Keywords: Myosin 1b, EphB2, membrane mechanics, optical tweezer, membrane nanotubes, transmembrane receptor diffusion, actin flows, TIRF-SIM

Figure 1 The cell boundary. Schematic representation of the cell boundary, the extracellular space is represented in green and the intracellular space in blue. The three functional layers as mentioned in the manuscript are highlighted on the left side from top to bottom: actin cortex, PM-actin linkers, and the PM. Modified from reference 8.

The last years that I spent at Curie have been both challenging and incredibly rewarding and I am happy to look back on this time while writing my acknowledgements, just before leaving Curie for good.

I would like to start thanking my two thesis directors Evelyne and Patricia, who, ever since I joined the lab, have supported, pushed, comforted and inspired me. It has been a tremendous pleasure to work with you, spending numerous hours discussing science, being confused by the data, and often times realizing that maybe it is the questions and not the answers that I enjoy most in life. I have always appreciated working with you, the freedom you gave me to explore science and the guidance you offered when I got lost. I am extremely grateful for the opportunities you gave me, notably to explore science outside the lab.

Thank you very much to my jury members Didier Marguet, Alba Diz-Muñoz, Roland Wedlich-Söldner, and a layer of even more gratitude to my 'rapporteurs' Pieta Mattila and Jure Derganc who were willing to read my manuscript, came to Paris in summer and made the experience of defending my PhD very stimulating and enjoyable.

I would like to thank Guy Tran van Nhieu for being my external thesis advisor, delving into my little bubble of desperation once a year and offering plenty of good advice throughout this PhD.

Thank you to the BMBC platform for continuous support: John, Fanny, Fahima, Aude, and Anna.

Team Coudrier, thank you! Olga and Priscilla for a biological perspective; and Maïté for a thousand 'petits conseils' and a lot of blotting magic.

Team Bassereau Superstar, thank you so much! It has been a great privilege to work with you during all these years. I have always appreciated the spirit in our team and everybody's willingness to help! A special shout-out to the Bassriers/Coudereaus: Feng and Julian, for at least three group meetings a week! Thank you to all the theoreticians I have had the pleasure to interact and discuss my experiments with: Pierre Sens, Madan Rao, and Françoise Brochard-Wyart.

Thank you to Bruno Goud and his team for many Tuesday morning Rab-ventures and some ERC-worthy dinners. v Table 1 Selection regulating membrane shape at the Golgi apparatus 1 and endosomes 2 . It is also involved at the plasma membrane, where it is required for efficient EphB2-driven cell segregation through cell retraction 3 . Work performed by Ayako Yamada showed that Myosin 1b can elongate membranes along actin bundles in vitro 4 in a way reminiscent of membrane tube elongation at the Golgi apparatus. Subsequently, work performed on neurons by Olga Iuliano showed effects on axon formation by Myosin 1b, linked to changes in actin wave dynamics [START_REF] Iuliano | Myosin 1b promotes axon formation by regulating actin wave propagation and growth cone dynamics[END_REF] .

List of Figures

In an effort to consolidate these observations into a coherent mechanistic model, and taking into account that Myosin 1b can interact with membrane receptors 3 and has been reported to change the mechanical properties of the plasma membrane [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF][START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] we thus hypothesized that the mechanism of action of Myosin 1b at the plasma membrane has a mechanical origin. By such a general effect, we thought to be able to explain the variety of biological phenotypes, linking them to one fundamental change when Myosin 1b is absent, i.e. altered deformability of the membrane and/or inefficient coupling between the underlying actin cytoskeleton and the plasma membrane.

Using optical tweezers we characterized the effect of Myosin 1b and ERM proteins, as a benchmark for plasma membrane-cortex linkers, on effective membrane tension, membrane-cortex friction and membrane-cortex adhesion. Yet, to our surprise, we did not observe any striking difference in the assessed parameters. The results are presented and discussed in part A of this thesis.

This prompted us to pursue a secondary hypothesis during the last year of this thesis. Inspired by the many demonstrations showing a functional dependence of receptor signaling on actin dynamics, we hypothesized that for EphB2, and potentially other receptors, Myosin 1b might alter the diffusive and thus functional landscape within the membrane, or the actin flows that happen downstream of EphB2 activation.

We thus characterized the effect of Myosin 1b on diffusivity, clustering behavior and immobilization of EphB2. Furthermore, we studied the effect of Myosin 1b on actin cytoskeleton dynamics. We studied the dynamics of EphB2 by employing FRAP, FCS, and fluorescence anisotropy. Using TIRF-SIM imaging and subsequent PIV analysis, we studied the dynamics of actin. The obtained results are described and discussed in part B of this thesis.

Introduction

The cell boundary is a defining feature of all living organisms, as it separates the cell from its surrounding environment. It serves as an integration hub for cell signaling, allows exchange with the surroundings, and is fundamental to both cell migration and morphology. In a simplified view, this interface can be reduced to 3 main functional layers [START_REF] Honigmann | Compartmentalization of the Cell Membrane[END_REF] (Figure 1). The plasma membrane, which separates inside from outside by a thin lipid bilayer, is highly enriched in proteins that can interact with either side of the leaflet or span the bilayer. Secondly, the underlying actin cytoskeleton often referred to as the cellular cortex, which is a highly dynamic network of semi-flexible polymers, conferring rigidity to the cell that allows it to withstand mechanical stresses from the inside and outside. The interplay and intricate balance between rigidity and constant turnover defines cellular morphology, while allowing for dynamic deformations required for, e.g. cell migration. Thirdly, the interface between the plasma membrane and the actin cytoskeleton is populated by a variety of proteins that link both.

In this thesis, we have focused on two fundamental processes happening at the cell boundary: This schematic view of the PM underlined by actin (green). Glycerophospholipids (GPL) form the majority of the PM lipid content. In addition one finds sphingomyelin (SM) and glycosphingolipids (GSL) that can form nano-domains (lipid rafts) together with cholesterol (red). Integral, bilayer-spanning transmembrane (TM) proteins can have affinities for 'raft' and 'non-raft' phases. Peripheral proteins can be attached to the leaflets of the plasma membrane through lipid anchors, e.g. acylation or glycosylphosphatidylinositol (GPI). Proteins binding to actin and the plasma membrane can serve as pickets, to form the membrane skeleton, as posited in the picket-fence model. Modified from reference 11.

1. The contribution of membrane-cortex linkers to the cell membrane's mechanical properties.

2. The contribution of membrane-cortex linkers to the dynamics of transmembrane receptors and the underlying actin cortex.

A detailed introduction regarding both processes precedes the two chapters that describe and discuss our results. This general introduction aims at giving an overview of the current state-of-the-art on the different components involved in these processes.

The plasma membrane

The conceptual view of the plasma membrane has been predicted to an impressive degree by Singer and Nicolson in their 'fluid-mosaic model' in the early 70s [START_REF] Singer | The Fluid Mosaic Model of the Structure of Cell Membranes[END_REF] . Nowadays we know much more about the heterogeneity and asymmetry of involved lipids [START_REF] Van Meer | Membrane lipids: Where they are and how they behave[END_REF] , their spatial segregation in short-lived nanodomains [START_REF] Lingwood | Lipid rafts as a membrane-organize principle[END_REF] , and the abundance of proteins within the lipid bilayer [START_REF] Engelman | Membranes are more mosaic than fluid[END_REF] . Yet, conceptually, one may still think about the plasma membrane as a composite material consisting of amphiphilic lipids that assemble into a bilayer, bilayer-spanning transmembrane proteins (integral), and proteins interacting with either side of the leaflet (peripheral) [START_REF] Suzuki | New Insights into the Organization of Plasma Membrane and Its Role in Signal Transduction[END_REF] (Figure 2). Functionally, the majority of proteins serve the purpose of extracellular signal integration and ion exchange through the membrane, nutrient uptake, and the control of actin cytoskeletal dynamics. For the lipids, one might differentiate between majority species that establish the biophysical properties of the plasma membrane and maintain an efficient boundary from those that are closely linked to protein function and regulation, e.g. PI(4,5)P2.

Lipid composition of the PM

The PM's lipids are generally synthesized at the ER and subsequently trafficked to the PM in a controlled way, with sorting mechanisms that allow maintaining a specific lipid composition [START_REF] Ikonen | Protein and lipid sorting from the trans-Golgi network to the plasma membrane in polarized cells[END_REF][START_REF] Roux | Role of curvature and phase transition in lipid sorting and fission of membrane tubules[END_REF][START_REF] Harayama | Understanding the diversity of membrane lipid composition[END_REF] . The main constituents of the eukaryotic plasma membrane are glycerophospholipids, cholesterol, and sphingomyelin. The family of glycerophospholipids, i.e. phosphatidyl-choline, phosphatidyl-serine, phosphatidylethanolamine, phosphatidyl-inositol, and phosphatidic acid all share a common hydrophobic di-acyl-glycerol backbone; yet they have a different polar headgroup.

Sphingolipids, with a ceramide backbone, preferentially interact with cholesterol [START_REF] Van Meer | Membrane lipids: Where they are and how they behave[END_REF] .

Variability in the hydrophobic acyl chains regarding both length and the degree of unsaturation fundamentally impacts the biophysical properties of the individual lipids and in consequence the plasma membrane [START_REF] Huang | Empirical Estimation of the Gel to Liquid-Crystalline Phase Transition Temperatures for Fully Hydrated Saturated Phosphatidylcholines[END_REF] . This adaptability is important for an organism's adaptability towards, e.g. changes in temperature [START_REF] Cooper | Thermal adaptation of cellular membranes in natural populations of Drosophila melanogaster[END_REF][START_REF] Muir | Lipid remodelling in the reef -building honeycomb worm, Sabellaria alveolata, reflects acclimation and local adaptation to temperature[END_REF] .

Furthermore, the PM is asymmetrically organized and lipids are differentially distributed between the inner and outer leaflet. This asymmetry is important for a variety of cellular processes, e.g. during apoptosis [START_REF] Fadok | Exposure of phosphatidylserine on the surface of apoptotic lymphocytes triggers specific recognition and removal by macrophages[END_REF] , and is maintained by the action of transmembrane proteins that catalyze transitions from one bilayer to the other [START_REF] Panatala | Inner workings and biological impact of phospholipid flippases[END_REF] .

Lipid-protein interactions

Lipids can affect protein function in two fundamental ways, either by changing local biophysical properties, or as a messenger and interaction hub. In the former case, the distribution of lipids in the lipid bilayer determines the lateral pressure profile and can, e.g. affect a transmembrane protein's opening probabilities 22,23 . In the latter example, lipids, e.g. phosphoinositides, can locally recruit proteins or act as messengers over large distances [START_REF] Di Paolo | Phosphoinositides in cell regulation and membrane dynamics[END_REF][START_REF] De Craene | Phosphoinositides, major actors in membrane trafficking and lipid signaling pathways[END_REF] .

Lateral organization of the PM

The spatial organization of the plasma membrane has remained a controversial topic, especially considering the biological relevance of observations made under nonphysiological conditions. Yet two main concepts that are now widely been accepted

involve the formation of short-lived, small lipid domains, termed 'lipid rafts' [START_REF] Simons | Functional rafts in cell membranes[END_REF][START_REF] Sezgin | The mystery of membrane organization: Composition, regulation and roles of lipid rafts[END_REF] , and spatial organization of the membrane via the underlying cytoskeletal network and connecting proteins, the 'picket-fence model' [START_REF] Kusumi | Paradigm shift of the plasma membrane concept from the two-dimensional II continuum fluid to the partitioned fluid: high-speed single-molecule tracking of membrane molecules[END_REF] .

The actin cytoskeleton

The eukaryotic cytoskeleton consists of different proteins able to form higher order, linear polymers. The current canonical members include microtubules, intermediate filaments, septins, and actin [START_REF] Mostowy | Septins: The fourth component of the cytoskeleton[END_REF] (Figure 3A, septin not displayed). Other proteins being able to form linear structures in vivo have been proposed to be included, e.g. cytidine triphosphate synthase filaments and Pil1 30 (Figure 3B). In this thesis we have worked only on actin and shall focus exclusively on actin from now on.

Nucleation and growth dynamics

Actin filaments are present in all eukaryotes and their structure is highly conserved throughout evolution [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] . The molecular building block is G-actin (globular actin), a protein of 42 kDa, consisting of four subdomains [START_REF] Otterbein | The crystal structure of uncomplexed actin in the ADP state[END_REF] , with a size of about 6 nm (Figure 4A). In humans, one can distinguish between highly specialized and stable actin fibers associated with Myosin II (actomyosin) optimized for contraction as present in muscle cells [START_REF] Szent-Györgyi | The Early History of the Biochemistry of Muscle Contraction[END_REF][START_REF] Banga | Myosin and Muscular Contraction[END_REF][START_REF] Balenovic | Ueber das Actomyosin des Kaninchenmuskels[END_REF][START_REF] Finck | On the Discovery of Actin[END_REF][START_REF] Halliburton | On muscle-plasma[END_REF] , and more diverse networks in non-muscle cells [START_REF] Herman | Actin isoforms[END_REF][START_REF] Perrin | The actin gene family: Function follows isoform[END_REF] . Non-muscle cells exhibit spatially segregated populations of different actin isoforms, with γ-actin being predominantly found in stress-fibers and actin arcs, while β-actin is preferentially incorporated into dynamic lamellipodial networks 40 , introduced hereafter. G-actin spontaneously forms polar filaments by polymerizing into a single-stranded, left-handed helix (Figure 4C). Growth is favored at the barbed end, a terminology dating back to the decoration of actin filaments with Myosin II subunits, yielding a pointed (-)

and barbed (+) end [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] when observed by electron microscopy (Figure 4C). At physiological concentrations, the difference in elongation kinetics at both extremities leads to a filament that is growing at the barbed and shrinking at the pointed end (Figure 4C). A steady-state filament of given length is thus constantly changing its microscopic constituents, and this flow of subunits along the filament is called 'treadmilling'. The total cellular concentration of actin has been estimated to be on the order of 100 μM, with roughly 70% being filamentous [START_REF] Abraham | The actin-based nanomachine at the leading edge of migrating cells[END_REF] .

Actin polymerization and different actin networks are controlled by multiple accessory proteins in cells (Figure 5). G-actin binding proteins, i.e. Thymosin-β-4 and profilin, control the available pool of free monomers [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] and differentially favor incorporation in either linear filaments or branched networks [START_REF] Suarez | Internetwork competition for monomers governs actin cytoskeleton organization[END_REF][START_REF] Suarez | Profilin regulates F-Actin network homeostasis by favoring formin over Arp2/3 complex[END_REF][START_REF] Burke | Homeostatic actin cytoskeleton networks are regulated by assembly factor competition for monomers[END_REF] . These two distinct morphologies, linear vs. branched, are generated by different proteins. Formins and other related proteins, e.g. Ena-VASP, bind to the barbed end and prevent capping of filaments, while still allowing elongation by addition of actin subunits. This 'leaky capping' leads to linear elongation of filaments [START_REF] Chesarone | Unleashing formins to remodel the actin and microtubule cytoskeletons[END_REF] , whereas the Arp2/3 complex, binds laterally to filaments and induces branching at 35 ° or 70 °, depending on the mechanical load [START_REF] Svitkina | Ultrastructure of the actin cytoskeleton[END_REF] . Arp2/3 is itself regulated by nucleation promoting factors, e.g. members of the WAVE complex [START_REF] Rotty | New insights into the regulation and cellular functions of the ARP2/3 complex[END_REF] .

Individual filaments can be assembled into higher order, parallel arrays by bundling proteins, e.g. fascin, leading to increased stiffness. Bundled actin filaments are found in a variety of cellular structures, e.g. membrane protrusions, stress fibers, and cell-cell junctions [START_REF] Stevenson | Actin-bundling proteins in cancer progression at a glance[END_REF] .

In order to maintain a dynamic equilibrium with free actin monomers, some proteins induce depolymerization of actin structures. These actin depolymerizing factors, e.g. cofilin and gelsolin, disassemble actin structures by severing and de-branching. The increased availability of barbed ends generates new nucleation points and maintains a stable pool of G-actin [START_REF] Kanellos | Cellular functions of the ADF/cofilin family at a glance[END_REF] .

Over the last decades in vitro approaches have been instrumental to identify and functionally characterize the numerous regulatory interaction partners of the actin cytoskeleton and have led to a good understanding of its basic biochemistry and biophysical properties. In cells, all the described networks and regulatory proteins coexist in a tightly regulated ecosystem of interactions. It is noteworthy that a lot of the described actin dynamics happen in proximity of cell membranes, on the one hand because key regulators are specifically localized to membranes, e.g. the plasma membrane through interactions with PI(4,5)P2, and on the other hand because signaling cascades lead to changes in actin dynamics in immediate vicinity to the plasma membrane (Figure 6).

Control of actin dynamics and network crosstalk.

Within cells all the described proteins regulating the dynamics of different actin networks coexist and require a system-wide control [START_REF] Michelot | Building distinct actin filament networks in a common cytoplasm[END_REF][START_REF] Goehring | Organelle growth control through limiting pools of cytoplasmic components[END_REF][START_REF] Mohapatra | The Limiting-Pool Mechanism Fails to Control the Size of Multiple Organelles[END_REF] . The control of these different functional actin networks is achieved through Rho GTPases [START_REF] Etienne-Manneville | Rho GTPases in cell biology[END_REF][START_REF] Ridley | Rho GTPase signalling in cell migration[END_REF] , e.g. Rho, Rac and Cdc42, which serve different functions yet share a common biochemical cycle of activation (Figure 6). Their recruitment to membranes in response to activation restricts their activity and induces actin dynamics generally close to membranes.

All of the different actin networks and their regulatory factor, together with signaling inputs create an intricate network of feedback loops which governs the balance between, e.g. branched and linear actin filaments, as shown in Figure 7 [START_REF] Suarez | Internetwork competition for monomers governs actin cytoskeleton organization[END_REF][START_REF] Suarez | Profilin regulates F-Actin network homeostasis by favoring formin over Arp2/3 complex[END_REF][START_REF] Burke | Homeostatic actin cytoskeleton networks are regulated by assembly factor competition for monomers[END_REF] .

Actin structures at the ventral surface

The actin cytoskeleton shows a remarkable morphological and functional complexity in cells [START_REF] Carlier | Global treadmilling coordinates actin turnover and controls the size of actin networks[END_REF] .

The ventral side of adherent cells is characterized by a complex actomyosin network with the presence of long bundles spanning multiple μm in length (Figure 8, Figure 9A).

One can distinguish dorsal fibers, that originate at focal adhesions and are generated in a formin-dependent manner, and transverse arcs which originate from annealing of actomyosin bundles in the lamella and are not linked to focal adhesions. Both structures can become stress fibers when the respective free end(s) is/are bound to focal adhesions [START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF] . Ventral stress fibers can connect and bridge adhesion sites [START_REF] Endlich | Movement of stress fibers away from focal adhesions identifies focal adhesions as sites of stress fiber assembly in stationary cells[END_REF][START_REF] Rossier | Force generated by actomyosin contraction builds bridges between adhesive contacts[END_REF] . They have been shown to be distinct in composition from cortical and lamellipodial networks by preferential incorporation of different actin isoforms [START_REF] Dugina | beta-and gammacytoplasmic actins display distinct distribution and functional diversity[END_REF] .

Adherent cells generate inward facing traction stresses on their substrate [START_REF] Burton | Keratocytes generate traction forces in two phases[END_REF] which are predominantly localized to the cell periphery [START_REF] Cai | Nonmuscle myosin IIA-dependent force inhibits cell spreading and drives F-actin flow[END_REF] . The generation of these stresses depends on Myosin II contractility [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterened substrates[END_REF] and limits cell spreading [START_REF] Cai | Nonmuscle myosin IIA-dependent force inhibits cell spreading and drives F-actin flow[END_REF] . Roughly two-thirds of contractile stresses originate from Myosin II isoform A, whereas isoform B accounts for one third [START_REF] Cai | Nonmuscle myosin IIA-dependent force inhibits cell spreading and drives F-actin flow[END_REF] . Efficient force transmission along the cell is necessary to achieve force balance on the cell scale and led to the concept of cytoskeletal coherence, which defines coherence as the ability of the highly dynamic actin network to establish force transmission that can span the entire cell body [START_REF] Cai | Force propagation across cells: mechanical coherence of dynamic cytoskeletons[END_REF] . By using the spreading process of adherent cells as a model for coherence, in which isotropic spreading occurs with remarkable symmetry, Myosin II was shown to establish and maintain such cell wide coherence of the ventral cytoskeletal network in adherent cells [START_REF] Cai | Cytoskeletal coherence requires myosin-IIA contractility[END_REF] .

2.4 Actin structures at the cell edge

Filopodia

At the cell edge, linear actin bundles can generate finger-like protrusions, e.g.

filopodia and microvilli [START_REF] Khurana | The role of actin bundling proteins in the assembly of filopodia in epithelial cells[END_REF] . Filopodia are dynamic, finger-like protrusions (Figure 8, Figure 9B) that serve a variety of cellular functions, e.g. establishment of focal adhesion points during migration or sensing of the environment [START_REF] Mattila | Filopodia: Molecular architecture and cellular functions[END_REF] . They consist of parallel actin filaments which are bundled by fascin, or related proteins, e.g. villin [START_REF] Khurana | The role of actin bundling proteins in the assembly of filopodia in epithelial cells[END_REF] . The origin of these parallel filaments remains debated as there is evidence supporting two main theories: The 'convergent elongation' model posits that actin filaments originating from Arp2/3 are bundled at the membrane and the elongation of that bundle, possibly through Ena-VASP, drives the formation of a filopodium [START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF] . The 'filament nucleation' model proposes the local, formin-based generation of new actin filaments at the nascent filopodial tip. It was notably based on the observation that filopodia form in absence of Arp2/3 [START_REF] Steffen | Filopodia formation in the absence of functional WAVE-and Arp2/3-complexes[END_REF] and the involvement of formins in the generation of filopodia [START_REF] Yang | Novel roles of formin mDia2 in lamellipodia and filopodia formation in motile cells[END_REF] . The motor proteins Myosin X is important for functional filopodia, probably due to its ability to control actin dynamics at the cell edge [START_REF] Tokuo | The motor activity of myosin-X promotes actin fiber convergence at the cell periphery to initiate filopodia formation[END_REF] , and is involved in transport along the filopodial core towards the tip [START_REF] Almagro | The motor protein myosin-X transports VE-cadherin along filopodia to allow the formation of early endothelial cell-cell contacts[END_REF] . Finally the 'inversed Bin/amphiphysin/Rvs' (I-BAR) domain containing proteins IRSp53 and MIM drive filopodia formation [START_REF] Mattila | Missing-in-metastasis and IRSp53 deform PI(4,5)P2-rich membranes by an inverse BAR domain-like mechanism[END_REF] . A mechanism has been proposed, based on the ability of I-BAR domains to sense negative membrane curvature, which could in turn locally stabilize membrane deformations followed by recruitment of actin nucleators to the nascent protrusion [START_REF] Prévost | IRSp53 senses negative membrane curvature and phase separates along membrane tubules[END_REF] .

Lamellipodia

Cells migrating in 2D often have a thin plasma membrane sheet (Figure 8, Figure 9C&D), called lamellipodium, which is, after decade spanning debate [START_REF] Small | Visualizing branched actin filaments in lamellipodia by electron tomography[END_REF][START_REF] Urban | Electron tomography reveals unbranched networks of actin filaments in lamellipodia[END_REF][START_REF] Small | Unravelling the structure of the lamellipodium[END_REF] , apparently characterized by a highly branched Arp2/3 driven network [START_REF] Svitkina | The Actin Cytoskeleton and Actin-Based Motility[END_REF][START_REF] Svitkina | Ultrastructure of protrusive actin filament arrays[END_REF] . Super-resolution imaging has been able to resolve two separate functional layers of actin within the lamellipodium, one that closely resembles the ventral surface of cells, and another one which is more dorsal and more homogenous [START_REF] Xu | Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton[END_REF] . The lamellipodial actin network is characterized by cycles of extension and contraction [START_REF] Giannone | Periodic lamellipodial contractions correlate with rearward actin waves[END_REF] and is separated kinetically from an underlying, less dynamic yet more persistent 'lamella', as established by analysis of actin flow profiles [START_REF] Ponti | Two distinct actin networks drive the protrusion of migrating cells[END_REF] . The transition between these zones is characterized by assembly of actin arcs, which are created from retrograde actin originating in the lamellipodium by Myosin II driven bundling [START_REF] Burnette | A role for actin arcs in the leading-edge advance of migrating cells[END_REF] .

Cell migration

Much of our understanding considering how cells move is based on work performed on adhesive 2-dimensional substrates with keratocytes which are both stereotypic in shape and highly motile. In these cells, both cell shape and movement can be predicted at astonishingly high accuracy by taking into account only the interaction between dynamic actin growth towards the cell edge and deformation of the excess plasma membrane [START_REF] Keren | Mechanism of shape determination in motile cells[END_REF] . Plasma membrane-localized actin regulators, e.g. Ena-VASP, are important under these conditions, and their mislocalization leads to reduced motional persistence and altered leading edge shape [START_REF] Lacayo | Emergence of large-scale cell morphology and movement from local actin filament growth dynamics[END_REF] . Furthermore, Myosin II is important for symmetry breaking of actin to engage in motion [START_REF] Yam | Actin-myosin network reorganization breaks symmetry at the cell rear to spontaneously initiate polarized cell motility[END_REF] and drives the depolymerization of actin at the cell rear leading to a cell spanning actin flow [START_REF] Wilson | Myosin II contributes to cell-scale actin network treadmilling through network disassembly[END_REF] . In keratocyte-derived lamellipodial fragments, decreasing actin density towards the rear has been hypothesized to be sufficient by itself to reach a threshold mechanical sensitivity where membrane tension alone can induce network collapse at the rear, thus theoretically allowing for a motion that only involves actin dynamics and a membrane [START_REF] Ofer | Actin disassembly clock determines shape and speed of lamellipodial fragments[END_REF][START_REF] Mogilner | Actin disassembly 'clock' and membrane tension determine cell shape and turning: A mathematical model[END_REF] .

