REF]

Figure 2 - 16 :

 216 Figure 2-16: An actomyosin cable at the boundary of a model MDCK wound of radius 37.5µm. A) Phospho-myosinII light chain (red) B) F-actin (green) C) Merge with dapi (blue) co-localization of actin and myosin is seen on the leading edge. Red stars indicate positions where lamellipodia are present. D) Cross section of a wound of radius 25um. Red arrows indicate the the actin cable present on both sides of the wound. Scale bar 25µm. [2]

Figure 2 -

 2 Figure 2-17: A pluricellular acto-myosin cable is present at on the two borders of a migrating finger protrusion. A) phosphorylated myosin light chain (red) B) GFP-actin C) colocalization on the boundaries in the form of a pluricellular acto-myosin cable (arrows)and at the leader lamella (zoom). D,E) Confocal section demonstrating the colocalization of F-actin and pMLC in the basal plane at the cable (triangles). The red line depicts the section plane. Scale bars of the x-z sections: 5µm.[START_REF] Reffay | Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells[END_REF]

Figure 2 -

 2 Figure 2-18: A) Phase contrast image of cells confined inside a two dimensional circle of radius 150µm. B) The radial velocity field averaged over all angles. Radial oscillations are present at the half-radius of the patch. and C) The orthoradial velocity. Cell domains rotate collectively in both directions[START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF]

Figure 2 - 19 :

 219 Figure 2-19: Influence of confinement on tissue morphogenesis. Here cell confinement in small circular islands leads to the formation of a tri-dimensional peripheral rim. A) A confocal section of the rim, 15µm above the basal plane. The dashed line delineates the edge of the adhesive treatment. (scale 20µm) B) The three dimensional reconstruction of the tissue C) The dynamics of the development of the rim over 60 hours for R=50µm. A representative plot taken from two replicates.[START_REF] Deforet | Emergence of collective modes and tri-dimensional structures from epithelial confinement[END_REF]

Figure 2 -

 2 Figure 2-20: A) The migration of MDCK cells in tracks of diferent widths. (scale 100 µm) B) The displacement of the cell front over time for tracks of width 20,100, and 400µm C)The velocity of the cell front for different widths for untreated, and blebbistatin treated conditions. The speed of the untreated front increases with confinement below 100µm.[START_REF] Vedula | Emerging modes of collective cell migration induced by geometrical constraints[END_REF]

Figure 2 - 21 :

 221 Figure 2-21: Modes of cell migration in 3D. Cells take on either a spherical amoeboid or an elongated spindle-like shape. Arrows on the right represent individual and collective migrational modes between which cells can switch. Thick arrows on the left represent the direction of migration.[START_REF] Friedl | Plasticity of cell migration: a multiscale tuning model[END_REF]

Figure 2 - 22 :

 222 Figure 2-22: Schematic of an epithelial tissue in vivo (B) that is comprised of a tubular network (A) which ends in spherical sacs or acini (C).In all these cases the polarity of the inner surface is apical (red) and the basement membrane faces the outside of the tissue (green).[START_REF] Wang | Normal morphogenesis of epithelial tissues and progression of epithelial tumors[END_REF]

Figure 2 - 23 :

 223 Figure 2-23: Three types of tube architecture in vivo. A) Multicellular tube: many cells can wrap around a central lumen, forming adherens junctions with neighboring cells B) Unicellular tube: a single cell can encircle a central lumen and form an autocellular adherens junction. C) Intracellular tube: a lumen can hollow out of a single cell. In all three cases the apical surface (green) faces the inside of the lumen and the basal surface (blue) faces the outside.[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]

Figure 2 - 24 :

 224 Figure2-24: Wrapping forms a tube from an already polarized epithelial tissue. A) Wrapping: a lumen is formed through myosin mediated contractions.[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF] Scanning electron micrograph of the initial wrapping stages of the B) chick neural plate to form the C) neural fold and later the neural tube. Arrows and colors represent the distribution of different signaling gradients.[START_REF] Briscoe | Regulatory pathways linking progenitor patterning , cell fates and neurogenesis in the ventral neural tube Regulatory pathways linking progenitor patterning , cell fates and neurogenesis in the ventral neural tube[END_REF]

Figure 2 -

 2 [START_REF] Nelson | Epithelial Cell Polarity From the Outside Looking In[END_REF] shows four examples of branching. The primary trachea branches are formed through budding and the new buds initially have a diameter of only around 2µm but they go through 3 expansion cycles which can leave them up to 40x their original size[START_REF] Lubarsky | Tube Morphogenesis : Making and Shaping Biological Tubes[END_REF]. The collecting system in the kidney is also constructed through a continuous reiterated branching forming a complex tubular network.

Figure 2 -

 2 Figure 2-25:Budding/branching: a lumen is formed off an existing tube. apical surface (green), basal surface (blue)[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]. Branching morphogenesis in various epithelial tissues in a mouse at embryonic day 13.5-15. A) salivary gland B) lung C) kidney. Immunofluorescent labeling of E-cadherin (green). D) mammary epithelium marked with red and green fluorescent proteins.[START_REF] Lu | Patterning Mechanisms of Branched Organs[END_REF]

Figure 2 - 26 :

 226 Figure 2-26: Branching tips in various tissues. Tip cells inhibit each of their neighbors and therefore acquire the role of a leading cell. A) Drosophila trachea tip cells generated form through mutual inhibition through notch signaling B) Drosophila air sacs during larval development. Leading tip cells form filopodial like protrusions C) Mammary gland forms a multilayered tip. Tip cells mutually inhibit other cells locally through TGF-β signaling[START_REF] Lu | Patterning Mechanisms of Branched Organs[END_REF]

Figure 2 - 27 :

 227 Figure 2-27: The four steps in intercalation of stalk cells. A) Two cells pair together, arranging themselves across the lumen from each other. B) One cell reaches around the lumen, to form an autocellular junction with itself. C) With the help of the force being applied by the tip cell, a second cell zips upward with respect to the other, elongating the length of the autocellular junction. This leads to the termination (D) where one cell is now stacked above the other, each of which forms an autocellular junction. [59] E) images from a time-lapse of the cell intercalation of a tracheal branch stalk. adherens junctions (green)and nuclei (red) scale 5µm[START_REF] Caussinus | Tip-cell migration controls stalkcell intercalation during Drosophila tracheal tube elongation[END_REF]

Figure 2 -

 2 Figure 2-28: Cavitation: a lumen forms through the apoptosis and clearing of central cells inside a cell aggregate.[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]

Figure 2 - 29 :

 229 Figure 2-29: Cord hollowing: a lumen forms inside a cord shaped cell aggregate through the development of apical-basal polarity of cells inside the bulk.[48] B) Cross-section of zebrafish midbrain neurulation. Embryonic stages listed on the top right. Zic2a protein (green) phallodin (red)[START_REF] Nyholm | A novel genetic mechanism regulates dorsolateral hinge-point formation during zebrafish cranial neurulation[END_REF]

Figure 2 - 30 :

 230 Figure2-30: Cell hollowing: a lumen forms through the fusion of cytoplasmic vesicles producing a lumen inside a single cell.[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]

Figure 2 - 31 :

 231 Figure 2-31: Cell assembly: a lumen forms through the migration and coordinated shape change of mesenchymal cells into a tube[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]

Figure 2 - 32 :

 232 Figure2-32: Cell wrapping: a lumen forms inside a single cell that fuses to itself forming an adherens junction free tube.[START_REF] Baer | Cellular and molecular mechanisms underlying the formation of biological tubes[END_REF]

  -33. Cells comprising the tube can elongate, rearrange, proliferate or be recruited to change the tube dimensions.

Figure 2 - 33 :

 233 Figure 2-33: Five different manners in which tubes can elongate. When cell number is fixed A) cell elongation and B) rearrangement can cause tube length increase. Cell division either C) locally or D) along the tube drive tube growth. Finally E) external cells can be incorporated into the tube.[START_REF] Andrew | Morphogenesis of epithelial tubes: Insights into tube formation, elongation, and elaboration[END_REF]

Figure 2 -

 2 Figure 2-34: A-C) Chitin (red) develops in the tracheal lumen and helps the tube expand. D) When the tube reaches its full size a rigid cuticle forms on the inside of the tube on a residual chitin membrane while the chitin cylinder is degraded and cleared. The red arrow represents the apical side of the cell and the green arrow the basal surface.[75] E) A drosophila trachea ∼9h-10h after fertilization when circumferential apical actin bundles begin to form. The yellow arrow points to one such oriented bundle. (actin-GFP marking, scale bar=10µm) F) A confocal projection of an adult, wild type, trachea. The circumferential actin rings are far more well defined than in the embryonic tube. Adherens junctions marked in green delineate the boundaries between the tube cells. Actin(red) DE-cadherin(green) bar=50µm[START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF]

Figure 2 -

 2 Figure 2-35: A) The egg chamber at stage 9. The apical-polarity axis is illustrated with the basal lamina facing outward. B) A schematic of the change in actin orientation during development.The actin is initially aligned in each cell but randomly oriented across the cell layer. As the chamber begins to rotates the actin becomes globally oriented.[START_REF] Gates | Drosophila egg chamber elongation: Insights into how tissues and organs are shaped[END_REF]

Figure 2 -

 2 Figure 2-36: A)Schematic of drosophila egg chamber at stage 11. The apical side of the cell faces the germline and the basal surface points outward. B) Organization of cells at the apical side. Image obtained from a projection of a confocal stack. C) Parallel actin-rich bundles resembling stress fibers organized at the basal side. D) Ypet-zyxin marks the zyxin focal adhesion protein and E) red phallodin staining , both observed at the basal side of the cells. The arrows represent the direction of egg chamber elongation. (scale 10µm)[START_REF] Colombelli | Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization[END_REF]

Figure 2 -

 2 Figure 2-37: A) Circular arcs at two points along a 2D curve that define the radius of curvature at these locations. An instantaneously coincident position fitting circle that is situated above the line possesses the opposite sign of curvature as that of a coincident circle with a center that fits a circle below the line. B) The two principle curvatures on a surface.