Retrograde flow is defined as the property of actin structures to move 'backwards' from the barbed end. Beyond the effect of the previously described tread milling that is inherent for actin, Myosin II can have an additional effect on this retrograde flow.

Blocking Myosin II activity with Blebbistatin can decrease retrograde flow by around 50 % in neuronal growth cones and is responsible for severing of actin bundles in the lamella [START_REF] Medeiros | Myosin II functions in actin-bundle turnover in neuronal growth cones[END_REF] . The retrograde flow is slowed down by counteracting Arp2/3 activity [START_REF] Yang | Arp2/3 complex-dependent actin networks constrain myosin II function in driving retrograde actin flow[END_REF] . In line with these results, siRNA depletion of both Myosin II isoforms A & B in CHO cells leads to altered protrusion and retraction behavior of the lamellipodium, while each isoform has additional, specific effects [START_REF] Vicente-Manzanares | Regulation of protrusion, adhesion dynamics, and polarity by myosins IIA and IIB in migrating cells[END_REF] . In fibroblasts, only Myosin II A affects retrograde flow significantly [START_REF] Cai | Nonmuscle myosin IIA-dependent force inhibits cell spreading and drives F-actin flow[END_REF] .

Yet, some cells can also move without extensive generation of traction forces on the underlying substrate through actin at the leading edge in an adhesion independent way. Such motion is generally referred to as 'amoeboid' (Figure 10), yet it is found in a variety of cells from vegetative Dictyostelium discoideum 92 cells to leukocytes [START_REF] Smith | Neutrophil traction stresses are concentrated in the uropod during migration[END_REF] , and in 3-dimensional environments. While the term amoeboid covers a variety of motion mechanisms, it generally critically depends on Myosin II contractility located at the back of the cell and creates blebbing at the cell front [START_REF] Lämmermann | Mechanical modes of 'amoeboid' cell migration[END_REF] . By changing the balance between actin polymerization and contractility, cells can switch between both types of motion in a dynamic way [START_REF] Bergert | Cell mechanics control rapid transitions between blebs and lamellipodia during migration[END_REF] .

Actomyosin contractility 2.6.1 In vitro

In vitro assemblies of Myosin II and actin tend to self-organize, first by creating local foci of high Myosin II densities, followed by generation of an actin shells through coalescence of the foci 96 (Figure 11D). Myosin II activity depends on local actin geometry, notably the orientation of the polar actin filaments relative to each other, i.e.

parallel vs antiparallel, where contractile efficiency scales with the relative abundance of antiparallel filaments [START_REF] Reymann | Actin network architecture can determine myosin motor activity[END_REF] . The generation of contractility and its dominance over extension has been explained considering different geometries and dimensionalities by filament buckling (Figure 11 A-C) [START_REF] Lenz | Contractile units in disordered actomyosin bundles arise from f-actin buckling[END_REF][START_REF] Lenz | Requirements for contractility in disordered cytoskeletal bundles[END_REF] , high Young's moduli [START_REF] Soares E Silva | Active multistage coarsening of actin networks driven by myosin motors[END_REF] , or independently of these two phenomena, because random networks with contractile stresses have lower energy than those with expansive stresses 100 . In vitro experiments confirmed that Myosin II induces actin buckling, buckling-dependent severing, and describe an increased severing rate of phalloidin-stabilized F-actin due to local attachment to the membrane 101 .

In vivo

In the cellular context, both extensile and contractile actomyosin filaments might be expected due to different filament polarities, yet predominantly contraction has been observed 102 , corresponding to highly polarized inward-facing traction forces on the substrate (Figure 11E). Recent theoretical work suggests that nevertheless efficient extensile fibers might exist in vivo 103 . It has been suggested that formin-enriched nodes account for optimized contractile network properties in vivo because they could create high densities of anti-parallel branch encounters 104 . Indeed such actin asters concentrated around local nodes have been visualized at the ventral surface of cells using advanced imaging [START_REF] Xu | Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton[END_REF] . In order to create contractile stresses, Myosin II gets

The cellular cortex governs cellular mechanics

Seminal work by Warren H. Lewis in 1939 proposed the presence of a superficial contractile 'plasmagel' layer, which would be under tension and play a fundamental role in cell movement and shape 106,107 . Actin was identified as the key protein in this functional layer 108,109 , called the 'cortex'. Part of the cortex is the membrane skeleton, a composite of actin and accessory proteins that forms a corralling network at immediate apposition to the plasma membrane, only few nanometers apart 110 . It consists of a branched actin network and highly dynamic small actin filaments 111 .

As the actin network is much stiffer than the plasma membrane 112 , it is the cortex that defines cell shape 113 and confers a mechanical stability to cells towards external

Plasma membrane-actin linkers

Many receptors residing in the plasma membrane have cytosolic domains that directly or indirectly lead to attachment to this actin cortex, and both layers are in close proximity and mechanically interconnected 132 . Furthermore, specific peripheral proteins link the plasma membrane and the actin cytoskeleton (Figure 12). The importance of connections between the membrane and actin is highlighted by the fact that embryo cell shape changes during early development both in Caenorhabditis elegans and Drosophila melanogaster are not induced by ad hoc generation of From left to right : Direct interaction between a transmembrane protein and actin, coupling via an adaptor / adaptor complex, direct binding of a peripheral protein to both actin and the plasma membrane, or via an adaptor complex. Adapted from reference 135 actomyosin contractility. Rather, pre-existing contractility is exploited during apical constriction, probably through increased linkage of the membrane to the underlying cortex 133 .

In general all these proteins share a domain architecture which enables them to bind both the plasma membrane and actin filaments 134,135 . Within this group one can emphasize three particular groups:

 BAR domain proteins sense membrane curvature through their peculiar shape and bridge actin dynamics to membranes with specific curvature.

 Class 1 myosins are monomeric motor proteins that act in conjunction with bound light chains, fulfil a wide range of cellular functions and, for certain subtypes, show sensitivity to external forces.

 Ezrin-Radixin-Moesin (ERM) proteins bridge the cortex and are involved in bleb behavior and the formation and maintenance of the immunological synapse.

Many of these proteins are recruited specifically via binding domains for PI(4,5)P2

which is highly enriched at the plasma membrane 10 , yet other ways of plasma membrane recruitment exist, e.g. via electrostatic interactions with phosphatidylserine.

The importance of PI (4,5)P2 for cortex integrity is illustrated by the effects of competitively masking PI (4,5)P2 by overexpression of PH domains 136,137 , or neomycin treatment 138 . Furthermore, the interaction with the plasma membrane can be mediated indirectly by, e.g. interaction between an actin binding protein and the cytosolic domain of a trans-membrane receptor in response to biochemical cues, thus locally increasing connectivity to the underlying actin.

In this thesis we have focused on two of the above mentioned protein families: Class 1 Myosins and ERM.

Class 1 Myosins

Early work on the microvilli-covered surface of enterocytes identified proteinaceous cross-bridges connecting the plasma membrane to underlying actin structures 139,140 .

Addition of a 110 kDa protein to actin bundles in vitro reconstituted the regular pattern of cross bridges along the actin core 141 and was the first vertebrate myosin 1 to be identified 142,143 . The Myosin 1 family consists of, to this date, 8 (subtypes a -h) singleheaded, monomeric motor proteins that bind calmodulin or related calmodulin-like light chains 144 . All class 1 myosins comprise a motor domain at the N-terminus that is linked to a tail domain by a regulatory neck domain, which serves as a lever arm for force transmission 145 (Figure 13A). Class 1 myosins bind to negative membrane lipids and interact with actin in an ATP-dependent way [146][147][148] . Based on their tail structure, members of the myosin 1 family can be sub-grouped into short-and long-tailed myosin 1s 149 . The length of the tail domain correlates with their ATP turnover rates. Long-tailed isoforms, i.e. e and f, have short actin binding lifetimes, while short-tailed myosin 1, i.e.

a-d, g, and h, have long actin-bound lifetimes 150 .

While many class 1 myosins show cell-type specific expression profiles, both myosin 1b and myosin 1c are found in virtually all cells. The following introduction thus primarily focuses on these two myosin 1s.

Conserved motor and variable regulatory neck domain.

The motor domain of myosin 1 is highly conserved and shares structural homology with myosin II 151 . Its ATPase activity is regulated by calcium ions and binding of calmodulin to the regulatory neck 142,[152][153][154][155][156][157][158] . Calmodulin binding is mediated by IQ domains, a common domain that shares a pattern in amino acid composition 159 . The identification of mammalian myosin 1b revealed the existence of splice isoforms that differ in the number of calmodulin-binding sites 160 .

3.1.2 Catch-bond behavior of myosin 1.

Kinetic analysis of short-tailed myosin 1s showed that they have prolonged actin attachment times in comparison to other myosin classes. This suggested that they might be involved in tension maintenance and sensing 161,162 . The length of the lever arm and its large 30° rotation required for ADP release suggested force dependent behavior for myosin 1s. An opposing force to this large rotation could hinder the release of ADP, thus prolonging the actin bound state, as a function of lever arm length 163,164 .

This was confirmed by single molecule studies in vitro showing that Myosin 1b detachment from actin decreased by almost two orders of magnitude when experiencing loads of around 2 pN 165 and that force sensing is controlled both by the lever arm length 166 and the binding of calcium to calmodulin 167 (Figure 14). Alternative splice isoforms of myosin 1b have different numbers of IQ motifs with different binding affinities for calmodulin. Calmodulin binding stabilizes the lever arm and is important for the in vitro motility of myosin 1b 168 .

A bond with prolonged lifetime with increasing force, up to a critical point, is called 'catch bond', in contrast to 'slip bonds' whose detachment increases with increasing force. Recent crystallographic evidence confirms the role of lever arm rotation in controlling the release of ADP and thus mechanistically explains myosin 1b's high sensitivity to external force 169 . Myosin 1c, although qualitatively similar, is less sensitive to calmodulin, calcium 170 and much less strain-sensitive 171,172 (Figure 13B&C). In comparison to unloaded conditions, Myosin 1b detaches 100 times slower from actin 165 , whereas Myosin 1c only slows down by a factor of 5 171 . Myosin 1c's mechanism of tension sensing is different from Myosin 1b and depends on the isomerization upon binding of ATP 171 , rather than ADP release (Figure 13B). This

Tail domains drive lipid interactions and govern function.

Myosin 1s share a 'tail-homology' domain, characterized by high density of positive charges 175,176 , yet tail length varies between isoforms. Myosin 1b binds specifically to phosphoinositides, i.e. PI(4,5)P2 and PI (3,4,5)P3, through a non-canonical pleckstrin homology domain 177 , while Myosin 1c preferentially binds to the PI(4,5)P2 headgroup.

Pleckstrin homology domains allow specific binding to phosphoinositides 178 via a β1loop-β2 structure 179,180 . Myosin 1c binds phosphatidylserine only at un-physiologically high concentrations 181,182 , yet Myosin 1e binds anionic phospholipids, including The binding strength between Myosin 1c and PI (4,5)P2 is in the range of 6 to 16 pN and thus below the force required for lipid extraction that is around 27 pN at equivalent force loading rates 184,185 .

3.1.4 Myosin 1's cellular functions converge towards actin.

When looking at the scientific literature involving myosin 1, it is striking to see an impressive plethora of different cellular functions that are affected by class 1 myosins.

While little mechanistic insight exists so far, all the different observed phenotypes converge towards a role regarding the control/interaction with dynamic actin.

As mentioned above, we focus mainly on the ubiquitously expressed myosin 1b and myosin 1c. They should a priori be expected to have a more general function as they are found in virtually all cell types.

Myosin 1b

Myosin 1b concentrates to membranes ruffles at the leading edge of cells, yet it is excluded from stable actin bundles and stress fibers due to negative regulation by tropomyosin 186 . The recruitment towards actin-rich protrusions depends on its binding to PI(4,5)P2 177 . Furthermore it is enriched in the mitotic cleavage furrow 187 . Myosin 1b regulates endosomal traffic and morphology 2 , lysosome positioning 188 , and is involved in trans-Golgi-network membrane remodeling through interaction with actin filaments [START_REF] Almeida | Myosin 1b promotes the formation of post-Golgi carriers by regulating actin assembly and membrane remodelling at the trans-Golgi network[END_REF] .

Furthermore, it is found in the developing brain and required for axon formation, likely by changing the dynamics of actin waves and the actin network in the growth cone [START_REF] Iuliano | Myosin 1b promotes axon formation by regulating actin wave propagation and growth cone dynamics[END_REF] .

Myosin 1b also functions as an effector of EphB2 and controls the efficiency of cell repulsion and dynamic actin structures 3 after EphB2 activation. Myosin 1b is involved in secretory granule biogenesis 189 and together with myosin 1c in surfactant exocytosis 190 . Its deregulation has been implied in cancer progression 191,192

Myosin 1c

Myosin 1c is found in membrane protrusions in B cells and recruited to the

Other short-tail class 1 myosins

In the brush border both myosin 1a and myosin 1d are expressed, yet they show distinct localization profiles, which seem to be governed by competitive binding along the actin core of the microvillus 196 . Myosin 1a regulates vesicle shedding at microvillar tips in isolated brush borders after ATP addition 197 . It furthermore affects the characteristic tether length upon elongation from microvilli and changes the propensity to form multiple tubes and their coalescence dynamics [START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] .

Myosin 1g is recruited to the plasma membrane of lymphocytes through its PH domain 198 . It controls meandering motility with higher average speeds and polarization dynamics 199 . CD44 surface levels and recycling depend on myosin 1g 200 .

Finally, myosin 1d is found in the developing brain 201 and is involved in laterality determination 202 .

Long-tail class 1 myosins

Myosin 1e is localized to the lamellipodial tip and affects actin dynamics and the formation of adhesions 203 . Myosin 1e is involved in Xenopus laevis cortical granule exocytosis, possibly controlling actin distribution around the coat 204,205 . Furthermore, via its SH3 domain, it interacts with synaptojanin-1 and dynamin and is involved in receptor endocytosis 206 .

Myosin 1f regulates adhesion in neutrophils and slightly affects cortex thickness, i.e.

KO cells are more adhesive and have a thinner cortex 207 . During the early steps of yeast endocytosis the long-tailed class 1 myosin Myo5 is localized at both the tip and base of buds with actin 208,209 .

Reported mechanical effects of class 1 myosins

Several studies have identified effects of class 1 myosins on cellular mechanics, notably effective membrane tension and cell stiffness.

In prechordal plate progenitor cells from Danio rerio, myosin 1b depletion reduces effective membrane tension, increases blebbing propensity and respective bleb sizes [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF] .

Myosin 1c ensembles are able to generate pN forces parallel to lipid bilayers 210 .

Myosin 1a influences effective membrane tension in enterocytes [START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] , and within this report the authors provide data that is represented in a way that suggests an effect on the coalescence behavior of multiple tubes for all myosin 1 subtypes 7 . Myosin 1g depletion leads to a decrease in cell elasticity in Jurkat cells 211 , furthermore it is involved in Blymphocyte stiffness 212 and regulates effective membrane tension in lymphocytes 199 . In a similar fashion, cortical tension in Dictyostelium discoideum is reduced upon depletion of myosin 1, but only when depleting two isoforms at the same time, while single overexpression does lead to significant effects 213 .

In conclusion, myosin 1b bridges the actin cortex to the plasma membrane and is a likely candidate to dynamically respond to force due to its catch bond property. In contrast to myosin 1c its biochemical properties suggest that it is best suited to serve as an anchor between the plasma membrane and actin. Its described cellular roles point to two main directions: On the one hand it might change the plasma membrane's mechanical properties, e.g. effective membrane tension. On the other hand many observations suggest an effect on actin dynamics.

Ezrin-Radixin-Moesin

In contrast to class 1 myosins, Ezrin-Radixin-Moesin (ERM) do not have a motor

domain, yet they are also consistently involved in cellular processes that depend on actin dynamics and the linkage between the plasma membrane and actin, notably in the spatial organization of the immunological synapse, i.e. the interaction interface between a lymphocyte and a target or antigen presenting cell.

ERM link actin to the plasma membrane.

The ERM family 214 has initially been described in the context of epithelial membrane protrusions 215,216 , controlling their morphogenesis during development [217][218][219] and in cell culture 220,221 . Based on a common ancestral protein The ERM family is characterized by a general architecture in three domains 222 (Figure 15A). Their C-terminus has an actin-binding domain 226 , yet it is auto-inhibited by interaction with its own N-terminus [227][228][229][230][231] . Unmasking of the actin-binding domain depends on threonine phosphorylation at the C-terminus [232][233][234] and PI(4,5)P2 binding 235 (Figure 15B). These two events act sequentially 236 and in synergy 237 . This sequential activation permits binding of the N-terminal FERM domain to PI (4,5)P2 and binding of its C-terminus to actin. Moesin has been implicated in the mechanical rigidity and organization of the cell cortex during mitosis [238][239][240] , potentially by aligning the plasma membrane and actin filaments 239 . Furthermore, in the developing zebrafish mesendoderm, ezrin depletion reduces effective membrane tension and friction between the plasma membrane and the cortex, while increasing membrane bleb frequency [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF] . In cultured mammalian cells, ezrin and moesin are found in stabilized blebs, and ezrin precedes actin cortex formation before bleb retraction 241 . In epithelial kidney cells, ezrin changes cell height and stiffness 242 . Phosphomimetic ezrin (T567E) increases effective membrane tension in lymphocytes and slows migratory speed 243 .

ERM controls spatial organization of receptors.

Beyond their mechanical role at the cortex, ERM proteins have been implicated in cellular signaling 244 . ERM proteins interact with the polybasic cytoplasmic domain of CD44 245,246 , CD43, ICAM-2, which has been proposed as a general mode of interaction between receptors and ERM proteins 247 . In subsequent studies, this interaction was linked to microvillar growth in response to epidermal growth factor stimulation 248 .

Interaction of ERM with both actin and CD44 was shown to be required for Ras activation downstream of hepatocyte growth factor, proposing an active role of actin in signal transduction 249 .

In lymphocytes, ERM influence cell morphology 250 , polarity establishment 251 On a side note, from an evolutionary perspective, ERM proteins are intriguing, as the FERM domain arose in conjunction with cadherin and receptor tyrosine kinases, thus suggesting a potential co-evolution between adhesion, signaling, and FERM domains 244 .

Plasma membrane blebbing

While general membrane deformation is generally driven by actin-generated pushing forces, one notable exception is membrane blebbing. A bleb is defined as a plasma membrane protrusion that is detached from the underlying actin cortex and assumes a roughly spherical shape due to hydrostatic pressure (Figure 16). First descriptions of blebs can be found associated to osmotic shocks on fibroblasts 263 . While being a hallmark of apoptotic/necrotic processes 264 , blebbing can occur under physiological conditions as well [265][266][267][268] . It can account for motion in the amoeboid mode, e.g. in While lamellipodial protrusion based motion depends on Rac signaling, amoeboid motion is independent of Rac, yet depends on Rho/ROCK 273 and requires Ezrin 274 . In (Figure 16B). In agreement with the establishment of a new cortex, the retracting bleb is more rigid than the expanding one 280 . The fact that an initially free plasma membrane is decorated with a functional cortex has established blebs as a model system to study the composition of the cell cortex using proteomic approaches, showing enrichment in actin and actin-regulating proteins, as well as plasma membrane-actin linkers 282 . The finding that both the formin mDia1 and the Arp2/3 complex contribute to cortical actin in M2 melanoma cells suggests the co-existence of two, probably interacting, actin networks which control blebbing propensity and dynamics 283 .

Dictyostelium discoideum

Eph receptors 4.1 Introduction

The Eph receptors, overexpressed in an erythropoietin-producing human hepatocellular carcinoma (hence its name), were first identified as a putative new class of receptor tyrosine kinase by inference from homologies with different growth factor receptors. They are overexpressed in a variety of cancers, i.e. colon carcinoma, lung adenocarcinoma; and mammary carcinoma 284 . For reasons of clarity, a coherent nomenclature has been agreed on: Ligands are named ephrins (Eph family receptor interacting proteins ), and receptors are named Eph receptors 285 (Figure 17A). Different screening methods led to identification of two subclasses, represented by Elk (EphB1)

and Eck (EphA2) respectively, that show tissue-specific expression profiles 286,287 . EphB receptors are evolutionary conserved structures found in Hydra where they show opposing gradients along tissue boundaries 288 .

The ephrins can be divided into two main subclasses, i.e. GPI-anchored proteins (ephrin-As), and transmembrane proteins (ephrin-Bs) 285 (Figure 17B). The different Eph receptors are separated into groups according to their relative affinity for these two ligand classes: Generally EphA receptors preferentially bind ephrin-As, and EphB receptors bind ephrin-Bs due to differences in their structure [289][290][291][292] , yet there are notable exceptions to this, e.g. ephrin-A5 can bind to EphB2 receptors 293 .

A first subclass of ephrins showed only weak activation of the receptor, i.e. large quantities of soluble ligand were needed to achieve efficient phosphorylation. This

finding was explained by a potential requirement for membrane binding of the ligand via a GPI-anchor for full activation 294 . In line with this finding, efficient activation requires membrane-bound or artificially clustered ligands. The requirement of ligands to be pre-clustered or membrane-bound suggests that ligand dimerization and/or aggregation at a membrane is of critical importance for efficient stimulation of Eph receptors and thus establishes a role of Eph receptor signaling in cell-to-cell communication (Figure 17C). The different ligands were shown to be specific yet overlapping in their receptor binding behavior 295 .

Bidirectional signaling in the Eph/ephrin system

The ligand itself is phosphorylated in response to Eph receptor binding, and can act as a signaling molecule itself, thus Eph receptor and ligand contact can induce bidirectional signaling 296-299 (Figure 18A). By convention, signaling that happens downstream of the Eph receptor is called 'forward signaling', while signaling downstream of ephrins is called 'reverse signalling' 300 . As most detail is known about the B subclass of receptors, and we have worked on the functional interaction between Myosin 1b and EphB2, the following paragraphs are mainly focusing on the EphB receptor subtype.

Evidence from crystal structures indicates that clustering of receptors is indeed an inherent property, driven by initial hetero-dimerization between ligand and receptor (EphB2 and ephrin-B2), with subsequent formation of tetramers and higher-order structures, in which each ligand can be bound by two receptors 301 . Cellular response to stimulation with ephrin-B1 is sensitive to differences in ligand oligomerization state 302,303 and density 304 . Notably, phospho-tyrosine phosphatase is recruited only upon stimulation with multimeric/tetrameric ligands, but not with dimers 302 .

Comparative studies have shown that accordingly only clustered ephrin-B1 induces growth cone collapse. In inversed signaling conditions, i.e. EphB2 being the ligand for ephrin-B, only unclustered EphB2 led to similar phenotypes 305 .

The recruitment of receptors into an existing cluster, i.e. condensation or cluster propagation, does not depend on direct ligand binding, i.e. 'free' receptors can be recruited into an existing cluster without the need to interact with a ligand themselves 306 . Interaction sites that allow these homotypic receptor interactions have been identified by crystallography 307,308 . Furthermore, different receptors tend to form clusters of different sizes 309 . Artificial clustering of EphB2 shows that receptor dimers are weakly phosphorylated, yet trimers and higher order oligomers show comparably high phosphorylation levels. This led to a proposed critical threshold of receptor trimers required for efficient activation, in which the relative amount of multimers determines signaling output 310 . Analysis of EphB2 cluster size distributions after stimulation with immobile, nano-clustered ephrin-B1 311 for 60 minutes revealed a switch from a trimer dominated population, to a broad distribution with 28-mers as average clusters.

Kinase-deficient receptor strikingly only assembled into a well-peaked distribution around 12-mers. This cluster distribution was changed fundamentally when stimulating with soluble, pre-clustered ligands, yielding a switch from heptamers (unstimulated) towards 11-mers and 22-mers, for the case of kinase-deficient and wildtype EphB2 respectively 312 .

Trafficking and phosphatase activity control the effective receptor surface concentration

Just like other receptor tyrosine kinases, Eph receptors can phosphorylate each other at a low basal level without ligand binding. It has been shown for EphA that such receptors are recycled through vesicular trafficking, dephosphorylated in the perinuclear region by the phosphatase PTP1B, and then recycled to the plasma membrane. This cycle was suggested to maintain a ligand-sensitive pool at the plasma membrane. Ubiquitination of EphA after ligand binding switches the transport towards the lysosome 313 . In the case of EphA3, dephosphorylation by PTP1B can happen directly at the membrane 314 . In a similar way, negative regulation of the epidermal growth factor receptor (EGFR) membrane recycling by Eph has been described, which modulates EGFR signaling outcome 315 .