Figure 2 -

 2 Figure 2-38: Geometric confinement controls lamellipodia formation at regions of high curvature. A) A NIH3T3 cell is confined to a square of size 30µmx30µm. Stained for Factin with green phallodin. B) The adhesive micro-patterned island used in A) stained for fibronectin in red. (scale 10µm)[START_REF] Brock | Geometric determinants of directional cell motility revealed using microcontact printing[END_REF]

  ticellular confinement can dictate the formation of protrusions and the pattern of cell migration. Additionally, Rolli et al. extended their study to explore negatively curved populations and they revealed that in contrast to convex curvature concave regions inhibit protrusion formation.

Figure 2 -

 2 Figure 2-39:The expansion of a cell cluster of radius 104µm incubated for 9h and then released from circular confinement. (scale 100µm)[START_REF] Rolli | Switchable adhesive substrates : Revealing geometry dependence in collective cell behavior[END_REF]

Figure 2 -

 2 Figure 2-40: a) The developing contour of an MDCK monolayer invading free space b) Apredicted contour from the model[START_REF] Mark | Physical model of the dynamic instability in an expanding cell culture[END_REF]

Figure 2 - 41 :

 241 Figure 2-41: Frequency map of branching patterns of engineered mammary epithelial tubules inside prepatterned gelled collagen. A) Curved tubules B) Bifurcated tubules. C) Immunofluorescence staining of actin(red) nuclei (green) of a fractal tree. Branching sites are marked by arrows. D)-F) Calculated concentration distributions of diffusible inhibitors for the geometries of A)B)andC) respectively. Branching occurred on the fractal tree at positions where the inhibitor was at a local minimum (scale 50µm)[START_REF] Nelson | Tissue geometry determines sites of mammary branching morphogenesis in organotypic cultures[END_REF]

Figure 2 - 42 :

 242 Figure 2-42: Chick heart fibroblasts cultured on : A) spherical beads of diameter 72µm and B) 29µm[START_REF]Cell behaviour: A tribute to Michael Abercrombie[END_REF]. Cells on the smaller bead show decreased spreading[START_REF]Cell behaviour: A tribute to Michael Abercrombie[END_REF]. C) Chick heart fibroblasts on a glass wire of diameter of 245µm and 108 µm. On the smaller wire fibroblasts tend to orient along the longitudinal axis of the wire. [92] D) Chick heart fibroblasts growing on an undulating wire of 8µm diameter. Cells preferentially grow on the concave surface rather than the convex surface of the wire. (A,B,D: scale 50µm)[START_REF] Curtis | Control of Cell Behavior : Topological Factors[END_REF]

Figure 2 -

 2 Figure 2-43: A representation of the Dunn & Heath hypothesis displaying the limiting microfilament bundle of ∼ 15 µm, present in a migrating cell, which rises ∼ 1 µ m above the substrate near at the rear of the on A) a cell migrating circumferentially on a cylindrical substrate B) a cell attempting to migrate over the ridge of a prism of angle 4 • [93]

  -44) below a diameter of 250µm [97]. Even at 250µm the cells are still slightly aligned with an orientation of around 40 • where 45 • represents a random configuration.

Figure 2 -

 2 Figure 2-44: L929 fibroblasts attached to PLGA fibers of diameter A) 10µm B) 20µm C) 30µm D) 50µm E) 102µm F) 242µm G) Average orientation angle of fibroblasts on fibers, where an angle of 0 • corresponds to the longitudinal direction. An angle of 45• which corresponds to a random orientation was obtained for cells seeded on a flat surface.[START_REF] Hwang | Controlled cellular orientation on PLGA microfibers with defined diameters[END_REF]

  study of the actin fiber orientation of cells on curved surfaces established contrasting cytoskeletal organization inside single epithelial cells (rat IAR-2, canine MDCK) and fibroblasts (rat REF, human AGO 1532). The actin in REF and AGO fibroblasts was shown to align longitudinally (Fig. 2-45) whereas the actin in IAR-2 and MDCK cells was shown to align circumferentially (Fig. 2-46). It was shown that in all three cases the alignment of actin was related to the presence of microtubules.

Figure 2 -

 2 Figure 2-45: Human AGO 1523 fibroblasts seeded on glass wires of diameter 32µm. The actin aligns in the longitudinal direction in the control condition. A-D) control condition A) scanning electron microscopy image of fibroblast B-C) fluorescent microscopy image where actin is labeled D) image of tubulin E) image of actin after colcemid incubation. Bars 20µm.Arrows mark the direction of the wire's long axis[START_REF] Svitkina | Transverse pattern of microfilament bundles induced in epitheliocytes by cylindrical substrata[END_REF]

Figure 2 -

 2 Figure 2-46: IAR-2 epithelial cells on cylindrical substrates of diameter 32µm. The actin aligns in the circumferential direction in the control condition. A-D) control condition A) scanning electron microscopy image of fibroblast B-C) fluorescent microscopy image where actin is labeled D) tubulin E) after colcemid incubation, actin is labeled. Bars 20µm.Arrows mark the direction of the wire's long axis[START_REF] Svitkina | Transverse pattern of microfilament bundles induced in epitheliocytes by cylindrical substrata[END_REF].

Figure 2 - 47 :

 247 Figure 2-47: Different cross sections of A)MDCK cells and B) NIH-3T3 fibroblast cell on a 2-photon polymerized wires of R=3-4.5µm. Both cells elongate to over 100µm in length on these fibers, fully wrapping around the circumference. The MDCK nucleus partially bends around the small wire, but the NIH-3T3 nucleus remains undeformed. (Alexa 488-phallodin: green, DAPI: blue) [99]

Figure 2 -

 2 Figure 2-48: a) A schematic of neuron cytoskeleton. b) A fluorescence micrograph of a neural growth cone. Microtubules (green) and actin-filaments (red) form protrusions at the growth cone which is at the end of the axon. (scale 20µm) c)The axon is comprised of neurofilaments (a type of intermediate filament) that wraps microtubules which transport materials between the cell body and the axon terminal end d) the growth cone which is comprised of both dendritic actin and parallel actin bundles in the form of filopodia. e) microtubules (green), f) intermediate filaments (purple), g) actin filaments(red)[START_REF] Fletcher | Cell mechanics and the cytoskeleton[END_REF]

Figure 2 - 49 :

 249 Figure 2-49:The orientation of DRG neurite outgrowths on glass wires of different diameters. A) A neuron on a 35µm diameter filament with a highly directed outgrowth orientation B) A neuron on a 250µm diameter filament with less oriented outgrowths. A-B) neurofilament (green). C)The normalized distributions of outgrowth direction where an angle of 0 represents the longitudinal direction of the filament. The black line is a fit derived from a Boltzmann model where the probability of an outgrowth in a certain direction depends on the neurofilament bending stiffness and adhesion energy with the surface.[START_REF] Smeal | Substrate Curvature Influences the Direction of Nerve Outgrowth[END_REF]

Figure 2 -

 2 Figure2-50: A) A summary of the two competing forces felt by a cell adhering to a curved substrate. The cell feels both pure bending as well as a myosin activated contractility from its stress-fibers. Cells are modeled to feel a superposition of the two effects as is depicted in the the bottom image. B) A schematic of a cell confined to a cylinder. A cell is contractile on both curved and flat substrates but when attached to a wire, it also experiences pure bending.[START_REF] Biton | The cellular response to curvature-induced stress[END_REF]

Figure 2 -

 2 Figure 2-51: A) glass balls are partially embedded in polyacrylamide gel and fibroblasts are seeded onto the spherical substrates B)The cell spreading area when seeded on glass micro balls embedded in polyacrylamide gel. Spreading area increased with ball diameter and three linear trends were reported. ntotal=95[START_REF] Lee | Micro glass ball embedded gels to study cell mechanobiological responses to substrate curvatures[END_REF]

Figure 2 -

 2 Figure 2-52: Glioblastoma (DBTRG-05MG) cell migrating on a 400nm wire. As the cell elongates along the fiber blebbing is inhibited I) II) arrows show position of leading protrusion, III), IV) stars show cell blebbing . Scale 50µm [109]

Figure 2 -

 2 Figure 2-53: A) Average migration speed of a cancer cells, simulated over 5 hours, moving inside a spherical lumen. Error bars Standard error of the mean. B) Cross sectional views of the lumen. Below 10µm the lumen confines the cell completely and the migration speed decreases.[START_REF] Kim | Integrating focal adhesion dynamics, cytoskeleton remodeling, and actin motor activity for predicting cell migration on 3D curved surfaces of the extracellular matrix[END_REF]

Figure 2 - 54 :

 254 Figure 2-54: Confocal images of HBMEC and HUVEC cells on wires of various diameters. HBMEC : A) d= 498µm , d=87µm , d=13µm, ZO-1 a tight junction protein(red) DAPI nuclear staining (blue). HUVEC: B) d=372µm , d=90µm, d=14µm VE-Cadherin (red) DAPI (blue). C) Orientation of HBMEC(red) and HUVEC(blue) grown on the outside of glass wires. The orientation angle is the angle between the cell long axis and the wire long axis. The number of cells N = 923 for HBMEC and N = 1306 for HUVEC. Error bars represent the SE. D) Average number of HBMEC(red) and HUVEC(blue) cells around the wire perimeter. The solid blue and red lines represent fits to a power law where N ∝ d α .For HBMEC α = 0.86 and the x-axis intercept where N=1 is at d=9.8µm. For HUVEC, however, α = 0.80 and the x-axis intercept where N=1 is at d=4.4µm. The dotted line shows α = 1 E) Parallel and F) perpendicular indices for actin fiber distribution in confluent monolayers of HBMEC and HUVEC cells in 2D on large and small wires under static conditions and for large wires under shear stress (SS). Error bars are the SE.[START_REF] Ye | Brain microvascular endothelial cells resist elongation due to curvature and shear stress[END_REF]

  After a fluorosilane treatment, this pattern became antiadhesive. Remolding the negative pattern then yielded the desired PDMS substrate with the structure of the initial wafer. Each molding step employed a vacuum chamber to remove air bubbles from the PDMS before overnight curing at 65 • C. The surface of the final PDMS substrate contained cylindrical PDMS pillars of height 100µm and diameter 100µm and 200µm. The pillar height depended on the spin coating parameters used and could be modulated through different rotation speeds. While SU-8 can be spun up to a thickness of around 200µm other types of photoresist or multiple coats result in deeper molds and therefore higher pillars; however, for initial trials 100µm proved sufficient.