Tissue patterning and homeostasis

Different Eph receptors are involved in patterning and maintenance of homeostasis in a variety of tissues 316 . During development, Eph-signaling is involved in embryonic tissue separation 317,318 . EphB2 and EphB3 in conjunction with their ligand ephrin-B1 maintain separation of stem cells from differentiated cell types in the colon by directing cell migration 319,320 , and controlling proliferation rates 320-322 (Figure 19). In agreement with these findings they can act as tumor supressors 323,324 and potential therapeutic target 320,325,326 . In contrast, ephrin-B2 activation of EphB3 and EphB4 abolishes contact inhibition of locomotion in prostate cancer cells 327

Retinal development depends on multiple Eph receptors 328 . Experiments in the mouse retina evidenced the generation of gradients for different receptors [329][330][331] . Yet, even at uniform distribution prior to any gradient generation, axon pathfinding is impaired, independently of EphB2's kinase activity 332 Opposing gradients could be observed for corresponding ligands, and subclasses A and B distributed separately along perpendicular axes. This suggested that Eph receptors and their ligands could specify tissue organization and guide cell fate decisions along gradients 333 . Taken together, these results suggest that the Eph system can not only drive cellular behavior along gradients, but can establish these gradients de novo from homogeneous cell populations. During wound healing ephrin-B1 allows for re-epithelialization by reducing cortical tension and cell-cell adhesion 334 By exploiting different splice isoforms, repulsive signals by Eph-ephrin interaction can be shifted to adhesion, notably through the loss/removal of Eph's kinase domain 340 . Similarly, synaptogenesis and synaptic plasticity do strongly depend on

EphB2, yet are independent of its kinase activity 341,342 Activation of Eph receptors can induce repulsive signals, inducing neuronal growth cone collapse and axon guidance both in vitro 343,344 and in vivo 342,344 , and positioning of cells in the brain 345 . Similarly, reverse signaling through ephrin-B1 is involved in axon guidance in mice 346 . In vivo it is required for patterning of the somite 347,348 and the skeleton 349 . It induces cell sorting in zebrafish embryos 350 , after bidirectional signaling 351 . In the developing brain cell segregation is independent of reverse signaling 336 . Modeling and experiments suggest that heterotypic repulsion is necessary and sufficient to achieve cell segregation and border sharpening 352,353 , even independently of EphB2 kinase activity 353 . The establishment of tissue boundaries involves supra-cellular, long-range force generation and leads to propagation of mechanical waves, independently of specific signals 354 .

Switching from strong adhesion to repulsion.

Cell repulsion mediated by Eph/ephrin follows the fundamental stages of contact inhibition of locomotion 355 (Figure 20). In cell culture contact between two cells expressing the ligand and receptor respectively, increases membrane ruffling and an increase in tyrosine phosphorylation at the interface is followed by cellular retraction.

Separation of engaged receptor -ligand complexes is achieved through full length clathrin-mediated 356 trans-endocytosis of either receptor or ligand in the case of the B subclass. The directionality of this endocytic activity depends on the cell type [357][358][359] .

Receptor clusters can preferentially localize to filopodia 358 , and increase actin dynamics by activating Rac 357,359 . In subclass A, metalloproteases, e.g. ADAM10, cleave the ligand in trans conformation (i.e. the metalloprotease is located on the outer leaflet of the receptor expressing cell and cleaves the ligand) 360,361 . Metalloprotease-based cleavage of EphB2 in response to stimulation with ephrin-B2 has also been reported 362 . ADAM10

has furthermore been involved in cleavage of E-cadherin thus further facilitating separation of cell-cell contacts downstream of EphB activation 363 .

Eph signaling drives actin dynamics.

Activation of Eph receptors feeds into Rac and RhoA signaling 317 (Figure 18B).

Thereby, stimulation induces cytoskeletal rearrangements that lead to cell retraction, characterized by reversible lamellipodial collapse dependent on Cdc42 303 and Myosin II contractility. Optogenetic activation has allowed the local activation under controlled conditions. In cell culture, stimulation of EphB2 induces cell rounding and deadhesion 339 . The deadhesion can be explained by altered FAK signaling 364,365 . Ligandbound EphA receptors experience radial flow originating from actomyosin contractility, and tend to be assembled into large scale aggregates if not hindered by mechanical resistance [366][367][368] . CD44 was shown to be excluded from EphA clusters 366 . In order to allow re-spreading after stimulation-induced deadhesion, the internalization of receptor-ligand complexes is important, probably because engaged signaling hubs need to be deactivated as described before 369 . The resulting 500 μL of transfection mix was added to the corresponding well, containing 1.5 mL freshly added, pre-warmed full medium.

Transfection

For depletion of Myo1b and the respective control, 125000 cells were seeded per well in a 6 well plate (TPP 92006) 24 hours prior transfection. A final concentration of 15 nM siRNA was used. Cells were assessed ~48 hours after transfection. For depletion of Ezrin, ERM, and respective controls, 80000 cells were seeded out 24h prior treatment and transfected twice, the secondary transfection following 48 hours after the first.

Cells were assessed after a total of ~96 hours. The respective concentrations of siRNA were 20 nM for Ezrin, and 10 nM for each siRNA of Ezrin, Radixin, and Moesin, thus yielding a total of 30 nM for ERM depletion.

Drug treatments

Part A

LatrunculinA (LatA) (Sigma L5163) was used at 100 nM for 20 minutes, and S-nitro-Blebbistatin (BS) (Cayman Chemical 13891) at 20 μM for 15 minutes at 37 °C before the respective measurements. In both cases, DMSO concentration within the cell medium was at 0.1%, as in the corresponding DMSO control.

Part B

In the FRAP experiments, all drugs were used at a final dilution of 1:1000 (corresponding to 0. Penta-chloro-pseudilin (PClP) treatment for TIRF-SIM datasets was done at 1 μM for 30 minutes before imaging and stimulation.

Optical Tweezer

The The glass cover slips were fixed on a custom-made experimental chamber using vacuum grease (Sigma Z273554). The cells were maintained in experimental medium throughout the experiment supplemented with carboxylated polystyrene beads (Spherotech CP-30-10, 3.07 μm nominal diameter, 0.001 % suspension) used for tether pulling. The temperature was maintained at ~37 °C throughout the experiment using a custom-built objective-heater based on a resistive collar.

Bead tracking

Image sequences of the bead were used to track its position over time using a simple MATLAB script, by fitting a circle to the bead. See Annex for the used code.

Tube pulling from cells

Using a custom LabVIEW program to control the piezo stage, tubes were pulled, by trapping an isolated floating bead, bringing it into contact with the cell for a short period (~3 seconds), and then moving the cell away from the trap center in x direction using the piezo. For measuring the static tether force, the tube was about 10 μm long and held steady for at least 10 seconds. For the dynamical force measurements, the initial tether had a length of about 10 μm. While the initial force overshoot for tether formation varied widely, a relaxation of the force to a stable plateau could generally be observed within the first 10 seconds after tube formation.

Tether step elongations

Once the tether holding force was stabilized, step elongation of the tube was performed by imposing a step-displacement of the piezo stage away from the trap center of 5 μm at a speed of 75 μm/s. The force relaxation was then recorded.

The change in force is monitored by imaging the bead holding the tube at high temporal resolution (175 fps). This allows following the peak in force upon step elongation and the subsequent relaxation.

Exclusion of data sets for tube elongation

Tube elongations, in which bead displacements perpendicular to the pulling direction larger than 1 pixel were detected, were not assessed.

Constant elongation

Once the tether holding force was stabilized, constant speed elongation of the tube was performed by imposing a continuous displacement of the piezo stage away from the trap center at a speed ranging between 0.1 and 15 μm/s and adjusting the displacement to allow detection of the plateau (between 2 μm at 0.1 μm/s and 40 μm at 15 μm/s). The force was continuously monitored by imaging the bead holding the tube at 95 frames per second.

Micropipette aspiration

Cells were grown to confluency on Laminin-coated glass coverslips in order to yield cells of sufficient height to allow approaching a micropipette roughly parallel to their side. 45 minutes before the experiment the coverslip was scratched manually with a fine forceps to create cell free areas. Pipets with a diameter of roughly 5 μm were used.

By controlling the basin height and initial establishment of the null position at which no net flow was observable, a quantifiable suction pressure was created and the cell was brought in contact with the micropipette, using the micropipette micromanipulators. Bleb formation was considered to happen if a clear protrusion formed inside the pipet within 2 seconds of cell contact to the micropipette.

Stimulation of EphB2 with ephrin-B1

Global Ephrin-B1 (200 g/mL in PBS, R&D systems 7654-EB) was pre-clustered with goat anti-human IgG Fc (molar ratio 2:1, i.e. 9 g ephrin-B1:6.75 g anti-IgG; Jackson ImmunoResearch 109-005-098) for 1h on ice; pre-diluted in 500 L serum-free DMEM and used at 1 μg/mL final ephrin-B1 concentration.

Local

In this case, we used beads coated with Ephrin-B1tethered to a lipid bilayer. The bead coating was achieved as follows: SUVs were formed from a 200 µg lipid mixture containing EggPC 97.9%, DOGS Ni-NTA 2%, BodipyTexasRed Ceramide 0.1%, w/w. The lipid mixture was dried under nitrogen until all solvent had evaporated, and subsequently left in a vacuum for 30 minutes to ensure full evaporation. 100 µL SLB buffer (10 mM HEPES, 150 mM NaCl, pH 7.4) was added to the dried lipids and left at room temperature for 30 minutes for rehydration. Vortexing of the solution gave an opaque liquid that was sonicated in a sonicator bath for 5 minutes, which was sufficient to yield a translucent SUV solution. The SUV solution was stored at -20 °C for up to 2 months in aliquots of 10 µL. A 10 µL SUV aliquot was diluted with 140 µL SLB buffer and sonicated for 3 minutes in a sonicator bath. 1 µL of silica beads (Kisker Biotech PSI-1.5, 1.5 µm, plain surface, 50 mg/mL) was added to the solution and 0.75 µL of a 1 M CaCl2 solution to induce SUV fusion with the silica particles. The mixture was incubated at 37 °C for 30 to 45 minutes in a shaker at 550 rpm and subsequently washed 3 times with 1 mL of SLB buffer supplemented with 5% BSA (SLB/BSA). The beads were pelleted at RT and 500 g in a benchtop centrifuge. After the final wash, the beads were resuspended in 200 µL SLB/BSA, half of which was used for ephrin-B1 coupling. 5 µL of recombinant biotinylated ephrin-B1 stock solution (200 µg/mL in PBS, stored at -80 °C) was added and incubated in a turning wheel at 8 °C in the cold room for 2 hours. Washing with cold SLB/BSA buffer was performed in a pre-cooled centrifuge as previously described. The resulting solution (~100 µL) was kept on ice and used for two consecutive days. The final concentration of beads varied widely depending on the loss during washing steps and was calibrated for each batch to give reasonable amounts of beads per chamber. To locally stimulate a cell expressing EphB2_YFP (checked by fluorescence), a lipid-coated bead (again checked by fluorescence) was deposited on the lamellipodial protrusions using the optical tweezer, either at the edge, or in most cases due to poor visibility close to the edge in order to mimic physiological activation geometry.

FRAP

In

Ventral FRAP

Ventral FRAP was performed using a 100x CFI Plan Apo oil immersion objective (NA 1.4) with circular bleaching spots of a nominal diameter of 30 pixels, a 100% laser power, and 50 bleach repetitions per area (Figure 21A). In theory this should correspond to a bleach radius of 1.65 μm with a physical pixel value of 11 μm, yet the actual bleach radius was observed to be considerably larger, on the order of 2.6 μm at half-width.

Equatorial FRAP

A 60x CFI Plan Apo oil immersion objective (NA 1.4) was used and bleaching was performed on the edge of the cell using a squared region. Detection after the bleach was manually chosen to be at a focal plane which showed little sensitivity of the cell edge position to variations in z, i.e. the position of the cell edge did not change much when changing the focus. As the set-up's camera was changed during the time all experiments were performed bleaching sizes were different for some experimental conditions (same input in bleach area in pixels resulted in different effective bleach sizes). We also found that the region was not controlled in z (control bleaching of a fixed cell showed that 'local' bleaching in one focal plane in fact bleached the entire cell in z).

This precluded estimation of Deff from the equatorial FRAP data (within the time of this thesis). Thus we decided to represent these FRAP results based on the recovery halftimes which were reasonably robust within experimental sets, and to normalize them to the respective control condition that had identical bleaching areas (i.e. LatA normalized to DMSO, siMyo1b normalized to sicontrol).

Analysis of recovery data

Using ImageJ we measured the average intensity in the bleach area over time and doubly normalized it by background subtraction and correction for bleaching during recovery (Figure 22A), where 𝑓 𝑛𝑜𝑟𝑚 (𝑡) = (𝑓(𝑡) -𝑓 𝐵𝐺 (𝑡))/(𝑓 𝑟𝑒𝑓 (𝑡)/𝑓 𝑟𝑒𝑓 (0)).

with fnorm being the normalized fluorescence intensity, fBG the background intensity, and (𝑓 𝑟𝑒𝑓 (𝑡)/𝑓 𝑟𝑒𝑓 (0) the bleaching factor due to imaging obtained from a reference cell.

From there, we calculated the halftime of recovery with:

𝐹(𝑡) = (𝑓 𝑛𝑜𝑟𝑚 (𝑡) -𝑓 𝑏𝑙𝑒𝑎𝑐ℎ )/(𝑓 𝑝𝑙𝑎𝑡𝑒𝑎𝑢 -𝑓 𝑏𝑙𝑒𝑎𝑐ℎ )
where fbleach is the normalized intensity after bleaching, and fplateau is the normalized fluorescence intensity after full recovery. This gives the halftime of recovery 𝜏 at 𝐹(𝜏) = 0.5 (Figure 22B).

The mobile fraction (MF) was similarly calculated with:

𝑀𝐹 = 𝐹(∞) = (𝑓 𝑛𝑜𝑟𝑚 (𝑡) -𝑓 𝑏𝑙𝑒𝑎𝑐ℎ )/(𝑓 𝑝𝑟𝑒𝑏𝑙𝑒𝑎𝑐ℎ -𝑓 𝑏𝑙𝑒𝑎𝑐ℎ )
where fprebleach is the normalized intensity before the bleach and 𝐹(∞) is the value of the stable plateau after full recovery (Figure 22B). In the case of ventral FRAP we calculated the effective diffusion coefficient from the obtained halftime 𝜏 and the effective bleach radius reff with 371 : 𝐷 𝑒𝑓𝑓 = 0.224 𝑟 𝑒𝑓𝑓 2 /𝜏

The obtained bleach profiles from the set-up were not perfectly uniform and exhibited effective radii that were bigger than the nominal values. We thus measured the half width of the bleach profile and considered this as the effective radius to estimate the effective diffusion coefficients (Figure 23). Here ⟨⟩ denotes the time-average, 𝛿𝐼(𝑡) = 𝐼(𝑡) -〈𝐼(𝑡)〉 and 𝜏 is the time lag. Traces that showed effects of drift or sporadic high intense bursts were discarded from further analysis. We find 3 timescales as described in 373 . The first timescale of about 20-120 µs corresponds to the triplet state, a second timescale (0. For all the data reported in this manuscript we fitted each raw 10 s autocorrelation (G(𝜏)) versus time lag (𝜏; 5.10 -6 s) to:

𝐺(𝜏) = 1 𝑁 𝐺 𝑇 (𝜏)𝐺 𝐷 (𝜏)
where N reflects the number of moving particles in the confocal volume and GT(𝜏) is the correlation function associated to blinking/triplet kinetics:

𝐺 𝑇 (𝜏) = 1 + 𝑇 1 -𝑇 𝑒 (-𝜏 𝜏 𝑇 ⁄ )
Where T is the fraction of molecules in the dark state and 𝜏T corresponds to the lifetime of the dark state.

GD(𝜏) is the correlation function associated to diffusion which in this case contains two diffusional timescales 𝜏 𝐷1 and 𝜏 𝐷2 :

𝐺 𝐷 (𝜏) = 𝑓 * 𝐺 𝐷1 (𝜏) + (1 -𝑓) * 𝐺 𝐷2 (𝜏) = 𝑓 (1 + 𝜏 𝜏 𝐷1 ⁄ ) * √ 1 + 𝜏 𝑆 2 𝜏 𝐷1 ⁄ + 1 -𝑓 1 + 𝜏 𝜏 𝐷2 ⁄
The fraction f corresponds to the intracellular diffusing pool of unbound fluorophores that has a timescale of 𝜏 𝐷1 . S is the structure factor that accounts for timescales arising from the fact that the intracellular fluorophores diffuse in a volume rather than a plane. Free fitting of S converged to a value of about 0.2, consistent with earlier reports. In order to limit the number of free parameters, S was thus fixed to 0.2.

The diffusion time of interest is finally calculated with 𝜏 𝐷2 . The diffusion coefficient was calculated by:

𝐷 𝐹𝐶𝑆 = 𝑤 𝑥𝑦 2 4𝜏 𝐷2 ⁄
where wxy is the width of the point spread function which is calibrated using a Rhodamin 6G solution. For 488 nm excitation wavelength wxy was 223±30 nm.

Fluorescence anisotropy measurements

HomoFRET The method is based on a grating that leads to a patterned excitation of the sample by using the first order beams, hence structured illumination 375,376 . Using the grating and a polarizer, the set-up creates an illumination pattern with different angles and phases (here: 3 angles and 3 phases) and allows subsequent reconstruction of an image with higher resolution due to improved gathering of high-frequency information from the sample (Figure 24). While this allows improving the lateral resolution considerably, total internal reflection illumination restricts the excitation to a thin sheet in z, thus further reducing out-of-focus contributions in a high background conditions as in the cell.

Reconstruction of SIM data

Reconstruction of TIRF-SIM datasets was performed with the Fiji plugin FairSIM 377 (Figure 25). This required transformation of the 3x3 image montages (3 angles at 3

polarizations each) into single image stacks, done with Fiji using the stack manipulation functions. Stacks were then imported into FairSIM with background subtraction using the graphical user interface (Figure 25A). This resulted to be a critical step as both high levels of background and "over-subtraction" of intensities resulted in unsuccessful reconstructions.

Taking into consideration the origin of images, i.e. TIRF-SIM data, following parameters were chosen in agreement with the manual's suggestion:

The optical transfer function (OTF) was estimated with an NA of 1.49, an emission wavelength of 610 nm and an OTF compensation of 0.25, allowing for deviations due to system aberrations (Figure 25B). No attenuation was chosen as TIRF illumination is already restricted to an almost 2-dimensional excitation sheet. Reconstruction parameters were obtained from fitting the peak in the high frequency domain (small yellow circle, top right) excluding 70% of the lower frequency intensity (large yellow circle) (Figure 25C). These allow to define which information remains and which gets rejected during reconstruction. Subsequent reconstruction was performed with a Wiener filter set to 0.099 and an APO cutoff of 0.2 (Figure 25D).

Particle image velocimetry

Data treatment prior PIV analysis

The reconstructed TIRF-SIM datasets were treated to allow robust estimation of actin flow profiles as follows (Figure 26): Reconstructed images were subjected to a bandpass filter with the limits of 3 to 15 pixels, thus enhancing the filamentous structures over background, and reducing reconstruction artifacts, e.g. honeycomb patterns.

In order to follow the actin filaments over time, we employed a ridge detection using the Fiji plugin developed by Steger et al. 378 , with following parameters: line width 2 pixels, high contrast limit 200, low contrast limit 75. The resulting binary image sequences were averaged stepwise over three frames and the resulting frames subjected to a 1 pixel Gaussian blur. The resulting data was used for flow profile analysis using particle image velocimetry (PIV) (Figure 26). PIV analysis

PIV analysis was performed using PIVlab, a freely available Matlab App 379,380 . We used the FFT window deforming algorithm for PIV, with an iterative interrogation area size of 64, 32 and 16 pixels respectively and shifting the interrogation area by half its width to find the best correlation between subsequent frames (Figure 27A). This allowed sampling of a wide variety of flow velocities, with high vector resolution and

Statistics

Data sets for were analyzed for statistical significance using the statistical toolbox of Excel. One-way ANOVA was employed to check for the presence of statistically

Assessment of protein expression

Western Blot

After washing with PBS, cells were lysed in 1.5x SDS-loading buffer supplemented with β-mercapto-ethanol pre-heated to 95°C. After treatment with benzonase, cell lysates were analyzed by SDS-PAGE and transferred to nitrocellulose membranes.

Myo1b, Ezrin and ERM were detected with antibodies as indicated on the respective figures.

Fluorescence microscopy

Transfected cells were imaged using a conventional confocal microscope at the Early interest in cell membranes, and particularly the peculiar shapes of the erythrocyte membrane, led to efforts to understand the membrane's elastic properties that govern membrane shape and deformations. Fundamental theoretical models of membrane elasticity were generated for lipid bilayers, which offered the advantage of homogeneity. The membrane could thus be treated as a continuous, two-dimensional layer without need to include molecular details 381,382 . Three main elastic deformations were described: Stretching, bending and shearing 382-384 (Figure 28).

W s = 1 2 κ S ( ΔA A ) 2 , ( 1
)
where κs is the elastic stretching modulus, with dimensions of an energy per unit area. For pure lipid vesicles of phosphatidylcholine this value is around 250 mJ.m -2 , with little variation depending on chain length and unsaturation 385 . It must be noted that changes in membrane thickness were not considered in the model 381 .

Membrane shear

Shear is the in-plane deformation of a membrane at constant area. The shear energy

Wshear per unit area is proportional to a quadratic function of the extension ratio of the membrane, with:

𝑊 𝑠ℎ𝑒𝑎𝑟 = 1 2 𝜅 𝑠ℎ𝑒𝑎𝑟 (𝜆 2 + 𝜆 -2 ), ( 2
)
where λ is the extension ratio 𝑥 𝑝𝑜𝑠𝑡 𝑥 𝑝𝑟𝑒 ⁄ with 𝑥 being the edge length before and after shearing, and κshear is the shear modulus of the membrane with dimensions of an energy per unit area 384 . In pure lipid membranes, the fluidity of the bilayer results in a shear modulus of 0 as lipids can move around freely. This is fundamentally different in the case of biological membranes, a fact that is discussed hereafter.

Membrane bending

Membrane bending accounts for out of plane deformations of the membrane. In a first instance one can define the bending energy per unit area g which is a function of the two principal curvatures c1 and c2, as well as a spontaneous curvature c0 which can arise from lipid asymmetry, with:

g = 1 2 𝜅 𝑏 (𝑐 1 + 𝑐 2 -𝑐 0 ) 2 + 1 2 𝜅 𝑐 ̅̅̅𝑐 1 𝑐 2 , ( 3
)
where 𝜅 𝑏 and 𝜅 𝐶 ̅̅̅ are elastic bending moduli relative to the mean and Gaussian curvature respectively.

As the second term of equation 3, which is related to the Gaussian curvature c1c2, is shape-independent for closed surfaces, the energy of the membrane can be described by the Canham-Helfrich Hamiltonian, as:

ℋ 𝐶-𝐻 = 1 2 𝜅 𝑏 ∮ (c 1 + c 2 -c 0 ) 2 𝑑𝑆 , (4)
with 𝜅 𝑏 being the bending elastic modulus of the membrane with dimensions of an energy 386 and S the surface. In contrast to the stretching modulus, bending moduli vary strongly depending on acyl chain length and degree of unsaturation. For a DOPC lipid bilayer, 𝜅 𝑏 is on the order of 0.85.10 -19 J 385 .

In-plane membrane tension

The in-plane membrane tension 𝜎 𝑚 with the dimensions of a force per unit length can be defined as the change in free energy F over a change in surface S with:

σ 𝑚 = 𝜕𝐹 ∂S , (5)
One can describe three distinct regimes for this tension (Figure 28D): A floppy regime where the membrane is not 'tense' and 𝜎 𝑚 = 0, and a tense regime, which can itself be separated into two distinct regimes.

By application of external stresses, the entropic-tense regime is found at macroscopically flat surface area, which microscopically is characterized by thermal membrane undulations, which are controlled in their amplitude by the bending modulus of the membrane. The apparent area can be further expanded to match the microscopic area and undulations are increasingly suppressed, leading to the stretchtense regime 383,387 .

For a plane membrane in the stretch-tense regime one readily gets:

σ 𝑚 = 𝜅 𝑆 ( Δ𝐴 𝐴 ) ( 6
)
At lower tensions, i.e. in the entropic-tense regime below 10 -5 N/m, the description of tension becomes more complex, and scales exponentially with the relative area change.

Studying cellular membranes

While some methods have been conceptually proposed to directly assess membrane tension without any perturbation to the system, e.g. exploiting mechanosensitive ion channels 388 , most experimental approaches have focused on generating membrane tethers from cells. In general, tethers can be generated from hydrodynamic flows 389,390 , pulling with an AFM cantilever or by pulling with a bead that is either held by a micropipette 391 or an optical tweezer 392-394 (Figure 29A).