Figure 3 - 1 :

 31 Figure 3-1: A schematic of the PDMS pillar assay. Cell were seeded on the bottom on the surfaces. The cells grew to confluence on the flat portion of the substrate before progressing up the pillars.

Figure 3 - 2 :

 32 Figure 3-2: SEM images of the surface of a glass wire pulled manually. Defects are submicron sized. A) scale 50µm B) 20µm C) 5µm, D) 1µm

Figure 3 -

 3 Figure 3-3: A) A schematic of the wires assay B) A wire aligned on a PDMS support. Cells are seeded on the support, grow to confluence and then progress onto the glass wire. (scale 100µm)

Figure 3 - 4 :

 34 Figure 3-4: PS fibers formed with different concentrations of polystyrene. All concentrations yield rough surfaces. A) 30wt% B) 35%wt C)35%wt D) 40%wt[START_REF] Kim | Unique Surface Morphology of Electrospun Polystyrene Fibers from a N,N-Dimethylformamide Solution[END_REF]

Figure 3 -

 3 Figure 3-5: A) A cleaned glass slide B) The slide is covered with a protein repellent layer C) An additional layer of photoresist is added D) Photolithography attacks the resin E) A plasma is used to remove the exposed anti-adhesive layer. F) The resin is dissolved G) Cells are cultured directly on the slide, attached to the regions of bare glass[123].

3. 3

 3 Cell culture 3.3.1 Cell lines Three different types of cells were used over the course of the study: MDCK, NIH3T3, and HEK-HT.

Figure 3 - 6 :

 36 Figure 3-6: An Ibidi chamber placed on top of micropatterned tracks. MDCK cells were seeded in both wells and grown to confluence before the insert was removed.

Figure 3 -

 3 Figure 3-7: A) MDCK wt cells B) NIH3T3 cells C) HEK-HT cells (scale: 100µm)

  Time lapse experiments were conducted under an automated inverted phase contrast video microscope (Olympus Ix71 & Leica DMIRB, CoolSnapHQ2) equipped with a 10x and 20x objective. The temperature, humidity, and CO 2 of the microscope environment were regulated (Life Imaging Services) while data acquisition and the motion of the motorized stage were controlled through MetaMorph software (Prior).

Figure 3 - 8 :

 38 Figure 3-8: An example of an image taken of a wire using a 10x objective on an inverted video microscope. The location of the front is clearly visible on the side of the wire (red arrows) however the front is much more weakly defined on the lateral face of the wire (yellow arrow). (scale 50 µm)

Figure 3 -

 3 Figure 3-9: A) A cross section of the upper half of a wire reconstructed from consecutive confocal stacks in z. Images of cells on a wire were taken at subsequent z planes across many microns (represented by yellow dotted lines) starting from the top of the wire. (MDCK cells marked for ezrin, scale 20µm) B) A projection taken of the maximum values in x -y-over all the z planes of an image stack for MDCK cells marked for F-actin and a 30µm scale.

Figure 3 -Figure 3 - 11 :

 3311 Figure 3-10: A) Parameters employed to characterize cell alignment: The angles obtained at θ (t=0) from the image projection yields the actual orientation on the surface of the wire. The angles measured at an off axis displacement b on a cylinder of radius r, however, require correction.(adapted from [97]) B) A schematic denoting the opening angle α

Figure 3 -

 3 Figure3-12: FFT image analysis. A) Overlapping subwindows were taking across an image. The green box is representative of the size of a single window which is of dimension 7µmx7µm. B) A subwindow image. C) A subwindows with a windowing mask applied over it D) The FFT norm of the windowed image. E) A threshold applied to the FFT. F) An ellipse is fit over the thresholded FFT in E. The major axis of the ellipse give the orientation of the subwindows. Ellipses of eccentricity above a threshold were used for analysis.

  -13) dividing the area with the cells to that of the background over time defines the velocity of the front. Measuring the orientation of features inside the kymograph provides additional information about the velocity profile in the bulk over time. The OrientationJ 1 [130] plugin for ImageJ 2 was used to measure local orientation in kymograph images.