Cortex contribution to effective membrane tension

In the cellular context, the membrane is underlined by a cytoskeletal network (cortex) and generally presents large excess areas 395,396 as compared to the cortex. Early on it became clear that this cytoskeleton affects the mechanics of membrane tethers although the actual tether is devoid of actin, leading to the conceptual parameter of 'effective membrane-tension' (𝜎 𝑒𝑓𝑓 ): it convolutes the contributions from in-plane membrane tension (𝜎 𝑚 ) and the additional effects originating from membrane interactions with the underlying actin cortex which are generally represented by an adhesion energy (𝑊) 392,397-401 (Figure 29B). This adhesion energy can be directly measured on a larger scale, by micropipette aspiration 402,403 (Figure 29A), and notably depends on PI(4,5)P2 levels 136 and of course on the presence of the actin cortex 398 (Figure 29C). W is on the order of 10 -5 J.m -2 in cells 136,404 . In summary, because of the large excess of membrane area the contribution of W dominates the effective membrane tension, thus cell membrane mechanics is generally assumed to be dominated by adhesion of the plasma membrane to the actin cortex.

Tether pulling from cells

In a large vesicle, i.e. pure lipid environment of flat nanoscale geometry, tube generation is characterized by a critical energy barrier which when overcome leads to formation of a tube of length-independent radius 405 . The initial energy barrier for tube formation is critically dependent on the initial patch size, i.e. the interaction area of membrane with pulling probe 406 . In order to form a membrane tether in cells this force barrier is considerably higher as a patch of membrane has to be separated from the underlying actin cortex 407,408 . Upon formation of a membrane tether two opposing processes govern the tether's equilibrium radius and the force required to hold it. While the surface tension 𝜎 𝑒𝑓𝑓 drives the system towards smaller radii, i.e. minimizing the tether surface, it eventually reaches a point where further reduction in radius is unfavorable due to the membrane's bending rigidity 𝜅 𝑏 405 . When the distance between two tethers is below a threshold value, coalescence of tethers can be observed 405,409 .

The equilibrium radius req and tether force ftether are related to effective membrane tension and bending rigidity by 410 :

r 𝑒𝑞 = √ 𝜅 𝑏 2𝜎 𝑒𝑓𝑓 𝑓 𝑡𝑒𝑡ℎ𝑒𝑟 = 2𝜋 √ 2𝜎 𝑒𝑓𝑓 𝜅 𝑏 (7) with 𝜎 𝑒𝑓𝑓 = 𝜎 𝑚 + 𝑊.

Combining both equations, one finds:

κ 𝑏 = 𝑓 𝑡𝑒𝑡ℎ𝑒𝑟 𝑟 𝑒𝑞 2𝜋 𝜎 𝑒𝑓𝑓 = 𝑓 𝑡𝑒𝑡ℎ𝑒𝑟 4𝜋𝑟 𝑒𝑞 (8)
Thus, in theory, one can readily deduce both the effective membrane tension and bending rigidity from tether forces, yet it is difficult to precisely measure the tube radius as it is below the optical resolution, of the order of 100 nm and below. As the bending rigidity is generally assumed to be reasonably stable in between experimental 58 samples, one can compare tether forces to observe changes in effective membrane tension.

Following table shows a selection of published tether forces for different cell lines:

Dynamic tether pulling

Holding a tether, or elongation at very low speeds (0.1 μm.s -1 ), gives a tether of constant radius over wide ranges of length in most cases 395,396 , and thus a constant force. Yet for example in outer hair cells a different behavior was observed, leading to length-dependent tether forces 411 .

During elongation at constant speed three main dissipation mechanisms come into play: flow of lipids into the tether, slippage within the bilayer, and membrane slippage along the cortex 410 . The tether radius decreases with increasing pulling velocity, due to inherent tether elasticity and membrane viscosity 412 . At the neck, slippage between the inner and outer monolayer is expected, although in pure lipid bilayers such effects emerge only upon very fast tether elongation, i.e. around 100 μm.s -1 elongation rates 413 .

Furthermore, in cells compressive resistance of the proteinaceous core at the cytosolic membrane leaflet leads to high effective viscosities during flow into the tube 391,412 .

Elongation at constant speed is an experimental way to assess the friction between the actin cortex and the plasma membrane. As a membrane tether is elongated, lipids have to flow from the cell body into the tube in order to equilibrate the difference in tension that is created by the pulling (Figure 30B). This imbalance is reflected by an increase in the force required to hold the tether (Figure 30A). It is a function of the cortex -plasma membrane linker density and of a phenomenological surface viscosity. This surface viscosity can be understood in terms of an effective friction between the plasma membrane and the cortex. Its measurement should a priori allow probing the properties of the linkers and should be dependent on the linker density. In this scenario, three dynamic ranges can be distinguished: At very slow pulling, the membrane, including proteins that might bind actin, flow as a viscous sheet, because individual detachment happens faster than the elongation. At intermediate speeds, bonds between actin and linkers persist and are 'felt' by the lipids that have to flow around them in order to equilibrate the rising tension in the tube. Finally, at very high speeds, the friction force is higher than the interaction energy between actin and the linkers, thus rupturing these bonds and leading to generalized slippage along the actin 390 . In the intermediate range, which is commonly assessed, the increase in force 𝑓 scales non-linearly with pulling speed 𝐿 390 :

𝑓(𝐿 ) ≅ 2𝜋(2𝜅 𝑏 2 𝜈𝜂 𝑒 𝐿 ln (𝑅 𝑟 𝑡 ⁄ )) 1 3 ⁄ ( 9
)
where: 𝐿 is the speed of tether elongation, 𝜅 𝑏 is the bending rigidity of the membrane, 𝜈 is the density of cortex-membrane linkers, 𝜂 𝑒 is the surface viscosity, 𝑅is the cell's 'radius', and 𝑟 𝑡 is the tether radius.

60

A more recent approach consists in imposing step-displacements at high speed and monitoring the subsequent relaxation dynamics. Phenomenologically this has been interpreted as the build-up of a diffusive barrier at the tube neck for a non-specified minority component, thus leading to non-exponential relaxation kinetics (Figure 30C).

The relaxation of the force 𝑓over time can then be understood as the initial creation of a concentration gradient of the slower component, relative to the majority component, that relaxes over time 𝑡, with 414 :

𝑓(𝑡) = √𝑓 𝑝𝑒𝑎𝑘 2 -(𝑓 𝑝𝑒𝑎𝑘 2 -𝑓 0 2 ) (1 -𝑒 𝑡 𝜏 𝑐𝑟𝑜𝑠𝑠 ⁄ (𝑒𝑟𝑓𝑐√𝑡 𝜏 𝑐𝑟𝑜𝑠𝑠 ⁄
)) (10) where: 𝑓 𝑝𝑒𝑎𝑘 is the peak force immediately after tether elongation, 𝑓 0 is the force after full relaxation of the tether, and 𝜏 𝑐𝑟𝑜𝑠𝑠 is the characteristic time of relaxation.

An effect of membrane cortex interaction was proposed to affect the relaxation time if actin-binding proteins were significantly contributing to the postulated concentration gradient 414 .

Tension regulation

Different results considering the effect of protein expression and activation on effective membrane tension in various cell lines might be explained by different availability of buffering mechanisms, e.g. the presence of membrane invaginations that disassemble upon stresses [415][416][417][418][419] , or compensatory endocytosis and exocytosis 417,[420][421][422] .

In line with this, changes in tension reciprocally influence endocytosis and exocytosis events 423,424 , and phagocytosis increases the effective membrane tension 425

Experimental observations

Effective membrane tension in keratocytes is polarized, i.e. the leading-edge lamellipodium during migration has a higher tension than the cell body 432 . Large surface area changes are buffered within 10 minutes with no persistent effect on tether force after this time, yet cytoskeletal drugs change effective membrane tension persistently 433 . Cholesterol depletion increases effective membrane tension in various cell lines 401,[434][435][436] .

The gradient in effective membrane tension in migrating cells might be explained by the role of local actin polymerization towards the leading edge which locally increases tension 437,438 . Accordingly, lamellipodial extension rates and effective membrane tension are coupled 439,440 . Effective membrane tension is dynamically adapted during cell spreading through a feedback loop which couples the induction of actomyosin contraction and exocytosis events to increases in effective membrane tension 421 .

Depletion of MLCK, an activator of Myosin II contractility, has been shown to reduce effective membrane in some cells 441 , whereas this effect was absent in another cell line 442 . Effective membrane tension has furthermore been reported to play a role during polarity establishment 443,444 and increases during mitosis 445 .

Evidence generated in silico, in cellulo and from theoretical arguments suggests that a feedback loop between membrane tension and the recruitment and spatial organization of membrane curvature sensing proteins exists [446][447][448] .

Taken together, the literature regarding the role of effective membrane tension in cells suggests that it plays a role in many cellular functions. Cells have developed a variety of dynamic processes that set the effective membrane tension, and regulate and adapt it, either locally or globally, to fulfil specific functions through, e.g. changes in contractility, membrane trafficking, and actin dynamics. Yet, we are still at a descriptive stage in which the various experimental results do not obviously paint a coherent picture of how cells respond to changes in effective membrane tension, how effective membrane tension is regulated within cells, and how changes in effective membrane tension propagate in space and time.

The overarching goal of this part of the thesis was to characterize the effect of two types of plasma membrane -actin linkers on membrane mechanics.

This was motivated by the initial observation that cell contraction after activation of EphB2 was less efficient in absence of Myosin 1b (this work). As the EphB2 receptor was still activated in cells (tyrosine phosphorylation), and Myosin II activity was still induced after depletion of Myosin 1b 3 (MLCK phosphorylation), we hypothesized that Myosin 1b could play a mechanical role in this process by coupling the Myosin IIgenerated contractile forces to the membrane. In line with this hypothesis, former literature evidenced a role of Myosin 1b in the control of membrane tension [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF][START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] , while

showing the exclusion of Myosin 1b from tropomyosin-decorated actin structures 186 .

Taken together this suggested a position of Myosin 1b at the plasma membrane rather than at the contractile apparatus, and accordingly biochemical evidence showed that Myosin 1b interacts, either directly or indirectly, with the EphB2 receptor 3 . We thus hypothesized, that reduced contractility in absence of Myosin 1b was due to a decreased coupling between the cortex and the plasma membrane, and figured that such a decrease in linkage should translate into a change in the membrane's mechanical properties, routinely assessed by tube pulling from cells.

We thus sought to characterize the effect of Myosin 1b depletion and overexpression in the cellular system in which we had seen reduced contractility.

As we surprisingly did not observe an effect on effective membrane tension in HEK293T cells, we expanded the initial study and assessed the role of Myosin 1b in a more general way, thus performing experiments on NIH3T3 cells, experimentally assessing cortex-plasma membrane interaction in a broader way by performing dynamic tether pulling experiments, and including the ERM protein family as a benchmark in our study.

Most of the work of this chapter has been submitted to the journal 'Molecular Biology

of the Cell' and is presented in the format adapted to the requirements of the journal (i.e.

Results and Discussion together). Initial results and additional experiments that were

undertaken in this project are presented following the general organization of this thesis with separate Results and Discussion.

Unpublished Results

Unless specifically stated all experiments were performed on a HEK293T cell line stably expressing YFP-tagged EphB2 receptor 3 , referred to as EphHEK cells. While the first method allowed for 'physiological' activation of EphB2 at membrane contact sites, it did not offer any spatiotemporal control of receptor activation, whereas global stimulation did not allow studying local activation events. We thus developed an optical tweezer-based approach to locally stimulate the EphB2 receptor with its ligand ephrin-B1. It is based on coupling the ligand to a lipid bilayer covered bead, allowing the diffusion of ephrin-B1 along the bead surface and thus clustering, that we control with an optical tweezer and bring in contact with cells (Figure 31, detailed protocol in Methods section).

Local activation of

We observed a clear recruitment of the EphB2 receptor to the bead contact site (Figure 32). To check the increase in phospho-tyrosines, a hallmark of receptor tyrosine kinase activity and thus of EphB2 activation, we used a previously characterized mCherry-labelled dimeric SH2 domain (dSH2_mCherry) 313,449 . We showed that local increases in EphB2 receptors around the beads coincided with increases in the dSH2 marker in cells depleted for Myosin 1b, thereby qualitatively confirming previous biochemical evidence of functional receptor phosphorylation in absence of Myosin 1b 3 (Figure 32). To quantify the contraction we measured the apparent surface area from the ventral EphB2 signal before activation and after 15 minutes. We chose 15 minutes as the 'endpoint' as most of the contraction happens within this time frame. The results obtained with this approach are summarized in Figure 33, showing that local receptor activation induced by the bead is sufficient to specifically induce a contractile response from cells, as expected from previous reports on EphB-driven contractility 450 .

While cells show considerable activity, i.e. protrusion dynamics, at steady state, untreated cells maintained their area over 15 minutes, with a slight tendency of area increases within our data. Addition of non-coated carboxylated beads as a negative control regarding any potential effect of adhesion, again showed no change in apparent surface area, yet an increased spread. The contractility after activation with ephrin-B1 coated beads (mean of relative area 82 %) was reduced after depletion of Myosin 1b using siRNA (92 %) consistent with previously observed effects of global stimulation 3 .

Based on our results, the observation that EphB2-driven cell sorting loses efficiency in absence of Myosin 1b 3 , and on the generally accepted role of Myosin 1b in the control of effective membrane tension [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF][START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] , we hypothesized that Myosin 1b depletion could affect the coupling between cortical actin and the plasma membrane, and in consequence the transmission of Myosin II-driven cytoskeletal contraction to the plasma membrane. We have thus used different mechanical methods for measuring the effective membrane tension and the friction at the interface with the cortex (submitted paper), or the adhesion energy between cortex and membrane (see below).

Micropipette aspiration on HEK293T cells does not reveal any mesoscale difference in membrane to cortex adhesion.

Micropipette aspiration has been employed to characterize the adhesion energy between the plasma membrane and the actin cortex 403,407,408,451 . In practice, such measurements allow identifying the critical pressure Pbleb at which a membrane bleb forms inside the micropipette, equivalent to the detachment of the plasma membrane from its underlying cortex. Ignoring the contribution of membrane tension as it is negligible quantitatively (see previous Introduction), the relationship between critical blebbing pressure and membrane-cortex adhesion is described through 402 :

P 𝑏𝑙𝑒𝑏 = ρ 𝑙 α * 𝑘 𝐵 𝑇 𝐿 𝑙 -2 𝜎 𝑐 𝑅 ( 11
)
where 𝜌 𝑙 is the linker density, 𝐿 𝑙 is the characteristic linker length, 𝜎 𝑐 is the cortex tension, 𝑅 is the cell's radius (assumed to be spherical) and 𝛼 * is a dimensionless ratio proportional to the critical force of detachment per link:

α * = ̅ 𝜎 𝑛 * 𝐿 𝑙 ρ 𝑙 𝑘 𝐵 𝑇 ( 12
)
Where 𝜎 𝑛 * is the critical normal stress exerted on the membrane and is obtained from As we studied adherent cells with complex morphology we only report comparative measurements of the critical pressure between control and Myosin 1b depleted cells, without inferring the actual adhesion energy between the cortex and the plasma membrane. We employed a micropipette connected to a height-controlled water reservoir to measure the critical blebbing pressure in Myosin 1b-depleted and control 68 conditions (Figure 34A). As shown in Figure 34B, we measured a critical blebbing pressure (defined as the pressure at 50% bleb formation probability 403 ) of the order of

Introduction

The different linker types that connect the PM to the cortical actin network in eukaryotic cells contribute to a variety of key processes. ERM proteins and the Myosin 1 family represent two important classes of cortical linkers that attach the actin cortex to the PM via interaction with PIP2 and membrane partners 177,452 . Myo1b is a motor protein able to deform membranes 4 . It has been implicated in a variety of cellular functions, e.g. cell segregation 3 , cell motility 191,192 , control of organelle shape [START_REF] Almeida | Myosin 1b promotes the formation of post-Golgi carriers by regulating actin assembly and membrane remodelling at the trans-Golgi network[END_REF]2 and filopodia formation 3 . It shows catch-bond behavior, i.e. it is sensitive to mechanical loads of a few pN which increase its actin attachment lifetime by two orders of magnitude 165 . Ezrin is required for the formation of protrusions, e.g. microvilli, and its actin interaction is regulated by phosphorylation 227,236 .

Sheetz and colleagues have emphasized the role of PM-actin linkers in cell membrane tension 394,398,453 . In general, membrane tension is defined as the variation of mechanical energy upon area change. Since PM and actin cortex are mechanically coupled in cells, membrane tension encompasses two contributions: the in-plane PM tension σm 398 and the interaction between the actin cortex and the PM, represented by an adhesion energy W0. Both contributions are difficult to distinguish experimentally.

Practically, an effective (membrane) tension 𝜎 𝑒𝑓𝑓 = 𝜎 𝑚 + 𝑊 0 398 is generally measured using two main methods: micropipette aspiration and tether pulling 454,455 . The most prominent technique is pulling membrane tethers from cells, using either OT or AFM 393,456 . The static force ftether -required to hold the tether when pulling is stopped and equilibrium is reached -depends directly on the effective tension 398 (Equation 7):

𝑓 𝑡𝑒𝑡ℎ𝑒𝑟 = 2𝜋√2𝜅 𝑏 𝜎 𝑒𝑓𝑓
where 𝜅 𝑏 is the bending rigidity of the membrane. 𝜅 𝑏 is generally assumed to remain stable over different experimental conditions and can in principle be deduced from measurements of the tube radius 433 . Equation 7supposes that no actin polymerizes in the tether, which is true at short times, i.e. less than a few minutes 414 .

Myosin 1s and Ezrin have been reported to influence tether force in cells. Using AFM, Diz-Muñoz and colleagues showed that Myo1b or Ezrin depletion decrease membrane tether force in zebrafish progenitor cells [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF] . A similar result was obtained with Myosin 1g in lymphocytes 199 . Overexpression of Myosin 1s has also been reported to change the coalescence of multiple tubes [START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] . OT-based tether pulling showed that Ezrin phosphorylation increases the tether force in lymphoblasts 243 . Globally, this data has been interpreted as evidence that Myosin 1s and Ezrin contribute to effective membrane tension in general.

Our data on adhesive HEK293T cells expressing YFP EphB2 (EphHEK) revealed that Myo1b depletion perturbs acto-myosin stress fiber distribution after EphB2 stimulation 3 . This suggested a role of Myo1b in cell contraction independent of the activation of Myosin II. A loss in coupling between the PM and the actin cortex in the absence of Myo1b would a priori support a contribution of Myo1b to effective membrane tension. We used OT-based tether pulling on EphHEK cells to measure the effect of Myo1b and rigor mutant expression on membrane mechanics and compared it to the expression of Ezrin and ERM. We performed three kinds of experiments to probe these effects. We measured static tether force and performed dynamic tube pulling assays since PM-actin linkers are also expected to affect membrane friction on the cytoskeleton upon tube pulling 453 . We deduced friction from the force vs. pulling speed scaling and measured the force relaxation time that is related to this friction.

Results & Discussion

Effective membrane tension in EphHEK cells is dominated by actin.

In order to measure the effective membrane tension, tethers were pulled from adherent cells as depicted in Figure 35A with a typical length of 10 μm. As previously shown, the initial force overshoot depends on the interaction area between the bead and the PM 406 and is not well controlled under experimental conditions (Figure 35A step 3 and Figure 36A). Upon tube formation the force next decreases and rapidly reaches a plateau. To measure the static tether force, we waited 10 seconds to let the force equilibrate (Figure 35A -step 4). As a previous report showed the presence of multiple tethers and different coalescence depending on Myo1b expression [START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] , special care was taken to ensure the measurement of forces for single tethers. In agreement with previous reports 395 , we confirmed that the tether force doesn't depend on tether length over a broad range in EphHEK cells (Figure 36B). We measured a tether force of 16.5±4.9 pN which is at the lower end of values reported for adherent cells 393 . In line with previous findings 401,425 we observed a marked decrease of the tether force when actin was depolymerized by LatrunculinA (LatA) (Figure 35B). Our measurements indicate that around 70% of the effective membrane tension directly depends on actin in EphHEK cells. This value is likely underestimated due to experimental constraints. LatA treatment was done at low concentrations for short periods of time to avoid complete cell detachment from the substrate that precludes tether pulling. When Myosin II activity was blocked using non-cytotoxic Blebbistatin (BS) 457 , the tether force decreased to 11.6±2.4 pN, suggesting that contractility influences the static tether force in EphHEK, as reported for other adherent cells 423 . As previous results involve Myo1b in EphB2-driven cell repulsion and given that EphB2 stimulation with ephrin-B1 induces cell contraction 450 , we checked if activation of EphB2 and the resulting contraction would alter effective membrane tension, as expected from the effects of BS. For technical reasons, the tether force measurements were performed within a time frame of 10 to 50 minutes after induction of cell contraction. Under these conditions, we did not observe any difference in tether force (Figure 36C), suggesting that any potential increase in effective membrane tension upon contraction was only transient and undetectable within our experimental approach. Alternatively, the observed effects upon BS treatment might be linked to a global reduction in cortical contractility, yet ephrin-B1-induced contraction might specifically be localized to the ventral surface, not affecting effective membrane tension locally probed by the tether force 431 .

Neither Myo1b nor ERM contribute to effective membrane tension in EphHEK cells.

Next we studied the effect of cellular levels of Myo1b and ERM on tether force.

Assuming that the membrane bending rigidity is not changed in these conditions, a change in tether force directly reflects a change in effective membrane tension.

Neither overexpression of mCherry-Myo1b nor its rigor mutant, which lacks motor activity 458 and stays bound to actin 1 , changed tether force as compared to controls (Figure 35C, Figure 42A&B, Figure 37A&B). Similarly, depletion of Myo1b by siRNA did not affect the measured tether forces (Figure 35C; Figure 37C). As overexpression of Myo1b had previously been suggested to affect the effective membrane tension in NIH3T3 cells [START_REF] Nambiar | Control of cell membrane tension by myosin-I[END_REF] , we checked if a difference was detectable in the effective membrane tension as deduced from the static tether force in NIH3T3 cells overexpressing mCherry-Myo1b. Yet, the measured tether forces in NIH3T3 cells were in the same range as in EphHEK cells (Figure 36D). Nambiar and colleagues 7 revealed changes in coalescence dynamics from the analysis of force-time integrals. These integrals contain contributions from static and dynamic forces during elongation, coalescence events of tubes, and the initial energy barrier for tube formation. As such, it seems difficult to extract the contribution of membrane tension from this data.

Concomitantly we tested if manipulation of Ezrin expression affects the effective membrane tension in EphHEK cells. We overexpressed mCherry-Ezrin and depleted Ezrin or ERM using siRNA 459 (Figure 37). Yet, none of these perturbations led to a change in effective membrane tension in EphHEK cells (Figure 35D).

Taken together, this data indicates that neither Myo1b nor ERM contribute significantly to the effective membrane tension in EphHEK cells. The abundance of actin-PM linkers or dominant contribution of adhesion to the substrate may preclude observing a significant effect. Previous papers based on static tether force measurements have reported effects of myosin I isoforms on effective membrane tension in non-adherent cells such as lymphocytes 199 , or in cells with high blebbing propensity shortly after plating [START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF] . Differences between these results and ours might be due to a different regulation of effective membrane tension between adherent and non-adherent cells. Indeed, MLCK alters effective membrane tension in de-adhered smooth muscle cells 441 , but does not in adherent keratocytes 442 . Alternatively, considering that our force measurements were performed within 1 and up to 5 days (for depletion) after transfection, changes in tension could be compensated. For example, keratocytes equilibrate membrane tension even after massive increases of the membrane area within ten minutes 433 .

Dynamical measurements to probe the PM-actin interface

As shown in 453 , another way to probe the effect of PM-actin linkers is dynamic tube pulling. Either the force is measured during tether extension at controlled speed 390,453 , or the force relaxation is measured after a fast step elongation 414,460 . Brochard and colleagues had shown from previously published data that PM-actin links -including membrane proteins bound to the cytoskeleton -produce a friction on the lipids when the tether is extended and a tension gradient builds up between the tube and the adjacent membrane 390 . In this regime, force increases with pulling speed and the density of links. Similar effects could also arise from the sorting of membrane constituents out of the tether upon pulling. As tube elongation stops, lipids and proteins flow into the tether to equilibrate the tension 407,411,460 . Datar and colleagues calculated 414 that this tension gradient, reflected by the tether force, is dissipated with a characteristic relaxation time that depends on membrane-component diffusion, and thus possibly on the density of actin-PM linkers. Here, we performed both types of dynamic tether pulling experiments varying the expression levels of Myo1b and ERM.

Neither Myo1b nor ERM contribute to effective PM-cortex friction in EphHEK cells

We first probed the dependence of tether force on pulling velocity in an intermediate regime (Figure 38A) as proposed in 390 . As expected, the plateau force increases with the pulling velocity 𝐿 (Figure 38B) and scaled as 𝐿 1 3 ⁄ (Figure 38C, black line).

From this data, we extract an effective surface viscosity on the order of 10 -9 Pa.m.s, supposing a membrane bending rigidity of 50 kBT and a density of linkers of 103 μm -2 as in 390 , but we do not detect any difference neither after depletion of Myo1b or ERM (Figure 38C), nor overexpression of mCherry-Myo1b-rigor (Figure 41A). The effective surface viscosity is low as compared to other cell types considered in 390 , suggesting a low friction between actin and the PM in EphHEK cells. After calculating the force variation for a higher effective surface viscosity on the order of 10 -8 Pa.m.s (Figure 38C, red line) or a doubling (Figure 38C, upper dashed) or reduction by 90% (Figure 38C, lower dashed) of the assumed cortex-PM linker density, we conclude that the data obtained with this approach is too spread to detect any difference between PM-cortex interfaces in the same cell type. In contrast, with similar spread in data, significant differences could be detected between different cell types 390 .

Myo1b-rigor mutant and ERM affect force relaxation dynamics.

We then asked if any effect of membrane linkers could be detected with stepelongations at high speed. A 5 μm extension at 75 μm/s was applied on a preformed tube with static tether force 𝑓 0 (Figure 39A). During elongation we observed a rise up to a peak force 𝑓 𝑝𝑒𝑎𝑘 when elongation is stopped, defined as t=0. We measured the force relaxation over time f(t) at constant tether length. We fitted our data using the expression from 414 . This two-component model was initially developed assuming that during step elongation a minority membrane component accumulates at the neck and behaves as a barrier, eventually passing the neck during the relaxation phase. It accounted well for the force relaxation of axonal tethers. More generally, it should to be valid for any situation where a composition gradient exists between the tether and the cell membrane, and to be sensitive to PM-cortex linker density 414 . Early work on tether pulling from cells generally considered a single exponential relaxation for the force 407,411,461 . Recent work both on vesicles with a reconstituted actin cortex and cellular membranes revealed that the force relaxation cannot be satisfyingly described with a single relaxation time but rather contains both a fast exponential decay (on the order of seconds) independent of actin and a linear slow decay that depends on actin and appears diffusive 460 . We confirmed that a single exponential decay does not account properly for our data (Figure 41A). A double-exponential fits as well as equation 10. However, since the long-time term was phenomenological in 460 and we do not observe a slow relaxation in EphHEK cells (Figure 41C,D), our data is correctly described by a simple model of a composition gradient across the neck. We thus used this model to analyze our experiments and fitted the force relaxation data (Figure 39B) with equation 10, with the relaxation time τ as the only free parameter. τ is expected to depend on the diffusion of the minority component in the cell membrane. Our data set fit well with equation 10 (Figure 39B), giving a relaxation time τ=0.69±0.31 s (Figure 39D).

We first analyzed the impact of actin depolymerization by LatA treatment. We observed a 3-fold decrease of the peak force. As this peak force originates from a variety of processes, we do not further comment on it. Likewise, we found a 3-fold reduction of the characteristic relaxation time (τ=0.22±0.09 s) after LatA treatment (Figure 39D,E).

Similarly, a reduction of peak forces and relaxation times after LatA treatment was previously reported by 414 , but the values are different, probably due to cellular differences. This suggests that F-actin affects concentration gradients across tether necks, probably due to actin-PM links reducing diffusion of membrane components.

Neither depletion of endogenous Myo1b nor overexpression of mCherry-Myo1b

changes the relaxation time (Figure 40A, Figure 42C). However, overexpression of the rigor mutant increases it significantly. The rigor mutant is permanently attached to actin, whereas WT Myo1b is bound to actin only during 20% of its ATPase cycle if not under load 165 . This indicates that the force relaxation time is only sensitive to PM-actin linkers when a substantial fraction of them is engaged. Moreover, it suggests that if Myo1b is overexpressed, its catch-bond is not under sufficient load to significantly affect the force relaxation dynamics. hereafter). The relatively low density of Myosin 1b among linkers seems the most likely explanation for the absence of an observable effect. Indeed, at whole cell protein levels 462,463 , i.e. not only the plasma membrane bound part, and only considering Myosin 1c and ERM as linkers, i.e. neglecting all other contributions to membranecortex adhesion, one finds that full depletion of Myosin 1b with no compensatory effects, would lead to a maximum of ~20 % in linker density reduction assuming comparable binding strengths (Figure 43).

Tension buffering in cells is generally efficient

In this chapter we have used all available mechanical methods that are usually recognized for measuring the effective plasma membrane tension and probing the mechanics of the cortex-membrane interface. However, we could not detect any influence of Myosin 1b. Considering evidence on other cell types showing efficient cellular processes that buffer membrane tension 415,433 the lack of effect is actually less surprising than the fact that in some cells, e.g. lymphocytes, strong changes in effective membrane tension after depletion or overexpression of proteins can reproducibly be observed. This suggests that cells might react differently to perturbations and show either highly efficient compensation mechanisms, or on the contrary high tolerance towards such changes. While one might posit that every cell type is different and thus propose a continuum distribution of effects and importance of compensation, fundamental biological reasons might underlie the presence of different buffering systems and the vast array of cortex -plasma membrane linkers. Our results and previous reports 441,442 indicate, that indeed both the relative density at the plasma membrane-actin interface, and a fully established adhesion to the substrate might fundamentally change the measured parameters. Furthermore, a feedback loop between effective membrane tension and adhesion formation has phenomenologically been described 422,464 , in which cycles of increasing local membrane tension at the cell edge are critical for the positioning of new adhesion sites. Controlling this process might be the principle role of class 1 myosins and ERM, which disappears once adhesion has been established.

As we do not observe a striking phenotype in absence of Myosin 1b regarding adhesion at steady-state, its effect on the dynamics of cell spreading could be studied using traction-force microscopy and/or reflective interference contrast microscopy.

Another set of experiments that remains to be performed is to measure if de-adhered and recently sedimented cells, that have not fully established their adhesion to the substrate, reveal a difference in effective membrane tension in absence of Myosin 1b, as one might expect if the adhesion to the substrate dominates the effective membrane tension throughout the cell. In that case it would mask any potential contribution of Myosin 1s or ERM, or lead to a shift in the cellular control system, thus abrogating the potential roles of Myosin 1 and/or ERM in effective tension that are at play when the cells are rounded. If that is the case, it would be interesting to map effective membrane tension over the cell cycle in cells depleted for Myosin 1s and/or ERMs, as their effect should dynamically become dominant during mitosis, when cells round up to divide.

Furthermore, one might suspect a phenotype regarding mitosis in the absence of Myosin 1b, as has been described for Moesin 238,240 . In any case, the phenotypes which have been described in EphHEK cells concerning the role of Myosin 1b as an effector for EphB2 3 are clearly not coupled to a change in effective membrane tension nor membrane cortex friction, at least within the resolution limit of current methods, as these were observed under the same conditions as our mechanical measurements.

In order to better understand these potential compensation mechanisms and circumvent them experimentally, one might use different systems to perform ad-hoc perturbations to the distribution of PM-actin linkers, using e.g. optogenetics or

Rapamycin based approaches [465][466][467] . This would allow the (reversible) removal of a specific protein of interest away from the PM-actin interface within seconds, thus circumventing long-term adaptation occurring after plasmid-based transfections.

Secondly, one might employ the Calcium-mediated actin reset as described in 468 , during which the entire cortical actin is disassembled and reassembled within minutes as a benchmark for potential changes in static tether force due to cortical dynamics, but independently of adhesion.

Tension propagation vs. tension regulation

Recent evidence suggests that membrane tension gradients dissipate very slowly in biological membranes as compared to pure model lipid membranes, which has been attributed to the presence of a dense network of connections between the plasma membrane and the underlying actin cortex 431 . This is in striking contrast to in silico results which for bare membranes suggest almost instantaneous tension equilibration 469 as well as theoretical arguments made for cells 470 . This is intriguing, as on the one hand, a slow effective tension relaxation along the plasma membrane would explain the observed tension gradients in migrating cells 432 , but it sheds doubt on the conceptual idea that local changes in effective membrane tension by themselves without a need for signaling 470 can be a determining factor in changing cellular behavior on a global level 431 .

In light of the obtained results in this work, it would be interesting to assess if instead of tension regulation, the presence and the density of Myosin 1s and ERM might affect relaxation of tension gradients along the membrane. This could experimentally be achieved through overexpression of mechanosensitive channels and Ca 2+ imaging as performed in 431 .

Dynamic tether experiments to assess cortex-membrane friction

Both ways of dynamic tether pulling presented in this thesis (i.e. constant speed elongation and step elongation) have been employed to study the mechanical properties of the plasma membrane-actin interface. To our knowledge, this is the first comparative study in which both techniques have been employed on the very same cell type and varying protein expression conditions. Both techniques show different results and suggest that although related, they actually assess different parameters in cells, or at the least have considerable differences in their sensitivity to detect changes. Notably, constant speed elongation is impressively noisy 390,411 , and based on parameter sensitivity estimation, this method should only be able to reveal massive changes.

While it thus allows to probe a parameter over a vast range of pulling speeds, it seems not to be particularly suited to investigate differences within a given cell type, or to compare closely related cells. In conclusion we find that step elongation is a better suited tool to study changes in cells, at least when studying the effects of PM-actin linkers as done in this work, due to increased signal-to-noise.

The biology of friction.

It has to be noted that while the role of tension in biology is well appreciated and multiple demonstrations of its functional relevance exist, the case of friction is more mitigated. In order to reveal changes in friction we employed tether elongations at a speed of 75 μm/s in order to capture the entire relaxation after pulling. While the fact that we only observe differences at high pulling speeds does not preclude an effect of friction at lower speeds, the fast relaxation we observe suggests that only large and steep flows might actually reveal the effect of linkers on cortical friction, whereas at a lower shear level, the cell is able to readily compensate any stress parallel to its surface.

The one example in which a steep and large flow can practically occur under real biological conditions would be the transition period for cells in the blood flow that start to adhere to a vessel's endothelium. In that case, one could hypothesize that the density of cortex-linkers plays a role in extravasation efficiency.

What is the relevance of a catch-bond in vivo?

Actin binding domains experience continuous stresses of around 2 pN in cells originating from persistent cortical actomyosin contractions 471 which means that Myosin 1b should a priori be constantly engaged in its catch-bond state. Thus it remains an open question if, why, and how the catch-bond properties are relevant in cells. In order to actually study this question, one would need a Myosin 1b with ideally identical properties, yet with abolished catch-bond behavior. Unfortunately, the structure of Myosin 1b's tail domain is not known at this point and currently precludes the design of such a specific catch-bond mutant. Meanwhile, the three cellular splice isoforms of Myosin 1b have different catch-bond behavior, and thus it would be instructive to study them in detail to distinguish the individual contributions of the different isoforms, assuming that the different catch-bond behavior indeed drives cellular function. This would as well help to better understand the conundrum of Myosin 1b which seems to be functionally involved in seemingly different processes, from PM-related cell functions 3,[START_REF] Diz-Muñoz | Control of directed cell migration in vivo by membrane-to-cortex attachment[END_REF] and organelle morphology [START_REF] Almeida | Myosin 1b promotes the formation of post-Golgi carriers by regulating actin assembly and membrane remodelling at the trans-Golgi network[END_REF]2 , to axon differentiation [START_REF] Iuliano | Myosin 1b promotes axon formation by regulating actin wave propagation and growth cone dynamics[END_REF] .

It is a nice and generally simple task to come up with ever more complicated experiments once reaching the end of one's own project. I will thus limit my scientific curiosity and fantasy to two main points which I consider of fundamental importance at this step for the field.

Development of new experimental approaches

The goal here is fairly simple yet non-obvious: Instead of pulling local tubes in a reasonably inefficient and tedious way; it would be fantastic to have a tool which allows the observation of effective and/or on plane membrane tension in real-time at the cellular scale. Ideally the reporter would be protein-based and thus allow expression in cells, ultimately even tissues. Obvious candidates to serve as starting points are mechanosensitive channels, which have already almost 20 years ago been suggested as a tool 388 . Interesting eukaryotic candidates which have recently gained considerable attention are the Piezo-family members both as research subjects [427][428][429][430] and tools 431 .

The fundamental problem in this approach is (at least) two-fold: 1. Mechanosensitive channels tend to have open probability transitions that are affected by higher tensions than what is observed as resting values in the plasma-membrane. Thus, the mechanics of the receptor would need to be fundamentally changed in order to allow a dynamic response range within the biologically relevant tension ranges. This might be achieved through rational design of mutants, as has been performed to optimize fluorescent molecules 472 and transmembrane receptors 473 . 2. Ideally one needs to ensure that the developed system is tension-sensitive but not curvature-sensing.

Alternatively, one might conceive a FRET-based tension sensor (Figure 44), e.g.

using DNA origami which could be calibrated in liposomes, resembling the FRET-based sensors developed for adhesion molecules 471 . The principal problem would be that such a sensor critically depends on the lipid-to-lipid distance, which might be changing enough to detect changes if one is in the stretched-tense situation, yet in cells the entropic-tense regime is more likely to be dominant, where lipid-to-lipid distance changes should be negligibly small. Thus, although conceptionally appealing, such an idea is likely not going to work in cells, while it might be useful to characterize, e.g.

local changes in tension by protein binding on liposomes. Thirdly, one might be able to deduce membrane tension from the emission fluctuations of membrane dyes, e.g. laurdan, that are sensitive to hydration, which is a function of tension, packing density, and local curvature 474,475 .

Systematic characterization of mechanical properties

In

Definition of a membrane-adjacent mesh that hinders diffusion

Hindered diffusion of the Band 3 transmembrane protein and a regulatory role of membrane-adjacent cytoskeletal structures in restricting its diffusion in the erythrocyte membrane are demonstrated early in the literature and reveal fundamental principles of the interplay between transmembrane proteins and the underlying cytoskeletal network [479][480][481][482] . Results from single particle tracking (SPT) and fluorescence recovery after photobleaching (FRAP) of E-cadherin and the transferrin receptor revealed that the membrane is 'felt' by some receptors as a compartmentalized fluid with discrete domains that constitute diffusive barriers, giving rise to four principal modes of motion, i.e. immobilized, Brownian, Brownian with superimposed ballistic motion, and confined

Brownian. The dominant mode was confined Brownian motion (64%), whereas ballistic motion was only observed in around 2% of analyzed tracks 483 . The important role of intracellular boundaries, i.e. cortical barriers, was demonstrated by treatment with cytoskeletal drugs 484 and in comparative studies where transmembrane receptors encounter more barriers than GPI-anchored proteins 485 . The measured effective mesh size for the presumed cytoskeletal barriers did not correspond well to assumed sizes of a perfect mesh, suggesting that a dynamic, metabolically active grid was present and encounters with the barrier were probabilistic. This allowed explaining the differences between effective mesh size as probed by barrier-free paths, i.e. the average length a molecule can be dragged along the membrane before encountering a barrier, and ultrastructural information from electron microcopy, and the different temperaturedependent scaling between diffusion coefficients and barrier-free paths 486 . Depending on cell types, and acquisition speeds, effective compartment sizes range from tens to hundreds of nanometers 487 , possibly depending on different cytoskeletal elements, e.g. spectrin in red blood cells and actin 488 .

In the case of transmembrane receptors, immobilization of the receptor on the actin cytoskeleton can be induced by ligand binding 489 . This is illustrated by the behavior of, e.g. the transferrin receptor. Its local diffusion is unhindered, while its reduced hop frequency leads to a much lower effective diffusion coefficient, due to corralling by the actin cytoskeleton 490 . Furthermore, such corralling and tethering to the underlying actin has been proposed to be responsible for the greatly reduced diffusion coefficients upon clustering [491][492][493][494] , that is not readily explained by increases in effective radii of oligomers as would be expected from Brownian motion since in 2D, diffusion coefficients change only logarithmically with cluster size 493 .

There are two ways how an underlying actin cortex might regulate the diffusion and create boundaries for transmembrane proteins: firstly, through direct interaction and binding to the protein, thus immobilizing it along at the boundary, and secondly simply by spatially inhibiting the passage, thus restricting the available space for diffusion without affecting individual microscopic diffusion 495 . The finding that lipids experience similar compartmentalization in cellular membranes led to the membrane-protein picket model, in which a large population of transmembrane proteins is immobilized in the plasma membrane (up to 30% of total membrane proteins 496 ) by its interaction with the underlying actin cytoskeleton, functioning as pickets that maintain the fence, i.e.

the actin mesh, in close proximity to the plasma membrane 497,498 . This creates two kinds of diffusion barriers. 'Free' transmembrane proteins can sterically 499 or specifically 500 experience reduced diffusion due to the fence. In addition, the high density of immobilized pickets creates additional diffusion barriers within the plasma membrane as immobilized 'obstacles', thus slowing down macroscopic diffusion of both lipids 501,502 and proteins 503,504 . Beyond these steric effects on thermal fluctuations, active control of nanocluster formation by dynamic actin structures has been demonstrated conceptually in a minimal in vitro system 505 and for GPI-anchored proteins 373,506 , in which trans-bilayer control is exerted through phosphatidyl-serine mediated coupling 507 . Both active and steric effects on lipid and protein diffusion, and a higher sensitivity of proteins to actin density have been reproduced in vitro 508 .

Intra-bilayer obstacles beyond pickets

Beyond the role of immobilized transmembrane pickets and the underlying actin fence, the plasma membrane itself can generate diffusion barriers and lateral segregation of constituents that is independent of actin. The most notable case is the presence of lipid rafts, short-lived, small scale assemblies of specific membrane lipids, specifically cholesterol and sphingomyelin, which are more ordered, i.e. more densely packed, than a standard phospholipid bilayer and can serve as a local hub for enrichment of some proteins and exclusion of others [START_REF] Lingwood | Lipid rafts as a membrane-organize principle[END_REF][START_REF] Simons | Functional rafts in cell membranes[END_REF][START_REF] Sezgin | The mystery of membrane organization: Composition, regulation and roles of lipid rafts[END_REF]509 . By the generation of line Furthermore, using advanced experimental approaches, e.g. high speed single particle tracking 498,514 and advanced fluorescence correlation spectroscopy 515,516 , one can characterize compartment sizes and distinguish between specific immobilization and 94 steric hindrance. HomoFRET measurements 517 and other polarization-sensitive methods 518 , super-resolution microscopy, and image correlation spectroscopy methods 519 all give information about the organization of proteins within the membrane, e.g. their relative packing density and cluster-sizes.

Functional consequences for signaling

Diffusion and cluster formation are of fundamental functional importance for membrane receptors, e.g. to integrate extracellular inputs into effective signaling outputs 520 . Immunoglobulin E receptors (FcεRI) cluster show increased diffusion and delayed immobilization after ligand binding when actin is disrupted 488 . Similar effects were described for CD36, which in macrophages shows a receptor-specific linear diffusive motion that is actin and microtubule dependent but cholesterol independent.

Furthermore, cytoskeletal perturbation led to decreased clustering and reduced signaling output after activation 521 . Similar findings were made for the insulin receptor 522 . Integrins show a complex diffusion profile with co-existence of multiple populations of different diffusion and immobilization behavior that depends on actin integrity 523 . It was hypothesized that a small fraction of integrins has to be already immobilized on actin in order to be activated upon mechanical stresses. In this scenario the immobilized molecules serve as a hub that is required as a nucleation point, which is growing through the mobile fraction that can efficiently be recruited 524 .

In the case of the antibody-binding Fcγ receptors, diffusion is slowed down upon cholesterol depletion, and controlled by tyrosine kinases, yet independently of receptor phosphorylation. This happens by increase in effective actin mesh size through Syk In summary, the diffusion of transmembrane receptors in the membrane, its regulation through the actin cytoskeleton, and in some cases the ability to form higher order oligomers after ligand binding are of fundamental importance for successful receptor engagement and signaling output. While the importance of cluster formation in EphB2-driven signaling is well established, how EphB2 diffuses and how it depends on actin has not been studied to our knowledge.

Working hypotheses 1. Diffusion of transmembrane receptors

The influence of the organization and interaction of the actin cortex on transmembrane receptor behavior has been identified and studied, in most detail in the context of the immunological synapse 528,529 . Considering the ability of Myosin 1b to interact with EphB2 we thus decided to study the behavior of EphB2 within the plasma membrane and how it is affected by Myosin 1b. We envisioned three possible scenarios:

Myosin 1b changes the dynamic cortical actin network.

If Myosin 1b is involved in controlling the geometry of the dynamic cortical actin network, its depletion might lead to increased lateral diffusivity of EphB2 receptors and alter clustering efficiency by increasing the likelihood of encounters. Such effects have been described for other receptors depending on actin 521,525,526,530 . As EphB2-driven signaling is known to be sensitive to cluster size 310 this might explain the observed difference in cellular behavior after stimulation. One explanation for a change in effective diffusion coefficient might be a change in the confinement size, thus leading to macroscopically larger effective diffusion rates. In that case one would expect increased EphB2 diffusion after depletion of Myosin 1b, an observation that when observed, might be followed up using more advanced methods like high-speed single particle tracking.

Myosin 1b immobilizes EphB2 by linking it to actin.

Myosin 1b could pin a subset of EphB2 receptors to the actin cortex via its interaction with both EphB2 and actin. This immobilized population might serve as a nucleation hub for efficient engagement in signaling, and a loss of it would lead to different outcomes when cells are stimulated. In this case, depletion of Myosin 1b would be expected to increase the mobile fraction as observed by FRAP, while the diffusivity of EphB2 might stay constant regardless of Myosin 1b.

Myosin 1b changes the steady-state distribution of EphB2 receptor clusters.

Lastly, we postulated that even without affecting immobilization to actin and EphB2's diffusion coefficient, Myosin 1b might be directly involved in the determination of steady-state cluster size distribution. We employed fluorescence anisotropy measurements to assess this question.

Actin geometry and dynamics

Secondly, beyond an effect of Myosin 1b on EphB2 diffusion or clustering, we also hypothesized that Myosin 1b could be important for the generation of actin flows which are fundamentally linked to cellular contraction. We thus employed TIRF-SIM imaging of the ventral actin cytoskeleton before and after stimulation of EphB2 with its ligand in the presence and absence of Myosin 1b. We quantified and compared the generated flows by performing particle image velocimetry (PIV) on the obtained datasets.

The following scenarios could explain the reduced contractile efficiency:

Myosin 1b controls actomyosin network geometry.

It is well established that actin network structure controls network contractility [START_REF] Reymann | Actin network architecture can determine myosin motor activity[END_REF]531 .

If Myosin 1b was important for the generation of Myosin II-driven contraction within the ventral side by e.g. changing the actin geometry at the ventral surface or controlling connectivity of the network, its absence could lead to reduced flow, thus explaining why cells were contracting less, although signaling was functional and Myosin II was successfully activated.

Myosin 1b acts as a molecular clutch for actin flows.

In contrast, Myosin 1b might as well function like a clutch which is necessary to couple the generated flows to the plasma membrane in order to allow for efficient contraction. Depletion of Myosin 1b could thus lead to increased flow velocities.

These increased flows and the observed reduction in contractility might be mechanistically linked because the actin generated flows need to be efficiently coupled to the plasma membrane in order to allow the cell to contract.

Myosin 1b changes large scale coherence of the cytoskeleton.

Related to but different from the first hypothesis, Myosin 1b might alter the cytoskeletal coherence of the cells ventral surface rather than its network geometry.

Cytoskeletal coherence is the concept that a locally highly dynamic network, as is the case for actin, needs a controlled spatial organization in order to create, e.g. forces across the cell body or well aligned traction forces, as can be observed in cells [START_REF] Cai | Force propagation across cells: mechanical coherence of dynamic cytoskeletons[END_REF][START_REF] Cai | Cytoskeletal coherence requires myosin-IIA contractility[END_REF] . If Myosin 1b were required in such coherence, one might expect random or chaotic local variations in flow that do not coalesce into spatially well-oriented flows.

We have used different techniques to test these hypotheses that we present hereafter.

97

Figure 46 Effect of drug treatments on cell morphology.

Representative fluorescence micrographs of EphHEK cells after treatment with respective drugs. The micrographs show the ventral focal plane of EphB2-YFP that was used as a marker for the plasma membrane due to its homogeneous distribution within the plasma membrane.

Results

EphB2 diffusion

Ventral FRAP reveals no influence of Myosin 1b on EphB2's diffusion coefficient.

Bleaching a circular spot at the ventral surface of EphHEK cells allows the estimation of an effective diffusion coefficient that represents the weighted average of the molecule population's diffusion coefficients (Figure 47A). We treated the cells with mild doses of cytoskeletal drugs which show clear changes in morphology yet maintain a stable adhesion within the experimental time frame. We used LatA to depolymerize actin 532 , CK-666 to specifically inhibit the Arp2/3 complex 533 and thus the maintenance of branched actin networks, and SMIFH2 534 to inhibit formins and thus the maintenance of linear actin structures.

Figure 46 shows representative images that reveal clear differences in the cellular morphology corresponding to the drug's expected effects, visualized by imaging the plasma membrane-localized EphB2-YFP receptor. In comparison to DMSO treated

99

Equatorial FRAP reveals actin-dependent changes in EphB2 diffusivity after activation.

In order to exclude any specific effect of the ventral surface and the specific nature of adhesion sites that are present at the interface and might thus change the diffusion of EphB2 we performed FRAP analysis at the equatorial plane of cells, both before and after stimulation of EphB2 with ephrin-B1 (Figure 47A). As the geometry of the bleach is not controlled in Z in this approach we plot recovery halftimes normalized by the value of the respective control experiment (either DMSO, or the sicontrol) that allow comparing the different conditions to each other. We observed a large spread in the We observed a marked decrease in mobile fraction after stimulation with ephrin-B1 in both control conditions in agreement with a large fraction of the receptors getting engaged in large, quasi-immobile clusters. After LatA treatment the average was and stimulation with ephrin-B1. These measurements were performed towards the cell center where actin flows were only marginally detectable (see e.g. Figure 54). In agreement with the FRAP results, FCS of EphB2 revealed no difference in the characteristic diffusion time in absence of Myosin 1b and after stimulation at the ventral side. Again, the measurement after stimulation detects only diffusion of the mobile molecules (Figure 50). Representative raw data and fitting results underpinning In summary, we did not observe any effect of Myosin 1b on EphB2 diffusion, both before and after receptor stimulation with ephrin-B1. Nevertheless, we saw a stimulation-dependent effect of LatA treatment that was more pronounced after receptor stimulation, yet only observable at the equatorial plane.