Figure 3 - 13 :

 313 Figure 3-13: An example of a kymograph image formed from a timelapse of cell front migrating on a wire. The dotted green line represents the position of the front over time. The slope of this line yields the average front velocity. The yellow box represents a region of interest (ROI) window used for OrientationJ analysis. (scale: 20h, 100µm)

Figure 3 - 14 : 1

 3141 Figure 3-14: An example of the image analysis obtained with OrientationJ. A) The original kymograph of the cell migration. B) A mask designed to isolate the region of the kymograph representing the section of the wire covered with cells C) The color map generated by the OrientationJ algorithm of of the orientation at each spatial point overlayed on the original kymograph. D) The color map representing the calculated velocities with a color whose value is defined on the adjacent scale. E) The rescaled color map of the velocity profiles with the leading font all placed at the left axis. F) Velocity profiles at different time points extracted from the kymograph, renormalized by the length of the front. x = 0 corresponds to front edge. (scale: 20h, 100µm)

Figure 4 - 1 :

 41 Figure 4-1: MDCK lifeAct cells A) migrated up PDMS pillars and reach over the top edge to invade the pillar's top. (scale 50µmB) The top of a pillar fully invaded by cells. (scale 100µm)

Figure 4 - 2 :

 42 Figure 4-2: A) A schematic of the wire assay with glass wires aligned on the edge of a PDMS substrate B) The convention used for θ in this thesis. An angle of θ = 0 describes a longitudinal orientation whereas a θ = π/2 represents the circumferential direction. C) MDCK E-Cadherin GFP cells confluent on a PDMS support and the attached glass wire. (scale: 100µm)

Figure 4 - 3 :

 43 Figure 4-3: Polarity of a monolayer of MDCK cells. Ezrin (red), phallodin (green), and DAPI (blue) are stained for : A) cells on a flat glass substrate (scale 20µm) B) cells on a glass wire (scale 10µm)

Figure 4 - 4 :

 44 Figure 4-4: A MDCK dome formed off the side of a wire. Ezrin (red) marks the apical surface. Dapi (blue) marks the cell nucleus and phallodin (green) marks the actin fibers. (scale 20µm)

Figure 4 - 5 :

 45 Figure 4-5: A) Elongated MDCK LifeAct-GFP cell on a wire of radius = 1µm (scale 50µm) B) A cross section drawn through the MDCK LifeAct-GFP cell in (A) demonstrating that the cell is fully wrapped around the wire. (scale 5µm) C) Phase image of a chain of cells on a wire of radius 4µm. The cells near the leading edge (red arrows) are highly elongated. (scale 100µm)

Figure 4 - 6 :

 46 Figure 4-6: The density along the migrating front depends on the distance from the leading edge (x = 0). Above 300µm the two density profiles overlap. Below 200µm, however, the R=10µm are less dense. (n R=10 , n R=40 = 5)

Figure 4 -

 4 Figure 4-7 details an example of a cell splitting from a monolayer. In this case the cell undergoes two uniaxial migrational modes, moving away from the monolayer at 96 µm/h and changing directions and then moving back towards the front at a speed of 100 µm/h later. These individual migrating cells displaced the fastest when "rounded up" as seen in figure4-8. Individual cells, however, were not always in a round shape, but could undergo cycles of elongation and retraction.

Figure 4 - 7 :

 47 Figure 4-7: A-D) Migration of a cell escaping a migrating monolayer moving on a wire of R = 5µm. There are 2h between successive images. (scale: 50µm) E) The kymograph of the migrating cell. (scale: 10h, 50µm) F) The position of the migrating cell front over time (blue) and the trajectory of a cell broken away form the front (green).

Figure 4 - 8 :

 48 Figure 4-8: A single cell MDCK-lifeAct cell rounded up in its 'fast migration mode' (see Figure 4-5B). The phase image of the wire is merged with the z projection of the fluoresent one. (scale 10µm)

Figure 4 - 9 :

 49 Figure 4-9: MDCK cells migrating in adhesive micropatterned tracks of width A) 200µm B) 50µm C) 20µm (scale 100µm)

Figure 4 - 10 :Figure 4 -

 4104 Figure 4-10: The orientation of the actin cytoskeleton inside a flat monolayer. A) The nuclei marked in DAPI (blue) indicate the position of the cells. B) Phallodin (green) shows an actin cytoskeleton that isn't coordinated across the population. C) Merge of DAPI and phallodin. (scale 20µm)

Figure 4 - 12 :

 412 Figure 4-12: Distribution of the orientation of actin on two different wires. A) R= 25µm B) R=85µm. (n angles > 2500 per radius)

Figure 4 -

 4 [START_REF] Pellegrin | Actin stress fibres[END_REF] shows an abrupt transition where fibers are randomly oriented above R=40µm and circumferential below R=35µm.

Figure 4 - 13 :

 413 Figure 4-13: The order parameter defined as S = cos(2θ) for the actin fibers measured on wires of varying radius. At a radius of 30µm and below the actin cytoskeleton transitions from an unordered to an ordered state. (n angles > 2500 per radius)

  [START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF][START_REF] Chhabra | The many faces of actin: matching assembly factors with cellular structures[END_REF][START_REF] Parsons | Cell adhesion: integrating cytoskeletal dynamics and cellular tension[END_REF][START_REF] Vicente-Manzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF][START_REF] Cramer | Identification of novel graded polarity actin filament bundles in locomoting heart fibroblasts: implications for the generation of motile force[END_REF][START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF][START_REF] Versaevel | Spatial coordination between cell and nuclear shape within micropatterned endothelial cells[END_REF][START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF][START_REF] Yeung | Effects of Substrate Stiffness on Cell Morphology, Cytoskeletal Structure, and Adhesion[END_REF][START_REF] Pellegrin | Actin stress fibres[END_REF][START_REF] Ingber | Tensegrity I. Cell structure and hierarchical systems biology[END_REF]. As well, the continuity of the actin fibers is again reminiscent of the drosophila trachea where the fibers relay circumferentially across cell boundaries(sec. 2.5.1 , Fig.2-34)[START_REF] Matusek | The Drosophila formin DAAM regulates the tracheal cuticle pattern through organizing the actin cytoskeleton[END_REF].

Figure 4 - 14 :Figure 4 - 15 :

 414415 Figure 4-14: Aligned actin fibers are seen to move through cell-cell boundaries. A) Immunofluorescent staining of F-actin (phallodin:green) B) MDCK LifeAct cells. (scale 20µm)

Figure 4 - 16 :Figure 4 - 17 :

 416417 Figure 4-16: Cells on PS wires. A) MDCK LifeAct cell on a wire of R=3µm. The cell wraps around the wire and elongates to a length of 95µm while preserving adhesion with its neighbor on the right. B) Cadherin-gfp, histone-Mcherry labeled cells show that at later times at small radii (here: R=1µm) multiple cells, over ten times shorter in length, wrap around the circumference of the wire. C) A transmission image of B showing multiple cells wrapping around the wire D) MDCK LifeAct cells show aligned actin streaks in the longitudinal direction corresponding with the rough features of the wires. E) MDCK LifeAct cell on a PS wire with aligned circumferential actin fibers. (A-E:scale 10µm)

Figure 4 -

 4 Figure 4-19 compares the order parameter of the actin in tracks to wires for the same lateral confinement. Whereas the order parameter of the actin in wires transitions abruptly from random to ordered at R=40µm the alignment of the actin in the tracks increases linearly with confinement below a width of 200µm. We conclude that the transverse actin orientation observed on wires is a consequence of curvature and not confinement.

Figure 4 - 18 :Figure 4 - 19 :

 418419 Figure 4-18: Confining a monolayer to adhesive tracks orients cells actin cytoskeleton. A) Track of width 100 µm and B) Track of width 50µm. The insets show the aligned actin fibers in the two cases. The effective radius of a track is the radius of a wire with the identical lateral confinement. (scale: 20µm)

  Figure 4-20 shows the density of focal adhesions (FAs) on the wires of radius 10µm. On wires of radius R < 40 µm, we measured an increase in the number of FAs per cell as well as a decrease of their size compared to the flat control (Figure 4-21). Furthermore several of these FAs were found to be spaced along the same fibers (Figure 4-20D). The situation on wires is therefore different from that on flat surfaces where stress fibers are anchored to the surface via only two FAs at their extremities.

Figure 4 - 20 :

 420 Figure 4-20: Focal adhesions are present at high density in cells seeded on wire of radius 10µm A) vinculin staining B) F-actin C) merge. (A-C: scale 10µm) D) inset of C showing multiple adhesions along single fiber. (D: scale 2µm)

Figure 4 - 22 :

 422 Figure 4-22: The ablation of an actin fiber on a wire of R=10µm A) 0s B) 2.5s C) 5s after retracts. The fibers ablated on curved surfaces retracted only up to 0.5µm.

Figure 4 -

 4 Figure 4-23: A) Actin cable of leading cell on wire of radius 10µ. B) Cable 2s and C) 10s after ablation. (scale 10µm) B) The speed of initial retraction 5s after ablation of the actin cables on the leading edge of monolayers. Cables on R < 20µm and those on a flat substrate are compared. (p < 0.001)

Figure 4 - 24 :

 424 Figure 4-24: Collective migration on a wire of R = 20µm A) An image of the progressing front with one image taken every 10 hours. The red arrow marks the position of the leading cell. B) A kymograph of the front progression (scale: x=100µm y=20h) C) The position of the leading front over time.

Figure 4 - 25 :

 425 Figure 4-25: The velocity profile of a migrating front on wires of R = 40µm and R = 20µm ( 5 kymographs formed from a time lapse sampled every 30 minutes for 24h were averaged)

Figure 4 -

 4 Figure 4-26: A oscillatory or frontward and backward motion is visible in the kymographs on a wire of R= 4µm (scale:10h, 50µm)

Figure 4 - 27 :

 427 Figure 4-27: The velocity of a collectively migrating monolayer on wires (black) and tracks (red). The bottom x axis in black displays a radius and the top x axis in red displays the corresponding width, w where w = 2πR. The points from the wires and tracks are therefore each plotted at equivalent lateral confinement

Figure 4 - 28 :

 428 Figure 4-28: The kymograph of the progression of a front of cells on a wire of radius 40µm. Mitomycin was added at the point of the blue dotted line. (scale: x-50µm, y-10 hours)

Figure 4 -

 4 Figure 4-29: A) The cell density along a front for wires R= 40µm (red) and R=85µm (green). The solid line represents the density of the active cells marked by Ki-67 along the wire(ρ active ), and the empty symbols represents the entire cell density(ρ cell ). B) The ratio of the density of active cells along the wire to density of all cells along the wire (ρ active /ρ cell ) is plotted versus the density of all the cells along the wire (ρ cell ). In both graphs x = 0 represents the position at the leading edge.