Figure 49 Mobile fractions

The left panel shows the mobile fractions of EphB2-YFP calculated from ventral FRAP for the different conditions as indicated on the bottom. n =DMSO (11), LatA (11), CK666 (11), SMIFH2 (12), sicontrol( 10), siMyo1b( 6), siERM (7). The right panel shows the mobile fractions of EphB2-YFP after equatorial FRAP, before and after global stimulation of cells with ephrin-B1. n=DMSO(14/18), LatA (16/16), sicontrol(15/12), siMyo1b (14/14). We decided to investigate the cluster size at higher precision and in a more quantitative way in collaboration with Satyajit Mayor's lab at NCBS in Bangalore. We Treatment with PClP freezes actin dynamics.

Treatment with 1 μM PClP abolishes actin dynamics in a cell-wide manner and activation of EphB2 after PClP treatment did not induce any change in the observed flows (Figure 54B). This concentration of PClP is supposed to be low enough to restrict the inhibition effect to all class 1 myosins, and should in principle not affect Myosin II 535 . This very striking observation thus suggests a very important role for class 1 myosins in actin flows parallel to the plasma membrane that was not envisaged before.

Depletion of Myosin 1b affects flow profiles in two distinct ways.

Cells transfected with control siRNA exhibited similar flows as untreated cells and DMSO treated cells. When Myosin 1b was depleted, visual inspection of the heatmaps suggested a slightly increased presence of (disperse) F-actin flows throughout the cell, i.e. a higher number of 'yellow' regions in the cell body (Figure 55). This observation requires further analysis of the data, e.g. binning of flow velocities and comparing the 106 relative change in bin size between sicontrol and siMyosin 1b cells and quantitative analysis of vector scatter plots limited to central cell regions. in flow rates, with a strong correlation (yet to be quantified). These flows tended to propagate over time and showed clear directionality towards the cell body. In cells initially lacking a clear lamellipodial structure, stimulation of EphB2 led to a different outcome. The flows increased in a dispersed cell-wide manner that did not show a clear spatial coherence over time. This resulted in two fundamentally different total average flow maps, in which the prior case showed extended areas of large flows, whereas the latter one exhibits increased flows, yet with an apparently random localization throughout the cell.

This difference in behavior is epitomized by plotting the individual axial components of flow vectors (Figure 56). Activation in control conditions led to increased flows concentrating around contraction axes (dashed lines). In contrast, in the case of expanded flows after depletion of Myosin 1b, we observed a shift along the axis of increased flows (dashed mask), while the lack in spatial coherence in the latter case resulted in condensed flow vector distribution.

Discussion

The results of this second part of the thesis have been performed over the course of the last 9 months and are thus to be considered preliminary. A number of control experiments are still to be performed and more data needs to be analyzed to conclude on the experimental observations.

Diffusion & spatial organization of EphB2

EphB2 shows fast diffusion in the EphHEK plasma membrane.

Our ventral FRAP experiments suggest an effective diffusion coefficient of EphB2 on the order of 0.3 μm 2. s -1 . This is in line with predictions for proteins with a single transmembrane domain 536,537 , and consistent with previously reported values of transmembrane protein diffusion in HEK293 cells, e.g. the dopamine transporter (0.36 μm 2 .s -1 ) 538 and the β2-adrenergic receptor (0.4-1.2 μm 2 .s -1 ) 539 . The diffusion of EphB2 is roughly 3 to 4 times lower than what has been reported for the macroscopic diffusion of lipids in cells 497 . Although the effective bleaching radii had to be estimated and thus Deff in Figure 47 can only feature as a rough estimate, it agrees well with the results obtained from FCS, that give a ventral effective diffusion coefficient for EphB2 on the order of 0.5 µm 2 .s -1

One might consider that EphB2's relatively high diffusion constant is related to its biological function in which efficient spatial exploration of free receptors would allow the efficient formation of functional signaling complexes upon local ligand binding.

Such mechanism has been proposed for Rhodopsin which exhibits similarly high diffusion in isolated rods 540 . It would be interesting to compare EphB2 diffusion to that of its deactivating phosphatase PTP1B 314 , which is present at the plasma membrane at low concentrations, and model how relative differences in diffusion might create a dynamic regulatory network for receptor signaling.

Myosin 1b has no obvious effect on EphB2 diffusion or spatial organization.

Using both FRAP and FCS we find no evidence for a role of Myosin 1b in the regulation of EphB2 receptor diffusion. Furthermore, our results regarding EphB2's fluorescence anisotropy suggest that the EphB2 receptor distribution is likely unaffected directly by Myosin 1b. Yet, we did not experimentally characterize the dynamics of EphB2 anisotropy just after stimulation with ephrin-B1 but only after 30 minutes of activation at which big cluster formation and contraction have happened.

Before activation we did not detect a difference in anisotropy values between control and Myosin 1b depletion, yet the strength of the data was considerably reduced due to the wide spread in anisotropy values we observe at given EphB2 intensities and thus makes it hard to firmly conclude. Still, the fact that Myosin 1b remains homogeneously distributed in the plasma membrane after receptor stimulation makes it unlikely that it would act as a direct effector that drives receptor condensation. A recent publication has shown an elegant approach to studying such problems at high spatial and temporal resolution: Using nano-patterned substrates to locally activate Eph receptors and enhanced number and brightness analysis allowed quantification of the heterogeneous cluster population of EphB at steady state and its change towards higher order oligomers over time after ligand binding 311,312 . In order to study clustering behavior after stimulation in more detail, it thus seems ideal to employ the experimental system used in these publications and characterize both the potential change in steady state distribution (missed in the anisotropy measurements due to the high spread) and its behavior over time after activation with ephrin-B1. As a default, one might as well resort to more classical approaches, e.g. PALM/STORM imaging, something that we had envisioned earlier and for which we already possess the required plasmid, i.e. mEos3.2 472 tagged EphB2, but we did not have the time to proceed during this thesis.

Myosin 1b depletion changes mobile fractions after stimulation

We observe a striking effect of Myosin 1b depletion on the mobile fractions of EphB2 obtained from our equatorial FRAP results after stimulation with ephrin-B1(Figure 49).

Whereas in all other conditions, including LatA treatment albeit at higher spread, lead to a reduction in the mobile fraction, corresponding to the expected immobilization of the receptors after clustering, we do not observe such change in mobile fraction after depletion of Myosin 1b. This result is in contradiction with the macroscopic clusters we observed under the same conditions (Figure 48), the homogeneous distribution of

Effects of cytoskeletal drugs.

The coalescence of EphB2 clusters into large scale structures after LatA treatment suggests that EphB2 clusters are spatially separated to a certain extent by the underlying actin cytoskeleton which precludes large scale coalescence after stimulation, either through binding or because it acts as a diffusion barrier for large clusters.

In the light of this it seems puzzling that only LatA treatment after activation shows a significant effect on effective receptor diffusion. Considering the non-significant decrease in recovery halftime at the equatorial plane after LatA treatment before stimulation of EphB2 it is tempting and reasonable to speculate that with higher precision methods one might expect a generalized effect of LatA. Previous reports suggest that upon LatA treatment confinement areas (as probed for lipids) increase roughly by a factor of 2 497 . In light of this and the fact that the confinement size in HEK293 cells is on the order of 70 nm 28 , only methods offering high spatial and temporal precision, e.g. high-speed single particle tracking of EphB2 or advanced FCS, would allow a detailed characterization of confinement zone size and microscopic diffusion coefficients. In that case, one might additionally be able to distinguish between mere confinement, i.e. the actin mesh being a passive boundary for EphB2, or local immobilization of receptors to the actin mesh via either direct or mediated binding 487 .

Different effects of LatA at the ventral and equatorial plane.

Considering the absence of any effect of LatA treatment on EphB2 diffusion and mobile fraction at the ventral side, one might speculate that this is related to the ventral's side specific function and composition, i.e. integrin-mediated adhesion and presence of stress fibers. It might thus be less sensitive to the drug treatments. As we did observe a clear change in morphology upon drug treatment, this would imply that a specifically stable subset of actin structures withstands these treatments better than, e.g. the cortex, and is sufficient to restrict the diffusion of EphB2. Indeed, at the concentrations used in our experiments, cells maintained attached to the substrate during the course of the experiments, yet do detach at higher concentrations of LatA (250 nM).

TIRF-SIM

PIV treatment of TIRF-SIM datasets successfully recovers actin flow speeds.

With the analysis described in this thesis we find F-actin flow speeds (dynamic range between 1 and 40 nm/s) that are in excellent agreement with reported values throughout the literature, and compatible with results obtained from methods ranging from speckle microscopy to spatio-temporal image correlation spectrosocopy [541][542][543][544] .

PClP blocks actin flows at low concentrations.

We find that PClP treatment, a drug that at this concentration should be specific for The availability and lack of alternatives makes PClP a particularly attractive compound for cell biological studies in which depletion is inefficient or not possible, e.g. in primary cells [START_REF] Iuliano | Myosin 1b promotes axon formation by regulating actin wave propagation and growth cone dynamics[END_REF]190,545 . Yet, considering its massive effects on actin flows, an off-target effect that goes beyond blockage of class 1 myosins should be at least considered in the interpretation of experimental results. For now no conclusive evidence is present, yet our and other's observations regarding the effect on actin flows pose an urgent issue, that is of fundamental importance to the biological community working on class 1 myosins. If PClP treatment were to be specific beyond doubt, this would mean that class 1 Myosins would be a newly identified essential factor for in-plane actin flows. In this case, it would be of fundamental interest to quantify the relative abundance of all different isoforms, e.g. using quantitative mass spectrometry, and secondly start systematic knock-down experiments to identify the isoforms that are relevant for inplane actin flows.

Myosin 1b depletion changes actin flow dynamics.

We observe an intriguing yet non-trivial effect of Myosin 1b depletion on actin flows.

At steady-state we see a slightly increased magnitude of flows around the cell. After activation, cells exhibit two distinct behaviors. One subpopulation shows increased coordinated flow velocities that tend to expand over large areas and start locally (class 1), while others show a generalized and disorganized, yet less pronounced, increase in flows around the cell's ventral surface (class 2). There is a correlation between the presence of a lamellipodial structure at steady-state (already being quite dynamic) and class 1 behavior, suggesting that pre-existing lamellipodial actin flows are sufficient to

Clutch hypothesis

In a clutch model, one would expect that the absence of Myosin 1b would combine both increased actin flows and reduced contractility. As the flows would be sufficiently generated by activated Myosin II but experience less counteracting force by membrane attachment they should increase in magnitude. Yet, in absence of Myosin 1b, these flows would less efficiently be transmitted to the membrane thus explaining the decrease in contractility. This hypothesis is supported by recent evidence showing that Myosin 1c puts E-cadherins under tension by linking them to actin 546 . In the case of Myosin 1b a similar mechanism could potentially couple EphB2 to underlying actin dynamics. Interestingly, due to its catch-bond behavior and the spatial restriction of physiological EphB2 activation at cell contact sites through ligand binding might additionally serve as a geometrical cue defining an axis of contraction in cellulo.

Altered network geometry

Another alternative is that Myosin 1b might simply change the local architecture of the actin network and thus lead to reduced contractility. In vitro studies have shown that contractility is a function of the actin network geometry (ordered bundles, disordered network, disordered bundles) and their connectivity, governed by crosslinkers and notably Arp2/3 531,547 . This scenario, which is in agreement with recent in vitro results in the lab (unpublished, Julien Pernier), does however not offer an obvious mechanistic link between flow speed increases and reduced contractility that we observe.

Nevertheless, it would be consistent with reported phase diagrams of the percolation dynamics in active gels, in which at intermediate motor activity levels subtle changes in network connectivity would a priori be sufficient to switch the systems behavior from global contractility to local contractility and non-contractile active solutions 548 . In such a scenario the cells would be predicted to be close to the transition point in the phase diagram but consistently in the global contraction phase. Myosin 1b depletion could lead to a small loss in network connectivity that might be sufficient to shift the system towards either local contractions or, at a slightly higher loss in connectivity, to active solutions without large scale order.

The obtained results strongly suggest that actin dynamics are changed after depletion of Myosin 1b, which is specifically striking after induction of EphB2-driven cell contraction.

In order to understand this phenotype and get down to a mechanistic understanding two main hypotheses are promising:

Clutch hypothesis of Myosin 1b

To evidence the role of Myosin 1b as a clutch, potentially specific for EphB2, one In conclusion, even if the mechanism by which Myosin 1b changes cellular response to EphB2 stimulation is still not fully elucidated, I have finally been able to pinpoint its function to a reasonably well-defined and quantifiable observation, i.e. changed actin flow dynamics. Future experiments will hopefully be able to dissect the mechanism that causes this observation, and follow it up considering other reported phenotypes of Myosin 1b depletion. This will allow concluding on whether Myosin 1b has a common underlying mechanism shared between all those biological processes.

Résumé

La myosine 1b, un moteur moléculaire nonconventionnel, est impliquée dans une variété de processus cellulaires, contrôlant, par exemple la morphologie endom embranaire, le développement des axones et la ségrégation cellulaire. Le mécanisme par lequel la myosine 1b est capable de remplir ses fonctions dans une variété de régions cellulaires reste inconnu à ce jour, mais les phénotypes décrits suggèrent un rôle de la myosine 1b à l'interface entre les membranes et l'actine. Notamment, elle est nécessaire pour une ségrégation cellulaire efficace après l'activation du récepteur EphB2 qui induit la contraction cellulaire. Cette thèse présente une caractérisation détaillée des effets de la myosine 1b sur (1) les propriétés mécaniques de la membrane cellulaire, étudiées par tirage de tubes membranaires à l'aide d'une pince optique, et (2) la dynamique du cytosquelette d'actine et des protéines transmembranaires, étudiées à l'aide d'une variété de méthodes basées sur l'imagerie microscopique. Dans cette thèse nous montrons que les myosines de classe 1 ne changent pas généralem ent la tension membranaire effective dans les cellules adhérentes, probablement en raison de mécanismes de compensation efficaces. De plus, nous montrons que la friction entre le cortex d'actine et la membrane plasmique dépend de la densité totale des liens entre membrane et cortex et de la fraction relative des protéines liées. L'inefficacité de la contraction cellulaire observée en absence de la myosine 1b est donc indépendante d'un changement global et persistant de la tension membranaire effective. Dans la deuxième partie de cette thèse, nous montrons que la myosine 1b ne modifie pas la dynamique du récepteur EphB2, c'est-à-dire son comportement de diffusion et de clustering, dans la membrane plasmique. Enfin, en utilisant la microscopie TIRF-SIM et une description quantitative des flux d'actine, nous révélons que la myosine 1b a un effet intrigant mais non-intuitif sur la dynamique de l'actine à la surfac e ventrale des cellules. En conclusion, même si le mécanisme par lequel la myosine 1b change la réponse cellulaire après stimulation des récepteurs EphB2 reste encore inconnu, nous avons finalem ent été en mesure de lier sa fonction à une observation bien définie et quantifiable, à savoir la modification de la dynamique des flux d'actine. Les expériences futures seront en mesure de répondre à cette observation et de disséquer son mécanisme sousjacent. Cela permettra de conclure si la myosine 1b a un effet commun qui régit tous ses rôles biologiques décrits.

Mots Clés

Myosine 1b, EphB2, mécanique membranaire, pince optique, nanotubes membranaires, diffusion de récepteurs transmembranaires, flux d'actine, TIRF-SIM

Abstract

The unconventional m otor protein myosin 1b is involved in a variety of cellular processes, controlling, e.g. endom embrane shape, axon developm ent, and cell segregation. The m echanism by which myosin 1b is able to fulfil its functions in a variety of cellular locations rem ains unknown to date, yet the described phenotypes suggest a role of myosin 1b at the interface between m embranes and actin. Notably, it is required for efficient cell segregation after activation of the EphB2 receptor which induces cell contraction. This thesis presents a detailed characterization of the effects of myosin 1b on (1) the m echanical properties of the cell membrane, studied by membrane tether pulling with an optical tweezer, and (2) the dynamics of the actin cytoskeleton and transm embrane proteins, studied by a variety of microscopy-based m ethods. Here w e show that class 1 myosins do not generally change effective m embrane tension in adherent cells, likely due to efficient com pensation mechanisms. Furtherm ore, we show that friction between the actin cortex and the plasm a m embrane depends on the total density of membrane-cortex linkers and the relative fraction of bound proteins. The observed deficiency in cell contraction in absence of myosin 1b is thus independent of a persistent, global change in effective m embrane tension. In the second part of this thesis, we show that myosin 1b likely does not change EphB2's receptor dynamics in the plasm a membrane, i.e. its diffusion and clustering behavior. Finally, using TIRF-SIM im aging and quantitative description of actin flows, we reveal that m yosin 1b has an intriguing yet non-intuitive effect on actin dynamics at the cellular ventral surface. In conclusion, even if the m echanism by which myosin 1b changes cellular response to EphB2 stimulation still rem ains unknown, we have finally been able t o pinpoint its function to a well -defined and quantifiable observation, i.e. changed actin flow dynamics. Future experim ents will be able to address this observation and dissect its underlying mechanism. This will allow concluding on whether myosin 1b has a comm on effect that governs all its described biological roles.

Figure 1

 1 Figure 1 The cell boundary. ..............................................................................................................

Figure 2

 2 Figure 2 Schematic view of plasma membrane organization. .......................................................

Figure 3

 3 Figure 3 Cytoskeletal elements .........................................................................................................

Figure 4

 4 Figure 4 Actin biochemistry ..............................................................................................................

Figure 5

 5 Figure 5 Actin modifications by actin-binding proteins. ..................................................................

Figure 6

 6 Figure 6 Control of actin dynamics by Rho GTPases. ......................................................................

Figure 7 F

 7 Figure 7 F-actin homeostasis through inter-network crosstalk..........................................................

Figure 8

 8 Figure 8 Cellular actin structures and their machineries. ...............................................................

Figure 9

 9 Figure 9 Actin structures at the leading edge ...............................................................................

Figure 10

 10 Figure 10 Amoeboid vs. lamellipodial motion ................................................................................

Figure 11

 11 Figure 11 Actomyosin contractility. ................................................................................................

Figure 12 PM

 12 Figure 12 PM-actin linkers ................................................................................................................

Figure 13

 13 Figure 13 Class 1 myosins ................................................................................................................

Figure 14

 14 Figure 14 Regulation of myosin 1b's catch-bond. .........................................................................

Figure 15

 15 Figure 15 ERM structure & Ezrin activation ......................................................................................

Figure 16

 16 Figure 16 Bleb dynamics in cells. ....................................................................................................

Figure 17

 17 Figure 17 Eph-ephrin signaling ........................................................................................................

Figure 18

 18 Figure 18 Eph/ephrin as a signaling hub ........................................................................................

Figure 19

 19 Figure 19 Cell sorting by EphB2/ephrin-B in intestinal crypts. ........................................................

Figure 20

 20 Figure 20 Cell repulsion through contact inhibition of locomotion. ..............................................

Figure 21

 21 Figure 21 Ventral vs. equatorial FRAP .............................................................................................

Figure 22 FRAP

 22 Figure 22 FRAP data analysis ..........................................................................................................

Figure 23

 23 Figure 23 Lateral bleach profile in ventral FRAP. ............................................................................

Figure 24

 24 Figure 24 Working principle of SIM ..................................................................................................

Figure 25

 25 Figure 25 TIRF-SIM reconstruction using fairSIM ...............................................................................

Figure 26

 26 Figure 26 Binary ridge map creation from TIRF-SIM data ...............................................................

Figure 27

 27 Figure 27 PIV analysis ......................................................................................................................

Figure 28

 28 Figure 28 Lipid membrane deformations .......................................................................................

Figure 29

 29 Figure 29 Studying membrane mechanics in cells. .......................................................................

Figure 30

 30 Figure 30 Dynamic tether pulling. ...................................................................................................

Figure 31

 31 Figure 31 Local stimulation of EphB2 with ephrin-B1 coated beads. ............................................

Figure 32

 32 Figure 32 Beads induce receptor recruitment and tyrosine phosphorylation. .............................

Figure 33

 33 Figure 33 Cell contraction after local stimulation with ephrin-B1 beads. ......................................

Figure 34

 34 Figure 34 Micropipet aspiration ......................................................................................................

Figure 35 72 Figure 73 Figure 75 Figure 77 Figure 78 Figure 80 Figure 81 Figure 88 Figure 93 Figure 97 Figure 98 Figure 99 Figure

 35727375777880818893979899 Figure 35 Measuring tether force as a reporter for effective membrane tension. .......................

58 viii 1 Preface

 581 of published tether forces for different cell lines, as summarized in 378 . ............ Previous work in the lab of Evelyne Coudrier has established a role of Myosin 1b in

Figure 2

 2 Figure 2 Schematic view of plasma membrane organization.This schematic view of the PM underlined by actin (green). Glycerophospholipids (GPL) form the majority of the PM lipid content. In addition one finds sphingomyelin (SM) and glycosphingolipids (GSL) that can form nano-domains (lipid rafts) together with cholesterol (red). Integral, bilayer-spanning transmembrane (TM) proteins can have affinities for 'raft' and 'non-raft' phases. Peripheral proteins can be attached to the leaflets of the plasma membrane through lipid anchors, e.g. acylation or glycosylphosphatidylinositol (GPI). Proteins binding to actin and the plasma membrane can serve as pickets, to form the membrane skeleton, as posited in the picket-fence model. Modified from reference 11.

Figure 3

 3 Figure 3 Cytoskeletal elements (A) Schematic representation of the three canonical cytoskeletal elements actin (top), microtubules (middle), and intermediate filaments (bottom). (reference 29) | (B) Proposed cytoskeleton-like structures as found in vivo by fluorescence microscopy, and their respective in vitro structures imaged by electron microscopy (inset). (modified from reference 30) Cytidine triphosphate synthase (CtpS) from Drosophila egg chambers and Phosphorylation inhibited by long chain bases (Pil1) from fission yeast.

Figure 4

 4 Figure 4 Actin biochemistry (A) Structure of the actin subunit [PDB: 1ATN]. Ribbon diagram (left) and space-filling representation (right), each with ATP bound. N (amino terminus), C (carboxyl terminus), 1-4 label the four domains. The ribbon diagram shows the DNase-I binding loop, whereas the space-filled subunit shows both the nucleotide binding cleft and the barbed end groove. |(B) Nucleation rates from monomers, to dimers, trimers and polymers. |(C) Polarized actin filament elongation. The left-hand side shows an electron micrograph from a negatively stained actin filament decorated with Myosin head fragments, giving rise to a pointed end (top) and a barbed end (bottom). Elongation is clearly favored at the barbed end. The right-hand side shows the respective rate constants for elongation and disassembly at both ends. | Association rates in units of μM -1 .sec -1 ; dissociation rates in units sec -1 . Modified from reference 31.

Figure 5

 5 Figure 5 Actin modifications by actin-binding proteins. Overview of different actin modifications that are mediated by actin-binding proteins in cells. Reference 31.

Figure 6

 6 Figure 6 Control of actin dynamics by Rho GTPases.(A) Schematic representation of the Rho GTPase cycle: Activation of Rho GTPases involves a nucleotide exchange (GDP  GTP) that is catalyzed by a guanine nucleotide exchange factor (GEF). GTPase-activating proteins (GAP) trigger hydrolysis of GTP, returning the GTPase to its inactive GDP-bound state. Membrane localization is controlled by a lipid anchor that can be masked by the guanine nucleotide exchange inhibitior (GDI). Reference 53 | (B) Overview of the different Rho GTPases (Cdc42, RhoA, Rac) that control cellular actin dynamics in the lamellipodium. Rac is involved in recruiting Arp2/3 and its activator WAVE to generated branched networks at the leading edge (center). Furthermore RhoA can drive actin polymerization through formin activation (mDia). Both Cdc42 and focal adhesion signaling control the activation of Rac, which is limited by negative feedbacks through Arpin (an Arp2/3 inhibitor) and SRGAP (a GAP for Rac). Towards the cell center, RhoC controls actin filament severing through LIMK/cofilin, and contractility through ROCK. Reference 54.

Figure 7 F

 7 Figure 7 F-actin homeostasis through inter-network crosstalk. F-actin networks are controlled by signaling and are dynamically interconnected by a limited pool of G-actin subunits. E.g., disassembly of stress fibers can drive polymerization of branched networks by increasing the available amount of G-actin. Reference 42

Figure 8

 8 Figure 8 Cellular actin structures and their machineries. Branched actin filaments (red) are generated from Arp2/3 and its regulatory interaction partners, e.g. WASP and WASH, at different locations in the cell. The leading edge of the cell is characterized by and broad actin network that decreases in density towards the cell center. Linear actin filament bundles (green) are found in thin membrane protrusions at the front, as well as in stress fibers. The stress fibers containing Myosin II link focal adhesions at the ventral surface yet are also found in the dorsal parts of the cell. The right-hand side shows the architecture of filopodia (top) and lamellipodia (bottom) in more detail. Reference 55

Figure 9

 9 Figure 9 Actin structures at the leading edge (A) Confocal fluorescen micrograph showing the presence of lamellipodia, filopodia, focal adhesions and ventral stress fibers in a cell. Myosin II is represented in red, Actin in turquoise. Modified from reference 62|(B) Electron micrograph showing the ultrastructure of actin at the leading edge in false colors, highlighting long bundled filaments (turquoise) that are rooted in an actin meshwork (lamella, violet) which is separated from the leading edge through a high-density mesh of actin (lamellipodium, orange). Modified from reference 77|(C&D) Super-resolved dorsal and ventral side of a lamellipodium through dual-objective STORM imaging. Whereas the dorsal side (C) shows a homogeneous mesh, the ventral side (D) shows prominent stress fibers. Modified from reference 79.