-30 and 4 - 31 .

 431 The first graph highlights the variation in the velocity versus radius trend for the different drugs. The number of experiments represented in this plot are : R = 10µm : n control = 54 n bleb = 75 n c3 = 54 n HGF = 90 n N SC = 39 R = 40µm : n control = 27 n bleb = 14 n c3 = 46 n HGF = 34 n N SC = 32 R = 85µm : n control = 19 n bleb = 32 n c3 = 15 n HGF = 71 n N SC = 13

Figure 4 - 30 :

 430 Figure 4-30: Four different drugs were tested on the migrating front: NSC, HGF, C3 transferase and blebbistatin. Wires of radius 10, 40, and 85µm were employed.

Figure 4 - 31 :

 431 Figure 4-31: Impact of NSC, HGF, C3 transferase and blebbistatin on front velocity for wires of radius R=10, 40, and 85µm. Results from the t-tests done for each condition with respect to the control are displayed.

  expected the velocity at R=40 and 85µm to increase with C3 transferase treatment as it does in the presence of blebbistatin. One possibility is that C3 transferase can interact with other pathways during longterm use which influence migration. Studies of the role of C3 transferase on migration are usually limited to a few hours while in this work we employed the drug for tens of hours. Another possibility is that Rho inhibition through C3 transferase could be acting on a pathway or mechanism unaffected by blebbistatin that influences cell contractility, cell-cell adhesion, or cell migration differently. Although more experiments are needed to probe the differences between C3 and blebbistatin at large radii, C3 and NSC both indicate that different mechanisms are at play at high versus low curvature.

Figure 4 -

 4  The speed of migrating fronts is disrupted when a defect on the wire or a dust particle is encountered. The leading front, moving on a wire of radius 10µm encounters a dust particle at t=35h. Defects cause the front to adopt a slower, linear trend over the span of tens of hours, long after the front has moved past the defect.

  Cells spread from the aggregate onto the adhesive area migrating collectively away from the bulk by permeating through the lower layers. The confined monolayer migrates with a constant velocity and the speed is defined by the level of expression of E-cadherin (Fig.4-33B).

Figure 4 -

 4 Figure 4-33: A) A schematic of cell aggregates spreading on adhesive tracks. (scale: 100µm) B)The linear progression of a front of murine sarcoma cells confined to a 100µm wide track collectively migrating away from an aggregate. The black points represent a cell line expressing a density of 100% of E-cadherin and the pink markers represent cells expressing only 48% E-cadherin. The dashed lines represent the theoretical prediction. C) Schematic of the aggregate feeding the migrating film through permeation. D) Schematic of the aggregate moving on the track.[START_REF] Douezan | Spreading dynamics of cellular aggregates confined to adhesive bands[END_REF]

Figure 4 -

 4 Figure 4-34: A kymograph illustrating a cell migrating up to a critical radius where it can no longer progress. At which point, the cell oscillates around this location during tens of hours. (scale: x=50µm. y=10h)

Figure 4 -Figure 4 -

 44 Figure 4-35: A cell front at the critical radius below which it cannot migrate. A) A single cell wraps fully around the wire at the leading edge. B-C) The cell oscillates sending out protrusions in front of itself that fail to propel the cell forward. During the oscillations the bulk behind the leading cell continues to densify. D) When the bulk densifies sufficiently the monolayer detaches from the leading edge at the front and a cyst develops and stabilizes in the tip. (scale: 20µm)

Figure 4 - 37 : 5 Conclusion

 4375 Figure 4-37: Blebs are sometimes observed in an oscillating cell at the edge of a high curvature zone. A) A cell at the tip of a cone. B-D) The same cell going through blebbing and unblebbing cycles. (scale: 20 µm)

Figure 5 - 1 :

 51 Figure 5-1: Fibroblasts migrating in tracks of width 20 to 1µm. [150]

Figure 5 - 2 :

 52 Figure 5-2: Multiphoton microscopy images of GFP labeled carcinoma cells migrating on ECM fibers (purple) at arrow head location(scale 25µm).[START_REF] Condeelis | Intravital imaging of cell movement in tumours[END_REF]

Figure 5 - 3 :

 53 Figure 5-3: Collective invasive strands of cancer cells migrating along striated muscle fibers.(scale: 100µm)[START_REF] Alexander | Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model[END_REF]

Figure 5 - 4 :

 54 Figure 5-4: MDCK LifeAct-GFP cells grown in a cylindrical tube manufactured inside a block of PDMS (scale: 100µm)

OrientationJ: http://bigwww.epfl.ch/demo/orientation/

ImageJ: (National Institutes of Health, Bethseda) http://imagej.nih.gov/ij/

3.7. IMAGE PROCESSING

Acknowledgments