Figure 10

 10 Figure 10 Amoeboid vs. lamellipodial motion (A) Schematic depiction of the differences between amoeboid (left) and lamellipodial (right) motion. Amoeboid motion is characterized by generation of blebs at the leading edge of cells with a homogeneous cortex. Blebs are subsequently lined by a newly assembling cortex. Lamellipodial motion is characterized by a large actin dense structure at the leading edge, i.e. a lamellipodium.|(B) Representative images of cells migrating in lamellipodial (top) and amoeboid mode (bottom) derived from common precursor cells through adhesion-based selection (suspSL suspension subline; adhSL adhesion subline). The left-hand panel shows a DIC micrograph, the arrow highlights the lamellipodium, arrow heads indicate matured blebs, and the asterisk shows a nascent/young bleb. The right-hand panel show the respective fluorescence micrographs through staining with Lifeact-mCherry, in which one can clearly observe the lack of cortex in the newly assembling bleb, and the high density of actin in the lamellipodium. Reference 95

Figure 11

 11 Figure 11 Actomyosin contractility. (A) Schematic depiction of Myosin II and actin, the key players in actomyosin contractility. |(B) The basic outcome of Myosin II activity on actin can lead to both contraction or extension depending on the filament orientation (parallel vs. anti-parallel). |(C) Cross-linked actin bundles can lead to contraction by Myosin II assemblies through creation of tensile and contractile stresses on the filament, eventually leading to filament buckling. |(D) Reconstitution of actomyosin contractility in vitro by addition of Myosin II filaments to a pre-assembled, homogeneous actin network. |(E) Cells create highly polarized, inward facing traction forces that show symmetry over cellular length scales. Modified from reference 102

Figure 12 PM

 12 Figure 12 PM-actin linkersSchematic depiciton of the fundamental ways that proteins couple the actin cortex to the plasma membrane. From left to right : Direct interaction between a transmembrane protein and actin, coupling via an adaptor / adaptor complex, direct binding of a peripheral protein to both actin and the plasma membrane, or via an adaptor complex. Adapted from reference 135

Figure 13

 13 Figure 13 Class 1 myosins (A) Domains of class 1 myosins, with the N-terminal motor domain (blue), the neck / lever arm bound to calmodulin light chains (yellow), and the C-terminal tail domain. The shown structure is not a crystal structure but a predicted Myosin 1a structure from homology inference. Reference 144|(B) Schematic representation of the molecular origin of different force-sensitivities between myosin 1b and myosin 1c based on different rate-limiting steps during their ATPase cycle. | (C) Characterization of different sensitivities to force of myosin 1b and myosin 1c: Effect of force on the duty ratio (top), the generated power (middle), and the motility rate (bottom). Modified from reference 172

  difference is partly controlled by the N-terminal region of Myosin 1c and Myosin 1b as evidenced by biochemical studies swapping domains 173 and crystallography 174 . Due to its catch bond behavior, Myosin 1b can form and elongate membrane tubes from GUVs along bundled actin in vitro 4 .

Figure 14

 14 Figure 14 Regulation of myosin 1b's catch-bond. (A) The negative effect of calcium on catch-bond behavior. Upon addition of calcium, the increase in actin attachment lifetime is lost. |(B) Catch-bond behavior is regulated by the length of the lever arm. Myosin 1b isoforms with different length due to alternative splicing in the IQ domains ( a : 6, b : 5, c : 4 IQ domains) show decreased attachment lifetimes with decreasing lever arm length. The IQ mutant which has only one IQ domain shows similar behavior as upon calcium treatment. Reference 172

immunological synapse 193 .

 193 It can bind to G-actin and promotes G-actin accumulation and membrane ruffling at the leading edge of endothelial cells 194 . It is involved in the translocation of the glucose transporter GLUT4 to the plasma membrane downstream of insulin signaling 195 .

Figure 15

 15 Figure 15 ERM structure & Ezrin activation (A) Domains of ERM proteins: The N-terminal part contains a FERM domain that binds to phosphoinositides, and the C-terminus contains the actin binding site, connected via an α-helical domain. | (B) Ezrin is activated through sequential phosphorylation and unmasking of its binding domains. Ezrin has an autoinhibited conformation which masks both its binding sites for PI(4,5)P2 and actin. Upon phosphorylation at its C-terminus and PI(4,5)P2 binding Ezrin can efficiently couple actin to the plasma membrane and interact with other adaptor proteins, e.g. EBP50. Reference 225

  and are phosphorylation targets252 . Furthermore, they have been shown to be important in the establishment of the immunological synapse. Both Ezrin and Moesin were shown to colocalize with CD43 and drive its spatial segregation, i.e. the exclusion from the central zone of the immunological synapse between antigen presenting cells and T cells, and towards the distal pole[253][254][255] . Subsequent work described a functional link between early ERM dephosphorylation at the synapse site and increased deformability, supposedly driven by decreased actin membrane linkage, thus facilitation the synapse formation256 . Direct comparison of Ezrin and Moesin in T cell activation, showed that both proteins have complementary functions with differences in cellular localization257,258 . In B cells, a role of Ezrin has been established in tuning humoral activity, by means of changed B cell receptor diffusion and altered clustering behavior[259][260][261] , as well as functional differences between Ezrin and Moesin, based on a non-conserved tyrosine residue relevant for JNK signaling262

  269 . Bleb formation is driven by increases in cell contractility. It can be induced by injection of the catalytic subunit of MLCK 270 . It critically depends on cortex tension, and can be experimentally induced by laser ablation 271 . The importance of cortical integrity in the control of blebbing propensity is highlighted by observation of impaired cell movement and increased membrane blebbing in cells with disturbed cortices 272 .

Figure 16

 16 Figure 16 Bleb dynamics in cells. (A) Hydrostatic generation of blebs can be triggered by either a loss in membrane-cortex attachment (left) or cortex disassembly (right) leading to bleb expansion. |(B) Assembly of a contractile cortex along the bleb surface allows the bleb to retract.|(C) Fluorescence end electron micrograph of blebs in a cell. Fluorescence signals : plasma membrane (red) and actin (green). Reference 267

Figure 17

 17 Figure 17 Eph-ephrin signaling (A) Both Eph receptors and corresponding ephrins are associated to the cell membrane, drive cell-cell communication and are involved in a variety of cellular properties. |(B) Domain architecture of Eph and ephrins. Both Ephs and ephrin-Bs can be directly phosphorylated and recruit accessory proteins, whereas the GPI-linked ephrin-As do not have an intracellular domain that can itself serve as a hub for proteins. |(C) Clustering. Upon ligand-binding, the receptor-ligand complexes get phosphorylated and clustering leads to signal amplification. Both Eph receptors and their ephrin ligands engage in signaling, i.e. Eph-ephrin interaction can drive bidirectional signaling. Modified from reference 316.

Figure 19

 19 Figure 19 Cell sorting by EphB2/ephrin-B in intestinal crypts. EphB2/ephrin-B signalling maintains the stem cell niche at the bottom of intestinal crypts. Stem cells (green) are maintained in the crypt through a repulsive opposing gradient between EphB2 (stem cells) and ephrin-B (differentiated cells that move out of the crypt). The right inset shows the dual function of this gradient, controlling both proliferation and migration. Reference 316

Figure 20

 20 Figure 20 Cell repulsion through contact inhibition of locomotion. (A) Cellular contact at the leading edge activates receptors that elicit a CIL response.|(B) In a first step, protrusion formation is inhibited at the leading edge through changes in Rho GTPase activity, i.e. activation of RhoA and inhibition of Rac. |(C) This initial phase is followed by the sequential steps of contraction and repolarization, which can happen in different order depending on the cell type and involved receptors. |(D) The inversion of cell polarity and detachment of the cell-cell contact leads to migration away from the contact site. Reference 355

  Transfection of cells with protein-encoding plasmids was performed using Lipofectamine™ 2000(Invitrogen 11668-019). 250000 cells per well were seeded in a 6 well plate (TPP 92006) 24 hours prior transfection with 0.5 μg (for mCherry and mCherry-CAAX) or 1 μg of DNA per well. The transfection mix was prepared as follows:5 μL of Lipofectamine™ 2000 and the respective amount of DNA were added to 250 μL of OptiMEM (gibco 31985-062) each in a separate 2 mL microtube (Sarstedt 72.695.500). After 5 minutes of incubation at room temperature, both solutions were mixed by pipetting up and down several times and incubated at room temperature for 15 minutes. The resulting 500 μL of transfection mix was added to the corresponding well, containing 1.5 mL freshly added, pre-warmed full medium. The medium was exchanged for full medium 6-8 hours after transfection and cells for assessed after ~24 hours of transfection.Part BTransfection of cells with protein-encoding plasmids was performed using FuGene®6 (Promega E2691). 250000 cells per well were seeded in a 6 well plate (TPP 92006) 24 hours prior transfection with 1 μg of DNA per well. The transfection mix was prepared as follows: 3 μL of FuGENE®6 was added to 100 μL of OptiMEM (gibco 31985-062) medium in a 2 mL microtube (Sarstedt 72.695.500). After 5 minutes of incubation at room temperature, DNA was added and mixed by carefully pipetting up and down and incubated at room temperature for 15 minutes. The resulting ~100 μL of transfection mix were added to the corresponding well, containing 1.5 mL freshly added, prewarmed full medium. siRNA Cells were transfected with siRNA using Lipofectamine™ RNAiMAX (Invitrogen 13778-030). The transfection mix was prepared as follows: 5 μL of Lipofectamine™ RNAiMAX and the respective amount of siRNA were added to 250 μL of OptiMEM (gibco 31985-062) each in a separate 2 mL microtube (Sarstedt 72.695.500). After 5 minutes of incubation at room temperature, both solutions were united and mixed by pipetting up and down several times and left to incubate at room temperature for 30 minutes.

  custom-built optical tweezer (OT) set-up consisted of a 1064 nm Ytterbium fiber laser (IPG Photonics) and a Nikon C1 Plus confocal microscope. We employed a Nikon CFI Plan Fluor 100x, NA 1.3 oil immersion objective which was surrounded by a resistive collar to allow heating of the objective to maintain a stable temperature of 37°C within the experimental chamber. The sample chamber was fixed on a voltagecontrolled piezo-drive (MadCityLabs Nano-LP100). Bright field images of the bead were acquired using an EM-CCD camera at a frame rate of ~ 180 frames per second (iXon DU-897, Andor), and analyzed by a custom MATLAB script. Forces were calculated from bead positions following the equation = 𝑘(𝑥 -𝑥 0 ) , where k is the trap stiffness, x the position of the bead, and x0 the reference position at equilibrium. Trap stiffness calibration was obtained using the viscous drag method, including Faxen's correction for calibration close to surfaces 370 , with a trap stiffness adjusted to 44 pN/μm at 3W input power (400mW at the back focal plane of the objective).Experimental chamberCells were grown on 25 mm circular glass cover slips (VWR ECN 631-1584) prepared in the following way: 1) Cleaning with Isopropanol, Ethanol, water, Ethanol and then dried under a cell culture hood. 2) Coating with a 20 μg/mL solution of Laminin (Sigma L2020) for ~2 hours at 37 °C. Cells were analyzed 16-20 hours after seeding out 250000 cells per glass coverslip. The medium was exchanged for CO2 independent DMEM medium (gibco 21063-029), supplemented with 1.5 mg/mL β-Casein (Sigma C6905) to passivate the surface (experiment medium), 1 hour before a measurement.

Figure 21

 21 Figure 21 Ventral vs. equatorial FRAP Representative images of overexpressed CAAX_mCherry before and after a bleach pulse in (A) ventral and (B) equatorial position.

Figure 22

 22 Figure 22 FRAP data analysis (A) Representative example of fluorescence recovery after photobleaching of EphB2_YFP in a sicontroltreated EphHEK cell. The red curve shows the average intensity within the bleached region of interest, the dashed black line the background intensity, and the solid black line the bleaching due to imaging of a non-bleached reference cell.|(B) Normalization of fluorescence recovery over time: Red line shows the normalization as described in the main text, allowing to identify the mobile fraction, whereas the black line shows the normalization that allow determining the halftime of recovery.

Figure 23

 23 Figure 23 Lateral bleach profile in ventral FRAP. Lateral intensity profile through the bleached area immediately after the bleach in a cell at 37 °C. The red arrow shows the bleach diameter at 50 % bleach efficiency.

  3-3 ms) arising from free/unbound fluorophore in the cytosol very close to the plasma membrane and a third timescale of around 10-200 ms corresponding to membrane bound EphB2-YFP diffusing through the confocal spot.

  measurements were performed in the lab of Satyajit Mayor at the NCBS in Bangalore, India, with Thomas van Zanten. HomoFRET allows studying the local organization of proteins, e.g. their relative packing in the membrane, by analyzing the anisotropy of emission after polarized excitation, i.e. the relative loss in excitation polarization during the time of fluorescence emission 374 . The following paragraph details the actual experimental procedure, details on the interpretation are found in the respective results. Homo-FRET between like-fluorophores was measured as steady state emission anisotropy in a total internal reflection fluorescence microscopy mode. The measurements were carried out on a Nikon Eclipse Ti-E microscope with polarized laser excitation equipped with an 100x 1.45 NA TIRF objective with a dual camera imaging arrangement as described in 373 . The emission was split into Ipa (parallel) and Ipe (perpendicular) components by means of a high-performance wire grid polarizer (Moxtek) and then collected onto two separate EMCCD cameras (Photometrics Evolve 512 EMCCDs). Anisotropy r is calculated as: 𝑟 = (𝐼 𝑝𝑎 -𝐼 𝑝𝑒 ) (𝐼 𝑝𝑎 +2𝐼 𝑝𝑒)where Ipa is the intensity measured in the parallel direction and Ipe the intensity in the perpendicular direction with respect to the plane of polarization of the excitation beam. For analysis, the images were background subtracted (buffer image taken with identical imaging conditions) and the Ipa and Ipe images were aligned (Registration) using the affine transformation function in Matlab (Mathworks, USA). An image of fluorescein in water was used to compute the G-factor image (Ipa/Ipe) which was then corrected onto the Ipe image. This G factor allows normalizing the data according to different detection sensitivities regarding polarization in the optical set-up. Roughly 1.6x1.6 μm regions on the membrane with no apparent endosomal presence were selected and the extracted intensities in the Ipa and G-factor corrected Ipe channels were used to compute the emission anisotropies for each ROI. The anisotropy values were binned based on total intensity values (Ipa+2Ipe) and the binned data was plotted using GraphPad Prism software.11. TIRF-SIMTIRF-SIM (total internal reflection fluorescence -structured illumination microscopy) datasets were obtained on a commercial Nikon N-STORM set-up in the imaging facility of NCBS in Bangalore, India. Actin was labelled by expression of mCherry-tractin, and excited at 561 nm. The set-up was aligned in a rough way on a daily basis ensuring centered fiber entry into the microscope, and accurate base-voltage in the piezo system controlling the TIRF-SIM grating.

Figure 24

 24 Figure 24 Working principle of SIM Representation of resolution improvement through patterned excitation: A sample (A) is illuminated with a pattern (B), creating Moiré fringes that reveal otherwise unresolved details (C). From reference 376.

Figure 25 TIRF

 25 Figure 25 TIRF-SIM reconstruction using fairSIM (A) Import of TIRF-SIM datasets defining the acquisition details, pixel size, and background correction. | (B) Optical transfer function (OTF) approximation by providing the numerical aperture of the system, the fluorophores emission wavelength, and attenuation to account for deviations from a 'perfect' OTF . | (C) Reconstruction parameter estimation through fitting. For TIRF datasets, the recommended exclusion to fit the correlation peaks( small yellow circle on the upper right) is 0.7 (representing the large yellow circle on the right. | (D) Reconstruction was performed with the Wiener filter set to 0.099, and the standard APO cutoff of 2. (See main text for details)

  reproducible results. Sub-pixel localization was estimated using a linear deformation and 2x3 pixel Gaussian fit. In order to reduce noise, recover spatially coherent flows and fill the flow map, individual frame-to-frame flows were averaged over 10 frames, yielding a final effective time resolution of roughly 1 flow profile per 60 to 90 seconds (depending on the initial time resolution) (Figure27B). Vector validation was performed excluding spurious vectors larger than 40 nm/s.

Figure 26

 26 Figure 26 Binary ridge map creation from TIRF-SIM data (A) Input data after reconstruction. | (B) Result after applying a bandpass filter (3-15 px) that biases the image towards larger actin structures and reduces small-scale reconstruction artifacts. | (C) Results from the ridge detection performed with the indicated parameters. | (D) Resulting binary map from ridge detection with a 1 pixel Gaussian blur.

Figure 27

 27 Figure 27 PIV analysis (A) Upper left window showing the average projection of two consecutive time frames in which the cell visibly retracted towards the lower left. Flow vectors obtained from applying the PIV algorithm at reducing interrogation window size, with 50 % shifts, as indicated on top of each image. The amount of vectors inversely scales with the size in interrogation area, at the cost of increasing false correlations.| (B) Heatmap of flows for an individual frame after iterative PIV analysis (left), recovering the general flow direction. Single frame sampling is insufficient to generate flow maps that cover the cell surface. The right shows the average of ten individual PIV heatmaps that allows full sampling of the cells surface and favors flows of coherent directionality during the time of averaging.

  equatorial plane to assess expression and localization of fluorescently tagged proteins prior to tube pulling.

Figure 28

 28 Figure 28 Lipid membrane deformations (A-C) The three principal membrane deformations: (A) Stretching of a membrane sheet to increase its area. |(B) Shearing a membrane along an axis while maintaining a constant area. Reference 382|(C) Bending a membrane leading to a compressed and an extended surface (left) (reference 382). Curvature can be characterized by two principal curvatures that are the inversed respective radii R1 and R2.(Reference 369) |(D) Regime changes in membrane tension through application of external forces. The left-hand side shows the transition from a floppy membrane (a1) to the entropic tense regime (a2), whereas the right-hand side shows the transition from the macroscopically flat entropic tense regime (b1) to the stretch tense regime (b2). Reference 383

Figure 29

 29 Figure 29 Studying membrane mechanics in cells. (A) Schematic representation of the four main methods to study membrane mechanics in cells : (I) Shear by hydrodynalic flows, (II) Micropipet aspiration, (III&IV) Membrane tether formation : dorsal tethers through AFM (III) and lateral tether pulling by optical tweezers. Reference 393 |(B) Schematic representation of the principal contributions to tether holding force, i.e. in plane membrane tension Tm and membrane-cortex adhesion energy 𝛾. |(C) Energy-dependent polarization of tether forces in epithelial cells. The basolateral membrane (bottom) has a lower tether holding force than the apical side, yet after ATP depletion and blebbing, both show equal tether holding force. Reference 394

Figure 30

 30 Figure 30 Dynamic tether pulling. (A) Non-linear scaling law of tether holding force 𝑓 with elongation velocity 𝐿 for different cell types (corresponding to different symbols)as described and theoretically explained in reference 390|(B) Schematic depiction of lipid flows from the cell into the tether. Reference 390 |(C) Schematic depiction of the initially homogeneous tether immediately after step elongation with the minority component 𝜙 2 being retained at the tether neck (left) and after full equilibration (right). Reference 414

Figure 31

 31 Figure 31 Local stimulation of EphB2 with ephrin-B1 coated beads. (A) Schematic depiction of the contact between a ligand-coated bead and the cell (left). Diffusible ephrin-B1 is able to locally induce EphB2 clustering and activate the cell (right). | (B) Experimental data showing a cell's ventral surface before (left) and 15 minutes after bead contact. The position of the bead is indicated with an asterisk in both frames. The yellow outline is the cell shape before activation.

  EphB2 with bead-coupled ligands induces cellular contraction. Previous studies on the interaction between EphB2 and Myosin 1b used two main sets of experiments: growth of two cell lines expressing EphB2 and ephrin-B1 respectively, with subsequent description of random cell -cell encounters and 'global' stimulation of EphB2 by adding soluble, pre-clustered ephrin-B1 into the medium 3 .

Figure 32

 32 Figure 32 Beads induce receptor recruitment and tyrosine phosphorylation. (A) Intensity-scaled fluorescence micrographs of EphHEK cells depleted of Myosin 1b by siRNA (siMyo1b) and expressing dSH2_mCherry after 1 minute of bead contact. The left cell was contacted from above, whereas the right one is in contact with a bead at its extremity. The upper panels show the fluorescence signal from EphB2_YFP and the lower ones from dSH2_mCherry, a dual SH2 domain probe that detects phosphotyrosines. On the right of each micrograph a zoom of the bead-contact site is depicted. |(B) Line profiles of the intensity along the white line in (A). One can see a clear correlation in intensity peaks between EphB2-YFP (top black lines) and dSH2-mCherry (bottom red lines).

Figure 33

 33 Figure 33 Cell contraction after local stimulation with ephrin-B1 beads.The plot shows the cell surface after 15 minutes relative to its initial area. A value above 100% means the cell expanded during the 15 minute time frame, whereas a value under 100% means that it contracted. | Untreated (n=24): Cells were imaged at time point 0 and after 15 minutes without any perturbation besides imaging; Adhesive beads (n=20): A carboxylated bead that sticks to the cell surface is deposited on the cell; +Efnb1: An ephrin-B1 coated bead was deposited close to the cell edge of a lamellipodial protrusion, either on control cells that were not treated with siRNA (n=21) or cells depleted of Myosin 1b using siRNA(siMyosin1b) (n=14).

  taking the kinetics of binding/unbinding of the linkers under stress into account. The first term of equation 9 represents the contribution of the detachment of a certain amount of linkers to the critical pressure through detachment, while the second term is the contribution of cortex contractility which creates a stress on the linkers and thus reduces critical blebbing pressure 402 . The critical blebbing pressure was previously shown to change in response to Myosin II inhibition in Dictyostelium discoideum 403 and related experiments have revealed a role for membrane cytoskeleton attachment in bleb behavior in Paramecium (unpublished C. Campillo, C. Sykes' lab).

750

  Pa with no clear difference between control cells and cells after Myosin 1b depletion. Critical blebbing pressure thus does not seem to depend on Myosin 1b in EphHEK cells. As we could not detect a difference at large scales as probed by micropipette aspiration we thus resorted to more local measurements, employing optical tweezer based tube pulling.

Figure 34

 34 Figure 34 Micropipet aspiration (A) Schematic depiction of the experimental procedure: A micropipet with a suction pressure ΔP is brought into contact with a cell. If the critical pressure is overcome, the plasma membrane detaches from the cortex and forms a bleb in the micropipette that is observable by brightfield microscopy. | (B) Fraction of cells forming a bleb in the micropipette as a function of applied suction pressure in [Pa]. Data for sicontrol cells is shown as black circles, data for Myosin 1b depleted cells as red dots. For each suction pressure 10 cells were probed.

Figure 35 Figure 36

 3536 Figure 35 Measuring tether force as a reporter for effective membrane tension. (A) Force regimes observed during tether pulling from cells corresponding to the steps depicted on the right. A bead at equilibrium position (1) is brought into contact with a cell (2). When the stage is pulled away from the trap, an initial force peak required to detach the membrane from the underlying actin cortex (3) is quickly followed by a stable force ftether (4). |(B) Tether forces in EphHEK cells treated with 0.1% DMSO (n=16), 100 nM LatA (n=22), or 20μM BS (n=15). (**p =2.10 -7 ; *p=0.0022) |(C) Tether forces in EphHEK cells overexpressing mCherry (mCh, n=36), mCh-CAAX (n=23), mCh-Myo1b (n=44), mCh-Myo1b-rigor (n=40), treated with control siRNA (sicontrol, n=39), or Myo1b siRNA (siMyo1b, n=43). Grey box indicates mean±S.D. for mCh-CAAX |(D) Tether forces in EphHEK cells overexpressing mCh-CAAX (n=23), mCh-Ezrin (n=49), treated with control siRNA(sicontrol, n=36), Ezrin siRNA (siEzrin, n=47), or ERM siRNA mix (siERM, n=38). Grey box indicates mean±S.D. for mCh-CAAX |(mean±S.D.)

Figure 37

 37 Figure 37 Expression levels of proteins. (A) Western Blots showing expression levels of proteins after expressing mCherry labeled constructs. The expression of mCherry-Myo1b is of the same order than the endogenous Myo1b (*) while expression of mCherry-Myo1b rigor mutant is quite low (line CAAX_mCH versus with line Myo1b_mCH and Myo1b_rigor_mCH) but this reflects a low transfection efficiency. Expression level of Ezrin_mCh is superior to the endogenous ezrin (*) and ERM. |(B) Representative fluorescence images of cells expressing fluorescentlylabeled proteins and used for tube experiments. Note that we selected cells with similar expression levels of fluorescent proteins. CAAX and Myo1b constructs are clearly predominantly localized to the plasma membrane, yet Ezrin shows a broad, cytosolic staining. |(C) Western Blots showing expression levels of proteins after depletion using siRNA. All siRNA treatments reduce the protein level below detection. GABDH and actin are the loading controls. Note that Ezrin and Radixin are not well separated and correspond to one band (upper band) when detected with anti-ERM antibodies. Thus, this band is only partially reduced in cells treated with Ezrin siRNA. The lower band is unchanged and corresponds to Moesin.

Figure 38

 38 Figure 38 Elongation of membrane tethers at constant speed to assess PM cortex friction. (A) Elongation of a relaxed membrane tether with holding force ftether (1) at constant speed leads to a force increase that rapidly plateaus at fstrai n (2). fplateau is defined as the difference between ftether and fstrai n.|(B) Representative data of the bead displacement from trap center measured during tube elongation at 0.5 and 2μm/s. |(C) Plot of plateau forces versus pulling speeds. Each data point represents one tether elongation. si_control (•), si_Myo1b (○), si_ERM (□). Fitting with equation 9 as detailed in reference 372, assuming typical values for linker density ν~10 3 μm -2 , bending rigidity κ ~50kBT, and ln(R/rt) ~5, one finds an effective surface viscosity of ηe ~10 -9 Pa.m.s (black line). Imposing an effective viscosity of 10 -8 Pa.m.s yields the red line, while dashed lines represent a theoretical doubling (upper) or reduction to 10% (lower) of linker density ν.

Figure 39

 39 Figure 39 Step elongation of existing membrane tethers to assess tether relaxation. (A) Three force regimes observed during step elongation of an existing membrane tether (left) corresponding to the sketches on the right. A relaxed membrane tether with holding force ftether (1) is elongated by imposing a fast step displacement of a piezo-controlled stage leading to a peak in force (2). Over time the force relaxes back to the initial value of the tether force (ftether).|(B) Individual tube force dataset (grey) and corresponding fit (red) as developed in reference 396 and detailed in the introduction.| (C) Plot of forces over time during step-elongation of tethers for EphHEK cells. Mean (black line) ± S.D. (grey area), n=13.|(D) Comparison of peak forces and characteristic relaxation times τ as obtained from fits of untreated EphHEK cells and those treated with LatA as shown in panels C & E. |(E) Plot of forces over time during step-elongation of tethers for EphHEK cells treated with LatA. Mean (black line) ± S.D. (grey area), n=16. In (C) and (E), for graphic purposes, a rolling average filter was applied to plot the dataset; analysis was performed on full dataset.

Figure 40

 40 Figure 40 Relaxation times for step-elongated tethers. (A) Relaxation times obtained from fitting individual data sets for EphHEK cells overexpressing mCh (n=27), mCh-CAAX (n=35), mCh-Myo1b (n=34), mCh-Myo1b-rigor (n=30), treated with control siRNA (sicontrol, n=38) or Myo1b siRNA (siMyo1b, n=34).|(B) Relaxation times obtained from fitting individual data sets for EphHEK cells overexpressing mCh (n=27), mCh-CAAX (n=35), mCh-Ezrin (n=33), treated with control siRNA (sicontrol, n=28), Ezrin siRNA (siEzrin, n=34), or ERM siRNA mix (siERM, n=32). (mean±S.D.)

Figure 42 Figure 43

 4243 Figure 42 All measurements in the different conditions. (A/B) All individual ftether measurements as summarized in Figure 1 for all probed conditions.|(A) Myosin1b variants and drug treatments|(B) Ezrin variants. |(C/D) All individual fit results for relaxation time τ as summarized in Figure 4 for all probed conditions.|(C) Myosin1b variants and drug treatments.|(D) Ezrin variants. The orange error bars correspond to the statistical error (i.e. standard error of the mean)

Figure 44 A

 44 Figure 44 A FRET-based membrane tension sensor (A) Scheme of the proposed dual FRET-based membrane tension sensor. Lipid anchors allow incorporation of the sensor into cells from the outside. Both FRET pairs are connected by a TATA box allowing low pN force resolution. While one FRET pair is close to the membrane, the other pair is positioned at a distance. |(B) Calibration approach to dissect tension and local curvature effects. As both FRET pairs are positioned at a different distance from the membrane the relative change in FRET efficiency is different depending on the local curvature. Whereas positive membrane curvature decreases FRET efficiency in the distal FRET couple, negative membrane curvature decreases FRET efficiency at the proximal FRET couple. Both should in turn respond in a proportional way to in-plane tension. Calibration with liposome would allow characterizing the parameter space of FRET efficiencies that correspond to given combinations of tension and curvature.

1 .

 1 light of the variety in different cell lines both regarding absolute values of effective membrane tension and the different contribution of proteins to it, it would be interesting to systematically measure and compare effective membrane tension in different cell types and correlate it to, e.g. relative abundance of cortex-membrane linkers, adhesion phenotype. The influence of actin on receptor dynamics in the membrane Proteins in the cell membrane are mobile and move laterally in the membrane 476 , yet consistently exhibit lower diffusion than lipids within the membrane 477,478 .

Figure 45

 45 Figure 45 Hindered diffusion in the plasma membrane. (A) The classical picket-fence model as conceptualized by Kusumi and others. The fence (membrane cytoskeleton) is held in close apposition to the membrane by membrane skeleton bound proteins (pickets). Reference 28|(B) 3 examples of diffusion hindrance in the plasma membrane: 1. Phosphorylation of transmembrane proteins can immobilize other proteins if they interact with the phosphorylated residues. 2. Raftlike nanodomains can partition membrane constituents and limit diffusion by confinement of raft molecules and by hindrance through increased line tension for non-raft molecules. 3. Hydrophobic mismatch can separate and restrict transmembrane proteins based on the length of their transmembrane domains. |(C) Changing diffusion through different 'fences': The actin cytoskeleton (1), extracellular matrix proteins (2), large immobile clusters of proteins (3) and endomembrane systems like the endoplasmic reticulum (4) can all limit diffusion and with the exception of case (3) create discrete compartments. Adapted from reference 513.

  kinase and promotes increased diffusion and clustering of Fcγ receptors 525 . A similar feedback promoting receptor engagement by means of altered actin structures, here driven by cofilin-mediated severing, has been demonstrated between the toll-like receptor and the B cell receptor 526 . CD1d in antigen presenting cells is equally restricted in motion by interaction with actin that prevents coalescence of nanoclusters, modulating the activation of natural killer T cells 527 . During phagocytosis activation of Fcγ drives the creation of an integrin and actin-based diffusion barrier. This barrier locally excludes CD45, a phosphatase, thus allowing amplification of signaling 514 .

Figure 47

 47 Figure 47 Diffusion assessed by FRAP experiments (A) Schematic depiciton of the two types of FRAP experiments. The left side represents ventral FRAP, i.e. bleaching of a well-defined area at the ventral side of cells. The right side shows equatorial FRAP, in which bleaching was performed on the side of the cell at roughly 5 μm from the substrate without controlling the exact bleach profile. |(B) The left panel shows the effective diffusion coefficient of EphB2-YFP obtained from ventral FRAP for the different conditions as indicated on the bottom. n =12(DMSO), 12(LatA), 11(CK666), 12(SMIFH2), 10(sicontrol), 8(siMyo1b), 7(siERM). The right panel shows the halftimes of equatorial FRAP, normalized to the respective control condition. The left part of this panel shows the data before, and the right after global stimulation of cells with ephrin-B1. n=DMSO(14/9), LatA(16/17), sicontrol(13/11), siMyo1b(14/15).

  data, probably due to the aforementioned lack in control of the bleach geometry. While depletion of Myosin 1b did not change the recovery halftimes both before and after activation, mild LatA treatment seemed to reduce recovery halftimes, i.e. increase large scale diffusivity, albeit in a non-significant way before stimulation of EphB2. The same treatment led to significantly reduced recovery halftimes after activation of EphB2 (Figure47B).Stimulation led to rapid formation of large, visible clusters of EphB2 that seemed almost completely immobile (Figure48), thus the normalized halftimes after stimulation with ephrin-B1 represent the contribution of the remaining mobile, probably unclustered, population of EphB2. The mobile fractions were comparable between both experimental approaches (ventral vs. equatorial FRAP) before stimulation (Figure49).

Figure 48 Formation 48 .

 4848 Figure 48 Formation of macroscopic EphB2 clusters upon global stimulation. Representative fluorescence micrographs of EphB2_YFP at the equatorial plane before and after global stimulation with ephrin-B1 in EphHEK cells, treated as indicated. Scale bar 10 μm

Figure 50 can

 50 Figure 50 can be found in the Appendix.

Figure 51 Ventral

 51 Figure 51 Ventral EphB2 clusters after global stimulation Representative fluorescence micrographs of EphB2_YFP and Myosin1b_mCherry at the ventral surface of EphHEK cells, after transfection with Myosin 1b_mCherry. Before (top) and after (bottom) global stimulation with ephrin-B1. Scale bar 10 μm

2 .

 2 EphB2's spatial organization in the PM.Global stimulation of cells with ephrin-B1 leads to the formation of large EphB2 clusters both at the equatorial plane and the ventral surface, which seem quite heterogeneous in size. These clusters coalesce into large scale aggregates after LatA treatment, yet do not seem fundamentally different in absence of Myosin 1b. Myosin 1b itself is not enriched in these clusters after activation but remains homogeneously distributed in the membrane (Figure51).

Figure 52

 52 Figure 52 HomoFRET of EphB2_YFP after Myosin 1b depletion Representative images (top) and fluorescence anisotropy of EphB2_YFP as a function of EphB2_YFP intensity (bottom) for control and siMyosin1b cells.

  performed fluorescence anisotropy measurements to address homoFRET within the EphB2_YFP population (see M&M section for experimental details) which was homogeneously distributed along the ventral cell surface.Fluorescence anisotropy is based on homoFRET, i.e. FRET between two identical fluorophores. As such the fluorescence anisotropy depends on the rotational freedom of the fluorophores to each other. In other words, if homoFRET happens between two fluorophores which are close enough to each to undergo FRET, the fluorescence anisotropy is a measure of their rotational freedom. For instance, a tightly packed dimer will show a lower anisotropy than two monomers that are close to each other yet less densely packed. From this statement it becomes clear that in a first approximation, fluorescence anisotropy will be a function of relative packing, i.e. fluorophore density, with a downward facing slope of anisotropy values with increasing fluorophore density, reflected by the intensity per pixel. From the experimental point of view, one is interested in the anisotropy value that carries the information of density-independent, cluster related spatial organization which is obtained from the plateau that is reached, in our case at around 30000 to 45000 arbitrary units. It must be noted that the absolute anisotropy value has no meaning by itself as it largely depends on the experimental set-up and configuration. It does nevertheless allow for a relative comparison in between conditions.

Figure 53

 53 Figure 53 HomoFRET of EphB2_YFP after PClP treatment Representative images (top) and fluorescence anisotropy of EphB2_YFP as a function of EphB2_YFP intensity (bottom) for control and PClP-treated cells.

Figure 54

 54 Figure 54 Heatmaps of actin flowsHeatmaps of actin flows for DMSO (A) and PClP-treated (B) cells. The dynamic range of colors goes from 1 nm.s -1 (blue) to 30 nm.s -1 (red). The left panel shows the steady state dynamics before activation, averaging over 25 frames (unstimulated). The peak frame is the 10 frame average after activation which shows the highest flows, and the last frame is the last 10 frame average after stimulation. The total average is the average of all frames after stimulation, i.e. 200 frames.

Figure 55

 55 Figure 55 Heatmaps of actin flows: Effect of Myosin 1b depletionHeatmaps of actin flows for control (top) and siMyosin1b-treated (bottom) cells. The dynamic range of colors goes from 1 nm.s -1 (blue) to 30 nm.s -1 (red). The left-most panel shows the steady state dynamics before activation, averaging over 25 frames. The peak frame is the 10 frame average after activation which shows the highest flows, and the last frame is the last 10 frame average after stimulation. The total average is the average of all frames after stimulation, i.e. 200 frames.

Figure 56

 56 Figure 56 Scatter plots for actin flow vectors Total amount of flow vectors obtained before activation (left) and over the timecourse after activation (right) for DMSO (A), sicontrol (B), and siMyosin1b (C) treated cells. The plot coordinates represent X and Y components of detected flow vectors ranging from 0 to 40 nm.s -1 . Negative flow values represent movement to the left and bottom whereas positive values represent movement to the right/top.

class 1

 1 myosins535 , completely stops actin flows in HEK293T cells. The same effect is observed as well in U2OS cells and is found in PClP from different chemical syntheses (personal communication Satyajit Mayor's lab). While one explanation might lay in the blockage of all class 1 myosins, it is a remarkably strong phenotype and should be studied in detail. The finding is particularly surprising as the flow of actin, especially in the lamellipodium is considered to arise from two main contributors, i.e. Myosin IIdriven contractility and the retrograde flow of polymerizing actin barbed ends. The fact that we see a cell-wide loss in dynamics suggests that both processes are affected by the PClP treatment. Two experiments are particularly interesting to be done as a consequence: First, characterization of specific inhibition of Myosin-2 by Blebbistatin, and second, control of actin polymerization at the leading edge of cells after PClP treatment. This could be done by overexpressing photo-convertible actin dyes, e.g. tractin_mEos.

  polarize the system sufficiently to create large directional flows in response to EphB2 stimulation. Yet, non-intuitively but in agreement with our data on contractile deficiency in absence of Myosin 1b, this increased actin flow does not correlate well with efficient contraction of the cells in response to EphB2 stimulation. Taken together, the observed results are in good agreement with a role of Myosin 1b acting as a clutch during cellular contraction or altering actin network geometry. As we do not have an in situ control of siRNA treatment efficiency per cell (of a generally very efficient depletion), the observation of two different phenotypes in actin flows after Myosin 1b depletion might in principal be related to differences in cellular depletion efficiency. The correlation between pre-existing lamellipodial flows and the distinction of class 1 and class 2 flow behavior after activation might be further investigated employing cells on micro-patterns, thus allowing for a more controlled cell shape and stereotypic cell organization.

  might go back to our initially developed system of bead-based receptor activation which allows spatial control of receptor engagement. In line with the findings for Myosin 1c, an ideal experiment would include a FRET-based axial tension sensor, which would allow detection of Myosin 1b-dependent tension build-up at local activation sites. It is not trivial to generate such a reporter without changing the molecular properties and at the same time get specific results. One idea might be the low level expression of a membrane-linked FRET tension sensor that has the Myosin 1b binding-domain of EphB2 (which still is not fully characterized and needs to be specific). Such an approach would evade any pitfalls of reduced receptor activation after inclusion of a tension sensor within EphB2, while still conserving specificity for Myosin 1b. Yet, it is puzzling that such a clutch-like behavior of Myosin 1b would not translate into any change regarding the plasma membrane's mechanical properties. Yet, as we highlighted in the first part of this thesis, we do not and cannot exclude a local and short-lived effect of Myosin 1b during EphB2 activation and contraction that might be detected if the right experimental tools were available (see Perspective Part A).

Figure 57 Molecular

 57 Figure 57 Molecular FRET sensor for Myosin1b generated axial tension (A) Schematic representation of the described axial stress sensor for Myosin1b -dependent stresses on EphB2. A CAAX domain localizes the sensor to the PM and is coupled to EphB2's binding domain for Myosin 1b with an interspersed FRET sensor. Such design prevents potential loss in receptor function due to addition of the stress sensor. Upon local stimulation the FRET efficiency is a readout of Myosin 1b-specific local stresses in response to EphB2 activation. | (B) Overview of the proposed SLB-based experiments to study the control of actin geometry by Myosin 1b. The top row depicts the well characterized addition of Myosin II to a pre-assembled actin network leading to contraction and coalescence. The lower row depicts some potential outcomes of addition of Myosin 1b, e.g. a change of filament orientation before addition of Myosin II (left), or hindered/enhanced network compaction (right bottom/top triangle respectively)

Figure 58

 58 Figure 58 Active gel contraction (A) Actin network contractility is a function of actin architecture (ordered bundles (red), disordered networks (green), disordered bundles (blue)) and network connectivity. Adapted from Ref.531| (B) Active gel phase diagram depending on contractility and motor activity. Four main phases can be distinguished: Active solutions that are not contractile at low connectivity (grey), pre-stressed, non-contractile gels at medium to high connectivity and low motor activity (turquoise), a global contractile regime at medium connectivity and medium motor activity (salmon), and local contractility at medium connectivity and high motor activity (rosé) Adapted from Ref. 548.

  stresses, e.g. osmotic pressure 114 . Tension within the cortex arises from the action of Myosin II and plays a major role in cellular processes such as cell division 115 . During cell division, the dynamics of the cortex and its thickness are controlled by α-actinin,

	an actin filament crosslinker. Successful cytokinesis requires the right balance between
	cortex stability and the possibility of disassembly 116 . Beyond generation of tension,
	Myosin II changes the network's viscoelastic properties 117 . After first approaches based
	on deformable plates 115 , micropipette aspiration of cells, initially applied to study the
	mechanical properties of spectrin network in red blood cells 118 has been instrumental
	to quantitatively characterize the apparent viscosity and cortical tension in detail 119 . In
	endothelial cells, stiffness and viscoelasticity strongly depend on actin 120-123 (up to 50%
	reduction in stiffness upon Cytochalasin D treatment which blocks actin filament
	polymerization 124 ). In line with these observations, AFM mapping and correlative
	fluorescence microscopy show correlation between elastic moduli and relative density of
	actin and intermediate filaments 125 . This has been corroborated by the effects of drug
	treatments specifically disturbing actin organization 126 . When measured in suspended
	fibroblasts to avoid the contribution of stress fibers and adhesions sites the cortex
	shear modulus is on the order of 200 Pa 127 . The importance of adhesion in determining
	the cellular mechanical properties is highlighted by comparison of identical cells in
	different conditions, showing that spread cells are stiffer than rounded cells 128 .
	Laser ablation experiments in Caenorhabditis elegans embryos have shown that the
	mechanical properties of the cortex are isotropic, yet significant anisotropies are
	created during development by cortical flows, that are driven by Myosin II
	contractility 129 . Recent evidence suggests that feedback regulation by Rho can explain
	how the creation of localized Myosin II foci does not lead to large scale aggregation of
	these foci and ensures efficient morphogenesis in the Caenorhabditis elegans
	embryo 130 . Along these lines but at much larger length scales, Myosin II distribution is
	sufficient to predict the flow profile of cells in the developing Drosophila melanogaster
	embryo 131 .

  Phosphorylation of intracellular residues (serine/threonine yellow, tyrosine orange) can recruit proteins through, e.g. SAM, PDZ, and SH2 domains. Domain names are depicted on EphA and recruitment is shown on EphB for reasons of readability, but apply to both subtypes. Whereas ephrin-B can recruit accessory proteins to its intracellular domain, ephrin-A needs interaction partners to bridge the plasma membrane, e.g. the nerve growth factor receptor p75 in neurons.|(B) Schematic representation of the EphB2 signaling cascade after stimulation with ephrin-B1. Reference 299 4.3 Eph receptors can discriminate ligand quantities.

Figure 18 Eph/ephrin as a signaling hub (A)

  1 vol. % DMSO), with the following concentrations and treatment

	times at 37 °C:
	LatA	100 nM	10 minutes
	CK-666	50 μM	15 minutes
	SMIFH2	25 μM	15 minutes

Table 1

 1 Selection of published tether forces for different cell lines, as summarized in 393 .

	Cell type	Cell line	Tether Force [pN]
	Neurons	Chick dorsal root ganglion	7
		mouse cortical neurons	15
		rat dorsal root ganglia neurons	32
	Endothelial cells	EA hy926	30
	Chinese hamster ovary		30
	Melanoma	M2 & A7	30
	Neutrophil	L-60	8
			40
	Macrophage	RAW 264.7	30
		(mouse peritoneum)	70
	Fibroblast	NIH3T3/WTCL3	30
		MEFs	15
	Astrocyte/glioblastoma		30
	Microglia		60
	Keratocyte		55
			40

  Myosin 1b after EphB2 clustering and the absence of an effect of Myosin 1b during fluorescence anisotropy experiments. The obvious consequence at this stage is to redo the FRAP experiments to be able to confirm or discard this observation. If reproducible it would suggest that the EphB2 clusters that form after stimulation remain mobile after depletion of Myosin 1b thus explaining the unchanged mobile fraction. It will be of interest to include ventral FRAP after global stimulation that we have not yet performed in order to be able to compare it directly to the interface that we studied by fluorescence anisotropy and where we did not see any Myosin 1b clustering after EphB2 stimulation. One caveat to consider is that we cannot strictly rule out that mCherry-labelled Myosin 1b, as imaged in Figure51, might have a lower affinity to EphB2 than endogenous Myosin 1b and thus not report on local clusters of Myosin 1b.

Acknowledgements

Submitted MBoC manuscript

membrane tether pulling assay to a single type of PM-actin linker might thus strongly vary from one cell type to another, explaining the apparent discrepancy between our results and previous reports. Our work highlights the limitations of the tether pulling approach and the importance to design new assays and to further develop theories describing the impact of PM-actin linkers on membrane mechanics. So far, how linkers contribute to membrane tension remains an open question. While we were able to successfully induce a specific response by stimulating EphHEK cells with ligand-covered beads a couple of limitations apply to this particular system that considerably limited further exploitation of this system. Notably, the bead, probably due to its strong adhesion with the plasma membrane through ligand-receptor interactions, strongly adheres to the cell's surface and we were not able to remove the bead from the cell surface with the optical tweezer once contact was made, reminiscent of the reported occurrence in cellulo of trans-endocytosis to remove engaged receptorligand from the cell surface. As the lab of Evelyne Coudrier evidenced increased filopodia formation around the area of cell to cell contact between ligand and receptor expressing cells we initially thought to potentially be able to quantify, e.g. pushing forces or at least an increase in filopodia density at the contact site between the cell and the bead. Yet, we never observed such an increase, probably because the adhesion area of the bead thus creating a large energy barrier for membrane tube formation. A potential work-around would be to use a ligand-covered GUV instead of a bead, that might be deformable enough to allow for membrane protrusions to form at the interface, yet again only if the adhesion area would stay sufficiently small. Ideally one would want a structure that has an adhesion area that is similar to the tip area of a filopodium, e.g. a thin AFM cantilever, yet highly deformable to allow protrusion generation.

Supplementary Figures

Critical blebbing pressure is Myosin 1b independent

We did not observe any striking difference in critical blebbing pressure after depletion of Myosin 1b. Membrane-cortex detachment depends on the density of linkers, on the critical force per linker and on the cortical contractibility. The population of linkers at the plasma membrane is diverse. Considering that this pressure is largely dependent on the density of linkers one might posit that Myosin 1b is simply not abundant enough at the plasma membrane to reveal a fundamental change in blebbing pressure, or that efficient compensatory mechanisms exist (see

TIRF-SIM & PIV analysis of actin flows

In order to study our hypotheses considering a potential effect of Myosin 1b on actin network dynamics and geometry we have, again collaborating with the team of Satyajit

Mayor at NCBS Bangalore, used total internal reflection fluorescence -structural illumination microscopy (TIRF-SIM) to study the dynamics of the ventral actin cytoskeleton (see M&M for experimental details).

In a first instance, we have used the obtained datasets to study the flows of the ventral actin cytoskeleton, both at steady-state, and after global stimulation of EphB2

with ephrin-B1. To do this, we have performed particle image velocimetry on image sequences from tractin-mCherry labelled actin filaments.

Iterative PIV and time-averaging recovers coherent flow features in EphHEK cells.

In order to reduce the contribution of SIM reconstruction artifacts and relatively high background noise in the acquired TIRF-SIM datasets, probably due to unbound tractin-mCherry, we performed additional steps of image treatment prior to the PIV analysis.

The treatment (detailed in the Methods section) consisted of applying a bandpass filter and performing a ridge detection algorithm. Using the map of ridges as an input, we performed PIV and were able to recover quantitative actin flow profiles in an unbiased way. In order to focus the analysis on flows which have a persisting directionality on the timescale of minutes, as expected from a cell which is, e.g. contracting after stimulation, and to obtain satisfactory signal to noise in the detection of flow vectors we performed time-averaging over 10 frames, leading to an effective time resolution of 75 seconds over a period of around 25 minutes. The time-averaging interval was chosen empirically using the flows in a lamellipodium as a benchmark, where both extensions and retrograde flows are visible qualitatively by eye, and 10-frame time-averages were able to recover these feature in a robust way, giving consistent outputs that match previously reported flow velocities in lamellipodia and full mapping of a given region of interest.

Stimulation of EphHEK cells with ephrin-B1 increases lamellipodial actin flows.

We represent the obtained PIV results in heat maps, in which the local flow velocity is color-coded in a dynamic range where speeds below 1 nm.s -1 are blue and flows above 30 nm.s -1 are red. The directionality of a given flow vector is indicated with super-imposed black arrows with lengths proportional to the flow velocity. Before stimulation, each cell was imaged over ~2 minutes and then imaged for ~20 minutes after stimulation. The frame-times depended on the exposure time and varied slightly to account for different expression levels of tractin-mCherry. Flow vectors where therefore